Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3744,2,Mod(1585,3744)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3744, 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("3744.1585");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3744.m (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: | \(29.8959905168\) |
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: | \( x^{16} + 2x^{14} - 16x^{12} - 72x^{10} + 26x^{8} + 360x^{6} + 725x^{4} + 1000x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{20} \) |
Twist minimal: | no (minimal twist has level 936) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1585.8 | ||
Root | \(-1.90184 - 0.0324487i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3744.1585 |
Dual form | 3744.2.m.h.1585.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3744\mathbb{Z}\right)^\times\).
\(n\) | \(703\) | \(2017\) | \(2081\) | \(2341\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | −1.66251 | −0.743496 | −0.371748 | − | 0.928334i | \(-0.621241\pi\) | ||||
−0.371748 | + | 0.928334i | \(0.621241\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.57266i | 1.35034i | 0.737662 | + | 0.675170i | \(0.235930\pi\) | ||||
−0.737662 | + | 0.675170i | \(0.764070\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.02749 | 0.309799 | 0.154899 | − | 0.987930i | \(-0.450495\pi\) | ||||
0.154899 | + | 0.987930i | \(0.450495\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.87826 | − | 3.07768i | 0.520936 | − | 0.853596i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.05251 | 1.22541 | 0.612707 | − | 0.790310i | \(-0.290081\pi\) | ||||
0.612707 | + | 0.790310i | \(0.290081\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.16083 | −0.266312 | −0.133156 | − | 0.991095i | \(-0.542511\pi\) | ||||
−0.133156 | + | 0.991095i | \(0.542511\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.17513 | 1.70463 | 0.852317 | − | 0.523026i | \(-0.175197\pi\) | ||||
0.852317 | + | 0.523026i | \(0.175197\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.23607 | −0.447214 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.29792i | 0.798104i | 0.916928 | + | 0.399052i | \(0.130661\pi\) | ||||
−0.916928 | + | 0.399052i | \(0.869339\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.98872i | − | 1.43482i | −0.696653 | − | 0.717408i | \(-0.745328\pi\) | ||
0.696653 | − | 0.717408i | \(-0.254672\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 5.93958i | − | 1.00397i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.83470 | −1.61682 | −0.808408 | − | 0.588623i | \(-0.799670\pi\) | ||||
−0.808408 | + | 0.588623i | \(0.799670\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.62054i | − | 0.253087i | −0.991961 | − | 0.126543i | \(-0.959612\pi\) | ||
0.991961 | − | 0.126543i | \(-0.0403883\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.35114i | 0.358546i | 0.983799 | + | 0.179273i | \(0.0573745\pi\) | ||||
−0.983799 | + | 0.179273i | \(0.942626\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.73877i | 1.12882i | 0.825496 | + | 0.564408i | \(0.190895\pi\) | ||||
−0.825496 | + | 0.564408i | \(0.809105\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.76393 | −0.823419 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 11.2521i | − | 1.54560i | −0.634652 | − | 0.772798i | \(-0.718857\pi\) | ||
0.634652 | − | 0.772798i | \(-0.281143\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.70820 | −0.230334 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.73249 | 1.26706 | 0.633531 | − | 0.773717i | \(-0.281605\pi\) | ||||
0.633531 | + | 0.773717i | \(0.281605\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 11.4127i | − | 1.46124i | −0.682782 | − | 0.730622i | \(-0.739230\pi\) | ||
0.682782 | − | 0.730622i | \(-0.260770\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.12262 | + | 5.11667i | −0.387314 | + | 0.634645i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.23901 | 0.884386 | 0.442193 | − | 0.896920i | \(-0.354201\pi\) | ||||
0.442193 | + | 0.896920i | \(0.354201\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.5672i | 1.25410i | 0.778981 | + | 0.627048i | \(0.215737\pi\) | ||||
−0.778981 | + | 0.627048i | \(0.784263\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.41606i | 0.516860i | 0.966030 | + | 0.258430i | \(0.0832052\pi\) | ||||
−0.966030 | + | 0.258430i | \(0.916795\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.67086i | 0.418334i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.94427 | 0.781292 | 0.390646 | − | 0.920541i | \(-0.372252\pi\) | ||||
0.390646 | + | 0.920541i | \(0.372252\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.29753 | 0.252187 | 0.126093 | − | 0.992018i | \(-0.459756\pi\) | ||||
0.126093 | + | 0.992018i | \(0.459756\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.39984 | −0.911090 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.02546i | 0.956697i | 0.878170 | + | 0.478349i | \(0.158764\pi\) | ||||
−0.878170 | + | 0.478349i | \(0.841236\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.9955 | + | 6.71040i | 1.15264 | + | 0.703441i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.92989 | 0.198002 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.5614i | 1.17388i | 0.809630 | + | 0.586940i | \(0.199668\pi\) | ||||
−0.809630 | + | 0.586940i | \(0.800332\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.96879i | 0.792924i | 0.918051 | + | 0.396462i | \(0.129762\pi\) | ||||
−0.918051 | + | 0.396462i | \(0.870238\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.7082 | 1.15364 | 0.576822 | − | 0.816870i | \(-0.304293\pi\) | ||||
0.576822 | + | 0.816870i | \(0.304293\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.65626i | 0.256791i | 0.991723 | + | 0.128395i | \(0.0409826\pi\) | ||||
−0.991723 | + | 0.128395i | \(0.959017\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.1564 | 1.16437 | 0.582184 | − | 0.813057i | \(-0.302198\pi\) | ||||
0.582184 | + | 0.813057i | \(0.302198\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.05251 | 0.475300 | 0.237650 | − | 0.971351i | \(-0.423623\pi\) | ||||
0.237650 | + | 0.971351i | \(0.423623\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.5912 | −1.26739 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.0509i | 1.65473i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.94427 | −0.904025 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0300 | 1.07600 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.00000 | 0.532414 | 0.266207 | − | 0.963916i | \(-0.414230\pi\) | ||||
0.266207 | + | 0.963916i | \(0.414230\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 16.5646i | − | 1.44726i | −0.690189 | − | 0.723629i | \(-0.742473\pi\) | ||
0.690189 | − | 0.723629i | \(-0.257527\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 4.14725i | − | 0.359612i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.6020i | 1.16209i | 0.813870 | + | 0.581047i | \(0.197357\pi\) | ||||
−0.813870 | + | 0.581047i | \(0.802643\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.3642i | 1.64245i | 0.570607 | + | 0.821223i | \(0.306708\pi\) | ||||
−0.570607 | + | 0.821223i | \(0.693292\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.92989 | − | 3.16228i | 0.161385 | − | 0.264443i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 7.14533i | − | 0.593387i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.04250 | −0.576944 | −0.288472 | − | 0.957488i | \(-0.593147\pi\) | ||||
−0.288472 | + | 0.957488i | \(0.593147\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3.57266i | − | 0.290739i | −0.989377 | − | 0.145370i | \(-0.953563\pi\) | ||
0.989377 | − | 0.145370i | \(-0.0464371\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.2813i | 1.06678i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 0.555029i | − | 0.0442961i | −0.999755 | − | 0.0221481i | \(-0.992949\pi\) | ||
0.999755 | − | 0.0221481i | \(-0.00705053\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 29.2070i | 2.30183i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.23901 | 0.567003 | 0.283501 | − | 0.958972i | \(-0.408504\pi\) | ||||
0.283501 | + | 0.958972i | \(0.408504\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.32611i | 0.566911i | 0.958985 | + | 0.283456i | \(0.0914809\pi\) | ||||
−0.958985 | + | 0.283456i | \(0.908519\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.94427 | − | 11.5614i | −0.457252 | − | 0.889337i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 11.2521i | − | 0.855482i | −0.903901 | − | 0.427741i | \(-0.859310\pi\) | ||
0.903901 | − | 0.427741i | \(-0.140690\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 7.98872i | − | 0.603891i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.8772i | 1.63518i | 0.575804 | + | 0.817588i | \(0.304689\pi\) | ||||
−0.575804 | + | 0.817588i | \(0.695311\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.8658i | 0.956305i | 0.878277 | + | 0.478152i | \(0.158693\pi\) | ||||
−0.878277 | + | 0.478152i | \(0.841307\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16.3503 | 1.20210 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.19139 | 0.379632 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.92989 | 0.139642 | 0.0698209 | − | 0.997560i | \(-0.477757\pi\) | ||||
0.0698209 | + | 0.997560i | \(0.477757\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.41606i | 0.317875i | 0.987289 | + | 0.158937i | \(0.0508068\pi\) | ||||
−0.987289 | + | 0.158937i | \(0.949193\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.1825 | 1.65168 | 0.825841 | − | 0.563903i | \(-0.190701\pi\) | ||||
0.825841 | + | 0.563903i | \(0.190701\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.0000 | −1.27599 | −0.637993 | − | 0.770042i | \(-0.720235\pi\) | ||||
−0.637993 | + | 0.770042i | \(0.720235\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.3550 | −1.07771 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.69417i | 0.188169i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.19274 | −0.0825033 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.5146i | 0.723856i | 0.932206 | + | 0.361928i | \(0.117881\pi\) | ||||
−0.932206 | + | 0.361928i | \(0.882119\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 3.90879i | − | 0.266577i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 28.5410 | 1.93749 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.48993 | − | 15.5500i | 0.638362 | − | 1.04601i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.98872i | 0.534964i | 0.963563 | + | 0.267482i | \(0.0861916\pi\) | ||||
−0.963563 | + | 0.267482i | \(0.913808\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.35250 | −0.288886 | −0.144443 | − | 0.989513i | \(-0.546139\pi\) | ||||
−0.144443 | + | 0.989513i | \(0.546139\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.43486 | −0.0948185 | −0.0474092 | − | 0.998876i | \(-0.515096\pi\) | ||||
−0.0474092 | + | 0.998876i | \(0.515096\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.3503 | 1.07114 | 0.535571 | − | 0.844490i | \(-0.320096\pi\) | ||||
0.535571 | + | 0.844490i | \(0.320096\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 12.8658i | − | 0.839270i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 7.07107i | − | 0.457389i | −0.973498 | − | 0.228695i | \(-0.926554\pi\) | ||
0.973498 | − | 0.228695i | \(-0.0734457\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 15.9774i | − | 1.02920i | −0.857431 | − | 0.514599i | \(-0.827941\pi\) | ||
0.857431 | − | 0.514599i | \(-0.172059\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.58258 | 0.612209 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.18034 | + | 3.57266i | −0.138732 | + | 0.227323i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 22.5042i | − | 1.42045i | −0.703973 | − | 0.710227i | \(-0.748592\pi\) | ||
0.703973 | − | 0.710227i | \(-0.251408\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.39984 | 0.528093 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.5955 | 1.40947 | 0.704735 | − | 0.709471i | \(-0.251066\pi\) | ||||
0.704735 | + | 0.709471i | \(0.251066\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 35.1361i | − | 2.18325i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.3503 | 1.00820 | 0.504100 | − | 0.863645i | \(-0.331824\pi\) | ||||
0.504100 | + | 0.863645i | \(0.331824\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.7067i | 1.14914i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 7.58124i | − | 0.462237i | −0.972926 | − | 0.231118i | \(-0.925762\pi\) | ||
0.972926 | − | 0.231118i | \(-0.0742384\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.98872i | 0.485280i | 0.970116 | + | 0.242640i | \(0.0780134\pi\) | ||||
−0.970116 | + | 0.242640i | \(0.921987\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.29753 | −0.138546 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.1231i | 1.08891i | 0.838790 | + | 0.544455i | \(0.183263\pi\) | ||||
−0.838790 | + | 0.544455i | \(0.816737\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.19704i | − | 0.369684i | −0.982768 | − | 0.184842i | \(-0.940823\pi\) | ||
0.982768 | − | 0.184842i | \(-0.0591774\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.90617i | 0.172754i | 0.996263 | + | 0.0863769i | \(0.0275289\pi\) | ||||
−0.996263 | + | 0.0863769i | \(0.972471\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.78966 | 0.341753 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.52786 | 0.501639 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.877578 | −0.0512687 | −0.0256343 | − | 0.999671i | \(-0.508161\pi\) | ||||
−0.0256343 | + | 0.999671i | \(0.508161\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.1803 | −0.942056 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.3550 | − | 25.1605i | 0.888005 | − | 1.45507i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.39984 | −0.484159 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 18.9737i | 1.08643i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.7521 | −0.841944 | −0.420972 | − | 0.907074i | \(-0.638311\pi\) | ||||
−0.420972 | + | 0.907074i | \(0.638311\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.5254 | 1.39071 | 0.695354 | − | 0.718667i | \(-0.255248\pi\) | ||||
0.695354 | + | 0.718667i | \(0.255248\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.47214 | 0.365827 | 0.182913 | − | 0.983129i | \(-0.441447\pi\) | ||||
0.182913 | + | 0.983129i | \(0.441447\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −31.1025 | −1.74689 | −0.873446 | − | 0.486921i | \(-0.838120\pi\) | ||||
−0.873446 | + | 0.486921i | \(0.838120\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.41606i | 0.247252i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.86510 | −0.326343 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.19992 | + | 6.88191i | −0.232970 | + | 0.381740i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −27.6480 | −1.52428 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.9955 | −0.604369 | −0.302185 | − | 0.953249i | \(-0.597716\pi\) | ||||
−0.302185 | + | 0.953249i | \(0.597716\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.0349 | −0.657537 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.52786 | 0.301122 | 0.150561 | − | 0.988601i | \(-0.451892\pi\) | ||||
0.150561 | + | 0.988601i | \(0.451892\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 8.20830i | − | 0.444504i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.41606i | 0.238445i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.4750i | 1.09916i | 0.835442 | + | 0.549578i | \(0.185212\pi\) | ||||
−0.835442 | + | 0.549578i | \(0.814788\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.5912 | 0.727522 | 0.363761 | − | 0.931492i | \(-0.381493\pi\) | ||||
0.363761 | + | 0.931492i | \(0.381493\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 20.5942i | − | 1.09612i | −0.836439 | − | 0.548060i | \(-0.815367\pi\) | ||
0.836439 | − | 0.548060i | \(-0.184633\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 17.5680i | − | 0.932415i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.1142i | 1.69493i | 0.530855 | + | 0.847463i | \(0.321871\pi\) | ||||
−0.530855 | + | 0.847463i | \(0.678129\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.6525 | −0.929078 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 7.34173i | − | 0.384284i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.1246 | −1.62469 | −0.812346 | − | 0.583176i | \(-0.801810\pi\) | ||||
−0.812346 | + | 0.583176i | \(0.801810\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 40.2000 | 2.08708 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 26.0746i | − | 1.35009i | −0.737777 | − | 0.675045i | \(-0.764124\pi\) | ||
0.737777 | − | 0.675045i | \(-0.235876\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.2276 | + | 8.07262i | 0.681258 | + | 0.415761i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.3954 | −0.996273 | −0.498137 | − | 0.867099i | \(-0.665982\pi\) | ||||
−0.498137 | + | 0.867099i | \(0.665982\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 3.57494i | − | 0.182671i | −0.995820 | − | 0.0913354i | \(-0.970886\pi\) | ||
0.995820 | − | 0.0913354i | \(-0.0291135\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 6.10284i | − | 0.311030i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35.3980i | 1.79475i | 0.441270 | + | 0.897374i | \(0.354528\pi\) | ||||
−0.441270 | + | 0.897374i | \(0.645472\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 41.3050 | 2.08888 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.5449 | −0.580887 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.5562 | 1.03169 | 0.515843 | − | 0.856683i | \(-0.327479\pi\) | ||||
0.515843 | + | 0.856683i | \(0.327479\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 30.4149i | − | 1.51885i | −0.650596 | − | 0.759424i | \(-0.725481\pi\) | ||
0.650596 | − | 0.759424i | \(-0.274519\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.5868 | − | 15.0049i | −1.22475 | − | 0.747447i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.1050 | −0.500887 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 34.6842i | − | 1.71502i | −0.514466 | − | 0.857511i | \(-0.672010\pi\) | ||
0.514466 | − | 0.857511i | \(-0.327990\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 34.7709i | 1.71097i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.81966 | −0.187500 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.96879i | 0.389301i | 0.980873 | + | 0.194650i | \(0.0623572\pi\) | ||||
−0.980873 | + | 0.194650i | \(0.937643\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.39984 | −0.409383 | −0.204692 | − | 0.978827i | \(-0.565619\pi\) | ||||
−0.204692 | + | 0.978827i | \(0.565619\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.2978 | −0.548022 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 40.7737 | 1.97318 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 1.82688i | − | 0.0879975i | −0.999032 | − | 0.0439987i | \(-0.985990\pi\) | ||
0.999032 | − | 0.0439987i | \(-0.0140098\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.18034 | −0.393122 | −0.196561 | − | 0.980492i | \(-0.562977\pi\) | ||||
−0.196561 | + | 0.980492i | \(0.562977\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.48993 | −0.453965 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.81966 | −0.0868476 | −0.0434238 | − | 0.999057i | \(-0.513827\pi\) | ||||
−0.0434238 | + | 0.999057i | \(0.513827\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 11.2521i | − | 0.534604i | −0.963613 | − | 0.267302i | \(-0.913868\pi\) | ||
0.963613 | − | 0.267302i | \(-0.0861321\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 15.0049i | − | 0.711301i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.86163i | 0.229435i | 0.993398 | + | 0.114717i | \(0.0365962\pi\) | ||||
−0.993398 | + | 0.114717i | \(0.963404\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1.66509i | − | 0.0784059i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18.2802 | − | 11.1561i | −0.856987 | − | 0.523005i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.0199i | 0.796159i | 0.917351 | + | 0.398079i | \(0.130323\pi\) | ||||
−0.917351 | + | 0.398079i | \(0.869677\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.9124 | −1.02056 | −0.510282 | − | 0.860007i | \(-0.670459\pi\) | ||||
−0.510282 | + | 0.860007i | \(0.670459\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.57266i | 0.166036i | 0.996548 | + | 0.0830179i | \(0.0264559\pi\) | ||||
−0.996548 | + | 0.0830179i | \(0.973544\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.59584i | 0.397768i | 0.980023 | + | 0.198884i | \(0.0637317\pi\) | ||||
−0.980023 | + | 0.198884i | \(0.936268\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.8626i | 1.19422i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.41577i | 0.111077i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.59569 | 0.119099 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.2858i | 1.33810i | 0.743216 | + | 0.669052i | \(0.233300\pi\) | ||||
−0.743216 | + | 0.669052i | \(0.766700\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.4721 | + | 30.2681i | −0.842257 | + | 1.38011i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 19.2209i | − | 0.872776i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.843392i | 0.0382177i | 0.999817 | + | 0.0191089i | \(0.00608291\pi\) | ||||
−0.999817 | + | 0.0191089i | \(0.993917\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.02920i | 0.0915767i | 0.998951 | + | 0.0457883i | \(0.0145800\pi\) | ||||
−0.998951 | + | 0.0457883i | \(0.985420\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.7153i | 0.978008i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −37.7530 | −1.69346 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.5347 | −1.50122 | −0.750609 | − | 0.660747i | \(-0.770240\pi\) | ||||
−0.750609 | + | 0.660747i | \(0.770240\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.24525 | 0.278462 | 0.139231 | − | 0.990260i | \(-0.455537\pi\) | ||||
0.139231 | + | 0.990260i | \(0.455537\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 13.2482i | − | 0.589536i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.58258 | 0.424740 | 0.212370 | − | 0.977189i | \(-0.431882\pi\) | ||||
0.212370 | + | 0.977189i | \(0.431882\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.7771 | −0.697937 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.4650 | −0.857729 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.95148i | 0.349706i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.19274 | −0.0522547 | −0.0261274 | − | 0.999659i | \(-0.508318\pi\) | ||||
−0.0261274 | + | 0.999659i | \(0.508318\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.0664i | 1.05235i | 0.850376 | + | 0.526176i | \(0.176375\pi\) | ||||
−0.850376 | + | 0.526176i | \(0.823625\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 40.3631i | − | 1.75824i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 43.8328 | 1.90577 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.98752 | − | 3.04381i | −0.216034 | − | 0.131842i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 4.41606i | − | 0.190923i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.92236 | −0.255094 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.20845 | −0.137942 | −0.0689711 | − | 0.997619i | \(-0.521972\pi\) | ||||
−0.0689711 | + | 0.997619i | \(0.521972\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20.2100 | −0.865703 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 42.1895i | − | 1.80389i | −0.431847 | − | 0.901947i | \(-0.642138\pi\) | ||
0.431847 | − | 0.901947i | \(-0.357862\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 4.98915i | − | 0.212545i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.8096i | 1.05501i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.4525 | 1.03609 | 0.518043 | − | 0.855355i | \(-0.326661\pi\) | ||||
0.518043 | + | 0.855355i | \(0.326661\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.23607 | + | 4.41606i | 0.306053 | + | 0.186779i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.627058i | 0.0264274i | 0.999913 | + | 0.0132137i | \(0.00420617\pi\) | ||||
−0.999913 | + | 0.0132137i | \(0.995794\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.39984 | −0.353384 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.4553 | −1.10906 | −0.554532 | − | 0.832163i | \(-0.687103\pi\) | ||||
−0.554532 | + | 0.832163i | \(0.687103\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.6215i | 1.03038i | 0.857077 | + | 0.515188i | \(0.172278\pi\) | ||||
−0.857077 | + | 0.515188i | \(0.827722\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18.2802 | −0.762335 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 44.5588i | − | 1.85501i | −0.373816 | − | 0.927503i | \(-0.621951\pi\) | ||
0.373816 | − | 0.927503i | \(-0.378049\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.20830i | 0.340538i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 11.5614i | − | 0.478824i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.5174 | 0.434100 | 0.217050 | − | 0.976160i | \(-0.430356\pi\) | ||||
0.217050 | + | 0.976160i | \(0.430356\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.27354i | 0.382110i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 26.6637i | − | 1.09495i | −0.836823 | − | 0.547474i | \(-0.815589\pi\) | ||
0.836823 | − | 0.547474i | \(-0.184411\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 30.0098i | − | 1.23028i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −46.6653 | −1.90669 | −0.953347 | − | 0.301877i | \(-0.902387\pi\) | ||||
−0.953347 | + | 0.301877i | \(0.902387\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.4164 | 0.792012 | 0.396006 | − | 0.918248i | \(-0.370396\pi\) | ||||
0.396006 | + | 0.918248i | \(0.370396\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.5324 | 0.672139 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.7082 | −0.637576 | −0.318788 | − | 0.947826i | \(-0.603276\pi\) | ||||
−0.318788 | + | 0.947826i | \(0.603276\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.8175 | + | 14.5354i | 0.963552 | + | 0.588040i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.96497 | 0.281313 | 0.140656 | − | 0.990058i | \(-0.455079\pi\) | ||||
0.140656 | + | 0.990058i | \(0.455079\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 3.36861i | − | 0.135615i | −0.997698 | − | 0.0678075i | \(-0.978400\pi\) | ||
0.997698 | − | 0.0678075i | \(-0.0216004\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.7781 | 1.19688 | 0.598442 | − | 0.801166i | \(-0.295787\pi\) | ||||
0.598442 | + | 0.801166i | \(0.295787\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −32.2450 | −1.29187 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.81966 | −0.352786 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −49.6899 | −1.98127 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 22.2794i | − | 0.886928i | −0.896292 | − | 0.443464i | \(-0.853749\pi\) | ||
0.896292 | − | 0.443464i | \(-0.146251\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.97505 | −0.395848 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.8262 | + | 17.7396i | −0.428948 | + | 0.702867i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 43.9983 | 1.73783 | 0.868914 | − | 0.494963i | \(-0.164818\pi\) | ||||
0.868914 | + | 0.494963i | \(0.164818\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.8734 | 1.33584 | 0.667918 | − | 0.744235i | \(-0.267186\pi\) | ||||
0.667918 | + | 0.744235i | \(0.267186\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.5603 | 1.43733 | 0.718667 | − | 0.695354i | \(-0.244753\pi\) | ||||
0.718667 | + | 0.695354i | \(0.244753\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.0000 | 0.392534 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 33.3688i | 1.30582i | 0.757435 | + | 0.652911i | \(0.226452\pi\) | ||||
−0.757435 | + | 0.652911i | \(0.773548\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.5388i | 1.07603i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 36.4126i | − | 1.41843i | −0.704991 | − | 0.709216i | \(-0.749049\pi\) | ||
0.704991 | − | 0.709216i | \(-0.250951\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.3038 | 1.80101 | 0.900504 | − | 0.434847i | \(-0.143198\pi\) | ||||
0.900504 | + | 0.434847i | \(0.143198\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.89484i | 0.267370i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 35.1361i | 1.36047i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 11.7264i | − | 0.452692i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.6525 | −0.487717 | −0.243859 | − | 0.969811i | \(-0.578413\pi\) | ||||
−0.243859 | + | 0.969811i | \(0.578413\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 17.8187i | − | 0.684830i | −0.939549 | − | 0.342415i | \(-0.888755\pi\) | ||
0.939549 | − | 0.342415i | \(-0.111245\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −41.3050 | −1.58514 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.5174 | 0.402438 | 0.201219 | − | 0.979546i | \(-0.435510\pi\) | ||||
0.201219 | + | 0.979546i | \(0.435510\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 22.6134i | − | 0.864012i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −34.6304 | − | 21.1344i | −1.31931 | − | 0.805156i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.91735 | −0.187065 | −0.0935324 | − | 0.995616i | \(-0.529816\pi\) | ||||
−0.0935324 | + | 0.995616i | \(0.529816\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 32.1931i | − | 1.22115i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 8.18782i | − | 0.310136i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 26.8021i | − | 1.01230i | −0.862445 | − | 0.506151i | \(-0.831068\pi\) | ||
0.862445 | − | 0.506151i | \(-0.168932\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.4164 | 0.430578 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −28.4698 | −1.07072 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.39984 | 0.315463 | 0.157731 | − | 0.987482i | \(-0.449582\pi\) | ||||
0.157731 | + | 0.987482i | \(0.449582\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 65.3089i | − | 2.44584i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.20845 | + | 5.25731i | −0.119989 | + | 0.196612i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.0349 | 0.448826 | 0.224413 | − | 0.974494i | \(-0.427953\pi\) | ||||
0.224413 | + | 0.974494i | \(0.427953\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 41.8295i | 1.55781i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 9.61045i | − | 0.356923i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.3607 | 0.829312 | 0.414656 | − | 0.909978i | \(-0.363902\pi\) | ||||
0.414656 | + | 0.909978i | \(0.363902\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.8792i | 0.439367i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −46.8519 | −1.73051 | −0.865256 | − | 0.501330i | \(-0.832844\pi\) | ||||
−0.865256 | + | 0.501330i | \(0.832844\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.43798 | 0.273982 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.9434 | −0.733631 | −0.366816 | − | 0.930294i | \(-0.619552\pi\) | ||||
−0.366816 | + | 0.930294i | \(0.619552\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 47.5918i | − | 1.74597i | −0.487744 | − | 0.872987i | \(-0.662180\pi\) | ||
0.487744 | − | 0.872987i | \(-0.337820\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.7082 | 0.428955 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.48993 | −0.346755 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 54.5410 | 1.99023 | 0.995115 | − | 0.0987222i | \(-0.0314755\pi\) | ||||
0.995115 | + | 0.0987222i | \(0.0314755\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.93958i | 0.216164i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 8.50651i | − | 0.309174i | −0.987979 | − | 0.154587i | \(-0.950595\pi\) | ||
0.987979 | − | 0.154587i | \(-0.0494047\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 16.4304i | − | 0.595601i | −0.954628 | − | 0.297800i | \(-0.903747\pi\) | ||
0.954628 | − | 0.297800i | \(-0.0962530\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 43.4306i | 1.57229i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.2802 | − | 29.9535i | 0.660058 | − | 1.08156i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 24.1653i | − | 0.871422i | −0.900087 | − | 0.435711i | \(-0.856497\pi\) | ||
0.900087 | − | 0.435711i | \(-0.143503\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.3176 | −1.09045 | −0.545224 | − | 0.838290i | \(-0.683555\pi\) | ||||
−0.545224 | + | 0.838290i | \(0.683555\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.8633i | 0.641669i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.88118i | 0.0674001i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.8576i | 0.388517i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.922740i | 0.0329340i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.4996 | −1.44366 | −0.721828 | − | 0.692072i | \(-0.756698\pi\) | ||||
−0.721828 | + | 0.692072i | \(0.756698\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.0509i | 0.641817i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −35.1246 | − | 21.4360i | −1.24731 | − | 0.761214i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.4896i | 0.761201i | 0.924740 | + | 0.380601i | \(0.124283\pi\) | ||||
−0.924740 | + | 0.380601i | \(0.875717\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 39.1002i | 1.38327i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.53744i | 0.160123i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 48.5569i | − | 1.71141i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.6480 | 0.972053 | 0.486026 | − | 0.873944i | \(-0.338446\pi\) | ||||
0.486026 | + | 0.873944i | \(0.338446\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.7863 | 1.74823 | 0.874116 | − | 0.485717i | \(-0.161441\pi\) | ||||
0.874116 | + | 0.485717i | \(0.161441\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.0349 | −0.421564 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 2.72927i | − | 0.0954852i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.5874 | 0.648705 | 0.324352 | − | 0.945936i | \(-0.394854\pi\) | ||||
0.324352 | + | 0.945936i | \(0.394854\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.1803 | −0.494296 | −0.247148 | − | 0.968978i | \(-0.579493\pi\) | ||||
−0.247148 | + | 0.968978i | \(0.579493\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.3326 | −1.26341 | −0.631704 | − | 0.775209i | \(-0.717644\pi\) | ||||
−0.631704 | + | 0.775209i | \(0.717644\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.3319i | 1.08820i | 0.839020 | + | 0.544100i | \(0.183129\pi\) | ||||
−0.839020 | + | 0.544100i | \(0.816871\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −29.1223 | −1.00903 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 12.1797i | − | 0.421496i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 45.0184i | − | 1.55421i | −0.629372 | − | 0.777104i | \(-0.716688\pi\) | ||
0.629372 | − | 0.777104i | \(-0.283312\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.5279 | 0.363030 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.88240 | + | 19.2209i | 0.339965 | + | 0.661219i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 35.5275i | − | 1.22074i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −80.4000 | −2.75608 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.5041 | 1.01020 | 0.505101 | − | 0.863060i | \(-0.331455\pi\) | ||||
0.505101 | + | 0.863060i | \(0.331455\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.4905 | 0.426667 | 0.213334 | − | 0.976979i | \(-0.431568\pi\) | ||||
0.213334 | + | 0.976979i | \(0.431568\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.5276i | 0.939231i | 0.882871 | + | 0.469615i | \(0.155607\pi\) | ||||
−0.882871 | + | 0.469615i | \(0.844393\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 12.0602i | − | 0.410535i | −0.978706 | − | 0.205267i | \(-0.934194\pi\) | ||
0.978706 | − | 0.205267i | \(-0.0658064\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.7067i | 0.636047i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.13514 | 0.242043 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.5967 | − | 22.2794i | 0.460708 | − | 0.754908i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 42.9792i | 1.45296i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.4430 | −0.724078 | −0.362039 | − | 0.932163i | \(-0.617919\pi\) | ||||
−0.362039 | + | 0.932163i | \(0.617919\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.1050 | 0.340447 | 0.170223 | − | 0.985405i | \(-0.445551\pi\) | ||||
0.170223 | + | 0.985405i | \(0.445551\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.5146i | 0.353845i | 0.984225 | + | 0.176923i | \(0.0566142\pi\) | ||||
−0.984225 | + | 0.176923i | \(0.943386\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −30.7706 | −1.03318 | −0.516589 | − | 0.856234i | \(-0.672798\pi\) | ||||
−0.516589 | + | 0.856234i | \(0.672798\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.4360i | 0.718940i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 8.98339i | − | 0.300618i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 36.3709i | − | 1.21575i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 34.3349 | 1.14513 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 56.8514i | − | 1.89399i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 21.3894i | − | 0.711009i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.81234i | 0.192996i | 0.995333 | + | 0.0964978i | \(0.0307641\pi\) | ||||
−0.995333 | + | 0.0964978i | \(0.969236\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.8757 | 1.35427 | 0.677136 | − | 0.735858i | \(-0.263221\pi\) | ||||
0.677136 | + | 0.735858i | \(0.263221\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.36068 | 0.0781271 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 59.1799 | 1.95429 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.41641 | −0.178671 | −0.0893354 | − | 0.996002i | \(-0.528474\pi\) | ||||
−0.0893354 | + | 0.996002i | \(0.528474\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 32.5225 | + | 19.8480i | 1.07049 | + | 0.653303i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.9911 | 0.723062 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.86474i | 0.225225i | 0.993639 | + | 0.112612i | \(0.0359218\pi\) | ||||
−0.993639 | + | 0.112612i | \(0.964078\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.69094 | 0.219287 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.63072 | −0.282255 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.6525 | −1.00137 | −0.500686 | − | 0.865629i | \(-0.666919\pi\) | ||||
−0.500686 | + | 0.865629i | \(0.666919\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36.4825 | −1.18930 | −0.594648 | − | 0.803986i | \(-0.702709\pi\) | ||||
−0.594648 | + | 0.803986i | \(0.702709\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 13.2482i | − | 0.431420i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −49.9325 | −1.62259 | −0.811294 | − | 0.584638i | \(-0.801236\pi\) | ||||
−0.811294 | + | 0.584638i | \(0.801236\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.5912 | + | 8.29451i | 0.441190 | + | 0.269251i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32.7005 | −1.05927 | −0.529637 | − | 0.848224i | \(-0.677672\pi\) | ||||
−0.529637 | + | 0.848224i | \(0.677672\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.20845 | −0.103823 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −48.5952 | −1.56922 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −32.8197 | −1.05870 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 7.34173i | − | 0.236339i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 5.25945i | − | 0.169132i | −0.996418 | − | 0.0845662i | \(-0.973050\pi\) | ||
0.996418 | − | 0.0845662i | \(-0.0269505\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.05841i | 0.130240i | 0.997877 | + | 0.0651202i | \(0.0207431\pi\) | ||||
−0.997877 | + | 0.0651202i | \(0.979257\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −69.1816 | −2.21786 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 15.1924i | − | 0.486048i | −0.970020 | − | 0.243024i | \(-0.921861\pi\) | ||
0.970020 | − | 0.243024i | \(-0.0781393\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.27354i | 0.296384i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 24.4543i | − | 0.779971i | −0.920821 | − | 0.389985i | \(-0.872480\pi\) | ||
0.920821 | − | 0.389985i | \(-0.127520\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −38.5410 | −1.22802 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.2209i | 0.611189i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.1803 | 0.323389 | 0.161695 | − | 0.986841i | \(-0.448304\pi\) | ||||
0.161695 | + | 0.986841i | \(0.448304\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 29.9251 | 0.948691 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 12.9968i | − | 0.411612i | −0.978593 | − | 0.205806i | \(-0.934018\pi\) | ||
0.978593 | − | 0.205806i | \(-0.0659817\pi\) | |||||||
\(998\) | 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 | 3744.2.m.h.1585.8 | 16 | ||
3.2 | odd | 2 | inner | 3744.2.m.h.1585.12 | 16 | ||
4.3 | odd | 2 | 936.2.m.h.181.1 | ✓ | 16 | ||
8.3 | odd | 2 | 936.2.m.h.181.13 | yes | 16 | ||
8.5 | even | 2 | inner | 3744.2.m.h.1585.11 | 16 | ||
12.11 | even | 2 | 936.2.m.h.181.15 | yes | 16 | ||
13.12 | even | 2 | inner | 3744.2.m.h.1585.9 | 16 | ||
24.5 | odd | 2 | inner | 3744.2.m.h.1585.7 | 16 | ||
24.11 | even | 2 | 936.2.m.h.181.3 | yes | 16 | ||
39.38 | odd | 2 | inner | 3744.2.m.h.1585.5 | 16 | ||
52.51 | odd | 2 | 936.2.m.h.181.16 | yes | 16 | ||
104.51 | odd | 2 | 936.2.m.h.181.4 | yes | 16 | ||
104.77 | even | 2 | inner | 3744.2.m.h.1585.6 | 16 | ||
156.155 | even | 2 | 936.2.m.h.181.2 | yes | 16 | ||
312.77 | odd | 2 | inner | 3744.2.m.h.1585.10 | 16 | ||
312.155 | even | 2 | 936.2.m.h.181.14 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
936.2.m.h.181.1 | ✓ | 16 | 4.3 | odd | 2 | ||
936.2.m.h.181.2 | yes | 16 | 156.155 | even | 2 | ||
936.2.m.h.181.3 | yes | 16 | 24.11 | even | 2 | ||
936.2.m.h.181.4 | yes | 16 | 104.51 | odd | 2 | ||
936.2.m.h.181.13 | yes | 16 | 8.3 | odd | 2 | ||
936.2.m.h.181.14 | yes | 16 | 312.155 | even | 2 | ||
936.2.m.h.181.15 | yes | 16 | 12.11 | even | 2 | ||
936.2.m.h.181.16 | yes | 16 | 52.51 | odd | 2 | ||
3744.2.m.h.1585.5 | 16 | 39.38 | odd | 2 | inner | ||
3744.2.m.h.1585.6 | 16 | 104.77 | even | 2 | inner | ||
3744.2.m.h.1585.7 | 16 | 24.5 | odd | 2 | inner | ||
3744.2.m.h.1585.8 | 16 | 1.1 | even | 1 | trivial | ||
3744.2.m.h.1585.9 | 16 | 13.12 | even | 2 | inner | ||
3744.2.m.h.1585.10 | 16 | 312.77 | odd | 2 | inner | ||
3744.2.m.h.1585.11 | 16 | 8.5 | even | 2 | inner | ||
3744.2.m.h.1585.12 | 16 | 3.2 | odd | 2 | inner |