Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,2,Mod(1199,1200)]
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, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.1199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.o (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: | \(9.58204824255\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 240) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1199.2 | ||
Root | \(1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.1199 |
Dual form | 1200.2.o.f.1199.1 |
$q$-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 | ||||||||
\(7\) | 2.44949 | 0.925820 | 0.462910 | − | 0.886405i | \(-0.346805\pi\) | ||||
0.462910 | + | 0.886405i | \(0.346805\pi\) | |||||||
\(8\) | 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 | ||||||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.00000 | 1.45521 | 0.727607 | − | 0.685994i | \(-0.240633\pi\) | ||||
0.727607 | + | 0.685994i | \(0.240633\pi\) | |||||||
\(18\) | 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 | ||||||||
\(23\) | − | 2.44949i | − | 0.510754i | −0.966842 | − | 0.255377i | \(-0.917800\pi\) | ||
0.966842 | − | 0.255377i | \(-0.0821996\pi\) | |||||||
\(24\) | 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 | \(0.342379\pi\) | ||||
−0.475191 | + | 0.879883i | \(0.657621\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.00000 | − | 6.00000i | 1.04447 | − | 1.04447i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000i | 0.328798i | 0.986394 | + | 0.164399i | \(0.0525685\pi\) | ||||
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.44949 | − | 2.44949i | −0.392232 | − | 0.392232i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.00000i | − | 0.937043i | −0.883452 | − | 0.468521i | \(-0.844787\pi\) | ||
0.883452 | − | 0.468521i | \(-0.155213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.44949 | 0.373544 | 0.186772 | − | 0.982403i | \(-0.440197\pi\) | ||||
0.186772 | + | 0.982403i | \(0.440197\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.2474i | 1.78647i | 0.449586 | + | 0.893237i | \(0.351571\pi\) | ||||
−0.449586 | + | 0.893237i | \(0.648429\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.34847 | + | 7.34847i | −1.02899 | + | 1.02899i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 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 | \(-0.720152\pi\) | ||||
−0.637793 | + | 0.770208i | \(0.720152\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.00000 | 1.02430 | 0.512148 | − | 0.858898i | \(-0.328850\pi\) | ||||
0.512148 | + | 0.858898i | \(0.328850\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 7.34847i | − | 0.925820i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.34847 | 0.897758 | 0.448879 | − | 0.893592i | \(-0.351823\pi\) | ||||
0.448879 | + | 0.893592i | \(0.351823\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | 14.0000i | 1.63858i | 0.573382 | + | 0.819288i | \(0.305631\pi\) | ||||
−0.573382 | + | 0.819288i | \(0.694369\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.0000 | −1.36753 | ||||||||
\(78\) | 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 | ||||||||
\(83\) | 7.34847i | 0.806599i | 0.915068 | + | 0.403300i | \(0.132137\pi\) | ||||
−0.915068 | + | 0.403300i | \(0.867863\pi\) | |||||||
\(84\) | 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 | ||||||||
\(97\) | 10.0000i | 1.01535i | 0.861550 | + | 0.507673i | \(0.169494\pi\) | ||||
−0.861550 | + | 0.507673i | \(0.830506\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14.6969i | 1.47710i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.0000i | 1.19404i | 0.802225 | + | 0.597022i | \(0.203650\pi\) | ||||
−0.802225 | + | 0.597022i | \(0.796350\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.2474 | −1.20678 | −0.603388 | − | 0.797447i | \(-0.706183\pi\) | ||||
−0.603388 | + | 0.797447i | \(0.706183\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 2.44949i | − | 0.236801i | −0.992966 | − | 0.118401i | \(-0.962223\pi\) | ||
0.992966 | − | 0.118401i | \(-0.0377767\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.00000 | −0.383131 | −0.191565 | − | 0.981480i | \(-0.561356\pi\) | ||||
−0.191565 | + | 0.981480i | \(0.561356\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.44949 | − | 2.44949i | −0.232495 | − | 0.232495i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.00000 | 0.554700 | ||||||||
\(118\) | 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 | ||||||||
\(127\) | 7.34847 | 0.652071 | 0.326036 | − | 0.945357i | \(-0.394287\pi\) | ||||
0.326036 | + | 0.945357i | \(0.394287\pi\) | |||||||
\(128\) | 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 | ||||||||
\(133\) | 12.0000i | 1.04053i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00000 | −0.512615 | −0.256307 | − | 0.966595i | \(-0.582506\pi\) | ||||
−0.256307 | + | 0.966595i | \(0.582506\pi\) | |||||||
\(138\) | 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 | ||||||||
\(143\) | − | 9.79796i | − | 0.819346i | ||||||
\(144\) | 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 | \(-0.706236\pi\) | ||
0.603522 | − | 0.797347i | \(-0.293764\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 18.0000i | − | 1.45521i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 10.0000i | − | 0.798087i | −0.916932 | − | 0.399043i | \(-0.869342\pi\) | ||
0.916932 | − | 0.399043i | \(-0.130658\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.34847 | − | 7.34847i | 0.582772 | − | 0.582772i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 6.00000i | − | 0.472866i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.34847 | 0.575577 | 0.287788 | − | 0.957694i | \(-0.407080\pi\) | ||||
0.287788 | + | 0.957694i | \(0.407080\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 17.1464i | − | 1.32683i | −0.748251 | − | 0.663415i | \(-0.769106\pi\) | ||
0.748251 | − | 0.663415i | \(-0.230894\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.6969 | 1.12390 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.0000 | 1.36851 | 0.684257 | − | 0.729241i | \(-0.260127\pi\) | ||||
0.684257 | + | 0.729241i | \(0.260127\pi\) | |||||||
\(174\) | 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 | \(-0.619330\pi\) | ||||
−0.366167 | + | 0.930549i | \(0.619330\pi\) | |||||||
\(180\) | 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 | ||||||||
\(187\) | −29.3939 | −2.14949 | ||||||||
\(188\) | 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 | ||||||||
\(193\) | 10.0000i | 0.719816i | 0.932988 | + | 0.359908i | \(0.117192\pi\) | ||||
−0.932988 | + | 0.359908i | \(0.882808\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 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 | ||||||||
\(207\) | −7.34847 | −0.510754 | ||||||||
\(208\) | 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 | ||||||||
\(217\) | 24.0000i | 1.62923i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −17.1464 | − | 17.1464i | −1.15865 | − | 1.15865i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000i | 0.807207i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.44949 | 0.164030 | 0.0820150 | − | 0.996631i | \(-0.473864\pi\) | ||||
0.0820150 | + | 0.996631i | \(0.473864\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.44949i | 0.162578i | 0.996691 | + | 0.0812892i | \(0.0259037\pi\) | ||||
−0.996691 | + | 0.0812892i | \(0.974096\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.0000 | −1.45380 | −0.726900 | − | 0.686743i | \(-0.759040\pi\) | ||||
−0.726900 | + | 0.686743i | \(0.759040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.6969 | − | 14.6969i | 0.966988 | − | 0.966988i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | 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 | \(-0.397362\pi\) | ||||
0.316889 | + | 0.948463i | \(0.397362\pi\) | |||||||
\(240\) | 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 | ||||||||
\(247\) | −9.79796 | −0.623429 | ||||||||
\(248\) | 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 | ||||||||
\(253\) | 12.0000i | 0.754434i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.00000 | 0.374270 | 0.187135 | − | 0.982334i | \(-0.440080\pi\) | ||||
0.187135 | + | 0.982334i | \(0.440080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.89898i | 0.304408i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 2.44949i | − | 0.151042i | −0.997144 | − | 0.0755210i | \(-0.975938\pi\) | ||
0.997144 | − | 0.0755210i | \(-0.0240620\pi\) | |||||||
\(264\) | 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 | \(-0.903817\pi\) | ||
0.954693 | − | 0.297592i | \(-0.0961834\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.00000 | − | 6.00000i | −0.363137 | − | 0.363137i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 2.00000i | − | 0.120168i | −0.998193 | − | 0.0600842i | \(-0.980863\pi\) | ||
0.998193 | − | 0.0600842i | \(-0.0191369\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 29.3939 | 1.75977 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000i | 0.357930i | 0.983855 | + | 0.178965i | \(0.0572749\pi\) | ||||
−0.983855 | + | 0.178965i | \(0.942725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.9444 | 1.60168 | 0.800839 | − | 0.598880i | \(-0.204387\pi\) | ||||
0.800839 | + | 0.598880i | \(0.204387\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 14.6969i | − | 0.867533i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.2474 | − | 12.2474i | −0.717958 | − | 0.717958i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | 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 | ||||||||
\(307\) | 2.44949 | 0.139800 | 0.0698999 | − | 0.997554i | \(-0.477732\pi\) | ||||
0.0698999 | + | 0.997554i | \(0.477732\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | 10.0000i | 0.565233i | 0.959233 | + | 0.282617i | \(0.0912024\pi\) | ||||
−0.959233 | + | 0.282617i | \(0.908798\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.0000 | −1.01098 | −0.505490 | − | 0.862832i | \(-0.668688\pi\) | ||||
−0.505490 | + | 0.862832i | \(0.668688\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.00000 | + | 3.00000i | 0.167444 | + | 0.167444i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 29.3939i | 1.63552i | ||||||||
\(324\) | 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 | \(-0.818974\pi\) | ||
0.842597 | − | 0.538545i | \(-0.181026\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.00000 | 0.328798 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 14.0000i | − | 0.762629i | −0.924445 | − | 0.381314i | \(-0.875472\pi\) | ||
0.924445 | − | 0.381314i | \(-0.124528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.34847 | + | 7.34847i | −0.399114 | + | 0.399114i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 48.0000i | − | 2.59935i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.5959 | −1.05808 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 7.34847i | − | 0.394486i | −0.980355 | − | 0.197243i | \(-0.936801\pi\) | ||
0.980355 | − | 0.197243i | \(-0.0631989\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.00000 | −0.107058 | −0.0535288 | − | 0.998566i | \(-0.517047\pi\) | ||||
−0.0535288 | + | 0.998566i | \(0.517047\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.34847 | + | 7.34847i | −0.392232 | + | 0.392232i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.00000 | −0.319348 | −0.159674 | − | 0.987170i | \(-0.551044\pi\) | ||||
−0.159674 | + | 0.987170i | \(0.551044\pi\) | |||||||
\(354\) | 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 | \(-0.416753\pi\) | ||||
0.258558 | + | 0.965996i | \(0.416753\pi\) | |||||||
\(360\) | 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 | ||||||||
\(367\) | −7.34847 | −0.383587 | −0.191793 | − | 0.981435i | \(-0.561430\pi\) | ||||
−0.191793 | + | 0.981435i | \(0.561430\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −18.0000 | −0.937043 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.6969 | −0.763027 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 26.0000i | − | 1.34623i | −0.739538 | − | 0.673114i | \(-0.764956\pi\) | ||
0.739538 | − | 0.673114i | \(-0.235044\pi\) | |||||||
\(374\) | 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 | ||||||||
\(383\) | 2.44949i | 0.125163i | 0.998040 | + | 0.0625815i | \(0.0199333\pi\) | ||||
−0.998040 | + | 0.0625815i | \(0.980067\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 7.34847i | − | 0.373544i | ||||||
\(388\) | 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 | ||||||||
\(397\) | 2.00000i | 0.100377i | 0.998740 | + | 0.0501886i | \(0.0159822\pi\) | ||||
−0.998740 | + | 0.0501886i | \(0.984018\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −14.6969 | − | 14.6969i | −0.735767 | − | 0.735767i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.0000i | 1.19850i | 0.800561 | + | 0.599251i | \(0.204535\pi\) | ||||
−0.800561 | + | 0.599251i | \(0.795465\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.5959 | −0.976142 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 9.79796i | − | 0.485667i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.0000 | −0.791149 | −0.395575 | − | 0.918434i | \(-0.629455\pi\) | ||||
−0.395575 | + | 0.918434i | \(0.629455\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.34847 | − | 7.34847i | 0.362473 | − | 0.362473i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24.0000 | −1.18096 | ||||||||
\(414\) | 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 | ||||||||
\(423\) | 36.7423 | 1.78647 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.5959 | 0.948313 | ||||||||
\(428\) | 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 | ||||||||
\(433\) | − | 2.00000i | − | 0.0961139i | −0.998845 | − | 0.0480569i | \(-0.984697\pi\) | ||
0.998845 | − | 0.0480569i | \(-0.0153029\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.0000 | 0.574038 | ||||||||
\(438\) | 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 | ||||||||
\(443\) | − | 17.1464i | − | 0.814651i | −0.913283 | − | 0.407326i | \(-0.866461\pi\) | ||
0.913283 | − | 0.407326i | \(-0.133539\pi\) | |||||||
\(444\) | 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 | ||||||||
\(457\) | 22.0000i | 1.02912i | 0.857455 | + | 0.514558i | \(0.172044\pi\) | ||||
−0.857455 | + | 0.514558i | \(0.827956\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 22.0454 | + | 22.0454i | 1.02899 | + | 1.02899i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 12.0000i | − | 0.558896i | −0.960161 | − | 0.279448i | \(-0.909849\pi\) | ||
0.960161 | − | 0.279448i | \(-0.0901514\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.44949 | 0.113837 | 0.0569187 | − | 0.998379i | \(-0.481872\pi\) | ||||
0.0569187 | + | 0.998379i | \(0.481872\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.1464i | 0.793442i | 0.917939 | + | 0.396721i | \(0.129852\pi\) | ||||
−0.917939 | + | 0.396721i | \(0.870148\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.0000 | 0.831163 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.2474 | + | 12.2474i | 0.564333 | + | 0.564333i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.0000 | −0.551761 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.0000i | 0.824163i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −29.3939 | −1.34304 | −0.671520 | − | 0.740986i | \(-0.734358\pi\) | ||||
−0.671520 | + | 0.740986i | \(0.734358\pi\) | |||||||
\(480\) | 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 | ||||||||
\(487\) | −22.0454 | −0.998973 | −0.499486 | − | 0.866322i | \(-0.666478\pi\) | ||||
−0.499486 | + | 0.866322i | \(0.666478\pi\) | |||||||
\(488\) | 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 | ||||||||
\(497\) | −12.0000 | −0.538274 | ||||||||
\(498\) | 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 | ||||||||
\(503\) | − | 36.7423i | − | 1.63826i | −0.573608 | − | 0.819130i | \(-0.694457\pi\) | ||
0.573608 | − | 0.819130i | \(-0.305543\pi\) | |||||||
\(504\) | 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 | ||||||||
\(517\) | − | 60.0000i | − | 2.63880i | ||||||
\(518\) | 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 | ||||||||
\(523\) | 2.44949 | 0.107109 | 0.0535544 | − | 0.998565i | \(-0.482945\pi\) | ||||
0.0535544 | + | 0.998565i | \(0.482945\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 58.7878i | 2.56083i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.0000 | 0.739130 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 29.3939i | 1.27559i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0000 | 0.519778 | ||||||||
\(534\) | 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 | ||||||||
\(547\) | 41.6413 | 1.78045 | 0.890227 | − | 0.455517i | \(-0.150545\pi\) | ||||
0.890227 | + | 0.455517i | \(0.150545\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 24.0000i | − | 1.02430i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 12.0000i | − | 0.510292i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.0000 | 0.762684 | 0.381342 | − | 0.924434i | \(-0.375462\pi\) | ||||
0.381342 | + | 0.924434i | \(0.375462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.89898i | 0.207205i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 36.0000 | − | 36.0000i | 1.51992 | − | 1.51992i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 12.2474i | − | 0.516168i | −0.966122 | − | 0.258084i | \(-0.916909\pi\) | ||
0.966122 | − | 0.258084i | \(-0.0830912\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −22.0454 | −0.925820 | ||||||||
\(568\) | 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 | \(0.0657246\pi\) | ||||
−0.978759 | + | 0.205016i | \(0.934275\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.0000 | + | 18.0000i | −0.751961 | + | 0.751961i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.0000i | 1.58196i | 0.611842 | + | 0.790980i | \(0.290429\pi\) | ||||
−0.611842 | + | 0.790980i | \(0.709571\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.2474 | − | 12.2474i | −0.508987 | − | 0.508987i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.0000i | 0.746766i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 29.3939 | 1.21737 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 36.7423i | − | 1.51652i | −0.651953 | − | 0.758259i | \(-0.726050\pi\) | ||
0.651953 | − | 0.758259i | \(-0.273950\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −48.0000 | −1.97781 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.0454 | + | 22.0454i | −0.906827 | + | 0.906827i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.0000 | 1.72473 | 0.862367 | − | 0.506284i | \(-0.168981\pi\) | ||||
0.862367 | + | 0.506284i | \(0.168981\pi\) | |||||||
\(594\) | 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 | ||||||||
\(603\) | − | 22.0454i | − | 0.897758i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.9444 | 1.09364 | 0.546819 | − | 0.837251i | \(-0.315838\pi\) | ||||
0.546819 | + | 0.837251i | \(0.315838\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.4949 | −0.990957 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 38.0000i | − | 1.53481i | −0.641165 | − | 0.767403i | \(-0.721549\pi\) | ||
0.641165 | − | 0.767403i | \(-0.278451\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.00000 | 0.241551 | 0.120775 | − | 0.992680i | \(-0.461462\pi\) | ||||
0.120775 | + | 0.992680i | \(0.461462\pi\) | |||||||
\(618\) | 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 | ||||||||
\(623\) | 29.3939i | 1.17764i | ||||||||
\(624\) | 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 | ||||||||
\(637\) | − | 2.00000i | − | 0.0792429i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.6969i | 0.581402i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.0000i | 0.710957i | 0.934684 | + | 0.355479i | \(0.115682\pi\) | ||||
−0.934684 | + | 0.355479i | \(0.884318\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −36.7423 | −1.44898 | −0.724488 | − | 0.689287i | \(-0.757924\pi\) | ||||
−0.724488 | + | 0.689287i | \(0.757924\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.9444i | 1.05929i | 0.848218 | + | 0.529647i | \(0.177675\pi\) | ||||
−0.848218 | + | 0.529647i | \(0.822325\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 48.0000 | 1.88416 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −29.3939 | − | 29.3939i | −1.15204 | − | 1.15204i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.0000 | 0.704394 | 0.352197 | − | 0.935926i | \(-0.385435\pi\) | ||||
0.352197 | + | 0.935926i | \(0.385435\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 42.0000 | 1.63858 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.3939 | −1.14502 | −0.572511 | − | 0.819897i | \(-0.694031\pi\) | ||||
−0.572511 | + | 0.819897i | \(0.694031\pi\) | |||||||
\(660\) | 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 | ||||||||
\(673\) | − | 26.0000i | − | 1.00223i | −0.865382 | − | 0.501113i | \(-0.832924\pi\) | ||
0.865382 | − | 0.501113i | \(-0.167076\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.0000 | 0.691796 | 0.345898 | − | 0.938272i | \(-0.387574\pi\) | ||||
0.345898 | + | 0.938272i | \(0.387574\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.4949i | 0.940028i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.00000 | − | 3.00000i | −0.114960 | − | 0.114960i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.8434i | 1.21845i | 0.792996 | + | 0.609226i | \(0.208520\pi\) | ||||
−0.792996 | + | 0.609226i | \(0.791480\pi\) | |||||||
\(684\) | 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 | \(0.188852\pi\) | ||||
−0.829102 | + | 0.559098i | \(0.811148\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 36.0000i | 1.36753i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 36.0000i | − | 1.36360i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.0454 | − | 22.0454i | 0.833834 | − | 0.833834i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.0000i | 1.13308i | 0.824033 | + | 0.566542i | \(0.191719\pi\) | ||||
−0.824033 | + | 0.566542i | \(0.808281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.79796 | −0.369537 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 29.3939i | 1.10547i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.0000 | −0.375558 | −0.187779 | − | 0.982211i | \(-0.560129\pi\) | ||||
−0.187779 | + | 0.982211i | \(0.560129\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.6969 | −0.551178 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.0000 | 0.898807 | ||||||||
\(714\) | 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 | \(-0.441516\pi\) | ||||
0.182701 | + | 0.983169i | \(0.441516\pi\) | |||||||
\(720\) | 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 | ||||||||
\(727\) | 26.9444 | 0.999312 | 0.499656 | − | 0.866224i | \(-0.333460\pi\) | ||||
0.499656 | + | 0.866224i | \(0.333460\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 1.00000i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.6969 | 0.543586 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 34.0000i | − | 1.25582i | −0.778287 | − | 0.627909i | \(-0.783911\pi\) | ||
0.778287 | − | 0.627909i | \(-0.216089\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −36.0000 | −1.32608 | ||||||||
\(738\) | 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 | ||||||||
\(743\) | 41.6413i | 1.52767i | 0.645410 | + | 0.763836i | \(0.276686\pi\) | ||||
−0.645410 | + | 0.763836i | \(0.723314\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 22.0454 | 0.806599 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 6.00000i | − | 0.219235i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.5959i | 0.715065i | 0.933901 | + | 0.357533i | \(0.116382\pi\) | ||||
−0.933901 | + | 0.357533i | \(0.883618\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −30.0000 | + | 30.0000i | −1.09326 | + | 1.09326i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 2.00000i | − | 0.0726912i | −0.999339 | − | 0.0363456i | \(-0.988428\pi\) | ||
0.999339 | − | 0.0363456i | \(-0.0115717\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −14.6969 | − | 14.6969i | −0.533465 | − | 0.533465i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 48.0000i | − | 1.74000i | −0.493053 | − | 0.869999i | \(-0.664119\pi\) | ||
0.493053 | − | 0.869999i | \(-0.335881\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.79796 | −0.354710 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 19.5959i | − | 0.707568i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.0000 | −0.504853 | −0.252426 | − | 0.967616i | \(-0.581229\pi\) | ||||
−0.252426 | + | 0.967616i | \(0.581229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.34847 | + | 7.34847i | −0.264649 | + | 0.264649i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −42.0000 | −1.51064 | −0.755318 | − | 0.655359i | \(-0.772517\pi\) | ||||
−0.755318 | + | 0.655359i | \(0.772517\pi\) | |||||||
\(774\) | 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 | ||||||||
\(787\) | −46.5403 | −1.65898 | −0.829491 | − | 0.558520i | \(-0.811370\pi\) | ||||
−0.829491 | + | 0.558520i | \(0.811370\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.00000 | + | 3.00000i | 0.106803 | + | 0.106803i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.6969 | 0.522563 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.0000i | 0.568177i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42.0000 | −1.48772 | −0.743858 | − | 0.668338i | \(-0.767006\pi\) | ||||
−0.743858 | + | 0.668338i | \(0.767006\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 73.4847i | 2.59970i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 36.0000 | 1.27200 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 68.5857i | − | 2.42034i | ||||||
\(804\) | 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 | \(-0.758443\pi\) | ||
0.725610 | − | 0.688106i | \(-0.241557\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.0000 | + | 12.0000i | 0.420858 | + | 0.420858i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.0000i | 0.419827i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 14.6969 | 0.513553 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.00000i | 0.209401i | 0.994504 | + | 0.104701i | \(0.0333885\pi\) | ||||
−0.994504 | + | 0.104701i | \(0.966612\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.7423 | 1.28076 | 0.640379 | − | 0.768059i | \(-0.278777\pi\) | ||||
0.640379 | + | 0.768059i | \(0.278777\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.1464i | 0.596240i | 0.954528 | + | 0.298120i | \(0.0963595\pi\) | ||||
−0.954528 | + | 0.298120i | \(0.903640\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.0000 | 0.694629 | 0.347314 | − | 0.937749i | \(-0.387094\pi\) | ||||
0.347314 | + | 0.937749i | \(0.387094\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.44949 | + | 2.44949i | 0.0849719 | + | 0.0849719i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.00000 | −0.207888 | ||||||||
\(834\) | 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 | \(-0.609839\pi\) | ||||
−0.338263 | + | 0.941052i | \(0.609839\pi\) | |||||||
\(840\) | 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 | ||||||||
\(847\) | 31.8434 | 1.09415 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −33.0000 | + | 33.0000i | −1.13256 | + | 1.13256i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.89898 | 0.167935 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 14.0000i | − | 0.479351i | −0.970853 | − | 0.239675i | \(-0.922959\pi\) | ||
0.970853 | − | 0.239675i | \(-0.0770410\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.00000 | −0.204956 | −0.102478 | − | 0.994735i | \(-0.532677\pi\) | ||||
−0.102478 | + | 0.994735i | \(0.532677\pi\) | |||||||
\(858\) | 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 | ||||||||
\(863\) | − | 7.34847i | − | 0.250145i | −0.992148 | − | 0.125072i | \(-0.960084\pi\) | ||
0.992148 | − | 0.125072i | \(-0.0399163\pi\) | |||||||
\(864\) | 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 | ||||||||
\(873\) | 30.0000 | 1.01535 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 58.0000i | − | 1.95852i | −0.202606 | − | 0.979260i | \(-0.564941\pi\) | ||
0.202606 | − | 0.979260i | \(-0.435059\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.34847 | + | 7.34847i | −0.247858 | + | 0.247858i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.0000i | 0.606435i | 0.952921 | + | 0.303218i | \(0.0980609\pi\) | ||||
−0.952921 | + | 0.303218i | \(0.901939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 56.3383 | 1.89593 | 0.947967 | − | 0.318369i | \(-0.103135\pi\) | ||||
0.947967 | + | 0.318369i | \(0.103135\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 41.6413i | − | 1.39818i | −0.715034 | − | 0.699089i | \(-0.753589\pi\) | ||
0.715034 | − | 0.699089i | \(-0.246411\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.0000 | 0.603701 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 44.0908 | 1.47710 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −60.0000 | −2.00782 | ||||||||
\(894\) | 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 | ||||||||
\(907\) | −12.2474 | −0.406670 | −0.203335 | − | 0.979109i | \(-0.565178\pi\) | ||||
−0.203335 | + | 0.979109i | \(0.565178\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | − | 36.0000i | − | 1.19143i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.0000 | −0.396275 | ||||||||
\(918\) | 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 | ||||||||
\(923\) | − | 9.79796i | − | 0.322504i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 36.7423i | 1.20678i | ||||||||
\(928\) | 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 | ||||||||
\(937\) | 38.0000i | 1.24141i | 0.784046 | + | 0.620703i | \(0.213153\pi\) | ||||
−0.784046 | + | 0.620703i | \(0.786847\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.2474 | − | 12.2474i | −0.399680 | − | 0.399680i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 12.0000i | − | 0.391189i | −0.980685 | − | 0.195594i | \(-0.937336\pi\) | ||
0.980685 | − | 0.195594i | \(-0.0626636\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.6969 | −0.478598 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.0454i | 0.716379i | 0.933649 | + | 0.358190i | \(0.116606\pi\) | ||||
−0.933649 | + | 0.358190i | \(0.883394\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.0000 | −0.908918 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.0454 | − | 22.0454i | 0.714871 | − | 0.714871i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.0000 | 0.971795 | 0.485898 | − | 0.874016i | \(-0.338493\pi\) | ||||
0.485898 | + | 0.874016i | \(0.338493\pi\) | |||||||
\(954\) | 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 | ||||||||
\(963\) | −7.34847 | −0.236801 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −56.3383 | −1.81172 | −0.905858 | − | 0.423581i | \(-0.860773\pi\) | ||||
−0.905858 | + | 0.423581i | \(0.860773\pi\) | |||||||
\(968\) | 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 | ||||||||
\(973\) | 12.0000i | 0.384702i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.0000 | 0.575871 | 0.287936 | − | 0.957650i | \(-0.407031\pi\) | ||||
0.287936 | + | 0.957650i | \(0.407031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 58.7878i | − | 1.87886i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.0000i | 0.383131i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31.8434i | 1.01565i | 0.861462 | + | 0.507823i | \(0.169550\pi\) | ||||
−0.861462 | + | 0.507823i | \(0.830450\pi\) | |||||||
\(984\) | 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 | \(-0.950262\pi\) | ||
0.987817 | − | 0.155621i | \(-0.0497379\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.0000 | + | 24.0000i | 0.761617 | + | 0.761617i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.0000i | 0.443384i | 0.975117 | + | 0.221692i | \(0.0711580\pi\) | ||||
−0.975117 | + | 0.221692i | \(0.928842\pi\) | |||||||
\(998\) | 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.o.f.1199.2 | 4 | ||
3.2 | odd | 2 | 1200.2.o.e.1199.1 | 4 | |||
4.3 | odd | 2 | inner | 1200.2.o.f.1199.3 | 4 | ||
5.2 | odd | 4 | 1200.2.h.k.1151.4 | 4 | |||
5.3 | odd | 4 | 240.2.h.a.191.1 | ✓ | 4 | ||
5.4 | even | 2 | 1200.2.o.e.1199.3 | 4 | |||
12.11 | even | 2 | 1200.2.o.e.1199.4 | 4 | |||
15.2 | even | 4 | 1200.2.h.k.1151.2 | 4 | |||
15.8 | even | 4 | 240.2.h.a.191.3 | yes | 4 | ||
15.14 | odd | 2 | inner | 1200.2.o.f.1199.4 | 4 | ||
20.3 | even | 4 | 240.2.h.a.191.4 | yes | 4 | ||
20.7 | even | 4 | 1200.2.h.k.1151.1 | 4 | |||
20.19 | odd | 2 | 1200.2.o.e.1199.2 | 4 | |||
40.3 | even | 4 | 960.2.h.c.191.1 | 4 | |||
40.13 | odd | 4 | 960.2.h.c.191.4 | 4 | |||
60.23 | odd | 4 | 240.2.h.a.191.2 | yes | 4 | ||
60.47 | odd | 4 | 1200.2.h.k.1151.3 | 4 | |||
60.59 | even | 2 | inner | 1200.2.o.f.1199.1 | 4 | ||
120.53 | even | 4 | 960.2.h.c.191.2 | 4 | |||
120.83 | odd | 4 | 960.2.h.c.191.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
240.2.h.a.191.1 | ✓ | 4 | 5.3 | odd | 4 | ||
240.2.h.a.191.2 | yes | 4 | 60.23 | odd | 4 | ||
240.2.h.a.191.3 | yes | 4 | 15.8 | even | 4 | ||
240.2.h.a.191.4 | yes | 4 | 20.3 | even | 4 | ||
960.2.h.c.191.1 | 4 | 40.3 | even | 4 | |||
960.2.h.c.191.2 | 4 | 120.53 | even | 4 | |||
960.2.h.c.191.3 | 4 | 120.83 | odd | 4 | |||
960.2.h.c.191.4 | 4 | 40.13 | odd | 4 | |||
1200.2.h.k.1151.1 | 4 | 20.7 | even | 4 | |||
1200.2.h.k.1151.2 | 4 | 15.2 | even | 4 | |||
1200.2.h.k.1151.3 | 4 | 60.47 | odd | 4 | |||
1200.2.h.k.1151.4 | 4 | 5.2 | odd | 4 | |||
1200.2.o.e.1199.1 | 4 | 3.2 | odd | 2 | |||
1200.2.o.e.1199.2 | 4 | 20.19 | odd | 2 | |||
1200.2.o.e.1199.3 | 4 | 5.4 | even | 2 | |||
1200.2.o.e.1199.4 | 4 | 12.11 | even | 2 | |||
1200.2.o.f.1199.1 | 4 | 60.59 | even | 2 | inner | ||
1200.2.o.f.1199.2 | 4 | 1.1 | even | 1 | trivial | ||
1200.2.o.f.1199.3 | 4 | 4.3 | odd | 2 | inner | ||
1200.2.o.f.1199.4 | 4 | 15.14 | odd | 2 | inner |