Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(1,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, 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("4012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.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: | \(32.0359812909\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 4012.1 |
$q$-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 | ||||||||
\(3\) | 0.967697 | 0.558700 | 0.279350 | − | 0.960189i | \(-0.409881\pi\) | ||||
0.279350 | + | 0.960189i | \(0.409881\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.19923 | −1.43074 | −0.715369 | − | 0.698747i | \(-0.753741\pi\) | ||||
−0.715369 | + | 0.698747i | \(0.753741\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.75414 | 1.41893 | 0.709466 | − | 0.704740i | \(-0.248936\pi\) | ||||
0.709466 | + | 0.704740i | \(0.248936\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.06356 | −0.687854 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.41425 | 1.63246 | 0.816229 | − | 0.577728i | \(-0.196061\pi\) | ||||
0.816229 | + | 0.577728i | \(0.196061\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.0945861 | −0.0262335 | −0.0131167 | − | 0.999914i | \(-0.504175\pi\) | ||||
−0.0131167 | + | 0.999914i | \(0.504175\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.09588 | −0.799353 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.489351 | 0.112265 | 0.0561324 | − | 0.998423i | \(-0.482123\pi\) | ||||
0.0561324 | + | 0.998423i | \(0.482123\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.63287 | 0.792757 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.45421 | 1.34580 | 0.672898 | − | 0.739735i | \(-0.265049\pi\) | ||||
0.672898 | + | 0.739735i | \(0.265049\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.23506 | 1.04701 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.89999 | −0.943004 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.50307 | −1.20759 | −0.603795 | − | 0.797140i | \(-0.706345\pi\) | ||||
−0.603795 | + | 0.797140i | \(0.706345\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.96708 | 0.892113 | 0.446057 | − | 0.895005i | \(-0.352828\pi\) | ||||
0.446057 | + | 0.895005i | \(0.352828\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.23935 | 0.912055 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −12.0103 | −2.03012 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.39405 | −0.557979 | −0.278990 | − | 0.960294i | \(-0.589999\pi\) | ||||
−0.278990 | + | 0.960294i | \(0.589999\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.0915307 | −0.0146566 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.13947 | 1.27117 | 0.635585 | − | 0.772031i | \(-0.280759\pi\) | ||||
0.635585 | + | 0.772031i | \(0.280759\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.71512 | −0.566551 | −0.283275 | − | 0.959039i | \(-0.591421\pi\) | ||||
−0.283275 | + | 0.959039i | \(0.591421\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.60181 | 0.984139 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.50432 | −1.38635 | −0.693174 | − | 0.720770i | \(-0.743788\pi\) | ||||
−0.693174 | + | 0.720770i | \(0.743788\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.09357 | 1.01337 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.967697 | 0.135505 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.30050 | 0.865441 | 0.432720 | − | 0.901528i | \(-0.357554\pi\) | ||||
0.432720 | + | 0.901528i | \(0.357554\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −17.3214 | −2.33562 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.473543 | 0.0627223 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.32942 | −1.19451 | −0.597255 | − | 0.802051i | \(-0.703742\pi\) | ||||
−0.597255 | + | 0.802051i | \(0.703742\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.74690 | −0.976018 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.302602 | 0.0375332 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.16771 | 0.753505 | 0.376753 | − | 0.926314i | \(-0.377041\pi\) | ||||
0.376753 | + | 0.926314i | \(0.377041\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.24572 | 0.751896 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.60812 | 1.02160 | 0.510798 | − | 0.859701i | \(-0.329350\pi\) | ||||
0.510798 | + | 0.859701i | \(0.329350\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.03033 | 0.705796 | 0.352898 | − | 0.935662i | \(-0.385196\pi\) | ||||
0.352898 | + | 0.935662i | \(0.385196\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.06595 | 0.584965 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 20.3259 | 2.31635 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.60416 | −0.855534 | −0.427767 | − | 0.903889i | \(-0.640700\pi\) | ||||
−0.427767 | + | 0.903889i | \(0.640700\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.44898 | 0.160998 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.92704 | 0.979870 | 0.489935 | − | 0.871759i | \(-0.337021\pi\) | ||||
0.489935 | + | 0.871759i | \(0.337021\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.19923 | −0.347005 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.29300 | −0.674680 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.79783 | 0.720569 | 0.360284 | − | 0.932843i | \(-0.382680\pi\) | ||||
0.360284 | + | 0.932843i | \(0.382680\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.355089 | −0.0372235 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.80662 | 0.498424 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.56554 | −0.160621 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.47723 | 0.556129 | 0.278064 | − | 0.960562i | \(-0.410307\pi\) | ||||
0.278064 | + | 0.960562i | \(0.410307\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.1726 | −1.12289 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.2743 | 1.91787 | 0.958935 | − | 0.283627i | \(-0.0915378\pi\) | ||||
0.958935 | + | 0.283627i | \(0.0915378\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.85323 | −0.478203 | −0.239101 | − | 0.970995i | \(-0.576853\pi\) | ||||
−0.239101 | + | 0.970995i | \(0.576853\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.6224 | −1.13423 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.24811 | 0.410680 | 0.205340 | − | 0.978691i | \(-0.434170\pi\) | ||||
0.205340 | + | 0.978691i | \(0.434170\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.7879 | −1.12908 | −0.564538 | − | 0.825407i | \(-0.690946\pi\) | ||||
−0.564538 | + | 0.825407i | \(0.690946\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.28442 | −0.311743 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.23556 | 0.492520 | 0.246260 | − | 0.969204i | \(-0.420798\pi\) | ||||
0.246260 | + | 0.969204i | \(0.420798\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −20.6485 | −1.92548 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.195184 | 0.0180448 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.75414 | 0.344141 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.3141 | 1.66492 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.87654 | 0.710203 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.751995 | −0.0672605 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.9340 | 1.23644 | 0.618221 | − | 0.786004i | \(-0.287854\pi\) | ||||
0.618221 | + | 0.786004i | \(0.287854\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.59511 | −0.316532 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.24344 | 0.196010 | 0.0980052 | − | 0.995186i | \(-0.468754\pi\) | ||||
0.0980052 | + | 0.995186i | \(0.468754\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.83709 | 0.159296 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 15.6762 | 1.34919 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.45912 | 0.551839 | 0.275920 | − | 0.961181i | \(-0.411018\pi\) | ||||
0.275920 | + | 0.961181i | \(0.411018\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.8781 | −1.00749 | −0.503743 | − | 0.863853i | \(-0.668044\pi\) | ||||
−0.503743 | + | 0.863853i | \(0.668044\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.19730 | −0.774553 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.512113 | −0.0428250 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.8048 | 1.72774 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.86443 | 0.566168 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.38363 | 0.195275 | 0.0976375 | − | 0.995222i | \(-0.468871\pi\) | ||||
0.0976375 | + | 0.995222i | \(0.468871\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.52333 | 0.205346 | 0.102673 | − | 0.994715i | \(-0.467260\pi\) | ||||
0.102673 | + | 0.994715i | \(0.467260\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.06356 | −0.166829 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.8908 | −1.27638 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.0785 | 0.963970 | 0.481985 | − | 0.876179i | \(-0.339916\pi\) | ||||
0.481985 | + | 0.876179i | \(0.339916\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.09698 | 0.483522 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.2300 | 1.90959 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.98874 | −0.155770 | −0.0778850 | − | 0.996962i | \(-0.524817\pi\) | ||||
−0.0778850 | + | 0.996962i | \(0.524817\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −16.7619 | −1.30491 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.09011 | 0.316502 | 0.158251 | − | 0.987399i | \(-0.449414\pi\) | ||||
0.158251 | + | 0.987399i | \(0.449414\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9911 | −0.999312 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00981 | −0.0772218 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.4486 | −0.794389 | −0.397194 | − | 0.917735i | \(-0.630016\pi\) | ||||
−0.397194 | + | 0.917735i | \(0.630016\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 19.6531 | 1.48564 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.967697 | 0.0727366 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.99677 | 0.597707 | 0.298853 | − | 0.954299i | \(-0.403396\pi\) | ||||
0.298853 | + | 0.954299i | \(0.403396\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.9418 | 1.18494 | 0.592472 | − | 0.805591i | \(-0.298152\pi\) | ||||
0.592472 | + | 0.805591i | \(0.298152\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.02806 | −0.667373 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.8583 | 0.798322 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.41425 | 0.395929 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −18.3953 | −1.33806 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.8272 | 0.783429 | 0.391715 | − | 0.920087i | \(-0.371882\pi\) | ||||
0.391715 | + | 0.920087i | \(0.371882\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.34664 | −0.672786 | −0.336393 | − | 0.941722i | \(-0.609207\pi\) | ||||
−0.336393 | + | 0.941722i | \(0.609207\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.292827 | 0.0209698 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.4269 | −1.24161 | −0.620807 | − | 0.783964i | \(-0.713195\pi\) | ||||
−0.620807 | + | 0.783964i | \(0.713195\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.44086 | 0.527469 | 0.263734 | − | 0.964595i | \(-0.415046\pi\) | ||||
0.263734 | + | 0.964595i | \(0.415046\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.96847 | 0.420984 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −24.4134 | −1.71349 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −26.0400 | −1.81871 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −13.3187 | −0.925711 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.64947 | 0.183268 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.0756 | −1.03785 | −0.518923 | − | 0.854821i | \(-0.673667\pi\) | ||||
−0.518923 | + | 0.854821i | \(0.673667\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.33005 | 0.570766 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.8855 | 0.810585 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.6471 | 1.26585 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.83553 | 0.394329 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.0945861 | −0.00636255 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.1230 | 1.28057 | 0.640286 | − | 0.768137i | \(-0.278816\pi\) | ||||
0.640286 | + | 0.768137i | \(0.278816\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.8029 | −0.720191 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.26372 | 0.282993 | 0.141496 | − | 0.989939i | \(-0.454809\pi\) | ||||
0.141496 | + | 0.989939i | \(0.454809\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.2755 | 1.73634 | 0.868169 | − | 0.496269i | \(-0.165297\pi\) | ||||
0.868169 | + | 0.496269i | \(0.165297\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 19.6693 | 1.29414 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.9285 | 1.24005 | 0.620025 | − | 0.784582i | \(-0.287122\pi\) | ||||
0.620025 | + | 0.784582i | \(0.287122\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 30.4065 | 1.98350 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.35852 | −0.477987 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.77782 | 0.373736 | 0.186868 | − | 0.982385i | \(-0.440166\pi\) | ||||
0.186868 | + | 0.982385i | \(0.440166\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.15928 | −0.590001 | −0.295001 | − | 0.955497i | \(-0.595320\pi\) | ||||
−0.295001 | + | 0.955497i | \(0.595320\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.1022 | 1.03295 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −22.6939 | −1.44986 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0462858 | −0.00294509 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.63867 | 0.547453 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.28759 | −0.144392 | −0.0721958 | − | 0.997390i | \(-0.523001\pi\) | ||||
−0.0721958 | + | 0.997390i | \(0.523001\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 34.9447 | 2.19695 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.09588 | −0.193872 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.8830 | 0.678863 | 0.339432 | − | 0.940631i | \(-0.389765\pi\) | ||||
0.339432 | + | 0.940631i | \(0.389765\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.7418 | −0.791734 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.4195 | 0.830645 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.24016 | 0.384785 | 0.192393 | − | 0.981318i | \(-0.438375\pi\) | ||||
0.192393 | + | 0.981318i | \(0.438375\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.1567 | −1.23822 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.57824 | 0.402582 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.8170 | 0.964377 | 0.482188 | − | 0.876068i | \(-0.339842\pi\) | ||||
0.482188 | + | 0.876068i | \(0.339842\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.1698 | −1.28597 | −0.642987 | − | 0.765877i | \(-0.722305\pi\) | ||||
−0.642987 | + | 0.765877i | \(0.722305\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.343619 | −0.0207968 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 28.3439 | 1.70920 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30.0769 | 1.80715 | 0.903573 | − | 0.428433i | \(-0.140934\pi\) | ||||
0.903573 | + | 0.428433i | \(0.140934\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.2499 | −0.613644 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.2552 | −0.790737 | −0.395369 | − | 0.918523i | \(-0.629383\pi\) | ||||
−0.395369 | + | 0.918523i | \(0.629383\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.59404 | −0.570306 | −0.285153 | − | 0.958482i | \(-0.592044\pi\) | ||||
−0.285153 | + | 0.958482i | \(0.592044\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.51497 | −0.0897392 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 30.5567 | 1.80370 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.30030 | 0.310709 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −30.0303 | −1.75439 | −0.877195 | − | 0.480135i | \(-0.840588\pi\) | ||||
−0.877195 | + | 0.480135i | \(0.840588\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.19923 | −0.186266 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −26.5298 | −1.53942 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.610478 | −0.0353049 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.9471 | −0.803897 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.6517 | 1.07151 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 29.8469 | 1.70903 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.9818 | −0.855054 | −0.427527 | − | 0.904002i | \(-0.640615\pi\) | ||||
−0.427527 | + | 0.904002i | \(0.640615\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.69645 | −0.267172 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.3729 | 1.04183 | 0.520915 | − | 0.853609i | \(-0.325591\pi\) | ||||
0.520915 | + | 0.853609i | \(0.325591\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 33.4922 | 1.89309 | 0.946544 | − | 0.322574i | \(-0.104548\pi\) | ||||
0.946544 | + | 0.322574i | \(0.104548\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 24.7841 | 1.39643 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.0899 | −1.12836 | −0.564180 | − | 0.825652i | \(-0.690808\pi\) | ||||
−0.564180 | + | 0.825652i | \(0.690808\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −35.2092 | −1.97134 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.11088 | 0.229447 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.489351 | 0.0272282 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.495163 | −0.0274667 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.4071 | −0.630815 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −35.6806 | −1.96713 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.08344 | 0.169481 | 0.0847405 | − | 0.996403i | \(-0.472994\pi\) | ||||
0.0847405 | + | 0.996403i | \(0.472994\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.00384 | 0.383808 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.7319 | −1.07807 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.0227 | −1.47202 | −0.736009 | − | 0.676971i | \(-0.763292\pi\) | ||||
−0.736009 | + | 0.676971i | \(0.763292\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.06644 | 0.275171 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.8930 | 1.45634 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.351279 | 0.0189673 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −19.9815 | −1.07577 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −34.8592 | −1.87134 | −0.935669 | − | 0.352879i | \(-0.885203\pi\) | ||||
−0.935669 | + | 0.352879i | \(0.885203\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.1338 | −0.917152 | −0.458576 | − | 0.888655i | \(-0.651640\pi\) | ||||
−0.458576 | + | 0.888655i | \(0.651640\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.463471 | 0.0247383 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.5647 | 0.562303 | 0.281151 | − | 0.959663i | \(-0.409284\pi\) | ||||
0.281151 | + | 0.959663i | \(0.409284\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −27.5393 | −1.46164 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.63287 | 0.192272 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.0374 | −1.58531 | −0.792657 | − | 0.609668i | \(-0.791303\pi\) | ||||
−0.792657 | + | 0.609668i | \(0.791303\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7605 | −0.987397 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.7225 | 0.930191 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.2924 | −1.00981 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.3908 | −0.698992 | −0.349496 | − | 0.936938i | \(-0.613647\pi\) | ||||
−0.349496 | + | 0.936938i | \(0.613647\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.7963 | −0.874380 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.6530 | 1.22800 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.587075 | −0.0303976 | −0.0151988 | − | 0.999884i | \(-0.504838\pi\) | ||||
−0.0151988 | + | 0.999884i | \(0.504838\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.727703 | −0.0375784 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.615100 | 0.0316792 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.3833 | 0.892921 | 0.446461 | − | 0.894803i | \(-0.352684\pi\) | ||||
0.446461 | + | 0.894803i | \(0.352684\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.4839 | 0.690801 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.7571 | −1.11174 | −0.555868 | − | 0.831271i | \(-0.687614\pi\) | ||||
−0.555868 | + | 0.831271i | \(0.687614\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −65.0270 | −3.31408 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.66638 | 0.389704 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.95005 | 0.149573 | 0.0747867 | − | 0.997200i | \(-0.476172\pi\) | ||||
0.0747867 | + | 0.997200i | \(0.476172\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.45421 | 0.326403 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.17097 | 0.109511 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 24.3274 | 1.22405 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.89442 | 0.396209 | 0.198105 | − | 0.980181i | \(-0.436521\pi\) | ||||
0.198105 | + | 0.980181i | \(0.436521\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.77775 | 0.0889987 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 39.3098 | 1.96304 | 0.981519 | − | 0.191363i | \(-0.0612908\pi\) | ||||
0.981519 | + | 0.191363i | \(0.0612908\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.469816 | −0.0234032 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.63561 | −0.230345 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.3763 | −0.910877 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.8331 | 0.782895 | 0.391448 | − | 0.920200i | \(-0.371974\pi\) | ||||
0.391448 | + | 0.920200i | \(0.371974\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.25047 | 0.308313 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.75414 | 0.184729 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −28.5596 | −1.40194 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.4944 | −0.562883 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.3553 | 1.23869 | 0.619344 | − | 0.785120i | \(-0.287399\pi\) | ||||
0.619344 | + | 0.785120i | \(0.287399\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.4296 | −1.53179 | −0.765894 | − | 0.642967i | \(-0.777703\pi\) | ||||
−0.765894 | + | 0.642967i | \(0.777703\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 19.6128 | 0.953605 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.23506 | 0.253937 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −35.0240 | −1.69493 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.495570 | −0.0239263 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.6013 | 1.04050 | 0.520249 | − | 0.854015i | \(-0.325839\pi\) | ||||
0.520249 | + | 0.854015i | \(0.325839\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.07192 | −0.243741 | −0.121871 | − | 0.992546i | \(-0.538889\pi\) | ||||
−0.121871 | + | 0.992546i | \(0.538889\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 20.1327 | 0.965291 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.15837 | 0.151085 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.9908 | −0.715470 | −0.357735 | − | 0.933823i | \(-0.616451\pi\) | ||||
−0.357735 | + | 0.933823i | \(0.616451\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.6380 | −0.697049 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.2757 | 0.488211 | 0.244106 | − | 0.969749i | \(-0.421506\pi\) | ||||
0.244106 | + | 0.969749i | \(0.421506\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −21.7478 | −1.03094 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.30664 | 0.109100 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.0309 | −1.55882 | −0.779411 | − | 0.626513i | \(-0.784482\pi\) | ||||
−0.779411 | + | 0.626513i | \(0.784482\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 44.0691 | 2.07513 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.44182 | 0.114727 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.13601 | 0.0532571 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.19815 | −0.289937 | −0.144969 | − | 0.989436i | \(-0.546308\pi\) | ||||
−0.144969 | + | 0.989436i | \(0.546308\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.89999 | −0.228712 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.7754 | −1.01418 | −0.507091 | − | 0.861892i | \(-0.669279\pi\) | ||||
−0.507091 | + | 0.861892i | \(0.669279\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.5267 | −0.953956 | −0.476978 | − | 0.878915i | \(-0.658268\pi\) | ||||
−0.476978 | + | 0.878915i | \(0.658268\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −15.3775 | −0.713114 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.23887 | 0.288700 | 0.144350 | − | 0.989527i | \(-0.453891\pi\) | ||||
0.144350 | + | 0.989527i | \(0.453891\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.1544 | 1.06917 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.6883 | 0.538570 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −20.1146 | −0.924870 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.56178 | 0.117542 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.0015 | −0.595297 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.5147 | 0.754577 | 0.377289 | − | 0.926096i | \(-0.376856\pi\) | ||||
0.377289 | + | 0.926096i | \(0.376856\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.321030 | 0.0146377 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 23.4473 | 1.06689 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.5229 | −0.795674 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.1432 | −1.27529 | −0.637646 | − | 0.770330i | \(-0.720092\pi\) | ||||
−0.637646 | + | 0.770330i | \(0.720092\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.92450 | −0.0870287 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 42.9324 | 1.93751 | 0.968757 | − | 0.248013i | \(-0.0797774\pi\) | ||||
0.968757 | + | 0.248013i | \(0.0797774\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.50307 | −0.292883 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 35.7438 | 1.60657 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 32.3161 | 1.44957 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.9294 | 0.623565 | 0.311783 | − | 0.950153i | \(-0.399074\pi\) | ||||
0.311783 | + | 0.950153i | \(0.399074\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.95799 | 0.176830 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −38.3172 | −1.70848 | −0.854240 | − | 0.519879i | \(-0.825977\pi\) | ||||
−0.854240 | + | 0.519879i | \(0.825977\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −61.6630 | −2.74397 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.5714 | −0.558316 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −23.1595 | −1.02653 | −0.513263 | − | 0.858231i | \(-0.671564\pi\) | ||||
−0.513263 | + | 0.858231i | \(0.671564\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.6387 | 1.00148 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.39782 | −0.105866 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.5266 | 0.684183 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −51.4588 | −2.26315 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.1110 | −0.443825 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −34.4628 | −1.50984 | −0.754921 | − | 0.655815i | \(-0.772325\pi\) | ||||
−0.754921 | + | 0.655815i | \(0.772325\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.8131 | −0.647730 | −0.323865 | − | 0.946103i | \(-0.604982\pi\) | ||||
−0.323865 | + | 0.946103i | \(0.604982\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 19.0183 | 0.830026 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.96708 | 0.216369 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.6568 | 0.811166 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.06356 | −0.0895510 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.769880 | −0.0333472 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.5907 | −0.587576 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.73845 | 0.333939 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 38.4064 | 1.65428 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.9944 | −1.50452 | −0.752262 | − | 0.658864i | \(-0.771037\pi\) | ||||
−0.752262 | + | 0.658864i | \(0.771037\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.4268 | 0.662028 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 37.7122 | 1.61541 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.90475 | 0.124198 | 0.0620991 | − | 0.998070i | \(-0.480221\pi\) | ||||
0.0620991 | + | 0.998070i | \(0.480221\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 19.2519 | 0.821649 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.18228 | −0.135570 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.5471 | −1.21395 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.5076 | 0.446022 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −46.7718 | −1.98179 | −0.990893 | − | 0.134651i | \(-0.957009\pi\) | ||||
−0.990893 | + | 0.134651i | \(0.957009\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.351399 | 0.0148626 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.23935 | 0.221206 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.56674 | 0.0660303 | 0.0330152 | − | 0.999455i | \(-0.489489\pi\) | ||||
0.0330152 | + | 0.999455i | \(0.489489\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.7498 | −0.704668 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.43967 | 0.228445 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.1198 | 1.43037 | 0.715187 | − | 0.698933i | \(-0.246341\pi\) | ||||
0.715187 | + | 0.698933i | \(0.246341\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.4531 | 1.77661 | 0.888303 | − | 0.459257i | \(-0.151884\pi\) | ||||
0.888303 | + | 0.459257i | \(0.151884\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.4775 | 0.437702 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 33.7881 | 1.40906 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.93398 | 0.371927 | 0.185963 | − | 0.982557i | \(-0.440459\pi\) | ||||
0.185963 | + | 0.982557i | \(0.440459\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.04471 | −0.375885 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 33.5134 | 1.39037 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 34.1125 | 1.41280 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.624439 | −0.0258174 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.4493 | 1.25678 | 0.628390 | − | 0.777899i | \(-0.283714\pi\) | ||||
0.628390 | + | 0.777899i | \(0.283714\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.43064 | 0.100153 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.8639 | −0.693689 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.0563 | 0.987872 | 0.493936 | − | 0.869498i | \(-0.335558\pi\) | ||||
0.493936 | + | 0.869498i | \(0.335558\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0103 | −0.492376 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.20050 | 0.294697 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 41.8664 | 1.71062 | 0.855308 | − | 0.518120i | \(-0.173368\pi\) | ||||
0.855308 | + | 0.518120i | \(0.173368\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.7687 | 1.66299 | 0.831495 | − | 0.555532i | \(-0.187485\pi\) | ||||
0.831495 | + | 0.555532i | \(0.187485\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.7275 | −0.518302 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −58.5910 | −2.38206 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.9424 | −1.58062 | −0.790312 | − | 0.612705i | \(-0.790081\pi\) | ||||
−0.790312 | + | 0.612705i | \(0.790081\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −23.6248 | −0.957325 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.898977 | 0.0363687 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.4953 | 0.545068 | 0.272534 | − | 0.962146i | \(-0.412138\pi\) | ||||
0.272534 | + | 0.962146i | \(0.412138\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −25.1988 | −1.01611 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.8878 | 0.559101 | 0.279551 | − | 0.960131i | \(-0.409815\pi\) | ||||
0.279551 | + | 0.960131i | \(0.409815\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.4746 | 0.863135 | 0.431568 | − | 0.902081i | \(-0.357961\pi\) | ||||
0.431568 | + | 0.902081i | \(0.357961\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −31.6256 | −1.26909 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 25.5200 | 1.02244 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.7695 | −0.950779 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.56388 | 0.102392 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.39405 | −0.135330 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.3546 | −0.730685 | −0.365343 | − | 0.930873i | \(-0.619048\pi\) | ||||
−0.365343 | + | 0.930873i | \(0.619048\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.5886 | −0.579844 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −44.5780 | −1.76903 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.670953 | −0.0265841 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17.7634 | −0.702709 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −37.9184 | −1.49769 | −0.748843 | − | 0.662747i | \(-0.769390\pi\) | ||||
−0.748843 | + | 0.662747i | \(0.769390\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.51867 | −0.0993266 | −0.0496633 | − | 0.998766i | \(-0.515815\pi\) | ||||
−0.0496633 | + | 0.998766i | \(0.515815\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.5016 | 0.452874 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.2313 | 0.598806 | 0.299403 | − | 0.954127i | \(-0.403212\pi\) | ||||
0.299403 | + | 0.954127i | \(0.403212\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.41425 | 0.212528 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 18.0447 | 0.707229 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.2562 | 0.401358 | 0.200679 | − | 0.979657i | \(-0.435685\pi\) | ||||
0.200679 | + | 0.979657i | \(0.435685\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.17728 | −0.280439 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.4440 | −0.485485 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.3376 | −0.948059 | −0.474029 | − | 0.880509i | \(-0.657201\pi\) | ||||
−0.474029 | + | 0.880509i | \(0.657201\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.7069 | 0.416451 | 0.208226 | − | 0.978081i | \(-0.433231\pi\) | ||||
0.208226 | + | 0.978081i | \(0.433231\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.0915307 | −0.00355476 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.87727 | −0.227911 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −41.9722 | −1.62517 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.5053 | 0.715456 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −50.5118 | −1.94999 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.7882 | 1.10970 | 0.554851 | − | 0.831950i | \(-0.312775\pi\) | ||||
0.554851 | + | 0.831950i | \(0.312775\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.6517 | −0.987336 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.6003 | −0.983898 | −0.491949 | − | 0.870624i | \(-0.663715\pi\) | ||||
−0.491949 | + | 0.870624i | \(0.663715\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.5623 | 0.789109 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.12598 | 0.158108 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.6100 | 0.597301 | 0.298650 | − | 0.954363i | \(-0.403464\pi\) | ||||
0.298650 | + | 0.954363i | \(0.403464\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.6642 | −0.789538 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.4268 | 0.970092 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.595940 | −0.0227035 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.7545 | −1.28408 | −0.642042 | − | 0.766670i | \(-0.721912\pi\) | ||||
−0.642042 | + | 0.766670i | \(0.721912\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −41.9437 | −1.59331 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 38.0007 | 1.44145 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.13947 | 0.308304 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.3171 | 0.692816 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.9310 | −1.20602 | −0.603010 | − | 0.797734i | \(-0.706032\pi\) | ||||
−0.603010 | + | 0.797734i | \(0.706032\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.66088 | −0.0626414 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 29.4243 | 1.10818 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 72.3586 | 2.72133 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.9943 | 0.638233 | 0.319117 | − | 0.947715i | \(-0.396614\pi\) | ||||
0.319117 | + | 0.947715i | \(0.396614\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.6917 | 0.588483 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 32.0585 | 1.20060 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.63837 | 0.0612714 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.59118 | 0.208806 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.7022 | −0.958531 | −0.479265 | − | 0.877670i | \(-0.659097\pi\) | ||||
−0.479265 | + | 0.877670i | \(0.659097\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.2197 | −0.678537 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.86341 | −0.329634 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −34.0439 | −1.26436 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.6313 | −1.50693 | −0.753465 | − | 0.657488i | \(-0.771619\pi\) | ||||
−0.753465 | + | 0.657488i | \(0.771619\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11.2351 | 0.416114 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.71512 | −0.137409 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.01414 | −0.148265 | −0.0741327 | − | 0.997248i | \(-0.523619\pi\) | ||||
−0.0741327 | + | 0.997248i | \(0.523619\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −21.9609 | −0.810039 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 33.3935 | 1.23007 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.98360 | 0.146539 | 0.0732695 | − | 0.997312i | \(-0.476657\pi\) | ||||
0.0732695 | + | 0.997312i | \(0.476657\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.0447906 | −0.00164542 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.07133 | −0.112676 | −0.0563381 | − | 0.998412i | \(-0.517942\pi\) | ||||
−0.0563381 | + | 0.998412i | \(0.517942\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.62579 | −0.279387 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18.4215 | −0.674008 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.9480 | 0.582727 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −54.1734 | −1.97682 | −0.988408 | − | 0.151822i | \(-0.951486\pi\) | ||||
−0.988408 | + | 0.151822i | \(0.951486\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.21370 | −0.0806716 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.07272 | −0.293796 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.9569 | −0.579965 | −0.289982 | − | 0.957032i | \(-0.593649\pi\) | ||||
−0.289982 | + | 0.957032i | \(0.593649\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 33.8159 | 1.22744 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.0484 | 1.19800 | 0.599002 | − | 0.800748i | \(-0.295564\pi\) | ||||
0.599002 | + | 0.800748i | \(0.295564\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −44.2535 | −1.60208 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.60181 | 0.238689 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.0945861 | −0.00341531 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.46725 | 0.233215 | 0.116607 | − | 0.993178i | \(-0.462798\pi\) | ||||
0.116607 | + | 0.993178i | \(0.462798\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.5314 | 0.379281 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.0822 | 0.866178 | 0.433089 | − | 0.901351i | \(-0.357424\pi\) | ||||
0.433089 | + | 0.901351i | \(0.357424\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.0029 | 0.934052 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12.3302 | −0.442342 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.98305 | 0.142708 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 46.6065 | 1.66771 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 31.8650 | 1.13876 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −38.6419 | −1.37919 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.2172 | −0.863252 | −0.431626 | − | 0.902053i | \(-0.642060\pi\) | ||||
−0.431626 | + | 0.902053i | \(0.642060\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.03859 | 0.214979 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.6550 | 0.698853 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.882434 | 0.0313361 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −19.5056 | −0.691793 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.93205 | 0.0684366 | 0.0342183 | − | 0.999414i | \(-0.489106\pi\) | ||||
0.0342183 | + | 0.999414i | \(0.489106\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.50432 | −0.336239 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.0278 | −0.495646 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.6497 | 1.15218 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −77.5173 | −2.73213 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.3060 | 0.538797 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.9018 | −0.910660 | −0.455330 | − | 0.890323i | \(-0.650479\pi\) | ||||
−0.455330 | + | 0.890323i | \(0.650479\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.5728 | −0.546836 | −0.273418 | − | 0.961895i | \(-0.588154\pi\) | ||||
−0.273418 | + | 0.961895i | \(0.588154\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.4860 | −0.718474 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.36243 | 0.222866 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.81800 | −0.0636037 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.732749 | 0.0256043 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.5587 | −1.06651 | −0.533253 | − | 0.845956i | \(-0.679031\pi\) | ||||
−0.533253 | + | 0.845956i | \(0.679031\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.37212 | 0.291834 | 0.145917 | − | 0.989297i | \(-0.453387\pi\) | ||||
0.145917 | + | 0.989297i | \(0.453387\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 27.4283 | 0.954931 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.5016 | −0.539042 | −0.269521 | − | 0.962994i | \(-0.586865\pi\) | ||||
−0.269521 | + | 0.962994i | \(0.586865\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.0173 | −0.834155 | −0.417077 | − | 0.908871i | \(-0.636946\pi\) | ||||
−0.417077 | + | 0.908871i | \(0.636946\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.1053 | 1.00965 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.09357 | 0.245778 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.0852 | −0.452832 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −24.3386 | −0.841267 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.6950 | 1.02519 | 0.512593 | − | 0.858632i | \(-0.328685\pi\) | ||||
0.512593 | + | 0.858632i | \(0.328685\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.2899 | 0.458272 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.8270 | −0.441785 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 41.5613 | 1.42975 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 68.7538 | 2.36241 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.28412 | −0.318630 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.9059 | −0.750926 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.4158 | 0.596307 | 0.298154 | − | 0.954518i | \(-0.403629\pi\) | ||||
0.298154 | + | 0.954518i | \(0.403629\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.23060 | 0.110484 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.3879 | −0.525641 | −0.262821 | − | 0.964845i | \(-0.584653\pi\) | ||||
−0.262821 | + | 0.964845i | \(0.584653\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.6185 | −0.464656 | −0.232328 | − | 0.972637i | \(-0.574634\pi\) | ||||
−0.232328 | + | 0.972637i | \(0.574634\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 29.5696 | 1.00773 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.3267 | 0.998293 | 0.499146 | − | 0.866518i | \(-0.333647\pi\) | ||||
0.499146 | + | 0.866518i | \(0.333647\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 33.4273 | 1.13656 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.967697 | 0.0328647 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −41.1708 | −1.39662 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.583379 | −0.0197671 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.3026 | −0.382535 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.82309 | −0.0954380 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.1989 | 0.783372 | 0.391686 | − | 0.920099i | \(-0.371892\pi\) | ||||
0.391686 | + | 0.920099i | \(0.371892\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −29.0602 | −0.980178 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.8370 | 0.702016 | 0.351008 | − | 0.936372i | \(-0.385839\pi\) | ||||
0.351008 | + | 0.936372i | \(0.385839\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.4308 | 1.15869 | 0.579344 | − | 0.815083i | \(-0.303309\pi\) | ||||
0.579344 | + | 0.815083i | \(0.303309\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.09588 | −0.104067 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.0059 | −0.369543 | −0.184772 | − | 0.982781i | \(-0.559155\pi\) | ||||
−0.184772 | + | 0.982781i | \(0.559155\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 52.3102 | 1.75443 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.84513 | 0.262822 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.65095 | −0.155638 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.5835 | −0.855162 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.590758 | −0.0197248 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −32.3012 | −1.07731 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.30050 | 0.209900 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.4966 | −0.449137 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −51.0014 | −1.69534 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.9867 | −0.364809 | −0.182404 | − | 0.983224i | \(-0.558388\pi\) | ||||
−0.182404 | + | 0.983224i | \(0.558388\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −39.7738 | −1.31921 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.52025 | −0.0503682 | −0.0251841 | − | 0.999683i | \(-0.508017\pi\) | ||||
−0.0251841 | + | 0.999683i | \(0.508017\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 48.3332 | 1.59960 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 28.8828 | 0.954836 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.42219 | 0.278125 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.0388 | −0.661018 | −0.330509 | − | 0.943803i | \(-0.607220\pi\) | ||||
−0.330509 | + | 0.943803i | \(0.607220\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.4978 | −0.477719 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.814208 | −0.0268000 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.7681 | −0.584210 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.0149 | 0.328934 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.7997 | 0.780843 | 0.390421 | − | 0.920636i | \(-0.372329\pi\) | ||||
0.390421 | + | 0.920636i | \(0.372329\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.47124 | 0.113765 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.7794 | 0.582070 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −17.3214 | −0.566471 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.7349 | 1.42876 | 0.714378 | − | 0.699760i | \(-0.246710\pi\) | ||||
0.714378 | + | 0.699760i | \(0.246710\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32.4103 | 1.05767 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.9657 | −0.455267 | −0.227634 | − | 0.973747i | \(-0.573099\pi\) | ||||
−0.227634 | + | 0.973747i | \(0.573099\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 52.5338 | 1.71074 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 58.8506 | 1.91441 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.4707 | −0.665207 | −0.332604 | − | 0.943067i | \(-0.607927\pi\) | ||||
−0.332604 | + | 0.943067i | \(0.607927\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.570385 | −0.0185155 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.4409 | −0.630415 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.89960 | 0.191107 | 0.0955533 | − | 0.995424i | \(-0.469538\pi\) | ||||
0.0955533 | + | 0.995424i | \(0.469538\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −34.6387 | −1.12088 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −34.0719 | −1.10139 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 24.2484 | 0.783023 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.32815 | −0.204134 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.76624 | −0.282488 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 29.9020 | 0.962580 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.8452 | −0.606020 | −0.303010 | − | 0.952987i | \(-0.597992\pi\) | ||||
−0.303010 | + | 0.952987i | \(0.597992\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.473543 | 0.0152124 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.9339 | −0.896440 | −0.448220 | − | 0.893923i | \(-0.647942\pi\) | ||||
−0.448220 | + | 0.893923i | \(0.647942\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −44.5920 | −1.42955 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.479168 | −0.0153457 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.0387 | −0.353159 | −0.176579 | − | 0.984286i | \(-0.556503\pi\) | ||||
−0.176579 | + | 0.984286i | \(0.556503\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.8052 | 1.17630 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24.3251 | 0.776640 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.7116 | 0.851966 | 0.425983 | − | 0.904731i | \(-0.359928\pi\) | ||||
0.425983 | + | 0.904731i | \(0.359928\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 55.7525 | 1.77642 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −34.5280 | −1.09904 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −23.9782 | −0.762461 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.24329 | −0.166559 | −0.0832793 | − | 0.996526i | \(-0.526539\pi\) | ||||
−0.0832793 | + | 0.996526i | \(0.526539\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.98383 | 0.0946891 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.8050 | −0.754669 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.6894 | 0.655241 | 0.327620 | − | 0.944809i | \(-0.393753\pi\) | ||||
0.327620 | + | 0.944809i | \(0.393753\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16.6308 | 0.526177 |
(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 | 4012.2.a.j.1.13 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.a.j.1.13 | ✓ | 21 | 1.1 | even | 1 | trivial |