Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,2,Mod(1151,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("1200.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.58204824255\) |
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: | \( 3 \) |
Twist minimal: | no (minimal twist has level 240) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1151.3 | ||
Root | \(1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.1151 |
Dual form | 1200.2.h.k.1151.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 1.22474 | − | 1.22474i | 0.707107 | − | 0.707107i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.44949i | − | 0.925820i | −0.886405 | − | 0.462910i | \(-0.846805\pi\) | ||
0.886405 | − | 0.462910i | \(-0.153195\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 3.00000i | − | 1.00000i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.89898 | −1.47710 | −0.738549 | − | 0.674200i | \(-0.764489\pi\) | ||||
−0.738549 | + | 0.674200i | \(0.764489\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.00000i | − | 1.45521i | −0.685994 | − | 0.727607i | \(-0.740633\pi\) | ||
0.685994 | − | 0.727607i | \(-0.259367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.89898i | 1.12390i | 0.827170 | + | 0.561951i | \(0.189949\pi\) | ||||
−0.827170 | + | 0.561951i | \(0.810051\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.00000 | − | 3.00000i | −0.654654 | − | 0.654654i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.44949 | −0.510754 | −0.255377 | − | 0.966842i | \(-0.582200\pi\) | ||||
−0.255377 | + | 0.966842i | \(0.582200\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.67423 | − | 3.67423i | −0.707107 | − | 0.707107i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9.79796i | − | 1.75977i | −0.475191 | − | 0.879883i | \(-0.657621\pi\) | ||
0.475191 | − | 0.879883i | \(-0.342379\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.00000 | + | 6.00000i | −1.04447 | + | 1.04447i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.44949 | − | 2.44949i | 0.392232 | − | 0.392232i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000i | 0.937043i | 0.883452 | + | 0.468521i | \(0.155213\pi\) | ||||
−0.883452 | + | 0.468521i | \(0.844787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.44949i | 0.373544i | 0.982403 | + | 0.186772i | \(0.0598025\pi\) | ||||
−0.982403 | + | 0.186772i | \(0.940197\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.2474 | −1.78647 | −0.893237 | − | 0.449586i | \(-0.851571\pi\) | ||||
−0.893237 | + | 0.449586i | \(0.851571\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.34847 | − | 7.34847i | −1.02899 | − | 1.02899i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 6.00000i | − | 0.824163i | −0.911147 | − | 0.412082i | \(-0.864802\pi\) | ||
0.911147 | − | 0.412082i | \(-0.135198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.00000 | + | 6.00000i | 0.794719 | + | 0.794719i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.79796 | 1.27559 | 0.637793 | − | 0.770208i | \(-0.279848\pi\) | ||||
0.637793 | + | 0.770208i | \(0.279848\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.00000 | 1.02430 | 0.512148 | − | 0.858898i | \(-0.328850\pi\) | ||||
0.512148 | + | 0.858898i | \(0.328850\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.34847 | −0.925820 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 7.34847i | − | 0.897758i | −0.893592 | − | 0.448879i | \(-0.851823\pi\) | ||
0.893592 | − | 0.448879i | \(-0.148177\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.00000 | + | 3.00000i | −0.361158 | + | 0.361158i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.89898 | −0.581402 | −0.290701 | − | 0.956814i | \(-0.593888\pi\) | ||||
−0.290701 | + | 0.956814i | \(0.593888\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.0000 | 1.63858 | 0.819288 | − | 0.573382i | \(-0.194369\pi\) | ||||
0.819288 | + | 0.573382i | \(0.194369\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.0000i | 1.36753i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 4.89898i | − | 0.551178i | −0.961276 | − | 0.275589i | \(-0.911127\pi\) | ||
0.961276 | − | 0.275589i | \(-0.0888729\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.34847 | 0.806599 | 0.403300 | − | 0.915068i | \(-0.367863\pi\) | ||||
0.403300 | + | 0.915068i | \(0.367863\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.0000i | 1.27200i | 0.771690 | + | 0.635999i | \(0.219412\pi\) | ||||
−0.771690 | + | 0.635999i | \(0.780588\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 4.89898i | − | 0.513553i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.0000 | − | 12.0000i | −1.24434 | − | 1.24434i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0000 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14.6969i | 1.47710i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 12.0000i | − | 1.19404i | −0.802225 | − | 0.597022i | \(-0.796350\pi\) | ||
0.802225 | − | 0.597022i | \(-0.203650\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 12.2474i | − | 1.20678i | −0.797447 | − | 0.603388i | \(-0.793817\pi\) | ||
0.797447 | − | 0.603388i | \(-0.206183\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.44949 | 0.236801 | 0.118401 | − | 0.992966i | \(-0.462223\pi\) | ||||
0.118401 | + | 0.992966i | \(0.462223\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.00000 | 0.383131 | 0.191565 | − | 0.981480i | \(-0.438644\pi\) | ||||
0.191565 | + | 0.981480i | \(0.438644\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.44949 | + | 2.44949i | −0.232495 | + | 0.232495i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 6.00000i | − | 0.554700i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.6969 | −1.34727 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.0000 | 1.18182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.34847 | + | 7.34847i | 0.662589 | + | 0.662589i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 7.34847i | − | 0.652071i | −0.945357 | − | 0.326036i | \(-0.894287\pi\) | ||
0.945357 | − | 0.326036i | \(-0.105713\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.00000 | + | 3.00000i | 0.264135 | + | 0.264135i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.89898 | −0.428026 | −0.214013 | − | 0.976831i | \(-0.568653\pi\) | ||||
−0.214013 | + | 0.976831i | \(0.568653\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.0000 | 1.04053 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.00000i | 0.512615i | 0.966595 | + | 0.256307i | \(0.0825059\pi\) | ||||
−0.966595 | + | 0.256307i | \(0.917494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.89898i | 0.415526i | 0.978179 | + | 0.207763i | \(0.0666183\pi\) | ||||
−0.978179 | + | 0.207763i | \(0.933382\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.0000 | + | 15.0000i | −1.26323 | + | 1.26323i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.79796 | −0.819346 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.22474 | − | 1.22474i | 0.101015 | − | 0.101015i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 18.0000i | − | 1.47462i | −0.675556 | − | 0.737309i | \(-0.736096\pi\) | ||
0.675556 | − | 0.737309i | \(-0.263904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.5959i | 1.59469i | 0.603522 | + | 0.797347i | \(0.293764\pi\) | ||||
−0.603522 | + | 0.797347i | \(0.706236\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −18.0000 | −1.45521 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0000 | 0.798087 | 0.399043 | − | 0.916932i | \(-0.369342\pi\) | ||||
0.399043 | + | 0.916932i | \(0.369342\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.34847 | − | 7.34847i | −0.582772 | − | 0.582772i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.00000i | 0.472866i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.34847i | 0.575577i | 0.957694 | + | 0.287788i | \(0.0929199\pi\) | ||||
−0.957694 | + | 0.287788i | \(0.907080\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.1464 | 1.32683 | 0.663415 | − | 0.748251i | \(-0.269106\pi\) | ||||
0.663415 | + | 0.748251i | \(0.269106\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.6969 | 1.12390 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.0000i | 1.36851i | 0.729241 | + | 0.684257i | \(0.239873\pi\) | ||||
−0.729241 | + | 0.684257i | \(0.760127\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.0000 | − | 12.0000i | 0.901975 | − | 0.901975i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.79796 | 0.732334 | 0.366167 | − | 0.930549i | \(-0.380670\pi\) | ||||
0.366167 | + | 0.930549i | \(0.380670\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.79796 | − | 9.79796i | 0.724286 | − | 0.724286i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 29.3939i | 2.14949i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.00000 | + | 9.00000i | −0.654654 | + | 0.654654i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.6969 | 1.06343 | 0.531717 | − | 0.846922i | \(-0.321547\pi\) | ||||
0.531717 | + | 0.846922i | \(0.321547\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.0000 | 0.719816 | 0.359908 | − | 0.932988i | \(-0.382808\pi\) | ||||
0.359908 | + | 0.932988i | \(0.382808\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 18.0000i | − | 1.28245i | −0.767354 | − | 0.641223i | \(-0.778427\pi\) | ||
0.767354 | − | 0.641223i | \(-0.221573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 14.6969i | − | 1.04184i | −0.853606 | − | 0.520919i | \(-0.825589\pi\) | ||
0.853606 | − | 0.520919i | \(-0.174411\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.00000 | − | 9.00000i | −0.634811 | − | 0.634811i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.34847i | 0.510754i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 24.0000i | − | 1.66011i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.00000 | + | 6.00000i | −0.411113 | + | 0.411113i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −24.0000 | −1.62923 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.1464 | − | 17.1464i | 1.15865 | − | 1.15865i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 12.0000i | − | 0.807207i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.44949i | 0.164030i | 0.996631 | + | 0.0820150i | \(0.0261355\pi\) | ||||
−0.996631 | + | 0.0820150i | \(0.973864\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.44949 | −0.162578 | −0.0812892 | − | 0.996691i | \(-0.525904\pi\) | ||||
−0.0812892 | + | 0.996691i | \(0.525904\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.0000 | 1.45380 | 0.726900 | − | 0.686743i | \(-0.240960\pi\) | ||||
0.726900 | + | 0.686743i | \(0.240960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.6969 | + | 14.6969i | 0.966988 | + | 0.966988i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 18.0000i | − | 1.17922i | −0.807688 | − | 0.589610i | \(-0.799282\pi\) | ||
0.807688 | − | 0.589610i | \(-0.200718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.00000 | − | 6.00000i | −0.389742 | − | 0.389742i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.79796 | −0.633777 | −0.316889 | − | 0.948463i | \(-0.602638\pi\) | ||||
−0.316889 | + | 0.948463i | \(0.602638\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.00000 | 0.257663 | 0.128831 | − | 0.991667i | \(-0.458877\pi\) | ||||
0.128831 | + | 0.991667i | \(0.458877\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.0227 | + | 11.0227i | −0.707107 | + | 0.707107i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.79796i | 0.623429i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.00000 | − | 9.00000i | 0.570352 | − | 0.570352i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.4949 | 1.54610 | 0.773052 | − | 0.634343i | \(-0.218729\pi\) | ||||
0.773052 | + | 0.634343i | \(0.218729\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0000 | 0.754434 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 6.00000i | − | 0.374270i | −0.982334 | − | 0.187135i | \(-0.940080\pi\) | ||
0.982334 | − | 0.187135i | \(-0.0599201\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.89898i | 0.304408i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.44949 | −0.151042 | −0.0755210 | − | 0.997144i | \(-0.524062\pi\) | ||||
−0.0755210 | + | 0.997144i | \(0.524062\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.6969 | + | 14.6969i | 0.899438 | + | 0.899438i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.0000i | 1.09748i | 0.835993 | + | 0.548740i | \(0.184892\pi\) | ||||
−0.835993 | + | 0.548740i | \(0.815108\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.79796i | 0.595184i | 0.954693 | + | 0.297592i | \(0.0961834\pi\) | ||||
−0.954693 | + | 0.297592i | \(0.903817\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.00000 | − | 6.00000i | −0.363137 | − | 0.363137i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00000 | 0.120168 | 0.0600842 | − | 0.998193i | \(-0.480863\pi\) | ||||
0.0600842 | + | 0.998193i | \(0.480863\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −29.3939 | −1.75977 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.00000i | − | 0.357930i | −0.983855 | − | 0.178965i | \(-0.942725\pi\) | ||
0.983855 | − | 0.178965i | \(-0.0572749\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.9444i | 1.60168i | 0.598880 | + | 0.800839i | \(0.295613\pi\) | ||||
−0.598880 | + | 0.800839i | \(0.704387\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.6969 | 0.867533 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −19.0000 | −1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.2474 | + | 12.2474i | −0.717958 | + | 0.717958i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.00000i | 0.350524i | 0.984522 | + | 0.175262i | \(0.0560772\pi\) | ||||
−0.984522 | + | 0.175262i | \(0.943923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.0000 | + | 18.0000i | 1.04447 | + | 1.04447i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.89898 | −0.283315 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.00000 | 0.345834 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.6969 | − | 14.6969i | −0.844317 | − | 0.844317i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.44949i | − | 0.139800i | −0.997554 | − | 0.0698999i | \(-0.977732\pi\) | ||
0.997554 | − | 0.0698999i | \(-0.0222680\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.0000 | − | 15.0000i | −0.853320 | − | 0.853320i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.4949 | 1.38898 | 0.694489 | − | 0.719503i | \(-0.255630\pi\) | ||||
0.694489 | + | 0.719503i | \(0.255630\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.0000 | 0.565233 | 0.282617 | − | 0.959233i | \(-0.408798\pi\) | ||||
0.282617 | + | 0.959233i | \(0.408798\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.0000i | 1.01098i | 0.862832 | + | 0.505490i | \(0.168688\pi\) | ||||
−0.862832 | + | 0.505490i | \(0.831312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.00000 | − | 3.00000i | 0.167444 | − | 0.167444i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 29.3939 | 1.63552 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.89898 | − | 4.89898i | 0.270914 | − | 0.270914i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 30.0000i | 1.65395i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.5959i | 1.07709i | 0.842597 | + | 0.538545i | \(0.181026\pi\) | ||||
−0.842597 | + | 0.538545i | \(0.818974\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.00000i | 0.328798i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.34847 | + | 7.34847i | 0.399114 | + | 0.399114i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 48.0000i | 2.59935i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 19.5959i | − | 1.05808i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.34847 | 0.394486 | 0.197243 | − | 0.980355i | \(-0.436801\pi\) | ||||
0.197243 | + | 0.980355i | \(0.436801\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.34847 | − | 7.34847i | −0.392232 | − | 0.392232i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 6.00000i | − | 0.319348i | −0.987170 | − | 0.159674i | \(-0.948956\pi\) | ||
0.987170 | − | 0.159674i | \(-0.0510443\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −18.0000 | + | 18.0000i | −0.952661 | + | 0.952661i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.79796 | −0.517116 | −0.258558 | − | 0.965996i | \(-0.583247\pi\) | ||||
−0.258558 | + | 0.965996i | \(0.583247\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.00000 | −0.263158 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.9217 | − | 15.9217i | 0.835672 | − | 0.835672i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.34847i | 0.383587i | 0.981435 | + | 0.191793i | \(0.0614304\pi\) | ||||
−0.981435 | + | 0.191793i | \(0.938570\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 18.0000 | 0.937043 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.6969 | −0.763027 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.0000 | −1.34623 | −0.673114 | − | 0.739538i | \(-0.735044\pi\) | ||||
−0.673114 | + | 0.739538i | \(0.735044\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.6969i | 0.754931i | 0.926024 | + | 0.377466i | \(0.123204\pi\) | ||||
−0.926024 | + | 0.377466i | \(0.876796\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.00000 | − | 9.00000i | −0.461084 | − | 0.461084i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.44949 | 0.125163 | 0.0625815 | − | 0.998040i | \(-0.480067\pi\) | ||||
0.0625815 | + | 0.998040i | \(0.480067\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.34847 | 0.373544 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.0000i | 0.912636i | 0.889817 | + | 0.456318i | \(0.150832\pi\) | ||||
−0.889817 | + | 0.456318i | \(0.849168\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.6969i | 0.743256i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.00000 | + | 6.00000i | −0.302660 | + | 0.302660i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.00000 | −0.100377 | −0.0501886 | − | 0.998740i | \(-0.515982\pi\) | ||||
−0.0501886 | + | 0.998740i | \(0.515982\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 14.6969 | − | 14.6969i | 0.735767 | − | 0.735767i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 24.0000i | − | 1.19850i | −0.800561 | − | 0.599251i | \(-0.795465\pi\) | ||
0.800561 | − | 0.599251i | \(-0.204535\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 19.5959i | − | 0.976142i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.79796 | 0.485667 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.0000 | 0.791149 | 0.395575 | − | 0.918434i | \(-0.370545\pi\) | ||||
0.395575 | + | 0.918434i | \(0.370545\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.34847 | + | 7.34847i | 0.362473 | + | 0.362473i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 24.0000i | − | 1.18096i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.00000 | + | 6.00000i | 0.293821 | + | 0.293821i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.00000 | −0.389896 | −0.194948 | − | 0.980814i | \(-0.562454\pi\) | ||||
−0.194948 | + | 0.980814i | \(0.562454\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 36.7423i | 1.78647i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 19.5959i | − | 0.948313i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.0000 | + | 12.0000i | −0.579365 | + | 0.579365i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.4949 | −1.17988 | −0.589939 | − | 0.807448i | \(-0.700848\pi\) | ||||
−0.589939 | + | 0.807448i | \(0.700848\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.00000 | −0.0961139 | −0.0480569 | − | 0.998845i | \(-0.515303\pi\) | ||||
−0.0480569 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 12.0000i | − | 0.574038i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 24.4949i | − | 1.16908i | −0.811366 | − | 0.584539i | \(-0.801275\pi\) | ||
0.811366 | − | 0.584539i | \(-0.198725\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 3.00000i | − | 0.142857i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.1464 | −0.814651 | −0.407326 | − | 0.913283i | \(-0.633539\pi\) | ||||
−0.407326 | + | 0.913283i | \(0.633539\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −22.0454 | − | 22.0454i | −1.04271 | − | 1.04271i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 6.00000i | − | 0.283158i | −0.989927 | − | 0.141579i | \(-0.954782\pi\) | ||
0.989927 | − | 0.141579i | \(-0.0452178\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 29.3939i | − | 1.38410i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 24.0000 | + | 24.0000i | 1.12762 | + | 1.12762i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.0000 | −1.02912 | −0.514558 | − | 0.857455i | \(-0.672044\pi\) | ||||
−0.514558 | + | 0.857455i | \(0.672044\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −22.0454 | + | 22.0454i | −1.02899 | + | 1.02899i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.0000i | 0.558896i | 0.960161 | + | 0.279448i | \(0.0901514\pi\) | ||||
−0.960161 | + | 0.279448i | \(0.909849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.44949i | 0.113837i | 0.998379 | + | 0.0569187i | \(0.0181276\pi\) | ||||
−0.998379 | + | 0.0569187i | \(0.981872\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.1464 | −0.793442 | −0.396721 | − | 0.917939i | \(-0.629852\pi\) | ||||
−0.396721 | + | 0.917939i | \(0.629852\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.0000 | −0.831163 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.2474 | − | 12.2474i | 0.564333 | − | 0.564333i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 12.0000i | − | 0.551761i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −18.0000 | −0.824163 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.3939 | 1.34304 | 0.671520 | − | 0.740986i | \(-0.265642\pi\) | ||||
0.671520 | + | 0.740986i | \(0.265642\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.00000 | −0.182384 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.34847 | + | 7.34847i | 0.334367 | + | 0.334367i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.0454i | 0.998973i | 0.866322 | + | 0.499486i | \(0.166478\pi\) | ||||
−0.866322 | + | 0.499486i | \(0.833522\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.00000 | + | 9.00000i | 0.406994 | + | 0.406994i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.6969 | −0.663264 | −0.331632 | − | 0.943409i | \(-0.607599\pi\) | ||||
−0.331632 | + | 0.943409i | \(0.607599\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.0000i | 0.538274i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 4.89898i | − | 0.219308i | −0.993970 | − | 0.109654i | \(-0.965026\pi\) | ||
0.993970 | − | 0.109654i | \(-0.0349744\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.0000 | − | 21.0000i | 0.938211 | − | 0.938211i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −36.7423 | −1.63826 | −0.819130 | − | 0.573608i | \(-0.805543\pi\) | ||||
−0.819130 | + | 0.573608i | \(0.805543\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.0227 | + | 11.0227i | −0.489535 | + | 0.489535i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 24.0000i | − | 1.06378i | −0.846813 | − | 0.531891i | \(-0.821482\pi\) | ||
0.846813 | − | 0.531891i | \(-0.178518\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 34.2929i | − | 1.51703i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 18.0000 | − | 18.0000i | 0.794719 | − | 0.794719i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 60.0000 | 2.63880 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.0454 | + | 22.0454i | 0.967686 | + | 0.967686i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.44949i | 0.107109i | 0.998565 | + | 0.0535544i | \(0.0170550\pi\) | ||||
−0.998565 | + | 0.0535544i | \(0.982945\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −58.7878 | −2.56083 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.0000 | −0.739130 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 29.3939i | − | 1.27559i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0000i | 0.519778i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.0000 | − | 12.0000i | 0.517838 | − | 0.517838i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.89898 | −0.211014 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.00000 | −0.0859867 | −0.0429934 | − | 0.999075i | \(-0.513689\pi\) | ||||
−0.0429934 | + | 0.999075i | \(0.513689\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.2474 | − | 12.2474i | 0.525588 | − | 0.525588i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 41.6413i | − | 1.78045i | −0.455517 | − | 0.890227i | \(-0.650545\pi\) | ||
0.455517 | − | 0.890227i | \(-0.349455\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 24.0000i | − | 1.02430i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.0000 | −0.510292 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 18.0000i | − | 0.762684i | −0.924434 | − | 0.381342i | \(-0.875462\pi\) | ||
0.924434 | − | 0.381342i | \(-0.124538\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.89898i | 0.207205i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 36.0000 | + | 36.0000i | 1.51992 | + | 1.51992i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.2474 | −0.516168 | −0.258084 | − | 0.966122i | \(-0.583091\pi\) | ||||
−0.258084 | + | 0.966122i | \(0.583091\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 22.0454i | 0.925820i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 30.0000i | − | 1.25767i | −0.777541 | − | 0.628833i | \(-0.783533\pi\) | ||
0.777541 | − | 0.628833i | \(-0.216467\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 9.79796i | − | 0.410032i | −0.978759 | − | 0.205016i | \(-0.934275\pi\) | ||
0.978759 | − | 0.205016i | \(-0.0657246\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.0000 | − | 18.0000i | 0.751961 | − | 0.751961i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.0000 | −1.58196 | −0.790980 | − | 0.611842i | \(-0.790429\pi\) | ||||
−0.790980 | + | 0.611842i | \(0.790429\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.2474 | − | 12.2474i | 0.508987 | − | 0.508987i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 18.0000i | − | 0.746766i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 29.3939i | 1.21737i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.7423 | 1.51652 | 0.758259 | − | 0.651953i | \(-0.226050\pi\) | ||||
0.758259 | + | 0.651953i | \(0.226050\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 48.0000 | 1.97781 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.0454 | − | 22.0454i | −0.906827 | − | 0.906827i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.0000i | 1.72473i | 0.506284 | + | 0.862367i | \(0.331019\pi\) | ||||
−0.506284 | + | 0.862367i | \(0.668981\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.0000 | − | 18.0000i | −0.736691 | − | 0.736691i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.0000 | −1.14214 | −0.571072 | − | 0.820900i | \(-0.693472\pi\) | ||||
−0.571072 | + | 0.820900i | \(0.693472\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.0454 | −0.897758 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 26.9444i | − | 1.09364i | −0.837251 | − | 0.546819i | \(-0.815838\pi\) | ||
0.837251 | − | 0.546819i | \(-0.184162\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.4949 | −0.990957 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −38.0000 | −1.53481 | −0.767403 | − | 0.641165i | \(-0.778451\pi\) | ||||
−0.767403 | + | 0.641165i | \(0.778451\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 6.00000i | − | 0.241551i | −0.992680 | − | 0.120775i | \(-0.961462\pi\) | ||
0.992680 | − | 0.120775i | \(-0.0385381\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.89898i | 0.196907i | 0.995142 | + | 0.0984533i | \(0.0313895\pi\) | ||||
−0.995142 | + | 0.0984533i | \(0.968610\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.00000 | + | 9.00000i | 0.361158 | + | 0.361158i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 29.3939 | 1.17764 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −29.3939 | − | 29.3939i | −1.17388 | − | 1.17388i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.0000i | 0.478471i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.00000 | 0.0792429 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.6969i | 0.581402i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 18.0000i | − | 0.710957i | −0.934684 | − | 0.355479i | \(-0.884318\pi\) | ||
0.934684 | − | 0.355479i | \(-0.115682\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 36.7423i | − | 1.44898i | −0.689287 | − | 0.724488i | \(-0.742076\pi\) | ||
0.689287 | − | 0.724488i | \(-0.257924\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −26.9444 | −1.05929 | −0.529647 | − | 0.848218i | \(-0.677675\pi\) | ||||
−0.529647 | + | 0.848218i | \(0.677675\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −48.0000 | −1.88416 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −29.3939 | + | 29.3939i | −1.15204 | + | 1.15204i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.0000i | 0.704394i | 0.935926 | + | 0.352197i | \(0.114565\pi\) | ||||
−0.935926 | + | 0.352197i | \(0.885435\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 42.0000i | − | 1.63858i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.3939 | 1.14502 | 0.572511 | − | 0.819897i | \(-0.305969\pi\) | ||||
0.572511 | + | 0.819897i | \(0.305969\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.0000 | −1.55582 | −0.777910 | − | 0.628376i | \(-0.783720\pi\) | ||||
−0.777910 | + | 0.628376i | \(0.783720\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14.6969 | − | 14.6969i | −0.570782 | − | 0.570782i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.00000 | + | 3.00000i | 0.115987 | + | 0.115987i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −39.1918 | −1.51298 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.0000 | −1.00223 | −0.501113 | − | 0.865382i | \(-0.667076\pi\) | ||||
−0.501113 | + | 0.865382i | \(0.667076\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 18.0000i | − | 0.691796i | −0.938272 | − | 0.345898i | \(-0.887574\pi\) | ||
0.938272 | − | 0.345898i | \(-0.112426\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.4949i | 0.940028i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.00000 | + | 3.00000i | −0.114960 | + | 0.114960i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.8434 | 1.21845 | 0.609226 | − | 0.792996i | \(-0.291480\pi\) | ||||
0.609226 | + | 0.792996i | \(0.291480\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.9444 | − | 26.9444i | 1.02799 | − | 1.02799i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 12.0000i | − | 0.457164i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 29.3939i | − | 1.11820i | −0.829102 | − | 0.559098i | \(-0.811148\pi\) | ||
0.829102 | − | 0.559098i | \(-0.188852\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 36.0000 | 1.36753 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 36.0000 | 1.36360 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.0454 | − | 22.0454i | −0.833834 | − | 0.833834i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 30.0000i | − | 1.13308i | −0.824033 | − | 0.566542i | \(-0.808281\pi\) | ||
0.824033 | − | 0.566542i | \(-0.191719\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 9.79796i | − | 0.369537i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −29.3939 | −1.10547 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.0000 | 0.375558 | 0.187779 | − | 0.982211i | \(-0.439871\pi\) | ||||
0.187779 | + | 0.982211i | \(0.439871\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.6969 | −0.551178 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.0000i | 0.898807i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.0000 | + | 12.0000i | −0.448148 | + | 0.448148i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.79796 | −0.365402 | −0.182701 | − | 0.983169i | \(-0.558484\pi\) | ||||
−0.182701 | + | 0.983169i | \(0.558484\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.0000 | −1.11726 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.89898 | − | 4.89898i | 0.182195 | − | 0.182195i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 26.9444i | − | 0.999312i | −0.866224 | − | 0.499656i | \(-0.833460\pi\) | ||
0.866224 | − | 0.499656i | \(-0.166540\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 1.00000i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.6969 | 0.543586 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.0000 | −1.25582 | −0.627909 | − | 0.778287i | \(-0.716089\pi\) | ||||
−0.627909 | + | 0.778287i | \(0.716089\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 36.0000i | 1.32608i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.6969i | 0.540636i | 0.962771 | + | 0.270318i | \(0.0871288\pi\) | ||||
−0.962771 | + | 0.270318i | \(0.912871\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.0000 | + | 12.0000i | 0.440831 | + | 0.440831i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.6413 | 1.52767 | 0.763836 | − | 0.645410i | \(-0.223314\pi\) | ||||
0.763836 | + | 0.645410i | \(0.223314\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 22.0454i | − | 0.806599i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 6.00000i | − | 0.219235i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 19.5959i | − | 0.715065i | −0.933901 | − | 0.357533i | \(-0.883618\pi\) | ||
0.933901 | − | 0.357533i | \(-0.116382\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 30.0000 | − | 30.0000i | 1.09326 | − | 1.09326i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000 | 0.0726912 | 0.0363456 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363456 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.6969 | − | 14.6969i | 0.533465 | − | 0.533465i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 48.0000i | 1.74000i | 0.493053 | + | 0.869999i | \(0.335881\pi\) | ||||
−0.493053 | + | 0.869999i | \(0.664119\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 9.79796i | − | 0.354710i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19.5959 | 0.707568 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.0000 | 0.504853 | 0.252426 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252426 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.34847 | − | 7.34847i | −0.264649 | − | 0.264649i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 42.0000i | − | 1.51064i | −0.655359 | − | 0.755318i | \(-0.727483\pi\) | ||
0.655359 | − | 0.755318i | \(-0.272517\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.00000 | + | 6.00000i | 0.215249 | + | 0.215249i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −29.3939 | −1.05314 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.0000 | 0.858788 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.5403i | 1.65898i | 0.558520 | + | 0.829491i | \(0.311370\pi\) | ||||
−0.558520 | + | 0.829491i | \(0.688630\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.00000 | + | 3.00000i | −0.106803 | + | 0.106803i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.6969 | 0.522563 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.0000 | 0.568177 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.0000i | 1.48772i | 0.668338 | + | 0.743858i | \(0.267006\pi\) | ||||
−0.668338 | + | 0.743858i | \(0.732994\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 73.4847i | 2.59970i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 36.0000 | 1.27200 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −68.5857 | −2.42034 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22.0454 | + | 22.0454i | 0.776035 | + | 0.776035i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 12.0000i | − | 0.421898i | −0.977497 | − | 0.210949i | \(-0.932345\pi\) | ||
0.977497 | − | 0.210949i | \(-0.0676553\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.1918i | 1.37621i | 0.725610 | + | 0.688106i | \(0.241557\pi\) | ||||
−0.725610 | + | 0.688106i | \(0.758443\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.0000 | + | 12.0000i | 0.420858 | + | 0.420858i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.0000 | −0.419827 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14.6969 | −0.513553 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 6.00000i | − | 0.209401i | −0.994504 | − | 0.104701i | \(-0.966612\pi\) | ||
0.994504 | − | 0.104701i | \(-0.0333885\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.7423i | 1.28076i | 0.768059 | + | 0.640379i | \(0.221223\pi\) | ||||
−0.768059 | + | 0.640379i | \(0.778777\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.1464 | −0.596240 | −0.298120 | − | 0.954528i | \(-0.596360\pi\) | ||||
−0.298120 | + | 0.954528i | \(0.596360\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.0000 | −0.694629 | −0.347314 | − | 0.937749i | \(-0.612906\pi\) | ||||
−0.347314 | + | 0.937749i | \(0.612906\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.44949 | − | 2.44949i | 0.0849719 | − | 0.0849719i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 6.00000i | − | 0.207888i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −36.0000 | + | 36.0000i | −1.24434 | + | 1.24434i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.5959 | 0.676526 | 0.338263 | − | 0.941052i | \(-0.390161\pi\) | ||||
0.338263 | + | 0.941052i | \(0.390161\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.34847 | − | 7.34847i | −0.253095 | − | 0.253095i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 31.8434i | − | 1.09415i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 33.0000 | + | 33.0000i | 1.13256 | + | 1.13256i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.89898 | 0.167935 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.0000 | −0.479351 | −0.239675 | − | 0.970853i | \(-0.577041\pi\) | ||||
−0.239675 | + | 0.970853i | \(0.577041\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.00000i | 0.204956i | 0.994735 | + | 0.102478i | \(0.0326771\pi\) | ||||
−0.994735 | + | 0.102478i | \(0.967323\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 53.8888i | − | 1.83866i | −0.393486 | − | 0.919331i | \(-0.628731\pi\) | ||
0.393486 | − | 0.919331i | \(-0.371269\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.0000 | − | 18.0000i | 0.613438 | − | 0.613438i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.34847 | −0.250145 | −0.125072 | − | 0.992148i | \(-0.539916\pi\) | ||||
−0.125072 | + | 0.992148i | \(0.539916\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −23.2702 | + | 23.2702i | −0.790296 | + | 0.790296i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.0000i | 0.814144i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 14.6969i | − | 0.497987i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 30.0000i | 1.01535i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 58.0000 | 1.95852 | 0.979260 | − | 0.202606i | \(-0.0649409\pi\) | ||||
0.979260 | + | 0.202606i | \(0.0649409\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.34847 | + | 7.34847i | 0.247858 | + | 0.247858i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 18.0000i | − | 0.606435i | −0.952921 | − | 0.303218i | \(-0.901939\pi\) | ||
0.952921 | − | 0.303218i | \(-0.0980609\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 56.3383i | 1.89593i | 0.318369 | + | 0.947967i | \(0.396865\pi\) | ||||
−0.318369 | + | 0.947967i | \(0.603135\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 41.6413 | 1.39818 | 0.699089 | − | 0.715034i | \(-0.253589\pi\) | ||||
0.699089 | + | 0.715034i | \(0.253589\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.0000 | −0.603701 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 44.0908 | 1.47710 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 60.0000i | − | 2.00782i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.00000 | + | 6.00000i | −0.200334 | + | 0.200334i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.0000 | −1.19933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.34847 | − | 7.34847i | 0.244542 | − | 0.244542i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.2474i | 0.406670i | 0.979109 | + | 0.203335i | \(0.0651780\pi\) | ||||
−0.979109 | + | 0.203335i | \(0.934822\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −36.0000 | −1.19404 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.4949 | −0.811552 | −0.405776 | − | 0.913973i | \(-0.632999\pi\) | ||||
−0.405776 | + | 0.913973i | \(0.632999\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36.0000 | −1.19143 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.0000i | 0.396275i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 34.2929i | − | 1.13122i | −0.824674 | − | 0.565608i | \(-0.808641\pi\) | ||
0.824674 | − | 0.565608i | \(-0.191359\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.00000 | − | 3.00000i | −0.0988534 | − | 0.0988534i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.79796 | −0.322504 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −36.7423 | −1.20678 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 54.0000i | 1.77168i | 0.463988 | + | 0.885841i | \(0.346418\pi\) | ||||
−0.463988 | + | 0.885841i | \(0.653582\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.89898i | 0.160558i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 30.0000 | − | 30.0000i | 0.982156 | − | 0.982156i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.0000 | −1.24141 | −0.620703 | − | 0.784046i | \(-0.713153\pi\) | ||||
−0.620703 | + | 0.784046i | \(0.713153\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.2474 | − | 12.2474i | 0.399680 | − | 0.399680i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.0000i | 0.391189i | 0.980685 | + | 0.195594i | \(0.0626636\pi\) | ||||
−0.980685 | + | 0.195594i | \(0.937336\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 14.6969i | − | 0.478598i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.0454 | −0.716379 | −0.358190 | − | 0.933649i | \(-0.616606\pi\) | ||||
−0.358190 | + | 0.933649i | \(0.616606\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.0000 | 0.908918 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.0454 | + | 22.0454i | 0.714871 | + | 0.714871i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.0000i | 0.971795i | 0.874016 | + | 0.485898i | \(0.161507\pi\) | ||||
−0.874016 | + | 0.485898i | \(0.838493\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.6969 | 0.474589 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −65.0000 | −2.09677 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 7.34847i | − | 0.236801i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 56.3383i | 1.81172i | 0.423581 | + | 0.905858i | \(0.360773\pi\) | ||||
−0.423581 | + | 0.905858i | \(0.639227\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 36.0000 | − | 36.0000i | 1.15649 | − | 1.15649i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 53.8888 | 1.72937 | 0.864687 | − | 0.502312i | \(-0.167517\pi\) | ||||
0.864687 | + | 0.502312i | \(0.167517\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.0000 | 0.384702 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 18.0000i | − | 0.575871i | −0.957650 | − | 0.287936i | \(-0.907031\pi\) | ||
0.957650 | − | 0.287936i | \(-0.0929689\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 58.7878i | − | 1.87886i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 12.0000i | − | 0.383131i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31.8434 | 1.01565 | 0.507823 | − | 0.861462i | \(-0.330450\pi\) | ||||
0.507823 | + | 0.861462i | \(0.330450\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 36.7423 | + | 36.7423i | 1.16952 | + | 1.16952i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 6.00000i | − | 0.190789i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.79796i | 0.311242i | 0.987817 | + | 0.155621i | \(0.0497379\pi\) | ||||
−0.987817 | + | 0.155621i | \(0.950262\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.0000 | + | 24.0000i | 0.761617 | + | 0.761617i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.0000 | −0.443384 | −0.221692 | − | 0.975117i | \(-0.571158\pi\) | ||||
−0.221692 | + | 0.975117i | \(0.571158\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.34847 | + | 7.34847i | 0.232495 | + | 0.232495i |
(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 | 1200.2.h.k.1151.3 | 4 | ||
3.2 | odd | 2 | inner | 1200.2.h.k.1151.1 | 4 | ||
4.3 | odd | 2 | inner | 1200.2.h.k.1151.2 | 4 | ||
5.2 | odd | 4 | 1200.2.o.f.1199.1 | 4 | |||
5.3 | odd | 4 | 1200.2.o.e.1199.4 | 4 | |||
5.4 | even | 2 | 240.2.h.a.191.2 | yes | 4 | ||
12.11 | even | 2 | inner | 1200.2.h.k.1151.4 | 4 | ||
15.2 | even | 4 | 1200.2.o.e.1199.2 | 4 | |||
15.8 | even | 4 | 1200.2.o.f.1199.3 | 4 | |||
15.14 | odd | 2 | 240.2.h.a.191.4 | yes | 4 | ||
20.3 | even | 4 | 1200.2.o.e.1199.1 | 4 | |||
20.7 | even | 4 | 1200.2.o.f.1199.4 | 4 | |||
20.19 | odd | 2 | 240.2.h.a.191.3 | yes | 4 | ||
40.19 | odd | 2 | 960.2.h.c.191.2 | 4 | |||
40.29 | even | 2 | 960.2.h.c.191.3 | 4 | |||
60.23 | odd | 4 | 1200.2.o.f.1199.2 | 4 | |||
60.47 | odd | 4 | 1200.2.o.e.1199.3 | 4 | |||
60.59 | even | 2 | 240.2.h.a.191.1 | ✓ | 4 | ||
120.29 | odd | 2 | 960.2.h.c.191.1 | 4 | |||
120.59 | even | 2 | 960.2.h.c.191.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
240.2.h.a.191.1 | ✓ | 4 | 60.59 | even | 2 | ||
240.2.h.a.191.2 | yes | 4 | 5.4 | even | 2 | ||
240.2.h.a.191.3 | yes | 4 | 20.19 | odd | 2 | ||
240.2.h.a.191.4 | yes | 4 | 15.14 | odd | 2 | ||
960.2.h.c.191.1 | 4 | 120.29 | odd | 2 | |||
960.2.h.c.191.2 | 4 | 40.19 | odd | 2 | |||
960.2.h.c.191.3 | 4 | 40.29 | even | 2 | |||
960.2.h.c.191.4 | 4 | 120.59 | even | 2 | |||
1200.2.h.k.1151.1 | 4 | 3.2 | odd | 2 | inner | ||
1200.2.h.k.1151.2 | 4 | 4.3 | odd | 2 | inner | ||
1200.2.h.k.1151.3 | 4 | 1.1 | even | 1 | trivial | ||
1200.2.h.k.1151.4 | 4 | 12.11 | even | 2 | inner | ||
1200.2.o.e.1199.1 | 4 | 20.3 | even | 4 | |||
1200.2.o.e.1199.2 | 4 | 15.2 | even | 4 | |||
1200.2.o.e.1199.3 | 4 | 60.47 | odd | 4 | |||
1200.2.o.e.1199.4 | 4 | 5.3 | odd | 4 | |||
1200.2.o.f.1199.1 | 4 | 5.2 | odd | 4 | |||
1200.2.o.f.1199.2 | 4 | 60.23 | odd | 4 | |||
1200.2.o.f.1199.3 | 4 | 15.8 | even | 4 | |||
1200.2.o.f.1199.4 | 4 | 20.7 | even | 4 |