Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,3,Mod(685,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.685");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.0655186332\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.339738624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 588) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 685.7 | ||
Root | \(1.60021 + 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.685 |
Dual form | 1764.3.d.h.685.2 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.37964i | 1.07593i | 0.842968 | + | 0.537964i | \(0.180806\pi\) | ||||
−0.842968 | + | 0.537964i | \(0.819194\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.59159 | 0.781054 | 0.390527 | − | 0.920592i | \(-0.372293\pi\) | ||||
0.390527 | + | 0.920592i | \(0.372293\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 21.0158i | 1.61660i | 0.588769 | + | 0.808301i | \(0.299613\pi\) | ||||
−0.588769 | + | 0.808301i | \(0.700387\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 5.48622i | − 0.322719i | −0.986896 | − | 0.161359i | \(-0.948412\pi\) | ||||
0.986896 | − | 0.161359i | \(-0.0515878\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.24098i | 0.381104i | 0.981677 | + | 0.190552i | \(0.0610278\pi\) | ||||
−0.981677 | + | 0.190552i | \(0.938972\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −28.0556 | −1.21981 | −0.609905 | − | 0.792474i | \(-0.708792\pi\) | ||||
−0.609905 | + | 0.792474i | \(0.708792\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.94054 | −0.157621 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −40.3447 | −1.39120 | −0.695599 | − | 0.718431i | \(-0.744861\pi\) | ||||
−0.695599 | + | 0.718431i | \(0.744861\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 40.5101i | 1.30678i | 0.757023 | + | 0.653388i | \(0.226653\pi\) | ||||
−0.757023 | + | 0.653388i | \(0.773347\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 66.6370 | 1.80100 | 0.900500 | − | 0.434856i | \(-0.143201\pi\) | ||||
0.900500 | + | 0.434856i | \(0.143201\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 33.6357i | 0.820383i | 0.911999 | + | 0.410191i | \(0.134538\pi\) | ||||
−0.911999 | + | 0.410191i | \(0.865462\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.932907 | 0.0216955 | 0.0108478 | − | 0.999941i | \(-0.496547\pi\) | ||||
0.0108478 | + | 0.999941i | \(0.496547\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 85.6544i | − 1.82243i | −0.411927 | − | 0.911217i | \(-0.635144\pi\) | ||||
0.411927 | − | 0.911217i | \(-0.364856\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 44.5954 | 0.841422 | 0.420711 | − | 0.907195i | \(-0.361781\pi\) | ||||
0.420711 | + | 0.907195i | \(0.361781\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 46.2197i | 0.840358i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 63.6950i | − 1.07958i | −0.841801 | − | 0.539788i | \(-0.818504\pi\) | ||||
0.841801 | − | 0.539788i | \(-0.181496\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 32.0084i | − 0.524727i | −0.964969 | − | 0.262364i | \(-0.915498\pi\) | ||||
0.964969 | − | 0.262364i | \(-0.0845020\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −113.058 | −1.73935 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −47.7341 | −0.712450 | −0.356225 | − | 0.934400i | \(-0.615936\pi\) | ||||
−0.356225 | + | 0.934400i | \(0.615936\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.9676 | −0.210811 | −0.105405 | − | 0.994429i | \(-0.533614\pi\) | ||||
−0.105405 | + | 0.994429i | \(0.533614\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 140.298i | 1.92188i | 0.276750 | + | 0.960942i | \(0.410742\pi\) | ||||
−0.276750 | + | 0.960942i | \(0.589258\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −122.307 | −1.54820 | −0.774098 | − | 0.633066i | \(-0.781796\pi\) | ||||
−0.774098 | + | 0.633066i | \(0.781796\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 33.1852i | 0.399822i | 0.979814 | + | 0.199911i | \(0.0640652\pi\) | ||||
−0.979814 | + | 0.199911i | \(0.935935\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 29.5139 | 0.347222 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 36.1246i | 0.405894i | 0.979190 | + | 0.202947i | \(0.0650519\pi\) | ||||
−0.979190 | + | 0.202947i | \(0.934948\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −38.9539 | −0.410041 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 16.2175i | − 0.167191i | −0.996500 | − | 0.0835956i | \(-0.973360\pi\) | ||||
0.996500 | − | 0.0835956i | \(-0.0266404\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 119.464i | 1.18281i | 0.806373 | + | 0.591407i | \(0.201427\pi\) | ||||
−0.806373 | + | 0.591407i | \(0.798573\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.93188i | 0.0867173i | 0.999060 | + | 0.0433586i | \(0.0138058\pi\) | ||||
−0.999060 | + | 0.0433586i | \(0.986194\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −173.856 | −1.62482 | −0.812410 | − | 0.583086i | \(-0.801845\pi\) | ||||
−0.812410 | + | 0.583086i | \(0.801845\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −160.315 | −1.47078 | −0.735388 | − | 0.677646i | \(-0.763000\pi\) | ||||
−0.735388 | + | 0.677646i | \(0.763000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 81.4420 | 0.720725 | 0.360363 | − | 0.932812i | \(-0.382653\pi\) | ||||
0.360363 | + | 0.932812i | \(0.382653\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 150.929i | − 1.31243i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −47.1846 | −0.389955 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 113.292i | 0.906339i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 117.172 | 0.922613 | 0.461307 | − | 0.887241i | \(-0.347381\pi\) | ||||
0.461307 | + | 0.887241i | \(0.347381\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 244.150i | − 1.86374i | −0.362795 | − | 0.931869i | \(-0.618177\pi\) | ||||
0.362795 | − | 0.931869i | \(-0.381823\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −245.412 | −1.79133 | −0.895663 | − | 0.444733i | \(-0.853299\pi\) | ||||
−0.895663 | + | 0.444733i | \(0.853299\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.1371i | 0.123288i | 0.998098 | + | 0.0616441i | \(0.0196344\pi\) | ||||
−0.998098 | + | 0.0616441i | \(0.980366\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 180.559i | 1.26265i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 217.040i | − 1.49683i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −134.242 | −0.900952 | −0.450476 | − | 0.892789i | \(-0.648746\pi\) | ||||
−0.450476 | + | 0.892789i | \(0.648746\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 199.009 | 1.31794 | 0.658971 | − | 0.752168i | \(-0.270992\pi\) | ||||
0.658971 | + | 0.752168i | \(0.270992\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −217.930 | −1.40600 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 77.0189i | − 0.490566i | −0.969451 | − | 0.245283i | \(-0.921119\pi\) | ||||
0.969451 | − | 0.245283i | \(-0.0788810\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −230.379 | −1.41337 | −0.706684 | − | 0.707529i | \(-0.749810\pi\) | ||||
−0.706684 | + | 0.707529i | \(0.749810\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 229.231i | 1.37264i | 0.727298 | + | 0.686321i | \(0.240776\pi\) | ||||
−0.727298 | + | 0.686321i | \(0.759224\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −272.665 | −1.61340 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 112.473i | − 0.650133i | −0.945691 | − | 0.325066i | \(-0.894613\pi\) | ||||
0.945691 | − | 0.325066i | \(-0.105387\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −105.494 | −0.589352 | −0.294676 | − | 0.955597i | \(-0.595212\pi\) | ||||
−0.294676 | + | 0.955597i | \(0.595212\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 15.2683i | − 0.0843553i | −0.999110 | − | 0.0421776i | \(-0.986570\pi\) | ||||
0.999110 | − | 0.0421776i | \(-0.0134295\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 358.483i | 1.93775i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 47.1353i | − 0.252061i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 306.186 | 1.60307 | 0.801534 | − | 0.597950i | \(-0.204018\pi\) | ||||
0.801534 | + | 0.597950i | \(0.204018\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.84100 | −0.00953885 | −0.00476943 | − | 0.999989i | \(-0.501518\pi\) | ||||
−0.00476943 | + | 0.999989i | \(0.501518\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 255.334 | 1.29611 | 0.648056 | − | 0.761593i | \(-0.275582\pi\) | ||||
0.648056 | + | 0.761593i | \(0.275582\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 36.6483i | 0.184162i | 0.995752 | + | 0.0920812i | \(0.0293519\pi\) | ||||
−0.995752 | + | 0.0920812i | \(0.970648\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −180.948 | −0.882673 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 62.2116i | 0.297663i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −126.571 | −0.599862 | −0.299931 | − | 0.953961i | \(-0.596964\pi\) | ||||
−0.299931 | + | 0.953961i | \(0.596964\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.01871i | 0.0233428i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 115.297 | 0.521708 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 212.193i | 0.951536i | 0.879571 | + | 0.475768i | \(0.157830\pi\) | ||||
−0.879571 | + | 0.475768i | \(0.842170\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 105.489i | − 0.464708i | −0.972631 | − | 0.232354i | \(-0.925357\pi\) | ||||
0.972631 | − | 0.232354i | \(-0.0746428\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 6.99086i | − 0.0305278i | −0.999884 | − | 0.0152639i | \(-0.995141\pi\) | ||||
0.999884 | − | 0.0152639i | \(-0.00485883\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −336.046 | −1.44226 | −0.721128 | − | 0.692801i | \(-0.756376\pi\) | ||||
−0.721128 | + | 0.692801i | \(0.756376\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 460.790 | 1.96081 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 232.382 | 0.972309 | 0.486155 | − | 0.873873i | \(-0.338399\pi\) | ||||
0.486155 | + | 0.873873i | \(0.338399\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 63.7346i | 0.264459i | 0.991219 | + | 0.132229i | \(0.0422136\pi\) | ||||
−0.991219 | + | 0.132229i | \(0.957786\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −152.175 | −0.616094 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 415.450i | 1.65518i | 0.561334 | + | 0.827589i | \(0.310288\pi\) | ||||
−0.561334 | + | 0.827589i | \(0.689712\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −241.043 | −0.952737 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 265.598i | 1.03345i | 0.856150 | + | 0.516727i | \(0.172850\pi\) | ||||
−0.856150 | + | 0.516727i | \(0.827150\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −156.373 | −0.594575 | −0.297288 | − | 0.954788i | \(-0.596082\pi\) | ||||
−0.297288 | + | 0.954788i | \(0.596082\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 239.907i | 0.905310i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 332.861i | 1.23740i | 0.785626 | + | 0.618701i | \(0.212341\pi\) | ||||
−0.785626 | + | 0.618701i | \(0.787659\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 209.089i | 0.771546i | 0.922594 | + | 0.385773i | \(0.126065\pi\) | ||||
−0.922594 | + | 0.385773i | \(0.873935\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −33.8555 | −0.123111 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −263.231 | −0.950293 | −0.475146 | − | 0.879907i | \(-0.657605\pi\) | ||||
−0.475146 | + | 0.879907i | \(0.657605\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −391.519 | −1.39331 | −0.696653 | − | 0.717408i | \(-0.745328\pi\) | ||||
−0.696653 | + | 0.717408i | \(0.745328\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 109.394i | − 0.386550i | −0.981145 | − | 0.193275i | \(-0.938089\pi\) | ||||
0.981145 | − | 0.193275i | \(-0.0619109\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 258.901 | 0.895853 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 35.3685i | 0.120712i | 0.998177 | + | 0.0603558i | \(0.0192235\pi\) | ||||
−0.998177 | + | 0.0603558i | \(0.980776\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 342.656 | 1.16155 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 589.613i | − 1.97195i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 172.194 | 0.564569 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 125.621i | − 0.409189i | −0.978847 | − | 0.204594i | \(-0.934412\pi\) | ||||
0.978847 | − | 0.204594i | \(-0.0655875\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 315.735i | − 1.01523i | −0.861585 | − | 0.507613i | \(-0.830528\pi\) | ||||
0.861585 | − | 0.507613i | \(-0.169472\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 51.6046i | 0.164871i | 0.996596 | + | 0.0824355i | \(0.0262698\pi\) | ||||
−0.996596 | + | 0.0824355i | \(0.973730\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.99391 | 0.0157537 | 0.00787683 | − | 0.999969i | \(-0.497493\pi\) | ||||
0.00787683 | + | 0.999969i | \(0.497493\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −346.625 | −1.08660 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 39.7256 | 0.122990 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 82.8137i | − 0.254811i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 454.780 | 1.37396 | 0.686980 | − | 0.726677i | \(-0.258936\pi\) | ||||
0.686980 | + | 0.726677i | \(0.258936\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 256.792i | − 0.766545i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −183.824 | −0.545471 | −0.272736 | − | 0.962089i | \(-0.587928\pi\) | ||||
−0.272736 | + | 0.962089i | \(0.587928\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 348.046i | 1.02066i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −144.776 | −0.417223 | −0.208611 | − | 0.977999i | \(-0.566894\pi\) | ||||
−0.208611 | + | 0.977999i | \(0.566894\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 187.069i | − 0.536015i | −0.963417 | − | 0.268007i | \(-0.913635\pi\) | ||||
0.963417 | − | 0.268007i | \(-0.0863651\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 222.601i | − 0.630597i | −0.948993 | − | 0.315299i | \(-0.897895\pi\) | ||||
0.948993 | − | 0.315299i | \(-0.102105\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 80.5201i | − 0.226817i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −62.9856 | −0.175447 | −0.0877237 | − | 0.996145i | \(-0.527959\pi\) | ||||
−0.0877237 | + | 0.996145i | \(0.527959\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 308.568 | 0.854759 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −754.750 | −2.06781 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 547.100i | 1.49074i | 0.666653 | + | 0.745368i | \(0.267726\pi\) | ||||
−0.666653 | + | 0.745368i | \(0.732274\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.4417 | −0.0869750 | −0.0434875 | − | 0.999054i | \(-0.513847\pi\) | ||||
−0.0434875 | + | 0.999054i | \(0.513847\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 847.878i | − 2.24901i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 508.859 | 1.34263 | 0.671317 | − | 0.741170i | \(-0.265729\pi\) | ||||
0.671317 | + | 0.741170i | \(0.265729\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.2839i | 0.0686263i | 0.999411 | + | 0.0343131i | \(0.0109244\pi\) | ||||
−0.999411 | + | 0.0343131i | \(0.989076\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 360.128 | 0.925779 | 0.462890 | − | 0.886416i | \(-0.346813\pi\) | ||||
0.462890 | + | 0.886416i | \(0.346813\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 153.919i | 0.393656i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 657.970i | − 1.66575i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 570.992i | − 1.43827i | −0.694872 | − | 0.719134i | \(-0.744539\pi\) | ||||
0.694872 | − | 0.719134i | \(-0.255461\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −68.4014 | −0.170577 | −0.0852885 | − | 0.996356i | \(-0.527181\pi\) | ||||
−0.0852885 | + | 0.996356i | \(0.527181\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −851.353 | −2.11254 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 572.518 | 1.40668 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.3649i | 0.0375671i | 0.999824 | + | 0.0187835i | \(0.00597934\pi\) | ||||
−0.999824 | + | 0.0187835i | \(0.994021\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −178.524 | −0.430179 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 366.079i | − 0.873696i | −0.899535 | − | 0.436848i | \(-0.856095\pi\) | ||||
0.899535 | − | 0.436848i | \(-0.143905\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 607.135 | 1.44213 | 0.721063 | − | 0.692870i | \(-0.243654\pi\) | ||||
0.721063 | + | 0.692870i | \(0.243654\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 21.6186i | 0.0508674i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 586.353 | 1.36045 | 0.680224 | − | 0.733004i | \(-0.261882\pi\) | ||||
0.680224 | + | 0.733004i | \(0.261882\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 518.769i | − 1.19808i | −0.800719 | − | 0.599040i | \(-0.795549\pi\) | ||||
0.800719 | − | 0.599040i | \(-0.204451\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 203.150i | − 0.464875i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 221.524i | 0.504610i | 0.967648 | + | 0.252305i | \(0.0811886\pi\) | ||||
−0.967648 | + | 0.252305i | \(0.918811\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 226.415 | 0.511095 | 0.255548 | − | 0.966796i | \(-0.417744\pi\) | ||||
0.255548 | + | 0.966796i | \(0.417744\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −194.337 | −0.436713 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 378.422 | 0.842810 | 0.421405 | − | 0.906873i | \(-0.361537\pi\) | ||||
0.421405 | + | 0.906873i | \(0.361537\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 288.984i | 0.640763i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 438.153 | 0.958760 | 0.479380 | − | 0.877607i | \(-0.340862\pi\) | ||||
0.479380 | + | 0.877607i | \(0.340862\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 46.3981i | 0.100647i | 0.998733 | + | 0.0503234i | \(0.0160252\pi\) | ||||
−0.998733 | + | 0.0503234i | \(0.983975\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 367.455 | 0.793639 | 0.396820 | − | 0.917897i | \(-0.370114\pi\) | ||||
0.396820 | + | 0.917897i | \(0.370114\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 529.465i | 1.13376i | 0.823801 | + | 0.566879i | \(0.191849\pi\) | ||||
−0.823801 | + | 0.566879i | \(0.808151\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.01516 | 0.0169454 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 28.5334i | − 0.0600702i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 289.761i | − 0.604928i | −0.953161 | − | 0.302464i | \(-0.902191\pi\) | ||||
0.953161 | − | 0.302464i | \(-0.0978093\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1400.43i | 2.91150i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 87.2445 | 0.179886 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 439.636 | 0.902744 | 0.451372 | − | 0.892336i | \(-0.350935\pi\) | ||||
0.451372 | + | 0.892336i | \(0.350935\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 320.561 | 0.652874 | 0.326437 | − | 0.945219i | \(-0.394152\pi\) | ||||
0.326437 | + | 0.945219i | \(0.394152\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 221.340i | 0.448965i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 771.973 | 1.54704 | 0.773520 | − | 0.633772i | \(-0.218494\pi\) | ||||
0.773520 | + | 0.633772i | \(0.218494\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 101.632i | 0.202052i | 0.994884 | + | 0.101026i | \(0.0322126\pi\) | ||||
−0.994884 | + | 0.101026i | \(0.967787\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −642.675 | −1.27262 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 605.407i | 1.18941i | 0.803946 | + | 0.594703i | \(0.202730\pi\) | ||||
−0.803946 | + | 0.594703i | \(0.797270\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −48.0503 | −0.0933016 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 735.907i | − 1.42342i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 383.293i | − 0.735688i | −0.929888 | − | 0.367844i | \(-0.880096\pi\) | ||||
0.929888 | − | 0.367844i | \(-0.119904\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 448.095i | − 0.856777i | −0.903595 | − | 0.428389i | \(-0.859081\pi\) | ||||
0.903595 | − | 0.428389i | \(-0.140919\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 222.247 | 0.421721 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 258.119 | 0.487937 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −706.882 | −1.32623 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 935.282i | − 1.74819i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −271.258 | −0.501400 | −0.250700 | − | 0.968065i | \(-0.580661\pi\) | ||||
−0.250700 | + | 0.968065i | \(0.580661\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 862.435i | − 1.58245i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −590.544 | −1.07961 | −0.539803 | − | 0.841791i | \(-0.681501\pi\) | ||||
−0.539803 | + | 0.841791i | \(0.681501\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 292.135i | − 0.530191i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −188.295 | −0.338051 | −0.169026 | − | 0.985612i | \(-0.554062\pi\) | ||||
−0.169026 | + | 0.985612i | \(0.554062\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.6058i | 0.0350730i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 204.157i | 0.362623i | 0.983426 | + | 0.181312i | \(0.0580342\pi\) | ||||
−0.983426 | + | 0.181312i | \(0.941966\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 438.129i | 0.775449i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 660.913 | 1.16153 | 0.580767 | − | 0.814070i | \(-0.302753\pi\) | ||||
0.580767 | + | 0.814070i | \(0.302753\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −533.978 | −0.935162 | −0.467581 | − | 0.883950i | \(-0.654874\pi\) | ||||
−0.467581 | + | 0.883950i | \(0.654874\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 110.554 | 0.192268 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 53.4337i | 0.0926062i | 0.998927 | + | 0.0463031i | \(0.0147440\pi\) | ||||
−0.998927 | + | 0.0463031i | \(0.985256\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 383.145 | 0.657196 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 413.063i | 0.703684i | 0.936059 | + | 0.351842i | \(0.114445\pi\) | ||||
−0.936059 | + | 0.351842i | \(0.885555\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −293.333 | −0.498018 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 122.452i | − 0.206496i | −0.994656 | − | 0.103248i | \(-0.967076\pi\) | ||||
0.994656 | − | 0.103248i | \(-0.0329235\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 645.136 | 1.07702 | 0.538511 | − | 0.842619i | \(-0.318987\pi\) | ||||
0.538511 | + | 0.842619i | \(0.318987\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 683.488i | 1.13725i | 0.822596 | + | 0.568626i | \(0.192525\pi\) | ||||
−0.822596 | + | 0.568626i | \(0.807475\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 253.836i | − 0.419564i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 257.253i | − 0.423811i | −0.977290 | − | 0.211905i | \(-0.932033\pi\) | ||||
0.977290 | − | 0.211905i | \(-0.0679669\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1800.10 | 2.94615 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 885.713 | 1.44488 | 0.722441 | − | 0.691433i | \(-0.243020\pi\) | ||||
0.722441 | + | 0.691433i | \(0.243020\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −46.0724 | −0.0746717 | −0.0373358 | − | 0.999303i | \(-0.511887\pi\) | ||||
−0.0373358 | + | 0.999303i | \(0.511887\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 1096.33i | − 1.77112i | −0.464522 | − | 0.885562i | \(-0.653774\pi\) | ||||
0.464522 | − | 0.885562i | \(-0.346226\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −707.986 | −1.13278 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 365.585i | − 0.581217i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 606.319 | 0.960886 | 0.480443 | − | 0.877026i | \(-0.340476\pi\) | ||||
0.480443 | + | 0.877026i | \(0.340476\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 630.343i | 0.992666i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −939.184 | −1.46519 | −0.732593 | − | 0.680667i | \(-0.761690\pi\) | ||||
−0.732593 | + | 0.680667i | \(0.761690\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 992.960i | 1.54426i | 0.635464 | + | 0.772131i | \(0.280809\pi\) | ||||
−0.635464 | + | 0.772131i | \(0.719191\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 265.184i | 0.409867i | 0.978776 | + | 0.204933i | \(0.0656978\pi\) | ||||
−0.978776 | + | 0.204933i | \(0.934302\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 547.241i | − 0.843206i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1134.14 | 1.73682 | 0.868409 | − | 0.495849i | \(-0.165143\pi\) | ||||
0.868409 | + | 0.495849i | \(0.165143\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1313.44 | 2.00525 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 924.147 | 1.40235 | 0.701174 | − | 0.712990i | \(-0.252660\pi\) | ||||
0.701174 | + | 0.712990i | \(0.252660\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 234.367i | − 0.354564i | −0.984160 | − | 0.177282i | \(-0.943269\pi\) | ||||
0.984160 | − | 0.177282i | \(-0.0567305\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1131.90 | 1.69700 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 275.003i | − 0.409840i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −465.127 | −0.691125 | −0.345563 | − | 0.938396i | \(-0.612312\pi\) | ||||
−0.345563 | + | 0.938396i | \(0.612312\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1295.93i | 1.91422i | 0.289724 | + | 0.957110i | \(0.406437\pi\) | ||||
−0.289724 | + | 0.957110i | \(0.593563\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.2612 | −0.0238085 | −0.0119042 | − | 0.999929i | \(-0.503789\pi\) | ||||
−0.0119042 | + | 0.999929i | \(0.503789\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 1320.23i | − 1.92734i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 937.209i | 1.36025i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 68.5364i | 0.0991843i | 0.998770 | + | 0.0495922i | \(0.0157922\pi\) | ||||
−0.998770 | + | 0.0495922i | \(0.984208\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −92.1912 | −0.132649 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 184.533 | 0.264753 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −923.360 | −1.31720 | −0.658602 | − | 0.752491i | \(-0.728852\pi\) | ||||
−0.658602 | + | 0.752491i | \(0.728852\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 482.518i | 0.686369i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −912.863 | −1.28754 | −0.643768 | − | 0.765221i | \(-0.722630\pi\) | ||||
−0.643768 | + | 0.765221i | \(0.722630\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 1136.54i | − 1.59402i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −971.345 | −1.35852 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 545.020i | 0.758025i | 0.925391 | + | 0.379013i | \(0.123736\pi\) | ||||
−0.925391 | + | 0.379013i | \(0.876264\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 158.980 | 0.219283 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 750.292i | − 1.03204i | −0.856577 | − | 0.516019i | \(-0.827413\pi\) | ||||
0.856577 | − | 0.516019i | \(-0.172587\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 5.11813i | − 0.00700155i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 926.599i | 1.26412i | 0.774920 | + | 0.632059i | \(0.217790\pi\) | ||||
−0.774920 | + | 0.632059i | \(0.782210\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −410.112 | −0.556461 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 488.147 | 0.660551 | 0.330275 | − | 0.943885i | \(-0.392858\pi\) | ||||
0.330275 | + | 0.943885i | \(0.392858\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1091.72 | 1.46935 | 0.734674 | − | 0.678421i | \(-0.237335\pi\) | ||||
0.734674 | + | 0.678421i | \(0.237335\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 722.173i | − 0.969360i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −480.443 | −0.639738 | −0.319869 | − | 0.947462i | \(-0.603639\pi\) | ||||
−0.319869 | + | 0.947462i | \(0.603639\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1070.60i | 1.41801i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 941.400 | 1.24359 | 0.621796 | − | 0.783179i | \(-0.286403\pi\) | ||||
0.621796 | + | 0.783179i | \(0.286403\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 1192.34i | − 1.56681i | −0.621509 | − | 0.783407i | \(-0.713480\pi\) | ||||
0.621509 | − | 0.783407i | \(-0.286520\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1338.60 | 1.74524 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 908.294i | 1.18114i | 0.806988 | + | 0.590568i | \(0.201096\pi\) | ||||
−0.806988 | + | 0.590568i | \(0.798904\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1189.38i | 1.53866i | 0.638854 | + | 0.769328i | \(0.279409\pi\) | ||||
−0.638854 | + | 0.769328i | \(0.720591\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 159.632i | − 0.205976i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −243.556 | −0.312652 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −128.595 | −0.164654 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 414.334 | 0.527814 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1057.12i | − 1.34323i | −0.740902 | − | 0.671613i | \(-0.765602\pi\) | ||||
0.740902 | − | 0.671613i | \(-0.234398\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 672.682 | 0.848275 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1037.94i | 1.30231i | 0.758945 | + | 0.651154i | \(0.225715\pi\) | ||||
−0.758945 | + | 0.651154i | \(0.774285\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −469.919 | −0.588133 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1205.38i | 1.50109i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1087.36 | −1.34408 | −0.672041 | − | 0.740514i | \(-0.734582\pi\) | ||||
−0.672041 | + | 0.740514i | \(0.734582\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 926.995i | − 1.14303i | −0.820593 | − | 0.571514i | \(-0.806356\pi\) | ||||
0.820593 | − | 0.571514i | \(-0.193644\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 1239.36i | − 1.52068i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.75517i | 0.00826826i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 430.300 | 0.524117 | 0.262058 | − | 0.965052i | \(-0.415599\pi\) | ||||
0.262058 | + | 0.965052i | \(0.415599\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1044.74 | −1.26942 | −0.634712 | − | 0.772749i | \(-0.718881\pi\) | ||||
−0.634712 | + | 0.772749i | \(0.718881\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 610.313 | 0.737984 | 0.368992 | − | 0.929433i | \(-0.379703\pi\) | ||||
0.368992 | + | 0.929433i | \(0.379703\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1413.90i | 1.70555i | 0.522279 | + | 0.852775i | \(0.325082\pi\) | ||||
−0.522279 | + | 0.852775i | \(0.674918\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1233.18 | −1.47687 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46.3303i | 0.0552209i | 0.999619 | + | 0.0276105i | \(0.00878980\pi\) | ||||
−0.999619 | + | 0.0276105i | \(0.991210\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 786.696 | 0.935430 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1466.84i | − 1.73591i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1869.54 | −2.19688 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 773.111i | − 0.906343i | −0.891423 | − | 0.453172i | \(-0.850292\pi\) | ||||
0.891423 | − | 0.453172i | \(-0.149708\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 438.159i | 0.511271i | 0.966773 | + | 0.255636i | \(0.0822847\pi\) | ||||
−0.966773 | + | 0.255636i | \(0.917715\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 72.3419i | − 0.0842164i | −0.999113 | − | 0.0421082i | \(-0.986593\pi\) | ||||
0.999113 | − | 0.0421082i | \(-0.0134074\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −426.495 | −0.494200 | −0.247100 | − | 0.968990i | \(-0.579478\pi\) | ||||
−0.247100 | + | 0.968990i | \(0.579478\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 605.064 | 0.699496 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1050.82 | −1.20922 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1003.17i | − 1.15175i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 416.485 | 0.474898 | 0.237449 | − | 0.971400i | \(-0.423689\pi\) | ||||
0.237449 | + | 0.971400i | \(0.423689\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 1249.01i | − 1.41771i | −0.705353 | − | 0.708857i | \(-0.749211\pi\) | ||||
0.705353 | − | 0.708857i | \(-0.250789\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 81.5906 | 0.0924016 | 0.0462008 | − | 0.998932i | \(-0.485289\pi\) | ||||
0.0462008 | + | 0.998932i | \(0.485289\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 917.730i | − 1.03464i | −0.855791 | − | 0.517322i | \(-0.826929\pi\) | ||||
0.855791 | − | 0.517322i | \(-0.173071\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 620.222 | 0.694537 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 567.520i | − 0.634100i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1634.37i | − 1.81798i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 244.660i | − 0.271543i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 82.1380 | 0.0907602 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1451.40 | −1.60022 | −0.800110 | − | 0.599853i | \(-0.795226\pi\) | ||||
−0.800110 | + | 0.599853i | \(0.795226\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 562.064 | 0.616975 | 0.308487 | − | 0.951228i | \(-0.400177\pi\) | ||||
0.308487 | + | 0.951228i | \(0.400177\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 285.114i | 0.312282i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 538.158 | 0.585591 | 0.292795 | − | 0.956175i | \(-0.405414\pi\) | ||||
0.292795 | + | 0.956175i | \(0.405414\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 314.556i | − 0.340797i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −262.586 | −0.283876 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 827.080i | 0.890291i | 0.895458 | + | 0.445145i | \(0.146848\pi\) | ||||
−0.895458 | + | 0.445145i | \(0.853152\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 253.571 | 0.271199 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1501.10i | 1.60203i | 0.598644 | + | 0.801016i | \(0.295707\pi\) | ||||
−0.598644 | + | 0.801016i | \(0.704293\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 766.672i | − 0.814742i | −0.913263 | − | 0.407371i | \(-0.866446\pi\) | ||||
0.913263 | − | 0.407371i | \(-0.133554\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 943.671i | − 1.00071i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1362.23 | −1.43847 | −0.719237 | − | 0.694765i | \(-0.755508\pi\) | ||||
−0.719237 | + | 0.694765i | \(0.755508\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2948.47 | −3.10692 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1431.37 | −1.50196 | −0.750980 | − | 0.660325i | \(-0.770419\pi\) | ||||
−0.750980 | + | 0.660325i | \(0.770419\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1647.17i | 1.72479i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −680.067 | −0.707666 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 9.90391i | − 0.0102631i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −426.276 | −0.440823 | −0.220411 | − | 0.975407i | \(-0.570740\pi\) | ||||
−0.220411 | + | 0.975407i | \(0.570740\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1728.41i | − 1.78003i | −0.455934 | − | 0.890013i | \(-0.650695\pi\) | ||||
0.455934 | − | 0.890013i | \(-0.349305\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 712.320 | 0.729089 | 0.364545 | − | 0.931186i | \(-0.381225\pi\) | ||||
0.364545 | + | 0.931186i | \(0.381225\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 310.368i | 0.317025i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1042.56i | 1.06059i | 0.847812 | + | 0.530297i | \(0.177920\pi\) | ||||
−0.847812 | + | 0.530297i | \(0.822080\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1373.61i | 1.39452i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −26.1733 | −0.0264644 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1397.41 | 1.41010 | 0.705052 | − | 0.709156i | \(-0.250924\pi\) | ||||
0.705052 | + | 0.709156i | \(0.250924\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −197.155 | −0.198146 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 717.962i | 0.720122i | 0.932929 | + | 0.360061i | \(0.117244\pi\) | ||||
−0.932929 | + | 0.360061i | \(0.882756\pi\) | |||||||
\(998\) | 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 | 1764.3.d.h.685.7 | 8 | ||
3.2 | odd | 2 | 588.3.d.c.97.5 | yes | 8 | ||
7.2 | even | 3 | 1764.3.z.m.325.4 | 8 | |||
7.3 | odd | 6 | 1764.3.z.m.901.4 | 8 | |||
7.4 | even | 3 | 1764.3.z.l.901.1 | 8 | |||
7.5 | odd | 6 | 1764.3.z.l.325.1 | 8 | |||
7.6 | odd | 2 | inner | 1764.3.d.h.685.2 | 8 | ||
12.11 | even | 2 | 2352.3.f.j.97.1 | 8 | |||
21.2 | odd | 6 | 588.3.m.e.325.1 | 8 | |||
21.5 | even | 6 | 588.3.m.f.325.4 | 8 | |||
21.11 | odd | 6 | 588.3.m.f.313.4 | 8 | |||
21.17 | even | 6 | 588.3.m.e.313.1 | 8 | |||
21.20 | even | 2 | 588.3.d.c.97.4 | ✓ | 8 | ||
84.83 | odd | 2 | 2352.3.f.j.97.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.3.d.c.97.4 | ✓ | 8 | 21.20 | even | 2 | ||
588.3.d.c.97.5 | yes | 8 | 3.2 | odd | 2 | ||
588.3.m.e.313.1 | 8 | 21.17 | even | 6 | |||
588.3.m.e.325.1 | 8 | 21.2 | odd | 6 | |||
588.3.m.f.313.4 | 8 | 21.11 | odd | 6 | |||
588.3.m.f.325.4 | 8 | 21.5 | even | 6 | |||
1764.3.d.h.685.2 | 8 | 7.6 | odd | 2 | inner | ||
1764.3.d.h.685.7 | 8 | 1.1 | even | 1 | trivial | ||
1764.3.z.l.325.1 | 8 | 7.5 | odd | 6 | |||
1764.3.z.l.901.1 | 8 | 7.4 | even | 3 | |||
1764.3.z.m.325.4 | 8 | 7.2 | even | 3 | |||
1764.3.z.m.901.4 | 8 | 7.3 | odd | 6 | |||
2352.3.f.j.97.1 | 8 | 12.11 | even | 2 | |||
2352.3.f.j.97.8 | 8 | 84.83 | odd | 2 |