Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [288,3,Mod(271,288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(288, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("288.271");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 288.b (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: | \(7.84743161358\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-6}, \sqrt{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 271.1 | ||
Root | \(1.58114 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 288.271 |
Dual form | 288.3.b.c.271.4 |
$q$-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 \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | − 4.89898i | − 0.979796i | −0.871780 | − | 0.489898i | \(-0.837034\pi\) | ||||
0.871780 | − | 0.489898i | \(-0.162966\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 7.74597i | − 1.10657i | −0.832993 | − | 0.553283i | \(-0.813375\pi\) | ||||
0.832993 | − | 0.553283i | \(-0.186625\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −12.6491 | −1.14992 | −0.574960 | − | 0.818182i | \(-0.694982\pi\) | ||||
−0.574960 | + | 0.818182i | \(0.694982\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15.4919i | 1.19169i | 0.803101 | + | 0.595844i | \(0.203182\pi\) | ||||
−0.803101 | + | 0.595844i | \(0.796818\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −25.2982 | −1.48813 | −0.744065 | − | 0.668107i | \(-0.767105\pi\) | ||||
−0.744065 | + | 0.668107i | \(0.767105\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.00000 | −0.421053 | −0.210526 | − | 0.977588i | \(-0.567518\pi\) | ||||
−0.210526 | + | 0.977588i | \(0.567518\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 39.1918i | − 1.70399i | −0.523548 | − | 0.851996i | \(-0.675392\pi\) | ||||
0.523548 | − | 0.851996i | \(-0.324608\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.0400000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 24.4949i | − 0.844652i | −0.906444 | − | 0.422326i | \(-0.861214\pi\) | ||||
0.906444 | − | 0.422326i | \(-0.138786\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.74597i | 0.249870i | 0.992165 | + | 0.124935i | \(0.0398722\pi\) | ||||
−0.992165 | + | 0.124935i | \(0.960128\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −37.9473 | −1.08421 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 46.4758i | − 1.25610i | −0.778172 | − | 0.628051i | \(-0.783853\pi\) | ||||
0.778172 | − | 0.628051i | \(-0.216147\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −25.2982 | −0.617030 | −0.308515 | − | 0.951220i | \(-0.599832\pi\) | ||||
−0.308515 | + | 0.951220i | \(0.599832\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 40.0000 | 0.930233 | 0.465116 | − | 0.885250i | \(-0.346013\pi\) | ||||
0.465116 | + | 0.885250i | \(0.346013\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 39.1918i | 0.833869i | 0.908937 | + | 0.416934i | \(0.136896\pi\) | ||||
−0.908937 | + | 0.416934i | \(0.863104\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −11.0000 | −0.224490 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 14.6969i | − 0.277301i | −0.990341 | − | 0.138650i | \(-0.955724\pi\) | ||||
0.990341 | − | 0.138650i | \(-0.0442764\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 61.9677i | 1.12669i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 25.2982 | 0.428783 | 0.214392 | − | 0.976748i | \(-0.431223\pi\) | ||||
0.214392 | + | 0.976748i | \(0.431223\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 15.4919i | − 0.253966i | −0.991905 | − | 0.126983i | \(-0.959471\pi\) | ||||
0.991905 | − | 0.126983i | \(-0.0405294\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 75.8947 | 1.16761 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −80.0000 | −1.19403 | −0.597015 | − | 0.802230i | \(-0.703647\pi\) | ||||
−0.597015 | + | 0.802230i | \(0.703647\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.0000 | −0.136986 | −0.0684932 | − | 0.997652i | \(-0.521819\pi\) | ||||
−0.0684932 | + | 0.997652i | \(0.521819\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 97.9796i | 1.27246i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 54.2218i | − 0.686351i | −0.939271 | − | 0.343176i | \(-0.888497\pi\) | ||||
0.939271 | − | 0.343176i | \(-0.111503\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 139.140 | 1.67639 | 0.838194 | − | 0.545372i | \(-0.183612\pi\) | ||||
0.838194 | + | 0.545372i | \(0.183612\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 123.935i | 1.45806i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 50.5964 | 0.568499 | 0.284250 | − | 0.958750i | \(-0.408256\pi\) | ||||
0.284250 | + | 0.958750i | \(0.408256\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 120.000 | 1.31868 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 39.1918i | 0.412546i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 50.0000 | 0.515464 | 0.257732 | − | 0.966216i | \(-0.417025\pi\) | ||||
0.257732 | + | 0.966216i | \(0.417025\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 122.474i | 1.21262i | 0.795229 | + | 0.606309i | \(0.207351\pi\) | ||||
−0.795229 | + | 0.606309i | \(0.792649\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 178.157i | − 1.72968i | −0.502046 | − | 0.864841i | \(-0.667419\pi\) | ||||
0.502046 | − | 0.864841i | \(-0.332581\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 25.2982 | 0.236432 | 0.118216 | − | 0.992988i | \(-0.462282\pi\) | ||||
0.118216 | + | 0.992988i | \(0.462282\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 46.4758i | − 0.426383i | −0.977010 | − | 0.213192i | \(-0.931614\pi\) | ||||
0.977010 | − | 0.213192i | \(-0.0683859\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 50.5964 | 0.447756 | 0.223878 | − | 0.974617i | \(-0.428128\pi\) | ||||
0.223878 | + | 0.974617i | \(0.428128\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −192.000 | −1.66957 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 195.959i | 1.64672i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 39.0000 | 0.322314 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 127.373i | − 1.01899i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 116.190i | 0.914878i | 0.889241 | + | 0.457439i | \(0.151233\pi\) | ||||
−0.889241 | + | 0.457439i | \(0.848767\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −50.5964 | −0.386232 | −0.193116 | − | 0.981176i | \(-0.561859\pi\) | ||||
−0.193116 | + | 0.981176i | \(0.561859\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 61.9677i | 0.465923i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 126.491 | 0.923293 | 0.461646 | − | 0.887064i | \(-0.347259\pi\) | ||||
0.461646 | + | 0.887064i | \(0.347259\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 208.000 | 1.49640 | 0.748201 | − | 0.663472i | \(-0.230918\pi\) | ||||
0.748201 | + | 0.663472i | \(0.230918\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 195.959i | − 1.37034i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −120.000 | −0.827586 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 122.474i | − 0.821976i | −0.911641 | − | 0.410988i | \(-0.865184\pi\) | ||||
0.911641 | − | 0.410988i | \(-0.134816\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 178.157i | 1.17985i | 0.807458 | + | 0.589925i | \(0.200843\pi\) | ||||
−0.807458 | + | 0.589925i | \(0.799157\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 37.9473 | 0.244821 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 77.4597i | − 0.493374i | −0.969095 | − | 0.246687i | \(-0.920658\pi\) | ||||
0.969095 | − | 0.246687i | \(-0.0793419\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −303.579 | −1.88558 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −200.000 | −1.22699 | −0.613497 | − | 0.789697i | \(-0.710238\pi\) | ||||
−0.613497 | + | 0.789697i | \(0.710238\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 39.1918i | − 0.234682i | −0.993092 | − | 0.117341i | \(-0.962563\pi\) | ||||
0.993092 | − | 0.117341i | \(-0.0374370\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −71.0000 | −0.420118 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 181.262i | 1.04776i | 0.851793 | + | 0.523879i | \(0.175516\pi\) | ||||
−0.851793 | + | 0.523879i | \(0.824484\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 7.74597i | − 0.0442627i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −278.280 | −1.55464 | −0.777320 | − | 0.629106i | \(-0.783421\pi\) | ||||
−0.777320 | + | 0.629106i | \(0.783421\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 325.331i | − 1.79741i | −0.438557 | − | 0.898703i | \(-0.644510\pi\) | ||||
0.438557 | − | 0.898703i | \(-0.355490\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −227.684 | −1.23072 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 320.000 | 1.71123 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 195.959i | − 1.02596i | −0.858399 | − | 0.512982i | \(-0.828541\pi\) | ||||
0.858399 | − | 0.512982i | \(-0.171459\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 170.000 | 0.880829 | 0.440415 | − | 0.897795i | \(-0.354831\pi\) | ||||
0.440415 | + | 0.897795i | \(0.354831\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 132.272i | − 0.671434i | −0.941963 | − | 0.335717i | \(-0.891021\pi\) | ||||
0.941963 | − | 0.335717i | \(-0.108979\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 69.7137i | 0.350320i | 0.984540 | + | 0.175160i | \(0.0560443\pi\) | ||||
−0.984540 | + | 0.175160i | \(0.943956\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −189.737 | −0.934663 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 123.935i | 0.604563i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 101.193 | 0.484176 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −272.000 | −1.28910 | −0.644550 | − | 0.764562i | \(-0.722955\pi\) | ||||
−0.644550 | + | 0.764562i | \(0.722955\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 195.959i | − 0.911438i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 60.0000 | 0.276498 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 391.918i | − 1.77339i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 193.649i | − 0.868382i | −0.900821 | − | 0.434191i | \(-0.857034\pi\) | ||||
0.900821 | − | 0.434191i | \(-0.142966\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 215.035 | 0.947290 | 0.473645 | − | 0.880716i | \(-0.342938\pi\) | ||||
0.473645 | + | 0.880716i | \(0.342938\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 108.444i | 0.473553i | 0.971564 | + | 0.236776i | \(0.0760908\pi\) | ||||
−0.971564 | + | 0.236776i | \(0.923909\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −252.982 | −1.08576 | −0.542880 | − | 0.839810i | \(-0.682666\pi\) | ||||
−0.542880 | + | 0.839810i | \(0.682666\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 192.000 | 0.817021 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 195.959i | 0.819913i | 0.912105 | + | 0.409956i | \(0.134456\pi\) | ||||
−0.912105 | + | 0.409956i | \(0.865544\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −202.000 | −0.838174 | −0.419087 | − | 0.907946i | \(-0.637650\pi\) | ||||
−0.419087 | + | 0.907946i | \(0.637650\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 53.8888i | 0.219954i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 123.935i | − 0.501763i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −316.228 | −1.25987 | −0.629936 | − | 0.776647i | \(-0.716919\pi\) | ||||
−0.629936 | + | 0.776647i | \(0.716919\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 495.742i | 1.95945i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 202.386 | 0.787493 | 0.393747 | − | 0.919219i | \(-0.371179\pi\) | ||||
0.393747 | + | 0.919219i | \(0.371179\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −360.000 | −1.38996 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 156.767i | 0.596074i | 0.954554 | + | 0.298037i | \(0.0963318\pi\) | ||||
−0.954554 | + | 0.298037i | \(0.903668\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −72.0000 | −0.271698 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 73.4847i | 0.273177i | 0.990628 | + | 0.136589i | \(0.0436139\pi\) | ||||
−0.990628 | + | 0.136589i | \(0.956386\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 69.7137i | − 0.257246i | −0.991694 | − | 0.128623i | \(-0.958944\pi\) | ||||
0.991694 | − | 0.128623i | \(-0.0410557\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.6491 | −0.0459968 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 15.4919i | − 0.0559276i | −0.999609 | − | 0.0279638i | \(-0.991098\pi\) | ||||
0.999609 | − | 0.0279638i | \(-0.00890231\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 202.386 | 0.720234 | 0.360117 | − | 0.932907i | \(-0.382737\pi\) | ||||
0.360117 | + | 0.932907i | \(0.382737\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 160.000 | 0.565371 | 0.282686 | − | 0.959213i | \(-0.408775\pi\) | ||||
0.282686 | + | 0.959213i | \(0.408775\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 195.959i | 0.682785i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 351.000 | 1.21453 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 259.646i | 0.886164i | 0.896481 | + | 0.443082i | \(0.146115\pi\) | ||||
−0.896481 | + | 0.443082i | \(0.853885\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 123.935i | − 0.420120i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 607.157 | 2.03063 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 309.839i | − 1.02936i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −75.8947 | −0.248835 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −80.0000 | −0.260586 | −0.130293 | − | 0.991476i | \(-0.541592\pi\) | ||||
−0.130293 | + | 0.991476i | \(0.541592\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 391.918i | − 1.26019i | −0.776519 | − | 0.630094i | \(-0.783016\pi\) | ||||
0.776519 | − | 0.630094i | \(-0.216984\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 230.000 | 0.734824 | 0.367412 | − | 0.930058i | \(-0.380244\pi\) | ||||
0.367412 | + | 0.930058i | \(0.380244\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 504.595i | 1.59178i | 0.605440 | + | 0.795891i | \(0.292997\pi\) | ||||
−0.605440 | + | 0.795891i | \(0.707003\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 309.839i | 0.971281i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 202.386 | 0.626581 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.4919i | 0.0476675i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 303.579 | 0.922731 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 352.000 | 1.06344 | 0.531722 | − | 0.846919i | \(-0.321545\pi\) | ||||
0.531722 | + | 0.846919i | \(0.321545\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 391.918i | 1.16991i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −550.000 | −1.63205 | −0.816024 | − | 0.578018i | \(-0.803826\pi\) | ||||
−0.816024 | + | 0.578018i | \(0.803826\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 97.9796i | − 0.287330i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 294.347i | − 0.858154i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 366.824 | 1.05713 | 0.528565 | − | 0.848893i | \(-0.322730\pi\) | ||||
0.528565 | + | 0.848893i | \(0.322730\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 573.202i | − 1.64241i | −0.570632 | − | 0.821206i | \(-0.693302\pi\) | ||||
0.570632 | − | 0.821206i | \(-0.306698\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 354.175 | 1.00333 | 0.501664 | − | 0.865062i | \(-0.332721\pi\) | ||||
0.501664 | + | 0.865062i | \(0.332721\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −297.000 | −0.822715 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 48.9898i | 0.134219i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 503.488i | 1.37190i | 0.727648 | + | 0.685951i | \(0.240613\pi\) | ||||
−0.727648 | + | 0.685951i | \(0.759387\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −113.842 | −0.306852 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 201.395i | 0.539933i | 0.962870 | + | 0.269967i | \(0.0870127\pi\) | ||||
−0.962870 | + | 0.269967i | \(0.912987\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 379.473 | 1.00656 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −152.000 | −0.401055 | −0.200528 | − | 0.979688i | \(-0.564266\pi\) | ||||
−0.200528 | + | 0.979688i | \(0.564266\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 431.110i | 1.12561i | 0.826588 | + | 0.562807i | \(0.190279\pi\) | ||||
−0.826588 | + | 0.562807i | \(0.809721\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 480.000 | 1.24675 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 24.4949i | − 0.0629689i | −0.999504 | − | 0.0314844i | \(-0.989977\pi\) | ||||
0.999504 | − | 0.0314844i | \(-0.0100235\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 991.484i | 2.53576i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −265.631 | −0.672484 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 46.4758i | 0.117068i | 0.998285 | + | 0.0585338i | \(0.0186425\pi\) | ||||
−0.998285 | + | 0.0585338i | \(0.981357\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −480.666 | −1.19867 | −0.599334 | − | 0.800499i | \(-0.704568\pi\) | ||||
−0.599334 | + | 0.800499i | \(0.704568\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −120.000 | −0.297767 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 587.878i | 1.44442i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 62.0000 | 0.151589 | 0.0757946 | − | 0.997123i | \(-0.475851\pi\) | ||||
0.0757946 | + | 0.997123i | \(0.475851\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 195.959i | − 0.474477i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 681.645i | − 1.64252i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 63.2456 | 0.150944 | 0.0754720 | − | 0.997148i | \(-0.475954\pi\) | ||||
0.0754720 | + | 0.997148i | \(0.475954\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 15.4919i | − 0.0367979i | −0.999831 | − | 0.0183990i | \(-0.994143\pi\) | ||||
0.999831 | − | 0.0183990i | \(-0.00585690\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −25.2982 | −0.0595252 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −120.000 | −0.281030 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 587.878i | − 1.36399i | −0.731359 | − | 0.681993i | \(-0.761114\pi\) | ||||
0.731359 | − | 0.681993i | \(-0.238886\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −370.000 | −0.854503 | −0.427252 | − | 0.904133i | \(-0.640518\pi\) | ||||
−0.427252 | + | 0.904133i | \(0.640518\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 313.535i | 0.717471i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 426.028i | − 0.970451i | −0.874389 | − | 0.485226i | \(-0.838737\pi\) | ||||
0.874389 | − | 0.485226i | \(-0.161263\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −240.333 | −0.542513 | −0.271256 | − | 0.962507i | \(-0.587439\pi\) | ||||
−0.271256 | + | 0.962507i | \(0.587439\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 247.871i | − 0.557013i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.2982 | −0.0563435 | −0.0281717 | − | 0.999603i | \(-0.508969\pi\) | ||||
−0.0281717 | + | 0.999603i | \(0.508969\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 320.000 | 0.709534 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 587.878i | − 1.29204i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −130.000 | −0.284464 | −0.142232 | − | 0.989833i | \(-0.545428\pi\) | ||||
−0.142232 | + | 0.989833i | \(0.545428\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 759.342i | − 1.64716i | −0.567198 | − | 0.823581i | \(-0.691973\pi\) | ||||
0.567198 | − | 0.823581i | \(-0.308027\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 503.488i | − 1.08745i | −0.839265 | − | 0.543723i | \(-0.817014\pi\) | ||||
0.839265 | − | 0.543723i | \(-0.182986\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 366.824 | 0.785491 | 0.392745 | − | 0.919647i | \(-0.371525\pi\) | ||||
0.392745 | + | 0.919647i | \(0.371525\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 619.677i | 1.32127i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −505.964 | −1.06969 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.00000 | −0.0168421 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 783.837i | − 1.63640i | −0.574932 | − | 0.818201i | \(-0.694972\pi\) | ||||
0.574932 | − | 0.818201i | \(-0.305028\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 720.000 | 1.49688 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 244.949i | − 0.505049i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 255.617i | − 0.524881i | −0.964948 | − | 0.262440i | \(-0.915473\pi\) | ||||
0.964948 | − | 0.262440i | \(-0.0845273\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −657.754 | −1.33962 | −0.669810 | − | 0.742532i | \(-0.733625\pi\) | ||||
−0.669810 | + | 0.742532i | \(0.733625\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 619.677i | 1.25695i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 352.000 | 0.705411 | 0.352705 | − | 0.935734i | \(-0.385262\pi\) | ||||
0.352705 | + | 0.935734i | \(0.385262\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 235.151i | 0.467497i | 0.972297 | + | 0.233749i | \(0.0750992\pi\) | ||||
−0.972297 | + | 0.233749i | \(0.924901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 600.000 | 1.18812 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 759.342i | 1.49183i | 0.666041 | + | 0.745915i | \(0.267988\pi\) | ||||
−0.666041 | + | 0.745915i | \(0.732012\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 77.4597i | 0.151584i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −872.789 | −1.69474 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 495.742i | − 0.958882i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −936.034 | −1.79661 | −0.898305 | − | 0.439372i | \(-0.855201\pi\) | ||||
−0.898305 | + | 0.439372i | \(0.855201\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −920.000 | −1.75908 | −0.879541 | − | 0.475823i | \(-0.842150\pi\) | ||||
−0.879541 | + | 0.475823i | \(0.842150\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 195.959i | − 0.371839i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1007.00 | −1.90359 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 391.918i | − 0.735306i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 123.935i | − 0.231655i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 139.140 | 0.258145 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 511.234i | 0.944979i | 0.881336 | + | 0.472490i | \(0.156645\pi\) | ||||
−0.881336 | + | 0.472490i | \(0.843355\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −227.684 | −0.417769 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.0000 | 0.0731261 | 0.0365631 | − | 0.999331i | \(-0.488359\pi\) | ||||
0.0365631 | + | 0.999331i | \(0.488359\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 195.959i | 0.355643i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −420.000 | −0.759494 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 308.636i | − 0.554104i | −0.960855 | − | 0.277052i | \(-0.910643\pi\) | ||||
0.960855 | − | 0.277052i | \(-0.0893574\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 619.677i | 1.10855i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −88.5438 | −0.157271 | −0.0786357 | − | 0.996903i | \(-0.525056\pi\) | ||||
−0.0786357 | + | 0.996903i | \(0.525056\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 247.871i | − 0.438710i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −328.877 | −0.577991 | −0.288995 | − | 0.957330i | \(-0.593321\pi\) | ||||
−0.288995 | + | 0.957330i | \(0.593321\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −368.000 | −0.644483 | −0.322242 | − | 0.946657i | \(-0.604436\pi\) | ||||
−0.322242 | + | 0.946657i | \(0.604436\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 39.1918i | − 0.0681597i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 710.000 | 1.23050 | 0.615251 | − | 0.788331i | \(-0.289055\pi\) | ||||
0.615251 | + | 0.788331i | \(0.289055\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 1077.78i | − 1.85504i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 185.903i | 0.318873i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 101.193 | 0.172390 | 0.0861950 | − | 0.996278i | \(-0.472529\pi\) | ||||
0.0861950 | + | 0.996278i | \(0.472529\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 61.9677i | − 0.105208i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 961.332 | 1.62113 | 0.810567 | − | 0.585646i | \(-0.199159\pi\) | ||||
0.810567 | + | 0.585646i | \(0.199159\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 960.000 | 1.61345 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 195.959i | 0.327144i | 0.986531 | + | 0.163572i | \(0.0523016\pi\) | ||||
−0.986531 | + | 0.163572i | \(0.947698\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.0000 | −0.0366057 | −0.0183028 | − | 0.999832i | \(-0.505826\pi\) | ||||
−0.0183028 | + | 0.999832i | \(0.505826\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 191.060i | − 0.315802i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 240.125i | 0.395593i | 0.980243 | + | 0.197797i | \(0.0633785\pi\) | ||||
−0.980243 | + | 0.197797i | \(0.936621\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −607.157 | −0.993711 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 790.089i | − 1.28889i | −0.764651 | − | 0.644444i | \(-0.777089\pi\) | ||||
0.764651 | − | 0.644444i | \(-0.222911\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1113.12 | 1.80409 | 0.902044 | − | 0.431645i | \(-0.142067\pi\) | ||||
0.902044 | + | 0.431645i | \(0.142067\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.0000 | −0.0516963 | −0.0258481 | − | 0.999666i | \(-0.508229\pi\) | ||||
−0.0258481 | + | 0.999666i | \(0.508229\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 391.918i | − 0.629082i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −599.000 | −0.958400 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1175.76i | 1.86924i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 116.190i | 0.184135i | 0.995753 | + | 0.0920677i | \(0.0293476\pi\) | ||||
−0.995753 | + | 0.0920677i | \(0.970652\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 569.210 | 0.896394 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 170.411i | − 0.267522i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1239.61 | −1.93387 | −0.966937 | − | 0.255017i | \(-0.917919\pi\) | ||||
−0.966937 | + | 0.255017i | \(0.917919\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1000.00 | 1.55521 | 0.777605 | − | 0.628753i | \(-0.216434\pi\) | ||||
0.777605 | + | 0.628753i | \(0.216434\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 823.029i | 1.27207i | 0.771661 | + | 0.636034i | \(0.219426\pi\) | ||||
−0.771661 | + | 0.636034i | \(0.780574\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −320.000 | −0.493066 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 328.232i | − 0.502652i | −0.967903 | − | 0.251326i | \(-0.919133\pi\) | ||||
0.967903 | − | 0.251326i | \(-0.0808666\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 247.871i | 0.378429i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 708.350 | 1.07489 | 0.537443 | − | 0.843300i | \(-0.319390\pi\) | ||||
0.537443 | + | 0.843300i | \(0.319390\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 728.121i | − 1.10154i | −0.834656 | − | 0.550772i | \(-0.814333\pi\) | ||||
0.834656 | − | 0.550772i | \(-0.185667\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 303.579 | 0.456509 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −960.000 | −1.43928 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 195.959i | 0.292041i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1070.00 | 1.58990 | 0.794948 | − | 0.606678i | \(-0.207498\pi\) | ||||
0.794948 | + | 0.606678i | \(0.207498\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1092.47i | 1.61370i | 0.590759 | + | 0.806848i | \(0.298828\pi\) | ||||
−0.590759 | + | 0.806848i | \(0.701172\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 387.298i | − 0.570395i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 594.508 | 0.870437 | 0.435218 | − | 0.900325i | \(-0.356671\pi\) | ||||
0.435218 | + | 0.900325i | \(0.356671\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 619.677i | − 0.904638i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 227.684 | 0.330456 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.00000 | −0.0115774 | −0.00578871 | − | 0.999983i | \(-0.501843\pi\) | ||||
−0.00578871 | + | 0.999983i | \(0.501843\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 1018.99i | − 1.46617i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 640.000 | 0.918221 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1249.24i | 1.78208i | 0.453922 | + | 0.891041i | \(0.350024\pi\) | ||||
−0.453922 | + | 0.891041i | \(0.649976\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 371.806i | 0.528885i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 948.683 | 1.34184 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 914.024i | 1.28917i | 0.764531 | + | 0.644587i | \(0.222971\pi\) | ||||
−0.764531 | + | 0.644587i | \(0.777029\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 303.579 | 0.425777 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −960.000 | −1.34266 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1175.76i | 1.63526i | 0.575741 | + | 0.817632i | \(0.304714\pi\) | ||||
−0.575741 | + | 0.817632i | \(0.695286\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1380.00 | −1.91401 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 24.4949i | − 0.0337861i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 549.964i | 0.756484i | 0.925707 | + | 0.378242i | \(0.123471\pi\) | ||||
−0.925707 | + | 0.378242i | \(0.876529\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1011.93 | −1.38431 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 945.008i | 1.28923i | 0.764506 | + | 0.644617i | \(0.222983\pi\) | ||||
−0.764506 | + | 0.644617i | \(0.777017\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1011.93 | 1.37304 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1072.00 | 1.45061 | 0.725304 | − | 0.688428i | \(-0.241699\pi\) | ||||
0.725304 | + | 0.688428i | \(0.241699\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 431.110i | 0.580229i | 0.956992 | + | 0.290115i | \(0.0936934\pi\) | ||||
−0.956992 | + | 0.290115i | \(0.906307\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −600.000 | −0.805369 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 195.959i | − 0.261628i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 1293.58i | − 1.72247i | −0.508205 | − | 0.861236i | \(-0.669691\pi\) | ||||
0.508205 | − | 0.861236i | \(-0.330309\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 872.789 | 1.15601 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 790.089i | 1.04371i | 0.853034 | + | 0.521855i | \(0.174760\pi\) | ||||
−0.853034 | + | 0.521855i | \(0.825240\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 733.648 | 0.964058 | 0.482029 | − | 0.876155i | \(-0.339900\pi\) | ||||
0.482029 | + | 0.876155i | \(0.339900\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −360.000 | −0.471822 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 391.918i | 0.510976i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 938.000 | 1.21977 | 0.609883 | − | 0.792491i | \(-0.291216\pi\) | ||||
0.609883 | + | 0.792491i | \(0.291216\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 426.211i | − 0.551373i | −0.961248 | − | 0.275686i | \(-0.911095\pi\) | ||||
0.961248 | − | 0.275686i | \(-0.0889051\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.74597i | 0.00999480i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 202.386 | 0.259802 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −379.473 | −0.483406 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 520.000 | 0.660737 | 0.330368 | − | 0.943852i | \(-0.392827\pi\) | ||||
0.330368 | + | 0.943852i | \(0.392827\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 391.918i | − 0.495472i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 240.000 | 0.302648 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 83.2827i | 0.104495i | 0.998634 | + | 0.0522476i | \(0.0166385\pi\) | ||||
−0.998634 | + | 0.0522476i | \(0.983362\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 991.484i | − 1.24091i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 126.491 | 0.157523 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1487.23i | 1.84749i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 430.070 | 0.531607 | 0.265803 | − | 0.964027i | \(-0.414363\pi\) | ||||
0.265803 | + | 0.964027i | \(0.414363\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −872.000 | −1.07522 | −0.537608 | − | 0.843195i | \(-0.680672\pi\) | ||||
−0.537608 | + | 0.843195i | \(0.680672\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 979.796i | 1.20220i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −320.000 | −0.391677 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 1053.28i | − 1.28292i | −0.767155 | − | 0.641462i | \(-0.778328\pi\) | ||||
0.767155 | − | 0.641462i | \(-0.221672\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 240.125i | 0.291768i | 0.989302 | + | 0.145884i | \(0.0466026\pi\) | ||||
−0.989302 | + | 0.145884i | \(0.953397\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1087.82 | 1.31539 | 0.657693 | − | 0.753286i | \(-0.271533\pi\) | ||||
0.657693 | + | 0.753286i | \(0.271533\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 1533.70i | − 1.85006i | −0.379892 | − | 0.925031i | \(-0.624039\pi\) | ||||
0.379892 | − | 0.925031i | \(-0.375961\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 278.280 | 0.334070 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −192.000 | −0.229940 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 783.837i | − 0.934251i | −0.884191 | − | 0.467126i | \(-0.845290\pi\) | ||||
0.884191 | − | 0.467126i | \(-0.154710\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 241.000 | 0.286564 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 347.828i | 0.411630i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 302.093i | − 0.356662i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1821.47 | −2.14039 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1037.96i | − 1.21683i | −0.793617 | − | 0.608417i | \(-0.791805\pi\) | ||||
0.793617 | − | 0.608417i | \(-0.208195\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −936.034 | −1.09222 | −0.546111 | − | 0.837713i | \(-0.683892\pi\) | ||||
−0.546111 | + | 0.837713i | \(0.683892\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −872.000 | −1.01513 | −0.507567 | − | 0.861612i | \(-0.669455\pi\) | ||||
−0.507567 | + | 0.861612i | \(0.669455\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 352.727i | 0.408721i | 0.978896 | + | 0.204361i | \(0.0655115\pi\) | ||||
−0.978896 | + | 0.204361i | \(0.934488\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 888.000 | 1.02659 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 685.857i | 0.789249i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1239.35i | − 1.42291i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −986.631 | −1.12758 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 480.250i | 0.547605i | 0.961786 | + | 0.273803i | \(0.0882815\pi\) | ||||
−0.961786 | + | 0.273803i | \(0.911718\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −404.772 | −0.459446 | −0.229723 | − | 0.973256i | \(-0.573782\pi\) | ||||
−0.229723 | + | 0.973256i | \(0.573782\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1720.00 | 1.94790 | 0.973952 | − | 0.226752i | \(-0.0728108\pi\) | ||||
0.973952 | + | 0.226752i | \(0.0728108\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 548.686i | 0.618586i | 0.950967 | + | 0.309293i | \(0.100092\pi\) | ||||
−0.950967 | + | 0.309293i | \(0.899908\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 900.000 | 1.01237 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 313.535i | − 0.351103i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1363.29i | 1.52323i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 189.737 | 0.211053 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 371.806i | 0.412660i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1593.79 | −1.76109 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 760.000 | 0.837927 | 0.418964 | − | 0.908003i | \(-0.362393\pi\) | ||||
0.418964 | + | 0.908003i | \(0.362393\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1371.71i | − 1.50572i | −0.658179 | − | 0.752862i | \(-0.728673\pi\) | ||||
0.658179 | − | 0.752862i | \(-0.271327\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1760.00 | −1.92771 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 391.918i | 0.427392i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1231.61i | 1.34016i | 0.742288 | + | 0.670081i | \(0.233741\pi\) | ||||
−0.742288 | + | 0.670081i | \(0.766259\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 46.4758i | − 0.0502441i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 430.070 | 0.462938 | 0.231469 | − | 0.972842i | \(-0.425647\pi\) | ||||
0.231469 | + | 0.972842i | \(0.425647\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 88.0000 | 0.0945220 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 1567.67i | − 1.67666i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1330.00 | −1.41942 | −0.709712 | − | 0.704492i | \(-0.751175\pi\) | ||||
−0.709712 | + | 0.704492i | \(0.751175\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 563.383i | − 0.598706i | −0.954142 | − | 0.299353i | \(-0.903229\pi\) | ||||
0.954142 | − | 0.299353i | \(-0.0967709\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 991.484i | 1.05141i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1037.23 | −1.09528 | −0.547638 | − | 0.836715i | \(-0.684473\pi\) | ||||
−0.547638 | + | 0.836715i | \(0.684473\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 154.919i | − 0.163245i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.2982 | −0.0265459 | −0.0132729 | − | 0.999912i | \(-0.504225\pi\) | ||||
−0.0132729 | + | 0.999912i | \(0.504225\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −960.000 | −1.00524 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 979.796i | − 1.02168i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 901.000 | 0.937565 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 832.827i | − 0.863033i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1107.67i | − 1.14547i | −0.819739 | − | 0.572737i | \(-0.805882\pi\) | ||||
0.819739 | − | 0.572737i | \(-0.194118\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 746.298 | 0.768587 | 0.384293 | − | 0.923211i | \(-0.374445\pi\) | ||||
0.384293 | + | 0.923211i | \(0.374445\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 1611.16i | − 1.65587i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −480.666 | −0.491982 | −0.245991 | − | 0.969272i | \(-0.579113\pi\) | ||||
−0.245991 | + | 0.969272i | \(0.579113\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −640.000 | −0.653728 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 548.686i | − 0.558175i | −0.960266 | − | 0.279087i | \(-0.909968\pi\) | ||||
0.960266 | − | 0.279087i | \(-0.0900319\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −648.000 | −0.657868 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 1567.67i | − 1.58511i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1185.13i | 1.19590i | 0.801535 | + | 0.597948i | \(0.204017\pi\) | ||||
−0.801535 | + | 0.597948i | \(0.795983\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 341.526 | 0.343242 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 666.153i | − 0.668158i | −0.942545 | − | 0.334079i | \(-0.891575\pi\) | ||||
0.942545 | − | 0.334079i | \(-0.108425\pi\) | |||||||
\(998\) | 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 | 288.3.b.c.271.1 | 4 | ||
3.2 | odd | 2 | inner | 288.3.b.c.271.3 | 4 | ||
4.3 | odd | 2 | 72.3.b.c.19.3 | yes | 4 | ||
8.3 | odd | 2 | inner | 288.3.b.c.271.4 | 4 | ||
8.5 | even | 2 | 72.3.b.c.19.4 | yes | 4 | ||
12.11 | even | 2 | 72.3.b.c.19.2 | yes | 4 | ||
16.3 | odd | 4 | 2304.3.g.y.1279.1 | 8 | |||
16.5 | even | 4 | 2304.3.g.y.1279.8 | 8 | |||
16.11 | odd | 4 | 2304.3.g.y.1279.6 | 8 | |||
16.13 | even | 4 | 2304.3.g.y.1279.3 | 8 | |||
24.5 | odd | 2 | 72.3.b.c.19.1 | ✓ | 4 | ||
24.11 | even | 2 | inner | 288.3.b.c.271.2 | 4 | ||
48.5 | odd | 4 | 2304.3.g.y.1279.4 | 8 | |||
48.11 | even | 4 | 2304.3.g.y.1279.2 | 8 | |||
48.29 | odd | 4 | 2304.3.g.y.1279.7 | 8 | |||
48.35 | even | 4 | 2304.3.g.y.1279.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.3.b.c.19.1 | ✓ | 4 | 24.5 | odd | 2 | ||
72.3.b.c.19.2 | yes | 4 | 12.11 | even | 2 | ||
72.3.b.c.19.3 | yes | 4 | 4.3 | odd | 2 | ||
72.3.b.c.19.4 | yes | 4 | 8.5 | even | 2 | ||
288.3.b.c.271.1 | 4 | 1.1 | even | 1 | trivial | ||
288.3.b.c.271.2 | 4 | 24.11 | even | 2 | inner | ||
288.3.b.c.271.3 | 4 | 3.2 | odd | 2 | inner | ||
288.3.b.c.271.4 | 4 | 8.3 | odd | 2 | inner | ||
2304.3.g.y.1279.1 | 8 | 16.3 | odd | 4 | |||
2304.3.g.y.1279.2 | 8 | 48.11 | even | 4 | |||
2304.3.g.y.1279.3 | 8 | 16.13 | even | 4 | |||
2304.3.g.y.1279.4 | 8 | 48.5 | odd | 4 | |||
2304.3.g.y.1279.5 | 8 | 48.35 | even | 4 | |||
2304.3.g.y.1279.6 | 8 | 16.11 | odd | 4 | |||
2304.3.g.y.1279.7 | 8 | 48.29 | odd | 4 | |||
2304.3.g.y.1279.8 | 8 | 16.5 | even | 4 |