Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4140,2,Mod(1241,4140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4140, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4140.1241");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4140.i (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: | \(33.0580664368\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 62x^{14} + 1303x^{12} + 12842x^{10} + 65359x^{8} + 170834x^{6} + 207293x^{4} + 91366x^{2} + 9604 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1241.15 | ||
Root | \(1.41255i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4140.1241 |
Dual form | 4140.2.i.a.1241.2 |
$q$-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 \(\left(\mathbb{Z}/4140\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(2071\) | \(3961\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.35549i | 1.64622i | 0.567881 | + | 0.823111i | \(0.307763\pi\) | ||||
−0.567881 | + | 0.823111i | \(0.692237\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.0533304 | −0.0160797 | −0.00803986 | − | 0.999968i | \(-0.502559\pi\) | ||||
−0.00803986 | + | 0.999968i | \(0.502559\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.90540 | −1.36051 | −0.680257 | − | 0.732974i | \(-0.738132\pi\) | ||||
−0.680257 | + | 0.732974i | \(0.738132\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.18157 | −0.286572 | −0.143286 | − | 0.989681i | \(-0.545767\pi\) | ||||
−0.143286 | + | 0.989681i | \(0.545767\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.30903i | − | 1.21797i | −0.793180 | − | 0.608987i | \(-0.791576\pi\) | ||
0.793180 | − | 0.608987i | \(-0.208424\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.90776 | − | 4.40005i | 0.397795 | − | 0.917474i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.23248i | 0.600256i | 0.953899 | + | 0.300128i | \(0.0970293\pi\) | ||||
−0.953899 | + | 0.300128i | \(0.902971\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.80149 | −1.22158 | −0.610792 | − | 0.791791i | \(-0.709149\pi\) | ||||
−0.610792 | + | 0.791791i | \(0.709149\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 4.35549i | − | 0.736213i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.86073i | − | 0.799100i | −0.916711 | − | 0.399550i | \(-0.869166\pi\) | ||
0.916711 | − | 0.399550i | \(-0.130834\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.15866i | − | 0.493299i | −0.969105 | − | 0.246650i | \(-0.920670\pi\) | ||
0.969105 | − | 0.246650i | \(-0.0793297\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.5277i | 1.60546i | 0.596340 | + | 0.802732i | \(0.296621\pi\) | ||||
−0.596340 | + | 0.802732i | \(0.703379\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 11.6729i | − | 1.70266i | −0.524629 | − | 0.851331i | \(-0.675796\pi\) | ||
0.524629 | − | 0.851331i | \(-0.324204\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −11.9703 | −1.71005 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.20332 | 0.852091 | 0.426046 | − | 0.904702i | \(-0.359906\pi\) | ||||
0.426046 | + | 0.904702i | \(0.359906\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0533304 | 0.00719107 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.11933i | 0.536291i | 0.963378 | + | 0.268145i | \(0.0864108\pi\) | ||||
−0.963378 | + | 0.268145i | \(0.913589\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 0.265744i | − | 0.0340250i | −0.999855 | − | 0.0170125i | \(-0.994584\pi\) | ||
0.999855 | − | 0.0170125i | \(-0.00541551\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.90540 | 0.608440 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.6537i | − | 1.54589i | −0.634470 | − | 0.772947i | \(-0.718782\pi\) | ||
0.634470 | − | 0.772947i | \(-0.281218\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.13167i | 0.134304i | 0.997743 | + | 0.0671520i | \(0.0213912\pi\) | ||||
−0.997743 | + | 0.0671520i | \(0.978609\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.67564 | 1.13245 | 0.566224 | − | 0.824251i | \(-0.308404\pi\) | ||||
0.566224 | + | 0.824251i | \(0.308404\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 0.232280i | − | 0.0264708i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3.25652i | − | 0.366387i | −0.983077 | − | 0.183193i | \(-0.941357\pi\) | ||
0.983077 | − | 0.183193i | \(-0.0586434\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.8978 | 1.96454 | 0.982268 | − | 0.187484i | \(-0.0600334\pi\) | ||||
0.982268 | + | 0.187484i | \(0.0600334\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.18157 | 0.128159 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.1425 | 1.28710 | 0.643552 | − | 0.765402i | \(-0.277460\pi\) | ||||
0.643552 | + | 0.765402i | \(0.277460\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 21.3654i | − | 2.23971i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.30903i | 0.544695i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.81245i | − | 0.691699i | −0.938290 | − | 0.345850i | \(-0.887591\pi\) | ||
0.938290 | − | 0.345850i | \(-0.112409\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.69296i | 0.765478i | 0.923857 | + | 0.382739i | \(0.125019\pi\) | ||||
−0.923857 | + | 0.382739i | \(0.874981\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.66586i | 0.361208i | 0.983556 | + | 0.180604i | \(0.0578053\pi\) | ||||
−0.983556 | + | 0.180604i | \(0.942195\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.44772 | −0.429977 | −0.214988 | − | 0.976617i | \(-0.568971\pi\) | ||||
−0.214988 | + | 0.976617i | \(0.568971\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.59386i | 0.248447i | 0.992254 | + | 0.124224i | \(0.0396440\pi\) | ||||
−0.992254 | + | 0.124224i | \(0.960356\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.3149 | 1.25256 | 0.626278 | − | 0.779600i | \(-0.284577\pi\) | ||||
0.626278 | + | 0.779600i | \(0.284577\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.90776 | + | 4.40005i | −0.177899 | + | 0.410307i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 5.14631i | − | 0.471762i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9972 | −0.999741 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.5250 | 1.91004 | 0.955019 | − | 0.296544i | \(-0.0958343\pi\) | ||||
0.955019 | + | 0.296544i | \(0.0958343\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.36869i | 0.818546i | 0.912412 | + | 0.409273i | \(0.134218\pi\) | ||||
−0.912412 | + | 0.409273i | \(0.865782\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 23.1234 | 2.00506 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.29045 | 0.281122 | 0.140561 | − | 0.990072i | \(-0.455109\pi\) | ||||
0.140561 | + | 0.990072i | \(0.455109\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.68501 | 0.227740 | 0.113870 | − | 0.993496i | \(-0.463675\pi\) | ||||
0.113870 | + | 0.993496i | \(0.463675\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.261607 | 0.0218767 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 3.23248i | − | 0.268442i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.517635 | −0.0424063 | −0.0212032 | − | 0.999775i | \(-0.506750\pi\) | ||||
−0.0212032 | + | 0.999775i | \(0.506750\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.1978 | −1.56230 | −0.781149 | − | 0.624345i | \(-0.785366\pi\) | ||||
−0.781149 | + | 0.624345i | \(0.785366\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.80149 | 0.546309 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 13.7067i | − | 1.09391i | −0.837161 | − | 0.546956i | \(-0.815786\pi\) | ||
0.837161 | − | 0.546956i | \(-0.184214\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.1644 | + | 8.30922i | 1.51037 | + | 0.654858i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.0108 | −1.17574 | −0.587869 | − | 0.808956i | \(-0.700033\pi\) | ||||
−0.587869 | + | 0.808956i | \(0.700033\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 12.6143i | − | 0.976126i | −0.872808 | − | 0.488063i | \(-0.837704\pi\) | ||
0.872808 | − | 0.488063i | \(-0.162296\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.0630 | 0.850997 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 4.49207i | − | 0.341526i | −0.985312 | − | 0.170763i | \(-0.945377\pi\) | ||
0.985312 | − | 0.170763i | \(-0.0546232\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.35549i | 0.329244i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 9.66095i | − | 0.722093i | −0.932548 | − | 0.361047i | \(-0.882420\pi\) | ||
0.932548 | − | 0.361047i | \(-0.117580\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 0.575728i | − | 0.0427935i | −0.999771 | − | 0.0213967i | \(-0.993189\pi\) | ||
0.999771 | − | 0.0213967i | \(-0.00681132\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.86073i | 0.357368i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.0630135 | 0.00460800 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.8620 | −1.29245 | −0.646224 | − | 0.763148i | \(-0.723653\pi\) | ||||
−0.646224 | + | 0.763148i | \(0.723653\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.760186 | 0.0547194 | 0.0273597 | − | 0.999626i | \(-0.491290\pi\) | ||||
0.0273597 | + | 0.999626i | \(0.491290\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.2534i | 1.65674i | 0.560184 | + | 0.828368i | \(0.310731\pi\) | ||||
−0.560184 | + | 0.828368i | \(0.689269\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 14.2715i | − | 1.01168i | −0.862628 | − | 0.505839i | \(-0.831183\pi\) | ||
0.862628 | − | 0.505839i | \(-0.168817\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −14.0790 | −0.988154 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.15866i | 0.220610i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.283132i | 0.0195847i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.56124 | 0.176323 | 0.0881616 | − | 0.996106i | \(-0.471901\pi\) | ||||
0.0881616 | + | 0.996106i | \(0.471901\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 10.5277i | − | 0.717985i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 29.6238i | − | 2.01100i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.79607 | 0.389886 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.2514 | −1.22221 | −0.611104 | − | 0.791551i | \(-0.709274\pi\) | ||||
−0.611104 | + | 0.791551i | \(0.709274\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.6784 | 1.04061 | 0.520304 | − | 0.853981i | \(-0.325819\pi\) | ||||
0.520304 | + | 0.853981i | \(0.325819\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2.23945i | − | 0.147987i | −0.997259 | − | 0.0739936i | \(-0.976426\pi\) | ||
0.997259 | − | 0.0739936i | \(-0.0235744\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 19.5141i | − | 1.27841i | −0.769035 | − | 0.639206i | \(-0.779263\pi\) | ||
0.769035 | − | 0.639206i | \(-0.220737\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.6729i | 0.761454i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 26.8368i | − | 1.73593i | −0.496626 | − | 0.867965i | \(-0.665428\pi\) | ||
0.496626 | − | 0.867965i | \(-0.334572\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 14.2600i | − | 0.918566i | −0.888290 | − | 0.459283i | \(-0.848106\pi\) | ||
0.888290 | − | 0.459283i | \(-0.151894\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.9703 | 0.764756 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.0429i | 1.65707i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.23056 | −0.267031 | −0.133515 | − | 0.991047i | \(-0.542627\pi\) | ||||
−0.133515 | + | 0.991047i | \(0.542627\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.101741 | + | 0.234657i | −0.00639643 | + | 0.0147527i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 27.1291i | − | 1.69226i | −0.532973 | − | 0.846132i | \(-0.678925\pi\) | ||
0.532973 | − | 0.846132i | \(-0.321075\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.1709 | 1.31550 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.78709 | −0.541835 | −0.270918 | − | 0.962603i | \(-0.587327\pi\) | ||||
−0.270918 | + | 0.962603i | \(0.587327\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.20332 | −0.381067 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 24.9826i | − | 1.52322i | −0.648037 | − | 0.761609i | \(-0.724410\pi\) | ||
0.648037 | − | 0.761609i | \(-0.275590\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.35815 | −0.325484 | −0.162742 | − | 0.986669i | \(-0.552034\pi\) | ||||
−0.162742 | + | 0.986669i | \(0.552034\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.0533304 | −0.00321594 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.2055 | −0.673274 | −0.336637 | − | 0.941634i | \(-0.609290\pi\) | ||||
−0.336637 | + | 0.941634i | \(0.609290\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.8269 | 1.42139 | 0.710696 | − | 0.703499i | \(-0.248380\pi\) | ||||
0.710696 | + | 0.703499i | \(0.248380\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.56706i | 0.509259i | 0.967039 | + | 0.254630i | \(0.0819535\pi\) | ||||
−0.967039 | + | 0.254630i | \(0.918046\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.7575 | 0.812080 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.6039 | −0.917876 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.8009 | 1.44888 | 0.724442 | − | 0.689336i | \(-0.242097\pi\) | ||||
0.724442 | + | 0.689336i | \(0.242097\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 4.11933i | − | 0.239837i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.35831 | + | 21.5840i | −0.541205 | + | 1.24824i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −45.8534 | −2.64295 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.265744i | 0.0152164i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.8960 | 0.621866 | 0.310933 | − | 0.950432i | \(-0.399358\pi\) | ||||
0.310933 | + | 0.950432i | \(0.399358\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 21.6067i | − | 1.22520i | −0.790392 | − | 0.612602i | \(-0.790123\pi\) | ||
0.790392 | − | 0.612602i | \(-0.209877\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 27.6548i | − | 1.56314i | −0.623816 | − | 0.781572i | \(-0.714418\pi\) | ||
0.623816 | − | 0.781572i | \(-0.285582\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 10.6630i | − | 0.598895i | −0.954113 | − | 0.299447i | \(-0.903198\pi\) | ||
0.954113 | − | 0.299447i | \(-0.0968023\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 0.172389i | − | 0.00965194i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.27298i | 0.349038i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.90540 | −0.272103 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 50.8411 | 2.80296 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.0311 | 1.04604 | 0.523022 | − | 0.852319i | \(-0.324805\pi\) | ||||
0.523022 | + | 0.852319i | \(0.324805\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.6537i | 0.691345i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 9.01836i | − | 0.491261i | −0.969364 | − | 0.245631i | \(-0.921005\pi\) | ||
0.969364 | − | 0.245631i | \(-0.0789950\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.362726 | 0.0196427 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 21.6482i | − | 1.16889i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.8249i | 1.22530i | 0.790353 | + | 0.612652i | \(0.209897\pi\) | ||||
−0.790353 | + | 0.612652i | \(0.790103\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.0814 | 0.753761 | 0.376880 | − | 0.926262i | \(-0.376997\pi\) | ||||
0.376880 | + | 0.926262i | \(0.376997\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 21.2950i | − | 1.13342i | −0.823917 | − | 0.566710i | \(-0.808216\pi\) | ||
0.823917 | − | 0.566710i | \(-0.191784\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 1.13167i | − | 0.0600626i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −35.4491 | −1.87093 | −0.935465 | − | 0.353418i | \(-0.885019\pi\) | ||||
−0.935465 | + | 0.353418i | \(0.885019\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.18576 | −0.483461 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.67564 | −0.506446 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.0679i | 1.04753i | 0.851861 | + | 0.523767i | \(0.175474\pi\) | ||||
−0.851861 | + | 0.523767i | \(0.824526\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 27.0185i | 1.40273i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0961i | 0.574535i | 0.957850 | + | 0.287267i | \(0.0927468\pi\) | ||||
−0.957850 | + | 0.287267i | \(0.907253\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 15.8566i | − | 0.816656i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.876305i | 0.0450128i | 0.999747 | + | 0.0225064i | \(0.00716461\pi\) | ||||
−0.999747 | + | 0.0225064i | \(0.992835\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.0864 | −0.719781 | −0.359890 | − | 0.932995i | \(-0.617186\pi\) | ||||
−0.359890 | + | 0.932995i | \(0.617186\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.232280i | 0.0118381i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.8276 | −0.853193 | −0.426596 | − | 0.904442i | \(-0.640287\pi\) | ||||
−0.426596 | + | 0.904442i | \(0.640287\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.25415 | + | 5.19896i | −0.113997 | + | 0.262923i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.25652i | 0.163853i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −36.4052 | −1.82713 | −0.913563 | − | 0.406697i | \(-0.866680\pi\) | ||||
−0.913563 | + | 0.406697i | \(0.866680\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.8784 | −1.14249 | −0.571246 | − | 0.820779i | \(-0.693540\pi\) | ||||
−0.571246 | + | 0.820779i | \(0.693540\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 33.3640 | 1.66198 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.259225i | 0.0128493i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.58108 | −0.374860 | −0.187430 | − | 0.982278i | \(-0.560016\pi\) | ||||
−0.187430 | + | 0.982278i | \(0.560016\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.9417 | −0.882854 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.8978 | −0.878567 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.6066 | 1.64179 | 0.820895 | − | 0.571079i | \(-0.193475\pi\) | ||||
0.820895 | + | 0.571079i | \(0.193475\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.2672i | 1.52387i | 0.647655 | + | 0.761934i | \(0.275750\pi\) | ||||
−0.647655 | + | 0.761934i | \(0.724250\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.18157 | −0.0573145 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.15744 | 0.0560127 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.9116 | 1.53713 | 0.768564 | − | 0.639772i | \(-0.220971\pi\) | ||||
0.768564 | + | 0.639772i | \(0.220971\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 5.65026i | − | 0.271534i | −0.990741 | − | 0.135767i | \(-0.956650\pi\) | ||
0.990741 | − | 0.135767i | \(-0.0433499\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −23.3600 | − | 10.1283i | −1.11746 | − | 0.484504i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.1206 | −0.960305 | −0.480152 | − | 0.877185i | \(-0.659419\pi\) | ||||
−0.480152 | + | 0.877185i | \(0.659419\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.5062i | 1.35437i | 0.735813 | + | 0.677185i | \(0.236800\pi\) | ||||
−0.735813 | + | 0.677185i | \(0.763200\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.1425 | −0.575611 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.4642i | 0.541029i | 0.962716 | + | 0.270515i | \(0.0871938\pi\) | ||||
−0.962716 | + | 0.270515i | \(0.912806\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.168452i | 0.00793211i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 21.3654i | 1.00163i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 6.50050i | − | 0.304080i | −0.988374 | − | 0.152040i | \(-0.951416\pi\) | ||
0.988374 | − | 0.152040i | \(-0.0485843\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 18.0113i | − | 0.838872i | −0.907785 | − | 0.419436i | \(-0.862228\pi\) | ||
0.907785 | − | 0.419436i | \(-0.137772\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.5620 | −0.676753 | −0.338376 | − | 0.941011i | \(-0.609878\pi\) | ||||
−0.338376 | + | 0.941011i | \(0.609878\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.1466 | −0.747174 | −0.373587 | − | 0.927595i | \(-0.621872\pi\) | ||||
−0.373587 | + | 0.927595i | \(0.621872\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 55.1131 | 2.54488 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 0.561448i | − | 0.0258154i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 5.30903i | − | 0.243595i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −30.0188 | −1.37160 | −0.685798 | − | 0.727792i | \(-0.740547\pi\) | ||||
−0.685798 | + | 0.727792i | \(0.740547\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.8438i | 1.08719i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.81245i | 0.309337i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.2977 | 0.602576 | 0.301288 | − | 0.953533i | \(-0.402583\pi\) | ||||
0.301288 | + | 0.953533i | \(0.402583\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.53612i | 0.159583i | 0.996812 | + | 0.0797915i | \(0.0254255\pi\) | ||||
−0.996812 | + | 0.0797915i | \(0.974575\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 3.81939i | − | 0.172017i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.92896 | −0.221094 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.9990 | 1.25341 | 0.626705 | − | 0.779257i | \(-0.284403\pi\) | ||||
0.626705 | + | 0.779257i | \(0.284403\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.91684 | 0.174643 | 0.0873217 | − | 0.996180i | \(-0.472169\pi\) | ||||
0.0873217 | + | 0.996180i | \(0.472169\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 7.69296i | − | 0.342332i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 16.1501i | − | 0.715839i | −0.933752 | − | 0.357920i | \(-0.883486\pi\) | ||
0.933752 | − | 0.357920i | \(-0.116514\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 42.1422i | 1.86426i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 3.66586i | − | 0.161537i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.622519i | 0.0273783i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.1551 | 1.05825 | 0.529126 | − | 0.848543i | \(-0.322520\pi\) | ||||
0.529126 | + | 0.848543i | \(0.322520\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.30455i | 0.0570439i | 0.999593 | + | 0.0285220i | \(0.00908005\pi\) | ||||
−0.999593 | + | 0.0285220i | \(0.990920\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.03642 | 0.350072 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.7209 | − | 16.7885i | −0.683519 | − | 0.729933i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.4945i | 0.671140i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.44772 | 0.192292 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.638382 | 0.0274971 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.5323 | −0.667784 | −0.333892 | − | 0.942611i | \(-0.608362\pi\) | ||||
−0.333892 | + | 0.942611i | \(0.608362\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 2.59386i | − | 0.111109i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.6332 | 0.625671 | 0.312836 | − | 0.949807i | \(-0.398721\pi\) | ||||
0.312836 | + | 0.949807i | \(0.398721\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.1613 | 0.731096 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.1837 | 0.603154 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.5916 | −0.491154 | −0.245577 | − | 0.969377i | \(-0.578977\pi\) | ||||
−0.245577 | + | 0.969377i | \(0.578977\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 51.6427i | − | 2.18425i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.21549 | −0.219807 | −0.109903 | − | 0.993942i | \(-0.535054\pi\) | ||||
−0.109903 | + | 0.993942i | \(0.535054\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.3149 | −0.560160 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.94892 | 0.375158 | 0.187579 | − | 0.982250i | \(-0.439936\pi\) | ||||
0.187579 | + | 0.982250i | \(0.439936\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 2.90991i | − | 0.121776i | −0.998145 | − | 0.0608879i | \(-0.980607\pi\) | ||
0.998145 | − | 0.0608879i | \(-0.0193932\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.90776 | − | 4.40005i | 0.0795590 | − | 0.183495i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.2025 | 1.50713 | 0.753565 | − | 0.657373i | \(-0.228332\pi\) | ||||
0.753565 | + | 0.657373i | \(0.228332\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 77.9536i | 3.23406i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.330825 | −0.0137014 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 21.5893i | − | 0.891088i | −0.895260 | − | 0.445544i | \(-0.853010\pi\) | ||
0.895260 | − | 0.445544i | \(-0.146990\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 36.1093i | 1.48786i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 13.2330i | − | 0.543412i | −0.962380 | − | 0.271706i | \(-0.912412\pi\) | ||
0.962380 | − | 0.271706i | \(-0.0875879\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.14631i | 0.210978i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.9912i | 1.18455i | 0.805736 | + | 0.592275i | \(0.201770\pi\) | ||||
−0.805736 | + | 0.592275i | \(0.798230\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.30240 | −0.0939170 | −0.0469585 | − | 0.998897i | \(-0.514953\pi\) | ||||
−0.0469585 | + | 0.998897i | \(0.514953\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.9972 | 0.447098 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 47.3449 | 1.92167 | 0.960836 | − | 0.277118i | \(-0.0893792\pi\) | ||||
0.960836 | + | 0.277118i | \(0.0893792\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 57.2601i | 2.31650i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.90409i | 0.117295i | 0.998279 | + | 0.0586475i | \(0.0186788\pi\) | ||||
−0.998279 | + | 0.0586475i | \(0.981321\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.3417 | −0.537118 | −0.268559 | − | 0.963263i | \(-0.586547\pi\) | ||||
−0.268559 | + | 0.963263i | \(0.586547\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.1961i | 0.851943i | 0.904737 | + | 0.425971i | \(0.140068\pi\) | ||||
−0.904737 | + | 0.425971i | \(0.859932\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 52.8867i | 2.11886i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.74329i | 0.229000i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.0046i | 1.07503i | 0.843253 | + | 0.537517i | \(0.180638\pi\) | ||||
−0.843253 | + | 0.537517i | \(0.819362\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −21.5250 | −0.854195 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 58.7192 | 2.32654 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.03440 | −0.0408565 | −0.0204282 | − | 0.999791i | \(-0.506503\pi\) | ||||
−0.0204282 | + | 0.999791i | \(0.506503\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 23.0638i | − | 0.909546i | −0.890608 | − | 0.454773i | \(-0.849720\pi\) | ||
0.890608 | − | 0.454773i | \(-0.150280\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 24.0526i | − | 0.945604i | −0.881169 | − | 0.472802i | \(-0.843243\pi\) | ||
0.881169 | − | 0.472802i | \(-0.156757\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 0.219685i | − | 0.00862341i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 44.7405i | − | 1.75083i | −0.483370 | − | 0.875416i | \(-0.660587\pi\) | ||
0.483370 | − | 0.875416i | \(-0.339413\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 9.36869i | − | 0.366065i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.7570 | −0.847533 | −0.423767 | − | 0.905771i | \(-0.639292\pi\) | ||||
−0.423767 | + | 0.905771i | \(0.639292\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.8400i | 0.616104i | 0.951370 | + | 0.308052i | \(0.0996770\pi\) | ||||
−0.951370 | + | 0.308052i | \(0.900323\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −23.1234 | −0.896688 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.2231 | + | 6.16678i | 0.550719 | + | 0.238779i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.0141722i | 0.000547112i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.9845 | −1.15582 | −0.577909 | − | 0.816101i | \(-0.696131\pi\) | ||||
−0.577909 | + | 0.816101i | \(0.696131\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 46.0816 | 1.77106 | 0.885530 | − | 0.464582i | \(-0.153795\pi\) | ||||
0.885530 | + | 0.464582i | \(0.153795\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29.6716 | 1.13869 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 10.1398i | − | 0.387988i | −0.981003 | − | 0.193994i | \(-0.937856\pi\) | ||
0.981003 | − | 0.193994i | \(-0.0621443\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.29045 | −0.125722 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −30.4298 | −1.15928 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −46.2807 | −1.76060 | −0.880301 | − | 0.474416i | \(-0.842659\pi\) | ||||
−0.880301 | + | 0.474416i | \(0.842659\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.68501 | −0.101848 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.73217i | 0.141366i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.8970 | 0.562653 | 0.281327 | − | 0.959612i | \(-0.409226\pi\) | ||||
0.281327 | + | 0.959612i | \(0.409226\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.8058 | −0.973283 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −33.5066 | −1.26015 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 37.5138i | − | 1.40886i | −0.709773 | − | 0.704431i | \(-0.751202\pi\) | ||
0.709773 | − | 0.704431i | \(-0.248798\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.9756 | + | 29.9269i | −0.485939 | + | 1.12077i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.261607 | −0.00978355 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 18.5872i | − | 0.693186i | −0.938016 | − | 0.346593i | \(-0.887339\pi\) | ||
0.938016 | − | 0.346593i | \(-0.112661\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.9666 | −0.594629 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.23248i | 0.120051i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.682442i | 0.0253104i | 0.999920 | + | 0.0126552i | \(0.00402838\pi\) | ||||
−0.999920 | + | 0.0126552i | \(0.995972\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 12.4392i | − | 0.460082i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 23.5325i | − | 0.869191i | −0.900626 | − | 0.434596i | \(-0.856891\pi\) | ||
0.900626 | − | 0.434596i | \(-0.143109\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.674826i | 0.0248575i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.6626 | −1.31187 | −0.655935 | − | 0.754817i | \(-0.727726\pi\) | ||||
−0.655935 | + | 0.754817i | \(0.727726\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −53.4011 | −1.95910 | −0.979548 | − | 0.201209i | \(-0.935513\pi\) | ||||
−0.979548 | + | 0.201209i | \(0.935513\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.517635 | 0.0189647 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 19.3720i | − | 0.707837i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.4014i | 0.999891i | 0.866057 | + | 0.499945i | \(0.166647\pi\) | ||||
−0.866057 | + | 0.499945i | \(0.833353\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.1978 | 0.698681 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 17.3599i | − | 0.630955i | −0.948933 | − | 0.315478i | \(-0.897835\pi\) | ||
0.948933 | − | 0.315478i | \(-0.102165\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 36.9950i | − | 1.34107i | −0.741879 | − | 0.670534i | \(-0.766065\pi\) | ||
0.741879 | − | 0.670534i | \(-0.233935\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.2976 | −0.408999 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 20.2070i | − | 0.729631i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.63844i | 0.0951447i | 0.998868 | + | 0.0475724i | \(0.0151485\pi\) | ||||
−0.998868 | + | 0.0475724i | \(0.984852\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.74882 | −0.0629009 | −0.0314504 | − | 0.999505i | \(-0.510013\pi\) | ||||
−0.0314504 | + | 0.999505i | \(0.510013\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.80149 | −0.244317 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.7694 | −0.600826 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 0.0603522i | − | 0.00215957i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.7067i | 0.489213i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.2802i | 1.61407i | 0.590506 | + | 0.807033i | \(0.298928\pi\) | ||||
−0.590506 | + | 0.807033i | \(0.701072\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 57.9928i | 2.06199i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.30358i | 0.0462915i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.0454 | 0.639202 | 0.319601 | − | 0.947552i | \(-0.396451\pi\) | ||||
0.319601 | + | 0.947552i | \(0.396451\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.7923i | 0.487936i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.516006 | −0.0182094 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19.1644 | − | 8.30922i | −0.675456 | − | 0.292862i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 15.7188i | − | 0.552645i | −0.961065 | − | 0.276322i | \(-0.910884\pi\) | ||
0.961065 | − | 0.276322i | \(-0.0891158\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.6749 | −0.515306 | −0.257653 | − | 0.966238i | \(-0.582949\pi\) | ||||
−0.257653 | + | 0.966238i | \(0.582949\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.0108 | 0.525806 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 55.8920 | 1.95541 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 41.8173i | − | 1.45943i | −0.683750 | − | 0.729717i | \(-0.739652\pi\) | ||
0.683750 | − | 0.729717i | \(-0.260348\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 48.6855 | 1.69707 | 0.848534 | − | 0.529140i | \(-0.177485\pi\) | ||||
0.848534 | + | 0.529140i | \(0.177485\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −44.5025 | −1.54750 | −0.773752 | − | 0.633489i | \(-0.781622\pi\) | ||||
−0.773752 | + | 0.633489i | \(0.781622\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.2852 | −0.878191 | −0.439096 | − | 0.898440i | \(-0.644701\pi\) | ||||
−0.439096 | + | 0.898440i | \(0.644701\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.1438 | 0.490052 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.6143i | 0.436537i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33.0296 | −1.14031 | −0.570154 | − | 0.821538i | \(-0.693117\pi\) | ||||
−0.570154 | + | 0.821538i | \(0.693117\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.5511 | 0.639693 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.0630 | −0.380577 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 47.8980i | − | 1.64580i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.3875 | − | 9.27310i | −0.733153 | − | 0.317878i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.6648 | 0.399394 | 0.199697 | − | 0.979858i | \(-0.436004\pi\) | ||||
0.199697 | + | 0.979858i | \(0.436004\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 30.5236i | − | 1.04267i | −0.853353 | − | 0.521333i | \(-0.825435\pi\) | ||
0.853353 | − | 0.521333i | \(-0.174565\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.7320 | 1.15092 | 0.575460 | − | 0.817830i | \(-0.304823\pi\) | ||||
0.575460 | + | 0.817830i | \(0.304823\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 0.442368i | − | 0.0150584i | −0.999972 | − | 0.00752920i | \(-0.997603\pi\) | ||
0.999972 | − | 0.00752920i | \(-0.00239664\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.49207i | 0.152735i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.173671i | 0.00589139i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 62.0714i | 2.10321i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 4.35549i | − | 0.147243i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.3839 | 0.789618 | 0.394809 | − | 0.918763i | \(-0.370811\pi\) | ||||
0.394809 | + | 0.918763i | \(0.370811\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.6795 | 0.663019 | 0.331509 | − | 0.943452i | \(-0.392442\pi\) | ||||
0.331509 | + | 0.943452i | \(0.392442\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.1161 | −0.811571 | −0.405785 | − | 0.913968i | \(-0.633002\pi\) | ||||
−0.405785 | + | 0.913968i | \(0.633002\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.3880i | 0.483103i | 0.970388 | + | 0.241552i | \(0.0776563\pi\) | ||||
−0.970388 | + | 0.241552i | \(0.922344\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 93.7522i | 3.14435i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −61.9716 | −2.07380 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.66095i | 0.322930i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 21.9856i | − | 0.733262i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.32964 | −0.244186 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.575728i | 0.0191378i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.153589i | 0.00509983i | 0.999997 | + | 0.00254992i | \(0.000811665\pi\) | ||||
−0.999997 | + | 0.00254992i | \(0.999188\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.89188 | −0.0626809 | −0.0313405 | − | 0.999509i | \(-0.509978\pi\) | ||||
−0.0313405 | + | 0.999509i | \(0.509978\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.954495 | −0.0315892 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −40.8053 | −1.34751 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.3096i | 1.26372i | 0.775084 | + | 0.631859i | \(0.217708\pi\) | ||||
−0.775084 | + | 0.631859i | \(0.782292\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 5.55127i | − | 0.182722i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 4.86073i | − | 0.159820i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.4363i | 0.736113i | 0.929804 | + | 0.368056i | \(0.119977\pi\) | ||||
−0.929804 | + | 0.368056i | \(0.880023\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 63.5508i | 2.08279i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.0630135 | −0.00206076 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.3629i | 0.567221i | 0.958940 | + | 0.283610i | \(0.0915322\pi\) | ||||
−0.958940 | + | 0.283610i | \(0.908468\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.9128 | −0.420946 | −0.210473 | − | 0.977600i | \(-0.567500\pi\) | ||||
−0.210473 | + | 0.977600i | \(0.567500\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.8983 | − | 6.02595i | −0.452589 | − | 0.196232i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 43.8747i | − | 1.42574i | −0.701297 | − | 0.712869i | \(-0.747395\pi\) | ||
0.701297 | − | 0.712869i | \(-0.252605\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −47.4629 | −1.54071 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48.0731 | −1.55724 | −0.778621 | − | 0.627495i | \(-0.784080\pi\) | ||||
−0.778621 | + | 0.627495i | \(0.784080\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.8620 | 0.578001 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.3315i | 0.462790i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.2602 | 0.492265 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.760186 | −0.0244713 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.9967 | 0.353630 | 0.176815 | − | 0.984244i | \(-0.443421\pi\) | ||||
0.176815 | + | 0.984244i | \(0.443421\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47.4613 | −1.52311 | −0.761553 | − | 0.648103i | \(-0.775563\pi\) | ||||
−0.761553 | + | 0.648103i | \(0.775563\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.6945i | 0.374910i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.8494 | −0.347102 | −0.173551 | − | 0.984825i | \(-0.555524\pi\) | ||||
−0.173551 | + | 0.984825i | \(0.555524\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.647566 | −0.0206963 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −53.0065 | −1.69064 | −0.845322 | − | 0.534257i | \(-0.820591\pi\) | ||||
−0.845322 | + | 0.534257i | \(0.820591\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 23.2534i | − | 0.740915i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 46.3226 | + | 20.0843i | 1.47297 | + | 0.638645i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.1662 | −1.14886 | −0.574429 | − | 0.818555i | \(-0.694776\pi\) | ||||
−0.574429 | + | 0.818555i | \(0.694776\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.2715i | 0.452436i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.7675 | −0.499363 | −0.249681 | − | 0.968328i | \(-0.580326\pi\) | ||||
−0.249681 | + | 0.968328i | \(0.580326\pi\) | |||||||
\(998\) | 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 | 4140.2.i.a.1241.15 | yes | 16 | |
3.2 | odd | 2 | 4140.2.i.b.1241.15 | yes | 16 | ||
23.22 | odd | 2 | 4140.2.i.b.1241.2 | yes | 16 | ||
69.68 | even | 2 | inner | 4140.2.i.a.1241.2 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4140.2.i.a.1241.2 | ✓ | 16 | 69.68 | even | 2 | inner | |
4140.2.i.a.1241.15 | yes | 16 | 1.1 | even | 1 | trivial | |
4140.2.i.b.1241.2 | yes | 16 | 23.22 | odd | 2 | ||
4140.2.i.b.1241.15 | yes | 16 | 3.2 | odd | 2 |