Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5520,2,Mod(1471,5520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5520.1471");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5520.be (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: | \(44.0774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.16 | ||
Character | \(\chi\) | \(=\) | 5520.1471 |
Dual form | 5520.2.be.c.1471.15 |
$q$-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 \(\left(\mathbb{Z}/5520\mathbb{Z}\right)^\times\).
\(n\) | \(1201\) | \(1381\) | \(1841\) | \(4417\) | \(4831\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.60511 | 1.36260 | 0.681302 | − | 0.732002i | \(-0.261414\pi\) | ||||
0.681302 | + | 0.732002i | \(0.261414\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.78590 | 1.74452 | 0.872258 | − | 0.489046i | \(-0.162655\pi\) | ||||
0.872258 | + | 0.489046i | \(0.162655\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.896503 | 0.248645 | 0.124323 | − | 0.992242i | \(-0.460324\pi\) | ||||
0.124323 | + | 0.992242i | \(0.460324\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.83315i | 1.65728i | 0.559781 | + | 0.828641i | \(0.310885\pi\) | ||||
−0.559781 | + | 0.828641i | \(0.689115\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.90832 | 0.437798 | 0.218899 | − | 0.975748i | \(-0.429753\pi\) | ||||
0.218899 | + | 0.975748i | \(0.429753\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.60511i | 0.786700i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.77275 | − | 0.469990i | 0.995186 | − | 0.0979997i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.39299 | 0.258672 | 0.129336 | − | 0.991601i | \(-0.458715\pi\) | ||||
0.129336 | + | 0.991601i | \(0.458715\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.12061i | 0.201268i | 0.994924 | + | 0.100634i | \(0.0320871\pi\) | ||||
−0.994924 | + | 0.100634i | \(0.967913\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.78590i | 1.00720i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.60511i | 0.609375i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.48133i | − | 1.22992i | −0.788557 | − | 0.614961i | \(-0.789172\pi\) | ||
0.788557 | − | 0.614961i | \(-0.210828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.896503i | 0.143555i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.19938 | 0.499660 | 0.249830 | − | 0.968290i | \(-0.419625\pi\) | ||||
0.249830 | + | 0.968290i | \(0.419625\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.53782 | 0.387014 | 0.193507 | − | 0.981099i | \(-0.438014\pi\) | ||||
0.193507 | + | 0.981099i | \(0.438014\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 5.80647i | − | 0.846961i | −0.905905 | − | 0.423480i | \(-0.860808\pi\) | ||
0.905905 | − | 0.423480i | \(-0.139192\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.99683 | 0.856690 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.83315 | −0.956832 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.67178i | 0.366998i | 0.983020 | + | 0.183499i | \(0.0587424\pi\) | ||||
−0.983020 | + | 0.183499i | \(0.941258\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.78590i | 0.780171i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.90832i | 0.252763i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.58667i | 0.857511i | 0.903420 | + | 0.428756i | \(0.141048\pi\) | ||||
−0.903420 | + | 0.428756i | \(0.858952\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.597564i | 0.0765102i | 0.999268 | + | 0.0382551i | \(0.0121800\pi\) | ||||
−0.999268 | + | 0.0382551i | \(0.987820\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.60511 | −0.454201 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.896503i | 0.111197i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.41745 | −0.661846 | −0.330923 | − | 0.943658i | \(-0.607360\pi\) | ||||
−0.330923 | + | 0.943658i | \(0.607360\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.469990 | + | 4.77275i | 0.0565801 | + | 0.574571i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.72842i | − | 0.442482i | −0.975219 | − | 0.221241i | \(-0.928989\pi\) | ||
0.975219 | − | 0.221241i | \(-0.0710108\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.479048 | 0.0560683 | 0.0280342 | − | 0.999607i | \(-0.491075\pi\) | ||||
0.0280342 | + | 0.999607i | \(0.491075\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 1.00000i | − | 0.115470i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 20.8588 | 2.37708 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.03711 | 0.116684 | 0.0583422 | − | 0.998297i | \(-0.481419\pi\) | ||||
0.0583422 | + | 0.998297i | \(0.481419\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.2088 | −1.23033 | −0.615163 | − | 0.788400i | \(-0.710910\pi\) | ||||
−0.615163 | + | 0.788400i | \(0.710910\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.83315 | −0.741159 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.39299i | 0.149344i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 5.21573i | − | 0.552866i | −0.961033 | − | 0.276433i | \(-0.910848\pi\) | ||
0.961033 | − | 0.276433i | \(-0.0891524\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.23199 | 0.338805 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.12061 | −0.116202 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.90832i | 0.195789i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.73433i | − | 0.480698i | −0.970687 | − | 0.240349i | \(-0.922738\pi\) | ||
0.970687 | − | 0.240349i | \(-0.0772619\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.78590 | −0.581505 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.362853 | −0.0361052 | −0.0180526 | − | 0.999837i | \(-0.505747\pi\) | ||||
−0.0180526 | + | 0.999837i | \(0.505747\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.7189 | −1.15470 | −0.577348 | − | 0.816498i | \(-0.695912\pi\) | ||||
−0.577348 | + | 0.816498i | \(0.695912\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.60511 | −0.351823 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.6988 | 1.22764 | 0.613818 | − | 0.789447i | \(-0.289633\pi\) | ||||
0.613818 | + | 0.789447i | \(0.289633\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 8.37783i | − | 0.802451i | −0.915979 | − | 0.401225i | \(-0.868584\pi\) | ||
0.915979 | − | 0.401225i | \(-0.131416\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.48133 | 0.710096 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 7.77619i | − | 0.731522i | −0.930709 | − | 0.365761i | \(-0.880809\pi\) | ||
0.930709 | − | 0.365761i | \(-0.119191\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.469990 | + | 4.77275i | 0.0438268 | + | 0.445061i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.896503 | −0.0828817 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 24.6343i | 2.25822i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.4767 | 2.04334 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.19938i | 0.288479i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.02772i | 0.446138i | 0.974803 | + | 0.223069i | \(0.0716075\pi\) | ||||
−0.974803 | + | 0.223069i | \(0.928392\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.53782i | 0.223443i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 16.0105i | − | 1.39885i | −0.714707 | − | 0.699424i | \(-0.753440\pi\) | ||
0.714707 | − | 0.699424i | \(-0.246560\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.87970 | 0.596545 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 23.3183i | − | 1.99222i | −0.0881386 | − | 0.996108i | \(-0.528092\pi\) | ||
0.0881386 | − | 0.996108i | \(-0.471908\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.21510i | 0.187882i | 0.995578 | + | 0.0939412i | \(0.0299466\pi\) | ||||
−0.995578 | + | 0.0939412i | \(0.970053\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.80647 | 0.488993 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.18708 | 0.433765 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.39299i | 0.115682i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.99683i | 0.494610i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.16837i | 0.341486i | 0.985316 | + | 0.170743i | \(0.0546168\pi\) | ||||
−0.985316 | + | 0.170743i | \(0.945383\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 5.22123i | − | 0.424897i | −0.977172 | − | 0.212449i | \(-0.931856\pi\) | ||
0.977172 | − | 0.212449i | \(-0.0681439\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 6.83315i | − | 0.552427i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.12061 | −0.0900098 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 1.91699i | − | 0.152992i | −0.997070 | − | 0.0764961i | \(-0.975627\pi\) | ||
0.997070 | − | 0.0764961i | \(-0.0243733\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.67178 | −0.211886 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 17.2063 | − | 1.69437i | 1.35605 | − | 0.133535i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.45209i | 0.662019i | 0.943627 | + | 0.331010i | \(0.107389\pi\) | ||||
−0.943627 | + | 0.331010i | \(0.892611\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.78590 | −0.450432 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 19.2777i | − | 1.49175i | −0.666084 | − | 0.745877i | \(-0.732031\pi\) | ||
0.666084 | − | 0.745877i | \(-0.267969\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.1963 | −0.938176 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.90832 | −0.145933 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.99198 | −0.151447 | −0.0757236 | − | 0.997129i | \(-0.524127\pi\) | ||||
−0.0757236 | + | 0.997129i | \(0.524127\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.60511 | −0.272521 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.58667 | −0.495084 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.5461i | 1.68517i | 0.538563 | + | 0.842586i | \(0.318968\pi\) | ||||
−0.538563 | + | 0.842586i | \(0.681032\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.37594i | − | 0.176602i | −0.996094 | − | 0.0883011i | \(-0.971856\pi\) | ||
0.996094 | − | 0.0883011i | \(-0.0281438\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.597564 | −0.0441732 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.48133 | 0.550038 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 39.5359i | 2.89115i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 3.60511i | − | 0.262233i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.63031 | 0.190323 | 0.0951613 | − | 0.995462i | \(-0.469663\pi\) | ||||
0.0951613 | + | 0.995462i | \(0.469663\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.1946 | −1.45364 | −0.726818 | − | 0.686830i | \(-0.759002\pi\) | ||||
−0.726818 | + | 0.686830i | \(0.759002\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.896503 | −0.0641999 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.4159 | 1.88205 | 0.941027 | − | 0.338332i | \(-0.109863\pi\) | ||||
0.941027 | + | 0.338332i | \(0.109863\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.4192 | −1.51837 | −0.759185 | − | 0.650875i | \(-0.774402\pi\) | ||||
−0.759185 | + | 0.650875i | \(0.774402\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 5.41745i | − | 0.382117i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.02189 | 0.352467 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.19938i | 0.223455i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.77275 | + | 0.469990i | −0.331729 | + | 0.0326666i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.0413 | 0.763746 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.342786i | 0.0235984i | 0.999930 | + | 0.0117992i | \(0.00375588\pi\) | ||||
−0.999930 | + | 0.0117992i | \(0.996244\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.72842 | 0.255467 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.53782i | 0.173078i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.03993i | 0.274249i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.479048i | 0.0323711i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.12593i | 0.412075i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6.96417i | − | 0.466355i | −0.972434 | − | 0.233178i | \(-0.925088\pi\) | ||
0.972434 | − | 0.233178i | \(-0.0749124\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.1845 | −1.14058 | −0.570289 | − | 0.821444i | \(-0.693169\pi\) | ||||
−0.570289 | + | 0.821444i | \(0.693169\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.6155i | 1.03190i | 0.856619 | + | 0.515950i | \(0.172561\pi\) | ||||
−0.856619 | + | 0.515950i | \(0.827439\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 20.8588i | 1.37241i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.8244 | 0.840153 | 0.420076 | − | 0.907489i | \(-0.362003\pi\) | ||||
0.420076 | + | 0.907489i | \(0.362003\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.80647 | 0.378772 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.03711i | 0.0673677i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.9984i | 0.711429i | 0.934595 | + | 0.355714i | \(0.115762\pi\) | ||||
−0.934595 | + | 0.355714i | \(0.884238\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.3738i | 0.732652i | 0.930487 | + | 0.366326i | \(0.119384\pi\) | ||||
−0.930487 | + | 0.366326i | \(0.880616\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.99683i | 0.383123i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.71081 | 0.108856 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 11.2088i | − | 0.710329i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.2561 | 1.46791 | 0.733957 | − | 0.679195i | \(-0.237671\pi\) | ||||
0.733957 | + | 0.679195i | \(0.237671\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.6147 | − | 2.71932i | 1.73612 | − | 0.170962i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 6.83315i | − | 0.427908i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −27.6478 | −1.72462 | −0.862312 | − | 0.506378i | \(-0.830984\pi\) | ||||
−0.862312 | + | 0.506378i | \(0.830984\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 26.9710i | − | 1.67590i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.39299 | −0.0862240 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.5536 | −1.45237 | −0.726187 | − | 0.687497i | \(-0.758709\pi\) | ||||
−0.726187 | + | 0.687497i | \(0.758709\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.67178 | −0.164126 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.21573 | 0.319198 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.7515 | −0.655533 | −0.327766 | − | 0.944759i | \(-0.606296\pi\) | ||||
−0.327766 | + | 0.944759i | \(0.606296\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.0996i | 1.22096i | 0.792030 | + | 0.610482i | \(0.209024\pi\) | ||||
−0.792030 | + | 0.610482i | \(0.790976\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.23199i | 0.195609i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.78590 | −0.348903 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.5831 | 0.996384 | 0.498192 | − | 0.867067i | \(-0.333998\pi\) | ||||
0.498192 | + | 0.867067i | \(0.333998\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 1.12061i | − | 0.0670893i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.61074i | 0.573329i | 0.958031 | + | 0.286664i | \(0.0925464\pi\) | ||||
−0.958031 | + | 0.286664i | \(0.907454\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.3850 | −1.68731 | −0.843657 | − | 0.536883i | \(-0.819602\pi\) | ||||
−0.843657 | + | 0.536883i | \(0.819602\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.90832 | −0.113039 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.5341 | 0.680838 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −29.6919 | −1.74658 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.73433 | 0.277531 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.9347i | 1.45670i | 0.685204 | + | 0.728351i | \(0.259713\pi\) | ||||
−0.685204 | + | 0.728351i | \(0.740287\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.58667 | −0.383491 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 5.78590i | − | 0.335732i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.27878 | − | 0.421347i | 0.247448 | − | 0.0243671i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.14913 | 0.527347 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 0.362853i | − | 0.0208454i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.597564 | −0.0342164 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.09513i | 0.519086i | 0.965731 | + | 0.259543i | \(0.0835720\pi\) | ||||
−0.965731 | + | 0.259543i | \(0.916428\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 11.7189i | − | 0.666664i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.14205i | − | 0.0647596i | −0.999476 | − | 0.0323798i | \(-0.989691\pi\) | ||
0.999476 | − | 0.0323798i | \(-0.0103086\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.0497i | 1.58546i | 0.609572 | + | 0.792731i | \(0.291341\pi\) | ||||
−0.609572 | + | 0.792731i | \(0.708659\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 3.60511i | − | 0.203125i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.0554 | 1.01409 | 0.507047 | − | 0.861918i | \(-0.330737\pi\) | ||||
0.507047 | + | 0.861918i | \(0.330737\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.05971 | 0.451257 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.6988i | 0.708776i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.0398i | 0.725555i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.896503 | −0.0497290 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.37783 | 0.463295 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 20.9330i | − | 1.15407i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.0971i | 0.939742i | 0.882735 | + | 0.469871i | \(0.155700\pi\) | ||||
−0.882735 | + | 0.469871i | \(0.844300\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.48133i | 0.409974i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 5.41745i | − | 0.295987i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.9130i | 1.03026i | 0.857113 | + | 0.515129i | \(0.172256\pi\) | ||||
−0.857113 | + | 0.515129i | \(0.827744\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.77619 | 0.422345 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.48376i | 0.351115i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.61655 | −0.195275 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.77275 | + | 0.469990i | −0.256956 | + | 0.0253034i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.3614i | 1.41515i | 0.706636 | + | 0.707577i | \(0.250212\pi\) | ||||
−0.706636 | + | 0.707577i | \(0.749788\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.87666 | −0.421628 | −0.210814 | − | 0.977526i | \(-0.567611\pi\) | ||||
−0.210814 | + | 0.977526i | \(0.567611\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 0.896503i | − | 0.0478518i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.97831 | 0.531092 | 0.265546 | − | 0.964098i | \(-0.414448\pi\) | ||||
0.265546 | + | 0.964098i | \(0.414448\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.72842 | 0.197884 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −24.6343 | −1.30378 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.21862 | −0.169872 | −0.0849362 | − | 0.996386i | \(-0.527069\pi\) | ||||
−0.0849362 | + | 0.996386i | \(0.527069\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.3583 | −0.808333 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 22.4767i | 1.17972i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.479048i | 0.0250745i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.7708 | −0.927630 | −0.463815 | − | 0.885932i | \(-0.653520\pi\) | ||||
−0.463815 | + | 0.885932i | \(0.653520\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.19938 | −0.166553 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.63208i | 0.500073i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 0.136042i | − | 0.00704396i | −0.999994 | − | 0.00352198i | \(-0.998879\pi\) | ||
0.999994 | − | 0.00352198i | \(-0.00112108\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.24882 | 0.0643175 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.4857 | 1.87415 | 0.937073 | − | 0.349135i | \(-0.113524\pi\) | ||||
0.937073 | + | 0.349135i | \(0.113524\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.02772 | −0.257578 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.13045 | −0.466544 | −0.233272 | − | 0.972412i | \(-0.574943\pi\) | ||||
−0.233272 | + | 0.972412i | \(0.574943\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.8588i | 1.06306i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.53782 | −0.129005 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.2289i | 0.822838i | 0.911446 | + | 0.411419i | \(0.134967\pi\) | ||||
−0.911446 | + | 0.411419i | \(0.865033\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.21151 | + | 32.6129i | 0.162413 | + | 1.64930i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.0105 | 0.807625 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.03711i | 0.0521828i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.37479 | −0.269753 | −0.134877 | − | 0.990862i | \(-0.543064\pi\) | ||||
−0.134877 | + | 0.990862i | \(0.543064\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.87970i | 0.344416i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.28928i | 0.164259i | 0.996622 | + | 0.0821294i | \(0.0261721\pi\) | ||||
−0.996622 | + | 0.0821294i | \(0.973828\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.00463i | 0.0500443i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 43.2862i | − | 2.14562i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.9778 | −1.03728 | −0.518642 | − | 0.854992i | \(-0.673562\pi\) | ||||
−0.518642 | + | 0.854992i | \(0.673562\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 23.3183 | 1.15021 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 23.7457i | 1.16845i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 11.2088i | − | 0.550219i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.21510 | −0.108474 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.7118 | −1.35381 | −0.676904 | − | 0.736071i | \(-0.736679\pi\) | ||||
−0.676904 | + | 0.736071i | \(0.736679\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 36.2909i | − | 1.76871i | −0.466813 | − | 0.884356i | \(-0.654598\pi\) | ||
0.466813 | − | 0.884356i | \(-0.345402\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.80647i | 0.282320i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 6.83315i | − | 0.331456i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.15428i | 0.104253i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.18708i | 0.250435i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.7066 | 0.997401 | 0.498700 | − | 0.866774i | \(-0.333811\pi\) | ||||
0.498700 | + | 0.866774i | \(0.333811\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 27.4933i | − | 1.32125i | −0.750718 | − | 0.660623i | \(-0.770292\pi\) | ||
0.750718 | − | 0.660623i | \(-0.229708\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.39299 | −0.0667888 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.10792 | − | 0.896890i | 0.435691 | − | 0.0429041i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.92167i | − | 0.139444i | −0.997566 | − | 0.0697219i | \(-0.977789\pi\) | ||
0.997566 | − | 0.0697219i | \(-0.0222112\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.99683 | −0.285563 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 37.6891i | − | 1.79066i | −0.445401 | − | 0.895331i | \(-0.646939\pi\) | ||
0.445401 | − | 0.895331i | \(-0.353061\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.21573 | 0.247249 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.16837 | −0.197157 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.73059 | 0.270443 | 0.135222 | − | 0.990815i | \(-0.456825\pi\) | ||||
0.135222 | + | 0.990815i | \(0.456825\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.5113 | 0.871664 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.22123 | 0.245315 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.23199i | 0.151518i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 27.3237i | − | 1.27815i | −0.769146 | − | 0.639073i | \(-0.779318\pi\) | ||
0.769146 | − | 0.639073i | \(-0.220682\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.83315 | 0.318944 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.2426 | 0.942793 | 0.471397 | − | 0.881921i | \(-0.343750\pi\) | ||||
0.471397 | + | 0.881921i | \(0.343750\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.5699i | 0.723596i | 0.932257 | + | 0.361798i | \(0.117837\pi\) | ||||
−0.932257 | + | 0.361798i | \(0.882163\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 1.12061i | − | 0.0519672i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.1385 | 0.931898 | 0.465949 | − | 0.884812i | \(-0.345713\pi\) | ||||
0.465949 | + | 0.884812i | \(0.345713\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.5305 | −0.901835 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.91699 | 0.0883301 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.6836 | 0.675152 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.90832 | −0.0875596 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 2.67178i | − | 0.122333i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.6339 | −1.26263 | −0.631313 | − | 0.775528i | \(-0.717484\pi\) | ||||
−0.631313 | + | 0.775528i | \(0.717484\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 6.70703i | − | 0.305814i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.69437 | + | 17.2063i | 0.0770963 | + | 0.782913i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.73433 | 0.214975 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.3891i | 0.833289i | 0.909070 | + | 0.416644i | \(0.136794\pi\) | ||||
−0.909070 | + | 0.416644i | \(0.863206\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.45209 | −0.382217 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.8576i | 0.941292i | 0.882322 | + | 0.470646i | \(0.155979\pi\) | ||||
−0.882322 | + | 0.470646i | \(0.844021\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.51851i | 0.428692i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 5.78590i | − | 0.260057i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 13.4414i | − | 0.602928i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 19.8572i | − | 0.888930i | −0.895796 | − | 0.444465i | \(-0.853394\pi\) | ||
0.895796 | − | 0.444465i | \(-0.146606\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.2777 | 0.861264 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.9821 | 0.712609 | 0.356304 | − | 0.934370i | \(-0.384037\pi\) | ||||
0.356304 | + | 0.934370i | \(0.384037\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 0.362853i | − | 0.0161468i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 12.1963i | − | 0.541656i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 37.8962 | 1.67972 | 0.839861 | − | 0.542802i | \(-0.182637\pi\) | ||||
0.839861 | + | 0.542802i | \(0.182637\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.72702 | 0.0763989 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 1.90832i | − | 0.0842543i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 11.7189i | − | 0.516396i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 33.5957i | − | 1.47754i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 1.99198i | − | 0.0874381i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 5.78555i | − | 0.253470i | −0.991937 | − | 0.126735i | \(-0.959550\pi\) | ||
0.991937 | − | 0.126735i | \(-0.0404497\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.70649 | −0.336981 | −0.168491 | − | 0.985703i | \(-0.553889\pi\) | ||||
−0.168491 | + | 0.985703i | \(0.553889\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 3.60511i | − | 0.157340i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.65731 | −0.333558 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.5582 | − | 4.48628i | 0.980792 | − | 0.195056i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 6.58667i | − | 0.285837i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.86826 | 0.124238 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.6988i | 0.549016i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22.5461 | −0.972934 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 34.6971 | 1.49451 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.0098 | −0.731308 | −0.365654 | − | 0.930751i | \(-0.619155\pi\) | ||||
−0.365654 | + | 0.930751i | \(0.619155\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.37594 | 0.101961 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.37783 | 0.358867 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 42.6426i | 1.82327i | 0.411006 | + | 0.911633i | \(0.365178\pi\) | ||||
−0.411006 | + | 0.911633i | \(0.634822\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 0.597564i | − | 0.0255034i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.65827 | 0.113246 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.73891 | 0.158995 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.48133i | 0.317565i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 13.2254i | − | 0.560380i | −0.959945 | − | 0.280190i | \(-0.909603\pi\) | ||
0.959945 | − | 0.280190i | \(-0.0903974\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.27516 | 0.0962292 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −39.5359 | −1.66921 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −39.8356 | −1.67887 | −0.839436 | − | 0.543459i | \(-0.817114\pi\) | ||||
−0.839436 | + | 0.543459i | \(0.817114\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.77619 | 0.327147 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.60511 | 0.151400 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 32.1739i | − | 1.34880i | −0.738366 | − | 0.674401i | \(-0.764402\pi\) | ||
0.738366 | − | 0.674401i | \(-0.235598\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.64594 | −0.319972 | −0.159986 | − | 0.987119i | \(-0.551145\pi\) | ||||
−0.159986 | + | 0.987119i | \(0.551145\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.63031i | 0.109883i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.77275 | + | 0.469990i | −0.199037 | + | 0.0195999i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.02954 | 0.292643 | 0.146322 | − | 0.989237i | \(-0.453257\pi\) | ||||
0.146322 | + | 0.989237i | \(0.453257\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 20.1946i | − | 0.839258i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −40.4090 | −1.67645 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.4587i | 0.640233i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 0.896503i | − | 0.0370658i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.6939i | 1.26687i | 0.773794 | + | 0.633437i | \(0.218357\pi\) | ||||
−0.773794 | + | 0.633437i | \(0.781643\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.13848i | 0.0881147i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 26.4159i | 1.08660i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.5473 | −1.25443 | −0.627214 | − | 0.778847i | \(-0.715805\pi\) | ||||
−0.627214 | + | 0.778847i | \(0.715805\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24.6343 | −1.00991 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 21.4192i | − | 0.876631i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.82194i | 0.360455i | 0.983625 | + | 0.180227i | \(0.0576834\pi\) | ||||
−0.983625 | + | 0.180227i | \(0.942317\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.7517 | −1.17280 | −0.586402 | − | 0.810020i | \(-0.699456\pi\) | ||||
−0.586402 | + | 0.810020i | \(0.699456\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.41745 | 0.220615 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.4767i | 0.913808i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 24.5794i | − | 0.997646i | −0.866704 | − | 0.498823i | \(-0.833766\pi\) | ||
0.866704 | − | 0.498823i | \(-0.166234\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.02189i | 0.203497i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 5.20552i | − | 0.210593i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 28.1696i | − | 1.13776i | −0.822420 | − | 0.568880i | \(-0.807377\pi\) | ||
0.822420 | − | 0.568880i | \(-0.192623\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.19938 | −0.129012 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.7417i | 1.31813i | 0.752086 | + | 0.659065i | \(0.229048\pi\) | ||||
−0.752086 | + | 0.659065i | \(0.770952\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.77997 | −0.192123 | −0.0960615 | − | 0.995375i | \(-0.530625\pi\) | ||||
−0.0960615 | + | 0.995375i | \(0.530625\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.469990 | − | 4.77275i | −0.0188600 | − | 0.191524i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 18.8033i | − | 0.753338i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.0413i | 0.440949i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 51.1210 | 2.03833 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 46.4708 | 1.84997 | 0.924987 | − | 0.379998i | \(-0.124075\pi\) | ||||
0.924987 | + | 0.379998i | \(0.124075\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.342786 | −0.0136245 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.02772 | −0.199519 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.37617 | 0.213012 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.72842i | 0.147494i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 23.9541i | − | 0.946130i | −0.881027 | − | 0.473065i | \(-0.843147\pi\) | ||
0.881027 | − | 0.473065i | \(-0.156853\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.7394 | −1.33055 | −0.665277 | − | 0.746597i | \(-0.731686\pi\) | ||||
−0.665277 | + | 0.746597i | \(0.731686\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.53782 | −0.0999266 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 45.6913i | − | 1.79631i | −0.439679 | − | 0.898155i | \(-0.644908\pi\) | ||
0.439679 | − | 0.898155i | \(-0.355092\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 38.1098i | 1.49594i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.03993 | −0.158337 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 45.2004 | 1.76883 | 0.884415 | − | 0.466701i | \(-0.154558\pi\) | ||||
0.884415 | + | 0.466701i | \(0.154558\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.0105 | 0.625584 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.479048 | −0.0186894 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.6885 | −1.00068 | −0.500342 | − | 0.865828i | \(-0.666792\pi\) | ||||
−0.500342 | + | 0.865828i | \(0.666792\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.39395i | 0.365382i | 0.983170 | + | 0.182691i | \(0.0584809\pi\) | ||||
−0.983170 | + | 0.182691i | \(0.941519\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.12593 | −0.237912 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.87970i | 0.266783i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.64839 | − | 0.654692i | 0.257427 | − | 0.0253498i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.96417 | 0.269250 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.45745i | 0.133473i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.2138 | −0.894826 | −0.447413 | − | 0.894328i | \(-0.647655\pi\) | ||||
−0.447413 | + | 0.894328i | \(0.647655\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000i | 0.0384900i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 46.6887i | 1.79439i | 0.441631 | + | 0.897197i | \(0.354400\pi\) | ||||
−0.441631 | + | 0.897197i | \(0.645600\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 17.0678i | − | 0.655001i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 17.1845i | − | 0.658513i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 41.3680i | − | 1.58290i | −0.611233 | − | 0.791451i | \(-0.709326\pi\) | ||
0.611233 | − | 0.791451i | \(-0.290674\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.3183 | 0.890946 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.6155 | −0.595768 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.39526i | 0.0912522i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 38.1418i | − | 1.45098i | −0.688231 | − | 0.725492i | \(-0.741612\pi\) | ||
0.688231 | − | 0.725492i | \(-0.258388\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −20.8588 | −0.792361 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.21510 | −0.0840236 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.8619i | 0.828077i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.8244i | 0.485063i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.8658i | 0.788091i | 0.919091 | + | 0.394045i | \(0.128925\pi\) | ||||
−0.919091 | + | 0.394045i | \(0.871075\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 14.2767i | − | 0.538458i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.80647i | 0.218684i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.30813 | −0.0491971 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 19.2856i | − | 0.724284i | −0.932123 | − | 0.362142i | \(-0.882045\pi\) | ||
0.932123 | − | 0.362142i | \(-0.117955\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.03711 | −0.0388948 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.526677 | + | 5.34840i | 0.0197242 | + | 0.200299i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.18708i | 0.193986i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.9984 | −0.410744 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 6.24028i | − | 0.232723i | −0.993207 | − | 0.116362i | \(-0.962877\pi\) | ||
0.993207 | − | 0.116362i | \(-0.0371231\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −42.2479 | −1.57339 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.3738 | −0.422997 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.39299 | −0.0517344 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.0658 | 0.521673 | 0.260836 | − | 0.965383i | \(-0.416002\pi\) | ||||
0.260836 | + | 0.965383i | \(0.416002\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.3413i | 0.641391i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.8930i | 1.06719i | 0.845740 | + | 0.533594i | \(0.179159\pi\) | ||||
−0.845740 | + | 0.533594i | \(0.820841\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.99683 | −0.221196 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −31.3448 | −1.15460 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.3784i | 1.15427i | 0.816648 | + | 0.577136i | \(0.195830\pi\) | ||||
−0.816648 | + | 0.577136i | \(0.804170\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.71081i | 0.0628482i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −41.8112 | −1.53390 | −0.766952 | − | 0.641705i | \(-0.778227\pi\) | ||||
−0.766952 | + | 0.641705i | \(0.778227\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.16837 | −0.152717 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.2088 | 0.410109 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 45.7805 | 1.67278 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.4288 | 1.25632 | 0.628162 | − | 0.778082i | \(-0.283807\pi\) | ||||
0.628162 | + | 0.778082i | \(0.283807\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23.2561i | 0.847501i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.22123 | 0.190020 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 29.7038i | − | 1.07960i | −0.841792 | − | 0.539802i | \(-0.818499\pi\) | ||
0.841792 | − | 0.539802i | \(-0.181501\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.71932 | + | 27.6147i | 0.0987049 | + | 1.00235i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.5094 | 0.743464 | 0.371732 | − | 0.928340i | \(-0.378764\pi\) | ||||
0.371732 | + | 0.928340i | \(0.378764\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 30.2030i | − | 1.09342i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.83315 | 0.247053 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.90497i | 0.213216i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 15.5406i | − | 0.560407i | −0.959941 | − | 0.280203i | \(-0.909598\pi\) | ||
0.959941 | − | 0.280203i | \(-0.0904019\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 27.6478i | − | 0.995712i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.79100i | 0.172320i | 0.996281 | + | 0.0861601i | \(0.0274597\pi\) | ||||
−0.996281 | + | 0.0861601i | \(0.972540\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.12061i | − | 0.0402536i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 26.9710 | 0.967580 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.10544 | 0.218750 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 21.5723i | − | 0.771917i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 1.39299i | − | 0.0497814i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.91699 | 0.0684202 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.9512 | −0.390369 | −0.195185 | − | 0.980767i | \(-0.562531\pi\) | ||||
−0.195185 | + | 0.980767i | \(0.562531\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 23.5536i | − | 0.838529i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 28.0340i | − | 0.996775i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.535718i | 0.0190239i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 2.67178i | − | 0.0947584i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 25.2060i | − | 0.892842i | −0.894823 | − | 0.446421i | \(-0.852698\pi\) | ||
0.894823 | − | 0.446421i | \(-0.147302\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 39.6765 | 1.40365 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.21573i | 0.184289i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.77173 | 0.0978121 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.69437 | + | 17.2063i | 0.0597185 | + | 0.606442i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 10.7515i | − | 0.378472i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.1100 | 0.882822 | 0.441411 | − | 0.897305i | \(-0.354478\pi\) | ||||
0.441411 | + | 0.897305i | \(0.354478\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 23.2579i | − | 0.816694i | −0.912827 | − | 0.408347i | \(-0.866105\pi\) | ||
0.912827 | − | 0.408347i | \(-0.133895\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.0996 | −0.704924 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.45209 | −0.296064 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.84297 | 0.169434 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.23199 | −0.112935 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.86939 | −0.274643 | −0.137322 | − | 0.990526i | \(-0.543849\pi\) | ||||
−0.137322 | + | 0.990526i | \(0.543849\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.03369i | 0.245179i | 0.992457 | + | 0.122590i | \(0.0391199\pi\) | ||||
−0.992457 | + | 0.122590i | \(0.960880\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 5.78590i | − | 0.201439i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40.1544 | −1.39631 | −0.698153 | − | 0.715948i | \(-0.745995\pi\) | ||||
−0.698153 | + | 0.715948i | \(0.745995\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.2379 | 0.425039 | 0.212520 | − | 0.977157i | \(-0.431833\pi\) | ||||
0.212520 | + | 0.977157i | \(0.431833\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.5831i | 0.575262i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 40.9772i | 1.41978i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.2777 | 0.667132 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.12061 | 0.0387340 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34.4547 | 1.18951 | 0.594755 | − | 0.803907i | \(-0.297249\pi\) | ||||
0.594755 | + | 0.803907i | \(0.297249\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0596 | −0.933089 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.61074 | −0.331011 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 12.1963i | − | 0.419565i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 81.0310 | 2.78426 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 28.3850i | − | 0.974171i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.51615 | − | 35.7065i | −0.120532 | − | 1.22400i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.870115 | −0.0297922 | −0.0148961 | − | 0.999889i | \(-0.504742\pi\) | ||||
−0.0148961 | + | 0.999889i | \(0.504742\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 1.90832i | − | 0.0652631i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.2563 | −0.760262 | −0.380131 | − | 0.924933i | \(-0.624121\pi\) | ||||
−0.380131 | + | 0.924933i | \(0.624121\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 2.78660i | − | 0.0950776i | −0.998869 | − | 0.0475388i | \(-0.984862\pi\) | ||
0.998869 | − | 0.0475388i | \(-0.0151378\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.5341i | 0.393082i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 37.0567i | − | 1.26142i | −0.776017 | − | 0.630712i | \(-0.782763\pi\) | ||
0.776017 | − | 0.630712i | \(-0.217237\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 1.99198i | − | 0.0677293i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 29.6919i | − | 1.00839i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.00064 | 0.203558 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.85676 | −0.164565 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.73433i | 0.160233i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 3.60511i | − | 0.121875i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.3614 | −0.687556 | −0.343778 | − | 0.939051i | \(-0.611707\pi\) | ||||
−0.343778 | + | 0.939051i | \(0.611707\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24.9347 | −0.841027 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.41977i | − | 0.115215i | −0.998339 | − | 0.0576075i | \(-0.981653\pi\) | ||
0.998339 | − | 0.0576075i | \(-0.0183472\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.38232i | 0.147477i | 0.997278 | + | 0.0737383i | \(0.0234930\pi\) | ||||
−0.997278 | + | 0.0737383i | \(0.976507\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 6.58667i | − | 0.221408i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 22.1798i | − | 0.744725i | −0.928087 | − | 0.372363i | \(-0.878548\pi\) | ||
0.928087 | − | 0.372363i | \(-0.121452\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.1255i | 0.607910i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.78590 | 0.193835 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 11.0806i | − | 0.370798i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.5461 | −0.753631 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.421347 | + | 4.27878i | 0.0140684 | + | 0.142864i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.56100i | 0.0520624i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.2567 | −0.608219 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.14913i | 0.304464i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.37594 | 0.0789789 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43.2997 | −1.43774 | −0.718872 | − | 0.695143i | \(-0.755341\pi\) | ||||
−0.718872 | + | 0.695143i | \(0.755341\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.362853 | 0.0120351 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.4352 | 0.975231 | 0.487616 | − | 0.873058i | \(-0.337867\pi\) | ||||
0.487616 | + | 0.873058i | \(0.337867\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −64.8531 | −2.14632 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 0.597564i | − | 0.0197549i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 57.7198i | − | 1.90608i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.5277 | 1.13896 | 0.569482 | − | 0.822004i | \(-0.307144\pi\) | ||||
0.569482 | + | 0.822004i | \(0.307144\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.09513 | −0.299695 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 3.34254i | − | 0.110021i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.48133i | 0.245984i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.7189 | 0.384899 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.6789 | 0.514408 | 0.257204 | − | 0.966357i | \(-0.417199\pi\) | ||||
0.257204 | + | 0.966357i | \(0.417199\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.4439 | 0.375057 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.14205 | 0.0373890 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −39.5359 | −1.29296 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.0438i | 0.654802i | 0.944885 | + | 0.327401i | \(0.106173\pi\) | ||||
−0.944885 | + | 0.327401i | \(0.893827\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −28.0497 | −0.915367 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 55.6519i | − | 1.81420i | −0.420914 | − | 0.907100i | \(-0.638291\pi\) | ||
0.420914 | − | 0.907100i | \(-0.361709\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.2698 | − | 1.50368i | 0.497255 | − | 0.0489665i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.60511 | 0.117274 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.0016i | 0.454992i | 0.973779 | + | 0.227496i | \(0.0730539\pi\) | ||||
−0.973779 | + | 0.227496i | \(0.926946\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.429468 | 0.0139411 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.0554i | 0.585487i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.92621i | 0.191969i | 0.995383 | + | 0.0959843i | \(0.0305999\pi\) | ||||
−0.995383 | + | 0.0959843i | \(0.969400\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.63031i | 0.0851148i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.05971i | 0.260534i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 84.0651i | − | 2.71460i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.7442 | 0.959491 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.6988 | −0.409212 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 20.1946i | − | 0.650086i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 2.92295i | − | 0.0939957i | −0.998895 | − | 0.0469979i | \(-0.985035\pi\) | ||
0.998895 | − | 0.0469979i | \(-0.0149654\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13.0398 | −0.418899 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.1539 | 0.999777 | 0.499888 | − | 0.866090i | \(-0.333374\pi\) | ||||
0.499888 | + | 0.866090i | \(0.333374\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.98569i | 0.256009i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 0.896503i | − | 0.0287111i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 23.0997i | − | 0.739025i | −0.929226 | − | 0.369513i | \(-0.879525\pi\) | ||
0.929226 | − | 0.369513i | \(-0.120475\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 30.1777i | − | 0.964484i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.37783i | 0.267484i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.8305 | 0.536809 | 0.268404 | − | 0.963306i | \(-0.413504\pi\) | ||||
0.268404 | + | 0.963306i | \(0.413504\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.4159i | 0.841680i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 20.9330 | 0.666304 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.1124 | − | 1.19275i | 0.385151 | − | 0.0379272i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.9784i | 0.856998i | 0.903542 | + | 0.428499i | \(0.140958\pi\) | ||||
−0.903542 | + | 0.428499i | \(0.859042\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17.0971 | −0.542560 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 21.4192i | − | 0.679035i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.7616 | 1.25926 | 0.629632 | − | 0.776894i | \(-0.283206\pi\) | ||||
0.629632 | + | 0.776894i | \(0.283206\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.48133 | −0.236699 |
(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 | 5520.2.be.c.1471.16 | yes | 32 | |
4.3 | odd | 2 | 5520.2.be.d.1471.15 | yes | 32 | ||
23.22 | odd | 2 | 5520.2.be.d.1471.16 | yes | 32 | ||
92.91 | even | 2 | inner | 5520.2.be.c.1471.15 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5520.2.be.c.1471.15 | ✓ | 32 | 92.91 | even | 2 | inner | |
5520.2.be.c.1471.16 | yes | 32 | 1.1 | even | 1 | trivial | |
5520.2.be.d.1471.15 | yes | 32 | 4.3 | odd | 2 | ||
5520.2.be.d.1471.16 | yes | 32 | 23.22 | odd | 2 |