Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2112,2,Mod(1,2112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2112, 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("2112.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2112 = 2^{6} \cdot 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2112.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: | \(16.8644049069\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 1056) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.254102\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2112.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.508203 | −0.227275 | −0.113638 | − | 0.993522i | \(-0.536250\pi\) | ||||
−0.113638 | + | 0.993522i | \(0.536250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.87086 | 1.46305 | 0.731525 | − | 0.681815i | \(-0.238809\pi\) | ||||
0.731525 | + | 0.681815i | \(0.238809\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.508203 | −0.140950 | −0.0704751 | − | 0.997514i | \(-0.522452\pi\) | ||||
−0.0704751 | + | 0.997514i | \(0.522452\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.508203 | −0.131218 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.36266 | 1.78571 | 0.892854 | − | 0.450347i | \(-0.148700\pi\) | ||||
0.892854 | + | 0.450347i | \(0.148700\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.36266 | 1.23028 | 0.615139 | − | 0.788418i | \(-0.289100\pi\) | ||||
0.615139 | + | 0.788418i | \(0.289100\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.87086 | 0.844692 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.50820 | 0.522997 | 0.261498 | − | 0.965204i | \(-0.415783\pi\) | ||||
0.261498 | + | 0.965204i | \(0.415783\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.74173 | −0.948346 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.36266 | −1.36721 | −0.683606 | − | 0.729851i | \(-0.739589\pi\) | ||||
−0.683606 | + | 0.729851i | \(0.739589\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.7253 | −1.92632 | −0.963162 | − | 0.268920i | \(-0.913333\pi\) | ||||
−0.963162 | + | 0.268920i | \(0.913333\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.96719 | −0.332515 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.72532 | −1.43443 | −0.717217 | − | 0.696850i | \(-0.754584\pi\) | ||||
−0.717217 | + | 0.696850i | \(0.754584\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.508203 | −0.0813777 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.37907 | 1.30859 | 0.654295 | − | 0.756239i | \(-0.272965\pi\) | ||||
0.654295 | + | 0.756239i | \(0.272965\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.37907 | −0.362804 | −0.181402 | − | 0.983409i | \(-0.558064\pi\) | ||||
−0.181402 | + | 0.983409i | \(0.558064\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.508203 | −0.0757585 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.49180 | 0.801061 | 0.400530 | − | 0.916283i | \(-0.368826\pi\) | ||||
0.400530 | + | 0.916283i | \(0.368826\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.98359 | 1.14051 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.36266 | 1.03098 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.2499 | 1.68266 | 0.841329 | − | 0.540524i | \(-0.181774\pi\) | ||||
0.841329 | + | 0.540524i | \(0.181774\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.508203 | −0.0685261 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.36266 | 0.710302 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.01641 | −0.132325 | −0.0661624 | − | 0.997809i | \(-0.521076\pi\) | ||||
−0.0661624 | + | 0.997809i | \(0.521076\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.23353 | 0.926158 | 0.463079 | − | 0.886317i | \(-0.346745\pi\) | ||||
0.463079 | + | 0.886317i | \(0.346745\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.87086 | 0.487683 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.258271 | 0.0320345 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.7581 | −1.55865 | −0.779327 | − | 0.626617i | \(-0.784439\pi\) | ||||
−0.779327 | + | 0.626617i | \(0.784439\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.50820 | 0.301952 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.5082 | 1.24709 | 0.623547 | − | 0.781786i | \(-0.285691\pi\) | ||||
0.623547 | + | 0.781786i | \(0.285691\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.7581 | 1.72731 | 0.863655 | − | 0.504084i | \(-0.168170\pi\) | ||||
0.863655 | + | 0.504084i | \(0.168170\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.74173 | −0.547528 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.87086 | 0.441126 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.14554 | −0.128884 | −0.0644418 | − | 0.997921i | \(-0.520527\pi\) | ||||
−0.0644418 | + | 0.997921i | \(0.520527\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.00000 | −0.878114 | −0.439057 | − | 0.898459i | \(-0.644687\pi\) | ||||
−0.439057 | + | 0.898459i | \(0.644687\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.74173 | −0.405848 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.36266 | −0.789360 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.96719 | −0.206217 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.7253 | −1.11216 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.72532 | −0.279612 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.01641 | 0.306270 | 0.153135 | − | 0.988205i | \(-0.451063\pi\) | ||||
0.153135 | + | 0.988205i | \(0.451063\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.637339 | 0.0634176 | 0.0317088 | − | 0.999497i | \(-0.489905\pi\) | ||||
0.0317088 | + | 0.999497i | \(0.489905\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.0164 | −1.28254 | −0.641272 | − | 0.767313i | \(-0.721593\pi\) | ||||
−0.641272 | + | 0.767313i | \(0.721593\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.96719 | −0.191978 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.72532 | −0.650161 | −0.325081 | − | 0.945686i | \(-0.605391\pi\) | ||||
−0.325081 | + | 0.945686i | \(0.605391\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.508203 | −0.0486771 | −0.0243385 | − | 0.999704i | \(-0.507748\pi\) | ||||
−0.0243385 | + | 0.999704i | \(0.507748\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.72532 | −0.828171 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.725323 | −0.0682326 | −0.0341163 | − | 0.999418i | \(-0.510862\pi\) | ||||
−0.0341163 | + | 0.999418i | \(0.510862\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.27468 | −0.118864 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.508203 | −0.0469834 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 28.4999 | 2.61258 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.37907 | 0.755515 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.95078 | 0.442811 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.14554 | −0.101650 | −0.0508252 | − | 0.998708i | \(-0.516185\pi\) | ||||
−0.0508252 | + | 0.998708i | \(0.516185\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.37907 | −0.209465 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.7253 | 0.937076 | 0.468538 | − | 0.883443i | \(-0.344781\pi\) | ||||
0.468538 | + | 0.883443i | \(0.344781\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20.7581 | 1.79996 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.508203 | −0.0437392 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.7089 | −1.00036 | −0.500180 | − | 0.865921i | \(-0.666733\pi\) | ||||
−0.500180 | + | 0.865921i | \(0.666733\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.39547 | 0.627276 | 0.313638 | − | 0.949543i | \(-0.398452\pi\) | ||||
0.313638 | + | 0.949543i | \(0.398452\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.49180 | 0.462493 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.508203 | −0.0424981 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.74173 | 0.310734 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.98359 | 0.658476 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.4119 | 0.852975 | 0.426487 | − | 0.904494i | \(-0.359751\pi\) | ||||
0.426487 | + | 0.904494i | \(0.359751\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.6290 | −1.35325 | −0.676624 | − | 0.736328i | \(-0.736558\pi\) | ||||
−0.676624 | + | 0.736328i | \(0.736558\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.36266 | 0.595236 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.45065 | 0.437806 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.01641 | 0.559970 | 0.279985 | − | 0.960004i | \(-0.409670\pi\) | ||||
0.279985 | + | 0.960004i | \(0.409670\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.2499 | 0.971483 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.70892 | 0.765170 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.75814 | 0.685990 | 0.342995 | − | 0.939337i | \(-0.388559\pi\) | ||||
0.342995 | + | 0.939337i | \(0.388559\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.508203 | −0.0395636 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.70892 | −0.441769 | −0.220885 | − | 0.975300i | \(-0.570894\pi\) | ||||
−0.220885 | + | 0.975300i | \(0.570894\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7417 | −0.980133 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.36266 | 0.410093 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.36266 | −0.559773 | −0.279886 | − | 0.960033i | \(-0.590297\pi\) | ||||
−0.279886 | + | 0.960033i | \(0.590297\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.3546 | −1.38748 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.01641 | −0.0763978 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.98359 | −0.521978 | −0.260989 | − | 0.965342i | \(-0.584049\pi\) | ||||
−0.260989 | + | 0.965342i | \(0.584049\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.98359 | 0.370428 | 0.185214 | − | 0.982698i | \(-0.440702\pi\) | ||||
0.185214 | + | 0.982698i | \(0.440702\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.23353 | 0.534718 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.43424 | 0.326012 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.36266 | 0.538411 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.87086 | 0.281564 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.54102 | −0.328576 | −0.164288 | − | 0.986412i | \(-0.552533\pi\) | ||||
−0.164288 | + | 0.986412i | \(0.552533\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.4671 | 1.47325 | 0.736625 | − | 0.676301i | \(-0.236418\pi\) | ||||
0.736625 | + | 0.676301i | \(0.236418\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.258271 | 0.0184951 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.63734 | 0.615385 | 0.307692 | − | 0.951486i | \(-0.400443\pi\) | ||||
0.307692 | + | 0.951486i | \(0.400443\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.74173 | 0.548797 | 0.274398 | − | 0.961616i | \(-0.411521\pi\) | ||||
0.274398 | + | 0.961616i | \(0.411521\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.7581 | −0.899890 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −28.4999 | −2.00030 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.25827 | −0.297411 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.50820 | 0.174332 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.36266 | 0.370943 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.0716 | −1.31294 | −0.656471 | − | 0.754351i | \(-0.727951\pi\) | ||||
−0.656471 | + | 0.754351i | \(0.727951\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.5082 | 0.720010 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.20905 | 0.0824566 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −41.5163 | −2.81831 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.7581 | 0.997262 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.74173 | −0.251696 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.74173 | −0.316115 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.2088 | −1.47405 | −0.737024 | − | 0.675866i | \(-0.763770\pi\) | ||||
−0.737024 | + | 0.675866i | \(0.763770\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.7089 | 1.03807 | 0.519037 | − | 0.854752i | \(-0.326291\pi\) | ||||
0.519037 | + | 0.854752i | \(0.326291\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.87086 | 0.254684 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −23.1044 | −1.51362 | −0.756809 | − | 0.653636i | \(-0.773243\pi\) | ||||
−0.756809 | + | 0.653636i | \(0.773243\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.79095 | −0.182061 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.14554 | −0.0744110 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.7417 | 1.01825 | 0.509124 | − | 0.860693i | \(-0.329969\pi\) | ||||
0.509124 | + | 0.860693i | \(0.329969\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.74173 | −0.369857 | −0.184929 | − | 0.982752i | \(-0.559205\pi\) | ||||
−0.184929 | + | 0.982752i | \(0.559205\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.05729 | −0.259211 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.72532 | −0.173408 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.00000 | −0.506979 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.4671 | 1.92306 | 0.961532 | − | 0.274694i | \(-0.0885766\pi\) | ||||
0.961532 | + | 0.274694i | \(0.0885766\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.50820 | 0.157689 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.74173 | −0.234316 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.0000 | −0.873296 | −0.436648 | − | 0.899632i | \(-0.643834\pi\) | ||||
−0.436648 | + | 0.899632i | \(0.643834\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −33.7745 | −2.09865 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.36266 | −0.455737 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −26.7253 | −1.64795 | −0.823977 | − | 0.566623i | \(-0.808250\pi\) | ||||
−0.823977 | + | 0.566623i | \(0.808250\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.22546 | −0.382427 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.00000 | 0.122398 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −27.2335 | −1.66046 | −0.830229 | − | 0.557423i | \(-0.811790\pi\) | ||||
−0.830229 | + | 0.557423i | \(0.811790\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.8216 | −0.778859 | −0.389430 | − | 0.921056i | \(-0.627328\pi\) | ||||
−0.389430 | + | 0.921056i | \(0.627328\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.96719 | −0.119060 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.74173 | −0.285937 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.5082 | 0.751545 | 0.375773 | − | 0.926712i | \(-0.377377\pi\) | ||||
0.375773 | + | 0.926712i | \(0.377377\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.7253 | −0.642108 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.3955 | −0.799107 | −0.399554 | − | 0.916710i | \(-0.630835\pi\) | ||||
−0.399554 | + | 0.916710i | \(0.630835\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.1372 | 1.85091 | 0.925457 | − | 0.378852i | \(-0.123681\pi\) | ||||
0.925457 | + | 0.378852i | \(0.123681\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.72532 | −0.161434 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 32.4342 | 1.91453 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 37.2088 | 2.18875 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.01641 | 0.176825 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.8297 | 1.27531 | 0.637653 | − | 0.770324i | \(-0.279905\pi\) | ||||
0.637653 | + | 0.770324i | \(0.279905\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.516541 | 0.0300742 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.27468 | −0.0737165 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.20905 | −0.530801 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.637339 | 0.0366142 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.67610 | −0.210493 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.0552 | −0.802171 | −0.401085 | − | 0.916041i | \(-0.631367\pi\) | ||||
−0.401085 | + | 0.916041i | \(0.631367\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.0164 | −0.740478 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.5082 | 0.595866 | 0.297933 | − | 0.954587i | \(-0.403703\pi\) | ||||
0.297933 | + | 0.954587i | \(0.403703\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.69251 | 0.152190 | 0.0760948 | − | 0.997101i | \(-0.475755\pi\) | ||||
0.0760948 | + | 0.997101i | \(0.475755\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.96719 | −0.110838 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.54102 | 0.367380 | 0.183690 | − | 0.982984i | \(-0.441196\pi\) | ||||
0.183690 | + | 0.982984i | \(0.441196\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.36266 | −0.412230 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.72532 | −0.375371 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 39.4835 | 2.19692 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.40976 | 0.133670 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.508203 | −0.0281037 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 21.2580 | 1.17199 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.7253 | −1.68882 | −0.844408 | − | 0.535700i | \(-0.820048\pi\) | ||||
−0.844408 | + | 0.535700i | \(0.820048\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.72532 | −0.478145 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.48373 | 0.354244 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.1760 | −1.64379 | −0.821895 | − | 0.569639i | \(-0.807083\pi\) | ||||
−0.821895 | + | 0.569639i | \(0.807083\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.725323 | −0.0393941 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.7253 | −0.580809 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.80736 | 0.205578 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.27468 | −0.0686263 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.0328 | −0.968052 | −0.484026 | − | 0.875054i | \(-0.660826\pi\) | ||||
−0.484026 | + | 0.875054i | \(0.660826\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.21712 | 0.118680 | 0.0593398 | − | 0.998238i | \(-0.481100\pi\) | ||||
0.0593398 | + | 0.998238i | \(0.481100\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.508203 | −0.0271259 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.4835 | −0.717652 | −0.358826 | − | 0.933404i | \(-0.616823\pi\) | ||||
−0.358826 | + | 0.933404i | \(0.616823\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.34030 | −0.283434 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 28.4999 | 1.50837 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.4999 | −1.08194 | −0.540971 | − | 0.841041i | \(-0.681943\pi\) | ||||
−0.540971 | + | 0.841041i | \(0.681943\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.75814 | 0.513586 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.50013 | −0.392575 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.0328 | −0.941305 | −0.470653 | − | 0.882319i | \(-0.655981\pi\) | ||||
−0.470653 | + | 0.882319i | \(0.655981\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.37907 | 0.436197 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 47.4178 | 2.46181 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.2335 | −0.581650 | −0.290825 | − | 0.956776i | \(-0.593930\pi\) | ||||
−0.290825 | + | 0.956776i | \(0.593930\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.95078 | 0.255657 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.74173 | 0.192709 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.24186 | −0.371990 | −0.185995 | − | 0.982551i | \(-0.559551\pi\) | ||||
−0.185995 | + | 0.982551i | \(0.559551\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.14554 | −0.0586879 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.9588 | 1.22424 | 0.612120 | − | 0.790765i | \(-0.290317\pi\) | ||||
0.612120 | + | 0.790765i | \(0.290317\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.96719 | −0.100257 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.37907 | −0.120935 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.47539 | −0.328315 | −0.164158 | − | 0.986434i | \(-0.552491\pi\) | ||||
−0.164158 | + | 0.986434i | \(0.552491\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.4671 | 0.933919 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.7253 | 0.541021 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.582168 | 0.0292921 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.1924 | −0.963238 | −0.481619 | − | 0.876381i | \(-0.659951\pi\) | ||||
−0.481619 | + | 0.876381i | \(0.659951\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 20.7581 | 1.03921 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.7745 | 0.587993 | 0.293996 | − | 0.955807i | \(-0.405015\pi\) | ||||
0.293996 | + | 0.955807i | \(0.405015\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.45065 | 0.271516 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.508203 | −0.0252528 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.72532 | −0.432498 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −35.1924 | −1.74015 | −0.870075 | − | 0.492919i | \(-0.835930\pi\) | ||||
−0.870075 | + | 0.492919i | \(0.835930\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.7089 | −0.577558 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.93437 | −0.193598 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.06563 | 0.199574 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.39547 | 0.362158 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.9836 | −0.731996 | −0.365998 | − | 0.930616i | \(-0.619272\pi\) | ||||
−0.365998 | + | 0.930616i | \(0.619272\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.4178 | −1.23879 | −0.619395 | − | 0.785080i | \(-0.712622\pi\) | ||||
−0.619395 | + | 0.785080i | \(0.712622\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.49180 | 0.267020 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −34.9117 | −1.69347 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 28.0000 | 1.35501 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.508203 | −0.0245363 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.2088 | 1.26243 | 0.631216 | − | 0.775607i | \(-0.282556\pi\) | ||||
0.631216 | + | 0.775607i | \(0.282556\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.2747 | 0.734054 | 0.367027 | − | 0.930210i | \(-0.380376\pi\) | ||||
0.367027 | + | 0.930210i | \(0.380376\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.74173 | 0.179402 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.4506 | 0.643432 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.42022 | −0.306420 | −0.153210 | − | 0.988194i | \(-0.548961\pi\) | ||||
−0.153210 | + | 0.988194i | \(0.548961\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.98359 | 0.380171 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.4999 | −0.783932 | −0.391966 | − | 0.919980i | \(-0.628205\pi\) | ||||
−0.391966 | + | 0.919980i | \(0.628205\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.01641 | −0.0481823 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.4119 | 0.492465 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.4999 | −0.495519 | −0.247760 | − | 0.968822i | \(-0.579694\pi\) | ||||
−0.247760 | + | 0.968822i | \(0.579694\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.37907 | 0.394555 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.6290 | −0.781299 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.999731 | 0.0468681 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.7745 | −0.737902 | −0.368951 | − | 0.929449i | \(-0.620283\pi\) | ||||
−0.368951 | + | 0.929449i | \(0.620283\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.36266 | 0.343660 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.6537 | −0.822217 | −0.411108 | − | 0.911586i | \(-0.634858\pi\) | ||||
−0.411108 | + | 0.911586i | \(0.634858\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.4999 | −1.69629 | −0.848146 | − | 0.529762i | \(-0.822281\pi\) | ||||
−0.848146 | + | 0.529762i | \(0.822281\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.45065 | 0.252768 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.03281 | 0.279165 | 0.139583 | − | 0.990210i | \(-0.455424\pi\) | ||||
0.139583 | + | 0.990210i | \(0.455424\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −49.3850 | −2.28039 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.01641 | 0.323299 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.37907 | −0.109390 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −25.4283 | −1.16673 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.2499 | 0.560886 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.65970 | −0.304289 | −0.152145 | − | 0.988358i | \(-0.548618\pi\) | ||||
−0.152145 | + | 0.988358i | \(0.548618\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.43424 | 0.202184 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.70892 | 0.441771 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.53295 | −0.0696076 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.2583 | 0.736733 | 0.368366 | − | 0.929681i | \(-0.379917\pi\) | ||||
0.368366 | + | 0.929681i | \(0.379917\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.75814 | 0.396057 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.7581 | 0.756284 | 0.378142 | − | 0.925748i | \(-0.376563\pi\) | ||||
0.378142 | + | 0.925748i | \(0.376563\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −54.2088 | −2.44144 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.508203 | −0.0228420 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 40.6758 | 1.82456 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.0328 | 0.628195 | 0.314098 | − | 0.949391i | \(-0.398298\pi\) | ||||
0.314098 | + | 0.949391i | \(0.398298\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.70892 | −0.255056 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.74173 | 0.345187 | 0.172593 | − | 0.984993i | \(-0.444785\pi\) | ||||
0.172593 | + | 0.984993i | \(0.444785\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.323898 | −0.0144133 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.7417 | −0.565880 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.7006 | 1.13916 | 0.569579 | − | 0.821937i | \(-0.307106\pi\) | ||||
0.569579 | + | 0.821937i | \(0.307106\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 57.1267 | 2.52714 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.36266 | 0.236767 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.61498 | 0.291491 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.49180 | 0.241529 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.36266 | −0.323185 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.7089 | −0.863463 | −0.431732 | − | 0.902002i | \(-0.642097\pi\) | ||||
−0.431732 | + | 0.902002i | \(0.642097\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.3463 | −1.06459 | −0.532294 | − | 0.846560i | \(-0.678670\pi\) | ||||
−0.532294 | + | 0.846560i | \(0.678670\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −18.3546 | −0.801060 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −78.9669 | −3.43985 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.7089 | −0.726475 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.01641 | −0.0441083 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.25827 | −0.184446 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.41783 | 0.147766 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.98359 | −0.301364 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.98359 | 0.343878 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.9753 | 0.643837 | 0.321918 | − | 0.946767i | \(-0.395672\pi\) | ||||
0.321918 | + | 0.946767i | \(0.395672\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.98359 | 0.213866 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.258271 | 0.0110631 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.8461 | −0.891316 | −0.445658 | − | 0.895203i | \(-0.647030\pi\) | ||||
−0.445658 | + | 0.895203i | \(0.647030\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.23353 | 0.308719 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −39.4835 | −1.68205 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.43424 | −0.188563 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.43424 | 0.188223 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.13720 | −0.0481849 | −0.0240924 | − | 0.999710i | \(-0.507670\pi\) | ||||
−0.0240924 | + | 0.999710i | \(0.507670\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.20905 | 0.0511374 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.36266 | 0.310852 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.9341 | 1.38801 | 0.694003 | − | 0.719972i | \(-0.255845\pi\) | ||||
0.694003 | + | 0.719972i | \(0.255845\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.368611 | 0.0155076 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.87086 | 0.162561 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.91202 | 0.415533 | 0.207767 | − | 0.978178i | \(-0.433381\pi\) | ||||
0.207767 | + | 0.978178i | \(0.433381\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.0880 | 1.34284 | 0.671420 | − | 0.741077i | \(-0.265685\pi\) | ||||
0.671420 | + | 0.741077i | \(0.265685\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.54102 | −0.189704 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.8932 | −0.495982 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.1924 | −1.29856 | −0.649278 | − | 0.760551i | \(-0.724929\pi\) | ||||
−0.649278 | + | 0.760551i | \(0.724929\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.4671 | 0.850582 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −30.9669 | −1.28472 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.2499 | 0.507340 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.258271 | 0.0106782 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.4671 | 0.927314 | 0.463657 | − | 0.886015i | \(-0.346537\pi\) | ||||
0.463657 | + | 0.886015i | \(0.346537\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −57.5163 | −2.36992 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.63734 | 0.355293 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.6045 | 0.435476 | 0.217738 | − | 0.976007i | \(-0.430132\pi\) | ||||
0.217738 | + | 0.976007i | \(0.430132\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.4837 | −0.593775 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.74173 | 0.316848 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.5082 | 0.429354 | 0.214677 | − | 0.976685i | \(-0.431130\pi\) | ||||
0.214677 | + | 0.976685i | \(0.431130\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.5163 | 1.12241 | 0.561206 | − | 0.827676i | \(-0.310338\pi\) | ||||
0.561206 | + | 0.827676i | \(0.310338\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.7581 | −0.519551 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.508203 | −0.0206614 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −46.0796 | −1.87032 | −0.935158 | − | 0.354232i | \(-0.884742\pi\) | ||||
−0.935158 | + | 0.354232i | \(0.884742\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −28.4999 | −1.15487 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.79095 | −0.112910 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.2335 | 1.26151 | 0.630755 | − | 0.775982i | \(-0.282745\pi\) | ||||
0.630755 | + | 0.775982i | \(0.282745\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.25827 | −0.171710 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 49.6594 | 1.99921 | 0.999607 | − | 0.0280467i | \(-0.00892871\pi\) | ||||
0.999607 | + | 0.0280467i | \(0.00892871\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.00000 | −0.321547 | −0.160774 | − | 0.986991i | \(-0.551399\pi\) | ||||
−0.160774 | + | 0.986991i | \(0.551399\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.50820 | 0.100651 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.74173 | 0.310166 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.1926 | 0.847706 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.36266 | 0.214164 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −64.2416 | −2.56148 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.1760 | −1.28091 | −0.640453 | − | 0.767998i | \(-0.721253\pi\) | ||||
−0.640453 | + | 0.767998i | \(0.721253\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19.0716 | −0.758027 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.582168 | 0.0231026 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.05729 | −0.160756 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.5082 | 0.415698 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.5327 | 0.968983 | 0.484491 | − | 0.874796i | \(-0.339005\pi\) | ||||
0.484491 | + | 0.874796i | \(0.339005\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.4178 | −0.765765 | −0.382882 | − | 0.923797i | \(-0.625069\pi\) | ||||
−0.382882 | + | 0.923797i | \(0.625069\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.20905 | 0.0476063 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.97526 | −0.195597 | −0.0977987 | − | 0.995206i | \(-0.531180\pi\) | ||||
−0.0977987 | + | 0.995206i | \(0.531180\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.01641 | −0.0398975 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −41.5163 | −1.62715 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32.2499 | −1.26204 | −0.631019 | − | 0.775768i | \(-0.717363\pi\) | ||||
−0.631019 | + | 0.775768i | \(0.717363\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.45065 | −0.212974 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.7581 | 0.575770 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.4835 | −0.447332 | −0.223666 | − | 0.974666i | \(-0.571802\pi\) | ||||
−0.223666 | + | 0.974666i | \(0.571802\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.9833 | 1.78854 | 0.894272 | − | 0.447524i | \(-0.147694\pi\) | ||||
0.894272 | + | 0.447524i | \(0.147694\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.74173 | −0.145317 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.5494 | −0.409086 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.4671 | −0.715047 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.23353 | 0.279247 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.4014 | 0.940606 | 0.470303 | − | 0.882505i | \(-0.344145\pi\) | ||||
0.470303 | + | 0.882505i | \(0.344145\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.74173 | −0.182509 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.15388 | 0.351812 | 0.175906 | − | 0.984407i | \(-0.443714\pi\) | ||||
0.175906 | + | 0.984407i | \(0.443714\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.6761 | 0.448088 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.2088 | −0.851042 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.4014 | −1.01022 | −0.505111 | − | 0.863054i | \(-0.668549\pi\) | ||||
−0.505111 | + | 0.863054i | \(0.668549\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.95051 | 0.227357 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.7089 | 0.599333 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.22546 | −0.237171 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.5163 | −0.970685 | −0.485342 | − | 0.874324i | \(-0.661305\pi\) | ||||
−0.485342 | + | 0.874324i | \(0.661305\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.87086 | 0.147042 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.75841 | −0.142564 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 61.6922 | 2.33676 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.1044 | −0.873888 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.10439 | −0.268329 | −0.134165 | − | 0.990959i | \(-0.542835\pi\) | ||||
−0.134165 | + | 0.990959i | \(0.542835\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −46.7909 | −1.76475 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.79095 | −0.105113 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.46705 | 0.0927830 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.77454 | 0.141756 | 0.0708780 | − | 0.997485i | \(-0.477420\pi\) | ||||
0.0708780 | + | 0.997485i | \(0.477420\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.14554 | −0.0429612 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −26.9013 | −1.00746 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.258271 | 0.00965878 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.7417 | 0.587886 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.9424 | −0.706434 | −0.353217 | − | 0.935541i | \(-0.614912\pi\) | ||||
−0.353217 | + | 0.935541i | \(0.614912\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −50.3847 | −1.87643 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.74173 | −0.213537 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 34.9117 | 1.29659 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.2583 | 0.602986 | 0.301493 | − | 0.953468i | \(-0.402515\pi\) | ||||
0.301493 | + | 0.953468i | \(0.402515\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.5163 | −0.647863 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.4918 | 0.572203 | 0.286101 | − | 0.958199i | \(-0.407641\pi\) | ||||
0.286101 | + | 0.958199i | \(0.407641\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.05729 | −0.149655 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.7581 | −0.469952 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.89561 | −0.106517 | −0.0532584 | − | 0.998581i | \(-0.516961\pi\) | ||||
−0.0532584 | + | 0.998581i | \(0.516961\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.72532 | −0.100117 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.53295 | −0.202984 | −0.101492 | − | 0.994836i | \(-0.532362\pi\) | ||||
−0.101492 | + | 0.994836i | \(0.532362\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.29135 | −0.193860 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.00000 | −0.292705 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −26.0328 | −0.951218 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.2416 | 0.446702 | 0.223351 | − | 0.974738i | \(-0.428300\pi\) | ||||
0.223351 | + | 0.974738i | \(0.428300\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 30.4671 | 1.11028 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.45091 | 0.307560 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.9669 | 0.907438 | 0.453719 | − | 0.891145i | \(-0.350097\pi\) | ||||
0.453719 | + | 0.891145i | \(0.350097\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.50820 | 0.0910420 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.6043 | −1.14565 | −0.572827 | − | 0.819677i | \(-0.694153\pi\) | ||||
−0.572827 | + | 0.819677i | \(0.694153\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.96719 | −0.0712169 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.74173 | −0.135283 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.516541 | 0.0186512 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.04922 | −0.182080 | −0.0910398 | − | 0.995847i | \(-0.529019\pi\) | ||||
−0.0910398 | + | 0.995847i | \(0.529019\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.0000 | −0.504198 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.2827 | 1.37693 | 0.688467 | − | 0.725267i | \(-0.258284\pi\) | ||||
0.688467 | + | 0.725267i | \(0.258284\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 50.8566 | 1.82682 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −33.7745 | −1.21165 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 44.9341 | 1.60993 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.5082 | 0.376013 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.36266 | −0.263120 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.56576 | −0.127267 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.5878 | 1.01905 | 0.509523 | − | 0.860457i | \(-0.329822\pi\) | ||||
0.509523 | + | 0.860457i | \(0.329822\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −26.7253 | −0.951447 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.80763 | −0.0998277 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.67610 | −0.130542 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.22546 | −0.220794 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.49180 | 0.265373 | 0.132687 | − | 0.991158i | \(-0.457640\pi\) | ||||
0.132687 | + | 0.991158i | \(0.457640\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40.4342 | 1.43046 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.00000 | 0.0706665 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.7581 | 0.520803 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.93410 | −0.173904 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.2335 | −0.958666 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.65375 | 0.198775 | 0.0993876 | − | 0.995049i | \(-0.468312\pi\) | ||||
0.0993876 | + | 0.995049i | \(0.468312\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.3463 | 0.854913 | 0.427456 | − | 0.904036i | \(-0.359410\pi\) | ||||
0.427456 | + | 0.904036i | \(0.359410\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.8216 | −0.449675 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.45091 | −0.155909 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.7581 | −0.446351 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.96719 | −0.0687391 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.84612 | −0.238931 | −0.119466 | − | 0.992838i | \(-0.538118\pi\) | ||||
−0.119466 | + | 0.992838i | \(0.538118\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 46.9669 | 1.63716 | 0.818582 | − | 0.574390i | \(-0.194761\pi\) | ||||
0.818582 | + | 0.574390i | \(0.194761\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.74173 | −0.165086 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35.5491 | −1.23616 | −0.618081 | − | 0.786114i | \(-0.712090\pi\) | ||||
−0.618081 | + | 0.786114i | \(0.712090\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.1432 | −0.977452 | −0.488726 | − | 0.872437i | \(-0.662538\pi\) | ||||
−0.488726 | + | 0.872437i | \(0.662538\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.5082 | 0.433905 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 58.7805 | 2.03662 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.90129 | 0.100403 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.7253 | −0.370721 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46.3603 | 1.60053 | 0.800267 | − | 0.599644i | \(-0.204691\pi\) | ||||
0.800267 | + | 0.599644i | \(0.204691\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.2088 | 0.869268 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.3955 | −0.461365 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.47539 | 0.222760 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.87086 | 0.133004 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 31.1372 | 1.06863 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.8849 | −0.750204 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.7006 | −0.743014 | −0.371507 | − | 0.928430i | \(-0.621159\pi\) | ||||
−0.371507 | + | 0.928430i | \(0.621159\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.72532 | −0.0932041 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −47.7969 | −1.63271 | −0.816355 | − | 0.577550i | \(-0.804009\pi\) | ||||
−0.816355 | + | 0.577550i | \(0.804009\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.758136 | −0.0258673 | −0.0129336 | − | 0.999916i | \(-0.504117\pi\) | ||||
−0.0129336 | + | 0.999916i | \(0.504117\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 32.4342 | 1.10536 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.4423 | −0.525662 | −0.262831 | − | 0.964842i | \(-0.584656\pi\) | ||||
−0.262831 | + | 0.964842i | \(0.584656\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.74173 | 0.127223 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 37.2088 | 1.26368 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.14554 | −0.0388599 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.48373 | 0.219693 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.01641 | 0.102090 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 19.1638 | 0.647855 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.2499 | 0.953932 | 0.476966 | − | 0.878922i | \(-0.341736\pi\) | ||||
0.476966 | + | 0.878922i | \(0.341736\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21.8297 | 0.736298 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.20905 | 0.108116 | 0.0540578 | − | 0.998538i | \(-0.482784\pi\) | ||||
0.0540578 | + | 0.998538i | \(0.482784\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −56.1760 | −1.89047 | −0.945236 | − | 0.326388i | \(-0.894168\pi\) | ||||
−0.945236 | + | 0.326388i | \(0.894168\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.516541 | 0.0173633 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −51.9833 | −1.74543 | −0.872715 | − | 0.488231i | \(-0.837642\pi\) | ||||
−0.872715 | + | 0.488231i | \(0.837642\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.43424 | −0.148720 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 29.4506 | 0.985528 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.54909 | 0.118633 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.27468 | −0.0425602 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 78.9669 | 2.63369 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 90.1921 | 3.00473 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.20905 | −0.306458 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.53268 | −0.0841891 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.8685 | 1.62265 | 0.811326 | − | 0.584595i | \(-0.198746\pi\) | ||||
0.811326 | + | 0.584595i | \(0.198746\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.637339 | 0.0211392 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.0245 | 0.663440 | 0.331720 | − | 0.943378i | \(-0.392371\pi\) | ||||
0.331720 | + | 0.943378i | \(0.392371\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.00000 | −0.264761 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.67610 | −0.121528 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 41.5163 | 1.37099 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.3051 | −0.669804 | −0.334902 | − | 0.942253i | \(-0.608703\pi\) | ||||
−0.334902 | + | 0.942253i | \(0.608703\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.0552 | −0.463134 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.34030 | −0.175778 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 41.3731 | 1.36034 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13.0164 | −0.427515 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29.7417 | −0.975794 | −0.487897 | − | 0.872901i | \(-0.662236\pi\) | ||||
−0.487897 | + | 0.872901i | \(0.662236\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 42.8133 | 1.40315 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.5082 | 0.344023 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.74173 | −0.122368 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.5163 | 0.376220 | 0.188110 | − | 0.982148i | \(-0.439764\pi\) | ||||
0.188110 | + | 0.982148i | \(0.439764\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.69251 | 0.0878667 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.0880 | 0.980840 | 0.490420 | − | 0.871486i | \(-0.336843\pi\) | ||||
0.490420 | + | 0.871486i | \(0.336843\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.0164 | 0.684388 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.96719 | −0.0639926 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.51654 | −0.146768 | −0.0733839 | − | 0.997304i | \(-0.523380\pi\) | ||||
−0.0733839 | + | 0.997304i | \(0.523380\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.50013 | −0.243465 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.54102 | 0.212107 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.1700 | 1.00970 | 0.504848 | − | 0.863208i | \(-0.331549\pi\) | ||||
0.504848 | + | 0.863208i | \(0.331549\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.30776 | 0.0746774 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.36266 | −0.238001 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −45.3236 | −1.46358 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 84.0325 | 2.71073 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.72532 | −0.216720 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.4014 | −0.334834 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.0796 | −0.967296 | −0.483648 | − | 0.875263i | \(-0.660689\pi\) | ||||
−0.483648 | + | 0.875263i | \(0.660689\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 39.4835 | 1.26839 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48.4999 | 1.55643 | 0.778217 | − | 0.627995i | \(-0.216124\pi\) | ||||
0.778217 | + | 0.627995i | \(0.216124\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.6269 | 0.917736 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.40976 | 0.0771742 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −53.2252 | −1.70282 | −0.851412 | − | 0.524497i | \(-0.824253\pi\) | ||||
−0.851412 | + | 0.524497i | \(0.824253\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.00000 | 0.0639203 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.508203 | −0.0162257 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −31.0081 | −0.989004 | −0.494502 | − | 0.869177i | \(-0.664650\pi\) | ||||
−0.494502 | + | 0.869177i | \(0.664650\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.38952 | −0.139862 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21.2580 | 0.676650 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.96719 | −0.189745 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.2416 | 1.15125 | 0.575626 | − | 0.817713i | \(-0.304758\pi\) | ||||
0.575626 | + | 0.817713i | \(0.304758\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −30.7253 | −0.975039 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.93437 | −0.124728 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.76647 | 0.150956 | 0.0754779 | − | 0.997147i | \(-0.475952\pi\) | ||||
0.0754779 | + | 0.997147i | \(0.475952\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.72532 | −0.276057 |
(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 | 2112.2.a.bh.1.2 | 3 | ||
3.2 | odd | 2 | 6336.2.a.cy.1.2 | 3 | |||
4.3 | odd | 2 | 2112.2.a.bg.1.2 | 3 | |||
8.3 | odd | 2 | 1056.2.a.n.1.2 | yes | 3 | ||
8.5 | even | 2 | 1056.2.a.m.1.2 | ✓ | 3 | ||
12.11 | even | 2 | 6336.2.a.cz.1.2 | 3 | |||
24.5 | odd | 2 | 3168.2.a.bg.1.2 | 3 | |||
24.11 | even | 2 | 3168.2.a.bh.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1056.2.a.m.1.2 | ✓ | 3 | 8.5 | even | 2 | ||
1056.2.a.n.1.2 | yes | 3 | 8.3 | odd | 2 | ||
2112.2.a.bg.1.2 | 3 | 4.3 | odd | 2 | |||
2112.2.a.bh.1.2 | 3 | 1.1 | even | 1 | trivial | ||
3168.2.a.bg.1.2 | 3 | 24.5 | odd | 2 | |||
3168.2.a.bh.1.2 | 3 | 24.11 | even | 2 | |||
6336.2.a.cy.1.2 | 3 | 3.2 | odd | 2 | |||
6336.2.a.cz.1.2 | 3 | 12.11 | even | 2 |