Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6040,2,Mod(1,6040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6040, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6040.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6040 = 2^{3} \cdot 5 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6040.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2296428209\) |
Analytic rank: | \(1\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 5 x^{18} - 29 x^{17} + 165 x^{16} + 325 x^{15} - 2208 x^{14} - 1891 x^{13} + 15895 x^{12} + \cdots - 5628 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-0.237601\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6040.1 |
$q$-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 | ||||||||
\(3\) | 0.237601 | 0.137179 | 0.0685896 | − | 0.997645i | \(-0.478150\pi\) | ||||
0.0685896 | + | 0.997645i | \(0.478150\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.27350 | 1.61523 | 0.807615 | − | 0.589709i | \(-0.200758\pi\) | ||||
0.807615 | + | 0.589709i | \(0.200758\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.94355 | −0.981182 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.02953 | −0.611926 | −0.305963 | − | 0.952043i | \(-0.598978\pi\) | ||||
−0.305963 | + | 0.952043i | \(0.598978\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.81969 | −1.33674 | −0.668371 | − | 0.743828i | \(-0.733008\pi\) | ||||
−0.668371 | + | 0.743828i | \(0.733008\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.237601 | 0.0613484 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.46461 | −1.32536 | −0.662681 | − | 0.748902i | \(-0.730581\pi\) | ||||
−0.662681 | + | 0.748902i | \(0.730581\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.56063 | 0.816864 | 0.408432 | − | 0.912789i | \(-0.366076\pi\) | ||||
0.408432 | + | 0.912789i | \(0.366076\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.01539 | 0.221576 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.164087 | −0.0342144 | −0.0171072 | − | 0.999854i | \(-0.505446\pi\) | ||||
−0.0171072 | + | 0.999854i | \(0.505446\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.41219 | −0.271777 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.17670 | −1.33268 | −0.666340 | − | 0.745648i | \(-0.732140\pi\) | ||||
−0.666340 | + | 0.745648i | \(0.732140\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.23553 | 1.47914 | 0.739572 | − | 0.673077i | \(-0.235028\pi\) | ||||
0.739572 | + | 0.673077i | \(0.235028\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.482219 | −0.0839435 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.27350 | 0.722353 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.02949 | 1.15564 | 0.577821 | − | 0.816164i | \(-0.303903\pi\) | ||||
0.577821 | + | 0.816164i | \(0.303903\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.14516 | −0.183373 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.73949 | −1.20871 | −0.604353 | − | 0.796717i | \(-0.706568\pi\) | ||||
−0.604353 | + | 0.796717i | \(0.706568\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.47560 | 0.530023 | 0.265012 | − | 0.964245i | \(-0.414624\pi\) | ||||
0.265012 | + | 0.964245i | \(0.414624\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.94355 | −0.438798 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.39739 | 1.07902 | 0.539510 | − | 0.841979i | \(-0.318609\pi\) | ||||
0.539510 | + | 0.841979i | \(0.318609\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.2628 | 1.60897 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.29840 | −0.181812 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.18979 | −0.712872 | −0.356436 | − | 0.934320i | \(-0.616008\pi\) | ||||
−0.356436 | + | 0.934320i | \(0.616008\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.02953 | −0.273662 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.846010 | 0.112057 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.8741 | −1.80625 | −0.903126 | − | 0.429377i | \(-0.858733\pi\) | ||||
−0.903126 | + | 0.429377i | \(0.858733\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.9562 | −1.53084 | −0.765420 | − | 0.643531i | \(-0.777469\pi\) | ||||
−0.765420 | + | 0.643531i | \(0.777469\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −12.5792 | −1.58484 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.81969 | −0.597809 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.08848 | −0.988165 | −0.494082 | − | 0.869415i | \(-0.664496\pi\) | ||||
−0.494082 | + | 0.869415i | \(0.664496\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.0389872 | −0.00469351 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.838605 | −0.0995241 | −0.0497621 | − | 0.998761i | \(-0.515846\pi\) | ||||
−0.0497621 | + | 0.998761i | \(0.515846\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.52854 | −0.530026 | −0.265013 | − | 0.964245i | \(-0.585376\pi\) | ||||
−0.265013 | + | 0.964245i | \(0.585376\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.237601 | 0.0274358 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.67319 | −0.988402 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.6713 | 1.31312 | 0.656561 | − | 0.754273i | \(-0.272011\pi\) | ||||
0.656561 | + | 0.754273i | \(0.272011\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.49510 | 0.943900 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.71143 | −0.736675 | −0.368337 | − | 0.929692i | \(-0.620073\pi\) | ||||
−0.368337 | + | 0.929692i | \(0.620073\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.46461 | −0.592720 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.70519 | −0.182816 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.26146 | −0.769713 | −0.384856 | − | 0.922976i | \(-0.625749\pi\) | ||||
−0.384856 | + | 0.922976i | \(0.625749\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −20.5969 | −2.15915 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.95677 | 0.202908 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.56063 | 0.365313 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.11104 | 0.315878 | 0.157939 | − | 0.987449i | \(-0.449515\pi\) | ||||
0.157939 | + | 0.987449i | \(0.449515\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.97401 | 0.600411 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.834076 | 0.0829937 | 0.0414969 | − | 0.999139i | \(-0.486787\pi\) | ||||
0.0414969 | + | 0.999139i | \(0.486787\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.2189 | −1.00690 | −0.503448 | − | 0.864025i | \(-0.667936\pi\) | ||||
−0.503448 | + | 0.864025i | \(0.667936\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.01539 | 0.0990918 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.3395 | −1.19291 | −0.596453 | − | 0.802648i | \(-0.703424\pi\) | ||||
−0.596453 | + | 0.802648i | \(0.703424\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.18989 | −0.592884 | −0.296442 | − | 0.955051i | \(-0.595800\pi\) | ||||
−0.296442 | + | 0.955051i | \(0.595800\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.67022 | 0.158530 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19.4597 | −1.83061 | −0.915305 | − | 0.402761i | \(-0.868050\pi\) | ||||
−0.915305 | + | 0.402761i | \(0.868050\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.164087 | −0.0153012 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.1870 | 1.31159 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −23.3530 | −2.14077 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.88101 | −0.625547 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.83891 | −0.165809 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.01836 | −0.622779 | −0.311389 | − | 0.950282i | \(-0.600794\pi\) | ||||
−0.311389 | + | 0.950282i | \(0.600794\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.825806 | 0.0727082 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.02148 | 0.176618 | 0.0883090 | − | 0.996093i | \(-0.471854\pi\) | ||||
0.0883090 | + | 0.996093i | \(0.471854\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.2163 | 1.31942 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.41219 | −0.121542 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.48501 | −0.468616 | −0.234308 | − | 0.972162i | \(-0.575282\pi\) | ||||
−0.234308 | + | 0.972162i | \(0.575282\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.0354 | 1.78420 | 0.892099 | − | 0.451840i | \(-0.149232\pi\) | ||||
0.892099 | + | 0.451840i | \(0.149232\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.75763 | 0.148019 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.78170 | 0.817987 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.17670 | −0.595993 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.67606 | 0.220717 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.61132 | 0.541620 | 0.270810 | − | 0.962633i | \(-0.412708\pi\) | ||||
0.270810 | + | 0.962633i | \(0.412708\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.00000 | 0.0813788 | ||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 16.0853 | 1.30042 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.23553 | 0.661494 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.5833 | 1.48311 | 0.741555 | − | 0.670892i | \(-0.234088\pi\) | ||||
0.741555 | + | 0.670892i | \(0.234088\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.23310 | −0.0977912 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.701225 | −0.0552642 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.12360 | 0.166333 | 0.0831666 | − | 0.996536i | \(-0.473497\pi\) | ||||
0.0831666 | + | 0.996536i | \(0.473497\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.482219 | −0.0375407 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.9362 | −0.923650 | −0.461825 | − | 0.886971i | \(-0.652805\pi\) | ||||
−0.461825 | + | 0.886971i | \(0.652805\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.2294 | 0.786878 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.4809 | −0.801492 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.81892 | −0.366376 | −0.183188 | − | 0.983078i | \(-0.558642\pi\) | ||||
−0.183188 | + | 0.983078i | \(0.558642\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.27350 | 0.323046 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.29650 | −0.247780 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.2951 | −0.918975 | −0.459488 | − | 0.888184i | \(-0.651967\pi\) | ||||
−0.459488 | + | 0.888184i | \(0.651967\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.56893 | −0.488264 | −0.244132 | − | 0.969742i | \(-0.578503\pi\) | ||||
−0.244132 | + | 0.969742i | \(0.578503\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.84082 | −0.209999 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.02949 | 0.516818 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.0906 | 0.811023 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.03501 | −0.438983 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.1704 | 1.24241 | 0.621205 | − | 0.783648i | \(-0.286644\pi\) | ||||
0.621205 | + | 0.783648i | \(0.286644\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.9716 | −1.14966 | −0.574829 | − | 0.818274i | \(-0.694931\pi\) | ||||
−0.574829 | + | 0.818274i | \(0.694931\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.14516 | −0.0820070 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.95356 | 0.424173 | 0.212087 | − | 0.977251i | \(-0.431974\pi\) | ||||
0.212087 | + | 0.977251i | \(0.431974\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.7828 | −1.33148 | −0.665739 | − | 0.746184i | \(-0.731884\pi\) | ||||
−0.665739 | + | 0.746184i | \(0.731884\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.92183 | −0.135556 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −30.6696 | −2.15259 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.73949 | −0.540550 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.482997 | 0.0335706 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.22639 | −0.499860 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.9244 | −1.09628 | −0.548141 | − | 0.836386i | \(-0.684664\pi\) | ||||
−0.548141 | + | 0.836386i | \(0.684664\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.199254 | −0.0136526 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.47560 | 0.237034 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 35.1945 | 2.38916 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.07599 | −0.0727085 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 26.3377 | 1.77167 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.63255 | 0.511113 | 0.255557 | − | 0.966794i | \(-0.417741\pi\) | ||||
0.255557 | + | 0.966794i | \(0.417741\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.94355 | −0.196236 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.2914 | −0.683062 | −0.341531 | − | 0.939871i | \(-0.610945\pi\) | ||||
−0.341531 | + | 0.939871i | \(0.610945\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.5034 | −0.958414 | −0.479207 | − | 0.877702i | \(-0.659076\pi\) | ||||
−0.479207 | + | 0.877702i | \(0.659076\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.06076 | −0.135588 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −27.1081 | −1.77591 | −0.887954 | − | 0.459932i | \(-0.847874\pi\) | ||||
−0.887954 | + | 0.459932i | \(0.847874\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.39739 | 0.482553 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.77311 | 0.180133 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.9948 | 1.22867 | 0.614335 | − | 0.789045i | \(-0.289424\pi\) | ||||
0.614335 | + | 0.789045i | \(0.289424\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.70051 | −0.496033 | −0.248017 | − | 0.968756i | \(-0.579779\pi\) | ||||
−0.248017 | + | 0.968756i | \(0.579779\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.25503 | 0.401260 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.2628 | 0.719554 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.1611 | −1.09194 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.59464 | −0.101056 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.17780 | −0.0743422 | −0.0371711 | − | 0.999309i | \(-0.511835\pi\) | ||||
−0.0371711 | + | 0.999309i | \(0.511835\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.333019 | 0.0209367 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.29840 | −0.0813088 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.8865 | 1.30286 | 0.651432 | − | 0.758707i | \(-0.274169\pi\) | ||||
0.651432 | + | 0.758707i | \(0.274169\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 30.0405 | 1.86663 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 21.1250 | 1.30760 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.2224 | 0.692003 | 0.346001 | − | 0.938234i | \(-0.387539\pi\) | ||||
0.346001 | + | 0.938234i | \(0.387539\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.18979 | −0.318806 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.72533 | −0.105589 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.8636 | 0.784307 | 0.392154 | − | 0.919900i | \(-0.371730\pi\) | ||||
0.392154 | + | 0.919900i | \(0.371730\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.7540 | 1.86817 | 0.934085 | − | 0.357050i | \(-0.116218\pi\) | ||||
0.934085 | + | 0.357050i | \(0.116218\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.89386 | −0.296190 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.02953 | −0.122385 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.904791 | 0.0543636 | 0.0271818 | − | 0.999631i | \(-0.491347\pi\) | ||||
0.0271818 | + | 0.999631i | \(0.491347\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −24.2417 | −1.45131 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.5608 | 0.808970 | 0.404485 | − | 0.914545i | \(-0.367451\pi\) | ||||
0.404485 | + | 0.914545i | \(0.367451\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.26259 | −0.193941 | −0.0969705 | − | 0.995287i | \(-0.530915\pi\) | ||||
−0.0969705 | + | 0.995287i | \(0.530915\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.846010 | 0.0501133 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −33.0747 | −1.95234 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.8619 | 0.756584 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.739186 | 0.0433319 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.8087 | 0.981975 | 0.490987 | − | 0.871167i | \(-0.336636\pi\) | ||||
0.490987 | + | 0.871167i | \(0.336636\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.8741 | −0.807780 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.86609 | 0.166307 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.790847 | 0.0457359 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.8530 | 0.856110 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.198178 | 0.0113850 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.9562 | −0.684613 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.9288 | −1.13740 | −0.568699 | − | 0.822546i | \(-0.692553\pi\) | ||||
−0.568699 | + | 0.822546i | \(0.692553\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.42802 | −0.138125 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.71747 | 0.267503 | 0.133752 | − | 0.991015i | \(-0.457298\pi\) | ||||
0.133752 | + | 0.991015i | \(0.457298\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.7915 | 1.06216 | 0.531080 | − | 0.847322i | \(-0.321786\pi\) | ||||
0.531080 | + | 0.847322i | \(0.321786\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −12.5792 | −0.708760 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.1265 | 1.35508 | 0.677540 | − | 0.735486i | \(-0.263046\pi\) | ||||
0.677540 | + | 0.735486i | \(0.263046\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.5653 | 0.815502 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.93189 | −0.163642 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.4574 | −1.08264 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.81969 | −0.267348 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.47073 | −0.0813313 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 31.6128 | 1.74287 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.6036 | −1.29737 | −0.648686 | − | 0.761056i | \(-0.724681\pi\) | ||||
−0.648686 | + | 0.761056i | \(0.724681\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −20.6916 | −1.13389 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.08848 | −0.441921 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.47693 | 0.134927 | 0.0674634 | − | 0.997722i | \(-0.478509\pi\) | ||||
0.0674634 | + | 0.997722i | \(0.478509\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.62364 | −0.251122 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.7142 | −0.905127 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.2171 | 0.983629 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.0389872 | −0.00209900 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.0865 | −0.809884 | −0.404942 | − | 0.914342i | \(-0.632708\pi\) | ||||
−0.404942 | + | 0.914342i | \(0.632708\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.7748 | −1.75439 | −0.877197 | − | 0.480131i | \(-0.840589\pi\) | ||||
−0.877197 | + | 0.480131i | \(0.840589\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.80634 | 0.363296 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.4770 | −0.664081 | −0.332041 | − | 0.943265i | \(-0.607737\pi\) | ||||
−0.332041 | + | 0.943265i | \(0.607737\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.838605 | −0.0445085 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.54870 | −0.293668 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.8290 | 1.62709 | 0.813546 | − | 0.581501i | \(-0.197534\pi\) | ||||
0.813546 | + | 0.581501i | \(0.197534\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.32194 | −0.332734 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.63494 | −0.0858120 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.52854 | −0.237035 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.44434 | 0.440791 | 0.220395 | − | 0.975411i | \(-0.429265\pi\) | ||||
0.220395 | + | 0.975411i | \(0.429265\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 22.7815 | 1.18596 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.1786 | −1.15145 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −30.2385 | −1.56569 | −0.782845 | − | 0.622217i | \(-0.786232\pi\) | ||||
−0.782845 | + | 0.622217i | \(0.786232\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.237601 | 0.0122697 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 34.5895 | 1.78145 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −35.8112 | −1.83950 | −0.919748 | − | 0.392509i | \(-0.871607\pi\) | ||||
−0.919748 | + | 0.392509i | \(0.871607\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.66757 | −0.0854323 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.15450 | −0.467773 | −0.233887 | − | 0.972264i | \(-0.575144\pi\) | ||||
−0.233887 | + | 0.972264i | \(0.575144\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.67319 | −0.442027 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.2306 | −0.520049 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.9144 | −0.553382 | −0.276691 | − | 0.960959i | \(-0.589238\pi\) | ||||
−0.276691 | + | 0.960959i | \(0.589238\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.896669 | 0.0453465 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.480307 | 0.0242283 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.6713 | 0.587246 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.97111 | 0.349870 | 0.174935 | − | 0.984580i | \(-0.444028\pi\) | ||||
0.174935 | + | 0.984580i | \(0.444028\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.61542 | 0.180997 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.2016 | 0.659256 | 0.329628 | − | 0.944111i | \(-0.393077\pi\) | ||||
0.329628 | + | 0.944111i | \(0.393077\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −39.6927 | −1.97723 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.49510 | 0.422125 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.2666 | −0.707167 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.5141 | −0.866018 | −0.433009 | − | 0.901390i | \(-0.642548\pi\) | ||||
−0.433009 | + | 0.901390i | \(0.642548\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.30325 | −0.0642844 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −59.2909 | −2.91751 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.71143 | −0.329451 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.99803 | 0.244755 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.8073 | 0.772237 | 0.386119 | − | 0.922449i | \(-0.373816\pi\) | ||||
0.386119 | + | 0.922449i | \(0.373816\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.6010 | 0.857819 | 0.428909 | − | 0.903347i | \(-0.358898\pi\) | ||||
0.428909 | + | 0.903347i | \(0.358898\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −21.7746 | −1.05872 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.46461 | −0.265072 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −51.0950 | −2.47266 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.32414 | 0.112211 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.38829 | −0.163208 | −0.0816041 | − | 0.996665i | \(-0.526004\pi\) | ||||
−0.0816041 | + | 0.996665i | \(0.526004\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.89980 | 0.475754 | 0.237877 | − | 0.971295i | \(-0.423548\pi\) | ||||
0.237877 | + | 0.971295i | \(0.423548\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.70519 | −0.0817578 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.584251 | −0.0279485 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.6328 | 1.27112 | 0.635558 | − | 0.772053i | \(-0.280770\pi\) | ||||
0.635558 | + | 0.772053i | \(0.280770\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −33.1526 | −1.57869 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.4998 | 0.546374 | 0.273187 | − | 0.961961i | \(-0.411922\pi\) | ||||
0.273187 | + | 0.961961i | \(0.411922\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.26146 | −0.344226 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.57086 | 0.0742990 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.0921 | 1.18417 | 0.592085 | − | 0.805876i | \(-0.298305\pi\) | ||||
0.592085 | + | 0.805876i | \(0.298305\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.7075 | 0.739638 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.237601 | 0.0111635 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −20.5969 | −0.965600 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.49466 | 0.210251 | 0.105126 | − | 0.994459i | \(-0.466476\pi\) | ||||
0.105126 | + | 0.994459i | \(0.466476\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.71709 | 0.360203 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.1580 | −1.35802 | −0.679011 | − | 0.734128i | \(-0.737591\pi\) | ||||
−0.679011 | + | 0.734128i | \(0.737591\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.97403 | 0.324110 | 0.162055 | − | 0.986782i | \(-0.448188\pi\) | ||||
0.162055 | + | 0.986782i | \(0.448188\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.95677 | 0.0907432 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.6575 | 1.46493 | 0.732467 | − | 0.680802i | \(-0.238369\pi\) | ||||
0.732467 | + | 0.680802i | \(0.238369\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −34.5661 | −1.59611 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.41542 | 0.203452 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.05382 | −0.324335 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.56063 | 0.163373 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15.2764 | 0.699457 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −29.8506 | −1.36391 | −0.681954 | − | 0.731395i | \(-0.738870\pi\) | ||||
−0.681954 | + | 0.731395i | \(0.738870\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −33.8800 | −1.54479 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.166612 | −0.00758110 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.11104 | 0.141265 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.7584 | 0.804709 | 0.402355 | − | 0.915484i | \(-0.368192\pi\) | ||||
0.402355 | + | 0.915484i | \(0.368192\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.504570 | 0.0228174 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.08870 | 0.139391 | 0.0696955 | − | 0.997568i | \(-0.477797\pi\) | ||||
0.0696955 | + | 0.997568i | \(0.477797\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 39.2179 | 1.76628 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.97401 | 0.268512 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.58378 | −0.160754 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 38.0808 | 1.70473 | 0.852366 | − | 0.522945i | \(-0.175167\pi\) | ||||
0.852366 | + | 0.522945i | \(0.175167\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.83605 | −0.126706 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −37.5152 | −1.67272 | −0.836361 | − | 0.548180i | \(-0.815321\pi\) | ||||
−0.836361 | + | 0.548180i | \(0.815321\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.834076 | 0.0371159 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.43052 | 0.107943 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.8821 | 1.54612 | 0.773061 | − | 0.634331i | \(-0.218724\pi\) | ||||
0.773061 | + | 0.634331i | \(0.218724\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.3527 | −0.856114 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.02830 | −0.222005 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.2189 | −0.450298 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.0132 | −0.660281 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.14498 | −0.0502591 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −44.4217 | −1.94615 | −0.973075 | − | 0.230490i | \(-0.925967\pi\) | ||||
−0.973075 | + | 0.230490i | \(0.925967\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.2976 | 1.01873 | 0.509366 | − | 0.860550i | \(-0.329880\pi\) | ||||
0.509366 | + | 0.860550i | \(0.329880\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.01539 | 0.0443152 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −45.0039 | −1.96040 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9731 | −0.998829 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 40.8390 | 1.77226 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 37.3020 | 1.61573 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.3395 | −0.533484 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.92132 | −0.126064 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −22.8582 | −0.984571 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.2569 | −1.60180 | −0.800899 | − | 0.598799i | \(-0.795645\pi\) | ||||
−0.800899 | + | 0.598799i | \(0.795645\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.56079 | −0.0669797 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.18989 | −0.265146 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.59085 | −0.410075 | −0.205038 | − | 0.978754i | \(-0.565732\pi\) | ||||
−0.205038 | + | 0.978754i | \(0.565732\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 35.1938 | 1.50203 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.5536 | −1.08862 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 49.8772 | 2.12099 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.67022 | 0.0708967 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.3090 | 0.775777 | 0.387889 | − | 0.921706i | \(-0.373205\pi\) | ||||
0.387889 | + | 0.921706i | \(0.373205\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.7513 | −0.708504 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.63514 | 0.111256 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.2883 | −0.560034 | −0.280017 | − | 0.959995i | \(-0.590340\pi\) | ||||
−0.280017 | + | 0.959995i | \(0.590340\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.4597 | −0.818674 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 36.3038 | 1.52462 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.45598 | 0.186804 | 0.0934022 | − | 0.995628i | \(-0.470226\pi\) | ||||
0.0934022 | + | 0.995628i | \(0.470226\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.1551 | −1.47120 | −0.735598 | − | 0.677418i | \(-0.763099\pi\) | ||||
−0.735598 | + | 0.677418i | \(0.763099\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.07972 | 0.170433 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.164087 | −0.00684289 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.5308 | −1.06286 | −0.531430 | − | 0.847102i | \(-0.678345\pi\) | ||||
−0.531430 | + | 0.847102i | \(0.678345\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.79486 | −0.157709 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −28.6813 | −1.18990 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.5328 | 0.436225 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 14.1870 | 0.586559 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.1426 | −1.03775 | −0.518873 | − | 0.854852i | \(-0.673648\pi\) | ||||
−0.518873 | + | 0.854852i | \(0.673648\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29.3236 | 1.20826 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.41457 | 0.0581878 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.2215 | 0.789333 | 0.394667 | − | 0.918824i | \(-0.370860\pi\) | ||||
0.394667 | + | 0.918824i | \(0.370860\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23.3530 | −0.957379 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.46282 | −0.182651 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −46.5042 | −1.90011 | −0.950054 | − | 0.312084i | \(-0.898973\pi\) | ||||
−0.950054 | + | 0.312084i | \(0.898973\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.9252 | −0.608814 | −0.304407 | − | 0.952542i | \(-0.598458\pi\) | ||||
−0.304407 | + | 0.952542i | \(0.598458\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 23.8088 | 0.969569 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.88101 | −0.279753 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.4843 | 1.15614 | 0.578070 | − | 0.815987i | \(-0.303806\pi\) | ||||
0.578070 | + | 0.815987i | \(0.303806\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.28715 | −0.295290 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −35.6531 | −1.44237 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.66993 | 0.148227 | 0.0741135 | − | 0.997250i | \(-0.476387\pi\) | ||||
0.0741135 | + | 0.997250i | \(0.476387\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.83891 | −0.0741522 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.29051 | −0.293505 | −0.146752 | − | 0.989173i | \(-0.546882\pi\) | ||||
−0.146752 | + | 0.989173i | \(0.546882\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.93223 | 0.359017 | 0.179508 | − | 0.983756i | \(-0.442549\pi\) | ||||
0.179508 | + | 0.983756i | \(0.442549\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.231722 | 0.00929870 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −31.0318 | −1.24326 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.71700 | −0.0685704 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −38.4134 | −1.53164 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.16658 | 0.205678 | 0.102839 | − | 0.994698i | \(-0.467207\pi\) | ||||
0.102839 | + | 0.994698i | \(0.467207\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.78366 | −0.150387 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.01836 | −0.278515 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −54.2832 | −2.15078 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.46847 | 0.0976513 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.5346 | −0.771570 | −0.385785 | − | 0.922589i | \(-0.626069\pi\) | ||||
−0.385785 | + | 0.922589i | \(0.626069\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.9124 | 1.21907 | 0.609533 | − | 0.792761i | \(-0.291357\pi\) | ||||
0.609533 | + | 0.792761i | \(0.291357\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.825806 | 0.0325161 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.2644 | 1.30776 | 0.653879 | − | 0.756599i | \(-0.273140\pi\) | ||||
0.653879 | + | 0.756599i | \(0.273140\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 28.1578 | 1.10529 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.36227 | 0.327743 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 48.1848 | 1.88562 | 0.942808 | − | 0.333336i | \(-0.108174\pi\) | ||||
0.942808 | + | 0.333336i | \(0.108174\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.02148 | 0.0789859 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.3300 | 0.520052 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.0500 | 0.703129 | 0.351565 | − | 0.936164i | \(-0.385650\pi\) | ||||
0.351565 | + | 0.936164i | \(0.385650\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.7920 | 0.575342 | 0.287671 | − | 0.957729i | \(-0.407119\pi\) | ||||
0.287671 | + | 0.957729i | \(0.407119\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.25788 | 0.243036 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.2163 | 0.590064 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.17760 | 0.0455969 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.81350 | 0.0701141 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.2655 | 0.936761 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.5320 | 0.483073 | 0.241537 | − | 0.970392i | \(-0.422349\pi\) | ||||
0.241537 | + | 0.970392i | \(0.422349\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.41219 | −0.0543554 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.5499 | 0.520765 | 0.260382 | − | 0.965506i | \(-0.416151\pi\) | ||||
0.260382 | + | 0.965506i | \(0.416151\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.2950 | 0.510216 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.44524 | −0.0937018 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.48253 | −0.0949914 | −0.0474957 | − | 0.998871i | \(-0.515124\pi\) | ||||
−0.0474957 | + | 0.998871i | \(0.515124\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.48501 | −0.209572 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.44604 | −0.131475 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25.0132 | 0.952926 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.2056 | −0.426282 | −0.213141 | − | 0.977021i | \(-0.568369\pi\) | ||||
−0.213141 | + | 0.977021i | \(0.568369\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 25.5299 | 0.969802 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.0354 | 0.797917 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 42.2933 | 1.60197 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.44091 | −0.243618 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 49.3595 | 1.86428 | 0.932141 | − | 0.362095i | \(-0.117938\pi\) | ||||
0.932141 | + | 0.362095i | \(0.117938\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.0294 | 0.944001 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.75763 | 0.0661962 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.56442 | 0.134054 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.1001 | 1.01777 | 0.508883 | − | 0.860836i | \(-0.330058\pi\) | ||||
0.508883 | + | 0.860836i | \(0.330058\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −34.3549 | −1.28841 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.35134 | −0.0506081 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.78170 | 0.365815 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.51319 | 0.168548 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.1601 | 1.34854 | 0.674272 | − | 0.738483i | \(-0.264457\pi\) | ||||
0.674272 | + | 0.738483i | \(0.264457\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −43.6704 | −1.62637 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.82965 | −0.0680455 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.17670 | −0.266536 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.4147 | 0.720053 | 0.360026 | − | 0.932942i | \(-0.382768\pi\) | ||||
0.360026 | + | 0.932942i | \(0.382768\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.9991 | −0.888855 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.9928 | −0.702473 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.2990 | 0.712825 | 0.356413 | − | 0.934329i | \(-0.384000\pi\) | ||||
0.356413 | + | 0.934329i | \(0.384000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.67606 | 0.0987078 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.4158 | 0.604683 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.2703 | 1.29744 | 0.648720 | − | 0.761027i | \(-0.275305\pi\) | ||||
0.648720 | + | 0.761027i | \(0.275305\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.07750 | −0.149791 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.91163 | 0.143504 | 0.0717520 | − | 0.997423i | \(-0.477141\pi\) | ||||
0.0717520 | + | 0.997423i | \(0.477141\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.61132 | 0.242220 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19.7554 | 0.722812 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −52.7330 | −1.92682 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.9269 | −0.398727 | −0.199364 | − | 0.979926i | \(-0.563888\pi\) | ||||
−0.199364 | + | 0.979926i | \(0.563888\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.279847 | −0.0101982 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.00000 | 0.0363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.733083 | −0.0266444 | −0.0133222 | − | 0.999911i | \(-0.504241\pi\) | ||||
−0.0133222 | + | 0.999911i | \(0.504241\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.0791257 | 0.00287208 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.956193 | 0.0346620 | 0.0173310 | − | 0.999850i | \(-0.494483\pi\) | ||||
0.0173310 | + | 0.999850i | \(0.494483\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26.4525 | −0.957644 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 16.0853 | 0.581566 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 66.8688 | 2.41449 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.4489 | 0.845590 | 0.422795 | − | 0.906225i | \(-0.361049\pi\) | ||||
0.422795 | + | 0.906225i | \(0.361049\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.96266 | 0.178726 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.0156 | 0.396205 | 0.198103 | − | 0.980181i | \(-0.436522\pi\) | ||||
0.198103 | + | 0.980181i | \(0.436522\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.23553 | 0.295829 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.13767 | 0.256062 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −27.5574 | −0.987348 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.70197 | 0.0609014 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.1349 | 0.362192 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.5833 | 0.663267 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.1718 | −0.362584 | −0.181292 | − | 0.983429i | \(-0.558028\pi\) | ||||
−0.181292 | + | 0.983429i | \(0.558028\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.66646 | 0.0949284 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −83.1608 | −2.95686 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 57.6254 | 2.04634 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.23310 | −0.0437336 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.05676 | 0.214542 | 0.107271 | − | 0.994230i | \(-0.465789\pi\) | ||||
0.107271 | + | 0.994230i | \(0.465789\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40.4238 | −1.43009 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.3744 | 0.755228 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.19081 | 0.324336 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.701225 | −0.0247149 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.05641 | 0.107591 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.09326 | 0.319702 | 0.159851 | − | 0.987141i | \(-0.448899\pi\) | ||||
0.159851 | + | 0.987141i | \(0.448899\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.31290 | −0.221676 | −0.110838 | − | 0.993838i | \(-0.535353\pi\) | ||||
−0.110838 | + | 0.993838i | \(0.535353\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.30718 | 0.256274 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.12360 | 0.0743864 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.3753 | 0.432957 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 60.6280 | 2.11852 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37.6187 | −1.31290 | −0.656450 | − | 0.754369i | \(-0.727943\pi\) | ||||
−0.656450 | + | 0.754369i | \(0.727943\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.1888 | 1.47061 | 0.735305 | − | 0.677737i | \(-0.237039\pi\) | ||||
0.735305 | + | 0.677737i | \(0.237039\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.482219 | −0.0167887 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.72001 | 0.164131 | 0.0820655 | − | 0.996627i | \(-0.473848\pi\) | ||||
0.0820655 | + | 0.996627i | \(0.473848\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.3958 | −1.57666 | −0.788330 | − | 0.615253i | \(-0.789054\pi\) | ||||
−0.788330 | + | 0.615253i | \(0.789054\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.214980 | 0.00745756 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −61.5467 | −2.13247 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.9362 | −0.413069 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −11.6302 | −0.401997 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.32046 | 0.218207 | 0.109103 | − | 0.994030i | \(-0.465202\pi\) | ||||
0.109103 | + | 0.994030i | \(0.465202\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.5051 | 0.776037 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.22207 | 0.110974 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.2294 | 0.351903 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −29.4060 | −1.01040 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.775197 | −0.0266047 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.15345 | −0.0395396 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.5429 | −1.31968 | −0.659842 | − | 0.751404i | \(-0.729377\pi\) | ||||
−0.659842 | + | 0.751404i | \(0.729377\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.4809 | −0.358438 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 38.4681 | 1.31405 | 0.657023 | − | 0.753871i | \(-0.271816\pi\) | ||||
0.657023 | + | 0.753871i | \(0.271816\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.61818 | −0.157570 | −0.0787851 | − | 0.996892i | \(-0.525104\pi\) | ||||
−0.0787851 | + | 0.996892i | \(0.525104\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.85860 | −0.267820 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.05034 | 0.0697943 | 0.0348971 | − | 0.999391i | \(-0.488890\pi\) | ||||
0.0348971 | + | 0.999391i | \(0.488890\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.81892 | −0.163848 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.05601 | 0.103788 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23.6872 | −0.803533 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.9839 | 1.32092 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.15748 | −0.309934 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.27350 | 0.144471 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −55.4576 | −1.87267 | −0.936335 | − | 0.351107i | \(-0.885805\pi\) | ||||
−0.936335 | + | 0.351107i | \(0.885805\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.99377 | 0.134707 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.3974 | −0.956734 | −0.478367 | − | 0.878160i | \(-0.658771\pi\) | ||||
−0.478367 | + | 0.878160i | \(0.658771\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.6982 | 0.831160 | 0.415580 | − | 0.909557i | \(-0.363579\pi\) | ||||
0.415580 | + | 0.909557i | \(0.363579\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.29650 | −0.110811 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −38.3374 | −1.28724 | −0.643622 | − | 0.765343i | \(-0.722569\pi\) | ||||
−0.643622 | + | 0.765343i | \(0.722569\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29.9929 | −1.00593 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.2410 | −0.577597 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.3393 | 0.881413 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.2951 | −0.410978 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.187906 | 0.00627401 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −59.1039 | −1.97123 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.3601 | 0.944813 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.52908 | 0.117440 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.56893 | −0.218358 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.77151 | 0.258049 | 0.129024 | − | 0.991641i | \(-0.458815\pi\) | ||||
0.129024 | + | 0.991641i | \(0.458815\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.45514 | −0.0814319 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.3165 | 0.639984 | 0.319992 | − | 0.947420i | \(-0.396320\pi\) | ||||
0.319992 | + | 0.947420i | \(0.396320\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.6210 | 0.450790 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.84082 | −0.0939146 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.63881 | 0.285279 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.3484 | −1.23201 | −0.616005 | − | 0.787742i | \(-0.711250\pi\) | ||||
−0.616005 | + | 0.787742i | \(0.711250\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.73512 | −0.156027 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.04182 | 0.133038 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.02949 | 0.231128 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 30.0797 | 0.987948 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.9336 | 0.457146 | 0.228573 | − | 0.973527i | \(-0.426594\pi\) | ||||
0.228573 | + | 0.973527i | \(0.426594\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 40.1026 | 1.31431 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.12088 | 0.0366959 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.0906 | 0.362701 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.3733 | −1.05759 | −0.528794 | − | 0.848750i | \(-0.677356\pi\) | ||||
−0.528794 | + | 0.848750i | \(0.677356\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.46489 | 0.145706 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.7927 | 0.775621 | 0.387811 | − | 0.921739i | \(-0.373231\pi\) | ||||
0.387811 | + | 0.921739i | \(0.373231\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.26995 | 0.0413552 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.03501 | −0.196319 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.6485 | −0.865961 | −0.432981 | − | 0.901403i | \(-0.642538\pi\) | ||||
−0.432981 | + | 0.901403i | \(0.642538\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.8262 | 0.708507 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.73249 | 0.185889 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.4232 | 0.855932 | 0.427966 | − | 0.903795i | \(-0.359230\pi\) | ||||
0.427966 | + | 0.903795i | \(0.359230\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.1704 | 0.555622 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.46074 | 0.111870 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −23.4402 | −0.756923 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 36.8240 | 1.18787 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 36.3220 | 1.17046 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.9716 | −0.514143 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.5130 | 1.62439 | 0.812195 | − | 0.583386i | \(-0.198273\pi\) | ||||
0.812195 | + | 0.583386i | \(0.198273\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.62311 | −0.148516 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.7689 | 1.08370 | 0.541848 | − | 0.840476i | \(-0.317725\pi\) | ||||
0.541848 | + | 0.840476i | \(0.317725\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 89.8947 | 2.88189 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.14516 | −0.0366746 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.09686 | 0.0670844 | 0.0335422 | − | 0.999437i | \(-0.489321\pi\) | ||||
0.0335422 | + | 0.999437i | \(0.489321\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.7373 | 0.471007 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.2202 | 0.581727 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 54.3369 | 1.73308 | 0.866540 | − | 0.499108i | \(-0.166339\pi\) | ||||
0.866540 | + | 0.499108i | \(0.166339\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.95356 | 0.189696 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.51123 | 0.239085 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.570299 | −0.0181345 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −57.9400 | −1.84053 | −0.920263 | − | 0.391300i | \(-0.872025\pi\) | ||||
−0.920263 | + | 0.391300i | \(0.872025\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.60825 | −0.177972 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18.7828 | −0.595455 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.5055 | −0.902779 | −0.451390 | − | 0.892327i | \(-0.649072\pi\) | ||||
−0.451390 | + | 0.892327i | \(0.649072\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.92701 | −0.314077 |
(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 | 6040.2.a.p.1.10 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6040.2.a.p.1.10 | ✓ | 19 | 1.1 | even | 1 | trivial |