Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8028,2,Mod(4013,8028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8028, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8028.4013");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8028 = 2^{2} \cdot 3^{2} \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8028.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(64.1039027427\) |
Analytic rank: | \(0\) |
Dimension: | \(76\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4013.3 | ||
Character | \(\chi\) | \(=\) | 8028.4013 |
Dual form | 8028.2.h.a.4013.4 |
$q$-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 \(\left(\mathbb{Z}/8028\mathbb{Z}\right)^\times\).
\(n\) | \(893\) | \(2233\) | \(4015\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | −3.84036 | −1.71746 | −0.858731 | − | 0.512427i | \(-0.828747\pi\) | ||||
−0.858731 | + | 0.512427i | \(0.828747\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.75909 | 0.664875 | 0.332438 | − | 0.943125i | \(-0.392129\pi\) | ||||
0.332438 | + | 0.943125i | \(0.392129\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.98889 | 1.80572 | 0.902859 | − | 0.429936i | \(-0.141464\pi\) | ||||
0.902859 | + | 0.429936i | \(0.141464\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.14669i | 1.42743i | 0.700434 | + | 0.713717i | \(0.252990\pi\) | ||||
−0.700434 | + | 0.713717i | \(0.747010\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.41667i | 1.79881i | 0.437119 | + | 0.899404i | \(0.355999\pi\) | ||||
−0.437119 | + | 0.899404i | \(0.644001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.31871 | 1.90844 | 0.954222 | − | 0.299101i | \(-0.0966867\pi\) | ||||
0.954222 | + | 0.299101i | \(0.0966867\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.63152 | −0.548711 | −0.274355 | − | 0.961628i | \(-0.588464\pi\) | ||||
−0.274355 | + | 0.961628i | \(0.588464\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.74838 | 1.94968 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.44889i | 1.01183i | 0.862582 | + | 0.505917i | \(0.168846\pi\) | ||||
−0.862582 | + | 0.505917i | \(0.831154\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.99898 | 0.897843 | 0.448922 | − | 0.893571i | \(-0.351808\pi\) | ||||
0.448922 | + | 0.893571i | \(0.351808\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.75556 | −1.14190 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.71440 | 0.939441 | 0.469721 | − | 0.882815i | \(-0.344355\pi\) | ||||
0.469721 | + | 0.882815i | \(0.344355\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.69328i | − | 0.420620i | −0.977635 | − | 0.210310i | \(-0.932553\pi\) | ||
0.977635 | − | 0.210310i | \(-0.0674473\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.69616 | −1.17365 | −0.586827 | − | 0.809713i | \(-0.699623\pi\) | ||||
−0.586827 | + | 0.809713i | \(0.699623\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.4380i | 1.66840i | 0.551459 | + | 0.834202i | \(0.314071\pi\) | ||||
−0.551459 | + | 0.834202i | \(0.685929\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.90559 | −0.557941 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.06965i | 0.421649i | 0.977524 | + | 0.210825i | \(0.0676149\pi\) | ||||
−0.977524 | + | 0.210825i | \(0.932385\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −22.9995 | −3.10125 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.03626 | −0.134910 | −0.0674548 | − | 0.997722i | \(-0.521488\pi\) | ||||
−0.0674548 | + | 0.997722i | \(0.521488\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 9.82914i | − | 1.25849i | −0.777206 | − | 0.629246i | \(-0.783364\pi\) | ||
0.777206 | − | 0.629246i | \(-0.216636\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 19.7651i | − | 2.45156i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.69857i | − | 0.207514i | −0.994603 | − | 0.103757i | \(-0.966914\pi\) | ||
0.994603 | − | 0.103757i | \(-0.0330864\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.83513 | 0.929858 | 0.464929 | − | 0.885348i | \(-0.346080\pi\) | ||||
0.464929 | + | 0.885348i | \(0.346080\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.44707 | 0.637531 | 0.318765 | − | 0.947834i | \(-0.396732\pi\) | ||||
0.318765 | + | 0.947834i | \(0.396732\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.5350 | 1.20058 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.91980i | 0.778538i | 0.921124 | + | 0.389269i | \(0.127272\pi\) | ||||
−0.921124 | + | 0.389269i | \(0.872728\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 8.11970i | − | 0.891253i | −0.895219 | − | 0.445626i | \(-0.852981\pi\) | ||
0.895219 | − | 0.445626i | \(-0.147019\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 28.4827i | − | 3.08938i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 9.06835i | − | 0.961243i | −0.876928 | − | 0.480621i | \(-0.840411\pi\) | ||
0.876928 | − | 0.480621i | \(-0.159589\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.05351i | 0.949066i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −31.9469 | −3.27768 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.305441i | 0.0310129i | 0.999880 | + | 0.0155064i | \(0.00493605\pi\) | ||||
−0.999880 | + | 0.0155064i | \(0.995064\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.669968i | 0.0666643i | 0.999444 | + | 0.0333321i | \(0.0106119\pi\) | ||||
−0.999444 | + | 0.0333321i | \(0.989388\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 7.99641i | − | 0.787910i | −0.919130 | − | 0.393955i | \(-0.871107\pi\) | ||
0.919130 | − | 0.393955i | \(-0.128893\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.13989 | −0.303545 | −0.151772 | − | 0.988415i | \(-0.548498\pi\) | ||||
−0.151772 | + | 0.988415i | \(0.548498\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.26082 | 0.503895 | 0.251948 | − | 0.967741i | \(-0.418929\pi\) | ||||
0.251948 | + | 0.967741i | \(0.418929\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.35771 | −0.409939 | −0.204969 | − | 0.978768i | \(-0.565709\pi\) | ||||
−0.204969 | + | 0.978768i | \(0.565709\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.1060 | 0.942390 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.0466i | 1.19598i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 24.8668 | 2.26062 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −18.2355 | −1.63103 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.65602 | −0.235684 | −0.117842 | − | 0.993032i | \(-0.537598\pi\) | ||||
−0.117842 | + | 0.993032i | \(0.537598\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 7.82739i | − | 0.683883i | −0.939721 | − | 0.341941i | \(-0.888916\pi\) | ||
0.939721 | − | 0.341941i | \(-0.111084\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.6334 | 1.26888 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.24368 | −0.789741 | −0.394870 | − | 0.918737i | \(-0.629210\pi\) | ||||
−0.394870 | + | 0.918737i | \(0.629210\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.3748 | −0.964795 | −0.482398 | − | 0.875952i | \(-0.660234\pi\) | ||||
−0.482398 | + | 0.875952i | \(0.660234\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 30.8230i | 2.57755i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 20.9257i | − | 1.73779i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.4080 | −1.26228 | −0.631138 | − | 0.775671i | \(-0.717412\pi\) | ||||
−0.631138 | + | 0.775671i | \(0.717412\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.8560i | 1.53448i | 0.641361 | + | 0.767239i | \(0.278370\pi\) | ||||
−0.641361 | + | 0.767239i | \(0.721630\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.1979 | −1.54201 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.0313i | 1.19962i | 0.800141 | + | 0.599812i | \(0.204758\pi\) | ||||
−0.800141 | + | 0.599812i | \(0.795242\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.62910 | −0.364824 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 13.3802i | − | 1.04802i | −0.851712 | − | 0.524010i | \(-0.824435\pi\) | ||
0.851712 | − | 0.524010i | \(-0.175565\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.3366 | −0.877252 | −0.438626 | − | 0.898670i | \(-0.644535\pi\) | ||||
−0.438626 | + | 0.898670i | \(0.644535\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.4884 | −1.03757 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.8260 | 0.975146 | 0.487573 | − | 0.873082i | \(-0.337882\pi\) | ||||
0.487573 | + | 0.873082i | \(0.337882\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.1483 | 1.29629 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.2660i | 1.51475i | 0.652979 | + | 0.757376i | \(0.273519\pi\) | ||||
−0.652979 | + | 0.757376i | \(0.726481\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.7440 | 1.31890 | 0.659452 | − | 0.751747i | \(-0.270788\pi\) | ||||
0.659452 | + | 0.751747i | \(0.270788\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21.9454 | −1.61346 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 44.4177i | 3.24814i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.399844 | −0.0289317 | −0.0144659 | − | 0.999895i | \(-0.504605\pi\) | ||||
−0.0144659 | + | 0.999895i | \(0.504605\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 9.86875i | − | 0.710368i | −0.934796 | − | 0.355184i | \(-0.884418\pi\) | ||
0.934796 | − | 0.355184i | \(-0.115582\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 7.40836i | − | 0.527824i | −0.964547 | − | 0.263912i | \(-0.914987\pi\) | ||
0.964547 | − | 0.263912i | \(-0.0850128\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.3243 | 0.873649 | 0.436825 | − | 0.899547i | \(-0.356103\pi\) | ||||
0.436825 | + | 0.899547i | \(0.356103\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.58511i | 0.672743i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.3432i | 0.722399i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 49.8198 | 3.44611 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.20156 | −0.495776 | −0.247888 | − | 0.968789i | \(-0.579737\pi\) | ||||
−0.247888 | + | 0.968789i | \(0.579737\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 29.5560 | 2.01570 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.79367 | 0.596953 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −38.1713 | −2.56768 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.1797 | + | 8.64024i | −0.815616 | + | 0.578593i | ||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.6670i | 0.774367i | 0.922003 | + | 0.387183i | \(0.126552\pi\) | ||||
−0.922003 | + | 0.387183i | \(0.873448\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 6.50468i | − | 0.429842i | −0.976631 | − | 0.214921i | \(-0.931051\pi\) | ||
0.976631 | − | 0.214921i | \(-0.0689493\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.5344 | −1.47628 | −0.738138 | − | 0.674650i | \(-0.764295\pi\) | ||||
−0.738138 | + | 0.674650i | \(0.764295\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 43.9261i | − | 2.86542i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 22.3441i | − | 1.44532i | −0.691204 | − | 0.722659i | \(-0.742920\pi\) | ||
0.691204 | − | 0.722659i | \(-0.257080\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.7219 | 1.65689 | 0.828446 | − | 0.560070i | \(-0.189226\pi\) | ||||
0.828446 | + | 0.560070i | \(0.189226\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.9989 | 0.958243 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 42.8138i | 2.72418i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 19.9642i | − | 1.26013i | −0.776542 | − | 0.630065i | \(-0.783028\pi\) | ||
0.776542 | − | 0.630065i | \(-0.216972\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.7599 | −0.990817 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 12.5567i | − | 0.783265i | −0.920122 | − | 0.391632i | \(-0.871911\pi\) | ||
0.920122 | − | 0.391632i | \(-0.128089\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.0522 | 0.624611 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.3133 | 1.49922 | 0.749612 | − | 0.661877i | \(-0.230240\pi\) | ||||
0.749612 | + | 0.661877i | \(0.230240\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 11.7886i | − | 0.724167i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.07527 | −0.309445 | −0.154722 | − | 0.987958i | \(-0.549448\pi\) | ||||
−0.154722 | + | 0.987958i | \(0.549448\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.814354i | 0.0494685i | 0.999694 | + | 0.0247342i | \(0.00787395\pi\) | ||||
−0.999694 | + | 0.0247342i | \(0.992126\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 58.3820 | 3.52057 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.1934i | 1.57381i | 0.617074 | + | 0.786905i | \(0.288318\pi\) | ||||
−0.617074 | + | 0.786905i | \(0.711682\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.6745i | 1.47196i | 0.677004 | + | 0.735979i | \(0.263278\pi\) | ||||
−0.677004 | + | 0.735979i | \(0.736722\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.0745 | 0.836642 | 0.418321 | − | 0.908299i | \(-0.362619\pi\) | ||||
0.418321 | + | 0.908299i | \(0.362619\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 4.73774i | − | 0.279660i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −38.0071 | −2.23571 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.5077 | −0.847548 | −0.423774 | − | 0.905768i | \(-0.639295\pi\) | ||||
−0.423774 | + | 0.905768i | \(0.639295\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.97961 | 0.231702 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 13.5436i | − | 0.783249i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.5383 | −0.780333 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 37.7475i | 2.16141i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 34.6272i | 1.97628i | 0.153553 | + | 0.988140i | \(0.450929\pi\) | ||||
−0.153553 | + | 0.988140i | \(0.549071\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.71486 | 0.437470 | 0.218735 | − | 0.975784i | \(-0.429807\pi\) | ||||
0.218735 | + | 0.975784i | \(0.429807\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 28.4539i | − | 1.60831i | −0.594420 | − | 0.804155i | \(-0.702618\pi\) | ||
0.594420 | − | 0.804155i | \(-0.297382\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 31.4378i | 1.76572i | 0.469632 | + | 0.882862i | \(0.344387\pi\) | ||||
−0.469632 | + | 0.882862i | \(0.655613\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 32.6328i | 1.82709i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 61.6972i | 3.43292i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 50.1719i | 2.78304i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.1205i | 1.10928i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.4935i | 0.686703i | 0.939207 | + | 0.343351i | \(0.111562\pi\) | ||||
−0.939207 | + | 0.343351i | \(0.888438\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.52314i | 0.356397i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 34.8365i | − | 1.89766i | −0.315781 | − | 0.948832i | \(-0.602266\pi\) | ||
0.315781 | − | 0.948832i | \(-0.397734\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 29.9383 | 1.62125 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.1840 | −1.03584 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.8567i | 0.636501i | 0.948007 | + | 0.318251i | \(0.103095\pi\) | ||||
−0.948007 | + | 0.318251i | \(0.896905\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.7922 | 1.59474 | 0.797371 | − | 0.603489i | \(-0.206223\pi\) | ||||
0.797371 | + | 0.603489i | \(0.206223\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 19.2735i | − | 1.02583i | −0.858441 | − | 0.512913i | \(-0.828566\pi\) | ||
0.858441 | − | 0.512913i | \(-0.171434\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −30.0897 | −1.59700 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 2.05711i | − | 0.108570i | −0.998525 | − | 0.0542850i | \(-0.982712\pi\) | ||
0.998525 | − | 0.0542850i | \(-0.0172879\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 50.2009 | 2.64215 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −20.9187 | −1.09494 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.8162 | −0.982199 | −0.491100 | − | 0.871103i | \(-0.663405\pi\) | ||||
−0.491100 | + | 0.871103i | \(0.663405\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.39981i | 0.280344i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.51663i | 0.440974i | 0.975390 | + | 0.220487i | \(0.0707647\pi\) | ||||
−0.975390 | + | 0.220487i | \(0.929235\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −28.0438 | −1.44433 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.8622 | −1.53392 | −0.766959 | − | 0.641696i | \(-0.778231\pi\) | ||||
−0.766959 | + | 0.641696i | \(0.778231\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.4880 | 0.944691 | 0.472346 | − | 0.881413i | \(-0.343407\pi\) | ||||
0.472346 | + | 0.881413i | \(0.343407\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −40.4583 | −2.06195 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.9103i | 0.908088i | 0.890979 | + | 0.454044i | \(0.150019\pi\) | ||||
−0.890979 | + | 0.454044i | \(0.849981\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 19.5172i | − | 0.987025i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 26.5745i | − | 1.33711i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 2.78904i | − | 0.139978i | −0.997548 | − | 0.0699891i | \(-0.977704\pi\) | ||
0.997548 | − | 0.0699891i | \(-0.0222964\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.26702i | 0.362898i | 0.983400 | + | 0.181449i | \(0.0580787\pi\) | ||||
−0.983400 | + | 0.181449i | \(0.941921\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25.7282i | 1.28161i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 34.2229 | 1.69637 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 21.1416i | − | 1.04538i | −0.852521 | − | 0.522692i | \(-0.824928\pi\) | ||
0.852521 | − | 0.522692i | \(-0.175072\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.82288 | −0.0896980 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 31.1826i | 1.53069i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 35.1158i | − | 1.71552i | −0.514051 | − | 0.857760i | \(-0.671856\pi\) | ||
0.514051 | − | 0.857760i | \(-0.328144\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.0049i | 1.21866i | 0.792916 | + | 0.609331i | \(0.208562\pi\) | ||||
−0.792916 | + | 0.609331i | \(0.791438\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 72.3006i | 3.50709i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 17.2904i | − | 0.836740i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.81487 | 0.280093 | 0.140046 | − | 0.990145i | \(-0.455275\pi\) | ||||
0.140046 | + | 0.990145i | \(0.455275\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.534136 | 0.0256689 | 0.0128345 | − | 0.999918i | \(-0.495915\pi\) | ||||
0.0128345 | + | 0.999918i | \(0.495915\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −21.8909 | −1.04718 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 26.9522i | − | 1.28636i | −0.765717 | − | 0.643178i | \(-0.777616\pi\) | ||
0.765717 | − | 0.643178i | \(-0.222384\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 12.8170i | − | 0.608955i | −0.952520 | − | 0.304477i | \(-0.901518\pi\) | ||
0.952520 | − | 0.304477i | \(-0.0984818\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 34.8257i | 1.65090i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.0760 | 1.65534 | 0.827669 | − | 0.561217i | \(-0.189667\pi\) | ||||
0.827669 | + | 0.561217i | \(0.189667\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 16.1298i | − | 0.759521i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 34.7688i | − | 1.62998i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.87919i | 0.275017i | 0.990501 | + | 0.137508i | \(0.0439094\pi\) | ||||
−0.990501 | + | 0.137508i | \(0.956091\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.4554i | 0.486958i | 0.969906 | + | 0.243479i | \(0.0782887\pi\) | ||||
−0.969906 | + | 0.243479i | \(0.921711\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.1470 | −0.750413 | −0.375206 | − | 0.926941i | \(-0.622428\pi\) | ||||
−0.375206 | + | 0.926941i | \(0.622428\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −33.4585 | −1.54827 | −0.774137 | − | 0.633018i | \(-0.781816\pi\) | ||||
−0.774137 | + | 0.633018i | \(0.781816\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 2.98795i | − | 0.137971i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −46.0915 | −2.11929 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 81.0940 | 3.72085 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.2904i | 1.61246i | 0.591602 | + | 0.806230i | \(0.298496\pi\) | ||||
−0.591602 | + | 0.806230i | \(0.701504\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.4102i | 1.34099i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 1.17301i | − | 0.0532634i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.4665 | −0.700852 | −0.350426 | − | 0.936590i | \(-0.613963\pi\) | ||||
−0.350426 | + | 0.936590i | \(0.613963\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.32103 | −0.104747 | −0.0523733 | − | 0.998628i | \(-0.516679\pi\) | ||||
−0.0523733 | + | 0.998628i | \(0.516679\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −40.4127 | −1.82009 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.7827 | 0.618240 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.10308 | −0.183679 | −0.0918396 | − | 0.995774i | \(-0.529275\pi\) | ||||
−0.0918396 | + | 0.995774i | \(0.529275\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.19123 | −0.276053 | −0.138027 | − | 0.990429i | \(-0.544076\pi\) | ||||
−0.138027 | + | 0.990429i | \(0.544076\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 2.57292i | − | 0.114493i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 21.3919i | − | 0.948178i | −0.880477 | − | 0.474089i | \(-0.842777\pi\) | ||
0.880477 | − | 0.474089i | \(-0.157223\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.58190 | 0.423878 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 30.7091i | 1.35321i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 68.5010i | 3.01267i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.3684 | 0.936166 | 0.468083 | − | 0.883684i | \(-0.344945\pi\) | ||||
0.468083 | + | 0.883684i | \(0.344945\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.1591i | 0.881498i | 0.897630 | + | 0.440749i | \(0.145287\pi\) | ||||
−0.897630 | + | 0.440749i | \(0.854713\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 37.0758i | 1.61505i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.0751 | −0.698917 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.8615 | 0.600408 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.0583 | 0.521327 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −23.3901 | −1.00748 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.9544i | 1.02988i | 0.857226 | + | 0.514941i | \(0.172186\pi\) | ||||
−0.857226 | + | 0.514941i | \(0.827814\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20.2035 | −0.865421 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.7380 | 1.31426 | 0.657132 | − | 0.753776i | \(-0.271770\pi\) | ||||
0.657132 | + | 0.753776i | \(0.271770\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 45.3278i | 1.93103i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.1726i | 0.517631i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.09972 | −0.131339 | −0.0656697 | − | 0.997841i | \(-0.520918\pi\) | ||||
−0.0656697 | + | 0.997841i | \(0.520918\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 39.6097i | − | 1.67531i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.04850 | 0.0863340 | 0.0431670 | − | 0.999068i | \(-0.486255\pi\) | ||||
0.0431670 | + | 0.999068i | \(0.486255\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.7352 | 0.704054 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 40.2770 | 1.68850 | 0.844250 | − | 0.535950i | \(-0.180046\pi\) | ||||
0.844250 | + | 0.535950i | \(0.180046\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 29.3204i | − | 1.22702i | −0.789687 | − | 0.613509i | \(-0.789757\pi\) | ||
0.789687 | − | 0.613509i | \(-0.210243\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −25.6531 | −1.06981 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.782350 | 0.0325696 | 0.0162848 | − | 0.999867i | \(-0.494816\pi\) | ||||
0.0162848 | + | 0.999867i | \(0.494816\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 14.2833i | − | 0.592572i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.3838i | 0.761380i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.9552 | −0.864912 | −0.432456 | − | 0.901655i | \(-0.642353\pi\) | ||||
−0.432456 | + | 0.901655i | \(0.642353\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 41.5851 | 1.71348 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.7414 | −1.09814 | −0.549069 | − | 0.835777i | \(-0.685018\pi\) | ||||
−0.549069 | + | 0.835777i | \(0.685018\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 50.1038i | − | 2.05405i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 8.10910i | − | 0.331329i | −0.986182 | − | 0.165664i | \(-0.947023\pi\) | ||
0.986182 | − | 0.165664i | \(-0.0529768\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 38.3430i | − | 1.56404i | −0.623251 | − | 0.782022i | \(-0.714188\pi\) | ||
0.623251 | − | 0.782022i | \(-0.285812\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −95.4976 | −3.88253 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.02394i | − | 0.0415606i | −0.999784 | − | 0.0207803i | \(-0.993385\pi\) | ||
0.999784 | − | 0.0207803i | \(-0.00661506\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −58.8678 | −2.38154 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.8647i | 0.681158i | 0.940216 | + | 0.340579i | \(0.110623\pi\) | ||||
−0.940216 | + | 0.340579i | \(0.889377\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 21.4891i | − | 0.865118i | −0.901606 | − | 0.432559i | \(-0.857611\pi\) | ||
0.901606 | − | 0.432559i | \(-0.142389\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 34.4819i | − | 1.38594i | −0.720964 | − | 0.692972i | \(-0.756301\pi\) | ||
0.720964 | − | 0.692972i | \(-0.243699\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 15.9521i | − | 0.639106i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.2890 | 0.851561 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 42.3818i | 1.68987i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.7254i | 0.506591i | 0.967389 | + | 0.253296i | \(0.0815145\pi\) | ||||
−0.967389 | + | 0.253296i | \(0.918485\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.2001 | 0.404778 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 20.1008i | − | 0.796425i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.5625 | −1.16765 | −0.583824 | − | 0.811880i | \(-0.698444\pi\) | ||||
−0.583824 | + | 0.811880i | \(0.698444\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.8720 | 0.586494 | 0.293247 | − | 0.956037i | \(-0.405264\pi\) | ||||
0.293247 | + | 0.956037i | \(0.405264\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 7.74488i | − | 0.304483i | −0.988343 | − | 0.152241i | \(-0.951351\pi\) | ||
0.988343 | − | 0.152241i | \(-0.0486491\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.20605 | −0.243609 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.7105 | 0.653934 | 0.326967 | − | 0.945036i | \(-0.393973\pi\) | ||||
0.326967 | + | 0.945036i | \(0.393973\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 30.0600i | 1.17454i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 9.24886i | − | 0.360285i | −0.983641 | − | 0.180142i | \(-0.942344\pi\) | ||
0.983641 | − | 0.180142i | \(-0.0576558\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 8.04614i | − | 0.312958i | −0.987681 | − | 0.156479i | \(-0.949986\pi\) | ||
0.987681 | − | 0.156479i | \(-0.0500144\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −56.1975 | −2.17925 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 14.3389i | − | 0.555204i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 58.8657i | − | 2.27248i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.1004 | −0.929003 | −0.464502 | − | 0.885572i | \(-0.653767\pi\) | ||||
−0.464502 | + | 0.885572i | \(0.653767\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.6147i | 0.715420i | 0.933833 | + | 0.357710i | \(0.116442\pi\) | ||||
−0.933833 | + | 0.357710i | \(0.883558\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.537300i | 0.0206197i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.45352i | 0.361729i | 0.983508 | + | 0.180864i | \(0.0578895\pi\) | ||||
−0.983508 | + | 0.180864i | \(0.942110\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 35.4991 | 1.35635 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.7985 | −0.601877 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.23717i | 0.237273i | 0.992938 | + | 0.118637i | \(0.0378523\pi\) | ||||
−0.992938 | + | 0.118637i | \(0.962148\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 43.6832 | 1.65700 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.9752 | 0.756615 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 38.5793i | − | 1.45712i | −0.684981 | − | 0.728560i | \(-0.740190\pi\) | ||
0.684981 | − | 0.728560i | \(-0.259810\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 47.5364 | 1.79287 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.17854i | 0.0443234i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.8480i | 1.00830i | 0.863616 | + | 0.504149i | \(0.168194\pi\) | ||||
−0.863616 | + | 0.504149i | \(0.831806\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.1549 | −0.492656 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 118.371i | − | 4.42684i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.1810i | 0.640742i | 0.947292 | + | 0.320371i | \(0.103808\pi\) | ||||
−0.947292 | + | 0.320371i | \(0.896192\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 14.0664i | − | 0.523862i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 53.1179i | 1.97275i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.7727 | −1.51218 | −0.756088 | − | 0.654470i | \(-0.772892\pi\) | ||||
−0.756088 | + | 0.654470i | \(0.772892\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 57.0799i | − | 2.11118i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.0337 | −0.444475 | −0.222238 | − | 0.974993i | \(-0.571336\pi\) | ||||
−0.222238 | + | 0.974993i | \(0.571336\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 10.1726i | − | 0.374711i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.1979i | 1.62585i | 0.582370 | + | 0.812924i | \(0.302125\pi\) | ||||
−0.582370 | + | 0.812924i | \(0.697875\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.0993i | 0.627314i | 0.949536 | + | 0.313657i | \(0.101554\pi\) | ||||
−0.949536 | + | 0.313657i | \(0.898446\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 59.1724 | 2.16791 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.52336 | −0.201819 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.52779 | −0.274693 | −0.137346 | − | 0.990523i | \(-0.543857\pi\) | ||||
−0.137346 | + | 0.990523i | \(0.543857\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 72.4138i | − | 2.63541i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.3568i | 0.703536i | 0.936087 | + | 0.351768i | \(0.114419\pi\) | ||||
−0.936087 | + | 0.351768i | \(0.885581\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.85457 | −0.139728 | −0.0698640 | − | 0.997557i | \(-0.522257\pi\) | ||||
−0.0698640 | + | 0.997557i | \(0.522257\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.25428 | 0.335027 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 5.33331i | − | 0.192575i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.7949 | 1.54322 | 0.771612 | − | 0.636094i | \(-0.219451\pi\) | ||||
0.771612 | + | 0.636094i | \(0.219451\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41.9392 | 1.50845 | 0.754224 | − | 0.656617i | \(-0.228013\pi\) | ||||
0.754224 | + | 0.656617i | \(0.228013\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 48.7320 | 1.75050 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 22.4046i | − | 0.802729i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 46.9237 | 1.67906 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 57.7255i | − | 2.06031i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.73416i | 0.275693i | 0.990454 | + | 0.137847i | \(0.0440181\pi\) | ||||
−0.990454 | + | 0.137847i | \(0.955982\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.66562 | −0.272558 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 50.5875 | 1.79642 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.6414i | 1.43959i | 0.694185 | + | 0.719796i | \(0.255765\pi\) | ||||
−0.694185 | + | 0.719796i | \(0.744235\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −84.8320 | −3.00114 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.6219 | 1.15120 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.7774 | 0.626571 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45.1580 | 1.58767 | 0.793835 | − | 0.608133i | \(-0.208081\pi\) | ||||
0.793835 | + | 0.608133i | \(0.208081\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 30.6080i | − | 1.07479i | −0.843329 | − | 0.537397i | \(-0.819408\pi\) | ||
0.843329 | − | 0.537397i | \(-0.180592\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 51.3849i | 1.79994i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −64.0221 | −2.23985 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 47.9518i | − | 1.67353i | −0.547563 | − | 0.836765i | \(-0.684444\pi\) | ||
0.547563 | − | 0.836765i | \(-0.315556\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.8971i | 1.21644i | 0.793770 | + | 0.608218i | \(0.208115\pi\) | ||||
−0.793770 | + | 0.608218i | \(0.791885\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 47.2514 | 1.64309 | 0.821545 | − | 0.570143i | \(-0.193112\pi\) | ||||
0.821545 | + | 0.570143i | \(0.193112\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 4.89282i | − | 0.169935i | −0.996384 | − | 0.0849674i | \(-0.972921\pi\) | ||
0.996384 | − | 0.0849674i | \(-0.0270786\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 28.9665i | − | 1.00363i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 43.5366 | 1.50665 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.46132 | 0.292117 | 0.146059 | − | 0.989276i | \(-0.453341\pi\) | ||||
0.146059 | + | 0.989276i | \(0.453341\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.690425 | −0.0238078 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 51.8004 | 1.78199 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 43.7431 | 1.50303 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.0376 | −0.515482 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 42.5391i | − | 1.45651i | −0.685306 | − | 0.728255i | \(-0.740332\pi\) | ||
0.685306 | − | 0.728255i | \(-0.259668\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 51.7346i | − | 1.76722i | −0.468223 | − | 0.883610i | \(-0.655106\pi\) | ||
0.468223 | − | 0.883610i | \(-0.344894\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.9477i | 1.49947i | 0.661736 | + | 0.749737i | \(0.269820\pi\) | ||||
−0.661736 | + | 0.749737i | \(0.730180\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.2934 | −1.13332 | −0.566661 | − | 0.823951i | \(-0.691765\pi\) | ||||
−0.566661 | + | 0.823951i | \(0.691765\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −49.2567 | −1.67478 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 41.4419i | 1.40582i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.74203 | 0.296212 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −32.0780 | −1.08443 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 21.7256i | − | 0.733621i | −0.930296 | − | 0.366811i | \(-0.880450\pi\) | ||
0.930296 | − | 0.366811i | \(-0.119550\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.9824i | 1.11121i | 0.831448 | + | 0.555603i | \(0.187513\pi\) | ||||
−0.831448 | + | 0.555603i | \(0.812487\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 45.4984i | − | 1.53114i | −0.643350 | − | 0.765572i | \(-0.722456\pi\) | ||
0.643350 | − | 0.765572i | \(-0.277544\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.28662i | 0.110354i | 0.998477 | + | 0.0551770i | \(0.0175723\pi\) | ||||
−0.998477 | + | 0.0551770i | \(0.982428\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.67220 | −0.156700 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 95.1494i | 3.18405i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 77.8288i | − | 2.60153i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 27.2389i | 0.908468i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.7666 | −0.758466 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −68.1435 | −2.26517 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −52.6858 | −1.74940 | −0.874702 | − | 0.484662i | \(-0.838943\pi\) | ||||
−0.874702 | + | 0.484662i | \(0.838943\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 13.9976i | − | 0.463760i | −0.972744 | − | 0.231880i | \(-0.925512\pi\) | ||
0.972744 | − | 0.231880i | \(-0.0744877\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 48.6280i | − | 1.60935i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 13.7691i | − | 0.454696i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 43.0324i | − | 1.41951i | −0.704450 | − | 0.709754i | \(-0.748806\pi\) | ||
0.704450 | − | 0.709754i | \(-0.251194\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 40.3250i | 1.32731i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 55.7061 | 1.83161 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.80809i | 0.190557i | 0.995451 | + | 0.0952786i | \(0.0303742\pi\) | ||||
−0.995451 | + | 0.0952786i | \(0.969626\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.4895 | −1.06480 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 170.580i | − | 5.57856i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.80069i | 0.156832i | 0.996921 | + | 0.0784158i | \(0.0249862\pi\) | ||||
−0.996921 | + | 0.0784158i | \(0.975014\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 6.34405i | − | 0.206810i | −0.994639 | − | 0.103405i | \(-0.967026\pi\) | ||
0.994639 | − | 0.103405i | \(-0.0329738\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.08744i | 0.230799i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.0695i | 0.327214i | 0.986526 | + | 0.163607i | \(0.0523129\pi\) | ||||
−0.986526 | + | 0.163607i | \(0.947687\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.0344i | 0.910034i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 57.2952 | 1.85597 | 0.927986 | − | 0.372615i | \(-0.121539\pi\) | ||||
0.927986 | + | 0.372615i | \(0.121539\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.53555 | 0.0496891 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.2605 | −0.525079 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.01021 | −0.193878 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 37.8996i | 1.22003i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.1170i | 1.06497i | 0.846439 | + | 0.532486i | \(0.178742\pi\) | ||||
−0.846439 | + | 0.532486i | \(0.821258\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.24321 | −0.0719880 | −0.0359940 | − | 0.999352i | \(-0.511460\pi\) | ||||
−0.0359940 | + | 0.999352i | \(0.511460\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.0093 | −0.641468 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.1526 | −0.452783 | −0.226392 | − | 0.974036i | \(-0.572693\pi\) | ||||
−0.226392 | + | 0.974036i | \(0.572693\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 54.3093i | − | 1.73573i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.01691 | 0.223805 | 0.111902 | − | 0.993719i | \(-0.464306\pi\) | ||||
0.111902 | + | 0.993719i | \(0.464306\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 28.4508i | 0.906517i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.2526 | 0.643996 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 36.6977i | − | 1.16574i | −0.812565 | − | 0.582871i | \(-0.801929\pi\) | ||
0.812565 | − | 0.582871i | \(-0.198071\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −47.3299 | −1.50046 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.38591 | 0.0755625 | 0.0377812 | − | 0.999286i | \(-0.487971\pi\) | ||||
0.0377812 | + | 0.999286i | \(0.487971\pi\) | |||||||
\(998\) | 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 | 8028.2.h.a.4013.3 | ✓ | 76 | |
3.2 | odd | 2 | inner | 8028.2.h.a.4013.73 | yes | 76 | |
223.222 | odd | 2 | inner | 8028.2.h.a.4013.74 | yes | 76 | |
669.668 | even | 2 | inner | 8028.2.h.a.4013.4 | yes | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8028.2.h.a.4013.3 | ✓ | 76 | 1.1 | even | 1 | trivial | |
8028.2.h.a.4013.4 | yes | 76 | 669.668 | even | 2 | inner | |
8028.2.h.a.4013.73 | yes | 76 | 3.2 | odd | 2 | inner | |
8028.2.h.a.4013.74 | yes | 76 | 223.222 | odd | 2 | inner |