Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8624,2,Mod(1,8624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8624, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8624.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8624 = 2^{4} \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8624.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: | \(68.8629867032\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.98988261376.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 12x^{6} + 37x^{4} - 28x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 4312) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.917853\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8624.1 |
$q$-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 | ||||||||
\(3\) | −2.61511 | −1.50984 | −0.754919 | − | 0.655819i | \(-0.772324\pi\) | ||||
−0.754919 | + | 0.655819i | \(0.772324\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.436116 | −0.195037 | −0.0975186 | − | 0.995234i | \(-0.531091\pi\) | ||||
−0.0975186 | + | 0.995234i | \(0.531091\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.83882 | 1.27961 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.35072 | −1.48402 | −0.742011 | − | 0.670388i | \(-0.766128\pi\) | ||||
−0.742011 | + | 0.670388i | \(0.766128\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.14049 | 0.294474 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.06594 | −1.71374 | −0.856870 | − | 0.515532i | \(-0.827594\pi\) | ||||
−0.856870 | + | 0.515532i | \(0.827594\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.05866 | −1.84878 | −0.924391 | − | 0.381446i | \(-0.875426\pi\) | ||||
−0.924391 | + | 0.381446i | \(0.875426\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.66843 | 1.39046 | 0.695232 | − | 0.718786i | \(-0.255302\pi\) | ||||
0.695232 | + | 0.718786i | \(0.255302\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.80980 | −0.961961 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.19362 | −0.422163 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.59608 | −0.853471 | −0.426735 | − | 0.904377i | \(-0.640336\pi\) | ||||
−0.426735 | + | 0.904377i | \(0.640336\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.04174 | −0.546313 | −0.273156 | − | 0.961970i | \(-0.588068\pi\) | ||||
−0.273156 | + | 0.961970i | \(0.588068\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.61511 | −0.455233 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.94108 | −1.63430 | −0.817151 | − | 0.576423i | \(-0.804448\pi\) | ||||
−0.817151 | + | 0.576423i | \(0.804448\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13.9927 | 2.24063 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.37935 | −0.996287 | −0.498144 | − | 0.867095i | \(-0.665985\pi\) | ||||
−0.498144 | + | 0.867095i | \(0.665985\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.2263 | −1.71199 | −0.855995 | − | 0.516985i | \(-0.827054\pi\) | ||||
−0.855995 | + | 0.516985i | \(0.827054\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.67417 | −0.249571 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.72113 | 1.27211 | 0.636054 | − | 0.771645i | \(-0.280566\pi\) | ||||
0.636054 | + | 0.771645i | \(0.280566\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 18.4782 | 2.58747 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.97098 | 0.682816 | 0.341408 | − | 0.939915i | \(-0.389096\pi\) | ||||
0.341408 | + | 0.939915i | \(0.389096\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.436116 | −0.0588059 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 21.0743 | 2.79136 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.27182 | 0.295766 | 0.147883 | − | 0.989005i | \(-0.452754\pi\) | ||||
0.147883 | + | 0.989005i | \(0.452754\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.55092 | 0.454649 | 0.227325 | − | 0.973819i | \(-0.427002\pi\) | ||||
0.227325 | + | 0.973819i | \(0.427002\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.33354 | 0.289439 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.31705 | −1.13826 | −0.569130 | − | 0.822248i | \(-0.692720\pi\) | ||||
−0.569130 | + | 0.822248i | \(0.692720\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −17.4387 | −2.09937 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.846083 | 0.100412 | 0.0502058 | − | 0.998739i | \(-0.484012\pi\) | ||||
0.0502058 | + | 0.998739i | \(0.484012\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.23751 | −0.495963 | −0.247981 | − | 0.968765i | \(-0.579767\pi\) | ||||
−0.247981 | + | 0.968765i | \(0.579767\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.5782 | 1.45240 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.05255 | 0.905982 | 0.452991 | − | 0.891515i | \(-0.350357\pi\) | ||||
0.452991 | + | 0.891515i | \(0.350357\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.77990 | −0.642211 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.08729 | −0.997459 | −0.498730 | − | 0.866758i | \(-0.666200\pi\) | ||||
−0.498730 | + | 0.866758i | \(0.666200\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.08157 | 0.334243 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.0193 | 1.28860 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.5680 | −1.54420 | −0.772102 | − | 0.635499i | \(-0.780794\pi\) | ||||
−0.772102 | + | 0.635499i | \(0.780794\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.95450 | 0.824843 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.51451 | 0.360581 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.77894 | 0.789832 | 0.394916 | − | 0.918717i | \(-0.370774\pi\) | ||||
0.394916 | + | 0.918717i | \(0.370774\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.83882 | 0.385816 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.3656 | 1.52893 | 0.764466 | − | 0.644664i | \(-0.223003\pi\) | ||||
0.764466 | + | 0.644664i | \(0.223003\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.848117 | 0.0835675 | 0.0417837 | − | 0.999127i | \(-0.486696\pi\) | ||||
0.0417837 | + | 0.999127i | \(0.486696\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.706671 | −0.0683165 | −0.0341582 | − | 0.999416i | \(-0.510875\pi\) | ||||
−0.0341582 | + | 0.999416i | \(0.510875\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.3151 | −0.988007 | −0.494003 | − | 0.869460i | \(-0.664467\pi\) | ||||
−0.494003 | + | 0.869460i | \(0.664467\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 25.9971 | 2.46753 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.02990 | −0.661318 | −0.330659 | − | 0.943750i | \(-0.607271\pi\) | ||||
−0.330659 | + | 0.943750i | \(0.607271\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.90821 | −0.271192 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −20.5405 | −1.89897 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.6827 | 1.50423 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.27821 | 0.382655 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.6486 | −0.944913 | −0.472456 | − | 0.881354i | \(-0.656633\pi\) | ||||
−0.472456 | + | 0.881354i | \(0.656633\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 29.3580 | 2.58482 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.21567 | 0.630436 | 0.315218 | − | 0.949019i | \(-0.397922\pi\) | ||||
0.315218 | + | 0.949019i | \(0.397922\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.956674 | 0.0823374 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.31089 | −0.111997 | −0.0559985 | − | 0.998431i | \(-0.517834\pi\) | ||||
−0.0559985 | + | 0.998431i | \(0.517834\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −23.1181 | −1.96085 | −0.980425 | − | 0.196891i | \(-0.936915\pi\) | ||||
−0.980425 | + | 0.196891i | \(0.936915\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −22.8067 | −1.92067 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.35072 | −0.447450 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00443 | 0.166458 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.76648 | −0.390485 | −0.195243 | − | 0.980755i | \(-0.562549\pi\) | ||||
−0.195243 | + | 0.980755i | \(0.562549\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.4369 | −1.17486 | −0.587428 | − | 0.809277i | \(-0.699859\pi\) | ||||
−0.587428 | + | 0.809277i | \(0.699859\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −27.1249 | −2.19292 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.32655 | 0.106551 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.808657 | 0.0645378 | 0.0322689 | − | 0.999479i | \(-0.489727\pi\) | ||||
0.0322689 | + | 0.999479i | \(0.489727\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.9997 | −1.03094 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.14137 | −0.246051 | −0.123026 | − | 0.992403i | \(-0.539260\pi\) | ||||
−0.123026 | + | 0.992403i | \(0.539260\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.14049 | 0.0887873 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.6576 | −0.979477 | −0.489738 | − | 0.871869i | \(-0.662908\pi\) | ||||
−0.489738 | + | 0.871869i | \(0.662908\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.6302 | 1.20232 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −30.9358 | −2.36572 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.0515 | 1.29640 | 0.648202 | − | 0.761468i | \(-0.275521\pi\) | ||||
0.648202 | + | 0.761468i | \(0.275521\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.94108 | −0.446559 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.2221 | 1.06301 | 0.531503 | − | 0.847056i | \(-0.321627\pi\) | ||||
0.531503 | + | 0.847056i | \(0.321627\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.2350 | −1.05808 | −0.529038 | − | 0.848598i | \(-0.677447\pi\) | ||||
−0.529038 | + | 0.848598i | \(0.677447\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.28607 | −0.686446 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.33546 | 0.318750 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.06594 | −0.516712 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.9411 | 0.864026 | 0.432013 | − | 0.901867i | \(-0.357803\pi\) | ||||
0.432013 | + | 0.901867i | \(0.357803\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.3821 | −1.53912 | −0.769560 | − | 0.638574i | \(-0.779525\pi\) | ||||
−0.769560 | + | 0.638574i | \(0.779525\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.10246 | −0.437006 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.5184 | −1.39063 | −0.695316 | − | 0.718705i | \(-0.744735\pi\) | ||||
−0.695316 | + | 0.718705i | \(0.744735\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.9552 | 1.20192 | 0.600960 | − | 0.799279i | \(-0.294785\pi\) | ||||
0.600960 | + | 0.799279i | \(0.294785\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 24.3652 | 1.71859 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.78214 | 0.194313 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 25.5989 | 1.77925 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.05866 | −0.557429 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.9112 | 1.02653 | 0.513264 | − | 0.858231i | \(-0.328436\pi\) | ||||
0.513264 | + | 0.858231i | \(0.328436\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.21260 | −0.151605 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.89596 | 0.333901 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.0816 | 0.748823 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 37.8078 | 2.54323 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.6191 | −0.778071 | −0.389035 | − | 0.921223i | \(-0.627192\pi\) | ||||
−0.389035 | + | 0.921223i | \(0.627192\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −18.4640 | −1.23093 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.51440 | 0.299631 | 0.149815 | − | 0.988714i | \(-0.452132\pi\) | ||||
0.149815 | + | 0.988714i | \(0.452132\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.4513 | −1.48362 | −0.741811 | − | 0.670610i | \(-0.766033\pi\) | ||||
−0.741811 | + | 0.670610i | \(0.766033\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.00725878 | −0.000475538 0 | −0.000237769 | − | 1.00000i | \(-0.500076\pi\) | ||||
−0.000237769 | 1.00000i | \(0.500076\pi\) | ||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.80342 | −0.248108 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −21.0583 | −1.36789 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.0145 | −0.971208 | −0.485604 | − | 0.874179i | \(-0.661400\pi\) | ||||
−0.485604 | + | 0.874179i | \(0.661400\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.70871 | 0.625393 | 0.312697 | − | 0.949853i | \(-0.398768\pi\) | ||||
0.312697 | + | 0.949853i | \(0.398768\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.6960 | 1.39180 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 43.1196 | 2.74363 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 23.7643 | 1.50600 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.9288 | −0.879180 | −0.439590 | − | 0.898199i | \(-0.644876\pi\) | ||||
−0.439590 | + | 0.898199i | \(0.644876\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.66843 | 0.419240 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.05866 | −0.504653 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.271755 | −0.0169516 | −0.00847582 | − | 0.999964i | \(-0.502698\pi\) | ||||
−0.00847582 | + | 0.999964i | \(0.502698\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −17.6435 | −1.09211 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.5145 | 0.710015 | 0.355008 | − | 0.934863i | \(-0.384478\pi\) | ||||
0.355008 | + | 0.934863i | \(0.384478\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.16792 | −0.133175 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 38.0970 | 2.33150 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.1884 | 1.41382 | 0.706910 | − | 0.707303i | \(-0.250088\pi\) | ||||
0.706910 | + | 0.707303i | \(0.250088\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.18642 | −0.436544 | −0.218272 | − | 0.975888i | \(-0.570042\pi\) | ||||
−0.218272 | + | 0.975888i | \(0.570042\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.80980 | −0.290042 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.57038 | −0.514944 | −0.257472 | − | 0.966286i | \(-0.582890\pi\) | ||||
−0.257472 | + | 0.966286i | \(0.582890\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.6767 | −0.699066 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.3151 | 0.615347 | 0.307673 | − | 0.951492i | \(-0.400450\pi\) | ||||
0.307673 | + | 0.951492i | \(0.400450\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.4650 | −1.21652 | −0.608260 | − | 0.793738i | \(-0.708132\pi\) | ||||
−0.608260 | + | 0.793738i | \(0.708132\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.19085 | −0.544419 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.9274 | 1.93691 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −20.3428 | −1.19252 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.10593 | −0.123030 | −0.0615149 | − | 0.998106i | \(-0.519593\pi\) | ||||
−0.0615149 | + | 0.998106i | \(0.519593\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.990779 | −0.0576854 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.19362 | −0.127287 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −35.6809 | −2.06348 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −40.1827 | −2.30844 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.54862 | −0.0886734 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.3468 | 0.818813 | 0.409407 | − | 0.912352i | \(-0.365736\pi\) | ||||
0.409407 | + | 0.912352i | \(0.365736\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.21792 | −0.126173 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.5229 | −0.710106 | −0.355053 | − | 0.934846i | \(-0.615537\pi\) | ||||
−0.355053 | + | 0.934846i | \(0.615537\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.6964 | −0.830689 | −0.415344 | − | 0.909664i | \(-0.636339\pi\) | ||||
−0.415344 | + | 0.909664i | \(0.636339\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −26.2674 | −1.47532 | −0.737661 | − | 0.675172i | \(-0.764070\pi\) | ||||
−0.737661 | + | 0.675172i | \(0.764070\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.59608 | −0.257331 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.84803 | 0.103147 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 56.9419 | 3.16833 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 25.7359 | 1.42757 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 26.9751 | 1.49173 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.25285 | 0.508582 | 0.254291 | − | 0.967128i | \(-0.418158\pi\) | ||||
0.254291 | + | 0.967128i | \(0.418158\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −38.1620 | −2.09127 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.06332 | 0.222003 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.92236 | −0.486032 | −0.243016 | − | 0.970022i | \(-0.578137\pi\) | ||||
−0.243016 | + | 0.970022i | \(0.578137\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.3840 | 0.998482 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.04174 | −0.164719 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.60530 | 0.409456 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.5631 | −0.889155 | −0.444577 | − | 0.895740i | \(-0.646646\pi\) | ||||
−0.444577 | + | 0.895740i | \(0.646646\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.5218 | −1.74085 | −0.870425 | − | 0.492300i | \(-0.836156\pi\) | ||||
−0.870425 | + | 0.492300i | \(0.836156\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.7375 | 0.626499 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.5285 | 0.666823 | 0.333411 | − | 0.942781i | \(-0.391800\pi\) | ||||
0.333411 | + | 0.942781i | \(0.391800\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.368991 | −0.0195840 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.26763 | 0.383571 | 0.191785 | − | 0.981437i | \(-0.438572\pi\) | ||||
0.191785 | + | 0.981437i | \(0.438572\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 45.9419 | 2.41800 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.61511 | −0.137258 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.84805 | 0.0967312 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.2478 | −0.587129 | −0.293565 | − | 0.955939i | \(-0.594842\pi\) | ||||
−0.293565 | + | 0.955939i | \(0.594842\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −24.4892 | −1.27486 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.952535 | −0.0493204 | −0.0246602 | − | 0.999696i | \(-0.507850\pi\) | ||||
−0.0246602 | + | 0.999696i | \(0.507850\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.1880 | −0.577747 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.5923 | 1.26657 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.4617 | 1.30788 | 0.653941 | − | 0.756545i | \(-0.273114\pi\) | ||||
0.653941 | + | 0.756545i | \(0.273114\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 27.8474 | 1.42666 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.64514 | 0.492844 | 0.246422 | − | 0.969163i | \(-0.420745\pi\) | ||||
0.246422 | + | 0.969163i | \(0.420745\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −43.0957 | −2.19068 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −37.0886 | −1.88047 | −0.940234 | − | 0.340530i | \(-0.889394\pi\) | ||||
−0.940234 | + | 0.340530i | \(0.889394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −47.1187 | −2.38289 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.8698 | −0.951856 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.51185 | −0.176700 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.4869 | 0.626702 | 0.313351 | − | 0.949637i | \(-0.398548\pi\) | ||||
0.313351 | + | 0.949637i | \(0.398548\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.60116 | −0.279709 | −0.139854 | − | 0.990172i | \(-0.544663\pi\) | ||||
−0.139854 | + | 0.990172i | \(0.544663\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.2755 | 0.810740 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.52071 | 0.125255 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.94108 | −0.492761 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.1717 | 1.04687 | 0.523437 | − | 0.852064i | \(-0.324649\pi\) | ||||
0.523437 | + | 0.852064i | \(0.324649\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.42813 | 0.169097 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.96311 | 0.194542 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 60.4565 | 2.96057 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −32.2398 | −1.57502 | −0.787508 | − | 0.616305i | \(-0.788629\pi\) | ||||
−0.787508 | + | 0.616305i | \(0.788629\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.2682 | 1.47518 | 0.737592 | − | 0.675247i | \(-0.235963\pi\) | ||||
0.737592 | + | 0.675247i | \(0.235963\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 33.4789 | 1.62780 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 33.9858 | 1.64855 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.9927 | 0.675576 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.6229 | 1.08971 | 0.544854 | − | 0.838531i | \(-0.316585\pi\) | ||||
0.544854 | + | 0.838531i | \(0.316585\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.5421 | 1.08330 | 0.541651 | − | 0.840603i | \(-0.317799\pi\) | ||||
0.541651 | + | 0.840603i | \(0.317799\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.24180 | −0.251325 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −53.7386 | −2.57066 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 39.5964 | 1.88983 | 0.944917 | − | 0.327309i | \(-0.106142\pi\) | ||||
0.944917 | + | 0.327309i | \(0.106142\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.23658 | 0.106263 | 0.0531316 | − | 0.998588i | \(-0.483080\pi\) | ||||
0.0531316 | + | 0.998588i | \(0.483080\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.35334 | 0.301177 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.4649 | 0.589569 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 36.9835 | 1.74536 | 0.872680 | − | 0.488292i | \(-0.162380\pi\) | ||||
0.872680 | + | 0.488292i | \(0.162380\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.37935 | −0.300392 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 37.7541 | 1.77384 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.3347 | −1.13833 | −0.569164 | − | 0.822224i | \(-0.692733\pi\) | ||||
−0.569164 | + | 0.822224i | \(0.692733\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 15.5000 | 0.723478 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.1287 | 1.40323 | 0.701617 | − | 0.712555i | \(-0.252462\pi\) | ||||
0.701617 | + | 0.712555i | \(0.252462\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.7841 | 1.47713 | 0.738566 | − | 0.674181i | \(-0.235503\pi\) | ||||
0.738566 | + | 0.674181i | \(0.235503\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.46909 | −0.160875 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.6186 | 0.861566 | 0.430783 | − | 0.902456i | \(-0.358237\pi\) | ||||
0.430783 | + | 0.902456i | \(0.358237\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.11473 | −0.0974416 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.2263 | −0.516184 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 38.7605 | 1.77846 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 19.0827 | 0.873737 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.03306 | −0.138584 | −0.0692920 | − | 0.997596i | \(-0.522074\pi\) | ||||
−0.0692920 | + | 0.997596i | \(0.522074\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 53.1919 | 2.42534 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.39252 | −0.154046 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.1684 | 1.18580 | 0.592902 | − | 0.805274i | \(-0.297982\pi\) | ||||
0.592902 | + | 0.805274i | \(0.297982\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.21506 | 0.371498 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.27373 | −0.373388 | −0.186694 | − | 0.982418i | \(-0.559777\pi\) | ||||
−0.186694 | + | 0.982418i | \(0.559777\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32.4756 | 1.46263 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.67417 | −0.0752485 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.19942 | 0.232758 | 0.116379 | − | 0.993205i | \(-0.462871\pi\) | ||||
0.116379 | + | 0.993205i | \(0.462871\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 33.1012 | 1.47885 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.64659 | 0.251769 | 0.125884 | − | 0.992045i | \(-0.459823\pi\) | ||||
0.125884 | + | 0.992045i | \(0.459823\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.70117 | −0.298198 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −40.8747 | −1.81531 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 36.1578 | 1.60266 | 0.801332 | − | 0.598220i | \(-0.204125\pi\) | ||||
0.801332 | + | 0.598220i | \(0.204125\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.6776 | 0.780487 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.369878 | −0.0162988 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.72113 | 0.383555 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −44.5917 | −1.95736 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.1005 | −1.53778 | −0.768891 | − | 0.639379i | \(-0.779191\pi\) | ||||
−0.768891 | + | 0.639379i | \(0.779191\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.7048 | −0.817902 | −0.408951 | − | 0.912556i | \(-0.634105\pi\) | ||||
−0.408951 | + | 0.912556i | \(0.634105\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21.4927 | 0.936238 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.4679 | 0.933388 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.72113 | 0.378465 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 34.1341 | 1.47851 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.308191 | 0.0133242 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −37.1923 | −1.60497 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.4129 | 1.22157 | 0.610784 | − | 0.791798i | \(-0.290855\pi\) | ||||
0.610784 | + | 0.791798i | \(0.290855\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 37.2261 | 1.59752 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.49858 | 0.192698 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.19216 | 0.393028 | 0.196514 | − | 0.980501i | \(-0.437038\pi\) | ||||
0.196514 | + | 0.980501i | \(0.437038\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.6314 | 0.581773 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 37.0382 | 1.57788 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11.3377 | −0.481260 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.6178 | −0.577007 | −0.288503 | − | 0.957479i | \(-0.593158\pi\) | ||||
−0.288503 | + | 0.957479i | \(0.593158\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 60.0686 | 2.54063 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.4782 | 0.780151 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.3944 | −0.648796 | −0.324398 | − | 0.945921i | \(-0.605162\pi\) | ||||
−0.324398 | + | 0.945921i | \(0.605162\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.06585 | 0.128981 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.99274 | −0.167384 | −0.0836922 | − | 0.996492i | \(-0.526671\pi\) | ||||
−0.0836922 | + | 0.996492i | \(0.526671\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.4481 | −1.44161 | −0.720803 | − | 0.693140i | \(-0.756227\pi\) | ||||
−0.720803 | + | 0.693140i | \(0.756227\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −31.2273 | −1.30454 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −32.0738 | −1.33757 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.9857 | −0.873648 | −0.436824 | − | 0.899547i | \(-0.643897\pi\) | ||||
−0.436824 | + | 0.899547i | \(0.643897\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 55.9168 | 2.32382 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.97098 | 0.205877 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.95803 | 0.370369 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.525053 | −0.0216713 | −0.0108356 | − | 0.999941i | \(-0.503449\pi\) | ||||
−0.0108356 | + | 0.999941i | \(0.503449\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.5123 | 1.01001 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 51.0429 | 2.09963 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.3978 | 0.468054 | 0.234027 | − | 0.972230i | \(-0.424810\pi\) | ||||
0.234027 | + | 0.972230i | \(0.424810\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −44.3397 | −1.81470 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.48217 | 0.142278 | 0.0711388 | − | 0.997466i | \(-0.477337\pi\) | ||||
0.0711388 | + | 0.997466i | \(0.477337\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.0794 | −0.451938 | −0.225969 | − | 0.974135i | \(-0.572555\pi\) | ||||
−0.225969 | + | 0.974135i | \(0.572555\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −35.7665 | −1.45653 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.436116 | −0.0177306 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.2845 | −0.458022 | −0.229011 | − | 0.973424i | \(-0.573549\pi\) | ||||
−0.229011 | + | 0.973424i | \(0.573549\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −46.6643 | −1.88784 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.0939 | −0.569248 | −0.284624 | − | 0.958639i | \(-0.591869\pi\) | ||||
−0.284624 | + | 0.958639i | \(0.591869\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.27561 | −0.293381 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.7251 | −0.512294 | −0.256147 | − | 0.966638i | \(-0.582453\pi\) | ||||
−0.256147 | + | 0.966638i | \(0.582453\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.41318 | 0.378348 | 0.189174 | − | 0.981944i | \(-0.439419\pi\) | ||||
0.189174 | + | 0.981944i | \(0.439419\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.6280 | −0.587002 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.1832 | 0.887329 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 21.0743 | 0.841627 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 70.2430 | 2.80077 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.18518 | −0.246228 | −0.123114 | − | 0.992393i | \(-0.539288\pi\) | ||||
−0.123114 | + | 0.992393i | \(0.539288\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −38.9944 | −1.54989 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.64404 | 0.184293 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.24797 | 0.128488 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.4679 | −1.16391 | −0.581956 | − | 0.813220i | \(-0.697713\pi\) | ||||
−0.581956 | + | 0.813220i | \(0.697713\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.7043 | −0.501008 | −0.250504 | − | 0.968116i | \(-0.580596\pi\) | ||||
−0.250504 | + | 0.968116i | \(0.580596\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.8035 | −0.504137 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 44.9669 | 1.76783 | 0.883916 | − | 0.467646i | \(-0.154898\pi\) | ||||
0.883916 | + | 0.467646i | \(0.154898\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.27182 | 0.0891768 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.0416 | −0.588622 | −0.294311 | − | 0.955710i | \(-0.595090\pi\) | ||||
−0.294311 | + | 0.955710i | \(0.595090\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.14687 | −0.122958 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.2670 | −0.634638 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.5218 | 1.11105 | 0.555525 | − | 0.831500i | \(-0.312517\pi\) | ||||
0.555525 | + | 0.831500i | \(0.312517\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.2979 | −0.789497 | −0.394749 | − | 0.918789i | \(-0.629168\pi\) | ||||
−0.394749 | + | 0.918789i | \(0.629168\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −98.8718 | −3.83986 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −30.6486 | −1.18672 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 30.3852 | 1.17476 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.55092 | 0.137082 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.39334 | −0.0922565 | −0.0461283 | − | 0.998936i | \(-0.514688\pi\) | ||||
−0.0461283 | + | 0.998936i | \(0.514688\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.5509 | 0.406104 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.4381 | −0.708635 | −0.354318 | − | 0.935125i | \(-0.615287\pi\) | ||||
−0.354318 | + | 0.935125i | \(0.615287\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.8057 | −0.452394 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.1922 | 0.963951 | 0.481976 | − | 0.876185i | \(-0.339919\pi\) | ||||
0.481976 | + | 0.876185i | \(0.339919\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.571701 | 0.0218436 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 58.7126 | 2.24003 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −26.5983 | −1.01331 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.6772 | 0.938767 | 0.469383 | − | 0.882995i | \(-0.344476\pi\) | ||||
0.469383 | + | 0.882995i | \(0.344476\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.0822 | 0.382439 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 45.0761 | 1.70738 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.0189825 | 0.000717986 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.68273 | 0.252403 | 0.126202 | − | 0.992005i | \(-0.459721\pi\) | ||||
0.126202 | + | 0.992005i | \(0.459721\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 80.1117 | 3.02147 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.94639 | 0.374603 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.4584 | −0.918556 | −0.459278 | − | 0.888293i | \(-0.651892\pi\) | ||||
−0.459278 | + | 0.888293i | \(0.651892\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 30.9123 | 1.15930 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.2836 | −0.759628 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.33354 | 0.0872693 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 39.2647 | 1.46637 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.7612 | −1.03532 | −0.517659 | − | 0.855587i | \(-0.673197\pi\) | ||||
−0.517659 | + | 0.855587i | \(0.673197\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25.3894 | −0.944242 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.1062 | 0.821005 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.47341 | 0.165909 | 0.0829547 | − | 0.996553i | \(-0.473564\pi\) | ||||
0.0829547 | + | 0.996553i | \(0.473564\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −39.3977 | −1.45918 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 79.3241 | 2.93391 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.3028 | −0.639093 | −0.319546 | − | 0.947571i | \(-0.603531\pi\) | ||||
−0.319546 | + | 0.947571i | \(0.603531\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.31705 | −0.343198 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.9235 | 1.43182 | 0.715912 | − | 0.698190i | \(-0.246011\pi\) | ||||
0.715912 | + | 0.698190i | \(0.246011\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −112.763 | −4.14244 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.0704 | 0.662938 | 0.331469 | − | 0.943466i | \(-0.392456\pi\) | ||||
0.331469 | + | 0.943466i | \(0.392456\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.07874 | 0.0761591 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −34.8845 | −1.27636 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.6433 | 0.388381 | 0.194191 | − | 0.980964i | \(-0.437792\pi\) | ||||
0.194191 | + | 0.980964i | \(0.437792\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 36.4255 | 1.32742 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.29615 | 0.229140 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.5106 | −0.454704 | −0.227352 | − | 0.973813i | \(-0.573007\pi\) | ||||
−0.227352 | + | 0.973813i | \(0.573007\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −17.4387 | −0.632985 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.89546 | −0.141210 | −0.0706052 | − | 0.997504i | \(-0.522493\pi\) | ||||
−0.0706052 | + | 0.997504i | \(0.522493\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11.8296 | 0.427700 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.1559 | −0.438923 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.2686 | 1.09151 | 0.545757 | − | 0.837944i | \(-0.316242\pi\) | ||||
0.545757 | + | 0.837944i | \(0.316242\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.710672 | 0.0255942 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.84529 | 0.282175 | 0.141088 | − | 0.989997i | \(-0.454940\pi\) | ||||
0.141088 | + | 0.989997i | \(0.454940\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.6302 | 0.525531 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 51.4090 | 1.84192 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.846083 | 0.0302752 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.0821 | 0.360304 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.352668 | −0.0125873 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.1333 | −0.717673 | −0.358837 | − | 0.933400i | \(-0.616826\pi\) | ||||
−0.358837 | + | 0.933400i | \(0.616826\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −30.1118 | −1.07201 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.0000 | −0.674709 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.66937 | 0.201072 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.1420 | −0.465513 | −0.232756 | − | 0.972535i | \(-0.574774\pi\) | ||||
−0.232756 | + | 0.972535i | \(0.574774\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −61.6229 | −2.18006 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −55.9239 | −1.97598 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.23751 | −0.149538 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −60.6403 | −2.13464 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.6861 | −0.481176 | −0.240588 | − | 0.970627i | \(-0.577340\pi\) | ||||
−0.240588 | + | 0.970627i | \(0.577340\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.85644 | −0.170533 | −0.0852664 | − | 0.996358i | \(-0.527174\pi\) | ||||
−0.0852664 | + | 0.996358i | \(0.527174\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.7933 | 0.659111 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.37000 | 0.0479892 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 90.4686 | 3.16510 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.05140 | 0.0715945 | 0.0357972 | − | 0.999359i | \(-0.488603\pi\) | ||||
0.0357972 | + | 0.999359i | \(0.488603\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −48.4903 | −1.69027 | −0.845133 | − | 0.534557i | \(-0.820479\pi\) | ||||
−0.845133 | + | 0.534557i | \(0.820479\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.5782 | 0.437916 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.9782 | −1.18154 | −0.590769 | − | 0.806841i | \(-0.701176\pi\) | ||||
−0.590769 | + | 0.806841i | \(0.701176\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.72044 | 0.268142 | 0.134071 | − | 0.990972i | \(-0.457195\pi\) | ||||
0.134071 | + | 0.990972i | \(0.457195\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.4125 | 0.777482 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.52020 | 0.191034 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.67243 | 0.230633 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.333364 | 0.0115090 | 0.00575450 | − | 0.999983i | \(-0.498168\pi\) | ||||
0.00575450 | + | 0.999983i | \(0.498168\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.87605 | −0.271588 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −26.9751 | −0.929073 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.81658 | −0.234497 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 53.5184 | 1.83675 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −66.2913 | −2.27244 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.39326 | 0.0477044 | 0.0238522 | − | 0.999715i | \(-0.492407\pi\) | ||||
0.0238522 | + | 0.999715i | \(0.492407\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13.4916 | 0.461403 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.5232 | −0.461944 | −0.230972 | − | 0.972960i | \(-0.574191\pi\) | ||||
−0.230972 | + | 0.972960i | \(0.574191\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.5872 | −1.14598 | −0.572991 | − | 0.819562i | \(-0.694217\pi\) | ||||
−0.572991 | + | 0.819562i | \(0.694217\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30.5039 | −1.03837 | −0.519183 | − | 0.854663i | \(-0.673764\pi\) | ||||
−0.519183 | + | 0.854663i | \(0.673764\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.43645 | −0.252847 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −86.1090 | −2.92442 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.05255 | 0.273164 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 49.8529 | 1.68920 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 29.8620 | 1.01068 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.25529 | 0.278761 | 0.139381 | − | 0.990239i | \(-0.455489\pi\) | ||||
0.139381 | + | 0.990239i | \(0.455489\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.50725 | 0.185755 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.1220 | 0.846383 | 0.423192 | − | 0.906040i | \(-0.360910\pi\) | ||||
0.423192 | + | 0.906040i | \(0.360910\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.3039 | −0.784238 | −0.392119 | − | 0.919914i | \(-0.628258\pi\) | ||||
−0.392119 | + | 0.919914i | \(0.628258\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.59100 | 0.0870955 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 51.9301 | 1.74364 | 0.871820 | − | 0.489826i | \(-0.162940\pi\) | ||||
0.871820 | + | 0.489826i | \(0.162940\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.77990 | −0.193634 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −70.2806 | −2.35185 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.20247 | −0.207326 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 93.3096 | 3.11552 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.9801 | 0.466262 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −35.1246 | −1.17017 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.20810 | 0.206364 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.0978 | −0.932973 | −0.466487 | − | 0.884528i | \(-0.654480\pi\) | ||||
−0.466487 | + | 0.884528i | \(0.654480\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 58.9857 | 1.95643 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.1123 | −1.69343 | −0.846714 | − | 0.532049i | \(-0.821422\pi\) | ||||
−0.846714 | + | 0.532049i | \(0.821422\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.08729 | −0.300745 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.04981 | 0.133882 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.05588 | −0.133791 | −0.0668956 | − | 0.997760i | \(-0.521309\pi\) | ||||
−0.0668956 | + | 0.997760i | \(0.521309\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −37.5184 | −1.23627 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.52715 | −0.149013 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 47.8146 | 1.57213 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.25577 | 0.106934 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.71675 | −0.0563246 | −0.0281623 | − | 0.999603i | \(-0.508966\pi\) | ||||
−0.0281623 | + | 0.999603i | \(0.508966\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 32.7487 | 1.07214 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.08157 | 0.100778 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.89546 | −0.127259 | −0.0636296 | − | 0.997974i | \(-0.520268\pi\) | ||||
−0.0636296 | + | 0.997974i | \(0.520268\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 38.4327 | 1.25420 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.6407 | 1.22705 | 0.613525 | − | 0.789675i | \(-0.289751\pi\) | ||||
0.613525 | + | 0.789675i | \(0.289751\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −42.5402 | −1.38530 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.0897 | 0.360367 | 0.180184 | − | 0.983633i | \(-0.442331\pi\) | ||||
0.180184 | + | 0.983633i | \(0.442331\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.6737 | 0.736020 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 68.6921 | 2.22750 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.4833 | 0.760699 | 0.380350 | − | 0.924843i | \(-0.375804\pi\) | ||||
0.380350 | + | 0.924843i | \(0.375804\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.20770 | −0.168517 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.0193 | 0.388528 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.7478 | −0.701543 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.71279 | −0.0874183 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.32510 | 0.300186 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.1743 | −0.713078 | −0.356539 | − | 0.934280i | \(-0.616043\pi\) | ||||
−0.356539 | + | 0.934280i | \(0.616043\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −148.910 | −4.78367 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.5159 | 1.33231 | 0.666155 | − | 0.745813i | \(-0.267939\pi\) | ||||
0.666155 | + | 0.745813i | \(0.267939\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −67.3023 | −2.15540 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.9729 | −0.894934 | −0.447467 | − | 0.894301i | \(-0.647674\pi\) | ||||
−0.447467 | + | 0.894301i | \(0.647674\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.5680 | −0.465595 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −39.5978 | −1.26426 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.3066 | −0.870945 | −0.435473 | − | 0.900202i | \(-0.643419\pi\) | ||||
−0.435473 | + | 0.900202i | \(0.643419\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.51231 | 0.271225 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −74.8615 | −2.38046 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45.5649 | −1.44742 | −0.723708 | − | 0.690106i | \(-0.757564\pi\) | ||||
−0.723708 | + | 0.690106i | \(0.757564\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24.1973 | −0.767877 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.39442 | −0.234419 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.6148 | −0.652877 | −0.326438 | − | 0.945219i | \(-0.605849\pi\) | ||||
−0.326438 | + | 0.945219i | \(0.605849\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 21.8070 | 0.689942 |
(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 | 8624.2.a.de.1.2 | 8 | ||
4.3 | odd | 2 | 4312.2.a.bi.1.7 | yes | 8 | ||
7.6 | odd | 2 | inner | 8624.2.a.de.1.7 | 8 | ||
28.27 | even | 2 | 4312.2.a.bi.1.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4312.2.a.bi.1.2 | ✓ | 8 | 28.27 | even | 2 | ||
4312.2.a.bi.1.7 | yes | 8 | 4.3 | odd | 2 | ||
8624.2.a.de.1.2 | 8 | 1.1 | even | 1 | trivial | ||
8624.2.a.de.1.7 | 8 | 7.6 | odd | 2 | inner |