Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.36497.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 3x^{3} + 5x^{2} + x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 501) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.33419\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.19539 | −0.534593 | −0.267296 | − | 0.963614i | \(-0.586130\pi\) | ||||
−0.267296 | + | 0.963614i | \(0.586130\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.77240 | −0.669905 | −0.334953 | − | 0.942235i | \(-0.608720\pi\) | ||||
−0.334953 | + | 0.942235i | \(0.608720\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.47298 | 1.65017 | 0.825083 | − | 0.565011i | \(-0.191128\pi\) | ||||
0.825083 | + | 0.565011i | \(0.191128\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.71582 | −1.30793 | −0.653966 | − | 0.756524i | \(-0.726896\pi\) | ||||
−0.653966 | + | 0.756524i | \(0.726896\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.19539 | 0.308647 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.92365 | 1.19416 | 0.597080 | − | 0.802182i | \(-0.296327\pi\) | ||||
0.597080 | + | 0.802182i | \(0.296327\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.56490 | 1.96492 | 0.982461 | − | 0.186466i | \(-0.0597035\pi\) | ||||
0.982461 | + | 0.186466i | \(0.0597035\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.77240 | 0.386770 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.04298 | 0.843019 | 0.421509 | − | 0.906824i | \(-0.361500\pi\) | ||||
0.421509 | + | 0.906824i | \(0.361500\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.57105 | −0.714210 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.38643 | 1.74302 | 0.871508 | − | 0.490381i | \(-0.163142\pi\) | ||||
0.871508 | + | 0.490381i | \(0.163142\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.0932685 | 0.0167515 | 0.00837576 | − | 0.999965i | \(-0.497334\pi\) | ||||
0.00837576 | + | 0.999965i | \(0.497334\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.47298 | −0.952724 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.11871 | 0.358127 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.65649 | −0.272325 | −0.136162 | − | 0.990687i | \(-0.543477\pi\) | ||||
−0.136162 | + | 0.990687i | \(0.543477\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.71582 | 0.755135 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.208144 | 0.0325066 | 0.0162533 | − | 0.999868i | \(-0.494826\pi\) | ||||
0.0162533 | + | 0.999868i | \(0.494826\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.12542 | −0.934118 | −0.467059 | − | 0.884226i | \(-0.654686\pi\) | ||||
−0.467059 | + | 0.884226i | \(0.654686\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.19539 | −0.178198 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.00671 | 0.730304 | 0.365152 | − | 0.930948i | \(-0.381017\pi\) | ||||
0.365152 | + | 0.930948i | \(0.381017\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.85859 | −0.551227 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.92365 | −0.689449 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.99915 | −1.23613 | −0.618064 | − | 0.786128i | \(-0.712083\pi\) | ||||
−0.618064 | + | 0.786128i | \(0.712083\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.54233 | −0.882167 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.56490 | −1.13445 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.4797 | 1.75491 | 0.877454 | − | 0.479661i | \(-0.159240\pi\) | ||||
0.877454 | + | 0.479661i | \(0.159240\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.91008 | −1.26886 | −0.634428 | − | 0.772982i | \(-0.718764\pi\) | ||||
−0.634428 | + | 0.772982i | \(0.718764\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.77240 | −0.223302 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.63722 | 0.699211 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.73622 | −0.578621 | −0.289311 | − | 0.957235i | \(-0.593426\pi\) | ||||
−0.289311 | + | 0.957235i | \(0.593426\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.04298 | −0.486717 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.89736 | 0.818566 | 0.409283 | − | 0.912408i | \(-0.365779\pi\) | ||||
0.409283 | + | 0.912408i | \(0.365779\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.90100 | 0.339536 | 0.169768 | − | 0.985484i | \(-0.445698\pi\) | ||||
0.169768 | + | 0.985484i | \(0.445698\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.57105 | 0.412350 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.70033 | −1.10546 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.36024 | −0.265548 | −0.132774 | − | 0.991146i | \(-0.542388\pi\) | ||||
−0.132774 | + | 0.991146i | \(0.542388\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.8094 | −1.73530 | −0.867651 | − | 0.497174i | \(-0.834371\pi\) | ||||
−0.867651 | + | 0.497174i | \(0.834371\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.88566 | −0.638390 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.38643 | −1.00633 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.84740 | −0.831823 | −0.415911 | − | 0.909405i | \(-0.636537\pi\) | ||||
−0.415911 | + | 0.909405i | \(0.636537\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.35833 | 0.876191 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.0932685 | −0.00967149 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.2384 | −1.05043 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.91792 | 0.600873 | 0.300437 | − | 0.953802i | \(-0.402868\pi\) | ||||
0.300437 | + | 0.953802i | \(0.402868\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.47298 | 0.550056 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.16294 | −0.115717 | −0.0578585 | − | 0.998325i | \(-0.518427\pi\) | ||||
−0.0578585 | + | 0.998325i | \(0.518427\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.22124 | 0.711530 | 0.355765 | − | 0.934575i | \(-0.384220\pi\) | ||||
0.355765 | + | 0.934575i | \(0.384220\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.11871 | −0.206765 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.75773 | −0.846642 | −0.423321 | − | 0.905980i | \(-0.639136\pi\) | ||||
−0.423321 | + | 0.905980i | \(0.639136\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.78303 | 0.553914 | 0.276957 | − | 0.960882i | \(-0.410674\pi\) | ||||
0.276957 | + | 0.960882i | \(0.410674\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.65649 | 0.157227 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.11997 | −0.293502 | −0.146751 | − | 0.989173i | \(-0.546882\pi\) | ||||
−0.146751 | + | 0.989173i | \(0.546882\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.83292 | −0.450672 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.71582 | −0.435977 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.72669 | −0.799974 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.9536 | 1.72305 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.208144 | −0.0187677 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.2457 | 0.916405 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.95298 | −0.262034 | −0.131017 | − | 0.991380i | \(-0.541824\pi\) | ||||
−0.131017 | + | 0.991380i | \(0.541824\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.12542 | 0.539313 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.3913 | 1.51948 | 0.759741 | − | 0.650225i | \(-0.225326\pi\) | ||||
0.759741 | + | 0.650225i | \(0.225326\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.1805 | −1.31631 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.19539 | 0.102882 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.3829 | 1.57056 | 0.785278 | − | 0.619143i | \(-0.212520\pi\) | ||||
0.785278 | + | 0.619143i | \(0.212520\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.44917 | 0.716649 | 0.358325 | − | 0.933597i | \(-0.383348\pi\) | ||||
0.358325 | + | 0.933597i | \(0.383348\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.00671 | −0.421641 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −25.8096 | −2.15831 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.2204 | −0.931804 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.85859 | 0.318251 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.3049 | −1.00805 | −0.504027 | − | 0.863688i | \(-0.668149\pi\) | ||||
−0.504027 | + | 0.863688i | \(0.668149\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.43183 | −0.523415 | −0.261708 | − | 0.965147i | \(-0.584286\pi\) | ||||
−0.261708 | + | 0.965147i | \(0.584286\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.92365 | 0.398053 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.111492 | −0.00895524 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.09719 | 0.326992 | 0.163496 | − | 0.986544i | \(-0.447723\pi\) | ||||
0.163496 | + | 0.986544i | \(0.447723\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.99915 | 0.713679 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.16578 | −0.564743 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.8003 | 0.845946 | 0.422973 | − | 0.906142i | \(-0.360986\pi\) | ||||
0.422973 | + | 0.906142i | \(0.360986\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.54233 | 0.509320 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.23892 | 0.710686 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.56490 | 0.654974 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.62825 | 0.503936 | 0.251968 | − | 0.967736i | \(-0.418922\pi\) | ||||
0.251968 | + | 0.967736i | \(0.418922\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.32934 | 0.478453 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.4797 | −1.01320 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.54195 | 0.488969 | 0.244484 | − | 0.969653i | \(-0.421381\pi\) | ||||
0.244484 | + | 0.969653i | \(0.421381\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.10198 | −0.304898 | −0.152449 | − | 0.988311i | \(-0.548716\pi\) | ||||
−0.152449 | + | 0.988311i | \(0.548716\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.91008 | 0.732574 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.98014 | 0.145583 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 26.9471 | 1.97056 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.77240 | 0.128923 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.92293 | 0.211496 | 0.105748 | − | 0.994393i | \(-0.466276\pi\) | ||||
0.105748 | + | 0.994393i | \(0.466276\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.63895 | −0.405900 | −0.202950 | − | 0.979189i | \(-0.565053\pi\) | ||||
−0.202950 | + | 0.979189i | \(0.565053\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.63722 | −0.403690 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.0864 | 1.14611 | 0.573054 | − | 0.819518i | \(-0.305759\pi\) | ||||
0.573054 | + | 0.819518i | \(0.305759\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.0123 | −0.780642 | −0.390321 | − | 0.920679i | \(-0.627636\pi\) | ||||
−0.390321 | + | 0.920679i | \(0.627636\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.73622 | 0.334067 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.6365 | −1.16766 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.248812 | −0.0173778 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.04298 | 0.281006 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 46.8756 | 3.24245 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.8916 | 1.78245 | 0.891227 | − | 0.453558i | \(-0.149846\pi\) | ||||
0.891227 | + | 0.453558i | \(0.149846\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.89736 | −0.472599 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.32224 | 0.499373 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.165309 | −0.0112219 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.90100 | −0.196031 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.2190 | −1.56188 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.7188 | −1.38743 | −0.693715 | − | 0.720249i | \(-0.744027\pi\) | ||||
−0.693715 | + | 0.720249i | \(0.744027\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.57105 | −0.238070 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.9100 | 1.45422 | 0.727110 | − | 0.686521i | \(-0.240863\pi\) | ||||
0.727110 | + | 0.686521i | \(0.240863\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.3308 | 1.21133 | 0.605667 | − | 0.795719i | \(-0.292907\pi\) | ||||
0.605667 | + | 0.795719i | \(0.292907\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.70033 | 0.638235 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.98209 | −0.129851 | −0.0649255 | − | 0.997890i | \(-0.520681\pi\) | ||||
−0.0649255 | + | 0.997890i | \(0.520681\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.98496 | −0.390416 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.36024 | 0.153314 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.2205 | −1.50201 | −0.751004 | − | 0.660297i | \(-0.770430\pi\) | ||||
−0.751004 | + | 0.660297i | \(0.770430\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.7187 | 0.690450 | 0.345225 | − | 0.938520i | \(-0.387803\pi\) | ||||
0.345225 | + | 0.938520i | \(0.387803\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.61250 | 0.294682 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −40.3905 | −2.56999 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.8094 | 1.00188 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.4880 | 0.788233 | 0.394116 | − | 0.919061i | \(-0.371051\pi\) | ||||
0.394116 | + | 0.919061i | \(0.371051\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.1271 | 1.39112 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.88566 | 0.368574 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.7839 | −0.735060 | −0.367530 | − | 0.930012i | \(-0.619796\pi\) | ||||
−0.367530 | + | 0.930012i | \(0.619796\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.93596 | 0.182432 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.38643 | 0.581005 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.92203 | 0.426830 | 0.213415 | − | 0.976962i | \(-0.431541\pi\) | ||||
0.213415 | + | 0.976962i | \(0.431541\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.7575 | 0.660825 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.84740 | 0.480253 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.7673 | 1.20523 | 0.602617 | − | 0.798030i | \(-0.294125\pi\) | ||||
0.602617 | + | 0.798030i | \(0.294125\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.0726 | −1.70529 | −0.852644 | − | 0.522492i | \(-0.825003\pi\) | ||||
−0.852644 | + | 0.522492i | \(0.825003\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.35833 | −0.505869 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −19.5443 | −1.17857 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.78055 | 0.587656 | 0.293828 | − | 0.955858i | \(-0.405071\pi\) | ||||
0.293828 | + | 0.955858i | \(0.405071\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.0932685 | 0.00558384 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.42891 | 0.144896 | 0.0724482 | − | 0.997372i | \(-0.476919\pi\) | ||||
0.0724482 | + | 0.997372i | \(0.476919\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.70418 | −0.457966 | −0.228983 | − | 0.973430i | \(-0.573540\pi\) | ||||
−0.228983 | + | 0.973430i | \(0.573540\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.2384 | 0.606468 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.368915 | −0.0217763 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.24232 | 0.426019 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.91792 | −0.346914 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.192909 | 0.0112698 | 0.00563492 | − | 0.999984i | \(-0.498206\pi\) | ||||
0.00563492 | + | 0.999984i | \(0.498206\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.1134 | −0.938161 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.47298 | −0.317575 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −19.0659 | −1.10261 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.8567 | 0.625771 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.16294 | 0.0668093 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.8464 | 0.678321 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.67881 | 0.267034 | 0.133517 | − | 0.991047i | \(-0.457373\pi\) | ||||
0.133517 | + | 0.991047i | \(0.457373\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.22124 | −0.410802 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.460674 | −0.0261225 | −0.0130612 | − | 0.999915i | \(-0.504158\pi\) | ||||
−0.0130612 | + | 0.999915i | \(0.504158\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0147 | 0.792157 | 0.396079 | − | 0.918217i | \(-0.370371\pi\) | ||||
0.396079 | + | 0.918217i | \(0.370371\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.11871 | 0.119376 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.70071 | −0.376349 | −0.188175 | − | 0.982136i | \(-0.560257\pi\) | ||||
−0.188175 | + | 0.982136i | \(0.560257\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 51.3718 | 2.87627 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.75773 | 0.488809 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 42.1706 | 2.34643 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.8404 | 0.934139 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.78303 | −0.319802 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.87392 | −0.489235 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.2154 | 1.22107 | 0.610535 | − | 0.791989i | \(-0.290954\pi\) | ||||
0.610535 | + | 0.791989i | \(0.290954\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.65649 | −0.0907749 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.66161 | 0.309327 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.4236 | −0.949125 | −0.474562 | − | 0.880222i | \(-0.657394\pi\) | ||||
−0.474562 | + | 0.880222i | \(0.657394\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.11997 | 0.169453 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.510457 | 0.0276428 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.2458 | 1.03918 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.83292 | 0.260195 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.9645 | 1.17911 | 0.589557 | − | 0.807727i | \(-0.299302\pi\) | ||||
0.589557 | + | 0.807727i | \(0.299302\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.50882 | −0.241352 | −0.120676 | − | 0.992692i | \(-0.538506\pi\) | ||||
−0.120676 | + | 0.992692i | \(0.538506\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.71582 | 0.251712 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.5941 | −1.52191 | −0.760955 | − | 0.648805i | \(-0.775269\pi\) | ||||
−0.760955 | + | 0.648805i | \(0.775269\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.24500 | −0.437599 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.72669 | 0.461865 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.6985 | −1.19798 | −0.598991 | − | 0.800756i | \(-0.704431\pi\) | ||||
−0.598991 | + | 0.800756i | \(0.704431\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 54.3575 | 2.86092 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.9536 | −0.994804 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.46781 | −0.181514 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.7463 | 1.08295 | 0.541474 | − | 0.840717i | \(-0.317866\pi\) | ||||
0.541474 | + | 0.840717i | \(0.317866\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.208144 | 0.0108355 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.9501 | 0.828089 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.7331 | −0.969961 | −0.484981 | − | 0.874525i | \(-0.661173\pi\) | ||||
−0.484981 | + | 0.874525i | \(0.661173\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.2457 | −0.529087 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −44.2647 | −2.27975 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.8017 | 0.657581 | 0.328790 | − | 0.944403i | \(-0.393359\pi\) | ||||
0.328790 | + | 0.944403i | \(0.393359\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.95298 | 0.151286 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.7589 | −1.06073 | −0.530364 | − | 0.847770i | \(-0.677945\pi\) | ||||
−0.530364 | + | 0.847770i | \(0.677945\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.5956 | 0.590969 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.12542 | −0.311373 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.4763 | 1.13959 | 0.569797 | − | 0.821785i | \(-0.307022\pi\) | ||||
0.569797 | + | 0.821785i | \(0.307022\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.9062 | 1.00670 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.3913 | −0.877274 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.82140 | 0.141960 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.0948 | 0.908153 | 0.454076 | − | 0.890963i | \(-0.349969\pi\) | ||||
0.454076 | + | 0.890963i | \(0.349969\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 15.1805 | 0.759973 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.90969 | 0.0953655 | 0.0476828 | − | 0.998863i | \(-0.484816\pi\) | ||||
0.0476828 | + | 0.998863i | \(0.484816\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.439837 | −0.0219099 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.19539 | −0.0593992 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.06592 | −0.449381 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.9762 | −0.592186 | −0.296093 | − | 0.955159i | \(-0.595684\pi\) | ||||
−0.296093 | + | 0.955159i | \(0.595684\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.3829 | −0.906761 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −23.8915 | −1.17562 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.8983 | 0.927680 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.44917 | −0.413758 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.4154 | −1.33933 | −0.669666 | − | 0.742663i | \(-0.733563\pi\) | ||||
−0.669666 | + | 0.742663i | \(0.733563\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.3718 | −0.895386 | −0.447693 | − | 0.894187i | \(-0.647754\pi\) | ||||
−0.447693 | + | 0.894187i | \(0.647754\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.00671 | 0.243435 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.5826 | −0.852882 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.5647 | 0.850014 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 25.8096 | 1.24610 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.66607 | 0.417430 | 0.208715 | − | 0.977977i | \(-0.433072\pi\) | ||||
0.208715 | + | 0.977977i | \(0.433072\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.56610 | 0.219433 | 0.109716 | − | 0.993963i | \(-0.465006\pi\) | ||||
0.109716 | + | 0.993963i | \(0.465006\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.2204 | 0.537977 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 34.6277 | 1.65647 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.5648 | 0.504232 | 0.252116 | − | 0.967697i | \(-0.418873\pi\) | ||||
0.252116 | + | 0.967697i | \(0.418873\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.85859 | −0.183742 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.9577 | −0.568127 | −0.284064 | − | 0.958805i | \(-0.591683\pi\) | ||||
−0.284064 | + | 0.958805i | \(0.591683\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.38067 | 0.444687 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.3049 | 0.582000 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.17792 | 0.338747 | 0.169374 | − | 0.985552i | \(-0.445826\pi\) | ||||
0.169374 | + | 0.985552i | \(0.445826\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.13917 | 0.0536413 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.43183 | 0.302194 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.99143 | −0.468405 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.32645 | 0.155605 | 0.0778025 | − | 0.996969i | \(-0.475210\pi\) | ||||
0.0778025 | + | 0.996969i | \(0.475210\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.92365 | −0.229816 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.3336 | −0.993603 | −0.496802 | − | 0.867864i | \(-0.665492\pi\) | ||||
−0.496802 | + | 0.867864i | \(0.665492\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −41.5946 | −1.93306 | −0.966531 | − | 0.256548i | \(-0.917415\pi\) | ||||
−0.966531 | + | 0.256548i | \(0.917415\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.111492 | 0.00517031 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.7058 | 1.32834 | 0.664172 | − | 0.747579i | \(-0.268784\pi\) | ||||
0.664172 | + | 0.747579i | \(0.268784\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.39449 | 0.387622 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.09719 | −0.188789 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −33.5243 | −1.54145 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −30.5857 | −1.40337 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.99915 | −0.412043 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.5130 | 0.982956 | 0.491478 | − | 0.870890i | \(-0.336457\pi\) | ||||
0.491478 | + | 0.870890i | \(0.336457\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.81168 | 0.356182 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.16578 | 0.326054 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.07420 | −0.321223 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.0631 | 1.49823 | 0.749117 | − | 0.662438i | \(-0.230478\pi\) | ||||
0.749117 | + | 0.662438i | \(0.230478\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.8003 | −0.488407 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.46205 | −0.201370 | −0.100685 | − | 0.994918i | \(-0.532103\pi\) | ||||
−0.100685 | + | 0.994918i | \(0.532103\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 46.2155 | 2.08144 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.54233 | −0.294056 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.2249 | −0.548362 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.1803 | −0.679565 | −0.339783 | − | 0.940504i | \(-0.610354\pi\) | ||||
−0.339783 | + | 0.940504i | \(0.610354\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.8467 | 1.24162 | 0.620811 | − | 0.783961i | \(-0.286804\pi\) | ||||
0.620811 | + | 0.783961i | \(0.286804\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.39016 | 0.0618615 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.23892 | −0.410315 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.39072 | 0.238939 | 0.119470 | − | 0.992838i | \(-0.461881\pi\) | ||||
0.119470 | + | 0.992838i | \(0.461881\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.14174 | −0.227457 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.56490 | −0.378150 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.63218 | −0.380379 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.4017 | 1.20512 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.62825 | −0.290948 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.40308 | −0.280524 | −0.140262 | − | 0.990114i | \(-0.544795\pi\) | ||||
−0.140262 | + | 0.990114i | \(0.544795\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.8147 | 1.34743 | 0.673717 | − | 0.738989i | \(-0.264697\pi\) | ||||
0.673717 | + | 0.738989i | \(0.264697\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.32934 | −0.276235 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.459221 | 0.0200040 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.65435 | −0.289320 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.4797 | 0.584969 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.981568 | −0.0425164 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.4689 | 0.452609 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.54195 | −0.282306 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −21.1180 | −0.909616 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.3284 | 0.959973 | 0.479987 | − | 0.877276i | \(-0.340642\pi\) | ||||
0.479987 | + | 0.877276i | \(0.340642\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.10198 | 0.176033 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.91295 | −0.296118 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.6182 | −0.753298 | −0.376649 | − | 0.926356i | \(-0.622924\pi\) | ||||
−0.376649 | + | 0.926356i | \(0.622924\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.91008 | −0.422952 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 80.3938 | 3.42489 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.18330 | 0.177892 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.98014 | −0.0840523 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 39.2928 | 1.66489 | 0.832445 | − | 0.554108i | \(-0.186941\pi\) | ||||
0.832445 | + | 0.554108i | \(0.186941\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28.8864 | 1.22176 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −26.9471 | −1.13771 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.37113 | 0.0999313 | 0.0499656 | − | 0.998751i | \(-0.484089\pi\) | ||||
0.0499656 | + | 0.998751i | \(0.484089\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.72956 | 0.156904 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.77240 | −0.0744339 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 41.0333 | 1.72020 | 0.860102 | − | 0.510121i | \(-0.170400\pi\) | ||||
0.860102 | + | 0.510121i | \(0.170400\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.0112 | −1.46517 | −0.732586 | − | 0.680674i | \(-0.761687\pi\) | ||||
−0.732586 | + | 0.680674i | \(0.761687\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.92293 | −0.122107 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.4377 | −0.602093 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.96953 | −0.165254 | −0.0826269 | − | 0.996581i | \(-0.526331\pi\) | ||||
−0.0826269 | + | 0.996581i | \(0.526331\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.63895 | 0.234347 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 28.0206 | 1.16249 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −49.2522 | −2.03982 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.63722 | 0.233070 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.6634 | 0.852870 | 0.426435 | − | 0.904518i | \(-0.359769\pi\) | ||||
0.426435 | + | 0.904518i | \(0.359769\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.798835 | 0.0329154 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.0864 | −0.661706 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.9249 | 1.10567 | 0.552836 | − | 0.833290i | \(-0.313546\pi\) | ||||
0.552836 | + | 0.833290i | \(0.313546\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.4318 | 0.427661 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.0123 | 0.450704 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.1015 | 1.59764 | 0.798822 | − | 0.601568i | \(-0.205457\pi\) | ||||
0.798822 | + | 0.601568i | \(0.205457\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.7034 | −0.926093 | −0.463046 | − | 0.886334i | \(-0.653244\pi\) | ||||
−0.463046 | + | 0.886334i | \(0.653244\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.73622 | −0.192874 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.6568 | −0.921131 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.0805 | 1.34270 | 0.671348 | − | 0.741142i | \(-0.265716\pi\) | ||||
0.671348 | + | 0.741142i | \(0.265716\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 16.6365 | 0.674147 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −23.6107 | −0.955189 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.34105 | −0.134944 | −0.0674719 | − | 0.997721i | \(-0.521493\pi\) | ||||
−0.0674719 | + | 0.997721i | \(0.521493\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.248812 | 0.0100331 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.4996 | −0.583731 | −0.291866 | − | 0.956459i | \(-0.594276\pi\) | ||||
−0.291866 | + | 0.956459i | \(0.594276\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.7308 | 1.67730 | 0.838652 | − | 0.544668i | \(-0.183344\pi\) | ||||
0.838652 | + | 0.544668i | \(0.183344\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.04298 | −0.162239 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.9088 | 0.557243 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.60768 | 0.224307 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −46.8756 | −1.87203 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.15596 | −0.325199 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.8326 | 0.988569 | 0.494285 | − | 0.869300i | \(-0.335430\pi\) | ||||
0.494285 | + | 0.869300i | \(0.335430\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −25.8916 | −1.02910 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.52995 | 0.140082 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.1964 | 0.720967 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.89736 | 0.272855 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.2163 | −1.03548 | −0.517742 | − | 0.855537i | \(-0.673227\pi\) | ||||
−0.517742 | + | 0.855537i | \(0.673227\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.5950 | 0.930495 | 0.465247 | − | 0.885181i | \(-0.345965\pi\) | ||||
0.465247 | + | 0.885181i | \(0.345965\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.32224 | −0.288313 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.6851 | −0.420074 | −0.210037 | − | 0.977693i | \(-0.567358\pi\) | ||||
−0.210037 | + | 0.977693i | \(0.567358\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 73.7742 | 2.89589 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.165309 | 0.00647899 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20.4734 | −0.801188 | −0.400594 | − | 0.916256i | \(-0.631196\pi\) | ||||
−0.400594 | + | 0.916256i | \(0.631196\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.7893 | −0.812305 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.90100 | 0.113179 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.85694 | −0.306063 | −0.153031 | − | 0.988221i | \(-0.548904\pi\) | ||||
−0.153031 | + | 0.988221i | \(0.548904\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.7399 | 0.495525 | 0.247762 | − | 0.968821i | \(-0.420305\pi\) | ||||
0.247762 | + | 0.968821i | \(0.420305\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.2190 | 0.901752 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 18.1465 | 0.703691 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 37.9491 | 1.46940 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.7188 | 0.801033 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −54.2377 | −2.09382 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.3912 | 0.400552 | 0.200276 | − | 0.979740i | \(-0.435816\pi\) | ||||
0.200276 | + | 0.979740i | \(0.435816\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.57105 | 0.137450 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.74331 | 0.259166 | 0.129583 | − | 0.991569i | \(-0.458636\pi\) | ||||
0.129583 | + | 0.991569i | \(0.458636\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.4889 | −0.402528 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.9100 | −0.839594 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.1693 | 1.03960 | 0.519802 | − | 0.854287i | \(-0.326006\pi\) | ||||
0.519802 | + | 0.854287i | \(0.326006\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.9746 | −0.839608 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.3308 | −0.699363 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 42.4383 | 1.61677 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.0429 | 0.572258 | 0.286129 | − | 0.958191i | \(-0.407631\pi\) | ||||
0.286129 | + | 0.958191i | \(0.407631\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.70033 | −0.368485 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.1000 | −0.383116 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.02483 | 0.0388181 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.98209 | 0.0749695 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.8197 | −1.69282 | −0.846409 | − | 0.532534i | \(-0.821240\pi\) | ||||
−0.846409 | + | 0.532534i | \(0.821240\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.1876 | −0.535097 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.98496 | 0.225407 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.06120 | 0.0775195 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.2478 | −0.422421 | −0.211211 | − | 0.977441i | \(-0.567741\pi\) | ||||
−0.211211 | + | 0.977441i | \(0.567741\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.36024 | −0.0885160 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.377082 | 0.0141218 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 30.8524 | 1.15382 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 23.2205 | 0.867185 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.9546 | −0.818769 | −0.409385 | − | 0.912362i | \(-0.634257\pi\) | ||||
−0.409385 | + | 0.912362i | \(0.634257\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.7990 | −0.476658 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.7187 | −0.398632 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −33.5194 | −1.24488 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −45.2750 | −1.67916 | −0.839579 | − | 0.543238i | \(-0.817198\pi\) | ||||
−0.839579 | + | 0.543238i | \(0.817198\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.1594 | −1.11549 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.84016 | −0.178775 | −0.0893876 | − | 0.995997i | \(-0.528491\pi\) | ||||
−0.0893876 | + | 0.995997i | \(0.528491\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.61250 | −0.170135 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.9213 | −0.954822 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.1540 | −0.778163 | −0.389081 | − | 0.921203i | \(-0.627208\pi\) | ||||
−0.389081 | + | 0.921203i | \(0.627208\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 40.3905 | 1.48378 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.9429 | −0.768320 | −0.384160 | − | 0.923267i | \(-0.625509\pi\) | ||||
−0.384160 | + | 0.923267i | \(0.625509\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.7091 | 0.538898 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.8094 | −0.578434 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.5222 | 0.567170 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.2708 | 0.776184 | 0.388092 | − | 0.921621i | \(-0.373134\pi\) | ||||
0.388092 | + | 0.921621i | \(0.373134\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.4880 | −0.455086 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.68852 | 0.279814 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.7271 | −1.26218 | −0.631089 | − | 0.775710i | \(-0.717392\pi\) | ||||
−0.631089 | + | 0.775710i | \(0.717392\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −22.1271 | −0.803164 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35.2988 | −1.27958 | −0.639789 | − | 0.768550i | \(-0.720978\pi\) | ||||
−0.639789 | + | 0.768550i | \(0.720978\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.2499 | −0.371070 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.88566 | −0.212797 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −63.5678 | −2.29530 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −48.1317 | −1.73567 | −0.867837 | − | 0.496849i | \(-0.834490\pi\) | ||||
−0.867837 | + | 0.496849i | \(0.834490\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.7839 | 0.424387 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.0122 | −0.396080 | −0.198040 | − | 0.980194i | \(-0.563458\pi\) | ||||
−0.198040 | + | 0.980194i | \(0.563458\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.333067 | −0.0119641 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.93596 | −0.105327 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.78273 | 0.0638730 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 37.7491 | 1.35077 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.38643 | −0.335444 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.89773 | −0.174807 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.1662 | −0.754495 | −0.377248 | − | 0.926112i | \(-0.623129\pi\) | ||||
−0.377248 | + | 0.926112i | \(0.623129\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.92203 | −0.246431 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.52984 | 0.196618 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 46.7341 | 1.65958 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.7575 | −0.381528 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.97801 | 0.105486 | 0.0527432 | − | 0.998608i | \(-0.483204\pi\) | ||||
0.0527432 | + | 0.998608i | \(0.483204\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.6513 | 0.872100 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.84740 | −0.277274 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.8771 | 0.560292 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.56588 | 0.301907 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.7673 | −0.695842 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.95543 | 0.0687491 | 0.0343746 | − | 0.999409i | \(-0.489056\pi\) | ||||
0.0343746 | + | 0.999409i | \(0.489056\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.0091 | 0.527040 | 0.263520 | − | 0.964654i | \(-0.415116\pi\) | ||||
0.263520 | + | 0.964654i | \(0.415116\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.0726 | 0.984549 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.9105 | −0.452237 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −52.4636 | −1.83547 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.35833 | 0.292064 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.80545 | −0.0630107 | −0.0315053 | − | 0.999504i | \(-0.510030\pi\) | ||||
−0.0315053 | + | 0.999504i | \(0.510030\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 47.0093 | 1.63864 | 0.819321 | − | 0.573335i | \(-0.194351\pi\) | ||||
0.819321 | + | 0.573335i | \(0.194351\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 19.5443 | 0.680446 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 51.7029 | 1.79788 | 0.898942 | − | 0.438067i | \(-0.144337\pi\) | ||||
0.898942 | + | 0.438067i | \(0.144337\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.5559 | 0.748669 | 0.374334 | − | 0.927294i | \(-0.377871\pi\) | ||||
0.374334 | + | 0.927294i | \(0.377871\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.78055 | −0.339283 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.9983 | −0.658253 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.19539 | 0.0413680 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.0932685 | −0.00322383 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.1997 | 1.07713 | 0.538566 | − | 0.842583i | \(-0.318966\pi\) | ||||
0.538566 | + | 0.842583i | \(0.318966\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 59.1051 | 2.03811 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.42891 | −0.0836560 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.0441 | −0.379928 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −33.5933 | −1.15428 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.70418 | 0.264407 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.69713 | −0.229575 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.4350 | 1.14479 | 0.572397 | − | 0.819977i | \(-0.306014\pi\) | ||||
0.572397 | + | 0.819977i | \(0.306014\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.2384 | −0.350145 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.7565 | −0.777349 | −0.388674 | − | 0.921375i | \(-0.627067\pi\) | ||||
−0.388674 | + | 0.921375i | \(0.627067\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46.6685 | 1.59231 | 0.796154 | − | 0.605094i | \(-0.206864\pi\) | ||||
0.796154 | + | 0.605094i | \(0.206864\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.368915 | 0.0125726 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.56673 | −0.0533321 | −0.0266661 | − | 0.999644i | \(-0.508489\pi\) | ||||
−0.0266661 | + | 0.999644i | \(0.508489\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.92331 | −0.269401 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.24232 | −0.245962 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.9176 | −0.438199 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.3351 | 0.756798 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.91792 | 0.200291 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −18.1595 | −0.613904 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −49.6890 | −1.67788 | −0.838939 | − | 0.544225i | \(-0.816824\pi\) | ||||
−0.838939 | + | 0.544225i | \(0.816824\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.192909 | −0.00650665 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.5704 | −0.524580 | −0.262290 | − | 0.964989i | \(-0.584478\pi\) | ||||
−0.262290 | + | 0.964989i | \(0.584478\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48.1084 | −1.61898 | −0.809488 | − | 0.587136i | \(-0.800255\pi\) | ||||
−0.809488 | + | 0.587136i | \(0.800255\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16.1134 | 0.541647 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.74435 | 0.327183 | 0.163592 | − | 0.986528i | \(-0.447692\pi\) | ||||
0.163592 | + | 0.986528i | \(0.447692\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.23386 | 0.175538 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.47298 | 0.183352 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 42.8820 | 1.43499 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.82016 | −0.261399 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19.0659 | 0.636593 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.875458 | 0.0291982 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −44.3086 | −1.47613 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.8567 | −0.361289 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.90345 | 0.162996 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.915262 | −0.0303908 | −0.0151954 | − | 0.999885i | \(-0.504837\pi\) | ||||
−0.0151954 | + | 0.999885i | \(0.504837\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.16294 | −0.0385723 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.6329 | 0.849256 | 0.424628 | − | 0.905368i | \(-0.360405\pi\) | ||||
0.424628 | + | 0.905368i | \(0.360405\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −86.5244 | −2.86354 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.8464 | −0.391629 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −30.8244 | −1.01791 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.78251 | 0.223734 | 0.111867 | − | 0.993723i | \(-0.464317\pi\) | ||||
0.111867 | + | 0.993723i | \(0.464317\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.67881 | −0.154172 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −32.5267 | −1.07063 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.91540 | 0.194497 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.22124 | 0.237177 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 53.5883 | 1.75817 | 0.879087 | − | 0.476662i | \(-0.158153\pi\) | ||||
0.879087 | + | 0.476662i | \(0.158153\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −33.0484 | −1.08312 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.460674 | 0.0150818 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −32.2121 | −1.05345 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.20311 | 0.300653 | 0.150326 | − | 0.988636i | \(-0.451968\pi\) | ||||
0.150326 | + | 0.988636i | \(0.451968\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.0147 | −0.457352 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.3226 | 0.923290 | 0.461645 | − | 0.887065i | \(-0.347259\pi\) | ||||
0.461645 | + | 0.887065i | \(0.347259\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.841520 | 0.0274037 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.11871 | −0.0689215 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.4865 | 0.633226 | 0.316613 | − | 0.948555i | \(-0.397454\pi\) | ||||
0.316613 | + | 0.948555i | \(0.397454\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.6806 | −0.444091 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.70071 | 0.217285 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.1670 | 1.75464 | 0.877320 | − | 0.479905i | \(-0.159329\pi\) | ||||
0.877320 | + | 0.479905i | \(0.159329\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.49403 | −0.113064 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −51.3718 | −1.66061 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −32.5819 | −1.05212 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9913 | −0.999719 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.75773 | −0.282214 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.74072 | 0.216991 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.3548 | 1.32988 | 0.664941 | − | 0.746896i | \(-0.268457\pi\) | ||||
0.664941 | + | 0.746896i | \(0.268457\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −42.1706 | −1.35471 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.4978 | 1.20336 | 0.601681 | − | 0.798736i | \(-0.294498\pi\) | ||||
0.601681 | + | 0.798736i | \(0.294498\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.9753 | −0.480087 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −16.8404 | −0.539325 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −49.6720 | −1.58915 | −0.794574 | − | 0.607168i | \(-0.792306\pi\) | ||||
−0.794574 | + | 0.607168i | \(0.792306\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −42.9487 | −1.37265 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.78303 | 0.184638 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.92643 | 0.0933387 | 0.0466694 | − | 0.998910i | \(-0.485139\pi\) | ||||
0.0466694 | + | 0.998910i | \(0.485139\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.2294 | −0.612701 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.87392 | 0.282460 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24.7649 | −0.787479 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45.1038 | −1.43277 | −0.716385 | − | 0.697705i | \(-0.754204\pi\) | ||||
−0.716385 | + | 0.697705i | \(0.754204\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −22.2154 | −0.704985 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.1640 | 0.417326 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.6044 | 0.937581 | 0.468790 | − | 0.883309i | \(-0.344690\pi\) | ||||
0.468790 | + | 0.883309i | \(0.344690\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.65649 | 0.0524089 |
(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 | 8016.2.a.p.1.4 | 5 | ||
4.3 | odd | 2 | 501.2.a.b.1.1 | ✓ | 5 | ||
12.11 | even | 2 | 1503.2.a.d.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
501.2.a.b.1.1 | ✓ | 5 | 4.3 | odd | 2 | ||
1503.2.a.d.1.5 | 5 | 12.11 | even | 2 | |||
8016.2.a.p.1.4 | 5 | 1.1 | even | 1 | trivial |