Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5390,2,Mod(1,5390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5390, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5390.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5390 = 2 \cdot 5 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5390.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: | \(43.0393666895\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5390.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.732051 | 0.422650 | 0.211325 | − | 0.977416i | \(-0.432222\pi\) | ||||
0.211325 | + | 0.977416i | \(0.432222\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.732051 | 0.298858 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.46410 | −0.821367 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0.732051 | 0.211325 | ||||||||
\(13\) | −5.46410 | −1.51547 | −0.757735 | − | 0.652563i | \(-0.773694\pi\) | ||||
−0.757735 | + | 0.652563i | \(0.773694\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.732051 | 0.189015 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.46410 | −0.840168 | −0.420084 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420084 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(18\) | −2.46410 | −0.580794 | ||||||||
\(19\) | −3.26795 | −0.749719 | −0.374859 | − | 0.927082i | \(-0.622309\pi\) | ||||
−0.374859 | + | 0.927082i | \(0.622309\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 2.19615 | 0.457929 | 0.228965 | − | 0.973435i | \(-0.426466\pi\) | ||||
0.228965 | + | 0.973435i | \(0.426466\pi\) | |||||||
\(24\) | 0.732051 | 0.149429 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.46410 | −1.07160 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.26795 | −0.235452 | −0.117726 | − | 0.993046i | \(-0.537560\pi\) | ||||
−0.117726 | + | 0.993046i | \(0.537560\pi\) | |||||||
\(30\) | 0.732051 | 0.133654 | ||||||||
\(31\) | −2.00000 | −0.359211 | −0.179605 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179605 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.732051 | 0.127434 | ||||||||
\(34\) | −3.46410 | −0.594089 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.46410 | −0.410684 | ||||||||
\(37\) | −2.73205 | −0.449146 | −0.224573 | − | 0.974457i | \(-0.572099\pi\) | ||||
−0.224573 | + | 0.974457i | \(0.572099\pi\) | |||||||
\(38\) | −3.26795 | −0.530131 | ||||||||
\(39\) | −4.00000 | −0.640513 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −8.19615 | −1.28002 | −0.640012 | − | 0.768365i | \(-0.721071\pi\) | ||||
−0.640012 | + | 0.768365i | \(0.721071\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −2.46410 | −0.367327 | ||||||||
\(46\) | 2.19615 | 0.323805 | ||||||||
\(47\) | 6.92820 | 1.01058 | 0.505291 | − | 0.862949i | \(-0.331385\pi\) | ||||
0.505291 | + | 0.862949i | \(0.331385\pi\) | |||||||
\(48\) | 0.732051 | 0.105662 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −2.53590 | −0.355097 | ||||||||
\(52\) | −5.46410 | −0.757735 | ||||||||
\(53\) | −10.7321 | −1.47416 | −0.737080 | − | 0.675805i | \(-0.763796\pi\) | ||||
−0.737080 | + | 0.675805i | \(0.763796\pi\) | |||||||
\(54\) | −4.00000 | −0.544331 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.39230 | −0.316869 | ||||||||
\(58\) | −1.26795 | −0.166490 | ||||||||
\(59\) | 6.92820 | 0.901975 | 0.450988 | − | 0.892530i | \(-0.351072\pi\) | ||||
0.450988 | + | 0.892530i | \(0.351072\pi\) | |||||||
\(60\) | 0.732051 | 0.0945074 | ||||||||
\(61\) | −8.92820 | −1.14314 | −0.571570 | − | 0.820554i | \(-0.693665\pi\) | ||||
−0.571570 | + | 0.820554i | \(0.693665\pi\) | |||||||
\(62\) | −2.00000 | −0.254000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.46410 | −0.677738 | ||||||||
\(66\) | 0.732051 | 0.0901092 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | −3.46410 | −0.420084 | ||||||||
\(69\) | 1.60770 | 0.193544 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.53590 | 0.300956 | 0.150478 | − | 0.988613i | \(-0.451919\pi\) | ||||
0.150478 | + | 0.988613i | \(0.451919\pi\) | |||||||
\(72\) | −2.46410 | −0.290397 | ||||||||
\(73\) | −6.39230 | −0.748163 | −0.374081 | − | 0.927396i | \(-0.622042\pi\) | ||||
−0.374081 | + | 0.927396i | \(0.622042\pi\) | |||||||
\(74\) | −2.73205 | −0.317594 | ||||||||
\(75\) | 0.732051 | 0.0845299 | ||||||||
\(76\) | −3.26795 | −0.374859 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.00000 | −0.452911 | ||||||||
\(79\) | −1.80385 | −0.202949 | −0.101474 | − | 0.994838i | \(-0.532356\pi\) | ||||
−0.101474 | + | 0.994838i | \(0.532356\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 4.46410 | 0.496011 | ||||||||
\(82\) | −8.19615 | −0.905114 | ||||||||
\(83\) | −4.39230 | −0.482118 | −0.241059 | − | 0.970510i | \(-0.577495\pi\) | ||||
−0.241059 | + | 0.970510i | \(0.577495\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.46410 | −0.375735 | ||||||||
\(86\) | 2.00000 | 0.215666 | ||||||||
\(87\) | −0.928203 | −0.0995138 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 3.46410 | 0.367194 | 0.183597 | − | 0.983002i | \(-0.441226\pi\) | ||||
0.183597 | + | 0.983002i | \(0.441226\pi\) | |||||||
\(90\) | −2.46410 | −0.259739 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.19615 | 0.228965 | ||||||||
\(93\) | −1.46410 | −0.151820 | ||||||||
\(94\) | 6.92820 | 0.714590 | ||||||||
\(95\) | −3.26795 | −0.335285 | ||||||||
\(96\) | 0.732051 | 0.0747146 | ||||||||
\(97\) | 16.5885 | 1.68430 | 0.842151 | − | 0.539241i | \(-0.181289\pi\) | ||||
0.842151 | + | 0.539241i | \(0.181289\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.46410 | −0.247652 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −19.8564 | −1.97579 | −0.987893 | − | 0.155136i | \(-0.950418\pi\) | ||||
−0.987893 | + | 0.155136i | \(0.950418\pi\) | |||||||
\(102\) | −2.53590 | −0.251091 | ||||||||
\(103\) | 8.39230 | 0.826918 | 0.413459 | − | 0.910523i | \(-0.364320\pi\) | ||||
0.413459 | + | 0.910523i | \(0.364320\pi\) | |||||||
\(104\) | −5.46410 | −0.535799 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.7321 | −1.04239 | ||||||||
\(107\) | −19.8564 | −1.91959 | −0.959796 | − | 0.280700i | \(-0.909433\pi\) | ||||
−0.959796 | + | 0.280700i | \(0.909433\pi\) | |||||||
\(108\) | −4.00000 | −0.384900 | ||||||||
\(109\) | 1.66025 | 0.159023 | 0.0795117 | − | 0.996834i | \(-0.474664\pi\) | ||||
0.0795117 | + | 0.996834i | \(0.474664\pi\) | |||||||
\(110\) | 1.00000 | 0.0953463 | ||||||||
\(111\) | −2.00000 | −0.189832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19.8564 | −1.86793 | −0.933967 | − | 0.357360i | \(-0.883677\pi\) | ||||
−0.933967 | + | 0.357360i | \(0.883677\pi\) | |||||||
\(114\) | −2.39230 | −0.224060 | ||||||||
\(115\) | 2.19615 | 0.204792 | ||||||||
\(116\) | −1.26795 | −0.117726 | ||||||||
\(117\) | 13.4641 | 1.24476 | ||||||||
\(118\) | 6.92820 | 0.637793 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.732051 | 0.0668268 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −8.92820 | −0.808322 | ||||||||
\(123\) | −6.00000 | −0.541002 | ||||||||
\(124\) | −2.00000 | −0.179605 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.9282 | 1.32466 | 0.662332 | − | 0.749211i | \(-0.269567\pi\) | ||||
0.662332 | + | 0.749211i | \(0.269567\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.46410 | 0.128907 | ||||||||
\(130\) | −5.46410 | −0.479233 | ||||||||
\(131\) | 11.6603 | 1.01876 | 0.509381 | − | 0.860541i | \(-0.329875\pi\) | ||||
0.509381 | + | 0.860541i | \(0.329875\pi\) | |||||||
\(132\) | 0.732051 | 0.0637168 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | −4.00000 | −0.344265 | ||||||||
\(136\) | −3.46410 | −0.297044 | ||||||||
\(137\) | 12.9282 | 1.10453 | 0.552265 | − | 0.833668i | \(-0.313763\pi\) | ||||
0.552265 | + | 0.833668i | \(0.313763\pi\) | |||||||
\(138\) | 1.60770 | 0.136856 | ||||||||
\(139\) | 3.66025 | 0.310459 | 0.155229 | − | 0.987878i | \(-0.450388\pi\) | ||||
0.155229 | + | 0.987878i | \(0.450388\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.07180 | 0.427122 | ||||||||
\(142\) | 2.53590 | 0.212808 | ||||||||
\(143\) | −5.46410 | −0.456931 | ||||||||
\(144\) | −2.46410 | −0.205342 | ||||||||
\(145\) | −1.26795 | −0.105297 | ||||||||
\(146\) | −6.39230 | −0.529031 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.73205 | −0.224573 | ||||||||
\(149\) | −10.7321 | −0.879204 | −0.439602 | − | 0.898193i | \(-0.644880\pi\) | ||||
−0.439602 | + | 0.898193i | \(0.644880\pi\) | |||||||
\(150\) | 0.732051 | 0.0597717 | ||||||||
\(151\) | −13.1244 | −1.06804 | −0.534022 | − | 0.845470i | \(-0.679320\pi\) | ||||
−0.534022 | + | 0.845470i | \(0.679320\pi\) | |||||||
\(152\) | −3.26795 | −0.265066 | ||||||||
\(153\) | 8.53590 | 0.690086 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.00000 | −0.160644 | ||||||||
\(156\) | −4.00000 | −0.320256 | ||||||||
\(157\) | −11.4641 | −0.914935 | −0.457467 | − | 0.889226i | \(-0.651243\pi\) | ||||
−0.457467 | + | 0.889226i | \(0.651243\pi\) | |||||||
\(158\) | −1.80385 | −0.143506 | ||||||||
\(159\) | −7.85641 | −0.623054 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 4.46410 | 0.350733 | ||||||||
\(163\) | −4.00000 | −0.313304 | −0.156652 | − | 0.987654i | \(-0.550070\pi\) | ||||
−0.156652 | + | 0.987654i | \(0.550070\pi\) | |||||||
\(164\) | −8.19615 | −0.640012 | ||||||||
\(165\) | 0.732051 | 0.0569901 | ||||||||
\(166\) | −4.39230 | −0.340909 | ||||||||
\(167\) | 13.8564 | 1.07224 | 0.536120 | − | 0.844141i | \(-0.319889\pi\) | ||||
0.536120 | + | 0.844141i | \(0.319889\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.8564 | 1.29665 | ||||||||
\(170\) | −3.46410 | −0.265684 | ||||||||
\(171\) | 8.05256 | 0.615795 | ||||||||
\(172\) | 2.00000 | 0.152499 | ||||||||
\(173\) | 12.9282 | 0.982913 | 0.491457 | − | 0.870902i | \(-0.336465\pi\) | ||||
0.491457 | + | 0.870902i | \(0.336465\pi\) | |||||||
\(174\) | −0.928203 | −0.0703669 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 5.07180 | 0.381220 | ||||||||
\(178\) | 3.46410 | 0.259645 | ||||||||
\(179\) | −6.00000 | −0.448461 | −0.224231 | − | 0.974536i | \(-0.571987\pi\) | ||||
−0.224231 | + | 0.974536i | \(0.571987\pi\) | |||||||
\(180\) | −2.46410 | −0.183663 | ||||||||
\(181\) | −14.0000 | −1.04061 | −0.520306 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520306 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.53590 | −0.483148 | ||||||||
\(184\) | 2.19615 | 0.161903 | ||||||||
\(185\) | −2.73205 | −0.200864 | ||||||||
\(186\) | −1.46410 | −0.107353 | ||||||||
\(187\) | −3.46410 | −0.253320 | ||||||||
\(188\) | 6.92820 | 0.505291 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.26795 | −0.237082 | ||||||||
\(191\) | −12.0000 | −0.868290 | −0.434145 | − | 0.900843i | \(-0.642949\pi\) | ||||
−0.434145 | + | 0.900843i | \(0.642949\pi\) | |||||||
\(192\) | 0.732051 | 0.0528312 | ||||||||
\(193\) | −8.39230 | −0.604091 | −0.302046 | − | 0.953293i | \(-0.597670\pi\) | ||||
−0.302046 | + | 0.953293i | \(0.597670\pi\) | |||||||
\(194\) | 16.5885 | 1.19098 | ||||||||
\(195\) | −4.00000 | −0.286446 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.2487 | 1.72765 | 0.863825 | − | 0.503793i | \(-0.168062\pi\) | ||||
0.863825 | + | 0.503793i | \(0.168062\pi\) | |||||||
\(198\) | −2.46410 | −0.175116 | ||||||||
\(199\) | 10.9282 | 0.774680 | 0.387340 | − | 0.921937i | \(-0.373394\pi\) | ||||
0.387340 | + | 0.921937i | \(0.373394\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −2.92820 | −0.206540 | ||||||||
\(202\) | −19.8564 | −1.39709 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.53590 | −0.177548 | ||||||||
\(205\) | −8.19615 | −0.572444 | ||||||||
\(206\) | 8.39230 | 0.584720 | ||||||||
\(207\) | −5.41154 | −0.376128 | ||||||||
\(208\) | −5.46410 | −0.378867 | ||||||||
\(209\) | −3.26795 | −0.226049 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.0718 | 0.899900 | 0.449950 | − | 0.893054i | \(-0.351442\pi\) | ||||
0.449950 | + | 0.893054i | \(0.351442\pi\) | |||||||
\(212\) | −10.7321 | −0.737080 | ||||||||
\(213\) | 1.85641 | 0.127199 | ||||||||
\(214\) | −19.8564 | −1.35736 | ||||||||
\(215\) | 2.00000 | 0.136399 | ||||||||
\(216\) | −4.00000 | −0.272166 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.66025 | 0.112447 | ||||||||
\(219\) | −4.67949 | −0.316211 | ||||||||
\(220\) | 1.00000 | 0.0674200 | ||||||||
\(221\) | 18.9282 | 1.27325 | ||||||||
\(222\) | −2.00000 | −0.134231 | ||||||||
\(223\) | 18.5359 | 1.24126 | 0.620628 | − | 0.784105i | \(-0.286878\pi\) | ||||
0.620628 | + | 0.784105i | \(0.286878\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.46410 | −0.164273 | ||||||||
\(226\) | −19.8564 | −1.32083 | ||||||||
\(227\) | 6.92820 | 0.459841 | 0.229920 | − | 0.973209i | \(-0.426153\pi\) | ||||
0.229920 | + | 0.973209i | \(0.426153\pi\) | |||||||
\(228\) | −2.39230 | −0.158434 | ||||||||
\(229\) | −3.60770 | −0.238403 | −0.119202 | − | 0.992870i | \(-0.538033\pi\) | ||||
−0.119202 | + | 0.992870i | \(0.538033\pi\) | |||||||
\(230\) | 2.19615 | 0.144810 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.26795 | −0.0832449 | ||||||||
\(233\) | 19.8564 | 1.30084 | 0.650418 | − | 0.759576i | \(-0.274594\pi\) | ||||
0.650418 | + | 0.759576i | \(0.274594\pi\) | |||||||
\(234\) | 13.4641 | 0.880176 | ||||||||
\(235\) | 6.92820 | 0.451946 | ||||||||
\(236\) | 6.92820 | 0.450988 | ||||||||
\(237\) | −1.32051 | −0.0857762 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.73205 | 0.306091 | 0.153045 | − | 0.988219i | \(-0.451092\pi\) | ||||
0.153045 | + | 0.988219i | \(0.451092\pi\) | |||||||
\(240\) | 0.732051 | 0.0472537 | ||||||||
\(241\) | −6.73205 | −0.433650 | −0.216825 | − | 0.976211i | \(-0.569570\pi\) | ||||
−0.216825 | + | 0.976211i | \(0.569570\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 15.2679 | 0.979439 | ||||||||
\(244\) | −8.92820 | −0.571570 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | 17.8564 | 1.13618 | ||||||||
\(248\) | −2.00000 | −0.127000 | ||||||||
\(249\) | −3.21539 | −0.203767 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.19615 | 0.138071 | ||||||||
\(254\) | 14.9282 | 0.936679 | ||||||||
\(255\) | −2.53590 | −0.158804 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.33975 | 0.395462 | 0.197731 | − | 0.980256i | \(-0.436643\pi\) | ||||
0.197731 | + | 0.980256i | \(0.436643\pi\) | |||||||
\(258\) | 1.46410 | 0.0911510 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −5.46410 | −0.338869 | ||||||||
\(261\) | 3.12436 | 0.193393 | ||||||||
\(262\) | 11.6603 | 0.720373 | ||||||||
\(263\) | −24.0000 | −1.47990 | −0.739952 | − | 0.672660i | \(-0.765152\pi\) | ||||
−0.739952 | + | 0.672660i | \(0.765152\pi\) | |||||||
\(264\) | 0.732051 | 0.0450546 | ||||||||
\(265\) | −10.7321 | −0.659265 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.53590 | 0.155194 | ||||||||
\(268\) | −4.00000 | −0.244339 | ||||||||
\(269\) | −7.60770 | −0.463849 | −0.231925 | − | 0.972734i | \(-0.574502\pi\) | ||||
−0.231925 | + | 0.972734i | \(0.574502\pi\) | |||||||
\(270\) | −4.00000 | −0.243432 | ||||||||
\(271\) | 20.3923 | 1.23874 | 0.619372 | − | 0.785098i | \(-0.287387\pi\) | ||||
0.619372 | + | 0.785098i | \(0.287387\pi\) | |||||||
\(272\) | −3.46410 | −0.210042 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.9282 | 0.781021 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 1.60770 | 0.0967719 | ||||||||
\(277\) | 20.9282 | 1.25745 | 0.628727 | − | 0.777626i | \(-0.283576\pi\) | ||||
0.628727 | + | 0.777626i | \(0.283576\pi\) | |||||||
\(278\) | 3.66025 | 0.219527 | ||||||||
\(279\) | 4.92820 | 0.295044 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.60770 | 0.0959071 | 0.0479535 | − | 0.998850i | \(-0.484730\pi\) | ||||
0.0479535 | + | 0.998850i | \(0.484730\pi\) | |||||||
\(282\) | 5.07180 | 0.302021 | ||||||||
\(283\) | −23.7128 | −1.40958 | −0.704790 | − | 0.709416i | \(-0.748959\pi\) | ||||
−0.704790 | + | 0.709416i | \(0.748959\pi\) | |||||||
\(284\) | 2.53590 | 0.150478 | ||||||||
\(285\) | −2.39230 | −0.141708 | ||||||||
\(286\) | −5.46410 | −0.323099 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.46410 | −0.145199 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | −1.26795 | −0.0744565 | ||||||||
\(291\) | 12.1436 | 0.711870 | ||||||||
\(292\) | −6.39230 | −0.374081 | ||||||||
\(293\) | −14.5359 | −0.849196 | −0.424598 | − | 0.905382i | \(-0.639585\pi\) | ||||
−0.424598 | + | 0.905382i | \(0.639585\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.92820 | 0.403376 | ||||||||
\(296\) | −2.73205 | −0.158797 | ||||||||
\(297\) | −4.00000 | −0.232104 | ||||||||
\(298\) | −10.7321 | −0.621691 | ||||||||
\(299\) | −12.0000 | −0.693978 | ||||||||
\(300\) | 0.732051 | 0.0422650 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −13.1244 | −0.755222 | ||||||||
\(303\) | −14.5359 | −0.835066 | ||||||||
\(304\) | −3.26795 | −0.187430 | ||||||||
\(305\) | −8.92820 | −0.511227 | ||||||||
\(306\) | 8.53590 | 0.487965 | ||||||||
\(307\) | −3.60770 | −0.205902 | −0.102951 | − | 0.994686i | \(-0.532828\pi\) | ||||
−0.102951 | + | 0.994686i | \(0.532828\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.14359 | 0.349497 | ||||||||
\(310\) | −2.00000 | −0.113592 | ||||||||
\(311\) | −11.0718 | −0.627824 | −0.313912 | − | 0.949452i | \(-0.601640\pi\) | ||||
−0.313912 | + | 0.949452i | \(0.601640\pi\) | |||||||
\(312\) | −4.00000 | −0.226455 | ||||||||
\(313\) | −11.8038 | −0.667193 | −0.333596 | − | 0.942716i | \(-0.608262\pi\) | ||||
−0.333596 | + | 0.942716i | \(0.608262\pi\) | |||||||
\(314\) | −11.4641 | −0.646957 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.80385 | −0.101474 | ||||||||
\(317\) | −0.588457 | −0.0330511 | −0.0165255 | − | 0.999863i | \(-0.505260\pi\) | ||||
−0.0165255 | + | 0.999863i | \(0.505260\pi\) | |||||||
\(318\) | −7.85641 | −0.440565 | ||||||||
\(319\) | −1.26795 | −0.0709915 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −14.5359 | −0.811315 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.3205 | 0.629890 | ||||||||
\(324\) | 4.46410 | 0.248006 | ||||||||
\(325\) | −5.46410 | −0.303094 | ||||||||
\(326\) | −4.00000 | −0.221540 | ||||||||
\(327\) | 1.21539 | 0.0672112 | ||||||||
\(328\) | −8.19615 | −0.452557 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.732051 | 0.0402981 | ||||||||
\(331\) | 22.7846 | 1.25236 | 0.626178 | − | 0.779680i | \(-0.284618\pi\) | ||||
0.626178 | + | 0.779680i | \(0.284618\pi\) | |||||||
\(332\) | −4.39230 | −0.241059 | ||||||||
\(333\) | 6.73205 | 0.368914 | ||||||||
\(334\) | 13.8564 | 0.758189 | ||||||||
\(335\) | −4.00000 | −0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.7846 | −1.02326 | −0.511631 | − | 0.859205i | \(-0.670959\pi\) | ||||
−0.511631 | + | 0.859205i | \(0.670959\pi\) | |||||||
\(338\) | 16.8564 | 0.916868 | ||||||||
\(339\) | −14.5359 | −0.789482 | ||||||||
\(340\) | −3.46410 | −0.187867 | ||||||||
\(341\) | −2.00000 | −0.108306 | ||||||||
\(342\) | 8.05256 | 0.435433 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.00000 | 0.107833 | ||||||||
\(345\) | 1.60770 | 0.0865554 | ||||||||
\(346\) | 12.9282 | 0.695025 | ||||||||
\(347\) | −36.9282 | −1.98241 | −0.991205 | − | 0.132336i | \(-0.957752\pi\) | ||||
−0.991205 | + | 0.132336i | \(0.957752\pi\) | |||||||
\(348\) | −0.928203 | −0.0497569 | ||||||||
\(349\) | 26.3923 | 1.41275 | 0.706374 | − | 0.707839i | \(-0.250330\pi\) | ||||
0.706374 | + | 0.707839i | \(0.250330\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21.8564 | 1.16661 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −3.80385 | −0.202458 | −0.101229 | − | 0.994863i | \(-0.532278\pi\) | ||||
−0.101229 | + | 0.994863i | \(0.532278\pi\) | |||||||
\(354\) | 5.07180 | 0.269563 | ||||||||
\(355\) | 2.53590 | 0.134592 | ||||||||
\(356\) | 3.46410 | 0.183597 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.00000 | −0.317110 | ||||||||
\(359\) | 4.05256 | 0.213886 | 0.106943 | − | 0.994265i | \(-0.465894\pi\) | ||||
0.106943 | + | 0.994265i | \(0.465894\pi\) | |||||||
\(360\) | −2.46410 | −0.129870 | ||||||||
\(361\) | −8.32051 | −0.437921 | ||||||||
\(362\) | −14.0000 | −0.735824 | ||||||||
\(363\) | 0.732051 | 0.0384227 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.39230 | −0.334589 | ||||||||
\(366\) | −6.53590 | −0.341637 | ||||||||
\(367\) | 8.39230 | 0.438075 | 0.219037 | − | 0.975716i | \(-0.429708\pi\) | ||||
0.219037 | + | 0.975716i | \(0.429708\pi\) | |||||||
\(368\) | 2.19615 | 0.114482 | ||||||||
\(369\) | 20.1962 | 1.05137 | ||||||||
\(370\) | −2.73205 | −0.142033 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.46410 | −0.0759101 | ||||||||
\(373\) | −2.39230 | −0.123869 | −0.0619344 | − | 0.998080i | \(-0.519727\pi\) | ||||
−0.0619344 | + | 0.998080i | \(0.519727\pi\) | |||||||
\(374\) | −3.46410 | −0.179124 | ||||||||
\(375\) | 0.732051 | 0.0378029 | ||||||||
\(376\) | 6.92820 | 0.357295 | ||||||||
\(377\) | 6.92820 | 0.356821 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.8564 | 1.73909 | 0.869543 | − | 0.493857i | \(-0.164413\pi\) | ||||
0.869543 | + | 0.493857i | \(0.164413\pi\) | |||||||
\(380\) | −3.26795 | −0.167642 | ||||||||
\(381\) | 10.9282 | 0.559869 | ||||||||
\(382\) | −12.0000 | −0.613973 | ||||||||
\(383\) | 26.5359 | 1.35592 | 0.677961 | − | 0.735098i | \(-0.262864\pi\) | ||||
0.677961 | + | 0.735098i | \(0.262864\pi\) | |||||||
\(384\) | 0.732051 | 0.0373573 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.39230 | −0.427157 | ||||||||
\(387\) | −4.92820 | −0.250515 | ||||||||
\(388\) | 16.5885 | 0.842151 | ||||||||
\(389\) | −22.3923 | −1.13533 | −0.567667 | − | 0.823258i | \(-0.692154\pi\) | ||||
−0.567667 | + | 0.823258i | \(0.692154\pi\) | |||||||
\(390\) | −4.00000 | −0.202548 | ||||||||
\(391\) | −7.60770 | −0.384738 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.53590 | 0.430579 | ||||||||
\(394\) | 24.2487 | 1.22163 | ||||||||
\(395\) | −1.80385 | −0.0907614 | ||||||||
\(396\) | −2.46410 | −0.123826 | ||||||||
\(397\) | −9.60770 | −0.482196 | −0.241098 | − | 0.970501i | \(-0.577508\pi\) | ||||
−0.241098 | + | 0.970501i | \(0.577508\pi\) | |||||||
\(398\) | 10.9282 | 0.547781 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 9.46410 | 0.472615 | 0.236307 | − | 0.971678i | \(-0.424063\pi\) | ||||
0.236307 | + | 0.971678i | \(0.424063\pi\) | |||||||
\(402\) | −2.92820 | −0.146046 | ||||||||
\(403\) | 10.9282 | 0.544373 | ||||||||
\(404\) | −19.8564 | −0.987893 | ||||||||
\(405\) | 4.46410 | 0.221823 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.73205 | −0.135423 | ||||||||
\(408\) | −2.53590 | −0.125546 | ||||||||
\(409\) | −35.1244 | −1.73679 | −0.868394 | − | 0.495875i | \(-0.834847\pi\) | ||||
−0.868394 | + | 0.495875i | \(0.834847\pi\) | |||||||
\(410\) | −8.19615 | −0.404779 | ||||||||
\(411\) | 9.46410 | 0.466830 | ||||||||
\(412\) | 8.39230 | 0.413459 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −5.41154 | −0.265963 | ||||||||
\(415\) | −4.39230 | −0.215610 | ||||||||
\(416\) | −5.46410 | −0.267900 | ||||||||
\(417\) | 2.67949 | 0.131215 | ||||||||
\(418\) | −3.26795 | −0.159841 | ||||||||
\(419\) | −17.0718 | −0.834012 | −0.417006 | − | 0.908904i | \(-0.636921\pi\) | ||||
−0.417006 | + | 0.908904i | \(0.636921\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.14359 | −0.396894 | −0.198447 | − | 0.980112i | \(-0.563590\pi\) | ||||
−0.198447 | + | 0.980112i | \(0.563590\pi\) | |||||||
\(422\) | 13.0718 | 0.636325 | ||||||||
\(423\) | −17.0718 | −0.830059 | ||||||||
\(424\) | −10.7321 | −0.521194 | ||||||||
\(425\) | −3.46410 | −0.168034 | ||||||||
\(426\) | 1.85641 | 0.0899432 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −19.8564 | −0.959796 | ||||||||
\(429\) | −4.00000 | −0.193122 | ||||||||
\(430\) | 2.00000 | 0.0964486 | ||||||||
\(431\) | −21.1244 | −1.01752 | −0.508762 | − | 0.860907i | \(-0.669897\pi\) | ||||
−0.508762 | + | 0.860907i | \(0.669897\pi\) | |||||||
\(432\) | −4.00000 | −0.192450 | ||||||||
\(433\) | 7.80385 | 0.375029 | 0.187514 | − | 0.982262i | \(-0.439957\pi\) | ||||
0.187514 | + | 0.982262i | \(0.439957\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.928203 | −0.0445039 | ||||||||
\(436\) | 1.66025 | 0.0795117 | ||||||||
\(437\) | −7.17691 | −0.343318 | ||||||||
\(438\) | −4.67949 | −0.223595 | ||||||||
\(439\) | 22.2487 | 1.06187 | 0.530937 | − | 0.847412i | \(-0.321840\pi\) | ||||
0.530937 | + | 0.847412i | \(0.321840\pi\) | |||||||
\(440\) | 1.00000 | 0.0476731 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 18.9282 | 0.900323 | ||||||||
\(443\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(444\) | −2.00000 | −0.0949158 | ||||||||
\(445\) | 3.46410 | 0.164214 | ||||||||
\(446\) | 18.5359 | 0.877700 | ||||||||
\(447\) | −7.85641 | −0.371595 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.6077 | 0.925344 | 0.462672 | − | 0.886529i | \(-0.346891\pi\) | ||||
0.462672 | + | 0.886529i | \(0.346891\pi\) | |||||||
\(450\) | −2.46410 | −0.116159 | ||||||||
\(451\) | −8.19615 | −0.385942 | ||||||||
\(452\) | −19.8564 | −0.933967 | ||||||||
\(453\) | −9.60770 | −0.451409 | ||||||||
\(454\) | 6.92820 | 0.325157 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.39230 | −0.112030 | ||||||||
\(457\) | 2.00000 | 0.0935561 | 0.0467780 | − | 0.998905i | \(-0.485105\pi\) | ||||
0.0467780 | + | 0.998905i | \(0.485105\pi\) | |||||||
\(458\) | −3.60770 | −0.168577 | ||||||||
\(459\) | 13.8564 | 0.646762 | ||||||||
\(460\) | 2.19615 | 0.102396 | ||||||||
\(461\) | −1.60770 | −0.0748778 | −0.0374389 | − | 0.999299i | \(-0.511920\pi\) | ||||
−0.0374389 | + | 0.999299i | \(0.511920\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.5167 | −0.814068 | −0.407034 | − | 0.913413i | \(-0.633437\pi\) | ||||
−0.407034 | + | 0.913413i | \(0.633437\pi\) | |||||||
\(464\) | −1.26795 | −0.0588631 | ||||||||
\(465\) | −1.46410 | −0.0678961 | ||||||||
\(466\) | 19.8564 | 0.919830 | ||||||||
\(467\) | −4.05256 | −0.187530 | −0.0937650 | − | 0.995594i | \(-0.529890\pi\) | ||||
−0.0937650 | + | 0.995594i | \(0.529890\pi\) | |||||||
\(468\) | 13.4641 | 0.622378 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 6.92820 | 0.319574 | ||||||||
\(471\) | −8.39230 | −0.386697 | ||||||||
\(472\) | 6.92820 | 0.318896 | ||||||||
\(473\) | 2.00000 | 0.0919601 | ||||||||
\(474\) | −1.32051 | −0.0606529 | ||||||||
\(475\) | −3.26795 | −0.149944 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 26.4449 | 1.21083 | ||||||||
\(478\) | 4.73205 | 0.216439 | ||||||||
\(479\) | −8.78461 | −0.401379 | −0.200690 | − | 0.979655i | \(-0.564318\pi\) | ||||
−0.200690 | + | 0.979655i | \(0.564318\pi\) | |||||||
\(480\) | 0.732051 | 0.0334134 | ||||||||
\(481\) | 14.9282 | 0.680667 | ||||||||
\(482\) | −6.73205 | −0.306637 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 16.5885 | 0.753243 | ||||||||
\(486\) | 15.2679 | 0.692568 | ||||||||
\(487\) | −6.19615 | −0.280774 | −0.140387 | − | 0.990097i | \(-0.544835\pi\) | ||||
−0.140387 | + | 0.990097i | \(0.544835\pi\) | |||||||
\(488\) | −8.92820 | −0.404161 | ||||||||
\(489\) | −2.92820 | −0.132418 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.7128 | 1.25066 | 0.625331 | − | 0.780360i | \(-0.284964\pi\) | ||||
0.625331 | + | 0.780360i | \(0.284964\pi\) | |||||||
\(492\) | −6.00000 | −0.270501 | ||||||||
\(493\) | 4.39230 | 0.197819 | ||||||||
\(494\) | 17.8564 | 0.803398 | ||||||||
\(495\) | −2.46410 | −0.110753 | ||||||||
\(496\) | −2.00000 | −0.0898027 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.21539 | −0.144085 | ||||||||
\(499\) | 39.8564 | 1.78422 | 0.892109 | − | 0.451820i | \(-0.149225\pi\) | ||||
0.892109 | + | 0.451820i | \(0.149225\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 10.1436 | 0.453182 | ||||||||
\(502\) | −12.0000 | −0.535586 | ||||||||
\(503\) | 32.7846 | 1.46179 | 0.730897 | − | 0.682488i | \(-0.239102\pi\) | ||||
0.730897 | + | 0.682488i | \(0.239102\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.8564 | −0.883598 | ||||||||
\(506\) | 2.19615 | 0.0976309 | ||||||||
\(507\) | 12.3397 | 0.548027 | ||||||||
\(508\) | 14.9282 | 0.662332 | ||||||||
\(509\) | −24.9282 | −1.10492 | −0.552462 | − | 0.833538i | \(-0.686311\pi\) | ||||
−0.552462 | + | 0.833538i | \(0.686311\pi\) | |||||||
\(510\) | −2.53590 | −0.112291 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 13.0718 | 0.577134 | ||||||||
\(514\) | 6.33975 | 0.279634 | ||||||||
\(515\) | 8.39230 | 0.369809 | ||||||||
\(516\) | 1.46410 | 0.0644535 | ||||||||
\(517\) | 6.92820 | 0.304702 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.46410 | 0.415428 | ||||||||
\(520\) | −5.46410 | −0.239617 | ||||||||
\(521\) | 10.3923 | 0.455295 | 0.227648 | − | 0.973744i | \(-0.426897\pi\) | ||||
0.227648 | + | 0.973744i | \(0.426897\pi\) | |||||||
\(522\) | 3.12436 | 0.136749 | ||||||||
\(523\) | −33.1769 | −1.45073 | −0.725363 | − | 0.688367i | \(-0.758328\pi\) | ||||
−0.725363 | + | 0.688367i | \(0.758328\pi\) | |||||||
\(524\) | 11.6603 | 0.509381 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.0000 | −1.04645 | ||||||||
\(527\) | 6.92820 | 0.301797 | ||||||||
\(528\) | 0.732051 | 0.0318584 | ||||||||
\(529\) | −18.1769 | −0.790301 | ||||||||
\(530\) | −10.7321 | −0.466170 | ||||||||
\(531\) | −17.0718 | −0.740853 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 44.7846 | 1.93984 | ||||||||
\(534\) | 2.53590 | 0.109739 | ||||||||
\(535\) | −19.8564 | −0.858467 | ||||||||
\(536\) | −4.00000 | −0.172774 | ||||||||
\(537\) | −4.39230 | −0.189542 | ||||||||
\(538\) | −7.60770 | −0.327991 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.00000 | −0.172133 | ||||||||
\(541\) | −17.2679 | −0.742407 | −0.371204 | − | 0.928552i | \(-0.621055\pi\) | ||||
−0.371204 | + | 0.928552i | \(0.621055\pi\) | |||||||
\(542\) | 20.3923 | 0.875924 | ||||||||
\(543\) | −10.2487 | −0.439814 | ||||||||
\(544\) | −3.46410 | −0.148522 | ||||||||
\(545\) | 1.66025 | 0.0711175 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.7846 | −0.546630 | −0.273315 | − | 0.961925i | \(-0.588120\pi\) | ||||
−0.273315 | + | 0.961925i | \(0.588120\pi\) | |||||||
\(548\) | 12.9282 | 0.552265 | ||||||||
\(549\) | 22.0000 | 0.938937 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | 4.14359 | 0.176523 | ||||||||
\(552\) | 1.60770 | 0.0684280 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 20.9282 | 0.889154 | ||||||||
\(555\) | −2.00000 | −0.0848953 | ||||||||
\(556\) | 3.66025 | 0.155229 | ||||||||
\(557\) | −46.3923 | −1.96571 | −0.982853 | − | 0.184393i | \(-0.940968\pi\) | ||||
−0.982853 | + | 0.184393i | \(0.940968\pi\) | |||||||
\(558\) | 4.92820 | 0.208627 | ||||||||
\(559\) | −10.9282 | −0.462214 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.53590 | −0.107066 | ||||||||
\(562\) | 1.60770 | 0.0678165 | ||||||||
\(563\) | −18.9282 | −0.797729 | −0.398864 | − | 0.917010i | \(-0.630596\pi\) | ||||
−0.398864 | + | 0.917010i | \(0.630596\pi\) | |||||||
\(564\) | 5.07180 | 0.213561 | ||||||||
\(565\) | −19.8564 | −0.835365 | ||||||||
\(566\) | −23.7128 | −0.996724 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.53590 | 0.106404 | ||||||||
\(569\) | −6.00000 | −0.251533 | −0.125767 | − | 0.992060i | \(-0.540139\pi\) | ||||
−0.125767 | + | 0.992060i | \(0.540139\pi\) | |||||||
\(570\) | −2.39230 | −0.100203 | ||||||||
\(571\) | 24.3923 | 1.02079 | 0.510393 | − | 0.859941i | \(-0.329500\pi\) | ||||
0.510393 | + | 0.859941i | \(0.329500\pi\) | |||||||
\(572\) | −5.46410 | −0.228466 | ||||||||
\(573\) | −8.78461 | −0.366982 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.19615 | 0.0915859 | ||||||||
\(576\) | −2.46410 | −0.102671 | ||||||||
\(577\) | 3.41154 | 0.142024 | 0.0710122 | − | 0.997475i | \(-0.477377\pi\) | ||||
0.0710122 | + | 0.997475i | \(0.477377\pi\) | |||||||
\(578\) | −5.00000 | −0.207973 | ||||||||
\(579\) | −6.14359 | −0.255319 | ||||||||
\(580\) | −1.26795 | −0.0526487 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 12.1436 | 0.503368 | ||||||||
\(583\) | −10.7321 | −0.444476 | ||||||||
\(584\) | −6.39230 | −0.264515 | ||||||||
\(585\) | 13.4641 | 0.556672 | ||||||||
\(586\) | −14.5359 | −0.600472 | ||||||||
\(587\) | 42.5885 | 1.75781 | 0.878907 | − | 0.476993i | \(-0.158273\pi\) | ||||
0.878907 | + | 0.476993i | \(0.158273\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.53590 | 0.269307 | ||||||||
\(590\) | 6.92820 | 0.285230 | ||||||||
\(591\) | 17.7513 | 0.730190 | ||||||||
\(592\) | −2.73205 | −0.112287 | ||||||||
\(593\) | 48.2487 | 1.98134 | 0.990669 | − | 0.136293i | \(-0.0435189\pi\) | ||||
0.990669 | + | 0.136293i | \(0.0435189\pi\) | |||||||
\(594\) | −4.00000 | −0.164122 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10.7321 | −0.439602 | ||||||||
\(597\) | 8.00000 | 0.327418 | ||||||||
\(598\) | −12.0000 | −0.490716 | ||||||||
\(599\) | −25.1769 | −1.02870 | −0.514350 | − | 0.857580i | \(-0.671967\pi\) | ||||
−0.514350 | + | 0.857580i | \(0.671967\pi\) | |||||||
\(600\) | 0.732051 | 0.0298858 | ||||||||
\(601\) | −39.5167 | −1.61192 | −0.805959 | − | 0.591971i | \(-0.798350\pi\) | ||||
−0.805959 | + | 0.591971i | \(0.798350\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.85641 | 0.401384 | ||||||||
\(604\) | −13.1244 | −0.534022 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −14.5359 | −0.590481 | ||||||||
\(607\) | −7.07180 | −0.287035 | −0.143518 | − | 0.989648i | \(-0.545841\pi\) | ||||
−0.143518 | + | 0.989648i | \(0.545841\pi\) | |||||||
\(608\) | −3.26795 | −0.132533 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.92820 | −0.361492 | ||||||||
\(611\) | −37.8564 | −1.53151 | ||||||||
\(612\) | 8.53590 | 0.345043 | ||||||||
\(613\) | 27.1769 | 1.09767 | 0.548833 | − | 0.835932i | \(-0.315072\pi\) | ||||
0.548833 | + | 0.835932i | \(0.315072\pi\) | |||||||
\(614\) | −3.60770 | −0.145595 | ||||||||
\(615\) | −6.00000 | −0.241943 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.3205 | −0.697297 | −0.348649 | − | 0.937253i | \(-0.613359\pi\) | ||||
−0.348649 | + | 0.937253i | \(0.613359\pi\) | |||||||
\(618\) | 6.14359 | 0.247132 | ||||||||
\(619\) | 12.7846 | 0.513857 | 0.256928 | − | 0.966430i | \(-0.417290\pi\) | ||||
0.256928 | + | 0.966430i | \(0.417290\pi\) | |||||||
\(620\) | −2.00000 | −0.0803219 | ||||||||
\(621\) | −8.78461 | −0.352514 | ||||||||
\(622\) | −11.0718 | −0.443939 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.00000 | −0.160128 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −11.8038 | −0.471777 | ||||||||
\(627\) | −2.39230 | −0.0955395 | ||||||||
\(628\) | −11.4641 | −0.457467 | ||||||||
\(629\) | 9.46410 | 0.377358 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.0718 | −1.31657 | −0.658284 | − | 0.752770i | \(-0.728717\pi\) | ||||
−0.658284 | + | 0.752770i | \(0.728717\pi\) | |||||||
\(632\) | −1.80385 | −0.0717532 | ||||||||
\(633\) | 9.56922 | 0.380342 | ||||||||
\(634\) | −0.588457 | −0.0233706 | ||||||||
\(635\) | 14.9282 | 0.592408 | ||||||||
\(636\) | −7.85641 | −0.311527 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.26795 | −0.0501986 | ||||||||
\(639\) | −6.24871 | −0.247195 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 47.5692 | 1.87887 | 0.939436 | − | 0.342725i | \(-0.111350\pi\) | ||||
0.939436 | + | 0.342725i | \(0.111350\pi\) | |||||||
\(642\) | −14.5359 | −0.573686 | ||||||||
\(643\) | −36.7321 | −1.44857 | −0.724285 | − | 0.689500i | \(-0.757830\pi\) | ||||
−0.724285 | + | 0.689500i | \(0.757830\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.46410 | 0.0576489 | ||||||||
\(646\) | 11.3205 | 0.445399 | ||||||||
\(647\) | 33.4641 | 1.31561 | 0.657805 | − | 0.753188i | \(-0.271485\pi\) | ||||
0.657805 | + | 0.753188i | \(0.271485\pi\) | |||||||
\(648\) | 4.46410 | 0.175366 | ||||||||
\(649\) | 6.92820 | 0.271956 | ||||||||
\(650\) | −5.46410 | −0.214320 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.00000 | −0.156652 | ||||||||
\(653\) | −5.66025 | −0.221503 | −0.110751 | − | 0.993848i | \(-0.535326\pi\) | ||||
−0.110751 | + | 0.993848i | \(0.535326\pi\) | |||||||
\(654\) | 1.21539 | 0.0475255 | ||||||||
\(655\) | 11.6603 | 0.455604 | ||||||||
\(656\) | −8.19615 | −0.320006 | ||||||||
\(657\) | 15.7513 | 0.614516 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.2487 | −0.710869 | −0.355434 | − | 0.934701i | \(-0.615667\pi\) | ||||
−0.355434 | + | 0.934701i | \(0.615667\pi\) | |||||||
\(660\) | 0.732051 | 0.0284950 | ||||||||
\(661\) | 46.0000 | 1.78919 | 0.894596 | − | 0.446875i | \(-0.147463\pi\) | ||||
0.894596 | + | 0.446875i | \(0.147463\pi\) | |||||||
\(662\) | 22.7846 | 0.885549 | ||||||||
\(663\) | 13.8564 | 0.538138 | ||||||||
\(664\) | −4.39230 | −0.170454 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.73205 | 0.260862 | ||||||||
\(667\) | −2.78461 | −0.107821 | ||||||||
\(668\) | 13.8564 | 0.536120 | ||||||||
\(669\) | 13.5692 | 0.524616 | ||||||||
\(670\) | −4.00000 | −0.154533 | ||||||||
\(671\) | −8.92820 | −0.344669 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.00000 | 0.0770943 | 0.0385472 | − | 0.999257i | \(-0.487727\pi\) | ||||
0.0385472 | + | 0.999257i | \(0.487727\pi\) | |||||||
\(674\) | −18.7846 | −0.723556 | ||||||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | 16.8564 | 0.648323 | ||||||||
\(677\) | 31.8564 | 1.22434 | 0.612171 | − | 0.790726i | \(-0.290297\pi\) | ||||
0.612171 | + | 0.790726i | \(0.290297\pi\) | |||||||
\(678\) | −14.5359 | −0.558248 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.46410 | −0.132842 | ||||||||
\(681\) | 5.07180 | 0.194352 | ||||||||
\(682\) | −2.00000 | −0.0765840 | ||||||||
\(683\) | −42.2487 | −1.61660 | −0.808301 | − | 0.588769i | \(-0.799613\pi\) | ||||
−0.808301 | + | 0.588769i | \(0.799613\pi\) | |||||||
\(684\) | 8.05256 | 0.307897 | ||||||||
\(685\) | 12.9282 | 0.493961 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.64102 | −0.100761 | ||||||||
\(688\) | 2.00000 | 0.0762493 | ||||||||
\(689\) | 58.6410 | 2.23404 | ||||||||
\(690\) | 1.60770 | 0.0612039 | ||||||||
\(691\) | 6.53590 | 0.248637 | 0.124319 | − | 0.992242i | \(-0.460325\pi\) | ||||
0.124319 | + | 0.992242i | \(0.460325\pi\) | |||||||
\(692\) | 12.9282 | 0.491457 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −36.9282 | −1.40178 | ||||||||
\(695\) | 3.66025 | 0.138841 | ||||||||
\(696\) | −0.928203 | −0.0351835 | ||||||||
\(697\) | 28.3923 | 1.07544 | ||||||||
\(698\) | 26.3923 | 0.998963 | ||||||||
\(699\) | 14.5359 | 0.549798 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.9090 | −0.903029 | −0.451515 | − | 0.892264i | \(-0.649116\pi\) | ||||
−0.451515 | + | 0.892264i | \(0.649116\pi\) | |||||||
\(702\) | 21.8564 | 0.824917 | ||||||||
\(703\) | 8.92820 | 0.336734 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 5.07180 | 0.191015 | ||||||||
\(706\) | −3.80385 | −0.143160 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 5.07180 | 0.190610 | ||||||||
\(709\) | −9.32051 | −0.350039 | −0.175020 | − | 0.984565i | \(-0.555999\pi\) | ||||
−0.175020 | + | 0.984565i | \(0.555999\pi\) | |||||||
\(710\) | 2.53590 | 0.0951706 | ||||||||
\(711\) | 4.44486 | 0.166695 | ||||||||
\(712\) | 3.46410 | 0.129823 | ||||||||
\(713\) | −4.39230 | −0.164493 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.46410 | −0.204346 | ||||||||
\(716\) | −6.00000 | −0.224231 | ||||||||
\(717\) | 3.46410 | 0.129369 | ||||||||
\(718\) | 4.05256 | 0.151240 | ||||||||
\(719\) | −27.7128 | −1.03351 | −0.516757 | − | 0.856132i | \(-0.672861\pi\) | ||||
−0.516757 | + | 0.856132i | \(0.672861\pi\) | |||||||
\(720\) | −2.46410 | −0.0918316 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −8.32051 | −0.309657 | ||||||||
\(723\) | −4.92820 | −0.183282 | ||||||||
\(724\) | −14.0000 | −0.520306 | ||||||||
\(725\) | −1.26795 | −0.0470905 | ||||||||
\(726\) | 0.732051 | 0.0271690 | ||||||||
\(727\) | 4.00000 | 0.148352 | 0.0741759 | − | 0.997245i | \(-0.476367\pi\) | ||||
0.0741759 | + | 0.997245i | \(0.476367\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.21539 | −0.0820515 | ||||||||
\(730\) | −6.39230 | −0.236590 | ||||||||
\(731\) | −6.92820 | −0.256249 | ||||||||
\(732\) | −6.53590 | −0.241574 | ||||||||
\(733\) | −26.0000 | −0.960332 | −0.480166 | − | 0.877178i | \(-0.659424\pi\) | ||||
−0.480166 | + | 0.877178i | \(0.659424\pi\) | |||||||
\(734\) | 8.39230 | 0.309766 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.19615 | 0.0809513 | ||||||||
\(737\) | −4.00000 | −0.147342 | ||||||||
\(738\) | 20.1962 | 0.743431 | ||||||||
\(739\) | −43.7128 | −1.60800 | −0.804001 | − | 0.594628i | \(-0.797299\pi\) | ||||
−0.804001 | + | 0.594628i | \(0.797299\pi\) | |||||||
\(740\) | −2.73205 | −0.100432 | ||||||||
\(741\) | 13.0718 | 0.480204 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.78461 | 0.322276 | 0.161138 | − | 0.986932i | \(-0.448484\pi\) | ||||
0.161138 | + | 0.986932i | \(0.448484\pi\) | |||||||
\(744\) | −1.46410 | −0.0536766 | ||||||||
\(745\) | −10.7321 | −0.393192 | ||||||||
\(746\) | −2.39230 | −0.0875885 | ||||||||
\(747\) | 10.8231 | 0.395996 | ||||||||
\(748\) | −3.46410 | −0.126660 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0.732051 | 0.0267307 | ||||||||
\(751\) | −32.3923 | −1.18201 | −0.591006 | − | 0.806667i | \(-0.701269\pi\) | ||||
−0.591006 | + | 0.806667i | \(0.701269\pi\) | |||||||
\(752\) | 6.92820 | 0.252646 | ||||||||
\(753\) | −8.78461 | −0.320129 | ||||||||
\(754\) | 6.92820 | 0.252310 | ||||||||
\(755\) | −13.1244 | −0.477644 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.3731 | 1.06758 | 0.533791 | − | 0.845616i | \(-0.320767\pi\) | ||||
0.533791 | + | 0.845616i | \(0.320767\pi\) | |||||||
\(758\) | 33.8564 | 1.22972 | ||||||||
\(759\) | 1.60770 | 0.0583556 | ||||||||
\(760\) | −3.26795 | −0.118541 | ||||||||
\(761\) | 29.6603 | 1.07518 | 0.537592 | − | 0.843205i | \(-0.319334\pi\) | ||||
0.537592 | + | 0.843205i | \(0.319334\pi\) | |||||||
\(762\) | 10.9282 | 0.395887 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −12.0000 | −0.434145 | ||||||||
\(765\) | 8.53590 | 0.308616 | ||||||||
\(766\) | 26.5359 | 0.958781 | ||||||||
\(767\) | −37.8564 | −1.36692 | ||||||||
\(768\) | 0.732051 | 0.0264156 | ||||||||
\(769\) | 7.80385 | 0.281414 | 0.140707 | − | 0.990051i | \(-0.455062\pi\) | ||||
0.140707 | + | 0.990051i | \(0.455062\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.64102 | 0.167142 | ||||||||
\(772\) | −8.39230 | −0.302046 | ||||||||
\(773\) | −12.9282 | −0.464995 | −0.232498 | − | 0.972597i | \(-0.574690\pi\) | ||||
−0.232498 | + | 0.972597i | \(0.574690\pi\) | |||||||
\(774\) | −4.92820 | −0.177141 | ||||||||
\(775\) | −2.00000 | −0.0718421 | ||||||||
\(776\) | 16.5885 | 0.595491 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −22.3923 | −0.802803 | ||||||||
\(779\) | 26.7846 | 0.959658 | ||||||||
\(780\) | −4.00000 | −0.143223 | ||||||||
\(781\) | 2.53590 | 0.0907416 | ||||||||
\(782\) | −7.60770 | −0.272051 | ||||||||
\(783\) | 5.07180 | 0.181251 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.4641 | −0.409171 | ||||||||
\(786\) | 8.53590 | 0.304465 | ||||||||
\(787\) | −45.8564 | −1.63460 | −0.817302 | − | 0.576209i | \(-0.804531\pi\) | ||||
−0.817302 | + | 0.576209i | \(0.804531\pi\) | |||||||
\(788\) | 24.2487 | 0.863825 | ||||||||
\(789\) | −17.5692 | −0.625481 | ||||||||
\(790\) | −1.80385 | −0.0641780 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.46410 | −0.0875580 | ||||||||
\(793\) | 48.7846 | 1.73239 | ||||||||
\(794\) | −9.60770 | −0.340964 | ||||||||
\(795\) | −7.85641 | −0.278638 | ||||||||
\(796\) | 10.9282 | 0.387340 | ||||||||
\(797\) | 46.3923 | 1.64330 | 0.821650 | − | 0.569993i | \(-0.193054\pi\) | ||||
0.821650 | + | 0.569993i | \(0.193054\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −8.53590 | −0.301601 | ||||||||
\(802\) | 9.46410 | 0.334189 | ||||||||
\(803\) | −6.39230 | −0.225580 | ||||||||
\(804\) | −2.92820 | −0.103270 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10.9282 | 0.384930 | ||||||||
\(807\) | −5.56922 | −0.196046 | ||||||||
\(808\) | −19.8564 | −0.698546 | ||||||||
\(809\) | 31.1769 | 1.09612 | 0.548061 | − | 0.836438i | \(-0.315366\pi\) | ||||
0.548061 | + | 0.836438i | \(0.315366\pi\) | |||||||
\(810\) | 4.46410 | 0.156853 | ||||||||
\(811\) | 18.8756 | 0.662814 | 0.331407 | − | 0.943488i | \(-0.392477\pi\) | ||||
0.331407 | + | 0.943488i | \(0.392477\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.9282 | 0.523555 | ||||||||
\(814\) | −2.73205 | −0.0957583 | ||||||||
\(815\) | −4.00000 | −0.140114 | ||||||||
\(816\) | −2.53590 | −0.0887742 | ||||||||
\(817\) | −6.53590 | −0.228662 | ||||||||
\(818\) | −35.1244 | −1.22809 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.19615 | −0.286222 | ||||||||
\(821\) | −47.9090 | −1.67203 | −0.836017 | − | 0.548703i | \(-0.815122\pi\) | ||||
−0.836017 | + | 0.548703i | \(0.815122\pi\) | |||||||
\(822\) | 9.46410 | 0.330098 | ||||||||
\(823\) | −25.1244 | −0.875780 | −0.437890 | − | 0.899029i | \(-0.644274\pi\) | ||||
−0.437890 | + | 0.899029i | \(0.644274\pi\) | |||||||
\(824\) | 8.39230 | 0.292360 | ||||||||
\(825\) | 0.732051 | 0.0254867 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.85641 | 0.0645536 | 0.0322768 | − | 0.999479i | \(-0.489724\pi\) | ||||
0.0322768 | + | 0.999479i | \(0.489724\pi\) | |||||||
\(828\) | −5.41154 | −0.188064 | ||||||||
\(829\) | 46.2487 | 1.60628 | 0.803142 | − | 0.595788i | \(-0.203160\pi\) | ||||
0.803142 | + | 0.595788i | \(0.203160\pi\) | |||||||
\(830\) | −4.39230 | −0.152459 | ||||||||
\(831\) | 15.3205 | 0.531463 | ||||||||
\(832\) | −5.46410 | −0.189434 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.67949 | 0.0927832 | ||||||||
\(835\) | 13.8564 | 0.479521 | ||||||||
\(836\) | −3.26795 | −0.113024 | ||||||||
\(837\) | 8.00000 | 0.276520 | ||||||||
\(838\) | −17.0718 | −0.589735 | ||||||||
\(839\) | 4.14359 | 0.143053 | 0.0715264 | − | 0.997439i | \(-0.477213\pi\) | ||||
0.0715264 | + | 0.997439i | \(0.477213\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.3923 | −0.944562 | ||||||||
\(842\) | −8.14359 | −0.280647 | ||||||||
\(843\) | 1.17691 | 0.0405351 | ||||||||
\(844\) | 13.0718 | 0.449950 | ||||||||
\(845\) | 16.8564 | 0.579878 | ||||||||
\(846\) | −17.0718 | −0.586940 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −10.7321 | −0.368540 | ||||||||
\(849\) | −17.3590 | −0.595759 | ||||||||
\(850\) | −3.46410 | −0.118818 | ||||||||
\(851\) | −6.00000 | −0.205677 | ||||||||
\(852\) | 1.85641 | 0.0635994 | ||||||||
\(853\) | 13.2154 | 0.452486 | 0.226243 | − | 0.974071i | \(-0.427356\pi\) | ||||
0.226243 | + | 0.974071i | \(0.427356\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.05256 | 0.275392 | ||||||||
\(856\) | −19.8564 | −0.678678 | ||||||||
\(857\) | 20.5359 | 0.701493 | 0.350746 | − | 0.936470i | \(-0.385928\pi\) | ||||
0.350746 | + | 0.936470i | \(0.385928\pi\) | |||||||
\(858\) | −4.00000 | −0.136558 | ||||||||
\(859\) | −28.7846 | −0.982118 | −0.491059 | − | 0.871126i | \(-0.663390\pi\) | ||||
−0.491059 | + | 0.871126i | \(0.663390\pi\) | |||||||
\(860\) | 2.00000 | 0.0681994 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −21.1244 | −0.719498 | ||||||||
\(863\) | 37.5167 | 1.27708 | 0.638541 | − | 0.769588i | \(-0.279538\pi\) | ||||
0.638541 | + | 0.769588i | \(0.279538\pi\) | |||||||
\(864\) | −4.00000 | −0.136083 | ||||||||
\(865\) | 12.9282 | 0.439572 | ||||||||
\(866\) | 7.80385 | 0.265186 | ||||||||
\(867\) | −3.66025 | −0.124309 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.80385 | −0.0611913 | ||||||||
\(870\) | −0.928203 | −0.0314690 | ||||||||
\(871\) | 21.8564 | 0.740576 | ||||||||
\(872\) | 1.66025 | 0.0562233 | ||||||||
\(873\) | −40.8756 | −1.38343 | ||||||||
\(874\) | −7.17691 | −0.242763 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.67949 | −0.158105 | ||||||||
\(877\) | 13.3205 | 0.449802 | 0.224901 | − | 0.974382i | \(-0.427794\pi\) | ||||
0.224901 | + | 0.974382i | \(0.427794\pi\) | |||||||
\(878\) | 22.2487 | 0.750858 | ||||||||
\(879\) | −10.6410 | −0.358913 | ||||||||
\(880\) | 1.00000 | 0.0337100 | ||||||||
\(881\) | −24.9282 | −0.839853 | −0.419926 | − | 0.907558i | \(-0.637944\pi\) | ||||
−0.419926 | + | 0.907558i | \(0.637944\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −56.3923 | −1.89775 | −0.948876 | − | 0.315649i | \(-0.897778\pi\) | ||||
−0.948876 | + | 0.315649i | \(0.897778\pi\) | |||||||
\(884\) | 18.9282 | 0.636624 | ||||||||
\(885\) | 5.07180 | 0.170487 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.8564 | 0.465253 | 0.232626 | − | 0.972566i | \(-0.425268\pi\) | ||||
0.232626 | + | 0.972566i | \(0.425268\pi\) | |||||||
\(888\) | −2.00000 | −0.0671156 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.46410 | 0.116117 | ||||||||
\(891\) | 4.46410 | 0.149553 | ||||||||
\(892\) | 18.5359 | 0.620628 | ||||||||
\(893\) | −22.6410 | −0.757653 | ||||||||
\(894\) | −7.85641 | −0.262758 | ||||||||
\(895\) | −6.00000 | −0.200558 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.78461 | −0.293310 | ||||||||
\(898\) | 19.6077 | 0.654317 | ||||||||
\(899\) | 2.53590 | 0.0845769 | ||||||||
\(900\) | −2.46410 | −0.0821367 | ||||||||
\(901\) | 37.1769 | 1.23854 | ||||||||
\(902\) | −8.19615 | −0.272902 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.8564 | −0.660414 | ||||||||
\(905\) | −14.0000 | −0.465376 | ||||||||
\(906\) | −9.60770 | −0.319194 | ||||||||
\(907\) | 59.0333 | 1.96017 | 0.980085 | − | 0.198580i | \(-0.0636331\pi\) | ||||
0.980085 | + | 0.198580i | \(0.0636331\pi\) | |||||||
\(908\) | 6.92820 | 0.229920 | ||||||||
\(909\) | 48.9282 | 1.62285 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.53590 | 0.0840181 | 0.0420090 | − | 0.999117i | \(-0.486624\pi\) | ||||
0.0420090 | + | 0.999117i | \(0.486624\pi\) | |||||||
\(912\) | −2.39230 | −0.0792171 | ||||||||
\(913\) | −4.39230 | −0.145364 | ||||||||
\(914\) | 2.00000 | 0.0661541 | ||||||||
\(915\) | −6.53590 | −0.216070 | ||||||||
\(916\) | −3.60770 | −0.119202 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 13.8564 | 0.457330 | ||||||||
\(919\) | 47.3731 | 1.56269 | 0.781347 | − | 0.624097i | \(-0.214533\pi\) | ||||
0.781347 | + | 0.624097i | \(0.214533\pi\) | |||||||
\(920\) | 2.19615 | 0.0724050 | ||||||||
\(921\) | −2.64102 | −0.0870244 | ||||||||
\(922\) | −1.60770 | −0.0529466 | ||||||||
\(923\) | −13.8564 | −0.456089 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.73205 | −0.0898293 | ||||||||
\(926\) | −17.5167 | −0.575633 | ||||||||
\(927\) | −20.6795 | −0.679204 | ||||||||
\(928\) | −1.26795 | −0.0416225 | ||||||||
\(929\) | 46.3923 | 1.52208 | 0.761041 | − | 0.648704i | \(-0.224689\pi\) | ||||
0.761041 | + | 0.648704i | \(0.224689\pi\) | |||||||
\(930\) | −1.46410 | −0.0480098 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 19.8564 | 0.650418 | ||||||||
\(933\) | −8.10512 | −0.265350 | ||||||||
\(934\) | −4.05256 | −0.132604 | ||||||||
\(935\) | −3.46410 | −0.113288 | ||||||||
\(936\) | 13.4641 | 0.440088 | ||||||||
\(937\) | 42.7846 | 1.39771 | 0.698856 | − | 0.715262i | \(-0.253693\pi\) | ||||
0.698856 | + | 0.715262i | \(0.253693\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.64102 | −0.281989 | ||||||||
\(940\) | 6.92820 | 0.225973 | ||||||||
\(941\) | −26.7846 | −0.873153 | −0.436577 | − | 0.899667i | \(-0.643809\pi\) | ||||
−0.436577 | + | 0.899667i | \(0.643809\pi\) | |||||||
\(942\) | −8.39230 | −0.273436 | ||||||||
\(943\) | −18.0000 | −0.586161 | ||||||||
\(944\) | 6.92820 | 0.225494 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.00000 | 0.0650256 | ||||||||
\(947\) | 12.6795 | 0.412028 | 0.206014 | − | 0.978549i | \(-0.433951\pi\) | ||||
0.206014 | + | 0.978549i | \(0.433951\pi\) | |||||||
\(948\) | −1.32051 | −0.0428881 | ||||||||
\(949\) | 34.9282 | 1.13382 | ||||||||
\(950\) | −3.26795 | −0.106026 | ||||||||
\(951\) | −0.430781 | −0.0139690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.4641 | 1.08401 | 0.542004 | − | 0.840376i | \(-0.317666\pi\) | ||||
0.542004 | + | 0.840376i | \(0.317666\pi\) | |||||||
\(954\) | 26.4449 | 0.856184 | ||||||||
\(955\) | −12.0000 | −0.388311 | ||||||||
\(956\) | 4.73205 | 0.153045 | ||||||||
\(957\) | −0.928203 | −0.0300045 | ||||||||
\(958\) | −8.78461 | −0.283818 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.732051 | 0.0236268 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 14.9282 | 0.481305 | ||||||||
\(963\) | 48.9282 | 1.57669 | ||||||||
\(964\) | −6.73205 | −0.216825 | ||||||||
\(965\) | −8.39230 | −0.270158 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.0718 | 0.420361 | 0.210180 | − | 0.977663i | \(-0.432595\pi\) | ||||
0.210180 | + | 0.977663i | \(0.432595\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 8.28719 | 0.266223 | ||||||||
\(970\) | 16.5885 | 0.532623 | ||||||||
\(971\) | −29.0718 | −0.932958 | −0.466479 | − | 0.884532i | \(-0.654478\pi\) | ||||
−0.466479 | + | 0.884532i | \(0.654478\pi\) | |||||||
\(972\) | 15.2679 | 0.489720 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −6.19615 | −0.198538 | ||||||||
\(975\) | −4.00000 | −0.128103 | ||||||||
\(976\) | −8.92820 | −0.285785 | ||||||||
\(977\) | 21.7128 | 0.694654 | 0.347327 | − | 0.937744i | \(-0.387089\pi\) | ||||
0.347327 | + | 0.937744i | \(0.387089\pi\) | |||||||
\(978\) | −2.92820 | −0.0936336 | ||||||||
\(979\) | 3.46410 | 0.110713 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.09103 | −0.130617 | ||||||||
\(982\) | 27.7128 | 0.884351 | ||||||||
\(983\) | −25.1769 | −0.803019 | −0.401509 | − | 0.915855i | \(-0.631514\pi\) | ||||
−0.401509 | + | 0.915855i | \(0.631514\pi\) | |||||||
\(984\) | −6.00000 | −0.191273 | ||||||||
\(985\) | 24.2487 | 0.772628 | ||||||||
\(986\) | 4.39230 | 0.139879 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 17.8564 | 0.568088 | ||||||||
\(989\) | 4.39230 | 0.139667 | ||||||||
\(990\) | −2.46410 | −0.0783143 | ||||||||
\(991\) | −4.00000 | −0.127064 | −0.0635321 | − | 0.997980i | \(-0.520237\pi\) | ||||
−0.0635321 | + | 0.997980i | \(0.520237\pi\) | |||||||
\(992\) | −2.00000 | −0.0635001 | ||||||||
\(993\) | 16.6795 | 0.529308 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.9282 | 0.346447 | ||||||||
\(996\) | −3.21539 | −0.101884 | ||||||||
\(997\) | 37.7128 | 1.19438 | 0.597188 | − | 0.802101i | \(-0.296284\pi\) | ||||
0.597188 | + | 0.802101i | \(0.296284\pi\) | |||||||
\(998\) | 39.8564 | 1.26163 | ||||||||
\(999\) | 10.9282 | 0.345753 |
(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 | 5390.2.a.bs.1.2 | 2 | ||
7.6 | odd | 2 | 770.2.a.j.1.1 | ✓ | 2 | ||
21.20 | even | 2 | 6930.2.a.bv.1.2 | 2 | |||
28.27 | even | 2 | 6160.2.a.t.1.2 | 2 | |||
35.13 | even | 4 | 3850.2.c.x.1849.1 | 4 | |||
35.27 | even | 4 | 3850.2.c.x.1849.4 | 4 | |||
35.34 | odd | 2 | 3850.2.a.bd.1.2 | 2 | |||
77.76 | even | 2 | 8470.2.a.br.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.a.j.1.1 | ✓ | 2 | 7.6 | odd | 2 | ||
3850.2.a.bd.1.2 | 2 | 35.34 | odd | 2 | |||
3850.2.c.x.1849.1 | 4 | 35.13 | even | 4 | |||
3850.2.c.x.1849.4 | 4 | 35.27 | even | 4 | |||
5390.2.a.bs.1.2 | 2 | 1.1 | even | 1 | trivial | ||
6160.2.a.t.1.2 | 2 | 28.27 | even | 2 | |||
6930.2.a.bv.1.2 | 2 | 21.20 | even | 2 | |||
8470.2.a.br.1.1 | 2 | 77.76 | even | 2 |