Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [528,4,Mod(1,528)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(528, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("528.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 528 = 2^{4} \cdot 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 528.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: | \(31.1530084830\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 132) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 528.1 |
$q$-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 | ||||||||
\(5\) | 10.0000 | 0.894427 | 0.447214 | − | 0.894427i | \(-0.352416\pi\) | ||||
0.447214 | + | 0.894427i | \(0.352416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.00000 | −0.431959 | −0.215980 | − | 0.976398i | \(-0.569295\pi\) | ||||
−0.215980 | + | 0.976398i | \(0.569295\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 18.0000 | 0.384023 | 0.192012 | − | 0.981393i | \(-0.438499\pi\) | ||||
0.192012 | + | 0.981393i | \(0.438499\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −30.0000 | −0.516398 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 46.0000 | 0.656273 | 0.328136 | − | 0.944630i | \(-0.393579\pi\) | ||||
0.328136 | + | 0.944630i | \(0.393579\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −40.0000 | −0.482980 | −0.241490 | − | 0.970403i | \(-0.577636\pi\) | ||||
−0.241490 | + | 0.970403i | \(0.577636\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 24.0000 | 0.249392 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −44.0000 | −0.398897 | −0.199449 | − | 0.979908i | \(-0.563915\pi\) | ||||
−0.199449 | + | 0.979908i | \(0.563915\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −25.0000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 186.000 | 1.19101 | 0.595506 | − | 0.803351i | \(-0.296952\pi\) | ||||
0.595506 | + | 0.803351i | \(0.296952\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 72.0000 | 0.417148 | 0.208574 | − | 0.978007i | \(-0.433118\pi\) | ||||
0.208574 | + | 0.978007i | \(0.433118\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −33.0000 | −0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −80.0000 | −0.386356 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −114.000 | −0.506527 | −0.253263 | − | 0.967397i | \(-0.581504\pi\) | ||||
−0.253263 | + | 0.967397i | \(0.581504\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −54.0000 | −0.221716 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 174.000 | 0.662786 | 0.331393 | − | 0.943493i | \(-0.392481\pi\) | ||||
0.331393 | + | 0.943493i | \(0.392481\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 416.000 | 1.47534 | 0.737668 | − | 0.675164i | \(-0.235927\pi\) | ||||
0.737668 | + | 0.675164i | \(0.235927\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 90.0000 | 0.298142 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 156.000 | 0.484148 | 0.242074 | − | 0.970258i | \(-0.422172\pi\) | ||||
0.242074 | + | 0.970258i | \(0.422172\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −279.000 | −0.813411 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −138.000 | −0.378899 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −62.0000 | −0.160686 | −0.0803430 | − | 0.996767i | \(-0.525602\pi\) | ||||
−0.0803430 | + | 0.996767i | \(0.525602\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 110.000 | 0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 120.000 | 0.278849 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 348.000 | 0.767894 | 0.383947 | − | 0.923355i | \(-0.374565\pi\) | ||||
0.383947 | + | 0.923355i | \(0.374565\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −446.000 | −0.936138 | −0.468069 | − | 0.883692i | \(-0.655050\pi\) | ||||
−0.468069 | + | 0.883692i | \(0.655050\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −72.0000 | −0.143986 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 180.000 | 0.343481 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 956.000 | 1.74319 | 0.871597 | − | 0.490223i | \(-0.163085\pi\) | ||||
0.871597 | + | 0.490223i | \(0.163085\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 132.000 | 0.230303 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 444.000 | 0.742156 | 0.371078 | − | 0.928602i | \(-0.378988\pi\) | ||||
0.371078 | + | 0.928602i | \(0.378988\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 306.000 | 0.490611 | 0.245305 | − | 0.969446i | \(-0.421112\pi\) | ||||
0.245305 | + | 0.969446i | \(0.421112\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 75.0000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −88.0000 | −0.130241 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 664.000 | 0.945644 | 0.472822 | − | 0.881158i | \(-0.343235\pi\) | ||||
0.472822 | + | 0.881158i | \(0.343235\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 124.000 | 0.163985 | 0.0819926 | − | 0.996633i | \(-0.473872\pi\) | ||||
0.0819926 | + | 0.996633i | \(0.473872\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 460.000 | 0.586988 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −558.000 | −0.687631 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 602.000 | 0.716987 | 0.358494 | − | 0.933532i | \(-0.383290\pi\) | ||||
0.358494 | + | 0.933532i | \(0.383290\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −144.000 | −0.165882 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −216.000 | −0.240840 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −400.000 | −0.431991 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1522.00 | 1.59315 | 0.796576 | − | 0.604539i | \(-0.206643\pi\) | ||||
0.796576 | + | 0.604539i | \(0.206643\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 99.0000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1090.00 | 1.07385 | 0.536926 | − | 0.843629i | \(-0.319585\pi\) | ||||
0.536926 | + | 0.843629i | \(0.319585\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1392.00 | 1.33163 | 0.665815 | − | 0.746117i | \(-0.268084\pi\) | ||||
0.665815 | + | 0.746117i | \(0.268084\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 240.000 | 0.223063 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −308.000 | −0.278276 | −0.139138 | − | 0.990273i | \(-0.544433\pi\) | ||||
−0.139138 | + | 0.990273i | \(0.544433\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 978.000 | 0.859407 | 0.429704 | − | 0.902970i | \(-0.358618\pi\) | ||||
0.429704 | + | 0.902970i | \(0.358618\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 342.000 | 0.292443 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1162.00 | 0.967361 | 0.483680 | − | 0.875245i | \(-0.339300\pi\) | ||||
0.483680 | + | 0.875245i | \(0.339300\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −440.000 | −0.356784 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 162.000 | 0.128008 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −368.000 | −0.283483 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −522.000 | −0.382660 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1500.00 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 984.000 | 0.687527 | 0.343763 | − | 0.939056i | \(-0.388298\pi\) | ||||
0.343763 | + | 0.939056i | \(0.388298\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1248.00 | −0.851785 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2012.00 | −1.34190 | −0.670951 | − | 0.741501i | \(-0.734114\pi\) | ||||
−0.670951 | + | 0.741501i | \(0.734114\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 320.000 | 0.208628 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −270.000 | −0.172133 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1286.00 | −0.801974 | −0.400987 | − | 0.916084i | \(-0.631333\pi\) | ||||
−0.400987 | + | 0.916084i | \(0.631333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −464.000 | −0.283136 | −0.141568 | − | 0.989929i | \(-0.545214\pi\) | ||||
−0.141568 | + | 0.989929i | \(0.545214\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −468.000 | −0.279523 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 198.000 | 0.115787 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1860.00 | 1.06527 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 837.000 | 0.469623 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2894.00 | −1.59118 | −0.795590 | − | 0.605836i | \(-0.792839\pi\) | ||||
−0.795590 | + | 0.605836i | \(0.792839\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −976.000 | −0.525998 | −0.262999 | − | 0.964796i | \(-0.584712\pi\) | ||||
−0.262999 | + | 0.964796i | \(0.584712\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 414.000 | 0.218758 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 720.000 | 0.373108 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1646.00 | 0.836720 | 0.418360 | − | 0.908281i | \(-0.362605\pi\) | ||||
0.418360 | + | 0.908281i | \(0.362605\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 186.000 | 0.0927721 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 352.000 | 0.172307 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3268.00 | −1.57037 | −0.785183 | − | 0.619264i | \(-0.787431\pi\) | ||||
−0.785183 | + | 0.619264i | \(0.787431\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −330.000 | −0.155700 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1608.00 | −0.745094 | −0.372547 | − | 0.928013i | \(-0.621516\pi\) | ||||
−0.372547 | + | 0.928013i | \(0.621516\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1873.00 | −0.852526 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −360.000 | −0.160993 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4070.00 | −1.78865 | −0.894325 | − | 0.447418i | \(-0.852343\pi\) | ||||
−0.894325 | + | 0.447418i | \(0.852343\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 200.000 | 0.0863919 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1044.00 | −0.443344 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −52.0000 | −0.0217132 | −0.0108566 | − | 0.999941i | \(-0.503456\pi\) | ||||
−0.0108566 | + | 0.999941i | \(0.503456\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1798.00 | 0.738366 | 0.369183 | − | 0.929357i | \(-0.379638\pi\) | ||||
0.369183 | + | 0.929357i | \(0.379638\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1338.00 | 0.540480 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1140.00 | −0.453051 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 506.000 | 0.197874 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 216.000 | 0.0831306 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3852.00 | 1.45927 | 0.729636 | − | 0.683836i | \(-0.239690\pi\) | ||||
0.729636 | + | 0.683836i | \(0.239690\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1958.00 | −0.730259 | −0.365129 | − | 0.930957i | \(-0.618975\pi\) | ||||
−0.365129 | + | 0.930957i | \(0.618975\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −540.000 | −0.198309 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1630.00 | −0.589506 | −0.294753 | − | 0.955573i | \(-0.595237\pi\) | ||||
−0.294753 | + | 0.955573i | \(0.595237\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4504.00 | 1.60442 | 0.802211 | − | 0.597040i | \(-0.203657\pi\) | ||||
0.802211 | + | 0.597040i | \(0.203657\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2868.00 | −1.00643 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1488.00 | −0.514469 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1740.00 | 0.592814 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −396.000 | −0.132966 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −440.000 | −0.145624 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3776.00 | −1.23199 | −0.615997 | − | 0.787749i | \(-0.711246\pi\) | ||||
−0.615997 | + | 0.787749i | \(0.711246\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1332.00 | −0.428484 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4160.00 | 1.31958 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −576.000 | −0.180191 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −918.000 | −0.283254 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 828.000 | 0.252024 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1728.00 | 0.518903 | 0.259452 | − | 0.965756i | \(-0.416458\pi\) | ||||
0.259452 | + | 0.965756i | \(0.416458\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −225.000 | −0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4716.00 | −1.37891 | −0.689454 | − | 0.724330i | \(-0.742149\pi\) | ||||
−0.689454 | + | 0.724330i | \(0.742149\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1766.00 | 0.509609 | 0.254805 | − | 0.966993i | \(-0.417989\pi\) | ||||
0.254805 | + | 0.966993i | \(0.417989\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 264.000 | 0.0751945 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4382.00 | 1.23208 | 0.616039 | − | 0.787715i | \(-0.288736\pi\) | ||||
0.616039 | + | 0.787715i | \(0.288736\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1560.00 | 0.433035 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1992.00 | −0.545968 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1264.00 | −0.342098 | −0.171049 | − | 0.985263i | \(-0.554716\pi\) | ||||
−0.171049 | + | 0.985263i | \(0.554716\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3010.00 | 0.804528 | 0.402264 | − | 0.915524i | \(-0.368223\pi\) | ||||
0.402264 | + | 0.915524i | \(0.368223\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2790.00 | −0.727537 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −720.000 | −0.185476 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −372.000 | −0.0946769 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5404.00 | −1.35895 | −0.679477 | − | 0.733697i | \(-0.737793\pi\) | ||||
−0.679477 | + | 0.733697i | \(0.737793\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −484.000 | −0.120272 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1380.00 | −0.338898 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1618.00 | 0.392716 | 0.196358 | − | 0.980532i | \(-0.437088\pi\) | ||||
0.196358 | + | 0.980532i | \(0.437088\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 912.000 | 0.218799 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1674.00 | 0.397004 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −48.0000 | −0.0112540 | −0.00562701 | − | 0.999984i | \(-0.501791\pi\) | ||||
−0.00562701 | + | 0.999984i | \(0.501791\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −620.000 | −0.143722 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1806.00 | −0.413953 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1814.00 | −0.411158 | −0.205579 | − | 0.978641i | \(-0.565908\pi\) | ||||
−0.205579 | + | 0.978641i | \(0.565908\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1016.00 | −0.227740 | −0.113870 | − | 0.993496i | \(-0.536325\pi\) | ||||
−0.113870 | + | 0.993496i | \(0.536325\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 432.000 | 0.0957723 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −275.000 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6914.00 | 1.49972 | 0.749859 | − | 0.661597i | \(-0.230121\pi\) | ||||
0.749859 | + | 0.661597i | \(0.230121\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 648.000 | 0.139049 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6098.00 | −1.29458 | −0.647289 | − | 0.762245i | \(-0.724097\pi\) | ||||
−0.647289 | + | 0.762245i | \(0.724097\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4192.00 | −0.880525 | −0.440262 | − | 0.897869i | \(-0.645115\pi\) | ||||
−0.440262 | + | 0.897869i | \(0.645115\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1200.00 | 0.249410 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1392.00 | −0.286297 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2797.00 | −0.569306 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4566.00 | −0.919806 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9314.00 | 1.85710 | 0.928549 | − | 0.371210i | \(-0.121057\pi\) | ||||
0.928549 | + | 0.371210i | \(0.121057\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3480.00 | 0.686825 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −297.000 | −0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −792.000 | −0.153186 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3328.00 | −0.637285 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3270.00 | −0.619989 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4460.00 | −0.837308 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1384.00 | −0.257293 | −0.128647 | − | 0.991690i | \(-0.541063\pi\) | ||||
−0.128647 | + | 0.991690i | \(0.541063\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4176.00 | −0.768817 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7916.00 | −1.44333 | −0.721664 | − | 0.692243i | \(-0.756623\pi\) | ||||
−0.721664 | + | 0.692243i | \(0.756623\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 218.000 | 0.0393677 | 0.0196838 | − | 0.999806i | \(-0.493734\pi\) | ||||
0.0196838 | + | 0.999806i | \(0.493734\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −720.000 | −0.128785 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 666.000 | 0.118001 | 0.0590005 | − | 0.998258i | \(-0.481209\pi\) | ||||
0.0590005 | + | 0.998258i | \(0.481209\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2046.00 | 0.359103 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 924.000 | 0.160662 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1840.00 | −0.316967 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −450.000 | −0.0768046 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2934.00 | −0.496179 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1248.00 | −0.209132 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2500.00 | 0.415143 | 0.207572 | − | 0.978220i | \(-0.433444\pi\) | ||||
0.207572 | + | 0.978220i | \(0.433444\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1026.00 | −0.168842 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9560.00 | 1.55916 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6678.00 | −1.07945 | −0.539724 | − | 0.841842i | \(-0.681471\pi\) | ||||
−0.539724 | + | 0.841842i | \(0.681471\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3486.00 | −0.558506 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 792.000 | 0.125775 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4976.00 | 0.783320 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1320.00 | 0.205990 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1892.00 | 0.292703 | 0.146351 | − | 0.989233i | \(-0.453247\pi\) | ||||
0.146351 | + | 0.989233i | \(0.453247\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7350.00 | −1.12733 | −0.563663 | − | 0.826005i | \(-0.690608\pi\) | ||||
−0.563663 | + | 0.826005i | \(0.690608\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −486.000 | −0.0739053 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2370.00 | 0.357344 | 0.178672 | − | 0.983909i | \(-0.442820\pi\) | ||||
0.178672 | + | 0.983909i | \(0.442820\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4440.00 | 0.663805 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1104.00 | 0.163669 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −912.000 | −0.134077 | −0.0670383 | − | 0.997750i | \(-0.521355\pi\) | ||||
−0.0670383 | + | 0.997750i | \(0.521355\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5259.00 | −0.766730 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −363.000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3060.00 | 0.438816 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8464.00 | 1.20386 | 0.601931 | − | 0.798548i | \(-0.294398\pi\) | ||||
0.601931 | + | 0.798548i | \(0.294398\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1566.00 | 0.220929 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 496.000 | 0.0694098 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11890.0 | 1.65051 | 0.825256 | − | 0.564759i | \(-0.191031\pi\) | ||||
0.825256 | + | 0.564759i | \(0.191031\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4500.00 | 0.619677 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3348.00 | 0.457376 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9556.00 | 1.29514 | 0.647571 | − | 0.762005i | \(-0.275785\pi\) | ||||
0.647571 | + | 0.762005i | \(0.275785\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2952.00 | −0.396944 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5236.00 | −0.698556 | −0.349278 | − | 0.937019i | \(-0.613573\pi\) | ||||
−0.349278 | + | 0.937019i | \(0.613573\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −880.000 | −0.116491 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3744.00 | 0.491778 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8262.00 | −1.07686 | −0.538432 | − | 0.842669i | \(-0.680983\pi\) | ||||
−0.538432 | + | 0.842669i | \(0.680983\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2024.00 | −0.261785 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6036.00 | 0.774748 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6640.00 | 0.845809 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2402.00 | −0.303660 | −0.151830 | − | 0.988407i | \(-0.548517\pi\) | ||||
−0.151830 | + | 0.988407i | \(0.548517\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −960.000 | −0.120451 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6290.00 | 0.783311 | 0.391655 | − | 0.920112i | \(-0.371903\pi\) | ||||
0.391655 | + | 0.920112i | \(0.371903\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1296.00 | 0.160194 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 810.000 | 0.0993808 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1254.00 | −0.152724 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6950.00 | −0.840233 | −0.420117 | − | 0.907470i | \(-0.638011\pi\) | ||||
−0.420117 | + | 0.907470i | \(0.638011\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3858.00 | 0.463020 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2784.00 | −0.331699 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1240.00 | 0.146673 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1392.00 | 0.163469 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12660.0 | −1.47609 | −0.738045 | − | 0.674752i | \(-0.764251\pi\) | ||||
−0.738045 | + | 0.674752i | \(0.764251\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5342.00 | 0.618416 | 0.309208 | − | 0.950994i | \(-0.399936\pi\) | ||||
0.309208 | + | 0.950994i | \(0.399936\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1404.00 | 0.161383 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1150.00 | −0.131255 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3568.00 | 0.404374 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −594.000 | −0.0668499 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13560.0 | 1.51546 | 0.757729 | − | 0.652570i | \(-0.226309\pi\) | ||||
0.757729 | + | 0.652570i | \(0.226309\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4658.00 | 0.516973 | 0.258486 | − | 0.966015i | \(-0.416776\pi\) | ||||
0.258486 | + | 0.966015i | \(0.416776\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5580.00 | −0.615036 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1760.00 | 0.192660 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6392.00 | 0.694928 | 0.347464 | − | 0.937693i | \(-0.387043\pi\) | ||||
0.347464 | + | 0.937693i | \(0.387043\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2511.00 | −0.271137 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10772.0 | −1.15529 | −0.577645 | − | 0.816288i | \(-0.696028\pi\) | ||||
−0.577645 | + | 0.816288i | \(0.696028\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6020.00 | 0.641293 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8682.00 | 0.918668 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5606.00 | −0.589228 | −0.294614 | − | 0.955616i | \(-0.595191\pi\) | ||||
−0.294614 | + | 0.955616i | \(0.595191\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1914.00 | 0.199838 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2928.00 | 0.303685 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1440.00 | −0.148370 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17050.0 | 1.74522 | 0.872610 | − | 0.488418i | \(-0.162426\pi\) | ||||
0.872610 | + | 0.488418i | \(0.162426\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1242.00 | −0.126300 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8438.00 | −0.852488 | −0.426244 | − | 0.904608i | \(-0.640163\pi\) | ||||
−0.426244 | + | 0.904608i | \(0.640163\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5064.00 | −0.508302 | −0.254151 | − | 0.967164i | \(-0.581796\pi\) | ||||
−0.254151 | + | 0.967164i | \(0.581796\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2160.00 | −0.215414 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14268.0 | 1.41380 | 0.706900 | − | 0.707314i | \(-0.250093\pi\) | ||||
0.706900 | + | 0.707314i | \(0.250093\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7648.00 | −0.752989 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4938.00 | −0.483081 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4576.00 | 0.444830 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1000.00 | 0.0965961 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −558.000 | −0.0535620 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18312.0 | 1.74676 | 0.873379 | − | 0.487042i | \(-0.161924\pi\) | ||||
0.873379 | + | 0.487042i | \(0.161924\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2052.00 | −0.194518 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1056.00 | −0.0994817 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15220.0 | 1.42496 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4376.00 | −0.407178 | −0.203589 | − | 0.979056i | \(-0.565261\pi\) | ||||
−0.203589 | + | 0.979056i | \(0.565261\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9804.00 | 0.906651 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17380.0 | −1.59745 | −0.798725 | − | 0.601696i | \(-0.794492\pi\) | ||||
−0.798725 | + | 0.601696i | \(0.794492\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8556.00 | 0.781629 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 990.000 | 0.0898933 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3552.00 | −0.320581 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11324.0 | −1.01590 | −0.507948 | − | 0.861388i | \(-0.669596\pi\) | ||||
−0.507948 | + | 0.861388i | \(0.669596\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4824.00 | 0.430180 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2392.00 | −0.212036 | −0.106018 | − | 0.994364i | \(-0.533810\pi\) | ||||
−0.106018 | + | 0.994364i | \(0.533810\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10900.0 | 0.960482 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5619.00 | 0.492206 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1238.00 | −0.107806 | −0.0539031 | − | 0.998546i | \(-0.517166\pi\) | ||||
−0.0539031 | + | 0.998546i | \(0.517166\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2448.00 | −0.211924 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1080.00 | 0.0929496 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13920.0 | 1.19105 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1716.00 | 0.145976 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12210.0 | 1.03268 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21738.0 | 1.82794 | 0.913972 | − | 0.405777i | \(-0.132999\pi\) | ||||
0.913972 | + | 0.405777i | \(0.132999\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22016.0 | −1.84071 | −0.920356 | − | 0.391081i | \(-0.872101\pi\) | ||||
−0.920356 | + | 0.391081i | \(0.872101\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −600.000 | −0.0498784 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3312.00 | 0.273763 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10231.0 | −0.840881 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3132.00 | 0.255965 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3132.00 | 0.254525 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3080.00 | −0.248897 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 156.000 | 0.0125361 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3069.00 | −0.245253 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9490.00 | 0.754172 | 0.377086 | − | 0.926178i | \(-0.376926\pi\) | ||||
0.377086 | + | 0.926178i | \(0.376926\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5394.00 | −0.426296 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9780.00 | 0.768677 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21632.0 | −1.69089 | −0.845446 | − | 0.534061i | \(-0.820665\pi\) | ||||
−0.845446 | + | 0.534061i | \(0.820665\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4014.00 | −0.312046 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7440.00 | −0.575235 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5312.00 | −0.408480 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3420.00 | 0.261569 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4854.00 | −0.369247 | −0.184624 | − | 0.982809i | \(-0.559107\pi\) | ||||
−0.184624 | + | 0.982809i | \(0.559107\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7488.00 | 0.566563 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1518.00 | −0.114242 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5308.00 | 0.397346 | 0.198673 | − | 0.980066i | \(-0.436337\pi\) | ||||
0.198673 | + | 0.980066i | \(0.436337\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11620.0 | 0.865234 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −648.000 | −0.0479955 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12490.0 | −0.920225 | −0.460113 | − | 0.887861i | \(-0.652191\pi\) | ||||
−0.460113 | + | 0.887861i | \(0.652191\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7448.00 | 0.545865 | 0.272933 | − | 0.962033i | \(-0.412006\pi\) | ||||
0.272933 | + | 0.962033i | \(0.412006\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11556.0 | −0.842511 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1100.00 | 0.0797794 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10994.0 | 0.793217 | 0.396608 | − | 0.917988i | \(-0.370187\pi\) | ||||
0.396608 | + | 0.917988i | \(0.370187\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5874.00 | 0.421615 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −992.000 | −0.0708349 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −682.000 | −0.0484486 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1620.00 | 0.114494 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5148.00 | 0.361977 | 0.180989 | − | 0.983485i | \(-0.442070\pi\) | ||||
0.180989 | + | 0.983485i | \(0.442070\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2880.00 | −0.201474 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4890.00 | 0.340351 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22314.0 | −1.54524 | −0.772619 | − | 0.634870i | \(-0.781054\pi\) | ||||
−0.772619 | + | 0.634870i | \(0.781054\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3680.00 | −0.253555 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13512.0 | −0.926314 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15588.0 | 1.06329 | 0.531643 | − | 0.846968i | \(-0.321575\pi\) | ||||
0.531643 | + | 0.846968i | \(0.321575\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21638.0 | −1.46861 | −0.734303 | − | 0.678822i | \(-0.762491\pi\) | ||||
−0.734303 | + | 0.678822i | \(0.762491\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8604.00 | 0.581065 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1210.00 | 0.0813116 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7496.00 | 0.501241 | 0.250620 | − | 0.968085i | \(-0.419365\pi\) | ||||
0.250620 | + | 0.968085i | \(0.419365\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4464.00 | 0.297029 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2808.00 | 0.185924 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2106.00 | 0.138761 | 0.0693805 | − | 0.997590i | \(-0.477898\pi\) | ||||
0.0693805 | + | 0.997590i | \(0.477898\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5220.00 | −0.342261 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26962.0 | 1.75924 | 0.879619 | − | 0.475680i | \(-0.157798\pi\) | ||||
0.879619 | + | 0.475680i | \(0.157798\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17740.0 | 1.15191 | 0.575954 | − | 0.817482i | \(-0.304631\pi\) | ||||
0.575954 | + | 0.817482i | \(0.304631\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1188.00 | 0.0767678 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4816.00 | −0.309709 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11875.0 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1320.00 | 0.0840761 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5244.00 | −0.332420 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19360.0 | −1.22141 | −0.610705 | − | 0.791858i | \(-0.709114\pi\) | ||||
−0.610705 | + | 0.791858i | \(0.709114\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11328.0 | 0.711292 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9840.00 | 0.614943 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5022.00 | −0.312369 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3996.00 | 0.247385 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19158.0 | −1.18049 | −0.590246 | − | 0.807223i | \(-0.700969\pi\) | ||||
−0.590246 | + | 0.807223i | \(0.700969\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11228.0 | −0.688630 | −0.344315 | − | 0.938854i | \(-0.611889\pi\) | ||||
−0.344315 | + | 0.938854i | \(0.611889\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12480.0 | −0.761860 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22628.0 | 1.37496 | 0.687480 | − | 0.726204i | \(-0.258717\pi\) | ||||
0.687480 | + | 0.726204i | \(0.258717\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3828.00 | 0.231529 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1728.00 | 0.104033 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28338.0 | 1.69824 | 0.849121 | − | 0.528199i | \(-0.177132\pi\) | ||||
0.849121 | + | 0.528199i | \(0.177132\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20120.0 | −1.20023 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2754.00 | 0.163537 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17052.0 | 1.00797 | 0.503985 | − | 0.863713i | \(-0.331867\pi\) | ||||
0.503985 | + | 0.863713i | \(0.331867\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21354.0 | −1.25654 | −0.628271 | − | 0.777995i | \(-0.716237\pi\) | ||||
−0.628271 | + | 0.777995i | \(0.716237\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2484.00 | −0.145506 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3200.00 | 0.186603 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8184.00 | −0.475091 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5184.00 | −0.299589 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4906.00 | −0.282256 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22198.0 | −1.27143 | −0.635713 | − | 0.771925i | \(-0.719294\pi\) | ||||
−0.635713 | + | 0.771925i | \(0.719294\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 675.000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32974.0 | −1.87193 | −0.935963 | − | 0.352099i | \(-0.885468\pi\) | ||||
−0.935963 | + | 0.352099i | \(0.885468\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12176.0 | −0.688177 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14148.0 | 0.796112 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22572.0 | −1.26456 | −0.632279 | − | 0.774740i | \(-0.717880\pi\) | ||||
−0.632279 | + | 0.774740i | \(0.717880\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12860.0 | −0.717307 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5298.00 | −0.294223 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1116.00 | −0.0617071 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2700.00 | −0.148644 | −0.0743219 | − | 0.997234i | \(-0.523679\pi\) | ||||
−0.0743219 | + | 0.997234i | \(0.523679\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −792.000 | −0.0434136 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4640.00 | −0.253245 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8004.00 | 0.434969 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13146.0 | −0.711341 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17382.0 | −0.936532 | −0.468266 | − | 0.883587i | \(-0.655121\pi\) | ||||
−0.468266 | + | 0.883587i | \(0.655121\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4560.00 | 0.244642 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4680.00 | −0.250013 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8720.00 | −0.463860 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20454.0 | 1.08345 | 0.541725 | − | 0.840556i | \(-0.317771\pi\) | ||||
0.541725 | + | 0.840556i | \(0.317771\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5976.00 | 0.315215 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3168.00 | −0.166399 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1980.00 | 0.103563 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3792.00 | 0.197510 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10236.0 | −0.530930 | −0.265465 | − | 0.964121i | \(-0.585525\pi\) | ||||
−0.265465 | + | 0.964121i | \(0.585525\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11136.0 | −0.575210 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9030.00 | −0.464494 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4650.00 | −0.238202 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9672.00 | −0.493418 | −0.246709 | − | 0.969090i | \(-0.579349\pi\) | ||||
−0.246709 | + | 0.969090i | \(0.579349\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19136.0 | 0.968222 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28078.0 | −1.41485 | −0.707425 | − | 0.706789i | \(-0.750143\pi\) | ||||
−0.707425 | + | 0.706789i | \(0.750143\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8370.00 | 0.420044 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10516.0 | 0.525593 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26776.0 | 1.33284 | 0.666422 | − | 0.745575i | \(-0.267825\pi\) | ||||
0.666422 | + | 0.745575i | \(0.267825\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2160.00 | 0.107084 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25280.0 | −1.24823 | −0.624114 | − | 0.781333i | \(-0.714540\pi\) | ||||
−0.624114 | + | 0.781333i | \(0.714540\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28940.0 | −1.42319 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1116.00 | 0.0546617 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2464.00 | 0.120204 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25160.0 | −1.22251 | −0.611253 | − | 0.791436i | \(-0.709334\pi\) | ||||
−0.611253 | + | 0.791436i | \(0.709334\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16212.0 | 0.784592 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9760.00 | −0.470467 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28910.0 | 1.38805 | 0.694024 | − | 0.719952i | \(-0.255836\pi\) | ||||
0.694024 | + | 0.719952i | \(0.255836\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1452.00 | 0.0694391 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10278.0 | 0.489589 | 0.244794 | − | 0.969575i | \(-0.421280\pi\) | ||||
0.244794 | + | 0.969575i | \(0.421280\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7824.00 | −0.371229 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4140.00 | 0.195663 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6264.00 | 0.294889 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29558.0 | −1.38607 | −0.693036 | − | 0.720903i | \(-0.743727\pi\) | ||||
−0.693036 | + | 0.720903i | \(0.743727\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4854.00 | −0.226735 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9762.00 | 0.454223 | 0.227112 | − | 0.973869i | \(-0.427072\pi\) | ||||
0.227112 | + | 0.973869i | \(0.427072\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1800.00 | −0.0834296 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2736.00 | −0.126324 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6960.00 | −0.320113 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4884.00 | 0.223769 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5022.00 | −0.229210 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16460.0 | 0.748385 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14824.0 | −0.671434 | −0.335717 | − | 0.941963i | \(-0.608979\pi\) | ||||
−0.335717 | + | 0.941963i | \(0.608979\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 144.000 | 0.00649751 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9296.00 | −0.417861 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8028.00 | −0.359499 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1860.00 | 0.0829779 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14946.0 | 0.664259 | 0.332130 | − | 0.943234i | \(-0.392233\pi\) | ||||
0.332130 | + | 0.943234i | \(0.392233\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7176.00 | 0.317733 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5418.00 | 0.238996 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3366.00 | 0.147925 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3520.00 | 0.154116 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5442.00 | 0.237382 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14774.0 | 0.642060 | 0.321030 | − | 0.947069i | \(-0.395971\pi\) | ||||
0.321030 | + | 0.947069i | \(0.395971\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22760.0 | −0.985464 | −0.492732 | − | 0.870181i | \(-0.664002\pi\) | ||||
−0.492732 | + | 0.870181i | \(0.664002\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3048.00 | 0.131486 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −32680.0 | −1.40458 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16640.0 | −0.712558 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1296.00 | −0.0552941 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16370.0 | 0.695879 | 0.347940 | − | 0.937517i | \(-0.386881\pi\) | ||||
0.347940 | + | 0.937517i | \(0.386881\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1784.00 | −0.0755605 | −0.0377803 | − | 0.999286i | \(-0.512029\pi\) | ||||
−0.0377803 | + | 0.999286i | \(0.512029\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 825.000 | 0.0348155 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22052.0 | 0.927235 | 0.463617 | − | 0.886036i | \(-0.346551\pi\) | ||||
0.463617 | + | 0.886036i | \(0.346551\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29738.0 | −1.24589 | −0.622945 | − | 0.782265i | \(-0.714064\pi\) | ||||
−0.622945 | + | 0.782265i | \(0.714064\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20742.0 | −0.865863 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12834.0 | −0.533820 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16080.0 | −0.666433 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1944.00 | −0.0802801 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −43956.0 | −1.80874 | −0.904368 | − | 0.426753i | \(-0.859657\pi\) | ||||
−0.904368 | + | 0.426753i | \(0.859657\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10207.0 | 0.418508 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18294.0 | 0.747424 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −18730.0 | −0.762523 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −968.000 | −0.0392690 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12576.0 | 0.508371 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5016.00 | 0.202052 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6438.00 | −0.258421 | −0.129210 | − | 0.991617i | \(-0.541244\pi\) | ||||
−0.129210 | + | 0.991617i | \(0.541244\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3600.00 | −0.143997 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2282.00 | −0.0909587 | −0.0454794 | − | 0.998965i | \(-0.514482\pi\) | ||||
−0.0454794 | + | 0.998965i | \(0.514482\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29972.0 | 1.19049 | 0.595245 | − | 0.803544i | \(-0.297055\pi\) | ||||
0.595245 | + | 0.803544i | \(0.297055\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4176.00 | 0.165293 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3716.00 | 0.146575 | 0.0732874 | − | 0.997311i | \(-0.476651\pi\) | ||||
0.0732874 | + | 0.997311i | \(0.476651\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −40700.0 | −1.59982 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8391.00 | 0.328689 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7304.00 | 0.285122 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17208.0 | 0.669427 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13698.0 | 0.531050 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12000.0 | 0.463627 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25194.0 | 0.970058 | 0.485029 | − | 0.874498i | \(-0.338809\pi\) | ||||
0.485029 | + | 0.874498i | \(0.338809\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27942.0 | −1.07220 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27194.0 | 1.03994 | 0.519971 | − | 0.854184i | \(-0.325943\pi\) | ||||
0.519971 | + | 0.854184i | \(0.325943\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14300.0 | 0.544998 | 0.272499 | − | 0.962156i | \(-0.412150\pi\) | ||||
0.272499 | + | 0.962156i | \(0.412150\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10440.0 | −0.396539 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4944.00 | −0.187151 | −0.0935757 | − | 0.995612i | \(-0.529830\pi\) | ||||
−0.0935757 | + | 0.995612i | \(0.529830\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7872.00 | −0.296984 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 891.000 | 0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6240.00 | −0.233834 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −520.000 | −0.0194209 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2376.00 | 0.0884418 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13392.0 | 0.496828 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2852.00 | −0.105454 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9984.00 | 0.367937 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17980.0 | 0.660415 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24332.0 | 0.890773 | 0.445386 | − | 0.895338i | \(-0.353066\pi\) | ||||
0.445386 | + | 0.895338i | \(0.353066\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9810.00 | 0.357951 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20796.0 | −0.756314 | −0.378157 | − | 0.925741i | \(-0.623442\pi\) | ||||
−0.378157 | + | 0.925741i | \(0.623442\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1364.00 | 0.0494434 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13380.0 | 0.483420 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16096.0 | 0.579647 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15392.0 | −0.552487 | −0.276243 | − | 0.961088i | \(-0.589090\pi\) | ||||
−0.276243 | + | 0.961088i | \(0.589090\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4152.00 | 0.148548 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7992.00 | 0.285005 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2850.00 | 0.101305 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12528.0 | 0.443876 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15150.0 | −0.535043 | −0.267522 | − | 0.963552i | \(-0.586205\pi\) | ||||
−0.267522 | + | 0.963552i | \(0.586205\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11160.0 | 0.392862 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 23748.0 | 0.833306 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5060.00 | 0.176984 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15610.0 | 0.544244 | 0.272122 | − | 0.962263i | \(-0.412275\pi\) | ||||
0.272122 | + | 0.962263i | \(0.412275\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −654.000 | −0.0227289 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −45222.0 | −1.56663 | −0.783313 | − | 0.621627i | \(-0.786472\pi\) | ||||
−0.783313 | + | 0.621627i | \(0.786472\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7656.00 | −0.264384 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2160.00 | 0.0743543 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14820.0 | 0.508538 | 0.254269 | − | 0.967134i | \(-0.418165\pi\) | ||||
0.254269 | + | 0.967134i | \(0.418165\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5508.00 | 0.188406 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1998.00 | −0.0681279 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5334.00 | 0.181307 | 0.0906533 | − | 0.995883i | \(-0.471104\pi\) | ||||
0.0906533 | + | 0.995883i | \(0.471104\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 38520.0 | 1.30521 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6138.00 | −0.207328 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10288.0 | 0.346420 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24607.0 | −0.825988 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2772.00 | −0.0927585 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19580.0 | −0.653163 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18400.0 | −0.611897 | −0.305948 | − | 0.952048i | \(-0.598973\pi\) | ||||
−0.305948 | + | 0.952048i | \(0.598973\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5520.00 | 0.183001 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14460.0 | 0.477903 | 0.238951 | − | 0.971032i | \(-0.423196\pi\) | ||||
0.238951 | + | 0.971032i | \(0.423196\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3712.00 | 0.122303 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1350.00 | 0.0443432 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9998.00 | −0.327394 | −0.163697 | − | 0.986511i | \(-0.552342\pi\) | ||||
−0.163697 | + | 0.986511i | \(0.552342\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6622.00 | 0.216180 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8802.00 | 0.286469 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 52548.0 | 1.70501 | 0.852503 | − | 0.522722i | \(-0.175084\pi\) | ||||
0.852503 | + | 0.522722i | \(0.175084\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16300.0 | −0.527270 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3744.00 | 0.120742 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18304.0 | −0.588507 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7096.00 | 0.227459 | 0.113729 | − | 0.993512i | \(-0.463720\pi\) | ||||
0.113729 | + | 0.993512i | \(0.463720\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7500.00 | −0.239683 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 45040.0 | 1.43504 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45202.0 | 1.43587 | 0.717935 | − | 0.696111i | \(-0.245088\pi\) | ||||
0.717935 | + | 0.696111i | \(0.245088\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3078.00 | 0.0974811 |
(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 | 528.4.a.e.1.1 | 1 | ||
3.2 | odd | 2 | 1584.4.a.f.1.1 | 1 | |||
4.3 | odd | 2 | 132.4.a.d.1.1 | ✓ | 1 | ||
8.3 | odd | 2 | 2112.4.a.e.1.1 | 1 | |||
8.5 | even | 2 | 2112.4.a.q.1.1 | 1 | |||
12.11 | even | 2 | 396.4.a.c.1.1 | 1 | |||
44.43 | even | 2 | 1452.4.a.i.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
132.4.a.d.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
396.4.a.c.1.1 | 1 | 12.11 | even | 2 | |||
528.4.a.e.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1452.4.a.i.1.1 | 1 | 44.43 | even | 2 | |||
1584.4.a.f.1.1 | 1 | 3.2 | odd | 2 | |||
2112.4.a.e.1.1 | 1 | 8.3 | odd | 2 | |||
2112.4.a.q.1.1 | 1 | 8.5 | even | 2 |