Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −2.00000 | −1.00000 | ||||||||
\(5\) | −3.46410 | −1.54919 | −0.774597 | − | 0.632456i | \(-0.782047\pi\) | ||||
−0.774597 | + | 0.632456i | \(0.782047\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.26795 | 0.683812 | 0.341906 | − | 0.939734i | \(-0.388927\pi\) | ||||
0.341906 | + | 0.939734i | \(0.388927\pi\) | |||||||
\(12\) | −2.00000 | −0.577350 | ||||||||
\(13\) | 1.46410 | 0.406069 | 0.203034 | − | 0.979172i | \(-0.434920\pi\) | ||||
0.203034 | + | 0.979172i | \(0.434920\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.46410 | −0.894427 | ||||||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | −5.00000 | −1.21268 | −0.606339 | − | 0.795206i | \(-0.707363\pi\) | ||||
−0.606339 | + | 0.795206i | \(0.707363\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.46410 | −1.71238 | −0.856191 | − | 0.516659i | \(-0.827175\pi\) | ||||
−0.856191 | + | 0.516659i | \(0.827175\pi\) | |||||||
\(20\) | 6.92820 | 1.54919 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.46410 | −0.305286 | −0.152643 | − | 0.988281i | \(-0.548779\pi\) | ||||
−0.152643 | + | 0.988281i | \(0.548779\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.00000 | 1.40000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.19615 | 0.964901 | 0.482451 | − | 0.875923i | \(-0.339747\pi\) | ||||
0.482451 | + | 0.875923i | \(0.339747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.26795 | −0.407336 | −0.203668 | − | 0.979040i | \(-0.565286\pi\) | ||||
−0.203668 | + | 0.979040i | \(0.565286\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.26795 | 0.394799 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | −1.00000 | −0.164399 | −0.0821995 | − | 0.996616i | \(-0.526194\pi\) | ||||
−0.0821995 | + | 0.996616i | \(0.526194\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.46410 | 0.234444 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.92820 | −0.599045 | −0.299523 | − | 0.954089i | \(-0.596827\pi\) | ||||
−0.299523 | + | 0.954089i | \(0.596827\pi\) | |||||||
\(44\) | −4.53590 | −0.683812 | ||||||||
\(45\) | −3.46410 | −0.516398 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.92820 | −0.281257 | −0.140629 | − | 0.990062i | \(-0.544912\pi\) | ||||
−0.140629 | + | 0.990062i | \(0.544912\pi\) | |||||||
\(48\) | 4.00000 | 0.577350 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.00000 | −0.700140 | ||||||||
\(52\) | −2.92820 | −0.406069 | ||||||||
\(53\) | −2.92820 | −0.402220 | −0.201110 | − | 0.979569i | \(-0.564455\pi\) | ||||
−0.201110 | + | 0.979569i | \(0.564455\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.85641 | −1.05936 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.46410 | −0.988644 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.92820 | −0.901975 | −0.450988 | − | 0.892530i | \(-0.648928\pi\) | ||||
−0.450988 | + | 0.892530i | \(0.648928\pi\) | |||||||
\(60\) | 6.92820 | 0.894427 | ||||||||
\(61\) | −1.73205 | −0.221766 | −0.110883 | − | 0.993833i | \(-0.535368\pi\) | ||||
−0.110883 | + | 0.993833i | \(0.535368\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | −5.07180 | −0.629079 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.535898 | 0.0654704 | 0.0327352 | − | 0.999464i | \(-0.489578\pi\) | ||||
0.0327352 | + | 0.999464i | \(0.489578\pi\) | |||||||
\(68\) | 10.0000 | 1.21268 | ||||||||
\(69\) | −1.46410 | −0.176257 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.80385 | 0.332755 | 0.166378 | − | 0.986062i | \(-0.446793\pi\) | ||||
0.166378 | + | 0.986062i | \(0.446793\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.19615 | −0.139999 | −0.0699995 | − | 0.997547i | \(-0.522300\pi\) | ||||
−0.0699995 | + | 0.997547i | \(0.522300\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.00000 | 0.808290 | ||||||||
\(76\) | 14.9282 | 1.71238 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.9282 | −1.45454 | −0.727268 | − | 0.686353i | \(-0.759210\pi\) | ||||
−0.727268 | + | 0.686353i | \(0.759210\pi\) | |||||||
\(80\) | −13.8564 | −1.54919 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.0000 | −1.09764 | −0.548821 | − | 0.835940i | \(-0.684923\pi\) | ||||
−0.548821 | + | 0.835940i | \(0.684923\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.3205 | 1.87867 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.19615 | 0.557086 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.92820 | 0.522388 | 0.261194 | − | 0.965286i | \(-0.415884\pi\) | ||||
0.261194 | + | 0.965286i | \(0.415884\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.92820 | 0.305286 | ||||||||
\(93\) | −2.26795 | −0.235175 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 25.8564 | 2.65281 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.3923 | 1.86746 | 0.933728 | − | 0.357984i | \(-0.116536\pi\) | ||||
0.933728 | + | 0.357984i | \(0.116536\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.26795 | 0.227937 | ||||||||
\(100\) | −14.0000 | −1.40000 | ||||||||
\(101\) | 8.85641 | 0.881245 | 0.440623 | − | 0.897692i | \(-0.354758\pi\) | ||||
0.440623 | + | 0.897692i | \(0.354758\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.19615 | −0.906124 | −0.453062 | − | 0.891479i | \(-0.649668\pi\) | ||||
−0.453062 | + | 0.891479i | \(0.649668\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.46410 | 0.334887 | 0.167444 | − | 0.985882i | \(-0.446449\pi\) | ||||
0.167444 | + | 0.985882i | \(0.446449\pi\) | |||||||
\(108\) | −2.00000 | −0.192450 | ||||||||
\(109\) | 9.46410 | 0.906497 | 0.453248 | − | 0.891384i | \(-0.350265\pi\) | ||||
0.453248 | + | 0.891384i | \(0.350265\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.00000 | −0.0949158 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.3205 | 1.62938 | 0.814688 | − | 0.579899i | \(-0.196908\pi\) | ||||
0.814688 | + | 0.579899i | \(0.196908\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.07180 | 0.472947 | ||||||||
\(116\) | −10.3923 | −0.964901 | ||||||||
\(117\) | 1.46410 | 0.135356 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.85641 | −0.532401 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | 4.53590 | 0.407336 | ||||||||
\(125\) | −6.92820 | −0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.85641 | −0.874615 | −0.437307 | − | 0.899312i | \(-0.644068\pi\) | ||||
−0.437307 | + | 0.899312i | \(0.644068\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.92820 | −0.345859 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.4641 | 1.52585 | 0.762923 | − | 0.646490i | \(-0.223764\pi\) | ||||
0.762923 | + | 0.646490i | \(0.223764\pi\) | |||||||
\(132\) | −4.53590 | −0.394799 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.46410 | −0.298142 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.1962 | 1.12742 | 0.563712 | − | 0.825972i | \(-0.309373\pi\) | ||||
0.563712 | + | 0.825972i | \(0.309373\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.53590 | 0.384730 | 0.192365 | − | 0.981323i | \(-0.438384\pi\) | ||||
0.192365 | + | 0.981323i | \(0.438384\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.92820 | −0.162384 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.32051 | 0.277675 | ||||||||
\(144\) | 4.00000 | 0.333333 | ||||||||
\(145\) | −18.0000 | −1.49482 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | 13.8564 | 1.13516 | 0.567581 | − | 0.823318i | \(-0.307880\pi\) | ||||
0.567581 | + | 0.823318i | \(0.307880\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.392305 | −0.0319253 | −0.0159627 | − | 0.999873i | \(-0.505081\pi\) | ||||
−0.0159627 | + | 0.999873i | \(0.505081\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.00000 | −0.404226 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.85641 | 0.631042 | ||||||||
\(156\) | −2.92820 | −0.234444 | ||||||||
\(157\) | 10.0000 | 0.798087 | 0.399043 | − | 0.916932i | \(-0.369342\pi\) | ||||
0.399043 | + | 0.916932i | \(0.369342\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.92820 | −0.232222 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.07180 | −0.318928 | −0.159464 | − | 0.987204i | \(-0.550977\pi\) | ||||
−0.159464 | + | 0.987204i | \(0.550977\pi\) | |||||||
\(164\) | −2.00000 | −0.156174 | ||||||||
\(165\) | −7.85641 | −0.611620 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.07180 | 0.392467 | 0.196234 | − | 0.980557i | \(-0.437129\pi\) | ||||
0.196234 | + | 0.980557i | \(0.437129\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.8564 | −0.835108 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.46410 | −0.570794 | ||||||||
\(172\) | 7.85641 | 0.599045 | ||||||||
\(173\) | −20.9282 | −1.59114 | −0.795571 | − | 0.605860i | \(-0.792829\pi\) | ||||
−0.795571 | + | 0.605860i | \(0.792829\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9.07180 | 0.683812 | ||||||||
\(177\) | −6.92820 | −0.520756 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.5885 | −1.16514 | −0.582568 | − | 0.812782i | \(-0.697952\pi\) | ||||
−0.582568 | + | 0.812782i | \(0.697952\pi\) | |||||||
\(180\) | 6.92820 | 0.516398 | ||||||||
\(181\) | 20.0000 | 1.48659 | 0.743294 | − | 0.668965i | \(-0.233262\pi\) | ||||
0.743294 | + | 0.668965i | \(0.233262\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.73205 | −0.128037 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.46410 | 0.254686 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.3397 | −0.829244 | ||||||||
\(188\) | 3.85641 | 0.281257 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.3923 | 0.751961 | 0.375980 | − | 0.926628i | \(-0.377306\pi\) | ||||
0.375980 | + | 0.926628i | \(0.377306\pi\) | |||||||
\(192\) | −8.00000 | −0.577350 | ||||||||
\(193\) | 27.3205 | 1.96657 | 0.983287 | − | 0.182064i | \(-0.0582779\pi\) | ||||
0.983287 | + | 0.182064i | \(0.0582779\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.07180 | −0.363199 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.46410 | 0.531795 | 0.265898 | − | 0.964001i | \(-0.414332\pi\) | ||||
0.265898 | + | 0.964001i | \(0.414332\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.32051 | 0.660713 | 0.330357 | − | 0.943856i | \(-0.392831\pi\) | ||||
0.330357 | + | 0.943856i | \(0.392831\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.535898 | 0.0377994 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 10.0000 | 0.700140 | ||||||||
\(205\) | −3.46410 | −0.241943 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.46410 | −0.101762 | ||||||||
\(208\) | 5.85641 | 0.406069 | ||||||||
\(209\) | −16.9282 | −1.17095 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.07180 | 0.0737855 | 0.0368928 | − | 0.999319i | \(-0.488254\pi\) | ||||
0.0368928 | + | 0.999319i | \(0.488254\pi\) | |||||||
\(212\) | 5.85641 | 0.402220 | ||||||||
\(213\) | 2.80385 | 0.192116 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.6077 | 0.928037 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.19615 | −0.0808285 | ||||||||
\(220\) | 15.7128 | 1.05936 | ||||||||
\(221\) | −7.32051 | −0.492431 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.4641 | −1.03555 | −0.517776 | − | 0.855516i | \(-0.673240\pi\) | ||||
−0.517776 | + | 0.855516i | \(0.673240\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.00000 | 0.466667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.9282 | 0.924447 | 0.462224 | − | 0.886763i | \(-0.347052\pi\) | ||||
0.462224 | + | 0.886763i | \(0.347052\pi\) | |||||||
\(228\) | 14.9282 | 0.988644 | ||||||||
\(229\) | 4.92820 | 0.325665 | 0.162832 | − | 0.986654i | \(-0.447937\pi\) | ||||
0.162832 | + | 0.986654i | \(0.447937\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.8564 | 0.907763 | 0.453882 | − | 0.891062i | \(-0.350039\pi\) | ||||
0.453882 | + | 0.891062i | \(0.350039\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.67949 | 0.435722 | ||||||||
\(236\) | 13.8564 | 0.901975 | ||||||||
\(237\) | −12.9282 | −0.839777 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.53590 | −0.552141 | −0.276071 | − | 0.961137i | \(-0.589032\pi\) | ||||
−0.276071 | + | 0.961137i | \(0.589032\pi\) | |||||||
\(240\) | −13.8564 | −0.894427 | ||||||||
\(241\) | −5.19615 | −0.334714 | −0.167357 | − | 0.985896i | \(-0.553523\pi\) | ||||
−0.167357 | + | 0.985896i | \(0.553523\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 3.46410 | 0.221766 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.9282 | −0.695345 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.0000 | −0.633724 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.535898 | 0.0338256 | 0.0169128 | − | 0.999857i | \(-0.494616\pi\) | ||||
0.0169128 | + | 0.999857i | \(0.494616\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.32051 | −0.208759 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 17.3205 | 1.08465 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 3.00000 | 0.187135 | 0.0935674 | − | 0.995613i | \(-0.470173\pi\) | ||||
0.0935674 | + | 0.995613i | \(0.470173\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 10.1436 | 0.629079 | ||||||||
\(261\) | 5.19615 | 0.321634 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.12436 | 0.254319 | 0.127159 | − | 0.991882i | \(-0.459414\pi\) | ||||
0.127159 | + | 0.991882i | \(0.459414\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.1436 | 0.623116 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.92820 | 0.301601 | ||||||||
\(268\) | −1.07180 | −0.0654704 | ||||||||
\(269\) | 10.5359 | 0.642385 | 0.321193 | − | 0.947014i | \(-0.395916\pi\) | ||||
0.321193 | + | 0.947014i | \(0.395916\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.5885 | 1.18991 | 0.594957 | − | 0.803758i | \(-0.297169\pi\) | ||||
0.594957 | + | 0.803758i | \(0.297169\pi\) | |||||||
\(272\) | −20.0000 | −1.21268 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.8756 | 0.957337 | ||||||||
\(276\) | 2.92820 | 0.176257 | ||||||||
\(277\) | −8.07180 | −0.484987 | −0.242494 | − | 0.970153i | \(-0.577965\pi\) | ||||
−0.242494 | + | 0.970153i | \(0.577965\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.26795 | −0.135779 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.1244 | 1.43914 | 0.719569 | − | 0.694421i | \(-0.244339\pi\) | ||||
0.719569 | + | 0.694421i | \(0.244339\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.6603 | −0.752574 | −0.376287 | − | 0.926503i | \(-0.622799\pi\) | ||||
−0.376287 | + | 0.926503i | \(0.622799\pi\) | |||||||
\(284\) | −5.60770 | −0.332755 | ||||||||
\(285\) | 25.8564 | 1.53160 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.3923 | 1.07818 | ||||||||
\(292\) | 2.39230 | 0.139999 | ||||||||
\(293\) | −9.00000 | −0.525786 | −0.262893 | − | 0.964825i | \(-0.584677\pi\) | ||||
−0.262893 | + | 0.964825i | \(0.584677\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.0000 | 1.39733 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.26795 | 0.131600 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.14359 | −0.123967 | ||||||||
\(300\) | −14.0000 | −0.808290 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.85641 | 0.508787 | ||||||||
\(304\) | −29.8564 | −1.71238 | ||||||||
\(305\) | 6.00000 | 0.343559 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.7321 | 1.01202 | 0.506011 | − | 0.862527i | \(-0.331120\pi\) | ||||
0.506011 | + | 0.862527i | \(0.331120\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.19615 | −0.523151 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.85641 | −0.105267 | −0.0526336 | − | 0.998614i | \(-0.516762\pi\) | ||||
−0.0526336 | + | 0.998614i | \(0.516762\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.9282 | −0.617699 | −0.308849 | − | 0.951111i | \(-0.599944\pi\) | ||||
−0.308849 | + | 0.951111i | \(0.599944\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 25.8564 | 1.45454 | ||||||||
\(317\) | 33.1962 | 1.86448 | 0.932241 | − | 0.361838i | \(-0.117851\pi\) | ||||
0.932241 | + | 0.361838i | \(0.117851\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.7846 | 0.659811 | ||||||||
\(320\) | 27.7128 | 1.54919 | ||||||||
\(321\) | 3.46410 | 0.193347 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 37.3205 | 2.07657 | ||||||||
\(324\) | −2.00000 | −0.111111 | ||||||||
\(325\) | 10.2487 | 0.568496 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.46410 | 0.523366 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.2487 | −1.77255 | −0.886275 | − | 0.463160i | \(-0.846716\pi\) | ||||
−0.886275 | + | 0.463160i | \(0.846716\pi\) | |||||||
\(332\) | 20.0000 | 1.09764 | ||||||||
\(333\) | −1.00000 | −0.0547997 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.85641 | −0.101426 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.0000 | 1.57973 | 0.789865 | − | 0.613280i | \(-0.210150\pi\) | ||||
0.789865 | + | 0.613280i | \(0.210150\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.3205 | 0.940721 | ||||||||
\(340\) | −34.6410 | −1.87867 | ||||||||
\(341\) | −5.14359 | −0.278541 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.07180 | 0.273056 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.6603 | 0.679638 | 0.339819 | − | 0.940491i | \(-0.389634\pi\) | ||||
0.339819 | + | 0.940491i | \(0.389634\pi\) | |||||||
\(348\) | −10.3923 | −0.557086 | ||||||||
\(349\) | −27.5885 | −1.47678 | −0.738388 | − | 0.674376i | \(-0.764413\pi\) | ||||
−0.738388 | + | 0.674376i | \(0.764413\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.46410 | 0.0781480 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.3205 | −1.13478 | −0.567388 | − | 0.823451i | \(-0.692046\pi\) | ||||
−0.567388 | + | 0.823451i | \(0.692046\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.71281 | −0.515503 | ||||||||
\(356\) | −9.85641 | −0.522388 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.7128 | −1.25151 | −0.625757 | − | 0.780018i | \(-0.715210\pi\) | ||||
−0.625757 | + | 0.780018i | \(0.715210\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.7128 | 1.93225 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.85641 | −0.307382 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.14359 | 0.216886 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.0526 | 1.20333 | 0.601667 | − | 0.798747i | \(-0.294503\pi\) | ||||
0.601667 | + | 0.798747i | \(0.294503\pi\) | |||||||
\(368\) | −5.85641 | −0.305286 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.53590 | 0.235175 | ||||||||
\(373\) | 34.8564 | 1.80480 | 0.902398 | − | 0.430903i | \(-0.141805\pi\) | ||||
0.902398 | + | 0.430903i | \(0.141805\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.92820 | −0.357771 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.60770 | 0.391816 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.0000 | −1.23280 | −0.616399 | − | 0.787434i | \(-0.711409\pi\) | ||||
−0.616399 | + | 0.787434i | \(0.711409\pi\) | |||||||
\(380\) | −51.7128 | −2.65281 | ||||||||
\(381\) | −9.85641 | −0.504959 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.0718 | 1.12782 | 0.563908 | − | 0.825838i | \(-0.309297\pi\) | ||||
0.563908 | + | 0.825838i | \(0.309297\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.92820 | −0.199682 | ||||||||
\(388\) | −36.7846 | −1.86746 | ||||||||
\(389\) | 34.7846 | 1.76365 | 0.881825 | − | 0.471577i | \(-0.156315\pi\) | ||||
0.881825 | + | 0.471577i | \(0.156315\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.32051 | 0.370214 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.4641 | 0.880947 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 44.7846 | 2.25336 | ||||||||
\(396\) | −4.53590 | −0.227937 | ||||||||
\(397\) | −10.5359 | −0.528782 | −0.264391 | − | 0.964416i | \(-0.585171\pi\) | ||||
−0.264391 | + | 0.964416i | \(0.585171\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 28.0000 | 1.40000 | ||||||||
\(401\) | −30.9282 | −1.54448 | −0.772240 | − | 0.635330i | \(-0.780864\pi\) | ||||
−0.772240 | + | 0.635330i | \(0.780864\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.32051 | −0.165406 | ||||||||
\(404\) | −17.7128 | −0.881245 | ||||||||
\(405\) | −3.46410 | −0.172133 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.26795 | −0.112418 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.26795 | −0.112143 | −0.0560714 | − | 0.998427i | \(-0.517857\pi\) | ||||
−0.0560714 | + | 0.998427i | \(0.517857\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.1962 | 0.650918 | ||||||||
\(412\) | 18.3923 | 0.906124 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 34.6410 | 1.70046 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.53590 | 0.222124 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.7128 | 1.15845 | 0.579223 | − | 0.815169i | \(-0.303356\pi\) | ||||
0.579223 | + | 0.815169i | \(0.303356\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.5359 | 0.903384 | 0.451692 | − | 0.892174i | \(-0.350821\pi\) | ||||
0.451692 | + | 0.892174i | \(0.350821\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.92820 | −0.0937524 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −35.0000 | −1.69775 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6.92820 | −0.334887 | ||||||||
\(429\) | 3.32051 | 0.160316 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.46410 | 0.455870 | 0.227935 | − | 0.973676i | \(-0.426803\pi\) | ||||
0.227935 | + | 0.973676i | \(0.426803\pi\) | |||||||
\(432\) | 4.00000 | 0.192450 | ||||||||
\(433\) | −0.411543 | −0.0197775 | −0.00988874 | − | 0.999951i | \(-0.503148\pi\) | ||||
−0.00988874 | + | 0.999951i | \(0.503148\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −18.0000 | −0.863034 | ||||||||
\(436\) | −18.9282 | −0.906497 | ||||||||
\(437\) | 10.9282 | 0.522767 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −35.4641 | −1.69261 | −0.846305 | − | 0.532699i | \(-0.821178\pi\) | ||||
−0.846305 | + | 0.532699i | \(0.821178\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.3923 | 1.15891 | 0.579457 | − | 0.815003i | \(-0.303265\pi\) | ||||
0.579457 | + | 0.815003i | \(0.303265\pi\) | |||||||
\(444\) | 2.00000 | 0.0949158 | ||||||||
\(445\) | −17.0718 | −0.809281 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.8564 | 0.655386 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.3205 | 0.534248 | 0.267124 | − | 0.963662i | \(-0.413927\pi\) | ||||
0.267124 | + | 0.963662i | \(0.413927\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.26795 | 0.106794 | ||||||||
\(452\) | −34.6410 | −1.62938 | ||||||||
\(453\) | −0.392305 | −0.0184321 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.6410 | 1.43333 | 0.716663 | − | 0.697419i | \(-0.245669\pi\) | ||||
0.716663 | + | 0.697419i | \(0.245669\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.00000 | −0.233380 | ||||||||
\(460\) | −10.1436 | −0.472947 | ||||||||
\(461\) | 24.2487 | 1.12938 | 0.564688 | − | 0.825305i | \(-0.308997\pi\) | ||||
0.564688 | + | 0.825305i | \(0.308997\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.3923 | −0.575919 | −0.287960 | − | 0.957643i | \(-0.592977\pi\) | ||||
−0.287960 | + | 0.957643i | \(0.592977\pi\) | |||||||
\(464\) | 20.7846 | 0.964901 | ||||||||
\(465\) | 7.85641 | 0.364332 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.46410 | −0.345397 | −0.172699 | − | 0.984975i | \(-0.555249\pi\) | ||||
−0.172699 | + | 0.984975i | \(0.555249\pi\) | |||||||
\(468\) | −2.92820 | −0.135356 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.0000 | 0.460776 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.90897 | −0.409635 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −52.2487 | −2.39734 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.92820 | −0.134073 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.7128 | −0.672246 | −0.336123 | − | 0.941818i | \(-0.609116\pi\) | ||||
−0.336123 | + | 0.941818i | \(0.609116\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.46410 | −0.0667573 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.7128 | 0.532401 | ||||||||
\(485\) | −63.7128 | −2.89305 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.9282 | 0.721776 | 0.360888 | − | 0.932609i | \(-0.382474\pi\) | ||||
0.360888 | + | 0.932609i | \(0.382474\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.07180 | −0.184133 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.8564 | −1.07662 | −0.538312 | − | 0.842745i | \(-0.680938\pi\) | ||||
−0.538312 | + | 0.842745i | \(0.680938\pi\) | |||||||
\(492\) | −2.00000 | −0.0901670 | ||||||||
\(493\) | −25.9808 | −1.17011 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.85641 | −0.353119 | ||||||||
\(496\) | −9.07180 | −0.407336 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.46410 | 0.244607 | 0.122303 | − | 0.992493i | \(-0.460972\pi\) | ||||
0.122303 | + | 0.992493i | \(0.460972\pi\) | |||||||
\(500\) | 13.8564 | 0.619677 | ||||||||
\(501\) | 5.07180 | 0.226591 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.7846 | 1.32803 | 0.664015 | − | 0.747719i | \(-0.268851\pi\) | ||||
0.664015 | + | 0.747719i | \(0.268851\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −30.6795 | −1.36522 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.8564 | −0.482150 | ||||||||
\(508\) | 19.7128 | 0.874615 | ||||||||
\(509\) | 21.9282 | 0.971951 | 0.485975 | − | 0.873973i | \(-0.338465\pi\) | ||||
0.485975 | + | 0.873973i | \(0.338465\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.46410 | −0.329548 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 31.8564 | 1.40376 | ||||||||
\(516\) | 7.85641 | 0.345859 | ||||||||
\(517\) | −4.37307 | −0.192327 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.9282 | −0.918646 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.8564 | −0.913736 | −0.456868 | − | 0.889535i | \(-0.651029\pi\) | ||||
−0.456868 | + | 0.889535i | \(0.651029\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.1769 | −1.36327 | −0.681636 | − | 0.731692i | \(-0.738731\pi\) | ||||
−0.681636 | + | 0.731692i | \(0.738731\pi\) | |||||||
\(524\) | −34.9282 | −1.52585 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.3397 | 0.493967 | ||||||||
\(528\) | 9.07180 | 0.394799 | ||||||||
\(529\) | −20.8564 | −0.906800 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.92820 | −0.300658 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.46410 | 0.0634173 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.0000 | −0.518805 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.5885 | −0.672692 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 6.92820 | 0.298142 | ||||||||
\(541\) | 16.9282 | 0.727800 | 0.363900 | − | 0.931438i | \(-0.381445\pi\) | ||||
0.363900 | + | 0.931438i | \(0.381445\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 20.0000 | 0.858282 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −32.7846 | −1.40434 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.6077 | −0.496309 | −0.248155 | − | 0.968720i | \(-0.579824\pi\) | ||||
−0.248155 | + | 0.968720i | \(0.579824\pi\) | |||||||
\(548\) | −26.3923 | −1.12742 | ||||||||
\(549\) | −1.73205 | −0.0739221 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −38.7846 | −1.65228 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.46410 | 0.147043 | ||||||||
\(556\) | −9.07180 | −0.384730 | ||||||||
\(557\) | 10.5167 | 0.445605 | 0.222803 | − | 0.974864i | \(-0.428479\pi\) | ||||
0.222803 | + | 0.974864i | \(0.428479\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.75129 | −0.243254 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.3397 | −0.478764 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.92820 | −0.249844 | −0.124922 | − | 0.992167i | \(-0.539868\pi\) | ||||
−0.124922 | + | 0.992167i | \(0.539868\pi\) | |||||||
\(564\) | 3.85641 | 0.162384 | ||||||||
\(565\) | −60.0000 | −2.52422 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.2487 | −1.10040 | −0.550202 | − | 0.835032i | \(-0.685449\pi\) | ||||
−0.550202 | + | 0.835032i | \(0.685449\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.9282 | 1.46170 | 0.730850 | − | 0.682538i | \(-0.239124\pi\) | ||||
0.730850 | + | 0.682538i | \(0.239124\pi\) | |||||||
\(572\) | −6.64102 | −0.277675 | ||||||||
\(573\) | 10.3923 | 0.434145 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.2487 | −0.427401 | ||||||||
\(576\) | −8.00000 | −0.333333 | ||||||||
\(577\) | −35.3205 | −1.47041 | −0.735206 | − | 0.677844i | \(-0.762915\pi\) | ||||
−0.735206 | + | 0.677844i | \(0.762915\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 27.3205 | 1.13540 | ||||||||
\(580\) | 36.0000 | 1.49482 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.64102 | −0.275043 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.07180 | −0.209693 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −41.9282 | −1.73056 | −0.865281 | − | 0.501287i | \(-0.832860\pi\) | ||||
−0.865281 | + | 0.501287i | \(0.832860\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.9282 | 0.697514 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.46410 | 0.307032 | ||||||||
\(592\) | −4.00000 | −0.164399 | ||||||||
\(593\) | 42.7128 | 1.75400 | 0.877002 | − | 0.480486i | \(-0.159540\pi\) | ||||
0.877002 | + | 0.480486i | \(0.159540\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −27.7128 | −1.13516 | ||||||||
\(597\) | 9.32051 | 0.381463 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.0000 | 1.63436 | 0.817178 | − | 0.576386i | \(-0.195537\pi\) | ||||
0.817178 | + | 0.576386i | \(0.195537\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.2487 | 1.64178 | 0.820890 | − | 0.571087i | \(-0.193478\pi\) | ||||
0.820890 | + | 0.571087i | \(0.193478\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.535898 | 0.0218235 | ||||||||
\(604\) | 0.784610 | 0.0319253 | ||||||||
\(605\) | 20.2872 | 0.824791 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −44.2487 | −1.79600 | −0.898000 | − | 0.439996i | \(-0.854980\pi\) | ||||
−0.898000 | + | 0.439996i | \(0.854980\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.82309 | −0.114210 | ||||||||
\(612\) | 10.0000 | 0.404226 | ||||||||
\(613\) | −32.6410 | −1.31836 | −0.659179 | − | 0.751986i | \(-0.729096\pi\) | ||||
−0.659179 | + | 0.751986i | \(0.729096\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.46410 | −0.139686 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.8564 | −0.799389 | −0.399694 | − | 0.916648i | \(-0.630884\pi\) | ||||
−0.399694 | + | 0.916648i | \(0.630884\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.1962 | 1.49504 | 0.747520 | − | 0.664240i | \(-0.231245\pi\) | ||||
0.747520 | + | 0.664240i | \(0.231245\pi\) | |||||||
\(620\) | −15.7128 | −0.631042 | ||||||||
\(621\) | −1.46410 | −0.0587524 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.85641 | 0.234444 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.9282 | −0.676047 | ||||||||
\(628\) | −20.0000 | −0.798087 | ||||||||
\(629\) | 5.00000 | 0.199363 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.0717968 | 0.00285818 | 0.00142909 | − | 0.999999i | \(-0.499545\pi\) | ||||
0.00142909 | + | 0.999999i | \(0.499545\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.07180 | 0.0426001 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 34.1436 | 1.35495 | ||||||||
\(636\) | 5.85641 | 0.232222 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.80385 | 0.110918 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.51666 | 0.0994021 | 0.0497011 | − | 0.998764i | \(-0.484173\pi\) | ||||
0.0497011 | + | 0.998764i | \(0.484173\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.2487 | 0.404170 | 0.202085 | − | 0.979368i | \(-0.435228\pi\) | ||||
0.202085 | + | 0.979368i | \(0.435228\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.6077 | 0.535802 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.9282 | −0.429632 | −0.214816 | − | 0.976655i | \(-0.568915\pi\) | ||||
−0.214816 | + | 0.976655i | \(0.568915\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.7128 | −0.616782 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.14359 | 0.318928 | ||||||||
\(653\) | 4.66025 | 0.182370 | 0.0911849 | − | 0.995834i | \(-0.470935\pi\) | ||||
0.0911849 | + | 0.995834i | \(0.470935\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −60.4974 | −2.36383 | ||||||||
\(656\) | 4.00000 | 0.156174 | ||||||||
\(657\) | −1.19615 | −0.0466664 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.4641 | −0.758214 | −0.379107 | − | 0.925353i | \(-0.623769\pi\) | ||||
−0.379107 | + | 0.925353i | \(0.623769\pi\) | |||||||
\(660\) | 15.7128 | 0.611620 | ||||||||
\(661\) | −38.6410 | −1.50296 | −0.751481 | − | 0.659755i | \(-0.770660\pi\) | ||||
−0.751481 | + | 0.659755i | \(0.770660\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.32051 | −0.284305 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.60770 | −0.294571 | ||||||||
\(668\) | −10.1436 | −0.392467 | ||||||||
\(669\) | −15.4641 | −0.597877 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.92820 | −0.151647 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.53590 | 0.329035 | 0.164517 | − | 0.986374i | \(-0.447393\pi\) | ||||
0.164517 | + | 0.986374i | \(0.447393\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.00000 | 0.269430 | ||||||||
\(676\) | 21.7128 | 0.835108 | ||||||||
\(677\) | 23.8564 | 0.916876 | 0.458438 | − | 0.888726i | \(-0.348409\pi\) | ||||
0.458438 | + | 0.888726i | \(0.348409\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.9282 | 0.533730 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.2487 | 1.38702 | 0.693509 | − | 0.720448i | \(-0.256064\pi\) | ||||
0.693509 | + | 0.720448i | \(0.256064\pi\) | |||||||
\(684\) | 14.9282 | 0.570794 | ||||||||
\(685\) | −45.7128 | −1.74660 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.92820 | 0.188023 | ||||||||
\(688\) | −15.7128 | −0.599045 | ||||||||
\(689\) | −4.28719 | −0.163329 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.1769 | 0.805608 | 0.402804 | − | 0.915286i | \(-0.368036\pi\) | ||||
0.402804 | + | 0.915286i | \(0.368036\pi\) | |||||||
\(692\) | 41.8564 | 1.59114 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.7128 | −0.596021 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.00000 | −0.189389 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.8564 | 0.524097 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.53590 | −0.322396 | −0.161198 | − | 0.986922i | \(-0.551536\pi\) | ||||
−0.161198 | + | 0.986922i | \(0.551536\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.46410 | 0.281514 | ||||||||
\(704\) | −18.1436 | −0.683812 | ||||||||
\(705\) | 6.67949 | 0.251564 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 13.8564 | 0.520756 | ||||||||
\(709\) | −1.32051 | −0.0495927 | −0.0247964 | − | 0.999693i | \(-0.507894\pi\) | ||||
−0.0247964 | + | 0.999693i | \(0.507894\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.9282 | −0.484846 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.32051 | 0.124354 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.5026 | −0.430172 | ||||||||
\(716\) | 31.1769 | 1.16514 | ||||||||
\(717\) | −8.53590 | −0.318779 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.0000 | −0.633993 | −0.316997 | − | 0.948427i | \(-0.602674\pi\) | ||||
−0.316997 | + | 0.948427i | \(0.602674\pi\) | |||||||
\(720\) | −13.8564 | −0.516398 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.19615 | −0.193247 | ||||||||
\(724\) | −40.0000 | −1.48659 | ||||||||
\(725\) | 36.3731 | 1.35086 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.6410 | 1.50729 | 0.753646 | − | 0.657281i | \(-0.228293\pi\) | ||||
0.753646 | + | 0.657281i | \(0.228293\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.6410 | 0.726449 | ||||||||
\(732\) | 3.46410 | 0.128037 | ||||||||
\(733\) | 21.9808 | 0.811878 | 0.405939 | − | 0.913900i | \(-0.366945\pi\) | ||||
0.405939 | + | 0.913900i | \(0.366945\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.21539 | 0.0447695 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.7846 | −1.24279 | −0.621393 | − | 0.783499i | \(-0.713433\pi\) | ||||
−0.621393 | + | 0.783499i | \(0.713433\pi\) | |||||||
\(740\) | −6.92820 | −0.254686 | ||||||||
\(741\) | −10.9282 | −0.401458 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.5359 | 0.753389 | 0.376695 | − | 0.926338i | \(-0.377061\pi\) | ||||
0.376695 | + | 0.926338i | \(0.377061\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −48.0000 | −1.75858 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.0000 | −0.365881 | ||||||||
\(748\) | 22.6795 | 0.829244 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.2487 | 0.884848 | 0.442424 | − | 0.896806i | \(-0.354119\pi\) | ||||
0.442424 | + | 0.896806i | \(0.354119\pi\) | |||||||
\(752\) | −7.71281 | −0.281257 | ||||||||
\(753\) | 0.535898 | 0.0195292 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.35898 | 0.0494585 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.8564 | −0.430928 | −0.215464 | − | 0.976512i | \(-0.569126\pi\) | ||||
−0.215464 | + | 0.976512i | \(0.569126\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.32051 | −0.120527 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.2487 | −1.38651 | −0.693257 | − | 0.720690i | \(-0.743825\pi\) | ||||
−0.693257 | + | 0.720690i | \(0.743825\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −20.7846 | −0.751961 | ||||||||
\(765\) | 17.3205 | 0.626224 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.1436 | −0.366264 | ||||||||
\(768\) | 16.0000 | 0.577350 | ||||||||
\(769\) | −13.1962 | −0.475865 | −0.237933 | − | 0.971282i | \(-0.576470\pi\) | ||||
−0.237933 | + | 0.971282i | \(0.576470\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.00000 | 0.108042 | ||||||||
\(772\) | −54.6410 | −1.96657 | ||||||||
\(773\) | −30.8564 | −1.10983 | −0.554914 | − | 0.831908i | \(-0.687249\pi\) | ||||
−0.554914 | + | 0.831908i | \(0.687249\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.8756 | −0.570270 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.46410 | −0.267429 | ||||||||
\(780\) | 10.1436 | 0.363199 | ||||||||
\(781\) | 6.35898 | 0.227542 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.19615 | 0.185695 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −34.6410 | −1.23639 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.5167 | 0.660048 | 0.330024 | − | 0.943973i | \(-0.392943\pi\) | ||||
0.330024 | + | 0.943973i | \(0.392943\pi\) | |||||||
\(788\) | −14.9282 | −0.531795 | ||||||||
\(789\) | 4.12436 | 0.146831 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.53590 | −0.0900524 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.1436 | 0.359756 | ||||||||
\(796\) | −18.6410 | −0.660713 | ||||||||
\(797\) | 7.85641 | 0.278288 | 0.139144 | − | 0.990272i | \(-0.455565\pi\) | ||||
0.139144 | + | 0.990272i | \(0.455565\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.64102 | 0.341075 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.92820 | 0.174129 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.71281 | −0.0957331 | ||||||||
\(804\) | −1.07180 | −0.0377994 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.5359 | 0.370881 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −54.9282 | −1.93117 | −0.965586 | − | 0.260083i | \(-0.916250\pi\) | ||||
−0.965586 | + | 0.260083i | \(0.916250\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.73205 | 0.0608205 | 0.0304103 | − | 0.999538i | \(-0.490319\pi\) | ||||
0.0304103 | + | 0.999538i | \(0.490319\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.5885 | 0.686997 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.1051 | 0.494081 | ||||||||
\(816\) | −20.0000 | −0.700140 | ||||||||
\(817\) | 29.3205 | 1.02579 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.92820 | 0.241943 | ||||||||
\(821\) | −43.3205 | −1.51190 | −0.755948 | − | 0.654632i | \(-0.772824\pi\) | ||||
−0.755948 | + | 0.654632i | \(0.772824\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43.5692 | −1.51873 | −0.759364 | − | 0.650666i | \(-0.774490\pi\) | ||||
−0.759364 | + | 0.650666i | \(0.774490\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.8756 | 0.552719 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.8038 | −1.21025 | −0.605124 | − | 0.796131i | \(-0.706877\pi\) | ||||
−0.605124 | + | 0.796131i | \(0.706877\pi\) | |||||||
\(828\) | 2.92820 | 0.101762 | ||||||||
\(829\) | −23.0526 | −0.800648 | −0.400324 | − | 0.916374i | \(-0.631102\pi\) | ||||
−0.400324 | + | 0.916374i | \(0.631102\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.07180 | −0.280008 | ||||||||
\(832\) | −11.7128 | −0.406069 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.5692 | −0.608008 | ||||||||
\(836\) | 33.8564 | 1.17095 | ||||||||
\(837\) | −2.26795 | −0.0783918 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.0000 | 1.51905 | 0.759524 | − | 0.650479i | \(-0.225432\pi\) | ||||
0.759524 | + | 0.650479i | \(0.225432\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.00000 | −0.0689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.1244 | 0.830887 | ||||||||
\(844\) | −2.14359 | −0.0737855 | ||||||||
\(845\) | 37.6077 | 1.29374 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −11.7128 | −0.402220 | ||||||||
\(849\) | −12.6603 | −0.434499 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.46410 | 0.0501888 | ||||||||
\(852\) | −5.60770 | −0.192116 | ||||||||
\(853\) | 3.71281 | 0.127124 | 0.0635621 | − | 0.997978i | \(-0.479754\pi\) | ||||
0.0635621 | + | 0.997978i | \(0.479754\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 25.8564 | 0.884270 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.2487 | −0.486727 | −0.243363 | − | 0.969935i | \(-0.578251\pi\) | ||||
−0.243363 | + | 0.969935i | \(0.578251\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.1962 | 0.450247 | 0.225123 | − | 0.974330i | \(-0.427721\pi\) | ||||
0.225123 | + | 0.974330i | \(0.427721\pi\) | |||||||
\(860\) | −27.2154 | −0.928037 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 49.3205 | 1.67889 | 0.839445 | − | 0.543445i | \(-0.182880\pi\) | ||||
0.839445 | + | 0.543445i | \(0.182880\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 72.4974 | 2.46499 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.00000 | 0.271694 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29.3205 | −0.994630 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.784610 | 0.0265855 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.3923 | 0.622485 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.39230 | 0.0808285 | ||||||||
\(877\) | 41.9282 | 1.41581 | 0.707907 | − | 0.706305i | \(-0.249639\pi\) | ||||
0.707907 | + | 0.706305i | \(0.249639\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.00000 | −0.303562 | ||||||||
\(880\) | −31.4256 | −1.05936 | ||||||||
\(881\) | 33.4641 | 1.12743 | 0.563717 | − | 0.825968i | \(-0.309371\pi\) | ||||
0.563717 | + | 0.825968i | \(0.309371\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43.5692 | −1.46622 | −0.733110 | − | 0.680110i | \(-0.761932\pi\) | ||||
−0.733110 | + | 0.680110i | \(0.761932\pi\) | |||||||
\(884\) | 14.6410 | 0.492431 | ||||||||
\(885\) | 24.0000 | 0.806751 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.85641 | 0.230216 | 0.115108 | − | 0.993353i | \(-0.463279\pi\) | ||||
0.115108 | + | 0.993353i | \(0.463279\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.26795 | 0.0759792 | ||||||||
\(892\) | 30.9282 | 1.03555 | ||||||||
\(893\) | 14.3923 | 0.481620 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 54.0000 | 1.80502 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.14359 | −0.0715725 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.7846 | −0.393039 | ||||||||
\(900\) | −14.0000 | −0.466667 | ||||||||
\(901\) | 14.6410 | 0.487763 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −69.2820 | −2.30301 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.8564 | −0.725730 | −0.362865 | − | 0.931842i | \(-0.618201\pi\) | ||||
−0.362865 | + | 0.931842i | \(0.618201\pi\) | |||||||
\(908\) | −27.8564 | −0.924447 | ||||||||
\(909\) | 8.85641 | 0.293748 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.7846 | 0.821151 | 0.410575 | − | 0.911827i | \(-0.365328\pi\) | ||||
0.410575 | + | 0.911827i | \(0.365328\pi\) | |||||||
\(912\) | −29.8564 | −0.988644 | ||||||||
\(913\) | −22.6795 | −0.750582 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.00000 | 0.198354 | ||||||||
\(916\) | −9.85641 | −0.325665 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.5359 | −0.611443 | −0.305721 | − | 0.952121i | \(-0.598898\pi\) | ||||
−0.305721 | + | 0.952121i | \(0.598898\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.7321 | 0.584291 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.10512 | 0.135122 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.00000 | −0.230159 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.19615 | −0.302041 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.21539 | −0.0726846 | −0.0363423 | − | 0.999339i | \(-0.511571\pi\) | ||||
−0.0363423 | + | 0.999339i | \(0.511571\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −27.7128 | −0.907763 | ||||||||
\(933\) | −1.85641 | −0.0607760 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 39.2820 | 1.28466 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.9282 | 0.618357 | 0.309179 | − | 0.951004i | \(-0.399946\pi\) | ||||
0.309179 | + | 0.951004i | \(0.399946\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.9282 | −0.356628 | ||||||||
\(940\) | −13.3590 | −0.435722 | ||||||||
\(941\) | −1.32051 | −0.0430473 | −0.0215237 | − | 0.999768i | \(-0.506852\pi\) | ||||
−0.0215237 | + | 0.999768i | \(0.506852\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.46410 | −0.0476777 | ||||||||
\(944\) | −27.7128 | −0.901975 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.9282 | 1.20001 | 0.600003 | − | 0.799998i | \(-0.295166\pi\) | ||||
0.600003 | + | 0.799998i | \(0.295166\pi\) | |||||||
\(948\) | 25.8564 | 0.839777 | ||||||||
\(949\) | −1.75129 | −0.0568492 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.1962 | 1.07646 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −55.3205 | −1.79201 | −0.896004 | − | 0.444047i | \(-0.853542\pi\) | ||||
−0.896004 | + | 0.444047i | \(0.853542\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −36.0000 | −1.16493 | ||||||||
\(956\) | 17.0718 | 0.552141 | ||||||||
\(957\) | 11.7846 | 0.380942 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 27.7128 | 0.894427 | ||||||||
\(961\) | −25.8564 | −0.834078 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.46410 | 0.111629 | ||||||||
\(964\) | 10.3923 | 0.334714 | ||||||||
\(965\) | −94.6410 | −3.04660 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.2487 | 0.393892 | 0.196946 | − | 0.980414i | \(-0.436898\pi\) | ||||
0.196946 | + | 0.980414i | \(0.436898\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 37.3205 | 1.19891 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.9282 | 0.896259 | 0.448129 | − | 0.893969i | \(-0.352090\pi\) | ||||
0.448129 | + | 0.893969i | \(0.352090\pi\) | |||||||
\(972\) | −2.00000 | −0.0641500 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.2487 | 0.328221 | ||||||||
\(976\) | −6.92820 | −0.221766 | ||||||||
\(977\) | −37.9808 | −1.21511 | −0.607556 | − | 0.794277i | \(-0.707850\pi\) | ||||
−0.607556 | + | 0.794277i | \(0.707850\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.1769 | 0.357216 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.46410 | 0.302166 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.7846 | 0.854296 | 0.427148 | − | 0.904182i | \(-0.359518\pi\) | ||||
0.427148 | + | 0.904182i | \(0.359518\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.8564 | −0.823854 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 21.8564 | 0.695345 | ||||||||
\(989\) | 5.75129 | 0.182880 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.1051 | 1.65517 | 0.827587 | − | 0.561338i | \(-0.189713\pi\) | ||||
0.827587 | + | 0.561338i | \(0.189713\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −32.2487 | −1.02338 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −32.2872 | −1.02357 | ||||||||
\(996\) | 20.0000 | 0.633724 | ||||||||
\(997\) | −41.1769 | −1.30409 | −0.652043 | − | 0.758182i | \(-0.726088\pi\) | ||||
−0.652043 | + | 0.758182i | \(0.726088\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.00000 | −0.0316386 |
(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 | 6027.2.a.n.1.1 | yes | 2 | |
7.6 | odd | 2 | 6027.2.a.l.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.l.1.2 | ✓ | 2 | 7.6 | odd | 2 | ||
6027.2.a.n.1.1 | yes | 2 | 1.1 | even | 1 | trivial |