Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(3025,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.3025");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3025.19 | ||
Character | \(\chi\) | \(=\) | 6048.3025 |
Dual form | 6048.2.c.f.3025.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.99001i | 1.33717i | 0.743634 | + | 0.668587i | \(0.233100\pi\) | ||||
−0.743634 | + | 0.668587i | \(0.766900\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 2.13956i | − 0.645101i | −0.946552 | − | 0.322550i | \(-0.895460\pi\) | ||||
0.946552 | − | 0.322550i | \(-0.104540\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 0.665739i | − 0.184643i | −0.995729 | − | 0.0923214i | \(-0.970571\pi\) | ||||
0.995729 | − | 0.0923214i | \(-0.0294287\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.04931 | −1.70971 | −0.854855 | − | 0.518867i | \(-0.826354\pi\) | ||||
−0.854855 | + | 0.518867i | \(0.826354\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1.39525i | − 0.320092i | −0.987110 | − | 0.160046i | \(-0.948836\pi\) | ||||
0.987110 | − | 0.160046i | \(-0.0511642\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.184371 | 0.0384439 | 0.0192220 | − | 0.999815i | \(-0.493881\pi\) | ||||
0.0192220 | + | 0.999815i | \(0.493881\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.94016 | −0.788032 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.27564i | 0.236880i | 0.992961 | + | 0.118440i | \(0.0377893\pi\) | ||||
−0.992961 | + | 0.118440i | \(0.962211\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.62308 | 1.36915 | 0.684573 | − | 0.728944i | \(-0.259989\pi\) | ||||
0.684573 | + | 0.728944i | \(0.259989\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 2.99001i | − 0.505404i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.69127i | 1.10004i | 0.835152 | + | 0.550019i | \(0.185379\pi\) | ||||
−0.835152 | + | 0.550019i | \(0.814621\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.274106 | 0.0428081 | 0.0214041 | − | 0.999771i | \(-0.493186\pi\) | ||||
0.0214041 | + | 0.999771i | \(0.493186\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.63971i | 0.402553i | 0.979535 | + | 0.201276i | \(0.0645089\pi\) | ||||
−0.979535 | + | 0.201276i | \(0.935491\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.77739 | −0.842719 | −0.421359 | − | 0.906894i | \(-0.638447\pi\) | ||||
−0.421359 | + | 0.906894i | \(0.638447\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 7.48353i | − 1.02794i | −0.857808 | − | 0.513971i | \(-0.828174\pi\) | ||||
0.857808 | − | 0.513971i | \(-0.171826\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.39730 | 0.862611 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 9.03787i | − 1.17663i | −0.808632 | − | 0.588315i | \(-0.799792\pi\) | ||||
0.808632 | − | 0.588315i | \(-0.200208\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 9.80298i | − 1.25514i | −0.778559 | − | 0.627571i | \(-0.784049\pi\) | ||||
0.778559 | − | 0.627571i | \(-0.215951\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.99057 | 0.246900 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 10.8191i | − 1.32177i | −0.750488 | − | 0.660884i | \(-0.770181\pi\) | ||||
0.750488 | − | 0.660884i | \(-0.229819\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.93573 | 0.941798 | 0.470899 | − | 0.882187i | \(-0.343930\pi\) | ||||
0.470899 | + | 0.882187i | \(0.343930\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.80408 | −0.328193 | −0.164097 | − | 0.986444i | \(-0.552471\pi\) | ||||
−0.164097 | + | 0.986444i | \(0.552471\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.13956i | 0.243825i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.98350 | −0.898214 | −0.449107 | − | 0.893478i | \(-0.648258\pi\) | ||||
−0.449107 | + | 0.893478i | \(0.648258\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.76125i | 0.742143i | 0.928604 | + | 0.371072i | \(0.121010\pi\) | ||||
−0.928604 | + | 0.371072i | \(0.878990\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 21.0775i | − 2.28618i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.7549 | −1.77602 | −0.888010 | − | 0.459825i | \(-0.847912\pi\) | ||||
−0.888010 | + | 0.459825i | \(0.847912\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.665739i | 0.0697884i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.17180 | 0.428018 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.107694 | −0.0109346 | −0.00546732 | − | 0.999985i | \(-0.501740\pi\) | ||||
−0.00546732 | + | 0.999985i | \(0.501740\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 14.8524i | − 1.47787i | −0.673775 | − | 0.738937i | \(-0.735328\pi\) | ||||
0.673775 | − | 0.738937i | \(-0.264672\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.1461 | 1.59092 | 0.795459 | − | 0.606007i | \(-0.207230\pi\) | ||||
0.795459 | + | 0.606007i | \(0.207230\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 15.6131i | − 1.50937i | −0.656084 | − | 0.754687i | \(-0.727789\pi\) | ||||
0.656084 | − | 0.754687i | \(-0.272211\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.15829i | 0.398292i | 0.979970 | + | 0.199146i | \(0.0638167\pi\) | ||||
−0.979970 | + | 0.199146i | \(0.936183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.4682 | −1.73734 | −0.868672 | − | 0.495388i | \(-0.835026\pi\) | ||||
−0.868672 | + | 0.495388i | \(0.835026\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.551270i | 0.0514062i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.04931 | 0.646209 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.42230 | 0.583845 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.16893i | 0.283437i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.37444 | 0.388169 | 0.194084 | − | 0.980985i | \(-0.437826\pi\) | ||||
0.194084 | + | 0.980985i | \(0.437826\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 5.76264i | − 0.503484i | −0.967794 | − | 0.251742i | \(-0.918997\pi\) | ||||
0.967794 | − | 0.251742i | \(-0.0810035\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.39525i | 0.120983i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.5191 | 0.898704 | 0.449352 | − | 0.893355i | \(-0.351655\pi\) | ||||
0.449352 | + | 0.893355i | \(0.351655\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.27000i | 0.616633i | 0.951284 | + | 0.308316i | \(0.0997656\pi\) | ||||
−0.951284 | + | 0.308316i | \(0.900234\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.42439 | −0.119113 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.81416 | −0.316749 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.06625i | 0.251197i | 0.992081 | + | 0.125599i | \(0.0400851\pi\) | ||||
−0.992081 | + | 0.125599i | \(0.959915\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.8992 | 1.29386 | 0.646930 | − | 0.762549i | \(-0.276053\pi\) | ||||
0.646930 | + | 0.762549i | \(0.276053\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 22.7931i | 1.83079i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 18.3211i | − 1.46219i | −0.682278 | − | 0.731093i | \(-0.739011\pi\) | ||||
0.682278 | − | 0.731093i | \(-0.260989\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.184371 | −0.0145304 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 22.0479i | − 1.72692i | −0.504415 | − | 0.863462i | \(-0.668292\pi\) | ||||
0.504415 | − | 0.863462i | \(-0.331708\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.2650 | 0.794332 | 0.397166 | − | 0.917747i | \(-0.369994\pi\) | ||||
0.397166 | + | 0.917747i | \(0.369994\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.5568 | 0.965907 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.5234i | 1.18022i | 0.807322 | + | 0.590111i | \(0.200916\pi\) | ||||
−0.807322 | + | 0.590111i | \(0.799084\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.94016 | 0.297848 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.2028i | 1.28580i | 0.765952 | + | 0.642898i | \(0.222268\pi\) | ||||
−0.765952 | + | 0.642898i | \(0.777732\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 10.5145i | − 0.781538i | −0.920489 | − | 0.390769i | \(-0.872209\pi\) | ||||
0.920489 | − | 0.390769i | \(-0.127791\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −20.0070 | −1.47094 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.0824i | 1.10293i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.3893 | 1.04117 | 0.520587 | − | 0.853808i | \(-0.325713\pi\) | ||||
0.520587 | + | 0.853808i | \(0.325713\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.3579 | 0.817562 | 0.408781 | − | 0.912632i | \(-0.365954\pi\) | ||||
0.408781 | + | 0.912632i | \(0.365954\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.44465i | 0.459163i | 0.973289 | + | 0.229581i | \(0.0737357\pi\) | ||||
−0.973289 | + | 0.229581i | \(0.926264\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.48055 | 0.459394 | 0.229697 | − | 0.973262i | \(-0.426226\pi\) | ||||
0.229697 | + | 0.973262i | \(0.426226\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1.27564i | − 0.0895321i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.819579i | 0.0572419i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.98521 | −0.206491 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 10.3150i | − 0.710112i | −0.934845 | − | 0.355056i | \(-0.884462\pi\) | ||||
0.934845 | − | 0.355056i | \(-0.115538\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.89277 | −0.538283 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.62308 | −0.517489 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.69300i | 0.315686i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.8589 | −1.59771 | −0.798854 | − | 0.601526i | \(-0.794560\pi\) | ||||
−0.798854 | + | 0.601526i | \(0.794560\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.88092i | 0.124841i | 0.998050 | + | 0.0624206i | \(0.0198820\pi\) | ||||
−0.998050 | + | 0.0624206i | \(0.980118\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 18.8128i | − 1.24319i | −0.783340 | − | 0.621594i | \(-0.786485\pi\) | ||||
0.783340 | − | 0.621594i | \(-0.213515\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.18759 | −0.601899 | −0.300949 | − | 0.953640i | \(-0.597304\pi\) | ||||
−0.300949 | + | 0.953640i | \(0.597304\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 17.2745i | − 1.12686i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.1200 | 1.88362 | 0.941808 | − | 0.336152i | \(-0.109126\pi\) | ||||
0.941808 | + | 0.336152i | \(0.109126\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.4640 | 1.64028 | 0.820142 | − | 0.572160i | \(-0.193894\pi\) | ||||
0.820142 | + | 0.572160i | \(0.193894\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.99001i | 0.191025i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.928871 | −0.0591027 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 2.72427i | − 0.171955i | −0.996297 | − | 0.0859773i | \(-0.972599\pi\) | ||||
0.996297 | − | 0.0859773i | \(-0.0274012\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 0.394471i | − 0.0248002i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.6181 | 1.09899 | 0.549494 | − | 0.835498i | \(-0.314821\pi\) | ||||
0.549494 | + | 0.835498i | \(0.314821\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 6.69127i | − 0.415775i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.42576 | 0.334567 | 0.167283 | − | 0.985909i | \(-0.446501\pi\) | ||||
0.167283 | + | 0.985909i | \(0.446501\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 22.3758 | 1.37454 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 17.6635i | − 1.07696i | −0.842637 | − | 0.538482i | \(-0.818998\pi\) | ||||
0.842637 | − | 0.538482i | \(-0.181002\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.5223 | −0.699929 | −0.349965 | − | 0.936763i | \(-0.613806\pi\) | ||||
−0.349965 | + | 0.936763i | \(0.613806\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.43020i | 0.508360i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.84872i | 0.471584i | 0.971804 | + | 0.235792i | \(0.0757684\pi\) | ||||
−0.971804 | + | 0.235792i | \(0.924232\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 31.1308 | 1.85711 | 0.928555 | − | 0.371195i | \(-0.121052\pi\) | ||||
0.928555 | + | 0.371195i | \(0.121052\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 24.7863i | − 1.47339i | −0.676224 | − | 0.736696i | \(-0.736385\pi\) | ||||
0.676224 | − | 0.736696i | \(-0.263615\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.274106 | −0.0161800 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.6928 | 1.92311 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.9898i | 1.69360i | 0.531909 | + | 0.846802i | \(0.321475\pi\) | ||||
−0.531909 | + | 0.846802i | \(0.678525\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.0233 | 1.57336 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 0.122743i | − 0.00709839i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 2.63971i | − 0.152151i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 29.3110 | 1.67834 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 18.8831i | − 1.07772i | −0.842397 | − | 0.538858i | \(-0.818856\pi\) | ||||
0.842397 | − | 0.538858i | \(-0.181144\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.147540 | 0.00836624 | 0.00418312 | − | 0.999991i | \(-0.498668\pi\) | ||||
0.00418312 | + | 0.999991i | \(0.498668\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.3154 | −1.31786 | −0.658932 | − | 0.752202i | \(-0.728992\pi\) | ||||
−0.658932 | + | 0.752202i | \(0.728992\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.43318i | − 0.0804954i | −0.999190 | − | 0.0402477i | \(-0.987185\pi\) | ||||
0.999190 | − | 0.0402477i | \(-0.0128147\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.72929 | 0.152811 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.83554i | 0.547264i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.62312i | 0.145505i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.77739 | 0.318518 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 23.3196i | − 1.28176i | −0.767640 | − | 0.640882i | \(-0.778569\pi\) | ||||
0.767640 | − | 0.640882i | \(-0.221431\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 32.3493 | 1.76743 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.484629 | 0.0263994 | 0.0131997 | − | 0.999913i | \(-0.495798\pi\) | ||||
0.0131997 | + | 0.999913i | \(0.495798\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 16.3100i | − 0.883237i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 10.0395i | − 0.538947i | −0.963008 | − | 0.269473i | \(-0.913150\pi\) | ||||
0.963008 | − | 0.269473i | \(-0.0868496\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.55791i | 0.511623i | 0.966727 | + | 0.255812i | \(0.0823427\pi\) | ||||
−0.966727 | + | 0.255812i | \(0.917657\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.2931 | −1.50589 | −0.752945 | − | 0.658083i | \(-0.771368\pi\) | ||||
−0.752945 | + | 0.658083i | \(0.771368\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 23.7279i | 1.25935i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.8316 | −1.36334 | −0.681671 | − | 0.731659i | \(-0.738746\pi\) | ||||
−0.681671 | + | 0.731659i | \(0.738746\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0533 | 0.897541 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 8.38424i | − 0.438851i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.78123 | 0.0929793 | 0.0464896 | − | 0.998919i | \(-0.485197\pi\) | ||||
0.0464896 | + | 0.998919i | \(0.485197\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.48353i | 0.388525i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.1074i | 1.14468i | 0.820017 | + | 0.572340i | \(0.193964\pi\) | ||||
−0.820017 | + | 0.572340i | \(0.806036\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.849241 | 0.0437381 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 35.4109i | − 1.81893i | −0.415776 | − | 0.909467i | \(-0.636490\pi\) | ||||
0.415776 | − | 0.909467i | \(-0.363510\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.1927 | −1.23619 | −0.618095 | − | 0.786104i | \(-0.712095\pi\) | ||||
−0.618095 | + | 0.786104i | \(0.712095\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.39730 | −0.326036 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.0465i | 0.661483i | 0.943721 | + | 0.330741i | \(0.107299\pi\) | ||||
−0.943721 | + | 0.330741i | \(0.892701\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.29969 | −0.0657279 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 23.8707i | − 1.20107i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 36.0707i | 1.81034i | 0.425053 | + | 0.905168i | \(0.360255\pi\) | ||||
−0.425053 | + | 0.905168i | \(0.639745\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.5149 | 0.774778 | 0.387389 | − | 0.921916i | \(-0.373377\pi\) | ||||
0.387389 | + | 0.921916i | \(0.373377\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 5.07499i | − 0.252803i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.3163 | 0.709635 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.6937 | −1.41881 | −0.709406 | − | 0.704800i | \(-0.751037\pi\) | ||||
−0.709406 | + | 0.704800i | \(0.751037\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.03787i | 0.444724i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −20.2162 | −0.992374 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 22.9355i | − 1.12047i | −0.828333 | − | 0.560236i | \(-0.810710\pi\) | ||||
0.828333 | − | 0.560236i | \(-0.189290\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 13.1562i | − 0.641193i | −0.947216 | − | 0.320596i | \(-0.896117\pi\) | ||||
0.947216 | − | 0.320596i | \(-0.103883\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 27.7754 | 1.34731 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.80298i | 0.474399i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −39.6373 | −1.90926 | −0.954631 | − | 0.297792i | \(-0.903750\pi\) | ||||
−0.954631 | + | 0.297792i | \(0.903750\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.5906 | 0.557010 | 0.278505 | − | 0.960435i | \(-0.410161\pi\) | ||||
0.278505 | + | 0.960435i | \(0.410161\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 0.257243i | − 0.0123056i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.88971 | 0.472010 | 0.236005 | − | 0.971752i | \(-0.424162\pi\) | ||||
0.236005 | + | 0.971752i | \(0.424162\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.14448i | 0.101888i | 0.998702 | + | 0.0509438i | \(0.0162229\pi\) | ||||
−0.998702 | + | 0.0509438i | \(0.983777\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 50.0974i | − 2.37485i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.65352 | −0.219613 | −0.109807 | − | 0.993953i | \(-0.535023\pi\) | ||||
−0.109807 | + | 0.993953i | \(0.535023\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 0.586465i | − 0.0276156i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.99057 | −0.0933192 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.0517 | 0.891203 | 0.445601 | − | 0.895232i | \(-0.352990\pi\) | ||||
0.445601 | + | 0.895232i | \(0.352990\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.0354i | 1.21259i | 0.795240 | + | 0.606294i | \(0.207345\pi\) | ||||
−0.795240 | + | 0.606294i | \(0.792655\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.6096 | −1.37607 | −0.688036 | − | 0.725676i | \(-0.741527\pi\) | ||||
−0.688036 | + | 0.725676i | \(0.741527\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 25.8983i | − 1.19843i | −0.800588 | − | 0.599216i | \(-0.795479\pi\) | ||||
0.800588 | − | 0.599216i | \(-0.204521\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.8191i | 0.499581i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.64782 | 0.259687 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.49750i | 0.252243i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.2498 | −0.879544 | −0.439772 | − | 0.898109i | \(-0.644941\pi\) | ||||
−0.439772 | + | 0.898109i | \(0.644941\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.45464 | 0.203114 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 0.322005i | − 0.0146215i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.32047 | −0.105150 | −0.0525752 | − | 0.998617i | \(-0.516743\pi\) | ||||
−0.0525752 | + | 0.998617i | \(0.516743\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.578109i | 0.0260897i | 0.999915 | + | 0.0130449i | \(0.00415242\pi\) | ||||
−0.999915 | + | 0.0130449i | \(0.995848\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 8.99235i | − 0.404995i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.93573 | −0.355966 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.3969i | 1.18169i | 0.806785 | + | 0.590845i | \(0.201205\pi\) | ||||
−0.806785 | + | 0.590845i | \(0.798795\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.40780 | 0.374885 | 0.187443 | − | 0.982276i | \(-0.439980\pi\) | ||||
0.187443 | + | 0.982276i | \(0.439980\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 44.4090 | 1.97617 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 32.9679i | − 1.46128i | −0.682764 | − | 0.730639i | \(-0.739222\pi\) | ||||
0.682764 | − | 0.730639i | \(-0.260778\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.80408 | 0.124045 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 48.2769i | 2.12733i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.3611i | 0.543638i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.9299 | −1.35506 | −0.677531 | − | 0.735494i | \(-0.736950\pi\) | ||||
−0.677531 | + | 0.735494i | \(0.736950\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.73852i | 0.119747i | 0.998206 | + | 0.0598735i | \(0.0190697\pi\) | ||||
−0.998206 | + | 0.0598735i | \(0.980930\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −53.7375 | −2.34084 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9660 | −0.998522 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 0.182483i | − 0.00790421i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 46.6833 | 2.01830 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 2.13956i | − 0.0921572i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 32.3372i | − 1.39029i | −0.718872 | − | 0.695143i | \(-0.755341\pi\) | ||||
0.718872 | − | 0.695143i | \(-0.244659\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.4333 | −0.532585 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 20.4045i | − 0.872434i | −0.899842 | − | 0.436217i | \(-0.856318\pi\) | ||||
0.899842 | − | 0.436217i | \(-0.143682\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.77983 | 0.0758232 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.98350 | 0.339493 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.16560i | 0.176502i | 0.996098 | + | 0.0882510i | \(0.0281278\pi\) | ||||
−0.996098 | + | 0.0882510i | \(0.971872\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.75736 | 0.0743285 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.37435i | 0.184357i | 0.995743 | + | 0.0921784i | \(0.0293830\pi\) | ||||
−0.995743 | + | 0.0921784i | \(0.970617\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 55.2202i | − 2.32313i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.59520 | −0.192641 | −0.0963204 | − | 0.995350i | \(-0.530707\pi\) | ||||
−0.0963204 | + | 0.995350i | \(0.530707\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.6111i | 1.28103i | 0.767944 | + | 0.640517i | \(0.221280\pi\) | ||||
−0.767944 | + | 0.640517i | \(0.778720\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.726450 | −0.0302951 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.32558 | −0.346598 | −0.173299 | − | 0.984869i | \(-0.555443\pi\) | ||||
−0.173299 | + | 0.984869i | \(0.555443\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 6.76125i | − 0.280504i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.0114 | −0.663126 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 24.4147i | − 1.00770i | −0.863791 | − | 0.503851i | \(-0.831916\pi\) | ||||
0.863791 | − | 0.503851i | \(-0.168084\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 10.6361i | − 0.438252i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.57185 | 0.228809 | 0.114404 | − | 0.993434i | \(-0.463504\pi\) | ||||
0.114404 | + | 0.993434i | \(0.463504\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.0775i | 0.864094i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.6835 | −1.17198 | −0.585988 | − | 0.810319i | \(-0.699294\pi\) | ||||
−0.585988 | + | 0.810319i | \(0.699294\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.9086 | −1.17921 | −0.589603 | − | 0.807693i | \(-0.700716\pi\) | ||||
−0.589603 | + | 0.807693i | \(0.700716\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 19.2027i | 0.780702i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.3353 | 0.419498 | 0.209749 | − | 0.977755i | \(-0.432735\pi\) | ||||
0.209749 | + | 0.977755i | \(0.432735\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.84624i | 0.155602i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 2.77963i | − 0.112268i | −0.998423 | − | 0.0561341i | \(-0.982123\pi\) | ||||
0.998423 | − | 0.0561341i | \(-0.0178774\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.1145 | −0.890296 | −0.445148 | − | 0.895457i | \(-0.646849\pi\) | ||||
−0.445148 | + | 0.895457i | \(0.646849\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 8.20284i | − 0.329700i | −0.986319 | − | 0.164850i | \(-0.947286\pi\) | ||||
0.986319 | − | 0.164850i | \(-0.0527140\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.7549 | 0.671272 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.1759 | −1.16704 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 47.1688i | − 1.88074i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.2572 | 1.12490 | 0.562450 | − | 0.826831i | \(-0.309859\pi\) | ||||
0.562450 | + | 0.826831i | \(0.309859\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.0796i | 0.519049i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 0.665739i | − 0.0263776i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 48.7144 | 1.92410 | 0.962051 | − | 0.272870i | \(-0.0879730\pi\) | ||||
0.962051 | + | 0.272870i | \(0.0879730\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.8806i | 0.941757i | 0.882198 | + | 0.470879i | \(0.156063\pi\) | ||||
−0.882198 | + | 0.470879i | \(0.843937\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.9383 | −1.33425 | −0.667127 | − | 0.744944i | \(-0.732476\pi\) | ||||
−0.667127 | + | 0.744944i | \(0.732476\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.3370 | −0.759045 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 35.4564i | − 1.38752i | −0.720208 | − | 0.693759i | \(-0.755953\pi\) | ||||
0.720208 | − | 0.693759i | \(-0.244047\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.2304 | 0.673246 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.40093i | 0.171436i | 0.996319 | + | 0.0857179i | \(0.0273184\pi\) | ||||
−0.996319 | + | 0.0857179i | \(0.972682\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 13.8183i | − 0.537470i | −0.963214 | − | 0.268735i | \(-0.913394\pi\) | ||||
0.963214 | − | 0.268735i | \(-0.0866056\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.17180 | −0.161776 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.235190i | 0.00910658i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.9740 | −0.809693 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.7125 | 1.10679 | 0.553393 | − | 0.832921i | \(-0.313333\pi\) | ||||
0.553393 | + | 0.832921i | \(0.313333\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 30.5789i | − 1.17524i | −0.809136 | − | 0.587621i | \(-0.800064\pi\) | ||||
0.809136 | − | 0.587621i | \(-0.199936\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.107694 | 0.00413290 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 10.0994i | − 0.386443i | −0.981155 | − | 0.193221i | \(-0.938106\pi\) | ||||
0.981155 | − | 0.193221i | \(-0.0618936\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 31.4521i | 1.20172i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.98208 | −0.189802 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.93187i | 0.0734916i | 0.999325 | + | 0.0367458i | \(0.0116992\pi\) | ||||
−0.999325 | + | 0.0367458i | \(0.988301\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.7374 | −0.824545 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.93226 | −0.0731895 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 23.6511i | − 0.893288i | −0.894712 | − | 0.446644i | \(-0.852619\pi\) | ||||
0.894712 | − | 0.446644i | \(-0.147381\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.33598 | 0.352113 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.8524i | 0.558584i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.8417i | 0.782728i | 0.920236 | + | 0.391364i | \(0.127997\pi\) | ||||
−0.920236 | + | 0.391364i | \(0.872003\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.40547 | 0.0526354 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 4.25893i | − 0.159275i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.81902 | 0.105132 | 0.0525658 | − | 0.998617i | \(-0.483260\pi\) | ||||
0.0525658 | + | 0.998617i | \(0.483260\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.1461 | −0.601311 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 5.02621i | − 0.186669i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.6918 | 0.544887 | 0.272444 | − | 0.962172i | \(-0.412168\pi\) | ||||
0.272444 | + | 0.962172i | \(0.412168\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 18.6082i | − 0.688248i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.7679i | 1.69048i | 0.534389 | + | 0.845239i | \(0.320542\pi\) | ||||
−0.534389 | + | 0.845239i | \(0.679458\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −23.1482 | −0.852673 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.7771i | 1.38965i | 0.719178 | + | 0.694826i | \(0.244519\pi\) | ||||
−0.719178 | + | 0.694826i | \(0.755481\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.38675 | −0.234307 | −0.117154 | − | 0.993114i | \(-0.537377\pi\) | ||||
−0.117154 | + | 0.993114i | \(0.537377\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.16812 | −0.335894 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.6131i | 0.570490i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −52.5372 | −1.91711 | −0.958554 | − | 0.284910i | \(-0.908036\pi\) | ||||
−0.958554 | + | 0.284910i | \(0.908036\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 47.5388i | 1.73012i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 3.80676i | − 0.138359i | −0.997604 | − | 0.0691794i | \(-0.977962\pi\) | ||||
0.997604 | − | 0.0691794i | \(-0.0220381\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.9307 | 0.939986 | 0.469993 | − | 0.882670i | \(-0.344256\pi\) | ||||
0.469993 | + | 0.882670i | \(0.344256\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 4.15829i | − 0.150540i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.01686 | −0.217256 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.2680 | −1.52422 | −0.762112 | − | 0.647445i | \(-0.775838\pi\) | ||||
−0.762112 | + | 0.647445i | \(0.775838\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 13.4481i | − 0.483696i | −0.970314 | − | 0.241848i | \(-0.922246\pi\) | ||||
0.970314 | − | 0.241848i | \(-0.0777536\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −30.0362 | −1.07893 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 0.382445i | − 0.0137025i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 16.9790i | − 0.607555i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 54.7804 | 1.95520 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1.40104i | − 0.0499418i | −0.999688 | − | 0.0249709i | \(-0.992051\pi\) | ||||
0.999688 | − | 0.0249709i | \(-0.00794932\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.4682 | 0.656654 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.52623 | −0.231753 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 19.3605i | − 0.685783i | −0.939375 | − | 0.342891i | \(-0.888594\pi\) | ||||
0.939375 | − | 0.342891i | \(-0.111406\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40.7266 | 1.44080 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.99950i | 0.211718i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 0.551270i | − 0.0194297i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.4386 | 0.507633 | 0.253816 | − | 0.967252i | \(-0.418314\pi\) | ||||
0.253816 | + | 0.967252i | \(0.418314\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 42.1307i | − 1.47941i | −0.672932 | − | 0.739705i | \(-0.734965\pi\) | ||||
0.672932 | − | 0.739705i | \(-0.265035\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 65.9234 | 2.30920 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.68305 | 0.128854 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 7.21315i | − 0.251741i | −0.992047 | − | 0.125870i | \(-0.959828\pi\) | ||||
0.992047 | − | 0.125870i | \(-0.0401723\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.47104 | 0.225566 | 0.112783 | − | 0.993620i | \(-0.464023\pi\) | ||||
0.112783 | + | 0.993620i | \(0.464023\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 55.8363i | − 1.94162i | −0.239850 | − | 0.970810i | \(-0.577098\pi\) | ||||
0.239850 | − | 0.970810i | \(-0.422902\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 14.1807i | − 0.492517i | −0.969204 | − | 0.246258i | \(-0.920799\pi\) | ||||
0.969204 | − | 0.246258i | \(-0.0792011\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.04931 | −0.244244 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30.6925i | 1.06216i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.4229 | 1.08484 | 0.542420 | − | 0.840108i | \(-0.317508\pi\) | ||||
0.542420 | + | 0.840108i | \(0.317508\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.3728 | 0.943888 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 37.5449i | 1.29159i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.42230 | −0.220673 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.23367i | 0.0422898i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.3929i | 0.800957i | 0.916306 | + | 0.400479i | \(0.131156\pi\) | ||||
−0.916306 | + | 0.400479i | \(0.868844\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.0033 | 0.819936 | 0.409968 | − | 0.912100i | \(-0.365540\pi\) | ||||
0.409968 | + | 0.912100i | \(0.365540\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 41.5626i | − 1.41810i | −0.705160 | − | 0.709048i | \(-0.749125\pi\) | ||||
0.705160 | − | 0.709048i | \(-0.250875\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.43323 | 0.116868 | 0.0584342 | − | 0.998291i | \(-0.481389\pi\) | ||||
0.0584342 | + | 0.998291i | \(0.481389\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −46.4151 | −1.57816 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.0812i | 0.579438i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.20273 | −0.244055 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 3.16893i | − 0.107129i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 47.9141i | 1.61794i | 0.587847 | + | 0.808972i | \(0.299976\pi\) | ||||
−0.587847 | + | 0.808972i | \(0.700024\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.7071 | −0.866095 | −0.433047 | − | 0.901371i | \(-0.642562\pi\) | ||||
−0.433047 | + | 0.901371i | \(0.642562\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 41.7112i | − 1.40369i | −0.712328 | − | 0.701847i | \(-0.752359\pi\) | ||||
0.712328 | − | 0.701847i | \(-0.247641\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32.6475 | −1.09620 | −0.548099 | − | 0.836414i | \(-0.684648\pi\) | ||||
−0.548099 | + | 0.836414i | \(0.684648\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.37444 | −0.146714 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.06089i | 0.269747i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −51.4365 | −1.71933 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.72428i | 0.324323i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 52.7537i | 1.75748i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 31.4385 | 1.04505 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 22.4610i | − 0.745804i | −0.927871 | − | 0.372902i | \(-0.878363\pi\) | ||||
0.927871 | − | 0.372902i | \(-0.121637\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.7360 | −0.687015 | −0.343507 | − | 0.939150i | \(-0.611615\pi\) | ||||
−0.343507 | + | 0.939150i | \(0.611615\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.4661 | 0.478757 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.76264i | 0.190299i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.9827 | 1.41787 | 0.708935 | − | 0.705274i | \(-0.249176\pi\) | ||||
0.708935 | + | 0.705274i | \(0.249176\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 5.28313i | − 0.173896i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 26.3647i | − 0.866865i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.62200 | −0.118834 | −0.0594170 | − | 0.998233i | \(-0.518924\pi\) | ||||
−0.0594170 | + | 0.998233i | \(0.518924\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1.39525i | − 0.0457274i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −45.0965 | −1.47481 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.8189 | 0.712793 | 0.356396 | − | 0.934335i | \(-0.384005\pi\) | ||||
0.356396 | + | 0.934335i | \(0.384005\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.8639i | 0.549747i | 0.961480 | + | 0.274873i | \(0.0886359\pi\) | ||||
−0.961480 | + | 0.274873i | \(0.911364\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.0505370 | 0.00164571 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.5568i | 0.603016i | 0.953464 | + | 0.301508i | \(0.0974900\pi\) | ||||
−0.953464 | + | 0.301508i | \(0.902510\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.86679i | 0.0605985i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36.6643 | −1.18767 | −0.593836 | − | 0.804586i | \(-0.702387\pi\) | ||||
−0.593836 | + | 0.804586i | \(0.702387\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 43.0242i | 1.39223i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.5191 | −0.339678 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.1114 | 0.874562 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 33.9604i | 1.09322i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.1440 | 0.358367 | 0.179184 | − | 0.983816i | \(-0.442654\pi\) | ||||
0.179184 | + | 0.983816i | \(0.442654\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 3.98773i | − 0.127972i | −0.997951 | − | 0.0639862i | \(-0.979619\pi\) | ||||
0.997951 | − | 0.0639862i | \(-0.0203814\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 7.27000i | − 0.233065i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32.7959 | 1.04923 | 0.524617 | − | 0.851338i | \(-0.324209\pi\) | ||||
0.524617 | + | 0.851338i | \(0.324209\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.8481i | 1.14571i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.0499 | 0.830864 | 0.415432 | − | 0.909624i | \(-0.363630\pi\) | ||||
0.415432 | + | 0.909624i | \(0.363630\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.2696 | −0.613980 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.486686i | 0.0154757i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.5053 | 0.556075 | 0.278037 | − | 0.960570i | \(-0.410316\pi\) | ||||
0.278037 | + | 0.960570i | \(0.410316\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.3769i | 0.614289i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 29.5008i | − 0.934300i | −0.884178 | − | 0.467150i | \(-0.845281\pi\) | ||||
0.884178 | − | 0.467150i | \(-0.154719\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6048.2.c.f.3025.19 | 24 | ||
3.2 | odd | 2 | inner | 6048.2.c.f.3025.5 | 24 | ||
4.3 | odd | 2 | 1512.2.c.g.757.8 | yes | 24 | ||
8.3 | odd | 2 | 1512.2.c.g.757.7 | ✓ | 24 | ||
8.5 | even | 2 | inner | 6048.2.c.f.3025.6 | 24 | ||
12.11 | even | 2 | 1512.2.c.g.757.17 | yes | 24 | ||
24.5 | odd | 2 | inner | 6048.2.c.f.3025.20 | 24 | ||
24.11 | even | 2 | 1512.2.c.g.757.18 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.g.757.7 | ✓ | 24 | 8.3 | odd | 2 | ||
1512.2.c.g.757.8 | yes | 24 | 4.3 | odd | 2 | ||
1512.2.c.g.757.17 | yes | 24 | 12.11 | even | 2 | ||
1512.2.c.g.757.18 | yes | 24 | 24.11 | even | 2 | ||
6048.2.c.f.3025.5 | 24 | 3.2 | odd | 2 | inner | ||
6048.2.c.f.3025.6 | 24 | 8.5 | even | 2 | inner | ||
6048.2.c.f.3025.19 | 24 | 1.1 | even | 1 | trivial | ||
6048.2.c.f.3025.20 | 24 | 24.5 | odd | 2 | inner |