Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(1,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.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: | \(29.9139683729\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 507.1 |
$q$-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 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | −8.00000 | −1.00000 | ||||||||
\(5\) | 12.0000 | 1.07331 | 0.536656 | − | 0.843801i | \(-0.319687\pi\) | ||||
0.536656 | + | 0.843801i | \(0.319687\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | −0.107990 | −0.0539949 | − | 0.998541i | \(-0.517195\pi\) | ||||
−0.0539949 | + | 0.998541i | \(0.517195\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 36.0000 | 0.986764 | 0.493382 | − | 0.869813i | \(-0.335760\pi\) | ||||
0.493382 | + | 0.869813i | \(0.335760\pi\) | |||||||
\(12\) | 24.0000 | 0.577350 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −36.0000 | −0.619677 | ||||||||
\(16\) | 64.0000 | 1.00000 | ||||||||
\(17\) | −78.0000 | −1.11281 | −0.556405 | − | 0.830911i | \(-0.687820\pi\) | ||||
−0.556405 | + | 0.830911i | \(0.687820\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −74.0000 | −0.893514 | −0.446757 | − | 0.894655i | \(-0.647421\pi\) | ||||
−0.446757 | + | 0.894655i | \(0.647421\pi\) | |||||||
\(20\) | −96.0000 | −1.07331 | ||||||||
\(21\) | 6.00000 | 0.0623480 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −96.0000 | −0.870321 | −0.435161 | − | 0.900353i | \(-0.643308\pi\) | ||||
−0.435161 | + | 0.900353i | \(0.643308\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 19.0000 | 0.152000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 16.0000 | 0.107990 | ||||||||
\(29\) | 18.0000 | 0.115259 | 0.0576296 | − | 0.998338i | \(-0.481646\pi\) | ||||
0.0576296 | + | 0.998338i | \(0.481646\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 214.000 | 1.23986 | 0.619928 | − | 0.784659i | \(-0.287162\pi\) | ||||
0.619928 | + | 0.784659i | \(0.287162\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −108.000 | −0.569709 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −24.0000 | −0.115907 | ||||||||
\(36\) | −72.0000 | −0.333333 | ||||||||
\(37\) | 286.000 | 1.27076 | 0.635380 | − | 0.772200i | \(-0.280844\pi\) | ||||
0.635380 | + | 0.772200i | \(0.280844\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 384.000 | 1.46270 | 0.731350 | − | 0.682002i | \(-0.238890\pi\) | ||||
0.731350 | + | 0.682002i | \(0.238890\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 524.000 | 1.85835 | 0.929177 | − | 0.369634i | \(-0.120517\pi\) | ||||
0.929177 | + | 0.369634i | \(0.120517\pi\) | |||||||
\(44\) | −288.000 | −0.986764 | ||||||||
\(45\) | 108.000 | 0.357771 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −300.000 | −0.931053 | −0.465527 | − | 0.885034i | \(-0.654135\pi\) | ||||
−0.465527 | + | 0.885034i | \(0.654135\pi\) | |||||||
\(48\) | −192.000 | −0.577350 | ||||||||
\(49\) | −339.000 | −0.988338 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 234.000 | 0.642481 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 558.000 | 1.44617 | 0.723087 | − | 0.690757i | \(-0.242723\pi\) | ||||
0.723087 | + | 0.690757i | \(0.242723\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 432.000 | 1.05911 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 222.000 | 0.515870 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −576.000 | −1.27100 | −0.635498 | − | 0.772102i | \(-0.719205\pi\) | ||||
−0.635498 | + | 0.772102i | \(0.719205\pi\) | |||||||
\(60\) | 288.000 | 0.619677 | ||||||||
\(61\) | 74.0000 | 0.155323 | 0.0776617 | − | 0.996980i | \(-0.475255\pi\) | ||||
0.0776617 | + | 0.996980i | \(0.475255\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −18.0000 | −0.0359966 | ||||||||
\(64\) | −512.000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −38.0000 | −0.0692901 | −0.0346451 | − | 0.999400i | \(-0.511030\pi\) | ||||
−0.0346451 | + | 0.999400i | \(0.511030\pi\) | |||||||
\(68\) | 624.000 | 1.11281 | ||||||||
\(69\) | 288.000 | 0.502480 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 456.000 | 0.762215 | 0.381107 | − | 0.924531i | \(-0.375543\pi\) | ||||
0.381107 | + | 0.924531i | \(0.375543\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 682.000 | 1.09345 | 0.546726 | − | 0.837311i | \(-0.315874\pi\) | ||||
0.546726 | + | 0.837311i | \(0.315874\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −57.0000 | −0.0877572 | ||||||||
\(76\) | 592.000 | 0.893514 | ||||||||
\(77\) | −72.0000 | −0.106561 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 704.000 | 1.00261 | 0.501305 | − | 0.865271i | \(-0.332853\pi\) | ||||
0.501305 | + | 0.865271i | \(0.332853\pi\) | |||||||
\(80\) | 768.000 | 1.07331 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 888.000 | 1.17435 | 0.587173 | − | 0.809462i | \(-0.300241\pi\) | ||||
0.587173 | + | 0.809462i | \(0.300241\pi\) | |||||||
\(84\) | −48.0000 | −0.0623480 | ||||||||
\(85\) | −936.000 | −1.19439 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −54.0000 | −0.0665449 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1020.00 | 1.21483 | 0.607415 | − | 0.794385i | \(-0.292207\pi\) | ||||
0.607415 | + | 0.794385i | \(0.292207\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 768.000 | 0.870321 | ||||||||
\(93\) | −642.000 | −0.715831 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −888.000 | −0.959020 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −110.000 | −0.115142 | −0.0575712 | − | 0.998341i | \(-0.518336\pi\) | ||||
−0.0575712 | + | 0.998341i | \(0.518336\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 324.000 | 0.328921 | ||||||||
\(100\) | −152.000 | −0.152000 | ||||||||
\(101\) | −990.000 | −0.975333 | −0.487667 | − | 0.873030i | \(-0.662152\pi\) | ||||
−0.487667 | + | 0.873030i | \(0.662152\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1208.00 | 1.15561 | 0.577805 | − | 0.816175i | \(-0.303910\pi\) | ||||
0.577805 | + | 0.816175i | \(0.303910\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 72.0000 | 0.0669189 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 996.000 | 0.899878 | 0.449939 | − | 0.893059i | \(-0.351446\pi\) | ||||
0.449939 | + | 0.893059i | \(0.351446\pi\) | |||||||
\(108\) | 216.000 | 0.192450 | ||||||||
\(109\) | 1402.00 | 1.23199 | 0.615997 | − | 0.787749i | \(-0.288754\pi\) | ||||
0.615997 | + | 0.787749i | \(0.288754\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −858.000 | −0.733673 | ||||||||
\(112\) | −128.000 | −0.107990 | ||||||||
\(113\) | 1926.00 | 1.60339 | 0.801694 | − | 0.597735i | \(-0.203932\pi\) | ||||
0.801694 | + | 0.597735i | \(0.203932\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1152.00 | −0.934127 | ||||||||
\(116\) | −144.000 | −0.115259 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 156.000 | 0.120172 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −35.0000 | −0.0262960 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1152.00 | −0.844491 | ||||||||
\(124\) | −1712.00 | −1.23986 | ||||||||
\(125\) | −1272.00 | −0.910169 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −988.000 | −0.690321 | −0.345161 | − | 0.938544i | \(-0.612176\pi\) | ||||
−0.345161 | + | 0.938544i | \(0.612176\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1572.00 | −1.07292 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2100.00 | −1.40059 | −0.700297 | − | 0.713851i | \(-0.746949\pi\) | ||||
−0.700297 | + | 0.713851i | \(0.746949\pi\) | |||||||
\(132\) | 864.000 | 0.569709 | ||||||||
\(133\) | 148.000 | 0.0964904 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −324.000 | −0.206559 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2496.00 | 1.55655 | 0.778276 | − | 0.627922i | \(-0.216094\pi\) | ||||
0.778276 | + | 0.627922i | \(0.216094\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2464.00 | −1.50355 | −0.751776 | − | 0.659418i | \(-0.770803\pi\) | ||||
−0.751776 | + | 0.659418i | \(0.770803\pi\) | |||||||
\(140\) | 192.000 | 0.115907 | ||||||||
\(141\) | 900.000 | 0.537544 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 576.000 | 0.333333 | ||||||||
\(145\) | 216.000 | 0.123709 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1017.00 | 0.570617 | ||||||||
\(148\) | −2288.00 | −1.27076 | ||||||||
\(149\) | −216.000 | −0.118761 | −0.0593806 | − | 0.998235i | \(-0.518913\pi\) | ||||
−0.0593806 | + | 0.998235i | \(0.518913\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 898.000 | 0.483962 | 0.241981 | − | 0.970281i | \(-0.422203\pi\) | ||||
0.241981 | + | 0.970281i | \(0.422203\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −702.000 | −0.370937 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2568.00 | 1.33075 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1510.00 | −0.767587 | −0.383793 | − | 0.923419i | \(-0.625383\pi\) | ||||
−0.383793 | + | 0.923419i | \(0.625383\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1674.00 | −0.834949 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 192.000 | 0.0939858 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 394.000 | 0.189328 | 0.0946640 | − | 0.995509i | \(-0.469822\pi\) | ||||
0.0946640 | + | 0.995509i | \(0.469822\pi\) | |||||||
\(164\) | −3072.00 | −1.46270 | ||||||||
\(165\) | −1296.00 | −0.611476 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −84.0000 | −0.0389228 | −0.0194614 | − | 0.999811i | \(-0.506195\pi\) | ||||
−0.0194614 | + | 0.999811i | \(0.506195\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −666.000 | −0.297838 | ||||||||
\(172\) | −4192.00 | −1.85835 | ||||||||
\(173\) | 1194.00 | 0.524729 | 0.262365 | − | 0.964969i | \(-0.415498\pi\) | ||||
0.262365 | + | 0.964969i | \(0.415498\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −38.0000 | −0.0164145 | ||||||||
\(176\) | 2304.00 | 0.986764 | ||||||||
\(177\) | 1728.00 | 0.733810 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3156.00 | 1.31782 | 0.658912 | − | 0.752220i | \(-0.271017\pi\) | ||||
0.658912 | + | 0.752220i | \(0.271017\pi\) | |||||||
\(180\) | −864.000 | −0.357771 | ||||||||
\(181\) | −1078.00 | −0.442691 | −0.221346 | − | 0.975195i | \(-0.571045\pi\) | ||||
−0.221346 | + | 0.975195i | \(0.571045\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −222.000 | −0.0896760 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3432.00 | 1.36392 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2808.00 | −1.09808 | ||||||||
\(188\) | 2400.00 | 0.931053 | ||||||||
\(189\) | 54.0000 | 0.0207827 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3192.00 | 1.20924 | 0.604620 | − | 0.796514i | \(-0.293325\pi\) | ||||
0.604620 | + | 0.796514i | \(0.293325\pi\) | |||||||
\(192\) | 1536.00 | 0.577350 | ||||||||
\(193\) | −722.000 | −0.269278 | −0.134639 | − | 0.990895i | \(-0.542988\pi\) | ||||
−0.134639 | + | 0.990895i | \(0.542988\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2712.00 | 0.988338 | ||||||||
\(197\) | −2796.00 | −1.01120 | −0.505601 | − | 0.862767i | \(-0.668729\pi\) | ||||
−0.505601 | + | 0.862767i | \(0.668729\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −340.000 | −0.121115 | −0.0605577 | − | 0.998165i | \(-0.519288\pi\) | ||||
−0.0605577 | + | 0.998165i | \(0.519288\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 114.000 | 0.0400047 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −36.0000 | −0.0124468 | ||||||||
\(204\) | −1872.00 | −0.642481 | ||||||||
\(205\) | 4608.00 | 1.56994 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −864.000 | −0.290107 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2664.00 | −0.881688 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1924.00 | −0.627742 | −0.313871 | − | 0.949466i | \(-0.601626\pi\) | ||||
−0.313871 | + | 0.949466i | \(0.601626\pi\) | |||||||
\(212\) | −4464.00 | −1.44617 | ||||||||
\(213\) | −1368.00 | −0.440065 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6288.00 | 1.99460 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −428.000 | −0.133892 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2046.00 | −0.631305 | ||||||||
\(220\) | −3456.00 | −1.05911 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5042.00 | −1.51407 | −0.757034 | − | 0.653375i | \(-0.773352\pi\) | ||||
−0.757034 | + | 0.653375i | \(0.773352\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 171.000 | 0.0506667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2676.00 | 0.782433 | 0.391217 | − | 0.920299i | \(-0.372054\pi\) | ||||
0.391217 | + | 0.920299i | \(0.372054\pi\) | |||||||
\(228\) | −1776.00 | −0.515870 | ||||||||
\(229\) | 2410.00 | 0.695447 | 0.347723 | − | 0.937597i | \(-0.386955\pi\) | ||||
0.347723 | + | 0.937597i | \(0.386955\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 216.000 | 0.0615228 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3726.00 | 1.04763 | 0.523816 | − | 0.851831i | \(-0.324508\pi\) | ||||
0.523816 | + | 0.851831i | \(0.324508\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3600.00 | −0.999311 | ||||||||
\(236\) | 4608.00 | 1.27100 | ||||||||
\(237\) | −2112.00 | −0.578857 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1248.00 | −0.337767 | −0.168884 | − | 0.985636i | \(-0.554016\pi\) | ||||
−0.168884 | + | 0.985636i | \(0.554016\pi\) | |||||||
\(240\) | −2304.00 | −0.619677 | ||||||||
\(241\) | 4210.00 | 1.12527 | 0.562635 | − | 0.826706i | \(-0.309788\pi\) | ||||
0.562635 | + | 0.826706i | \(0.309788\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −592.000 | −0.155323 | ||||||||
\(245\) | −4068.00 | −1.06080 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2664.00 | −0.678009 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7692.00 | −1.93432 | −0.967161 | − | 0.254165i | \(-0.918199\pi\) | ||||
−0.967161 | + | 0.254165i | \(0.918199\pi\) | |||||||
\(252\) | 144.000 | 0.0359966 | ||||||||
\(253\) | −3456.00 | −0.858802 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2808.00 | 0.689583 | ||||||||
\(256\) | 4096.00 | 1.00000 | ||||||||
\(257\) | 1326.00 | 0.321843 | 0.160921 | − | 0.986967i | \(-0.448553\pi\) | ||||
0.160921 | + | 0.986967i | \(0.448553\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −572.000 | −0.137229 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 162.000 | 0.0384197 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6048.00 | −1.41801 | −0.709003 | − | 0.705205i | \(-0.750855\pi\) | ||||
−0.709003 | + | 0.705205i | \(0.750855\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6696.00 | 1.55220 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3060.00 | −0.701382 | ||||||||
\(268\) | 304.000 | 0.0692901 | ||||||||
\(269\) | 6474.00 | 1.46739 | 0.733693 | − | 0.679481i | \(-0.237795\pi\) | ||||
0.733693 | + | 0.679481i | \(0.237795\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5978.00 | −1.33999 | −0.669996 | − | 0.742365i | \(-0.733704\pi\) | ||||
−0.669996 | + | 0.742365i | \(0.733704\pi\) | |||||||
\(272\) | −4992.00 | −1.11281 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 684.000 | 0.149988 | ||||||||
\(276\) | −2304.00 | −0.502480 | ||||||||
\(277\) | 8750.00 | 1.89797 | 0.948983 | − | 0.315327i | \(-0.102114\pi\) | ||||
0.948983 | + | 0.315327i | \(0.102114\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1926.00 | 0.413285 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8976.00 | −1.90556 | −0.952782 | − | 0.303656i | \(-0.901793\pi\) | ||||
−0.952782 | + | 0.303656i | \(0.901793\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −592.000 | −0.124349 | −0.0621745 | − | 0.998065i | \(-0.519804\pi\) | ||||
−0.0621745 | + | 0.998065i | \(0.519804\pi\) | |||||||
\(284\) | −3648.00 | −0.762215 | ||||||||
\(285\) | 2664.00 | 0.553690 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −768.000 | −0.157957 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1171.00 | 0.238347 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 330.000 | 0.0664775 | ||||||||
\(292\) | −5456.00 | −1.09345 | ||||||||
\(293\) | 4608.00 | 0.918779 | 0.459389 | − | 0.888235i | \(-0.348068\pi\) | ||||
0.459389 | + | 0.888235i | \(0.348068\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6912.00 | −1.36418 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −972.000 | −0.189903 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 456.000 | 0.0877572 | ||||||||
\(301\) | −1048.00 | −0.200683 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2970.00 | 0.563109 | ||||||||
\(304\) | −4736.00 | −0.893514 | ||||||||
\(305\) | 888.000 | 0.166711 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3166.00 | 0.588577 | 0.294289 | − | 0.955717i | \(-0.404917\pi\) | ||||
0.294289 | + | 0.955717i | \(0.404917\pi\) | |||||||
\(308\) | 576.000 | 0.106561 | ||||||||
\(309\) | −3624.00 | −0.667191 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2472.00 | 0.450721 | 0.225361 | − | 0.974275i | \(-0.427644\pi\) | ||||
0.225361 | + | 0.974275i | \(0.427644\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3094.00 | −0.558732 | −0.279366 | − | 0.960185i | \(-0.590124\pi\) | ||||
−0.279366 | + | 0.960185i | \(0.590124\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −216.000 | −0.0386356 | ||||||||
\(316\) | −5632.00 | −1.00261 | ||||||||
\(317\) | −2316.00 | −0.410345 | −0.205173 | − | 0.978726i | \(-0.565776\pi\) | ||||
−0.205173 | + | 0.978726i | \(0.565776\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 648.000 | 0.113734 | ||||||||
\(320\) | −6144.00 | −1.07331 | ||||||||
\(321\) | −2988.00 | −0.519545 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5772.00 | 0.994312 | ||||||||
\(324\) | −648.000 | −0.111111 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4206.00 | −0.711292 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 600.000 | 0.100544 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4426.00 | 0.734970 | 0.367485 | − | 0.930030i | \(-0.380219\pi\) | ||||
0.367485 | + | 0.930030i | \(0.380219\pi\) | |||||||
\(332\) | −7104.00 | −1.17435 | ||||||||
\(333\) | 2574.00 | 0.423587 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −456.000 | −0.0743700 | ||||||||
\(336\) | 384.000 | 0.0623480 | ||||||||
\(337\) | 866.000 | 0.139982 | 0.0699911 | − | 0.997548i | \(-0.477703\pi\) | ||||
0.0699911 | + | 0.997548i | \(0.477703\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5778.00 | −0.925716 | ||||||||
\(340\) | 7488.00 | 1.19439 | ||||||||
\(341\) | 7704.00 | 1.22345 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1364.00 | 0.214720 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3456.00 | 0.539318 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2556.00 | −0.395427 | −0.197714 | − | 0.980260i | \(-0.563352\pi\) | ||||
−0.197714 | + | 0.980260i | \(0.563352\pi\) | |||||||
\(348\) | 432.000 | 0.0665449 | ||||||||
\(349\) | 11014.0 | 1.68930 | 0.844650 | − | 0.535318i | \(-0.179808\pi\) | ||||
0.844650 | + | 0.535318i | \(0.179808\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9720.00 | 1.46556 | 0.732781 | − | 0.680465i | \(-0.238222\pi\) | ||||
0.732781 | + | 0.680465i | \(0.238222\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5472.00 | 0.818095 | ||||||||
\(356\) | −8160.00 | −1.21483 | ||||||||
\(357\) | −468.000 | −0.0693815 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2988.00 | 0.439277 | 0.219639 | − | 0.975581i | \(-0.429512\pi\) | ||||
0.219639 | + | 0.975581i | \(0.429512\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1383.00 | −0.201633 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 105.000 | 0.0151820 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8184.00 | 1.17362 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2068.00 | −0.294138 | −0.147069 | − | 0.989126i | \(-0.546984\pi\) | ||||
−0.147069 | + | 0.989126i | \(0.546984\pi\) | |||||||
\(368\) | −6144.00 | −0.870321 | ||||||||
\(369\) | 3456.00 | 0.487567 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1116.00 | −0.156172 | ||||||||
\(372\) | 5136.00 | 0.715831 | ||||||||
\(373\) | 902.000 | 0.125211 | 0.0626056 | − | 0.998038i | \(-0.480059\pi\) | ||||
0.0626056 | + | 0.998038i | \(0.480059\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3816.00 | 0.525486 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12818.0 | −1.73725 | −0.868623 | − | 0.495473i | \(-0.834995\pi\) | ||||
−0.868623 | + | 0.495473i | \(0.834995\pi\) | |||||||
\(380\) | 7104.00 | 0.959020 | ||||||||
\(381\) | 2964.00 | 0.398557 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1332.00 | 0.177708 | 0.0888538 | − | 0.996045i | \(-0.471680\pi\) | ||||
0.0888538 | + | 0.996045i | \(0.471680\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −864.000 | −0.114373 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4716.00 | 0.619452 | ||||||||
\(388\) | 880.000 | 0.115142 | ||||||||
\(389\) | 3054.00 | 0.398056 | 0.199028 | − | 0.979994i | \(-0.436221\pi\) | ||||
0.199028 | + | 0.979994i | \(0.436221\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7488.00 | 0.968502 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6300.00 | 0.808633 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8448.00 | 1.07611 | ||||||||
\(396\) | −2592.00 | −0.328921 | ||||||||
\(397\) | −11162.0 | −1.41110 | −0.705548 | − | 0.708663i | \(-0.749299\pi\) | ||||
−0.705548 | + | 0.708663i | \(0.749299\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −444.000 | −0.0557088 | ||||||||
\(400\) | 1216.00 | 0.152000 | ||||||||
\(401\) | 14820.0 | 1.84557 | 0.922787 | − | 0.385310i | \(-0.125905\pi\) | ||||
0.922787 | + | 0.385310i | \(0.125905\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 7920.00 | 0.975333 | ||||||||
\(405\) | 972.000 | 0.119257 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10296.0 | 1.25394 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9682.00 | 1.17052 | 0.585262 | − | 0.810844i | \(-0.300992\pi\) | ||||
0.585262 | + | 0.810844i | \(0.300992\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7488.00 | −0.898676 | ||||||||
\(412\) | −9664.00 | −1.15561 | ||||||||
\(413\) | 1152.00 | 0.137255 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10656.0 | 1.26044 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7392.00 | 0.868076 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −348.000 | −0.0405750 | −0.0202875 | − | 0.999794i | \(-0.506458\pi\) | ||||
−0.0202875 | + | 0.999794i | \(0.506458\pi\) | |||||||
\(420\) | −576.000 | −0.0669189 | ||||||||
\(421\) | −2486.00 | −0.287792 | −0.143896 | − | 0.989593i | \(-0.545963\pi\) | ||||
−0.143896 | + | 0.989593i | \(0.545963\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2700.00 | −0.310351 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1482.00 | −0.169147 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −148.000 | −0.0167734 | ||||||||
\(428\) | −7968.00 | −0.899878 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1812.00 | 0.202508 | 0.101254 | − | 0.994861i | \(-0.467715\pi\) | ||||
0.101254 | + | 0.994861i | \(0.467715\pi\) | |||||||
\(432\) | −1728.00 | −0.192450 | ||||||||
\(433\) | −6226.00 | −0.690999 | −0.345499 | − | 0.938419i | \(-0.612290\pi\) | ||||
−0.345499 | + | 0.938419i | \(0.612290\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −648.000 | −0.0714235 | ||||||||
\(436\) | −11216.0 | −1.23199 | ||||||||
\(437\) | 7104.00 | 0.777644 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12544.0 | −1.36376 | −0.681882 | − | 0.731462i | \(-0.738838\pi\) | ||||
−0.681882 | + | 0.731462i | \(0.738838\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3051.00 | −0.329446 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8556.00 | −0.917625 | −0.458812 | − | 0.888533i | \(-0.651725\pi\) | ||||
−0.458812 | + | 0.888533i | \(0.651725\pi\) | |||||||
\(444\) | 6864.00 | 0.733673 | ||||||||
\(445\) | 12240.0 | 1.30389 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 648.000 | 0.0685668 | ||||||||
\(448\) | 1024.00 | 0.107990 | ||||||||
\(449\) | −4116.00 | −0.432619 | −0.216310 | − | 0.976325i | \(-0.569402\pi\) | ||||
−0.216310 | + | 0.976325i | \(0.569402\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13824.0 | 1.44334 | ||||||||
\(452\) | −15408.0 | −1.60339 | ||||||||
\(453\) | −2694.00 | −0.279415 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6514.00 | 0.666766 | 0.333383 | − | 0.942791i | \(-0.391810\pi\) | ||||
0.333383 | + | 0.942791i | \(0.391810\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2106.00 | 0.214160 | ||||||||
\(460\) | 9216.00 | 0.934127 | ||||||||
\(461\) | −10500.0 | −1.06081 | −0.530405 | − | 0.847744i | \(-0.677960\pi\) | ||||
−0.530405 | + | 0.847744i | \(0.677960\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5542.00 | 0.556282 | 0.278141 | − | 0.960540i | \(-0.410282\pi\) | ||||
0.278141 | + | 0.960540i | \(0.410282\pi\) | |||||||
\(464\) | 1152.00 | 0.115259 | ||||||||
\(465\) | −7704.00 | −0.768311 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5220.00 | −0.517244 | −0.258622 | − | 0.965979i | \(-0.583268\pi\) | ||||
−0.258622 | + | 0.965979i | \(0.583268\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 76.0000 | 0.00748263 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4530.00 | 0.443166 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18864.0 | 1.83376 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1406.00 | −0.135814 | ||||||||
\(476\) | −1248.00 | −0.120172 | ||||||||
\(477\) | 5022.00 | 0.482058 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11592.0 | −1.10575 | −0.552873 | − | 0.833266i | \(-0.686468\pi\) | ||||
−0.552873 | + | 0.833266i | \(0.686468\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −576.000 | −0.0542627 | ||||||||
\(484\) | 280.000 | 0.0262960 | ||||||||
\(485\) | −1320.00 | −0.123584 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12170.0 | −1.13239 | −0.566196 | − | 0.824270i | \(-0.691586\pi\) | ||||
−0.566196 | + | 0.824270i | \(0.691586\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1182.00 | −0.109309 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1812.00 | 0.166547 | 0.0832733 | − | 0.996527i | \(-0.473463\pi\) | ||||
0.0832733 | + | 0.996527i | \(0.473463\pi\) | |||||||
\(492\) | 9216.00 | 0.844491 | ||||||||
\(493\) | −1404.00 | −0.128262 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3888.00 | 0.353036 | ||||||||
\(496\) | 13696.0 | 1.23986 | ||||||||
\(497\) | −912.000 | −0.0823115 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1330.00 | 0.119317 | 0.0596583 | − | 0.998219i | \(-0.480999\pi\) | ||||
0.0596583 | + | 0.998219i | \(0.480999\pi\) | |||||||
\(500\) | 10176.0 | 0.910169 | ||||||||
\(501\) | 252.000 | 0.0224721 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2688.00 | −0.238274 | −0.119137 | − | 0.992878i | \(-0.538013\pi\) | ||||
−0.119137 | + | 0.992878i | \(0.538013\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11880.0 | −1.04684 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7904.00 | 0.690321 | ||||||||
\(509\) | −5124.00 | −0.446203 | −0.223101 | − | 0.974795i | \(-0.571618\pi\) | ||||
−0.223101 | + | 0.974795i | \(0.571618\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1364.00 | −0.118082 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1998.00 | 0.171957 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14496.0 | 1.24033 | ||||||||
\(516\) | 12576.0 | 1.07292 | ||||||||
\(517\) | −10800.0 | −0.918730 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3582.00 | −0.302953 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −882.000 | −0.0741672 | −0.0370836 | − | 0.999312i | \(-0.511807\pi\) | ||||
−0.0370836 | + | 0.999312i | \(0.511807\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2320.00 | −0.193970 | −0.0969852 | − | 0.995286i | \(-0.530920\pi\) | ||||
−0.0969852 | + | 0.995286i | \(0.530920\pi\) | |||||||
\(524\) | 16800.0 | 1.40059 | ||||||||
\(525\) | 114.000 | 0.00947689 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16692.0 | −1.37972 | ||||||||
\(528\) | −6912.00 | −0.569709 | ||||||||
\(529\) | −2951.00 | −0.242541 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5184.00 | −0.423666 | ||||||||
\(532\) | −1184.00 | −0.0964904 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11952.0 | 0.965851 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9468.00 | −0.760846 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12204.0 | −0.975257 | ||||||||
\(540\) | 2592.00 | 0.206559 | ||||||||
\(541\) | −21422.0 | −1.70241 | −0.851205 | − | 0.524833i | \(-0.824128\pi\) | ||||
−0.851205 | + | 0.524833i | \(0.824128\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3234.00 | 0.255588 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16824.0 | 1.32231 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7040.00 | 0.550290 | 0.275145 | − | 0.961403i | \(-0.411274\pi\) | ||||
0.275145 | + | 0.961403i | \(0.411274\pi\) | |||||||
\(548\) | −19968.0 | −1.55655 | ||||||||
\(549\) | 666.000 | 0.0517745 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1332.00 | −0.102986 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1408.00 | −0.108272 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10296.0 | −0.787461 | ||||||||
\(556\) | 19712.0 | 1.50355 | ||||||||
\(557\) | 8400.00 | 0.638994 | 0.319497 | − | 0.947587i | \(-0.396486\pi\) | ||||
0.319497 | + | 0.947587i | \(0.396486\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1536.00 | −0.115907 | ||||||||
\(561\) | 8424.00 | 0.633978 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19044.0 | 1.42559 | 0.712797 | − | 0.701371i | \(-0.247428\pi\) | ||||
0.712797 | + | 0.701371i | \(0.247428\pi\) | |||||||
\(564\) | −7200.00 | −0.537544 | ||||||||
\(565\) | 23112.0 | 1.72094 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −162.000 | −0.0119989 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4698.00 | −0.346134 | −0.173067 | − | 0.984910i | \(-0.555368\pi\) | ||||
−0.173067 | + | 0.984910i | \(0.555368\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8728.00 | −0.639677 | −0.319838 | − | 0.947472i | \(-0.603629\pi\) | ||||
−0.319838 | + | 0.947472i | \(0.603629\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9576.00 | −0.698156 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1824.00 | −0.132289 | ||||||||
\(576\) | −4608.00 | −0.333333 | ||||||||
\(577\) | −2018.00 | −0.145599 | −0.0727993 | − | 0.997347i | \(-0.523193\pi\) | ||||
−0.0727993 | + | 0.997347i | \(0.523193\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2166.00 | 0.155468 | ||||||||
\(580\) | −1728.00 | −0.123709 | ||||||||
\(581\) | −1776.00 | −0.126817 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20088.0 | 1.42703 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11376.0 | −0.799894 | −0.399947 | − | 0.916538i | \(-0.630971\pi\) | ||||
−0.399947 | + | 0.916538i | \(0.630971\pi\) | |||||||
\(588\) | −8136.00 | −0.570617 | ||||||||
\(589\) | −15836.0 | −1.10783 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8388.00 | 0.583818 | ||||||||
\(592\) | 18304.0 | 1.27076 | ||||||||
\(593\) | 25596.0 | 1.77252 | 0.886258 | − | 0.463192i | \(-0.153296\pi\) | ||||
0.886258 | + | 0.463192i | \(0.153296\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1872.00 | 0.128982 | ||||||||
\(596\) | 1728.00 | 0.118761 | ||||||||
\(597\) | 1020.00 | 0.0699260 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3480.00 | 0.237377 | 0.118689 | − | 0.992932i | \(-0.462131\pi\) | ||||
0.118689 | + | 0.992932i | \(0.462131\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10010.0 | 0.679395 | 0.339698 | − | 0.940535i | \(-0.389675\pi\) | ||||
0.339698 | + | 0.940535i | \(0.389675\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −342.000 | −0.0230967 | ||||||||
\(604\) | −7184.00 | −0.483962 | ||||||||
\(605\) | −420.000 | −0.0282238 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3764.00 | 0.251690 | 0.125845 | − | 0.992050i | \(-0.459836\pi\) | ||||
0.125845 | + | 0.992050i | \(0.459836\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 108.000 | 0.00718618 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 5616.00 | 0.370937 | ||||||||
\(613\) | −13610.0 | −0.896742 | −0.448371 | − | 0.893848i | \(-0.647996\pi\) | ||||
−0.448371 | + | 0.893848i | \(0.647996\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −13824.0 | −0.906402 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6408.00 | −0.418114 | −0.209057 | − | 0.977903i | \(-0.567039\pi\) | ||||
−0.209057 | + | 0.977903i | \(0.567039\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6694.00 | 0.434660 | 0.217330 | − | 0.976098i | \(-0.430265\pi\) | ||||
0.217330 | + | 0.976098i | \(0.430265\pi\) | |||||||
\(620\) | −20544.0 | −1.33075 | ||||||||
\(621\) | 2592.00 | 0.167493 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2040.00 | −0.131189 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17639.0 | −1.12890 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7992.00 | 0.509043 | ||||||||
\(628\) | 12080.0 | 0.767587 | ||||||||
\(629\) | −22308.0 | −1.41411 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27250.0 | 1.71918 | 0.859592 | − | 0.510981i | \(-0.170718\pi\) | ||||
0.859592 | + | 0.510981i | \(0.170718\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5772.00 | 0.362427 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11856.0 | −0.740931 | ||||||||
\(636\) | 13392.0 | 0.834949 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4104.00 | 0.254072 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12630.0 | −0.778245 | −0.389122 | − | 0.921186i | \(-0.627222\pi\) | ||||
−0.389122 | + | 0.921186i | \(0.627222\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14798.0 | −0.907583 | −0.453792 | − | 0.891108i | \(-0.649929\pi\) | ||||
−0.453792 | + | 0.891108i | \(0.649929\pi\) | |||||||
\(644\) | −1536.00 | −0.0939858 | ||||||||
\(645\) | −18864.0 | −1.15158 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26232.0 | 1.59395 | 0.796976 | − | 0.604012i | \(-0.206432\pi\) | ||||
0.796976 | + | 0.604012i | \(0.206432\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20736.0 | −1.25417 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1284.00 | 0.0773025 | ||||||||
\(652\) | −3152.00 | −0.189328 | ||||||||
\(653\) | −30390.0 | −1.82121 | −0.910607 | − | 0.413274i | \(-0.864385\pi\) | ||||
−0.910607 | + | 0.413274i | \(0.864385\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25200.0 | −1.50328 | ||||||||
\(656\) | 24576.0 | 1.46270 | ||||||||
\(657\) | 6138.00 | 0.364484 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −28740.0 | −1.69886 | −0.849432 | − | 0.527698i | \(-0.823055\pi\) | ||||
−0.849432 | + | 0.527698i | \(0.823055\pi\) | |||||||
\(660\) | 10368.0 | 0.611476 | ||||||||
\(661\) | 9214.00 | 0.542183 | 0.271092 | − | 0.962554i | \(-0.412615\pi\) | ||||
0.271092 | + | 0.962554i | \(0.412615\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1776.00 | 0.103564 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1728.00 | −0.100312 | ||||||||
\(668\) | 672.000 | 0.0389228 | ||||||||
\(669\) | 15126.0 | 0.874148 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2664.00 | 0.153268 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16598.0 | 0.950677 | 0.475339 | − | 0.879803i | \(-0.342326\pi\) | ||||
0.475339 | + | 0.879803i | \(0.342326\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −513.000 | −0.0292524 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8610.00 | −0.488788 | −0.244394 | − | 0.969676i | \(-0.578589\pi\) | ||||
−0.244394 | + | 0.969676i | \(0.578589\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 220.000 | 0.0124342 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8028.00 | −0.451738 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −804.000 | −0.0450428 | −0.0225214 | − | 0.999746i | \(-0.507169\pi\) | ||||
−0.0225214 | + | 0.999746i | \(0.507169\pi\) | |||||||
\(684\) | 5328.00 | 0.297838 | ||||||||
\(685\) | 29952.0 | 1.67067 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7230.00 | −0.401516 | ||||||||
\(688\) | 33536.0 | 1.85835 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2270.00 | −0.124971 | −0.0624854 | − | 0.998046i | \(-0.519903\pi\) | ||||
−0.0624854 | + | 0.998046i | \(0.519903\pi\) | |||||||
\(692\) | −9552.00 | −0.524729 | ||||||||
\(693\) | −648.000 | −0.0355202 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −29568.0 | −1.61378 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −29952.0 | −1.62771 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11178.0 | −0.604851 | ||||||||
\(700\) | 304.000 | 0.0164145 | ||||||||
\(701\) | 1782.00 | 0.0960131 | 0.0480066 | − | 0.998847i | \(-0.484713\pi\) | ||||
0.0480066 | + | 0.998847i | \(0.484713\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21164.0 | −1.13544 | ||||||||
\(704\) | −18432.0 | −0.986764 | ||||||||
\(705\) | 10800.0 | 0.576953 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1980.00 | 0.105326 | ||||||||
\(708\) | −13824.0 | −0.733810 | ||||||||
\(709\) | 10690.0 | 0.566250 | 0.283125 | − | 0.959083i | \(-0.408629\pi\) | ||||
0.283125 | + | 0.959083i | \(0.408629\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6336.00 | 0.334203 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20544.0 | −1.07907 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −25248.0 | −1.31782 | ||||||||
\(717\) | 3744.00 | 0.195010 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11568.0 | 0.600019 | 0.300009 | − | 0.953936i | \(-0.403010\pi\) | ||||
0.300009 | + | 0.953936i | \(0.403010\pi\) | |||||||
\(720\) | 6912.00 | 0.357771 | ||||||||
\(721\) | −2416.00 | −0.124794 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12630.0 | −0.649675 | ||||||||
\(724\) | 8624.00 | 0.442691 | ||||||||
\(725\) | 342.000 | 0.0175194 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11644.0 | −0.594019 | −0.297010 | − | 0.954874i | \(-0.595989\pi\) | ||||
−0.297010 | + | 0.954874i | \(0.595989\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −40872.0 | −2.06800 | ||||||||
\(732\) | 1776.00 | 0.0896760 | ||||||||
\(733\) | 15010.0 | 0.756353 | 0.378177 | − | 0.925733i | \(-0.376551\pi\) | ||||
0.378177 | + | 0.925733i | \(0.376551\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12204.0 | 0.612451 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1368.00 | −0.0683730 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33410.0 | −1.66307 | −0.831534 | − | 0.555474i | \(-0.812537\pi\) | ||||
−0.831534 | + | 0.555474i | \(0.812537\pi\) | |||||||
\(740\) | −27456.0 | −1.36392 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6504.00 | 0.321142 | 0.160571 | − | 0.987024i | \(-0.448666\pi\) | ||||
0.160571 | + | 0.987024i | \(0.448666\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2592.00 | −0.127468 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7992.00 | 0.391448 | ||||||||
\(748\) | 22464.0 | 1.09808 | ||||||||
\(749\) | −1992.00 | −0.0971777 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13912.0 | −0.675973 | −0.337987 | − | 0.941151i | \(-0.609746\pi\) | ||||
−0.337987 | + | 0.941151i | \(0.609746\pi\) | |||||||
\(752\) | −19200.0 | −0.931053 | ||||||||
\(753\) | 23076.0 | 1.11678 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10776.0 | 0.519442 | ||||||||
\(756\) | −432.000 | −0.0207827 | ||||||||
\(757\) | −23974.0 | −1.15106 | −0.575528 | − | 0.817782i | \(-0.695204\pi\) | ||||
−0.575528 | + | 0.817782i | \(0.695204\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10368.0 | 0.495829 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 288.000 | 0.0137188 | 0.00685939 | − | 0.999976i | \(-0.497817\pi\) | ||||
0.00685939 | + | 0.999976i | \(0.497817\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2804.00 | −0.133043 | ||||||||
\(764\) | −25536.0 | −1.20924 | ||||||||
\(765\) | −8424.00 | −0.398131 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −12288.0 | −0.577350 | ||||||||
\(769\) | −1514.00 | −0.0709964 | −0.0354982 | − | 0.999370i | \(-0.511302\pi\) | ||||
−0.0354982 | + | 0.999370i | \(0.511302\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3978.00 | −0.185816 | ||||||||
\(772\) | 5776.00 | 0.269278 | ||||||||
\(773\) | −15816.0 | −0.735915 | −0.367957 | − | 0.929843i | \(-0.619943\pi\) | ||||
−0.367957 | + | 0.929843i | \(0.619943\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4066.00 | 0.188458 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1716.00 | 0.0792293 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −28416.0 | −1.30694 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16416.0 | 0.752126 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −486.000 | −0.0221816 | ||||||||
\(784\) | −21696.0 | −0.988338 | ||||||||
\(785\) | −18120.0 | −0.823861 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10154.0 | −0.459912 | −0.229956 | − | 0.973201i | \(-0.573858\pi\) | ||||
−0.229956 | + | 0.973201i | \(0.573858\pi\) | |||||||
\(788\) | 22368.0 | 1.01120 | ||||||||
\(789\) | 18144.0 | 0.818686 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3852.00 | −0.173150 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −20088.0 | −0.896161 | ||||||||
\(796\) | 2720.00 | 0.121115 | ||||||||
\(797\) | −17442.0 | −0.775191 | −0.387596 | − | 0.921830i | \(-0.626694\pi\) | ||||
−0.387596 | + | 0.921830i | \(0.626694\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23400.0 | 1.03609 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9180.00 | 0.404943 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 24552.0 | 1.07898 | ||||||||
\(804\) | −912.000 | −0.0400047 | ||||||||
\(805\) | 2304.00 | 0.100876 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19422.0 | −0.847196 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8778.00 | −0.381481 | −0.190740 | − | 0.981641i | \(-0.561089\pi\) | ||||
−0.190740 | + | 0.981641i | \(0.561089\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 430.000 | 0.0186182 | 0.00930909 | − | 0.999957i | \(-0.497037\pi\) | ||||
0.00930909 | + | 0.999957i | \(0.497037\pi\) | |||||||
\(812\) | 288.000 | 0.0124468 | ||||||||
\(813\) | 17934.0 | 0.773644 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4728.00 | 0.203208 | ||||||||
\(816\) | 14976.0 | 0.642481 | ||||||||
\(817\) | −38776.0 | −1.66047 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −36864.0 | −1.56994 | ||||||||
\(821\) | 32976.0 | 1.40179 | 0.700895 | − | 0.713264i | \(-0.252784\pi\) | ||||
0.700895 | + | 0.713264i | \(0.252784\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1168.00 | −0.0494701 | −0.0247351 | − | 0.999694i | \(-0.507874\pi\) | ||||
−0.0247351 | + | 0.999694i | \(0.507874\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2052.00 | −0.0865957 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17172.0 | 0.722042 | 0.361021 | − | 0.932558i | \(-0.382428\pi\) | ||||
0.361021 | + | 0.932558i | \(0.382428\pi\) | |||||||
\(828\) | 6912.00 | 0.290107 | ||||||||
\(829\) | 27146.0 | 1.13730 | 0.568649 | − | 0.822580i | \(-0.307466\pi\) | ||||
0.568649 | + | 0.822580i | \(0.307466\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26250.0 | −1.09579 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26442.0 | 1.09983 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1008.00 | −0.0417764 | ||||||||
\(836\) | 21312.0 | 0.881688 | ||||||||
\(837\) | −5778.00 | −0.238610 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30696.0 | −1.26310 | −0.631552 | − | 0.775334i | \(-0.717582\pi\) | ||||
−0.631552 | + | 0.775334i | \(0.717582\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24065.0 | −0.986715 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 26928.0 | 1.10018 | ||||||||
\(844\) | 15392.0 | 0.627742 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 70.0000 | 0.00283970 | ||||||||
\(848\) | 35712.0 | 1.44617 | ||||||||
\(849\) | 1776.00 | 0.0717929 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27456.0 | −1.10597 | ||||||||
\(852\) | 10944.0 | 0.440065 | ||||||||
\(853\) | −24842.0 | −0.997156 | −0.498578 | − | 0.866845i | \(-0.666144\pi\) | ||||
−0.498578 | + | 0.866845i | \(0.666144\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7992.00 | −0.319673 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11406.0 | 0.454634 | 0.227317 | − | 0.973821i | \(-0.427005\pi\) | ||||
0.227317 | + | 0.973821i | \(0.427005\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20540.0 | 0.815851 | 0.407925 | − | 0.913015i | \(-0.366252\pi\) | ||||
0.407925 | + | 0.913015i | \(0.366252\pi\) | |||||||
\(860\) | −50304.0 | −1.99460 | ||||||||
\(861\) | 2304.00 | 0.0911964 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9108.00 | −0.359258 | −0.179629 | − | 0.983734i | \(-0.557490\pi\) | ||||
−0.179629 | + | 0.983734i | \(0.557490\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14328.0 | 0.563198 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3513.00 | −0.137610 | ||||||||
\(868\) | 3424.00 | 0.133892 | ||||||||
\(869\) | 25344.0 | 0.989340 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −990.000 | −0.0383808 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2544.00 | 0.0982890 | ||||||||
\(876\) | 16368.0 | 0.631305 | ||||||||
\(877\) | 24046.0 | 0.925856 | 0.462928 | − | 0.886396i | \(-0.346799\pi\) | ||||
0.462928 | + | 0.886396i | \(0.346799\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13824.0 | −0.530457 | ||||||||
\(880\) | 27648.0 | 1.05911 | ||||||||
\(881\) | 7998.00 | 0.305856 | 0.152928 | − | 0.988237i | \(-0.451130\pi\) | ||||
0.152928 | + | 0.988237i | \(0.451130\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24032.0 | 0.915902 | 0.457951 | − | 0.888978i | \(-0.348584\pi\) | ||||
0.457951 | + | 0.888978i | \(0.348584\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 20736.0 | 0.787608 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15648.0 | −0.592343 | −0.296172 | − | 0.955135i | \(-0.595710\pi\) | ||||
−0.296172 | + | 0.955135i | \(0.595710\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1976.00 | 0.0745477 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2916.00 | 0.109640 | ||||||||
\(892\) | 40336.0 | 1.51407 | ||||||||
\(893\) | 22200.0 | 0.831909 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 37872.0 | 1.41444 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3852.00 | 0.142905 | ||||||||
\(900\) | −1368.00 | −0.0506667 | ||||||||
\(901\) | −43524.0 | −1.60932 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3144.00 | 0.115865 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12936.0 | −0.475146 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −808.000 | −0.0295802 | −0.0147901 | − | 0.999891i | \(-0.504708\pi\) | ||||
−0.0147901 | + | 0.999891i | \(0.504708\pi\) | |||||||
\(908\) | −21408.0 | −0.782433 | ||||||||
\(909\) | −8910.00 | −0.325111 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39144.0 | 1.42360 | 0.711799 | − | 0.702383i | \(-0.247880\pi\) | ||||
0.711799 | + | 0.702383i | \(0.247880\pi\) | |||||||
\(912\) | 14208.0 | 0.515870 | ||||||||
\(913\) | 31968.0 | 1.15880 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2664.00 | −0.0962504 | ||||||||
\(916\) | −19280.0 | −0.695447 | ||||||||
\(917\) | 4200.00 | 0.151250 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38248.0 | −1.37289 | −0.686445 | − | 0.727182i | \(-0.740830\pi\) | ||||
−0.686445 | + | 0.727182i | \(0.740830\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9498.00 | −0.339815 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1728.00 | −0.0615228 | ||||||||
\(925\) | 5434.00 | 0.193155 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10872.0 | 0.385203 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 54264.0 | 1.91641 | 0.958205 | − | 0.286084i | \(-0.0923536\pi\) | ||||
0.958205 | + | 0.286084i | \(0.0923536\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25086.0 | 0.883094 | ||||||||
\(932\) | −29808.0 | −1.04763 | ||||||||
\(933\) | −7416.00 | −0.260224 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −33696.0 | −1.17859 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12206.0 | 0.425563 | 0.212782 | − | 0.977100i | \(-0.431748\pi\) | ||||
0.212782 | + | 0.977100i | \(0.431748\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9282.00 | 0.322584 | ||||||||
\(940\) | 28800.0 | 0.999311 | ||||||||
\(941\) | −17664.0 | −0.611934 | −0.305967 | − | 0.952042i | \(-0.598980\pi\) | ||||
−0.305967 | + | 0.952042i | \(0.598980\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36864.0 | −1.27302 | ||||||||
\(944\) | −36864.0 | −1.27100 | ||||||||
\(945\) | 648.000 | 0.0223063 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 51984.0 | 1.78379 | 0.891897 | − | 0.452238i | \(-0.149374\pi\) | ||||
0.891897 | + | 0.452238i | \(0.149374\pi\) | |||||||
\(948\) | 16896.0 | 0.578857 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6948.00 | 0.236913 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13782.0 | 0.468460 | 0.234230 | − | 0.972181i | \(-0.424743\pi\) | ||||
0.234230 | + | 0.972181i | \(0.424743\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 38304.0 | 1.29789 | ||||||||
\(956\) | 9984.00 | 0.337767 | ||||||||
\(957\) | −1944.00 | −0.0656642 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4992.00 | −0.168092 | ||||||||
\(960\) | 18432.0 | 0.619677 | ||||||||
\(961\) | 16005.0 | 0.537243 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8964.00 | 0.299959 | ||||||||
\(964\) | −33680.0 | −1.12527 | ||||||||
\(965\) | −8664.00 | −0.289020 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14618.0 | −0.486125 | −0.243063 | − | 0.970011i | \(-0.578152\pi\) | ||||
−0.243063 | + | 0.970011i | \(0.578152\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −17316.0 | −0.574066 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18708.0 | −0.618299 | −0.309149 | − | 0.951013i | \(-0.600044\pi\) | ||||
−0.309149 | + | 0.951013i | \(0.600044\pi\) | |||||||
\(972\) | 1944.00 | 0.0641500 | ||||||||
\(973\) | 4928.00 | 0.162368 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4736.00 | 0.155323 | ||||||||
\(977\) | 48804.0 | 1.59814 | 0.799068 | − | 0.601241i | \(-0.205327\pi\) | ||||
0.799068 | + | 0.601241i | \(0.205327\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36720.0 | 1.19875 | ||||||||
\(980\) | 32544.0 | 1.06080 | ||||||||
\(981\) | 12618.0 | 0.410664 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 44736.0 | 1.45153 | 0.725766 | − | 0.687941i | \(-0.241485\pi\) | ||||
0.725766 | + | 0.687941i | \(0.241485\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33552.0 | −1.08534 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1800.00 | −0.0580493 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −50304.0 | −1.61737 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21004.0 | −0.673274 | −0.336637 | − | 0.941635i | \(-0.609289\pi\) | ||||
−0.336637 | + | 0.941635i | \(0.609289\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13278.0 | −0.424335 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4080.00 | −0.129995 | ||||||||
\(996\) | 21312.0 | 0.678009 | ||||||||
\(997\) | 9038.00 | 0.287098 | 0.143549 | − | 0.989643i | \(-0.454149\pi\) | ||||
0.143549 | + | 0.989643i | \(0.454149\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7722.00 | −0.244558 |
(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 | 507.4.a.c.1.1 | 1 | ||
3.2 | odd | 2 | 1521.4.a.f.1.1 | 1 | |||
13.5 | odd | 4 | 507.4.b.b.337.1 | 2 | |||
13.8 | odd | 4 | 507.4.b.b.337.2 | 2 | |||
13.12 | even | 2 | 39.4.a.a.1.1 | ✓ | 1 | ||
39.38 | odd | 2 | 117.4.a.a.1.1 | 1 | |||
52.51 | odd | 2 | 624.4.a.g.1.1 | 1 | |||
65.64 | even | 2 | 975.4.a.e.1.1 | 1 | |||
91.90 | odd | 2 | 1911.4.a.f.1.1 | 1 | |||
104.51 | odd | 2 | 2496.4.a.f.1.1 | 1 | |||
104.77 | even | 2 | 2496.4.a.o.1.1 | 1 | |||
156.155 | even | 2 | 1872.4.a.m.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.a.a.1.1 | ✓ | 1 | 13.12 | even | 2 | ||
117.4.a.a.1.1 | 1 | 39.38 | odd | 2 | |||
507.4.a.c.1.1 | 1 | 1.1 | even | 1 | trivial | ||
507.4.b.b.337.1 | 2 | 13.5 | odd | 4 | |||
507.4.b.b.337.2 | 2 | 13.8 | odd | 4 | |||
624.4.a.g.1.1 | 1 | 52.51 | odd | 2 | |||
975.4.a.e.1.1 | 1 | 65.64 | even | 2 | |||
1521.4.a.f.1.1 | 1 | 3.2 | odd | 2 | |||
1872.4.a.m.1.1 | 1 | 156.155 | even | 2 | |||
1911.4.a.f.1.1 | 1 | 91.90 | odd | 2 | |||
2496.4.a.f.1.1 | 1 | 104.51 | odd | 2 | |||
2496.4.a.o.1.1 | 1 | 104.77 | even | 2 |