Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,3,Mod(127,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(31.3897264543\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{21} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.1 | ||
Root | \(0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.127 |
Dual form | 1152.3.g.f.127.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | −4.29253 | −0.858506 | −0.429253 | − | 0.903184i | \(-0.641223\pi\) | ||||
−0.429253 | + | 0.903184i | \(0.641223\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.75787i | − 0.393982i | −0.980405 | − | 0.196991i | \(-0.936883\pi\) | ||||
0.980405 | − | 0.196991i | \(-0.0631170\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.7980i | 1.25436i | 0.778874 | + | 0.627180i | \(0.215791\pi\) | ||||
−0.778874 | + | 0.627180i | \(0.784209\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.5266 | 1.11743 | 0.558716 | − | 0.829359i | \(-0.311294\pi\) | ||||
0.558716 | + | 0.829359i | \(0.311294\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −22.8673 | −1.34513 | −0.672567 | − | 0.740037i | \(-0.734808\pi\) | ||||
−0.672567 | + | 0.740037i | \(0.734808\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 16.0399i | − 0.844204i | −0.906548 | − | 0.422102i | \(-0.861292\pi\) | ||||
0.906548 | − | 0.422102i | \(-0.138708\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 17.1117i | − 0.743986i | −0.928236 | − | 0.371993i | \(-0.878675\pi\) | ||||
0.928236 | − | 0.371993i | \(-0.121325\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.57420 | −0.262968 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 21.8667 | 0.754025 | 0.377013 | − | 0.926208i | \(-0.376951\pi\) | ||||
0.377013 | + | 0.926208i | \(0.376951\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 38.6944i | 1.24821i | 0.781341 | + | 0.624104i | \(0.214536\pi\) | ||||
−0.781341 | + | 0.624104i | \(0.785464\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 11.8383i | 0.338236i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 66.4204 | 1.79515 | 0.897573 | − | 0.440866i | \(-0.145329\pi\) | ||||
0.897573 | + | 0.440866i | \(0.145329\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −23.2392 | −0.566809 | −0.283405 | − | 0.959000i | \(-0.591464\pi\) | ||||
−0.283405 | + | 0.959000i | \(0.591464\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 47.9230i | − 1.11449i | −0.830349 | − | 0.557244i | \(-0.811859\pi\) | ||||
0.830349 | − | 0.557244i | \(-0.188141\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 14.8512i | − 0.315983i | −0.987441 | − | 0.157991i | \(-0.949498\pi\) | ||||
0.987441 | − | 0.157991i | \(-0.0505018\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 41.3941 | 0.844778 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −65.5589 | −1.23696 | −0.618480 | − | 0.785800i | \(-0.712251\pi\) | ||||
−0.618480 | + | 0.785800i | \(0.712251\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 59.2281i | − 1.07688i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 65.8428i | − 1.11598i | −0.829848 | − | 0.557990i | \(-0.811573\pi\) | ||||
0.829848 | − | 0.557990i | \(-0.188427\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −40.1123 | −0.657579 | −0.328790 | − | 0.944403i | \(-0.606641\pi\) | ||||
−0.328790 | + | 0.944403i | \(0.606641\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −62.3559 | −0.959321 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 74.8105i | − 1.11657i | −0.829648 | − | 0.558287i | \(-0.811459\pi\) | ||||
0.829648 | − | 0.558287i | \(-0.188541\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 122.681i | − 1.72790i | −0.503578 | − | 0.863950i | \(-0.667983\pi\) | ||||
0.503578 | − | 0.863950i | \(-0.332017\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −144.904 | −1.98498 | −0.992492 | − | 0.122312i | \(-0.960969\pi\) | ||||
−0.992492 | + | 0.122312i | \(0.960969\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 38.0530 | 0.494195 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 128.657i | − 1.62857i | −0.580467 | − | 0.814284i | \(-0.697130\pi\) | ||||
0.580467 | − | 0.814284i | \(-0.302870\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 22.0417i | 0.265563i | 0.991145 | + | 0.132781i | \(0.0423908\pi\) | ||||
−0.991145 | + | 0.132781i | \(0.957609\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 98.1584 | 1.15480 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 122.075 | 1.37163 | 0.685813 | − | 0.727778i | \(-0.259447\pi\) | ||||
0.685813 | + | 0.727778i | \(0.259447\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 40.0626i | − 0.440248i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 68.8516i | 0.724754i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −88.3072 | −0.910384 | −0.455192 | − | 0.890393i | \(-0.650429\pi\) | ||||
−0.455192 | + | 0.890393i | \(0.650429\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 104.345 | 1.03312 | 0.516560 | − | 0.856251i | \(-0.327212\pi\) | ||||
0.516560 | + | 0.856251i | \(0.327212\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 69.0609i | − 0.670494i | −0.942130 | − | 0.335247i | \(-0.891180\pi\) | ||||
0.942130 | − | 0.335247i | \(-0.108820\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 149.429i | − 1.39653i | −0.715839 | − | 0.698265i | \(-0.753956\pi\) | ||||
0.715839 | − | 0.698265i | \(-0.246044\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 54.3341 | 0.498478 | 0.249239 | − | 0.968442i | \(-0.419820\pi\) | ||||
0.249239 | + | 0.968442i | \(0.419820\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.32846 | −0.0560041 | −0.0280021 | − | 0.999608i | \(-0.508914\pi\) | ||||
−0.0280021 | + | 0.999608i | \(0.508914\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 73.4523i | 0.638716i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 63.0651i | 0.529958i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −69.3837 | −0.573419 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 135.533 | 1.08427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 16.5228i | − 0.130101i | −0.997882 | − | 0.0650504i | \(-0.979279\pi\) | ||||
0.997882 | − | 0.0650504i | \(-0.0207208\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 50.9799i | − 0.389159i | −0.980887 | − | 0.194580i | \(-0.937666\pi\) | ||||
0.980887 | − | 0.194580i | \(-0.0623343\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −44.2360 | −0.332601 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.0157 | −0.0731070 | −0.0365535 | − | 0.999332i | \(-0.511638\pi\) | ||||
−0.0365535 | + | 0.999332i | \(0.511638\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 65.7088i | − 0.472725i | −0.971665 | − | 0.236363i | \(-0.924045\pi\) | ||||
0.971665 | − | 0.236363i | \(-0.0759553\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 200.438i | 1.40166i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −93.8635 | −0.647335 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 94.7716 | 0.636051 | 0.318026 | − | 0.948082i | \(-0.396980\pi\) | ||||
0.318026 | + | 0.948082i | \(0.396980\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 269.769i | − 1.78655i | −0.449508 | − | 0.893276i | \(-0.648401\pi\) | ||||
0.449508 | − | 0.893276i | \(-0.351599\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 166.097i | − 1.07159i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 31.5058 | 0.200674 | 0.100337 | − | 0.994954i | \(-0.468008\pi\) | ||||
0.100337 | + | 0.994954i | \(0.468008\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −47.1918 | −0.293117 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 201.159i | 1.23410i | 0.786923 | + | 0.617051i | \(0.211673\pi\) | ||||
−0.786923 | + | 0.617051i | \(0.788327\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 266.393i | − 1.59517i | −0.603208 | − | 0.797584i | \(-0.706111\pi\) | ||||
0.603208 | − | 0.797584i | \(-0.293889\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 42.0224 | 0.248653 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 43.8456 | 0.253443 | 0.126721 | − | 0.991938i | \(-0.459555\pi\) | ||||
0.126721 | + | 0.991938i | \(0.459555\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 18.1308i | 0.103605i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 275.778i | 1.54066i | 0.637646 | + | 0.770330i | \(0.279908\pi\) | ||||
−0.637646 | + | 0.770330i | \(0.720092\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −79.0033 | −0.436482 | −0.218241 | − | 0.975895i | \(-0.570032\pi\) | ||||
−0.218241 | + | 0.975895i | \(0.570032\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −285.111 | −1.54114 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 315.522i | − 1.68728i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 142.409i | − 0.745598i | −0.927912 | − | 0.372799i | \(-0.878398\pi\) | ||||
0.927912 | − | 0.372799i | \(-0.121602\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −277.818 | −1.43947 | −0.719736 | − | 0.694248i | \(-0.755737\pi\) | ||||
−0.719736 | + | 0.694248i | \(0.755737\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.40848 | −0.0173019 | −0.00865095 | − | 0.999963i | \(-0.502754\pi\) | ||||
−0.00865095 | + | 0.999963i | \(0.502754\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 314.323i | 1.57951i | 0.613421 | + | 0.789756i | \(0.289793\pi\) | ||||
−0.613421 | + | 0.789756i | \(0.710207\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 60.3057i | − 0.297072i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 99.7548 | 0.486609 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 221.317 | 1.05894 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.54933i | 0.00734281i | 0.999993 | + | 0.00367140i | \(0.00116865\pi\) | ||||
−0.999993 | + | 0.00367140i | \(0.998831\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 205.711i | 0.956794i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 106.714 | 0.491772 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −332.184 | −1.50309 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 148.964i | 0.668001i | 0.942573 | + | 0.334000i | \(0.108399\pi\) | ||||
−0.942573 | + | 0.334000i | \(0.891601\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 237.803i | 1.04759i | 0.851844 | + | 0.523796i | \(0.175485\pi\) | ||||
−0.851844 | + | 0.523796i | \(0.824515\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 70.0590 | 0.305935 | 0.152967 | − | 0.988231i | \(-0.451117\pi\) | ||||
0.152967 | + | 0.988231i | \(0.451117\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.18107 | −0.0308200 | −0.0154100 | − | 0.999881i | \(-0.504905\pi\) | ||||
−0.0154100 | + | 0.999881i | \(0.504905\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 63.7491i | 0.271273i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 216.620i | 0.906359i | 0.891419 | + | 0.453180i | \(0.149710\pi\) | ||||
−0.891419 | + | 0.453180i | \(0.850290\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 385.001 | 1.59751 | 0.798757 | − | 0.601653i | \(-0.205491\pi\) | ||||
0.798757 | + | 0.601653i | \(0.205491\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −177.685 | −0.725247 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 233.005i | − 0.943340i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 85.4882i | 0.340590i | 0.985393 | + | 0.170295i | \(0.0544721\pi\) | ||||
−0.985393 | + | 0.170295i | \(0.945528\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 236.106 | 0.933226 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 54.2981 | 0.211277 | 0.105638 | − | 0.994405i | \(-0.466311\pi\) | ||||
0.105638 | + | 0.994405i | \(0.466311\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 183.179i | − 0.707255i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 501.827i | − 1.90809i | −0.299670 | − | 0.954043i | \(-0.596877\pi\) | ||||
0.299670 | − | 0.954043i | \(-0.403123\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 281.413 | 1.06194 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −284.911 | −1.05915 | −0.529574 | − | 0.848264i | \(-0.677648\pi\) | ||||
−0.529574 | + | 0.848264i | \(0.677648\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 241.190i | 0.889998i | 0.895531 | + | 0.444999i | \(0.146796\pi\) | ||||
−0.895531 | + | 0.444999i | \(0.853204\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 90.7105i | − 0.329856i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −242.877 | −0.876813 | −0.438407 | − | 0.898777i | \(-0.644457\pi\) | ||||
−0.438407 | + | 0.898777i | \(0.644457\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −105.341 | −0.374880 | −0.187440 | − | 0.982276i | \(-0.560019\pi\) | ||||
−0.187440 | + | 0.982276i | \(0.560019\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 223.867i | 0.791049i | 0.918455 | + | 0.395525i | \(0.129437\pi\) | ||||
−0.918455 | + | 0.395525i | \(0.870563\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 64.0907i | 0.223313i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 233.912 | 0.809384 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 421.057 | 1.43705 | 0.718527 | − | 0.695499i | \(-0.244817\pi\) | ||||
0.718527 | + | 0.695499i | \(0.244817\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 282.632i | 0.958075i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 248.575i | − 0.831353i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −132.166 | −0.439088 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 172.183 | 0.564536 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 122.865i | − 0.400211i | −0.979774 | − | 0.200106i | \(-0.935871\pi\) | ||||
0.979774 | − | 0.200106i | \(-0.0641285\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 437.535i | − 1.40686i | −0.710762 | − | 0.703432i | \(-0.751650\pi\) | ||||
0.710762 | − | 0.703432i | \(-0.248350\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 375.413 | 1.19940 | 0.599702 | − | 0.800223i | \(-0.295286\pi\) | ||||
0.599702 | + | 0.800223i | \(0.295286\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −388.867 | −1.22671 | −0.613355 | − | 0.789808i | \(-0.710180\pi\) | ||||
−0.613355 | + | 0.789808i | \(0.710180\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 301.716i | 0.945819i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 366.788i | 1.13557i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −95.5008 | −0.293849 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −40.9577 | −0.124491 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 15.4690i | − 0.0467341i | −0.999727 | − | 0.0233670i | \(-0.992561\pi\) | ||||
0.999727 | − | 0.0233670i | \(-0.00743864\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 321.126i | 0.958585i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −88.0105 | −0.261159 | −0.130579 | − | 0.991438i | \(-0.541684\pi\) | ||||
−0.130579 | + | 0.991438i | \(0.541684\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −533.904 | −1.56570 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 249.296i | − 0.726810i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 183.589i | 0.529076i | 0.964375 | + | 0.264538i | \(0.0852194\pi\) | ||||
−0.964375 | + | 0.264538i | \(0.914781\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −242.556 | −0.695003 | −0.347501 | − | 0.937679i | \(-0.612970\pi\) | ||||
−0.347501 | + | 0.937679i | \(0.612970\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.2850 | −0.0291360 | −0.0145680 | − | 0.999894i | \(-0.504637\pi\) | ||||
−0.0145680 | + | 0.999894i | \(0.504637\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 526.611i | 1.48341i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 137.976i | 0.384334i | 0.981362 | + | 0.192167i | \(0.0615515\pi\) | ||||
−0.981362 | + | 0.192167i | \(0.938448\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 103.723 | 0.287320 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 622.004 | 1.70412 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 400.180i | 1.09041i | 0.838303 | + | 0.545205i | \(0.183548\pi\) | ||||
−0.838303 | + | 0.545205i | \(0.816452\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 180.803i | 0.487340i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −644.881 | −1.72890 | −0.864451 | − | 0.502717i | \(-0.832334\pi\) | ||||
−0.864451 | + | 0.502717i | \(0.832334\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 317.649 | 0.842571 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 485.900i | 1.28206i | 0.767517 | + | 0.641029i | \(0.221492\pi\) | ||||
−0.767517 | + | 0.641029i | \(0.778508\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 168.828i | 0.440804i | 0.975409 | + | 0.220402i | \(0.0707370\pi\) | ||||
−0.975409 | + | 0.220402i | \(0.929263\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −163.344 | −0.424270 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 192.592 | 0.495095 | 0.247548 | − | 0.968876i | \(-0.420375\pi\) | ||||
0.247548 | + | 0.968876i | \(0.420375\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 391.297i | 1.00076i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 552.263i | 1.39813i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −62.0483 | −0.156293 | −0.0781465 | − | 0.996942i | \(-0.524900\pi\) | ||||
−0.0781465 | + | 0.996942i | \(0.524900\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −353.066 | −0.880464 | −0.440232 | − | 0.897884i | \(-0.645104\pi\) | ||||
−0.440232 | + | 0.897884i | \(0.645104\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 562.099i | 1.39479i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 916.466i | 2.25176i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −62.9725 | −0.153967 | −0.0769835 | − | 0.997032i | \(-0.524529\pi\) | ||||
−0.0769835 | + | 0.997032i | \(0.524529\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −181.586 | −0.439676 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 94.6146i | − 0.227987i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 398.741i | − 0.951650i | −0.879540 | − | 0.475825i | \(-0.842150\pi\) | ||||
0.879540 | − | 0.475825i | \(-0.157850\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 533.059 | 1.26617 | 0.633086 | − | 0.774081i | \(-0.281788\pi\) | ||||
0.633086 | + | 0.774081i | \(0.281788\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 150.334 | 0.353727 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 110.625i | 0.259075i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 284.282i | 0.659587i | 0.944053 | + | 0.329793i | \(0.106979\pi\) | ||||
−0.944053 | + | 0.329793i | \(0.893021\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −304.599 | −0.703462 | −0.351731 | − | 0.936101i | \(-0.614407\pi\) | ||||
−0.351731 | + | 0.936101i | \(0.614407\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −274.469 | −0.628075 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 204.615i | − 0.466094i | −0.972465 | − | 0.233047i | \(-0.925130\pi\) | ||||
0.972465 | − | 0.233047i | \(-0.0748696\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 625.828i | − 1.41270i | −0.707861 | − | 0.706352i | \(-0.750340\pi\) | ||||
0.707861 | − | 0.706352i | \(-0.249660\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −524.009 | −1.17755 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 557.532 | 1.24172 | 0.620860 | − | 0.783921i | \(-0.286783\pi\) | ||||
0.620860 | + | 0.783921i | \(0.286783\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 320.653i | − 0.710983i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 171.970i | 0.377955i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −312.142 | −0.683024 | −0.341512 | − | 0.939877i | \(-0.610939\pi\) | ||||
−0.341512 | + | 0.939877i | \(0.610939\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 603.187 | 1.30843 | 0.654216 | − | 0.756308i | \(-0.272999\pi\) | ||||
0.654216 | + | 0.756308i | \(0.272999\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 707.866i | − 1.52887i | −0.644702 | − | 0.764434i | \(-0.723019\pi\) | ||||
0.644702 | − | 0.764434i | \(-0.276981\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 195.220i | − 0.418031i | −0.977912 | − | 0.209015i | \(-0.932974\pi\) | ||||
0.977912 | − | 0.209015i | \(-0.0670259\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −206.318 | −0.439910 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 661.239 | 1.39797 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 105.449i | 0.221998i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 233.729i | − 0.487952i | −0.969781 | − | 0.243976i | \(-0.921548\pi\) | ||||
0.969781 | − | 0.243976i | \(-0.0784517\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 964.863 | 2.00595 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 379.061 | 0.781569 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 224.058i | 0.460078i | 0.973181 | + | 0.230039i | \(0.0738854\pi\) | ||||
−0.973181 | + | 0.230039i | \(0.926115\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 194.772i | − 0.396684i | −0.980133 | − | 0.198342i | \(-0.936444\pi\) | ||||
0.980133 | − | 0.198342i | \(-0.0635556\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −500.032 | −1.01426 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −338.339 | −0.680762 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 99.7462i | 0.199892i | 0.994993 | + | 0.0999461i | \(0.0318670\pi\) | ||||
−0.994993 | + | 0.0999461i | \(0.968133\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 772.172i | 1.53513i | 0.640969 | + | 0.767567i | \(0.278533\pi\) | ||||
−0.640969 | + | 0.767567i | \(0.721467\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −447.904 | −0.886939 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 292.306 | 0.574276 | 0.287138 | − | 0.957889i | \(-0.407296\pi\) | ||||
0.287138 | + | 0.957889i | \(0.407296\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 399.627i | 0.782048i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 296.446i | 0.575623i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 204.916 | 0.396356 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 412.035 | 0.790853 | 0.395427 | − | 0.918498i | \(-0.370597\pi\) | ||||
0.395427 | + | 0.918498i | \(0.370597\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 124.693i | − 0.238420i | −0.992869 | − | 0.119210i | \(-0.961964\pi\) | ||||
0.992869 | − | 0.119210i | \(-0.0380361\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 884.836i | − 1.67901i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 236.191 | 0.446486 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −337.586 | −0.633370 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 641.427i | 1.19893i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 571.154i | 1.05966i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −572.988 | −1.05913 | −0.529564 | − | 0.848270i | \(-0.677644\pi\) | ||||
−0.529564 | + | 0.848270i | \(0.677644\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −233.231 | −0.427946 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 682.433i | 1.24759i | 0.781587 | + | 0.623796i | \(0.214410\pi\) | ||||
−0.781587 | + | 0.623796i | \(0.785590\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 350.739i | − 0.636551i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −354.820 | −0.641627 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −856.125 | −1.53703 | −0.768515 | − | 0.639832i | \(-0.779004\pi\) | ||||
−0.768515 | + | 0.639832i | \(0.779004\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 696.158i | − 1.24536i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 680.745i | − 1.20914i | −0.796552 | − | 0.604570i | \(-0.793345\pi\) | ||||
0.796552 | − | 0.604570i | \(-0.206655\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 27.1651 | 0.0480798 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −343.401 | −0.603516 | −0.301758 | − | 0.953384i | \(-0.597574\pi\) | ||||
−0.301758 | + | 0.953384i | \(0.597574\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 329.137i | − 0.576422i | −0.957567 | − | 0.288211i | \(-0.906940\pi\) | ||||
0.957567 | − | 0.288211i | \(-0.0930604\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 112.495i | 0.195644i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 734.738 | 1.27338 | 0.636688 | − | 0.771122i | \(-0.280304\pi\) | ||||
0.636688 | + | 0.771122i | \(0.280304\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 60.7883 | 0.104627 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 904.579i | − 1.55159i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 433.815i | 0.739037i | 0.929223 | + | 0.369519i | \(0.120477\pi\) | ||||
−0.929223 | + | 0.369519i | \(0.879523\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 620.654 | 1.05374 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 425.075 | 0.716822 | 0.358411 | − | 0.933564i | \(-0.383319\pi\) | ||||
0.358411 | + | 0.933564i | \(0.383319\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 270.709i | − 0.454972i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 1048.73i | − 1.75081i | −0.483394 | − | 0.875403i | \(-0.660596\pi\) | ||||
0.483394 | − | 0.875403i | \(-0.339404\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −478.816 | −0.796699 | −0.398349 | − | 0.917234i | \(-0.630417\pi\) | ||||
−0.398349 | + | 0.917234i | \(0.630417\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 297.831 | 0.492283 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 18.7009i | − 0.0308088i | −0.999881 | − | 0.0154044i | \(-0.995096\pi\) | ||||
0.999881 | − | 0.0154044i | \(-0.00490356\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 215.737i | − 0.353089i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 314.964 | 0.513807 | 0.256904 | − | 0.966437i | \(-0.417298\pi\) | ||||
0.256904 | + | 0.966437i | \(0.417298\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −786.590 | −1.27486 | −0.637431 | − | 0.770507i | \(-0.720003\pi\) | ||||
−0.637431 | + | 0.770507i | \(0.720003\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 505.431i | 0.816528i | 0.912864 | + | 0.408264i | \(0.133866\pi\) | ||||
−0.912864 | + | 0.408264i | \(0.866134\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 336.667i | − 0.540396i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −417.425 | −0.667880 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1518.85 | −2.41471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 682.834i | 1.08215i | 0.840976 | + | 0.541073i | \(0.181982\pi\) | ||||
−0.840976 | + | 0.541073i | \(0.818018\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 70.9246i | 0.111692i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 601.316 | 0.943982 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −816.719 | −1.27413 | −0.637066 | − | 0.770809i | \(-0.719852\pi\) | ||||
−0.637066 | + | 0.770809i | \(0.719852\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1164.05i | − 1.81034i | −0.425045 | − | 0.905172i | \(-0.639742\pi\) | ||||
0.425045 | − | 0.905172i | \(-0.360258\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 471.519i | 0.728778i | 0.931247 | + | 0.364389i | \(0.118722\pi\) | ||||
−0.931247 | + | 0.364389i | \(0.881278\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 908.496 | 1.39984 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1187.25 | 1.81814 | 0.909071 | − | 0.416642i | \(-0.136793\pi\) | ||||
0.909071 | + | 0.416642i | \(0.136793\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 218.833i | 0.334096i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 245.640i | − 0.372747i | −0.982479 | − | 0.186373i | \(-0.940327\pi\) | ||||
0.982479 | − | 0.186373i | \(-0.0596734\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1244.70 | 1.88305 | 0.941527 | − | 0.336936i | \(-0.109391\pi\) | ||||
0.941527 | + | 0.336936i | \(0.109391\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 189.884 | 0.285540 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 374.176i | − 0.560984i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 553.468i | − 0.824841i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −852.278 | −1.26639 | −0.633193 | − | 0.773994i | \(-0.718256\pi\) | ||||
−0.633193 | + | 0.773994i | \(0.718256\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 555.765 | 0.820923 | 0.410461 | − | 0.911878i | \(-0.365368\pi\) | ||||
0.410461 | + | 0.911878i | \(0.365368\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 243.540i | 0.358675i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 335.241i | − 0.490836i | −0.969417 | − | 0.245418i | \(-0.921075\pi\) | ||||
0.969417 | − | 0.245418i | \(-0.0789253\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 42.9925 | 0.0627628 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −952.349 | −1.38222 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 1274.20i | − 1.84400i | −0.387192 | − | 0.921999i | \(-0.626555\pi\) | ||||
0.387192 | − | 0.921999i | \(-0.373445\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 282.057i | 0.405837i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 531.416 | 0.762434 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −676.056 | −0.964416 | −0.482208 | − | 0.876057i | \(-0.660165\pi\) | ||||
−0.482208 | + | 0.876057i | \(0.660165\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1065.37i | − 1.51547i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 287.771i | − 0.407031i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −62.3418 | −0.0879292 | −0.0439646 | − | 0.999033i | \(-0.513999\pi\) | ||||
−0.0439646 | + | 0.999033i | \(0.513999\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 662.127 | 0.928649 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 860.384i | − 1.20333i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 322.341i | − 0.448318i | −0.974553 | − | 0.224159i | \(-0.928036\pi\) | ||||
0.974553 | − | 0.224159i | \(-0.0719636\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −190.461 | −0.264163 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −143.756 | −0.198284 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 368.070i | 0.506287i | 0.967429 | + | 0.253143i | \(0.0814644\pi\) | ||||
−0.967429 | + | 0.253143i | \(0.918536\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1095.87i | 1.49913i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 430.587 | 0.587431 | 0.293715 | − | 0.955893i | \(-0.405108\pi\) | ||||
0.293715 | + | 0.955893i | \(0.405108\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1032.23 | 1.40059 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 818.050i | − 1.10697i | −0.832859 | − | 0.553485i | \(-0.813298\pi\) | ||||
0.832859 | − | 0.553485i | \(-0.186702\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 685.438i | 0.922528i | 0.887263 | + | 0.461264i | \(0.152604\pi\) | ||||
−0.887263 | + | 0.461264i | \(0.847396\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −406.810 | −0.546053 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −412.106 | −0.550208 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 104.336i | − 0.138929i | −0.997584 | − | 0.0694647i | \(-0.977871\pi\) | ||||
0.997584 | − | 0.0694647i | \(-0.0221291\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1157.99i | 1.53377i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −539.949 | −0.713274 | −0.356637 | − | 0.934243i | \(-0.616077\pi\) | ||||
−0.356637 | + | 0.934243i | \(0.616077\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1192.21 | −1.56663 | −0.783317 | − | 0.621623i | \(-0.786474\pi\) | ||||
−0.783317 | + | 0.621623i | \(0.786474\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 149.847i | − 0.196391i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 956.473i | − 1.24703i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −321.506 | −0.418083 | −0.209042 | − | 0.977907i | \(-0.567034\pi\) | ||||
−0.209042 | + | 0.977907i | \(0.567034\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1453.29 | 1.88006 | 0.940029 | − | 0.341094i | \(-0.110798\pi\) | ||||
0.940029 | + | 0.341094i | \(0.110798\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 254.385i | − 0.328239i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 372.753i | 0.478502i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1692.75 | 2.16741 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −135.240 | −0.172280 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 231.223i | − 0.293802i | −0.989151 | − | 0.146901i | \(-0.953070\pi\) | ||||
0.989151 | − | 0.146901i | \(-0.0469299\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.4531i | 0.0220646i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −582.696 | −0.734800 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −51.5068 | −0.0646259 | −0.0323129 | − | 0.999478i | \(-0.510287\pi\) | ||||
−0.0323129 | + | 0.999478i | \(0.510287\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 339.606i | 0.425039i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1999.38i | − 2.48988i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 202.572 | 0.251643 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −580.914 | −0.718065 | −0.359032 | − | 0.933325i | \(-0.616893\pi\) | ||||
−0.359032 | + | 0.933325i | \(0.616893\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1351.98i | 1.66706i | 0.552475 | + | 0.833529i | \(0.313683\pi\) | ||||
−0.552475 | + | 0.833529i | \(0.686317\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 863.480i | − 1.05948i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −768.678 | −0.940855 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −179.511 | −0.218650 | −0.109325 | − | 0.994006i | \(-0.534869\pi\) | ||||
−0.109325 | + | 0.994006i | \(0.534869\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 665.446i | − 0.808561i | −0.914635 | − | 0.404281i | \(-0.867522\pi\) | ||||
0.914635 | − | 0.404281i | \(-0.132478\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 901.166i | 1.08968i | 0.838540 | + | 0.544840i | \(0.183410\pi\) | ||||
−0.838540 | + | 0.544840i | \(0.816590\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −183.151 | −0.220930 | −0.110465 | − | 0.993880i | \(-0.535234\pi\) | ||||
−0.110465 | + | 0.993880i | \(0.535234\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −946.571 | −1.13634 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1143.50i | 1.36946i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 846.082i | 1.00844i | 0.863575 | + | 0.504220i | \(0.168220\pi\) | ||||
−0.863575 | + | 0.504220i | \(0.831780\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −362.846 | −0.431446 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −180.382 | −0.213470 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 191.351i | 0.225917i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1136.56i | − 1.33556i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −540.635 | −0.633804 | −0.316902 | − | 0.948458i | \(-0.602643\pi\) | ||||
−0.316902 | + | 0.948458i | \(0.602643\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1333.41 | −1.55590 | −0.777952 | − | 0.628323i | \(-0.783742\pi\) | ||||
−0.777952 | + | 0.628323i | \(0.783742\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 439.034i | 0.511099i | 0.966796 | + | 0.255549i | \(0.0822563\pi\) | ||||
−0.966796 | + | 0.255549i | \(0.917744\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1164.41i | 1.34926i | 0.738155 | + | 0.674631i | \(0.235697\pi\) | ||||
−0.738155 | + | 0.674631i | \(0.764303\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −188.208 | −0.217582 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1775.20 | 2.04281 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1086.74i | − 1.24769i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 373.783i | − 0.427181i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 404.456 | 0.461181 | 0.230591 | − | 0.973051i | \(-0.425934\pi\) | ||||
0.230591 | + | 0.973051i | \(0.425934\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 227.084 | 0.257757 | 0.128879 | − | 0.991660i | \(-0.458862\pi\) | ||||
0.128879 | + | 0.991660i | \(0.458862\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 673.730i | − 0.763001i | −0.924369 | − | 0.381501i | \(-0.875407\pi\) | ||||
0.924369 | − | 0.381501i | \(-0.124593\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1370.95i | − 1.54560i | −0.634648 | − | 0.772801i | \(-0.718855\pi\) | ||||
0.634648 | − | 0.772801i | \(-0.281145\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −45.5678 | −0.0512574 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −238.211 | −0.266754 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 1183.79i | − 1.32267i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 846.121i | 0.941180i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1499.15 | 1.66388 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 339.124 | 0.374723 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1469.46i | − 1.62013i | −0.586342 | − | 0.810063i | \(-0.699433\pi\) | ||||
0.586342 | − | 0.810063i | \(-0.300567\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 871.203i | − 0.956315i | −0.878274 | − | 0.478157i | \(-0.841305\pi\) | ||||
0.878274 | − | 0.478157i | \(-0.158695\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −304.131 | −0.333111 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −140.596 | −0.153322 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 256.361i | 0.278957i | 0.990225 | + | 0.139478i | \(0.0445426\pi\) | ||||
−0.990225 | + | 0.139478i | \(0.955457\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 1782.14i | − 1.93081i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −436.661 | −0.472066 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1399.93 | 1.50692 | 0.753462 | − | 0.657491i | \(-0.228382\pi\) | ||||
0.753462 | + | 0.657491i | \(0.228382\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 663.956i | − 0.713165i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1354.39i | 1.44854i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 365.610 | 0.390192 | 0.195096 | − | 0.980784i | \(-0.437498\pi\) | ||||
0.195096 | + | 0.980784i | \(0.437498\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 407.498 | 0.433048 | 0.216524 | − | 0.976277i | \(-0.430528\pi\) | ||||
0.216524 | + | 0.976277i | \(0.430528\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 397.661i | 0.421698i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1150.64i | − 1.21503i | −0.794307 | − | 0.607516i | \(-0.792166\pi\) | ||||
0.794307 | − | 0.607516i | \(-0.207834\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2104.96 | −2.21808 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1341.53 | 1.40769 | 0.703844 | − | 0.710355i | \(-0.251466\pi\) | ||||
0.703844 | + | 0.710355i | \(0.251466\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 611.295i | 0.640100i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 27.6219i | 0.0288029i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −536.260 | −0.558023 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1192.54 | 1.23579 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1227.25i | − 1.26914i | −0.772867 | − | 0.634568i | \(-0.781178\pi\) | ||||
0.772867 | − | 0.634568i | \(-0.218822\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1864.31i | 1.91999i | 0.280020 | + | 0.959994i | \(0.409659\pi\) | ||||
−0.280020 | + | 0.959994i | \(0.590341\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −181.217 | −0.186245 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1209.56 | 1.23803 | 0.619017 | − | 0.785378i | \(-0.287531\pi\) | ||||
0.619017 | + | 0.785378i | \(0.287531\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1684.38i | 1.72051i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1018.26i | − 1.03587i | −0.855420 | − | 0.517935i | \(-0.826701\pi\) | ||||
0.855420 | − | 0.517935i | \(-0.173299\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.6310 | 0.0148538 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −820.042 | −0.829163 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 1627.52i | − 1.64230i | −0.570712 | − | 0.821150i | \(-0.693333\pi\) | ||||
0.570712 | − | 0.821150i | \(-0.306667\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 1349.24i | − 1.35602i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 540.192 | 0.541817 | 0.270909 | − | 0.962605i | \(-0.412676\pi\) | ||||
0.270909 | + | 0.962605i | \(0.412676\pi\) | |||||||
\(998\) | 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 | 1152.3.g.f.127.1 | 8 | ||
3.2 | odd | 2 | 384.3.g.a.127.8 | yes | 8 | ||
4.3 | odd | 2 | inner | 1152.3.g.f.127.2 | 8 | ||
8.3 | odd | 2 | 1152.3.g.c.127.8 | 8 | |||
8.5 | even | 2 | 1152.3.g.c.127.7 | 8 | |||
12.11 | even | 2 | 384.3.g.a.127.4 | ✓ | 8 | ||
16.3 | odd | 4 | 2304.3.b.q.127.7 | 8 | |||
16.5 | even | 4 | 2304.3.b.q.127.2 | 8 | |||
16.11 | odd | 4 | 2304.3.b.t.127.2 | 8 | |||
16.13 | even | 4 | 2304.3.b.t.127.7 | 8 | |||
24.5 | odd | 2 | 384.3.g.b.127.1 | yes | 8 | ||
24.11 | even | 2 | 384.3.g.b.127.5 | yes | 8 | ||
48.5 | odd | 4 | 768.3.b.f.127.8 | 8 | |||
48.11 | even | 4 | 768.3.b.e.127.4 | 8 | |||
48.29 | odd | 4 | 768.3.b.e.127.1 | 8 | |||
48.35 | even | 4 | 768.3.b.f.127.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.3.g.a.127.4 | ✓ | 8 | 12.11 | even | 2 | ||
384.3.g.a.127.8 | yes | 8 | 3.2 | odd | 2 | ||
384.3.g.b.127.1 | yes | 8 | 24.5 | odd | 2 | ||
384.3.g.b.127.5 | yes | 8 | 24.11 | even | 2 | ||
768.3.b.e.127.1 | 8 | 48.29 | odd | 4 | |||
768.3.b.e.127.4 | 8 | 48.11 | even | 4 | |||
768.3.b.f.127.5 | 8 | 48.35 | even | 4 | |||
768.3.b.f.127.8 | 8 | 48.5 | odd | 4 | |||
1152.3.g.c.127.7 | 8 | 8.5 | even | 2 | |||
1152.3.g.c.127.8 | 8 | 8.3 | odd | 2 | |||
1152.3.g.f.127.1 | 8 | 1.1 | even | 1 | trivial | ||
1152.3.g.f.127.2 | 8 | 4.3 | odd | 2 | inner | ||
2304.3.b.q.127.2 | 8 | 16.5 | even | 4 | |||
2304.3.b.q.127.7 | 8 | 16.3 | odd | 4 | |||
2304.3.b.t.127.2 | 8 | 16.11 | odd | 4 | |||
2304.3.b.t.127.7 | 8 | 16.13 | even | 4 |