Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(5615,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.5615");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.j (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5615.16 | ||
Character | \(\chi\) | \(=\) | 6048.5615 |
Dual form | 6048.2.j.d.5615.15 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.27819 | −0.571625 | −0.285813 | − | 0.958285i | \(-0.592264\pi\) | ||||
−0.285813 | + | 0.958285i | \(0.592264\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 2.84853i | − 0.858865i | −0.903099 | − | 0.429433i | \(-0.858714\pi\) | ||||
0.903099 | − | 0.429433i | \(-0.141286\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 0.223683i | − 0.0620385i | −0.999519 | − | 0.0310192i | \(-0.990125\pi\) | ||||
0.999519 | − | 0.0310192i | \(-0.00987531\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.397844i | 0.0964913i | 0.998836 | + | 0.0482456i | \(0.0153630\pi\) | ||||
−0.998836 | + | 0.0482456i | \(0.984637\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.64862 | 1.06647 | 0.533234 | − | 0.845968i | \(-0.320977\pi\) | ||||
0.533234 | + | 0.845968i | \(0.320977\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.36177 | −1.53503 | −0.767517 | − | 0.641028i | \(-0.778508\pi\) | ||||
−0.767517 | + | 0.641028i | \(0.778508\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.36622 | −0.673244 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.6317 | 1.97425 | 0.987124 | − | 0.159957i | \(-0.0511356\pi\) | ||||
0.987124 | + | 0.159957i | \(0.0511356\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.67558i | 1.37857i | 0.724488 | + | 0.689287i | \(0.242076\pi\) | ||||
−0.724488 | + | 0.689287i | \(0.757924\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 1.27819i | − 0.216054i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.74489i | 0.780055i | 0.920803 | + | 0.390027i | \(0.127534\pi\) | ||||
−0.920803 | + | 0.390027i | \(0.872466\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 1.97843i | − 0.308979i | −0.987994 | − | 0.154490i | \(-0.950627\pi\) | ||||
0.987994 | − | 0.154490i | \(-0.0493733\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.62888 | −1.16339 | −0.581697 | − | 0.813406i | \(-0.697611\pi\) | ||||
−0.581697 | + | 0.813406i | \(0.697611\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.0724 | −1.61508 | −0.807538 | − | 0.589815i | \(-0.799201\pi\) | ||||
−0.807538 | + | 0.589815i | \(0.799201\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.295366 | −0.0405717 | −0.0202858 | − | 0.999794i | \(-0.506458\pi\) | ||||
−0.0202858 | + | 0.999794i | \(0.506458\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.64098i | 0.490949i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 7.25779i | − 0.944884i | −0.881362 | − | 0.472442i | \(-0.843373\pi\) | ||||
0.881362 | − | 0.472442i | \(-0.156627\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 9.45592i | − 1.21071i | −0.795957 | − | 0.605354i | \(-0.793032\pi\) | ||||
0.795957 | − | 0.605354i | \(-0.206968\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.285910i | 0.0354628i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.52321 | 0.430428 | 0.215214 | − | 0.976567i | \(-0.430955\pi\) | ||||
0.215214 | + | 0.976567i | \(0.430955\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.37710 | 0.994179 | 0.497089 | − | 0.867699i | \(-0.334402\pi\) | ||||
0.497089 | + | 0.867699i | \(0.334402\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.6704 | 1.24887 | 0.624437 | − | 0.781076i | \(-0.285329\pi\) | ||||
0.624437 | + | 0.781076i | \(0.285329\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.84853 | 0.324621 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.22135i | 0.587448i | 0.955890 | + | 0.293724i | \(0.0948947\pi\) | ||||
−0.955890 | + | 0.293724i | \(0.905105\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.11868i | 1.00091i | 0.865764 | + | 0.500453i | \(0.166833\pi\) | ||||
−0.865764 | + | 0.500453i | \(0.833167\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 0.508521i | − 0.0551569i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 8.94887i | − 0.948578i | −0.880369 | − | 0.474289i | \(-0.842705\pi\) | ||||
0.880369 | − | 0.474289i | \(-0.157295\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.223683 | 0.0234483 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.94184 | −0.609620 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.228078 | 0.0231578 | 0.0115789 | − | 0.999933i | \(-0.496314\pi\) | ||||
0.0115789 | + | 0.999933i | \(0.496314\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.36504 | 0.633346 | 0.316673 | − | 0.948535i | \(-0.397434\pi\) | ||||
0.316673 | + | 0.948535i | \(0.397434\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.6557i | 1.14847i | 0.818690 | + | 0.574236i | \(0.194701\pi\) | ||||
−0.818690 | + | 0.574236i | \(0.805299\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.01403i | 0.871419i | 0.900087 | + | 0.435709i | \(0.143502\pi\) | ||||
−0.900087 | + | 0.435709i | \(0.856498\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.45206i | 0.522213i | 0.965310 | + | 0.261106i | \(0.0840873\pi\) | ||||
−0.965310 | + | 0.261106i | \(0.915913\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.00229i | 0.658720i | 0.944204 | + | 0.329360i | \(0.106833\pi\) | ||||
−0.944204 | + | 0.329360i | \(0.893167\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.40976 | 0.877465 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.397844 | −0.0364703 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.88586 | 0.262351 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.6936 | 0.956469 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.48046i | 0.841255i | 0.907234 | + | 0.420627i | \(0.138190\pi\) | ||||
−0.907234 | + | 0.420627i | \(0.861810\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 6.34169i | − 0.554076i | −0.960859 | − | 0.277038i | \(-0.910647\pi\) | ||||
0.960859 | − | 0.277038i | \(-0.0893528\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.64862i | 0.403087i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.3108i | 0.966349i | 0.875524 | + | 0.483174i | \(0.160516\pi\) | ||||
−0.875524 | + | 0.483174i | \(0.839484\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.7583 | −1.84551 | −0.922757 | − | 0.385382i | \(-0.874070\pi\) | ||||
−0.922757 | + | 0.385382i | \(0.874070\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.637168 | −0.0532827 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.5893 | −1.12853 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.42505 | 0.198668 | 0.0993340 | − | 0.995054i | \(-0.468329\pi\) | ||||
0.0993340 | + | 0.995054i | \(0.468329\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.0398i | 1.63082i | 0.578887 | + | 0.815408i | \(0.303487\pi\) | ||||
−0.578887 | + | 0.815408i | \(0.696513\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 9.81087i | − 0.788028i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.5990i | 1.24494i | 0.782644 | + | 0.622470i | \(0.213871\pi\) | ||||
−0.782644 | + | 0.622470i | \(0.786129\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 7.36177i | − 0.580189i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.8755 | −1.00848 | −0.504242 | − | 0.863562i | \(-0.668228\pi\) | ||||
−0.504242 | + | 0.863562i | \(0.668228\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.55771 | −0.120539 | −0.0602697 | − | 0.998182i | \(-0.519196\pi\) | ||||
−0.0602697 | + | 0.998182i | \(0.519196\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9500 | 0.996151 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.60553 | 0.198095 | 0.0990474 | − | 0.995083i | \(-0.468420\pi\) | ||||
0.0990474 | + | 0.995083i | \(0.468420\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 3.36622i | − 0.254462i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 18.9293i | − 1.41484i | −0.706793 | − | 0.707420i | \(-0.749859\pi\) | ||||
0.706793 | − | 0.707420i | \(-0.250141\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.6813i | 1.16558i | 0.812621 | + | 0.582792i | \(0.198040\pi\) | ||||
−0.812621 | + | 0.582792i | \(0.801960\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 6.06488i | − 0.445899i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.13327 | 0.0828730 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.86888 | −0.279943 | −0.139971 | − | 0.990156i | \(-0.544701\pi\) | ||||
−0.139971 | + | 0.990156i | \(0.544701\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.1061 | −0.871419 | −0.435710 | − | 0.900087i | \(-0.643503\pi\) | ||||
−0.435710 | + | 0.900087i | \(0.643503\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.20058 | −0.370526 | −0.185263 | − | 0.982689i | \(-0.559314\pi\) | ||||
−0.185263 | + | 0.982689i | \(0.559314\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 15.5030i | − 1.09898i | −0.835501 | − | 0.549489i | \(-0.814823\pi\) | ||||
0.835501 | − | 0.549489i | \(-0.185177\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.6317i | 0.746196i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.52882i | 0.176620i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 13.2418i | − 0.915952i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.04096 | 0.622406 | 0.311203 | − | 0.950344i | \(-0.399268\pi\) | ||||
0.311203 | + | 0.950344i | \(0.399268\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.75118 | 0.665025 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.67558 | −0.521052 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.0889909 | 0.00598617 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.2327i | 0.685231i | 0.939476 | + | 0.342616i | \(0.111313\pi\) | ||||
−0.939476 | + | 0.342616i | \(0.888687\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.9987i | 0.730007i | 0.931006 | + | 0.365003i | \(0.118932\pi\) | ||||
−0.931006 | + | 0.365003i | \(0.881068\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.1988i | 1.59910i | 0.600600 | + | 0.799550i | \(0.294928\pi\) | ||||
−0.600600 | + | 0.799550i | \(0.705072\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.5448i | 1.41144i | 0.708489 | + | 0.705722i | \(0.249377\pi\) | ||||
−0.708489 | + | 0.705722i | \(0.750623\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.1527 | 0.923219 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.5708 | −1.33061 | −0.665307 | − | 0.746570i | \(-0.731699\pi\) | ||||
−0.665307 | + | 0.746570i | \(0.731699\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.0840 | −0.713984 | −0.356992 | − | 0.934107i | \(-0.616198\pi\) | ||||
−0.356992 | + | 0.934107i | \(0.616198\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.27819 | 0.0816608 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1.03982i | − 0.0661620i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.7016i | 1.30667i | 0.757068 | + | 0.653336i | \(0.226631\pi\) | ||||
−0.757068 | + | 0.653336i | \(0.773369\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.9702i | 1.31839i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.6516i | 0.664427i | 0.943204 | + | 0.332213i | \(0.107795\pi\) | ||||
−0.943204 | + | 0.332213i | \(0.892205\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.74489 | −0.294833 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.36313 | 0.392367 | 0.196184 | − | 0.980567i | \(-0.437145\pi\) | ||||
0.196184 | + | 0.980567i | \(0.437145\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.377535 | 0.0231918 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.3840 | −0.877007 | −0.438503 | − | 0.898730i | \(-0.644491\pi\) | ||||
−0.438503 | + | 0.898730i | \(0.644491\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.9317i | 0.785548i | 0.919635 | + | 0.392774i | \(0.128485\pi\) | ||||
−0.919635 | + | 0.392774i | \(0.871515\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.58880i | 0.578226i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.5242i | 0.812593i | 0.913741 | + | 0.406297i | \(0.133180\pi\) | ||||
−0.913741 | + | 0.406297i | \(0.866820\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.7882i | 1.24012i | 0.784554 | + | 0.620061i | \(0.212892\pi\) | ||||
−0.784554 | + | 0.620061i | \(0.787108\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.6119 | 1.04692 | 0.523459 | − | 0.852051i | \(-0.324641\pi\) | ||||
0.523459 | + | 0.852051i | \(0.324641\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.97843 | 0.116783 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.8417 | 0.990689 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.42581 | −0.141718 | −0.0708588 | − | 0.997486i | \(-0.522574\pi\) | ||||
−0.0708588 | + | 0.997486i | \(0.522574\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.27687i | 0.540120i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.64670i | 0.0952312i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 7.62888i | − 0.439721i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.0865i | 0.692071i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.15871 | 0.294423 | 0.147212 | − | 0.989105i | \(-0.452970\pi\) | ||||
0.147212 | + | 0.989105i | \(0.452970\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.1304 | −1.76524 | −0.882620 | − | 0.470086i | \(-0.844223\pi\) | ||||
−0.882620 | + | 0.470086i | \(0.844223\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.8080 | −1.23266 | −0.616330 | − | 0.787488i | \(-0.711381\pi\) | ||||
−0.616330 | + | 0.787488i | \(0.711381\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.309869 | −0.0174040 | −0.00870199 | − | 0.999962i | \(-0.502770\pi\) | ||||
−0.00870199 | + | 0.999962i | \(0.502770\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 30.2846i | − 1.69561i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.84943i | 0.102905i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.752966i | 0.0417670i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 11.0724i | − 0.610441i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.5893 | −1.57141 | −0.785706 | − | 0.618600i | \(-0.787700\pi\) | ||||
−0.785706 | + | 0.618600i | \(0.787700\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.50334 | −0.246044 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.7103 | 1.45500 | 0.727502 | − | 0.686106i | \(-0.240681\pi\) | ||||
0.727502 | + | 0.686106i | \(0.240681\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.8641 | 1.18401 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 11.0302i | − 0.592132i | −0.955168 | − | 0.296066i | \(-0.904325\pi\) | ||||
0.955168 | − | 0.296066i | \(-0.0956748\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 9.30132i | − 0.497888i | −0.968518 | − | 0.248944i | \(-0.919916\pi\) | ||||
0.968518 | − | 0.248944i | \(-0.0800836\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 18.4585i | − 0.982446i | −0.871034 | − | 0.491223i | \(-0.836550\pi\) | ||||
0.871034 | − | 0.491223i | \(-0.163450\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.7076 | −0.568298 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.70098 | 0.406442 | 0.203221 | − | 0.979133i | \(-0.434859\pi\) | ||||
0.203221 | + | 0.979133i | \(0.434859\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.60971 | 0.137353 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.6388 | −0.713888 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 36.0127i | 1.87985i | 0.341386 | + | 0.939923i | \(0.389104\pi\) | ||||
−0.341386 | + | 0.939923i | \(0.610896\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 0.295366i | − 0.0153346i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.8248i | 1.69960i | 0.527103 | + | 0.849801i | \(0.323278\pi\) | ||||
−0.527103 | + | 0.849801i | \(0.676722\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 2.37812i | − 0.122479i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.8200 | 1.42902 | 0.714509 | − | 0.699626i | \(-0.246650\pi\) | ||||
0.714509 | + | 0.699626i | \(0.246650\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.9047 | −0.608301 | −0.304151 | − | 0.952624i | \(-0.598373\pi\) | ||||
−0.304151 | + | 0.952624i | \(0.598373\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.64098 | −0.185561 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.8388 | 1.25938 | 0.629688 | − | 0.776848i | \(-0.283183\pi\) | ||||
0.629688 | + | 0.776848i | \(0.283183\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 2.92883i | − 0.148117i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 6.67390i | − 0.335800i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.49543i | 0.225619i | 0.993617 | + | 0.112810i | \(0.0359850\pi\) | ||||
−0.993617 | + | 0.112810i | \(0.964015\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 14.8094i | − 0.739545i | −0.929122 | − | 0.369772i | \(-0.879436\pi\) | ||||
0.929122 | − | 0.369772i | \(-0.120564\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.71689 | 0.0855246 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.5160 | 0.669962 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.4088 | −1.65196 | −0.825980 | − | 0.563699i | \(-0.809378\pi\) | ||||
−0.825980 | + | 0.563699i | \(0.809378\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.25779 | 0.357133 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 11.6554i | − 0.572143i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 6.31558i | − 0.308536i | −0.988029 | − | 0.154268i | \(-0.950698\pi\) | ||||
0.988029 | − | 0.154268i | \(-0.0493020\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 10.6716i | − 0.520104i | −0.965595 | − | 0.260052i | \(-0.916260\pi\) | ||||
0.965595 | − | 0.260052i | \(-0.0837397\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 1.33923i | − 0.0649622i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.45592 | 0.457604 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.8686 | 1.72773 | 0.863865 | − | 0.503723i | \(-0.168037\pi\) | ||||
0.863865 | + | 0.503723i | \(0.168037\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.43908 | 0.213328 | 0.106664 | − | 0.994295i | \(-0.465983\pi\) | ||||
0.106664 | + | 0.994295i | \(0.465983\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −34.2221 | −1.63706 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.7939i | 0.896985i | 0.893787 | + | 0.448493i | \(0.148039\pi\) | ||||
−0.893787 | + | 0.448493i | \(0.851961\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 30.9630i | − 1.47109i | −0.677473 | − | 0.735547i | \(-0.736925\pi\) | ||||
0.677473 | − | 0.735547i | \(-0.263075\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.4384i | 0.542232i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 24.6744i | − 1.16446i | −0.813025 | − | 0.582229i | \(-0.802181\pi\) | ||||
0.813025 | − | 0.582229i | \(-0.197819\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.63563 | −0.265372 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.285910 | −0.0134037 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.3915 | 0.626429 | 0.313214 | − | 0.949682i | \(-0.398594\pi\) | ||||
0.313214 | + | 0.949682i | \(0.398594\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.3835 | 0.576759 | 0.288379 | − | 0.957516i | \(-0.406884\pi\) | ||||
0.288379 | + | 0.957516i | \(0.406884\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.34707i | 0.155551i | 0.996971 | + | 0.0777757i | \(0.0247818\pi\) | ||||
−0.996971 | + | 0.0777757i | \(0.975218\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.05078i | 0.141173i | 0.997506 | + | 0.0705866i | \(0.0224871\pi\) | ||||
−0.997506 | + | 0.0705866i | \(0.977513\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.52321i | 0.162687i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.7311i | 0.999198i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.6483 | −0.717993 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.4934 | −0.936368 | −0.468184 | − | 0.883631i | \(-0.655092\pi\) | ||||
−0.468184 | + | 0.883631i | \(0.655092\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.06135 | 0.0483934 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.291528 | −0.0132376 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.9186i | 0.993226i | 0.867972 | + | 0.496613i | \(0.165423\pi\) | ||||
−0.867972 | + | 0.496613i | \(0.834577\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.2880i | 0.464291i | 0.972681 | + | 0.232146i | \(0.0745746\pi\) | ||||
−0.972681 | + | 0.232146i | \(0.925425\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.22974i | 0.190498i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.37710i | 0.375764i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.87931 | 0.0841294 | 0.0420647 | − | 0.999115i | \(-0.486606\pi\) | ||||
0.0420647 | + | 0.999115i | \(0.486606\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.5489 | 0.648702 | 0.324351 | − | 0.945937i | \(-0.394854\pi\) | ||||
0.324351 | + | 0.945937i | \(0.394854\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.13576 | −0.362036 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.7122 | −1.13967 | −0.569837 | − | 0.821758i | \(-0.692994\pi\) | ||||
−0.569837 | + | 0.821758i | \(0.692994\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.6704i | 0.472030i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 14.8983i | − 0.656496i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 31.5401i | 1.38713i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.03293i | 0.351929i | 0.984397 | + | 0.175965i | \(0.0563044\pi\) | ||||
−0.984397 | + | 0.175965i | \(0.943696\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.2938 | −0.756206 | −0.378103 | − | 0.925764i | \(-0.623423\pi\) | ||||
−0.378103 | + | 0.925764i | \(0.623423\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.05368 | −0.133020 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 31.1956 | 1.35633 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.442542 | −0.0191686 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 11.5217i | − 0.498125i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.84853i | 0.122695i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.58504i | 0.283113i | 0.989930 | + | 0.141557i | \(0.0452107\pi\) | ||||
−0.989930 | + | 0.141557i | \(0.954789\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 6.96879i | − 0.298510i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.4478 | 1.43012 | 0.715062 | − | 0.699061i | \(-0.246398\pi\) | ||||
0.715062 | + | 0.699061i | \(0.246398\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 49.4226 | 2.10547 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.22135 | −0.222035 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.92223 | 0.250933 | 0.125467 | − | 0.992098i | \(-0.459957\pi\) | ||||
0.125467 | + | 0.992098i | \(0.459957\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.70645i | 0.0721751i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.1453i | 0.975459i | 0.872995 | + | 0.487730i | \(0.162175\pi\) | ||||
−0.872995 | + | 0.487730i | \(0.837825\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 8.95028i | − 0.376541i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 1.41139i | − 0.0591686i | −0.999562 | − | 0.0295843i | \(-0.990582\pi\) | ||||
0.999562 | − | 0.0295843i | \(-0.00941835\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.82194 | 0.285489 | 0.142745 | − | 0.989760i | \(-0.454407\pi\) | ||||
0.142745 | + | 0.989760i | \(0.454407\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.7813 | 1.03345 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.97587 | 0.290409 | 0.145205 | − | 0.989402i | \(-0.453616\pi\) | ||||
0.145205 | + | 0.989402i | \(0.453616\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.11868 | −0.378307 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.841360i | 0.0348456i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 40.3481i | 1.66534i | 0.553766 | + | 0.832672i | \(0.313190\pi\) | ||||
−0.553766 | + | 0.832672i | \(0.686810\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.6809i | 1.47020i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.40544i | 0.263040i | 0.991314 | + | 0.131520i | \(0.0419858\pi\) | ||||
−0.991314 | + | 0.131520i | \(0.958014\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.508521 | 0.0208473 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.80603 | 0.114651 | 0.0573257 | − | 0.998356i | \(-0.481743\pi\) | ||||
0.0573257 | + | 0.998356i | \(0.481743\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.6165 | 0.473847 | 0.236924 | − | 0.971528i | \(-0.423861\pi\) | ||||
0.236924 | + | 0.971528i | \(0.423861\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.68868 | −0.149966 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 38.5388i | − 1.56424i | −0.623126 | − | 0.782122i | \(-0.714138\pi\) | ||||
0.623126 | − | 0.782122i | \(-0.285862\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.47671i | 0.100197i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 15.8274i | − 0.639261i | −0.947542 | − | 0.319631i | \(-0.896441\pi\) | ||||
0.947542 | − | 0.319631i | \(-0.103559\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 23.9040i | − 0.962339i | −0.876628 | − | 0.481170i | \(-0.840212\pi\) | ||||
0.876628 | − | 0.481170i | \(-0.159788\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.4193 | 1.26285 | 0.631424 | − | 0.775437i | \(-0.282471\pi\) | ||||
0.631424 | + | 0.775437i | \(0.282471\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.94887 | 0.358529 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.16256 | 0.126502 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.88772 | −0.0752685 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 6.94219i | − 0.276364i | −0.990407 | − | 0.138182i | \(-0.955874\pi\) | ||||
0.990407 | − | 0.138182i | \(-0.0441260\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 12.1179i | − 0.480883i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.223683i | 0.00886264i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.1823i | 1.23163i | 0.787892 | + | 0.615814i | \(0.211173\pi\) | ||||
−0.787892 | + | 0.615814i | \(0.788827\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.6881 | −0.894733 | −0.447366 | − | 0.894351i | \(-0.647638\pi\) | ||||
−0.447366 | + | 0.894351i | \(0.647638\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.7608 | 1.48453 | 0.742266 | − | 0.670106i | \(-0.233751\pi\) | ||||
0.742266 | + | 0.670106i | \(0.233751\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.6741 | −0.811528 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −47.8848 | −1.87388 | −0.936939 | − | 0.349494i | \(-0.886353\pi\) | ||||
−0.936939 | + | 0.349494i | \(0.886353\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.10591i | 0.316724i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.00120i | 0.272728i | 0.990659 | + | 0.136364i | \(0.0435417\pi\) | ||||
−0.990659 | + | 0.136364i | \(0.956458\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 41.8042i | − 1.62599i | −0.582267 | − | 0.812997i | \(-0.697834\pi\) | ||||
0.582267 | − | 0.812997i | \(-0.302166\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 5.94184i | − 0.230415i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −78.2677 | −3.03054 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26.9355 | −1.03983 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.2519 | 0.857747 | 0.428874 | − | 0.903364i | \(-0.358911\pi\) | ||||
0.428874 | + | 0.903364i | \(0.358911\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.2219 | −1.12309 | −0.561544 | − | 0.827447i | \(-0.689793\pi\) | ||||
−0.561544 | + | 0.827447i | \(0.689793\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.228078i | 0.00875283i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 35.0080i | − 1.33954i | −0.742567 | − | 0.669772i | \(-0.766392\pi\) | ||||
0.742567 | − | 0.669772i | \(-0.233608\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 14.4574i | − 0.552390i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.0660684i | 0.00251700i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.33849 | −0.0509185 | −0.0254593 | − | 0.999676i | \(-0.508105\pi\) | ||||
−0.0254593 | + | 0.999676i | \(0.508105\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 27.8113 | 1.05494 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.787107 | 0.0298138 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.0621 | 0.871044 | 0.435522 | − | 0.900178i | \(-0.356564\pi\) | ||||
0.435522 | + | 0.900178i | \(0.356564\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.0572i | 0.831903i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.36504i | 0.239382i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 46.8150i | − 1.75818i | −0.476660 | − | 0.879088i | \(-0.658153\pi\) | ||||
0.476660 | − | 0.879088i | \(-0.341847\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 56.5058i | − 2.11616i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.814424 | 0.0304577 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.8849 | −1.30099 | −0.650493 | − | 0.759512i | \(-0.725438\pi\) | ||||
−0.650493 | + | 0.759512i | \(0.725438\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.6557 | −0.434082 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −35.7885 | −1.32915 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 16.4491i | − 0.610063i | −0.952342 | − | 0.305032i | \(-0.901333\pi\) | ||||
0.952342 | − | 0.305032i | \(-0.0986671\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 3.03510i | − 0.112257i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 35.9855i | − 1.32915i | −0.747220 | − | 0.664577i | \(-0.768612\pi\) | ||||
0.747220 | − | 0.664577i | \(-0.231388\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 10.0360i | − 0.369680i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.44866 | 0.200432 | 0.100216 | − | 0.994966i | \(-0.468047\pi\) | ||||
0.100216 | + | 0.994966i | \(0.468047\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.2115 | 1.14504 | 0.572520 | − | 0.819891i | \(-0.305966\pi\) | ||||
0.572520 | + | 0.819891i | \(0.305966\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.09969 | −0.113564 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.01403 | −0.329365 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.1812i | 0.845894i | 0.906154 | + | 0.422947i | \(0.139004\pi\) | ||||
−0.906154 | + | 0.422947i | \(0.860996\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 25.6147i | − 0.932216i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 39.3962i | − 1.43188i | −0.698162 | − | 0.715940i | \(-0.745998\pi\) | ||||
0.698162 | − | 0.715940i | \(-0.254002\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.1356i | 0.621166i | 0.950546 | + | 0.310583i | \(0.100524\pi\) | ||||
−0.950546 | + | 0.310583i | \(0.899476\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.45206 | −0.197378 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.62344 | −0.0586192 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.9084 | −1.61944 | −0.809718 | − | 0.586819i | \(-0.800380\pi\) | ||||
−0.809718 | + | 0.586819i | \(0.800380\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.0273 | 0.972106 | 0.486053 | − | 0.873929i | \(-0.338436\pi\) | ||||
0.486053 | + | 0.873929i | \(0.338436\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 25.8377i | − 0.928117i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 9.19699i | − 0.329516i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 23.8624i | − 0.853866i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 19.9386i | − 0.711639i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.1562 | 1.21754 | 0.608769 | − | 0.793348i | \(-0.291664\pi\) | ||||
0.608769 | + | 0.793348i | \(0.291664\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.00229 | −0.248973 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.11513 | −0.0751104 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −46.2712 | −1.63901 | −0.819505 | − | 0.573072i | \(-0.805751\pi\) | ||||
−0.819505 | + | 0.573072i | \(0.805751\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 4.40509i | − 0.155841i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 30.3949i | − 1.07261i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.40976i | 0.331651i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.3429i | 0.926167i | 0.886315 | + | 0.463084i | \(0.153257\pi\) | ||||
−0.886315 | + | 0.463084i | \(0.846743\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.96401 | −0.104080 | −0.0520402 | − | 0.998645i | \(-0.516572\pi\) | ||||
−0.0520402 | + | 0.998645i | \(0.516572\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.4573 | 0.576475 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −35.4638 | −1.24072 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.3996 | −0.362949 | −0.181475 | − | 0.983396i | \(-0.558087\pi\) | ||||
−0.181475 | + | 0.983396i | \(0.558087\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.8598i | 1.38942i | 0.719288 | + | 0.694712i | \(0.244468\pi\) | ||||
−0.719288 | + | 0.694712i | \(0.755532\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.5060i | 0.956477i | 0.878230 | + | 0.478239i | \(0.158725\pi\) | ||||
−0.878230 | + | 0.478239i | \(0.841275\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.0086i | 1.32009i | 0.751225 | + | 0.660047i | \(0.229464\pi\) | ||||
−0.751225 | + | 0.660047i | \(0.770536\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 0.397844i | − 0.0137845i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.99106 | 0.0689034 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.9037 | 1.06691 | 0.533457 | − | 0.845827i | \(-0.320893\pi\) | ||||
0.533457 | + | 0.845827i | \(0.320893\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 84.0320 | 2.89765 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.5526 | −0.569425 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.88586i | 0.0991592i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 34.9308i | − 1.19741i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 25.3302i | − 0.867290i | −0.901084 | − | 0.433645i | \(-0.857227\pi\) | ||||
0.901084 | − | 0.433645i | \(-0.142773\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 39.1574i | − 1.33759i | −0.743447 | − | 0.668795i | \(-0.766810\pi\) | ||||
0.743447 | − | 0.668795i | \(-0.233190\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.2783 | −0.384810 | −0.192405 | − | 0.981316i | \(-0.561629\pi\) | ||||
−0.192405 | + | 0.981316i | \(0.561629\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.6543 | −0.532878 | −0.266439 | − | 0.963852i | \(-0.585847\pi\) | ||||
−0.266439 | + | 0.963852i | \(0.585847\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.33037 | −0.113236 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.8732 | 0.504539 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 0.788081i | − 0.0267031i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.6936i | 0.361511i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 14.6357i | − 0.494211i | −0.968989 | − | 0.247106i | \(-0.920521\pi\) | ||||
0.968989 | − | 0.247106i | \(-0.0794795\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 21.9054i | − 0.738013i | −0.929427 | − | 0.369007i | \(-0.879698\pi\) | ||||
0.929427 | − | 0.369007i | \(-0.120302\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.3852 | 1.22446 | 0.612230 | − | 0.790680i | \(-0.290273\pi\) | ||||
0.612230 | + | 0.790680i | \(0.290273\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.3554 | −0.347700 | −0.173850 | − | 0.984772i | \(-0.555621\pi\) | ||||
−0.173850 | + | 0.984772i | \(0.555621\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.48046 | −0.317964 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −51.4715 | −1.72243 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.1953i | 0.808759i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 81.6040i | 2.72165i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 0.117510i | − 0.00391481i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 20.0438i | − 0.666278i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.5615 | −0.350689 | −0.175344 | − | 0.984507i | \(-0.556104\pi\) | ||||
−0.175344 | + | 0.984507i | \(0.556104\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.4732 | −0.612044 | −0.306022 | − | 0.952024i | \(-0.598998\pi\) | ||||
−0.306022 | + | 0.952024i | \(0.598998\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.9749 | 0.859643 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.34169 | 0.209421 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.7252i | 0.914569i | 0.889320 | + | 0.457285i | \(0.151178\pi\) | ||||
−0.889320 | + | 0.457285i | \(0.848822\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 1.87381i | − 0.0616773i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 15.9723i | − 0.525167i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 57.6318i | 1.89084i | 0.325858 | + | 0.945419i | \(0.394347\pi\) | ||||
−0.325858 | + | 0.945419i | \(0.605653\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.64862 | −0.152353 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.44854 | −0.0473723 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44.9081 | −1.46708 | −0.733542 | − | 0.679644i | \(-0.762134\pi\) | ||||
−0.733542 | + | 0.679644i | \(0.762134\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.0167 | 0.815521 | 0.407761 | − | 0.913089i | \(-0.366310\pi\) | ||||
0.407761 | + | 0.913089i | \(0.366310\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.5648i | 0.474294i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 39.7909i | − 1.29303i | −0.762901 | − | 0.646516i | \(-0.776225\pi\) | ||||
0.762901 | − | 0.646516i | \(-0.223775\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 2.38678i | − 0.0774782i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 12.4544i | − 0.403437i | −0.979444 | − | 0.201718i | \(-0.935347\pi\) | ||||
0.979444 | − | 0.201718i | \(-0.0646526\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.94518 | 0.160022 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.3108 | −0.365246 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.9145 | −0.900466 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.4740 | 0.498125 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 6.97106i | − 0.224174i | −0.993698 | − | 0.112087i | \(-0.964246\pi\) | ||||
0.993698 | − | 0.112087i | \(-0.0357536\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 9.18374i | − 0.294720i | −0.989083 | − | 0.147360i | \(-0.952922\pi\) | ||||
0.989083 | − | 0.147360i | \(-0.0470776\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 21.7583i | − 0.697539i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.1316i | 1.25193i | 0.779851 | + | 0.625965i | \(0.215295\pi\) | ||||
−0.779851 | + | 0.625965i | \(0.784705\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.4912 | −0.814701 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 50.4121 | 1.60790 | 0.803948 | − | 0.594700i | \(-0.202729\pi\) | ||||
0.803948 | + | 0.594700i | \(0.202729\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.64735 | 0.211802 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 56.1620 | 1.78585 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 55.9071i | − 1.77595i | −0.459894 | − | 0.887974i | \(-0.652113\pi\) | ||||
0.459894 | − | 0.887974i | \(-0.347887\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.8158i | 0.628204i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 11.6669i | − 0.369494i | −0.982786 | − | 0.184747i | \(-0.940853\pi\) | ||||
0.982786 | − | 0.184747i | \(-0.0591466\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6048.2.j.d.5615.16 | 48 | ||
3.2 | odd | 2 | inner | 6048.2.j.d.5615.33 | 48 | ||
4.3 | odd | 2 | 1512.2.j.d.323.23 | ✓ | 48 | ||
8.3 | odd | 2 | inner | 6048.2.j.d.5615.34 | 48 | ||
8.5 | even | 2 | 1512.2.j.d.323.25 | yes | 48 | ||
12.11 | even | 2 | 1512.2.j.d.323.26 | yes | 48 | ||
24.5 | odd | 2 | 1512.2.j.d.323.24 | yes | 48 | ||
24.11 | even | 2 | inner | 6048.2.j.d.5615.15 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.d.323.23 | ✓ | 48 | 4.3 | odd | 2 | ||
1512.2.j.d.323.24 | yes | 48 | 24.5 | odd | 2 | ||
1512.2.j.d.323.25 | yes | 48 | 8.5 | even | 2 | ||
1512.2.j.d.323.26 | yes | 48 | 12.11 | even | 2 | ||
6048.2.j.d.5615.15 | 48 | 24.11 | even | 2 | inner | ||
6048.2.j.d.5615.16 | 48 | 1.1 | even | 1 | trivial | ||
6048.2.j.d.5615.33 | 48 | 3.2 | odd | 2 | inner | ||
6048.2.j.d.5615.34 | 48 | 8.3 | odd | 2 | inner |