Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5040,2,Mod(1009,5040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5040, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5040.1009");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5040 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5040.t (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: | \(40.2446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1009.1 | ||
Root | \(-1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5040.1009 |
Dual form | 5040.2.t.t.1009.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5040\mathbb{Z}\right)^\times\).
\(n\) | \(2017\) | \(2801\) | \(3151\) | \(3601\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.22474 | − | 0.224745i | −0.994936 | − | 0.100509i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.89898 | −1.47710 | −0.738549 | − | 0.674200i | \(-0.764489\pi\) | ||||
−0.738549 | + | 0.674200i | \(0.764489\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.44949i | 1.23407i | 0.786937 | + | 0.617033i | \(0.211666\pi\) | ||||
−0.786937 | + | 0.617033i | \(0.788334\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000i | 0.485071i | 0.970143 | + | 0.242536i | \(0.0779791\pi\) | ||||
−0.970143 | + | 0.242536i | \(0.922021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.55051 | 0.355711 | 0.177856 | − | 0.984057i | \(-0.443084\pi\) | ||||
0.177856 | + | 0.984057i | \(0.443084\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.89898i | 0.604479i | 0.953232 | + | 0.302240i | \(0.0977342\pi\) | ||||
−0.953232 | + | 0.302240i | \(0.902266\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.89898 | + | 1.00000i | 0.979796 | + | 0.200000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.89898 | 1.28111 | 0.640554 | − | 0.767913i | \(-0.278705\pi\) | ||||
0.640554 | + | 0.767913i | \(0.278705\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.89898 | −1.59830 | −0.799152 | − | 0.601129i | \(-0.794718\pi\) | ||||
−0.799152 | + | 0.601129i | \(0.794718\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.224745 | + | 2.22474i | −0.0379888 | + | 0.376051i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.00000i | − | 0.328798i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) | ||
0.986394 | − | 0.164399i | \(-0.0525685\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.10102 | 0.171951 | 0.0859753 | − | 0.996297i | \(-0.472599\pi\) | ||||
0.0859753 | + | 0.996297i | \(0.472599\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.898979i | 0.137093i | 0.997648 | + | 0.0685465i | \(0.0218362\pi\) | ||||
−0.997648 | + | 0.0685465i | \(0.978164\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 8.89898i | − | 1.29805i | −0.760767 | − | 0.649025i | \(-0.775177\pi\) | ||
0.760767 | − | 0.649025i | \(-0.224823\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.8990i | 1.49709i | 0.663084 | + | 0.748545i | \(0.269247\pi\) | ||||
−0.663084 | + | 0.748545i | \(0.730753\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.8990 | + | 1.10102i | 1.46962 | + | 0.148462i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.55051 | 0.201859 | 0.100930 | − | 0.994894i | \(-0.467818\pi\) | ||||
0.100930 | + | 0.994894i | \(0.467818\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.55051 | 0.454596 | 0.227298 | − | 0.973825i | \(-0.427011\pi\) | ||||
0.227298 | + | 0.973825i | \(0.427011\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | − | 9.89898i | 0.124035 | − | 1.22782i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8.00000i | − | 0.977356i | −0.872464 | − | 0.488678i | \(-0.837479\pi\) | ||
0.872464 | − | 0.488678i | \(-0.162521\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.10102 | −0.130667 | −0.0653335 | − | 0.997863i | \(-0.520811\pi\) | ||||
−0.0653335 | + | 0.997863i | \(0.520811\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.89898i | 0.339300i | 0.985504 | + | 0.169650i | \(0.0542637\pi\) | ||||
−0.985504 | + | 0.169650i | \(0.945736\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.89898i | 0.558291i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.89898 | 0.776196 | 0.388098 | − | 0.921618i | \(-0.373132\pi\) | ||||
0.388098 | + | 0.921618i | \(0.373132\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 2.44949i | − | 0.268866i | −0.990923 | − | 0.134433i | \(-0.957079\pi\) | ||
0.990923 | − | 0.134433i | \(-0.0429214\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.449490 | − | 4.44949i | 0.0487540 | − | 0.482615i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.0000 | −1.06000 | −0.529999 | − | 0.847998i | \(-0.677808\pi\) | ||||
−0.529999 | + | 0.847998i | \(0.677808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.44949 | 0.466433 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.44949 | − | 0.348469i | −0.353910 | − | 0.0357522i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 15.7980i | − | 1.60404i | −0.597297 | − | 0.802020i | \(-0.703759\pi\) | ||
0.597297 | − | 0.802020i | \(-0.296241\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.55051 | −0.353289 | −0.176644 | − | 0.984275i | \(-0.556524\pi\) | ||||
−0.176644 | + | 0.984275i | \(0.556524\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 12.8990i | − | 1.27097i | −0.772111 | − | 0.635487i | \(-0.780799\pi\) | ||
0.772111 | − | 0.635487i | \(-0.219201\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.00000i | 0.773389i | 0.922208 | + | 0.386695i | \(0.126383\pi\) | ||||
−0.922208 | + | 0.386695i | \(0.873617\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.89898 | −0.660802 | −0.330401 | − | 0.943841i | \(-0.607184\pi\) | ||||
−0.330401 | + | 0.943841i | \(0.607184\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 19.7980i | − | 1.86244i | −0.364464 | − | 0.931218i | \(-0.618748\pi\) | ||
0.364464 | − | 0.931218i | \(-0.381252\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.651531 | − | 6.44949i | 0.0607556 | − | 0.601418i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.00000 | 0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.0000 | 1.18182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.6742 | − | 3.32577i | −0.954733 | − | 0.297465i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 14.8990i | − | 1.32207i | −0.750355 | − | 0.661035i | \(-0.770117\pi\) | ||
0.750355 | − | 0.661035i | \(-0.229883\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.44949 | −0.563495 | −0.281747 | − | 0.959489i | \(-0.590914\pi\) | ||||
−0.281747 | + | 0.959489i | \(0.590914\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 1.55051i | − | 0.134446i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 1.79796i | − | 0.153610i | −0.997046 | − | 0.0768050i | \(-0.975528\pi\) | ||
0.997046 | − | 0.0768050i | \(-0.0244719\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.55051 | 0.131513 | 0.0657563 | − | 0.997836i | \(-0.479054\pi\) | ||||
0.0657563 | + | 0.997836i | \(0.479054\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 21.7980i | − | 1.82284i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.3485 | − | 1.55051i | −1.27462 | − | 0.128763i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.79796 | −0.311141 | −0.155570 | − | 0.987825i | \(-0.549722\pi\) | ||||
−0.155570 | + | 0.987825i | \(0.549722\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.5959 | −1.59469 | −0.797347 | − | 0.603522i | \(-0.793764\pi\) | ||||
−0.797347 | + | 0.603522i | \(0.793764\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.7980 | + | 2.00000i | 1.59021 | + | 0.160644i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 3.55051i | − | 0.283362i | −0.989912 | − | 0.141681i | \(-0.954749\pi\) | ||
0.989912 | − | 0.141681i | \(-0.0452507\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.89898 | 0.228472 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.10102i | 0.556195i | 0.960553 | + | 0.278097i | \(0.0897038\pi\) | ||||
−0.960553 | + | 0.278097i | \(0.910296\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.89898i | 0.379094i | 0.981872 | + | 0.189547i | \(0.0607020\pi\) | ||||
−0.981872 | + | 0.189547i | \(0.939298\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.79796 | −0.522920 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.24745i | 0.474985i | 0.971389 | + | 0.237492i | \(0.0763255\pi\) | ||||
−0.971389 | + | 0.237492i | \(0.923675\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | − | 4.89898i | 0.0755929 | − | 0.370328i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.7980 | −1.03131 | −0.515654 | − | 0.856797i | \(-0.672451\pi\) | ||||
−0.515654 | + | 0.856797i | \(0.672451\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.2474 | −0.761687 | −0.380843 | − | 0.924640i | \(-0.624366\pi\) | ||||
−0.380843 | + | 0.924640i | \(0.624366\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.449490 | + | 4.44949i | −0.0330471 | + | 0.327133i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 9.79796i | − | 0.716498i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.6969 | 0.918718 | 0.459359 | − | 0.888251i | \(-0.348079\pi\) | ||||
0.459359 | + | 0.888251i | \(0.348079\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 21.5959i | − | 1.55451i | −0.629187 | − | 0.777254i | \(-0.716612\pi\) | ||
0.629187 | − | 0.777254i | \(-0.283388\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.8990i | 1.34650i | 0.739417 | + | 0.673248i | \(0.235101\pi\) | ||||
−0.739417 | + | 0.673248i | \(0.764899\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.8990 | 1.19794 | 0.598968 | − | 0.800773i | \(-0.295577\pi\) | ||||
0.598968 | + | 0.800773i | \(0.295577\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 6.89898i | − | 0.484213i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.44949 | − | 0.247449i | −0.171080 | − | 0.0172826i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.59592 | −0.525421 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.202041 | − | 2.00000i | 0.0137791 | − | 0.136399i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.89898i | 0.604102i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.89898 | −0.598610 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.00000i | 0.267860i | 0.990991 | + | 0.133930i | \(0.0427597\pi\) | ||||
−0.990991 | + | 0.133930i | \(0.957240\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 7.34847i | − | 0.487735i | −0.969809 | − | 0.243868i | \(-0.921584\pi\) | ||
0.969809 | − | 0.243868i | \(-0.0784162\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.1464 | 1.26523 | 0.632616 | − | 0.774466i | \(-0.281981\pi\) | ||||
0.632616 | + | 0.774466i | \(0.281981\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 29.7980i | − | 1.95213i | −0.217481 | − | 0.976065i | \(-0.569784\pi\) | ||
0.217481 | − | 0.976065i | \(-0.430216\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.00000 | + | 19.7980i | −0.130466 | + | 1.29148i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.20204 | 0.401177 | 0.200588 | − | 0.979676i | \(-0.435715\pi\) | ||||
0.200588 | + | 0.979676i | \(0.435715\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.69694 | −0.560219 | −0.280110 | − | 0.959968i | \(-0.590371\pi\) | ||||
−0.280110 | + | 0.959968i | \(0.590371\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.22474 | + | 0.224745i | 0.142134 | + | 0.0143584i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.89898i | 0.438972i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.44949 | −0.407088 | −0.203544 | − | 0.979066i | \(-0.565246\pi\) | ||||
−0.203544 | + | 0.979066i | \(0.565246\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 14.2020i | − | 0.892875i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 8.69694i | − | 0.542500i | −0.962509 | − | 0.271250i | \(-0.912563\pi\) | ||
0.962509 | − | 0.271250i | \(-0.0874370\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.00000 | −0.124274 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.79796i | 0.604168i | 0.953281 | + | 0.302084i | \(0.0976823\pi\) | ||||
−0.953281 | + | 0.302084i | \(0.902318\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.44949 | − | 24.2474i | 0.150471 | − | 1.48951i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.1464 | 1.16738 | 0.583689 | − | 0.811977i | \(-0.301609\pi\) | ||||
0.583689 | + | 0.811977i | \(0.301609\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.0000 | −0.728948 | −0.364474 | − | 0.931214i | \(-0.618751\pi\) | ||||
−0.364474 | + | 0.931214i | \(0.618751\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −24.0000 | − | 4.89898i | −1.44725 | − | 0.295420i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.8990i | 0.895193i | 0.894236 | + | 0.447596i | \(0.147720\pi\) | ||||
−0.894236 | + | 0.447596i | \(0.852280\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.0000 | 1.07379 | 0.536895 | − | 0.843649i | \(-0.319597\pi\) | ||||
0.536895 | + | 0.843649i | \(0.319597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 3.75255i | − | 0.223066i | −0.993761 | − | 0.111533i | \(-0.964424\pi\) | ||
0.993761 | − | 0.111533i | \(-0.0355761\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 1.10102i | − | 0.0649912i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 18.2474i | − | 1.06603i | −0.846107 | − | 0.533014i | \(-0.821059\pi\) | ||
0.846107 | − | 0.533014i | \(-0.178941\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.44949 | − | 0.348469i | −0.200837 | − | 0.0202887i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.8990 | −0.745967 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.898979 | 0.0518163 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.89898 | − | 0.797959i | −0.452294 | − | 0.0456910i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 20.2474i | − | 1.15558i | −0.816184 | − | 0.577791i | \(-0.803915\pi\) | ||
0.816184 | − | 0.577791i | \(-0.196085\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 21.5959i | − | 1.22067i | −0.792142 | − | 0.610337i | \(-0.791034\pi\) | ||
0.792142 | − | 0.610337i | \(-0.208966\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 22.4949i | − | 1.26344i | −0.775197 | − | 0.631720i | \(-0.782349\pi\) | ||
0.775197 | − | 0.631720i | \(-0.217651\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −33.7980 | −1.89232 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.10102i | 0.172545i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.44949 | + | 21.7980i | −0.246813 | + | 1.20913i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.89898 | −0.490617 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.6969 | 1.02768 | 0.513838 | − | 0.857887i | \(-0.328223\pi\) | ||||
0.513838 | + | 0.857887i | \(0.328223\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.79796 | + | 17.7980i | −0.0982330 | + | 0.972406i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 9.59592i | − | 0.522723i | −0.965241 | − | 0.261361i | \(-0.915829\pi\) | ||
0.965241 | − | 0.261361i | \(-0.0841715\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 43.5959 | 2.36085 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 28.8990i | − | 1.55138i | −0.631115 | − | 0.775689i | \(-0.717402\pi\) | ||
0.631115 | − | 0.775689i | \(-0.282598\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.44949 | 0.452291 | 0.226145 | − | 0.974094i | \(-0.427388\pi\) | ||||
0.226145 | + | 0.974094i | \(0.427388\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 22.8990i | − | 1.21879i | −0.792867 | − | 0.609395i | \(-0.791412\pi\) | ||
0.792867 | − | 0.609395i | \(-0.208588\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.44949 | + | 0.247449i | 0.130005 | + | 0.0131332i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.5959 | 1.45646 | 0.728228 | − | 0.685334i | \(-0.240344\pi\) | ||||
0.728228 | + | 0.685334i | \(0.240344\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.5959 | −0.873469 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.651531 | − | 6.44949i | 0.0341027 | − | 0.337582i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.0000i | 1.67039i | 0.549957 | + | 0.835193i | \(0.314644\pi\) | ||||
−0.549957 | + | 0.835193i | \(0.685356\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.8990 | 0.565847 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 4.69694i | − | 0.243198i | −0.992579 | − | 0.121599i | \(-0.961198\pi\) | ||
0.992579 | − | 0.121599i | \(-0.0388022\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 30.6969i | 1.58097i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.6969 | 1.57680 | 0.788398 | − | 0.615166i | \(-0.210911\pi\) | ||||
0.788398 | + | 0.615166i | \(0.210911\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 7.10102i | − | 0.362845i | −0.983405 | − | 0.181423i | \(-0.941930\pi\) | ||
0.983405 | − | 0.181423i | \(-0.0580702\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.10102 | − | 10.8990i | 0.0561132 | − | 0.555463i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.1010 | 0.664248 | 0.332124 | − | 0.943236i | \(-0.392235\pi\) | ||||
0.332124 | + | 0.943236i | \(0.392235\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.79796 | −0.293215 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.3485 | − | 1.55051i | −0.772265 | − | 0.0780146i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.65153i | 0.133077i | 0.997784 | + | 0.0665383i | \(0.0211954\pi\) | ||||
−0.997784 | + | 0.0665383i | \(0.978805\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.3939 | 1.46786 | 0.733930 | − | 0.679225i | \(-0.237684\pi\) | ||||
0.733930 | + | 0.679225i | \(0.237684\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 39.5959i | − | 1.97241i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.79796i | 0.485667i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −34.4949 | −1.70566 | −0.852831 | − | 0.522186i | \(-0.825117\pi\) | ||||
−0.852831 | + | 0.522186i | \(0.825117\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 1.55051i | − | 0.0762956i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.550510 | + | 5.44949i | −0.0270235 | + | 0.267505i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.55051 | 0.0757474 | 0.0378737 | − | 0.999283i | \(-0.487942\pi\) | ||||
0.0378737 | + | 0.999283i | \(0.487942\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.20204 | −0.204795 | −0.102397 | − | 0.994744i | \(-0.532651\pi\) | ||||
−0.102397 | + | 0.994744i | \(0.532651\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.00000 | + | 9.79796i | −0.0970143 | + | 0.475271i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 3.55051i | − | 0.171821i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.79796 | −0.0866046 | −0.0433023 | − | 0.999062i | \(-0.513788\pi\) | ||||
−0.0433023 | + | 0.999062i | \(0.513788\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 0.202041i | − | 0.00970947i | −0.999988 | − | 0.00485474i | \(-0.998455\pi\) | ||
0.999988 | − | 0.00485474i | \(-0.00154532\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.49490i | 0.215020i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.3939 | −1.02107 | −0.510537 | − | 0.859856i | \(-0.670553\pi\) | ||||
−0.510537 | + | 0.859856i | \(0.670553\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.79796i | 0.465515i | 0.972535 | + | 0.232758i | \(0.0747749\pi\) | ||||
−0.972535 | + | 0.232758i | \(0.925225\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.2474 | + | 2.24745i | 1.05463 | + | 0.106539i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.0000 | −0.471929 | −0.235965 | − | 0.971762i | \(-0.575825\pi\) | ||||
−0.235965 | + | 0.971762i | \(0.575825\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.39388 | −0.253988 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.89898 | − | 1.00000i | −0.464071 | − | 0.0468807i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 29.5959i | − | 1.38444i | −0.721687 | − | 0.692219i | \(-0.756633\pi\) | ||
0.721687 | − | 0.692219i | \(-0.243367\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.3485 | −0.807999 | −0.403999 | − | 0.914759i | \(-0.632380\pi\) | ||||
−0.403999 | + | 0.914759i | \(0.632380\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 3.59592i | − | 0.167116i | −0.996503 | − | 0.0835582i | \(-0.973372\pi\) | ||
0.996503 | − | 0.0835582i | \(-0.0266285\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 10.4495i | − | 0.483545i | −0.970333 | − | 0.241772i | \(-0.922271\pi\) | ||
0.970333 | − | 0.241772i | \(-0.0777287\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.00000 | −0.369406 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 4.40408i | − | 0.202500i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.59592 | + | 1.55051i | 0.348525 | + | 0.0711423i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.30306 | −0.425068 | −0.212534 | − | 0.977154i | \(-0.568172\pi\) | ||||
−0.212534 | + | 0.977154i | \(0.568172\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.89898 | 0.405759 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.55051 | + | 35.1464i | −0.161220 | + | 1.59592i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 7.30306i | − | 0.330933i | −0.986215 | − | 0.165467i | \(-0.947087\pi\) | ||
0.986215 | − | 0.165467i | \(-0.0529130\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.5959 | 0.884351 | 0.442176 | − | 0.896928i | \(-0.354207\pi\) | ||||
0.442176 | + | 0.896928i | \(0.354207\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.7980i | 0.621429i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.10102i | 0.0493875i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.20204 | 0.277641 | 0.138821 | − | 0.990318i | \(-0.455669\pi\) | ||||
0.138821 | + | 0.990318i | \(0.455669\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 4.00000i | − | 0.178351i | −0.996016 | − | 0.0891756i | \(-0.971577\pi\) | ||
0.996016 | − | 0.0891756i | \(-0.0284232\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.89898 | + | 0.797959i | 0.351500 | + | 0.0355087i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.5505 | −1.39845 | −0.699226 | − | 0.714901i | \(-0.746472\pi\) | ||||
−0.699226 | + | 0.714901i | \(0.746472\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.89898 | 0.128243 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.89898 | + | 28.6969i | −0.127744 | + | 1.26454i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 43.5959i | 1.91735i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.6969 | −1.43248 | −0.716239 | − | 0.697855i | \(-0.754138\pi\) | ||||
−0.716239 | + | 0.697855i | \(0.754138\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.1464i | 1.44939i | 0.689069 | + | 0.724696i | \(0.258020\pi\) | ||||
−0.689069 | + | 0.724696i | \(0.741980\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 17.7980i | − | 0.775291i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.5959 | 0.634605 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.89898i | 0.212198i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.79796 | − | 17.7980i | 0.0777325 | − | 0.769473i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.89898 | 0.211014 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.59592 | 0.412561 | 0.206280 | − | 0.978493i | \(-0.433864\pi\) | ||||
0.206280 | + | 0.978493i | \(0.433864\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.3485 | + | 1.55051i | 0.657456 | + | 0.0664166i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 18.6969i | − | 0.799423i | −0.916641 | − | 0.399712i | \(-0.869110\pi\) | ||
0.916641 | − | 0.399712i | \(-0.130890\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.6969 | 0.455705 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 6.89898i | − | 0.293374i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.6969i | 0.537987i | 0.963142 | + | 0.268993i | \(0.0866909\pi\) | ||||
−0.963142 | + | 0.268993i | \(0.913309\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.00000 | −0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 30.0454i | − | 1.26626i | −0.774044 | − | 0.633131i | \(-0.781769\pi\) | ||
0.774044 | − | 0.633131i | \(-0.218231\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.44949 | + | 44.0454i | −0.187191 | + | 1.85300i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.7980 | 1.41688 | 0.708442 | − | 0.705769i | \(-0.249398\pi\) | ||||
0.708442 | + | 0.705769i | \(0.249398\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.1010 | 0.464563 | 0.232282 | − | 0.972649i | \(-0.425381\pi\) | ||||
0.232282 | + | 0.972649i | \(0.425381\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.89898 | + | 14.2020i | −0.120896 | + | 0.592266i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.49490i | 0.103864i | 0.998651 | + | 0.0519320i | \(0.0165379\pi\) | ||||
−0.998651 | + | 0.0519320i | \(0.983462\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.44949 | −0.101622 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 53.3939i | − | 2.21135i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 1.14643i | − | 0.0473182i | −0.999720 | − | 0.0236591i | \(-0.992468\pi\) | ||
0.999720 | − | 0.0236591i | \(-0.00753162\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.7980 | −0.568535 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.8990i | 0.447567i | 0.974639 | + | 0.223784i | \(0.0718409\pi\) | ||||
−0.974639 | + | 0.223784i | \(0.928159\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.44949 | − | 0.449490i | −0.182411 | − | 0.0184273i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.1010 | 0.535293 | 0.267647 | − | 0.963517i | \(-0.413754\pi\) | ||||
0.267647 | + | 0.963517i | \(0.413754\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.3939 | −1.60691 | −0.803455 | − | 0.595366i | \(-0.797007\pi\) | ||||
−0.803455 | + | 0.595366i | \(0.797007\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −28.9217 | − | 2.92168i | −1.17583 | − | 0.118783i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.3939i | 1.35542i | 0.735331 | + | 0.677708i | \(0.237027\pi\) | ||||
−0.735331 | + | 0.677708i | \(0.762973\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 39.5959 | 1.60188 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 27.7980i | − | 1.12275i | −0.827562 | − | 0.561374i | \(-0.810273\pi\) | ||
0.827562 | − | 0.561374i | \(-0.189727\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.5959i | 1.19149i | 0.803175 | + | 0.595743i | \(0.203142\pi\) | ||||
−0.803175 | + | 0.595743i | \(0.796858\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −41.5505 | −1.67006 | −0.835028 | − | 0.550207i | \(-0.814549\pi\) | ||||
−0.835028 | + | 0.550207i | \(0.814549\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.0000i | 0.400642i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.0000 | + | 9.79796i | 0.920000 | + | 0.391918i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.00000 | 0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.4949 | 1.69170 | 0.845848 | − | 0.533425i | \(-0.179095\pi\) | ||||
0.845848 | + | 0.533425i | \(0.179095\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.34847 | + | 33.1464i | −0.132880 | + | 1.31538i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 4.44949i | − | 0.176295i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.7980 | −1.01896 | −0.509479 | − | 0.860483i | \(-0.670162\pi\) | ||||
−0.509479 | + | 0.860483i | \(0.670162\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 25.1464i | − | 0.991678i | −0.868414 | − | 0.495839i | \(-0.834861\pi\) | ||
0.868414 | − | 0.495839i | \(-0.165139\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 46.2929i | 1.81996i | 0.414652 | + | 0.909980i | \(0.363903\pi\) | ||||
−0.414652 | + | 0.909980i | \(0.636097\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.59592 | −0.298166 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.2020i | 0.790567i | 0.918559 | + | 0.395283i | \(0.129354\pi\) | ||||
−0.918559 | + | 0.395283i | \(0.870646\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.3485 | + | 1.44949i | 0.560641 | + | 0.0566363i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.8990 | −0.658291 | −0.329145 | − | 0.944279i | \(-0.606761\pi\) | ||||
−0.329145 | + | 0.944279i | \(0.606761\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.9444 | −1.59255 | −0.796276 | − | 0.604933i | \(-0.793200\pi\) | ||||
−0.796276 | + | 0.604933i | \(0.793200\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.348469 | + | 3.44949i | −0.0135131 | + | 0.133765i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.0000i | 0.774403i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.3939 | −0.671483 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 17.7980i | − | 0.686061i | −0.939324 | − | 0.343030i | \(-0.888547\pi\) | ||
0.939324 | − | 0.343030i | \(-0.111453\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 36.4495i | − | 1.40087i | −0.713717 | − | 0.700434i | \(-0.752990\pi\) | ||
0.713717 | − | 0.700434i | \(-0.247010\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.7980 | −0.606270 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.59592i | 0.137594i | 0.997631 | + | 0.0687970i | \(0.0219161\pi\) | ||||
−0.997631 | + | 0.0687970i | \(0.978084\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.404082 | + | 4.00000i | −0.0154392 | + | 0.152832i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −48.4949 | −1.84751 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.1464 | −0.804448 | −0.402224 | − | 0.915541i | \(-0.631763\pi\) | ||||
−0.402224 | + | 0.915541i | \(0.631763\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.44949 | − | 0.348469i | −0.130847 | − | 0.0132182i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.20204i | 0.0834083i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.3031 | −0.426911 | −0.213455 | − | 0.976953i | \(-0.568472\pi\) | ||||
−0.213455 | + | 0.976953i | \(0.568472\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3.10102i | − | 0.116957i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.55051i | 0.133531i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.2929 | 1.06256 | 0.531280 | − | 0.847196i | \(-0.321711\pi\) | ||||
0.531280 | + | 0.847196i | \(0.321711\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 25.7980i | − | 0.966141i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.89898 | + | 48.4949i | −0.183211 | + | 1.81361i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.49490 | 0.167631 | 0.0838157 | − | 0.996481i | \(-0.473289\pi\) | ||||
0.0838157 | + | 0.996481i | \(0.473289\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.8990 | −0.480383 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 33.7980 | + | 6.89898i | 1.25522 | + | 0.256222i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.6969i | 0.841783i | 0.907111 | + | 0.420891i | \(0.138283\pi\) | ||||
−0.907111 | + | 0.420891i | \(0.861717\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.79796 | −0.0664999 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.6413i | 1.46419i | 0.681205 | + | 0.732093i | \(0.261456\pi\) | ||||
−0.681205 | + | 0.732093i | \(0.738544\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 39.1918i | 1.44365i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.49490 | 0.165347 | 0.0826737 | − | 0.996577i | \(-0.473654\pi\) | ||||
0.0826737 | + | 0.996577i | \(0.473654\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 44.6969i | − | 1.63977i | −0.572527 | − | 0.819886i | \(-0.694037\pi\) | ||
0.572527 | − | 0.819886i | \(-0.305963\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.44949 | + | 0.853572i | 0.309565 | + | 0.0312725i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.00000 | 0.292314 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.7980 | 1.52523 | 0.762615 | − | 0.646853i | \(-0.223915\pi\) | ||||
0.762615 | + | 0.646853i | \(0.223915\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 43.5959 | + | 4.40408i | 1.58662 | + | 0.160281i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 51.7980i | 1.88263i | 0.337531 | + | 0.941314i | \(0.390408\pi\) | ||||
−0.337531 | + | 0.941314i | \(0.609592\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.1010 | 0.764911 | 0.382456 | − | 0.923974i | \(-0.375078\pi\) | ||||
0.382456 | + | 0.923974i | \(0.375078\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.89898i | 0.249760i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.89898i | 0.249108i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.6969 | 1.46757 | 0.733785 | − | 0.679382i | \(-0.237752\pi\) | ||||
0.733785 | + | 0.679382i | \(0.237752\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1.34847i | − | 0.0485011i | −0.999706 | − | 0.0242505i | \(-0.992280\pi\) | ||
0.999706 | − | 0.0242505i | \(-0.00771994\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −43.5959 | − | 8.89898i | −1.56601 | − | 0.319661i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.70714 | 0.0611648 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.39388 | 0.193008 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.797959 | + | 7.89898i | −0.0284804 | + | 0.281927i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 50.4495i | 1.79833i | 0.437610 | + | 0.899165i | \(0.355825\pi\) | ||||
−0.437610 | + | 0.899165i | \(0.644175\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.7980 | −0.703934 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.7980i | 0.561002i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 0.944387i | − | 0.0334519i | −0.999860 | − | 0.0167260i | \(-0.994676\pi\) | ||
0.999860 | − | 0.0167260i | \(-0.00532429\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.7980 | 0.629647 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 14.2020i | − | 0.501179i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.44949 | − | 0.651531i | −0.227315 | − | 0.0229634i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 47.5959 | 1.67338 | 0.836692 | − | 0.547674i | \(-0.184487\pi\) | ||||
0.836692 | + | 0.547674i | \(0.184487\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.9444 | −0.524768 | −0.262384 | − | 0.964963i | \(-0.584509\pi\) | ||||
−0.262384 | + | 0.964963i | \(0.584509\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.59592 | − | 15.7980i | 0.0559026 | − | 0.553378i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.39388i | 0.0487656i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.20204 | −0.286253 | −0.143127 | − | 0.989704i | \(-0.545716\pi\) | ||||
−0.143127 | + | 0.989704i | \(0.545716\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.1918i | 1.36614i | 0.730352 | + | 0.683071i | \(0.239356\pi\) | ||||
−0.730352 | + | 0.683071i | \(0.760644\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.5959i | 0.542323i | 0.962534 | + | 0.271162i | \(0.0874078\pi\) | ||||
−0.962534 | + | 0.271162i | \(0.912592\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43.6413 | 1.51573 | 0.757863 | − | 0.652414i | \(-0.226244\pi\) | ||||
0.757863 | + | 0.652414i | \(0.226244\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 2.00000i | − | 0.0692959i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.10102 | − | 10.8990i | 0.0381024 | − | 0.377175i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.8990 | −1.27389 | −0.636947 | − | 0.770907i | \(-0.719803\pi\) | ||||
−0.636947 | + | 0.770907i | \(0.719803\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.5959 | 0.641239 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15.1237 | + | 1.52781i | 0.520272 | + | 0.0525581i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 13.0000i | − | 0.446685i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.79796 | 0.198751 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 33.8434i | − | 1.15877i | −0.815052 | − | 0.579387i | \(-0.803292\pi\) | ||
0.815052 | − | 0.579387i | \(-0.196708\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 53.1918i | − | 1.81700i | −0.417886 | − | 0.908499i | \(-0.637229\pi\) | ||
0.417886 | − | 0.908499i | \(-0.362771\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.6413 | 1.83022 | 0.915109 | − | 0.403206i | \(-0.132104\pi\) | ||||
0.915109 | + | 0.403206i | \(0.132104\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 45.3939i | − | 1.54523i | −0.634878 | − | 0.772613i | \(-0.718949\pi\) | ||
0.634878 | − | 0.772613i | \(-0.281051\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.40408 | − | 13.8990i | 0.0477402 | − | 0.472579i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −33.7980 | −1.14652 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.5959 | 1.20612 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.32577 | + | 10.6742i | −0.112431 | + | 0.360855i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 39.3939i | 1.33024i | 0.746738 | + | 0.665118i | \(0.231619\pi\) | ||||
−0.746738 | + | 0.665118i | \(0.768381\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.20204 | −0.276334 | −0.138167 | − | 0.990409i | \(-0.544121\pi\) | ||||
−0.138167 | + | 0.990409i | \(0.544121\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 22.2020i | − | 0.747158i | −0.927598 | − | 0.373579i | \(-0.878130\pi\) | ||
0.927598 | − | 0.373579i | \(-0.121870\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 2.69694i | − | 0.0905543i | −0.998974 | − | 0.0452772i | \(-0.985583\pi\) | ||
0.998974 | − | 0.0452772i | \(-0.0144171\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.8990 | −0.499696 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 13.7980i | − | 0.461731i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30.6969 | + | 3.10102i | 1.02609 | + | 0.103656i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −61.3939 | −2.04760 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.7980 | −0.726195 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.7980 | + | 2.30306i | 0.757830 | + | 0.0765564i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 41.7980i | − | 1.38788i | −0.720034 | − | 0.693939i | \(-0.755874\pi\) | ||
0.720034 | − | 0.693939i | \(-0.244126\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.5959 | −1.17935 | −0.589673 | − | 0.807642i | \(-0.700743\pi\) | ||||
−0.589673 | + | 0.807642i | \(0.700743\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.0000i | 0.397142i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.44949i | 0.212981i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.8990 | −0.887315 | −0.443658 | − | 0.896196i | \(-0.646319\pi\) | ||||
−0.443658 | + | 0.896196i | \(0.646319\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 4.89898i | − | 0.161252i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.00000 | − | 9.79796i | 0.0657596 | − | 0.322155i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.2929 | −0.928259 | −0.464129 | − | 0.885767i | \(-0.653633\pi\) | ||||
−0.464129 | + | 0.885767i | \(0.653633\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.55051 | −0.0508159 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.20204 | + | 21.7980i | −0.0720144 | + | 0.712869i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.1010i | 1.34271i | 0.741135 | + | 0.671356i | \(0.234288\pi\) | ||||
−0.741135 | + | 0.671356i | \(0.765712\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.5505 | 0.637328 | 0.318664 | − | 0.947868i | \(-0.396766\pi\) | ||||
0.318664 | + | 0.947868i | \(0.396766\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.19184i | 0.103940i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 44.0908i | − | 1.43276i | −0.697711 | − | 0.716379i | \(-0.745798\pi\) | ||
0.697711 | − | 0.716379i | \(-0.254202\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.8990 | −0.418719 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 2.20204i | − | 0.0713311i | −0.999364 | − | 0.0356656i | \(-0.988645\pi\) | ||
0.999364 | − | 0.0356656i | \(-0.0113551\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −28.2474 | − | 2.85357i | −0.914066 | − | 0.0923394i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.79796 | −0.0580591 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 48.1918 | 1.55458 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.85357 | + | 48.0454i | −0.156242 | + | 1.54664i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 36.2929i | − | 1.16710i | −0.812077 | − | 0.583550i | \(-0.801663\pi\) | ||
0.812077 | − | 0.583550i | \(-0.198337\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.55051 | −0.306490 | −0.153245 | − | 0.988188i | \(-0.548972\pi\) | ||||
−0.153245 | + | 0.988188i | \(0.548972\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1.55051i | − | 0.0497071i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 29.3939i | − | 0.940393i | −0.882562 | − | 0.470197i | \(-0.844183\pi\) | ||
0.882562 | − | 0.470197i | \(-0.155817\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.9898 | 1.56572 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 13.3031i | − | 0.424302i | −0.977237 | − | 0.212151i | \(-0.931953\pi\) | ||
0.977237 | − | 0.212151i | \(-0.0680468\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.24745 | − | 42.0454i | 0.135335 | − | 1.33968i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.60612 | −0.0828699 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.3031 | −0.994375 | −0.497187 | − | 0.867643i | \(-0.665634\pi\) | ||||
−0.497187 | + | 0.867643i | \(0.665634\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −37.5959 | − | 3.79796i | −1.19187 | − | 0.120403i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 57.3485i | − | 1.81624i | −0.418705 | − | 0.908122i | \(-0.637516\pi\) | ||
0.418705 | − | 0.908122i | \(-0.362484\pi\) | |||||||
\(998\) | 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 | 5040.2.t.t.1009.1 | 4 | ||
3.2 | odd | 2 | 560.2.g.e.449.4 | 4 | |||
4.3 | odd | 2 | 630.2.g.g.379.1 | 4 | |||
5.4 | even | 2 | inner | 5040.2.t.t.1009.2 | 4 | ||
12.11 | even | 2 | 70.2.c.a.29.3 | yes | 4 | ||
15.2 | even | 4 | 2800.2.a.bm.1.2 | 2 | |||
15.8 | even | 4 | 2800.2.a.bl.1.1 | 2 | |||
15.14 | odd | 2 | 560.2.g.e.449.2 | 4 | |||
20.3 | even | 4 | 3150.2.a.bs.1.2 | 2 | |||
20.7 | even | 4 | 3150.2.a.bt.1.2 | 2 | |||
20.19 | odd | 2 | 630.2.g.g.379.3 | 4 | |||
24.5 | odd | 2 | 2240.2.g.i.449.1 | 4 | |||
24.11 | even | 2 | 2240.2.g.j.449.3 | 4 | |||
60.23 | odd | 4 | 350.2.a.h.1.2 | 2 | |||
60.47 | odd | 4 | 350.2.a.g.1.1 | 2 | |||
60.59 | even | 2 | 70.2.c.a.29.2 | ✓ | 4 | ||
84.11 | even | 6 | 490.2.i.c.79.1 | 8 | |||
84.23 | even | 6 | 490.2.i.c.459.4 | 8 | |||
84.47 | odd | 6 | 490.2.i.f.459.3 | 8 | |||
84.59 | odd | 6 | 490.2.i.f.79.2 | 8 | |||
84.83 | odd | 2 | 490.2.c.e.99.4 | 4 | |||
120.29 | odd | 2 | 2240.2.g.i.449.3 | 4 | |||
120.59 | even | 2 | 2240.2.g.j.449.1 | 4 | |||
420.59 | odd | 6 | 490.2.i.f.79.3 | 8 | |||
420.83 | even | 4 | 2450.2.a.bq.1.1 | 2 | |||
420.167 | even | 4 | 2450.2.a.bl.1.2 | 2 | |||
420.179 | even | 6 | 490.2.i.c.79.4 | 8 | |||
420.299 | odd | 6 | 490.2.i.f.459.2 | 8 | |||
420.359 | even | 6 | 490.2.i.c.459.1 | 8 | |||
420.419 | odd | 2 | 490.2.c.e.99.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.c.a.29.2 | ✓ | 4 | 60.59 | even | 2 | ||
70.2.c.a.29.3 | yes | 4 | 12.11 | even | 2 | ||
350.2.a.g.1.1 | 2 | 60.47 | odd | 4 | |||
350.2.a.h.1.2 | 2 | 60.23 | odd | 4 | |||
490.2.c.e.99.1 | 4 | 420.419 | odd | 2 | |||
490.2.c.e.99.4 | 4 | 84.83 | odd | 2 | |||
490.2.i.c.79.1 | 8 | 84.11 | even | 6 | |||
490.2.i.c.79.4 | 8 | 420.179 | even | 6 | |||
490.2.i.c.459.1 | 8 | 420.359 | even | 6 | |||
490.2.i.c.459.4 | 8 | 84.23 | even | 6 | |||
490.2.i.f.79.2 | 8 | 84.59 | odd | 6 | |||
490.2.i.f.79.3 | 8 | 420.59 | odd | 6 | |||
490.2.i.f.459.2 | 8 | 420.299 | odd | 6 | |||
490.2.i.f.459.3 | 8 | 84.47 | odd | 6 | |||
560.2.g.e.449.2 | 4 | 15.14 | odd | 2 | |||
560.2.g.e.449.4 | 4 | 3.2 | odd | 2 | |||
630.2.g.g.379.1 | 4 | 4.3 | odd | 2 | |||
630.2.g.g.379.3 | 4 | 20.19 | odd | 2 | |||
2240.2.g.i.449.1 | 4 | 24.5 | odd | 2 | |||
2240.2.g.i.449.3 | 4 | 120.29 | odd | 2 | |||
2240.2.g.j.449.1 | 4 | 120.59 | even | 2 | |||
2240.2.g.j.449.3 | 4 | 24.11 | even | 2 | |||
2450.2.a.bl.1.2 | 2 | 420.167 | even | 4 | |||
2450.2.a.bq.1.1 | 2 | 420.83 | even | 4 | |||
2800.2.a.bl.1.1 | 2 | 15.8 | even | 4 | |||
2800.2.a.bm.1.2 | 2 | 15.2 | even | 4 | |||
3150.2.a.bs.1.2 | 2 | 20.3 | even | 4 | |||
3150.2.a.bt.1.2 | 2 | 20.7 | even | 4 | |||
5040.2.t.t.1009.1 | 4 | 1.1 | even | 1 | trivial | ||
5040.2.t.t.1009.2 | 4 | 5.4 | even | 2 | inner |