Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(2591,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.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: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.7 | ||
Character | \(\chi\) | \(=\) | 6048.2591 |
Dual form | 6048.2.h.i.2591.8 |
$q$-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 | ||||||||
\(5\) | − 2.76574i | − 1.23688i | −0.785834 | − | 0.618438i | \(-0.787766\pi\) | ||||
0.785834 | − | 0.618438i | \(-0.212234\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.55543 | 0.770493 | 0.385246 | − | 0.922814i | \(-0.374116\pi\) | ||||
0.385246 | + | 0.922814i | \(0.374116\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.32854 | −0.645822 | −0.322911 | − | 0.946429i | \(-0.604661\pi\) | ||||
−0.322911 | + | 0.946429i | \(0.604661\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 7.36547i | − 1.78639i | −0.449669 | − | 0.893195i | \(-0.648458\pi\) | ||||
0.449669 | − | 0.893195i | \(-0.351542\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.78261i | 0.408959i | 0.978871 | + | 0.204480i | \(0.0655503\pi\) | ||||
−0.978871 | + | 0.204480i | \(0.934450\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.87170 | 0.807305 | 0.403653 | − | 0.914912i | \(-0.367740\pi\) | ||||
0.403653 | + | 0.914912i | \(0.367740\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.64930 | −0.529861 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 7.32622i | − 1.36044i | −0.733006 | − | 0.680222i | \(-0.761883\pi\) | ||||
0.733006 | − | 0.680222i | \(-0.238117\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.17647i | 0.390905i | 0.980713 | + | 0.195453i | \(0.0626176\pi\) | ||||
−0.980713 | + | 0.195453i | \(0.937382\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.76574 | 0.467495 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.24968 | −0.205445 | −0.102723 | − | 0.994710i | \(-0.532755\pi\) | ||||
−0.102723 | + | 0.994710i | \(0.532755\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.52679i | 0.550792i | 0.961331 | + | 0.275396i | \(0.0888090\pi\) | ||||
−0.961331 | + | 0.275396i | \(0.911191\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 5.28762i | − 0.806355i | −0.915122 | − | 0.403178i | \(-0.867906\pi\) | ||||
0.915122 | − | 0.403178i | \(-0.132094\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.77479 | −0.842340 | −0.421170 | − | 0.906982i | \(-0.638380\pi\) | ||||
−0.421170 | + | 0.906982i | \(0.638380\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.29178i | 1.00160i | 0.865562 | + | 0.500801i | \(0.166961\pi\) | ||||
−0.865562 | + | 0.500801i | \(0.833039\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 7.06766i | − 0.953003i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.98108 | 0.648482 | 0.324241 | − | 0.945975i | \(-0.394891\pi\) | ||||
0.324241 | + | 0.945975i | \(0.394891\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.15465 | 0.403912 | 0.201956 | − | 0.979395i | \(-0.435270\pi\) | ||||
0.201956 | + | 0.979395i | \(0.435270\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.44014i | 0.798801i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 7.72509i | − 0.943770i | −0.881660 | − | 0.471885i | \(-0.843574\pi\) | ||||
0.881660 | − | 0.471885i | \(-0.156426\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.98532 | −0.947683 | −0.473842 | − | 0.880610i | \(-0.657133\pi\) | ||||
−0.473842 | + | 0.880610i | \(0.657133\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.7548 | −1.25875 | −0.629377 | − | 0.777100i | \(-0.716690\pi\) | ||||
−0.629377 | + | 0.777100i | \(0.716690\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.55543i | 0.291219i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 2.10858i | − 0.237234i | −0.992940 | − | 0.118617i | \(-0.962154\pi\) | ||||
0.992940 | − | 0.118617i | \(-0.0378461\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.1458 | 1.33318 | 0.666590 | − | 0.745425i | \(-0.267753\pi\) | ||||
0.666590 | + | 0.745425i | \(0.267753\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20.3710 | −2.20954 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 9.71061i | − 1.02932i | −0.857394 | − | 0.514661i | \(-0.827918\pi\) | ||||
0.857394 | − | 0.514661i | \(-0.172082\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 2.32854i | − 0.244098i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.93024 | 0.505832 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.6053 | 1.58448 | 0.792239 | − | 0.610211i | \(-0.208915\pi\) | ||||
0.792239 | + | 0.610211i | \(0.208915\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 8.43842i | − 0.839654i | −0.907604 | − | 0.419827i | \(-0.862091\pi\) | ||||
0.907604 | − | 0.419827i | \(-0.137909\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1.53472i | − 0.151221i | −0.997137 | − | 0.0756105i | \(-0.975909\pi\) | ||||
0.997137 | − | 0.0756105i | \(-0.0240905\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.42794 | −0.524739 | −0.262369 | − | 0.964967i | \(-0.584504\pi\) | ||||
−0.262369 | + | 0.964967i | \(0.584504\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.47199 | −0.715687 | −0.357843 | − | 0.933782i | \(-0.616488\pi\) | ||||
−0.357843 | + | 0.933782i | \(0.616488\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.64780i | 0.249084i | 0.992214 | + | 0.124542i | \(0.0397461\pi\) | ||||
−0.992214 | + | 0.124542i | \(0.960254\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 10.7081i | − 0.998536i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.36547 | 0.675192 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.46975 | −0.406341 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 6.50141i | − 0.581504i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.2079i | 1.70443i | 0.523195 | + | 0.852213i | \(0.324740\pi\) | ||||
−0.523195 | + | 0.852213i | \(0.675260\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.182412 | 0.0159374 | 0.00796869 | − | 0.999968i | \(-0.497463\pi\) | ||||
0.00796869 | + | 0.999968i | \(0.497463\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.78261 | −0.154572 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.55207i | 0.474345i | 0.971467 | + | 0.237173i | \(0.0762207\pi\) | ||||
−0.971467 | + | 0.237173i | \(0.923779\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 18.7949i | − 1.59416i | −0.603873 | − | 0.797080i | \(-0.706377\pi\) | ||||
0.603873 | − | 0.797080i | \(-0.293623\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.95044 | −0.497601 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20.2624 | −1.68270 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.82804i | 0.805144i | 0.915388 | + | 0.402572i | \(0.131884\pi\) | ||||
−0.915388 | + | 0.402572i | \(0.868116\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 8.96087i | − 0.729225i | −0.931159 | − | 0.364613i | \(-0.881201\pi\) | ||||
0.931159 | − | 0.364613i | \(-0.118799\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.01954 | 0.483501 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.4314 | 1.15175 | 0.575876 | − | 0.817537i | \(-0.304661\pi\) | ||||
0.575876 | + | 0.817537i | \(0.304661\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.87170i | 0.305133i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 14.4908i | − 1.13500i | −0.823372 | − | 0.567502i | \(-0.807910\pi\) | ||||
0.823372 | − | 0.567502i | \(-0.192090\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.88572 | −0.610215 | −0.305108 | − | 0.952318i | \(-0.598692\pi\) | ||||
−0.305108 | + | 0.952318i | \(0.598692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.57788 | −0.582914 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 15.8802i | − 1.20735i | −0.797230 | − | 0.603676i | \(-0.793702\pi\) | ||||
0.797230 | − | 0.603676i | \(-0.206298\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 2.64930i | − 0.200269i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.2503 | 1.36409 | 0.682046 | − | 0.731309i | \(-0.261090\pi\) | ||||
0.682046 | + | 0.731309i | \(0.261090\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.1717 | −1.79667 | −0.898335 | − | 0.439311i | \(-0.855223\pi\) | ||||
−0.898335 | + | 0.439311i | \(0.855223\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.45628i | 0.254110i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 18.8220i | − 1.37640i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.6845 | −1.35197 | −0.675983 | − | 0.736917i | \(-0.736281\pi\) | ||||
−0.675983 | + | 0.736917i | \(0.736281\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.89411 | 0.496249 | 0.248124 | − | 0.968728i | \(-0.420186\pi\) | ||||
0.248124 | + | 0.968728i | \(0.420186\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.10853i | 0.648956i | 0.945893 | + | 0.324478i | \(0.105189\pi\) | ||||
−0.945893 | + | 0.324478i | \(0.894811\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.53988i | 0.676264i | 0.941099 | + | 0.338132i | \(0.109795\pi\) | ||||
−0.941099 | + | 0.338132i | \(0.890205\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.32622 | 0.514200 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.75418 | 0.681261 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.55535i | 0.315100i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 16.0066i | − 1.10194i | −0.834525 | − | 0.550970i | \(-0.814258\pi\) | ||||
0.834525 | − | 0.550970i | \(-0.185742\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.6242 | −0.997361 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.17647 | −0.147748 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.1508i | 1.15369i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.28527i | 0.219998i | 0.993932 | + | 0.109999i | \(0.0350848\pi\) | ||||
−0.993932 | + | 0.109999i | \(0.964915\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.2772 | −0.881238 | −0.440619 | − | 0.897694i | \(-0.645241\pi\) | ||||
−0.440619 | + | 0.897694i | \(0.645241\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.23836 | 0.346160 | 0.173080 | − | 0.984908i | \(-0.444628\pi\) | ||||
0.173080 | + | 0.984908i | \(0.444628\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 6.32608i | − 0.414435i | −0.978295 | − | 0.207218i | \(-0.933559\pi\) | ||||
0.978295 | − | 0.207218i | \(-0.0664408\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.9716i | 1.04187i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.2297 | 1.11450 | 0.557249 | − | 0.830346i | \(-0.311857\pi\) | ||||
0.557249 | + | 0.830346i | \(0.311857\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.6743 | −1.78266 | −0.891328 | − | 0.453358i | \(-0.850226\pi\) | ||||
−0.891328 | + | 0.453358i | \(0.850226\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.76574i | 0.176696i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 4.15089i | − 0.264115i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.3083 | −1.02937 | −0.514685 | − | 0.857380i | \(-0.672091\pi\) | ||||
−0.514685 | + | 0.857380i | \(0.672091\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.89388 | 0.622023 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 1.98554i | − 0.123855i | −0.998081 | − | 0.0619274i | \(-0.980275\pi\) | ||||
0.998081 | − | 0.0619274i | \(-0.0197247\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 1.24968i | − 0.0776511i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.93854 | −0.366186 | −0.183093 | − | 0.983096i | \(-0.558611\pi\) | ||||
−0.183093 | + | 0.983096i | \(0.558611\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.1671 | 1.23886 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 11.1048i | − 0.677073i | −0.940953 | − | 0.338537i | \(-0.890068\pi\) | ||||
0.940953 | − | 0.338537i | \(-0.109932\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 23.6992i | − 1.43962i | −0.694170 | − | 0.719811i | \(-0.744228\pi\) | ||||
0.694170 | − | 0.719811i | \(-0.255772\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.77012 | −0.408254 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.7917 | −1.42951 | −0.714753 | − | 0.699377i | \(-0.753461\pi\) | ||||
−0.714753 | + | 0.699377i | \(0.753461\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.1589i | 1.32189i | 0.750434 | + | 0.660945i | \(0.229844\pi\) | ||||
−0.750434 | + | 0.660945i | \(0.770156\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 6.58388i | − 0.391371i | −0.980667 | − | 0.195686i | \(-0.937307\pi\) | ||||
0.980667 | − | 0.195686i | \(-0.0626932\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.52679 | −0.208180 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −37.2502 | −2.19119 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.1727i | 1.35376i | 0.736091 | + | 0.676882i | \(0.236669\pi\) | ||||
−0.736091 | + | 0.676882i | \(0.763331\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 13.7764i | − 0.802091i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.01543 | −0.521376 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.28762 | 0.304774 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 8.72494i | − 0.499589i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 12.7944i | − 0.730216i | −0.930965 | − | 0.365108i | \(-0.881032\pi\) | ||||
0.930965 | − | 0.365108i | \(-0.118968\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.6695 | −1.68240 | −0.841202 | − | 0.540720i | \(-0.818152\pi\) | ||||
−0.841202 | + | 0.540720i | \(0.818152\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.54381 | 0.256831 | 0.128416 | − | 0.991720i | \(-0.459011\pi\) | ||||
0.128416 | + | 0.991720i | \(0.459011\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 9.93868i | − 0.558212i | −0.960260 | − | 0.279106i | \(-0.909962\pi\) | ||||
0.960260 | − | 0.279106i | \(-0.0900381\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 18.7217i | − 1.04821i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.1298 | 0.730561 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.16902 | 0.342196 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 5.77479i | − 0.318375i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.7766i | 1.08702i | 0.839403 | + | 0.543509i | \(0.182905\pi\) | ||||
−0.839403 | + | 0.543509i | \(0.817095\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −21.3656 | −1.16733 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.5056 | −1.66175 | −0.830873 | − | 0.556462i | \(-0.812158\pi\) | ||||
−0.830873 | + | 0.556462i | \(0.812158\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.56182i | 0.301189i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.0080 | 1.50355 | 0.751773 | − | 0.659422i | \(-0.229199\pi\) | ||||
0.751773 | + | 0.659422i | \(0.229199\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.47317 | −0.346501 | −0.173251 | − | 0.984878i | \(-0.555427\pi\) | ||||
−0.173251 | + | 0.984878i | \(0.555427\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 33.5190i | − 1.78404i | −0.452000 | − | 0.892018i | \(-0.649289\pi\) | ||||
0.452000 | − | 0.892018i | \(-0.350711\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.0853i | 1.17217i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −33.2112 | −1.75282 | −0.876410 | − | 0.481565i | \(-0.840069\pi\) | ||||
−0.876410 | + | 0.481565i | \(0.840069\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.8223 | 0.832752 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 29.7450i | 1.55692i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 15.5534i | − 0.811883i | −0.913899 | − | 0.405941i | \(-0.866944\pi\) | ||||
0.913899 | − | 0.405941i | \(-0.133056\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.29178 | −0.378570 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.84450 | −0.406173 | −0.203086 | − | 0.979161i | \(-0.565097\pi\) | ||||
−0.203086 | + | 0.979161i | \(0.565097\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17.0594i | 0.878605i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.6551i | 1.78011i | 0.455851 | + | 0.890056i | \(0.349335\pi\) | ||||
−0.455851 | + | 0.890056i | \(0.650665\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.57082 | 0.335753 | 0.167877 | − | 0.985808i | \(-0.446309\pi\) | ||||
0.167877 | + | 0.985808i | \(0.446309\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.06766 | 0.360201 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.56366i | 0.383493i | 0.981444 | + | 0.191746i | \(0.0614151\pi\) | ||||
−0.981444 | + | 0.191746i | \(0.938585\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 28.5169i | − 1.44216i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.83178 | −0.293429 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.26100 | 0.464796 | 0.232398 | − | 0.972621i | \(-0.425343\pi\) | ||||
0.232398 | + | 0.972621i | \(0.425343\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.158397i | 0.00790995i | 0.999992 | + | 0.00395497i | \(0.00125891\pi\) | ||||
−0.999992 | + | 0.00395497i | \(0.998741\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 5.06800i | − 0.252455i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.19347 | −0.158294 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.79241 | −0.335863 | −0.167932 | − | 0.985799i | \(-0.553709\pi\) | ||||
−0.167932 | + | 0.985799i | \(0.553709\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.98108i | 0.245103i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 33.5922i | − 1.64898i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 35.2185 | 1.72054 | 0.860269 | − | 0.509841i | \(-0.170296\pi\) | ||||
0.860269 | + | 0.509841i | \(0.170296\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.1907 | −1.37393 | −0.686966 | − | 0.726689i | \(-0.741058\pi\) | ||||
−0.686966 | + | 0.726689i | \(0.741058\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 19.5134i | 0.946538i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.15465i | 0.152664i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.5840 | −0.895160 | −0.447580 | − | 0.894244i | \(-0.647714\pi\) | ||||
−0.447580 | + | 0.894244i | \(0.647714\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.1063 | −0.485680 | −0.242840 | − | 0.970066i | \(-0.578079\pi\) | ||||
−0.242840 | + | 0.970066i | \(0.578079\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.90174i | 0.330155i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 33.9732i | − 1.62145i | −0.585426 | − | 0.810726i | \(-0.699073\pi\) | ||||
0.585426 | − | 0.810726i | \(-0.300927\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.6709 | 0.887082 | 0.443541 | − | 0.896254i | \(-0.353722\pi\) | ||||
0.443541 | + | 0.896254i | \(0.353722\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −26.8570 | −1.27314 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.2721i | 0.862316i | 0.902276 | + | 0.431158i | \(0.141895\pi\) | ||||
−0.902276 | + | 0.431158i | \(0.858105\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.01249i | 0.424381i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.44014 | −0.301918 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.1665 | 1.08369 | 0.541843 | − | 0.840480i | \(-0.317727\pi\) | ||||
0.541843 | + | 0.840480i | \(0.317727\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 27.0478i | − 1.25974i | −0.776700 | − | 0.629870i | \(-0.783108\pi\) | ||||
0.776700 | − | 0.629870i | \(-0.216892\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.2067i | 1.31088i | 0.755249 | + | 0.655438i | \(0.227516\pi\) | ||||
−0.755249 | + | 0.655438i | \(0.772484\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.3299 | 0.987029 | 0.493514 | − | 0.869738i | \(-0.335712\pi\) | ||||
0.493514 | + | 0.869738i | \(0.335712\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.72509 | 0.356711 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 13.5122i | − 0.621291i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 4.72268i | − 0.216692i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.5415 | −1.02995 | −0.514973 | − | 0.857207i | \(-0.672198\pi\) | ||||
−0.514973 | + | 0.857207i | \(0.672198\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.90993 | 0.132681 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 43.1602i | − 1.95980i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.51090i | 0.204408i | 0.994763 | + | 0.102204i | \(0.0325895\pi\) | ||||
−0.994763 | + | 0.102204i | \(0.967410\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.4636 | 1.37480 | 0.687401 | − | 0.726278i | \(-0.258752\pi\) | ||||
0.687401 | + | 0.726278i | \(0.258752\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −53.9611 | −2.43028 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 7.98532i | − 0.358191i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 11.7384i | − 0.525482i | −0.964866 | − | 0.262741i | \(-0.915373\pi\) | ||||
0.964866 | − | 0.262741i | \(-0.0846265\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.7589 | 0.836419 | 0.418210 | − | 0.908351i | \(-0.362658\pi\) | ||||
0.418210 | + | 0.908351i | \(0.362658\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.3385 | −1.03855 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.97172i | 0.309016i | 0.987992 | + | 0.154508i | \(0.0493792\pi\) | ||||
−0.987992 | + | 0.154508i | \(0.950621\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 10.7548i | − 0.475764i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.24465 | −0.187041 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.7571 | −0.649017 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 40.2146i | − 1.76183i | −0.473270 | − | 0.880917i | \(-0.656926\pi\) | ||||
0.473270 | − | 0.880917i | \(-0.343074\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 29.6607i | − 1.29697i | −0.761226 | − | 0.648486i | \(-0.775402\pi\) | ||||
0.761226 | − | 0.648486i | \(-0.224598\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.0307 | 0.698309 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.00993 | −0.348258 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 8.21229i | − 0.355714i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.0123i | 0.649037i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.55543 | −0.110070 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.6687 | 1.74849 | 0.874243 | − | 0.485489i | \(-0.161359\pi\) | ||||
0.874243 | + | 0.485489i | \(0.161359\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.6656i | 0.885215i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.0822i | 0.773137i | 0.922261 | + | 0.386569i | \(0.126340\pi\) | ||||
−0.922261 | + | 0.386569i | \(0.873660\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.0598 | 0.556366 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.10858 | 0.0896660 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 21.7467i | − 0.921436i | −0.887547 | − | 0.460718i | \(-0.847592\pi\) | ||||
0.887547 | − | 0.460718i | \(-0.152408\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.3125i | 0.520762i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.1061 | 0.805228 | 0.402614 | − | 0.915370i | \(-0.368102\pi\) | ||||
0.402614 | + | 0.915370i | \(0.368102\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.32311 | 0.308086 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 1.98917i | − 0.0833903i | −0.999130 | − | 0.0416952i | \(-0.986724\pi\) | ||||
0.999130 | − | 0.0416952i | \(-0.0132758\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.5278i | 1.06831i | 0.845388 | + | 0.534153i | \(0.179369\pi\) | ||||
−0.845388 | + | 0.534153i | \(0.820631\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.2573 | −0.427759 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.8837 | 0.702879 | 0.351439 | − | 0.936211i | \(-0.385692\pi\) | ||||
0.351439 | + | 0.936211i | \(0.385692\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.1458i | 0.503894i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.6337i | 0.771727i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 41.7731 | 1.72416 | 0.862080 | − | 0.506773i | \(-0.169162\pi\) | ||||
0.862080 | + | 0.506773i | \(0.169162\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.87980 | −0.159864 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 29.6707i | − 1.21843i | −0.793006 | − | 0.609214i | \(-0.791485\pi\) | ||||
0.793006 | − | 0.609214i | \(-0.208515\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 20.3710i | − 0.835128i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.1882 | 1.27432 | 0.637158 | − | 0.770733i | \(-0.280110\pi\) | ||||
0.637158 | + | 0.770733i | \(0.280110\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.4671 | 1.40594 | 0.702972 | − | 0.711218i | \(-0.251856\pi\) | ||||
0.702972 | + | 0.711218i | \(0.251856\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.3622i | 0.502593i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.7335i | 0.476249i | 0.971235 | + | 0.238124i | \(0.0765326\pi\) | ||||
−0.971235 | + | 0.238124i | \(0.923467\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.4469 | 0.544002 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.772139 | 0.0311864 | 0.0155932 | − | 0.999878i | \(-0.495036\pi\) | ||||
0.0155932 | + | 0.999878i | \(0.495036\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.9376i | 0.641625i | 0.947143 | + | 0.320812i | \(0.103956\pi\) | ||||
−0.947143 | + | 0.320812i | \(0.896044\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 8.41774i | − 0.338337i | −0.985587 | − | 0.169169i | \(-0.945892\pi\) | ||||
0.985587 | − | 0.169169i | \(-0.0541083\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.71061 | 0.389047 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2277 | −1.24911 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.20446i | 0.367006i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 35.0824i | − 1.39661i | −0.715800 | − | 0.698305i | \(-0.753938\pi\) | ||||
0.715800 | − | 0.698305i | \(-0.246062\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 53.1240 | 2.10816 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.32854 | 0.0922603 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 7.02263i | − 0.277377i | −0.990336 | − | 0.138689i | \(-0.955711\pi\) | ||||
0.990336 | − | 0.138689i | \(-0.0442887\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.4292i | 0.766214i | 0.923704 | + | 0.383107i | \(0.125146\pi\) | ||||
−0.923704 | + | 0.383107i | \(0.874854\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.3921 | −0.447869 | −0.223935 | − | 0.974604i | \(-0.571890\pi\) | ||||
−0.223935 | + | 0.974604i | \(0.571890\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.7288 | 0.499650 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 37.4801i | − 1.46671i | −0.679845 | − | 0.733356i | \(-0.737953\pi\) | ||||
0.679845 | − | 0.733356i | \(-0.262047\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 0.504503i | − 0.0197126i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31.6058 | 1.23119 | 0.615594 | − | 0.788063i | \(-0.288916\pi\) | ||||
0.615594 | + | 0.788063i | \(0.288916\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.7889 | −1.50871 | −0.754356 | − | 0.656466i | \(-0.772051\pi\) | ||||
−0.754356 | + | 0.656466i | \(0.772051\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.93024i | 0.191186i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 28.3649i | − 1.09829i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.06151 | 0.311211 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.7203 | −0.490331 | −0.245166 | − | 0.969481i | \(-0.578842\pi\) | ||||
−0.245166 | + | 0.969481i | \(0.578842\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.8409i | 0.839414i | 0.907660 | + | 0.419707i | \(0.137867\pi\) | ||||
−0.907660 | + | 0.419707i | \(0.862133\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.6053i | 0.598876i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −28.5781 | −1.09351 | −0.546755 | − | 0.837293i | \(-0.684137\pi\) | ||||
−0.546755 | + | 0.837293i | \(0.684137\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.3556 | 0.586706 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 16.9792i | − 0.646857i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.4404i | 0.473254i | 0.971601 | + | 0.236627i | \(0.0760420\pi\) | ||||
−0.971601 | + | 0.236627i | \(0.923958\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −51.9817 | −1.97178 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.9765 | 0.983930 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 30.1067i | − 1.13711i | −0.822644 | − | 0.568557i | \(-0.807502\pi\) | ||||
0.822644 | − | 0.568557i | \(-0.192498\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 2.22769i | − 0.0840189i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.43842 | 0.317359 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 50.3032 | 1.88918 | 0.944589 | − | 0.328256i | \(-0.106461\pi\) | ||||
0.944589 | + | 0.328256i | \(0.106461\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.42663i | 0.315580i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.4574i | 0.615470i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.3376 | −0.646583 | −0.323291 | − | 0.946299i | \(-0.604789\pi\) | ||||
−0.323291 | + | 0.946299i | \(0.604789\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.53472 | 0.0571561 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 19.4094i | 0.720846i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.4708i | 1.57515i | 0.616217 | + | 0.787576i | \(0.288664\pi\) | ||||
−0.616217 | + | 0.787576i | \(0.711336\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −38.9459 | −1.44046 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.4759 | 0.756294 | 0.378147 | − | 0.925746i | \(-0.376561\pi\) | ||||
0.378147 | + | 0.925746i | \(0.376561\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 19.7410i | − 0.727168i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 5.95637i | − 0.219109i | −0.993981 | − | 0.109554i | \(-0.965058\pi\) | ||||
0.993981 | − | 0.109554i | \(-0.0349424\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.66621 | −0.0611274 | −0.0305637 | − | 0.999533i | \(-0.509730\pi\) | ||||
−0.0305637 | + | 0.999533i | \(0.509730\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.1818 | 0.995863 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 5.42794i | − 0.198333i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 49.1354i | − 1.79298i | −0.443068 | − | 0.896488i | \(-0.646110\pi\) | ||||
0.443068 | − | 0.896488i | \(-0.353890\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24.7834 | −0.901961 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.9665 | 1.34357 | 0.671785 | − | 0.740747i | \(-0.265528\pi\) | ||||
0.671785 | + | 0.740747i | \(0.265528\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.5213i | 1.32390i | 0.749550 | + | 0.661948i | \(0.230270\pi\) | ||||
−0.749550 | + | 0.661948i | \(0.769730\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 7.47199i | − 0.270504i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.5987 | −0.418804 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.9601 | 1.00827 | 0.504133 | − | 0.863626i | \(-0.331812\pi\) | ||||
0.504133 | + | 0.863626i | \(0.331812\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 13.1835i | − 0.474178i | −0.971488 | − | 0.237089i | \(-0.923807\pi\) | ||||
0.971488 | − | 0.237089i | \(-0.0761933\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 5.76612i | − 0.207125i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.28690 | −0.225252 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.4060 | −0.730183 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 39.9135i | − 1.42457i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.1472i | 1.28851i | 0.764812 | + | 0.644254i | \(0.222832\pi\) | ||||
−0.764812 | + | 0.644254i | \(0.777168\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.64780 | −0.0941448 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.34575 | −0.260855 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.63891i | 0.0580531i | 0.999579 | + | 0.0290266i | \(0.00924074\pi\) | ||||
−0.999579 | + | 0.0290266i | \(0.990759\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 42.5341i | 1.50475i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −27.4832 | −0.969861 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.7081 | 0.377411 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.2010i | 1.13213i | 0.824362 | + | 0.566063i | \(0.191534\pi\) | ||||
−0.824362 | + | 0.566063i | \(0.808466\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 18.6552i | − 0.655072i | −0.944839 | − | 0.327536i | \(-0.893782\pi\) | ||||
0.944839 | − | 0.327536i | \(-0.106218\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −40.0776 | −1.40386 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.42579 | 0.329767 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 6.85032i | − 0.239078i | −0.992830 | − | 0.119539i | \(-0.961858\pi\) | ||||
0.992830 | − | 0.119539i | \(-0.0381416\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.8948i | 0.728348i | 0.931331 | + | 0.364174i | \(0.118649\pi\) | ||||
−0.931331 | + | 0.364174i | \(0.881351\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −39.4714 | −1.37255 | −0.686277 | − | 0.727341i | \(-0.740756\pi\) | ||||
−0.686277 | + | 0.727341i | \(0.740756\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.23657 | 0.251336 | 0.125668 | − | 0.992072i | \(-0.459893\pi\) | ||||
0.125668 | + | 0.992072i | \(0.459893\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.36547i | 0.255199i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.8098i | 0.754760i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.32006 | 0.218193 | 0.109096 | − | 0.994031i | \(-0.465204\pi\) | ||||
0.109096 | + | 0.994031i | \(0.465204\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.6734 | −0.850808 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 20.9584i | 0.720992i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 4.46975i | − 0.153583i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.83837 | −0.165857 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.4940 | −0.975615 | −0.487807 | − | 0.872951i | \(-0.662203\pi\) | ||||
−0.487807 | + | 0.872951i | \(0.662203\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.4708i | 0.870067i | 0.900414 | + | 0.435034i | \(0.143264\pi\) | ||||
−0.900414 | + | 0.435034i | \(0.856736\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 48.0030i | − 1.63784i | −0.573907 | − | 0.818921i | \(-0.694573\pi\) | ||||
0.573907 | − | 0.818921i | \(-0.305427\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.5532 | 1.17621 | 0.588103 | − | 0.808786i | \(-0.299875\pi\) | ||||
0.588103 | + | 0.808786i | \(0.299875\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −43.9205 | −1.49334 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 5.38834i | − 0.182787i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.9882i | 0.609507i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.50141 | 0.219788 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.46779 | −0.150867 | −0.0754333 | − | 0.997151i | \(-0.524034\pi\) | ||||
−0.0754333 | + | 0.997151i | \(0.524034\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 47.9230i | − 1.61457i | −0.590164 | − | 0.807283i | \(-0.700937\pi\) | ||||
0.590164 | − | 0.807283i | \(-0.299063\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.50033i | 0.252406i | 0.992004 | + | 0.126203i | \(0.0402791\pi\) | ||||
−0.992004 | + | 0.126203i | \(0.959721\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.8246 | −0.397030 | −0.198515 | − | 0.980098i | \(-0.563612\pi\) | ||||
−0.198515 | + | 0.980098i | \(0.563612\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.2079 | −0.644213 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 10.2942i | − 0.344483i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 50.4755i | − 1.68721i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.9453 | 0.531804 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 53.7074 | 1.78925 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 66.8527i | 2.22226i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34.2557i | 1.13744i | 0.822531 | + | 0.568721i | \(0.192562\pi\) | ||||
−0.822531 | + | 0.568721i | \(0.807438\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.8731 | 0.459638 | 0.229819 | − | 0.973233i | \(-0.426187\pi\) | ||||
0.229819 | + | 0.973233i | \(0.426187\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31.0379 | 1.02720 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.182412i | 0.00602376i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.0500i | 0.628402i | 0.949356 | + | 0.314201i | \(0.101737\pi\) | ||||
−0.949356 | + | 0.314201i | \(0.898263\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.5942 | 0.612035 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.31077 | 0.108857 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 6.93319i | − 0.227470i | −0.993511 | − | 0.113735i | \(-0.963718\pi\) | ||||
0.993511 | − | 0.113735i | \(-0.0362816\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1.78261i | − 0.0584228i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −52.0567 | −1.70244 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.7279 | 0.546475 | 0.273238 | − | 0.961947i | \(-0.411905\pi\) | ||||
0.273238 | + | 0.961947i | \(0.411905\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.5223i | 0.440814i | 0.975408 | + | 0.220407i | \(0.0707386\pi\) | ||||
−0.975408 | + | 0.220407i | \(0.929261\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.6547i | 0.444658i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.4695 | 0.502692 | 0.251346 | − | 0.967897i | \(-0.419127\pi\) | ||||
0.251346 | + | 0.967897i | \(0.419127\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.0430 | 0.812931 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 16.4797i | − 0.533831i | −0.963720 | − | 0.266915i | \(-0.913996\pi\) | ||||
0.963720 | − | 0.266915i | \(-0.0860044\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 51.6765i | 1.67221i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.55207 | −0.179286 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.2630 | 0.847193 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 19.0673i | − 0.613798i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.1895i | 1.38888i | 0.719550 | + | 0.694441i | \(0.244348\pi\) | ||||
−0.719550 | + | 0.694441i | \(0.755652\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.5954 | 0.693029 | 0.346515 | − | 0.938045i | \(-0.387365\pi\) | ||||
0.346515 | + | 0.938045i | \(0.387365\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.7949 | 0.602536 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.08900i | 0.290783i | 0.989374 | + | 0.145391i | \(0.0464442\pi\) | ||||
−0.989374 | + | 0.145391i | \(0.953556\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 24.8148i | − 0.793085i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.7430 | 0.725388 | 0.362694 | − | 0.931908i | \(-0.381857\pi\) | ||||
0.362694 | + | 0.931908i | \(0.381857\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.1918 | 0.802678 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 20.4721i | − 0.650975i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.96925i | 0.189619i | 0.995495 | + | 0.0948097i | \(0.0302243\pi\) | ||||
−0.995495 | + | 0.0948097i | \(0.969776\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26.3848 | 0.836454 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42.1258 | −1.33414 | −0.667069 | − | 0.744996i | \(-0.732451\pi\) | ||||
−0.667069 | + | 0.744996i | \(0.732451\pi\) | |||||||
\(998\) | 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.h.i.2591.7 | ✓ | 24 | |
3.2 | odd | 2 | inner | 6048.2.h.i.2591.18 | yes | 24 | |
4.3 | odd | 2 | inner | 6048.2.h.i.2591.17 | yes | 24 | |
12.11 | even | 2 | inner | 6048.2.h.i.2591.8 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.h.i.2591.7 | ✓ | 24 | 1.1 | even | 1 | trivial | |
6048.2.h.i.2591.8 | yes | 24 | 12.11 | even | 2 | inner | |
6048.2.h.i.2591.17 | yes | 24 | 4.3 | odd | 2 | inner | |
6048.2.h.i.2591.18 | yes | 24 | 3.2 | odd | 2 | inner |