Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,2,Mod(449,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("560.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.g (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.47162251319\) |
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 | 449.4 | ||
Root | \(1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 560.449 |
Dual form | 560.2.g.e.449.2 |
$q$-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 \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.44949i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.22474 | + | 0.224745i | 0.994936 | + | 0.100509i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.89898 | 1.47710 | 0.738549 | − | 0.674200i | \(-0.235511\pi\) | ||||
0.738549 | + | 0.674200i | \(0.235511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.44949i | 1.23407i | 0.786937 | + | 0.617033i | \(0.211666\pi\) | ||||
−0.786937 | + | 0.617033i | \(0.788334\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.550510 | + | 5.44949i | −0.142141 | + | 1.40705i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.00000i | − | 0.485071i | −0.970143 | − | 0.242536i | \(-0.922021\pi\) | ||
0.970143 | − | 0.242536i | \(-0.0779791\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.55051 | 0.355711 | 0.177856 | − | 0.984057i | \(-0.443084\pi\) | ||||
0.177856 | + | 0.984057i | \(0.443084\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.44949 | 0.534522 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.89898i | − | 0.604479i | −0.953232 | − | 0.302240i | \(-0.902266\pi\) | ||
0.953232 | − | 0.302240i | \(-0.0977342\pi\) | |||||||
\(24\) | 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 | \(-0.721295\pi\) | ||||
−0.640554 | + | 0.767913i | \(0.721295\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.89898 | −1.59830 | −0.799152 | − | 0.601129i | \(-0.794718\pi\) | ||||
−0.799152 | + | 0.601129i | \(0.794718\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.0000i | 2.08893i | ||||||||
\(34\) | 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 | ||||||||
\(39\) | −10.8990 | −1.74523 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.10102 | −0.171951 | −0.0859753 | − | 0.996297i | \(-0.527401\pi\) | ||||
−0.0859753 | + | 0.996297i | \(0.527401\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.898979i | 0.137093i | 0.997648 | + | 0.0685465i | \(0.0218362\pi\) | ||||
−0.997648 | + | 0.0685465i | \(0.978164\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.67423 | − | 0.674235i | −0.994936 | − | 0.100509i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.89898i | 1.29805i | 0.760767 | + | 0.649025i | \(0.224823\pi\) | ||||
−0.760767 | + | 0.649025i | \(0.775177\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.89898 | 0.685994 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 10.8990i | − | 1.49709i | −0.663084 | − | 0.748545i | \(-0.730753\pi\) | ||
0.663084 | − | 0.748545i | \(-0.269247\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.8990 | + | 1.10102i | 1.46962 | + | 0.148462i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.79796i | 0.503052i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.55051 | −0.201859 | −0.100930 | − | 0.994894i | \(-0.532182\pi\) | ||||
−0.100930 | + | 0.994894i | \(0.532182\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.55051 | 0.454596 | 0.227298 | − | 0.973825i | \(-0.427011\pi\) | ||||
0.227298 | + | 0.973825i | \(0.427011\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.00000i | 0.377964i | ||||||||
\(64\) | 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 | ||||||||
\(69\) | 7.10102 | 0.854862 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.10102 | 0.130667 | 0.0653335 | − | 0.997863i | \(-0.479189\pi\) | ||||
0.0653335 | + | 0.997863i | \(0.479189\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.89898i | 0.339300i | 0.985504 | + | 0.169650i | \(0.0542637\pi\) | ||||
−0.985504 | + | 0.169650i | \(0.945736\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.44949 | + | 12.0000i | −0.282843 | + | 1.38564i | ||||
\(76\) | 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 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.44949i | 0.268866i | 0.990923 | + | 0.134433i | \(0.0429214\pi\) | ||||
−0.990923 | + | 0.134433i | \(0.957079\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.449490 | − | 4.44949i | 0.0487540 | − | 0.482615i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 16.8990i | − | 1.81176i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.44949 | 0.466433 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 21.7980i | − | 2.26034i | ||||||
\(94\) | 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 | ||||||||
\(99\) | −14.6969 | −1.47710 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.55051 | 0.353289 | 0.176644 | − | 0.984275i | \(-0.443476\pi\) | ||||
0.176644 | + | 0.984275i | \(0.443476\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 12.8990i | − | 1.27097i | −0.772111 | − | 0.635487i | \(-0.780799\pi\) | ||
0.772111 | − | 0.635487i | \(-0.219201\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.44949 | + | 0.550510i | 0.531816 | + | 0.0537243i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 8.00000i | − | 0.773389i | −0.922208 | − | 0.386695i | \(-0.873617\pi\) | ||
0.922208 | − | 0.386695i | \(-0.126383\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.89898 | −0.660802 | −0.330401 | − | 0.943841i | \(-0.607184\pi\) | ||||
−0.330401 | + | 0.943841i | \(0.607184\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.89898 | 0.464991 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.7980i | 1.86244i | 0.364464 | + | 0.931218i | \(0.381252\pi\) | ||||
−0.364464 | + | 0.931218i | \(0.618748\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.651531 | − | 6.44949i | 0.0607556 | − | 0.601418i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 13.3485i | − | 1.23407i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.00000 | −0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.0000 | 1.18182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 2.69694i | − | 0.243175i | ||||||
\(124\) | 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 | ||||||||
\(129\) | −2.20204 | −0.193879 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.44949 | 0.563495 | 0.281747 | − | 0.959489i | \(-0.409086\pi\) | ||||
0.281747 | + | 0.959489i | \(0.409086\pi\) | |||||||
\(132\) | 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 | \(0.0244719\pi\) | ||||
−0.997046 | + | 0.0768050i | \(0.975528\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.55051 | 0.131513 | 0.0657563 | − | 0.997836i | \(-0.479054\pi\) | ||||
0.0657563 | + | 0.997836i | \(0.479054\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −21.7980 | −1.83572 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 21.7980i | 1.82284i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.3485 | − | 1.55051i | −1.27462 | − | 0.128763i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 2.44949i | − | 0.202031i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.79796 | 0.311141 | 0.155570 | − | 0.987825i | \(-0.450278\pi\) | ||||
0.155570 | + | 0.987825i | \(0.450278\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.5959 | −1.59469 | −0.797347 | − | 0.603522i | \(-0.793764\pi\) | ||||
−0.797347 | + | 0.603522i | \(0.793764\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.00000i | 0.485071i | ||||||||
\(154\) | 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 | ||||||||
\(159\) | 26.6969 | 2.11720 | ||||||||
\(160\) | 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 | ||||||||
\(165\) | −2.69694 | + | 26.6969i | −0.209956 | + | 2.07835i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 4.89898i | − | 0.379094i | −0.981872 | − | 0.189547i | \(-0.939298\pi\) | ||
0.981872 | − | 0.189547i | \(-0.0607020\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.79796 | −0.522920 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.65153 | −0.355711 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 6.24745i | − | 0.474985i | −0.971389 | − | 0.237492i | \(-0.923675\pi\) | ||
0.971389 | − | 0.237492i | \(-0.0763255\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | − | 4.89898i | 0.0755929 | − | 0.370328i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 3.79796i | − | 0.285472i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.7980 | 1.03131 | 0.515654 | − | 0.856797i | \(-0.327549\pi\) | ||||
0.515654 | + | 0.856797i | \(0.327549\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.2474 | −0.761687 | −0.380843 | − | 0.924640i | \(-0.624366\pi\) | ||||
−0.380843 | + | 0.924640i | \(0.624366\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.69694i | 0.642896i | ||||||||
\(184\) | 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 | \(-0.651921\pi\) | ||||
−0.459359 | + | 0.888251i | \(0.651921\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 21.5959i | − | 1.55451i | −0.629187 | − | 0.777254i | \(-0.716612\pi\) | ||
0.629187 | − | 0.777254i | \(-0.283388\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −24.2474 | − | 2.44949i | −1.73640 | − | 0.175412i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 18.8990i | − | 1.34650i | −0.739417 | − | 0.673248i | \(-0.764899\pi\) | ||
0.739417 | − | 0.673248i | \(-0.235101\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.8990 | 1.19794 | 0.598968 | − | 0.800773i | \(-0.295577\pi\) | ||||
0.598968 | + | 0.800773i | \(0.295577\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 19.5959 | 1.38219 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.89898i | 0.484213i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.44949 | − | 0.247449i | −0.171080 | − | 0.0172826i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.69694i | 0.604479i | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 2.69694i | 0.184791i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.202041 | + | 2.00000i | −0.0137791 | + | 0.136399i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.89898i | 0.604102i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.10102 | −0.479842 | ||||||||
\(220\) | 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 | ||||||||
\(225\) | −14.6969 | − | 3.00000i | −0.979796 | − | 0.200000i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.34847i | 0.487735i | 0.969809 | + | 0.243868i | \(0.0784162\pi\) | ||||
−0.969809 | + | 0.243868i | \(0.921584\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.1464 | 1.26523 | 0.632616 | − | 0.774466i | \(-0.281981\pi\) | ||||
0.632616 | + | 0.774466i | \(0.281981\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.0000 | 0.789542 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 29.7980i | 1.95213i | 0.217481 | + | 0.976065i | \(0.430216\pi\) | ||||
−0.217481 | + | 0.976065i | \(0.569784\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.00000 | + | 19.7980i | −0.130466 | + | 1.29148i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.8990i | 1.09771i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.20204 | −0.401177 | −0.200588 | − | 0.979676i | \(-0.564285\pi\) | ||||
−0.200588 | + | 0.979676i | \(0.564285\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.69694 | −0.560219 | −0.280110 | − | 0.959968i | \(-0.590371\pi\) | ||||
−0.280110 | + | 0.959968i | \(0.590371\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 22.0454i | − | 1.41421i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.22474 | − | 0.224745i | −0.142134 | − | 0.0143584i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.89898i | 0.438972i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.00000 | −0.380235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.44949 | 0.407088 | 0.203544 | − | 0.979066i | \(-0.434754\pi\) | ||||
0.203544 | + | 0.979066i | \(0.434754\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 14.2020i | − | 0.892875i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.8990 | + | 1.10102i | 0.682521 | + | 0.0689486i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.69694i | 0.542500i | 0.962509 | + | 0.271250i | \(0.0874370\pi\) | ||||
−0.962509 | + | 0.271250i | \(0.912563\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.00000 | −0.124274 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.6969 | 1.28111 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 9.79796i | − | 0.604168i | −0.953281 | − | 0.302084i | \(-0.902318\pi\) | ||
0.953281 | − | 0.302084i | \(-0.0976823\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.44949 | − | 24.2474i | 0.150471 | − | 1.48951i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 24.4949i | 1.49906i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.1464 | −1.16738 | −0.583689 | − | 0.811977i | \(-0.698391\pi\) | ||||
−0.583689 | + | 0.811977i | \(0.698391\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.0000 | −0.728948 | −0.364474 | − | 0.931214i | \(-0.618751\pi\) | ||||
−0.364474 | + | 0.931214i | \(0.618751\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.8990i | 0.659636i | ||||||||
\(274\) | 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 | ||||||||
\(279\) | 26.6969 | 1.59830 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.0000 | −1.07379 | −0.536895 | − | 0.843649i | \(-0.680403\pi\) | ||||
−0.536895 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 3.75255i | − | 0.223066i | −0.993761 | − | 0.111533i | \(-0.964424\pi\) | ||
0.993761 | − | 0.111533i | \(-0.0355761\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.853572 | + | 8.44949i | −0.0505612 | + | 0.500505i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.10102i | 0.0649912i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 38.6969 | 2.26845 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.2474i | 1.06603i | 0.846107 | + | 0.533014i | \(0.178941\pi\) | ||||
−0.846107 | + | 0.533014i | \(0.821059\pi\) | |||||||
\(294\) | 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 | ||||||||
\(303\) | 8.69694i | 0.499626i | ||||||||
\(304\) | 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 | ||||||||
\(309\) | 31.5959 | 1.79743 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.0000 | −0.680458 | −0.340229 | − | 0.940343i | \(-0.610505\pi\) | ||||
−0.340229 | + | 0.940343i | \(0.610505\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 21.5959i | − | 1.22067i | −0.792142 | − | 0.610337i | \(-0.791034\pi\) | ||
0.792142 | − | 0.610337i | \(-0.208966\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.674235 | + | 6.67423i | −0.0379888 | + | 0.376051i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.4949i | 1.26344i | 0.775197 | + | 0.631720i | \(0.217651\pi\) | ||||
−0.775197 | + | 0.631720i | \(0.782349\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −33.7980 | −1.89232 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.5959 | 1.09374 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.10102i | − | 0.172545i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.44949 | + | 21.7980i | −0.246813 | + | 1.20913i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 16.8990i | − | 0.934516i | ||||||
\(328\) | 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 | ||||||||
\(333\) | 6.00000i | 0.328798i | ||||||||
\(334\) | 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 | ||||||||
\(339\) | −48.4949 | −2.63388 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −43.5959 | −2.36085 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 15.7980 | + | 1.59592i | 0.850534 | + | 0.0859213i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.8990i | 1.55138i | 0.631115 | + | 0.775689i | \(0.282598\pi\) | ||||
−0.631115 | + | 0.775689i | \(0.717402\pi\) | |||||||
\(348\) | 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 | \(0.208588\pi\) | ||||
−0.792867 | + | 0.609395i | \(0.791412\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.44949 | + | 0.247449i | 0.130005 | + | 0.0131332i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 4.89898i | − | 0.259281i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.5959 | −1.45646 | −0.728228 | − | 0.685334i | \(-0.759656\pi\) | ||||
−0.728228 | + | 0.685334i | \(0.759656\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.5959 | −0.873469 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 31.8434i | 1.67134i | ||||||||
\(364\) | 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 | ||||||||
\(369\) | 3.30306 | 0.171951 | ||||||||
\(370\) | 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 | ||||||||
\(375\) | −8.14643 | + | 26.1464i | −0.420680 | + | 1.35020i | ||||
\(376\) | 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 | ||||||||
\(381\) | 36.4949 | 1.86969 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.10102i | 0.362845i | 0.983405 | + | 0.181423i | \(0.0580702\pi\) | ||||
−0.983405 | + | 0.181423i | \(0.941930\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.10102 | − | 10.8990i | 0.0561132 | − | 0.555463i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 2.69694i | − | 0.137093i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.1010 | −0.664248 | −0.332124 | − | 0.943236i | \(-0.607765\pi\) | ||||
−0.332124 | + | 0.943236i | \(0.607765\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.79796 | −0.293215 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.7980i | 0.796902i | ||||||||
\(394\) | 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 | ||||||||
\(399\) | 3.79796 | 0.190136 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −29.3939 | −1.46786 | −0.733930 | − | 0.679225i | \(-0.762316\pi\) | ||||
−0.733930 | + | 0.679225i | \(0.762316\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 39.5959i | − | 1.97241i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −20.0227 | − | 2.02270i | −0.994936 | − | 0.100509i | ||||
\(406\) | 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 | ||||||||
\(411\) | −4.40408 | −0.217237 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.55051i | 0.0762956i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.550510 | + | 5.44949i | −0.0270235 | + | 0.267505i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.79796i | 0.185987i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.55051 | −0.0757474 | −0.0378737 | − | 0.999283i | \(-0.512058\pi\) | ||||
−0.0378737 | + | 0.999283i | \(0.512058\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.20204 | −0.204795 | −0.102397 | − | 0.994744i | \(-0.532651\pi\) | ||||
−0.102397 | + | 0.994744i | \(0.532651\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 26.6969i | − | 1.29805i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.00000 | − | 9.79796i | 0.0970143 | − | 0.475271i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 3.55051i | − | 0.171821i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −53.3939 | −2.57788 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.79796 | 0.0866046 | 0.0433023 | − | 0.999062i | \(-0.486212\pi\) | ||||
0.0433023 | + | 0.999062i | \(0.486212\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 0.202041i | − | 0.00970947i | −0.999988 | − | 0.00485474i | \(-0.998455\pi\) | ||
0.999988 | − | 0.00485474i | \(-0.00154532\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.79796 | − | 37.5959i | 0.182098 | − | 1.80259i | ||||
\(436\) | 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 | ||||||||
\(441\) | 3.00000 | 0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 9.79796i | − | 0.465515i | −0.972535 | − | 0.232758i | \(-0.925225\pi\) | ||
0.972535 | − | 0.232758i | \(-0.0747749\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.2474 | + | 2.24745i | 1.05463 | + | 0.106539i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.30306i | 0.440020i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.0000 | 0.471929 | 0.235965 | − | 0.971762i | \(-0.424175\pi\) | ||||
0.235965 | + | 0.971762i | \(0.424175\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.39388 | −0.253988 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 48.0000i | − | 2.25524i | ||||||
\(454\) | 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 | \(-0.367620\pi\) | ||||
0.403999 | + | 0.914759i | \(0.367620\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 3.59592i | − | 0.167116i | −0.996503 | − | 0.0835582i | \(-0.973372\pi\) | ||
0.996503 | − | 0.0835582i | \(-0.0266285\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.89898 | − | 48.4949i | 0.227185 | − | 2.24890i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.4495i | 0.483545i | 0.970333 | + | 0.241772i | \(0.0777287\pi\) | ||||
−0.970333 | + | 0.241772i | \(0.922271\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.00000 | −0.369406 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.69694 | 0.400734 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.40408i | 0.202500i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.59592 | + | 1.55051i | 0.348525 | + | 0.0711423i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 32.6969i | 1.49709i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.30306 | 0.425068 | 0.212534 | − | 0.977154i | \(-0.431828\pi\) | ||||
0.212534 | + | 0.977154i | \(0.431828\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.89898 | 0.405759 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 7.10102i | − | 0.323108i | ||||||
\(484\) | 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 | ||||||||
\(489\) | −17.3939 | −0.786578 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.5959 | −0.884351 | −0.442176 | − | 0.896928i | \(-0.645793\pi\) | ||||
−0.442176 | + | 0.896928i | \(0.645793\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.7980i | 0.621429i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −32.6969 | − | 3.30306i | −1.46962 | − | 0.148462i | ||||
\(496\) | 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 | ||||||||
\(501\) | 12.0000 | 0.536120 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.00000i | 0.178351i | 0.996016 | + | 0.0891756i | \(0.0284232\pi\) | ||||
−0.996016 | + | 0.0891756i | \(0.971577\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.89898 | + | 0.797959i | 0.351500 | + | 0.0355087i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 16.6515i | − | 0.739520i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 31.5505 | 1.39845 | 0.699226 | − | 0.714901i | \(-0.253528\pi\) | ||||
0.699226 | + | 0.714901i | \(0.253528\pi\) | |||||||
\(510\) | 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 | ||||||||
\(519\) | 15.3031 | 0.671730 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.6969 | 1.43248 | 0.716239 | − | 0.697855i | \(-0.245862\pi\) | ||||
0.716239 | + | 0.697855i | \(0.245862\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.1464i | 1.44939i | 0.689069 | + | 0.724696i | \(0.258020\pi\) | ||||
−0.689069 | + | 0.724696i | \(0.741980\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.0000 | + | 2.44949i | 0.523723 | + | 0.106904i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.7980i | 0.775291i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.5959 | 0.634605 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.65153 | 0.201859 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 4.89898i | − | 0.212198i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.79796 | − | 17.7980i | 0.0777325 | − | 0.769473i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 33.7980i | 1.45849i | ||||||||
\(538\) | 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 | ||||||||
\(543\) | − | 25.1010i | − | 1.07719i | ||||||
\(544\) | 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 | ||||||||
\(549\) | −10.6515 | −0.454596 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.6969 | −0.455705 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 6.89898i | − | 0.293374i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.8990 | + | 1.10102i | 0.462636 | + | 0.0467357i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 12.6969i | − | 0.537987i | −0.963142 | − | 0.268993i | \(-0.913309\pi\) | ||
0.963142 | − | 0.268993i | \(-0.0866909\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.00000 | −0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.0000 | 1.01328 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 30.0454i | 1.26626i | 0.774044 | + | 0.633131i | \(0.218231\pi\) | ||||
−0.774044 | + | 0.633131i | \(0.781769\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.44949 | + | 44.0454i | −0.187191 | + | 1.85300i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.00000i | 0.377964i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −33.7980 | −1.41688 | −0.708442 | − | 0.705769i | \(-0.750602\pi\) | ||||
−0.708442 | + | 0.705769i | \(0.750602\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.1010 | 0.464563 | 0.232282 | − | 0.972649i | \(-0.425381\pi\) | ||||
0.232282 | + | 0.972649i | \(0.425381\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 31.1010i | − | 1.29926i | ||||||
\(574\) | 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 | ||||||||
\(579\) | 52.8990 | 2.19841 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.44949 | 0.101622 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 53.3939i | − | 2.21135i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.00000 | − | 29.6969i | 0.124035 | − | 1.22782i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.14643i | 0.0473182i | 0.999720 | + | 0.0236591i | \(0.00753162\pi\) | ||||
−0.999720 | + | 0.0236591i | \(0.992468\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.7980 | −0.568535 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 46.2929 | 1.90423 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 10.8990i | − | 0.447567i | −0.974639 | − | 0.223784i | \(-0.928159\pi\) | ||
0.974639 | − | 0.223784i | \(-0.0718409\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.44949 | − | 0.449490i | −0.182411 | − | 0.0184273i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 41.3939i | 1.69414i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.1010 | −0.535293 | −0.267647 | − | 0.963517i | \(-0.586246\pi\) | ||||
−0.267647 | + | 0.963517i | \(0.586246\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.3939 | −1.60691 | −0.803455 | − | 0.595366i | \(-0.797007\pi\) | ||||
−0.803455 | + | 0.595366i | \(0.797007\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 24.0000i | 0.977356i | ||||||||
\(604\) | 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 | ||||||||
\(609\) | −16.8990 | −0.684781 | ||||||||
\(610\) | 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 | ||||||||
\(615\) | 0.606123 | − | 6.00000i | 0.0244412 | − | 0.241943i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 29.5959i | − | 1.19149i | −0.803175 | − | 0.595743i | \(-0.796858\pi\) | ||
0.803175 | − | 0.595743i | \(-0.203142\pi\) | |||||||
\(618\) | 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 | ||||||||
\(627\) | 18.6061i | 0.743057i | ||||||||
\(628\) | 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 | ||||||||
\(633\) | − | 29.3939i | − | 1.16830i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.34847 | − | 33.1464i | 0.132880 | − | 1.31538i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 4.44949i | − | 0.176295i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.30306 | −0.130667 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.7980 | 1.01896 | 0.509479 | − | 0.860483i | \(-0.329838\pi\) | ||||
0.509479 | + | 0.860483i | \(0.329838\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 25.1464i | − | 0.991678i | −0.868414 | − | 0.495839i | \(-0.834861\pi\) | ||
0.868414 | − | 0.495839i | \(-0.165139\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.89898 | − | 0.494897i | −0.192897 | − | 0.0194866i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 46.2929i | − | 1.81996i | −0.414652 | − | 0.909980i | \(-0.636097\pi\) | ||
0.414652 | − | 0.909980i | \(-0.363903\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.59592 | −0.298166 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.7980 | −0.854329 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 20.2020i | − | 0.790567i | −0.918559 | − | 0.395283i | \(-0.870646\pi\) | ||
0.918559 | − | 0.395283i | \(-0.129354\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.3485 | + | 1.44949i | 0.560641 | + | 0.0566363i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 8.69694i | − | 0.339300i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.8990 | 0.658291 | 0.329145 | − | 0.944279i | \(-0.393239\pi\) | ||||
0.329145 | + | 0.944279i | \(0.393239\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.9444 | −1.59255 | −0.796276 | − | 0.604933i | \(-0.793200\pi\) | ||||
−0.796276 | + | 0.604933i | \(0.793200\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 21.7980i | 0.846563i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.348469 | − | 3.44949i | 0.0135131 | − | 0.133765i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.0000i | 0.774403i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.79796 | −0.378811 | ||||||||
\(670\) | 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 | \(0.247010\pi\) | ||||
−0.713717 | + | 0.700434i | \(0.752990\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.7980 | −0.606270 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.0000 | −0.689761 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 3.59592i | − | 0.137594i | −0.997631 | − | 0.0687970i | \(-0.978084\pi\) | ||
0.997631 | − | 0.0687970i | \(-0.0219161\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.404082 | + | 4.00000i | −0.0154392 | + | 0.152832i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 46.8990i | 1.78931i | ||||||||
\(688\) | 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 | ||||||||
\(693\) | 14.6969i | 0.558291i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.44949 | + | 0.348469i | 0.130847 | + | 0.0132182i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.20204i | 0.0834083i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −72.9898 | −2.76073 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.3031 | 0.426911 | 0.213455 | − | 0.976953i | \(-0.431528\pi\) | ||||
0.213455 | + | 0.976953i | \(0.431528\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3.10102i | − | 0.116957i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −48.4949 | − | 4.89898i | −1.82642 | − | 0.184506i | ||||
\(706\) | 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 | ||||||||
\(711\) | −20.6969 | −0.776196 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.7980i | 0.966141i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.89898 | + | 48.4949i | −0.183211 | + | 1.81361i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 15.1918i | − | 0.567350i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.49490 | −0.167631 | −0.0838157 | − | 0.996481i | \(-0.526711\pi\) | ||||
−0.0838157 | + | 0.996481i | \(0.526711\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.8990 | −0.480383 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 21.3031i | − | 0.792269i | ||||||
\(724\) | 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 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 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 | ||||||||
\(735\) | 0.550510 | − | 5.44949i | 0.0203059 | − | 0.201007i | ||||
\(736\) | 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 | ||||||||
\(741\) | −16.8990 | −0.620800 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 44.6969i | 1.63977i | 0.572527 | + | 0.819886i | \(0.305963\pi\) | ||||
−0.572527 | + | 0.819886i | \(0.694037\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.44949 | + | 0.853572i | 0.309565 | + | 0.0312725i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 7.34847i | − | 0.268866i | ||||||
\(748\) | 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 | ||||||||
\(753\) | 15.7980i | 0.575710i | ||||||||
\(754\) | 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 | ||||||||
\(759\) | 34.7878 | 1.26272 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.1010 | −0.764911 | −0.382456 | − | 0.923974i | \(-0.624922\pi\) | ||||
−0.382456 | + | 0.923974i | \(0.624922\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.89898i | 0.249760i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.34847 | + | 13.3485i | −0.0487540 | + | 0.482615i | ||||
\(766\) | 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 | ||||||||
\(771\) | −21.3031 | −0.767211 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.34847i | 0.0485011i | 0.999706 | + | 0.0242505i | \(0.00771994\pi\) | ||||
−0.999706 | + | 0.0242505i | \(0.992280\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −43.5959 | − | 8.89898i | −1.56601 | − | 0.319661i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 4.89898i | − | 0.175750i | ||||||
\(778\) | 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 | ||||||||
\(789\) | 24.0000 | 0.854423 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.7980 | 0.703934 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.7980i | 0.561002i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 59.3939 | + | 6.00000i | 2.10648 | + | 0.212798i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.944387i | 0.0334519i | 0.999860 | + | 0.0167260i | \(0.00532429\pi\) | ||||
−0.999860 | + | 0.0167260i | \(0.994676\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.7980 | 0.629647 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −30.0000 | −1.06000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.2020i | 0.501179i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.44949 | − | 0.651531i | −0.227315 | − | 0.0229634i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 46.8990i | − | 1.65092i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −47.5959 | −1.67338 | −0.836692 | − | 0.547674i | \(-0.815513\pi\) | ||||
−0.836692 | + | 0.547674i | \(0.815513\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.9444 | −0.524768 | −0.262384 | − | 0.964963i | \(-0.584509\pi\) | ||||
−0.262384 | + | 0.964963i | \(0.584509\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 29.3939i | − | 1.03089i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.59592 | + | 15.7980i | −0.0559026 | + | 0.553378i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.39388i | 0.0487656i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13.3485 | −0.466433 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.20204 | 0.286253 | 0.143127 | − | 0.989704i | \(-0.454284\pi\) | ||||
0.143127 | + | 0.989704i | \(0.454284\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.1918i | 1.36614i | 0.730352 | + | 0.683071i | \(0.239356\pi\) | ||||
−0.730352 | + | 0.683071i | \(0.760644\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.0000 | + | 58.7878i | −0.417786 | + | 2.04673i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 15.5959i | − | 0.542323i | −0.962534 | − | 0.271162i | \(-0.912592\pi\) | ||
0.962534 | − | 0.271162i | \(-0.0874078\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43.6413 | 1.51573 | 0.757863 | − | 0.652414i | \(-0.226244\pi\) | ||||
0.757863 | + | 0.652414i | \(0.226244\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −36.4949 | −1.26599 | ||||||||
\(832\) | 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 | \(-0.280197\pi\) | ||||
0.636947 | + | 0.770907i | \(0.280197\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.5959 | 0.641239 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 44.0908i | − | 1.51857i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.1237 | − | 1.52781i | −0.520272 | − | 0.0525581i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 13.0000i | − | 0.446685i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.19184 | 0.315463 | ||||||||
\(850\) | 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 | ||||||||
\(855\) | −10.3485 | − | 1.04541i | −0.353910 | − | 0.0357522i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 53.1918i | 1.81700i | 0.417886 | + | 0.908499i | \(0.362771\pi\) | ||||
−0.417886 | + | 0.908499i | \(0.637229\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.6413 | 1.83022 | 0.915109 | − | 0.403206i | \(-0.132104\pi\) | ||||
0.915109 | + | 0.403206i | \(0.132104\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.69694 | −0.0919114 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 45.3939i | 1.54523i | 0.634878 | + | 0.772613i | \(0.281051\pi\) | ||||
−0.634878 | + | 0.772613i | \(0.718949\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.40408 | − | 13.8990i | 0.0477402 | − | 0.472579i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 31.8434i | 1.08146i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33.7980 | 1.14652 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.5959 | 1.20612 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 47.3939i | 1.60404i | ||||||||
\(874\) | 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 | ||||||||
\(879\) | −44.6969 | −1.50759 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.20204 | 0.276334 | 0.138167 | − | 0.990409i | \(-0.455879\pi\) | ||||
0.138167 | + | 0.990409i | \(0.455879\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 22.2020i | − | 0.747158i | −0.927598 | − | 0.373579i | \(-0.878130\pi\) | ||
0.927598 | − | 0.373579i | \(-0.121870\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.853572 | − | 8.44949i | 0.0286925 | − | 0.284026i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.69694i | 0.0905543i | 0.998974 | + | 0.0452772i | \(0.0144171\pi\) | ||||
−0.998974 | + | 0.0452772i | \(0.985583\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.8990 | −0.499696 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −44.0908 | −1.47710 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.7980i | 0.461731i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30.6969 | + | 3.10102i | 1.02609 | + | 0.103656i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 31.5959i | 1.05496i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 61.3939 | 2.04760 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.7980 | −0.726195 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.20204i | 0.0732793i | ||||||||
\(904\) | 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 | ||||||||
\(909\) | −10.6515 | −0.353289 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.5959 | 1.17935 | 0.589673 | − | 0.807642i | \(-0.299257\pi\) | ||||
0.589673 | + | 0.807642i | \(0.299257\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.0000i | 0.397142i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.95459 | + | 19.3485i | −0.0646168 | + | 0.639641i | ||||
\(916\) | 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 | ||||||||
\(921\) | 49.5959 | 1.63424 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.89898i | 0.161252i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.00000 | − | 9.79796i | 0.0657596 | − | 0.322155i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 38.6969i | 1.27097i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.2929 | 0.928259 | 0.464129 | − | 0.885767i | \(-0.346367\pi\) | ||||
0.464129 | + | 0.885767i | \(0.346367\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.55051 | −0.0508159 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 29.3939i | − | 0.962312i | ||||||
\(934\) | 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 | ||||||||
\(939\) | 52.8990 | 1.72629 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.5505 | −0.637328 | −0.318664 | − | 0.947868i | \(-0.603234\pi\) | ||||
−0.318664 | + | 0.947868i | \(0.603234\pi\) | |||||||
\(942\) | 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 | \(0.254202\pi\) | ||||
−0.697711 | + | 0.716379i | \(0.745798\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.8990 | −0.418719 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −55.1010 | −1.78677 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.20204i | 0.0713311i | 0.999364 | + | 0.0356656i | \(0.0113551\pi\) | ||||
−0.999364 | + | 0.0356656i | \(0.988645\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −28.2474 | − | 2.85357i | −0.914066 | − | 0.0923394i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 82.7878i | − | 2.67615i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.79796 | 0.0580591 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 48.1918 | 1.55458 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 24.0000i | 0.773389i | ||||||||
\(964\) | 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 | ||||||||
\(969\) | 7.59592 | 0.244016 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.55051 | 0.306490 | 0.153245 | − | 0.988188i | \(-0.451028\pi\) | ||||
0.153245 | + | 0.988188i | \(0.451028\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1.55051i | − | 0.0497071i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −53.3939 | − | 10.8990i | −1.70997 | − | 0.349047i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.3939i | 0.940393i | 0.882562 | + | 0.470197i | \(0.155817\pi\) | ||||
−0.882562 | + | 0.470197i | \(0.844183\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.9898 | 1.56572 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.6969 | 0.660802 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.3031i | 0.424302i | 0.977237 | + | 0.212151i | \(0.0680468\pi\) | ||||
−0.977237 | + | 0.212151i | \(0.931953\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.24745 | − | 42.0454i | 0.135335 | − | 1.33968i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21.7980i | 0.693837i | ||||||||
\(988\) | 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 | ||||||||
\(993\) | 45.7980i | 1.45335i | ||||||||
\(994\) | 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 | 560.2.g.e.449.4 | 4 | ||
3.2 | odd | 2 | 5040.2.t.t.1009.1 | 4 | |||
4.3 | odd | 2 | 70.2.c.a.29.3 | yes | 4 | ||
5.2 | odd | 4 | 2800.2.a.bm.1.2 | 2 | |||
5.3 | odd | 4 | 2800.2.a.bl.1.1 | 2 | |||
5.4 | even | 2 | inner | 560.2.g.e.449.2 | 4 | ||
8.3 | odd | 2 | 2240.2.g.j.449.3 | 4 | |||
8.5 | even | 2 | 2240.2.g.i.449.1 | 4 | |||
12.11 | even | 2 | 630.2.g.g.379.1 | 4 | |||
15.14 | odd | 2 | 5040.2.t.t.1009.2 | 4 | |||
20.3 | even | 4 | 350.2.a.h.1.2 | 2 | |||
20.7 | even | 4 | 350.2.a.g.1.1 | 2 | |||
20.19 | odd | 2 | 70.2.c.a.29.2 | ✓ | 4 | ||
28.3 | even | 6 | 490.2.i.f.79.2 | 8 | |||
28.11 | odd | 6 | 490.2.i.c.79.1 | 8 | |||
28.19 | even | 6 | 490.2.i.f.459.3 | 8 | |||
28.23 | odd | 6 | 490.2.i.c.459.4 | 8 | |||
28.27 | even | 2 | 490.2.c.e.99.4 | 4 | |||
40.19 | odd | 2 | 2240.2.g.j.449.1 | 4 | |||
40.29 | even | 2 | 2240.2.g.i.449.3 | 4 | |||
60.23 | odd | 4 | 3150.2.a.bs.1.2 | 2 | |||
60.47 | odd | 4 | 3150.2.a.bt.1.2 | 2 | |||
60.59 | even | 2 | 630.2.g.g.379.3 | 4 | |||
140.19 | even | 6 | 490.2.i.f.459.2 | 8 | |||
140.27 | odd | 4 | 2450.2.a.bl.1.2 | 2 | |||
140.39 | odd | 6 | 490.2.i.c.79.4 | 8 | |||
140.59 | even | 6 | 490.2.i.f.79.3 | 8 | |||
140.79 | odd | 6 | 490.2.i.c.459.1 | 8 | |||
140.83 | odd | 4 | 2450.2.a.bq.1.1 | 2 | |||
140.139 | even | 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 | 20.19 | odd | 2 | ||
70.2.c.a.29.3 | yes | 4 | 4.3 | odd | 2 | ||
350.2.a.g.1.1 | 2 | 20.7 | even | 4 | |||
350.2.a.h.1.2 | 2 | 20.3 | even | 4 | |||
490.2.c.e.99.1 | 4 | 140.139 | even | 2 | |||
490.2.c.e.99.4 | 4 | 28.27 | even | 2 | |||
490.2.i.c.79.1 | 8 | 28.11 | odd | 6 | |||
490.2.i.c.79.4 | 8 | 140.39 | odd | 6 | |||
490.2.i.c.459.1 | 8 | 140.79 | odd | 6 | |||
490.2.i.c.459.4 | 8 | 28.23 | odd | 6 | |||
490.2.i.f.79.2 | 8 | 28.3 | even | 6 | |||
490.2.i.f.79.3 | 8 | 140.59 | even | 6 | |||
490.2.i.f.459.2 | 8 | 140.19 | even | 6 | |||
490.2.i.f.459.3 | 8 | 28.19 | even | 6 | |||
560.2.g.e.449.2 | 4 | 5.4 | even | 2 | inner | ||
560.2.g.e.449.4 | 4 | 1.1 | even | 1 | trivial | ||
630.2.g.g.379.1 | 4 | 12.11 | even | 2 | |||
630.2.g.g.379.3 | 4 | 60.59 | even | 2 | |||
2240.2.g.i.449.1 | 4 | 8.5 | even | 2 | |||
2240.2.g.i.449.3 | 4 | 40.29 | even | 2 | |||
2240.2.g.j.449.1 | 4 | 40.19 | odd | 2 | |||
2240.2.g.j.449.3 | 4 | 8.3 | odd | 2 | |||
2450.2.a.bl.1.2 | 2 | 140.27 | odd | 4 | |||
2450.2.a.bq.1.1 | 2 | 140.83 | odd | 4 | |||
2800.2.a.bl.1.1 | 2 | 5.3 | odd | 4 | |||
2800.2.a.bm.1.2 | 2 | 5.2 | odd | 4 | |||
3150.2.a.bs.1.2 | 2 | 60.23 | odd | 4 | |||
3150.2.a.bt.1.2 | 2 | 60.47 | odd | 4 | |||
5040.2.t.t.1009.1 | 4 | 3.2 | odd | 2 | |||
5040.2.t.t.1009.2 | 4 | 15.14 | odd | 2 |