Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,4,Mod(863,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.863");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.f (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: | \(101.955300490\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.58594980096.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 21x^{6} + 341x^{4} - 2100x^{2} + 10000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 863.2 | ||
Root | \(-2.33962 - 1.35078i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.863 |
Dual form | 1728.4.f.d.863.3 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | −1.73205 | −0.154919 | −0.0774597 | − | 0.996995i | \(-0.524681\pi\) | ||||
−0.0774597 | + | 0.996995i | \(0.524681\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 13.0000i | − 0.701934i | −0.936388 | − | 0.350967i | \(-0.885853\pi\) | ||||
0.936388 | − | 0.350967i | \(-0.114147\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 22.5167i | 0.617184i | 0.951194 | + | 0.308592i | \(0.0998578\pi\) | ||||
−0.951194 | + | 0.308592i | \(0.900142\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 66.5432i | 1.41967i | 0.704366 | + | 0.709837i | \(0.251232\pi\) | ||||
−0.704366 | + | 0.709837i | \(0.748768\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 115.256i | − 1.64434i | −0.569244 | − | 0.822169i | \(-0.692764\pi\) | ||||
0.569244 | − | 0.822169i | \(-0.307236\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 66.5432 | 0.803477 | 0.401738 | − | 0.915754i | \(-0.368406\pi\) | ||||
0.401738 | + | 0.915754i | \(0.368406\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −115.256 | −1.04490 | −0.522448 | − | 0.852671i | \(-0.674981\pi\) | ||||
−0.522448 | + | 0.852671i | \(0.674981\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −122.000 | −0.976000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 207.846 | 1.33090 | 0.665449 | − | 0.746443i | \(-0.268240\pi\) | ||||
0.665449 | + | 0.746443i | \(0.268240\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 13.0000i | 0.0753184i | 0.999291 | + | 0.0376592i | \(0.0119901\pi\) | ||||
−0.999291 | + | 0.0376592i | \(0.988010\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 22.5167i | 0.108743i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 332.716i | − 1.47833i | −0.673525 | − | 0.739165i | \(-0.735220\pi\) | ||||
0.673525 | − | 0.739165i | \(-0.264780\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 345.769i | 1.31707i | 0.752549 | + | 0.658537i | \(0.228824\pi\) | ||||
−0.752549 | + | 0.658537i | \(0.771176\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −266.173 | −0.943976 | −0.471988 | − | 0.881605i | \(-0.656464\pi\) | ||||
−0.471988 | + | 0.881605i | \(0.656464\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 230.512 | 0.715398 | 0.357699 | − | 0.933837i | \(-0.383561\pi\) | ||||
0.357699 | + | 0.933837i | \(0.383561\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 174.000 | 0.507289 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 112.583 | 0.291783 | 0.145892 | − | 0.989301i | \(-0.453395\pi\) | ||||
0.145892 | + | 0.989301i | \(0.453395\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 39.0000i | − 0.0956138i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 135.100i | 0.298110i | 0.988829 | + | 0.149055i | \(0.0476232\pi\) | ||||
−0.988829 | + | 0.149055i | \(0.952377\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 399.259i | 0.838031i | 0.907979 | + | 0.419016i | \(0.137625\pi\) | ||||
−0.907979 | + | 0.419016i | \(0.862375\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 115.256i | − 0.219935i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 345.769 | 0.577961 | 0.288980 | − | 0.957335i | \(-0.406684\pi\) | ||||
0.288980 | + | 0.957335i | \(0.406684\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 85.0000 | 0.136281 | 0.0681404 | − | 0.997676i | \(-0.478293\pi\) | ||||
0.0681404 | + | 0.997676i | \(0.478293\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 292.717 | 0.433223 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 844.000i | 1.20199i | 0.799252 | + | 0.600996i | \(0.205229\pi\) | ||||
−0.799252 | + | 0.600996i | \(0.794771\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 1259.20i | − 1.66524i | −0.553842 | − | 0.832622i | \(-0.686839\pi\) | ||||
0.553842 | − | 0.832622i | \(-0.313161\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 199.630i | 0.254740i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 230.512i | 0.274542i | 0.990534 | + | 0.137271i | \(0.0438332\pi\) | ||||
−0.990534 | + | 0.137271i | \(0.956167\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 865.062 | 0.996518 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −115.256 | −0.124474 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −481.000 | −0.503486 | −0.251743 | − | 0.967794i | \(-0.581004\pi\) | ||||
−0.251743 | + | 0.967794i | \(0.581004\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 694.552 | 0.684263 | 0.342131 | − | 0.939652i | \(-0.388851\pi\) | ||||
0.342131 | + | 0.939652i | \(0.388851\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 632.000i | − 0.604590i | −0.953214 | − | 0.302295i | \(-0.902247\pi\) | ||||
0.953214 | − | 0.302295i | \(-0.0977528\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1311.16i | − 1.18462i | −0.805708 | − | 0.592312i | \(-0.798215\pi\) | ||||
0.805708 | − | 0.592312i | \(-0.201785\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 66.5432i | 0.0584742i | 0.999573 | + | 0.0292371i | \(0.00930778\pi\) | ||||
−0.999573 | + | 0.0292371i | \(0.990692\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 1498.33i | − 1.24736i | −0.781682 | − | 0.623678i | \(-0.785638\pi\) | ||||
0.781682 | − | 0.623678i | \(-0.214362\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 199.630 | 0.161874 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1498.33 | −1.15422 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 824.000 | 0.619083 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 427.817 | 0.306121 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 1201.00i | − 0.839146i | −0.907722 | − | 0.419573i | \(-0.862180\pi\) | ||||
0.907722 | − | 0.419573i | \(-0.137820\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 2274.18i | − 1.51677i | −0.651810 | − | 0.758383i | \(-0.725990\pi\) | ||||
0.651810 | − | 0.758383i | \(-0.274010\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 865.062i | − 0.563988i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 230.512i | 0.143752i | 0.997414 | + | 0.0718759i | \(0.0228986\pi\) | ||||
−0.997414 | + | 0.0718759i | \(0.977101\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1330.86 | −0.812104 | −0.406052 | − | 0.913850i | \(-0.633095\pi\) | ||||
−0.406052 | + | 0.913850i | \(0.633095\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1498.33 | −0.876201 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −360.000 | −0.206182 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1352.73 | 0.743759 | 0.371880 | − | 0.928281i | \(-0.378713\pi\) | ||||
0.371880 | + | 0.928281i | \(0.378713\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 319.000i | − 0.171920i | −0.996299 | − | 0.0859598i | \(-0.972604\pi\) | ||||
0.996299 | − | 0.0859598i | \(-0.0273957\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 22.5167i | − 0.0116683i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 1730.12i | − 0.879483i | −0.898124 | − | 0.439742i | \(-0.855070\pi\) | ||||
0.898124 | − | 0.439742i | \(-0.144930\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1498.33i | 0.733447i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3127.53 | −1.50287 | −0.751433 | − | 0.659809i | \(-0.770637\pi\) | ||||
−0.751433 | + | 0.659809i | \(0.770637\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3227.17 | 1.49537 | 0.747683 | − | 0.664055i | \(-0.231166\pi\) | ||||
0.747683 | + | 0.664055i | \(0.231166\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2231.00 | −1.01548 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3628.65 | 1.59469 | 0.797344 | − | 0.603526i | \(-0.206238\pi\) | ||||
0.797344 | + | 0.603526i | \(0.206238\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1586.00i | 0.685088i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 3576.68i | − 1.49349i | −0.665113 | − | 0.746743i | \(-0.731617\pi\) | ||||
0.665113 | − | 0.746743i | \(-0.268383\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3460.25i | 1.42098i | 0.703705 | + | 0.710492i | \(0.251528\pi\) | ||||
−0.703705 | + | 0.710492i | \(0.748472\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 576.281i | 0.229022i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2595.19 | 1.01486 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3572.94 | 1.35356 | 0.676778 | − | 0.736187i | \(-0.263376\pi\) | ||||
0.676778 | + | 0.736187i | \(0.263376\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3101.00 | 1.15655 | 0.578277 | − | 0.815841i | \(-0.303725\pi\) | ||||
0.578277 | + | 0.815841i | \(0.303725\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4480.82 | 1.62053 | 0.810266 | − | 0.586062i | \(-0.199323\pi\) | ||||
0.810266 | + | 0.586062i | \(0.199323\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 5.00000i | − 0.00178111i | −1.00000 | 0.000890554i | \(-0.999717\pi\) | |||||
1.00000 | 0.000890554i | \(-0.000283472\pi\) | ||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 2702.00i | − 0.934203i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 598.889i | − 0.204040i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1498.33i | 0.495893i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6055.43 | 1.97570 | 0.987851 | − | 0.155403i | \(-0.0496676\pi\) | ||||
0.987851 | + | 0.155403i | \(0.0496676\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 461.025 | 0.146240 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 169.000 | 0.0528685 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7669.52 | 2.33442 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 2032.00i | − 0.610192i | −0.952322 | − | 0.305096i | \(-0.901311\pi\) | ||||
0.952322 | − | 0.305096i | \(-0.0986885\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 2546.11i | − 0.744456i | −0.928141 | − | 0.372228i | \(-0.878594\pi\) | ||||
0.928141 | − | 0.372228i | \(-0.121406\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1730.12i | 0.499257i | 0.968342 | + | 0.249628i | \(0.0803085\pi\) | ||||
−0.968342 | + | 0.249628i | \(0.919692\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 4610.25i | − 1.29626i | −0.761532 | − | 0.648128i | \(-0.775552\pi\) | ||||
0.761532 | − | 0.648128i | \(-0.224448\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −399.259 | −0.110829 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6339.09 | −1.71566 | −0.857828 | − | 0.513937i | \(-0.828187\pi\) | ||||
−0.857828 | + | 0.513937i | \(0.828187\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2626.00 | 0.701890 | 0.350945 | − | 0.936396i | \(-0.385860\pi\) | ||||
0.350945 | + | 0.936396i | \(0.385860\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −301.377 | −0.0785888 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4428.00i | 1.14068i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 1714.73i | − 0.431206i | −0.976481 | − | 0.215603i | \(-0.930828\pi\) | ||||
0.976481 | − | 0.215603i | \(-0.0691718\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 2595.19i | − 0.644893i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4494.99i | 1.09101i | 0.838107 | + | 0.545506i | \(0.183662\pi\) | ||||
−0.838107 | + | 0.545506i | \(0.816338\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4325.31 | −1.03769 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3572.94 | −0.837708 | −0.418854 | − | 0.908054i | \(-0.637568\pi\) | ||||
−0.418854 | + | 0.908054i | \(0.637568\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −195.000 | −0.0452028 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5133.80 | 1.16362 | 0.581809 | − | 0.813325i | \(-0.302345\pi\) | ||||
0.581809 | + | 0.813325i | \(0.302345\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 1723.00i | − 0.386217i | −0.981177 | − | 0.193108i | \(-0.938143\pi\) | ||||
0.981177 | − | 0.193108i | \(-0.0618569\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 2747.03i | − 0.602372i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1463.95i | − 0.317546i | −0.987315 | − | 0.158773i | \(-0.949246\pi\) | ||||
0.987315 | − | 0.158773i | \(-0.0507538\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 4264.48i | − 0.905330i | −0.891681 | − | 0.452665i | \(-0.850473\pi\) | ||||
0.891681 | − | 0.452665i | \(-0.149527\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7519.38 | −1.57944 | −0.789719 | − | 0.613469i | \(-0.789774\pi\) | ||||
−0.789719 | + | 0.613469i | \(0.789774\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4494.99 | 0.924498 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8371.00 | −1.70385 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1621.20 | 0.323247 | 0.161624 | − | 0.986852i | \(-0.448327\pi\) | ||||
0.161624 | + | 0.986852i | \(0.448327\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 234.000i | − 0.0461831i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 7669.52i | − 1.48341i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3460.25i | 0.662609i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 691.537i | − 0.129827i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3792.96 | 0.705133 | 0.352567 | − | 0.935787i | \(-0.385309\pi\) | ||||
0.352567 | + | 0.935787i | \(0.385309\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3111.92 | −0.567398 | −0.283699 | − | 0.958913i | \(-0.591562\pi\) | ||||
−0.283699 | + | 0.958913i | \(0.591562\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 625.000 | 0.112866 | 0.0564330 | − | 0.998406i | \(-0.482027\pi\) | ||||
0.0564330 | + | 0.998406i | \(0.482027\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7588.11 | 1.34445 | 0.672226 | − | 0.740346i | \(-0.265339\pi\) | ||||
0.672226 | + | 0.740346i | \(0.265339\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4680.00i | 0.821410i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 7669.52i | − 1.32119i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 8118.27i | − 1.38560i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 2996.66i | − 0.502162i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 931.605 | 0.154700 | 0.0773499 | − | 0.997004i | \(-0.475354\pi\) | ||||
0.0773499 | + | 0.997004i | \(0.475354\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2738.00 | 0.442577 | 0.221288 | − | 0.975208i | \(-0.428974\pi\) | ||||
0.221288 | + | 0.975208i | \(0.428974\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −292.717 | −0.0464853 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 6721.00i | − 1.05802i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 9614.61i | − 1.48743i | −0.668495 | − | 0.743717i | \(-0.733061\pi\) | ||||
0.668495 | − | 0.743717i | \(-0.266939\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7253.21i | 1.11248i | 0.831022 | + | 0.556240i | \(0.187756\pi\) | ||||
−0.831022 | + | 0.556240i | \(0.812244\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 2189.87i | − 0.330184i | −0.986278 | − | 0.165092i | \(-0.947208\pi\) | ||||
0.986278 | − | 0.165092i | \(-0.0527921\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −598.889 | −0.0895373 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2431.00 | −0.354425 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −147.224 | −0.0211125 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 10895.0i | − 1.54963i | −0.632188 | − | 0.774815i | \(-0.717843\pi\) | ||||
0.632188 | − | 0.774815i | \(-0.282157\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 1463.58i | − 0.204813i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 6055.43i | − 0.840586i | −0.907389 | − | 0.420293i | \(-0.861927\pi\) | ||||
0.907389 | − | 0.420293i | \(-0.138073\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13830.7i | 1.88944i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10247.7 | 1.38888 | 0.694442 | − | 0.719549i | \(-0.255651\pi\) | ||||
0.694442 | + | 0.719549i | \(0.255651\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13485.0 | 1.79909 | 0.899543 | − | 0.436831i | \(-0.143899\pi\) | ||||
0.899543 | + | 0.436831i | \(0.143899\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −507.000 | −0.0671146 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2682.95 | 0.349694 | 0.174847 | − | 0.984596i | \(-0.444057\pi\) | ||||
0.174847 | + | 0.984596i | \(0.444057\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13284.0i | 1.71816i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 1461.85i | − 0.186212i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7253.21i | 0.916948i | 0.888708 | + | 0.458474i | \(0.151604\pi\) | ||||
−0.888708 | + | 0.458474i | \(0.848396\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 2996.66i | − 0.373182i | −0.982438 | − | 0.186591i | \(-0.940256\pi\) | ||||
0.982438 | − | 0.186591i | \(-0.0597440\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −865.062 | −0.106928 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7491.66 | 0.912402 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10435.0 | 1.26156 | 0.630779 | − | 0.775962i | \(-0.282735\pi\) | ||||
0.630779 | + | 0.775962i | \(0.282735\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1756.30 | 0.209254 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2181.00i | 0.257979i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4250.45i | 0.495580i | 0.968814 | + | 0.247790i | \(0.0797044\pi\) | ||||
−0.968814 | + | 0.247790i | \(0.920296\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7719.01i | 0.893591i | 0.894636 | + | 0.446795i | \(0.147435\pi\) | ||||
−0.894636 | + | 0.446795i | \(0.852565\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14061.3i | 1.60487i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5190.37 | 0.588243 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10834.1 | −1.21081 | −0.605406 | − | 0.795917i | \(-0.706989\pi\) | ||||
−0.605406 | + | 0.795917i | \(0.706989\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7493.00 | −0.831618 | −0.415809 | − | 0.909452i | \(-0.636502\pi\) | ||||
−0.415809 | + | 0.909452i | \(0.636502\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7669.52 | −0.839549 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 4217.00i | − 0.458466i | −0.973372 | − | 0.229233i | \(-0.926378\pi\) | ||||
0.973372 | − | 0.229233i | \(-0.0736217\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 6765.39i | − 0.725583i | −0.931870 | − | 0.362792i | \(-0.881824\pi\) | ||||
0.931870 | − | 0.362792i | \(-0.118176\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 399.259i | − 0.0425319i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 10488.3i | − 1.10239i | −0.834376 | − | 0.551196i | \(-0.814172\pi\) | ||||
0.834376 | − | 0.551196i | \(-0.185828\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7785.56 | −0.812877 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1498.33 | −0.154380 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10049.0 | −1.02860 | −0.514302 | − | 0.857609i | \(-0.671949\pi\) | ||||
−0.514302 | + | 0.857609i | \(0.671949\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8509.57 | 0.859718 | 0.429859 | − | 0.902896i | \(-0.358563\pi\) | ||||
0.429859 | + | 0.902896i | \(0.358563\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16061.0i | 1.61213i | 0.591824 | + | 0.806067i | \(0.298408\pi\) | ||||
−0.591824 | + | 0.806067i | \(0.701592\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9881.35i | 0.979131i | 0.871966 | + | 0.489566i | \(0.162845\pi\) | ||||
−0.871966 | + | 0.489566i | \(0.837155\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 5993.32i | − 0.582607i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8118.27 | −0.784193 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17518.9 | −1.67111 | −0.835554 | − | 0.549408i | \(-0.814853\pi\) | ||||
−0.835554 | + | 0.549408i | \(0.814853\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22140.0 | 2.09875 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 833.116 | 0.0779997 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 13984.0i | − 1.30118i | −0.759428 | − | 0.650591i | \(-0.774521\pi\) | ||||
0.759428 | − | 0.650591i | \(-0.225479\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6060.45i | 0.557035i | 0.960431 | + | 0.278517i | \(0.0898430\pi\) | ||||
−0.960431 | + | 0.278517i | \(0.910157\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 23955.6i | − 2.18845i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 4494.99i | − 0.405690i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10380.7 | −0.931274 | −0.465637 | − | 0.884976i | \(-0.654175\pi\) | ||||
−0.465637 | + | 0.884976i | \(0.654175\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4494.99 | −0.398453 | −0.199226 | − | 0.979953i | \(-0.563843\pi\) | ||||
−0.199226 | + | 0.979953i | \(0.563843\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1203.00 | −0.106006 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16189.5 | 1.40980 | 0.704898 | − | 0.709309i | \(-0.250993\pi\) | ||||
0.704898 | + | 0.709309i | \(0.250993\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 1105.00i | − 0.0956601i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1094.66i | 0.0936627i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5190.37i | 0.441532i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 8413.71i | − 0.707507i | −0.935339 | − | 0.353753i | \(-0.884905\pi\) | ||||
0.935339 | − | 0.353753i | \(-0.115095\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12576.7 | −1.05151 | −0.525755 | − | 0.850636i | \(-0.676217\pi\) | ||||
−0.525755 | + | 0.850636i | \(0.676217\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1498.33 | 0.123849 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1117.00 | 0.0918057 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23008.6 | −1.86982 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2271.00i | 0.183521i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3917.90i | 0.313091i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 3460.25i | − 0.274986i | −0.990503 | − | 0.137493i | \(-0.956095\pi\) | ||||
0.990503 | − | 0.137493i | \(-0.0439045\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 115.256i | − 0.00905878i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22957.4 | 1.79449 | 0.897247 | − | 0.441529i | \(-0.145564\pi\) | ||||
0.897247 | + | 0.441529i | \(0.145564\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13830.7 | 1.06935 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10972.0 | 0.843720 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10380.2 | 0.789627 | 0.394814 | − | 0.918761i | \(-0.370809\pi\) | ||||
0.394814 | + | 0.918761i | \(0.370809\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 17712.0i | − 1.34014i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10331.7i | 0.773408i | 0.922204 | + | 0.386704i | \(0.126386\pi\) | ||||
−0.922204 | + | 0.386704i | \(0.873614\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2595.19i | 0.193239i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 11986.6i | − 0.883140i | −0.897227 | − | 0.441570i | \(-0.854422\pi\) | ||||
0.897227 | − | 0.441570i | \(-0.145578\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16702.3 | 1.22412 | 0.612059 | − | 0.790812i | \(-0.290341\pi\) | ||||
0.612059 | + | 0.790812i | \(0.290341\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14061.3 | 1.01982 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24518.0 | −1.76897 | −0.884487 | − | 0.466565i | \(-0.845491\pi\) | ||||
−0.884487 | + | 0.466565i | \(0.845491\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16369.6 | −1.16889 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2535.00i | 0.180084i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19161.7i | 1.34734i | 0.739033 | + | 0.673669i | \(0.235283\pi\) | ||||
−0.739033 | + | 0.673669i | \(0.764717\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 865.062i | 0.0605166i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11986.6i | 0.830072i | 0.909805 | + | 0.415036i | \(0.136231\pi\) | ||||
−0.909805 | + | 0.415036i | \(0.863769\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2595.19 | 0.178810 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12908.7 | −0.880526 | −0.440263 | − | 0.897869i | \(-0.645115\pi\) | ||||
−0.440263 | + | 0.897869i | \(0.645115\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15835.0 | −1.07475 | −0.537374 | − | 0.843344i | \(-0.680583\pi\) | ||||
−0.537374 | + | 0.843344i | \(0.680583\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1427.21 | −0.0959080 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18344.0i | 1.22662i | 0.789841 | + | 0.613311i | \(0.210163\pi\) | ||||
−0.789841 | + | 0.613311i | \(0.789837\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15339.0i | 1.01563i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21560.0i | 1.42056i | 0.703922 | + | 0.710278i | \(0.251431\pi\) | ||||
−0.703922 | + | 0.710278i | \(0.748569\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21322.4i | 1.39126i | 0.718400 | + | 0.695630i | \(0.244875\pi\) | ||||
−0.718400 | + | 0.695630i | \(0.755125\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1397.41 | 0.0907376 | 0.0453688 | − | 0.998970i | \(-0.485554\pi\) | ||||
0.0453688 | + | 0.998970i | \(0.485554\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2996.66 | 0.192711 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14509.0 | 0.928576 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −38347.6 | −2.43087 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 11245.0i | − 0.709440i | −0.934973 | − | 0.354720i | \(-0.884576\pi\) | ||||
0.934973 | − | 0.354720i | \(-0.115424\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2080.19i | 0.130000i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11578.5i | 0.720185i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4494.99i | 0.276976i | 0.990364 | + | 0.138488i | \(0.0442242\pi\) | ||||
−0.990364 | + | 0.138488i | \(0.955776\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5988.89 | 0.367308 | 0.183654 | − | 0.982991i | \(-0.441207\pi\) | ||||
0.183654 | + | 0.982991i | \(0.441207\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5993.32 | 0.364176 | 0.182088 | − | 0.983282i | \(-0.441714\pi\) | ||||
0.182088 | + | 0.983282i | \(0.441714\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3042.00 | −0.183989 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10858.2 | −0.650712 | −0.325356 | − | 0.945592i | \(-0.605484\pi\) | ||||
−0.325356 | + | 0.945592i | \(0.605484\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3939.00i | 0.234976i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13217.3i | 0.781293i | 0.920541 | + | 0.390647i | \(0.127749\pi\) | ||||
−0.920541 | + | 0.390647i | \(0.872251\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 3792.96i | − 0.223191i | −0.993754 | − | 0.111595i | \(-0.964404\pi\) | ||||
0.993754 | − | 0.111595i | \(-0.0355961\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1498.33i | 0.0873726i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23955.6 | −1.39065 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8989.99 | −0.517220 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21965.0 | −1.25808 | −0.629041 | − | 0.777373i | \(-0.716552\pi\) | ||||
−0.629041 | + | 0.777373i | \(0.716552\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17292.8 | −0.981708 | −0.490854 | − | 0.871242i | \(-0.663315\pi\) | ||||
−0.490854 | + | 0.871242i | \(0.663315\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6253.00i | 0.353414i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 5372.82i | − 0.301003i | −0.988610 | − | 0.150502i | \(-0.951911\pi\) | ||||
0.988610 | − | 0.150502i | \(-0.0480889\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 399.259i | − 0.0222699i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7491.66i | 0.414237i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19031.4 | −1.04774 | −0.523869 | − | 0.851799i | \(-0.675512\pi\) | ||||
−0.523869 | + | 0.851799i | \(0.675512\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2305.12 | 0.125811 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 39852.0 | 2.16571 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7272.88 | 0.391859 | 0.195929 | − | 0.980618i | \(-0.437228\pi\) | ||||
0.195929 | + | 0.980618i | \(0.437228\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 22140.0i | − 1.18780i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 9029.18i | − 0.480307i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 16103.5i | − 0.853002i | −0.904487 | − | 0.426501i | \(-0.859746\pi\) | ||||
0.904487 | − | 0.426501i | \(-0.140254\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 1498.33i | − 0.0786998i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2595.19 | 0.135740 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19593.6 | 1.01630 | 0.508148 | − | 0.861270i | \(-0.330330\pi\) | ||||
0.508148 | + | 0.861270i | \(0.330330\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8216.00 | −0.424383 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −25357.2 | −1.29896 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 949.000i | − 0.0484133i | −0.999707 | − | 0.0242066i | \(-0.992294\pi\) | ||||
0.999707 | − | 0.0242066i | \(-0.00770597\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30678.1i | 1.55222i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 10314.2i | − 0.519732i | −0.965645 | − | 0.259866i | \(-0.916322\pi\) | ||||
0.965645 | − | 0.259866i | \(-0.0836784\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28014.7 | 1.39450 | 0.697251 | − | 0.716827i | \(-0.254406\pi\) | ||||
0.697251 | + | 0.716827i | \(0.254406\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1498.33 | −0.0739817 | −0.0369909 | − | 0.999316i | \(-0.511777\pi\) | ||||
−0.0369909 | + | 0.999316i | \(0.511777\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2343.00 | −0.115223 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17045.1 | −0.831528 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40261.0i | 1.95625i | 0.208015 | + | 0.978126i | \(0.433300\pi\) | ||||
−0.208015 | + | 0.978126i | \(0.566700\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 552.524i | 0.0266337i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 20761.5i | − 0.996815i | −0.866943 | − | 0.498408i | \(-0.833918\pi\) | ||||
0.866943 | − | 0.498408i | \(-0.166082\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 14752.8i | − 0.702744i | −0.936236 | − | 0.351372i | \(-0.885715\pi\) | ||||
0.936236 | − | 0.351372i | \(-0.114285\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 865.062 | 0.0410450 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8989.99 | −0.423220 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28877.0 | 1.35414 | 0.677068 | − | 0.735920i | \(-0.263250\pi\) | ||||
0.677068 | + | 0.735920i | \(0.263250\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −38119.0 | −1.77367 | −0.886833 | − | 0.462090i | \(-0.847100\pi\) | ||||
−0.886833 | + | 0.462090i | \(0.847100\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 1586.00i | − 0.0735107i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 23008.6i | 1.05824i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7785.56i | 0.356708i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2996.66i | 0.136249i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40325.2 | −1.82648 | −0.913239 | − | 0.407425i | \(-0.866427\pi\) | ||||
−0.913239 | + | 0.407425i | \(0.866427\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19478.3 | −0.875561 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −26568.0 | −1.18973 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2315.75 | −0.102921 | −0.0514606 | − | 0.998675i | \(-0.516388\pi\) | ||||
−0.0514606 | + | 0.998675i | \(0.516388\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 26568.0i | − 1.17636i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1913.92i | 0.0841104i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 2595.19i | − 0.113625i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 38956.6i | − 1.69301i | −0.532384 | − | 0.846503i | \(-0.678704\pi\) | ||||
0.532384 | − | 0.846503i | \(-0.321296\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25086.8 | 1.08621 | 0.543105 | − | 0.839665i | \(-0.317249\pi\) | ||||
0.543105 | + | 0.839665i | \(0.317249\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5417.04 | 0.232823 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17712.0 | −0.758463 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32424.0 | −1.37833 | −0.689163 | − | 0.724607i | \(-0.742021\pi\) | ||||
−0.689163 | + | 0.724607i | \(0.742021\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43277.0i | 1.83298i | 0.400059 | + | 0.916489i | \(0.368990\pi\) | ||||
−0.400059 | + | 0.916489i | \(0.631010\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42660.4i | 1.79377i | 0.442264 | + | 0.896885i | \(0.354176\pi\) | ||||
−0.442264 | + | 0.896885i | \(0.645824\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 13841.0i | − 0.579876i | −0.957045 | − | 0.289938i | \(-0.906365\pi\) | ||||
0.957045 | − | 0.289938i | \(-0.0936347\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 20054.6i | − 0.834154i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5589.63 | −0.231661 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25702.1 | −1.05761 | −0.528806 | − | 0.848743i | \(-0.677360\pi\) | ||||
−0.528806 | + | 0.848743i | \(0.677360\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18811.0 | 0.771290 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3864.21 | 0.157317 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 10712.0i | − 0.434556i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38347.6i | 1.54470i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23157.0i | 0.929522i | 0.885436 | + | 0.464761i | \(0.153860\pi\) | ||||
−0.885436 | + | 0.464761i | \(0.846140\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 11871.4i | − 0.473184i | −0.971609 | − | 0.236592i | \(-0.923969\pi\) | ||||
0.971609 | − | 0.236592i | \(-0.0760305\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3060.99 | −0.121583 | −0.0607914 | − | 0.998150i | \(-0.519362\pi\) | ||||
−0.0607914 | + | 0.998150i | \(0.519362\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −42644.8 | −1.68209 | −0.841046 | − | 0.540963i | \(-0.818060\pi\) | ||||
−0.841046 | + | 0.540963i | \(0.818060\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6285.00 | −0.247048 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19004.1 | −0.741851 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 5561.62i | − 0.214876i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34602.5i | 1.33232i | 0.745810 | + | 0.666159i | \(0.232063\pi\) | ||||
−0.745810 | + | 0.666159i | \(0.767937\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32848.0i | 1.25616i | 0.778148 | + | 0.628081i | \(0.216159\pi\) | ||||
−0.778148 | + | 0.628081i | \(0.783841\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23090.5 | 0.880019 | 0.440010 | − | 0.897993i | \(-0.354975\pi\) | ||||
0.440010 | + | 0.897993i | \(0.354975\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 48522.9 | 1.83680 | 0.918398 | − | 0.395657i | \(-0.129483\pi\) | ||||
0.918398 | + | 0.395657i | \(0.129483\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15613.0 | −0.589025 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15339.0 | 0.574806 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6195.00i | 0.231370i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2702.00i | 0.100241i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 12975.9i | − 0.479790i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 5993.32i | − 0.220138i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7519.38 | 0.275278 | 0.137639 | − | 0.990482i | \(-0.456049\pi\) | ||||
0.137639 | + | 0.990482i | \(0.456049\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44027.9 | 1.60122 | 0.800609 | − | 0.599188i | \(-0.204510\pi\) | ||||
0.800609 | + | 0.599188i | \(0.204510\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28353.0 | 1.02776 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −29564.4 | −1.06467 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 35671.0i | − 1.28039i | −0.768213 | − | 0.640195i | \(-0.778854\pi\) | ||||
0.768213 | − | 0.640195i | \(-0.221146\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 23008.6i | 0.820516i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 40591.4i | 1.44285i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38956.6i | 1.37581i | 0.725802 | + | 0.687904i | \(0.241469\pi\) | ||||
−0.725802 | + | 0.687904i | \(0.758531\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11578.5 | 0.407595 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4494.99 | −0.157221 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21605.0 | −0.753260 | −0.376630 | − | 0.926364i | \(-0.622917\pi\) | ||||
−0.376630 | + | 0.926364i | \(0.622917\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31476.6 | 1.09044 | 0.545221 | − | 0.838292i | \(-0.316446\pi\) | ||||
0.545221 | + | 0.838292i | \(0.316446\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 39852.0i | − 1.37620i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10349.0i | 0.355119i | 0.984110 | + | 0.177559i | \(0.0568202\pi\) | ||||
−0.984110 | + | 0.177559i | \(0.943180\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5656.17i | 0.193474i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 50943.3i | 1.73160i | 0.500391 | + | 0.865800i | \(0.333190\pi\) | ||||
−0.500391 | + | 0.865800i | \(0.666810\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6188.52 | −0.209692 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2996.66 | 0.100904 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29622.0 | 0.994327 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5371.09 | −0.179173 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5629.00i | 0.187194i | 0.995610 | + | 0.0935969i | \(0.0298365\pi\) | ||||
−0.995610 | + | 0.0935969i | \(0.970164\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22241.3i | 0.735073i | 0.930009 | + | 0.367537i | \(0.119799\pi\) | ||||
−0.930009 | + | 0.367537i | \(0.880201\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17301.2i | 0.570043i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 1844.10i | − 0.0603869i | −0.999544 | − | 0.0301934i | \(-0.990388\pi\) | ||||
0.999544 | − | 0.0301934i | \(-0.00961233\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5190.37 | −0.169443 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5762.81 | −0.186984 | −0.0934919 | − | 0.995620i | \(-0.529803\pi\) | ||||
−0.0934919 | + | 0.995620i | \(0.529803\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7761.00 | −0.251052 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30678.1 | 0.986356 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 9293.00i | − 0.297883i | −0.988846 | − | 0.148941i | \(-0.952413\pi\) | ||||
0.988846 | − | 0.148941i | \(-0.0475866\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.66025i | 0 0.000275928i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 54498.9i | − 1.73119i | −0.500744 | − | 0.865595i | \(-0.666940\pi\) | ||||
0.500744 | − | 0.865595i | \(-0.333060\pi\) | |||||||
\(998\) | 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 | 1728.4.f.d.863.2 | yes | 8 | |
3.2 | odd | 2 | inner | 1728.4.f.d.863.6 | yes | 8 | |
4.3 | odd | 2 | inner | 1728.4.f.d.863.4 | yes | 8 | |
8.3 | odd | 2 | inner | 1728.4.f.d.863.7 | yes | 8 | |
8.5 | even | 2 | inner | 1728.4.f.d.863.5 | yes | 8 | |
12.11 | even | 2 | inner | 1728.4.f.d.863.8 | yes | 8 | |
24.5 | odd | 2 | inner | 1728.4.f.d.863.1 | ✓ | 8 | |
24.11 | even | 2 | inner | 1728.4.f.d.863.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1728.4.f.d.863.1 | ✓ | 8 | 24.5 | odd | 2 | inner | |
1728.4.f.d.863.2 | yes | 8 | 1.1 | even | 1 | trivial | |
1728.4.f.d.863.3 | yes | 8 | 24.11 | even | 2 | inner | |
1728.4.f.d.863.4 | yes | 8 | 4.3 | odd | 2 | inner | |
1728.4.f.d.863.5 | yes | 8 | 8.5 | even | 2 | inner | |
1728.4.f.d.863.6 | yes | 8 | 3.2 | odd | 2 | inner | |
1728.4.f.d.863.7 | yes | 8 | 8.3 | odd | 2 | inner | |
1728.4.f.d.863.8 | yes | 8 | 12.11 | even | 2 | inner |