Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,4,Mod(1,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(138.772492334\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 2352.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.00000 | −0.536656 | −0.268328 | − | 0.963328i | \(-0.586471\pi\) | ||||
−0.268328 | + | 0.963328i | \(0.586471\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 30.0000 | 0.822304 | 0.411152 | − | 0.911567i | \(-0.365127\pi\) | ||||
0.411152 | + | 0.911567i | \(0.365127\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 53.0000 | 1.13074 | 0.565368 | − | 0.824839i | \(-0.308734\pi\) | ||||
0.565368 | + | 0.824839i | \(0.308734\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 18.0000 | 0.309839 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −84.0000 | −1.19841 | −0.599206 | − | 0.800595i | \(-0.704517\pi\) | ||||
−0.599206 | + | 0.800595i | \(0.704517\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 97.0000 | 1.17123 | 0.585614 | − | 0.810590i | \(-0.300854\pi\) | ||||
0.585614 | + | 0.810590i | \(0.300854\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −84.0000 | −0.761531 | −0.380765 | − | 0.924672i | \(-0.624339\pi\) | ||||
−0.380765 | + | 0.924672i | \(0.624339\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −89.0000 | −0.712000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −180.000 | −1.15259 | −0.576296 | − | 0.817241i | \(-0.695502\pi\) | ||||
−0.576296 | + | 0.817241i | \(0.695502\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −179.000 | −1.03708 | −0.518538 | − | 0.855055i | \(-0.673523\pi\) | ||||
−0.518538 | + | 0.855055i | \(0.673523\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −90.0000 | −0.474757 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −145.000 | −0.644266 | −0.322133 | − | 0.946694i | \(-0.604400\pi\) | ||||
−0.322133 | + | 0.946694i | \(0.604400\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −159.000 | −0.652830 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 126.000 | 0.479949 | 0.239974 | − | 0.970779i | \(-0.422861\pi\) | ||||
0.239974 | + | 0.970779i | \(0.422861\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 325.000 | 1.15261 | 0.576303 | − | 0.817236i | \(-0.304495\pi\) | ||||
0.576303 | + | 0.817236i | \(0.304495\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −54.0000 | −0.178885 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 366.000 | 1.13588 | 0.567942 | − | 0.823068i | \(-0.307740\pi\) | ||||
0.567942 | + | 0.823068i | \(0.307740\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 252.000 | 0.691903 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −768.000 | −1.99043 | −0.995216 | − | 0.0976975i | \(-0.968852\pi\) | ||||
−0.995216 | + | 0.0976975i | \(0.968852\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −180.000 | −0.441294 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −291.000 | −0.676209 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 264.000 | 0.582540 | 0.291270 | − | 0.956641i | \(-0.405922\pi\) | ||||
0.291270 | + | 0.956641i | \(0.405922\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 818.000 | 1.71695 | 0.858477 | − | 0.512852i | \(-0.171411\pi\) | ||||
0.858477 | + | 0.512852i | \(0.171411\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −318.000 | −0.606816 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 523.000 | 0.953651 | 0.476826 | − | 0.878998i | \(-0.341787\pi\) | ||||
0.476826 | + | 0.878998i | \(0.341787\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 252.000 | 0.439670 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 342.000 | 0.571661 | 0.285831 | − | 0.958280i | \(-0.407731\pi\) | ||||
0.285831 | + | 0.958280i | \(0.407731\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −43.0000 | −0.0689420 | −0.0344710 | − | 0.999406i | \(-0.510975\pi\) | ||||
−0.0344710 | + | 0.999406i | \(0.510975\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 267.000 | 0.411073 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1171.00 | 1.66769 | 0.833847 | − | 0.551996i | \(-0.186134\pi\) | ||||
0.833847 | + | 0.551996i | \(0.186134\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 810.000 | 1.07119 | 0.535597 | − | 0.844474i | \(-0.320087\pi\) | ||||
0.535597 | + | 0.844474i | \(0.320087\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 504.000 | 0.643135 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 540.000 | 0.665449 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −600.000 | −0.714605 | −0.357303 | − | 0.933989i | \(-0.616304\pi\) | ||||
−0.357303 | + | 0.933989i | \(0.616304\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 537.000 | 0.598756 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −582.000 | −0.628547 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 386.000 | 0.404045 | 0.202022 | − | 0.979381i | \(-0.435249\pi\) | ||||
0.202022 | + | 0.979381i | \(0.435249\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 270.000 | 0.274101 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 618.000 | 0.608845 | 0.304422 | − | 0.952537i | \(-0.401537\pi\) | ||||
0.304422 | + | 0.952537i | \(0.401537\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1475.00 | −1.41103 | −0.705515 | − | 0.708695i | \(-0.749284\pi\) | ||||
−0.705515 | + | 0.708695i | \(0.749284\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1884.00 | −1.70218 | −0.851090 | − | 0.525021i | \(-0.824058\pi\) | ||||
−0.851090 | + | 0.525021i | \(0.824058\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 413.000 | 0.362920 | 0.181460 | − | 0.983398i | \(-0.441918\pi\) | ||||
0.181460 | + | 0.983398i | \(0.441918\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 435.000 | 0.371967 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −882.000 | −0.734262 | −0.367131 | − | 0.930169i | \(-0.619660\pi\) | ||||
−0.367131 | + | 0.930169i | \(0.619660\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 504.000 | 0.408680 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 477.000 | 0.376912 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −431.000 | −0.323817 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −378.000 | −0.277098 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1284.00 | 0.918756 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2483.00 | −1.73489 | −0.867443 | − | 0.497536i | \(-0.834238\pi\) | ||||
−0.867443 | + | 0.497536i | \(0.834238\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −975.000 | −0.665457 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2118.00 | −1.41260 | −0.706300 | − | 0.707913i | \(-0.749637\pi\) | ||||
−0.706300 | + | 0.707913i | \(0.749637\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 162.000 | 0.103280 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3012.00 | 1.87834 | 0.939170 | − | 0.343453i | \(-0.111597\pi\) | ||||
0.939170 | + | 0.343453i | \(0.111597\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 37.0000 | 0.0225777 | 0.0112888 | − | 0.999936i | \(-0.496407\pi\) | ||||
0.0112888 | + | 0.999936i | \(0.496407\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1098.00 | −0.655803 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1590.00 | 0.929808 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1080.00 | 0.618546 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1644.00 | −0.903904 | −0.451952 | − | 0.892042i | \(-0.649272\pi\) | ||||
−0.451952 | + | 0.892042i | \(0.649272\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1088.00 | −0.586359 | −0.293179 | − | 0.956057i | \(-0.594713\pi\) | ||||
−0.293179 | + | 0.956057i | \(0.594713\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −756.000 | −0.399470 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1074.00 | 0.556553 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 506.000 | 0.257218 | 0.128609 | − | 0.991695i | \(-0.458949\pi\) | ||||
0.128609 | + | 0.991695i | \(0.458949\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2304.00 | 1.14918 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1844.00 | −0.886093 | −0.443047 | − | 0.896499i | \(-0.646102\pi\) | ||||
−0.443047 | + | 0.896499i | \(0.646102\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 540.000 | 0.254781 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −162.000 | −0.0750655 | −0.0375327 | − | 0.999295i | \(-0.511950\pi\) | ||||
−0.0375327 | + | 0.999295i | \(0.511950\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 612.000 | 0.278562 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 873.000 | 0.390409 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2724.00 | −1.19712 | −0.598560 | − | 0.801078i | \(-0.704260\pi\) | ||||
−0.598560 | + | 0.801078i | \(0.704260\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −792.000 | −0.336330 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1254.00 | 0.523622 | 0.261811 | − | 0.965119i | \(-0.415680\pi\) | ||||
0.261811 | + | 0.965119i | \(0.415680\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1807.00 | −0.742062 | −0.371031 | − | 0.928620i | \(-0.620996\pi\) | ||||
−0.371031 | + | 0.928620i | \(0.620996\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2454.00 | −0.991284 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 870.000 | 0.345750 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2520.00 | −0.985458 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −714.000 | −0.270488 | −0.135244 | − | 0.990812i | \(-0.543182\pi\) | ||||
−0.135244 | + | 0.990812i | \(0.543182\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3709.00 | −1.38331 | −0.691657 | − | 0.722226i | \(-0.743119\pi\) | ||||
−0.691657 | + | 0.722226i | \(0.743119\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 954.000 | 0.350345 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1044.00 | −0.377573 | −0.188787 | − | 0.982018i | \(-0.560455\pi\) | ||||
−0.188787 | + | 0.982018i | \(0.560455\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 136.000 | 0.0484462 | 0.0242231 | − | 0.999707i | \(-0.492289\pi\) | ||||
0.0242231 | + | 0.999707i | \(0.492289\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1569.00 | −0.550591 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −756.000 | −0.257567 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −756.000 | −0.253844 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2910.00 | 0.963105 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1484.00 | −0.484184 | −0.242092 | − | 0.970253i | \(-0.577834\pi\) | ||||
−0.242092 | + | 0.970253i | \(0.577834\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1026.00 | −0.330049 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1950.00 | −0.618553 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 129.000 | 0.0398037 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4452.00 | −1.35509 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2032.00 | 0.610192 | 0.305096 | − | 0.952322i | \(-0.401311\pi\) | ||||
0.305096 | + | 0.952322i | \(0.401311\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −801.000 | −0.237333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6198.00 | −1.81223 | −0.906114 | − | 0.423034i | \(-0.860965\pi\) | ||||
−0.906114 | + | 0.423034i | \(0.860965\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4591.00 | −1.32481 | −0.662406 | − | 0.749145i | \(-0.730464\pi\) | ||||
−0.662406 | + | 0.749145i | \(0.730464\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4530.00 | 1.27369 | 0.636846 | − | 0.770991i | \(-0.280239\pi\) | ||||
0.636846 | + | 0.770991i | \(0.280239\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2196.00 | −0.609580 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3513.00 | −0.962843 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1530.00 | −0.414090 | −0.207045 | − | 0.978331i | \(-0.566385\pi\) | ||||
−0.207045 | + | 0.978331i | \(0.566385\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5534.00 | 1.47915 | 0.739577 | − | 0.673072i | \(-0.235025\pi\) | ||||
0.739577 | + | 0.673072i | \(0.235025\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5141.00 | 1.32435 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2430.00 | −0.618454 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 468.000 | 0.117689 | 0.0588444 | − | 0.998267i | \(-0.481258\pi\) | ||||
0.0588444 | + | 0.998267i | \(0.481258\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2520.00 | −0.626210 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1512.00 | −0.371314 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2490.00 | −0.604365 | −0.302183 | − | 0.953250i | \(-0.597715\pi\) | ||||
−0.302183 | + | 0.953250i | \(0.597715\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1620.00 | −0.384197 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1572.00 | −0.368569 | −0.184285 | − | 0.982873i | \(-0.558997\pi\) | ||||
−0.184285 | + | 0.982873i | \(0.558997\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4608.00 | 1.06818 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1800.00 | 0.412578 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1806.00 | 0.409345 | 0.204672 | − | 0.978831i | \(-0.434387\pi\) | ||||
0.204672 | + | 0.978831i | \(0.434387\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6112.00 | 1.37003 | 0.685014 | − | 0.728530i | \(-0.259796\pi\) | ||||
0.685014 | + | 0.728530i | \(0.259796\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2670.00 | −0.585480 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4231.00 | −0.917748 | −0.458874 | − | 0.888501i | \(-0.651747\pi\) | ||||
−0.458874 | + | 0.888501i | \(0.651747\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1611.00 | −0.345692 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3816.00 | −0.810119 | −0.405060 | − | 0.914290i | \(-0.632749\pi\) | ||||
−0.405060 | + | 0.914290i | \(0.632749\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3997.00 | 0.839565 | 0.419783 | − | 0.907625i | \(-0.362106\pi\) | ||||
0.419783 | + | 0.907625i | \(0.362106\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1746.00 | 0.362892 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2143.00 | 0.436190 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1158.00 | −0.233275 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4608.00 | 0.918779 | 0.459389 | − | 0.888235i | \(-0.348068\pi\) | ||||
0.459389 | + | 0.888235i | \(0.348068\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1584.00 | −0.312624 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −810.000 | −0.158252 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4452.00 | −0.861090 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1854.00 | −0.351517 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4908.00 | −0.921414 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 631.000 | 0.117306 | 0.0586532 | − | 0.998278i | \(-0.481319\pi\) | ||||
0.0586532 | + | 0.998278i | \(0.481319\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4425.00 | 0.814658 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3894.00 | −0.709995 | −0.354998 | − | 0.934867i | \(-0.615518\pi\) | ||||
−0.354998 | + | 0.934867i | \(0.615518\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2185.00 | −0.394580 | −0.197290 | − | 0.980345i | \(-0.563214\pi\) | ||||
−0.197290 | + | 0.980345i | \(0.563214\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3504.00 | 0.620834 | 0.310417 | − | 0.950601i | \(-0.399531\pi\) | ||||
0.310417 | + | 0.950601i | \(0.399531\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5400.00 | −0.947780 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5652.00 | 0.982754 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8148.00 | −1.40361 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4717.00 | −0.805083 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1239.00 | −0.209532 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2945.00 | −0.489039 | −0.244519 | − | 0.969644i | \(-0.578630\pi\) | ||||
−0.244519 | + | 0.969644i | \(0.578630\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1305.00 | −0.214755 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3138.00 | −0.511783 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4277.00 | 0.691344 | 0.345672 | − | 0.938355i | \(-0.387651\pi\) | ||||
0.345672 | + | 0.938355i | \(0.387651\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2646.00 | 0.423926 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5370.00 | −0.852791 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1512.00 | −0.235952 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7188.00 | −1.11202 | −0.556012 | − | 0.831175i | \(-0.687669\pi\) | ||||
−0.556012 | + | 0.831175i | \(0.687669\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9406.00 | −1.44267 | −0.721335 | − | 0.692587i | \(-0.756471\pi\) | ||||
−0.721335 | + | 0.692587i | \(0.756471\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1431.00 | −0.217610 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3390.00 | 0.511137 | 0.255569 | − | 0.966791i | \(-0.417737\pi\) | ||||
0.255569 | + | 0.966791i | \(0.417737\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2052.00 | −0.306785 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4812.00 | 0.707431 | 0.353715 | − | 0.935353i | \(-0.384918\pi\) | ||||
0.353715 | + | 0.935353i | \(0.384918\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2550.00 | 0.371774 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1293.00 | 0.186956 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 258.000 | 0.0369982 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7099.00 | 1.00971 | 0.504857 | − | 0.863203i | \(-0.331545\pi\) | ||||
0.504857 | + | 0.863203i | \(0.331545\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1134.00 | 0.159983 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2963.00 | 0.411309 | 0.205655 | − | 0.978625i | \(-0.434068\pi\) | ||||
0.205655 | + | 0.978625i | \(0.434068\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3852.00 | −0.530444 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9540.00 | −1.30328 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11899.0 | 1.61269 | 0.806346 | − | 0.591444i | \(-0.201442\pi\) | ||||
0.806346 | + | 0.591444i | \(0.201442\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7449.00 | 1.00164 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2568.00 | −0.342607 | −0.171304 | − | 0.985218i | \(-0.554798\pi\) | ||||
−0.171304 | + | 0.985218i | \(0.554798\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2925.00 | 0.384202 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10146.0 | −1.32242 | −0.661212 | − | 0.750199i | \(-0.729957\pi\) | ||||
−0.661212 | + | 0.750199i | \(0.729957\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7056.00 | 0.912627 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6354.00 | 0.815565 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7026.00 | −0.894978 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6229.00 | −0.787467 | −0.393734 | − | 0.919225i | \(-0.628817\pi\) | ||||
−0.393734 | + | 0.919225i | \(0.628817\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2472.00 | −0.307845 | −0.153922 | − | 0.988083i | \(-0.549191\pi\) | ||||
−0.153922 | + | 0.988083i | \(0.549191\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9487.00 | −1.17266 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −486.000 | −0.0596285 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4350.00 | −0.529783 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7075.00 | −0.855345 | −0.427673 | − | 0.903934i | \(-0.640666\pi\) | ||||
−0.427673 | + | 0.903934i | \(0.640666\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9036.00 | −1.08446 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4860.00 | −0.574863 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −111.000 | −0.0130352 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4158.00 | 0.484801 | 0.242400 | − | 0.970176i | \(-0.422065\pi\) | ||||
0.242400 | + | 0.970176i | \(0.422065\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6595.00 | −0.763469 | −0.381735 | − | 0.924272i | \(-0.624673\pi\) | ||||
−0.381735 | + | 0.924272i | \(0.624673\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3294.00 | 0.378628 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7476.00 | 0.853269 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4770.00 | −0.536825 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1518.00 | −0.169651 | −0.0848254 | − | 0.996396i | \(-0.527033\pi\) | ||||
−0.0848254 | + | 0.996396i | \(0.527033\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8567.00 | 0.950817 | 0.475408 | − | 0.879765i | \(-0.342300\pi\) | ||||
0.475408 | + | 0.879765i | \(0.342300\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3240.00 | −0.357117 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8148.00 | −0.891926 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10640.0 | −1.15676 | −0.578382 | − | 0.815766i | \(-0.696316\pi\) | ||||
−0.578382 | + | 0.815766i | \(0.696316\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7032.00 | −0.754177 | −0.377088 | − | 0.926177i | \(-0.623075\pi\) | ||||
−0.377088 | + | 0.926177i | \(0.623075\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3600.00 | 0.383497 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4932.00 | 0.521869 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14814.0 | −1.55705 | −0.778525 | − | 0.627613i | \(-0.784032\pi\) | ||||
−0.778525 | + | 0.627613i | \(0.784032\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3780.00 | 0.394664 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3264.00 | 0.338534 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11251.0 | −1.15164 | −0.575820 | − | 0.817576i | \(-0.695317\pi\) | ||||
−0.575820 | + | 0.817576i | \(0.695317\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2268.00 | 0.230634 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3852.00 | −0.389166 | −0.194583 | − | 0.980886i | \(-0.562335\pi\) | ||||
−0.194583 | + | 0.980886i | \(0.562335\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 475.000 | 0.0476784 | 0.0238392 | − | 0.999716i | \(-0.492411\pi\) | ||||
0.0238392 | + | 0.999716i | \(0.492411\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3222.00 | −0.321326 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5934.00 | −0.587993 | −0.293997 | − | 0.955806i | \(-0.594985\pi\) | ||||
−0.293997 | + | 0.955806i | \(0.594985\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1518.00 | −0.148505 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9750.00 | 0.947792 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8633.00 | −0.833914 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6912.00 | −0.663477 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13368.0 | 1.27516 | 0.637578 | − | 0.770386i | \(-0.279936\pi\) | ||||
0.637578 | + | 0.770386i | \(0.279936\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7685.00 | −0.728494 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2316.00 | −0.216833 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6653.00 | −0.619048 | −0.309524 | − | 0.950892i | \(-0.600170\pi\) | ||||
−0.309524 | + | 0.950892i | \(0.600170\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5532.00 | 0.511586 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15444.0 | −1.41951 | −0.709754 | − | 0.704450i | \(-0.751194\pi\) | ||||
−0.709754 | + | 0.704450i | \(0.751194\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15120.0 | 1.38128 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1620.00 | −0.147098 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −683.000 | −0.0612731 | −0.0306366 | − | 0.999531i | \(-0.509753\pi\) | ||||
−0.0306366 | + | 0.999531i | \(0.509753\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 486.000 | 0.0433391 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9882.00 | −0.875977 | −0.437989 | − | 0.898980i | \(-0.644309\pi\) | ||||
−0.437989 | + | 0.898980i | \(0.644309\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3708.00 | −0.326740 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1836.00 | −0.160828 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4206.00 | 0.366263 | 0.183131 | − | 0.983088i | \(-0.441377\pi\) | ||||
0.183131 | + | 0.983088i | \(0.441377\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2619.00 | −0.225403 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8850.00 | 0.757238 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10980.0 | 0.934042 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8172.00 | 0.691158 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9060.00 | 0.761854 | 0.380927 | − | 0.924605i | \(-0.375605\pi\) | ||||
0.380927 | + | 0.924605i | \(0.375605\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15679.0 | 1.31089 | 0.655444 | − | 0.755243i | \(-0.272481\pi\) | ||||
0.655444 | + | 0.755243i | \(0.272481\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15036.0 | 1.24284 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5111.00 | −0.420071 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2376.00 | 0.194180 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6678.00 | 0.542695 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11304.0 | 0.913485 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3762.00 | −0.302313 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7711.00 | −0.612794 | −0.306397 | − | 0.951904i | \(-0.599124\pi\) | ||||
−0.306397 | + | 0.951904i | \(0.599124\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5421.00 | 0.428430 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2478.00 | −0.194763 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4292.00 | −0.335489 | −0.167745 | − | 0.985830i | \(-0.553648\pi\) | ||||
−0.167745 | + | 0.985830i | \(0.553648\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7362.00 | 0.572318 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17460.0 | −1.34995 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2610.00 | −0.199619 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9858.00 | −0.749905 | −0.374952 | − | 0.927044i | \(-0.622341\pi\) | ||||
−0.374952 | + | 0.927044i | \(0.622341\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17225.0 | 1.30329 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7560.00 | 0.568954 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13890.0 | 1.03978 | 0.519888 | − | 0.854235i | \(-0.325974\pi\) | ||||
0.519888 | + | 0.854235i | \(0.325974\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5292.00 | 0.394046 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19038.0 | 1.40266 | 0.701331 | − | 0.712836i | \(-0.252590\pi\) | ||||
0.701331 | + | 0.712836i | \(0.252590\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8053.00 | 0.590206 | 0.295103 | − | 0.955465i | \(-0.404646\pi\) | ||||
0.295103 | + | 0.955465i | \(0.404646\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2142.00 | 0.156166 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7476.00 | 0.542210 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17137.0 | −1.23643 | −0.618217 | − | 0.786007i | \(-0.712145\pi\) | ||||
−0.618217 | + | 0.786007i | \(0.712145\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11127.0 | 0.798657 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23040.0 | −1.63674 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2862.00 | −0.202272 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18144.0 | −1.27578 | −0.637890 | − | 0.770127i | \(-0.720193\pi\) | ||||
−0.637890 | + | 0.770127i | \(0.720193\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17363.0 | −1.21465 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3132.00 | 0.217992 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24702.0 | −1.71061 | −0.855303 | − | 0.518128i | \(-0.826629\pi\) | ||||
−0.855303 | + | 0.518128i | \(0.826629\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −408.000 | −0.0279704 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2172.00 | 0.148156 | 0.0740781 | − | 0.997252i | \(-0.476399\pi\) | ||||
0.0740781 | + | 0.997252i | \(0.476399\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4175.00 | 0.283364 | 0.141682 | − | 0.989912i | \(-0.454749\pi\) | ||||
0.141682 | + | 0.989912i | \(0.454749\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4707.00 | 0.317884 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2586.00 | 0.173778 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2261.00 | −0.151188 | −0.0755940 | − | 0.997139i | \(-0.524085\pi\) | ||||
−0.0755940 | + | 0.997139i | \(0.524085\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19398.0 | 1.28438 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16318.0 | −1.07517 | −0.537584 | − | 0.843210i | \(-0.680663\pi\) | ||||
−0.537584 | + | 0.843210i | \(0.680663\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2268.00 | 0.148707 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26550.0 | −1.73235 | −0.866177 | − | 0.499737i | \(-0.833430\pi\) | ||||
−0.866177 | + | 0.499737i | \(0.833430\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19925.0 | −1.29379 | −0.646893 | − | 0.762581i | \(-0.723932\pi\) | ||||
−0.646893 | + | 0.762581i | \(0.723932\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2268.00 | 0.146557 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3421.00 | 0.218944 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8730.00 | −0.556049 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12180.0 | 0.772096 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6832.00 | 0.431026 | 0.215513 | − | 0.976501i | \(-0.430858\pi\) | ||||
0.215513 | + | 0.976501i | \(0.430858\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4452.00 | 0.279544 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14898.0 | 0.931038 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3078.00 | 0.190554 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10212.0 | 0.629251 | 0.314625 | − | 0.949216i | \(-0.398121\pi\) | ||||
0.314625 | + | 0.949216i | \(0.398121\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3779.00 | −0.231772 | −0.115886 | − | 0.993263i | \(-0.536971\pi\) | ||||
−0.115886 | + | 0.993263i | \(0.536971\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5850.00 | 0.357122 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16998.0 | −1.03286 | −0.516430 | − | 0.856329i | \(-0.672739\pi\) | ||||
−0.516430 | + | 0.856329i | \(0.672739\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7920.00 | 0.479025 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21750.0 | −1.30344 | −0.651718 | − | 0.758462i | \(-0.725951\pi\) | ||||
−0.651718 | + | 0.758462i | \(0.725951\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12708.0 | 0.758080 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −387.000 | −0.0229807 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10944.0 | 0.646916 | 0.323458 | − | 0.946243i | \(-0.395155\pi\) | ||||
0.323458 | + | 0.946243i | \(0.395155\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10955.0 | 0.644630 | 0.322315 | − | 0.946633i | \(-0.395539\pi\) | ||||
0.322315 | + | 0.946633i | \(0.395539\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13356.0 | 0.782359 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15120.0 | 0.877734 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6096.00 | −0.352294 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24540.0 | 1.41186 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25103.0 | 1.43782 | 0.718908 | − | 0.695106i | \(-0.244642\pi\) | ||||
0.718908 | + | 0.695106i | \(0.244642\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2403.00 | 0.137024 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5604.00 | −0.318138 | −0.159069 | − | 0.987267i | \(-0.550849\pi\) | ||||
−0.159069 | + | 0.987267i | \(0.550849\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18594.0 | 1.04629 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10968.0 | −0.614464 | −0.307232 | − | 0.951635i | \(-0.599403\pi\) | ||||
−0.307232 | + | 0.951635i | \(0.599403\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18072.0 | −1.00802 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13773.0 | 0.764880 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −40704.0 | −2.25065 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8405.00 | −0.462723 | −0.231361 | − | 0.972868i | \(-0.574318\pi\) | ||||
−0.231361 | + | 0.972868i | \(0.574318\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −222.000 | −0.0121165 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10584.0 | −0.575176 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13590.0 | −0.735366 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 468.000 | 0.0252156 | 0.0126078 | − | 0.999921i | \(-0.495987\pi\) | ||||
0.0126078 | + | 0.999921i | \(0.495987\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14065.0 | −0.754583 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6588.00 | 0.351941 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25066.0 | −1.32775 | −0.663874 | − | 0.747844i | \(-0.731089\pi\) | ||||
−0.663874 | + | 0.747844i | \(0.731089\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10539.0 | 0.555898 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15036.0 | 0.789765 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9540.00 | −0.498987 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4590.00 | 0.239075 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11082.0 | −0.574811 | −0.287405 | − | 0.957809i | \(-0.592793\pi\) | ||||
−0.287405 | + | 0.957809i | \(0.592793\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16602.0 | −0.853990 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16020.0 | 0.820645 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13481.0 | −0.687734 | −0.343867 | − | 0.939018i | \(-0.611737\pi\) | ||||
−0.343867 | + | 0.939018i | \(0.611737\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27300.0 | −1.38130 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24317.0 | 1.22533 | 0.612666 | − | 0.790342i | \(-0.290097\pi\) | ||||
0.612666 | + | 0.790342i | \(0.290097\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15690.0 | 0.784191 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18217.0 | 0.906797 | 0.453399 | − | 0.891308i | \(-0.350211\pi\) | ||||
0.453399 | + | 0.891308i | \(0.350211\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15423.0 | −0.764613 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19782.0 | −0.976758 | −0.488379 | − | 0.872632i | \(-0.662412\pi\) | ||||
−0.488379 | + | 0.872632i | \(0.662412\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9864.00 | 0.485086 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7290.00 | 0.357064 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4921.00 | 0.239108 | 0.119554 | − | 0.992828i | \(-0.461854\pi\) | ||||
0.119554 | + | 0.992828i | \(0.461854\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1404.00 | −0.0679477 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6528.00 | 0.314673 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18098.0 | 0.868934 | 0.434467 | − | 0.900688i | \(-0.356937\pi\) | ||||
0.434467 | + | 0.900688i | \(0.356937\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7560.00 | 0.361542 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24468.0 | −1.16552 | −0.582762 | − | 0.812643i | \(-0.698028\pi\) | ||||
−0.582762 | + | 0.812643i | \(0.698028\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4536.00 | 0.214378 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13992.0 | 0.658699 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21719.0 | 1.01847 | 0.509237 | − | 0.860626i | \(-0.329928\pi\) | ||||
0.509237 | + | 0.860626i | \(0.329928\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7470.00 | 0.348931 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30306.0 | −1.41013 | −0.705065 | − | 0.709142i | \(-0.749082\pi\) | ||||
−0.705065 | + | 0.709142i | \(0.749082\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15931.0 | 0.738398 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12222.0 | 0.562129 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10260.0 | 0.470079 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4860.00 | 0.221816 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3036.00 | −0.138038 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27296.0 | −1.23634 | −0.618169 | − | 0.786046i | \(-0.712125\pi\) | ||||
−0.618169 | + | 0.786046i | \(0.712125\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4716.00 | 0.212793 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 43354.0 | 1.94142 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13824.0 | −0.616713 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −35100.0 | −1.55998 | −0.779991 | − | 0.625791i | \(-0.784776\pi\) | ||||
−0.779991 | + | 0.625791i | \(0.784776\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30744.0 | −1.36126 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5400.00 | −0.238202 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1290.00 | −0.0566913 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5418.00 | −0.236335 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 44394.0 | 1.92931 | 0.964654 | − | 0.263520i | \(-0.0848836\pi\) | ||||
0.964654 | + | 0.263520i | \(0.0848836\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8584.00 | 0.371671 | 0.185835 | − | 0.982581i | \(-0.440501\pi\) | ||||
0.185835 | + | 0.982581i | \(0.440501\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18336.0 | −0.790986 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11064.0 | 0.475528 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31525.0 | 1.34996 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9834.00 | −0.418038 | −0.209019 | − | 0.977912i | \(-0.567027\pi\) | ||||
−0.209019 | + | 0.977912i | \(0.567027\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43856.0 | −1.85750 | −0.928751 | − | 0.370704i | \(-0.879116\pi\) | ||||
−0.928751 | + | 0.370704i | \(0.879116\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8010.00 | 0.338027 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13266.0 | −0.557804 | −0.278902 | − | 0.960320i | \(-0.589970\pi\) | ||||
−0.278902 | + | 0.960320i | \(0.589970\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17453.0 | 0.731204 | 0.365602 | − | 0.930771i | \(-0.380863\pi\) | ||||
0.365602 | + | 0.930771i | \(0.380863\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12693.0 | 0.529862 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 972.000 | 0.0402844 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4833.00 | 0.199585 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 35172.0 | 1.44729 | 0.723643 | − | 0.690175i | \(-0.242466\pi\) | ||||
0.723643 | + | 0.690175i | \(0.242466\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8011.00 | 0.328468 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11448.0 | 0.467722 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3672.00 | −0.149492 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11991.0 | −0.484723 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12180.0 | 0.490629 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3503.00 | 0.140610 | 0.0703051 | − | 0.997526i | \(-0.477603\pi\) | ||||
0.0703051 | + | 0.997526i | \(0.477603\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5238.00 | −0.209516 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22848.0 | 0.910703 | 0.455352 | − | 0.890312i | \(-0.349514\pi\) | ||||
0.455352 | + | 0.890312i | \(0.349514\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13456.0 | 0.534474 | 0.267237 | − | 0.963631i | \(-0.413889\pi\) | ||||
0.267237 | + | 0.963631i | \(0.413889\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −40710.0 | −1.60578 | −0.802888 | − | 0.596130i | \(-0.796704\pi\) | ||||
−0.802888 | + | 0.596130i | \(0.796704\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16344.0 | 0.642442 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6429.00 | −0.251834 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 35130.0 | 1.37135 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27719.0 | 1.07833 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3474.00 | 0.134682 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2906.00 | 0.111891 | 0.0559456 | − | 0.998434i | \(-0.482183\pi\) | ||||
0.0559456 | + | 0.998434i | \(0.482183\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13824.0 | −0.530457 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19188.0 | −0.733780 | −0.366890 | − | 0.930264i | \(-0.619577\pi\) | ||||
−0.366890 | + | 0.930264i | \(0.619577\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17251.0 | 0.657466 | 0.328733 | − | 0.944423i | \(-0.393378\pi\) | ||||
0.328733 | + | 0.944423i | \(0.393378\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4752.00 | 0.180493 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2094.00 | 0.0792668 | 0.0396334 | − | 0.999214i | \(-0.487381\pi\) | ||||
0.0396334 | + | 0.999214i | \(0.487381\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2430.00 | 0.0913671 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 35502.0 | 1.33038 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7524.00 | −0.281005 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13356.0 | 0.497150 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32220.0 | 1.19532 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 64512.0 | 2.38536 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10842.0 | 0.398232 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40267.0 | 1.47414 | 0.737069 | − | 0.675817i | \(-0.236209\pi\) | ||||
0.737069 | + | 0.675817i | \(0.236209\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5562.00 | 0.202948 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17604.0 | −0.640227 | −0.320113 | − | 0.947379i | \(-0.603721\pi\) | ||||
−0.320113 | + | 0.947379i | \(0.603721\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24300.0 | 0.880846 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14724.0 | 0.531979 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3509.00 | −0.125953 | −0.0629767 | − | 0.998015i | \(-0.520059\pi\) | ||||
−0.0629767 | + | 0.998015i | \(0.520059\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1893.00 | −0.0677269 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18126.0 | 0.646397 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12905.0 | 0.458718 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13275.0 | −0.470343 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −34638.0 | −1.22329 | −0.611645 | − | 0.791133i | \(-0.709492\pi\) | ||||
−0.611645 | + | 0.791133i | \(0.709492\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11682.0 | 0.409916 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15120.0 | 0.528852 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17353.0 | −0.605014 | −0.302507 | − | 0.953147i | \(-0.597824\pi\) | ||||
−0.302507 | + | 0.953147i | \(0.597824\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6555.00 | 0.227811 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −46920.0 | −1.62545 | −0.812725 | − | 0.582648i | \(-0.802017\pi\) | ||||
−0.812725 | + | 0.582648i | \(0.802017\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10584.0 | −0.365496 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18354.0 | −0.629804 | −0.314902 | − | 0.949124i | \(-0.601972\pi\) | ||||
−0.314902 | + | 0.949124i | \(0.601972\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2279.00 | −0.0779552 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10512.0 | −0.358438 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35568.0 | 1.20898 | 0.604491 | − | 0.796612i | \(-0.293376\pi\) | ||||
0.604491 | + | 0.796612i | \(0.293376\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4284.00 | 0.145159 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16200.0 | 0.547201 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2250.00 | 0.0755262 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16956.0 | −0.567393 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22254.0 | 0.742364 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27343.0 | 0.909298 | 0.454649 | − | 0.890671i | \(-0.349765\pi\) | ||||
0.454649 | + | 0.890671i | \(0.349765\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 24444.0 | 0.810376 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −51024.0 | −1.68634 | −0.843171 | − | 0.537645i | \(-0.819314\pi\) | ||||
−0.843171 | + | 0.537645i | \(0.819314\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14151.0 | 0.464815 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2226.00 | −0.0728926 | −0.0364463 | − | 0.999336i | \(-0.511604\pi\) | ||||
−0.0364463 | + | 0.999336i | \(0.511604\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18000.0 | −0.587623 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3717.00 | 0.120973 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −35304.0 | −1.14550 | −0.572748 | − | 0.819731i | \(-0.694123\pi\) | ||||
−0.572748 | + | 0.819731i | \(0.694123\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6264.00 | 0.202627 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27300.0 | −0.877745 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2341.00 | 0.0750397 | 0.0375198 | − | 0.999296i | \(-0.488054\pi\) | ||||
0.0375198 | + | 0.999296i | \(0.488054\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8835.00 | 0.282347 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −816.000 | −0.0259989 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29015.0 | 0.921679 | 0.460840 | − | 0.887483i | \(-0.347548\pi\) | ||||
0.460840 | + | 0.887483i | \(0.347548\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3915.00 | 0.123989 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2352.4.a.f.1.1 | 1 | ||
4.3 | odd | 2 | 294.4.a.d.1.1 | 1 | |||
7.2 | even | 3 | 336.4.q.f.193.1 | 2 | |||
7.4 | even | 3 | 336.4.q.f.289.1 | 2 | |||
7.6 | odd | 2 | 2352.4.a.bf.1.1 | 1 | |||
12.11 | even | 2 | 882.4.a.o.1.1 | 1 | |||
28.3 | even | 6 | 294.4.e.i.79.1 | 2 | |||
28.11 | odd | 6 | 42.4.e.a.37.1 | yes | 2 | ||
28.19 | even | 6 | 294.4.e.i.67.1 | 2 | |||
28.23 | odd | 6 | 42.4.e.a.25.1 | ✓ | 2 | ||
28.27 | even | 2 | 294.4.a.c.1.1 | 1 | |||
84.11 | even | 6 | 126.4.g.b.37.1 | 2 | |||
84.23 | even | 6 | 126.4.g.b.109.1 | 2 | |||
84.47 | odd | 6 | 882.4.g.g.361.1 | 2 | |||
84.59 | odd | 6 | 882.4.g.g.667.1 | 2 | |||
84.83 | odd | 2 | 882.4.a.l.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.4.e.a.25.1 | ✓ | 2 | 28.23 | odd | 6 | ||
42.4.e.a.37.1 | yes | 2 | 28.11 | odd | 6 | ||
126.4.g.b.37.1 | 2 | 84.11 | even | 6 | |||
126.4.g.b.109.1 | 2 | 84.23 | even | 6 | |||
294.4.a.c.1.1 | 1 | 28.27 | even | 2 | |||
294.4.a.d.1.1 | 1 | 4.3 | odd | 2 | |||
294.4.e.i.67.1 | 2 | 28.19 | even | 6 | |||
294.4.e.i.79.1 | 2 | 28.3 | even | 6 | |||
336.4.q.f.193.1 | 2 | 7.2 | even | 3 | |||
336.4.q.f.289.1 | 2 | 7.4 | even | 3 | |||
882.4.a.l.1.1 | 1 | 84.83 | odd | 2 | |||
882.4.a.o.1.1 | 1 | 12.11 | even | 2 | |||
882.4.g.g.361.1 | 2 | 84.47 | odd | 6 | |||
882.4.g.g.667.1 | 2 | 84.59 | odd | 6 | |||
2352.4.a.f.1.1 | 1 | 1.1 | even | 1 | trivial | ||
2352.4.a.bf.1.1 | 1 | 7.6 | odd | 2 |