Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4140,2,Mod(2069,4140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4140, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4140.2069");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4140.n (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(33.0580664368\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2069.16 | ||
Character | \(\chi\) | \(=\) | 4140.2069 |
Dual form | 4140.2.n.b.2069.14 |
$q$-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 \(\left(\mathbb{Z}/4140\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(2071\) | \(3961\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | −1.55901 | + | 1.60296i | −0.697209 | + | 0.716868i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.21571 | 0.459496 | 0.229748 | − | 0.973250i | \(-0.426210\pi\) | ||||
0.229748 | + | 0.973250i | \(0.426210\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.73752 | 0.825394 | 0.412697 | − | 0.910868i | \(-0.364587\pi\) | ||||
0.412697 | + | 0.910868i | \(0.364587\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.99737i | 1.94072i | 0.241663 | + | 0.970360i | \(0.422307\pi\) | ||||
−0.241663 | + | 0.970360i | \(0.577693\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.391222i | 0.0948852i | 0.998874 | + | 0.0474426i | \(0.0151071\pi\) | ||||
−0.998874 | + | 0.0474426i | \(0.984893\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.94625i | 0.675917i | 0.941161 | + | 0.337958i | \(0.109736\pi\) | ||||
−0.941161 | + | 0.337958i | \(0.890264\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.74030 | + | 3.00169i | −0.779906 | + | 0.625896i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.138992 | − | 4.99807i | −0.0277984 | − | 0.999614i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.30404i | 0.613545i | 0.951783 | + | 0.306772i | \(0.0992490\pi\) | ||||
−0.951783 | + | 0.306772i | \(0.900751\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.96077 | 1.42980 | 0.714898 | − | 0.699229i | \(-0.246473\pi\) | ||||
0.714898 | + | 0.699229i | \(0.246473\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.89530 | + | 1.94874i | −0.320365 | + | 0.329398i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.84588 | 0.303461 | 0.151731 | − | 0.988422i | \(-0.451515\pi\) | ||||
0.151731 | + | 0.988422i | \(0.451515\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.35402i | − | 1.46085i | −0.682991 | − | 0.730426i | \(-0.739321\pi\) | ||
0.682991 | − | 0.730426i | \(-0.260679\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.89960 | −0.747182 | −0.373591 | − | 0.927593i | \(-0.621874\pi\) | ||||
−0.373591 | + | 0.927593i | \(0.621874\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.87774 | −0.419762 | −0.209881 | − | 0.977727i | \(-0.567308\pi\) | ||||
−0.209881 | + | 0.977727i | \(0.567308\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.52205 | −0.788864 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.95606i | 0.406046i | 0.979174 | + | 0.203023i | \(0.0650766\pi\) | ||||
−0.979174 | + | 0.203023i | \(0.934923\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.26782 | + | 4.38815i | −0.575472 | + | 0.591698i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 8.16713i | − | 1.06327i | −0.846974 | − | 0.531635i | \(-0.821578\pi\) | ||
0.846974 | − | 0.531635i | \(-0.178422\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.9163i | 1.65377i | 0.562375 | + | 0.826883i | \(0.309888\pi\) | ||||
−0.562375 | + | 0.826883i | \(0.690112\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −11.2165 | − | 10.9089i | −1.39124 | − | 1.35309i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.5479 | 1.28863 | 0.644315 | − | 0.764760i | \(-0.277143\pi\) | ||||
0.644315 | + | 0.764760i | \(0.277143\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 14.5479i | − | 1.72652i | −0.504762 | − | 0.863258i | \(-0.668420\pi\) | ||
0.504762 | − | 0.863258i | \(-0.331580\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.70779i | − | 0.199881i | −0.994993 | − | 0.0999406i | \(-0.968135\pi\) | ||
0.994993 | − | 0.0999406i | \(-0.0318653\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.32804 | 0.379265 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.9911i | 1.34911i | 0.738226 | + | 0.674554i | \(0.235664\pi\) | ||||
−0.738226 | + | 0.674554i | \(0.764336\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.9935i | 1.42622i | 0.701054 | + | 0.713108i | \(0.252713\pi\) | ||||
−0.701054 | + | 0.713108i | \(0.747287\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.627114 | − | 0.609917i | −0.0680201 | − | 0.0661548i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.1484 | −1.60573 | −0.802865 | − | 0.596161i | \(-0.796692\pi\) | ||||
−0.802865 | + | 0.596161i | \(0.796692\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.50678i | 0.891753i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.72274 | − | 4.59323i | −0.484543 | − | 0.471255i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.6909 | −1.39010 | −0.695049 | − | 0.718963i | \(-0.744617\pi\) | ||||
−0.695049 | + | 0.718963i | \(0.744617\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.21591i | 0.718009i | 0.933336 | + | 0.359005i | \(0.116884\pi\) | ||||
−0.933336 | + | 0.359005i | \(0.883116\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.9655 | 1.86873 | 0.934365 | − | 0.356316i | \(-0.115967\pi\) | ||||
0.934365 | + | 0.356316i | \(0.115967\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 4.17749i | − | 0.403853i | −0.979401 | − | 0.201927i | \(-0.935280\pi\) | ||
0.979401 | − | 0.201927i | \(-0.0647203\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 12.3782i | − | 1.18562i | −0.805343 | − | 0.592809i | \(-0.798019\pi\) | ||
0.805343 | − | 0.592809i | \(-0.201981\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 3.88175i | − | 0.365165i | −0.983191 | − | 0.182582i | \(-0.941554\pi\) | ||
0.983191 | − | 0.182582i | \(-0.0584456\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.01954 | − | 10.6752i | 0.0950729 | − | 0.995470i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.475613i | 0.0435993i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.50598 | −0.318725 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.22842 | + | 7.56923i | 0.735972 | + | 0.677012i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.06851i | 0.627229i | 0.949550 | + | 0.313615i | \(0.101540\pi\) | ||||
−0.949550 | + | 0.313615i | \(0.898460\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1.98669i | − | 0.173578i | −0.996227 | − | 0.0867889i | \(-0.972339\pi\) | ||
0.996227 | − | 0.0867889i | \(-0.0276606\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.58179i | 0.310581i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.4934i | 1.15282i | 0.817160 | + | 0.576411i | \(0.195547\pi\) | ||||
−0.817160 | + | 0.576411i | \(0.804453\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.96667 | 0.251630 | 0.125815 | − | 0.992054i | \(-0.459845\pi\) | ||||
0.125815 | + | 0.992054i | \(0.459845\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 19.1554i | 1.60186i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.29626 | − | 5.15102i | −0.439830 | − | 0.427769i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.85554 | 0.479704 | 0.239852 | − | 0.970809i | \(-0.422901\pi\) | ||||
0.239852 | + | 0.970809i | \(0.422901\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.14041 | 0.0928049 | 0.0464024 | − | 0.998923i | \(-0.485224\pi\) | ||||
0.0464024 | + | 0.998923i | \(0.485224\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.4109 | + | 12.7608i | −0.996867 | + | 1.02497i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.9077 | 1.34938 | 0.674692 | − | 0.738099i | \(-0.264276\pi\) | ||||
0.674692 | + | 0.738099i | \(0.264276\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.54712 | + | 3.64919i | −0.358364 | + | 0.287597i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.28818i | 0.727506i | 0.931495 | + | 0.363753i | \(0.118505\pi\) | ||||
−0.931495 | + | 0.363753i | \(0.881495\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.5641 | −1.28177 | −0.640885 | − | 0.767637i | \(-0.721433\pi\) | ||||
−0.640885 | + | 0.767637i | \(0.721433\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −35.9631 | −2.76640 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.5167 | −1.40780 | −0.703900 | − | 0.710299i | \(-0.748560\pi\) | ||||
−0.703900 | + | 0.710299i | \(0.748560\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.168974 | − | 6.07621i | −0.0127732 | − | 0.459318i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.89279i | 0.664678i | 0.943160 | + | 0.332339i | \(0.107838\pi\) | ||||
−0.943160 | + | 0.332339i | \(0.892162\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 21.4231i | − | 1.59237i | −0.605056 | − | 0.796183i | \(-0.706849\pi\) | ||
0.605056 | − | 0.796183i | \(-0.293151\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.87774 | + | 2.95889i | −0.211576 | + | 0.217542i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.07098i | 0.0783176i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.8622 | −1.72661 | −0.863303 | − | 0.504686i | \(-0.831608\pi\) | ||||
−0.863303 | + | 0.504686i | \(0.831608\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.6503i | 0.766626i | 0.923619 | + | 0.383313i | \(0.125217\pi\) | ||||
−0.923619 | + | 0.383313i | \(0.874783\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.9273 | −1.27727 | −0.638633 | − | 0.769512i | \(-0.720500\pi\) | ||||
−0.638633 | + | 0.769512i | \(0.720500\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.2721i | 1.43705i | 0.695500 | + | 0.718526i | \(0.255183\pi\) | ||||
−0.695500 | + | 0.718526i | \(0.744817\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.01676i | 0.281921i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.9942 | + | 14.5830i | 1.04724 | + | 1.01852i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.06543i | 0.557898i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.9786 | −1.37539 | −0.687693 | − | 0.726002i | \(-0.741376\pi\) | ||||
−0.687693 | + | 0.726002i | \(0.741376\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.63851 | − | 7.85389i | 0.520942 | − | 0.535631i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.67800 | 0.656985 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.73752 | −0.184146 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.6489i | 0.980963i | 0.871451 | + | 0.490482i | \(0.163179\pi\) | ||||
−0.871451 | + | 0.490482i | \(0.836821\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.4187i | 1.15612i | 0.815995 | + | 0.578059i | \(0.196190\pi\) | ||||
−0.815995 | + | 0.578059i | \(0.803810\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 8.28098i | − | 0.547222i | −0.961840 | − | 0.273611i | \(-0.911782\pi\) | ||
0.961840 | − | 0.273611i | \(-0.0882182\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 27.7224 | 1.81616 | 0.908078 | − | 0.418800i | \(-0.137549\pi\) | ||||
0.908078 | + | 0.418800i | \(0.137549\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.48643 | − | 4.61292i | 0.292662 | − | 0.300914i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 25.5089i | − | 1.65004i | −0.565107 | − | 0.825018i | \(-0.691165\pi\) | ||
0.565107 | − | 0.825018i | \(-0.308835\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.4544i | 0.866675i | 0.901232 | + | 0.433338i | \(0.142664\pi\) | ||||
−0.901232 | + | 0.433338i | \(0.857336\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.60891 | − | 8.85164i | 0.550003 | − | 0.565511i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.6160 | −1.31177 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.7914 | −0.807385 | −0.403693 | − | 0.914895i | \(-0.632274\pi\) | ||||
−0.403693 | + | 0.914895i | \(0.632274\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.2391 | + | 8.21720i | −0.643730 | + | 0.516611i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.361953 | −0.0225780 | −0.0112890 | − | 0.999936i | \(-0.503593\pi\) | ||||
−0.0112890 | + | 0.999936i | \(0.503593\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.24406 | 0.139439 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 16.5816i | − | 1.02247i | −0.859442 | − | 0.511233i | \(-0.829189\pi\) | ||
0.859442 | − | 0.511233i | \(-0.170811\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.73846 | − | 4.60852i | −0.291081 | − | 0.283099i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.28389i | 0.383136i | 0.981479 | + | 0.191568i | \(0.0613572\pi\) | ||||
−0.981479 | + | 0.191568i | \(0.938643\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.63929 | −0.342562 | −0.171281 | − | 0.985222i | \(-0.554791\pi\) | ||||
−0.171281 | + | 0.985222i | \(0.554791\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.380493 | − | 13.6823i | −0.0229446 | − | 0.825075i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 6.50942i | − | 0.391113i | −0.980692 | − | 0.195556i | \(-0.937349\pi\) | ||
0.980692 | − | 0.195556i | \(-0.0626513\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.2192 | −1.56411 | −0.782053 | − | 0.623212i | \(-0.785828\pi\) | ||||
−0.782053 | + | 0.623212i | \(0.785828\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.6516 | −1.04928 | −0.524638 | − | 0.851325i | \(-0.675799\pi\) | ||||
−0.524638 | + | 0.851325i | \(0.675799\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 11.3718i | − | 0.671256i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.8469 | 0.990997 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.9531i | 1.10725i | 0.832765 | + | 0.553626i | \(0.186756\pi\) | ||||
−0.832765 | + | 0.553626i | \(0.813244\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.0916 | + | 12.7326i | 0.762224 | + | 0.741322i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −21.0040 | − | 26.1722i | −1.21469 | − | 1.51358i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.95650 | −0.343327 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −20.7044 | − | 20.1366i | −1.18553 | − | 1.15302i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 25.7698i | − | 1.47076i | −0.677655 | − | 0.735380i | \(-0.737004\pi\) | ||
0.677655 | − | 0.735380i | \(-0.262996\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.09108i | 0.345394i | 0.984975 | + | 0.172697i | \(0.0552481\pi\) | ||||
−0.984975 | + | 0.172697i | \(0.944752\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.62159 | −0.0916577 | −0.0458288 | − | 0.998949i | \(-0.514593\pi\) | ||||
−0.0458288 | + | 0.998949i | \(0.514593\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.39354 | 0.302931 | 0.151466 | − | 0.988463i | \(-0.451601\pi\) | ||||
0.151466 | + | 0.988463i | \(0.451601\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.04488i | 0.506416i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.15264 | −0.0641345 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 34.9733 | − | 0.972577i | 1.93997 | − | 0.0539489i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.49851 | −0.192879 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.6809 | −1.02679 | −0.513397 | − | 0.858151i | \(-0.671613\pi\) | ||||
−0.513397 | + | 0.858151i | \(0.671613\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.4442 | + | 16.9079i | −0.898445 | + | 0.923777i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.4134 | 1.11199 | 0.555995 | − | 0.831186i | \(-0.312337\pi\) | ||||
0.555995 | + | 0.831186i | \(0.312337\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.7928 | 1.18015 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.2232 | −0.821975 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.7612 | 0.685059 | 0.342530 | − | 0.939507i | \(-0.388716\pi\) | ||||
0.342530 | + | 0.939507i | \(0.388716\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.1162 | 1.02327 | 0.511633 | − | 0.859204i | \(-0.329041\pi\) | ||||
0.511633 | + | 0.859204i | \(0.329041\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.8401 | 1.00276 | 0.501380 | − | 0.865227i | \(-0.332826\pi\) | ||||
0.501380 | + | 0.865227i | \(0.332826\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 23.3198 | + | 22.6803i | 1.23768 | + | 1.20374i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.2899 | −0.859748 | −0.429874 | − | 0.902889i | \(-0.641442\pi\) | ||||
−0.429874 | + | 0.902889i | \(0.641442\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.3196 | 0.543136 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.73752 | + | 2.66245i | 0.143288 | + | 0.139359i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.8454 | 1.40132 | 0.700658 | − | 0.713497i | \(-0.252890\pi\) | ||||
0.700658 | + | 0.713497i | \(0.252890\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.59371i | 0.186576i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −30.1882 | −1.56309 | −0.781544 | − | 0.623850i | \(-0.785567\pi\) | ||||
−0.781544 | + | 0.623850i | \(0.785567\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −23.1196 | −1.19072 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.8864i | 1.63790i | 0.573868 | + | 0.818948i | \(0.305442\pi\) | ||||
−0.573868 | + | 0.818948i | \(0.694558\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.8594i | 1.06586i | 0.846158 | + | 0.532932i | \(0.178910\pi\) | ||||
−0.846158 | + | 0.532932i | \(0.821090\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.18843 | + | 5.33473i | −0.264427 | + | 0.271883i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.9398 | 1.41660 | 0.708302 | − | 0.705909i | \(-0.249461\pi\) | ||||
0.708302 | + | 0.705909i | \(0.249461\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.17433 | − | 1.46329i | −0.0593883 | − | 0.0740015i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −19.2214 | − | 18.6943i | −0.967132 | − | 0.940611i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 0.0173642i | − | 0.000871486i | −1.00000 | 0.000435743i | \(-0.999861\pi\) | |||
1.00000 | 0.000435743i | \(-0.000138701\pi\) | ||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.6179 | 0.779921 | 0.389961 | − | 0.920832i | \(-0.372489\pi\) | ||||
0.389961 | + | 0.920832i | \(0.372489\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 55.7044i | 2.77484i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.05314 | 0.250475 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.5255 | −0.767685 | −0.383842 | − | 0.923399i | \(-0.625399\pi\) | ||||
−0.383842 | + | 0.923399i | \(0.625399\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 9.92888i | − | 0.488568i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −20.8281 | − | 20.2569i | −1.02241 | − | 0.994372i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.4486 | 0.705860 | 0.352930 | − | 0.935650i | \(-0.385185\pi\) | ||||
0.352930 | + | 0.935650i | \(0.385185\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 15.3048i | − | 0.745910i | −0.927849 | − | 0.372955i | \(-0.878345\pi\) | ||
0.927849 | − | 0.372955i | \(-0.121655\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.95535 | − | 0.0543766i | 0.0948485 | − | 0.00263765i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.7025i | 0.759898i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.09723 | −0.101020 | −0.0505101 | − | 0.998724i | \(-0.516085\pi\) | ||||
−0.0505101 | + | 0.998724i | \(0.516085\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.8785 | 0.715014 | 0.357507 | − | 0.933911i | \(-0.383627\pi\) | ||||
0.357507 | + | 0.933911i | \(0.383627\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.84375 | − | 11.0199i | −0.423054 | − | 0.527152i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.0823 | 1.00620 | 0.503101 | − | 0.864228i | \(-0.332192\pi\) | ||||
0.503101 | + | 0.864228i | \(0.332192\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.3629 | 0.777424 | 0.388712 | − | 0.921359i | \(-0.372920\pi\) | ||||
0.388712 | + | 0.921359i | \(0.372920\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.6165 | − | 24.2824i | 1.11953 | − | 1.15110i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.7204i | 0.741892i | 0.928655 | + | 0.370946i | \(0.120966\pi\) | ||||
−0.928655 | + | 0.370946i | \(0.879034\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 25.6068i | − | 1.20578i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.6361 | − | 13.2621i | −0.639269 | − | 0.621738i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.13286 | 0.0529929 | 0.0264964 | − | 0.999649i | \(-0.491565\pi\) | ||||
0.0264964 | + | 0.999649i | \(0.491565\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.8726i | 0.552964i | 0.961019 | + | 0.276482i | \(0.0891686\pi\) | ||||
−0.961019 | + | 0.276482i | \(0.910831\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 25.1156i | − | 1.16722i | −0.812033 | − | 0.583611i | \(-0.801639\pi\) | ||
0.812033 | − | 0.583611i | \(-0.198361\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.6360i | 1.41766i | 0.705377 | + | 0.708832i | \(0.250778\pi\) | ||||
−0.705377 | + | 0.708832i | \(0.749222\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.8232 | 0.592120 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.4128 | −0.616720 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.7256 | − | 0.409505i | 0.675656 | − | 0.0187894i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.0763 | 0.734547 | 0.367273 | − | 0.930113i | \(-0.380291\pi\) | ||||
0.367273 | + | 0.930113i | \(0.380291\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.9163i | 0.588933i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.3442 | − | 21.9460i | 0.969189 | − | 0.996516i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.99877i | 0.135887i | 0.997689 | + | 0.0679436i | \(0.0216438\pi\) | ||||
−0.997689 | + | 0.0679436i | \(0.978356\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 14.4568i | − | 0.652425i | −0.945296 | − | 0.326213i | \(-0.894227\pi\) | ||
0.945296 | − | 0.326213i | \(-0.105773\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.29261 | −0.0582163 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 17.6860i | − | 0.793327i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.94634 | 0.131896 | 0.0659480 | − | 0.997823i | \(-0.478993\pi\) | ||||
0.0659480 | + | 0.997823i | \(0.478993\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.06093i | 0.0473047i | 0.999720 | + | 0.0236523i | \(0.00752948\pi\) | ||||
−0.999720 | + | 0.0236523i | \(0.992471\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.5668 | − | 11.2496i | −0.514718 | − | 0.500603i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 13.5277i | − | 0.599606i | −0.954001 | − | 0.299803i | \(-0.903079\pi\) | ||
0.954001 | − | 0.299803i | \(-0.0969209\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 2.07618i | − | 0.0918446i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −29.5674 | + | 30.4011i | −1.30290 | + | 1.33963i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.87789 | −0.346469 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 42.8579 | 1.87764 | 0.938819 | − | 0.344410i | \(-0.111921\pi\) | ||||
0.938819 | + | 0.344410i | \(0.111921\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.9651 | −1.39774 | −0.698868 | − | 0.715251i | \(-0.746313\pi\) | ||||
−0.698868 | + | 0.715251i | \(0.746313\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.11443i | 0.135666i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.97966 | − | 22.4545i | 0.216507 | − | 0.976281i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 65.4535 | 2.83511 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.69637 | + | 6.51274i | 0.289509 | + | 0.281570i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.1167 | −0.651123 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.48281 | 0.364705 | 0.182352 | − | 0.983233i | \(-0.441629\pi\) | ||||
0.182352 | + | 0.983233i | \(0.441629\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.8419 | + | 19.2977i | 0.849932 | + | 0.826624i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.2068i | 0.778465i | 0.921139 | + | 0.389233i | \(0.127260\pi\) | ||||
−0.921139 | + | 0.389233i | \(0.872740\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.73454 | −0.414705 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.5778i | 0.619909i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 0.758851i | − | 0.0321536i | −0.999871 | − | 0.0160768i | \(-0.994882\pi\) | ||
0.999871 | − | 0.0160768i | \(-0.00511762\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 34.2843i | − | 1.45007i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.3844i | 0.606230i | 0.952954 | + | 0.303115i | \(0.0980266\pi\) | ||||
−0.952954 | + | 0.303115i | \(0.901973\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.22231 | + | 6.05168i | 0.261775 | + | 0.254596i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.59604 | −0.0669095 | −0.0334548 | − | 0.999440i | \(-0.510651\pi\) | ||||
−0.0334548 | + | 0.999440i | \(0.510651\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 0.106176i | − | 0.00444333i | −0.999998 | − | 0.00222167i | \(-0.999293\pi\) | ||
0.999998 | − | 0.00222167i | \(-0.000707179\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.5225 | + | 18.2771i | 0.647335 | + | 0.762206i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 34.0755i | − | 1.41858i | −0.704916 | − | 0.709291i | \(-0.749015\pi\) | ||
0.704916 | − | 0.709291i | \(-0.250985\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.7963i | 0.655341i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.09227i | 0.335148i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.7927 | −0.858208 | −0.429104 | − | 0.903255i | \(-0.641171\pi\) | ||||
−0.429104 | + | 0.903255i | \(0.641171\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.4544i | 0.966423i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.2505 | 1.24224 | 0.621120 | − | 0.783716i | \(-0.286678\pi\) | ||||
0.621120 | + | 0.783716i | \(0.286678\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.762390 | − | 0.741484i | −0.0312550 | − | 0.0303979i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 0.878003i | − | 0.0358742i | −0.999839 | − | 0.0179371i | \(-0.994290\pi\) | ||
0.999839 | − | 0.0179371i | \(-0.00570986\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.5102 | −0.918212 | −0.459106 | − | 0.888382i | \(-0.651830\pi\) | ||||
−0.459106 | + | 0.888382i | \(0.651830\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.46584 | − | 5.61996i | 0.222218 | − | 0.228484i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.5755i | 0.794544i | 0.917701 | + | 0.397272i | \(0.130043\pi\) | ||||
−0.917701 | + | 0.397272i | \(0.869957\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 20.1366i | − | 0.814641i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.4086 | −0.783904 | −0.391952 | − | 0.919986i | \(-0.628200\pi\) | ||||
−0.391952 | + | 0.919986i | \(0.628200\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 39.9822i | − | 1.60962i | −0.593530 | − | 0.804812i | \(-0.702266\pi\) | ||
0.593530 | − | 0.804812i | \(-0.297734\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 29.8654i | − | 1.20039i | −0.799854 | − | 0.600195i | \(-0.795090\pi\) | ||
0.799854 | − | 0.600195i | \(-0.204910\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.4161 | −0.737826 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.9614 | + | 1.38938i | −0.998454 | + | 0.0555753i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.722149i | 0.0287940i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.18510i | 0.286034i | 0.989720 | + | 0.143017i | \(0.0456804\pi\) | ||||
−0.989720 | + | 0.143017i | \(0.954320\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.3306 | − | 11.0199i | −0.449640 | − | 0.437310i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 38.6398i | − | 1.53096i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.3137 | 0.407365 | 0.203683 | − | 0.979037i | \(-0.434709\pi\) | ||||
0.203683 | + | 0.979037i | \(0.434709\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.4473 | 0.964107 | 0.482054 | − | 0.876142i | \(-0.339891\pi\) | ||||
0.482054 | + | 0.876142i | \(0.339891\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.3595 | 0.446590 | 0.223295 | − | 0.974751i | \(-0.428319\pi\) | ||||
0.223295 | + | 0.974751i | \(0.428319\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 22.3577i | − | 0.877616i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 36.7299 | 1.43735 | 0.718676 | − | 0.695345i | \(-0.244748\pi\) | ||||
0.718676 | + | 0.695345i | \(0.244748\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.18459 | + | 3.09726i | 0.124432 | + | 0.121020i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.22349 | −0.281387 | −0.140694 | − | 0.990053i | \(-0.544933\pi\) | ||||
−0.140694 | + | 0.990053i | \(0.544933\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.1450i | 1.36698i | 0.729959 | + | 0.683491i | \(0.239539\pi\) | ||||
−0.729959 | + | 0.683491i | \(0.760461\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.74149 | − | 5.58404i | −0.222645 | − | 0.216540i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.91772 | − | 12.3581i | −0.384016 | − | 0.478507i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 35.3587i | 1.36501i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 3.90352i | − | 0.150470i | −0.997166 | − | 0.0752349i | \(-0.976029\pi\) | ||
0.997166 | − | 0.0752349i | \(-0.0239707\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 43.7055i | − | 1.67974i | −0.542787 | − | 0.839870i | \(-0.682631\pi\) | ||
0.542787 | − | 0.839870i | \(-0.317369\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.6441 | −0.638744 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.323411 | 0.0123750 | 0.00618750 | − | 0.999981i | \(-0.498030\pi\) | ||||
0.00618750 | + | 0.999981i | \(0.498030\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.6295 | − | 21.0364i | −0.826420 | − | 0.803758i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20.6846 | −0.788021 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.1535 | 1.45143 | 0.725715 | − | 0.687996i | \(-0.241509\pi\) | ||||
0.725715 | + | 0.687996i | \(0.241509\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.62506 | + | 4.75547i | −0.175439 | + | 0.180385i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.65950 | 0.138613 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.16633 | 0.308438 | 0.154219 | − | 0.988037i | \(-0.450714\pi\) | ||||
0.154219 | + | 0.988037i | \(0.450714\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.43844i | 0.205115i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.77246i | 0.329922i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.35439i | 0.238644i | 0.992856 | + | 0.119322i | \(0.0380721\pi\) | ||||
−0.992856 | + | 0.119322i | \(0.961928\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −29.7757 | + | 23.8958i | −1.11511 | + | 0.894905i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −30.7055 | − | 29.8635i | −1.14832 | − | 1.11683i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 35.2797i | 1.31571i | 0.753144 | + | 0.657856i | \(0.228536\pi\) | ||||
−0.753144 | + | 0.657856i | \(0.771464\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.0566 | 0.858674 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16.5138 | − | 0.459235i | 0.613308 | − | 0.0170556i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.32193 | 0.0861154 | 0.0430577 | − | 0.999073i | \(-0.486290\pi\) | ||||
0.0430577 | + | 0.999073i | \(0.486290\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1.91683i | − | 0.0708965i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −48.5901 | −1.79472 | −0.897358 | − | 0.441304i | \(-0.854516\pi\) | ||||
−0.897358 | + | 0.441304i | \(0.854516\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28.8751 | 1.06363 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.8179 | −0.986512 | −0.493256 | − | 0.869884i | \(-0.664193\pi\) | ||||
−0.493256 | + | 0.869884i | \(0.664193\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.33417i | − | 0.0489458i | −0.999700 | − | 0.0244729i | \(-0.992209\pi\) | ||
0.999700 | − | 0.0244729i | \(-0.00779074\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.12882 | + | 9.38622i | −0.334454 | + | 0.343884i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 5.07863i | − | 0.185569i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 16.4951i | − | 0.601916i | −0.953637 | − | 0.300958i | \(-0.902694\pi\) | ||
0.953637 | − | 0.300958i | \(-0.0973065\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.77790 | + | 1.82803i | −0.0647044 | + | 0.0665288i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.93942 | −0.361254 | −0.180627 | − | 0.983552i | \(-0.557813\pi\) | ||||
−0.180627 | + | 0.983552i | \(0.557813\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 15.4267i | − | 0.559219i | −0.960114 | − | 0.279609i | \(-0.909795\pi\) | ||
0.960114 | − | 0.279609i | \(-0.0902049\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 15.0483i | − | 0.544787i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 57.1484 | 2.06351 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 28.4021i | − | 1.02421i | −0.858924 | − | 0.512103i | \(-0.828867\pi\) | ||
0.858924 | − | 0.512103i | \(-0.171133\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 44.4726i | − | 1.59957i | −0.600287 | − | 0.799785i | \(-0.704947\pi\) | ||
0.600287 | − | 0.799785i | \(-0.295053\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.10648 | − | 39.7885i | −0.0397460 | − | 1.42924i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27.5593 | 0.987415 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 39.8252i | − | 1.42506i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −26.3593 | + | 27.1025i | −0.940803 | + | 0.967330i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.4314 | 0.799594 | 0.399797 | − | 0.916604i | \(-0.369081\pi\) | ||||
0.399797 | + | 0.916604i | \(0.369081\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 4.71909i | − | 0.167792i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −90.3802 | −3.20950 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 3.18044i | − | 0.112657i | −0.998412 | − | 0.0563284i | \(-0.982061\pi\) | ||
0.998412 | − | 0.0563284i | \(-0.0179394\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.12584i | − | 0.0398292i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 4.67510i | − | 0.164981i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.23947 | − | 12.9780i | 0.0436856 | − | 0.457414i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.3367i | 0.398578i | 0.979941 | + | 0.199289i | \(0.0638632\pi\) | ||||
−0.979941 | + | 0.199289i | \(0.936137\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.6106 | 0.934424 | 0.467212 | − | 0.884145i | \(-0.345259\pi\) | ||||
0.467212 | + | 0.884145i | \(0.345259\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.8886 | − | 14.4803i | −0.521526 | − | 0.507224i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 14.4355i | − | 0.505033i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 7.15531i | − | 0.249722i | −0.992174 | − | 0.124861i | \(-0.960152\pi\) | ||
0.992174 | − | 0.124861i | \(-0.0398485\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.1559i | 0.946594i | 0.880903 | + | 0.473297i | \(0.156936\pi\) | ||||
−0.880903 | + | 0.473297i | \(0.843064\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 45.2505i | − | 1.57351i | −0.617262 | − | 0.786757i | \(-0.711758\pi\) | ||
0.617262 | − | 0.786757i | \(-0.288242\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.1757 | 1.25643 | 0.628216 | − | 0.778039i | \(-0.283785\pi\) | ||||
0.628216 | + | 0.778039i | \(0.283785\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 2.16034i | − | 0.0748515i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 25.8236 | − | 26.5517i | 0.893662 | − | 0.918860i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.2859 | 1.08011 | 0.540055 | − | 0.841630i | \(-0.318403\pi\) | ||||
0.540055 | + | 0.841630i | \(0.318403\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.0833 | 0.623563 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 56.0668 | − | 57.6477i | 1.92876 | − | 1.98314i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.26226 | −0.146453 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.90415 | + | 5.54078i | −0.236671 | + | 0.189935i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.6476i | 1.22055i | 0.792190 | + | 0.610275i | \(0.208941\pi\) | ||||
−0.792190 | + | 0.610275i | \(0.791059\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −31.9633 | −1.09185 | −0.545923 | − | 0.837835i | \(-0.683821\pi\) | ||||
−0.545923 | + | 0.837835i | \(0.683821\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.82627 | −0.335268 | −0.167634 | − | 0.985849i | \(-0.553613\pi\) | ||||
−0.167634 | + | 0.985849i | \(0.553613\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −50.8297 | −1.73026 | −0.865132 | − | 0.501544i | \(-0.832766\pi\) | ||||
−0.865132 | + | 0.501544i | \(0.832766\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28.8677 | − | 29.6817i | 0.981532 | − | 1.00921i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32.8260i | 1.11355i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 73.8074i | 2.50087i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.0034 | + | 9.20200i | 0.338176 | + | 0.311084i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 31.2256i | − | 1.05441i | −0.849737 | − | 0.527207i | \(-0.823239\pi\) | ||
0.849737 | − | 0.527207i | \(-0.176761\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.15796 | 0.173776 | 0.0868880 | − | 0.996218i | \(-0.472308\pi\) | ||||
0.0868880 | + | 0.996218i | \(0.472308\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.8664i | 0.702212i | 0.936336 | + | 0.351106i | \(0.114194\pi\) | ||||
−0.936336 | + | 0.351106i | \(0.885806\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.7224 | −0.930828 | −0.465414 | − | 0.885093i | \(-0.654095\pi\) | ||||
−0.465414 | + | 0.885093i | \(0.654095\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.59328i | 0.288209i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 8.47857i | − | 0.283724i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.2548 | − | 13.8639i | −0.476486 | − | 0.463420i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26.3027i | 0.877244i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.15647 | −0.0385277 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 34.3405 | + | 33.3988i | 1.14152 | + | 1.11021i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.816241 | −0.0271028 | −0.0135514 | − | 0.999908i | \(-0.504314\pi\) | ||||
−0.0135514 | + | 0.999908i | \(0.504314\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.2500 | −0.472122 | −0.236061 | − | 0.971738i | \(-0.575857\pi\) | ||||
−0.236061 | + | 0.971738i | \(0.575857\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 35.5699i | 1.17719i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 2.41524i | − | 0.0797583i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 35.8892i | − | 1.18388i | −0.805984 | − | 0.591938i | \(-0.798363\pi\) | ||
0.805984 | − | 0.591938i | \(-0.201637\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 101.797 | 3.35069 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.256563 | − | 9.22585i | −0.00843573 | − | 0.303344i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.73060i | 0.155206i | 0.996984 | + | 0.0776029i | \(0.0247266\pi\) | ||||
−0.996984 | + | 0.0776029i | \(0.975273\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 16.2693i | − | 0.533206i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.71674 | − | 1.66966i | −0.0561434 | − | 0.0546038i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.0761 | 0.427177 | 0.213588 | − | 0.976924i | \(-0.431485\pi\) | ||||
0.213588 | + | 0.976924i | \(0.431485\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.7022 | 1.22906 | 0.614528 | − | 0.788895i | \(-0.289346\pi\) | ||||
0.614528 | + | 0.788895i | \(0.289346\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28.0779 | + | 34.9868i | 0.914343 | + | 1.13933i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.5167 | −0.601713 | −0.300856 | − | 0.953669i | \(-0.597272\pi\) | ||||
−0.300856 | + | 0.953669i | \(0.597272\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.9500 | 0.387914 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51.4367i | 1.66620i | 0.553124 | + | 0.833099i | \(0.313436\pi\) | ||||
−0.553124 | + | 0.833099i | \(0.686564\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37.2013 | − | 38.2502i | 1.20381 | − | 1.23775i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.4041i | 0.529717i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 32.3739 | 1.04432 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.0721 | − | 16.6039i | −0.549569 | − | 0.534499i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 13.0661i | − | 0.420176i | −0.977682 | − | 0.210088i | \(-0.932625\pi\) | ||
0.977682 | − | 0.210088i | \(-0.0673750\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.4356 | 1.10509 | 0.552546 | − | 0.833482i | \(-0.313656\pi\) | ||||
0.552546 | + | 0.833482i | \(0.313656\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.60662 | 0.115623 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 50.9556i | 1.63022i | 0.579310 | + | 0.815108i | \(0.303322\pi\) | ||||
−0.579310 | + | 0.815108i | \(0.696678\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −41.4691 | −1.32536 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 41.2121i | 1.31446i | 0.753690 | + | 0.657230i | \(0.228272\pi\) | ||||
−0.753690 | + | 0.657230i | \(0.771728\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.9488 | − | 28.7368i | 0.890521 | − | 0.915630i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.3260 | − | 14.7071i | 0.582732 | − | 0.467659i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.20850 | −0.292518 | −0.146259 | − | 0.989246i | \(-0.546723\pi\) | ||||
−0.146259 | + | 0.989246i | \(0.546723\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −32.4955 | − | 31.6044i | −1.03018 | − | 1.00193i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 22.3782i | − | 0.708723i | −0.935108 | − | 0.354362i | \(-0.884698\pi\) | ||
0.935108 | − | 0.354362i | \(-0.115302\pi\) | |||||||
\(998\) | 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 | 4140.2.n.b.2069.16 | yes | 32 | |
3.2 | odd | 2 | inner | 4140.2.n.b.2069.18 | yes | 32 | |
5.4 | even | 2 | inner | 4140.2.n.b.2069.13 | ✓ | 32 | |
15.14 | odd | 2 | inner | 4140.2.n.b.2069.19 | yes | 32 | |
23.22 | odd | 2 | inner | 4140.2.n.b.2069.17 | yes | 32 | |
69.68 | even | 2 | inner | 4140.2.n.b.2069.15 | yes | 32 | |
115.114 | odd | 2 | inner | 4140.2.n.b.2069.20 | yes | 32 | |
345.344 | even | 2 | inner | 4140.2.n.b.2069.14 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4140.2.n.b.2069.13 | ✓ | 32 | 5.4 | even | 2 | inner | |
4140.2.n.b.2069.14 | yes | 32 | 345.344 | even | 2 | inner | |
4140.2.n.b.2069.15 | yes | 32 | 69.68 | even | 2 | inner | |
4140.2.n.b.2069.16 | yes | 32 | 1.1 | even | 1 | trivial | |
4140.2.n.b.2069.17 | yes | 32 | 23.22 | odd | 2 | inner | |
4140.2.n.b.2069.18 | yes | 32 | 3.2 | odd | 2 | inner | |
4140.2.n.b.2069.19 | yes | 32 | 15.14 | odd | 2 | inner | |
4140.2.n.b.2069.20 | yes | 32 | 115.114 | odd | 2 | inner |