Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(703,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.703");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.g (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: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.22581504.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{14}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 864) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 703.4 | ||
Root | \(-1.27597 - 0.609843i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.703 |
Dual form | 1728.3.g.k.703.3 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | −1.76102 | −0.352204 | −0.176102 | − | 0.984372i | \(-0.556349\pi\) | ||||
−0.176102 | + | 0.984372i | \(0.556349\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.0363i | 1.71947i | 0.510738 | + | 0.859736i | \(0.329372\pi\) | ||||
−0.510738 | + | 0.859736i | \(0.670628\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 13.3544i | − 1.21404i | −0.794687 | − | 0.607020i | \(-0.792365\pi\) | ||||
0.794687 | − | 0.607020i | \(-0.207635\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.15828 | −0.627560 | −0.313780 | − | 0.949496i | \(-0.601595\pi\) | ||||
−0.313780 | + | 0.949496i | \(0.601595\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.15828 | −0.244605 | −0.122302 | − | 0.992493i | \(-0.539028\pi\) | ||||
−0.122302 | + | 0.992493i | \(0.539028\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 8.87027i | − 0.466856i | −0.972374 | − | 0.233428i | \(-0.925006\pi\) | ||||
0.972374 | − | 0.233428i | \(-0.0749944\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 33.5947i | − 1.46064i | −0.683107 | − | 0.730319i | \(-0.739372\pi\) | ||||
0.683107 | − | 0.730319i | \(-0.260628\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −21.8988 | −0.875953 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 36.4649 | 1.25741 | 0.628706 | − | 0.777643i | \(-0.283585\pi\) | ||||
0.628706 | + | 0.777643i | \(0.283585\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.590023i | 0.0190330i | 0.999955 | + | 0.00951650i | \(0.00302924\pi\) | ||||
−0.999955 | + | 0.00951650i | \(0.996971\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 21.1962i | − 0.605604i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 69.8156 | 1.88691 | 0.943455 | − | 0.331502i | \(-0.107555\pi\) | ||||
0.943455 | + | 0.331502i | \(0.107555\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 57.5661 | 1.40405 | 0.702025 | − | 0.712152i | \(-0.252279\pi\) | ||||
0.702025 | + | 0.712152i | \(0.252279\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 23.5847i | − 0.548482i | −0.961661 | − | 0.274241i | \(-0.911573\pi\) | ||||
0.961661 | − | 0.274241i | \(-0.0884267\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 24.4804i | 0.520861i | 0.965493 | + | 0.260430i | \(0.0838644\pi\) | ||||
−0.965493 | + | 0.260430i | \(0.916136\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −95.8727 | −1.95659 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −29.9292 | −0.564702 | −0.282351 | − | 0.959311i | \(-0.591114\pi\) | ||||
−0.282351 | + | 0.959311i | \(0.591114\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 23.5174i | 0.427589i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 55.0130i | 0.932424i | 0.884673 | + | 0.466212i | \(0.154382\pi\) | ||||
−0.884673 | + | 0.466212i | \(0.845618\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.1645 | 0.183025 | 0.0915125 | − | 0.995804i | \(-0.470830\pi\) | ||||
0.0915125 | + | 0.995804i | \(0.470830\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.3669 | 0.221029 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 99.6989i | − 1.48804i | −0.668155 | − | 0.744022i | \(-0.732916\pi\) | ||||
0.668155 | − | 0.744022i | \(-0.267084\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 71.2023i | 1.00285i | 0.865201 | + | 0.501425i | \(0.167191\pi\) | ||||
−0.865201 | + | 0.501425i | \(0.832809\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 36.0508 | 0.493847 | 0.246924 | − | 0.969035i | \(-0.420580\pi\) | ||||
0.246924 | + | 0.969035i | \(0.420580\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 160.738 | 2.08751 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 108.284i | 1.37068i | 0.728223 | + | 0.685340i | \(0.240346\pi\) | ||||
−0.728223 | + | 0.685340i | \(0.759654\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 100.556i | 1.21152i | 0.795648 | + | 0.605760i | \(0.207131\pi\) | ||||
−0.795648 | + | 0.605760i | \(0.792869\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.32280 | 0.0861506 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 159.616 | 1.79344 | 0.896721 | − | 0.442596i | \(-0.145942\pi\) | ||||
0.896721 | + | 0.442596i | \(0.145942\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 98.1956i | − 1.07907i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 15.6207i | 0.164428i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −24.0242 | −0.247673 | −0.123836 | − | 0.992303i | \(-0.539520\pi\) | ||||
−0.123836 | + | 0.992303i | \(0.539520\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 22.5078 | 0.222850 | 0.111425 | − | 0.993773i | \(-0.464459\pi\) | ||||
0.111425 | + | 0.993773i | \(0.464459\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 135.290i | 1.31350i | 0.754109 | + | 0.656750i | \(0.228069\pi\) | ||||
−0.754109 | + | 0.656750i | \(0.771931\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 29.5388i | − 0.276063i | −0.990428 | − | 0.138032i | \(-0.955922\pi\) | ||||
0.990428 | − | 0.138032i | \(-0.0440776\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 130.246 | 1.19492 | 0.597460 | − | 0.801898i | \(-0.296176\pi\) | ||||
0.597460 | + | 0.801898i | \(0.296176\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −134.421 | −1.18957 | −0.594785 | − | 0.803885i | \(-0.702763\pi\) | ||||
−0.594785 | + | 0.803885i | \(0.702763\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 59.1608i | 0.514442i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 50.0503i | − 0.420591i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −57.3408 | −0.473891 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 82.5896 | 0.660717 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 40.3479i | − 0.317700i | −0.987303 | − | 0.158850i | \(-0.949221\pi\) | ||||
0.987303 | − | 0.158850i | \(-0.0507786\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 136.966i | − 1.04555i | −0.852472 | − | 0.522773i | \(-0.824898\pi\) | ||||
0.852472 | − | 0.522773i | \(-0.175102\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 106.765 | 0.802747 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 245.969 | 1.79539 | 0.897697 | − | 0.440614i | \(-0.145239\pi\) | ||||
0.897697 | + | 0.440614i | \(0.145239\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 157.526i | 1.13328i | 0.823966 | + | 0.566639i | \(0.191757\pi\) | ||||
−0.823966 | + | 0.566639i | \(0.808243\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 108.949i | 0.761882i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −64.2154 | −0.442865 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 184.731 | 1.23981 | 0.619904 | − | 0.784678i | \(-0.287172\pi\) | ||||
0.619904 | + | 0.784678i | \(0.287172\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 9.64832i | − 0.0638961i | −0.999490 | − | 0.0319481i | \(-0.989829\pi\) | ||||
0.999490 | − | 0.0319481i | \(-0.0101711\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 1.03904i | − 0.00670349i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 36.3166 | 0.231316 | 0.115658 | − | 0.993289i | \(-0.463102\pi\) | ||||
0.115658 | + | 0.993289i | \(0.463102\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 404.356 | 2.51153 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 126.095i | − 0.773588i | −0.922166 | − | 0.386794i | \(-0.873582\pi\) | ||||
0.922166 | − | 0.386794i | \(-0.126418\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 302.797i | − 1.81316i | −0.422039 | − | 0.906578i | \(-0.638685\pi\) | ||||
0.422039 | − | 0.906578i | \(-0.361315\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −102.443 | −0.606169 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 204.895 | 1.18436 | 0.592181 | − | 0.805805i | \(-0.298267\pi\) | ||||
0.592181 | + | 0.805805i | \(0.298267\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 263.581i | − 1.50618i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 320.815i | − 1.79226i | −0.443789 | − | 0.896131i | \(-0.646366\pi\) | ||||
0.443789 | − | 0.896131i | \(-0.353634\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −285.364 | −1.57660 | −0.788299 | − | 0.615292i | \(-0.789038\pi\) | ||||
−0.788299 | + | 0.615292i | \(0.789038\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −122.947 | −0.664576 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 55.5314i | 0.296960i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 132.634i | − 0.694417i | −0.937788 | − | 0.347208i | \(-0.887130\pi\) | ||||
0.937788 | − | 0.347208i | \(-0.112870\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 366.794 | 1.90049 | 0.950245 | − | 0.311504i | \(-0.100833\pi\) | ||||
0.950245 | + | 0.311504i | \(0.100833\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.3110 | −0.0726445 | −0.0363223 | − | 0.999340i | \(-0.511564\pi\) | ||||
−0.0363223 | + | 0.999340i | \(0.511564\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 214.542i | − 1.07810i | −0.842274 | − | 0.539049i | \(-0.818784\pi\) | ||||
0.842274 | − | 0.539049i | \(-0.181216\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 438.903i | 2.16208i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −101.375 | −0.494512 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −118.457 | −0.566782 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 223.579i | − 1.05962i | −0.848118 | − | 0.529808i | \(-0.822264\pi\) | ||||
0.848118 | − | 0.529808i | \(-0.177736\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 41.5331i | 0.193177i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.10170 | −0.0327267 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 33.9244 | 0.153504 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 287.564i | 1.28952i | 0.764384 | + | 0.644761i | \(0.223043\pi\) | ||||
−0.764384 | + | 0.644761i | \(0.776957\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 167.933i | − 0.739793i | −0.929073 | − | 0.369896i | \(-0.879393\pi\) | ||||
0.929073 | − | 0.369896i | \(-0.120607\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −28.4693 | −0.124320 | −0.0621601 | − | 0.998066i | \(-0.519799\pi\) | ||||
−0.0621601 | + | 0.998066i | \(0.519799\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 158.334 | 0.679545 | 0.339773 | − | 0.940508i | \(-0.389650\pi\) | ||||
0.339773 | + | 0.940508i | \(0.389650\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 43.1105i | − 0.183449i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.0236i | 0.121438i | 0.998155 | + | 0.0607188i | \(0.0193393\pi\) | ||||
−0.998155 | + | 0.0607188i | \(0.980661\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 301.579 | 1.25137 | 0.625683 | − | 0.780078i | \(-0.284820\pi\) | ||||
0.625683 | + | 0.780078i | \(0.284820\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 168.834 | 0.689117 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 72.3661i | 0.292980i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 111.785i | − 0.445359i | −0.974892 | − | 0.222680i | \(-0.928520\pi\) | ||||
0.974892 | − | 0.222680i | \(-0.0714804\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −448.637 | −1.77327 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 462.857 | 1.80100 | 0.900500 | − | 0.434856i | \(-0.143201\pi\) | ||||
0.900500 | + | 0.434856i | \(0.143201\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 840.323i | 3.24449i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 216.912i | 0.824759i | 0.911012 | + | 0.412380i | \(0.135302\pi\) | ||||
−0.911012 | + | 0.412380i | \(0.864698\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 52.7059 | 0.198890 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −431.963 | −1.60581 | −0.802906 | − | 0.596106i | \(-0.796714\pi\) | ||||
−0.802906 | + | 0.596106i | \(0.796714\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 278.164i | − 1.02644i | −0.858258 | − | 0.513218i | \(-0.828453\pi\) | ||||
0.858258 | − | 0.513218i | \(-0.171547\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 292.446i | 1.06344i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −271.579 | −0.980430 | −0.490215 | − | 0.871602i | \(-0.663082\pi\) | ||||
−0.490215 | + | 0.871602i | \(0.663082\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −343.222 | −1.22143 | −0.610715 | − | 0.791850i | \(-0.709118\pi\) | ||||
−0.610715 | + | 0.791850i | \(0.709118\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 242.067i | 0.855361i | 0.903930 | + | 0.427680i | \(0.140669\pi\) | ||||
−0.903930 | + | 0.427680i | \(0.859331\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 692.883i | 2.41423i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −271.709 | −0.940169 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 471.585 | 1.60950 | 0.804752 | − | 0.593611i | \(-0.202298\pi\) | ||||
0.804752 | + | 0.593611i | \(0.202298\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 96.8789i | − 0.328403i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 274.075i | 0.916637i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 283.873 | 0.943100 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −19.6609 | −0.0644620 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 115.907i | 0.377549i | 0.982021 | + | 0.188774i | \(0.0604515\pi\) | ||||
−0.982021 | + | 0.188774i | \(0.939549\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 394.948i | − 1.26993i | −0.772541 | − | 0.634964i | \(-0.781015\pi\) | ||||
0.772541 | − | 0.634964i | \(-0.218985\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 298.099 | 0.952394 | 0.476197 | − | 0.879339i | \(-0.342015\pi\) | ||||
0.476197 | + | 0.879339i | \(0.342015\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.5754 | 0.0491337 | 0.0245669 | − | 0.999698i | \(-0.492179\pi\) | ||||
0.0245669 | + | 0.999698i | \(0.492179\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 486.968i | − 1.52655i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 36.8850i | 0.114195i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 178.657 | 0.549713 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −294.654 | −0.895606 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 132.849i | 0.401355i | 0.979657 | + | 0.200678i | \(0.0643144\pi\) | ||||
−0.979657 | + | 0.200678i | \(0.935686\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 175.572i | 0.524094i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 64.2930 | 0.190781 | 0.0953903 | − | 0.995440i | \(-0.469590\pi\) | ||||
0.0953903 | + | 0.995440i | \(0.469590\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.87942 | 0.0231068 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 564.175i | − 1.64482i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 184.163i | 0.530728i | 0.964148 | + | 0.265364i | \(0.0854922\pi\) | ||||
−0.964148 | + | 0.265364i | \(0.914508\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 107.326 | 0.307525 | 0.153763 | − | 0.988108i | \(-0.450861\pi\) | ||||
0.153763 | + | 0.988108i | \(0.450861\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 444.637 | 1.25960 | 0.629798 | − | 0.776759i | \(-0.283138\pi\) | ||||
0.629798 | + | 0.776759i | \(0.283138\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 125.389i | − 0.353207i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 275.528i | − 0.767488i | −0.923440 | − | 0.383744i | \(-0.874635\pi\) | ||||
0.923440 | − | 0.383744i | \(-0.125365\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 282.318 | 0.782045 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −63.4862 | −0.173935 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 594.925i | 1.62105i | 0.585705 | + | 0.810525i | \(0.300818\pi\) | ||||
−0.585705 | + | 0.810525i | \(0.699182\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 360.237i | − 0.970990i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −478.902 | −1.28392 | −0.641960 | − | 0.766738i | \(-0.721878\pi\) | ||||
−0.641960 | + | 0.766738i | \(0.721878\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −297.491 | −0.789101 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 425.301i | − 1.12217i | −0.827760 | − | 0.561083i | \(-0.810385\pi\) | ||||
0.827760 | − | 0.561083i | \(-0.189615\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 386.549i | 1.00927i | 0.863334 | + | 0.504634i | \(0.168372\pi\) | ||||
−0.863334 | + | 0.504634i | \(0.831628\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −283.063 | −0.735227 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −186.277 | −0.478861 | −0.239430 | − | 0.970914i | \(-0.576961\pi\) | ||||
−0.239430 | + | 0.970914i | \(0.576961\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 139.696i | 0.357279i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 190.689i | − 0.482758i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −221.030 | −0.556750 | −0.278375 | − | 0.960472i | \(-0.589796\pi\) | ||||
−0.278375 | + | 0.960472i | \(0.589796\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −712.734 | −1.77739 | −0.888695 | − | 0.458498i | \(-0.848388\pi\) | ||||
−0.888695 | + | 0.458498i | \(0.848388\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 4.81357i | − 0.0119443i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 932.348i | − 2.29078i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 198.746 | 0.485933 | 0.242966 | − | 0.970035i | \(-0.421880\pi\) | ||||
0.242966 | + | 0.970035i | \(0.421880\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −662.154 | −1.60328 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 177.081i | − 0.426701i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 573.831i | − 1.36953i | −0.728766 | − | 0.684763i | \(-0.759906\pi\) | ||||
0.728766 | − | 0.684763i | \(-0.240094\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 83.4289 | 0.198168 | 0.0990842 | − | 0.995079i | \(-0.468409\pi\) | ||||
0.0990842 | + | 0.995079i | \(0.468409\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 91.0614 | 0.214262 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 134.380i | 0.314706i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 328.762i | − 0.762789i | −0.924412 | − | 0.381394i | \(-0.875444\pi\) | ||||
0.924412 | − | 0.381394i | \(-0.124556\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 445.063 | 1.02786 | 0.513930 | − | 0.857832i | \(-0.328189\pi\) | ||||
0.513930 | + | 0.857832i | \(0.328189\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −297.994 | −0.681908 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 459.120i | 1.04583i | 0.852385 | + | 0.522915i | \(0.175156\pi\) | ||||
−0.852385 | + | 0.522915i | \(0.824844\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 463.025i | 1.04520i | 0.852577 | + | 0.522602i | \(0.175039\pi\) | ||||
−0.852577 | + | 0.522602i | \(0.824961\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −281.087 | −0.631657 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 271.385 | 0.604420 | 0.302210 | − | 0.953241i | \(-0.402276\pi\) | ||||
0.302210 | + | 0.953241i | \(0.402276\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 768.762i | − 1.70457i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 172.924i | 0.380053i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 92.0749 | 0.201477 | 0.100738 | − | 0.994913i | \(-0.467879\pi\) | ||||
0.100738 | + | 0.994913i | \(0.467879\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −551.486 | −1.19628 | −0.598141 | − | 0.801391i | \(-0.704094\pi\) | ||||
−0.598141 | + | 0.801391i | \(0.704094\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 78.7518i | 0.170090i | 0.996377 | + | 0.0850452i | \(0.0271035\pi\) | ||||
−0.996377 | + | 0.0850452i | \(0.972897\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 637.095i | − 1.36423i | −0.731245 | − | 0.682114i | \(-0.761061\pi\) | ||||
0.731245 | − | 0.682114i | \(-0.238939\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1200.01 | 2.55865 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −314.961 | −0.665879 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 194.248i | 0.408944i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 201.640i | 0.420961i | 0.977598 | + | 0.210480i | \(0.0675028\pi\) | ||||
−0.977598 | + | 0.210480i | \(0.932497\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −569.575 | −1.18415 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 42.3071 | 0.0872312 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 164.086i | − 0.336932i | −0.985707 | − | 0.168466i | \(-0.946119\pi\) | ||||
0.985707 | − | 0.168466i | \(-0.0538814\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 30.3778i | − 0.0618692i | −0.999521 | − | 0.0309346i | \(-0.990152\pi\) | ||||
0.999521 | − | 0.0309346i | \(-0.00984836\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −151.631 | −0.307569 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −857.013 | −1.72437 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 37.8381i | − 0.0758279i | −0.999281 | − | 0.0379140i | \(-0.987929\pi\) | ||||
0.999281 | − | 0.0379140i | \(-0.0120713\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 252.844i | − 0.502672i | −0.967900 | − | 0.251336i | \(-0.919130\pi\) | ||||
0.967900 | − | 0.251336i | \(-0.0808699\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −39.6366 | −0.0784884 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 38.9887 | 0.0765986 | 0.0382993 | − | 0.999266i | \(-0.487806\pi\) | ||||
0.0382993 | + | 0.999266i | \(0.487806\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 433.919i | 0.849157i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 238.249i | − 0.462619i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 326.922 | 0.632345 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −254.943 | −0.489334 | −0.244667 | − | 0.969607i | \(-0.578679\pi\) | ||||
−0.244667 | + | 0.969607i | \(0.578679\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 193.808i | − 0.370571i | −0.982685 | − | 0.185285i | \(-0.940679\pi\) | ||||
0.982685 | − | 0.185285i | \(-0.0593209\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 2.45348i | − 0.00465556i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −599.601 | −1.13346 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −469.640 | −0.881126 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 52.0183i | 0.0972305i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1280.33i | 2.37537i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 519.448 | 0.960162 | 0.480081 | − | 0.877224i | \(-0.340607\pi\) | ||||
0.480081 | + | 0.877224i | \(0.340607\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −229.366 | −0.420855 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 859.658i | 1.57159i | 0.618490 | + | 0.785793i | \(0.287745\pi\) | ||||
−0.618490 | + | 0.785793i | \(0.712255\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 323.454i | − 0.587030i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1303.34 | −2.35685 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 603.829 | 1.08407 | 0.542037 | − | 0.840354i | \(-0.317653\pi\) | ||||
0.542037 | + | 0.840354i | \(0.317653\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 192.411i | 0.344206i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 102.473i | − 0.182013i | −0.995850 | − | 0.0910064i | \(-0.970992\pi\) | ||||
0.995850 | − | 0.0910064i | \(-0.0290084\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 236.718 | 0.418971 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −237.219 | −0.416905 | −0.208453 | − | 0.978032i | \(-0.566843\pi\) | ||||
−0.208453 | + | 0.978032i | \(0.566843\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 881.129i | − 1.54313i | −0.636149 | − | 0.771566i | \(-0.719474\pi\) | ||||
0.636149 | − | 0.771566i | \(-0.280526\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 735.683i | 1.27945i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −197.356 | −0.342038 | −0.171019 | − | 0.985268i | \(-0.554706\pi\) | ||||
−0.171019 | + | 0.985268i | \(0.554706\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1210.32 | −2.08317 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 399.687i | 0.685570i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 181.507i | 0.309210i | 0.987976 | + | 0.154605i | \(0.0494106\pi\) | ||||
−0.987976 | + | 0.154605i | \(0.950589\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.23366 | 0.00888568 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −828.164 | −1.39657 | −0.698283 | − | 0.715822i | \(-0.746052\pi\) | ||||
−0.698283 | + | 0.715822i | \(0.746052\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 88.1395i | 0.148134i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 97.1450i | − 0.162179i | −0.996707 | − | 0.0810893i | \(-0.974160\pi\) | ||||
0.996707 | − | 0.0810893i | \(-0.0258399\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −729.916 | −1.21450 | −0.607251 | − | 0.794510i | \(-0.707728\pi\) | ||||
−0.607251 | + | 0.794510i | \(0.707728\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 100.978 | 0.166906 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 711.346i | 1.17191i | 0.810345 | + | 0.585953i | \(0.199279\pi\) | ||||
−0.810345 | + | 0.585953i | \(0.800721\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 199.718i | − 0.326871i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −317.107 | −0.517304 | −0.258652 | − | 0.965971i | \(-0.583278\pi\) | ||||
−0.258652 | + | 0.965971i | \(0.583278\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 682.859 | 1.10674 | 0.553371 | − | 0.832935i | \(-0.313341\pi\) | ||||
0.553371 | + | 0.832935i | \(0.313341\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 87.7695i | 0.141792i | 0.997484 | + | 0.0708962i | \(0.0225859\pi\) | ||||
−0.997484 | + | 0.0708962i | \(0.977414\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1921.19i | 3.08378i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 402.029 | 0.643246 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −290.313 | −0.461547 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 150.666i | 0.238773i | 0.992848 | + | 0.119386i | \(0.0380927\pi\) | ||||
−0.992848 | + | 0.119386i | \(0.961907\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 71.0534i | 0.111895i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 782.156 | 1.22788 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −447.618 | −0.698312 | −0.349156 | − | 0.937065i | \(-0.613532\pi\) | ||||
−0.349156 | + | 0.937065i | \(0.613532\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 400.436i | − 0.622762i | −0.950285 | − | 0.311381i | \(-0.899209\pi\) | ||||
0.950285 | − | 0.311381i | \(-0.100791\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 253.680i | − 0.392086i | −0.980595 | − | 0.196043i | \(-0.937191\pi\) | ||||
0.980595 | − | 0.196043i | \(-0.0628092\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 734.668 | 1.13200 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −719.542 | −1.10190 | −0.550951 | − | 0.834537i | \(-0.685735\pi\) | ||||
−0.550951 | + | 0.834537i | \(0.685735\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 241.200i | 0.368245i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 475.052i | − 0.720868i | −0.932785 | − | 0.360434i | \(-0.882629\pi\) | ||||
0.932785 | − | 0.360434i | \(-0.117371\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −132.074 | −0.199809 | −0.0999046 | − | 0.994997i | \(-0.531854\pi\) | ||||
−0.0999046 | + | 0.994997i | \(0.531854\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −188.016 | −0.282730 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1225.03i | − 1.83662i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 149.096i | − 0.222199i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 919.525 | 1.36631 | 0.683154 | − | 0.730275i | \(-0.260608\pi\) | ||||
0.683154 | + | 0.730275i | \(0.260608\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −200.276 | −0.295829 | −0.147914 | − | 0.989000i | \(-0.547256\pi\) | ||||
−0.147914 | + | 0.989000i | \(0.547256\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 289.163i | − 0.425866i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1049.18i | 1.53613i | 0.640373 | + | 0.768064i | \(0.278780\pi\) | ||||
−0.640373 | + | 0.768064i | \(0.721220\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −433.156 | −0.632344 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 244.171 | 0.354384 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 1039.19i | − 1.50389i | −0.659225 | − | 0.751946i | \(-0.729116\pi\) | ||||
0.659225 | − | 0.751946i | \(-0.270884\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 277.405i | − 0.399145i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −239.376 | −0.343437 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 903.635 | 1.28907 | 0.644533 | − | 0.764576i | \(-0.277052\pi\) | ||||
0.644533 | + | 0.764576i | \(0.277052\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 619.284i | − 0.880915i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 270.911i | 0.383184i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −990.096 | −1.39647 | −0.698234 | − | 0.715869i | \(-0.746031\pi\) | ||||
−0.698234 | + | 0.715869i | \(0.746031\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.8216 | 0.0278003 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 191.861i | − 0.268338i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 775.482i | − 1.07856i | −0.842128 | − | 0.539278i | \(-0.818697\pi\) | ||||
0.842128 | − | 0.539278i | \(-0.181303\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1628.40 | −2.25853 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −798.539 | −1.10143 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 862.588i | 1.18650i | 0.805017 | + | 0.593252i | \(0.202156\pi\) | ||||
−0.805017 | + | 0.593252i | \(0.797844\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 98.0719i | 0.134161i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1013.12 | 1.38215 | 0.691075 | − | 0.722783i | \(-0.257137\pi\) | ||||
0.691075 | + | 0.722783i | \(0.257137\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1331.42 | −1.80654 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 1205.31i | − 1.63100i | −0.578755 | − | 0.815502i | \(-0.696461\pi\) | ||||
0.578755 | − | 0.815502i | \(-0.303539\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 762.230i | 1.02588i | 0.858424 | + | 0.512941i | \(0.171444\pi\) | ||||
−0.858424 | + | 0.512941i | \(0.828556\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −325.315 | −0.436664 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 355.538 | 0.474684 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 122.219i | − 0.162742i | −0.996684 | − | 0.0813709i | \(-0.974070\pi\) | ||||
0.996684 | − | 0.0813709i | \(-0.0259298\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.9909i | 0.0225044i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 279.583 | 0.369330 | 0.184665 | − | 0.982802i | \(-0.440880\pi\) | ||||
0.184665 | + | 0.982802i | \(0.440880\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 250.171 | 0.328740 | 0.164370 | − | 0.986399i | \(-0.447441\pi\) | ||||
0.164370 | + | 0.986399i | \(0.447441\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1567.69i | 2.05463i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 448.812i | − 0.585152i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 993.027 | 1.29132 | 0.645662 | − | 0.763624i | \(-0.276582\pi\) | ||||
0.645662 | + | 0.763624i | \(0.276582\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −631.978 | −0.817565 | −0.408782 | − | 0.912632i | \(-0.634047\pi\) | ||||
−0.408782 | + | 0.912632i | \(0.634047\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 12.9208i | − 0.0166720i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 510.627i | − 0.655490i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 950.867 | 1.21750 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −63.9541 | −0.0814702 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 881.763i | 1.12041i | 0.828354 | + | 0.560205i | \(0.189278\pi\) | ||||
−0.828354 | + | 0.560205i | \(0.810722\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 1617.94i | − 2.04543i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −91.0833 | −0.114859 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −442.306 | −0.554964 | −0.277482 | − | 0.960731i | \(-0.589500\pi\) | ||||
−0.277482 | + | 0.960731i | \(0.589500\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 101.796i | − 0.127405i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 481.439i | − 0.599550i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −712.077 | −0.884568 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −665.367 | −0.822456 | −0.411228 | − | 0.911533i | \(-0.634900\pi\) | ||||
−0.411228 | + | 0.911533i | \(0.634900\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1193.47i | 1.47160i | 0.677198 | + | 0.735801i | \(0.263194\pi\) | ||||
−0.677198 | + | 0.735801i | \(0.736806\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 222.055i | 0.272461i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −209.203 | −0.256062 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −359.355 | −0.437704 | −0.218852 | − | 0.975758i | \(-0.570231\pi\) | ||||
−0.218852 | + | 0.975758i | \(0.570231\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 1159.12i | − 1.40841i | −0.709999 | − | 0.704203i | \(-0.751304\pi\) | ||||
0.709999 | − | 0.704203i | \(-0.248696\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 160.002i | − 0.193473i | −0.995310 | − | 0.0967364i | \(-0.969160\pi\) | ||||
0.995310 | − | 0.0967364i | \(-0.0308404\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −992.384 | −1.19709 | −0.598543 | − | 0.801091i | \(-0.704253\pi\) | ||||
−0.598543 | + | 0.801091i | \(0.704253\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 398.665 | 0.478590 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 533.231i | 0.638600i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 84.8821i | 0.101171i | 0.998720 | + | 0.0505853i | \(0.0161087\pi\) | ||||
−0.998720 | + | 0.0505853i | \(0.983891\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 488.691 | 0.581083 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 180.403 | 0.213495 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 690.172i | − 0.814843i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 2345.43i | − 2.75609i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 626.933 | 0.734974 | 0.367487 | − | 0.930029i | \(-0.380218\pi\) | ||||
0.367487 | + | 0.930029i | \(0.380218\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1560.76 | 1.82119 | 0.910594 | − | 0.413302i | \(-0.135625\pi\) | ||||
0.910594 | + | 0.413302i | \(0.135625\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 172.848i | − 0.201220i | −0.994926 | − | 0.100610i | \(-0.967921\pi\) | ||||
0.994926 | − | 0.100610i | \(-0.0320794\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 66.7620i | 0.0773604i | 0.999252 | + | 0.0386802i | \(0.0123154\pi\) | ||||
−0.999252 | + | 0.0386802i | \(0.987685\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −360.823 | −0.417136 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1446.07 | 1.66406 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 813.372i | 0.933836i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 994.074i | 1.13609i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 903.899 | 1.03067 | 0.515336 | − | 0.856988i | \(-0.327667\pi\) | ||||
0.515336 | + | 0.856988i | \(0.327667\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 514.281 | 0.583747 | 0.291873 | − | 0.956457i | \(-0.405721\pi\) | ||||
0.291873 | + | 0.956457i | \(0.405721\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1668.73i | 1.88984i | 0.327299 | + | 0.944921i | \(0.393861\pi\) | ||||
−0.327299 | + | 0.944921i | \(0.606139\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1155.43i | − 1.30262i | −0.758810 | − | 0.651312i | \(-0.774219\pi\) | ||||
0.758810 | − | 0.651312i | \(-0.225781\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 485.640 | 0.546277 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 217.148 | 0.243167 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 564.961i | 0.631241i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21.5151i | 0.0239323i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 124.454 | 0.138129 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 502.531 | 0.555283 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 229.965i | − 0.253545i | −0.991932 | − | 0.126772i | \(-0.959538\pi\) | ||||
0.991932 | − | 0.126772i | \(-0.0404618\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.1180i | 0.0220835i | 0.999939 | + | 0.0110417i | \(0.00351476\pi\) | ||||
−0.999939 | + | 0.0110417i | \(0.996485\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1342.87 | 1.47083 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1648.57 | 1.79779 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 580.742i | 0.631929i | 0.948771 | + | 0.315964i | \(0.102328\pi\) | ||||
−0.948771 | + | 0.315964i | \(0.897672\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 580.889i | − 0.629348i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1528.88 | −1.65284 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 375.347 | 0.404033 | 0.202017 | − | 0.979382i | \(-0.435250\pi\) | ||||
0.202017 | + | 0.979382i | \(0.435250\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 850.417i | 0.913445i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 97.7918i | − 0.104590i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 339.330 | 0.362145 | 0.181073 | − | 0.983470i | \(-0.442043\pi\) | ||||
0.181073 | + | 0.983470i | \(0.442043\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 459.867 | 0.488700 | 0.244350 | − | 0.969687i | \(-0.421425\pi\) | ||||
0.244350 | + | 0.969687i | \(0.421425\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1933.91i | − 2.05081i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 424.359i | − 0.448109i | −0.974577 | − | 0.224055i | \(-0.928071\pi\) | ||||
0.974577 | − | 0.224055i | \(-0.0719294\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −294.113 | −0.309919 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −140.791 | −0.147734 | −0.0738670 | − | 0.997268i | \(-0.523534\pi\) | ||||
−0.0738670 | + | 0.997268i | \(0.523534\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 233.570i | 0.244576i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2960.56i | 3.08713i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 960.652 | 0.999638 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −645.932 | −0.669359 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 683.919i | − 0.707258i | −0.935386 | − | 0.353629i | \(-0.884947\pi\) | ||||
0.935386 | − | 0.353629i | \(-0.115053\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 983.197i | 1.01256i | 0.862369 | + | 0.506281i | \(0.168980\pi\) | ||||
−0.862369 | + | 0.506281i | \(0.831020\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1896.03 | −1.94864 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1008.88 | 1.03263 | 0.516315 | − | 0.856399i | \(-0.327303\pi\) | ||||
0.516315 | + | 0.856399i | \(0.327303\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 2131.59i | − 2.17731i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1681.75i | − 1.71084i | −0.517936 | − | 0.855419i | \(-0.673300\pi\) | ||||
0.517936 | − | 0.855419i | \(-0.326700\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.2019 | 0.0255857 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −792.321 | −0.801134 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 81.5243i | − 0.0822647i | −0.999154 | − | 0.0411323i | \(-0.986903\pi\) | ||||
0.999154 | − | 0.0411323i | \(-0.0130965\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 377.812i | 0.379710i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −549.116 | −0.550768 | −0.275384 | − | 0.961334i | \(-0.588805\pi\) | ||||
−0.275384 | + | 0.961334i | \(0.588805\pi\) | |||||||
\(998\) | 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 | 1728.3.g.k.703.4 | 8 | ||
3.2 | odd | 2 | 1728.3.g.n.703.6 | 8 | |||
4.3 | odd | 2 | inner | 1728.3.g.k.703.3 | 8 | ||
8.3 | odd | 2 | 864.3.g.c.703.5 | yes | 8 | ||
8.5 | even | 2 | 864.3.g.c.703.6 | yes | 8 | ||
12.11 | even | 2 | 1728.3.g.n.703.5 | 8 | |||
24.5 | odd | 2 | 864.3.g.a.703.4 | yes | 8 | ||
24.11 | even | 2 | 864.3.g.a.703.3 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.3.g.a.703.3 | ✓ | 8 | 24.11 | even | 2 | ||
864.3.g.a.703.4 | yes | 8 | 24.5 | odd | 2 | ||
864.3.g.c.703.5 | yes | 8 | 8.3 | odd | 2 | ||
864.3.g.c.703.6 | yes | 8 | 8.5 | even | 2 | ||
1728.3.g.k.703.3 | 8 | 4.3 | odd | 2 | inner | ||
1728.3.g.k.703.4 | 8 | 1.1 | even | 1 | trivial | ||
1728.3.g.n.703.5 | 8 | 12.11 | even | 2 | |||
1728.3.g.n.703.6 | 8 | 3.2 | odd | 2 |