Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,4,Mod(1,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.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: | \(79.6525785077\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 270) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1350.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.00000 | 0.215980 | 0.107990 | − | 0.994152i | \(-0.465559\pi\) | ||||
0.107990 | + | 0.994152i | \(0.465559\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −42.0000 | −1.15123 | −0.575613 | − | 0.817723i | \(-0.695236\pi\) | ||||
−0.575613 | + | 0.817723i | \(0.695236\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −20.0000 | −0.426692 | −0.213346 | − | 0.976977i | \(-0.568436\pi\) | ||||
−0.213346 | + | 0.976977i | \(0.568436\pi\) | |||||||
\(14\) | 8.00000 | 0.152721 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 93.0000 | 1.32681 | 0.663406 | − | 0.748259i | \(-0.269110\pi\) | ||||
0.663406 | + | 0.748259i | \(0.269110\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 59.0000 | 0.712396 | 0.356198 | − | 0.934410i | \(-0.384073\pi\) | ||||
0.356198 | + | 0.934410i | \(0.384073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −84.0000 | −0.814039 | ||||||||
\(23\) | 9.00000 | 0.0815926 | 0.0407963 | − | 0.999167i | \(-0.487011\pi\) | ||||
0.0407963 | + | 0.999167i | \(0.487011\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −40.0000 | −0.301717 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 16.0000 | 0.107990 | ||||||||
\(29\) | −120.000 | −0.768395 | −0.384197 | − | 0.923251i | \(-0.625522\pi\) | ||||
−0.384197 | + | 0.923251i | \(0.625522\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 47.0000 | 0.272305 | 0.136152 | − | 0.990688i | \(-0.456526\pi\) | ||||
0.136152 | + | 0.990688i | \(0.456526\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 186.000 | 0.938198 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 262.000 | 1.16412 | 0.582061 | − | 0.813145i | \(-0.302246\pi\) | ||||
0.582061 | + | 0.813145i | \(0.302246\pi\) | |||||||
\(38\) | 118.000 | 0.503740 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −126.000 | −0.479949 | −0.239974 | − | 0.970779i | \(-0.577139\pi\) | ||||
−0.239974 | + | 0.970779i | \(0.577139\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 178.000 | 0.631273 | 0.315637 | − | 0.948880i | \(-0.397782\pi\) | ||||
0.315637 | + | 0.948880i | \(0.397782\pi\) | |||||||
\(44\) | −168.000 | −0.575613 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 18.0000 | 0.0576947 | ||||||||
\(47\) | 144.000 | 0.446906 | 0.223453 | − | 0.974715i | \(-0.428267\pi\) | ||||
0.223453 | + | 0.974715i | \(0.428267\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −327.000 | −0.953353 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −80.0000 | −0.213346 | ||||||||
\(53\) | 741.000 | 1.92046 | 0.960228 | − | 0.279217i | \(-0.0900748\pi\) | ||||
0.960228 | + | 0.279217i | \(0.0900748\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 32.0000 | 0.0763604 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −240.000 | −0.543337 | ||||||||
\(59\) | 444.000 | 0.979727 | 0.489863 | − | 0.871799i | \(-0.337047\pi\) | ||||
0.489863 | + | 0.871799i | \(0.337047\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 221.000 | 0.463871 | 0.231936 | − | 0.972731i | \(-0.425494\pi\) | ||||
0.231936 | + | 0.972731i | \(0.425494\pi\) | |||||||
\(62\) | 94.0000 | 0.192549 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 538.000 | 0.981002 | 0.490501 | − | 0.871441i | \(-0.336814\pi\) | ||||
0.490501 | + | 0.871441i | \(0.336814\pi\) | |||||||
\(68\) | 372.000 | 0.663406 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −690.000 | −1.15335 | −0.576676 | − | 0.816973i | \(-0.695650\pi\) | ||||
−0.576676 | + | 0.816973i | \(0.695650\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1126.00 | 1.80532 | 0.902660 | − | 0.430355i | \(-0.141612\pi\) | ||||
0.902660 | + | 0.430355i | \(0.141612\pi\) | |||||||
\(74\) | 524.000 | 0.823159 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 236.000 | 0.356198 | ||||||||
\(77\) | −168.000 | −0.248641 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 665.000 | 0.947068 | 0.473534 | − | 0.880776i | \(-0.342978\pi\) | ||||
0.473534 | + | 0.880776i | \(0.342978\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −252.000 | −0.339375 | ||||||||
\(83\) | 75.0000 | 0.0991846 | 0.0495923 | − | 0.998770i | \(-0.484208\pi\) | ||||
0.0495923 | + | 0.998770i | \(0.484208\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 356.000 | 0.446378 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −336.000 | −0.407020 | ||||||||
\(89\) | 1086.00 | 1.29344 | 0.646718 | − | 0.762729i | \(-0.276141\pi\) | ||||
0.646718 | + | 0.762729i | \(0.276141\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −80.0000 | −0.0921569 | ||||||||
\(92\) | 36.0000 | 0.0407963 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 288.000 | 0.316010 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1544.00 | −1.61618 | −0.808090 | − | 0.589059i | \(-0.799499\pi\) | ||||
−0.808090 | + | 0.589059i | \(0.799499\pi\) | |||||||
\(98\) | −654.000 | −0.674122 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 132.000 | 0.130044 | 0.0650222 | − | 0.997884i | \(-0.479288\pi\) | ||||
0.0650222 | + | 0.997884i | \(0.479288\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 892.000 | 0.853314 | 0.426657 | − | 0.904413i | \(-0.359691\pi\) | ||||
0.426657 | + | 0.904413i | \(0.359691\pi\) | |||||||
\(104\) | −160.000 | −0.150859 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1482.00 | 1.35797 | ||||||||
\(107\) | −1140.00 | −1.02998 | −0.514990 | − | 0.857196i | \(-0.672205\pi\) | ||||
−0.514990 | + | 0.857196i | \(0.672205\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1735.00 | −1.52461 | −0.762307 | − | 0.647216i | \(-0.775933\pi\) | ||||
−0.762307 | + | 0.647216i | \(0.775933\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 64.0000 | 0.0539949 | ||||||||
\(113\) | −1434.00 | −1.19380 | −0.596900 | − | 0.802316i | \(-0.703601\pi\) | ||||
−0.596900 | + | 0.802316i | \(0.703601\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −480.000 | −0.384197 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 888.000 | 0.692771 | ||||||||
\(119\) | 372.000 | 0.286565 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 433.000 | 0.325319 | ||||||||
\(122\) | 442.000 | 0.328007 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 188.000 | 0.136152 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −686.000 | −0.479312 | −0.239656 | − | 0.970858i | \(-0.577035\pi\) | ||||
−0.239656 | + | 0.970858i | \(0.577035\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 114.000 | 0.0760323 | 0.0380161 | − | 0.999277i | \(-0.487896\pi\) | ||||
0.0380161 | + | 0.999277i | \(0.487896\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 236.000 | 0.153863 | ||||||||
\(134\) | 1076.00 | 0.693673 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 744.000 | 0.469099 | ||||||||
\(137\) | 159.000 | 0.0991554 | 0.0495777 | − | 0.998770i | \(-0.484212\pi\) | ||||
0.0495777 | + | 0.998770i | \(0.484212\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2276.00 | 1.38883 | 0.694417 | − | 0.719573i | \(-0.255663\pi\) | ||||
0.694417 | + | 0.719573i | \(0.255663\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1380.00 | −0.815542 | ||||||||
\(143\) | 840.000 | 0.491219 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2252.00 | 1.27655 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1048.00 | 0.582061 | ||||||||
\(149\) | 1398.00 | 0.768648 | 0.384324 | − | 0.923198i | \(-0.374434\pi\) | ||||
0.384324 | + | 0.923198i | \(0.374434\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2624.00 | 1.41416 | 0.707080 | − | 0.707134i | \(-0.250012\pi\) | ||||
0.707080 | + | 0.707134i | \(0.250012\pi\) | |||||||
\(152\) | 472.000 | 0.251870 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −336.000 | −0.175816 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 394.000 | 0.200284 | 0.100142 | − | 0.994973i | \(-0.468070\pi\) | ||||
0.100142 | + | 0.994973i | \(0.468070\pi\) | |||||||
\(158\) | 1330.00 | 0.669678 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 36.0000 | 0.0176223 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3346.00 | 1.60785 | 0.803923 | − | 0.594733i | \(-0.202742\pi\) | ||||
0.803923 | + | 0.594733i | \(0.202742\pi\) | |||||||
\(164\) | −504.000 | −0.239974 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 150.000 | 0.0701341 | ||||||||
\(167\) | −1491.00 | −0.690881 | −0.345440 | − | 0.938441i | \(-0.612270\pi\) | ||||
−0.345440 | + | 0.938441i | \(0.612270\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1797.00 | −0.817934 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 712.000 | 0.315637 | ||||||||
\(173\) | 2403.00 | 1.05605 | 0.528025 | − | 0.849229i | \(-0.322933\pi\) | ||||
0.528025 | + | 0.849229i | \(0.322933\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −672.000 | −0.287806 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2172.00 | 0.914597 | ||||||||
\(179\) | 2640.00 | 1.10236 | 0.551181 | − | 0.834386i | \(-0.314177\pi\) | ||||
0.551181 | + | 0.834386i | \(0.314177\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1073.00 | 0.440638 | 0.220319 | − | 0.975428i | \(-0.429290\pi\) | ||||
0.220319 | + | 0.975428i | \(0.429290\pi\) | |||||||
\(182\) | −160.000 | −0.0651648 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 72.0000 | 0.0288473 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3906.00 | −1.52746 | ||||||||
\(188\) | 576.000 | 0.223453 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1470.00 | −0.556887 | −0.278444 | − | 0.960453i | \(-0.589819\pi\) | ||||
−0.278444 | + | 0.960453i | \(0.589819\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4720.00 | 1.76038 | 0.880189 | − | 0.474623i | \(-0.157416\pi\) | ||||
0.880189 | + | 0.474623i | \(0.157416\pi\) | |||||||
\(194\) | −3088.00 | −1.14281 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1308.00 | −0.476676 | ||||||||
\(197\) | −765.000 | −0.276670 | −0.138335 | − | 0.990385i | \(-0.544175\pi\) | ||||
−0.138335 | + | 0.990385i | \(0.544175\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 668.000 | 0.237956 | 0.118978 | − | 0.992897i | \(-0.462038\pi\) | ||||
0.118978 | + | 0.992897i | \(0.462038\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 264.000 | 0.0919553 | ||||||||
\(203\) | −480.000 | −0.165958 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1784.00 | 0.603384 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −320.000 | −0.106673 | ||||||||
\(209\) | −2478.00 | −0.820128 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4601.00 | 1.50117 | 0.750583 | − | 0.660777i | \(-0.229773\pi\) | ||||
0.750583 | + | 0.660777i | \(0.229773\pi\) | |||||||
\(212\) | 2964.00 | 0.960228 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2280.00 | −0.728307 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 188.000 | 0.0588123 | ||||||||
\(218\) | −3470.00 | −1.07806 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1860.00 | −0.566141 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2158.00 | 0.648029 | 0.324014 | − | 0.946052i | \(-0.394967\pi\) | ||||
0.324014 | + | 0.946052i | \(0.394967\pi\) | |||||||
\(224\) | 128.000 | 0.0381802 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2868.00 | −0.844144 | ||||||||
\(227\) | 3123.00 | 0.913131 | 0.456566 | − | 0.889690i | \(-0.349079\pi\) | ||||
0.456566 | + | 0.889690i | \(0.349079\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2027.00 | 0.584925 | 0.292463 | − | 0.956277i | \(-0.405525\pi\) | ||||
0.292463 | + | 0.956277i | \(0.405525\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −960.000 | −0.271668 | ||||||||
\(233\) | −438.000 | −0.123152 | −0.0615758 | − | 0.998102i | \(-0.519613\pi\) | ||||
−0.0615758 | + | 0.998102i | \(0.519613\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1776.00 | 0.489863 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 744.000 | 0.202632 | ||||||||
\(239\) | −6414.00 | −1.73593 | −0.867965 | − | 0.496626i | \(-0.834572\pi\) | ||||
−0.867965 | + | 0.496626i | \(0.834572\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3431.00 | 0.917055 | 0.458527 | − | 0.888680i | \(-0.348377\pi\) | ||||
0.458527 | + | 0.888680i | \(0.348377\pi\) | |||||||
\(242\) | 866.000 | 0.230035 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 884.000 | 0.231936 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1180.00 | −0.303974 | ||||||||
\(248\) | 376.000 | 0.0962743 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7308.00 | −1.83776 | −0.918878 | − | 0.394541i | \(-0.870904\pi\) | ||||
−0.918878 | + | 0.394541i | \(0.870904\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −378.000 | −0.0939314 | ||||||||
\(254\) | −1372.00 | −0.338925 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −3729.00 | −0.905092 | −0.452546 | − | 0.891741i | \(-0.649484\pi\) | ||||
−0.452546 | + | 0.891741i | \(0.649484\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1048.00 | 0.251427 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 228.000 | 0.0537629 | ||||||||
\(263\) | −1956.00 | −0.458601 | −0.229301 | − | 0.973356i | \(-0.573644\pi\) | ||||
−0.229301 | + | 0.973356i | \(0.573644\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 472.000 | 0.108798 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2152.00 | 0.490501 | ||||||||
\(269\) | −990.000 | −0.224392 | −0.112196 | − | 0.993686i | \(-0.535788\pi\) | ||||
−0.112196 | + | 0.993686i | \(0.535788\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8495.00 | 1.90419 | 0.952093 | − | 0.305808i | \(-0.0989266\pi\) | ||||
0.952093 | + | 0.305808i | \(0.0989266\pi\) | |||||||
\(272\) | 1488.00 | 0.331703 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 318.000 | 0.0701134 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1366.00 | 0.296300 | 0.148150 | − | 0.988965i | \(-0.452668\pi\) | ||||
0.148150 | + | 0.988965i | \(0.452668\pi\) | |||||||
\(278\) | 4552.00 | 0.982053 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5520.00 | −1.17187 | −0.585935 | − | 0.810358i | \(-0.699273\pi\) | ||||
−0.585935 | + | 0.810358i | \(0.699273\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5438.00 | −1.14225 | −0.571123 | − | 0.820865i | \(-0.693492\pi\) | ||||
−0.571123 | + | 0.820865i | \(0.693492\pi\) | |||||||
\(284\) | −2760.00 | −0.576676 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1680.00 | 0.347344 | ||||||||
\(287\) | −504.000 | −0.103659 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3736.00 | 0.760432 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4504.00 | 0.902660 | ||||||||
\(293\) | −8253.00 | −1.64555 | −0.822774 | − | 0.568369i | \(-0.807575\pi\) | ||||
−0.822774 | + | 0.568369i | \(0.807575\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2096.00 | 0.411579 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2796.00 | 0.543517 | ||||||||
\(299\) | −180.000 | −0.0348149 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 712.000 | 0.136342 | ||||||||
\(302\) | 5248.00 | 0.999962 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 944.000 | 0.178099 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9290.00 | −1.72706 | −0.863531 | − | 0.504295i | \(-0.831752\pi\) | ||||
−0.863531 | + | 0.504295i | \(0.831752\pi\) | |||||||
\(308\) | −672.000 | −0.124321 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8112.00 | 1.47907 | 0.739533 | − | 0.673121i | \(-0.235047\pi\) | ||||
0.739533 | + | 0.673121i | \(0.235047\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7900.00 | 1.42663 | 0.713314 | − | 0.700845i | \(-0.247193\pi\) | ||||
0.713314 | + | 0.700845i | \(0.247193\pi\) | |||||||
\(314\) | 788.000 | 0.141622 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2660.00 | 0.473534 | ||||||||
\(317\) | −4419.00 | −0.782952 | −0.391476 | − | 0.920188i | \(-0.628035\pi\) | ||||
−0.391476 | + | 0.920188i | \(0.628035\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5040.00 | 0.884595 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 72.0000 | 0.0124609 | ||||||||
\(323\) | 5487.00 | 0.945216 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6692.00 | 1.13692 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1008.00 | −0.169687 | ||||||||
\(329\) | 576.000 | 0.0965225 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8200.00 | −1.36167 | −0.680835 | − | 0.732437i | \(-0.738383\pi\) | ||||
−0.680835 | + | 0.732437i | \(0.738383\pi\) | |||||||
\(332\) | 300.000 | 0.0495923 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2982.00 | −0.488526 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9556.00 | 1.54465 | 0.772327 | − | 0.635225i | \(-0.219093\pi\) | ||||
0.772327 | + | 0.635225i | \(0.219093\pi\) | |||||||
\(338\) | −3594.00 | −0.578366 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1974.00 | −0.313484 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2680.00 | −0.421885 | ||||||||
\(344\) | 1424.00 | 0.223189 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4806.00 | 0.746740 | ||||||||
\(347\) | −10116.0 | −1.56500 | −0.782500 | − | 0.622650i | \(-0.786056\pi\) | ||||
−0.782500 | + | 0.622650i | \(0.786056\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6751.00 | −1.03545 | −0.517726 | − | 0.855546i | \(-0.673221\pi\) | ||||
−0.517726 | + | 0.855546i | \(0.673221\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1344.00 | −0.203510 | ||||||||
\(353\) | −4062.00 | −0.612460 | −0.306230 | − | 0.951958i | \(-0.599068\pi\) | ||||
−0.306230 | + | 0.951958i | \(0.599068\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4344.00 | 0.646718 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5280.00 | 0.779488 | ||||||||
\(359\) | 8778.00 | 1.29049 | 0.645244 | − | 0.763977i | \(-0.276756\pi\) | ||||
0.645244 | + | 0.763977i | \(0.276756\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3378.00 | −0.492492 | ||||||||
\(362\) | 2146.00 | 0.311578 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −320.000 | −0.0460785 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −956.000 | −0.135975 | −0.0679875 | − | 0.997686i | \(-0.521658\pi\) | ||||
−0.0679875 | + | 0.997686i | \(0.521658\pi\) | |||||||
\(368\) | 144.000 | 0.0203981 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2964.00 | 0.414780 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2300.00 | −0.319275 | −0.159637 | − | 0.987176i | \(-0.551032\pi\) | ||||
−0.159637 | + | 0.987176i | \(0.551032\pi\) | |||||||
\(374\) | −7812.00 | −1.08008 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1152.00 | 0.158005 | ||||||||
\(377\) | 2400.00 | 0.327868 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.0000 | 0.00393042 | 0.00196521 | − | 0.999998i | \(-0.499374\pi\) | ||||
0.00196521 | + | 0.999998i | \(0.499374\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2940.00 | −0.393779 | ||||||||
\(383\) | −8127.00 | −1.08426 | −0.542128 | − | 0.840296i | \(-0.682381\pi\) | ||||
−0.542128 | + | 0.840296i | \(0.682381\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9440.00 | 1.24478 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6176.00 | −0.808090 | ||||||||
\(389\) | −7938.00 | −1.03463 | −0.517317 | − | 0.855794i | \(-0.673069\pi\) | ||||
−0.517317 | + | 0.855794i | \(0.673069\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 837.000 | 0.108258 | ||||||||
\(392\) | −2616.00 | −0.337061 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1530.00 | −0.195635 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −272.000 | −0.0343861 | −0.0171931 | − | 0.999852i | \(-0.505473\pi\) | ||||
−0.0171931 | + | 0.999852i | \(0.505473\pi\) | |||||||
\(398\) | 1336.00 | 0.168260 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4554.00 | 0.567122 | 0.283561 | − | 0.958954i | \(-0.408484\pi\) | ||||
0.283561 | + | 0.958954i | \(0.408484\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −940.000 | −0.116190 | ||||||||
\(404\) | 528.000 | 0.0650222 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −960.000 | −0.117350 | ||||||||
\(407\) | −11004.0 | −1.34017 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1001.00 | 0.121018 | 0.0605089 | − | 0.998168i | \(-0.480728\pi\) | ||||
0.0605089 | + | 0.998168i | \(0.480728\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3568.00 | 0.426657 | ||||||||
\(413\) | 1776.00 | 0.211601 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −640.000 | −0.0754293 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4956.00 | −0.579918 | ||||||||
\(419\) | −1794.00 | −0.209171 | −0.104585 | − | 0.994516i | \(-0.533352\pi\) | ||||
−0.104585 | + | 0.994516i | \(0.533352\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16129.0 | −1.86717 | −0.933586 | − | 0.358354i | \(-0.883338\pi\) | ||||
−0.933586 | + | 0.358354i | \(0.883338\pi\) | |||||||
\(422\) | 9202.00 | 1.06148 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5928.00 | 0.678984 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 884.000 | 0.100187 | ||||||||
\(428\) | −4560.00 | −0.514990 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13356.0 | −1.49266 | −0.746329 | − | 0.665577i | \(-0.768186\pi\) | ||||
−0.746329 | + | 0.665577i | \(0.768186\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11500.0 | 1.27634 | 0.638169 | − | 0.769896i | \(-0.279692\pi\) | ||||
0.638169 | + | 0.769896i | \(0.279692\pi\) | |||||||
\(434\) | 376.000 | 0.0415866 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6940.00 | −0.762307 | ||||||||
\(437\) | 531.000 | 0.0581263 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11149.0 | −1.21210 | −0.606051 | − | 0.795426i | \(-0.707247\pi\) | ||||
−0.606051 | + | 0.795426i | \(0.707247\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3720.00 | −0.400322 | ||||||||
\(443\) | −3849.00 | −0.412803 | −0.206401 | − | 0.978467i | \(-0.566175\pi\) | ||||
−0.206401 | + | 0.978467i | \(0.566175\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4316.00 | 0.458225 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 256.000 | 0.0269975 | ||||||||
\(449\) | 18048.0 | 1.89697 | 0.948483 | − | 0.316828i | \(-0.102618\pi\) | ||||
0.948483 | + | 0.316828i | \(0.102618\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5292.00 | 0.552529 | ||||||||
\(452\) | −5736.00 | −0.596900 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6246.00 | 0.645681 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4264.00 | 0.436458 | 0.218229 | − | 0.975898i | \(-0.429972\pi\) | ||||
0.218229 | + | 0.975898i | \(0.429972\pi\) | |||||||
\(458\) | 4054.00 | 0.413605 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10242.0 | −1.03475 | −0.517373 | − | 0.855760i | \(-0.673090\pi\) | ||||
−0.517373 | + | 0.855760i | \(0.673090\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3302.00 | −0.331441 | −0.165720 | − | 0.986173i | \(-0.552995\pi\) | ||||
−0.165720 | + | 0.986173i | \(0.552995\pi\) | |||||||
\(464\) | −1920.00 | −0.192099 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −876.000 | −0.0870814 | ||||||||
\(467\) | 1923.00 | 0.190548 | 0.0952739 | − | 0.995451i | \(-0.469627\pi\) | ||||
0.0952739 | + | 0.995451i | \(0.469627\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2152.00 | 0.211877 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3552.00 | 0.346386 | ||||||||
\(473\) | −7476.00 | −0.726738 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1488.00 | 0.143282 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12828.0 | −1.22749 | ||||||||
\(479\) | 15246.0 | 1.45430 | 0.727148 | − | 0.686481i | \(-0.240846\pi\) | ||||
0.727148 | + | 0.686481i | \(0.240846\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5240.00 | −0.496722 | ||||||||
\(482\) | 6862.00 | 0.648455 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1732.00 | 0.162660 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8206.00 | 0.763551 | 0.381776 | − | 0.924255i | \(-0.375313\pi\) | ||||
0.381776 | + | 0.924255i | \(0.375313\pi\) | |||||||
\(488\) | 1768.00 | 0.164003 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16806.0 | −1.54469 | −0.772346 | − | 0.635202i | \(-0.780917\pi\) | ||||
−0.772346 | + | 0.635202i | \(0.780917\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11160.0 | −1.01952 | ||||||||
\(494\) | −2360.00 | −0.214942 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 752.000 | 0.0680762 | ||||||||
\(497\) | −2760.00 | −0.249100 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5425.00 | −0.486686 | −0.243343 | − | 0.969940i | \(-0.578244\pi\) | ||||
−0.243343 | + | 0.969940i | \(0.578244\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −14616.0 | −1.29949 | ||||||||
\(503\) | 19665.0 | 1.74318 | 0.871589 | − | 0.490236i | \(-0.163090\pi\) | ||||
0.871589 | + | 0.490236i | \(0.163090\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −756.000 | −0.0664196 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2744.00 | −0.239656 | ||||||||
\(509\) | −14724.0 | −1.28218 | −0.641090 | − | 0.767466i | \(-0.721518\pi\) | ||||
−0.641090 | + | 0.767466i | \(0.721518\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4504.00 | 0.389912 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7458.00 | −0.639997 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6048.00 | −0.514489 | ||||||||
\(518\) | 2096.00 | 0.177786 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2058.00 | 0.173057 | 0.0865284 | − | 0.996249i | \(-0.472423\pi\) | ||||
0.0865284 | + | 0.996249i | \(0.472423\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11912.0 | −0.995938 | −0.497969 | − | 0.867195i | \(-0.665921\pi\) | ||||
−0.497969 | + | 0.867195i | \(0.665921\pi\) | |||||||
\(524\) | 456.000 | 0.0380161 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3912.00 | −0.324280 | ||||||||
\(527\) | 4371.00 | 0.361297 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12086.0 | −0.993343 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 944.000 | 0.0769316 | ||||||||
\(533\) | 2520.00 | 0.204790 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4304.00 | 0.346837 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1980.00 | −0.158669 | ||||||||
\(539\) | 13734.0 | 1.09752 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5170.00 | −0.410861 | −0.205430 | − | 0.978672i | \(-0.565859\pi\) | ||||
−0.205430 | + | 0.978672i | \(0.565859\pi\) | |||||||
\(542\) | 16990.0 | 1.34646 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2976.00 | 0.234550 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4186.00 | 0.327204 | 0.163602 | − | 0.986526i | \(-0.447689\pi\) | ||||
0.163602 | + | 0.986526i | \(0.447689\pi\) | |||||||
\(548\) | 636.000 | 0.0495777 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7080.00 | −0.547401 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2660.00 | 0.204547 | ||||||||
\(554\) | 2732.00 | 0.209515 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9104.00 | 0.694417 | ||||||||
\(557\) | −13026.0 | −0.990896 | −0.495448 | − | 0.868637i | \(-0.664996\pi\) | ||||
−0.495448 | + | 0.868637i | \(0.664996\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3560.00 | −0.269359 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11040.0 | −0.828638 | ||||||||
\(563\) | 10668.0 | 0.798584 | 0.399292 | − | 0.916824i | \(-0.369256\pi\) | ||||
0.399292 | + | 0.916824i | \(0.369256\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −10876.0 | −0.807690 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5520.00 | −0.407771 | ||||||||
\(569\) | −15372.0 | −1.13256 | −0.566281 | − | 0.824212i | \(-0.691618\pi\) | ||||
−0.566281 | + | 0.824212i | \(0.691618\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14989.0 | −1.09855 | −0.549273 | − | 0.835643i | \(-0.685095\pi\) | ||||
−0.549273 | + | 0.835643i | \(0.685095\pi\) | |||||||
\(572\) | 3360.00 | 0.245610 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1008.00 | −0.0732981 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1066.00 | 0.0769119 | 0.0384559 | − | 0.999260i | \(-0.487756\pi\) | ||||
0.0384559 | + | 0.999260i | \(0.487756\pi\) | |||||||
\(578\) | 7472.00 | 0.537706 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 300.000 | 0.0214219 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −31122.0 | −2.21088 | ||||||||
\(584\) | 9008.00 | 0.638277 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16506.0 | −1.16358 | ||||||||
\(587\) | 621.000 | 0.0436651 | 0.0218325 | − | 0.999762i | \(-0.493050\pi\) | ||||
0.0218325 | + | 0.999762i | \(0.493050\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2773.00 | 0.193989 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4192.00 | 0.291031 | ||||||||
\(593\) | 20187.0 | 1.39794 | 0.698972 | − | 0.715149i | \(-0.253641\pi\) | ||||
0.698972 | + | 0.715149i | \(0.253641\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5592.00 | 0.384324 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −360.000 | −0.0246179 | ||||||||
\(599\) | −18228.0 | −1.24337 | −0.621683 | − | 0.783269i | \(-0.713551\pi\) | ||||
−0.621683 | + | 0.783269i | \(0.713551\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11743.0 | −0.797017 | −0.398508 | − | 0.917165i | \(-0.630472\pi\) | ||||
−0.398508 | + | 0.917165i | \(0.630472\pi\) | |||||||
\(602\) | 1424.00 | 0.0964085 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10496.0 | 0.707080 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24418.0 | 1.63278 | 0.816389 | − | 0.577503i | \(-0.195973\pi\) | ||||
0.816389 | + | 0.577503i | \(0.195973\pi\) | |||||||
\(608\) | 1888.00 | 0.125935 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2880.00 | −0.190691 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2672.00 | −0.176054 | −0.0880270 | − | 0.996118i | \(-0.528056\pi\) | ||||
−0.0880270 | + | 0.996118i | \(0.528056\pi\) | |||||||
\(614\) | −18580.0 | −1.22122 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1344.00 | −0.0879080 | ||||||||
\(617\) | 8601.00 | 0.561205 | 0.280602 | − | 0.959824i | \(-0.409466\pi\) | ||||
0.280602 | + | 0.959824i | \(0.409466\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21308.0 | 1.38359 | 0.691794 | − | 0.722095i | \(-0.256821\pi\) | ||||
0.691794 | + | 0.722095i | \(0.256821\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16224.0 | 1.04586 | ||||||||
\(623\) | 4344.00 | 0.279356 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 15800.0 | 1.00878 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1576.00 | 0.100142 | ||||||||
\(629\) | 24366.0 | 1.54457 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19015.0 | −1.19964 | −0.599822 | − | 0.800134i | \(-0.704762\pi\) | ||||
−0.599822 | + | 0.800134i | \(0.704762\pi\) | |||||||
\(632\) | 5320.00 | 0.334839 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8838.00 | −0.553631 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6540.00 | 0.406788 | ||||||||
\(638\) | 10080.0 | 0.625503 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4416.00 | −0.272108 | −0.136054 | − | 0.990701i | \(-0.543442\pi\) | ||||
−0.136054 | + | 0.990701i | \(0.543442\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7580.00 | −0.464893 | −0.232446 | − | 0.972609i | \(-0.574673\pi\) | ||||
−0.232446 | + | 0.972609i | \(0.574673\pi\) | |||||||
\(644\) | 144.000 | 0.00881117 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10974.0 | 0.668369 | ||||||||
\(647\) | 14901.0 | 0.905439 | 0.452719 | − | 0.891653i | \(-0.350454\pi\) | ||||
0.452719 | + | 0.891653i | \(0.350454\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18648.0 | −1.12789 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13384.0 | 0.803923 | ||||||||
\(653\) | −12915.0 | −0.773971 | −0.386985 | − | 0.922086i | \(-0.626484\pi\) | ||||
−0.386985 | + | 0.922086i | \(0.626484\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2016.00 | −0.119987 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1152.00 | 0.0682517 | ||||||||
\(659\) | 28128.0 | 1.66269 | 0.831344 | − | 0.555758i | \(-0.187572\pi\) | ||||
0.831344 | + | 0.555758i | \(0.187572\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8362.00 | −0.492049 | −0.246024 | − | 0.969264i | \(-0.579124\pi\) | ||||
−0.246024 | + | 0.969264i | \(0.579124\pi\) | |||||||
\(662\) | −16400.0 | −0.962846 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 600.000 | 0.0350670 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1080.00 | −0.0626953 | ||||||||
\(668\) | −5964.00 | −0.345440 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9282.00 | −0.534020 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29708.0 | −1.70157 | −0.850787 | − | 0.525511i | \(-0.823874\pi\) | ||||
−0.850787 | + | 0.525511i | \(0.823874\pi\) | |||||||
\(674\) | 19112.0 | 1.09224 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7188.00 | −0.408967 | ||||||||
\(677\) | −6762.00 | −0.383877 | −0.191939 | − | 0.981407i | \(-0.561477\pi\) | ||||
−0.191939 | + | 0.981407i | \(0.561477\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6176.00 | −0.349062 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3948.00 | −0.221667 | ||||||||
\(683\) | 19155.0 | 1.07313 | 0.536563 | − | 0.843860i | \(-0.319722\pi\) | ||||
0.536563 | + | 0.843860i | \(0.319722\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5360.00 | −0.298317 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2848.00 | 0.157818 | ||||||||
\(689\) | −14820.0 | −0.819444 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22975.0 | −1.26485 | −0.632424 | − | 0.774622i | \(-0.717940\pi\) | ||||
−0.632424 | + | 0.774622i | \(0.717940\pi\) | |||||||
\(692\) | 9612.00 | 0.528025 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20232.0 | −1.10662 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11718.0 | −0.636802 | ||||||||
\(698\) | −13502.0 | −0.732175 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6450.00 | −0.347522 | −0.173761 | − | 0.984788i | \(-0.555592\pi\) | ||||
−0.173761 | + | 0.984788i | \(0.555592\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15458.0 | 0.829317 | ||||||||
\(704\) | −2688.00 | −0.143903 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8124.00 | −0.433075 | ||||||||
\(707\) | 528.000 | 0.0280870 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34538.0 | 1.82948 | 0.914740 | − | 0.404042i | \(-0.132395\pi\) | ||||
0.914740 | + | 0.404042i | \(0.132395\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8688.00 | 0.457299 | ||||||||
\(713\) | 423.000 | 0.0222181 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10560.0 | 0.551181 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 17556.0 | 0.912513 | ||||||||
\(719\) | 27114.0 | 1.40637 | 0.703186 | − | 0.711006i | \(-0.251760\pi\) | ||||
0.703186 | + | 0.711006i | \(0.251760\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3568.00 | 0.184299 | ||||||||
\(722\) | −6756.00 | −0.348244 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4292.00 | 0.220319 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −236.000 | −0.0120396 | −0.00601978 | − | 0.999982i | \(-0.501916\pi\) | ||||
−0.00601978 | + | 0.999982i | \(0.501916\pi\) | |||||||
\(728\) | −640.000 | −0.0325824 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16554.0 | 0.837581 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27128.0 | −1.36698 | −0.683489 | − | 0.729960i | \(-0.739538\pi\) | ||||
−0.683489 | + | 0.729960i | \(0.739538\pi\) | |||||||
\(734\) | −1912.00 | −0.0961488 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 288.000 | 0.0144237 | ||||||||
\(737\) | −22596.0 | −1.12935 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5249.00 | 0.261282 | 0.130641 | − | 0.991430i | \(-0.458296\pi\) | ||||
0.130641 | + | 0.991430i | \(0.458296\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5928.00 | 0.293293 | ||||||||
\(743\) | −13896.0 | −0.686130 | −0.343065 | − | 0.939312i | \(-0.611465\pi\) | ||||
−0.343065 | + | 0.939312i | \(0.611465\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4600.00 | −0.225761 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −15624.0 | −0.763730 | ||||||||
\(749\) | −4560.00 | −0.222455 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27665.0 | 1.34422 | 0.672111 | − | 0.740451i | \(-0.265388\pi\) | ||||
0.672111 | + | 0.740451i | \(0.265388\pi\) | |||||||
\(752\) | 2304.00 | 0.111726 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4800.00 | 0.231838 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8122.00 | 0.389959 | 0.194980 | − | 0.980807i | \(-0.437536\pi\) | ||||
0.194980 | + | 0.980807i | \(0.437536\pi\) | |||||||
\(758\) | 58.0000 | 0.00277923 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10584.0 | 0.504165 | 0.252083 | − | 0.967706i | \(-0.418885\pi\) | ||||
0.252083 | + | 0.967706i | \(0.418885\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6940.00 | −0.329286 | ||||||||
\(764\) | −5880.00 | −0.278444 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16254.0 | −0.766685 | ||||||||
\(767\) | −8880.00 | −0.418042 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18619.0 | −0.873106 | −0.436553 | − | 0.899679i | \(-0.643801\pi\) | ||||
−0.436553 | + | 0.899679i | \(0.643801\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 18880.0 | 0.880189 | ||||||||
\(773\) | −22251.0 | −1.03533 | −0.517667 | − | 0.855582i | \(-0.673199\pi\) | ||||
−0.517667 | + | 0.855582i | \(0.673199\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −12352.0 | −0.571406 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15876.0 | −0.731597 | ||||||||
\(779\) | −7434.00 | −0.341914 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28980.0 | 1.32777 | ||||||||
\(782\) | 1674.00 | 0.0765500 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5232.00 | −0.238338 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24854.0 | −1.12573 | −0.562865 | − | 0.826549i | \(-0.690301\pi\) | ||||
−0.562865 | + | 0.826549i | \(0.690301\pi\) | |||||||
\(788\) | −3060.00 | −0.138335 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5736.00 | −0.257837 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4420.00 | −0.197930 | ||||||||
\(794\) | −544.000 | −0.0243147 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2672.00 | 0.118978 | ||||||||
\(797\) | −3681.00 | −0.163598 | −0.0817991 | − | 0.996649i | \(-0.526067\pi\) | ||||
−0.0817991 | + | 0.996649i | \(0.526067\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13392.0 | 0.592960 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9108.00 | 0.401016 | ||||||||
\(803\) | −47292.0 | −2.07833 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1880.00 | −0.0821590 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1056.00 | 0.0459777 | ||||||||
\(809\) | −5142.00 | −0.223465 | −0.111732 | − | 0.993738i | \(-0.535640\pi\) | ||||
−0.111732 | + | 0.993738i | \(0.535640\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18484.0 | −0.800322 | −0.400161 | − | 0.916445i | \(-0.631046\pi\) | ||||
−0.400161 | + | 0.916445i | \(0.631046\pi\) | |||||||
\(812\) | −1920.00 | −0.0829788 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −22008.0 | −0.947641 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10502.0 | 0.449717 | ||||||||
\(818\) | 2002.00 | 0.0855725 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25014.0 | 1.06333 | 0.531665 | − | 0.846954i | \(-0.321566\pi\) | ||||
0.531665 | + | 0.846954i | \(0.321566\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32146.0 | 1.36153 | 0.680765 | − | 0.732502i | \(-0.261648\pi\) | ||||
0.680765 | + | 0.732502i | \(0.261648\pi\) | |||||||
\(824\) | 7136.00 | 0.301692 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3552.00 | 0.149625 | ||||||||
\(827\) | 10977.0 | 0.461557 | 0.230779 | − | 0.973006i | \(-0.425873\pi\) | ||||
0.230779 | + | 0.973006i | \(0.425873\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36602.0 | 1.53346 | 0.766731 | − | 0.641969i | \(-0.221882\pi\) | ||||
0.766731 | + | 0.641969i | \(0.221882\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1280.00 | −0.0533366 | ||||||||
\(833\) | −30411.0 | −1.26492 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −9912.00 | −0.410064 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3588.00 | −0.147906 | ||||||||
\(839\) | 11076.0 | 0.455764 | 0.227882 | − | 0.973689i | \(-0.426820\pi\) | ||||
0.227882 | + | 0.973689i | \(0.426820\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9989.00 | −0.409570 | ||||||||
\(842\) | −32258.0 | −1.32029 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18404.0 | 0.750583 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1732.00 | 0.0702624 | ||||||||
\(848\) | 11856.0 | 0.480114 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2358.00 | 0.0949838 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36848.0 | −1.47908 | −0.739538 | − | 0.673115i | \(-0.764956\pi\) | ||||
−0.739538 | + | 0.673115i | \(0.764956\pi\) | |||||||
\(854\) | 1768.00 | 0.0708428 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9120.00 | −0.364153 | ||||||||
\(857\) | 26961.0 | 1.07464 | 0.537322 | − | 0.843377i | \(-0.319436\pi\) | ||||
0.537322 | + | 0.843377i | \(0.319436\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −415.000 | −0.0164838 | −0.00824192 | − | 0.999966i | \(-0.502624\pi\) | ||||
−0.00824192 | + | 0.999966i | \(0.502624\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −26712.0 | −1.05547 | ||||||||
\(863\) | 45501.0 | 1.79475 | 0.897377 | − | 0.441265i | \(-0.145470\pi\) | ||||
0.897377 | + | 0.441265i | \(0.145470\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 23000.0 | 0.902508 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 752.000 | 0.0294062 | ||||||||
\(869\) | −27930.0 | −1.09029 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10760.0 | −0.418586 | ||||||||
\(872\) | −13880.0 | −0.539032 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1062.00 | 0.0411015 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35042.0 | −1.34924 | −0.674620 | − | 0.738165i | \(-0.735693\pi\) | ||||
−0.674620 | + | 0.738165i | \(0.735693\pi\) | |||||||
\(878\) | −22298.0 | −0.857085 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1080.00 | 0.0413009 | 0.0206505 | − | 0.999787i | \(-0.493426\pi\) | ||||
0.0206505 | + | 0.999787i | \(0.493426\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20164.0 | 0.768485 | 0.384243 | − | 0.923232i | \(-0.374463\pi\) | ||||
0.384243 | + | 0.923232i | \(0.374463\pi\) | |||||||
\(884\) | −7440.00 | −0.283070 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7698.00 | −0.291895 | ||||||||
\(887\) | −20067.0 | −0.759621 | −0.379811 | − | 0.925064i | \(-0.624011\pi\) | ||||
−0.379811 | + | 0.925064i | \(0.624011\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2744.00 | −0.103522 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8632.00 | 0.324014 | ||||||||
\(893\) | 8496.00 | 0.318374 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 512.000 | 0.0190901 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 36096.0 | 1.34136 | ||||||||
\(899\) | −5640.00 | −0.209238 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 68913.0 | 2.54809 | ||||||||
\(902\) | 10584.0 | 0.390697 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11472.0 | −0.422072 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26524.0 | 0.971020 | 0.485510 | − | 0.874231i | \(-0.338634\pi\) | ||||
0.485510 | + | 0.874231i | \(0.338634\pi\) | |||||||
\(908\) | 12492.0 | 0.456566 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35568.0 | 1.29355 | 0.646773 | − | 0.762683i | \(-0.276118\pi\) | ||||
0.646773 | + | 0.762683i | \(0.276118\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3150.00 | −0.114184 | ||||||||
\(914\) | 8528.00 | 0.308623 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8108.00 | 0.292463 | ||||||||
\(917\) | 456.000 | 0.0164214 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23704.0 | −0.850841 | −0.425420 | − | 0.904996i | \(-0.639874\pi\) | ||||
−0.425420 | + | 0.904996i | \(0.639874\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −20484.0 | −0.731675 | ||||||||
\(923\) | 13800.0 | 0.492126 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −6604.00 | −0.234364 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3840.00 | −0.135834 | ||||||||
\(929\) | −40590.0 | −1.43349 | −0.716746 | − | 0.697334i | \(-0.754369\pi\) | ||||
−0.716746 | + | 0.697334i | \(0.754369\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19293.0 | −0.679165 | ||||||||
\(932\) | −1752.00 | −0.0615758 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3846.00 | 0.134738 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12964.0 | 0.451991 | 0.225995 | − | 0.974128i | \(-0.427437\pi\) | ||||
0.225995 | + | 0.974128i | \(0.427437\pi\) | |||||||
\(938\) | 4304.00 | 0.149819 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29922.0 | 1.03659 | 0.518294 | − | 0.855203i | \(-0.326567\pi\) | ||||
0.518294 | + | 0.855203i | \(0.326567\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1134.00 | −0.0391603 | ||||||||
\(944\) | 7104.00 | 0.244932 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14952.0 | −0.513881 | ||||||||
\(947\) | −5241.00 | −0.179841 | −0.0899206 | − | 0.995949i | \(-0.528661\pi\) | ||||
−0.0899206 | + | 0.995949i | \(0.528661\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22520.0 | −0.770316 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2976.00 | 0.101316 | ||||||||
\(953\) | −26214.0 | −0.891033 | −0.445517 | − | 0.895274i | \(-0.646980\pi\) | ||||
−0.445517 | + | 0.895274i | \(0.646980\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −25656.0 | −0.867965 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 30492.0 | 1.02834 | ||||||||
\(959\) | 636.000 | 0.0214155 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27582.0 | −0.925850 | ||||||||
\(962\) | −10480.0 | −0.351236 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13724.0 | 0.458527 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18278.0 | −0.607840 | −0.303920 | − | 0.952698i | \(-0.598295\pi\) | ||||
−0.303920 | + | 0.952698i | \(0.598295\pi\) | |||||||
\(968\) | 3464.00 | 0.115018 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24942.0 | −0.824333 | −0.412166 | − | 0.911109i | \(-0.635228\pi\) | ||||
−0.412166 | + | 0.911109i | \(0.635228\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9104.00 | 0.299960 | ||||||||
\(974\) | 16412.0 | 0.539912 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3536.00 | 0.115968 | ||||||||
\(977\) | 11226.0 | 0.367607 | 0.183803 | − | 0.982963i | \(-0.441159\pi\) | ||||
0.183803 | + | 0.982963i | \(0.441159\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −45612.0 | −1.48904 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −33612.0 | −1.09226 | ||||||||
\(983\) | 23073.0 | 0.748641 | 0.374321 | − | 0.927299i | \(-0.377876\pi\) | ||||
0.374321 | + | 0.927299i | \(0.377876\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −22320.0 | −0.720906 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4720.00 | −0.151987 | ||||||||
\(989\) | 1602.00 | 0.0515072 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22037.0 | 0.706386 | 0.353193 | − | 0.935551i | \(-0.385096\pi\) | ||||
0.353193 | + | 0.935551i | \(0.385096\pi\) | |||||||
\(992\) | 1504.00 | 0.0481371 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5520.00 | −0.176141 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19082.0 | −0.606151 | −0.303076 | − | 0.952966i | \(-0.598014\pi\) | ||||
−0.303076 | + | 0.952966i | \(0.598014\pi\) | |||||||
\(998\) | −10850.0 | −0.344139 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1350.4.a.u.1.1 | 1 | ||
3.2 | odd | 2 | 1350.4.a.g.1.1 | 1 | |||
5.2 | odd | 4 | 1350.4.c.d.649.2 | 2 | |||
5.3 | odd | 4 | 1350.4.c.d.649.1 | 2 | |||
5.4 | even | 2 | 270.4.a.e.1.1 | ✓ | 1 | ||
15.2 | even | 4 | 1350.4.c.q.649.1 | 2 | |||
15.8 | even | 4 | 1350.4.c.q.649.2 | 2 | |||
15.14 | odd | 2 | 270.4.a.i.1.1 | yes | 1 | ||
20.19 | odd | 2 | 2160.4.a.o.1.1 | 1 | |||
45.4 | even | 6 | 810.4.e.q.541.1 | 2 | |||
45.14 | odd | 6 | 810.4.e.h.541.1 | 2 | |||
45.29 | odd | 6 | 810.4.e.h.271.1 | 2 | |||
45.34 | even | 6 | 810.4.e.q.271.1 | 2 | |||
60.59 | even | 2 | 2160.4.a.e.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
270.4.a.e.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
270.4.a.i.1.1 | yes | 1 | 15.14 | odd | 2 | ||
810.4.e.h.271.1 | 2 | 45.29 | odd | 6 | |||
810.4.e.h.541.1 | 2 | 45.14 | odd | 6 | |||
810.4.e.q.271.1 | 2 | 45.34 | even | 6 | |||
810.4.e.q.541.1 | 2 | 45.4 | even | 6 | |||
1350.4.a.g.1.1 | 1 | 3.2 | odd | 2 | |||
1350.4.a.u.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1350.4.c.d.649.1 | 2 | 5.3 | odd | 4 | |||
1350.4.c.d.649.2 | 2 | 5.2 | odd | 4 | |||
1350.4.c.q.649.1 | 2 | 15.2 | even | 4 | |||
1350.4.c.q.649.2 | 2 | 15.8 | even | 4 | |||
2160.4.a.e.1.1 | 1 | 60.59 | even | 2 | |||
2160.4.a.o.1.1 | 1 | 20.19 | odd | 2 |