Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8100,2,Mod(649,8100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8100.649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8100 = 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8100.d (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: | \(64.6788256372\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.4057180416.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 9x^{6} + 22x^{4} + 12x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | no (minimal twist has level 900) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.5 | ||
Root | \(2.28400i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8100.649 |
Dual form | 8100.2.d.s.649.4 |
$q$-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 \(\left(\mathbb{Z}/8100\mathbb{Z}\right)^\times\).
\(n\) | \(4051\) | \(6401\) | \(7777\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.0864793i | 0.0326861i | 0.999866 | + | 0.0163431i | \(0.00520239\pi\) | ||||
−0.999866 | + | 0.0163431i | \(0.994798\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.913521 | 0.275437 | 0.137718 | − | 0.990471i | \(-0.456023\pi\) | ||||
0.137718 | + | 0.990471i | \(0.456023\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 2.62499i | − 0.728040i | −0.931391 | − | 0.364020i | \(-0.881404\pi\) | ||||
0.931391 | − | 0.364020i | \(-0.118596\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 2.08648i | − 0.506046i | −0.967460 | − | 0.253023i | \(-0.918575\pi\) | ||||
0.967460 | − | 0.253023i | \(-0.0814248\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.93847 | −1.13296 | −0.566482 | − | 0.824074i | \(-0.691696\pi\) | ||||
−0.566482 | + | 0.824074i | \(0.691696\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.47698i | 1.76757i | 0.467891 | + | 0.883786i | \(0.345014\pi\) | ||||
−0.467891 | + | 0.883786i | \(0.654986\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.39798 | 0.445294 | 0.222647 | − | 0.974899i | \(-0.428530\pi\) | ||||
0.222647 | + | 0.974899i | \(0.428530\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.62499 | 0.651067 | 0.325533 | − | 0.945531i | \(-0.394456\pi\) | ||||
0.325533 | + | 0.945531i | \(0.394456\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 5.85199i | − 0.962062i | −0.876704 | − | 0.481031i | \(-0.840262\pi\) | ||||
0.876704 | − | 0.481031i | \(-0.159738\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.64994 | −1.03855 | −0.519273 | − | 0.854608i | \(-0.673797\pi\) | ||||
−0.519273 | + | 0.854608i | \(0.673797\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.24997i | 1.25811i | 0.777361 | + | 0.629055i | \(0.216558\pi\) | ||||
−0.777361 | + | 0.629055i | \(0.783442\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 2.68850i | − 0.392158i | −0.980588 | − | 0.196079i | \(-0.937179\pi\) | ||||
0.980588 | − | 0.196079i | \(-0.0628209\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.99252 | 0.998932 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 5.73642i | − 0.787958i | −0.919120 | − | 0.393979i | \(-0.871098\pi\) | ||||
0.919120 | − | 0.393979i | \(-0.128902\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.3384 | 1.60633 | 0.803164 | − | 0.595758i | \(-0.203148\pi\) | ||||
0.803164 | + | 0.595758i | \(0.203148\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.33645 | −0.811300 | −0.405650 | − | 0.914029i | \(-0.632955\pi\) | ||||
−0.405650 | + | 0.914029i | \(0.632955\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.16548i | 0.753233i | 0.926369 | + | 0.376617i | \(0.122913\pi\) | ||||
−0.926369 | + | 0.376617i | \(0.877087\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.3905 | 1.47048 | 0.735241 | − | 0.677806i | \(-0.237069\pi\) | ||||
0.735241 | + | 0.677806i | \(0.237069\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 5.31349i | − 0.621897i | −0.950427 | − | 0.310948i | \(-0.899353\pi\) | ||||
0.950427 | − | 0.310948i | \(-0.100647\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.0790006i | 0.00900296i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.4479 | 1.51301 | 0.756503 | − | 0.653991i | \(-0.226906\pi\) | ||||
0.756503 | + | 0.653991i | \(0.226906\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 6.07900i | − 0.667257i | −0.942705 | − | 0.333629i | \(-0.891727\pi\) | ||||
0.942705 | − | 0.333629i | \(-0.108273\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.13440 | −0.862244 | −0.431122 | − | 0.902294i | \(-0.641882\pi\) | ||||
−0.431122 | + | 0.902294i | \(0.641882\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.227007 | 0.0237968 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.1020i | 1.12723i | 0.826036 | + | 0.563617i | \(0.190591\pi\) | ||||
−0.826036 | + | 0.563617i | \(0.809409\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.0790 | 1.20191 | 0.600953 | − | 0.799285i | \(-0.294788\pi\) | ||||
0.600953 | + | 0.799285i | \(0.294788\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.36753i | 0.430346i | 0.976576 | + | 0.215173i | \(0.0690315\pi\) | ||||
−0.976576 | + | 0.215173i | \(0.930968\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 18.9614i | − 1.83307i | −0.399953 | − | 0.916536i | \(-0.630973\pi\) | ||||
0.399953 | − | 0.916536i | \(-0.369027\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.1904 | −1.45498 | −0.727490 | − | 0.686119i | \(-0.759313\pi\) | ||||
−0.727490 | + | 0.686119i | \(0.759313\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.60202i | 0.621066i | 0.950563 | + | 0.310533i | \(0.100507\pi\) | ||||
−0.950563 | + | 0.310533i | \(0.899493\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.180437 | 0.0165407 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.1655 | −0.924135 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 7.42492i | − 0.658855i | −0.944181 | − | 0.329427i | \(-0.893144\pi\) | ||||
0.944181 | − | 0.329427i | \(-0.106856\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.9614 | 1.39456 | 0.697279 | − | 0.716800i | \(-0.254394\pi\) | ||||
0.697279 | + | 0.716800i | \(0.254394\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 0.427076i | − 0.0370322i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 18.3905i | − 1.57121i | −0.618731 | − | 0.785603i | \(-0.712353\pi\) | ||||
0.618731 | − | 0.785603i | \(-0.287647\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.56147 | −0.471718 | −0.235859 | − | 0.971787i | \(-0.575790\pi\) | ||||
−0.235859 | + | 0.971787i | \(0.575790\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 2.39798i | − 0.200529i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 23.5560 | 1.92978 | 0.964891 | − | 0.262652i | \(-0.0845972\pi\) | ||||
0.964891 | + | 0.262652i | \(0.0845972\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.0229661 | 0.00186896 | 0.000934479 | − | 1.00000i | \(-0.499703\pi\) | ||||
0.000934479 | 1.00000i | \(0.499703\pi\) | ||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 12.1593i | − 0.970422i | −0.874397 | − | 0.485211i | \(-0.838743\pi\) | ||||
0.874397 | − | 0.485211i | \(-0.161257\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.733083 | −0.0577751 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 19.0654i | − 1.49332i | −0.665208 | − | 0.746658i | \(-0.731657\pi\) | ||||
0.665208 | − | 0.746658i | \(-0.268343\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.82290i | 0.141060i | 0.997510 | + | 0.0705300i | \(0.0224691\pi\) | ||||
−0.997510 | + | 0.0705300i | \(0.977531\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.10945 | 0.469957 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.7885i | 1.58052i | 0.612772 | + | 0.790259i | \(0.290054\pi\) | ||||
−0.612772 | + | 0.790259i | \(0.709946\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.12692 | −0.233717 | −0.116858 | − | 0.993149i | \(-0.537282\pi\) | ||||
−0.116858 | + | 0.993149i | \(0.537282\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.9249 | 1.70399 | 0.851996 | − | 0.523549i | \(-0.175392\pi\) | ||||
0.851996 | + | 0.523549i | \(0.175392\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1.90604i | − 0.139384i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.95396 | −0.575528 | −0.287764 | − | 0.957701i | \(-0.592912\pi\) | ||||
−0.287764 | + | 0.957701i | \(0.592912\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.18845i | 0.373473i | 0.982410 | + | 0.186736i | \(0.0597910\pi\) | ||||
−0.982410 | + | 0.186736i | \(0.940209\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 21.3384i | − 1.52030i | −0.649747 | − | 0.760150i | \(-0.725125\pi\) | ||||
0.649747 | − | 0.760150i | \(-0.274875\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.50608 | −0.673868 | −0.336934 | − | 0.941528i | \(-0.609390\pi\) | ||||
−0.336934 | + | 0.941528i | \(0.609390\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.207376i | 0.0145549i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.51140 | −0.312060 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.590570 | −0.0406565 | −0.0203282 | − | 0.999793i | \(-0.506471\pi\) | ||||
−0.0203282 | + | 0.999793i | \(0.506471\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.313486i | 0.0212808i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.47698 | −0.368422 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 5.76551i | − 0.386087i | −0.981190 | − | 0.193044i | \(-0.938164\pi\) | ||||
0.981190 | − | 0.193044i | \(-0.0618359\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 13.2561i | − 0.879838i | −0.898037 | − | 0.439919i | \(-0.855007\pi\) | ||||
0.898037 | − | 0.439919i | \(-0.144993\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.85001 | −0.518743 | −0.259372 | − | 0.965778i | \(-0.583515\pi\) | ||||
−0.259372 | + | 0.965778i | \(0.583515\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.9094i | 1.04226i | 0.853478 | + | 0.521129i | \(0.174489\pi\) | ||||
−0.853478 | + | 0.521129i | \(0.825511\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.4770 | 0.936438 | 0.468219 | − | 0.883612i | \(-0.344896\pi\) | ||||
0.468219 | + | 0.883612i | \(0.344896\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.65607 | 0.428755 | 0.214378 | − | 0.976751i | \(-0.431228\pi\) | ||||
0.214378 | + | 0.976751i | \(0.431228\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.9634i | 0.824843i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.6885 | 0.927130 | 0.463565 | − | 0.886063i | \(-0.346570\pi\) | ||||
0.463565 | + | 0.886063i | \(0.346570\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.74390i | 0.486855i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 17.0865i | − 1.06583i | −0.846170 | − | 0.532913i | \(-0.821097\pi\) | ||||
0.846170 | − | 0.532913i | \(-0.178903\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.506076 | 0.0314461 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 3.34258i | − 0.206112i | −0.994676 | − | 0.103056i | \(-0.967138\pi\) | ||||
0.994676 | − | 0.103056i | \(-0.0328622\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.82704 | 0.111397 | 0.0556983 | − | 0.998448i | \(-0.482261\pi\) | ||||
0.0556983 | + | 0.998448i | \(0.482261\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.0634 | −1.46175 | −0.730874 | − | 0.682513i | \(-0.760887\pi\) | ||||
−0.730874 | + | 0.682513i | \(0.760887\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.9310i | 0.837032i | 0.908209 | + | 0.418516i | \(0.137450\pi\) | ||||
−0.908209 | + | 0.418516i | \(0.862550\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.2478 | 1.14823 | 0.574114 | − | 0.818775i | \(-0.305347\pi\) | ||||
0.574114 | + | 0.818775i | \(0.305347\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.2749i | 1.32411i | 0.749457 | + | 0.662053i | \(0.230315\pi\) | ||||
−0.749457 | + | 0.662053i | \(0.769685\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 0.575082i | − 0.0339460i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.6466 | 0.743918 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.09062i | 0.122136i | 0.998134 | + | 0.0610678i | \(0.0194506\pi\) | ||||
−0.998134 | + | 0.0610678i | \(0.980549\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 22.2520 | 1.28686 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.713452 | −0.0411227 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1.74056i | − 0.0993391i | −0.998766 | − | 0.0496696i | \(-0.984183\pi\) | ||||
0.998766 | − | 0.0496696i | \(-0.0158168\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.7364 | 1.34597 | 0.672984 | − | 0.739657i | \(-0.265012\pi\) | ||||
0.672984 | + | 0.739657i | \(0.265012\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.8811i | 0.615036i | 0.951542 | + | 0.307518i | \(0.0994984\pi\) | ||||
−0.951542 | + | 0.307518i | \(0.900502\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 8.00748i | − 0.449745i | −0.974388 | − | 0.224872i | \(-0.927803\pi\) | ||||
0.974388 | − | 0.224872i | \(-0.0721965\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.19060 | 0.122650 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.3040i | 0.573331i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.232500 | 0.0128181 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.21953 | −0.231926 | −0.115963 | − | 0.993254i | \(-0.536995\pi\) | ||||
−0.115963 | + | 0.993254i | \(0.536995\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 6.39663i | − 0.348447i | −0.984706 | − | 0.174223i | \(-0.944259\pi\) | ||||
0.984706 | − | 0.174223i | \(-0.0557415\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.31150 | 0.179328 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.21006i | 0.0653373i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 13.5155i | − 0.725552i | −0.931876 | − | 0.362776i | \(-0.881829\pi\) | ||||
0.931876 | − | 0.362776i | \(-0.118171\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.817577 | −0.0437639 | −0.0218819 | − | 0.999761i | \(-0.506966\pi\) | ||||
−0.0218819 | + | 0.999761i | \(0.506966\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.9405i | 1.00810i | 0.863675 | + | 0.504049i | \(0.168157\pi\) | ||||
−0.863675 | + | 0.504049i | \(0.831843\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 36.4863 | 1.92568 | 0.962838 | − | 0.270081i | \(-0.0870505\pi\) | ||||
0.962838 | + | 0.270081i | \(0.0870505\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.38851 | 0.283606 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 19.4249i | − 1.01397i | −0.861954 | − | 0.506986i | \(-0.830759\pi\) | ||||
0.861954 | − | 0.506986i | \(-0.169241\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.496081 | 0.0257553 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 29.1768i | − 1.51072i | −0.655311 | − | 0.755359i | \(-0.727462\pi\) | ||||
0.655311 | − | 0.755359i | \(-0.272538\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 6.29466i | − 0.324192i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.8060 | 1.12010 | 0.560048 | − | 0.828460i | \(-0.310783\pi\) | ||||
0.560048 | + | 0.828460i | \(0.310783\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.67092i | 0.494161i | 0.968995 | + | 0.247080i | \(0.0794712\pi\) | ||||
−0.968995 | + | 0.247080i | \(0.920529\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.7289 | 0.797489 | 0.398744 | − | 0.917062i | \(-0.369446\pi\) | ||||
0.398744 | + | 0.917062i | \(0.369446\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.6870 | 0.894472 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.8999i | 1.14931i | 0.818394 | + | 0.574657i | \(0.194864\pi\) | ||||
−0.818394 | + | 0.574657i | \(0.805136\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.09998 | −0.304618 | −0.152309 | − | 0.988333i | \(-0.548671\pi\) | ||||
−0.152309 | + | 0.988333i | \(0.548671\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 9.51554i | − 0.474003i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 5.34592i | − 0.264987i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.8688 | 1.42747 | 0.713736 | − | 0.700415i | \(-0.247002\pi\) | ||||
0.713736 | + | 0.700415i | \(0.247002\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.06702i | 0.0525046i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.9423 | −0.876541 | −0.438270 | − | 0.898843i | \(-0.644409\pi\) | ||||
−0.438270 | + | 0.898843i | \(0.644409\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.723089 | −0.0352412 | −0.0176206 | − | 0.999845i | \(-0.505609\pi\) | ||||
−0.0176206 | + | 0.999845i | \(0.505609\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 0.547972i | − 0.0265182i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.19656 | 0.394815 | 0.197407 | − | 0.980322i | \(-0.436748\pi\) | ||||
0.197407 | + | 0.980322i | \(0.436748\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.7464i | 1.71786i | 0.512091 | + | 0.858931i | \(0.328871\pi\) | ||||
−0.512091 | + | 0.858931i | \(0.671129\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 41.8633i | − 2.00259i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.2688 | −0.871922 | −0.435961 | − | 0.899966i | \(-0.643591\pi\) | ||||
−0.435961 | + | 0.899966i | \(0.643591\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 29.8323i | − 1.41737i | −0.705523 | − | 0.708687i | \(-0.749288\pi\) | ||||
0.705523 | − | 0.708687i | \(-0.250712\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38.9423 | 1.83780 | 0.918901 | − | 0.394488i | \(-0.129078\pi\) | ||||
0.918901 | + | 0.394488i | \(0.129078\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.07486 | −0.286054 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 20.4905i | − 0.958504i | −0.877677 | − | 0.479252i | \(-0.840908\pi\) | ||||
0.877677 | − | 0.479252i | \(-0.159092\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.1715 | 1.31208 | 0.656039 | − | 0.754727i | \(-0.272231\pi\) | ||||
0.656039 | + | 0.754727i | \(0.272231\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 34.3195i | − 1.59496i | −0.603344 | − | 0.797481i | \(-0.706165\pi\) | ||||
0.603344 | − | 0.797481i | \(-0.293835\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.33096i | 0.200413i | 0.994967 | + | 0.100206i | \(0.0319503\pi\) | ||||
−0.994967 | + | 0.100206i | \(0.968050\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.533186 | −0.0246203 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.53652i | 0.346530i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 28.9850 | 1.32436 | 0.662180 | − | 0.749345i | \(-0.269631\pi\) | ||||
0.662180 | + | 0.749345i | \(0.269631\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.3614 | −0.700420 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 11.2189i | − 0.508376i | −0.967155 | − | 0.254188i | \(-0.918192\pi\) | ||||
0.967155 | − | 0.254188i | \(-0.0818083\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.5635 | 1.15366 | 0.576831 | − | 0.816863i | \(-0.304289\pi\) | ||||
0.576831 | + | 0.816863i | \(0.304289\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 5.00333i | − 0.225339i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.07152i | 0.0480643i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.9371 | −0.847742 | −0.423871 | − | 0.905723i | \(-0.639329\pi\) | ||||
−0.423871 | + | 0.905723i | \(0.639329\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 21.1790i | − 0.944324i | −0.881512 | − | 0.472162i | \(-0.843474\pi\) | ||||
0.881512 | − | 0.472162i | \(-0.156526\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −32.6560 | −1.44745 | −0.723725 | − | 0.690088i | \(-0.757572\pi\) | ||||
−0.723725 | + | 0.690088i | \(0.757572\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.459507 | 0.0203274 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 2.45600i | − 0.108015i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.06550 | −0.0904912 | −0.0452456 | − | 0.998976i | \(-0.514407\pi\) | ||||
−0.0452456 | + | 0.998976i | \(0.514407\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.34790i | 0.365028i | 0.983203 | + | 0.182514i | \(0.0584235\pi\) | ||||
−0.983203 | + | 0.182514i | \(0.941576\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 7.56346i | − 0.329469i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −48.8592 | −2.12431 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.4560i | 0.756103i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.38781 | 0.275143 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.2175 | −0.525273 | −0.262637 | − | 0.964895i | \(-0.584592\pi\) | ||||
−0.262637 | + | 0.964895i | \(0.584592\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 9.50193i | − 0.406273i | −0.979150 | − | 0.203137i | \(-0.934886\pi\) | ||||
0.979150 | − | 0.203137i | \(-0.0651136\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.8424 | −0.504501 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.16296i | 0.0494542i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 19.1999i | − 0.813526i | −0.913534 | − | 0.406763i | \(-0.866658\pi\) | ||||
0.913534 | − | 0.406763i | \(-0.133342\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.6561 | 0.915954 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 16.2209i | − 0.683628i | −0.939768 | − | 0.341814i | \(-0.888959\pi\) | ||||
0.939768 | − | 0.341814i | \(-0.111041\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.0573 | −1.17622 | −0.588111 | − | 0.808780i | \(-0.700128\pi\) | ||||
−0.588111 | + | 0.808780i | \(0.700128\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.5444 | 1.73858 | 0.869289 | − | 0.494305i | \(-0.164577\pi\) | ||||
0.869289 | + | 0.494305i | \(0.164577\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.4113i | 0.766473i | 0.923650 | + | 0.383236i | \(0.125191\pi\) | ||||
−0.923650 | + | 0.383236i | \(0.874809\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.525708 | 0.0218100 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 5.24034i | − 0.217033i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 35.8843i | − 1.48110i | −0.671999 | − | 0.740552i | \(-0.734564\pi\) | ||||
0.671999 | − | 0.740552i | \(-0.265436\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.9019 | −0.737635 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 47.6039i | 1.95486i | 0.211265 | + | 0.977429i | \(0.432242\pi\) | ||||
−0.211265 | + | 0.977429i | \(0.567758\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.8559 | −1.01558 | −0.507791 | − | 0.861480i | \(-0.669538\pi\) | ||||
−0.507791 | + | 0.861480i | \(0.669538\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.0965 | 0.942125 | 0.471062 | − | 0.882100i | \(-0.343871\pi\) | ||||
0.471062 | + | 0.882100i | \(0.343871\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 4.62697i | − 0.187803i | −0.995581 | − | 0.0939015i | \(-0.970066\pi\) | ||||
0.995581 | − | 0.0939015i | \(-0.0299339\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.05728 | −0.285507 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 12.1791i | − 0.491909i | −0.969281 | − | 0.245954i | \(-0.920899\pi\) | ||||
0.969281 | − | 0.245954i | \(-0.0791013\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 46.5369i | − 1.87350i | −0.349994 | − | 0.936752i | \(-0.613816\pi\) | ||||
0.349994 | − | 0.936752i | \(-0.386184\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.8040 | −0.635215 | −0.317608 | − | 0.948222i | \(-0.602879\pi\) | ||||
−0.317608 | + | 0.948222i | \(0.602879\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 0.703457i | − 0.0281834i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.2101 | −0.486847 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.6749 | −0.982292 | −0.491146 | − | 0.871077i | \(-0.663422\pi\) | ||||
−0.491146 | + | 0.871077i | \(0.663422\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 18.3553i | − 0.727262i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.51554 | −0.0598603 | −0.0299301 | − | 0.999552i | \(-0.509528\pi\) | ||||
−0.0299301 | + | 0.999552i | \(0.509528\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.3999i | 0.962236i | 0.876656 | + | 0.481118i | \(0.159769\pi\) | ||||
−0.876656 | + | 0.481118i | \(0.840231\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.9195i | 1.05832i | 0.848523 | + | 0.529158i | \(0.177492\pi\) | ||||
−0.848523 | + | 0.529158i | \(0.822508\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.2714 | 0.442442 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 8.18232i | − 0.320199i | −0.987101 | − | 0.160099i | \(-0.948819\pi\) | ||||
0.987101 | − | 0.160099i | \(-0.0511815\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.1101 | 0.588605 | 0.294303 | − | 0.955712i | \(-0.404913\pi\) | ||||
0.294303 | + | 0.955712i | \(0.404913\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.0601 | −1.32478 | −0.662392 | − | 0.749158i | \(-0.730458\pi\) | ||||
−0.662392 | + | 0.749158i | \(0.730458\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.3276i | 0.787089i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.78848 | −0.223462 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 29.4135i | − 1.13381i | −0.823785 | − | 0.566903i | \(-0.808141\pi\) | ||||
0.823785 | − | 0.566903i | \(-0.191859\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.9038i | 1.30303i | 0.758637 | + | 0.651514i | \(0.225866\pi\) | ||||
−0.758637 | + | 0.651514i | \(0.774134\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.960090 | −0.0368449 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.1078i | 1.11378i | 0.830586 | + | 0.556890i | \(0.188005\pi\) | ||||
−0.830586 | + | 0.556890i | \(0.811995\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.0580 | −0.573665 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.4216 | −0.396456 | −0.198228 | − | 0.980156i | \(-0.563519\pi\) | ||||
−0.198228 | + | 0.980156i | \(0.563519\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.8750i | 0.525552i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.75406 | 0.368406 | 0.184203 | − | 0.982888i | \(-0.441030\pi\) | ||||
0.184203 | + | 0.982888i | \(0.441030\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.8999i | 1.08998i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.04458i | 0.0392856i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.3079 | 1.21335 | 0.606674 | − | 0.794951i | \(-0.292503\pi\) | ||||
0.606674 | + | 0.794951i | \(0.292503\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 30.7289i | 1.15081i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.4905 | 0.689579 | 0.344789 | − | 0.938680i | \(-0.387950\pi\) | ||||
0.344789 | + | 0.938680i | \(0.387950\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.377701 | −0.0140663 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 51.4714i | 1.90897i | 0.298262 | + | 0.954484i | \(0.403593\pi\) | ||||
−0.298262 | + | 0.954484i | \(0.596407\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.2134 | 0.636661 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 6.64058i | − 0.245275i | −0.992452 | − | 0.122638i | \(-0.960865\pi\) | ||||
0.992452 | − | 0.122638i | \(-0.0391353\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.63229i | 0.207468i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.6058 | 1.42014 | 0.710068 | − | 0.704133i | \(-0.248664\pi\) | ||||
0.710068 | + | 0.704133i | \(0.248664\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 25.5904i | − 0.938821i | −0.882980 | − | 0.469410i | \(-0.844467\pi\) | ||||
0.882980 | − | 0.469410i | \(-0.155533\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.63977 | 0.0599160 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.1114 | 0.551424 | 0.275712 | − | 0.961240i | \(-0.411086\pi\) | ||||
0.275712 | + | 0.961240i | \(0.411086\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.2710i | 0.482341i | 0.970483 | + | 0.241170i | \(0.0775313\pi\) | ||||
−0.970483 | + | 0.241170i | \(0.922469\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.5174 | 0.671256 | 0.335628 | − | 0.941995i | \(-0.391052\pi\) | ||||
0.335628 | + | 0.941995i | \(0.391052\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 1.31366i | − 0.0475576i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 32.3882i | − 1.16947i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.01882 | 0.0728006 | 0.0364003 | − | 0.999337i | \(-0.488411\pi\) | ||||
0.0364003 | + | 0.999337i | \(0.488411\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.76154i | 0.207228i | 0.994618 | + | 0.103614i | \(0.0330407\pi\) | ||||
−0.994618 | + | 0.103614i | \(0.966959\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 32.8405 | 1.17663 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.3190 | 0.405025 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.33043i | 0.261302i | 0.991428 | + | 0.130651i | \(0.0417067\pi\) | ||||
−0.991428 | + | 0.130651i | \(0.958293\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.570938 | −0.0203002 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.6331i | 0.590659i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.12358i | 0.252330i | 0.992009 | + | 0.126165i | \(0.0402669\pi\) | ||||
−0.992009 | + | 0.126165i | \(0.959733\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.60950 | −0.198450 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 4.85398i | − 0.171293i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.0809 | 1.02243 | 0.511215 | − | 0.859453i | \(-0.329196\pi\) | ||||
0.511215 | + | 0.859453i | \(0.329196\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.3214 | 1.20519 | 0.602593 | − | 0.798048i | \(-0.294134\pi\) | ||||
0.602593 | + | 0.798048i | \(0.294134\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 40.7423i | − 1.42539i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.8768 | −1.49641 | −0.748206 | − | 0.663466i | \(-0.769085\pi\) | ||||
−0.748206 | + | 0.663466i | \(0.769085\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 46.2309i | 1.61151i | 0.592251 | + | 0.805753i | \(0.298239\pi\) | ||||
−0.592251 | + | 0.805753i | \(0.701761\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 23.6350i | − 0.821869i | −0.911665 | − | 0.410934i | \(-0.865203\pi\) | ||||
0.911665 | − | 0.410934i | \(-0.134797\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.8979 | 0.656352 | 0.328176 | − | 0.944617i | \(-0.393566\pi\) | ||||
0.328176 | + | 0.944617i | \(0.393566\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 14.5898i | − 0.505505i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.4309 | 0.360116 | 0.180058 | − | 0.983656i | \(-0.442371\pi\) | ||||
0.180058 | + | 0.983656i | \(0.442371\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.2497 | −0.801714 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 0.879104i | − 0.0302064i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 49.6072 | 1.70051 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.8809i | 1.36550i | 0.730654 | + | 0.682748i | \(0.239215\pi\) | ||||
−0.730654 | + | 0.682748i | \(0.760785\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.1269i | 0.619204i | 0.950866 | + | 0.309602i | \(0.100196\pi\) | ||||
−0.950866 | + | 0.309602i | \(0.899804\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.02081 | −0.137188 | −0.0685941 | − | 0.997645i | \(-0.521851\pi\) | ||||
−0.0685941 | + | 0.997645i | \(0.521851\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 43.9540i | − 1.49621i | −0.663580 | − | 0.748105i | \(-0.730964\pi\) | ||||
0.663580 | − | 0.748105i | \(-0.269036\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.2849 | 0.416737 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.1843 | 0.548384 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 49.5728i | − 1.67396i | −0.547237 | − | 0.836978i | \(-0.684320\pi\) | ||||
0.547237 | − | 0.836978i | \(-0.315680\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −51.0775 | −1.72085 | −0.860423 | − | 0.509580i | \(-0.829801\pi\) | ||||
−0.860423 | + | 0.509580i | \(0.829801\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 51.1113i | − 1.72003i | −0.510266 | − | 0.860017i | \(-0.670453\pi\) | ||||
0.510266 | − | 0.860017i | \(-0.329547\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33.9573i | 1.14017i | 0.821584 | + | 0.570087i | \(0.193091\pi\) | ||||
−0.821584 | + | 0.570087i | \(0.806909\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.642102 | 0.0215354 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.2771i | 0.444301i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.69264 | 0.289916 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.9689 | −0.398742 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.80397i | 0.192718i | 0.995347 | + | 0.0963588i | \(0.0307196\pi\) | ||||
−0.995347 | + | 0.0963588i | \(0.969280\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.19990 | 0.139149 | 0.0695744 | − | 0.997577i | \(-0.477836\pi\) | ||||
0.0695744 | + | 0.997577i | \(0.477836\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 5.55329i | − 0.183787i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.38033i | 0.0455827i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.2655 | −0.833431 | −0.416715 | − | 0.909037i | \(-0.636819\pi\) | ||||
−0.416715 | + | 0.909037i | \(0.636819\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 32.5249i | − 1.07057i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −36.3864 | −1.19380 | −0.596899 | − | 0.802317i | \(-0.703601\pi\) | ||||
−0.596899 | + | 0.802317i | \(0.703601\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −34.5324 | −1.13175 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.5425i | 0.573088i | 0.958067 | + | 0.286544i | \(0.0925064\pi\) | ||||
−0.958067 | + | 0.286544i | \(0.907494\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.3384 | −0.793410 | −0.396705 | − | 0.917946i | \(-0.629846\pi\) | ||||
−0.396705 | + | 0.917946i | \(0.629846\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 56.3714i | − 1.83571i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.05206i | 0.0991787i | 0.998770 | + | 0.0495893i | \(0.0157913\pi\) | ||||
−0.998770 | + | 0.0495893i | \(0.984209\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.9478 | −0.452766 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.6054i | 0.375934i | 0.982175 | + | 0.187967i | \(0.0601899\pi\) | ||||
−0.982175 | + | 0.187967i | \(0.939810\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.59040 | 0.0513566 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.8595 | −0.576112 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.8384i | 0.541486i | 0.962652 | + | 0.270743i | \(0.0872694\pi\) | ||||
−0.962652 | + | 0.270743i | \(0.912731\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.3864 | 0.590046 | 0.295023 | − | 0.955490i | \(-0.404673\pi\) | ||||
0.295023 | + | 0.955490i | \(0.404673\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 0.480952i | − 0.0154186i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.4687i | 0.942787i | 0.881923 | + | 0.471393i | \(0.156249\pi\) | ||||
−0.881923 | + | 0.471393i | \(0.843751\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.43094 | −0.237494 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 21.5541i | − 0.687469i | −0.939067 | − | 0.343735i | \(-0.888308\pi\) | ||||
0.939067 | − | 0.343735i | \(-0.111692\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −69.9349 | −2.22380 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.01027 | 0.286221 | 0.143110 | − | 0.989707i | \(-0.454290\pi\) | ||||
0.143110 | + | 0.989707i | \(0.454290\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.4998i | 0.965938i | 0.875638 | + | 0.482969i | \(0.160442\pi\) | ||||
−0.875638 | + | 0.482969i | \(0.839558\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8100.2.d.s.649.5 | 8 | ||
3.2 | odd | 2 | 8100.2.d.q.649.5 | 8 | |||
5.2 | odd | 4 | 8100.2.a.y.1.2 | 4 | |||
5.3 | odd | 4 | 8100.2.a.ba.1.3 | 4 | |||
5.4 | even | 2 | inner | 8100.2.d.s.649.4 | 8 | ||
9.2 | odd | 6 | 900.2.s.d.49.6 | 16 | |||
9.4 | even | 3 | 2700.2.s.d.2449.4 | 16 | |||
9.5 | odd | 6 | 900.2.s.d.349.3 | 16 | |||
9.7 | even | 3 | 2700.2.s.d.1549.5 | 16 | |||
15.2 | even | 4 | 8100.2.a.x.1.2 | 4 | |||
15.8 | even | 4 | 8100.2.a.z.1.3 | 4 | |||
15.14 | odd | 2 | 8100.2.d.q.649.4 | 8 | |||
45.2 | even | 12 | 900.2.i.d.301.4 | ✓ | 8 | ||
45.4 | even | 6 | 2700.2.s.d.2449.5 | 16 | |||
45.7 | odd | 12 | 2700.2.i.e.901.3 | 8 | |||
45.13 | odd | 12 | 2700.2.i.d.1801.2 | 8 | |||
45.14 | odd | 6 | 900.2.s.d.349.6 | 16 | |||
45.22 | odd | 12 | 2700.2.i.e.1801.3 | 8 | |||
45.23 | even | 12 | 900.2.i.e.601.1 | yes | 8 | ||
45.29 | odd | 6 | 900.2.s.d.49.3 | 16 | |||
45.32 | even | 12 | 900.2.i.d.601.4 | yes | 8 | ||
45.34 | even | 6 | 2700.2.s.d.1549.4 | 16 | |||
45.38 | even | 12 | 900.2.i.e.301.1 | yes | 8 | ||
45.43 | odd | 12 | 2700.2.i.d.901.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
900.2.i.d.301.4 | ✓ | 8 | 45.2 | even | 12 | ||
900.2.i.d.601.4 | yes | 8 | 45.32 | even | 12 | ||
900.2.i.e.301.1 | yes | 8 | 45.38 | even | 12 | ||
900.2.i.e.601.1 | yes | 8 | 45.23 | even | 12 | ||
900.2.s.d.49.3 | 16 | 45.29 | odd | 6 | |||
900.2.s.d.49.6 | 16 | 9.2 | odd | 6 | |||
900.2.s.d.349.3 | 16 | 9.5 | odd | 6 | |||
900.2.s.d.349.6 | 16 | 45.14 | odd | 6 | |||
2700.2.i.d.901.2 | 8 | 45.43 | odd | 12 | |||
2700.2.i.d.1801.2 | 8 | 45.13 | odd | 12 | |||
2700.2.i.e.901.3 | 8 | 45.7 | odd | 12 | |||
2700.2.i.e.1801.3 | 8 | 45.22 | odd | 12 | |||
2700.2.s.d.1549.4 | 16 | 45.34 | even | 6 | |||
2700.2.s.d.1549.5 | 16 | 9.7 | even | 3 | |||
2700.2.s.d.2449.4 | 16 | 9.4 | even | 3 | |||
2700.2.s.d.2449.5 | 16 | 45.4 | even | 6 | |||
8100.2.a.x.1.2 | 4 | 15.2 | even | 4 | |||
8100.2.a.y.1.2 | 4 | 5.2 | odd | 4 | |||
8100.2.a.z.1.3 | 4 | 15.8 | even | 4 | |||
8100.2.a.ba.1.3 | 4 | 5.3 | odd | 4 | |||
8100.2.d.q.649.4 | 8 | 15.14 | odd | 2 | |||
8100.2.d.q.649.5 | 8 | 3.2 | odd | 2 | |||
8100.2.d.s.649.4 | 8 | 5.4 | even | 2 | inner | ||
8100.2.d.s.649.5 | 8 | 1.1 | even | 1 | trivial |