Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,4,Mod(1,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("2352.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.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: | \(138.772492334\) |
Analytic rank: | \(0\) |
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 | \(\chi\) | \(=\) | 2352.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 15.0000 | 1.34164 | 0.670820 | − | 0.741620i | \(-0.265942\pi\) | ||||
0.670820 | + | 0.741620i | \(0.265942\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 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 | ||||||||
\(15\) | −45.0000 | −0.774597 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 84.0000 | 1.19841 | 0.599206 | − | 0.800595i | \(-0.295483\pi\) | ||||
0.599206 | + | 0.800595i | \(0.295483\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 104.000 | 1.25575 | 0.627875 | − | 0.778314i | \(-0.283925\pi\) | ||||
0.627875 | + | 0.778314i | \(0.283925\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 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 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 51.0000 | 0.326568 | 0.163284 | − | 0.986579i | \(-0.447791\pi\) | ||||
0.163284 | + | 0.986579i | \(0.447791\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 185.000 | 1.07184 | 0.535919 | − | 0.844269i | \(-0.319965\pi\) | ||||
0.535919 | + | 0.844269i | \(0.319965\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −27.0000 | −0.142427 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 44.0000 | 0.195501 | 0.0977507 | − | 0.995211i | \(-0.468835\pi\) | ||||
0.0977507 | + | 0.995211i | \(0.468835\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −264.000 | −1.08394 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 168.000 | 0.639932 | 0.319966 | − | 0.947429i | \(-0.396329\pi\) | ||||
0.319966 | + | 0.947429i | \(0.396329\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −326.000 | −1.15615 | −0.578076 | − | 0.815983i | \(-0.696196\pi\) | ||||
−0.578076 | + | 0.815983i | \(0.696196\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 135.000 | 0.447214 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −138.000 | −0.428284 | −0.214142 | − | 0.976802i | \(-0.568696\pi\) | ||||
−0.214142 | + | 0.976802i | \(0.568696\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −252.000 | −0.691903 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 639.000 | 1.65610 | 0.828051 | − | 0.560653i | \(-0.189450\pi\) | ||||
0.828051 | + | 0.560653i | \(0.189450\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 135.000 | 0.330971 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −312.000 | −0.725007 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 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 | \(0.773690\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1320.00 | 2.51886 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 166.000 | 0.302688 | 0.151344 | − | 0.988481i | \(-0.451640\pi\) | ||||
0.151344 | + | 0.988481i | \(0.451640\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −252.000 | −0.439670 | ||||||||
\(70\) | 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 | \(0.555915\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −300.000 | −0.461880 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 583.000 | 0.830286 | 0.415143 | − | 0.909756i | \(-0.363731\pi\) | ||||
0.415143 | + | 0.909756i | \(0.363731\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −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 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −153.000 | −0.188544 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1038.00 | 1.23627 | 0.618134 | − | 0.786073i | \(-0.287889\pi\) | ||||
0.618134 | + | 0.786073i | \(0.287889\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −555.000 | −0.618826 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 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 | ||||||||
\(99\) | 81.0000 | 0.0822304 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −642.000 | −0.632489 | −0.316244 | − | 0.948678i | \(-0.602422\pi\) | ||||
−0.316244 | + | 0.948678i | \(0.602422\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 464.000 | 0.443876 | 0.221938 | − | 0.975061i | \(-0.428762\pi\) | ||||
0.221938 | + | 0.975061i | \(0.428762\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −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 | \(0.498042\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −132.000 | −0.112873 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2184.00 | −1.81817 | −0.909086 | − | 0.416608i | \(-0.863219\pi\) | ||||
−0.909086 | + | 0.416608i | \(0.863219\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1260.00 | 1.02170 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 792.000 | 0.625816 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1250.00 | −0.939144 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −504.000 | −0.369465 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −375.000 | −0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 373.000 | 0.260617 | 0.130309 | − | 0.991473i | \(-0.458403\pi\) | ||||
0.130309 | + | 0.991473i | \(0.458403\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 978.000 | 0.667505 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1173.00 | −0.782332 | −0.391166 | − | 0.920320i | \(-0.627928\pi\) | ||||
−0.391166 | + | 0.920320i | \(0.627928\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −405.000 | −0.258199 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 30.0000 | 0.0187086 | 0.00935428 | − | 0.999956i | \(-0.497022\pi\) | ||||
0.00935428 | + | 0.999956i | \(0.497022\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −82.0000 | −0.0500370 | −0.0250185 | − | 0.999687i | \(-0.507964\pi\) | ||||
−0.0250185 | + | 0.999687i | \(0.507964\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 414.000 | 0.247270 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 792.000 | 0.463149 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 765.000 | 0.438136 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1434.00 | −0.788442 | −0.394221 | − | 0.919016i | \(-0.628986\pi\) | ||||
−0.394221 | + | 0.919016i | \(0.628986\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2671.00 | 1.43949 | 0.719745 | − | 0.694239i | \(-0.244259\pi\) | ||||
0.719745 | + | 0.694239i | \(0.244259\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 756.000 | 0.399470 | ||||||||
\(154\) | 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 | \(0.693982\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1917.00 | −0.956151 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1676.00 | −0.805365 | −0.402682 | − | 0.915340i | \(-0.631922\pi\) | ||||
−0.402682 | + | 0.915340i | \(0.631922\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −405.000 | −0.191086 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 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 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 936.000 | 0.418583 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3438.00 | −1.51090 | −0.755452 | − | 0.655204i | \(-0.772583\pi\) | ||||
−0.755452 | + | 0.655204i | \(0.772583\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −477.000 | −0.202562 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 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 | ||||||||
\(183\) | 2166.00 | 0.874947 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 660.000 | 0.262293 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 756.000 | 0.295637 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −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 | \(0.478317\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3960.00 | −1.45426 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1590.00 | −0.575040 | −0.287520 | − | 0.957775i | \(-0.592831\pi\) | ||||
−0.287520 | + | 0.957775i | \(0.592831\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5380.00 | −1.91647 | −0.958236 | − | 0.285977i | \(-0.907682\pi\) | ||||
−0.958236 | + | 0.285977i | \(0.907682\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −498.000 | −0.174757 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2520.00 | 0.858558 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 756.000 | 0.253844 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 936.000 | 0.309782 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5362.00 | 1.74946 | 0.874728 | − | 0.484614i | \(-0.161040\pi\) | ||||
0.874728 | + | 0.484614i | \(0.161040\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3258.00 | 1.04805 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4890.00 | −1.55114 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 654.000 | 0.201796 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7392.00 | 2.24995 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1573.00 | −0.472358 | −0.236179 | − | 0.971710i | \(-0.575895\pi\) | ||||
−0.236179 | + | 0.971710i | \(0.575895\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 900.000 | 0.266667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 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 | \(0.698763\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −468.000 | −0.131587 | −0.0657933 | − | 0.997833i | \(-0.520958\pi\) | ||||
−0.0657933 | + | 0.997833i | \(0.520958\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2070.00 | −0.574604 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1749.00 | −0.479366 | ||||||||
\(238\) | 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 | \(0.434148\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9152.00 | 2.35760 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1791.00 | 0.455823 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 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 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3780.00 | −0.928285 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5346.00 | −1.29757 | −0.648783 | − | 0.760974i | \(-0.724722\pi\) | ||||
−0.648783 | + | 0.760974i | \(0.724722\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 459.000 | 0.108856 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −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 | ||||||||
\(267\) | −3114.00 | −0.713759 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2415.00 | −0.547380 | −0.273690 | − | 0.961818i | \(-0.588244\pi\) | ||||
−0.273690 | + | 0.961818i | \(0.588244\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −475.000 | −0.106473 | −0.0532365 | − | 0.998582i | \(-0.516954\pi\) | ||||
−0.0532365 | + | 0.998582i | \(0.516954\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 900.000 | 0.197353 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3728.00 | 0.808642 | 0.404321 | − | 0.914617i | \(-0.367508\pi\) | ||||
0.404321 | + | 0.914617i | \(0.367508\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1665.00 | 0.357279 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1602.00 | 0.340097 | 0.170049 | − | 0.985436i | \(-0.445608\pi\) | ||||
0.170049 | + | 0.985436i | \(0.445608\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 686.000 | 0.144094 | 0.0720468 | − | 0.997401i | \(-0.477047\pi\) | ||||
0.0720468 | + | 0.997401i | \(0.477047\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4680.00 | −0.972699 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2143.00 | 0.436190 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −507.000 | −0.102134 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1101.00 | 0.219526 | 0.109763 | − | 0.993958i | \(-0.464991\pi\) | ||||
0.109763 | + | 0.993958i | \(0.464991\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2385.00 | 0.470712 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −243.000 | −0.0474757 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7392.00 | 1.42973 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1926.00 | 0.365168 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10830.0 | −2.03319 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2780.00 | 0.516818 | 0.258409 | − | 0.966036i | \(-0.416802\pi\) | ||||
0.258409 | + | 0.966036i | \(0.416802\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1392.00 | −0.256272 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 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 | \(0.665058\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4491.00 | 0.795709 | 0.397854 | − | 0.917449i | \(-0.369755\pi\) | ||||
0.397854 | + | 0.917449i | \(0.369755\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 459.000 | 0.0805613 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1179.00 | 0.205001 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8736.00 | 1.50490 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8800.00 | 1.50196 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −42.0000 | −0.00710277 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3964.00 | 0.658251 | 0.329126 | − | 0.944286i | \(-0.393246\pi\) | ||||
0.329126 | + | 0.944286i | \(0.393246\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 396.000 | 0.0651672 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2490.00 | 0.406099 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 161.000 | 0.0260244 | 0.0130122 | − | 0.999915i | \(-0.495858\pi\) | ||||
0.0130122 | + | 0.999915i | \(0.495858\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6552.00 | 1.04972 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1665.00 | 0.264413 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3780.00 | −0.589879 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 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 | ||||||||
\(351\) | −2376.00 | −0.361315 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4440.00 | 0.669454 | 0.334727 | − | 0.942315i | \(-0.391356\pi\) | ||||
0.334727 | + | 0.942315i | \(0.391356\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16290.0 | −2.43545 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −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 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3750.00 | 0.542215 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3270.00 | −0.468930 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2869.00 | −0.408067 | −0.204033 | − | 0.978964i | \(-0.565405\pi\) | ||||
−0.204033 | + | 0.978964i | \(0.565405\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1512.00 | 0.213311 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3064.00 | −0.425330 | −0.212665 | − | 0.977125i | \(-0.568214\pi\) | ||||
−0.212665 | + | 0.977125i | \(0.568214\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1125.00 | 0.154919 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4488.00 | 0.613113 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6040.00 | 0.818612 | 0.409306 | − | 0.912397i | \(-0.365771\pi\) | ||||
0.409306 | + | 0.912397i | \(0.365771\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1119.00 | −0.150467 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1842.00 | 0.245749 | 0.122874 | − | 0.992422i | \(-0.460789\pi\) | ||||
0.122874 | + | 0.992422i | \(0.460789\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2934.00 | −0.385384 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7830.00 | 1.02056 | 0.510279 | − | 0.860009i | \(-0.329542\pi\) | ||||
0.510279 | + | 0.860009i | \(0.329542\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7056.00 | 0.912627 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3519.00 | 0.451680 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8745.00 | 1.11395 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14764.0 | 1.86646 | 0.933229 | − | 0.359282i | \(-0.116978\pi\) | ||||
0.933229 | + | 0.359282i | \(0.116978\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6264.00 | 0.780073 | 0.390036 | − | 0.920799i | \(-0.372462\pi\) | ||||
0.390036 | + | 0.920799i | \(0.372462\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16280.0 | 2.01232 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1215.00 | 0.149071 | ||||||||
\(406\) | 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 | \(0.592721\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −90.0000 | −0.0108014 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8955.00 | −1.05924 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 246.000 | 0.0288889 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −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 | \(0.583382\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1242.00 | −0.142761 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8400.00 | 0.958729 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2376.00 | −0.267399 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 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 | ||||||||
\(435\) | −2295.00 | −0.252958 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8736.00 | 0.956292 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1267.00 | −0.137746 | −0.0688731 | − | 0.997625i | \(-0.521940\pi\) | ||||
−0.0688731 | + | 0.997625i | \(0.521940\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 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 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4302.00 | 0.455207 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11688.0 | 1.22849 | 0.614244 | − | 0.789116i | \(-0.289461\pi\) | ||||
0.614244 | + | 0.789116i | \(0.289461\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1512.00 | 0.157865 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8013.00 | −0.831090 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 551.000 | 0.0563998 | 0.0281999 | − | 0.999602i | \(-0.491023\pi\) | ||||
0.0281999 | + | 0.999602i | \(0.491023\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2268.00 | −0.230634 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13386.0 | −1.35238 | −0.676191 | − | 0.736726i | \(-0.736371\pi\) | ||||
−0.676191 | + | 0.736726i | \(0.736371\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6376.00 | 0.639995 | 0.319998 | − | 0.947418i | \(-0.396318\pi\) | ||||
0.319998 | + | 0.947418i | \(0.396318\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8325.00 | −0.830242 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5700.00 | 0.564806 | 0.282403 | − | 0.959296i | \(-0.408868\pi\) | ||||
0.282403 | + | 0.959296i | \(0.408868\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6756.00 | 0.660934 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2934.00 | −0.285212 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10400.0 | 1.00460 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5751.00 | 0.552034 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 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 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2535.00 | 0.237337 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15935.0 | −1.48272 | −0.741359 | − | 0.671109i | \(-0.765818\pi\) | ||||
−0.741359 | + | 0.671109i | \(0.765818\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5028.00 | 0.464978 | ||||||||
\(490\) | 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 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1215.00 | 0.110324 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19142.0 | −1.71726 | −0.858631 | − | 0.512594i | \(-0.828684\pi\) | ||||
−0.858631 | + | 0.512594i | \(0.828684\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9090.00 | −0.810601 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −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 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16641.0 | −1.45770 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19809.0 | 1.72499 | 0.862494 | − | 0.506068i | \(-0.168902\pi\) | ||||
0.862494 | + | 0.506068i | \(0.168902\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2808.00 | −0.241669 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6960.00 | 0.595523 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1242.00 | −0.105654 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10314.0 | 0.872321 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1794.00 | 0.150857 | 0.0754286 | − | 0.997151i | \(-0.475968\pi\) | ||||
0.0754286 | + | 0.997151i | \(0.475968\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6448.00 | −0.539104 | −0.269552 | − | 0.962986i | \(-0.586876\pi\) | ||||
−0.269552 | + | 0.962986i | \(0.586876\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15540.0 | 1.28450 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5111.00 | −0.420071 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1431.00 | 0.116949 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14784.0 | 1.20144 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5895.00 | −0.476380 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3636.00 | −0.292188 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7262.00 | 0.577112 | 0.288556 | − | 0.957463i | \(-0.406825\pi\) | ||||
0.288556 | + | 0.957463i | \(0.406825\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9096.00 | 0.718871 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 210.000 | 0.0165053 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14204.0 | −1.11027 | −0.555136 | − | 0.831759i | \(-0.687334\pi\) | ||||
−0.555136 | + | 0.831759i | \(0.687334\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6498.00 | −0.505151 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5304.00 | 0.410087 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1980.00 | −0.151435 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15825.0 | 1.20382 | 0.601909 | − | 0.798565i | \(-0.294407\pi\) | ||||
0.601909 | + | 0.798565i | \(0.294407\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28688.0 | −2.17061 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2268.00 | −0.170686 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 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 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3960.00 | 0.291761 | 0.145880 | − | 0.989302i | \(-0.453399\pi\) | ||||
0.145880 | + | 0.989302i | \(0.453399\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2530.00 | 0.185424 | 0.0927121 | − | 0.995693i | \(-0.470446\pi\) | ||||
0.0927121 | + | 0.995693i | \(0.470446\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7560.00 | 0.551175 | ||||||||
\(574\) | 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 | \(0.640360\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1095.00 | −0.0785952 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5751.00 | 0.408546 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11880.0 | 0.839620 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 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 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4770.00 | 0.331999 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21804.0 | −1.50992 | −0.754960 | − | 0.655770i | \(-0.772344\pi\) | ||||
−0.754960 | + | 0.655770i | \(0.772344\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16140.0 | 1.10648 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −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 | ||||||||
\(603\) | 1494.00 | 0.100896 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −18750.0 | −1.25999 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2737.00 | −0.183017 | −0.0915086 | − | 0.995804i | \(-0.529169\pi\) | ||||
−0.0915086 | + | 0.995804i | \(0.529169\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12144.0 | −0.804081 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26188.0 | −1.72549 | −0.862743 | − | 0.505642i | \(-0.831256\pi\) | ||||
−0.862743 | + | 0.505642i | \(0.831256\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7560.00 | −0.495689 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2358.00 | −0.153857 | −0.0769283 | − | 0.997037i | \(-0.524511\pi\) | ||||
−0.0769283 | + | 0.997037i | \(0.524511\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13766.0 | 0.893865 | 0.446932 | − | 0.894568i | \(-0.352516\pi\) | ||||
0.446932 | + | 0.894568i | \(0.352516\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2268.00 | −0.146557 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18125.0 | −1.16000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2808.00 | −0.178853 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3696.00 | 0.234291 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21287.0 | −1.34298 | −0.671491 | − | 0.741012i | \(-0.734346\pi\) | ||||
−0.671491 | + | 0.741012i | \(0.734346\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16086.0 | −1.01005 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5595.00 | 0.349655 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9774.00 | −0.605091 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21426.0 | 1.32024 | 0.660122 | − | 0.751159i | \(-0.270505\pi\) | ||||
0.660122 | + | 0.751159i | \(0.270505\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9962.00 | 0.610984 | 0.305492 | − | 0.952195i | \(-0.401179\pi\) | ||||
0.305492 | + | 0.952195i | \(0.401179\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14670.0 | 0.895551 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −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 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19167.0 | −1.14864 | −0.574321 | − | 0.818630i | \(-0.694734\pi\) | ||||
−0.574321 | + | 0.818630i | \(0.694734\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17595.0 | −1.04961 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1962.00 | −0.116507 | ||||||||
\(658\) | 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 | \(0.352522\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −22176.0 | −1.29901 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4284.00 | 0.248691 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4719.00 | 0.272716 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6498.00 | −0.373849 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4397.00 | 0.251845 | 0.125923 | − | 0.992040i | \(-0.459811\pi\) | ||||
0.125923 | + | 0.992040i | \(0.459811\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2700.00 | −0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4029.00 | −0.228725 | −0.114363 | − | 0.993439i | \(-0.536483\pi\) | ||||
−0.114363 | + | 0.993439i | \(0.536483\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2763.00 | −0.155475 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −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 | ||||||||
\(687\) | 12156.0 | 0.675081 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 56232.0 | 3.10924 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13984.0 | −0.769865 | −0.384932 | − | 0.922945i | \(-0.625775\pi\) | ||||
−0.384932 | + | 0.922945i | \(0.625775\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1230.00 | −0.0671317 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14112.0 | 0.766901 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1404.00 | 0.0759716 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31053.0 | −1.67312 | −0.836559 | − | 0.547877i | \(-0.815436\pi\) | ||||
−0.836559 | + | 0.547877i | \(0.815436\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4576.00 | 0.245501 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6210.00 | 0.331748 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15086.0 | 0.799107 | 0.399553 | − | 0.916710i | \(-0.369165\pi\) | ||||
0.399553 | + | 0.916710i | \(0.369165\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5247.00 | 0.276762 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15540.0 | 0.816238 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11880.0 | 0.621380 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14796.0 | 0.770665 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6378.00 | −0.330820 | −0.165410 | − | 0.986225i | \(-0.552895\pi\) | ||||
−0.165410 | + | 0.986225i | \(0.552895\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4611.00 | −0.237185 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5100.00 | 0.261254 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7363.00 | −0.375624 | −0.187812 | − | 0.982205i | \(-0.560140\pi\) | ||||
−0.187812 | + | 0.982205i | \(0.560140\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27384.0 | −1.38555 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32810.0 | −1.65329 | −0.826647 | − | 0.562720i | \(-0.809755\pi\) | ||||
−0.826647 | + | 0.562720i | \(0.809755\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1494.00 | 0.0746706 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24034.0 | 1.19635 | 0.598177 | − | 0.801364i | \(-0.295892\pi\) | ||||
0.598177 | + | 0.801364i | \(0.295892\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −27456.0 | −1.36116 | ||||||||
\(742\) | 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 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5373.00 | −0.263170 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29519.0 | −1.43431 | −0.717153 | − | 0.696916i | \(-0.754555\pi\) | ||||
−0.717153 | + | 0.696916i | \(0.754555\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15957.0 | −0.772252 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 40065.0 | 1.93128 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3742.00 | −0.179664 | −0.0898318 | − | 0.995957i | \(-0.528633\pi\) | ||||
−0.0898318 | + | 0.995957i | \(0.528633\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2268.00 | −0.108463 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10896.0 | 0.519027 | 0.259514 | − | 0.965739i | \(-0.416438\pi\) | ||||
0.259514 | + | 0.965739i | \(0.416438\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11340.0 | 0.535946 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 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 | ||||||||
\(771\) | 16038.0 | 0.749150 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11826.0 | −0.550261 | −0.275130 | − | 0.961407i | \(-0.588721\pi\) | ||||
−0.275130 | + | 0.961407i | \(0.588721\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18500.0 | 0.857470 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17472.0 | 0.803594 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9774.00 | −0.447812 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1377.00 | −0.0628480 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −33780.0 | −1.53587 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17714.0 | 0.802333 | 0.401166 | − | 0.916005i | \(-0.368605\pi\) | ||||
0.401166 | + | 0.916005i | \(0.368605\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2322.00 | 0.104772 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −63536.0 | −2.84518 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −28755.0 | −1.28281 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24939.0 | 1.10839 | 0.554194 | − | 0.832388i | \(-0.313027\pi\) | ||||
0.554194 | + | 0.832388i | \(0.313027\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11592.0 | −0.513261 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9342.00 | 0.412089 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1962.00 | −0.0862235 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7245.00 | 0.316030 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29064.0 | −1.26309 | −0.631543 | − | 0.775341i | \(-0.717578\pi\) | ||||
−0.631543 | + | 0.775341i | \(0.717578\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15370.0 | −0.665492 | −0.332746 | − | 0.943017i | \(-0.607975\pi\) | ||||
−0.332746 | + | 0.943017i | \(0.607975\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1425.00 | 0.0614722 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −25140.0 | −1.08051 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −33904.0 | −1.45184 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44031.0 | 1.87173 | 0.935866 | − | 0.352355i | \(-0.114619\pi\) | ||||
0.935866 | + | 0.352355i | \(0.114619\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4192.00 | 0.177550 | 0.0887752 | − | 0.996052i | \(-0.471705\pi\) | ||||
0.0887752 | + | 0.996052i | \(0.471705\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2700.00 | −0.113942 | ||||||||
\(826\) | 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 | \(0.611968\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11184.0 | −0.466870 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 45450.0 | 1.88367 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4995.00 | −0.206275 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 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 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4806.00 | −0.196355 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 83205.0 | 3.38738 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2058.00 | −0.0831924 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 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 | ||||||||
\(855\) | 14040.0 | 0.561588 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −41958.0 | −1.67241 | −0.836207 | − | 0.548415i | \(-0.815232\pi\) | ||||
−0.836207 | + | 0.548415i | \(0.815232\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5546.00 | 0.220288 | 0.110144 | − | 0.993916i | \(-0.464869\pi\) | ||||
0.110144 | + | 0.993916i | \(0.464869\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 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 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6429.00 | −0.251834 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5247.00 | 0.204824 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14608.0 | 0.568282 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1521.00 | 0.0589668 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32096.0 | 1.23581 | 0.617905 | − | 0.786253i | \(-0.287982\pi\) | ||||
0.617905 | + | 0.786253i | \(0.287982\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3303.00 | −0.126743 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8490.00 | 0.324671 | 0.162336 | − | 0.986736i | \(-0.448097\pi\) | ||||
0.162336 | + | 0.986736i | \(0.448097\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48352.0 | 1.84278 | 0.921390 | − | 0.388640i | \(-0.127055\pi\) | ||||
0.921390 | + | 0.388640i | \(0.127055\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7155.00 | −0.271766 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15492.0 | 0.586438 | 0.293219 | − | 0.956045i | \(-0.405274\pi\) | ||||
0.293219 | + | 0.956045i | \(0.405274\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 729.000 | 0.0274101 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14352.0 | −0.537818 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18180.0 | 0.678984 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22176.0 | −0.825457 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9435.00 | 0.350028 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 53676.0 | 1.98469 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −45480.0 | −1.67050 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8116.00 | 0.297119 | 0.148560 | − | 0.988903i | \(-0.452536\pi\) | ||||
0.148560 | + | 0.988903i | \(0.452536\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5778.00 | −0.210830 | ||||||||
\(910\) | 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 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 32490.0 | 1.17386 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26504.0 | −0.951345 | −0.475673 | − | 0.879622i | \(-0.657795\pi\) | ||||
−0.475673 | + | 0.879622i | \(0.657795\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8340.00 | −0.298385 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −95568.0 | −3.40808 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4400.00 | 0.156401 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4176.00 | 0.147959 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5430.00 | 0.191768 | 0.0958840 | − | 0.995393i | \(-0.469432\pi\) | ||||
0.0958840 | + | 0.995393i | \(0.469432\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12888.0 | −0.452234 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 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 | ||||||||
\(939\) | 16467.0 | 0.572290 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 48483.0 | 1.67960 | 0.839798 | − | 0.542898i | \(-0.182673\pi\) | ||||
0.839798 | + | 0.542898i | \(0.182673\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14112.0 | 0.487328 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −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 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13473.0 | −0.459403 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38478.0 | −1.30790 | −0.653948 | − | 0.756540i | \(-0.726888\pi\) | ||||
−0.653948 | + | 0.756540i | \(0.726888\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −37800.0 | −1.28082 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1377.00 | −0.0465121 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4434.00 | 0.148837 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3537.00 | −0.118357 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5475.00 | 0.182639 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27257.0 | −0.906438 | −0.453219 | − | 0.891399i | \(-0.649725\pi\) | ||||
−0.453219 | + | 0.891399i | \(0.649725\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −26208.0 | −0.868857 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34341.0 | 1.13497 | 0.567485 | − | 0.823384i | \(-0.307917\pi\) | ||||
0.567485 | + | 0.823384i | \(0.307917\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −26400.0 | −0.867156 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27426.0 | 0.898092 | 0.449046 | − | 0.893509i | \(-0.351764\pi\) | ||||
0.449046 | + | 0.893509i | \(0.351764\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9342.00 | 0.304976 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 126.000 | 0.00410079 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 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 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27384.0 | −0.880445 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47597.0 | −1.52570 | −0.762850 | − | 0.646576i | \(-0.776200\pi\) | ||||
−0.762850 | + | 0.646576i | \(0.776200\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11892.0 | −0.380042 | ||||||||
\(994\) | 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 | \(0.442858\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1188.00 | −0.0376243 |
(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 | 2352.4.a.q.1.1 | 1 | ||
4.3 | odd | 2 | 294.4.a.g.1.1 | 1 | |||
7.3 | odd | 6 | 336.4.q.d.289.1 | 2 | |||
7.5 | odd | 6 | 336.4.q.d.193.1 | 2 | |||
7.6 | odd | 2 | 2352.4.a.u.1.1 | 1 | |||
12.11 | even | 2 | 882.4.a.h.1.1 | 1 | |||
28.3 | even | 6 | 42.4.e.b.37.1 | yes | 2 | ||
28.11 | odd | 6 | 294.4.e.e.79.1 | 2 | |||
28.19 | even | 6 | 42.4.e.b.25.1 | ✓ | 2 | ||
28.23 | odd | 6 | 294.4.e.e.67.1 | 2 | |||
28.27 | even | 2 | 294.4.a.a.1.1 | 1 | |||
84.11 | even | 6 | 882.4.g.l.667.1 | 2 | |||
84.23 | even | 6 | 882.4.g.l.361.1 | 2 | |||
84.47 | odd | 6 | 126.4.g.a.109.1 | 2 | |||
84.59 | odd | 6 | 126.4.g.a.37.1 | 2 | |||
84.83 | odd | 2 | 882.4.a.r.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.4.e.b.25.1 | ✓ | 2 | 28.19 | even | 6 | ||
42.4.e.b.37.1 | yes | 2 | 28.3 | even | 6 | ||
126.4.g.a.37.1 | 2 | 84.59 | odd | 6 | |||
126.4.g.a.109.1 | 2 | 84.47 | odd | 6 | |||
294.4.a.a.1.1 | 1 | 28.27 | even | 2 | |||
294.4.a.g.1.1 | 1 | 4.3 | odd | 2 | |||
294.4.e.e.67.1 | 2 | 28.23 | odd | 6 | |||
294.4.e.e.79.1 | 2 | 28.11 | odd | 6 | |||
336.4.q.d.193.1 | 2 | 7.5 | odd | 6 | |||
336.4.q.d.289.1 | 2 | 7.3 | odd | 6 | |||
882.4.a.h.1.1 | 1 | 12.11 | even | 2 | |||
882.4.a.r.1.1 | 1 | 84.83 | odd | 2 | |||
882.4.g.l.361.1 | 2 | 84.23 | even | 6 | |||
882.4.g.l.667.1 | 2 | 84.11 | even | 6 | |||
2352.4.a.q.1.1 | 1 | 1.1 | even | 1 | trivial | ||
2352.4.a.u.1.1 | 1 | 7.6 | odd | 2 |