Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [96,4,Mod(1,96)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(96, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("96.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 96 = 2^{5} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 96.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: | \(5.66418336055\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 96.1 |
$q$-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 | ||||||||
\(5\) | 2.00000 | 0.178885 | 0.0894427 | − | 0.995992i | \(-0.471491\pi\) | ||||
0.0894427 | + | 0.995992i | \(0.471491\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −12.0000 | −0.647939 | −0.323970 | − | 0.946068i | \(-0.605018\pi\) | ||||
−0.323970 | + | 0.946068i | \(0.605018\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −60.0000 | −1.64461 | −0.822304 | − | 0.569049i | \(-0.807311\pi\) | ||||
−0.822304 | + | 0.569049i | \(0.807311\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −42.0000 | −0.896054 | −0.448027 | − | 0.894020i | \(-0.647873\pi\) | ||||
−0.448027 | + | 0.894020i | \(0.647873\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.00000 | −0.103280 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 10.0000 | 0.142668 | 0.0713340 | − | 0.997452i | \(-0.477274\pi\) | ||||
0.0713340 | + | 0.997452i | \(0.477274\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −132.000 | −1.59384 | −0.796918 | − | 0.604088i | \(-0.793538\pi\) | ||||
−0.796918 | + | 0.604088i | \(0.793538\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 36.0000 | 0.374088 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 48.0000 | 0.435161 | 0.217580 | − | 0.976042i | \(-0.430184\pi\) | ||||
0.217580 | + | 0.976042i | \(0.430184\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −121.000 | −0.968000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 226.000 | 1.44714 | 0.723571 | − | 0.690249i | \(-0.242499\pi\) | ||||
0.723571 | + | 0.690249i | \(0.242499\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 252.000 | 1.46002 | 0.730009 | − | 0.683438i | \(-0.239516\pi\) | ||||
0.730009 | + | 0.683438i | \(0.239516\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 180.000 | 0.949514 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −24.0000 | −0.115907 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −362.000 | −1.60844 | −0.804222 | − | 0.594329i | \(-0.797418\pi\) | ||||
−0.804222 | + | 0.594329i | \(0.797418\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 126.000 | 0.517337 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −94.0000 | −0.358057 | −0.179028 | − | 0.983844i | \(-0.557295\pi\) | ||||
−0.179028 | + | 0.983844i | \(0.557295\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 228.000 | 0.808597 | 0.404299 | − | 0.914627i | \(-0.367516\pi\) | ||||
0.404299 | + | 0.914627i | \(0.367516\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 18.0000 | 0.0596285 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 408.000 | 1.26623 | 0.633116 | − | 0.774057i | \(-0.281776\pi\) | ||||
0.633116 | + | 0.774057i | \(0.281776\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −199.000 | −0.580175 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −30.0000 | −0.0823694 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 346.000 | 0.896731 | 0.448366 | − | 0.893850i | \(-0.352006\pi\) | ||||
0.448366 | + | 0.893850i | \(0.352006\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −120.000 | −0.294196 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 396.000 | 0.920201 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 300.000 | 0.661978 | 0.330989 | − | 0.943635i | \(-0.392618\pi\) | ||||
0.330989 | + | 0.943635i | \(0.392618\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −466.000 | −0.978118 | −0.489059 | − | 0.872251i | \(-0.662660\pi\) | ||||
−0.489059 | + | 0.872251i | \(0.662660\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −108.000 | −0.215980 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −84.0000 | −0.160291 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −204.000 | −0.371979 | −0.185989 | − | 0.982552i | \(-0.559549\pi\) | ||||
−0.185989 | + | 0.982552i | \(0.559549\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −144.000 | −0.251240 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1056.00 | −1.76513 | −0.882564 | − | 0.470192i | \(-0.844185\pi\) | ||||
−0.882564 | + | 0.470192i | \(0.844185\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 330.000 | 0.529090 | 0.264545 | − | 0.964373i | \(-0.414778\pi\) | ||||
0.264545 | + | 0.964373i | \(0.414778\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 363.000 | 0.558875 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 720.000 | 1.06561 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −612.000 | −0.871587 | −0.435794 | − | 0.900047i | \(-0.643532\pi\) | ||||
−0.435794 | + | 0.900047i | \(0.643532\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −564.000 | −0.745868 | −0.372934 | − | 0.927858i | \(-0.621648\pi\) | ||||
−0.372934 | + | 0.927858i | \(0.621648\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 20.0000 | 0.0255212 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −678.000 | −0.835508 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1510.00 | −1.79842 | −0.899212 | − | 0.437514i | \(-0.855859\pi\) | ||||
−0.899212 | + | 0.437514i | \(0.855859\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 504.000 | 0.580589 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −756.000 | −0.842941 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −264.000 | −0.285114 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 594.000 | 0.621769 | 0.310884 | − | 0.950448i | \(-0.399375\pi\) | ||||
0.310884 | + | 0.950448i | \(0.399375\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −540.000 | −0.548202 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 554.000 | 0.545793 | 0.272896 | − | 0.962043i | \(-0.412018\pi\) | ||||
0.272896 | + | 0.962043i | \(0.412018\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1284.00 | −1.22831 | −0.614157 | − | 0.789184i | \(-0.710504\pi\) | ||||
−0.614157 | + | 0.789184i | \(0.710504\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 72.0000 | 0.0669189 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1356.00 | 1.22514 | 0.612568 | − | 0.790418i | \(-0.290137\pi\) | ||||
0.612568 | + | 0.790418i | \(0.290137\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 390.000 | 0.342708 | 0.171354 | − | 0.985209i | \(-0.445186\pi\) | ||||
0.171354 | + | 0.985209i | \(0.445186\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1086.00 | 0.928636 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −766.000 | −0.637692 | −0.318846 | − | 0.947807i | \(-0.603295\pi\) | ||||
−0.318846 | + | 0.947807i | \(0.603295\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 96.0000 | 0.0778439 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −378.000 | −0.298685 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −120.000 | −0.0924402 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2269.00 | 1.70473 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 282.000 | 0.206724 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −492.000 | −0.352047 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2388.00 | 1.66851 | 0.834255 | − | 0.551379i | \(-0.185898\pi\) | ||||
0.834255 | + | 0.551379i | \(0.185898\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −684.000 | −0.466844 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −396.000 | −0.264112 | −0.132056 | − | 0.991242i | \(-0.542158\pi\) | ||||
−0.132056 | + | 0.991242i | \(0.542158\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1584.00 | 1.03271 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −54.0000 | −0.0344265 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −110.000 | −0.0685981 | −0.0342990 | − | 0.999412i | \(-0.510920\pi\) | ||||
−0.0342990 | + | 0.999412i | \(0.510920\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 732.000 | 0.446672 | 0.223336 | − | 0.974742i | \(-0.428305\pi\) | ||||
0.223336 | + | 0.974742i | \(0.428305\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1224.00 | −0.731060 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2520.00 | 1.47366 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 452.000 | 0.258873 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 597.000 | 0.334964 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1934.00 | −1.06335 | −0.531676 | − | 0.846948i | \(-0.678438\pi\) | ||||
−0.531676 | + | 0.846948i | \(0.678438\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1092.00 | 0.588515 | 0.294257 | − | 0.955726i | \(-0.404928\pi\) | ||||
0.294257 | + | 0.955726i | \(0.404928\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 90.0000 | 0.0475560 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 504.000 | 0.261176 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −578.000 | −0.293818 | −0.146909 | − | 0.989150i | \(-0.546932\pi\) | ||||
−0.146909 | + | 0.989150i | \(0.546932\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1038.00 | −0.517728 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −576.000 | −0.281958 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2532.00 | −1.21670 | −0.608348 | − | 0.793670i | \(-0.708168\pi\) | ||||
−0.608348 | + | 0.793670i | \(0.708168\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 360.000 | 0.169854 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 648.000 | 0.300262 | 0.150131 | − | 0.988666i | \(-0.452030\pi\) | ||||
0.150131 | + | 0.988666i | \(0.452030\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −433.000 | −0.197087 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1188.00 | −0.531279 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3338.00 | 1.46696 | 0.733478 | − | 0.679713i | \(-0.237896\pi\) | ||||
0.733478 | + | 0.679713i | \(0.237896\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1452.00 | 0.627205 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −900.000 | −0.382193 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3804.00 | −1.58840 | −0.794202 | − | 0.607654i | \(-0.792111\pi\) | ||||
−0.794202 | + | 0.607654i | \(0.792111\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1854.00 | 0.761363 | 0.380682 | − | 0.924706i | \(-0.375689\pi\) | ||||
0.380682 | + | 0.924706i | \(0.375689\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1398.00 | 0.564717 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −724.000 | −0.287727 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −600.000 | −0.234633 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 324.000 | 0.124696 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1344.00 | −0.509154 | −0.254577 | − | 0.967052i | \(-0.581936\pi\) | ||||
−0.254577 | + | 0.967052i | \(0.581936\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1262.00 | −0.470677 | −0.235339 | − | 0.971913i | \(-0.575620\pi\) | ||||
−0.235339 | + | 0.971913i | \(0.575620\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 252.000 | 0.0925441 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4294.00 | −1.55297 | −0.776484 | − | 0.630137i | \(-0.782999\pi\) | ||||
−0.776484 | + | 0.630137i | \(0.782999\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4308.00 | −1.53460 | −0.767302 | − | 0.641286i | \(-0.778401\pi\) | ||||
−0.767302 | + | 0.641286i | \(0.778401\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 612.000 | 0.214762 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2712.00 | −0.937661 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −188.000 | −0.0640512 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 432.000 | 0.145054 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7920.00 | 2.62123 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1212.00 | −0.395438 | −0.197719 | − | 0.980259i | \(-0.563353\pi\) | ||||
−0.197719 | + | 0.980259i | \(0.563353\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3168.00 | 1.01910 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 456.000 | 0.144646 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3024.00 | −0.946002 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −990.000 | −0.305470 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −420.000 | −0.127838 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2172.00 | −0.652233 | −0.326116 | − | 0.945330i | \(-0.605740\pi\) | ||||
−0.326116 | + | 0.945330i | \(0.605740\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1089.00 | −0.322667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3948.00 | 1.15435 | 0.577176 | − | 0.816620i | \(-0.304155\pi\) | ||||
0.577176 | + | 0.816620i | \(0.304155\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3522.00 | −1.01633 | −0.508167 | − | 0.861259i | \(-0.669677\pi\) | ||||
−0.508167 | + | 0.861259i | \(0.669677\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2160.00 | −0.615228 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2774.00 | −0.779960 | −0.389980 | − | 0.920823i | \(-0.627518\pi\) | ||||
−0.389980 | + | 0.920823i | \(0.627518\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 816.000 | 0.226511 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1836.00 | 0.503211 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2784.00 | −0.753481 | −0.376741 | − | 0.926319i | \(-0.622955\pi\) | ||||
−0.376741 | + | 0.926319i | \(0.622955\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4686.00 | −1.25250 | −0.626249 | − | 0.779623i | \(-0.715410\pi\) | ||||
−0.626249 | + | 0.779623i | \(0.715410\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −398.000 | −0.103785 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5544.00 | 1.42816 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1692.00 | 0.430627 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2484.00 | 0.624656 | 0.312328 | − | 0.949974i | \(-0.398891\pi\) | ||||
0.312328 | + | 0.949974i | \(0.398891\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2880.00 | −0.715668 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −60.0000 | −0.0147347 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6658.00 | 1.61601 | 0.808005 | − | 0.589175i | \(-0.200547\pi\) | ||||
0.808005 | + | 0.589175i | \(0.200547\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4344.00 | 1.04217 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2034.00 | 0.482381 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2904.00 | −0.680868 | −0.340434 | − | 0.940268i | \(-0.610574\pi\) | ||||
−0.340434 | + | 0.940268i | \(0.610574\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 692.000 | 0.160412 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4530.00 | 1.03832 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1006.00 | −0.228018 | −0.114009 | − | 0.993480i | \(-0.536369\pi\) | ||||
−0.114009 | + | 0.993480i | \(0.536369\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −876.000 | −0.196359 | −0.0981794 | − | 0.995169i | \(-0.531302\pi\) | ||||
−0.0981794 | + | 0.995169i | \(0.531302\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1512.00 | −0.335203 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7260.00 | 1.59198 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2718.00 | 0.589562 | 0.294781 | − | 0.955565i | \(-0.404753\pi\) | ||||
0.294781 | + | 0.955565i | \(0.404753\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2268.00 | 0.486672 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5354.00 | 1.13663 | 0.568315 | − | 0.822811i | \(-0.307596\pi\) | ||||
0.568315 | + | 0.822811i | \(0.307596\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 780.000 | 0.163838 | 0.0819191 | − | 0.996639i | \(-0.473895\pi\) | ||||
0.0819191 | + | 0.996639i | \(0.473895\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 792.000 | 0.164611 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1128.00 | 0.231999 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4813.00 | −0.979646 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1782.00 | −0.358978 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3350.00 | −0.667949 | −0.333975 | − | 0.942582i | \(-0.608390\pi\) | ||||
−0.333975 | + | 0.942582i | \(0.608390\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 600.000 | 0.118418 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1620.00 | 0.316505 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2016.00 | −0.389927 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2736.00 | −0.523922 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1662.00 | −0.315114 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −932.000 | −0.174971 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9636.00 | 1.79139 | 0.895693 | − | 0.444673i | \(-0.146680\pi\) | ||||
0.895693 | + | 0.444673i | \(0.146680\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3852.00 | 0.709167 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7560.00 | 1.37842 | 0.689209 | − | 0.724562i | \(-0.257958\pi\) | ||||
0.689209 | + | 0.724562i | \(0.257958\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3526.00 | −0.636745 | −0.318373 | − | 0.947966i | \(-0.603136\pi\) | ||||
−0.318373 | + | 0.947966i | \(0.603136\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −216.000 | −0.0386356 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7634.00 | 1.35258 | 0.676290 | − | 0.736635i | \(-0.263586\pi\) | ||||
0.676290 | + | 0.736635i | \(0.263586\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13560.0 | −2.37998 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4068.00 | −0.707332 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1320.00 | −0.227389 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5082.00 | 0.867380 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1170.00 | −0.197863 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4896.00 | −0.820441 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7572.00 | −1.25739 | −0.628693 | − | 0.777654i | \(-0.716410\pi\) | ||||
−0.628693 | + | 0.777654i | \(0.716410\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3258.00 | −0.536148 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −408.000 | −0.0665416 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 162.000 | 0.0261861 | 0.0130930 | − | 0.999914i | \(-0.495832\pi\) | ||||
0.0130930 | + | 0.999914i | \(0.495832\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2298.00 | 0.368172 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15120.0 | −2.40116 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6504.00 | 1.02386 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −288.000 | −0.0449432 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6636.00 | −1.02663 | −0.513313 | − | 0.858202i | \(-0.671582\pi\) | ||||
−0.513313 | + | 0.858202i | \(0.671582\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4430.00 | 0.679463 | 0.339731 | − | 0.940523i | \(-0.389664\pi\) | ||||
0.339731 | + | 0.940523i | \(0.389664\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1134.00 | 0.172446 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8402.00 | 1.26684 | 0.633418 | − | 0.773810i | \(-0.281651\pi\) | ||||
0.633418 | + | 0.773810i | \(0.281651\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2112.00 | −0.315756 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 360.000 | 0.0533704 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11520.0 | −1.69360 | −0.846800 | − | 0.531912i | \(-0.821474\pi\) | ||||
−0.846800 | + | 0.531912i | \(0.821474\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10565.0 | 1.54031 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6807.00 | −0.984228 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 660.000 | 0.0946465 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7404.00 | 1.05309 | 0.526547 | − | 0.850146i | \(-0.323486\pi\) | ||||
0.526547 | + | 0.850146i | \(0.323486\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −846.000 | −0.119352 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4152.00 | −0.581027 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1910.00 | 0.265137 | 0.132568 | − | 0.991174i | \(-0.457678\pi\) | ||||
0.132568 | + | 0.991174i | \(0.457678\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1476.00 | 0.203254 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9492.00 | −1.29672 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10332.0 | −1.40031 | −0.700157 | − | 0.713989i | \(-0.746887\pi\) | ||||
−0.700157 | + | 0.713989i | \(0.746887\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7164.00 | −0.963315 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6624.00 | −0.883735 | −0.441868 | − | 0.897080i | \(-0.645684\pi\) | ||||
−0.441868 | + | 0.897080i | \(0.645684\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1440.00 | 0.190621 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2052.00 | 0.269532 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10210.0 | 1.33076 | 0.665382 | − | 0.746503i | \(-0.268268\pi\) | ||||
0.665382 | + | 0.746503i | \(0.268268\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 480.000 | 0.0620835 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1188.00 | 0.152485 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1224.00 | −0.155914 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4066.00 | −0.514022 | −0.257011 | − | 0.966408i | \(-0.582738\pi\) | ||||
−0.257011 | + | 0.966408i | \(0.582738\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4752.00 | −0.596234 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5510.00 | −0.686175 | −0.343088 | − | 0.939303i | \(-0.611473\pi\) | ||||
−0.343088 | + | 0.939303i | \(0.611473\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10584.0 | −1.30825 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 162.000 | 0.0198762 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21720.0 | 2.64526 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15450.0 | 1.86786 | 0.933928 | − | 0.357460i | \(-0.116357\pi\) | ||||
0.933928 | + | 0.357460i | \(0.116357\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 330.000 | 0.0396051 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3600.00 | −0.428921 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1128.00 | −0.133425 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2196.00 | −0.257886 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3084.00 | 0.359578 | 0.179789 | − | 0.983705i | \(-0.442458\pi\) | ||||
0.179789 | + | 0.983705i | \(0.442458\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10446.0 | 1.20928 | 0.604640 | − | 0.796499i | \(-0.293317\pi\) | ||||
0.604640 | + | 0.796499i | \(0.293317\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3672.00 | 0.422077 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1210.00 | −0.138103 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5592.00 | 0.633761 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7560.00 | −0.850816 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2184.00 | 0.244083 | 0.122041 | − | 0.992525i | \(-0.461056\pi\) | ||||
0.122041 | + | 0.992525i | \(0.461056\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −110.000 | −0.0122085 | −0.00610423 | − | 0.999981i | \(-0.501943\pi\) | ||||
−0.00610423 | + | 0.999981i | \(0.501943\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1356.00 | −0.149460 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6336.00 | −0.693574 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2412.00 | 0.262229 | 0.131114 | − | 0.991367i | \(-0.458144\pi\) | ||||
0.131114 | + | 0.991367i | \(0.458144\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1791.00 | −0.193392 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6540.00 | −0.701410 | −0.350705 | − | 0.936486i | \(-0.614058\pi\) | ||||
−0.350705 | + | 0.936486i | \(0.614058\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3020.00 | −0.321712 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5802.00 | 0.613927 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9670.00 | −1.01638 | −0.508191 | − | 0.861244i | \(-0.669686\pi\) | ||||
−0.508191 | + | 0.861244i | \(0.669686\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5640.00 | 0.588863 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3276.00 | −0.339779 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1008.00 | 0.103859 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6774.00 | −0.693379 | −0.346690 | − | 0.937980i | \(-0.612694\pi\) | ||||
−0.346690 | + | 0.937980i | \(0.612694\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −270.000 | −0.0274565 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14602.0 | 1.47523 | 0.737617 | − | 0.675219i | \(-0.235951\pi\) | ||||
0.737617 | + | 0.675219i | \(0.235951\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13620.0 | 1.36712 | 0.683558 | − | 0.729896i | \(-0.260431\pi\) | ||||
0.683558 | + | 0.729896i | \(0.260431\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1512.00 | −0.150790 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8508.00 | 0.843048 | 0.421524 | − | 0.906817i | \(-0.361495\pi\) | ||||
0.421524 | + | 0.906817i | \(0.361495\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2448.00 | 0.241019 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1734.00 | 0.169636 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13680.0 | −1.32982 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15972.0 | 1.54283 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3114.00 | 0.298910 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6312.00 | −0.602093 | −0.301047 | − | 0.953609i | \(-0.597336\pi\) | ||||
−0.301047 | + | 0.953609i | \(0.597336\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15204.0 | 1.44125 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1728.00 | 0.162788 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1188.00 | 0.111225 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10572.0 | −0.983702 | −0.491851 | − | 0.870679i | \(-0.663680\pi\) | ||||
−0.491851 | + | 0.870679i | \(0.663680\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7596.00 | 0.702460 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4332.00 | 0.398168 | 0.199084 | − | 0.979982i | \(-0.436203\pi\) | ||||
0.199084 | + | 0.979982i | \(0.436203\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2260.00 | 0.206461 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1080.00 | −0.0980654 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12672.0 | 1.14370 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3684.00 | 0.330498 | 0.165249 | − | 0.986252i | \(-0.447157\pi\) | ||||
0.165249 | + | 0.986252i | \(0.447157\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1944.00 | −0.173356 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11184.0 | 0.991391 | 0.495696 | − | 0.868496i | \(-0.334913\pi\) | ||||
0.495696 | + | 0.868496i | \(0.334913\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1108.00 | 0.0976344 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1299.00 | 0.113788 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12946.0 | 1.12735 | 0.563675 | − | 0.825997i | \(-0.309387\pi\) | ||||
0.563675 | + | 0.825997i | \(0.309387\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3960.00 | −0.342818 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3564.00 | 0.306734 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2568.00 | −0.219727 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24480.0 | −2.08245 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10014.0 | −0.846948 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17150.0 | −1.44214 | −0.721070 | − | 0.692862i | \(-0.756349\pi\) | ||||
−0.721070 | + | 0.692862i | \(0.756349\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7884.00 | −0.659165 | −0.329582 | − | 0.944127i | \(-0.606908\pi\) | ||||
−0.329582 | + | 0.944127i | \(0.606908\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4356.00 | −0.362117 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2520.00 | 0.208298 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9863.00 | −0.810635 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2700.00 | 0.220659 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3948.00 | 0.320838 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2712.00 | 0.219159 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11412.0 | 0.917065 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11940.0 | 0.954160 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5910.00 | 0.469669 | 0.234834 | − | 0.972035i | \(-0.424545\pi\) | ||||
0.234834 | + | 0.972035i | \(0.424545\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5562.00 | −0.439573 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 780.000 | 0.0613056 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 972.000 | 0.0759775 | 0.0379888 | − | 0.999278i | \(-0.487905\pi\) | ||||
0.0379888 | + | 0.999278i | \(0.487905\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4194.00 | −0.326039 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29832.0 | −2.30651 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7344.00 | 0.564735 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2172.00 | 0.166119 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2458.00 | 0.186982 | 0.0934908 | − | 0.995620i | \(-0.470197\pi\) | ||||
0.0934908 | + | 0.995620i | \(0.470197\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9576.00 | −0.724547 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1800.00 | 0.135465 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11316.0 | −0.847092 | −0.423546 | − | 0.905875i | \(-0.639215\pi\) | ||||
−0.423546 | + | 0.905875i | \(0.639215\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1532.00 | −0.114074 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −972.000 | −0.0719932 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1810.00 | 0.133355 | 0.0666776 | − | 0.997775i | \(-0.478760\pi\) | ||||
0.0666776 | + | 0.997775i | \(0.478760\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10500.0 | −0.769547 | −0.384773 | − | 0.923011i | \(-0.625720\pi\) | ||||
−0.384773 | + | 0.923011i | \(0.625720\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4032.00 | 0.293960 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5808.00 | −0.421235 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19438.0 | −1.40245 | −0.701226 | − | 0.712939i | \(-0.747363\pi\) | ||||
−0.701226 | + | 0.712939i | \(0.747363\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3786.00 | 0.271746 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6768.00 | 0.483277 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20760.0 | −1.47477 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −756.000 | −0.0534303 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15084.0 | 1.06062 | 0.530309 | − | 0.847804i | \(-0.322076\pi\) | ||||
0.530309 | + | 0.847804i | \(0.322076\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −33264.0 | −2.32703 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12882.0 | 0.896607 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5794.00 | 0.401233 | 0.200616 | − | 0.979670i | \(-0.435706\pi\) | ||||
0.200616 | + | 0.979670i | \(0.435706\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −240.000 | −0.0165362 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12924.0 | 0.886004 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25152.0 | −1.71566 | −0.857832 | − | 0.513930i | \(-0.828189\pi\) | ||||
−0.857832 | + | 0.513930i | \(0.828189\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11846.0 | −0.804007 | −0.402004 | − | 0.915638i | \(-0.631686\pi\) | ||||
−0.402004 | + | 0.915638i | \(0.631686\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1836.00 | −0.123993 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4538.00 | 0.304952 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8940.00 | −0.597798 | −0.298899 | − | 0.954285i | \(-0.596619\pi\) | ||||
−0.298899 | + | 0.954285i | \(0.596619\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8136.00 | 0.541359 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17136.0 | −1.13461 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4570.00 | −0.301110 | −0.150555 | − | 0.988602i | \(-0.548106\pi\) | ||||
−0.150555 | + | 0.988602i | \(0.548106\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 564.000 | 0.0369800 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17786.0 | 1.16051 | 0.580257 | − | 0.814433i | \(-0.302952\pi\) | ||||
0.580257 | + | 0.814433i | \(0.302952\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15804.0 | 1.02620 | 0.513099 | − | 0.858330i | \(-0.328497\pi\) | ||||
0.513099 | + | 0.858330i | \(0.328497\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1296.00 | −0.0837467 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18120.0 | 1.16527 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14141.0 | 0.905024 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −23760.0 | −1.51337 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3620.00 | −0.229474 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18468.0 | 1.16513 | 0.582567 | − | 0.812783i | \(-0.302048\pi\) | ||||
0.582567 | + | 0.812783i | \(0.302048\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3636.00 | 0.228307 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4776.00 | 0.298472 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8358.00 | 0.519868 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9504.00 | −0.588376 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7814.00 | −0.481489 | −0.240744 | − | 0.970589i | \(-0.577392\pi\) | ||||
−0.240744 | + | 0.970589i | \(0.577392\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5364.00 | −0.328982 | −0.164491 | − | 0.986379i | \(-0.552598\pi\) | ||||
−0.164491 | + | 0.986379i | \(0.552598\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1368.00 | −0.0835115 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3936.00 | 0.239166 | 0.119583 | − | 0.992824i | \(-0.461844\pi\) | ||||
0.119583 | + | 0.992824i | \(0.461844\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18000.0 | −1.08869 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9072.00 | 0.546175 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7610.00 | 0.456053 | 0.228026 | − | 0.973655i | \(-0.426773\pi\) | ||||
0.228026 | + | 0.973655i | \(0.426773\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −792.000 | −0.0472458 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2970.00 | 0.176363 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13620.0 | 0.805098 | 0.402549 | − | 0.915398i | \(-0.368124\pi\) | ||||
0.402549 | + | 0.915398i | \(0.368124\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8710.00 | 0.512526 | 0.256263 | − | 0.966607i | \(-0.417509\pi\) | ||||
0.256263 | + | 0.966607i | \(0.417509\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1260.00 | 0.0738075 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3168.00 | 0.184736 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10848.0 | 0.629739 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6516.00 | 0.376567 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27960.0 | 1.60862 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12094.0 | −0.692703 | −0.346352 | − | 0.938105i | \(-0.612580\pi\) | ||||
−0.346352 | + | 0.938105i | \(0.612580\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3267.00 | 0.186292 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16466.0 | 0.934771 | 0.467385 | − | 0.884054i | \(-0.345196\pi\) | ||||
0.467385 | + | 0.884054i | \(0.345196\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7128.00 | −0.402868 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11844.0 | −0.666466 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16428.0 | −0.920351 | −0.460176 | − | 0.887828i | \(-0.652214\pi\) | ||||
−0.460176 | + | 0.887828i | \(0.652214\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −220.000 | −0.0122712 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10566.0 | 0.586780 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14532.0 | −0.803520 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13332.0 | −0.733970 | −0.366985 | − | 0.930227i | \(-0.619610\pi\) | ||||
−0.366985 | + | 0.930227i | \(0.619610\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6480.00 | 0.355202 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1464.00 | 0.0799031 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −940.000 | −0.0510833 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8322.00 | 0.450310 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19118.0 | −1.03007 | −0.515033 | − | 0.857170i | \(-0.672221\pi\) | ||||
−0.515033 | + | 0.857170i | \(0.672221\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 47784.0 | 2.56360 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2448.00 | −0.130776 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6648.00 | −0.353640 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 798.000 | 0.0422701 | 0.0211351 | − | 0.999777i | \(-0.493272\pi\) | ||||
0.0211351 | + | 0.999777i | \(0.493272\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5508.00 | −0.290529 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12096.0 | 0.635342 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5040.00 | 0.263616 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8352.00 | 0.435023 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8856.00 | 0.459351 | 0.229675 | − | 0.973267i | \(-0.426234\pi\) | ||||
0.229675 | + | 0.973267i | \(0.426234\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15408.0 | 0.795872 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14058.0 | 0.723130 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −27346.0 | −1.40083 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13764.0 | 0.702171 | 0.351086 | − | 0.936343i | \(-0.385813\pi\) | ||||
0.351086 | + | 0.936343i | \(0.385813\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2280.00 | 0.115361 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20538.0 | −1.03491 | −0.517455 | − | 0.855711i | \(-0.673120\pi\) | ||||
−0.517455 | + | 0.855711i | \(0.673120\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1194.00 | 0.0599202 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12240.0 | 0.611759 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15900.0 | −0.791463 | −0.395731 | − | 0.918366i | \(-0.629509\pi\) | ||||
−0.395731 | + | 0.918366i | \(0.629509\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16632.0 | −0.824550 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20856.0 | 1.02979 | 0.514894 | − | 0.857254i | \(-0.327831\pi\) | ||||
0.514894 | + | 0.857254i | \(0.327831\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3868.00 | −0.190218 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5076.00 | −0.248623 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16272.0 | −0.793813 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10332.0 | 0.502024 | 0.251012 | − | 0.967984i | \(-0.419237\pi\) | ||||
0.251012 | + | 0.967984i | \(0.419237\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7452.00 | −0.360645 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2184.00 | 0.105277 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13806.0 | 0.662863 | 0.331432 | − | 0.943479i | \(-0.392468\pi\) | ||||
0.331432 | + | 0.943479i | \(0.392468\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8640.00 | 0.413191 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15554.0 | 0.740909 | 0.370455 | − | 0.928851i | \(-0.379202\pi\) | ||||
0.370455 | + | 0.928851i | \(0.379202\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4680.00 | −0.222054 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 180.000 | 0.00850708 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12600.0 | −0.593168 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13106.0 | 0.614583 | 0.307292 | − | 0.951615i | \(-0.400577\pi\) | ||||
0.307292 | + | 0.951615i | \(0.400577\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19974.0 | −0.933004 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18874.0 | 0.878203 | 0.439101 | − | 0.898438i | \(-0.355297\pi\) | ||||
0.439101 | + | 0.898438i | \(0.355297\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −30492.0 | −1.41330 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13032.0 | −0.601699 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12408.0 | 0.570684 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 63360.0 | 2.90294 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6102.00 | −0.278503 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1156.00 | −0.0525598 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15444.0 | −0.699516 | −0.349758 | − | 0.936840i | \(-0.613736\pi\) | ||||
−0.349758 | + | 0.936840i | \(0.613736\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8712.00 | 0.393099 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9192.00 | 0.413186 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19572.0 | 0.876447 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2076.00 | −0.0926140 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −39286.0 | −1.74602 | −0.873012 | − | 0.487698i | \(-0.837837\pi\) | ||||
−0.873012 | + | 0.487698i | \(0.837837\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4080.00 | 0.180651 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13590.0 | −0.599474 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19800.0 | −0.870145 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1152.00 | −0.0504381 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3018.00 | 0.131646 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20018.0 | 0.869957 | 0.434979 | − | 0.900441i | \(-0.356756\pi\) | ||||
0.434979 | + | 0.900441i | \(0.356756\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8388.00 | 0.363184 | 0.181592 | − | 0.983374i | \(-0.441875\pi\) | ||||
0.181592 | + | 0.983374i | \(0.441875\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2628.00 | 0.113368 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5064.00 | −0.217649 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30096.0 | −1.28877 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4536.00 | 0.193530 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37942.0 | −1.61289 | −0.806446 | − | 0.591307i | \(-0.798612\pi\) | ||||
−0.806446 | + | 0.591307i | \(0.798612\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11628.0 | −0.492499 | −0.246249 | − | 0.969206i | \(-0.579198\pi\) | ||||
−0.246249 | + | 0.969206i | \(0.579198\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −21780.0 | −0.919130 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32388.0 | −1.36184 | −0.680920 | − | 0.732358i | \(-0.738420\pi\) | ||||
−0.680920 | + | 0.732358i | \(0.738420\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9846.00 | 0.412504 | 0.206252 | − | 0.978499i | \(-0.433873\pi\) | ||||
0.206252 | + | 0.978499i | \(0.433873\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8154.00 | −0.340384 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1990.00 | −0.0827724 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1296.00 | 0.0537125 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6804.00 | −0.280980 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16848.0 | −0.693275 | −0.346637 | − | 0.937999i | \(-0.612677\pi\) | ||||
−0.346637 | + | 0.937999i | \(0.612677\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26687.0 | 1.09422 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16062.0 | −0.656233 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −866.000 | −0.0352560 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27228.0 | −1.10456 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2340.00 | −0.0945920 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17376.0 | −0.699931 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18214.0 | 0.731108 | 0.365554 | − | 0.930790i | \(-0.380879\pi\) | ||||
0.365554 | + | 0.930790i | \(0.380879\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2376.00 | −0.0950380 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2446.00 | −0.0974956 | −0.0487478 | − | 0.998811i | \(-0.515523\pi\) | ||||
−0.0487478 | + | 0.998811i | \(0.515523\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26244.0 | 1.04241 | 0.521207 | − | 0.853430i | \(-0.325482\pi\) | ||||
0.521207 | + | 0.853430i | \(0.325482\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3384.00 | −0.133945 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25248.0 | −0.995889 | −0.497944 | − | 0.867209i | \(-0.665912\pi\) | ||||
−0.497944 | + | 0.867209i | \(0.665912\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6676.00 | 0.262417 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14439.0 | 0.565599 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 36720.0 | 1.43342 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8568.00 | 0.333313 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5346.00 | 0.207256 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5904.00 | 0.228105 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.0000 | −0.00130912 | −0.000654560 | − | 1.00000i | \(-0.500208\pi\) | ||||
−0.000654560 | 1.00000i | \(0.500208\pi\) | ||||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10050.0 | 0.385641 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19022.0 | −0.727432 | −0.363716 | − | 0.931510i | \(-0.618492\pi\) | ||||
−0.363716 | + | 0.931510i | \(0.618492\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12852.0 | −0.489812 | −0.244906 | − | 0.969547i | \(-0.578757\pi\) | ||||
−0.244906 | + | 0.969547i | \(0.578757\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1800.00 | −0.0683687 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −40104.0 | −1.51811 | −0.759053 | − | 0.651028i | \(-0.774338\pi\) | ||||
−0.759053 | + | 0.651028i | \(0.774338\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28656.0 | −1.08109 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4860.00 | −0.182734 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −53856.0 | −2.01817 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7608.00 | −0.284142 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6048.00 | 0.225125 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 56952.0 | 2.11285 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3460.00 | 0.127935 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8208.00 | 0.302486 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3708.00 | 0.136197 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42540.0 | −1.55735 | −0.778676 | − | 0.627427i | \(-0.784108\pi\) | ||||
−0.778676 | + | 0.627427i | \(0.784108\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4986.00 | 0.181931 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18528.0 | 0.673831 | 0.336915 | − | 0.941535i | \(-0.390616\pi\) | ||||
0.336915 | + | 0.941535i | \(0.390616\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33840.0 | 1.22666 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2796.00 | 0.101020 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4752.00 | 0.171129 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15756.0 | −0.565552 | −0.282776 | − | 0.959186i | \(-0.591255\pi\) | ||||
−0.282776 | + | 0.959186i | \(0.591255\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28908.0 | −1.03426 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 44352.0 | 1.58165 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 43802.0 | 1.55697 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11556.0 | −0.409438 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15542.0 | −0.548887 | −0.274444 | − | 0.961603i | \(-0.588494\pi\) | ||||
−0.274444 | + | 0.961603i | \(0.588494\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26268.0 | 0.924703 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22680.0 | −0.795831 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1200.00 | −0.0419724 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29702.0 | −1.03556 | −0.517781 | − | 0.855513i | \(-0.673242\pi\) | ||||
−0.517781 | + | 0.855513i | \(0.673242\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10578.0 | 0.367625 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2890.00 | 0.100118 | 0.0500591 | − | 0.998746i | \(-0.484059\pi\) | ||||
0.0500591 | + | 0.998746i | \(0.484059\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4512.00 | −0.155812 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 648.000 | 0.0223063 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9180.00 | −0.315005 | −0.157503 | − | 0.987519i | \(-0.550344\pi\) | ||||
−0.157503 | + | 0.987519i | \(0.550344\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13860.0 | −0.474093 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22902.0 | −0.780913 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37906.0 | 1.28845 | 0.644227 | − | 0.764835i | \(-0.277179\pi\) | ||||
0.644227 | + | 0.764835i | \(0.277179\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2688.00 | −0.0910802 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 40680.0 | 1.37408 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1320.00 | 0.0444474 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33713.0 | 1.13165 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12204.0 | 0.408378 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2524.00 | −0.0841973 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41916.0 | 1.39393 | 0.696964 | − | 0.717106i | \(-0.254534\pi\) | ||||
0.696964 | + | 0.717106i | \(0.254534\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3960.00 | 0.131283 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7764.00 | 0.256600 | 0.128300 | − | 0.991735i | \(-0.459048\pi\) | ||||
0.128300 | + | 0.991735i | \(0.459048\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8784.00 | −0.289416 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −15246.0 | −0.500782 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32666.0 | 1.06968 | 0.534840 | − | 0.844953i | \(-0.320372\pi\) | ||||
0.534840 | + | 0.844953i | \(0.320372\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 90600.0 | 2.95770 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3510.00 | 0.114236 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 53016.0 | 1.72019 | 0.860096 | − | 0.510133i | \(-0.170404\pi\) | ||||
0.860096 | + | 0.510133i | \(0.170404\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8588.00 | −0.277803 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14688.0 | 0.473682 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10944.0 | 0.351870 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17844.0 | −0.571981 | −0.285991 | − | 0.958232i | \(-0.592323\pi\) | ||||
−0.285991 | + | 0.958232i | \(0.592323\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22716.0 | 0.725952 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8616.00 | −0.274518 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −55834.0 | −1.77360 | −0.886801 | − | 0.462152i | \(-0.847077\pi\) | ||||
−0.886801 | + | 0.462152i | \(0.847077\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9774.00 | 0.309545 |
(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 | 96.4.a.b.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 288.4.a.e.1.1 | 1 | |||
4.3 | odd | 2 | 96.4.a.e.1.1 | yes | 1 | ||
5.4 | even | 2 | 2400.4.a.t.1.1 | 1 | |||
8.3 | odd | 2 | 192.4.a.d.1.1 | 1 | |||
8.5 | even | 2 | 192.4.a.j.1.1 | 1 | |||
12.11 | even | 2 | 288.4.a.f.1.1 | 1 | |||
16.3 | odd | 4 | 768.4.d.d.385.2 | 2 | |||
16.5 | even | 4 | 768.4.d.m.385.2 | 2 | |||
16.11 | odd | 4 | 768.4.d.d.385.1 | 2 | |||
16.13 | even | 4 | 768.4.d.m.385.1 | 2 | |||
20.19 | odd | 2 | 2400.4.a.c.1.1 | 1 | |||
24.5 | odd | 2 | 576.4.a.n.1.1 | 1 | |||
24.11 | even | 2 | 576.4.a.o.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.4.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
96.4.a.e.1.1 | yes | 1 | 4.3 | odd | 2 | ||
192.4.a.d.1.1 | 1 | 8.3 | odd | 2 | |||
192.4.a.j.1.1 | 1 | 8.5 | even | 2 | |||
288.4.a.e.1.1 | 1 | 3.2 | odd | 2 | |||
288.4.a.f.1.1 | 1 | 12.11 | even | 2 | |||
576.4.a.n.1.1 | 1 | 24.5 | odd | 2 | |||
576.4.a.o.1.1 | 1 | 24.11 | even | 2 | |||
768.4.d.d.385.1 | 2 | 16.11 | odd | 4 | |||
768.4.d.d.385.2 | 2 | 16.3 | odd | 4 | |||
768.4.d.m.385.1 | 2 | 16.13 | even | 4 | |||
768.4.d.m.385.2 | 2 | 16.5 | even | 4 | |||
2400.4.a.c.1.1 | 1 | 20.19 | odd | 2 | |||
2400.4.a.t.1.1 | 1 | 5.4 | even | 2 |