Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5586,2,Mod(1,5586)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5586, 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("5586.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5586.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: | \(44.6044345691\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 798) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5586.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.267949 | −0.119831 | −0.0599153 | − | 0.998203i | \(-0.519083\pi\) | ||||
−0.0599153 | + | 0.998203i | \(0.519083\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.267949 | −0.0847330 | ||||||||
\(11\) | −1.00000 | −0.301511 | −0.150756 | − | 0.988571i | \(-0.548171\pi\) | ||||
−0.150756 | + | 0.988571i | \(0.548171\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −5.46410 | −1.51547 | −0.757735 | − | 0.652563i | \(-0.773694\pi\) | ||||
−0.757735 | + | 0.652563i | \(0.773694\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.267949 | −0.0691842 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.73205 | −1.14769 | −0.573845 | − | 0.818964i | \(-0.694549\pi\) | ||||
−0.573845 | + | 0.818964i | \(0.694549\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −0.267949 | −0.0599153 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −2.73205 | −0.569672 | −0.284836 | − | 0.958576i | \(-0.591939\pi\) | ||||
−0.284836 | + | 0.958576i | \(0.591939\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.92820 | −0.985641 | ||||||||
\(26\) | −5.46410 | −1.07160 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | −0.267949 | −0.0489206 | ||||||||
\(31\) | 2.46410 | 0.442566 | 0.221283 | − | 0.975210i | \(-0.428976\pi\) | ||||
0.221283 | + | 0.975210i | \(0.428976\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −4.73205 | −0.811540 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.19615 | 1.01864 | 0.509321 | − | 0.860577i | \(-0.329897\pi\) | ||||
0.509321 | + | 0.860577i | \(0.329897\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −5.46410 | −0.874957 | ||||||||
\(40\) | −0.267949 | −0.0423665 | ||||||||
\(41\) | −5.26795 | −0.822715 | −0.411358 | − | 0.911474i | \(-0.634945\pi\) | ||||
−0.411358 | + | 0.911474i | \(0.634945\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.196152 | 0.0299130 | 0.0149565 | − | 0.999888i | \(-0.495239\pi\) | ||||
0.0149565 | + | 0.999888i | \(0.495239\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | −0.267949 | −0.0399435 | ||||||||
\(46\) | −2.73205 | −0.402819 | ||||||||
\(47\) | −11.4641 | −1.67221 | −0.836106 | − | 0.548569i | \(-0.815173\pi\) | ||||
−0.836106 | + | 0.548569i | \(0.815173\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.92820 | −0.696953 | ||||||||
\(51\) | −4.73205 | −0.662620 | ||||||||
\(52\) | −5.46410 | −0.757735 | ||||||||
\(53\) | 1.53590 | 0.210972 | 0.105486 | − | 0.994421i | \(-0.466360\pi\) | ||||
0.105486 | + | 0.994421i | \(0.466360\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.267949 | 0.0361303 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | 1.73205 | 0.225494 | 0.112747 | − | 0.993624i | \(-0.464035\pi\) | ||||
0.112747 | + | 0.993624i | \(0.464035\pi\) | |||||||
\(60\) | −0.267949 | −0.0345921 | ||||||||
\(61\) | −4.53590 | −0.580762 | −0.290381 | − | 0.956911i | \(-0.593782\pi\) | ||||
−0.290381 | + | 0.956911i | \(0.593782\pi\) | |||||||
\(62\) | 2.46410 | 0.312941 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.46410 | 0.181599 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | −0.928203 | −0.113398 | −0.0566990 | − | 0.998391i | \(-0.518058\pi\) | ||||
−0.0566990 | + | 0.998391i | \(0.518058\pi\) | |||||||
\(68\) | −4.73205 | −0.573845 | ||||||||
\(69\) | −2.73205 | −0.328900 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.1962 | −1.44742 | −0.723708 | − | 0.690106i | \(-0.757564\pi\) | ||||
−0.723708 | + | 0.690106i | \(0.757564\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −6.92820 | −0.810885 | −0.405442 | − | 0.914121i | \(-0.632883\pi\) | ||||
−0.405442 | + | 0.914121i | \(0.632883\pi\) | |||||||
\(74\) | 6.19615 | 0.720288 | ||||||||
\(75\) | −4.92820 | −0.569060 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.46410 | −0.618688 | ||||||||
\(79\) | −11.3923 | −1.28173 | −0.640867 | − | 0.767652i | \(-0.721425\pi\) | ||||
−0.640867 | + | 0.767652i | \(0.721425\pi\) | |||||||
\(80\) | −0.267949 | −0.0299576 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.26795 | −0.581748 | ||||||||
\(83\) | 3.00000 | 0.329293 | 0.164646 | − | 0.986353i | \(-0.447352\pi\) | ||||
0.164646 | + | 0.986353i | \(0.447352\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.26795 | 0.137528 | ||||||||
\(86\) | 0.196152 | 0.0211517 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −0.339746 | −0.0360130 | −0.0180065 | − | 0.999838i | \(-0.505732\pi\) | ||||
−0.0180065 | + | 0.999838i | \(0.505732\pi\) | |||||||
\(90\) | −0.267949 | −0.0282443 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.73205 | −0.284836 | ||||||||
\(93\) | 2.46410 | 0.255515 | ||||||||
\(94\) | −11.4641 | −1.18243 | ||||||||
\(95\) | −0.267949 | −0.0274910 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −5.73205 | −0.582002 | −0.291001 | − | 0.956723i | \(-0.593988\pi\) | ||||
−0.291001 | + | 0.956723i | \(0.593988\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −4.92820 | −0.492820 | ||||||||
\(101\) | 4.92820 | 0.490375 | 0.245187 | − | 0.969476i | \(-0.421151\pi\) | ||||
0.245187 | + | 0.969476i | \(0.421151\pi\) | |||||||
\(102\) | −4.73205 | −0.468543 | ||||||||
\(103\) | −6.00000 | −0.591198 | −0.295599 | − | 0.955312i | \(-0.595519\pi\) | ||||
−0.295599 | + | 0.955312i | \(0.595519\pi\) | |||||||
\(104\) | −5.46410 | −0.535799 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.53590 | 0.149180 | ||||||||
\(107\) | −1.33975 | −0.129518 | −0.0647591 | − | 0.997901i | \(-0.520628\pi\) | ||||
−0.0647591 | + | 0.997901i | \(0.520628\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 10.7321 | 1.02794 | 0.513972 | − | 0.857807i | \(-0.328174\pi\) | ||||
0.513972 | + | 0.857807i | \(0.328174\pi\) | |||||||
\(110\) | 0.267949 | 0.0255480 | ||||||||
\(111\) | 6.19615 | 0.588113 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.26795 | −0.495567 | −0.247783 | − | 0.968815i | \(-0.579702\pi\) | ||||
−0.247783 | + | 0.968815i | \(0.579702\pi\) | |||||||
\(114\) | 1.00000 | 0.0936586 | ||||||||
\(115\) | 0.732051 | 0.0682641 | ||||||||
\(116\) | 1.00000 | 0.0928477 | ||||||||
\(117\) | −5.46410 | −0.505156 | ||||||||
\(118\) | 1.73205 | 0.159448 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.267949 | −0.0244603 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | −4.53590 | −0.410661 | ||||||||
\(123\) | −5.26795 | −0.474995 | ||||||||
\(124\) | 2.46410 | 0.221283 | ||||||||
\(125\) | 2.66025 | 0.237940 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.92820 | 0.348572 | 0.174286 | − | 0.984695i | \(-0.444238\pi\) | ||||
0.174286 | + | 0.984695i | \(0.444238\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0.196152 | 0.0172703 | ||||||||
\(130\) | 1.46410 | 0.128410 | ||||||||
\(131\) | 0.464102 | 0.0405487 | 0.0202744 | − | 0.999794i | \(-0.493546\pi\) | ||||
0.0202744 | + | 0.999794i | \(0.493546\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.928203 | −0.0801845 | ||||||||
\(135\) | −0.267949 | −0.0230614 | ||||||||
\(136\) | −4.73205 | −0.405770 | ||||||||
\(137\) | 11.8564 | 1.01296 | 0.506481 | − | 0.862251i | \(-0.330946\pi\) | ||||
0.506481 | + | 0.862251i | \(0.330946\pi\) | |||||||
\(138\) | −2.73205 | −0.232568 | ||||||||
\(139\) | −8.19615 | −0.695189 | −0.347594 | − | 0.937645i | \(-0.613001\pi\) | ||||
−0.347594 | + | 0.937645i | \(0.613001\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.4641 | −0.965452 | ||||||||
\(142\) | −12.1962 | −1.02348 | ||||||||
\(143\) | 5.46410 | 0.456931 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −0.267949 | −0.0222520 | ||||||||
\(146\) | −6.92820 | −0.573382 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.19615 | 0.509321 | ||||||||
\(149\) | 1.60770 | 0.131708 | 0.0658538 | − | 0.997829i | \(-0.479023\pi\) | ||||
0.0658538 | + | 0.997829i | \(0.479023\pi\) | |||||||
\(150\) | −4.92820 | −0.402386 | ||||||||
\(151\) | 15.3923 | 1.25261 | 0.626304 | − | 0.779579i | \(-0.284567\pi\) | ||||
0.626304 | + | 0.779579i | \(0.284567\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −4.73205 | −0.382564 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.660254 | −0.0530329 | ||||||||
\(156\) | −5.46410 | −0.437478 | ||||||||
\(157\) | −1.46410 | −0.116848 | −0.0584240 | − | 0.998292i | \(-0.518608\pi\) | ||||
−0.0584240 | + | 0.998292i | \(0.518608\pi\) | |||||||
\(158\) | −11.3923 | −0.906323 | ||||||||
\(159\) | 1.53590 | 0.121805 | ||||||||
\(160\) | −0.267949 | −0.0211832 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 12.3923 | 0.970640 | 0.485320 | − | 0.874337i | \(-0.338703\pi\) | ||||
0.485320 | + | 0.874337i | \(0.338703\pi\) | |||||||
\(164\) | −5.26795 | −0.411358 | ||||||||
\(165\) | 0.267949 | 0.0208598 | ||||||||
\(166\) | 3.00000 | 0.232845 | ||||||||
\(167\) | −20.1962 | −1.56283 | −0.781413 | − | 0.624015i | \(-0.785501\pi\) | ||||
−0.781413 | + | 0.624015i | \(0.785501\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.8564 | 1.29665 | ||||||||
\(170\) | 1.26795 | 0.0972473 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 0.196152 | 0.0149565 | ||||||||
\(173\) | 20.7846 | 1.58022 | 0.790112 | − | 0.612962i | \(-0.210022\pi\) | ||||
0.790112 | + | 0.612962i | \(0.210022\pi\) | |||||||
\(174\) | 1.00000 | 0.0758098 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 1.73205 | 0.130189 | ||||||||
\(178\) | −0.339746 | −0.0254650 | ||||||||
\(179\) | −9.46410 | −0.707380 | −0.353690 | − | 0.935363i | \(-0.615073\pi\) | ||||
−0.353690 | + | 0.935363i | \(0.615073\pi\) | |||||||
\(180\) | −0.267949 | −0.0199718 | ||||||||
\(181\) | −1.46410 | −0.108826 | −0.0544129 | − | 0.998519i | \(-0.517329\pi\) | ||||
−0.0544129 | + | 0.998519i | \(0.517329\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.53590 | −0.335303 | ||||||||
\(184\) | −2.73205 | −0.201409 | ||||||||
\(185\) | −1.66025 | −0.122064 | ||||||||
\(186\) | 2.46410 | 0.180677 | ||||||||
\(187\) | 4.73205 | 0.346042 | ||||||||
\(188\) | −11.4641 | −0.836106 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.267949 | −0.0194391 | ||||||||
\(191\) | 13.4641 | 0.974228 | 0.487114 | − | 0.873338i | \(-0.338050\pi\) | ||||
0.487114 | + | 0.873338i | \(0.338050\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 27.5885 | 1.98586 | 0.992930 | − | 0.118699i | \(-0.0378723\pi\) | ||||
0.992930 | + | 0.118699i | \(0.0378723\pi\) | |||||||
\(194\) | −5.73205 | −0.411537 | ||||||||
\(195\) | 1.46410 | 0.104846 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.7846 | 1.19585 | 0.597927 | − | 0.801551i | \(-0.295991\pi\) | ||||
0.597927 | + | 0.801551i | \(0.295991\pi\) | |||||||
\(198\) | −1.00000 | −0.0710669 | ||||||||
\(199\) | −12.3923 | −0.878467 | −0.439234 | − | 0.898373i | \(-0.644750\pi\) | ||||
−0.439234 | + | 0.898373i | \(0.644750\pi\) | |||||||
\(200\) | −4.92820 | −0.348477 | ||||||||
\(201\) | −0.928203 | −0.0654704 | ||||||||
\(202\) | 4.92820 | 0.346747 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −4.73205 | −0.331310 | ||||||||
\(205\) | 1.41154 | 0.0985864 | ||||||||
\(206\) | −6.00000 | −0.418040 | ||||||||
\(207\) | −2.73205 | −0.189891 | ||||||||
\(208\) | −5.46410 | −0.378867 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.26795 | −0.500346 | −0.250173 | − | 0.968201i | \(-0.580488\pi\) | ||||
−0.250173 | + | 0.968201i | \(0.580488\pi\) | |||||||
\(212\) | 1.53590 | 0.105486 | ||||||||
\(213\) | −12.1962 | −0.835667 | ||||||||
\(214\) | −1.33975 | −0.0915831 | ||||||||
\(215\) | −0.0525589 | −0.00358449 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.7321 | 0.726866 | ||||||||
\(219\) | −6.92820 | −0.468165 | ||||||||
\(220\) | 0.267949 | 0.0180651 | ||||||||
\(221\) | 25.8564 | 1.73929 | ||||||||
\(222\) | 6.19615 | 0.415859 | ||||||||
\(223\) | −10.3205 | −0.691112 | −0.345556 | − | 0.938398i | \(-0.612310\pi\) | ||||
−0.345556 | + | 0.938398i | \(0.612310\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.92820 | −0.328547 | ||||||||
\(226\) | −5.26795 | −0.350419 | ||||||||
\(227\) | −18.6603 | −1.23852 | −0.619262 | − | 0.785184i | \(-0.712568\pi\) | ||||
−0.619262 | + | 0.785184i | \(0.712568\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | 27.3205 | 1.80539 | 0.902695 | − | 0.430281i | \(-0.141586\pi\) | ||||
0.902695 | + | 0.430281i | \(0.141586\pi\) | |||||||
\(230\) | 0.732051 | 0.0482700 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | 2.53590 | 0.166132 | 0.0830661 | − | 0.996544i | \(-0.473529\pi\) | ||||
0.0830661 | + | 0.996544i | \(0.473529\pi\) | |||||||
\(234\) | −5.46410 | −0.357199 | ||||||||
\(235\) | 3.07180 | 0.200382 | ||||||||
\(236\) | 1.73205 | 0.112747 | ||||||||
\(237\) | −11.3923 | −0.740010 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.9282 | −1.22436 | −0.612182 | − | 0.790717i | \(-0.709708\pi\) | ||||
−0.612182 | + | 0.790717i | \(0.709708\pi\) | |||||||
\(240\) | −0.267949 | −0.0172960 | ||||||||
\(241\) | −23.9808 | −1.54474 | −0.772368 | − | 0.635175i | \(-0.780928\pi\) | ||||
−0.772368 | + | 0.635175i | \(0.780928\pi\) | |||||||
\(242\) | −10.0000 | −0.642824 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −4.53590 | −0.290381 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.26795 | −0.335872 | ||||||||
\(247\) | −5.46410 | −0.347672 | ||||||||
\(248\) | 2.46410 | 0.156471 | ||||||||
\(249\) | 3.00000 | 0.190117 | ||||||||
\(250\) | 2.66025 | 0.168249 | ||||||||
\(251\) | 2.85641 | 0.180295 | 0.0901474 | − | 0.995928i | \(-0.471266\pi\) | ||||
0.0901474 | + | 0.995928i | \(0.471266\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.73205 | 0.171763 | ||||||||
\(254\) | 3.92820 | 0.246477 | ||||||||
\(255\) | 1.26795 | 0.0794021 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.92820 | 0.307413 | 0.153706 | − | 0.988117i | \(-0.450879\pi\) | ||||
0.153706 | + | 0.988117i | \(0.450879\pi\) | |||||||
\(258\) | 0.196152 | 0.0122119 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.46410 | 0.0907997 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0.464102 | 0.0286723 | ||||||||
\(263\) | 16.0526 | 0.989843 | 0.494922 | − | 0.868938i | \(-0.335197\pi\) | ||||
0.494922 | + | 0.868938i | \(0.335197\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | −0.411543 | −0.0252809 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.339746 | −0.0207921 | ||||||||
\(268\) | −0.928203 | −0.0566990 | ||||||||
\(269\) | −20.3205 | −1.23896 | −0.619482 | − | 0.785011i | \(-0.712657\pi\) | ||||
−0.619482 | + | 0.785011i | \(0.712657\pi\) | |||||||
\(270\) | −0.267949 | −0.0163069 | ||||||||
\(271\) | −23.0526 | −1.40034 | −0.700172 | − | 0.713975i | \(-0.746893\pi\) | ||||
−0.700172 | + | 0.713975i | \(0.746893\pi\) | |||||||
\(272\) | −4.73205 | −0.286923 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.8564 | 0.716272 | ||||||||
\(275\) | 4.92820 | 0.297182 | ||||||||
\(276\) | −2.73205 | −0.164450 | ||||||||
\(277\) | 19.8038 | 1.18990 | 0.594949 | − | 0.803763i | \(-0.297172\pi\) | ||||
0.594949 | + | 0.803763i | \(0.297172\pi\) | |||||||
\(278\) | −8.19615 | −0.491573 | ||||||||
\(279\) | 2.46410 | 0.147522 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.8564 | −1.66177 | −0.830887 | − | 0.556441i | \(-0.812166\pi\) | ||||
−0.830887 | + | 0.556441i | \(0.812166\pi\) | |||||||
\(282\) | −11.4641 | −0.682677 | ||||||||
\(283\) | 26.4449 | 1.57198 | 0.785992 | − | 0.618237i | \(-0.212153\pi\) | ||||
0.785992 | + | 0.618237i | \(0.212153\pi\) | |||||||
\(284\) | −12.1962 | −0.723708 | ||||||||
\(285\) | −0.267949 | −0.0158719 | ||||||||
\(286\) | 5.46410 | 0.323099 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 5.39230 | 0.317194 | ||||||||
\(290\) | −0.267949 | −0.0157345 | ||||||||
\(291\) | −5.73205 | −0.336019 | ||||||||
\(292\) | −6.92820 | −0.405442 | ||||||||
\(293\) | −30.4641 | −1.77973 | −0.889866 | − | 0.456222i | \(-0.849202\pi\) | ||||
−0.889866 | + | 0.456222i | \(0.849202\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.464102 | −0.0270210 | ||||||||
\(296\) | 6.19615 | 0.360144 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 1.60770 | 0.0931313 | ||||||||
\(299\) | 14.9282 | 0.863320 | ||||||||
\(300\) | −4.92820 | −0.284530 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 15.3923 | 0.885728 | ||||||||
\(303\) | 4.92820 | 0.283118 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 1.21539 | 0.0695930 | ||||||||
\(306\) | −4.73205 | −0.270513 | ||||||||
\(307\) | 24.5885 | 1.40334 | 0.701669 | − | 0.712503i | \(-0.252439\pi\) | ||||
0.701669 | + | 0.712503i | \(0.252439\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.00000 | −0.341328 | ||||||||
\(310\) | −0.660254 | −0.0374999 | ||||||||
\(311\) | 35.1244 | 1.99172 | 0.995860 | − | 0.0909031i | \(-0.0289754\pi\) | ||||
0.995860 | + | 0.0909031i | \(0.0289754\pi\) | |||||||
\(312\) | −5.46410 | −0.309344 | ||||||||
\(313\) | −31.7846 | −1.79657 | −0.898286 | − | 0.439411i | \(-0.855187\pi\) | ||||
−0.898286 | + | 0.439411i | \(0.855187\pi\) | |||||||
\(314\) | −1.46410 | −0.0826240 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.3923 | −0.640867 | ||||||||
\(317\) | −25.3923 | −1.42617 | −0.713087 | − | 0.701076i | \(-0.752704\pi\) | ||||
−0.713087 | + | 0.701076i | \(0.752704\pi\) | |||||||
\(318\) | 1.53590 | 0.0861289 | ||||||||
\(319\) | −1.00000 | −0.0559893 | ||||||||
\(320\) | −0.267949 | −0.0149788 | ||||||||
\(321\) | −1.33975 | −0.0747773 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.73205 | −0.263298 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 26.9282 | 1.49371 | ||||||||
\(326\) | 12.3923 | 0.686346 | ||||||||
\(327\) | 10.7321 | 0.593484 | ||||||||
\(328\) | −5.26795 | −0.290874 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.267949 | 0.0147501 | ||||||||
\(331\) | 15.5167 | 0.852873 | 0.426436 | − | 0.904518i | \(-0.359769\pi\) | ||||
0.426436 | + | 0.904518i | \(0.359769\pi\) | |||||||
\(332\) | 3.00000 | 0.164646 | ||||||||
\(333\) | 6.19615 | 0.339547 | ||||||||
\(334\) | −20.1962 | −1.10508 | ||||||||
\(335\) | 0.248711 | 0.0135886 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.9808 | −1.52421 | −0.762105 | − | 0.647454i | \(-0.775834\pi\) | ||||
−0.762105 | + | 0.647454i | \(0.775834\pi\) | |||||||
\(338\) | 16.8564 | 0.916868 | ||||||||
\(339\) | −5.26795 | −0.286116 | ||||||||
\(340\) | 1.26795 | 0.0687642 | ||||||||
\(341\) | −2.46410 | −0.133439 | ||||||||
\(342\) | 1.00000 | 0.0540738 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.196152 | 0.0105758 | ||||||||
\(345\) | 0.732051 | 0.0394123 | ||||||||
\(346\) | 20.7846 | 1.11739 | ||||||||
\(347\) | −6.39230 | −0.343157 | −0.171578 | − | 0.985170i | \(-0.554887\pi\) | ||||
−0.171578 | + | 0.985170i | \(0.554887\pi\) | |||||||
\(348\) | 1.00000 | 0.0536056 | ||||||||
\(349\) | 15.2679 | 0.817275 | 0.408637 | − | 0.912697i | \(-0.366004\pi\) | ||||
0.408637 | + | 0.912697i | \(0.366004\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.46410 | −0.291652 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 14.1962 | 0.755585 | 0.377792 | − | 0.925890i | \(-0.376683\pi\) | ||||
0.377792 | + | 0.925890i | \(0.376683\pi\) | |||||||
\(354\) | 1.73205 | 0.0920575 | ||||||||
\(355\) | 3.26795 | 0.173445 | ||||||||
\(356\) | −0.339746 | −0.0180065 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.46410 | −0.500193 | ||||||||
\(359\) | −0.928203 | −0.0489887 | −0.0244943 | − | 0.999700i | \(-0.507798\pi\) | ||||
−0.0244943 | + | 0.999700i | \(0.507798\pi\) | |||||||
\(360\) | −0.267949 | −0.0141222 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −1.46410 | −0.0769515 | ||||||||
\(363\) | −10.0000 | −0.524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.85641 | 0.0971688 | ||||||||
\(366\) | −4.53590 | −0.237095 | ||||||||
\(367\) | 24.5167 | 1.27976 | 0.639880 | − | 0.768475i | \(-0.278984\pi\) | ||||
0.639880 | + | 0.768475i | \(0.278984\pi\) | |||||||
\(368\) | −2.73205 | −0.142418 | ||||||||
\(369\) | −5.26795 | −0.274238 | ||||||||
\(370\) | −1.66025 | −0.0863125 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.46410 | 0.127758 | ||||||||
\(373\) | −15.3205 | −0.793266 | −0.396633 | − | 0.917977i | \(-0.629821\pi\) | ||||
−0.396633 | + | 0.917977i | \(0.629821\pi\) | |||||||
\(374\) | 4.73205 | 0.244689 | ||||||||
\(375\) | 2.66025 | 0.137375 | ||||||||
\(376\) | −11.4641 | −0.591216 | ||||||||
\(377\) | −5.46410 | −0.281416 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.1436 | 0.521041 | 0.260521 | − | 0.965468i | \(-0.416106\pi\) | ||||
0.260521 | + | 0.965468i | \(0.416106\pi\) | |||||||
\(380\) | −0.267949 | −0.0137455 | ||||||||
\(381\) | 3.92820 | 0.201248 | ||||||||
\(382\) | 13.4641 | 0.688883 | ||||||||
\(383\) | −6.78461 | −0.346677 | −0.173339 | − | 0.984862i | \(-0.555456\pi\) | ||||
−0.173339 | + | 0.984862i | \(0.555456\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 27.5885 | 1.40422 | ||||||||
\(387\) | 0.196152 | 0.00997099 | ||||||||
\(388\) | −5.73205 | −0.291001 | ||||||||
\(389\) | 17.3205 | 0.878185 | 0.439092 | − | 0.898442i | \(-0.355300\pi\) | ||||
0.439092 | + | 0.898442i | \(0.355300\pi\) | |||||||
\(390\) | 1.46410 | 0.0741377 | ||||||||
\(391\) | 12.9282 | 0.653807 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.464102 | 0.0234108 | ||||||||
\(394\) | 16.7846 | 0.845596 | ||||||||
\(395\) | 3.05256 | 0.153591 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | −19.3205 | −0.969669 | −0.484834 | − | 0.874606i | \(-0.661120\pi\) | ||||
−0.484834 | + | 0.874606i | \(0.661120\pi\) | |||||||
\(398\) | −12.3923 | −0.621170 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.92820 | −0.246410 | ||||||||
\(401\) | −0.392305 | −0.0195908 | −0.00979538 | − | 0.999952i | \(-0.503118\pi\) | ||||
−0.00979538 | + | 0.999952i | \(0.503118\pi\) | |||||||
\(402\) | −0.928203 | −0.0462946 | ||||||||
\(403\) | −13.4641 | −0.670695 | ||||||||
\(404\) | 4.92820 | 0.245187 | ||||||||
\(405\) | −0.267949 | −0.0133145 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.19615 | −0.307132 | ||||||||
\(408\) | −4.73205 | −0.234271 | ||||||||
\(409\) | 10.6603 | 0.527116 | 0.263558 | − | 0.964644i | \(-0.415104\pi\) | ||||
0.263558 | + | 0.964644i | \(0.415104\pi\) | |||||||
\(410\) | 1.41154 | 0.0697111 | ||||||||
\(411\) | 11.8564 | 0.584833 | ||||||||
\(412\) | −6.00000 | −0.295599 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.73205 | −0.134273 | ||||||||
\(415\) | −0.803848 | −0.0394593 | ||||||||
\(416\) | −5.46410 | −0.267900 | ||||||||
\(417\) | −8.19615 | −0.401367 | ||||||||
\(418\) | −1.00000 | −0.0489116 | ||||||||
\(419\) | −31.1769 | −1.52309 | −0.761546 | − | 0.648111i | \(-0.775559\pi\) | ||||
−0.761546 | + | 0.648111i | \(0.775559\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.2487 | −0.791914 | −0.395957 | − | 0.918269i | \(-0.629587\pi\) | ||||
−0.395957 | + | 0.918269i | \(0.629587\pi\) | |||||||
\(422\) | −7.26795 | −0.353798 | ||||||||
\(423\) | −11.4641 | −0.557404 | ||||||||
\(424\) | 1.53590 | 0.0745898 | ||||||||
\(425\) | 23.3205 | 1.13121 | ||||||||
\(426\) | −12.1962 | −0.590906 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.33975 | −0.0647591 | ||||||||
\(429\) | 5.46410 | 0.263809 | ||||||||
\(430\) | −0.0525589 | −0.00253461 | ||||||||
\(431\) | −20.4449 | −0.984794 | −0.492397 | − | 0.870371i | \(-0.663879\pi\) | ||||
−0.492397 | + | 0.870371i | \(0.663879\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 16.0000 | 0.768911 | 0.384455 | − | 0.923144i | \(-0.374389\pi\) | ||||
0.384455 | + | 0.923144i | \(0.374389\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.267949 | −0.0128472 | ||||||||
\(436\) | 10.7321 | 0.513972 | ||||||||
\(437\) | −2.73205 | −0.130692 | ||||||||
\(438\) | −6.92820 | −0.331042 | ||||||||
\(439\) | −2.46410 | −0.117605 | −0.0588026 | − | 0.998270i | \(-0.518728\pi\) | ||||
−0.0588026 | + | 0.998270i | \(0.518728\pi\) | |||||||
\(440\) | 0.267949 | 0.0127740 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 25.8564 | 1.22986 | ||||||||
\(443\) | 7.00000 | 0.332580 | 0.166290 | − | 0.986077i | \(-0.446821\pi\) | ||||
0.166290 | + | 0.986077i | \(0.446821\pi\) | |||||||
\(444\) | 6.19615 | 0.294056 | ||||||||
\(445\) | 0.0910347 | 0.00431546 | ||||||||
\(446\) | −10.3205 | −0.488690 | ||||||||
\(447\) | 1.60770 | 0.0760414 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.1244 | −1.09131 | −0.545653 | − | 0.838011i | \(-0.683718\pi\) | ||||
−0.545653 | + | 0.838011i | \(0.683718\pi\) | |||||||
\(450\) | −4.92820 | −0.232318 | ||||||||
\(451\) | 5.26795 | 0.248058 | ||||||||
\(452\) | −5.26795 | −0.247783 | ||||||||
\(453\) | 15.3923 | 0.723194 | ||||||||
\(454\) | −18.6603 | −0.875769 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | 23.9282 | 1.11931 | 0.559657 | − | 0.828724i | \(-0.310933\pi\) | ||||
0.559657 | + | 0.828724i | \(0.310933\pi\) | |||||||
\(458\) | 27.3205 | 1.27660 | ||||||||
\(459\) | −4.73205 | −0.220873 | ||||||||
\(460\) | 0.732051 | 0.0341320 | ||||||||
\(461\) | −39.8564 | −1.85630 | −0.928149 | − | 0.372209i | \(-0.878600\pi\) | ||||
−0.928149 | + | 0.372209i | \(0.878600\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.00000 | 0.185896 | 0.0929479 | − | 0.995671i | \(-0.470371\pi\) | ||||
0.0929479 | + | 0.995671i | \(0.470371\pi\) | |||||||
\(464\) | 1.00000 | 0.0464238 | ||||||||
\(465\) | −0.660254 | −0.0306185 | ||||||||
\(466\) | 2.53590 | 0.117473 | ||||||||
\(467\) | −16.9282 | −0.783344 | −0.391672 | − | 0.920105i | \(-0.628103\pi\) | ||||
−0.391672 | + | 0.920105i | \(0.628103\pi\) | |||||||
\(468\) | −5.46410 | −0.252578 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.07180 | 0.141691 | ||||||||
\(471\) | −1.46410 | −0.0674622 | ||||||||
\(472\) | 1.73205 | 0.0797241 | ||||||||
\(473\) | −0.196152 | −0.00901910 | ||||||||
\(474\) | −11.3923 | −0.523266 | ||||||||
\(475\) | −4.92820 | −0.226121 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.53590 | 0.0703240 | ||||||||
\(478\) | −18.9282 | −0.865756 | ||||||||
\(479\) | −23.8564 | −1.09003 | −0.545014 | − | 0.838427i | \(-0.683475\pi\) | ||||
−0.545014 | + | 0.838427i | \(0.683475\pi\) | |||||||
\(480\) | −0.267949 | −0.0122302 | ||||||||
\(481\) | −33.8564 | −1.54372 | ||||||||
\(482\) | −23.9808 | −1.09229 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.0000 | −0.454545 | ||||||||
\(485\) | 1.53590 | 0.0697416 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 38.8564 | 1.76075 | 0.880376 | − | 0.474277i | \(-0.157290\pi\) | ||||
0.880376 | + | 0.474277i | \(0.157290\pi\) | |||||||
\(488\) | −4.53590 | −0.205330 | ||||||||
\(489\) | 12.3923 | 0.560399 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −43.0000 | −1.94056 | −0.970281 | − | 0.241979i | \(-0.922203\pi\) | ||||
−0.970281 | + | 0.241979i | \(0.922203\pi\) | |||||||
\(492\) | −5.26795 | −0.237497 | ||||||||
\(493\) | −4.73205 | −0.213121 | ||||||||
\(494\) | −5.46410 | −0.245842 | ||||||||
\(495\) | 0.267949 | 0.0120434 | ||||||||
\(496\) | 2.46410 | 0.110641 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 3.00000 | 0.134433 | ||||||||
\(499\) | −7.07180 | −0.316577 | −0.158289 | − | 0.987393i | \(-0.550598\pi\) | ||||
−0.158289 | + | 0.987393i | \(0.550598\pi\) | |||||||
\(500\) | 2.66025 | 0.118970 | ||||||||
\(501\) | −20.1962 | −0.902298 | ||||||||
\(502\) | 2.85641 | 0.127488 | ||||||||
\(503\) | 41.6603 | 1.85754 | 0.928769 | − | 0.370658i | \(-0.120868\pi\) | ||||
0.928769 | + | 0.370658i | \(0.120868\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.32051 | −0.0587618 | ||||||||
\(506\) | 2.73205 | 0.121454 | ||||||||
\(507\) | 16.8564 | 0.748619 | ||||||||
\(508\) | 3.92820 | 0.174286 | ||||||||
\(509\) | 0.464102 | 0.0205709 | 0.0102855 | − | 0.999947i | \(-0.496726\pi\) | ||||
0.0102855 | + | 0.999947i | \(0.496726\pi\) | |||||||
\(510\) | 1.26795 | 0.0561457 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | 4.92820 | 0.217374 | ||||||||
\(515\) | 1.60770 | 0.0708435 | ||||||||
\(516\) | 0.196152 | 0.00863513 | ||||||||
\(517\) | 11.4641 | 0.504191 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.7846 | 0.912343 | ||||||||
\(520\) | 1.46410 | 0.0642051 | ||||||||
\(521\) | 23.8564 | 1.04517 | 0.522584 | − | 0.852588i | \(-0.324968\pi\) | ||||
0.522584 | + | 0.852588i | \(0.324968\pi\) | |||||||
\(522\) | 1.00000 | 0.0437688 | ||||||||
\(523\) | 9.66025 | 0.422413 | 0.211207 | − | 0.977441i | \(-0.432261\pi\) | ||||
0.211207 | + | 0.977441i | \(0.432261\pi\) | |||||||
\(524\) | 0.464102 | 0.0202744 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.0526 | 0.699925 | ||||||||
\(527\) | −11.6603 | −0.507929 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | −15.5359 | −0.675474 | ||||||||
\(530\) | −0.411543 | −0.0178763 | ||||||||
\(531\) | 1.73205 | 0.0751646 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 28.7846 | 1.24680 | ||||||||
\(534\) | −0.339746 | −0.0147022 | ||||||||
\(535\) | 0.358984 | 0.0155202 | ||||||||
\(536\) | −0.928203 | −0.0400923 | ||||||||
\(537\) | −9.46410 | −0.408406 | ||||||||
\(538\) | −20.3205 | −0.876079 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.267949 | −0.0115307 | ||||||||
\(541\) | 16.4449 | 0.707020 | 0.353510 | − | 0.935431i | \(-0.384988\pi\) | ||||
0.353510 | + | 0.935431i | \(0.384988\pi\) | |||||||
\(542\) | −23.0526 | −0.990192 | ||||||||
\(543\) | −1.46410 | −0.0628306 | ||||||||
\(544\) | −4.73205 | −0.202885 | ||||||||
\(545\) | −2.87564 | −0.123179 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 44.9808 | 1.92324 | 0.961619 | − | 0.274387i | \(-0.0884750\pi\) | ||||
0.961619 | + | 0.274387i | \(0.0884750\pi\) | |||||||
\(548\) | 11.8564 | 0.506481 | ||||||||
\(549\) | −4.53590 | −0.193587 | ||||||||
\(550\) | 4.92820 | 0.210139 | ||||||||
\(551\) | 1.00000 | 0.0426014 | ||||||||
\(552\) | −2.73205 | −0.116284 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 19.8038 | 0.841385 | ||||||||
\(555\) | −1.66025 | −0.0704739 | ||||||||
\(556\) | −8.19615 | −0.347594 | ||||||||
\(557\) | −0.267949 | −0.0113534 | −0.00567669 | − | 0.999984i | \(-0.501807\pi\) | ||||
−0.00567669 | + | 0.999984i | \(0.501807\pi\) | |||||||
\(558\) | 2.46410 | 0.104314 | ||||||||
\(559\) | −1.07180 | −0.0453322 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.73205 | 0.199787 | ||||||||
\(562\) | −27.8564 | −1.17505 | ||||||||
\(563\) | 11.8756 | 0.500499 | 0.250249 | − | 0.968181i | \(-0.419487\pi\) | ||||
0.250249 | + | 0.968181i | \(0.419487\pi\) | |||||||
\(564\) | −11.4641 | −0.482726 | ||||||||
\(565\) | 1.41154 | 0.0593840 | ||||||||
\(566\) | 26.4449 | 1.11156 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.1962 | −0.511739 | ||||||||
\(569\) | −42.6410 | −1.78760 | −0.893802 | − | 0.448461i | \(-0.851972\pi\) | ||||
−0.893802 | + | 0.448461i | \(0.851972\pi\) | |||||||
\(570\) | −0.267949 | −0.0112232 | ||||||||
\(571\) | 18.0526 | 0.755476 | 0.377738 | − | 0.925913i | \(-0.376702\pi\) | ||||
0.377738 | + | 0.925913i | \(0.376702\pi\) | |||||||
\(572\) | 5.46410 | 0.228466 | ||||||||
\(573\) | 13.4641 | 0.562471 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.4641 | 0.561492 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 20.6077 | 0.857910 | 0.428955 | − | 0.903326i | \(-0.358882\pi\) | ||||
0.428955 | + | 0.903326i | \(0.358882\pi\) | |||||||
\(578\) | 5.39230 | 0.224290 | ||||||||
\(579\) | 27.5885 | 1.14654 | ||||||||
\(580\) | −0.267949 | −0.0111260 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −5.73205 | −0.237601 | ||||||||
\(583\) | −1.53590 | −0.0636104 | ||||||||
\(584\) | −6.92820 | −0.286691 | ||||||||
\(585\) | 1.46410 | 0.0605332 | ||||||||
\(586\) | −30.4641 | −1.25846 | ||||||||
\(587\) | 1.14359 | 0.0472012 | 0.0236006 | − | 0.999721i | \(-0.492487\pi\) | ||||
0.0236006 | + | 0.999721i | \(0.492487\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.46410 | 0.101532 | ||||||||
\(590\) | −0.464102 | −0.0191068 | ||||||||
\(591\) | 16.7846 | 0.690427 | ||||||||
\(592\) | 6.19615 | 0.254660 | ||||||||
\(593\) | 22.5359 | 0.925438 | 0.462719 | − | 0.886505i | \(-0.346874\pi\) | ||||
0.462719 | + | 0.886505i | \(0.346874\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.60770 | 0.0658538 | ||||||||
\(597\) | −12.3923 | −0.507183 | ||||||||
\(598\) | 14.9282 | 0.610460 | ||||||||
\(599\) | 35.9090 | 1.46720 | 0.733600 | − | 0.679581i | \(-0.237838\pi\) | ||||
0.733600 | + | 0.679581i | \(0.237838\pi\) | |||||||
\(600\) | −4.92820 | −0.201193 | ||||||||
\(601\) | 21.9808 | 0.896614 | 0.448307 | − | 0.893880i | \(-0.352027\pi\) | ||||
0.448307 | + | 0.893880i | \(0.352027\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.928203 | −0.0377994 | ||||||||
\(604\) | 15.3923 | 0.626304 | ||||||||
\(605\) | 2.67949 | 0.108937 | ||||||||
\(606\) | 4.92820 | 0.200195 | ||||||||
\(607\) | 14.1769 | 0.575423 | 0.287712 | − | 0.957717i | \(-0.407106\pi\) | ||||
0.287712 | + | 0.957717i | \(0.407106\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.21539 | 0.0492097 | ||||||||
\(611\) | 62.6410 | 2.53418 | ||||||||
\(612\) | −4.73205 | −0.191282 | ||||||||
\(613\) | 19.8038 | 0.799870 | 0.399935 | − | 0.916544i | \(-0.369033\pi\) | ||||
0.399935 | + | 0.916544i | \(0.369033\pi\) | |||||||
\(614\) | 24.5885 | 0.992309 | ||||||||
\(615\) | 1.41154 | 0.0569189 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.5885 | −0.506792 | −0.253396 | − | 0.967363i | \(-0.581548\pi\) | ||||
−0.253396 | + | 0.967363i | \(0.581548\pi\) | |||||||
\(618\) | −6.00000 | −0.241355 | ||||||||
\(619\) | −31.4641 | −1.26465 | −0.632325 | − | 0.774704i | \(-0.717899\pi\) | ||||
−0.632325 | + | 0.774704i | \(0.717899\pi\) | |||||||
\(620\) | −0.660254 | −0.0265164 | ||||||||
\(621\) | −2.73205 | −0.109633 | ||||||||
\(622\) | 35.1244 | 1.40836 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5.46410 | −0.218739 | ||||||||
\(625\) | 23.9282 | 0.957128 | ||||||||
\(626\) | −31.7846 | −1.27037 | ||||||||
\(627\) | −1.00000 | −0.0399362 | ||||||||
\(628\) | −1.46410 | −0.0584240 | ||||||||
\(629\) | −29.3205 | −1.16909 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.9808 | −0.715803 | −0.357901 | − | 0.933759i | \(-0.616508\pi\) | ||||
−0.357901 | + | 0.933759i | \(0.616508\pi\) | |||||||
\(632\) | −11.3923 | −0.453162 | ||||||||
\(633\) | −7.26795 | −0.288875 | ||||||||
\(634\) | −25.3923 | −1.00846 | ||||||||
\(635\) | −1.05256 | −0.0417695 | ||||||||
\(636\) | 1.53590 | 0.0609023 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.00000 | −0.0395904 | ||||||||
\(639\) | −12.1962 | −0.482472 | ||||||||
\(640\) | −0.267949 | −0.0105916 | ||||||||
\(641\) | 34.9808 | 1.38166 | 0.690829 | − | 0.723019i | \(-0.257246\pi\) | ||||
0.690829 | + | 0.723019i | \(0.257246\pi\) | |||||||
\(642\) | −1.33975 | −0.0528756 | ||||||||
\(643\) | 23.8038 | 0.938732 | 0.469366 | − | 0.883004i | \(-0.344482\pi\) | ||||
0.469366 | + | 0.883004i | \(0.344482\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.0525589 | −0.00206950 | ||||||||
\(646\) | −4.73205 | −0.186180 | ||||||||
\(647\) | 46.5885 | 1.83158 | 0.915791 | − | 0.401656i | \(-0.131565\pi\) | ||||
0.915791 | + | 0.401656i | \(0.131565\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −1.73205 | −0.0679889 | ||||||||
\(650\) | 26.9282 | 1.05621 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.3923 | 0.485320 | ||||||||
\(653\) | −42.1244 | −1.64845 | −0.824227 | − | 0.566260i | \(-0.808390\pi\) | ||||
−0.824227 | + | 0.566260i | \(0.808390\pi\) | |||||||
\(654\) | 10.7321 | 0.419656 | ||||||||
\(655\) | −0.124356 | −0.00485898 | ||||||||
\(656\) | −5.26795 | −0.205679 | ||||||||
\(657\) | −6.92820 | −0.270295 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.4641 | −0.758214 | −0.379107 | − | 0.925353i | \(-0.623769\pi\) | ||||
−0.379107 | + | 0.925353i | \(0.623769\pi\) | |||||||
\(660\) | 0.267949 | 0.0104299 | ||||||||
\(661\) | −23.5167 | −0.914692 | −0.457346 | − | 0.889289i | \(-0.651200\pi\) | ||||
−0.457346 | + | 0.889289i | \(0.651200\pi\) | |||||||
\(662\) | 15.5167 | 0.603072 | ||||||||
\(663\) | 25.8564 | 1.00418 | ||||||||
\(664\) | 3.00000 | 0.116423 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.19615 | 0.240096 | ||||||||
\(667\) | −2.73205 | −0.105785 | ||||||||
\(668\) | −20.1962 | −0.781413 | ||||||||
\(669\) | −10.3205 | −0.399014 | ||||||||
\(670\) | 0.248711 | 0.00960856 | ||||||||
\(671\) | 4.53590 | 0.175106 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.9808 | 1.07858 | 0.539290 | − | 0.842120i | \(-0.318693\pi\) | ||||
0.539290 | + | 0.842120i | \(0.318693\pi\) | |||||||
\(674\) | −27.9808 | −1.07778 | ||||||||
\(675\) | −4.92820 | −0.189687 | ||||||||
\(676\) | 16.8564 | 0.648323 | ||||||||
\(677\) | 21.6410 | 0.831732 | 0.415866 | − | 0.909426i | \(-0.363479\pi\) | ||||
0.415866 | + | 0.909426i | \(0.363479\pi\) | |||||||
\(678\) | −5.26795 | −0.202314 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.26795 | 0.0486236 | ||||||||
\(681\) | −18.6603 | −0.715062 | ||||||||
\(682\) | −2.46410 | −0.0943553 | ||||||||
\(683\) | −38.8038 | −1.48479 | −0.742394 | − | 0.669964i | \(-0.766310\pi\) | ||||
−0.742394 | + | 0.669964i | \(0.766310\pi\) | |||||||
\(684\) | 1.00000 | 0.0382360 | ||||||||
\(685\) | −3.17691 | −0.121384 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27.3205 | 1.04234 | ||||||||
\(688\) | 0.196152 | 0.00747824 | ||||||||
\(689\) | −8.39230 | −0.319721 | ||||||||
\(690\) | 0.732051 | 0.0278687 | ||||||||
\(691\) | −18.5885 | −0.707138 | −0.353569 | − | 0.935408i | \(-0.615032\pi\) | ||||
−0.353569 | + | 0.935408i | \(0.615032\pi\) | |||||||
\(692\) | 20.7846 | 0.790112 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.39230 | −0.242649 | ||||||||
\(695\) | 2.19615 | 0.0833048 | ||||||||
\(696\) | 1.00000 | 0.0379049 | ||||||||
\(697\) | 24.9282 | 0.944223 | ||||||||
\(698\) | 15.2679 | 0.577900 | ||||||||
\(699\) | 2.53590 | 0.0959165 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.12436 | −0.155775 | −0.0778874 | − | 0.996962i | \(-0.524817\pi\) | ||||
−0.0778874 | + | 0.996962i | \(0.524817\pi\) | |||||||
\(702\) | −5.46410 | −0.206229 | ||||||||
\(703\) | 6.19615 | 0.233692 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 3.07180 | 0.115691 | ||||||||
\(706\) | 14.1962 | 0.534279 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.73205 | 0.0650945 | ||||||||
\(709\) | −21.1244 | −0.793342 | −0.396671 | − | 0.917961i | \(-0.629835\pi\) | ||||
−0.396671 | + | 0.917961i | \(0.629835\pi\) | |||||||
\(710\) | 3.26795 | 0.122644 | ||||||||
\(711\) | −11.3923 | −0.427245 | ||||||||
\(712\) | −0.339746 | −0.0127325 | ||||||||
\(713\) | −6.73205 | −0.252117 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.46410 | −0.0547543 | ||||||||
\(716\) | −9.46410 | −0.353690 | ||||||||
\(717\) | −18.9282 | −0.706887 | ||||||||
\(718\) | −0.928203 | −0.0346402 | ||||||||
\(719\) | 40.5359 | 1.51173 | 0.755867 | − | 0.654725i | \(-0.227216\pi\) | ||||
0.755867 | + | 0.654725i | \(0.227216\pi\) | |||||||
\(720\) | −0.267949 | −0.00998588 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −23.9808 | −0.891854 | ||||||||
\(724\) | −1.46410 | −0.0544129 | ||||||||
\(725\) | −4.92820 | −0.183029 | ||||||||
\(726\) | −10.0000 | −0.371135 | ||||||||
\(727\) | 0.267949 | 0.00993769 | 0.00496884 | − | 0.999988i | \(-0.498418\pi\) | ||||
0.00496884 | + | 0.999988i | \(0.498418\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.85641 | 0.0687087 | ||||||||
\(731\) | −0.928203 | −0.0343308 | ||||||||
\(732\) | −4.53590 | −0.167652 | ||||||||
\(733\) | 17.9090 | 0.661483 | 0.330741 | − | 0.943721i | \(-0.392701\pi\) | ||||
0.330741 | + | 0.943721i | \(0.392701\pi\) | |||||||
\(734\) | 24.5167 | 0.904926 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.73205 | −0.100705 | ||||||||
\(737\) | 0.928203 | 0.0341908 | ||||||||
\(738\) | −5.26795 | −0.193916 | ||||||||
\(739\) | −30.4449 | −1.11993 | −0.559966 | − | 0.828515i | \(-0.689186\pi\) | ||||
−0.559966 | + | 0.828515i | \(0.689186\pi\) | |||||||
\(740\) | −1.66025 | −0.0610322 | ||||||||
\(741\) | −5.46410 | −0.200729 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.21539 | −0.0445883 | −0.0222942 | − | 0.999751i | \(-0.507097\pi\) | ||||
−0.0222942 | + | 0.999751i | \(0.507097\pi\) | |||||||
\(744\) | 2.46410 | 0.0903383 | ||||||||
\(745\) | −0.430781 | −0.0157826 | ||||||||
\(746\) | −15.3205 | −0.560924 | ||||||||
\(747\) | 3.00000 | 0.109764 | ||||||||
\(748\) | 4.73205 | 0.173021 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.66025 | 0.0971387 | ||||||||
\(751\) | 6.60770 | 0.241118 | 0.120559 | − | 0.992706i | \(-0.461531\pi\) | ||||
0.120559 | + | 0.992706i | \(0.461531\pi\) | |||||||
\(752\) | −11.4641 | −0.418053 | ||||||||
\(753\) | 2.85641 | 0.104093 | ||||||||
\(754\) | −5.46410 | −0.198991 | ||||||||
\(755\) | −4.12436 | −0.150101 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.1244 | −0.622395 | −0.311198 | − | 0.950345i | \(-0.600730\pi\) | ||||
−0.311198 | + | 0.950345i | \(0.600730\pi\) | |||||||
\(758\) | 10.1436 | 0.368432 | ||||||||
\(759\) | 2.73205 | 0.0991672 | ||||||||
\(760\) | −0.267949 | −0.00971954 | ||||||||
\(761\) | 12.6795 | 0.459631 | 0.229816 | − | 0.973234i | \(-0.426188\pi\) | ||||
0.229816 | + | 0.973234i | \(0.426188\pi\) | |||||||
\(762\) | 3.92820 | 0.142304 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 13.4641 | 0.487114 | ||||||||
\(765\) | 1.26795 | 0.0458428 | ||||||||
\(766\) | −6.78461 | −0.245138 | ||||||||
\(767\) | −9.46410 | −0.341729 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 12.6077 | 0.454645 | 0.227323 | − | 0.973820i | \(-0.427003\pi\) | ||||
0.227323 | + | 0.973820i | \(0.427003\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.92820 | 0.177485 | ||||||||
\(772\) | 27.5885 | 0.992930 | ||||||||
\(773\) | 35.3205 | 1.27039 | 0.635195 | − | 0.772352i | \(-0.280920\pi\) | ||||
0.635195 | + | 0.772352i | \(0.280920\pi\) | |||||||
\(774\) | 0.196152 | 0.00705055 | ||||||||
\(775\) | −12.1436 | −0.436211 | ||||||||
\(776\) | −5.73205 | −0.205769 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.3205 | 0.620970 | ||||||||
\(779\) | −5.26795 | −0.188744 | ||||||||
\(780\) | 1.46410 | 0.0524232 | ||||||||
\(781\) | 12.1962 | 0.436413 | ||||||||
\(782\) | 12.9282 | 0.462312 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.392305 | 0.0140020 | ||||||||
\(786\) | 0.464102 | 0.0165540 | ||||||||
\(787\) | −22.0000 | −0.784215 | −0.392108 | − | 0.919919i | \(-0.628254\pi\) | ||||
−0.392108 | + | 0.919919i | \(0.628254\pi\) | |||||||
\(788\) | 16.7846 | 0.597927 | ||||||||
\(789\) | 16.0526 | 0.571486 | ||||||||
\(790\) | 3.05256 | 0.108605 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | 24.7846 | 0.880127 | ||||||||
\(794\) | −19.3205 | −0.685659 | ||||||||
\(795\) | −0.411543 | −0.0145959 | ||||||||
\(796\) | −12.3923 | −0.439234 | ||||||||
\(797\) | −2.32051 | −0.0821966 | −0.0410983 | − | 0.999155i | \(-0.513086\pi\) | ||||
−0.0410983 | + | 0.999155i | \(0.513086\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 54.2487 | 1.91918 | ||||||||
\(800\) | −4.92820 | −0.174238 | ||||||||
\(801\) | −0.339746 | −0.0120043 | ||||||||
\(802\) | −0.392305 | −0.0138528 | ||||||||
\(803\) | 6.92820 | 0.244491 | ||||||||
\(804\) | −0.928203 | −0.0327352 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.4641 | −0.474253 | ||||||||
\(807\) | −20.3205 | −0.715316 | ||||||||
\(808\) | 4.92820 | 0.173374 | ||||||||
\(809\) | −40.0526 | −1.40817 | −0.704086 | − | 0.710114i | \(-0.748643\pi\) | ||||
−0.704086 | + | 0.710114i | \(0.748643\pi\) | |||||||
\(810\) | −0.267949 | −0.00941477 | ||||||||
\(811\) | 22.9808 | 0.806964 | 0.403482 | − | 0.914988i | \(-0.367800\pi\) | ||||
0.403482 | + | 0.914988i | \(0.367800\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23.0526 | −0.808489 | ||||||||
\(814\) | −6.19615 | −0.217175 | ||||||||
\(815\) | −3.32051 | −0.116312 | ||||||||
\(816\) | −4.73205 | −0.165655 | ||||||||
\(817\) | 0.196152 | 0.00686250 | ||||||||
\(818\) | 10.6603 | 0.372727 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.41154 | 0.0492932 | ||||||||
\(821\) | −7.73205 | −0.269850 | −0.134925 | − | 0.990856i | \(-0.543079\pi\) | ||||
−0.134925 | + | 0.990856i | \(0.543079\pi\) | |||||||
\(822\) | 11.8564 | 0.413540 | ||||||||
\(823\) | −33.0718 | −1.15281 | −0.576405 | − | 0.817164i | \(-0.695545\pi\) | ||||
−0.576405 | + | 0.817164i | \(0.695545\pi\) | |||||||
\(824\) | −6.00000 | −0.209020 | ||||||||
\(825\) | 4.92820 | 0.171578 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.9808 | 1.18163 | 0.590813 | − | 0.806808i | \(-0.298807\pi\) | ||||
0.590813 | + | 0.806808i | \(0.298807\pi\) | |||||||
\(828\) | −2.73205 | −0.0949453 | ||||||||
\(829\) | 10.1436 | 0.352302 | 0.176151 | − | 0.984363i | \(-0.443635\pi\) | ||||
0.176151 | + | 0.984363i | \(0.443635\pi\) | |||||||
\(830\) | −0.803848 | −0.0279020 | ||||||||
\(831\) | 19.8038 | 0.686988 | ||||||||
\(832\) | −5.46410 | −0.189434 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −8.19615 | −0.283810 | ||||||||
\(835\) | 5.41154 | 0.187274 | ||||||||
\(836\) | −1.00000 | −0.0345857 | ||||||||
\(837\) | 2.46410 | 0.0851718 | ||||||||
\(838\) | −31.1769 | −1.07699 | ||||||||
\(839\) | 24.4449 | 0.843930 | 0.421965 | − | 0.906612i | \(-0.361340\pi\) | ||||
0.421965 | + | 0.906612i | \(0.361340\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | −16.2487 | −0.559968 | ||||||||
\(843\) | −27.8564 | −0.959426 | ||||||||
\(844\) | −7.26795 | −0.250173 | ||||||||
\(845\) | −4.51666 | −0.155378 | ||||||||
\(846\) | −11.4641 | −0.394144 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.53590 | 0.0527430 | ||||||||
\(849\) | 26.4449 | 0.907585 | ||||||||
\(850\) | 23.3205 | 0.799887 | ||||||||
\(851\) | −16.9282 | −0.580291 | ||||||||
\(852\) | −12.1962 | −0.417833 | ||||||||
\(853\) | −40.7321 | −1.39464 | −0.697319 | − | 0.716761i | \(-0.745624\pi\) | ||||
−0.697319 | + | 0.716761i | \(0.745624\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.267949 | −0.00916367 | ||||||||
\(856\) | −1.33975 | −0.0457916 | ||||||||
\(857\) | 18.0000 | 0.614868 | 0.307434 | − | 0.951569i | \(-0.400530\pi\) | ||||
0.307434 | + | 0.951569i | \(0.400530\pi\) | |||||||
\(858\) | 5.46410 | 0.186541 | ||||||||
\(859\) | 15.1769 | 0.517830 | 0.258915 | − | 0.965900i | \(-0.416635\pi\) | ||||
0.258915 | + | 0.965900i | \(0.416635\pi\) | |||||||
\(860\) | −0.0525589 | −0.00179224 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20.4449 | −0.696355 | ||||||||
\(863\) | 15.1244 | 0.514839 | 0.257420 | − | 0.966300i | \(-0.417128\pi\) | ||||
0.257420 | + | 0.966300i | \(0.417128\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −5.56922 | −0.189359 | ||||||||
\(866\) | 16.0000 | 0.543702 | ||||||||
\(867\) | 5.39230 | 0.183132 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.3923 | 0.386457 | ||||||||
\(870\) | −0.267949 | −0.00908433 | ||||||||
\(871\) | 5.07180 | 0.171851 | ||||||||
\(872\) | 10.7321 | 0.363433 | ||||||||
\(873\) | −5.73205 | −0.194001 | ||||||||
\(874\) | −2.73205 | −0.0924130 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.92820 | −0.234082 | ||||||||
\(877\) | 6.87564 | 0.232174 | 0.116087 | − | 0.993239i | \(-0.462965\pi\) | ||||
0.116087 | + | 0.993239i | \(0.462965\pi\) | |||||||
\(878\) | −2.46410 | −0.0831594 | ||||||||
\(879\) | −30.4641 | −1.02753 | ||||||||
\(880\) | 0.267949 | 0.00903257 | ||||||||
\(881\) | 9.21539 | 0.310474 | 0.155237 | − | 0.987877i | \(-0.450386\pi\) | ||||
0.155237 | + | 0.987877i | \(0.450386\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.1962 | 1.42001 | 0.710007 | − | 0.704195i | \(-0.248692\pi\) | ||||
0.710007 | + | 0.704195i | \(0.248692\pi\) | |||||||
\(884\) | 25.8564 | 0.869645 | ||||||||
\(885\) | −0.464102 | −0.0156006 | ||||||||
\(886\) | 7.00000 | 0.235170 | ||||||||
\(887\) | −26.9808 | −0.905925 | −0.452963 | − | 0.891529i | \(-0.649633\pi\) | ||||
−0.452963 | + | 0.891529i | \(0.649633\pi\) | |||||||
\(888\) | 6.19615 | 0.207929 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.0910347 | 0.00305149 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −10.3205 | −0.345556 | ||||||||
\(893\) | −11.4641 | −0.383632 | ||||||||
\(894\) | 1.60770 | 0.0537694 | ||||||||
\(895\) | 2.53590 | 0.0847657 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.9282 | 0.498438 | ||||||||
\(898\) | −23.1244 | −0.771670 | ||||||||
\(899\) | 2.46410 | 0.0821824 | ||||||||
\(900\) | −4.92820 | −0.164273 | ||||||||
\(901\) | −7.26795 | −0.242130 | ||||||||
\(902\) | 5.26795 | 0.175404 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.26795 | −0.175209 | ||||||||
\(905\) | 0.392305 | 0.0130407 | ||||||||
\(906\) | 15.3923 | 0.511375 | ||||||||
\(907\) | −31.8038 | −1.05603 | −0.528015 | − | 0.849235i | \(-0.677063\pi\) | ||||
−0.528015 | + | 0.849235i | \(0.677063\pi\) | |||||||
\(908\) | −18.6603 | −0.619262 | ||||||||
\(909\) | 4.92820 | 0.163458 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.53590 | −0.282807 | −0.141403 | − | 0.989952i | \(-0.545161\pi\) | ||||
−0.141403 | + | 0.989952i | \(0.545161\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | −3.00000 | −0.0992855 | ||||||||
\(914\) | 23.9282 | 0.791475 | ||||||||
\(915\) | 1.21539 | 0.0401796 | ||||||||
\(916\) | 27.3205 | 0.902695 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.73205 | −0.156181 | ||||||||
\(919\) | −47.1769 | −1.55622 | −0.778111 | − | 0.628126i | \(-0.783822\pi\) | ||||
−0.778111 | + | 0.628126i | \(0.783822\pi\) | |||||||
\(920\) | 0.732051 | 0.0241350 | ||||||||
\(921\) | 24.5885 | 0.810217 | ||||||||
\(922\) | −39.8564 | −1.31260 | ||||||||
\(923\) | 66.6410 | 2.19352 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −30.5359 | −1.00401 | ||||||||
\(926\) | 4.00000 | 0.131448 | ||||||||
\(927\) | −6.00000 | −0.197066 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | 0.196152 | 0.00643555 | 0.00321778 | − | 0.999995i | \(-0.498976\pi\) | ||||
0.00321778 | + | 0.999995i | \(0.498976\pi\) | |||||||
\(930\) | −0.660254 | −0.0216506 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.53590 | 0.0830661 | ||||||||
\(933\) | 35.1244 | 1.14992 | ||||||||
\(934\) | −16.9282 | −0.553908 | ||||||||
\(935\) | −1.26795 | −0.0414664 | ||||||||
\(936\) | −5.46410 | −0.178600 | ||||||||
\(937\) | −27.3923 | −0.894868 | −0.447434 | − | 0.894317i | \(-0.647662\pi\) | ||||
−0.447434 | + | 0.894317i | \(0.647662\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −31.7846 | −1.03725 | ||||||||
\(940\) | 3.07180 | 0.100191 | ||||||||
\(941\) | 19.7846 | 0.644960 | 0.322480 | − | 0.946576i | \(-0.395484\pi\) | ||||
0.322480 | + | 0.946576i | \(0.395484\pi\) | |||||||
\(942\) | −1.46410 | −0.0477030 | ||||||||
\(943\) | 14.3923 | 0.468678 | ||||||||
\(944\) | 1.73205 | 0.0563735 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.196152 | −0.00637747 | ||||||||
\(947\) | 1.60770 | 0.0522431 | 0.0261215 | − | 0.999659i | \(-0.491684\pi\) | ||||
0.0261215 | + | 0.999659i | \(0.491684\pi\) | |||||||
\(948\) | −11.3923 | −0.370005 | ||||||||
\(949\) | 37.8564 | 1.22887 | ||||||||
\(950\) | −4.92820 | −0.159892 | ||||||||
\(951\) | −25.3923 | −0.823402 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −52.2487 | −1.69250 | −0.846251 | − | 0.532785i | \(-0.821146\pi\) | ||||
−0.846251 | + | 0.532785i | \(0.821146\pi\) | |||||||
\(954\) | 1.53590 | 0.0497265 | ||||||||
\(955\) | −3.60770 | −0.116742 | ||||||||
\(956\) | −18.9282 | −0.612182 | ||||||||
\(957\) | −1.00000 | −0.0323254 | ||||||||
\(958\) | −23.8564 | −0.770766 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.267949 | −0.00864802 | ||||||||
\(961\) | −24.9282 | −0.804136 | ||||||||
\(962\) | −33.8564 | −1.09157 | ||||||||
\(963\) | −1.33975 | −0.0431727 | ||||||||
\(964\) | −23.9808 | −0.772368 | ||||||||
\(965\) | −7.39230 | −0.237967 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.58846 | −0.308344 | −0.154172 | − | 0.988044i | \(-0.549271\pi\) | ||||
−0.154172 | + | 0.988044i | \(0.549271\pi\) | |||||||
\(968\) | −10.0000 | −0.321412 | ||||||||
\(969\) | −4.73205 | −0.152015 | ||||||||
\(970\) | 1.53590 | 0.0493147 | ||||||||
\(971\) | −7.19615 | −0.230936 | −0.115468 | − | 0.993311i | \(-0.536837\pi\) | ||||
−0.115468 | + | 0.993311i | \(0.536837\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 38.8564 | 1.24504 | ||||||||
\(975\) | 26.9282 | 0.862393 | ||||||||
\(976\) | −4.53590 | −0.145191 | ||||||||
\(977\) | 0.143594 | 0.00459396 | 0.00229698 | − | 0.999997i | \(-0.499269\pi\) | ||||
0.00229698 | + | 0.999997i | \(0.499269\pi\) | |||||||
\(978\) | 12.3923 | 0.396262 | ||||||||
\(979\) | 0.339746 | 0.0108583 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.7321 | 0.342648 | ||||||||
\(982\) | −43.0000 | −1.37219 | ||||||||
\(983\) | −51.7128 | −1.64938 | −0.824691 | − | 0.565583i | \(-0.808651\pi\) | ||||
−0.824691 | + | 0.565583i | \(0.808651\pi\) | |||||||
\(984\) | −5.26795 | −0.167936 | ||||||||
\(985\) | −4.49742 | −0.143300 | ||||||||
\(986\) | −4.73205 | −0.150699 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.46410 | −0.173836 | ||||||||
\(989\) | −0.535898 | −0.0170406 | ||||||||
\(990\) | 0.267949 | 0.00851598 | ||||||||
\(991\) | 58.0333 | 1.84349 | 0.921745 | − | 0.387797i | \(-0.126764\pi\) | ||||
0.921745 | + | 0.387797i | \(0.126764\pi\) | |||||||
\(992\) | 2.46410 | 0.0782353 | ||||||||
\(993\) | 15.5167 | 0.492406 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.32051 | 0.105267 | ||||||||
\(996\) | 3.00000 | 0.0950586 | ||||||||
\(997\) | 61.3205 | 1.94204 | 0.971020 | − | 0.238998i | \(-0.0768190\pi\) | ||||
0.971020 | + | 0.238998i | \(0.0768190\pi\) | |||||||
\(998\) | −7.07180 | −0.223854 | ||||||||
\(999\) | 6.19615 | 0.196038 |
(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 | 5586.2.a.bm.1.2 | 2 | ||
7.3 | odd | 6 | 798.2.j.g.457.2 | ✓ | 4 | ||
7.5 | odd | 6 | 798.2.j.g.571.2 | yes | 4 | ||
7.6 | odd | 2 | 5586.2.a.bl.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
798.2.j.g.457.2 | ✓ | 4 | 7.3 | odd | 6 | ||
798.2.j.g.571.2 | yes | 4 | 7.5 | odd | 6 | ||
5586.2.a.bl.1.1 | 2 | 7.6 | odd | 2 | |||
5586.2.a.bm.1.2 | 2 | 1.1 | even | 1 | trivial |