Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,4,Mod(1,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.a (trivial) |
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: | yes |
Analytic conductor: | \(52.0396846251\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 882.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −15.0000 | −1.34164 | −0.670820 | − | 0.741620i | \(-0.734058\pi\) | ||||
−0.670820 | + | 0.741620i | \(0.734058\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −30.0000 | −0.948683 | ||||||||
\(11\) | 9.00000 | 0.246691 | 0.123346 | − | 0.992364i | \(-0.460638\pi\) | ||||
0.123346 | + | 0.992364i | \(0.460638\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 88.0000 | 1.87745 | 0.938723 | − | 0.344671i | \(-0.112010\pi\) | ||||
0.938723 | + | 0.344671i | \(0.112010\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −84.0000 | −1.19841 | −0.599206 | − | 0.800595i | \(-0.704517\pi\) | ||||
−0.599206 | + | 0.800595i | \(0.704517\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −104.000 | −1.25575 | −0.627875 | − | 0.778314i | \(-0.716075\pi\) | ||||
−0.627875 | + | 0.778314i | \(0.716075\pi\) | |||||||
\(20\) | −60.0000 | −0.670820 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 18.0000 | 0.174437 | ||||||||
\(23\) | 84.0000 | 0.761531 | 0.380765 | − | 0.924672i | \(-0.375661\pi\) | ||||
0.380765 | + | 0.924672i | \(0.375661\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 100.000 | 0.800000 | ||||||||
\(26\) | 176.000 | 1.32756 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −51.0000 | −0.326568 | −0.163284 | − | 0.986579i | \(-0.552209\pi\) | ||||
−0.163284 | + | 0.986579i | \(0.552209\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −185.000 | −1.07184 | −0.535919 | − | 0.844269i | \(-0.680035\pi\) | ||||
−0.535919 | + | 0.844269i | \(0.680035\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −168.000 | −0.847405 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 44.0000 | 0.195501 | 0.0977507 | − | 0.995211i | \(-0.468835\pi\) | ||||
0.0977507 | + | 0.995211i | \(0.468835\pi\) | |||||||
\(38\) | −208.000 | −0.887949 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −120.000 | −0.474342 | ||||||||
\(41\) | −168.000 | −0.639932 | −0.319966 | − | 0.947429i | \(-0.603671\pi\) | ||||
−0.319966 | + | 0.947429i | \(0.603671\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 326.000 | 1.15615 | 0.578076 | − | 0.815983i | \(-0.303804\pi\) | ||||
0.578076 | + | 0.815983i | \(0.303804\pi\) | |||||||
\(44\) | 36.0000 | 0.123346 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 168.000 | 0.538484 | ||||||||
\(47\) | −138.000 | −0.428284 | −0.214142 | − | 0.976802i | \(-0.568696\pi\) | ||||
−0.214142 | + | 0.976802i | \(0.568696\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 200.000 | 0.565685 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 352.000 | 0.938723 | ||||||||
\(53\) | −639.000 | −1.65610 | −0.828051 | − | 0.560653i | \(-0.810550\pi\) | ||||
−0.828051 | + | 0.560653i | \(0.810550\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −135.000 | −0.330971 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −102.000 | −0.230918 | ||||||||
\(59\) | 159.000 | 0.350848 | 0.175424 | − | 0.984493i | \(-0.443870\pi\) | ||||
0.175424 | + | 0.984493i | \(0.443870\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −722.000 | −1.51545 | −0.757726 | − | 0.652572i | \(-0.773690\pi\) | ||||
−0.757726 | + | 0.652572i | \(0.773690\pi\) | |||||||
\(62\) | −370.000 | −0.757904 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −1320.00 | −2.51886 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −166.000 | −0.302688 | −0.151344 | − | 0.988481i | \(-0.548360\pi\) | ||||
−0.151344 | + | 0.988481i | \(0.548360\pi\) | |||||||
\(68\) | −336.000 | −0.599206 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1086.00 | −1.81527 | −0.907637 | − | 0.419755i | \(-0.862116\pi\) | ||||
−0.907637 | + | 0.419755i | \(0.862116\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −218.000 | −0.349520 | −0.174760 | − | 0.984611i | \(-0.555915\pi\) | ||||
−0.174760 | + | 0.984611i | \(0.555915\pi\) | |||||||
\(74\) | 88.0000 | 0.138240 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −416.000 | −0.627875 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −583.000 | −0.830286 | −0.415143 | − | 0.909756i | \(-0.636269\pi\) | ||||
−0.415143 | + | 0.909756i | \(0.636269\pi\) | |||||||
\(80\) | −240.000 | −0.335410 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −336.000 | −0.452500 | ||||||||
\(83\) | −597.000 | −0.789509 | −0.394755 | − | 0.918787i | \(-0.629170\pi\) | ||||
−0.394755 | + | 0.918787i | \(0.629170\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1260.00 | 1.60784 | ||||||||
\(86\) | 652.000 | 0.817523 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 72.0000 | 0.0872185 | ||||||||
\(89\) | −1038.00 | −1.23627 | −0.618134 | − | 0.786073i | \(-0.712111\pi\) | ||||
−0.618134 | + | 0.786073i | \(0.712111\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 336.000 | 0.380765 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −276.000 | −0.302843 | ||||||||
\(95\) | 1560.00 | 1.68476 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 169.000 | 0.176901 | 0.0884503 | − | 0.996081i | \(-0.471809\pi\) | ||||
0.0884503 | + | 0.996081i | \(0.471809\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 400.000 | 0.400000 | ||||||||
\(101\) | 642.000 | 0.632489 | 0.316244 | − | 0.948678i | \(-0.397578\pi\) | ||||
0.316244 | + | 0.948678i | \(0.397578\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −464.000 | −0.443876 | −0.221938 | − | 0.975061i | \(-0.571238\pi\) | ||||
−0.221938 | + | 0.975061i | \(0.571238\pi\) | |||||||
\(104\) | 704.000 | 0.663778 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1278.00 | −1.17104 | ||||||||
\(107\) | −393.000 | −0.355072 | −0.177536 | − | 0.984114i | \(-0.556813\pi\) | ||||
−0.177536 | + | 0.984114i | \(0.556813\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.0000 | 0.0123024 | 0.00615118 | − | 0.999981i | \(-0.498042\pi\) | ||||
0.00615118 | + | 0.999981i | \(0.498042\pi\) | |||||||
\(110\) | −270.000 | −0.234032 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2184.00 | 1.81817 | 0.909086 | − | 0.416608i | \(-0.136781\pi\) | ||||
0.909086 | + | 0.416608i | \(0.136781\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1260.00 | −1.02170 | ||||||||
\(116\) | −204.000 | −0.163284 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 318.000 | 0.248087 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1250.00 | −0.939144 | ||||||||
\(122\) | −1444.00 | −1.07159 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −740.000 | −0.535919 | ||||||||
\(125\) | 375.000 | 0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −373.000 | −0.260617 | −0.130309 | − | 0.991473i | \(-0.541597\pi\) | ||||
−0.130309 | + | 0.991473i | \(0.541597\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2640.00 | −1.78110 | ||||||||
\(131\) | −1173.00 | −0.782332 | −0.391166 | − | 0.920320i | \(-0.627928\pi\) | ||||
−0.391166 | + | 0.920320i | \(0.627928\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −332.000 | −0.214033 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −672.000 | −0.423702 | ||||||||
\(137\) | −30.0000 | −0.0187086 | −0.00935428 | − | 0.999956i | \(-0.502978\pi\) | ||||
−0.00935428 | + | 0.999956i | \(0.502978\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 82.0000 | 0.0500370 | 0.0250185 | − | 0.999687i | \(-0.492036\pi\) | ||||
0.0250185 | + | 0.999687i | \(0.492036\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2172.00 | −1.28359 | ||||||||
\(143\) | 792.000 | 0.463149 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 765.000 | 0.438136 | ||||||||
\(146\) | −436.000 | −0.247148 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 176.000 | 0.0977507 | ||||||||
\(149\) | 1434.00 | 0.788442 | 0.394221 | − | 0.919016i | \(-0.371014\pi\) | ||||
0.394221 | + | 0.919016i | \(0.371014\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2671.00 | −1.43949 | −0.719745 | − | 0.694239i | \(-0.755741\pi\) | ||||
−0.719745 | + | 0.694239i | \(0.755741\pi\) | |||||||
\(152\) | −832.000 | −0.443974 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2775.00 | 1.43802 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2252.00 | −1.14477 | −0.572386 | − | 0.819984i | \(-0.693982\pi\) | ||||
−0.572386 | + | 0.819984i | \(0.693982\pi\) | |||||||
\(158\) | −1166.00 | −0.587101 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −480.000 | −0.237171 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1676.00 | 0.805365 | 0.402682 | − | 0.915340i | \(-0.368078\pi\) | ||||
0.402682 | + | 0.915340i | \(0.368078\pi\) | |||||||
\(164\) | −672.000 | −0.319966 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1194.00 | −0.558267 | ||||||||
\(167\) | 3030.00 | 1.40400 | 0.702001 | − | 0.712176i | \(-0.252290\pi\) | ||||
0.702001 | + | 0.712176i | \(0.252290\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5547.00 | 2.52481 | ||||||||
\(170\) | 2520.00 | 1.13691 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1304.00 | 0.578076 | ||||||||
\(173\) | 3438.00 | 1.51090 | 0.755452 | − | 0.655204i | \(-0.227417\pi\) | ||||
0.755452 | + | 0.655204i | \(0.227417\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 144.000 | 0.0616728 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2076.00 | −0.874173 | ||||||||
\(179\) | 1212.00 | 0.506085 | 0.253042 | − | 0.967455i | \(-0.418569\pi\) | ||||
0.253042 | + | 0.967455i | \(0.418569\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3032.00 | −1.24512 | −0.622560 | − | 0.782572i | \(-0.713907\pi\) | ||||
−0.622560 | + | 0.782572i | \(0.713907\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 672.000 | 0.269242 | ||||||||
\(185\) | −660.000 | −0.262293 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −756.000 | −0.295637 | ||||||||
\(188\) | −552.000 | −0.214142 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3120.00 | 1.19131 | ||||||||
\(191\) | −2520.00 | −0.954664 | −0.477332 | − | 0.878723i | \(-0.658396\pi\) | ||||
−0.477332 | + | 0.878723i | \(0.658396\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 365.000 | 0.136131 | 0.0680655 | − | 0.997681i | \(-0.478317\pi\) | ||||
0.0680655 | + | 0.997681i | \(0.478317\pi\) | |||||||
\(194\) | 338.000 | 0.125088 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1590.00 | 0.575040 | 0.287520 | − | 0.957775i | \(-0.407169\pi\) | ||||
0.287520 | + | 0.957775i | \(0.407169\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5380.00 | 1.91647 | 0.958236 | − | 0.285977i | \(-0.0923182\pi\) | ||||
0.958236 | + | 0.285977i | \(0.0923182\pi\) | |||||||
\(200\) | 800.000 | 0.282843 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1284.00 | 0.447237 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2520.00 | 0.858558 | ||||||||
\(206\) | −928.000 | −0.313868 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1408.00 | 0.469362 | ||||||||
\(209\) | −936.000 | −0.309782 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5362.00 | −1.74946 | −0.874728 | − | 0.484614i | \(-0.838960\pi\) | ||||
−0.874728 | + | 0.484614i | \(0.838960\pi\) | |||||||
\(212\) | −2556.00 | −0.828051 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −786.000 | −0.251074 | ||||||||
\(215\) | −4890.00 | −1.55114 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 28.0000 | 0.00869908 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −540.000 | −0.165485 | ||||||||
\(221\) | −7392.00 | −2.24995 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1573.00 | 0.472358 | 0.236179 | − | 0.971710i | \(-0.424105\pi\) | ||||
0.236179 | + | 0.971710i | \(0.424105\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4368.00 | 1.28564 | ||||||||
\(227\) | 921.000 | 0.269290 | 0.134645 | − | 0.990894i | \(-0.457011\pi\) | ||||
0.134645 | + | 0.990894i | \(0.457011\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4052.00 | −1.16927 | −0.584637 | − | 0.811295i | \(-0.698763\pi\) | ||||
−0.584637 | + | 0.811295i | \(0.698763\pi\) | |||||||
\(230\) | −2520.00 | −0.722452 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −408.000 | −0.115459 | ||||||||
\(233\) | 468.000 | 0.131587 | 0.0657933 | − | 0.997833i | \(-0.479042\pi\) | ||||
0.0657933 | + | 0.997833i | \(0.479042\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2070.00 | 0.574604 | ||||||||
\(236\) | 636.000 | 0.175424 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4932.00 | −1.33483 | −0.667415 | − | 0.744686i | \(-0.732599\pi\) | ||||
−0.667415 | + | 0.744686i | \(0.732599\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1537.00 | 0.410817 | 0.205408 | − | 0.978676i | \(-0.434148\pi\) | ||||
0.205408 | + | 0.978676i | \(0.434148\pi\) | |||||||
\(242\) | −2500.00 | −0.664075 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2888.00 | −0.757726 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9152.00 | −2.35760 | ||||||||
\(248\) | −1480.00 | −0.378952 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 750.000 | 0.189737 | ||||||||
\(251\) | 5319.00 | 1.33758 | 0.668789 | − | 0.743452i | \(-0.266813\pi\) | ||||
0.668789 | + | 0.743452i | \(0.266813\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 756.000 | 0.187863 | ||||||||
\(254\) | −746.000 | −0.184284 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 5346.00 | 1.29757 | 0.648783 | − | 0.760974i | \(-0.275278\pi\) | ||||
0.648783 | + | 0.760974i | \(0.275278\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −5280.00 | −1.25943 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2346.00 | −0.553192 | ||||||||
\(263\) | −774.000 | −0.181471 | −0.0907355 | − | 0.995875i | \(-0.528922\pi\) | ||||
−0.0907355 | + | 0.995875i | \(0.528922\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9585.00 | 2.22189 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −664.000 | −0.151344 | ||||||||
\(269\) | 2415.00 | 0.547380 | 0.273690 | − | 0.961818i | \(-0.411756\pi\) | ||||
0.273690 | + | 0.961818i | \(0.411756\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 475.000 | 0.106473 | 0.0532365 | − | 0.998582i | \(-0.483046\pi\) | ||||
0.0532365 | + | 0.998582i | \(0.483046\pi\) | |||||||
\(272\) | −1344.00 | −0.299603 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −60.0000 | −0.0132290 | ||||||||
\(275\) | 900.000 | 0.197353 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3728.00 | 0.808642 | 0.404321 | − | 0.914617i | \(-0.367508\pi\) | ||||
0.404321 | + | 0.914617i | \(0.367508\pi\) | |||||||
\(278\) | 164.000 | 0.0353815 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1602.00 | −0.340097 | −0.170049 | − | 0.985436i | \(-0.554392\pi\) | ||||
−0.170049 | + | 0.985436i | \(0.554392\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −686.000 | −0.144094 | −0.0720468 | − | 0.997401i | \(-0.522953\pi\) | ||||
−0.0720468 | + | 0.997401i | \(0.522953\pi\) | |||||||
\(284\) | −4344.00 | −0.907637 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1584.00 | 0.327496 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2143.00 | 0.436190 | ||||||||
\(290\) | 1530.00 | 0.309809 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −872.000 | −0.174760 | ||||||||
\(293\) | −1101.00 | −0.219526 | −0.109763 | − | 0.993958i | \(-0.535009\pi\) | ||||
−0.109763 | + | 0.993958i | \(0.535009\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2385.00 | −0.470712 | ||||||||
\(296\) | 352.000 | 0.0691202 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2868.00 | 0.557513 | ||||||||
\(299\) | 7392.00 | 1.42973 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5342.00 | −1.01787 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1664.00 | −0.313937 | ||||||||
\(305\) | 10830.0 | 2.03319 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2780.00 | −0.516818 | −0.258409 | − | 0.966036i | \(-0.583198\pi\) | ||||
−0.258409 | + | 0.966036i | \(0.583198\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5550.00 | 1.01683 | ||||||||
\(311\) | 4296.00 | 0.783292 | 0.391646 | − | 0.920116i | \(-0.371906\pi\) | ||||
0.391646 | + | 0.920116i | \(0.371906\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5489.00 | −0.991235 | −0.495618 | − | 0.868541i | \(-0.665058\pi\) | ||||
−0.495618 | + | 0.868541i | \(0.665058\pi\) | |||||||
\(314\) | −4504.00 | −0.809476 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2332.00 | −0.415143 | ||||||||
\(317\) | −4491.00 | −0.795709 | −0.397854 | − | 0.917449i | \(-0.630245\pi\) | ||||
−0.397854 | + | 0.917449i | \(0.630245\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −459.000 | −0.0805613 | ||||||||
\(320\) | −960.000 | −0.167705 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8736.00 | 1.50490 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8800.00 | 1.50196 | ||||||||
\(326\) | 3352.00 | 0.569479 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1344.00 | −0.226250 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3964.00 | −0.658251 | −0.329126 | − | 0.944286i | \(-0.606754\pi\) | ||||
−0.329126 | + | 0.944286i | \(0.606754\pi\) | |||||||
\(332\) | −2388.00 | −0.394755 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6060.00 | 0.992780 | ||||||||
\(335\) | 2490.00 | 0.406099 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 161.000 | 0.0260244 | 0.0130122 | − | 0.999915i | \(-0.495858\pi\) | ||||
0.0130122 | + | 0.999915i | \(0.495858\pi\) | |||||||
\(338\) | 11094.0 | 1.78531 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5040.00 | 0.803919 | ||||||||
\(341\) | −1665.00 | −0.264413 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2608.00 | 0.408761 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6876.00 | 1.06837 | ||||||||
\(347\) | 5916.00 | 0.915238 | 0.457619 | − | 0.889148i | \(-0.348702\pi\) | ||||
0.457619 | + | 0.889148i | \(0.348702\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 142.000 | 0.0217796 | 0.0108898 | − | 0.999941i | \(-0.496534\pi\) | ||||
0.0108898 | + | 0.999941i | \(0.496534\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 288.000 | 0.0436092 | ||||||||
\(353\) | −4440.00 | −0.669454 | −0.334727 | − | 0.942315i | \(-0.608644\pi\) | ||||
−0.334727 | + | 0.942315i | \(0.608644\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16290.0 | 2.43545 | ||||||||
\(356\) | −4152.00 | −0.618134 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2424.00 | 0.357856 | ||||||||
\(359\) | −2286.00 | −0.336074 | −0.168037 | − | 0.985781i | \(-0.553743\pi\) | ||||
−0.168037 | + | 0.985781i | \(0.553743\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3957.00 | 0.576906 | ||||||||
\(362\) | −6064.00 | −0.880433 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3270.00 | 0.468930 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2869.00 | 0.408067 | 0.204033 | − | 0.978964i | \(-0.434595\pi\) | ||||
0.204033 | + | 0.978964i | \(0.434595\pi\) | |||||||
\(368\) | 1344.00 | 0.190383 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1320.00 | −0.185469 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3064.00 | −0.425330 | −0.212665 | − | 0.977125i | \(-0.568214\pi\) | ||||
−0.212665 | + | 0.977125i | \(0.568214\pi\) | |||||||
\(374\) | −1512.00 | −0.209047 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1104.00 | −0.151421 | ||||||||
\(377\) | −4488.00 | −0.613113 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6040.00 | −0.818612 | −0.409306 | − | 0.912397i | \(-0.634229\pi\) | ||||
−0.409306 | + | 0.912397i | \(0.634229\pi\) | |||||||
\(380\) | 6240.00 | 0.842382 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5040.00 | −0.675049 | ||||||||
\(383\) | 1842.00 | 0.245749 | 0.122874 | − | 0.992422i | \(-0.460789\pi\) | ||||
0.122874 | + | 0.992422i | \(0.460789\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 730.000 | 0.0962591 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 676.000 | 0.0884503 | ||||||||
\(389\) | −7830.00 | −1.02056 | −0.510279 | − | 0.860009i | \(-0.670458\pi\) | ||||
−0.510279 | + | 0.860009i | \(0.670458\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7056.00 | −0.912627 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3180.00 | 0.406614 | ||||||||
\(395\) | 8745.00 | 1.11395 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14764.0 | 1.86646 | 0.933229 | − | 0.359282i | \(-0.116978\pi\) | ||||
0.933229 | + | 0.359282i | \(0.116978\pi\) | |||||||
\(398\) | 10760.0 | 1.35515 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1600.00 | 0.200000 | ||||||||
\(401\) | −6264.00 | −0.780073 | −0.390036 | − | 0.920799i | \(-0.627538\pi\) | ||||
−0.390036 | + | 0.920799i | \(0.627538\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16280.0 | −2.01232 | ||||||||
\(404\) | 2568.00 | 0.316244 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 396.000 | 0.0482285 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4751.00 | −0.574381 | −0.287191 | − | 0.957873i | \(-0.592721\pi\) | ||||
−0.287191 | + | 0.957873i | \(0.592721\pi\) | |||||||
\(410\) | 5040.00 | 0.607092 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1856.00 | −0.221938 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8955.00 | 1.05924 | ||||||||
\(416\) | 2816.00 | 0.331889 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1872.00 | −0.219049 | ||||||||
\(419\) | −4704.00 | −0.548462 | −0.274231 | − | 0.961664i | \(-0.588423\pi\) | ||||
−0.274231 | + | 0.961664i | \(0.588423\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4474.00 | −0.517932 | −0.258966 | − | 0.965886i | \(-0.583382\pi\) | ||||
−0.258966 | + | 0.965886i | \(0.583382\pi\) | |||||||
\(422\) | −10724.0 | −1.23705 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5112.00 | −0.585520 | ||||||||
\(425\) | −8400.00 | −0.958729 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1572.00 | −0.177536 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9780.00 | −1.09682 | ||||||||
\(431\) | 12804.0 | 1.43097 | 0.715484 | − | 0.698629i | \(-0.246206\pi\) | ||||
0.715484 | + | 0.698629i | \(0.246206\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5074.00 | 0.563143 | 0.281571 | − | 0.959540i | \(-0.409144\pi\) | ||||
0.281571 | + | 0.959540i | \(0.409144\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 56.0000 | 0.00615118 | ||||||||
\(437\) | −8736.00 | −0.956292 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1267.00 | 0.137746 | 0.0688731 | − | 0.997625i | \(-0.478060\pi\) | ||||
0.0688731 | + | 0.997625i | \(0.478060\pi\) | |||||||
\(440\) | −1080.00 | −0.117016 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14784.0 | −1.59096 | ||||||||
\(443\) | 6933.00 | 0.743559 | 0.371780 | − | 0.928321i | \(-0.378748\pi\) | ||||
0.371780 | + | 0.928321i | \(0.378748\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15570.0 | 1.65863 | ||||||||
\(446\) | 3146.00 | 0.334008 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11688.0 | −1.22849 | −0.614244 | − | 0.789116i | \(-0.710539\pi\) | ||||
−0.614244 | + | 0.789116i | \(0.710539\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1512.00 | −0.157865 | ||||||||
\(452\) | 8736.00 | 0.909086 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1842.00 | 0.190417 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 551.000 | 0.0563998 | 0.0281999 | − | 0.999602i | \(-0.491023\pi\) | ||||
0.0281999 | + | 0.999602i | \(0.491023\pi\) | |||||||
\(458\) | −8104.00 | −0.826801 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5040.00 | −0.510850 | ||||||||
\(461\) | 13386.0 | 1.35238 | 0.676191 | − | 0.736726i | \(-0.263629\pi\) | ||||
0.676191 | + | 0.736726i | \(0.263629\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6376.00 | −0.639995 | −0.319998 | − | 0.947418i | \(-0.603682\pi\) | ||||
−0.319998 | + | 0.947418i | \(0.603682\pi\) | |||||||
\(464\) | −816.000 | −0.0816419 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 936.000 | 0.0930458 | ||||||||
\(467\) | 5700.00 | 0.564806 | 0.282403 | − | 0.959296i | \(-0.408868\pi\) | ||||
0.282403 | + | 0.959296i | \(0.408868\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4140.00 | 0.406306 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1272.00 | 0.124044 | ||||||||
\(473\) | 2934.00 | 0.285212 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10400.0 | −1.00460 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9864.00 | −0.943868 | ||||||||
\(479\) | 19794.0 | 1.88812 | 0.944062 | − | 0.329769i | \(-0.106971\pi\) | ||||
0.944062 | + | 0.329769i | \(0.106971\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3872.00 | 0.367044 | ||||||||
\(482\) | 3074.00 | 0.290491 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5000.00 | −0.469572 | ||||||||
\(485\) | −2535.00 | −0.237337 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15935.0 | 1.48272 | 0.741359 | − | 0.671109i | \(-0.234182\pi\) | ||||
0.741359 | + | 0.671109i | \(0.234182\pi\) | |||||||
\(488\) | −5776.00 | −0.535794 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9963.00 | −0.915731 | −0.457865 | − | 0.889021i | \(-0.651386\pi\) | ||||
−0.457865 | + | 0.889021i | \(0.651386\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4284.00 | 0.391362 | ||||||||
\(494\) | −18304.0 | −1.66708 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2960.00 | −0.267960 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19142.0 | 1.71726 | 0.858631 | − | 0.512594i | \(-0.171316\pi\) | ||||
0.858631 | + | 0.512594i | \(0.171316\pi\) | |||||||
\(500\) | 1500.00 | 0.134164 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10638.0 | 0.945811 | ||||||||
\(503\) | −12192.0 | −1.08074 | −0.540372 | − | 0.841426i | \(-0.681717\pi\) | ||||
−0.540372 | + | 0.841426i | \(0.681717\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9630.00 | −0.848573 | ||||||||
\(506\) | 1512.00 | 0.132839 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1492.00 | −0.130309 | ||||||||
\(509\) | −19809.0 | −1.72499 | −0.862494 | − | 0.506068i | \(-0.831098\pi\) | ||||
−0.862494 | + | 0.506068i | \(0.831098\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10692.0 | 0.917517 | ||||||||
\(515\) | 6960.00 | 0.595523 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1242.00 | −0.105654 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10560.0 | −0.890551 | ||||||||
\(521\) | −1794.00 | −0.150857 | −0.0754286 | − | 0.997151i | \(-0.524032\pi\) | ||||
−0.0754286 | + | 0.997151i | \(0.524032\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6448.00 | 0.539104 | 0.269552 | − | 0.962986i | \(-0.413124\pi\) | ||||
0.269552 | + | 0.962986i | \(0.413124\pi\) | |||||||
\(524\) | −4692.00 | −0.391166 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1548.00 | −0.128319 | ||||||||
\(527\) | 15540.0 | 1.28450 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5111.00 | −0.420071 | ||||||||
\(530\) | 19170.0 | 1.57112 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14784.0 | −1.20144 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5895.00 | 0.476380 | ||||||||
\(536\) | −1328.00 | −0.107017 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4830.00 | 0.387056 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7262.00 | 0.577112 | 0.288556 | − | 0.957463i | \(-0.406825\pi\) | ||||
0.288556 | + | 0.957463i | \(0.406825\pi\) | |||||||
\(542\) | 950.000 | 0.0752878 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2688.00 | −0.211851 | ||||||||
\(545\) | −210.000 | −0.0165053 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14204.0 | 1.11027 | 0.555136 | − | 0.831759i | \(-0.312666\pi\) | ||||
0.555136 | + | 0.831759i | \(0.312666\pi\) | |||||||
\(548\) | −120.000 | −0.00935428 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1800.00 | 0.139550 | ||||||||
\(551\) | 5304.00 | 0.410087 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 7456.00 | 0.571796 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 328.000 | 0.0250185 | ||||||||
\(557\) | −15825.0 | −1.20382 | −0.601909 | − | 0.798565i | \(-0.705593\pi\) | ||||
−0.601909 | + | 0.798565i | \(0.705593\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28688.0 | 2.17061 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3204.00 | −0.240485 | ||||||||
\(563\) | 1059.00 | 0.0792745 | 0.0396372 | − | 0.999214i | \(-0.487380\pi\) | ||||
0.0396372 | + | 0.999214i | \(0.487380\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −32760.0 | −2.43933 | ||||||||
\(566\) | −1372.00 | −0.101890 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8688.00 | −0.641796 | ||||||||
\(569\) | −3960.00 | −0.291761 | −0.145880 | − | 0.989302i | \(-0.546601\pi\) | ||||
−0.145880 | + | 0.989302i | \(0.546601\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2530.00 | −0.185424 | −0.0927121 | − | 0.995693i | \(-0.529554\pi\) | ||||
−0.0927121 | + | 0.995693i | \(0.529554\pi\) | |||||||
\(572\) | 3168.00 | 0.231575 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8400.00 | 0.609225 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11831.0 | −0.853607 | −0.426803 | − | 0.904344i | \(-0.640360\pi\) | ||||
−0.426803 | + | 0.904344i | \(0.640360\pi\) | |||||||
\(578\) | 4286.00 | 0.308433 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3060.00 | 0.219068 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5751.00 | −0.408546 | ||||||||
\(584\) | −1744.00 | −0.123574 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2202.00 | −0.155228 | ||||||||
\(587\) | 4809.00 | 0.338141 | 0.169070 | − | 0.985604i | \(-0.445923\pi\) | ||||
0.169070 | + | 0.985604i | \(0.445923\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19240.0 | 1.34596 | ||||||||
\(590\) | −4770.00 | −0.332844 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 704.000 | 0.0488754 | ||||||||
\(593\) | 21804.0 | 1.50992 | 0.754960 | − | 0.655770i | \(-0.227656\pi\) | ||||
0.754960 | + | 0.655770i | \(0.227656\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5736.00 | 0.394221 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 14784.0 | 1.01097 | ||||||||
\(599\) | −14166.0 | −0.966289 | −0.483144 | − | 0.875541i | \(-0.660505\pi\) | ||||
−0.483144 | + | 0.875541i | \(0.660505\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5891.00 | −0.399832 | −0.199916 | − | 0.979813i | \(-0.564067\pi\) | ||||
−0.199916 | + | 0.979813i | \(0.564067\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10684.0 | −0.719745 | ||||||||
\(605\) | 18750.0 | 1.25999 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2737.00 | 0.183017 | 0.0915086 | − | 0.995804i | \(-0.470831\pi\) | ||||
0.0915086 | + | 0.995804i | \(0.470831\pi\) | |||||||
\(608\) | −3328.00 | −0.221987 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 21660.0 | 1.43768 | ||||||||
\(611\) | −12144.0 | −0.804081 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26188.0 | −1.72549 | −0.862743 | − | 0.505642i | \(-0.831256\pi\) | ||||
−0.862743 | + | 0.505642i | \(0.831256\pi\) | |||||||
\(614\) | −5560.00 | −0.365445 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2358.00 | 0.153857 | 0.0769283 | − | 0.997037i | \(-0.475489\pi\) | ||||
0.0769283 | + | 0.997037i | \(0.475489\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13766.0 | −0.893865 | −0.446932 | − | 0.894568i | \(-0.647484\pi\) | ||||
−0.446932 | + | 0.894568i | \(0.647484\pi\) | |||||||
\(620\) | 11100.0 | 0.719011 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8592.00 | 0.553871 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18125.0 | −1.16000 | ||||||||
\(626\) | −10978.0 | −0.700909 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9008.00 | −0.572386 | ||||||||
\(629\) | −3696.00 | −0.234291 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21287.0 | 1.34298 | 0.671491 | − | 0.741012i | \(-0.265654\pi\) | ||||
0.671491 | + | 0.741012i | \(0.265654\pi\) | |||||||
\(632\) | −4664.00 | −0.293551 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8982.00 | −0.562651 | ||||||||
\(635\) | 5595.00 | 0.349655 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −918.000 | −0.0569655 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1920.00 | −0.118585 | ||||||||
\(641\) | −21426.0 | −1.32024 | −0.660122 | − | 0.751159i | \(-0.729495\pi\) | ||||
−0.660122 | + | 0.751159i | \(0.729495\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9962.00 | −0.610984 | −0.305492 | − | 0.952195i | \(-0.598821\pi\) | ||||
−0.305492 | + | 0.952195i | \(0.598821\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17472.0 | 1.06413 | ||||||||
\(647\) | −18174.0 | −1.10432 | −0.552159 | − | 0.833739i | \(-0.686196\pi\) | ||||
−0.552159 | + | 0.833739i | \(0.686196\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1431.00 | 0.0865511 | ||||||||
\(650\) | 17600.0 | 1.06204 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6704.00 | 0.402682 | ||||||||
\(653\) | 19167.0 | 1.14864 | 0.574321 | − | 0.818630i | \(-0.305266\pi\) | ||||
0.574321 | + | 0.818630i | \(0.305266\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17595.0 | 1.04961 | ||||||||
\(656\) | −2688.00 | −0.159983 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13080.0 | −0.773178 | −0.386589 | − | 0.922252i | \(-0.626347\pi\) | ||||
−0.386589 | + | 0.922252i | \(0.626347\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15190.0 | 0.893831 | 0.446916 | − | 0.894576i | \(-0.352522\pi\) | ||||
0.446916 | + | 0.894576i | \(0.352522\pi\) | |||||||
\(662\) | −7928.00 | −0.465454 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4776.00 | −0.279134 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4284.00 | −0.248691 | ||||||||
\(668\) | 12120.0 | 0.702001 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4980.00 | 0.287155 | ||||||||
\(671\) | −6498.00 | −0.373849 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4397.00 | 0.251845 | 0.125923 | − | 0.992040i | \(-0.459811\pi\) | ||||
0.125923 | + | 0.992040i | \(0.459811\pi\) | |||||||
\(674\) | 322.000 | 0.0184020 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 22188.0 | 1.26240 | ||||||||
\(677\) | 4029.00 | 0.228725 | 0.114363 | − | 0.993439i | \(-0.463517\pi\) | ||||
0.114363 | + | 0.993439i | \(0.463517\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 10080.0 | 0.568456 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3330.00 | −0.186968 | ||||||||
\(683\) | −15021.0 | −0.841526 | −0.420763 | − | 0.907170i | \(-0.638238\pi\) | ||||
−0.420763 | + | 0.907170i | \(0.638238\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 450.000 | 0.0251002 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5216.00 | 0.289038 | ||||||||
\(689\) | −56232.0 | −3.10924 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13984.0 | 0.769865 | 0.384932 | − | 0.922945i | \(-0.374225\pi\) | ||||
0.384932 | + | 0.922945i | \(0.374225\pi\) | |||||||
\(692\) | 13752.0 | 0.755452 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11832.0 | 0.647171 | ||||||||
\(695\) | −1230.00 | −0.0671317 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14112.0 | 0.766901 | ||||||||
\(698\) | 284.000 | 0.0154005 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31053.0 | 1.67312 | 0.836559 | − | 0.547877i | \(-0.184564\pi\) | ||||
0.836559 | + | 0.547877i | \(0.184564\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4576.00 | −0.245501 | ||||||||
\(704\) | 576.000 | 0.0308364 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8880.00 | −0.473376 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15086.0 | 0.799107 | 0.399553 | − | 0.916710i | \(-0.369165\pi\) | ||||
0.399553 | + | 0.916710i | \(0.369165\pi\) | |||||||
\(710\) | 32580.0 | 1.72212 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8304.00 | −0.437086 | ||||||||
\(713\) | −15540.0 | −0.816238 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11880.0 | −0.621380 | ||||||||
\(716\) | 4848.00 | 0.253042 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4572.00 | −0.237640 | ||||||||
\(719\) | −6378.00 | −0.330820 | −0.165410 | − | 0.986225i | \(-0.552895\pi\) | ||||
−0.165410 | + | 0.986225i | \(0.552895\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 7914.00 | 0.407934 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −12128.0 | −0.622560 | ||||||||
\(725\) | −5100.00 | −0.261254 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7363.00 | 0.375624 | 0.187812 | − | 0.982205i | \(-0.439860\pi\) | ||||
0.187812 | + | 0.982205i | \(0.439860\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6540.00 | 0.331584 | ||||||||
\(731\) | −27384.0 | −1.38555 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32810.0 | −1.65329 | −0.826647 | − | 0.562720i | \(-0.809755\pi\) | ||||
−0.826647 | + | 0.562720i | \(0.809755\pi\) | |||||||
\(734\) | 5738.00 | 0.288547 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2688.00 | 0.134621 | ||||||||
\(737\) | −1494.00 | −0.0746706 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24034.0 | −1.19635 | −0.598177 | − | 0.801364i | \(-0.704108\pi\) | ||||
−0.598177 | + | 0.801364i | \(0.704108\pi\) | |||||||
\(740\) | −2640.00 | −0.131146 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8022.00 | 0.396095 | 0.198048 | − | 0.980192i | \(-0.436540\pi\) | ||||
0.198048 | + | 0.980192i | \(0.436540\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21510.0 | −1.05781 | ||||||||
\(746\) | −6128.00 | −0.300753 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3024.00 | −0.147819 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29519.0 | 1.43431 | 0.717153 | − | 0.696916i | \(-0.245445\pi\) | ||||
0.717153 | + | 0.696916i | \(0.245445\pi\) | |||||||
\(752\) | −2208.00 | −0.107071 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8976.00 | −0.433537 | ||||||||
\(755\) | 40065.0 | 1.93128 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3742.00 | −0.179664 | −0.0898318 | − | 0.995957i | \(-0.528633\pi\) | ||||
−0.0898318 | + | 0.995957i | \(0.528633\pi\) | |||||||
\(758\) | −12080.0 | −0.578846 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12480.0 | 0.595654 | ||||||||
\(761\) | −10896.0 | −0.519027 | −0.259514 | − | 0.965739i | \(-0.583562\pi\) | ||||
−0.259514 | + | 0.965739i | \(0.583562\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −10080.0 | −0.477332 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3684.00 | 0.173771 | ||||||||
\(767\) | 13992.0 | 0.658699 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17285.0 | −0.810550 | −0.405275 | − | 0.914195i | \(-0.632824\pi\) | ||||
−0.405275 | + | 0.914195i | \(0.632824\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1460.00 | 0.0680655 | ||||||||
\(773\) | 11826.0 | 0.550261 | 0.275130 | − | 0.961407i | \(-0.411279\pi\) | ||||
0.275130 | + | 0.961407i | \(0.411279\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18500.0 | −0.857470 | ||||||||
\(776\) | 1352.00 | 0.0625438 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15660.0 | −0.721643 | ||||||||
\(779\) | 17472.0 | 0.803594 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9774.00 | −0.447812 | ||||||||
\(782\) | −14112.0 | −0.645325 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 33780.0 | 1.53587 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17714.0 | −0.802333 | −0.401166 | − | 0.916005i | \(-0.631395\pi\) | ||||
−0.401166 | + | 0.916005i | \(0.631395\pi\) | |||||||
\(788\) | 6360.00 | 0.287520 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 17490.0 | 0.787679 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −63536.0 | −2.84518 | ||||||||
\(794\) | 29528.0 | 1.31979 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 21520.0 | 0.958236 | ||||||||
\(797\) | −24939.0 | −1.10839 | −0.554194 | − | 0.832388i | \(-0.686973\pi\) | ||||
−0.554194 | + | 0.832388i | \(0.686973\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11592.0 | 0.513261 | ||||||||
\(800\) | 3200.00 | 0.141421 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12528.0 | −0.551595 | ||||||||
\(803\) | −1962.00 | −0.0862235 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −32560.0 | −1.42292 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5136.00 | 0.223619 | ||||||||
\(809\) | 29064.0 | 1.26309 | 0.631543 | − | 0.775341i | \(-0.282422\pi\) | ||||
0.631543 | + | 0.775341i | \(0.282422\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15370.0 | 0.665492 | 0.332746 | − | 0.943017i | \(-0.392025\pi\) | ||||
0.332746 | + | 0.943017i | \(0.392025\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 792.000 | 0.0341027 | ||||||||
\(815\) | −25140.0 | −1.08051 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −33904.0 | −1.45184 | ||||||||
\(818\) | −9502.00 | −0.406149 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10080.0 | 0.429279 | ||||||||
\(821\) | −44031.0 | −1.87173 | −0.935866 | − | 0.352355i | \(-0.885381\pi\) | ||||
−0.935866 | + | 0.352355i | \(0.885381\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4192.00 | −0.177550 | −0.0887752 | − | 0.996052i | \(-0.528295\pi\) | ||||
−0.0887752 | + | 0.996052i | \(0.528295\pi\) | |||||||
\(824\) | −3712.00 | −0.156934 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33195.0 | −1.39577 | −0.697886 | − | 0.716209i | \(-0.745876\pi\) | ||||
−0.697886 | + | 0.716209i | \(0.745876\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16448.0 | −0.689098 | −0.344549 | − | 0.938768i | \(-0.611968\pi\) | ||||
−0.344549 | + | 0.938768i | \(0.611968\pi\) | |||||||
\(830\) | 17910.0 | 0.748994 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5632.00 | 0.234681 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −45450.0 | −1.88367 | ||||||||
\(836\) | −3744.00 | −0.154891 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9408.00 | −0.387821 | ||||||||
\(839\) | 16860.0 | 0.693769 | 0.346884 | − | 0.937908i | \(-0.387240\pi\) | ||||
0.346884 | + | 0.937908i | \(0.387240\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21788.0 | −0.893354 | ||||||||
\(842\) | −8948.00 | −0.366233 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −21448.0 | −0.874728 | ||||||||
\(845\) | −83205.0 | −3.38738 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −10224.0 | −0.414025 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −16800.0 | −0.677924 | ||||||||
\(851\) | 3696.00 | 0.148880 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29054.0 | −1.16623 | −0.583113 | − | 0.812391i | \(-0.698165\pi\) | ||||
−0.583113 | + | 0.812391i | \(0.698165\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3144.00 | −0.125537 | ||||||||
\(857\) | 41958.0 | 1.67241 | 0.836207 | − | 0.548415i | \(-0.184768\pi\) | ||||
0.836207 | + | 0.548415i | \(0.184768\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5546.00 | −0.220288 | −0.110144 | − | 0.993916i | \(-0.535131\pi\) | ||||
−0.110144 | + | 0.993916i | \(0.535131\pi\) | |||||||
\(860\) | −19560.0 | −0.775570 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 25608.0 | 1.01185 | ||||||||
\(863\) | 32538.0 | 1.28344 | 0.641719 | − | 0.766940i | \(-0.278222\pi\) | ||||
0.641719 | + | 0.766940i | \(0.278222\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −51570.0 | −2.02709 | ||||||||
\(866\) | 10148.0 | 0.398202 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5247.00 | −0.204824 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14608.0 | −0.568282 | ||||||||
\(872\) | 112.000 | 0.00434954 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −17472.0 | −0.676200 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32096.0 | 1.23581 | 0.617905 | − | 0.786253i | \(-0.287982\pi\) | ||||
0.617905 | + | 0.786253i | \(0.287982\pi\) | |||||||
\(878\) | 2534.00 | 0.0974013 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2160.00 | −0.0827427 | ||||||||
\(881\) | −8490.00 | −0.324671 | −0.162336 | − | 0.986736i | \(-0.551903\pi\) | ||||
−0.162336 | + | 0.986736i | \(0.551903\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48352.0 | −1.84278 | −0.921390 | − | 0.388640i | \(-0.872945\pi\) | ||||
−0.921390 | + | 0.388640i | \(0.872945\pi\) | |||||||
\(884\) | −29568.0 | −1.12498 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13866.0 | 0.525776 | ||||||||
\(887\) | 15492.0 | 0.586438 | 0.293219 | − | 0.956045i | \(-0.405274\pi\) | ||||
0.293219 | + | 0.956045i | \(0.405274\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 31140.0 | 1.17283 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6292.00 | 0.236179 | ||||||||
\(893\) | 14352.0 | 0.537818 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18180.0 | −0.678984 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −23376.0 | −0.868672 | ||||||||
\(899\) | 9435.00 | 0.350028 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 53676.0 | 1.98469 | ||||||||
\(902\) | −3024.00 | −0.111628 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 17472.0 | 0.642821 | ||||||||
\(905\) | 45480.0 | 1.67050 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8116.00 | −0.297119 | −0.148560 | − | 0.988903i | \(-0.547464\pi\) | ||||
−0.148560 | + | 0.988903i | \(0.547464\pi\) | |||||||
\(908\) | 3684.00 | 0.134645 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4446.00 | 0.161693 | 0.0808466 | − | 0.996727i | \(-0.474238\pi\) | ||||
0.0808466 | + | 0.996727i | \(0.474238\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5373.00 | −0.194765 | ||||||||
\(914\) | 1102.00 | 0.0398807 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16208.0 | −0.584637 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26504.0 | 0.951345 | 0.475673 | − | 0.879622i | \(-0.342205\pi\) | ||||
0.475673 | + | 0.879622i | \(0.342205\pi\) | |||||||
\(920\) | −10080.0 | −0.361226 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 26772.0 | 0.956279 | ||||||||
\(923\) | −95568.0 | −3.40808 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4400.00 | 0.156401 | ||||||||
\(926\) | −12752.0 | −0.452545 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1632.00 | −0.0577296 | ||||||||
\(929\) | −5430.00 | −0.191768 | −0.0958840 | − | 0.995393i | \(-0.530568\pi\) | ||||
−0.0958840 | + | 0.995393i | \(0.530568\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1872.00 | 0.0657933 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11400.0 | 0.399378 | ||||||||
\(935\) | 11340.0 | 0.396639 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33803.0 | −1.17854 | −0.589272 | − | 0.807935i | \(-0.700585\pi\) | ||||
−0.589272 | + | 0.807935i | \(0.700585\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8280.00 | 0.287302 | ||||||||
\(941\) | −48483.0 | −1.67960 | −0.839798 | − | 0.542898i | \(-0.817327\pi\) | ||||
−0.839798 | + | 0.542898i | \(0.817327\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14112.0 | −0.487328 | ||||||||
\(944\) | 2544.00 | 0.0877120 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5868.00 | 0.201676 | ||||||||
\(947\) | −37296.0 | −1.27979 | −0.639893 | − | 0.768464i | \(-0.721021\pi\) | ||||
−0.639893 | + | 0.768464i | \(0.721021\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19184.0 | −0.656205 | ||||||||
\(950\) | −20800.0 | −0.710359 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38478.0 | 1.30790 | 0.653948 | − | 0.756540i | \(-0.273112\pi\) | ||||
0.653948 | + | 0.756540i | \(0.273112\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37800.0 | 1.28082 | ||||||||
\(956\) | −19728.0 | −0.667415 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 39588.0 | 1.33510 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4434.00 | 0.148837 | ||||||||
\(962\) | 7744.00 | 0.259539 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6148.00 | 0.205408 | ||||||||
\(965\) | −5475.00 | −0.182639 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27257.0 | 0.906438 | 0.453219 | − | 0.891399i | \(-0.350275\pi\) | ||||
0.453219 | + | 0.891399i | \(0.350275\pi\) | |||||||
\(968\) | −10000.0 | −0.332037 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5070.00 | −0.167823 | ||||||||
\(971\) | 34341.0 | 1.13497 | 0.567485 | − | 0.823384i | \(-0.307917\pi\) | ||||
0.567485 | + | 0.823384i | \(0.307917\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 31870.0 | 1.04844 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11552.0 | −0.378863 | ||||||||
\(977\) | −27426.0 | −0.898092 | −0.449046 | − | 0.893509i | \(-0.648236\pi\) | ||||
−0.449046 | + | 0.893509i | \(0.648236\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9342.00 | −0.304976 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −19926.0 | −0.647520 | ||||||||
\(983\) | 12324.0 | 0.399872 | 0.199936 | − | 0.979809i | \(-0.435927\pi\) | ||||
0.199936 | + | 0.979809i | \(0.435927\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23850.0 | −0.771497 | ||||||||
\(986\) | 8568.00 | 0.276735 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −36608.0 | −1.17880 | ||||||||
\(989\) | 27384.0 | 0.880445 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47597.0 | 1.52570 | 0.762850 | − | 0.646576i | \(-0.223800\pi\) | ||||
0.762850 | + | 0.646576i | \(0.223800\pi\) | |||||||
\(992\) | −5920.00 | −0.189476 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −80700.0 | −2.57122 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11242.0 | 0.357109 | 0.178555 | − | 0.983930i | \(-0.442858\pi\) | ||||
0.178555 | + | 0.983930i | \(0.442858\pi\) | |||||||
\(998\) | 38284.0 | 1.21429 | ||||||||
\(999\) | 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 | 882.4.a.h.1.1 | 1 | ||
3.2 | odd | 2 | 294.4.a.g.1.1 | 1 | |||
7.2 | even | 3 | 882.4.g.l.361.1 | 2 | |||
7.3 | odd | 6 | 126.4.g.a.37.1 | 2 | |||
7.4 | even | 3 | 882.4.g.l.667.1 | 2 | |||
7.5 | odd | 6 | 126.4.g.a.109.1 | 2 | |||
7.6 | odd | 2 | 882.4.a.r.1.1 | 1 | |||
12.11 | even | 2 | 2352.4.a.q.1.1 | 1 | |||
21.2 | odd | 6 | 294.4.e.e.67.1 | 2 | |||
21.5 | even | 6 | 42.4.e.b.25.1 | ✓ | 2 | ||
21.11 | odd | 6 | 294.4.e.e.79.1 | 2 | |||
21.17 | even | 6 | 42.4.e.b.37.1 | yes | 2 | ||
21.20 | even | 2 | 294.4.a.a.1.1 | 1 | |||
84.47 | odd | 6 | 336.4.q.d.193.1 | 2 | |||
84.59 | odd | 6 | 336.4.q.d.289.1 | 2 | |||
84.83 | odd | 2 | 2352.4.a.u.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.4.e.b.25.1 | ✓ | 2 | 21.5 | even | 6 | ||
42.4.e.b.37.1 | yes | 2 | 21.17 | even | 6 | ||
126.4.g.a.37.1 | 2 | 7.3 | odd | 6 | |||
126.4.g.a.109.1 | 2 | 7.5 | odd | 6 | |||
294.4.a.a.1.1 | 1 | 21.20 | even | 2 | |||
294.4.a.g.1.1 | 1 | 3.2 | odd | 2 | |||
294.4.e.e.67.1 | 2 | 21.2 | odd | 6 | |||
294.4.e.e.79.1 | 2 | 21.11 | odd | 6 | |||
336.4.q.d.193.1 | 2 | 84.47 | odd | 6 | |||
336.4.q.d.289.1 | 2 | 84.59 | odd | 6 | |||
882.4.a.h.1.1 | 1 | 1.1 | even | 1 | trivial | ||
882.4.a.r.1.1 | 1 | 7.6 | odd | 2 | |||
882.4.g.l.361.1 | 2 | 7.2 | even | 3 | |||
882.4.g.l.667.1 | 2 | 7.4 | even | 3 | |||
2352.4.a.q.1.1 | 1 | 12.11 | even | 2 | |||
2352.4.a.u.1.1 | 1 | 84.83 | odd | 2 |