Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [608,2,Mod(1,608)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(608, 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("608.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 608 = 2^{5} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 608.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: | \(4.85490444289\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.15317.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 5x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.69353\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 608.1 |
$q$-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 | ||||||||
\(3\) | −2.56155 | −1.47891 | −0.739457 | − | 0.673204i | \(-0.764917\pi\) | ||||
−0.739457 | + | 0.673204i | \(0.764917\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.20608 | −1.88102 | −0.940508 | − | 0.339770i | \(-0.889651\pi\) | ||||
−0.940508 | + | 0.339770i | \(0.889651\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.74252 | −0.658611 | −0.329306 | − | 0.944223i | \(-0.606815\pi\) | ||||
−0.329306 | + | 0.944223i | \(0.606815\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.56155 | 1.18718 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.20608 | −1.87120 | −0.935602 | − | 0.353056i | \(-0.885142\pi\) | ||||
−0.935602 | + | 0.353056i | \(0.885142\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.82550 | 1.33835 | 0.669176 | − | 0.743104i | \(-0.266647\pi\) | ||||
0.669176 | + | 0.743104i | \(0.266647\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10.7741 | 2.78186 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.12957 | −1.24410 | −0.622052 | − | 0.782976i | \(-0.713701\pi\) | ||||
−0.622052 | + | 0.782976i | \(0.713701\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.46356 | 0.974029 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.463560 | −0.0966590 | −0.0483295 | − | 0.998831i | \(-0.515390\pi\) | ||||
−0.0483295 | + | 0.998831i | \(0.515390\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.6911 | 2.53822 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.43845 | −0.276829 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.82550 | 0.896072 | 0.448036 | − | 0.894015i | \(-0.352124\pi\) | ||||
0.448036 | + | 0.894015i | \(0.352124\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.63806 | 0.294205 | 0.147102 | − | 0.989121i | \(-0.453005\pi\) | ||||
0.147102 | + | 0.989121i | \(0.453005\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 15.8972 | 2.76735 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.32919 | 1.23886 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.63806 | 0.598094 | 0.299047 | − | 0.954238i | \(-0.403331\pi\) | ||||
0.299047 | + | 0.954238i | \(0.403331\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.3608 | −1.97931 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.28906 | −0.826012 | −0.413006 | − | 0.910728i | \(-0.635521\pi\) | ||||
−0.413006 | + | 0.910728i | \(0.635521\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.08298 | −0.165152 | −0.0825762 | − | 0.996585i | \(-0.526315\pi\) | ||||
−0.0825762 | + | 0.996585i | \(0.526315\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −14.9802 | −2.23311 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.555087 | 0.0809677 | 0.0404839 | − | 0.999180i | \(-0.487110\pi\) | ||||
0.0404839 | + | 0.999180i | \(0.487110\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.96362 | −0.566231 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13.1397 | 1.83992 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.65955 | 0.365317 | 0.182658 | − | 0.983176i | \(-0.441530\pi\) | ||||
0.182658 | + | 0.983176i | \(0.441530\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 26.1033 | 3.51977 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.56155 | 0.339286 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.85061 | 0.240929 | 0.120465 | − | 0.992718i | \(-0.461562\pi\) | ||||
0.120465 | + | 0.992718i | \(0.461562\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.32919 | −1.19448 | −0.597240 | − | 0.802063i | \(-0.703736\pi\) | ||||
−0.597240 | + | 0.802063i | \(0.703736\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.20608 | −0.781893 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −20.2964 | −2.51746 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.72751 | −0.577557 | −0.288778 | − | 0.957396i | \(-0.593249\pi\) | ||||
−0.288778 | + | 0.957396i | \(0.593249\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.18743 | 0.142950 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.4850 | 1.36302 | 0.681512 | − | 0.731807i | \(-0.261323\pi\) | ||||
0.681512 | + | 0.731807i | \(0.261323\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.00646614 | −0.000756804 0 | −0.000378402 | − | 1.00000i | \(-0.500120\pi\) | ||||
−0.000378402 | 1.00000i | \(0.500120\pi\) | ||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −32.5090 | −3.75381 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.8142 | 1.23240 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.76117 | −0.760691 | −0.380345 | − | 0.924844i | \(-0.624195\pi\) | ||||
−0.380345 | + | 0.924844i | \(0.624195\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.8972 | 1.30589 | 0.652944 | − | 0.757406i | \(-0.273534\pi\) | ||||
0.652944 | + | 0.757406i | \(0.273534\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 21.5754 | 2.34018 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −12.3608 | −1.32521 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.31909 | −0.775822 | −0.387911 | − | 0.921697i | \(-0.626803\pi\) | ||||
−0.387911 | + | 0.921697i | \(0.626803\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.40853 | −0.881454 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.19598 | −0.435103 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.20608 | 0.431535 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.4122 | −1.05720 | −0.528598 | − | 0.848873i | \(-0.677282\pi\) | ||||
−0.528598 | + | 0.848873i | \(0.677282\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −22.1033 | −2.22146 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.246211 | 0.0244989 | 0.0122495 | − | 0.999925i | \(-0.496101\pi\) | ||||
0.0122495 | + | 0.999925i | \(0.496101\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.710942 | −0.0700512 | −0.0350256 | − | 0.999386i | \(-0.511151\pi\) | ||||
−0.0350256 | + | 0.999386i | \(0.511151\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −18.7741 | −1.83216 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.6976 | 1.13085 | 0.565424 | − | 0.824800i | \(-0.308712\pi\) | ||||
0.565424 | + | 0.824800i | \(0.308712\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.99145 | −0.286529 | −0.143264 | − | 0.989684i | \(-0.545760\pi\) | ||||
−0.143264 | + | 0.989684i | \(0.545760\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.31909 | −0.884529 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.41216 | 0.603206 | 0.301603 | − | 0.953434i | \(-0.402478\pi\) | ||||
0.301603 | + | 0.953434i | \(0.402478\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.94977 | 0.181817 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 17.1863 | 1.58887 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.93839 | 0.819381 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 27.5155 | 2.50140 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.5482 | 1.22160 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −32.3495 | −2.89343 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.1434 | 1.60997 | 0.804984 | − | 0.593297i | \(-0.202174\pi\) | ||||
0.804984 | + | 0.593297i | \(0.202174\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.77410 | 0.244246 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.4652 | −1.08909 | −0.544546 | − | 0.838731i | \(-0.683298\pi\) | ||||
−0.544546 | + | 0.838731i | \(0.683298\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.74252 | 0.151096 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.05023 | 0.520721 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.41863 | 0.719252 | 0.359626 | − | 0.933097i | \(-0.382904\pi\) | ||||
0.359626 | + | 0.933097i | \(0.382904\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.3292 | −0.960929 | −0.480465 | − | 0.877014i | \(-0.659532\pi\) | ||||
−0.480465 | + | 0.877014i | \(0.659532\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.42188 | −0.119744 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −29.9474 | −2.50433 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20.2964 | −1.68553 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.1530 | 0.837407 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.321808 | −0.0263635 | −0.0131818 | − | 0.999913i | \(-0.504196\pi\) | ||||
−0.0131818 | + | 0.999913i | \(0.504196\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.95715 | 0.240650 | 0.120325 | − | 0.992735i | \(-0.461606\pi\) | ||||
0.120325 | + | 0.992735i | \(0.461606\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −18.2692 | −1.47698 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.88983 | −0.553404 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.52789 | 0.520982 | 0.260491 | − | 0.965476i | \(-0.416116\pi\) | ||||
0.260491 | + | 0.965476i | \(0.416116\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.81257 | −0.540272 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.807764 | 0.0636607 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.05023 | −0.160586 | −0.0802931 | − | 0.996771i | \(-0.525586\pi\) | ||||
−0.0802931 | + | 0.996771i | \(0.525586\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −66.8650 | −5.20543 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.2462 | 0.792876 | 0.396438 | − | 0.918062i | \(-0.370246\pi\) | ||||
0.396438 | + | 0.918062i | \(0.370246\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.2854 | 0.791187 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.56155 | −0.272359 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.05023 | 0.612047 | 0.306024 | − | 0.952024i | \(-0.401001\pi\) | ||||
0.306024 | + | 0.952024i | \(0.401001\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −22.1146 | −1.67170 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.74044 | −0.356313 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.75379 | −0.131084 | −0.0655422 | − | 0.997850i | \(-0.520878\pi\) | ||||
−0.0655422 | + | 0.997850i | \(0.520878\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.0203 | −0.819133 | −0.409567 | − | 0.912280i | \(-0.634320\pi\) | ||||
−0.409567 | + | 0.912280i | \(0.634320\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 23.8972 | 1.76653 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.3020 | −1.12502 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 31.8345 | 2.32797 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.50652 | 0.182323 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.2276 | 0.957113 | 0.478556 | − | 0.878057i | \(-0.341160\pi\) | ||||
0.478556 | + | 0.878057i | \(0.341160\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.47211 | 0.105965 | 0.0529824 | − | 0.998595i | \(-0.483127\pi\) | ||||
0.0529824 | + | 0.998595i | \(0.483127\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 51.9904 | 3.72311 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.84698 | 0.559074 | 0.279537 | − | 0.960135i | \(-0.409819\pi\) | ||||
0.279537 | + | 0.960135i | \(0.409819\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.8057 | 0.836882 | 0.418441 | − | 0.908244i | \(-0.362577\pi\) | ||||
0.418441 | + | 0.908244i | \(0.362577\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.1098 | 0.854156 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.40853 | −0.590163 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 22.2462 | 1.55374 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.65100 | −0.114752 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.20608 | 0.429284 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.5745 | 1.00335 | 0.501674 | − | 0.865056i | \(-0.332718\pi\) | ||||
0.501674 | + | 0.865056i | \(0.332718\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −29.4195 | −2.01579 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.55509 | 0.310654 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.85436 | −0.193767 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.0165634 | 0.00111925 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.7527 | −1.66505 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.6713 | −1.78604 | −0.893021 | − | 0.450014i | \(-0.851419\pi\) | ||||
−0.893021 | + | 0.450014i | \(0.851419\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 45.2001 | 3.01334 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.01656 | 0.266589 | 0.133294 | − | 0.991076i | \(-0.457444\pi\) | ||||
0.133294 | + | 0.991076i | \(0.457444\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.1834 | 1.53200 | 0.766002 | − | 0.642838i | \(-0.222243\pi\) | ||||
0.766002 | + | 0.642838i | \(0.222243\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −27.7012 | −1.82261 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.2692 | 1.45891 | 0.729453 | − | 0.684031i | \(-0.239775\pi\) | ||||
0.729453 | + | 0.684031i | \(0.239775\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.33474 | −0.152302 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 17.3191 | 1.12500 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.0818 | 1.49304 | 0.746519 | − | 0.665364i | \(-0.231724\pi\) | ||||
0.746519 | + | 0.665364i | \(0.231724\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.565184 | −0.0364067 | −0.0182033 | − | 0.999834i | \(-0.505795\pi\) | ||||
−0.0182033 | + | 0.999834i | \(0.505795\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.2462 | 1.42710 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 16.6713 | 1.06509 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.82550 | −0.307039 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −30.4753 | −1.93130 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.8441 | −1.00007 | −0.500037 | − | 0.866004i | \(-0.666680\pi\) | ||||
−0.500037 | + | 0.866004i | \(0.666680\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.87689 | 0.180869 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −55.2665 | −3.46092 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.0632 | 0.752479 | 0.376240 | − | 0.926522i | \(-0.377217\pi\) | ||||
0.376240 | + | 0.926522i | \(0.377217\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.33940 | −0.393911 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.1863 | 1.06380 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.2135 | −1.43140 | −0.715702 | − | 0.698406i | \(-0.753893\pi\) | ||||
−0.715702 | + | 0.698406i | \(0.753893\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.1863 | −0.687167 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.7482 | 1.14737 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.2964 | 1.60332 | 0.801661 | − | 0.597779i | \(-0.203950\pi\) | ||||
0.801661 | + | 0.597779i | \(0.203950\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.9560 | −0.787020 | −0.393510 | − | 0.919320i | \(-0.628739\pi\) | ||||
−0.393510 | + | 0.919320i | \(0.628739\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 21.5389 | 1.30359 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −78.7622 | −4.74954 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.8645 | −0.652782 | −0.326391 | − | 0.945235i | \(-0.605833\pi\) | ||||
−0.326391 | + | 0.945235i | \(0.605833\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.83405 | 0.349275 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.8470 | −0.945352 | −0.472676 | − | 0.881236i | \(-0.656712\pi\) | ||||
−0.472676 | + | 0.881236i | \(0.656712\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.6740 | 1.64505 | 0.822525 | − | 0.568729i | \(-0.192565\pi\) | ||||
0.822525 | + | 0.568729i | \(0.192565\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.7741 | −0.638203 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.21630 | 0.544021 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.31251 | 0.547795 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 26.6713 | 1.56350 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.3179 | −1.24541 | −0.622703 | − | 0.782458i | \(-0.713966\pi\) | ||||
−0.622703 | + | 0.782458i | \(0.713966\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.78382 | −0.453192 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.92712 | 0.518004 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.23691 | −0.129364 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.88711 | 0.108771 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.630683 | −0.0362318 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 39.2393 | 2.24684 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.6584 | 1.52147 | 0.760737 | − | 0.649060i | \(-0.224838\pi\) | ||||
0.760737 | + | 0.649060i | \(0.224838\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.82112 | 0.103600 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.0690 | −1.13801 | −0.569004 | − | 0.822335i | \(-0.692671\pi\) | ||||
−0.569004 | + | 0.822335i | \(0.692671\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.1397 | −0.629651 | −0.314826 | − | 0.949150i | \(-0.601946\pi\) | ||||
−0.314826 | + | 0.949150i | \(0.601946\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 26.1033 | 1.47075 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 33.1349 | 1.86104 | 0.930520 | − | 0.366242i | \(-0.119356\pi\) | ||||
0.930520 | + | 0.366242i | \(0.119356\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −29.9474 | −1.67673 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −29.9640 | −1.67243 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.12957 | 0.285417 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 61.2410 | 3.39704 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.66276 | 0.423751 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.967250 | −0.0533262 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.30241 | −0.236482 | −0.118241 | − | 0.992985i | \(-0.537726\pi\) | ||||
−0.118241 | + | 0.992985i | \(0.537726\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.9572 | 0.710048 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 19.8843 | 1.08639 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 31.3393 | 1.70716 | 0.853580 | − | 0.520962i | \(-0.174427\pi\) | ||||
0.853580 | + | 0.520962i | \(0.174427\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.4251 | −0.892089 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.1660 | −0.550517 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.1043 | 1.03154 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.99445 | −0.268892 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.6782 | 1.16375 | 0.581873 | − | 0.813280i | \(-0.302320\pi\) | ||||
0.581873 | + | 0.813280i | \(0.302320\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.50486 | 0.241140 | 0.120570 | − | 0.992705i | \(-0.461528\pi\) | ||||
0.120570 | + | 0.992705i | \(0.461528\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.94122 | −0.370495 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.4158 | −1.19307 | −0.596536 | − | 0.802586i | \(-0.703457\pi\) | ||||
−0.596536 | + | 0.802586i | \(0.703457\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −48.3070 | −2.56387 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −22.8962 | −1.21179 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.4940 | −0.606629 | −0.303314 | − | 0.952891i | \(-0.598093\pi\) | ||||
−0.303314 | + | 0.952891i | \(0.598093\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −70.4823 | −3.69936 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.0271971 | 0.00142356 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.7944 | 1.03326 | 0.516630 | − | 0.856209i | \(-0.327186\pi\) | ||||
0.516630 | + | 0.856209i | \(0.327186\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −18.8373 | −0.980629 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.63431 | −0.240602 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.6199 | −0.860546 | −0.430273 | − | 0.902699i | \(-0.641583\pi\) | ||||
−0.430273 | + | 0.902699i | \(0.641583\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 82.8650 | 4.27913 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23.2854 | 1.19926 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.3956 | −0.842185 | −0.421093 | − | 0.907018i | \(-0.638353\pi\) | ||||
−0.421093 | + | 0.907018i | \(0.638353\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −46.4753 | −2.38100 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30.6915 | 1.56826 | 0.784131 | − | 0.620595i | \(-0.213109\pi\) | ||||
0.784131 | + | 0.620595i | \(0.213109\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −45.4855 | −2.31816 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.85708 | −0.196066 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.24905 | −0.114031 | −0.0570156 | − | 0.998373i | \(-0.518158\pi\) | ||||
−0.0570156 | + | 0.998373i | \(0.518158\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.37787 | 0.120254 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 31.9303 | 1.61067 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 28.4380 | 1.43087 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.12582 | −0.207069 | −0.103535 | − | 0.994626i | \(-0.533015\pi\) | ||||
−0.103535 | + | 0.994626i | \(0.533015\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.46356 | −0.223458 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.3992 | −1.11856 | −0.559282 | − | 0.828977i | \(-0.688923\pi\) | ||||
−0.559282 | + | 0.828977i | \(0.688923\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.90447 | 0.393750 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 29.4426 | 1.46301 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −22.5781 | −1.11916 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.1992 | 0.652658 | 0.326329 | − | 0.945256i | \(-0.394188\pi\) | ||||
0.326329 | + | 0.945256i | \(0.394188\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −21.5648 | −1.06371 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.22473 | −0.158679 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −50.0406 | −2.45640 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 29.0203 | 1.42113 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.5984 | 1.54368 | 0.771842 | − | 0.635814i | \(-0.219336\pi\) | ||||
0.771842 | + | 0.635814i | \(0.219336\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.8587 | −1.26028 | −0.630139 | − | 0.776482i | \(-0.717002\pi\) | ||||
−0.630139 | + | 0.776482i | \(0.717002\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.97697 | 0.0961236 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −65.1000 | −3.15782 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.2563 | 0.786698 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 76.7119 | 3.70369 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.8972 | 1.53643 | 0.768217 | − | 0.640189i | \(-0.221144\pi\) | ||||
0.768217 | + | 0.640189i | \(0.221144\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.1006 | 1.11014 | 0.555071 | − | 0.831803i | \(-0.312691\pi\) | ||||
0.555071 | + | 0.831803i | \(0.312691\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 51.9904 | 2.49275 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.463560 | 0.0221751 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.7944 | −0.753826 | −0.376913 | − | 0.926249i | \(-0.623014\pi\) | ||||
−0.376913 | + | 0.926249i | \(0.623014\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.1166 | −0.672221 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −40.5584 | −1.92699 | −0.963494 | − | 0.267729i | \(-0.913727\pi\) | ||||
−0.963494 | + | 0.267729i | \(0.913727\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 30.7847 | 1.45933 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.824327 | 0.0389893 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.4026 | −1.43479 | −0.717393 | − | 0.696669i | \(-0.754665\pi\) | ||||
−0.717393 | + | 0.696669i | \(0.754665\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.8243 | 1.54564 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.57490 | −0.355900 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 35.3670 | 1.65803 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.33516 | 0.0624561 | 0.0312280 | − | 0.999512i | \(-0.490058\pi\) | ||||
0.0312280 | + | 0.999512i | \(0.490058\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.37862 | 0.344404 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.0604 | −1.07403 | −0.537016 | − | 0.843572i | \(-0.680448\pi\) | ||||
−0.537016 | + | 0.843572i | \(0.680448\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.29916 | −0.432168 | −0.216084 | − | 0.976375i | \(-0.569329\pi\) | ||||
−0.216084 | + | 0.976375i | \(0.569329\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 17.6487 | 0.818437 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.8344 | 0.871553 | 0.435777 | − | 0.900055i | \(-0.356474\pi\) | ||||
0.435777 | + | 0.900055i | \(0.356474\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.23778 | 0.380385 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.7215 | −0.770488 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.72104 | 0.309034 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.6911 | −0.582309 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.47211 | 0.433698 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.9701 | −0.501236 | −0.250618 | − | 0.968086i | \(-0.580634\pi\) | ||||
−0.250618 | + | 0.968086i | \(0.580634\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.5555 | 0.800460 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.06913 | −0.0941487 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 43.7944 | 1.98860 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.3895 | −0.878623 | −0.439311 | − | 0.898335i | \(-0.644777\pi\) | ||||
−0.439311 | + | 0.898335i | \(0.644777\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.25176 | 0.237493 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.1562 | −1.49632 | −0.748160 | − | 0.663518i | \(-0.769062\pi\) | ||||
−0.748160 | + | 0.663518i | \(0.769062\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −24.7527 | −1.11481 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 92.9682 | 4.17861 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20.0129 | −0.897703 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.8814 | 1.15861 | 0.579306 | − | 0.815110i | \(-0.303324\pi\) | ||||
0.579306 | + | 0.815110i | \(0.303324\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −26.2462 | −1.17259 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.3178 | −0.460048 | −0.230024 | − | 0.973185i | \(-0.573880\pi\) | ||||
−0.230024 | + | 0.973185i | \(0.573880\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.03558 | −0.0460829 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −26.3467 | −1.17010 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.21618 | −0.275527 | −0.137764 | − | 0.990465i | \(-0.543991\pi\) | ||||
−0.137764 | + | 0.990465i | \(0.543991\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.0112674 | 0.000498440 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.43845 | 0.0635090 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.99028 | 0.131767 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.44491 | −0.151507 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.6211 | −0.905165 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.8917 | 1.00290 | 0.501451 | − | 0.865186i | \(-0.332800\pi\) | ||||
0.501451 | + | 0.865186i | \(0.332800\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.02628 | −0.394692 | −0.197346 | − | 0.980334i | \(-0.563232\pi\) | ||||
−0.197346 | + | 0.980334i | \(0.563232\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 56.6476 | 2.47230 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.40256 | −0.366021 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.7851 | −0.990657 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.59105 | 0.286027 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −25.5223 | −1.10550 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −49.2010 | −2.12715 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.49242 | 0.193862 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.5985 | 1.05953 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.2937 | −0.915489 | −0.457744 | − | 0.889084i | \(-0.651342\pi\) | ||||
−0.457744 | + | 0.889084i | \(0.651342\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 28.2291 | 1.21143 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.5823 | 0.538966 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.60803 | −0.154268 | −0.0771341 | − | 0.997021i | \(-0.524577\pi\) | ||||
−0.0771341 | + | 0.997021i | \(0.524577\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −33.2264 | −1.41807 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.82550 | −0.205573 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.7815 | 0.501000 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 39.1969 | 1.66381 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −34.8645 | −1.47725 | −0.738627 | − | 0.674114i | \(-0.764526\pi\) | ||||
−0.738627 | + | 0.674114i | \(0.764526\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.22590 | −0.221032 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −81.5459 | −3.44287 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −41.3167 | −1.74129 | −0.870647 | − | 0.491909i | \(-0.836299\pi\) | ||||
−0.870647 | + | 0.491909i | \(0.836299\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −26.9701 | −1.13464 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12.1976 | 0.512253 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 41.0835 | 1.72231 | 0.861154 | − | 0.508344i | \(-0.169742\pi\) | ||||
0.861154 | + | 0.508344i | \(0.169742\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.8243 | 1.54105 | 0.770525 | − | 0.637410i | \(-0.219994\pi\) | ||||
0.770525 | + | 0.637410i | \(0.219994\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −33.8831 | −1.41549 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.88310 | −0.245342 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.7004 | 0.653617 | 0.326809 | − | 0.945091i | \(-0.394027\pi\) | ||||
0.326809 | + | 0.945091i | \(0.394027\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.77089 | −0.156713 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.7311 | −0.860072 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.5054 | −0.683582 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −72.2868 | −2.98869 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −34.3099 | −1.41612 | −0.708060 | − | 0.706152i | \(-0.750429\pi\) | ||||
−0.708060 | + | 0.706152i | \(0.750429\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.63806 | −0.0674952 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.1005 | −0.826822 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.11584 | 0.292213 | 0.146106 | − | 0.989269i | \(-0.453326\pi\) | ||||
0.146106 | + | 0.989269i | \(0.453326\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −37.5956 | −1.54127 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −30.2409 | −1.23768 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.8340 | 0.565244 | 0.282622 | − | 0.959231i | \(-0.408796\pi\) | ||||
0.282622 | + | 0.959231i | \(0.408796\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.2140 | 1.59957 | 0.799785 | − | 0.600286i | \(-0.204947\pi\) | ||||
0.799785 | + | 0.600286i | \(0.204947\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.8373 | −0.685666 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −115.732 | −4.70518 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.1733 | −1.42764 | −0.713821 | − | 0.700328i | \(-0.753037\pi\) | ||||
−0.713821 | + | 0.700328i | \(0.753037\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 21.5389 | 0.872800 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.67857 | 0.108363 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.24905 | 0.252397 | 0.126198 | − | 0.992005i | \(-0.459722\pi\) | ||||
0.126198 | + | 0.992005i | \(0.459722\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −56.9848 | −2.29785 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.0378 | −1.69238 | −0.846189 | − | 0.532883i | \(-0.821109\pi\) | ||||
−0.846189 | + | 0.532883i | \(0.821109\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.0633 | −1.24854 | −0.624269 | − | 0.781209i | \(-0.714603\pi\) | ||||
−0.624269 | + | 0.781209i | \(0.714603\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.666807 | 0.0267581 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.7537 | 0.510965 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 72.6090 | 2.90436 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −15.8972 | −0.634873 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.6617 | −0.744091 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.0378 | 1.59388 | 0.796940 | − | 0.604059i | \(-0.206451\pi\) | ||||
0.796940 | + | 0.604059i | \(0.206451\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −37.3333 | −1.48387 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −76.3127 | −3.02838 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.1264 | −0.757817 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 40.9046 | 1.61816 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.3619 | −0.804248 | −0.402124 | − | 0.915585i | \(-0.631728\pi\) | ||||
−0.402124 | + | 0.915585i | \(0.631728\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.7041 | −0.540435 | −0.270218 | − | 0.962799i | \(-0.587096\pi\) | ||||
−0.270218 | + | 0.962799i | \(0.587096\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.6681 | −0.459431 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −26.9588 | −1.05986 | −0.529930 | − | 0.848041i | \(-0.677782\pi\) | ||||
−0.529930 | + | 0.848041i | \(0.677782\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.4850 | −0.450827 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.31159 | 0.286564 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.7842 | 1.20468 | 0.602339 | − | 0.798240i | \(-0.294235\pi\) | ||||
0.602339 | + | 0.798240i | \(0.294235\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 52.4298 | 2.04860 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.0230295 | −0.000898466 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.57854 | −0.295218 | −0.147609 | − | 0.989046i | \(-0.547158\pi\) | ||||
−0.147609 | + | 0.989046i | \(0.547158\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 47.8191 | 1.85995 | 0.929974 | − | 0.367626i | \(-0.119829\pi\) | ||||
0.929974 | + | 0.367626i | \(0.119829\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 63.4054 | 2.46246 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.32919 | −0.284214 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.23691 | −0.0866135 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 68.3200 | 2.64140 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 57.8977 | 2.23512 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.2389 | 0.471777 | 0.235888 | − | 0.971780i | \(-0.424200\pi\) | ||||
0.235888 | + | 0.971780i | \(0.424200\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −18.2555 | −0.702655 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.3609 | 0.897832 | 0.448916 | − | 0.893574i | \(-0.351810\pi\) | ||||
0.448916 | + | 0.893574i | \(0.351810\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.1434 | 0.696280 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.2886 | −0.394262 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.7239 | −0.946033 | −0.473016 | − | 0.881054i | \(-0.656835\pi\) | ||||
−0.473016 | + | 0.881054i | \(0.656835\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −35.4094 | −1.35293 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −59.3856 | −2.26570 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.8336 | 0.488922 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.78837 | −0.258242 | −0.129121 | − | 0.991629i | \(-0.541215\pi\) | ||||
−0.129121 | + | 0.991629i | \(0.541215\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 38.5155 | 1.46308 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 47.6515 | 1.80752 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27.1306 | 1.02764 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −57.0438 | −2.15760 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.9175 | 1.01666 | 0.508330 | − | 0.861162i | \(-0.330263\pi\) | ||||
0.508330 | + | 0.861162i | \(0.330263\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.63806 | −0.137212 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.98056 | 0.225241 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.429028 | −0.0161353 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.5984 | −0.811146 | −0.405573 | − | 0.914063i | \(-0.632928\pi\) | ||||
−0.405573 | + | 0.914063i | \(0.632928\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −24.0803 | −0.903080 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.759341 | −0.0284376 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 125.961 | 4.71069 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −59.1253 | −2.20807 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.2575 | 0.830064 | 0.415032 | − | 0.909807i | \(-0.363770\pi\) | ||||
0.415032 | + | 0.909807i | \(0.363770\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.23883 | 0.0461365 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.44775 | 0.0538423 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 61.2410 | 2.27443 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 51.9118 | 1.92530 | 0.962651 | − | 0.270745i | \(-0.0872700\pi\) | ||||
0.962651 | + | 0.270745i | \(0.0872700\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −35.9848 | −1.33277 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.55520 | 0.205467 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.0575 | 0.740840 | 0.370420 | − | 0.928864i | \(-0.379214\pi\) | ||||
0.370420 | + | 0.928864i | \(0.379214\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −42.7044 | −1.57518 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29.3393 | 1.08073 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.36465 | −0.270913 | −0.135457 | − | 0.990783i | \(-0.543250\pi\) | ||||
−0.135457 | + | 0.990783i | \(0.543250\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.3608 | 0.454084 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.85436 | 0.104716 | 0.0523581 | − | 0.998628i | \(-0.483326\pi\) | ||||
0.0523581 | + | 0.998628i | \(0.483326\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.35355 | 0.0495902 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 42.3725 | 1.55033 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.3833 | −0.744790 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.3725 | 0.816385 | 0.408193 | − | 0.912896i | \(-0.366159\pi\) | ||||
0.408193 | + | 0.912896i | \(0.366159\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 40.5856 | 1.47902 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.4380 | −0.452666 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.07326 | 0.220736 | 0.110368 | − | 0.993891i | \(-0.464797\pi\) | ||||
0.110368 | + | 0.993891i | \(0.464797\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.36932 | −0.267489 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.1166 | 0.475478 | 0.237739 | − | 0.971329i | \(-0.423594\pi\) | ||||
0.237739 | + | 0.971329i | \(0.423594\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.21267 | 0.188711 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 76.8419 | 2.77823 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.93012 | 0.322448 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.5791 | −1.60757 | −0.803783 | − | 0.594923i | \(-0.797182\pi\) | ||||
−0.803783 | + | 0.594923i | \(0.797182\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −30.9004 | −1.11285 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.43920 | −0.159667 | −0.0798334 | − | 0.996808i | \(-0.525439\pi\) | ||||
−0.0798334 | + | 0.996808i | \(0.525439\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.7889 | 0.746758 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16.2387 | 0.582561 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.28906 | 0.189500 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −71.2771 | −2.55050 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.94122 | −0.248059 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −27.4568 | −0.979977 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.315342 | −0.0112407 | −0.00562036 | − | 0.999984i | \(-0.501789\pi\) | ||||
−0.00562036 | + | 0.999984i | \(0.501789\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 59.4625 | 2.11692 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.1733 | −0.397278 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −45.0180 | −1.59864 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 28.6542 | 1.01626 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.16712 | 0.218451 | 0.109225 | − | 0.994017i | \(-0.465163\pi\) | ||||
0.109225 | + | 0.994017i | \(0.465163\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.84736 | −0.100732 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −26.0673 | −0.921044 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.0401294 | 0.00141614 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.39752 | −0.119747 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −67.3597 | −2.37117 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.4057 | 0.717426 | 0.358713 | − | 0.933448i | \(-0.383216\pi\) | ||||
0.358713 | + | 0.933448i | \(0.383216\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.5763 | 1.28437 | 0.642184 | − | 0.766551i | \(-0.278029\pi\) | ||||
0.642184 | + | 0.766551i | \(0.278029\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 33.1874 | 1.16393 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.62342 | 0.302065 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.08298 | 0.0378885 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −29.9474 | −1.04645 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.6686 | 0.686439 | 0.343219 | − | 0.939255i | \(-0.388483\pi\) | ||||
0.343219 | + | 0.939255i | \(0.388483\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.7328 | 1.28042 | 0.640212 | − | 0.768198i | \(-0.278846\pi\) | ||||
0.640212 | + | 0.768198i | \(0.278846\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 201.753 | 7.02415 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.4920 | −0.955991 | −0.477995 | − | 0.878362i | \(-0.658636\pi\) | ||||
−0.477995 | + | 0.878362i | \(0.658636\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.1016 | −0.420307 | −0.210153 | − | 0.977668i | \(-0.567396\pi\) | ||||
−0.210153 | + | 0.977668i | \(0.567396\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.8299 | 0.965408 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.3317 | 0.704451 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −43.0964 | −1.49141 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.35627 | −0.0814445 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 51.4731 | 1.77705 | 0.888524 | − | 0.458829i | \(-0.151731\pi\) | ||||
0.888524 | + | 0.458829i | \(0.151731\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.71457 | −0.197054 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 40.5929 | 1.39809 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −43.2613 | −1.48824 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −47.9463 | −1.64745 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −70.8885 | −2.43289 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.68646 | −0.0578112 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.6187 | −1.45924 | −0.729619 | − | 0.683854i | \(-0.760303\pi\) | ||||
−0.729619 | + | 0.683854i | \(0.760303\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14.9802 | 0.512311 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.45501 | 0.118021 | 0.0590105 | − | 0.998257i | \(-0.481205\pi\) | ||||
0.0590105 | + | 0.998257i | \(0.481205\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.1161 | −0.583994 | −0.291997 | − | 0.956419i | \(-0.594320\pi\) | ||||
−0.291997 | + | 0.956419i | \(0.594320\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −23.6080 | −0.804560 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.0130 | 0.442969 | 0.221485 | − | 0.975164i | \(-0.428910\pi\) | ||||
0.221485 | + | 0.975164i | \(0.428910\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −33.8599 | −1.15127 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −23.8545 | −0.810141 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 41.9604 | 1.42341 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.8126 | −0.772974 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −37.0835 | −1.25509 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 56.3697 | 1.90564 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.908097 | 0.0306642 | 0.0153321 | − | 0.999882i | \(-0.495119\pi\) | ||||
0.0153321 | + | 0.999882i | \(0.495119\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 54.6070 | 1.84185 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.1332 | 0.981523 | 0.490761 | − | 0.871294i | \(-0.336719\pi\) | ||||
0.490761 | + | 0.871294i | \(0.336719\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.4780 | 1.05932 | 0.529660 | − | 0.848210i | \(-0.322319\pi\) | ||||
0.529660 | + | 0.848210i | \(0.322319\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 19.9387 | 0.670231 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −37.0933 | −1.24547 | −0.622736 | − | 0.782432i | \(-0.713979\pi\) | ||||
−0.622736 | + | 0.782432i | \(0.713979\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31.6153 | −1.06034 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 43.4426 | 1.45538 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.555087 | −0.0185753 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.37658 | 0.246572 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.72996 | 0.191318 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.90447 | 0.263629 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.6423 | −0.454492 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.83393 | −0.160863 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 46.3523 | 1.54080 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.0295 | 0.797886 | 0.398943 | − | 0.916976i | \(-0.369377\pi\) | ||||
0.398943 | + | 0.916976i | \(0.369377\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.876894 | 0.0290848 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.7644 | 1.51624 | 0.758121 | − | 0.652114i | \(-0.226118\pi\) | ||||
0.758121 | + | 0.652114i | \(0.226118\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −73.8350 | −2.44358 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −100.514 | −3.32288 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.7209 | 0.717288 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.91536 | 0.0961688 | 0.0480844 | − | 0.998843i | \(-0.484688\pi\) | ||||
0.0480844 | + | 0.998843i | \(0.484688\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −68.2868 | −2.25013 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 55.4210 | 1.82421 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 46.1711 | 1.51810 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.53206 | −0.0831637 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.4417 | −0.473815 | −0.236908 | − | 0.971532i | \(-0.576134\pi\) | ||||
−0.236908 | + | 0.971532i | \(0.576134\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.96362 | 0.129902 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 51.4078 | 1.68302 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −133.899 | −4.37896 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.3960 | 1.28701 | 0.643505 | − | 0.765442i | \(-0.277479\pi\) | ||||
0.643505 | + | 0.765442i | \(0.277479\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.5349 | 0.931200 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.5954 | 1.22558 | 0.612788 | − | 0.790247i | \(-0.290048\pi\) | ||||
0.612788 | + | 0.790247i | \(0.290048\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.45180 | 0.0798415 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10.5426 | −0.342952 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.3522 | 0.693854 | 0.346927 | − | 0.937892i | \(-0.387225\pi\) | ||||
0.346927 | + | 0.937892i | \(0.387225\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.0312023 | −0.00101287 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −84.8767 | −2.75232 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.5726 | 1.21709 | 0.608547 | − | 0.793518i | \(-0.291753\pi\) | ||||
0.608547 | + | 0.793518i | \(0.291753\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −55.6362 | −1.80035 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 76.7119 | 2.47974 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.6696 | −0.473707 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.3167 | −0.913444 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 41.6616 | 1.34253 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.19182 | −0.199322 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.5676 | −0.371990 | −0.185995 | − | 0.982551i | \(-0.559551\pi\) | ||||
−0.185995 | + | 0.982551i | \(0.559551\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13.1397 | −0.422107 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 60.2009 | 1.93194 | 0.965970 | − | 0.258656i | \(-0.0832796\pi\) | ||||
0.965970 | + | 0.258656i | \(0.0832796\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.7414 | 0.632879 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −156.872 | −5.02393 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41.2738 | 1.32047 | 0.660233 | − | 0.751061i | \(-0.270458\pi\) | ||||
0.660233 | + | 0.751061i | \(0.270458\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45.4229 | 1.45172 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.6542 | −0.340163 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.5610 | −0.528214 | −0.264107 | − | 0.964493i | \(-0.585077\pi\) | ||||
−0.264107 | + | 0.964493i | \(0.585077\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33.0050 | −1.05163 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.47766 | 0.0788649 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.502025 | 0.0159635 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.6243 | −1.13164 | −0.565821 | − | 0.824528i | \(-0.691441\pi\) | ||||
−0.565821 | + | 0.824528i | \(0.691441\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.0208 | 0.349736 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −49.6557 | −1.57419 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.0563 | 1.30027 | 0.650133 | − | 0.759821i | \(-0.274713\pi\) | ||||
0.650133 | + | 0.759821i | \(0.274713\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.23316 | −0.165570 |
(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 | 608.2.a.i.1.1 | ✓ | 4 | |
3.2 | odd | 2 | 5472.2.a.bt.1.4 | 4 | |||
4.3 | odd | 2 | 608.2.a.j.1.3 | yes | 4 | ||
8.3 | odd | 2 | 1216.2.a.w.1.2 | 4 | |||
8.5 | even | 2 | 1216.2.a.x.1.4 | 4 | |||
12.11 | even | 2 | 5472.2.a.bs.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
608.2.a.i.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
608.2.a.j.1.3 | yes | 4 | 4.3 | odd | 2 | ||
1216.2.a.w.1.2 | 4 | 8.3 | odd | 2 | |||
1216.2.a.x.1.4 | 4 | 8.5 | even | 2 | |||
5472.2.a.bs.1.4 | 4 | 12.11 | even | 2 | |||
5472.2.a.bt.1.4 | 4 | 3.2 | odd | 2 |