Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(2239,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("2240.2239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | no (minimal twist has level 1120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2239.7 | ||
Character | \(\chi\) | \(=\) | 2240.2239 |
Dual form | 2240.2.e.g.2239.8 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 3.06386i | − | 1.76892i | −0.466617 | − | 0.884460i | \(-0.654527\pi\) | ||
0.466617 | − | 0.884460i | \(-0.345473\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.39003 | − | 1.75152i | −0.621641 | − | 0.783303i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.46063 | − | 0.972270i | −0.930030 | − | 0.367483i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.38723 | −2.12908 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.46601i | 1.64806i | 0.566544 | + | 0.824032i | \(0.308280\pi\) | ||||
−0.566544 | + | 0.824032i | \(0.691720\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.22883 | −0.340816 | −0.170408 | − | 0.985374i | \(-0.554509\pi\) | ||||
−0.170408 | + | 0.985374i | \(0.554509\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.36640 | + | 4.25886i | −1.38560 | + | 1.09963i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.813283 | −0.197250 | −0.0986250 | − | 0.995125i | \(-0.531444\pi\) | ||||
−0.0986250 | + | 0.995125i | \(0.531444\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.68583 | 1.53383 | 0.766917 | − | 0.641746i | \(-0.221790\pi\) | ||||
0.766917 | + | 0.641746i | \(0.221790\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.97890 | + | 7.53902i | −0.650048 | + | 1.64515i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.51731 | −0.733410 | −0.366705 | − | 0.930337i | \(-0.619514\pi\) | ||||
−0.366705 | + | 0.930337i | \(0.619514\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.13563 | + | 4.86933i | −0.227126 | + | 0.973865i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10.3780i | 1.99724i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.09020 | 1.50231 | 0.751156 | − | 0.660125i | \(-0.229497\pi\) | ||||
0.751156 | + | 0.660125i | \(0.229497\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.00726 | −1.61775 | −0.808876 | − | 0.587980i | \(-0.799923\pi\) | ||||
−0.808876 | + | 0.587980i | \(0.799923\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 16.7471 | 2.91529 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.71740 | + | 5.66132i | 0.290294 | + | 0.956938i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.61599i | − | 0.758864i | −0.925220 | − | 0.379432i | \(-0.876119\pi\) | ||
0.925220 | − | 0.379432i | \(-0.123881\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.76496i | 0.602875i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.59512i | − | 0.405290i | −0.979252 | − | 0.202645i | \(-0.935046\pi\) | ||
0.979252 | − | 0.202645i | \(-0.0649538\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.61833 | 0.246793 | 0.123397 | − | 0.992357i | \(-0.460621\pi\) | ||||
0.123397 | + | 0.992357i | \(0.460621\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.87844 | + | 11.1873i | 1.32352 | + | 1.66771i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.97579i | 0.871658i | 0.900029 | + | 0.435829i | \(0.143545\pi\) | ||||
−0.900029 | + | 0.435829i | \(0.856455\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.10938 | + | 4.78479i | 0.729912 | + | 0.683541i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.49178i | 0.348919i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.51536i | 0.208151i | 0.994569 | + | 0.104076i | \(0.0331884\pi\) | ||||
−0.994569 | + | 0.104076i | \(0.966812\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.57381 | − | 7.59792i | 1.29093 | − | 1.02450i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 20.4844i | − | 2.71323i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.1846 | −1.32593 | −0.662963 | − | 0.748652i | \(-0.730701\pi\) | ||||
−0.662963 | + | 0.748652i | \(0.730701\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 3.16168i | − | 0.404811i | −0.979302 | − | 0.202406i | \(-0.935124\pi\) | ||
0.979302 | − | 0.202406i | \(-0.0648760\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 15.7166 | + | 6.21011i | 1.98010 | + | 0.782400i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.70811 | + | 2.15231i | 0.211865 | + | 0.266962i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.1445 | −1.60586 | −0.802931 | − | 0.596072i | \(-0.796727\pi\) | ||||
−0.802931 | + | 0.596072i | \(0.796727\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.7765i | 1.29734i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.4755i | 1.48057i | 0.672293 | + | 0.740285i | \(0.265310\pi\) | ||||
−0.672293 | + | 0.740285i | \(0.734690\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.65228 | 0.895631 | 0.447816 | − | 0.894126i | \(-0.352202\pi\) | ||||
0.447816 | + | 0.894126i | \(0.352202\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 14.9189 | + | 3.47940i | 1.72269 | + | 0.401767i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.31443 | − | 13.4498i | 0.605636 | − | 1.53275i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.19667i | 0.247145i | 0.992336 | + | 0.123572i | \(0.0394351\pi\) | ||||
−0.992336 | + | 0.123572i | \(0.960565\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 12.6350 | 1.40389 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 7.88172i | − | 0.865131i | −0.901603 | − | 0.432565i | \(-0.857608\pi\) | ||
0.901603 | − | 0.432565i | \(-0.142392\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.13049 | + | 1.42448i | 0.122619 | + | 0.154506i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 24.7872i | − | 2.65747i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.19849i | 0.127040i | 0.997981 | + | 0.0635198i | \(0.0202326\pi\) | ||||
−0.997981 | + | 0.0635198i | \(0.979767\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.02369 | + | 1.19475i | 0.316969 | + | 0.125244i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 27.5970i | 2.86167i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.29351 | − | 11.7103i | −0.953494 | − | 1.20146i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.813283 | −0.0825764 | −0.0412882 | − | 0.999147i | \(-0.513146\pi\) | ||||
−0.0412882 | + | 0.999147i | \(0.513146\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 34.9126i | − | 3.50885i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.76504i | 0.175628i | 0.996137 | + | 0.0878142i | \(0.0279882\pi\) | ||||
−0.996137 | + | 0.0878142i | \(0.972012\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.0600i | 0.991242i | 0.868539 | + | 0.495621i | \(0.165060\pi\) | ||||
−0.868539 | + | 0.495621i | \(0.834940\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 17.3455 | − | 5.26188i | 1.69275 | − | 0.513507i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.1445 | 1.27073 | 0.635366 | − | 0.772211i | \(-0.280849\pi\) | ||||
0.635366 | + | 0.772211i | \(0.280849\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.128572 | −0.0123149 | −0.00615747 | − | 0.999981i | \(-0.501960\pi\) | ||||
−0.00615747 | + | 0.999981i | \(0.501960\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.1427 | −1.34237 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.04955i | 0.192806i | 0.995342 | + | 0.0964028i | \(0.0307337\pi\) | ||||
−0.995342 | + | 0.0964028i | \(0.969266\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.88917 | + | 6.16063i | 0.455917 | + | 0.574482i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.84881 | 0.725622 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.00119 | + | 0.790730i | 0.183448 | + | 0.0724861i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −18.8773 | −1.71611 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.95109 | −0.716926 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.1073 | − | 4.77944i | 0.904022 | − | 0.427486i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.81155 | −0.515691 | −0.257846 | − | 0.966186i | \(-0.583013\pi\) | ||||
−0.257846 | + | 0.966186i | \(0.583013\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 4.95834i | − | 0.436557i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.1544 | −1.41142 | −0.705709 | − | 0.708501i | \(-0.749372\pi\) | ||||
−0.705709 | + | 0.708501i | \(0.749372\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.4513 | − | 6.50043i | −1.42651 | − | 0.563659i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 18.1772 | − | 14.4257i | 1.56445 | − | 1.24157i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 5.90852i | − | 0.504799i | −0.967623 | − | 0.252400i | \(-0.918780\pi\) | ||
0.967623 | − | 0.252400i | \(-0.0812197\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.82751 | 0.324645 | 0.162323 | − | 0.986738i | \(-0.448101\pi\) | ||||
0.162323 | + | 0.986738i | \(0.448101\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 18.3090 | 1.54189 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 6.71679i | − | 0.561686i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.2456 | − | 14.1701i | −0.933898 | − | 1.17676i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14.6599 | − | 15.6544i | 1.20913 | − | 1.29116i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.10275 | 0.581880 | 0.290940 | − | 0.956741i | \(-0.406032\pi\) | ||||
0.290940 | + | 0.956741i | \(0.406032\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 10.7144i | − | 0.871924i | −0.899965 | − | 0.435962i | \(-0.856408\pi\) | ||
0.899965 | − | 0.435962i | \(-0.143592\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.19462 | 0.419960 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.5204 | + | 15.7764i | 1.00566 | + | 1.26719i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.12741 | −0.409212 | −0.204606 | − | 0.978844i | \(-0.565591\pi\) | ||||
−0.204606 | + | 0.978844i | \(0.565591\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.64286 | 0.368202 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.65479 | + | 3.41977i | 0.682093 | + | 0.269516i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.3674 | 1.04701 | 0.523507 | − | 0.852021i | \(-0.324623\pi\) | ||||
0.523507 | + | 0.852021i | \(0.324623\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −23.2790 | − | 29.3328i | −1.81226 | − | 2.28356i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.3403i | 1.57398i | 0.616966 | + | 0.786990i | \(0.288362\pi\) | ||||
−0.616966 | + | 0.786990i | \(0.711638\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4900 | −0.883845 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −42.7039 | −3.26565 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.38042 | 0.561123 | 0.280561 | − | 0.959836i | \(-0.409479\pi\) | ||||
0.280561 | + | 0.959836i | \(0.409479\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.52866 | − | 10.8775i | 0.569113 | − | 0.822259i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 31.2043i | 2.34546i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.6037i | 1.09153i | 0.837937 | + | 0.545767i | \(0.183761\pi\) | ||||
−0.837937 | + | 0.545767i | \(0.816239\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.2568i | 0.836711i | 0.908283 | + | 0.418355i | \(0.137393\pi\) | ||||
−0.908283 | + | 0.418355i | \(0.862607\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.68693 | −0.716079 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.08499 | + | 6.41637i | −0.594420 | + | 0.471741i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4.44541i | − | 0.325081i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.0902 | − | 25.5364i | 0.733954 | − | 1.85750i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.19284i | 0.592813i | 0.955062 | + | 0.296406i | \(0.0957883\pi\) | ||||
−0.955062 | + | 0.296406i | \(0.904212\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.6355i | 1.26943i | 0.772747 | + | 0.634715i | \(0.218882\pi\) | ||||
−0.772747 | + | 0.634715i | \(0.781118\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.59439 | − | 5.23340i | 0.472234 | − | 0.374772i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 6.60429i | − | 0.470536i | −0.971931 | − | 0.235268i | \(-0.924403\pi\) | ||
0.971931 | − | 0.235268i | \(-0.0755968\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.35712 | 0.450644 | 0.225322 | − | 0.974284i | \(-0.427657\pi\) | ||||
0.225322 | + | 0.974284i | \(0.427657\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 40.2730i | 2.84064i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −19.9070 | − | 7.86585i | −1.39720 | − | 0.552075i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.54541 | + | 3.60730i | −0.317465 | + | 0.251945i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 22.4658 | 1.56148 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 36.5448i | 2.52786i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.97949i | 0.687016i | 0.939150 | + | 0.343508i | \(0.111615\pi\) | ||||
−0.939150 | + | 0.343508i | \(0.888385\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 38.2232 | 2.61901 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.24953 | − | 2.83454i | −0.153417 | − | 0.193314i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.1635 | + | 8.75748i | 1.50456 | + | 0.594497i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 23.4455i | − | 1.58430i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.999385 | 0.0672259 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.18795i | 0.481341i | 0.970607 | + | 0.240671i | \(0.0773673\pi\) | ||||
−0.970607 | + | 0.240671i | \(0.922633\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.25352 | − | 31.1015i | 0.483568 | − | 2.07343i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 3.43607i | − | 0.228060i | −0.993477 | − | 0.114030i | \(-0.963624\pi\) | ||
0.993477 | − | 0.114030i | \(-0.0363760\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.87652i | 0.322250i | 0.986934 | + | 0.161125i | \(0.0515122\pi\) | ||||
−0.986934 | + | 0.161125i | \(0.948488\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −41.2083 | − | 16.2827i | −2.71131 | − | 1.07132i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.4530i | 0.684802i | 0.939554 | + | 0.342401i | \(0.111240\pi\) | ||||
−0.939554 | + | 0.342401i | \(0.888760\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.4667 | − | 8.30653i | 0.682772 | − | 0.541858i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.73028 | 0.437179 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 16.9379i | − | 1.09562i | −0.836601 | − | 0.547812i | \(-0.815461\pi\) | ||
0.836601 | − | 0.547812i | \(-0.184539\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 17.7741i | − | 1.14493i | −0.819928 | − | 0.572466i | \(-0.805987\pi\) | ||
0.819928 | − | 0.572466i | \(-0.194013\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 7.57786i | − | 0.486120i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.27844 | − | 15.6002i | 0.0816765 | − | 0.996659i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.21574 | −0.522755 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −24.1485 | −1.53035 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.6509 | 0.987873 | 0.493937 | − | 0.869498i | \(-0.335557\pi\) | ||||
0.493937 | + | 0.869498i | \(0.335557\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 19.2256i | − | 1.20871i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.36440 | − | 3.46366i | 0.273309 | − | 0.216903i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.2065 | 1.32283 | 0.661414 | − | 0.750021i | \(-0.269957\pi\) | ||||
0.661414 | + | 0.750021i | \(0.269957\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.48799 | + | 11.3582i | −0.278870 | + | 0.705766i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −51.6739 | −3.19854 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.0849 | −0.806847 | −0.403423 | − | 0.915013i | \(-0.632180\pi\) | ||||
−0.403423 | + | 0.915013i | \(0.632180\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.65418 | − | 2.10640i | 0.163045 | − | 0.129395i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.67200 | 0.224723 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.357794i | 0.0218151i | 0.999941 | + | 0.0109075i | \(0.00347204\pi\) | ||||
−0.999941 | + | 0.0109075i | \(0.996528\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.151601 | 0.00920910 | 0.00460455 | − | 0.999989i | \(-0.498534\pi\) | ||||
0.00460455 | + | 0.999989i | \(0.498534\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.66055 | − | 9.26416i | 0.221547 | − | 0.560692i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −26.6158 | − | 6.20735i | −1.60499 | − | 0.374318i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.1822i | 1.75339i | 0.481047 | + | 0.876695i | \(0.340257\pi\) | ||||
−0.481047 | + | 0.876695i | \(0.659743\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 57.5314 | 3.44431 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.8389 | 1.42211 | 0.711054 | − | 0.703137i | \(-0.248218\pi\) | ||||
0.711054 | + | 0.703137i | \(0.248218\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.6344i | 0.869922i | 0.900449 | + | 0.434961i | \(0.143238\pi\) | ||||
−0.900449 | + | 0.434961i | \(0.856762\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −35.8788 | + | 28.4740i | −2.12528 | + | 1.68665i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.52316 | + | 6.38564i | −0.148937 | + | 0.376932i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3386 | −0.961092 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.49178i | 0.146071i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.4646 | 0.669771 | 0.334886 | − | 0.942259i | \(-0.391302\pi\) | ||||
0.334886 | + | 0.942259i | \(0.391302\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.1570 | + | 17.8386i | 0.824250 | + | 1.03860i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −56.7261 | −3.29158 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.32217 | 0.249957 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.98211 | − | 1.57345i | −0.229525 | − | 0.0906924i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.40784 | 0.310672 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.53773 | + | 4.39483i | −0.317090 | + | 0.251647i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.8117i | 0.788273i | 0.919052 | + | 0.394136i | \(0.128956\pi\) | ||||
−0.919052 | + | 0.394136i | \(0.871044\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 30.8224 | 1.75343 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.0932 | 1.36620 | 0.683099 | − | 0.730325i | \(-0.260632\pi\) | ||||
0.683099 | + | 0.730325i | \(0.260632\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.6899 | −1.22599 | −0.612994 | − | 0.790088i | \(-0.710035\pi\) | ||||
−0.612994 | + | 0.790088i | \(0.710035\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10.9694 | − | 36.1601i | −0.618058 | − | 2.03739i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.5279i | 0.703638i | 0.936068 | + | 0.351819i | \(0.114437\pi\) | ||||
−0.936068 | + | 0.351819i | \(0.885563\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 44.2211i | 2.47591i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 40.2730i | − | 2.24782i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.43747 | −0.302549 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.39549 | − | 5.98357i | 0.0774080 | − | 0.331909i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.393926i | 0.0217842i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.81008 | − | 14.7042i | 0.320320 | − | 0.810668i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.8936i | 1.58814i | 0.607828 | + | 0.794069i | \(0.292041\pi\) | ||||
−0.607828 | + | 0.794069i | \(0.707959\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 29.4834i | 1.61568i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 18.2713 | + | 23.0229i | 0.998269 | + | 1.25788i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 12.7694i | − | 0.695592i | −0.937570 | − | 0.347796i | \(-0.886930\pi\) | ||
0.937570 | − | 0.347796i | \(-0.113070\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.27954 | 0.341058 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 49.2337i | − | 2.66616i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.92019 | − | 16.7413i | −0.427650 | − | 0.903944i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 18.8753 | − | 14.9797i | 1.01621 | − | 0.806481i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −29.6898 | −1.59383 | −0.796916 | − | 0.604091i | \(-0.793537\pi\) | ||||
−0.796916 | + | 0.604091i | \(0.793537\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 29.5579i | − | 1.58220i | −0.611688 | − | 0.791099i | \(-0.709509\pi\) | ||
0.611688 | − | 0.791099i | \(-0.290491\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 12.7528i | − | 0.680692i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.0795 | −1.12195 | −0.560973 | − | 0.827834i | \(-0.689573\pi\) | ||||
−0.560973 | + | 0.827834i | \(0.689573\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.8511 | − | 17.3413i | 1.15973 | − | 0.920383i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.42268 | − | 6.13135i | 0.128222 | − | 0.324506i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.8898i | 0.785854i | 0.919570 | + | 0.392927i | \(0.128538\pi\) | ||||
−0.919570 | + | 0.392927i | \(0.871462\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 25.7003 | 1.35265 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 57.8372i | 3.03567i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.6369 | − | 13.4031i | −0.556761 | − | 0.701550i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.1814i | 1.31446i | 0.753691 | + | 0.657229i | \(0.228272\pi\) | ||||
−0.753691 | + | 0.657229i | \(0.771728\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.5756i | 0.862894i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.47334 | − | 3.72874i | 0.0764920 | − | 0.193587i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.2586i | 1.20428i | 0.798389 | + | 0.602142i | \(0.205686\pi\) | ||||
−0.798389 | + | 0.602142i | \(0.794314\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −14.6435 | − | 30.9672i | −0.756189 | − | 1.59914i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.94146 | −0.512011 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.86285i | 0.0956884i | 0.998855 | + | 0.0478442i | \(0.0152351\pi\) | ||||
−0.998855 | + | 0.0478442i | \(0.984765\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.8058i | 0.912216i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.15731i | 0.263526i | 0.991281 | + | 0.131763i | \(0.0420638\pi\) | ||||
−0.991281 | + | 0.131763i | \(0.957936\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −30.9448 | + | 9.38734i | −1.57709 | + | 0.478423i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.3367 | −0.525442 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.6749 | −0.541240 | −0.270620 | − | 0.962686i | \(-0.587229\pi\) | ||||
−0.270620 | + | 0.962686i | \(0.587229\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.86057 | 0.144665 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 49.4949i | 2.49669i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.84750 | − | 3.05344i | 0.193589 | − | 0.153635i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.1047 | −1.05922 | −0.529608 | − | 0.848243i | \(-0.677661\pi\) | ||||
−0.529608 | + | 0.848243i | \(0.677661\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −19.9164 | + | 50.4046i | −0.997067 | + | 2.52339i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.97650 | −0.198577 | −0.0992886 | − | 0.995059i | \(-0.531657\pi\) | ||||
−0.0992886 | + | 0.995059i | \(0.531657\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.0684 | 0.551355 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −17.5630 | − | 22.1304i | −0.872714 | − | 1.09967i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.2310 | 1.25066 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 24.1166i | − | 1.19249i | −0.802803 | − | 0.596244i | \(-0.796659\pi\) | ||
0.802803 | − | 0.596244i | \(-0.203341\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.1029 | −0.892949 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 25.0606 | + | 9.90221i | 1.23315 | + | 0.487256i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.8050 | + | 10.9558i | −0.677659 | + | 0.537801i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 11.7270i | − | 0.574271i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.64109 | −0.275585 | −0.137793 | − | 0.990461i | \(-0.544001\pi\) | ||||
−0.137793 | + | 0.990461i | \(0.544001\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.9114 | −0.726738 | −0.363369 | − | 0.931645i | \(-0.618374\pi\) | ||||
−0.363369 | + | 0.931645i | \(0.618374\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 38.1687i | − | 1.85583i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.923587 | − | 3.96014i | 0.0448005 | − | 0.192095i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.07400 | + | 7.77971i | −0.148761 | + | 0.376487i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −20.5793 | −0.993577 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.1329i | 0.825264i | 0.910898 | + | 0.412632i | \(0.135390\pi\) | ||||
−0.910898 | + | 0.412632i | \(0.864610\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.2171 | −0.875460 | −0.437730 | − | 0.899106i | \(-0.644217\pi\) | ||||
−0.437730 | + | 0.899106i | \(0.644217\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −43.4152 | + | 34.4550i | −2.08160 | + | 1.65199i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −23.5161 | −1.12493 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.5281 | −1.40930 | −0.704650 | − | 0.709555i | \(-0.748896\pi\) | ||||
−0.704650 | + | 0.709555i | \(0.748896\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −32.6348 | − | 30.5615i | −1.55404 | − | 1.45531i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.42623 | 0.210296 | 0.105148 | − | 0.994457i | \(-0.466468\pi\) | ||||
0.105148 | + | 0.994457i | \(0.466468\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.09918 | − | 1.66594i | 0.0995104 | − | 0.0789730i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 21.7618i | − | 1.02930i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.2925 | 0.627313 | 0.313657 | − | 0.949536i | \(-0.398446\pi\) | ||||
0.313657 | + | 0.949536i | \(0.398446\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.1850 | 0.667944 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −32.8274 | −1.54236 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.11039 | − | 6.95679i | −0.0989367 | − | 0.326139i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 12.2949i | − | 0.575130i | −0.957761 | − | 0.287565i | \(-0.907154\pi\) | ||
0.957761 | − | 0.287565i | \(-0.0928458\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 8.44023i | − | 0.393956i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.4068i | 1.09016i | 0.838383 | + | 0.545082i | \(0.183501\pi\) | ||||
−0.838383 | + | 0.545082i | \(0.816499\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.7828 | −1.01233 | −0.506165 | − | 0.862437i | \(-0.668937\pi\) | ||||
−0.506165 | + | 0.862437i | \(0.668937\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 48.3366 | − | 38.3606i | 2.24155 | − | 1.77893i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 32.6245i | − | 1.50968i | −0.655909 | − | 0.754840i | \(-0.727715\pi\) | ||
0.655909 | − | 0.754840i | \(-0.272285\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 32.3439 | + | 12.7800i | 1.49350 | + | 0.590128i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.7097i | 0.723863i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.84582i | 0.406731i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.59262 | + | 32.5555i | −0.348373 | + | 1.49375i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 9.67896i | − | 0.443169i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.7215 | 0.489879 | 0.244939 | − | 0.969538i | \(-0.421232\pi\) | ||||
0.244939 | + | 0.969538i | \(0.421232\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.67226i | 0.258633i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.4777 | − | 26.5170i | 0.476752 | − | 1.20657i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.13049 | + | 1.42448i | 0.0513328 | + | 0.0646823i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −35.7679 | −1.62080 | −0.810398 | − | 0.585880i | \(-0.800749\pi\) | ||||
−0.810398 | + | 0.585880i | \(0.800749\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 40.9557i | − | 1.85208i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.9944i | 1.03772i | 0.854859 | + | 0.518860i | \(0.173644\pi\) | ||||
−0.854859 | + | 0.518860i | \(0.826356\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.57962 | −0.296331 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −61.1501 | + | 48.5296i | −2.74849 | + | 2.18125i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.1296 | − | 30.6976i | 0.544085 | − | 1.37697i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 13.0307i | − | 0.583336i | −0.956520 | − | 0.291668i | \(-0.905790\pi\) | ||
0.956520 | − | 0.291668i | \(-0.0942103\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 62.3198 | 2.78424 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 12.3987i | − | 0.552832i | −0.961038 | − | 0.276416i | \(-0.910853\pi\) | ||
0.961038 | − | 0.276416i | \(-0.0891468\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.09150 | − | 2.45346i | 0.137570 | − | 0.109178i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 35.2037i | 1.56345i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 14.8884i | − | 0.659918i | −0.943995 | − | 0.329959i | \(-0.892965\pi\) | ||
0.943995 | − | 0.329959i | \(-0.107035\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.8294 | − | 7.44008i | −0.832964 | − | 0.329130i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 69.3854i | 3.06344i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.6203 | − | 13.9837i | 0.776442 | − | 0.616196i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −32.6637 | −1.43655 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 22.6126i | − | 0.992581i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.6065i | 1.77900i | 0.456932 | + | 0.889502i | \(0.348948\pi\) | ||||
−0.456932 | + | 0.889502i | \(0.651052\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.346454i | 0.0151494i | 0.999971 | + | 0.00757469i | \(0.00241112\pi\) | ||||
−0.999971 | + | 0.00757469i | \(0.997589\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −33.3270 | − | 23.0667i | −1.45451 | − | 1.00672i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.32545 | 0.319101 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.6285 | −0.462110 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 65.0515 | 2.82300 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.18896i | 0.138129i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.2713 | − | 23.0229i | −0.789938 | − | 0.995367i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 44.7437 | 1.93083 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −26.1537 | + | 27.9279i | −1.12652 | + | 1.20294i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.3137 | 0.615396 | 0.307698 | − | 0.951484i | \(-0.400441\pi\) | ||||
0.307698 | + | 0.951484i | \(0.400441\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 34.4892 | 1.48007 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.178719 | + | 0.225196i | 0.00765547 | + | 0.00964633i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.7534 | −1.69973 | −0.849865 | − | 0.527000i | \(-0.823317\pi\) | ||||
−0.849865 | + | 0.527000i | \(0.823317\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 20.1944i | 0.861874i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 54.0897 | 2.30430 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.13575 | − | 5.40519i | 0.0908215 | − | 0.229852i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 19.6588 | + | 24.7713i | 0.834471 | + | 1.05148i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 33.2813i | − | 1.41018i | −0.709120 | − | 0.705088i | \(-0.750908\pi\) | ||
0.709120 | − | 0.705088i | \(-0.249092\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.98865 | −0.0841110 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.6201 | −0.575041 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.3139i | 0.687549i | 0.939052 | + | 0.343774i | \(0.111706\pi\) | ||||
−0.939052 | + | 0.343774i | \(0.888294\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.58983 | − | 2.84894i | 0.151025 | − | 0.119856i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −31.0900 | − | 12.2846i | −1.30566 | − | 0.515905i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.54541 | 0.274398 | 0.137199 | − | 0.990544i | \(-0.456190\pi\) | ||||
0.137199 | + | 0.990544i | \(0.456190\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 39.5547i | − | 1.65531i | −0.561234 | − | 0.827657i | \(-0.689673\pi\) | ||
0.561234 | − | 0.827657i | \(-0.310327\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 25.1017 | 1.04864 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.99435 | − | 17.1269i | 0.166576 | − | 0.714242i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −40.4544 | −1.68414 | −0.842069 | − | 0.539369i | \(-0.818663\pi\) | ||||
−0.842069 | + | 0.539369i | \(0.818663\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 54.0326 | 2.24552 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.66315 | + | 19.3940i | −0.317921 | + | 0.804598i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.28298 | −0.343046 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.9101 | − | 13.7473i | −0.451076 | − | 0.568382i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 29.6642i | − | 1.22437i | −0.790714 | − | 0.612185i | \(-0.790291\pi\) | ||
0.790714 | − | 0.612185i | \(-0.209709\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −60.2210 | −2.48136 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.2346 | −0.832340 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.50273 | −0.267035 | −0.133517 | − | 0.991046i | \(-0.542627\pi\) | ||||
−0.133517 | + | 0.991046i | \(0.542627\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.39673 | − | 4.60425i | −0.0572605 | − | 0.188756i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 19.4773i | − | 0.797153i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.70631i | 0.192295i | 0.995367 | + | 0.0961474i | \(0.0306520\pi\) | ||||
−0.995367 | + | 0.0961474i | \(0.969348\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 21.0706i | − | 0.859490i | −0.902950 | − | 0.429745i | \(-0.858604\pi\) | ||
0.902950 | − | 0.429745i | \(-0.141396\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 83.9572 | 3.41900 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 26.2400 | + | 33.0638i | 1.06681 | + | 1.34424i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 8.45732i | − | 0.343272i | −0.985160 | − | 0.171636i | \(-0.945095\pi\) | ||
0.985160 | − | 0.171636i | \(-0.0549053\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −24.0999 | + | 60.9921i | −0.976575 | + | 2.47153i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 7.34322i | − | 0.297075i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.7547i | 1.60568i | 0.596198 | + | 0.802838i | \(0.296677\pi\) | ||||
−0.596198 | + | 0.802838i | \(0.703323\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.0523 | + | 13.9265i | 0.445670 | + | 0.561570i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.7088i | 0.793446i | 0.917938 | + | 0.396723i | \(0.129853\pi\) | ||||
−0.917938 | + | 0.396723i | \(0.870147\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −40.1553 | −1.61398 | −0.806990 | − | 0.590566i | \(-0.798905\pi\) | ||||
−0.806990 | + | 0.590566i | \(0.798905\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 36.5026i | − | 1.46480i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.16525 | − | 2.94904i | 0.0466849 | − | 0.118151i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.4207 | − | 11.0595i | −0.896828 | − | 0.442380i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 111.968 | 4.47157 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.75410i | 0.149686i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 25.4148i | − | 1.01175i | −0.862608 | − | 0.505873i | \(-0.831170\pi\) | ||
0.862608 | − | 0.505873i | \(-0.168830\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 30.5757 | 1.21528 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.07823 | + | 10.1790i | 0.320575 | + | 0.403942i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.27856 | − | 5.87968i | −0.248765 | − | 0.232962i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 79.6839i | − | 3.15225i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −44.0099 | −1.73829 | −0.869143 | − | 0.494561i | \(-0.835329\pi\) | ||||
−0.869143 | + | 0.494561i | \(0.835329\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 11.9892i | − | 0.472807i | −0.971655 | − | 0.236404i | \(-0.924031\pi\) | ||
0.971655 | − | 0.236404i | \(-0.0759687\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.68462 | + | 6.89224i | −0.341957 | + | 0.271382i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 15.1947i | − | 0.597366i | −0.954352 | − | 0.298683i | \(-0.903453\pi\) | ||
0.954352 | − | 0.298683i | \(-0.0965473\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 55.6693i | − | 2.18521i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 26.8317 | − | 67.9059i | 1.05162 | − | 2.66144i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 23.4965i | − | 0.919490i | −0.888051 | − | 0.459745i | \(-0.847941\pi\) | ||
0.888051 | − | 0.459745i | \(-0.152059\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.4552 | + | 28.2948i | 0.877395 | + | 1.10557i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −48.8768 | −1.90687 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 20.6544i | − | 0.804583i | −0.915512 | − | 0.402292i | \(-0.868214\pi\) | ||
0.915512 | − | 0.402292i | \(-0.131786\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 30.8321i | − | 1.19923i | −0.800289 | − | 0.599614i | \(-0.795321\pi\) | ||
0.800289 | − | 0.599614i | \(-0.204679\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 3.06197i | − | 0.118917i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.4823 | + | 37.8506i | 0.445263 | + | 1.46778i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28.4557 | −1.10181 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 22.0229 | 0.851453 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.2818 | 0.667155 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.7263i | 1.03022i | 0.857123 | + | 0.515111i | \(0.172249\pi\) | ||||
−0.857123 | + | 0.515111i | \(0.827751\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −50.5338 | − | 11.7855i | −1.94505 | − | 0.453625i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.9033 | 1.22614 | 0.613071 | − | 0.790028i | \(-0.289934\pi\) | ||||
0.613071 | + | 0.790028i | \(0.289934\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.00119 | + | 0.790730i | 0.0767985 | + | 0.0303454i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.5276 | −0.403420 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.92815 | −0.341626 | −0.170813 | − | 0.985303i | \(-0.554639\pi\) | ||||
−0.170813 | + | 0.985303i | \(0.554639\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.3489 | + | 8.21303i | −0.395410 | + | 0.313804i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.9410 | 0.570034 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1.86212i | − | 0.0709411i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.7006 | −0.559238 | −0.279619 | − | 0.960111i | \(-0.590208\pi\) | ||||
−0.279619 | + | 0.960111i | \(0.590208\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −33.9445 | + | 85.9070i | −1.28944 | + | 3.26334i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.32036 | − | 6.70395i | −0.201813 | − | 0.254295i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.11057i | 0.0799435i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 32.0267 | 1.21136 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.7065 | −0.668766 | −0.334383 | − | 0.942437i | \(-0.608528\pi\) | ||||
−0.334383 | + | 0.942437i | \(0.608528\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 30.8617i | − | 1.16397i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −25.4500 | − | 32.0685i | −0.958503 | − | 1.20777i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.71610 | − | 4.34311i | 0.0645405 | − | 0.163340i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.7222 | 1.60447 | 0.802234 | − | 0.597010i | \(-0.203645\pi\) | ||||
0.802234 | + | 0.597010i | \(0.203645\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 14.0306i | − | 0.526189i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 31.6813 | 1.18647 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.7646 | + | 9.33654i | −0.439970 | + | 0.349167i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −51.8954 | −1.93807 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.2758 | −0.979923 | −0.489961 | − | 0.871744i | \(-0.662989\pi\) | ||||
−0.489961 | + | 0.871744i | \(0.662989\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.78104 | − | 24.7539i | 0.364265 | − | 0.921885i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −54.4574 | −2.02529 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.18745 | + | 39.3938i | −0.341214 | + | 1.46305i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.4192i | 0.794393i | 0.917734 | + | 0.397196i | \(0.130017\pi\) | ||||
−0.917734 | + | 0.397196i | \(0.869983\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.6875 | 0.543981 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.31616 | −0.0486800 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.3586 | −0.936642 | −0.468321 | − | 0.883558i | \(-0.655141\pi\) | ||||
−0.468321 | + | 0.883558i | \(0.655141\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −47.7967 | − | 3.91696i | −1.76301 | − | 0.144479i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 71.8482i | − | 2.64656i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.43697i | 0.347145i | 0.984821 | + | 0.173572i | \(0.0555310\pi\) | ||||
−0.984821 | + | 0.173572i | \(0.944469\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25.1719i | 0.924711i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 40.7813 | 1.49612 | 0.748061 | − | 0.663630i | \(-0.230985\pi\) | ||||
0.748061 | + | 0.663630i | \(0.230985\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.87305 | − | 12.4406i | −0.361720 | − | 0.455788i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 50.3423i | 1.84193i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −32.3439 | − | 12.7800i | −1.18182 | − | 0.466973i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.1304i | 0.515624i | 0.966195 | + | 0.257812i | \(0.0830016\pi\) | ||||
−0.966195 | + | 0.257812i | \(0.916998\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 47.9520i | − | 1.74747i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.7664 | + | 14.8933i | −0.682980 | + | 0.542024i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.5846i | 0.566432i | 0.959056 | + | 0.283216i | \(0.0914013\pi\) | ||||
−0.959056 | + | 0.283216i | \(0.908599\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −58.9046 | −2.13810 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 10.6693i | − | 0.386763i | −0.981124 | − | 0.193382i | \(-0.938054\pi\) | ||
0.981124 | − | 0.193382i | \(-0.0619455\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.316368 | + | 0.125006i | 0.0114533 | + | 0.00452554i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.22068 | − | 9.09847i | −0.261064 | − | 0.328956i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.5152 | 0.451896 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 10.6332i | − | 0.383441i | −0.981450 | − | 0.191721i | \(-0.938593\pi\) | ||
0.981450 | − | 0.191721i | \(-0.0614068\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 64.9738i | − | 2.33998i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 48.0043 | 1.72659 | 0.863297 | − | 0.504696i | \(-0.168395\pi\) | ||||
0.863297 | + | 0.504696i | \(0.168395\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.2289 | − | 43.8593i | 0.367433 | − | 1.57547i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 34.8000 | + | 13.7506i | 1.24844 | + | 0.493298i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 17.3506i | − | 0.621648i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −68.1912 | −2.44007 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 83.9599i | 3.00048i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.12726 | + | 8.98076i | 0.254383 | + | 0.320537i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 52.3628i | − | 1.86653i | −0.359185 | − | 0.933266i | \(-0.616945\pi\) | ||
0.359185 | − | 0.933266i | \(-0.383055\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 40.0901i | 1.42725i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.99272 | − | 5.04318i | 0.0708528 | − | 0.179315i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.88516i | 0.137966i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.45371 | − | 8.13204i | −0.228890 | − | 0.288414i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −40.2475 | −1.42564 | −0.712820 | − | 0.701347i | \(-0.752582\pi\) | ||||
−0.712820 | + | 0.701347i | \(0.752582\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 4.86000i | − | 0.171935i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 7.65502i | − | 0.270477i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 41.8274i | 1.47606i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.04063 | − | 19.9126i | −0.212904 | − | 0.701827i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.09623 | 0.0385891 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.1962 | −0.569429 | −0.284714 | − | 0.958612i | \(-0.591899\pi\) | ||||
−0.284714 | + | 0.958612i | \(0.591899\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.9985 | 1.33431 | 0.667154 | − | 0.744920i | \(-0.267512\pi\) | ||||
0.667154 | + | 0.744920i | \(0.267512\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 0.464484i | − | 0.0162902i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.5811 | − | 23.4132i | −0.650866 | − | 0.820129i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.8199 | 0.378540 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −19.3130 | − | 7.63115i | −0.674851 | − | 0.266654i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.7149 | 0.897456 | 0.448728 | − | 0.893668i | \(-0.351877\pi\) | ||||
0.448728 | + | 0.893668i | \(0.351877\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 48.5297 | 1.69164 | 0.845819 | − | 0.533469i | \(-0.179112\pi\) | ||||
0.845819 | + | 0.533469i | \(0.179112\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −19.0185 | + | 81.5470i | −0.662137 | + | 2.83910i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.4578 | −0.363654 | −0.181827 | − | 0.983331i | \(-0.558201\pi\) | ||||
−0.181827 | + | 0.983331i | \(0.558201\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 13.7971i | − | 0.479195i | −0.970872 | − | 0.239597i | \(-0.922985\pi\) | ||
0.970872 | − | 0.239597i | \(-0.0770154\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 89.4102 | 3.10161 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.15537 | − | 3.89139i | −0.143975 | − | 0.134829i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 35.6264 | − | 28.2736i | 1.23290 | − | 0.978450i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 93.4772i | − | 3.23104i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40.8691 | −1.41096 | −0.705479 | − | 0.708731i | \(-0.749268\pi\) | ||||
−0.705479 | + | 0.708731i | \(0.749268\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36.4513 | 1.25694 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 73.0389i | − | 2.51559i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15.9714 | + | 20.1249i | 0.549434 | + | 0.692318i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 46.4499 | + | 18.3538i | 1.59604 | + | 0.630643i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 44.8376 | 1.53882 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.2359i | 0.556558i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.9104 | 0.681721 | 0.340860 | − | 0.940114i | \(-0.389282\pi\) | ||||
0.340860 | + | 0.940114i | \(0.389282\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 59.3598 | + | 74.7967i | 2.03006 | + | 2.55799i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −46.2728 | −1.58065 | −0.790324 | − | 0.612689i | \(-0.790088\pi\) | ||||
−0.790324 | + | 0.612689i | \(0.790088\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.6565 | −1.25070 | −0.625352 | − | 0.780343i | \(-0.715045\pi\) | ||||
−0.625352 | + | 0.780343i | \(0.715045\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19.5647 | + | 7.73060i | 0.666763 | + | 0.263458i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.1182 | −0.855032 | −0.427516 | − | 0.904008i | \(-0.640611\pi\) | ||||
−0.427516 | + | 0.904008i | \(0.640611\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.2590 | − | 12.9269i | −0.348817 | − | 0.439529i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 50.0591i | 1.70009i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.0070 | −0.407310 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.1524 | 0.547303 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.19462 | 0.175811 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −29.5171 | + | 1.93344i | −0.997862 | + | 0.0653622i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.7977i | 0.904896i | 0.891791 | + | 0.452448i | \(0.149449\pi\) | ||||
−0.891791 | + | 0.452448i | \(0.850551\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 35.1260i | − | 1.18477i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.7099i | 1.30417i | 0.758146 | + | 0.652084i | \(0.226105\pi\) | ||||
−0.758146 | + | 0.652084i | \(0.773895\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.3515 | −1.12237 | −0.561183 | − | 0.827692i | \(-0.689654\pi\) | ||||
−0.561183 | + | 0.827692i | \(0.689654\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 54.6548 | − | 43.3749i | 1.83720 | − | 1.45803i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.9373i | 1.03877i | 0.854539 | + | 0.519386i | \(0.173839\pi\) | ||||
−0.854539 | + | 0.519386i | \(0.826161\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.3001 | + | 5.65039i | 0.479609 | + | 0.189508i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 69.0629i | 2.31370i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 39.9531i | 1.33698i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.5787 | − | 20.2996i | 0.855001 | − | 0.678541i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 13.2425i | − | 0.442155i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −72.8705 | −2.43037 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.23242i | − | 0.0410578i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.82084 | + | 12.2006i | −0.160428 | + | 0.406012i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19.7165 | − | 15.6473i | 0.655397 | − | 0.520133i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.1073 | 0.634449 | 0.317224 | − | 0.948350i | \(-0.397249\pi\) | ||||
0.317224 | + | 0.948350i | \(0.397249\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 11.2737i | − | 0.373926i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 38.5483i | − | 1.27716i | −0.769554 | − | 0.638582i | \(-0.779521\pi\) | ||
0.769554 | − | 0.638582i | \(-0.220479\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 43.0815 | 1.42579 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.4651 | + | 16.9668i | 0.445144 | + | 0.560906i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 39.7500 | + | 15.7065i | 1.31266 | + | 0.518673i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.5994i | 0.481589i | 0.970576 | + | 0.240795i | \(0.0774080\pi\) | ||||
−0.970576 | + | 0.240795i | \(0.922592\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 42.3170 | 1.39439 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 15.3303i | − | 0.504602i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.4768 | + | 5.24205i | 0.739031 | + | 0.172357i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 64.2556i | − | 2.11043i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.4422i | 0.605068i | 0.953139 | + | 0.302534i | \(0.0978326\pi\) | ||||
−0.953139 | + | 0.302534i | \(0.902167\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.1605 | + | 31.9903i | 1.11956 | + | 1.04844i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 73.8181i | − | 2.41670i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.78622 | + | 6.17926i | −0.254636 | + | 0.202083i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.27094 | 0.106857 | 0.0534285 | − | 0.998572i | \(-0.482985\pi\) | ||||
0.0534285 | + | 0.998572i | \(0.482985\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 66.4549i | 2.16867i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.1015i | 0.753086i | 0.926399 | + | 0.376543i | \(0.122887\pi\) | ||||
−0.926399 | + | 0.376543i | \(0.877113\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.12785i | 0.297244i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −58.7531 | + | 17.8232i | −1.91124 | + | 0.579788i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.1476 | 0.979666 | 0.489833 | − | 0.871816i | \(-0.337058\pi\) | ||||
0.489833 | + | 0.871816i | \(0.337058\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.40334 | −0.305245 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 38.3838 | 1.24468 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.9517i | 0.516725i | 0.966048 | + | 0.258363i | \(0.0831829\pi\) | ||||
−0.966048 | + | 0.258363i | \(0.916817\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.3499 | − | 11.3883i | 0.464352 | − | 0.368517i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 135.487 | 4.37968 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.74468 | + | 14.5387i | −0.185505 | + | 0.469478i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 50.1307 | 1.61712 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −83.9572 | −2.70548 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 30.8888 | − | 24.5139i | 0.994347 | − | 0.789129i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.80814 | −0.122461 | −0.0612307 | − | 0.998124i | \(-0.519503\pi\) | ||||
−0.0612307 | + | 0.998124i | \(0.519503\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.6596i | 0.535185i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.7036 | 1.33833 | 0.669167 | − | 0.743112i | \(-0.266651\pi\) | ||||
0.669167 | + | 0.743112i | \(0.266651\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.41808 | − | 3.72137i | −0.301930 | − | 0.119302i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −18.3328 | − | 4.27559i | −0.587120 | − | 0.136928i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 55.5801i | 1.77816i | 0.457748 | + | 0.889082i | \(0.348656\pi\) | ||||
−0.457748 | + | 0.889082i | \(0.651344\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.55095 | −0.209369 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.821218 | 0.0262195 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 57.6224i | 1.83787i | 0.394409 | + | 0.918935i | \(0.370949\pi\) | ||||
−0.394409 | + | 0.918935i | \(0.629051\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.5675 | + | 9.18016i | −0.368572 | + | 0.292504i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −45.0516 | − | 17.8012i | −1.43401 | − | 0.566620i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.69217 | −0.181001 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 16.7139i | − | 0.530934i | −0.964120 | − | 0.265467i | \(-0.914474\pi\) | ||
0.964120 | − | 0.265467i | \(-0.0855261\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 88.5260 | 2.80929 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.83659 | − | 11.1346i | −0.280139 | − | 0.352991i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.3449 | −1.15106 | −0.575528 | − | 0.817782i | \(-0.695203\pi\) | ||||
−0.575528 | + | 0.817782i | \(0.695203\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 47.9047 | 1.51564 |
(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 | 2240.2.e.g.2239.7 | 48 | ||
4.3 | odd | 2 | inner | 2240.2.e.g.2239.4 | 48 | ||
5.4 | even | 2 | inner | 2240.2.e.g.2239.16 | 48 | ||
7.6 | odd | 2 | inner | 2240.2.e.g.2239.20 | 48 | ||
8.3 | odd | 2 | 1120.2.e.a.1119.19 | yes | 48 | ||
8.5 | even | 2 | 1120.2.e.a.1119.16 | yes | 48 | ||
20.19 | odd | 2 | inner | 2240.2.e.g.2239.19 | 48 | ||
28.27 | even | 2 | inner | 2240.2.e.g.2239.15 | 48 | ||
35.34 | odd | 2 | inner | 2240.2.e.g.2239.3 | 48 | ||
40.19 | odd | 2 | 1120.2.e.a.1119.4 | yes | 48 | ||
40.29 | even | 2 | 1120.2.e.a.1119.7 | yes | 48 | ||
56.13 | odd | 2 | 1120.2.e.a.1119.3 | ✓ | 48 | ||
56.27 | even | 2 | 1120.2.e.a.1119.8 | yes | 48 | ||
140.139 | even | 2 | inner | 2240.2.e.g.2239.8 | 48 | ||
280.69 | odd | 2 | 1120.2.e.a.1119.20 | yes | 48 | ||
280.139 | even | 2 | 1120.2.e.a.1119.15 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1120.2.e.a.1119.3 | ✓ | 48 | 56.13 | odd | 2 | ||
1120.2.e.a.1119.4 | yes | 48 | 40.19 | odd | 2 | ||
1120.2.e.a.1119.7 | yes | 48 | 40.29 | even | 2 | ||
1120.2.e.a.1119.8 | yes | 48 | 56.27 | even | 2 | ||
1120.2.e.a.1119.15 | yes | 48 | 280.139 | even | 2 | ||
1120.2.e.a.1119.16 | yes | 48 | 8.5 | even | 2 | ||
1120.2.e.a.1119.19 | yes | 48 | 8.3 | odd | 2 | ||
1120.2.e.a.1119.20 | yes | 48 | 280.69 | odd | 2 | ||
2240.2.e.g.2239.3 | 48 | 35.34 | odd | 2 | inner | ||
2240.2.e.g.2239.4 | 48 | 4.3 | odd | 2 | inner | ||
2240.2.e.g.2239.7 | 48 | 1.1 | even | 1 | trivial | ||
2240.2.e.g.2239.8 | 48 | 140.139 | even | 2 | inner | ||
2240.2.e.g.2239.15 | 48 | 28.27 | even | 2 | inner | ||
2240.2.e.g.2239.16 | 48 | 5.4 | even | 2 | inner | ||
2240.2.e.g.2239.19 | 48 | 20.19 | odd | 2 | inner | ||
2240.2.e.g.2239.20 | 48 | 7.6 | odd | 2 | inner |