Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, 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("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.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: | \(64.2636035467\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 9x^{8} + 14x^{7} + 27x^{6} - 27x^{5} - 34x^{4} + 14x^{3} + 17x^{2} + x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 503) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-0.858231\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-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 | ||||||||
\(3\) | 1.85823 | 1.07285 | 0.536425 | − | 0.843948i | \(-0.319774\pi\) | ||||
0.536425 | + | 0.843948i | \(0.319774\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.44291 | 0.645289 | 0.322644 | − | 0.946520i | \(-0.395428\pi\) | ||||
0.322644 | + | 0.946520i | \(0.395428\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.96509 | 0.742734 | 0.371367 | − | 0.928486i | \(-0.378889\pi\) | ||||
0.371367 | + | 0.928486i | \(0.378889\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.453023 | 0.151008 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.85614 | −0.861160 | −0.430580 | − | 0.902552i | \(-0.641691\pi\) | ||||
−0.430580 | + | 0.902552i | \(0.641691\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.84427 | −1.06621 | −0.533104 | − | 0.846050i | \(-0.678974\pi\) | ||||
−0.533104 | + | 0.846050i | \(0.678974\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.68126 | 0.692298 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.30329 | 0.316095 | 0.158047 | − | 0.987432i | \(-0.449480\pi\) | ||||
0.158047 | + | 0.987432i | \(0.449480\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.53196 | −0.810287 | −0.405143 | − | 0.914253i | \(-0.632778\pi\) | ||||
−0.405143 | + | 0.914253i | \(0.632778\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.65159 | 0.796842 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.20650 | −0.877115 | −0.438558 | − | 0.898703i | \(-0.644510\pi\) | ||||
−0.438558 | + | 0.898703i | \(0.644510\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.91801 | −0.583602 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.73287 | −0.910842 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.10402 | −0.205011 | −0.102506 | − | 0.994732i | \(-0.532686\pi\) | ||||
−0.102506 | + | 0.994732i | \(0.532686\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.53201 | 0.634368 | 0.317184 | − | 0.948364i | \(-0.397263\pi\) | ||||
0.317184 | + | 0.948364i | \(0.397263\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.30738 | −0.923896 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.83545 | 0.479278 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.61903 | −1.08816 | −0.544081 | − | 0.839033i | \(-0.683121\pi\) | ||||
−0.544081 | + | 0.839033i | \(0.683121\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.14353 | −1.14388 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.671095 | 0.104807 | 0.0524037 | − | 0.998626i | \(-0.483312\pi\) | ||||
0.0524037 | + | 0.998626i | \(0.483312\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.32289 | 0.659235 | 0.329617 | − | 0.944115i | \(-0.393080\pi\) | ||||
0.329617 | + | 0.944115i | \(0.393080\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.653672 | 0.0974436 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.378524 | 0.0552134 | 0.0276067 | − | 0.999619i | \(-0.491211\pi\) | ||||
0.0276067 | + | 0.999619i | \(0.491211\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.13843 | −0.448347 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.42182 | 0.339122 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.13700 | −0.980342 | −0.490171 | − | 0.871626i | \(-0.663066\pi\) | ||||
−0.490171 | + | 0.871626i | \(0.663066\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.12116 | −0.555697 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.56319 | −0.869316 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.8806 | 1.80709 | 0.903547 | − | 0.428489i | \(-0.140954\pi\) | ||||
0.903547 | + | 0.428489i | \(0.140954\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.51374 | −0.833999 | −0.417000 | − | 0.908907i | \(-0.636918\pi\) | ||||
−0.417000 | + | 0.908907i | \(0.636918\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.890231 | 0.112159 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.54693 | −0.688012 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.55189 | 0.922610 | 0.461305 | − | 0.887242i | \(-0.347381\pi\) | ||||
0.461305 | + | 0.887242i | \(0.347381\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.81664 | −0.941013 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.0744967 | −0.00884113 | −0.00442057 | − | 0.999990i | \(-0.501407\pi\) | ||||
−0.00442057 | + | 0.999990i | \(0.501407\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.29052 | 0.385126 | 0.192563 | − | 0.981285i | \(-0.438320\pi\) | ||||
0.192563 | + | 0.981285i | \(0.438320\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.42234 | −0.626118 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.61258 | −0.639612 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.57578 | −0.964850 | −0.482425 | − | 0.875937i | \(-0.660244\pi\) | ||||
−0.482425 | + | 0.875937i | \(0.660244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.1538 | −1.12820 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.8165 | −1.62632 | −0.813158 | − | 0.582042i | \(-0.802254\pi\) | ||||
−0.813158 | + | 0.582042i | \(0.802254\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.88053 | 0.203973 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.05152 | −0.219946 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.5415 | −1.85940 | −0.929700 | − | 0.368318i | \(-0.879934\pi\) | ||||
−0.929700 | + | 0.368318i | \(0.879934\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.55432 | −0.791908 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.56329 | 0.680582 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.09630 | −0.522869 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.01702 | −0.814005 | −0.407003 | − | 0.913427i | \(-0.633426\pi\) | ||||
−0.407003 | + | 0.913427i | \(0.633426\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.29390 | −0.130042 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.11148 | 0.906626 | 0.453313 | − | 0.891351i | \(-0.350242\pi\) | ||||
0.453313 | + | 0.891351i | \(0.350242\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.2943 | 1.50699 | 0.753494 | − | 0.657455i | \(-0.228367\pi\) | ||||
0.753494 | + | 0.657455i | \(0.228367\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.26891 | 0.514193 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.50420 | −0.338764 | −0.169382 | − | 0.985550i | \(-0.554177\pi\) | ||||
−0.169382 | + | 0.985550i | \(0.554177\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.49301 | 0.238787 | 0.119393 | − | 0.992847i | \(-0.461905\pi\) | ||||
0.119393 | + | 0.992847i | \(0.461905\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.2997 | −1.16743 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.5343 | −1.36727 | −0.683634 | − | 0.729825i | \(-0.739601\pi\) | ||||
−0.683634 | + | 0.729825i | \(0.739601\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.06959 | −0.565993 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.74154 | −0.161006 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.56109 | 0.234774 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.84244 | −0.258404 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.24705 | 0.112443 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.4250 | −1.02188 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.52702 | −0.490443 | −0.245222 | − | 0.969467i | \(-0.578861\pi\) | ||||
−0.245222 | + | 0.969467i | \(0.578861\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.03293 | 0.707260 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.2174 | 1.85377 | 0.926885 | − | 0.375346i | \(-0.122476\pi\) | ||||
0.926885 | + | 0.375346i | \(0.122476\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.94061 | −0.601827 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.82911 | −0.587756 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.6794 | 0.997835 | 0.498917 | − | 0.866650i | \(-0.333731\pi\) | ||||
0.498917 | + | 0.866650i | \(0.333731\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.8676 | 0.921778 | 0.460889 | − | 0.887458i | \(-0.347531\pi\) | ||||
0.460889 | + | 0.887458i | \(0.347531\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.703385 | 0.0592357 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.9798 | 0.918175 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.59300 | −0.132292 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.83192 | −0.481009 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.40209 | −0.606403 | −0.303202 | − | 0.952926i | \(-0.598056\pi\) | ||||
−0.303202 | + | 0.952926i | \(0.598056\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.09188 | −0.495750 | −0.247875 | − | 0.968792i | \(-0.579732\pi\) | ||||
−0.247875 | + | 0.968792i | \(0.579732\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.590422 | 0.0477328 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.09637 | 0.409350 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.22790 | 0.177806 | 0.0889028 | − | 0.996040i | \(-0.471664\pi\) | ||||
0.0889028 | + | 0.996040i | \(0.471664\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.2622 | −1.05176 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.26614 | −0.651463 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.7370 | 1.46759 | 0.733797 | − | 0.679368i | \(-0.237746\pi\) | ||||
0.733797 | + | 0.679368i | \(0.237746\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.65807 | −0.596180 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −22.7237 | −1.75841 | −0.879205 | − | 0.476443i | \(-0.841926\pi\) | ||||
−0.879205 | + | 0.476443i | \(0.841926\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.77838 | 0.136798 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.60006 | −0.122360 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.25141 | −0.171172 | −0.0855859 | − | 0.996331i | \(-0.527276\pi\) | ||||
−0.0855859 | + | 0.996331i | \(0.527276\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.73415 | −0.433461 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 25.7933 | 1.93874 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.8986 | −1.18832 | −0.594159 | − | 0.804348i | \(-0.702515\pi\) | ||||
−0.594159 | + | 0.804348i | \(0.702515\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.5942 | 1.23344 | 0.616718 | − | 0.787184i | \(-0.288462\pi\) | ||||
0.616718 | + | 0.787184i | \(0.288462\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.1040 | −0.894756 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.55066 | −0.702179 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.72239 | −0.272208 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.30051 | −0.676513 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.03640 | 0.147348 | 0.0736742 | − | 0.997282i | \(-0.476527\pi\) | ||||
0.0736742 | + | 0.997282i | \(0.476527\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.1384 | −1.08968 | −0.544841 | − | 0.838539i | \(-0.683410\pi\) | ||||
−0.544841 | + | 0.838539i | \(0.683410\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.3075 | −0.738134 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.01285 | −0.428398 | −0.214199 | − | 0.976790i | \(-0.568714\pi\) | ||||
−0.214199 | + | 0.976790i | \(0.568714\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.5513 | −1.66951 | −0.834753 | − | 0.550624i | \(-0.814390\pi\) | ||||
−0.834753 | + | 0.550624i | \(0.814390\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.0332 | 0.989823 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.16950 | −0.152269 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.968329 | 0.0676311 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.90564 | −0.132451 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.0878 | 0.697786 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.35555 | −0.162163 | −0.0810814 | − | 0.996707i | \(-0.525837\pi\) | ||||
−0.0810814 | + | 0.996707i | \(0.525837\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.138432 | −0.00948521 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.23754 | 0.425397 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.94071 | 0.471166 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.11455 | 0.413183 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.01020 | −0.337023 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.6268 | −0.912519 | −0.456260 | − | 0.889847i | \(-0.650811\pi\) | ||||
−0.456260 | + | 0.889847i | \(0.650811\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.32193 | −0.0881285 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.9812 | −0.795218 | −0.397609 | − | 0.917555i | \(-0.630160\pi\) | ||||
−0.397609 | + | 0.917555i | \(0.630160\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.2066 | 1.79786 | 0.898932 | − | 0.438087i | \(-0.144344\pi\) | ||||
0.898932 | + | 0.438087i | \(0.144344\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.4295 | −0.686208 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.4504 | 0.946679 | 0.473339 | − | 0.880880i | \(-0.343048\pi\) | ||||
0.473339 | + | 0.880880i | \(0.343048\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.546176 | 0.0356286 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.9358 | −1.03514 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.9361 | 1.54830 | 0.774148 | − | 0.633005i | \(-0.218179\pi\) | ||||
0.774148 | + | 0.633005i | \(0.218179\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.7734 | −0.887224 | −0.443612 | − | 0.896219i | \(-0.646303\pi\) | ||||
−0.443612 | + | 0.896219i | \(0.646303\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.66957 | −0.299553 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.52847 | −0.289313 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.5778 | 0.863934 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −27.5324 | −1.74479 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.26975 | 0.521982 | 0.260991 | − | 0.965341i | \(-0.415951\pi\) | ||||
0.260991 | + | 0.965341i | \(0.415951\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0144 | 0.755336 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.49447 | 0.218832 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.1486 | −1.25684 | −0.628418 | − | 0.777876i | \(-0.716297\pi\) | ||||
−0.628418 | + | 0.777876i | \(0.716297\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.0070 | −0.808214 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.500147 | −0.0309583 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 27.9229 | 1.72180 | 0.860900 | − | 0.508774i | \(-0.169901\pi\) | ||||
0.860900 | + | 0.508774i | \(0.169901\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.2980 | −0.632604 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −32.5962 | −1.99486 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.6165 | 0.708269 | 0.354135 | − | 0.935194i | \(-0.384775\pi\) | ||||
0.354135 | + | 0.935194i | \(0.384775\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.27787 | 0.199117 | 0.0995583 | − | 0.995032i | \(-0.468257\pi\) | ||||
0.0995583 | + | 0.995032i | \(0.468257\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −14.0377 | −0.849599 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.33426 | 0.502575 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.1157 | 0.607795 | 0.303897 | − | 0.952705i | \(-0.401712\pi\) | ||||
0.303897 | + | 0.952705i | \(0.401712\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.60008 | 0.0957944 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.7656 | 1.00015 | 0.500077 | − | 0.865981i | \(-0.333305\pi\) | ||||
0.500077 | + | 0.865981i | \(0.333305\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.4382 | −0.917705 | −0.458852 | − | 0.888513i | \(-0.651739\pi\) | ||||
−0.458852 | + | 0.888513i | \(0.651739\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.47010 | −0.560960 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.31876 | 0.0778440 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.3014 | −0.900084 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.8975 | −0.873306 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.52887 | −0.439841 | −0.219921 | − | 0.975518i | \(-0.570580\pi\) | ||||
−0.219921 | + | 0.975518i | \(0.570580\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.0284 | 1.16610 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.5178 | 0.784380 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.1709 | 0.935187 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.49487 | 0.489636 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.9312 | 0.972674 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.39874 | −0.538170 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.1932 | −0.981265 | −0.490632 | − | 0.871367i | \(-0.663234\pi\) | ||||
−0.490632 | + | 0.871367i | \(0.663234\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 28.4203 | 1.61677 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.1595 | −0.576094 | −0.288047 | − | 0.957616i | \(-0.593006\pi\) | ||||
−0.288047 | + | 0.957616i | \(0.593006\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.6909 | 1.50866 | 0.754329 | − | 0.656496i | \(-0.227962\pi\) | ||||
0.754329 | + | 0.656496i | \(0.227962\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.28452 | 0.0723746 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.3855 | 1.08880 | 0.544398 | − | 0.838827i | \(-0.316758\pi\) | ||||
0.544398 | + | 0.838827i | \(0.316758\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.15324 | 0.176548 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.51161 | −0.363443 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.60317 | −0.256127 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.2176 | 0.622241 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.63258 | 0.256182 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.743833 | 0.0410088 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.0579 | 1.43227 | 0.716135 | − | 0.697962i | \(-0.245910\pi\) | ||||
0.716135 | + | 0.697962i | \(0.245910\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.99857 | −0.164321 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.8967 | 0.595350 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.6240 | −0.633199 | −0.316600 | − | 0.948559i | \(-0.602541\pi\) | ||||
−0.316600 | + | 0.948559i | \(0.602541\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −27.0080 | −1.46687 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.0879 | −0.546292 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.9229 | −1.07574 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11.2787 | −0.607225 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.5102 | −1.31578 | −0.657888 | − | 0.753115i | \(-0.728550\pi\) | ||||
−0.657888 | + | 0.753115i | \(0.728550\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.6510 | 0.570133 | 0.285066 | − | 0.958508i | \(-0.407984\pi\) | ||||
0.285066 | + | 0.958508i | \(0.407984\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.1944 | 0.971146 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.04651 | 0.0557003 | 0.0278501 | − | 0.999612i | \(-0.491134\pi\) | ||||
0.0278501 | + | 0.999612i | \(0.491134\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.107492 | −0.00570508 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.75909 | 0.251878 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0194 | 1.26769 | 0.633847 | − | 0.773459i | \(-0.281475\pi\) | ||||
0.633847 | + | 0.773459i | \(0.281475\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.52528 | −0.343436 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.28191 | −0.277228 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.74793 | 0.248518 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.6963 | 0.975937 | 0.487969 | − | 0.872861i | \(-0.337738\pi\) | ||||
0.487969 | + | 0.872861i | \(0.337738\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.304022 | 0.0158267 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.0248 | −0.728133 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.3008 | −1.20647 | −0.603235 | − | 0.797564i | \(-0.706122\pi\) | ||||
−0.603235 | + | 0.797564i | \(0.706122\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −21.2302 | −1.09633 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.24415 | 0.218585 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.79951 | 0.503367 | 0.251683 | − | 0.967810i | \(-0.419016\pi\) | ||||
0.251683 | + | 0.967810i | \(0.419016\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.2705 | −0.526172 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.97295 | 0.100813 | 0.0504066 | − | 0.998729i | \(-0.483948\pi\) | ||||
0.0504066 | + | 0.998729i | \(0.483948\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.09844 | −0.412735 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.95837 | 0.0995496 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.61202 | −0.335243 | −0.167621 | − | 0.985851i | \(-0.553609\pi\) | ||||
−0.167621 | + | 0.985851i | \(0.553609\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.48230 | −0.277252 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 39.4268 | 1.98882 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.3741 | −0.622607 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.61750 | −0.382311 | −0.191156 | − | 0.981560i | \(-0.561224\pi\) | ||||
−0.191156 | + | 0.981560i | \(0.561224\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.8973 | −0.645670 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.8162 | 1.28920 | 0.644601 | − | 0.764519i | \(-0.277024\pi\) | ||||
0.644601 | + | 0.764519i | \(0.277024\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.5780 | −0.676368 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −14.6511 | −0.728018 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.9049 | 0.937081 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.6924 | −0.677044 | −0.338522 | − | 0.940958i | \(-0.609927\pi\) | ||||
−0.338522 | + | 0.940958i | \(0.609927\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.7029 | 1.07053 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 27.2765 | 1.34219 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21.3788 | −1.04944 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.1945 | 0.988930 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.0027 | −1.17261 | −0.586305 | − | 0.810091i | \(-0.699418\pi\) | ||||
−0.586305 | + | 0.810091i | \(0.699418\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.1293 | 1.51715 | 0.758573 | − | 0.651588i | \(-0.225897\pi\) | ||||
0.758573 | + | 0.651588i | \(0.225897\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.171480 | 0.00833765 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.80302 | −0.184474 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.8001 | −0.619439 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 20.4030 | 0.985064 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.0585 | −1.35153 | −0.675766 | − | 0.737116i | \(-0.736187\pi\) | ||||
−0.675766 | + | 0.737116i | \(0.736187\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.6011 | −0.990026 | −0.495013 | − | 0.868886i | \(-0.664837\pi\) | ||||
−0.495013 | + | 0.868886i | \(0.664837\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.96016 | −0.141929 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14.8572 | 0.710715 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 36.4050 | 1.73752 | 0.868758 | − | 0.495238i | \(-0.164919\pi\) | ||||
0.868758 | + | 0.495238i | \(0.164919\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.42178 | −0.0677038 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.1192 | 1.33598 | 0.667992 | − | 0.744169i | \(-0.267154\pi\) | ||||
0.667992 | + | 0.744169i | \(0.267154\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25.3109 | −1.19985 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.7548 | −0.650580 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.9493 | −0.611116 | −0.305558 | − | 0.952173i | \(-0.598843\pi\) | ||||
−0.305558 | + | 0.952173i | \(0.598843\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.91674 | −0.0902559 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.3201 | −0.531866 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.9002 | −0.511010 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.149626 | 0.00699919 | 0.00349960 | − | 0.999994i | \(-0.498886\pi\) | ||||
0.00349960 | + | 0.999994i | \(0.498886\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.16832 | −0.287912 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 38.9917 | 1.81603 | 0.908013 | − | 0.418942i | \(-0.137599\pi\) | ||||
0.908013 | + | 0.418942i | \(0.137599\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.1386 | 0.935918 | 0.467959 | − | 0.883750i | \(-0.344989\pi\) | ||||
0.467959 | + | 0.883750i | \(0.344989\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.47024 | 0.439172 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.8664 | −0.687936 | −0.343968 | − | 0.938981i | \(-0.611771\pi\) | ||||
−0.343968 | + | 0.938981i | \(0.611771\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.8401 | 0.685254 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.13995 | 0.190759 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.3468 | −0.567707 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.3063 | 0.472885 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.23322 | −0.148039 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.2515 | 1.61068 | 0.805342 | − | 0.592810i | \(-0.201982\pi\) | ||||
0.805342 | + | 0.592810i | \(0.201982\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.4453 | 1.16021 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −15.3604 | −0.698922 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.5678 | −0.525268 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.4362 | −1.24325 | −0.621626 | − | 0.783314i | \(-0.713528\pi\) | ||||
−0.621626 | + | 0.783314i | \(0.713528\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 34.8177 | 1.57451 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.83937 | 0.218398 | 0.109199 | − | 0.994020i | \(-0.465171\pi\) | ||||
0.109199 | + | 0.994020i | \(0.465171\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.43886 | −0.0648030 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.86698 | −0.0839145 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.146393 | −0.00656661 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.7739 | −0.750904 | −0.375452 | − | 0.926842i | \(-0.622512\pi\) | ||||
−0.375452 | + | 0.926842i | \(0.622512\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −42.2258 | −1.88651 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.1470 | 0.585036 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.30464 | 0.146764 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.5401 | −1.22069 | −0.610347 | − | 0.792134i | \(-0.708970\pi\) | ||||
−0.610347 | + | 0.792134i | \(0.708970\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.46617 | 0.286046 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 16.7163 | 0.738043 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.0682 | 0.972443 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.08112 | −0.0475475 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.18365 | −0.183642 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.7250 | 1.12703 | 0.563515 | − | 0.826106i | \(-0.309449\pi\) | ||||
0.563515 | + | 0.826106i | \(0.309449\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.5746 | 1.29321 | 0.646605 | − | 0.762825i | \(-0.276188\pi\) | ||||
0.646605 | + | 0.762825i | \(0.276188\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −10.6554 | −0.465039 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.60324 | 0.200520 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.30539 | −0.230669 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.28821 | 0.272885 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.57987 | −0.111746 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.05624 | −0.218601 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −29.5433 | −1.27489 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.96380 | 0.386098 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.1889 | −0.567035 | −0.283517 | − | 0.958967i | \(-0.591501\pi\) | ||||
−0.283517 | + | 0.958967i | \(0.591501\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 30.8358 | 1.32329 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.59718 | 0.154086 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.9543 | 0.767673 | 0.383836 | − | 0.923401i | \(-0.374603\pi\) | ||||
0.383836 | + | 0.923401i | \(0.374603\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.95088 | −0.125940 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.89935 | 0.166118 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.8522 | −0.716627 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −17.7473 | −0.753332 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.47412 | 0.401431 | 0.200716 | − | 0.979650i | \(-0.435673\pi\) | ||||
0.200716 | + | 0.979650i | \(0.435673\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.6183 | −0.702881 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.91706 | −0.292039 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.2995 | 1.40341 | 0.701704 | − | 0.712469i | \(-0.252423\pi\) | ||||
0.701704 | + | 0.712469i | \(0.252423\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.9716 | −0.882283 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −19.9532 | −0.837955 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.8525 | −1.20956 | −0.604780 | − | 0.796393i | \(-0.706739\pi\) | ||||
−0.604780 | + | 0.796393i | \(0.706739\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.7379 | −0.951550 | −0.475775 | − | 0.879567i | \(-0.657832\pi\) | ||||
−0.475775 | + | 0.879567i | \(0.657832\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.78409 | 0.158083 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.2746 | 0.511886 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.60031 | −0.191513 | −0.0957567 | − | 0.995405i | \(-0.530527\pi\) | ||||
−0.0957567 | + | 0.995405i | \(0.530527\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −28.1306 | −1.16907 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −29.1156 | −1.20792 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.3843 | 0.844231 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.51289 | −0.103895 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −32.6537 | −1.34776 | −0.673881 | − | 0.738839i | \(-0.735374\pi\) | ||||
−0.673881 | + | 0.738839i | \(0.735374\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.4749 | −0.514020 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.1733 | −0.459607 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −36.4077 | −1.49509 | −0.747543 | − | 0.664214i | \(-0.768767\pi\) | ||||
−0.747543 | + | 0.664214i | \(0.768767\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.69542 | 0.151497 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −43.7637 | −1.79113 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.2375 | 1.64406 | 0.822031 | − | 0.569443i | \(-0.192841\pi\) | ||||
0.822031 | + | 0.569443i | \(0.192841\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.80257 | 0.359065 | 0.179532 | − | 0.983752i | \(-0.442542\pi\) | ||||
0.179532 | + | 0.983752i | \(0.442542\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.42118 | 0.139321 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.10139 | −0.166745 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.3824 | −0.543176 | −0.271588 | − | 0.962414i | \(-0.587549\pi\) | ||||
−0.271588 | + | 0.962414i | \(0.587549\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.03143 | −0.163362 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.45515 | −0.0588689 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.6160 | −0.630725 | −0.315363 | − | 0.948971i | \(-0.602126\pi\) | ||||
−0.315363 | + | 0.948971i | \(0.602126\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.79938 | 0.0725580 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.29634 | 0.172964 | 0.0864820 | − | 0.996253i | \(-0.472437\pi\) | ||||
0.0864820 | + | 0.996253i | \(0.472437\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.8380 | 0.435614 | 0.217807 | − | 0.975992i | \(-0.430110\pi\) | ||||
0.217807 | + | 0.975992i | \(0.430110\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 19.9088 | 0.798913 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −34.4707 | −1.38104 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.89515 | −0.0758062 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.7454 | 0.748620 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.62653 | −0.343962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.5073 | −1.17467 | −0.587334 | − | 0.809345i | \(-0.699822\pi\) | ||||
−0.587334 | + | 0.809345i | \(0.699822\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.37716 | −0.173976 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.97499 | −0.316478 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.0649 | 0.478031 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.0337487 | −0.00133508 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.72732 | 0.305211 | 0.152605 | − | 0.988287i | \(-0.451234\pi\) | ||||
0.152605 | + | 0.988287i | \(0.451234\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.0167 | −0.395021 | −0.197511 | − | 0.980301i | \(-0.563286\pi\) | ||||
−0.197511 | + | 0.980301i | \(0.563286\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.5908 | 0.456387 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.6884 | 0.538147 | 0.269074 | − | 0.963120i | \(-0.413282\pi\) | ||||
0.269074 | + | 0.963120i | \(0.413282\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −39.6449 | −1.55620 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.8974 | 0.505491 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.1399 | 1.49253 | 0.746264 | − | 0.665650i | \(-0.231845\pi\) | ||||
0.746264 | + | 0.665650i | \(0.231845\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 30.6147 | 1.19622 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.49068 | 0.0581571 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.5253 | −1.22805 | −0.614026 | − | 0.789286i | \(-0.710451\pi\) | ||||
−0.614026 | + | 0.789286i | \(0.710451\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.1122 | −1.17123 | −0.585614 | − | 0.810590i | \(-0.699146\pi\) | ||||
−0.585614 | + | 0.810590i | \(0.699146\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.31012 | −0.361575 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.0147 | −0.388352 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.64405 | 0.179818 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −25.3218 | −0.978996 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.6042 | 0.718207 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.7982 | −1.57265 | −0.786327 | − | 0.617810i | \(-0.788020\pi\) | ||||
−0.786327 | + | 0.617810i | \(0.788020\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13.8106 | 0.531569 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.18994 | 0.122599 | 0.0612997 | − | 0.998119i | \(-0.480475\pi\) | ||||
0.0612997 | + | 0.998119i | \(0.480475\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.7542 | −0.604589 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.2638 | −0.853150 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.0239 | −0.957512 | −0.478756 | − | 0.877948i | \(-0.658912\pi\) | ||||
−0.478756 | + | 0.877948i | \(0.658912\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.8523 | 0.643892 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 50.5562 | 1.92884 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 27.4365 | 1.04525 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.5349 | −1.38985 | −0.694927 | − | 0.719081i | \(-0.744563\pi\) | ||||
−0.694927 | + | 0.719081i | \(0.744563\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.54263 | −0.0965864 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.6810 | 0.594813 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.874633 | 0.0331291 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 26.8522 | 1.01564 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.6252 | 1.53439 | 0.767196 | − | 0.641413i | \(-0.221652\pi\) | ||||
0.767196 | + | 0.641413i | \(0.221652\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23.3781 | 0.881723 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.01492 | 0.0382241 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.9049 | 0.673382 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.3401 | −1.10189 | −0.550945 | − | 0.834542i | \(-0.685733\pi\) | ||||
−0.550945 | + | 0.834542i | \(0.685733\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.88503 | −0.145700 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14.8574 | −0.556414 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.8428 | 0.592488 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 44.4788 | 1.66109 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.69273 | 0.212303 | 0.106152 | − | 0.994350i | \(-0.466147\pi\) | ||||
0.106152 | + | 0.994350i | \(0.466147\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30.0546 | 1.11929 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25.5942 | −0.951858 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.22154 | 0.119645 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.4072 | −1.16483 | −0.582414 | − | 0.812892i | \(-0.697892\pi\) | ||||
−0.582414 | + | 0.812892i | \(0.697892\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.7844 | 0.806829 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.63399 | 0.208381 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 47.6365 | 1.75949 | 0.879747 | − | 0.475441i | \(-0.157712\pi\) | ||||
0.879747 | + | 0.475441i | \(0.157712\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.41494 | −0.310390 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21.5693 | −0.794515 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.88794 | −0.363734 | −0.181867 | − | 0.983323i | \(-0.558214\pi\) | ||||
−0.181867 | + | 0.983323i | \(0.558214\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25.2307 | 0.926871 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.7935 | −0.652782 | −0.326391 | − | 0.945235i | \(-0.605833\pi\) | ||||
−0.326391 | + | 0.945235i | \(0.605833\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.6806 | −0.391305 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.71220 | −0.245586 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.88606 | −0.251611 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.7934 | 1.59804 | 0.799022 | − | 0.601302i | \(-0.205351\pi\) | ||||
0.799022 | + | 0.601302i | \(0.205351\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.3671 | 0.560009 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.79003 | −0.319902 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.950190 | 0.0345353 | 0.0172676 | − | 0.999851i | \(-0.494503\pi\) | ||||
0.0172676 | + | 0.999851i | \(0.494503\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 22.3255 | 0.810363 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.00434 | −0.181407 | −0.0907035 | − | 0.995878i | \(-0.528912\pi\) | ||||
−0.0907035 | + | 0.995878i | \(0.528912\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.89898 | 0.177355 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.851925 | 0.0308014 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −53.3605 | −1.92674 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.5794 | 0.597870 | 0.298935 | − | 0.954274i | \(-0.403369\pi\) | ||||
0.298935 | + | 0.954274i | \(0.403369\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −37.4408 | −1.34840 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.4696 | −1.09592 | −0.547958 | − | 0.836506i | \(-0.684595\pi\) | ||||
−0.547958 | + | 0.836506i | \(0.684595\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.3064 | −0.370218 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −24.1700 | −0.867093 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.37028 | −0.0849240 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.212773 | 0.00761363 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.22518 | 0.186733 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.21465 | 0.114736 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.7903 | −1.06191 | −0.530954 | − | 0.847400i | \(-0.678166\pi\) | ||||
−0.530954 | + | 0.847400i | \(0.678166\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 51.8872 | 1.84723 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −28.5611 | −1.01552 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.0406 | 0.889216 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −19.1361 | −0.678689 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.503125 | 0.0178216 | 0.00891081 | − | 0.999960i | \(-0.497164\pi\) | ||||
0.00891081 | + | 0.999960i | \(0.497164\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.493327 | 0.0174527 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.94673 | −0.280784 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.39820 | −0.331655 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.9273 | −0.420382 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21.5861 | 0.759867 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.1371 | −0.743142 | −0.371571 | − | 0.928405i | \(-0.621181\pi\) | ||||
−0.371571 | + | 0.928405i | \(0.621181\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.7238 | −0.552139 | −0.276069 | − | 0.961138i | \(-0.589032\pi\) | ||||
−0.276069 | + | 0.961138i | \(0.589032\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.09105 | 0.213622 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 27.0358 | 0.947023 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.2683 | −0.534169 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.42228 | −0.119584 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.7588 | −1.49229 | −0.746147 | − | 0.665781i | \(-0.768098\pi\) | ||||
−0.746147 | + | 0.665781i | \(0.768098\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.2920 | 1.16049 | 0.580243 | − | 0.814444i | \(-0.302958\pi\) | ||||
0.580243 | + | 0.814444i | \(0.302958\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.4870 | 0.539188 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.2343 | −0.494975 | −0.247487 | − | 0.968891i | \(-0.579605\pi\) | ||||
−0.247487 | + | 0.968891i | \(0.579605\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.3766 | −0.429855 | −0.214928 | − | 0.976630i | \(-0.568952\pi\) | ||||
−0.214928 | + | 0.976630i | \(0.568952\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.7973 | 0.652073 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.09029 | −0.141720 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −32.7882 | −1.13468 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.7166 | −0.577809 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.6864 | −1.09394 | −0.546969 | − | 0.837153i | \(-0.684218\pi\) | ||||
−0.546969 | + | 0.837153i | \(0.684218\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.7811 | −0.957970 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 31.1544 | 1.07301 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.56604 | 0.0882745 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.58565 | −0.191925 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.6877 | −0.984560 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27.8429 | 0.954443 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.2234 | 1.03483 | 0.517416 | − | 0.855734i | \(-0.326894\pi\) | ||||
0.517416 | + | 0.855734i | \(0.326894\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.30874 | −0.0789573 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −31.4206 | −1.07331 | −0.536653 | − | 0.843803i | \(-0.680312\pi\) | ||||
−0.536653 | + | 0.843803i | \(0.680312\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.5866 | −0.941244 | −0.470622 | − | 0.882335i | \(-0.655970\pi\) | ||||
−0.470622 | + | 0.882335i | \(0.655970\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.45056 | 0.0835149 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −40.3690 | −1.37418 | −0.687088 | − | 0.726574i | \(-0.741111\pi\) | ||||
−0.687088 | + | 0.726574i | \(0.741111\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.24859 | −0.110455 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −28.4336 | −0.965655 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.4937 | 0.830890 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.0315 | −0.983694 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.63190 | −0.122921 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −22.4511 | −0.758985 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.330616 | −0.0111641 | −0.00558205 | − | 0.999984i | \(-0.501777\pi\) | ||||
−0.00558205 | + | 0.999984i | \(0.501777\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.9904 | −0.471884 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.51734 | −0.152193 | −0.0760965 | − | 0.997100i | \(-0.524246\pi\) | ||||
−0.0760965 | + | 0.997100i | \(0.524246\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46.7445 | 1.57308 | 0.786539 | − | 0.617540i | \(-0.211871\pi\) | ||||
0.786539 | + | 0.617540i | \(0.211871\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 37.2174 | 1.25105 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.29057 | 0.311947 | 0.155973 | − | 0.987761i | \(-0.450149\pi\) | ||||
0.155973 | + | 0.987761i | \(0.450149\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.8611 | −0.364269 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 29.0008 | 0.971564 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.33693 | −0.0447387 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.9403 | −0.766808 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 30.0492 | 1.00332 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.89941 | −0.130053 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.30159 | −0.309881 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15.7854 | 0.525306 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 23.9439 | 0.795923 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.0423 | 0.798313 | 0.399156 | − | 0.916883i | \(-0.369303\pi\) | ||||
0.399156 | + | 0.916883i | \(0.369303\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.12771 | 0.136908 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.04735 | −0.200358 | −0.100179 | − | 0.994969i | \(-0.531941\pi\) | ||||
−0.100179 | + | 0.994969i | \(0.531941\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42.3179 | 1.40052 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −17.4650 | −0.577376 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 41.6940 | 1.37686 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.8990 | 1.15121 | 0.575606 | − | 0.817727i | \(-0.304766\pi\) | ||||
0.575606 | + | 0.817727i | \(0.304766\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31.9488 | −1.05275 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.286385 | 0.00942648 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.3144 | 0.635054 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.92866 | 0.227567 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.8343 | 1.30692 | 0.653460 | − | 0.756961i | \(-0.273317\pi\) | ||||
0.653460 | + | 0.756961i | \(0.273317\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.0848 | 0.363289 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.8788 | −0.618063 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.37108 | −0.175653 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.6822 | 0.348971 | 0.174485 | − | 0.984660i | \(-0.444174\pi\) | ||||
0.174485 | + | 0.984660i | \(0.444174\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 49.5978 | 1.61856 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.40329 | −0.0457459 | −0.0228729 | − | 0.999738i | \(-0.507281\pi\) | ||||
−0.0228729 | + | 0.999738i | \(0.507281\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.82296 | −0.0919281 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.4198 | −0.436546 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.93625 | −0.322885 | −0.161442 | − | 0.986882i | \(-0.551615\pi\) | ||||
−0.161442 | + | 0.986882i | \(0.551615\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.6496 | −0.410625 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 36.0227 | 1.16812 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.4560 | 0.371097 | 0.185548 | − | 0.982635i | \(-0.440594\pi\) | ||||
0.185548 | + | 0.982635i | \(0.440594\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.93834 | 0.0950823 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.85945 | 0.189409 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.9510 | 0.741126 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.5249 | −0.597578 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.58748 | −0.0511560 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21.8433 | −0.703160 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.0337 | 1.03014 | 0.515068 | − | 0.857150i | \(-0.327767\pi\) | ||||
0.515068 | + | 0.857150i | \(0.327767\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.55376 | −0.274786 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.7771 | 0.698859 | 0.349429 | − | 0.936963i | \(-0.386375\pi\) | ||||
0.349429 | + | 0.936963i | \(0.386375\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.3558 | 0.684636 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 20.8449 | 0.667572 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48.8640 | 1.56330 | 0.781649 | − | 0.623719i | \(-0.214379\pi\) | ||||
0.781649 | + | 0.623719i | \(0.214379\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 50.1012 | 1.60124 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.12939 | 0.0360586 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −43.9288 | −1.40111 | −0.700555 | − | 0.713598i | \(-0.747064\pi\) | ||||
−0.700555 | + | 0.713598i | \(0.747064\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.67600 | −0.276440 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.38221 | 0.0439963 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.1842 | −0.578225 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.0715 | −0.574060 | −0.287030 | − | 0.957922i | \(-0.592668\pi\) | ||||
−0.287030 | + | 0.957922i | \(0.592668\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 48.4215 | 1.53661 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −33.9824 | −1.07731 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.5966 | −1.15903 | −0.579514 | − | 0.814963i | \(-0.696757\pi\) | ||||
−0.579514 | + | 0.814963i | \(0.696757\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 31.3270 | 0.991143 |
(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 | 8048.2.a.p.1.8 | 10 | ||
4.3 | odd | 2 | 503.2.a.e.1.1 | ✓ | 10 | ||
12.11 | even | 2 | 4527.2.a.k.1.10 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
503.2.a.e.1.1 | ✓ | 10 | 4.3 | odd | 2 | ||
4527.2.a.k.1.10 | 10 | 12.11 | even | 2 | |||
8048.2.a.p.1.8 | 10 | 1.1 | even | 1 | trivial |