Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4009,2,Mod(1,4009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4009, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4009 = 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4009.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: | \(32.0120261703\) |
Analytic rank: | \(1\) |
Dimension: | \(71\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 4009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.08320 | −1.47304 | −0.736522 | − | 0.676414i | \(-0.763533\pi\) | ||||
−0.736522 | + | 0.676414i | \(0.763533\pi\) | |||||||
\(3\) | 2.50442 | 1.44593 | 0.722963 | − | 0.690886i | \(-0.242780\pi\) | ||||
0.722963 | + | 0.690886i | \(0.242780\pi\) | |||||||
\(4\) | 2.33972 | 1.16986 | ||||||||
\(5\) | −4.26568 | −1.90767 | −0.953834 | − | 0.300333i | \(-0.902902\pi\) | ||||
−0.953834 | + | 0.300333i | \(0.902902\pi\) | |||||||
\(6\) | −5.21720 | −2.12991 | ||||||||
\(7\) | −3.89477 | −1.47209 | −0.736043 | − | 0.676935i | \(-0.763308\pi\) | ||||
−0.736043 | + | 0.676935i | \(0.763308\pi\) | |||||||
\(8\) | −0.707698 | −0.250209 | ||||||||
\(9\) | 3.27211 | 1.09070 | ||||||||
\(10\) | 8.88625 | 2.81008 | ||||||||
\(11\) | −0.717906 | −0.216457 | −0.108228 | − | 0.994126i | \(-0.534518\pi\) | ||||
−0.108228 | + | 0.994126i | \(0.534518\pi\) | |||||||
\(12\) | 5.85963 | 1.69153 | ||||||||
\(13\) | 1.36066 | 0.377379 | 0.188689 | − | 0.982037i | \(-0.439576\pi\) | ||||
0.188689 | + | 0.982037i | \(0.439576\pi\) | |||||||
\(14\) | 8.11358 | 2.16845 | ||||||||
\(15\) | −10.6830 | −2.75835 | ||||||||
\(16\) | −3.20516 | −0.801290 | ||||||||
\(17\) | 1.14117 | 0.276776 | 0.138388 | − | 0.990378i | \(-0.455808\pi\) | ||||
0.138388 | + | 0.990378i | \(0.455808\pi\) | |||||||
\(18\) | −6.81646 | −1.60665 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −9.98048 | −2.23170 | ||||||||
\(21\) | −9.75414 | −2.12853 | ||||||||
\(22\) | 1.49554 | 0.318851 | ||||||||
\(23\) | 3.32840 | 0.694019 | 0.347009 | − | 0.937862i | \(-0.387197\pi\) | ||||
0.347009 | + | 0.937862i | \(0.387197\pi\) | |||||||
\(24\) | −1.77237 | −0.361784 | ||||||||
\(25\) | 13.1960 | 2.63920 | ||||||||
\(26\) | −2.83452 | −0.555896 | ||||||||
\(27\) | 0.681482 | 0.131151 | ||||||||
\(28\) | −9.11266 | −1.72213 | ||||||||
\(29\) | 8.60525 | 1.59796 | 0.798978 | − | 0.601361i | \(-0.205375\pi\) | ||||
0.798978 | + | 0.601361i | \(0.205375\pi\) | |||||||
\(30\) | 22.2549 | 4.06317 | ||||||||
\(31\) | −1.36901 | −0.245881 | −0.122941 | − | 0.992414i | \(-0.539232\pi\) | ||||
−0.122941 | + | 0.992414i | \(0.539232\pi\) | |||||||
\(32\) | 8.09238 | 1.43054 | ||||||||
\(33\) | −1.79794 | −0.312981 | ||||||||
\(34\) | −2.37729 | −0.407703 | ||||||||
\(35\) | 16.6138 | 2.80825 | ||||||||
\(36\) | 7.65582 | 1.27597 | ||||||||
\(37\) | −0.348108 | −0.0572287 | −0.0286143 | − | 0.999591i | \(-0.509109\pi\) | ||||
−0.0286143 | + | 0.999591i | \(0.509109\pi\) | |||||||
\(38\) | −2.08320 | −0.337939 | ||||||||
\(39\) | 3.40766 | 0.545662 | ||||||||
\(40\) | 3.01881 | 0.477316 | ||||||||
\(41\) | −3.19719 | −0.499316 | −0.249658 | − | 0.968334i | \(-0.580318\pi\) | ||||
−0.249658 | + | 0.968334i | \(0.580318\pi\) | |||||||
\(42\) | 20.3198 | 3.13541 | ||||||||
\(43\) | 9.29999 | 1.41823 | 0.709117 | − | 0.705090i | \(-0.249094\pi\) | ||||
0.709117 | + | 0.705090i | \(0.249094\pi\) | |||||||
\(44\) | −1.67970 | −0.253224 | ||||||||
\(45\) | −13.9578 | −2.08070 | ||||||||
\(46\) | −6.93371 | −1.02232 | ||||||||
\(47\) | −9.35756 | −1.36494 | −0.682470 | − | 0.730913i | \(-0.739094\pi\) | ||||
−0.682470 | + | 0.730913i | \(0.739094\pi\) | |||||||
\(48\) | −8.02706 | −1.15861 | ||||||||
\(49\) | 8.16924 | 1.16703 | ||||||||
\(50\) | −27.4899 | −3.88766 | ||||||||
\(51\) | 2.85798 | 0.400197 | ||||||||
\(52\) | 3.18356 | 0.441480 | ||||||||
\(53\) | −9.83068 | −1.35035 | −0.675174 | − | 0.737658i | \(-0.735931\pi\) | ||||
−0.675174 | + | 0.737658i | \(0.735931\pi\) | |||||||
\(54\) | −1.41966 | −0.193192 | ||||||||
\(55\) | 3.06236 | 0.412928 | ||||||||
\(56\) | 2.75632 | 0.368329 | ||||||||
\(57\) | 2.50442 | 0.331718 | ||||||||
\(58\) | −17.9265 | −2.35386 | ||||||||
\(59\) | −1.11151 | −0.144706 | −0.0723528 | − | 0.997379i | \(-0.523051\pi\) | ||||
−0.0723528 | + | 0.997379i | \(0.523051\pi\) | |||||||
\(60\) | −24.9953 | −3.22688 | ||||||||
\(61\) | −0.418657 | −0.0536036 | −0.0268018 | − | 0.999641i | \(-0.508532\pi\) | ||||
−0.0268018 | + | 0.999641i | \(0.508532\pi\) | |||||||
\(62\) | 2.85192 | 0.362194 | ||||||||
\(63\) | −12.7441 | −1.60561 | ||||||||
\(64\) | −10.4477 | −1.30596 | ||||||||
\(65\) | −5.80413 | −0.719914 | ||||||||
\(66\) | 3.74546 | 0.461034 | ||||||||
\(67\) | 5.87719 | 0.718013 | 0.359007 | − | 0.933335i | \(-0.383116\pi\) | ||||
0.359007 | + | 0.933335i | \(0.383116\pi\) | |||||||
\(68\) | 2.67003 | 0.323788 | ||||||||
\(69\) | 8.33570 | 1.00350 | ||||||||
\(70\) | −34.6099 | −4.13668 | ||||||||
\(71\) | −10.3544 | −1.22885 | −0.614423 | − | 0.788977i | \(-0.710611\pi\) | ||||
−0.614423 | + | 0.788977i | \(0.710611\pi\) | |||||||
\(72\) | −2.31567 | −0.272904 | ||||||||
\(73\) | 11.0662 | 1.29520 | 0.647602 | − | 0.761979i | \(-0.275772\pi\) | ||||
0.647602 | + | 0.761979i | \(0.275772\pi\) | |||||||
\(74\) | 0.725179 | 0.0843003 | ||||||||
\(75\) | 33.0483 | 3.81609 | ||||||||
\(76\) | 2.33972 | 0.268384 | ||||||||
\(77\) | 2.79608 | 0.318643 | ||||||||
\(78\) | −7.09883 | −0.803784 | ||||||||
\(79\) | 10.0203 | 1.12737 | 0.563687 | − | 0.825989i | \(-0.309382\pi\) | ||||
0.563687 | + | 0.825989i | \(0.309382\pi\) | |||||||
\(80\) | 13.6722 | 1.52860 | ||||||||
\(81\) | −8.10962 | −0.901069 | ||||||||
\(82\) | 6.66037 | 0.735515 | ||||||||
\(83\) | 1.29356 | 0.141987 | 0.0709936 | − | 0.997477i | \(-0.477383\pi\) | ||||
0.0709936 | + | 0.997477i | \(0.477383\pi\) | |||||||
\(84\) | −22.8219 | −2.49008 | ||||||||
\(85\) | −4.86788 | −0.527996 | ||||||||
\(86\) | −19.3737 | −2.08912 | ||||||||
\(87\) | 21.5512 | 2.31053 | ||||||||
\(88\) | 0.508061 | 0.0541595 | ||||||||
\(89\) | 11.1348 | 1.18029 | 0.590145 | − | 0.807297i | \(-0.299070\pi\) | ||||
0.590145 | + | 0.807297i | \(0.299070\pi\) | |||||||
\(90\) | 29.0768 | 3.06497 | ||||||||
\(91\) | −5.29945 | −0.555534 | ||||||||
\(92\) | 7.78751 | 0.811904 | ||||||||
\(93\) | −3.42857 | −0.355526 | ||||||||
\(94\) | 19.4937 | 2.01062 | ||||||||
\(95\) | −4.26568 | −0.437649 | ||||||||
\(96\) | 20.2667 | 2.06846 | ||||||||
\(97\) | −5.00956 | −0.508644 | −0.254322 | − | 0.967120i | \(-0.581852\pi\) | ||||
−0.254322 | + | 0.967120i | \(0.581852\pi\) | |||||||
\(98\) | −17.0182 | −1.71909 | ||||||||
\(99\) | −2.34907 | −0.236090 | ||||||||
\(100\) | 30.8749 | 3.08749 | ||||||||
\(101\) | −4.94851 | −0.492395 | −0.246197 | − | 0.969220i | \(-0.579181\pi\) | ||||
−0.246197 | + | 0.969220i | \(0.579181\pi\) | |||||||
\(102\) | −5.95374 | −0.589508 | ||||||||
\(103\) | −4.69978 | −0.463083 | −0.231542 | − | 0.972825i | \(-0.574377\pi\) | ||||
−0.231542 | + | 0.972825i | \(0.574377\pi\) | |||||||
\(104\) | −0.962935 | −0.0944236 | ||||||||
\(105\) | 41.6080 | 4.06052 | ||||||||
\(106\) | 20.4793 | 1.98912 | ||||||||
\(107\) | −6.63349 | −0.641284 | −0.320642 | − | 0.947200i | \(-0.603899\pi\) | ||||
−0.320642 | + | 0.947200i | \(0.603899\pi\) | |||||||
\(108\) | 1.59447 | 0.153428 | ||||||||
\(109\) | −2.35326 | −0.225401 | −0.112701 | − | 0.993629i | \(-0.535950\pi\) | ||||
−0.112701 | + | 0.993629i | \(0.535950\pi\) | |||||||
\(110\) | −6.37950 | −0.608261 | ||||||||
\(111\) | −0.871809 | −0.0827484 | ||||||||
\(112\) | 12.4834 | 1.17957 | ||||||||
\(113\) | 4.42555 | 0.416320 | 0.208160 | − | 0.978095i | \(-0.433252\pi\) | ||||
0.208160 | + | 0.978095i | \(0.433252\pi\) | |||||||
\(114\) | −5.21720 | −0.488636 | ||||||||
\(115\) | −14.1979 | −1.32396 | ||||||||
\(116\) | 20.1339 | 1.86938 | ||||||||
\(117\) | 4.45223 | 0.411609 | ||||||||
\(118\) | 2.31549 | 0.213158 | ||||||||
\(119\) | −4.44461 | −0.407437 | ||||||||
\(120\) | 7.56037 | 0.690164 | ||||||||
\(121\) | −10.4846 | −0.953146 | ||||||||
\(122\) | 0.872147 | 0.0789604 | ||||||||
\(123\) | −8.00709 | −0.721975 | ||||||||
\(124\) | −3.20309 | −0.287646 | ||||||||
\(125\) | −34.9615 | −3.12705 | ||||||||
\(126\) | 26.5485 | 2.36513 | ||||||||
\(127\) | −16.9923 | −1.50782 | −0.753912 | − | 0.656976i | \(-0.771835\pi\) | ||||
−0.753912 | + | 0.656976i | \(0.771835\pi\) | |||||||
\(128\) | 5.57991 | 0.493199 | ||||||||
\(129\) | 23.2911 | 2.05066 | ||||||||
\(130\) | 12.0912 | 1.06046 | ||||||||
\(131\) | 2.74282 | 0.239641 | 0.119820 | − | 0.992796i | \(-0.461768\pi\) | ||||
0.119820 | + | 0.992796i | \(0.461768\pi\) | |||||||
\(132\) | −4.20667 | −0.366143 | ||||||||
\(133\) | −3.89477 | −0.337719 | ||||||||
\(134\) | −12.2434 | −1.05767 | ||||||||
\(135\) | −2.90698 | −0.250193 | ||||||||
\(136\) | −0.807607 | −0.0692517 | ||||||||
\(137\) | −3.22948 | −0.275914 | −0.137957 | − | 0.990438i | \(-0.544053\pi\) | ||||
−0.137957 | + | 0.990438i | \(0.544053\pi\) | |||||||
\(138\) | −17.3649 | −1.47820 | ||||||||
\(139\) | −12.4364 | −1.05484 | −0.527421 | − | 0.849604i | \(-0.676841\pi\) | ||||
−0.527421 | + | 0.849604i | \(0.676841\pi\) | |||||||
\(140\) | 38.8717 | 3.28526 | ||||||||
\(141\) | −23.4352 | −1.97360 | ||||||||
\(142\) | 21.5704 | 1.81014 | ||||||||
\(143\) | −0.976825 | −0.0816862 | ||||||||
\(144\) | −10.4876 | −0.873970 | ||||||||
\(145\) | −36.7072 | −3.04837 | ||||||||
\(146\) | −23.0532 | −1.90789 | ||||||||
\(147\) | 20.4592 | 1.68745 | ||||||||
\(148\) | −0.814475 | −0.0669494 | ||||||||
\(149\) | −3.07642 | −0.252030 | −0.126015 | − | 0.992028i | \(-0.540219\pi\) | ||||
−0.126015 | + | 0.992028i | \(0.540219\pi\) | |||||||
\(150\) | −68.8462 | −5.62127 | ||||||||
\(151\) | 6.65967 | 0.541956 | 0.270978 | − | 0.962586i | \(-0.412653\pi\) | ||||
0.270978 | + | 0.962586i | \(0.412653\pi\) | |||||||
\(152\) | −0.707698 | −0.0574019 | ||||||||
\(153\) | 3.73405 | 0.301880 | ||||||||
\(154\) | −5.82479 | −0.469375 | ||||||||
\(155\) | 5.83975 | 0.469060 | ||||||||
\(156\) | 7.97296 | 0.638347 | ||||||||
\(157\) | 11.6680 | 0.931208 | 0.465604 | − | 0.884993i | \(-0.345837\pi\) | ||||
0.465604 | + | 0.884993i | \(0.345837\pi\) | |||||||
\(158\) | −20.8743 | −1.66067 | ||||||||
\(159\) | −24.6201 | −1.95250 | ||||||||
\(160\) | −34.5195 | −2.72900 | ||||||||
\(161\) | −12.9633 | −1.02165 | ||||||||
\(162\) | 16.8939 | 1.32731 | ||||||||
\(163\) | −12.9478 | −1.01415 | −0.507077 | − | 0.861901i | \(-0.669274\pi\) | ||||
−0.507077 | + | 0.861901i | \(0.669274\pi\) | |||||||
\(164\) | −7.48051 | −0.584130 | ||||||||
\(165\) | 7.66942 | 0.597064 | ||||||||
\(166\) | −2.69475 | −0.209153 | ||||||||
\(167\) | −9.79314 | −0.757816 | −0.378908 | − | 0.925434i | \(-0.623700\pi\) | ||||
−0.378908 | + | 0.925434i | \(0.623700\pi\) | |||||||
\(168\) | 6.90298 | 0.532577 | ||||||||
\(169\) | −11.1486 | −0.857585 | ||||||||
\(170\) | 10.1408 | 0.777761 | ||||||||
\(171\) | 3.27211 | 0.250225 | ||||||||
\(172\) | 21.7593 | 1.65913 | ||||||||
\(173\) | 10.9902 | 0.835572 | 0.417786 | − | 0.908545i | \(-0.362806\pi\) | ||||
0.417786 | + | 0.908545i | \(0.362806\pi\) | |||||||
\(174\) | −44.8953 | −3.40351 | ||||||||
\(175\) | −51.3954 | −3.88513 | ||||||||
\(176\) | 2.30100 | 0.173445 | ||||||||
\(177\) | −2.78367 | −0.209234 | ||||||||
\(178\) | −23.1961 | −1.73862 | ||||||||
\(179\) | −8.06631 | −0.602904 | −0.301452 | − | 0.953481i | \(-0.597471\pi\) | ||||
−0.301452 | + | 0.953481i | \(0.597471\pi\) | |||||||
\(180\) | −32.6572 | −2.43413 | ||||||||
\(181\) | −5.27084 | −0.391779 | −0.195889 | − | 0.980626i | \(-0.562759\pi\) | ||||
−0.195889 | + | 0.980626i | \(0.562759\pi\) | |||||||
\(182\) | 11.0398 | 0.818326 | ||||||||
\(183\) | −1.04849 | −0.0775069 | ||||||||
\(184\) | −2.35550 | −0.173650 | ||||||||
\(185\) | 1.48492 | 0.109173 | ||||||||
\(186\) | 7.14240 | 0.523706 | ||||||||
\(187\) | −0.819257 | −0.0599100 | ||||||||
\(188\) | −21.8940 | −1.59679 | ||||||||
\(189\) | −2.65422 | −0.193066 | ||||||||
\(190\) | 8.88625 | 0.644677 | ||||||||
\(191\) | −21.2805 | −1.53981 | −0.769903 | − | 0.638162i | \(-0.779695\pi\) | ||||
−0.769903 | + | 0.638162i | \(0.779695\pi\) | |||||||
\(192\) | −26.1654 | −1.88833 | ||||||||
\(193\) | 21.6556 | 1.55881 | 0.779404 | − | 0.626522i | \(-0.215522\pi\) | ||||
0.779404 | + | 0.626522i | \(0.215522\pi\) | |||||||
\(194\) | 10.4359 | 0.749255 | ||||||||
\(195\) | −14.5360 | −1.04094 | ||||||||
\(196\) | 19.1137 | 1.36527 | ||||||||
\(197\) | −4.59309 | −0.327244 | −0.163622 | − | 0.986523i | \(-0.552318\pi\) | ||||
−0.163622 | + | 0.986523i | \(0.552318\pi\) | |||||||
\(198\) | 4.89358 | 0.347772 | ||||||||
\(199\) | 27.3740 | 1.94049 | 0.970247 | − | 0.242119i | \(-0.0778423\pi\) | ||||
0.970247 | + | 0.242119i | \(0.0778423\pi\) | |||||||
\(200\) | −9.33878 | −0.660352 | ||||||||
\(201\) | 14.7189 | 1.03819 | ||||||||
\(202\) | 10.3087 | 0.725319 | ||||||||
\(203\) | −33.5155 | −2.35233 | ||||||||
\(204\) | 6.68686 | 0.468174 | ||||||||
\(205\) | 13.6382 | 0.952530 | ||||||||
\(206\) | 9.79057 | 0.682142 | ||||||||
\(207\) | 10.8909 | 0.756969 | ||||||||
\(208\) | −4.36113 | −0.302390 | ||||||||
\(209\) | −0.717906 | −0.0496586 | ||||||||
\(210\) | −86.6777 | −5.98133 | ||||||||
\(211\) | 1.00000 | 0.0688428 | ||||||||
\(212\) | −23.0010 | −1.57972 | ||||||||
\(213\) | −25.9318 | −1.77682 | ||||||||
\(214\) | 13.8189 | 0.944639 | ||||||||
\(215\) | −39.6707 | −2.70552 | ||||||||
\(216\) | −0.482283 | −0.0328152 | ||||||||
\(217\) | 5.33198 | 0.361958 | ||||||||
\(218\) | 4.90230 | 0.332026 | ||||||||
\(219\) | 27.7145 | 1.87277 | ||||||||
\(220\) | 7.16505 | 0.483067 | ||||||||
\(221\) | 1.55275 | 0.104449 | ||||||||
\(222\) | 1.81615 | 0.121892 | ||||||||
\(223\) | 10.1143 | 0.677305 | 0.338653 | − | 0.940911i | \(-0.390029\pi\) | ||||
0.338653 | + | 0.940911i | \(0.390029\pi\) | |||||||
\(224\) | −31.5180 | −2.10588 | ||||||||
\(225\) | 43.1788 | 2.87859 | ||||||||
\(226\) | −9.21929 | −0.613258 | ||||||||
\(227\) | −28.2840 | −1.87728 | −0.938639 | − | 0.344901i | \(-0.887912\pi\) | ||||
−0.938639 | + | 0.344901i | \(0.887912\pi\) | |||||||
\(228\) | 5.85963 | 0.388064 | ||||||||
\(229\) | 7.62003 | 0.503546 | 0.251773 | − | 0.967786i | \(-0.418986\pi\) | ||||
0.251773 | + | 0.967786i | \(0.418986\pi\) | |||||||
\(230\) | 29.5770 | 1.95025 | ||||||||
\(231\) | 7.00256 | 0.460734 | ||||||||
\(232\) | −6.08992 | −0.399823 | ||||||||
\(233\) | −22.4303 | −1.46946 | −0.734730 | − | 0.678360i | \(-0.762691\pi\) | ||||
−0.734730 | + | 0.678360i | \(0.762691\pi\) | |||||||
\(234\) | −9.27487 | −0.606317 | ||||||||
\(235\) | 39.9163 | 2.60385 | ||||||||
\(236\) | −2.60061 | −0.169285 | ||||||||
\(237\) | 25.0951 | 1.63010 | ||||||||
\(238\) | 9.25901 | 0.600173 | ||||||||
\(239\) | −8.70037 | −0.562780 | −0.281390 | − | 0.959593i | \(-0.590795\pi\) | ||||
−0.281390 | + | 0.959593i | \(0.590795\pi\) | |||||||
\(240\) | 34.2408 | 2.21024 | ||||||||
\(241\) | −13.4256 | −0.864816 | −0.432408 | − | 0.901678i | \(-0.642336\pi\) | ||||
−0.432408 | + | 0.901678i | \(0.642336\pi\) | |||||||
\(242\) | 21.8415 | 1.40403 | ||||||||
\(243\) | −22.3543 | −1.43403 | ||||||||
\(244\) | −0.979540 | −0.0627086 | ||||||||
\(245\) | −34.8473 | −2.22632 | ||||||||
\(246\) | 16.6804 | 1.06350 | ||||||||
\(247\) | 1.36066 | 0.0865766 | ||||||||
\(248\) | 0.968845 | 0.0615217 | ||||||||
\(249\) | 3.23963 | 0.205303 | ||||||||
\(250\) | 72.8317 | 4.60628 | ||||||||
\(251\) | −21.8720 | −1.38055 | −0.690273 | − | 0.723549i | \(-0.742510\pi\) | ||||
−0.690273 | + | 0.723549i | \(0.742510\pi\) | |||||||
\(252\) | −29.8176 | −1.87834 | ||||||||
\(253\) | −2.38948 | −0.150225 | ||||||||
\(254\) | 35.3984 | 2.22109 | ||||||||
\(255\) | −12.1912 | −0.763444 | ||||||||
\(256\) | 9.27137 | 0.579460 | ||||||||
\(257\) | −2.90751 | −0.181365 | −0.0906826 | − | 0.995880i | \(-0.528905\pi\) | ||||
−0.0906826 | + | 0.995880i | \(0.528905\pi\) | |||||||
\(258\) | −48.5199 | −3.02072 | ||||||||
\(259\) | 1.35580 | 0.0842455 | ||||||||
\(260\) | −13.5800 | −0.842197 | ||||||||
\(261\) | 28.1573 | 1.74290 | ||||||||
\(262\) | −5.71383 | −0.353002 | ||||||||
\(263\) | −18.0713 | −1.11432 | −0.557161 | − | 0.830405i | \(-0.688109\pi\) | ||||
−0.557161 | + | 0.830405i | \(0.688109\pi\) | |||||||
\(264\) | 1.27240 | 0.0783106 | ||||||||
\(265\) | 41.9345 | 2.57602 | ||||||||
\(266\) | 8.11358 | 0.497476 | ||||||||
\(267\) | 27.8863 | 1.70661 | ||||||||
\(268\) | 13.7510 | 0.839974 | ||||||||
\(269\) | 0.426291 | 0.0259914 | 0.0129957 | − | 0.999916i | \(-0.495863\pi\) | ||||
0.0129957 | + | 0.999916i | \(0.495863\pi\) | |||||||
\(270\) | 6.05582 | 0.368545 | ||||||||
\(271\) | −23.1458 | −1.40601 | −0.703004 | − | 0.711186i | \(-0.748158\pi\) | ||||
−0.703004 | + | 0.711186i | \(0.748158\pi\) | |||||||
\(272\) | −3.65765 | −0.221777 | ||||||||
\(273\) | −13.2720 | −0.803261 | ||||||||
\(274\) | 6.72766 | 0.406433 | ||||||||
\(275\) | −9.47349 | −0.571273 | ||||||||
\(276\) | 19.5032 | 1.17395 | ||||||||
\(277\) | 13.7558 | 0.826509 | 0.413254 | − | 0.910616i | \(-0.364392\pi\) | ||||
0.413254 | + | 0.910616i | \(0.364392\pi\) | |||||||
\(278\) | 25.9075 | 1.55383 | ||||||||
\(279\) | −4.47955 | −0.268184 | ||||||||
\(280\) | −11.7576 | −0.702650 | ||||||||
\(281\) | 26.4252 | 1.57639 | 0.788196 | − | 0.615424i | \(-0.211015\pi\) | ||||
0.788196 | + | 0.615424i | \(0.211015\pi\) | |||||||
\(282\) | 48.8203 | 2.90721 | ||||||||
\(283\) | 18.6998 | 1.11159 | 0.555795 | − | 0.831319i | \(-0.312414\pi\) | ||||
0.555795 | + | 0.831319i | \(0.312414\pi\) | |||||||
\(284\) | −24.2265 | −1.43758 | ||||||||
\(285\) | −10.6830 | −0.632809 | ||||||||
\(286\) | 2.03492 | 0.120327 | ||||||||
\(287\) | 12.4523 | 0.735036 | ||||||||
\(288\) | 26.4792 | 1.56030 | ||||||||
\(289\) | −15.6977 | −0.923395 | ||||||||
\(290\) | 76.4685 | 4.49038 | ||||||||
\(291\) | −12.5460 | −0.735462 | ||||||||
\(292\) | 25.8918 | 1.51521 | ||||||||
\(293\) | −28.9577 | −1.69173 | −0.845864 | − | 0.533399i | \(-0.820914\pi\) | ||||
−0.845864 | + | 0.533399i | \(0.820914\pi\) | |||||||
\(294\) | −42.6206 | −2.48568 | ||||||||
\(295\) | 4.74132 | 0.276050 | ||||||||
\(296\) | 0.246356 | 0.0143191 | ||||||||
\(297\) | −0.489240 | −0.0283886 | ||||||||
\(298\) | 6.40879 | 0.371251 | ||||||||
\(299\) | 4.52881 | 0.261908 | ||||||||
\(300\) | 77.3237 | 4.46428 | ||||||||
\(301\) | −36.2213 | −2.08776 | ||||||||
\(302\) | −13.8734 | −0.798325 | ||||||||
\(303\) | −12.3931 | −0.711967 | ||||||||
\(304\) | −3.20516 | −0.183828 | ||||||||
\(305\) | 1.78586 | 0.102258 | ||||||||
\(306\) | −7.77877 | −0.444683 | ||||||||
\(307\) | −0.0823094 | −0.00469764 | −0.00234882 | − | 0.999997i | \(-0.500748\pi\) | ||||
−0.00234882 | + | 0.999997i | \(0.500748\pi\) | |||||||
\(308\) | 6.54204 | 0.372767 | ||||||||
\(309\) | −11.7702 | −0.669584 | ||||||||
\(310\) | −12.1654 | −0.690946 | ||||||||
\(311\) | 15.6210 | 0.885786 | 0.442893 | − | 0.896574i | \(-0.353952\pi\) | ||||
0.442893 | + | 0.896574i | \(0.353952\pi\) | |||||||
\(312\) | −2.41159 | −0.136530 | ||||||||
\(313\) | −13.9639 | −0.789287 | −0.394644 | − | 0.918834i | \(-0.629132\pi\) | ||||
−0.394644 | + | 0.918834i | \(0.629132\pi\) | |||||||
\(314\) | −24.3068 | −1.37171 | ||||||||
\(315\) | 54.3623 | 3.06297 | ||||||||
\(316\) | 23.4447 | 1.31887 | ||||||||
\(317\) | −20.2316 | −1.13632 | −0.568161 | − | 0.822917i | \(-0.692345\pi\) | ||||
−0.568161 | + | 0.822917i | \(0.692345\pi\) | |||||||
\(318\) | 51.2886 | 2.87612 | ||||||||
\(319\) | −6.17777 | −0.345888 | ||||||||
\(320\) | 44.5666 | 2.49135 | ||||||||
\(321\) | −16.6130 | −0.927249 | ||||||||
\(322\) | 27.0052 | 1.50494 | ||||||||
\(323\) | 1.14117 | 0.0634967 | ||||||||
\(324\) | −18.9742 | −1.05412 | ||||||||
\(325\) | 17.9552 | 0.995978 | ||||||||
\(326\) | 26.9729 | 1.49389 | ||||||||
\(327\) | −5.89354 | −0.325914 | ||||||||
\(328\) | 2.26264 | 0.124933 | ||||||||
\(329\) | 36.4456 | 2.00931 | ||||||||
\(330\) | −15.9769 | −0.879501 | ||||||||
\(331\) | 1.62526 | 0.0893323 | 0.0446662 | − | 0.999002i | \(-0.485778\pi\) | ||||
0.0446662 | + | 0.999002i | \(0.485778\pi\) | |||||||
\(332\) | 3.02658 | 0.166105 | ||||||||
\(333\) | −1.13905 | −0.0624195 | ||||||||
\(334\) | 20.4011 | 1.11630 | ||||||||
\(335\) | −25.0702 | −1.36973 | ||||||||
\(336\) | 31.2636 | 1.70557 | ||||||||
\(337\) | 10.4019 | 0.566629 | 0.283315 | − | 0.959027i | \(-0.408566\pi\) | ||||
0.283315 | + | 0.959027i | \(0.408566\pi\) | |||||||
\(338\) | 23.2248 | 1.26326 | ||||||||
\(339\) | 11.0834 | 0.601969 | ||||||||
\(340\) | −11.3895 | −0.617681 | ||||||||
\(341\) | 0.982820 | 0.0532227 | ||||||||
\(342\) | −6.81646 | −0.368592 | ||||||||
\(343\) | −4.55393 | −0.245889 | ||||||||
\(344\) | −6.58158 | −0.354855 | ||||||||
\(345\) | −35.5574 | −1.91435 | ||||||||
\(346\) | −22.8949 | −1.23083 | ||||||||
\(347\) | −13.4195 | −0.720397 | −0.360199 | − | 0.932876i | \(-0.617291\pi\) | ||||
−0.360199 | + | 0.932876i | \(0.617291\pi\) | |||||||
\(348\) | 50.4236 | 2.70299 | ||||||||
\(349\) | −28.8807 | −1.54595 | −0.772973 | − | 0.634439i | \(-0.781231\pi\) | ||||
−0.772973 | + | 0.634439i | \(0.781231\pi\) | |||||||
\(350\) | 107.067 | 5.72296 | ||||||||
\(351\) | 0.927264 | 0.0494937 | ||||||||
\(352\) | −5.80957 | −0.309651 | ||||||||
\(353\) | 22.1950 | 1.18132 | 0.590661 | − | 0.806920i | \(-0.298867\pi\) | ||||
0.590661 | + | 0.806920i | \(0.298867\pi\) | |||||||
\(354\) | 5.79895 | 0.308211 | ||||||||
\(355\) | 44.1687 | 2.34423 | ||||||||
\(356\) | 26.0524 | 1.38077 | ||||||||
\(357\) | −11.1312 | −0.589124 | ||||||||
\(358\) | 16.8037 | 0.888104 | ||||||||
\(359\) | −22.5884 | −1.19217 | −0.596084 | − | 0.802922i | \(-0.703277\pi\) | ||||
−0.596084 | + | 0.802922i | \(0.703277\pi\) | |||||||
\(360\) | 9.87789 | 0.520610 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 10.9802 | 0.577107 | ||||||||
\(363\) | −26.2579 | −1.37818 | ||||||||
\(364\) | −12.3992 | −0.649896 | ||||||||
\(365\) | −47.2050 | −2.47082 | ||||||||
\(366\) | 2.18422 | 0.114171 | ||||||||
\(367\) | 11.3655 | 0.593277 | 0.296638 | − | 0.954990i | \(-0.404134\pi\) | ||||
0.296638 | + | 0.954990i | \(0.404134\pi\) | |||||||
\(368\) | −10.6680 | −0.556110 | ||||||||
\(369\) | −10.4615 | −0.544606 | ||||||||
\(370\) | −3.09338 | −0.160817 | ||||||||
\(371\) | 38.2883 | 1.98783 | ||||||||
\(372\) | −8.02189 | −0.415916 | ||||||||
\(373\) | 34.8016 | 1.80196 | 0.900980 | − | 0.433862i | \(-0.142849\pi\) | ||||
0.900980 | + | 0.433862i | \(0.142849\pi\) | |||||||
\(374\) | 1.70667 | 0.0882500 | ||||||||
\(375\) | −87.5582 | −4.52149 | ||||||||
\(376\) | 6.62233 | 0.341520 | ||||||||
\(377\) | 11.7088 | 0.603034 | ||||||||
\(378\) | 5.52926 | 0.284394 | ||||||||
\(379\) | 29.2686 | 1.50343 | 0.751714 | − | 0.659489i | \(-0.229227\pi\) | ||||
0.751714 | + | 0.659489i | \(0.229227\pi\) | |||||||
\(380\) | −9.98048 | −0.511988 | ||||||||
\(381\) | −42.5559 | −2.18020 | ||||||||
\(382\) | 44.3316 | 2.26820 | ||||||||
\(383\) | 15.6258 | 0.798443 | 0.399222 | − | 0.916854i | \(-0.369280\pi\) | ||||
0.399222 | + | 0.916854i | \(0.369280\pi\) | |||||||
\(384\) | 13.9744 | 0.713130 | ||||||||
\(385\) | −11.9272 | −0.607865 | ||||||||
\(386\) | −45.1130 | −2.29619 | ||||||||
\(387\) | 30.4306 | 1.54687 | ||||||||
\(388\) | −11.7210 | −0.595042 | ||||||||
\(389\) | 35.8233 | 1.81631 | 0.908156 | − | 0.418631i | \(-0.137490\pi\) | ||||
0.908156 | + | 0.418631i | \(0.137490\pi\) | |||||||
\(390\) | 30.2813 | 1.53335 | ||||||||
\(391\) | 3.79828 | 0.192087 | ||||||||
\(392\) | −5.78136 | −0.292003 | ||||||||
\(393\) | 6.86916 | 0.346503 | ||||||||
\(394\) | 9.56831 | 0.482044 | ||||||||
\(395\) | −42.7434 | −2.15066 | ||||||||
\(396\) | −5.49616 | −0.276192 | ||||||||
\(397\) | −22.2129 | −1.11483 | −0.557417 | − | 0.830233i | \(-0.688208\pi\) | ||||
−0.557417 | + | 0.830233i | \(0.688208\pi\) | |||||||
\(398\) | −57.0255 | −2.85843 | ||||||||
\(399\) | −9.75414 | −0.488318 | ||||||||
\(400\) | −42.2953 | −2.11476 | ||||||||
\(401\) | 30.8386 | 1.54001 | 0.770003 | − | 0.638041i | \(-0.220255\pi\) | ||||
0.770003 | + | 0.638041i | \(0.220255\pi\) | |||||||
\(402\) | −30.6625 | −1.52931 | ||||||||
\(403\) | −1.86275 | −0.0927904 | ||||||||
\(404\) | −11.5781 | −0.576032 | ||||||||
\(405\) | 34.5930 | 1.71894 | ||||||||
\(406\) | 69.8194 | 3.46508 | ||||||||
\(407\) | 0.249909 | 0.0123875 | ||||||||
\(408\) | −2.02259 | −0.100133 | ||||||||
\(409\) | 35.6269 | 1.76164 | 0.880819 | − | 0.473453i | \(-0.156993\pi\) | ||||
0.880819 | + | 0.473453i | \(0.156993\pi\) | |||||||
\(410\) | −28.4110 | −1.40312 | ||||||||
\(411\) | −8.08798 | −0.398951 | ||||||||
\(412\) | −10.9962 | −0.541742 | ||||||||
\(413\) | 4.32906 | 0.213019 | ||||||||
\(414\) | −22.6879 | −1.11505 | ||||||||
\(415\) | −5.51793 | −0.270865 | ||||||||
\(416\) | 11.0110 | 0.539857 | ||||||||
\(417\) | −31.1460 | −1.52523 | ||||||||
\(418\) | 1.49554 | 0.0731493 | ||||||||
\(419\) | −16.9440 | −0.827770 | −0.413885 | − | 0.910329i | \(-0.635828\pi\) | ||||
−0.413885 | + | 0.910329i | \(0.635828\pi\) | |||||||
\(420\) | 97.3509 | 4.75024 | ||||||||
\(421\) | −19.9914 | −0.974319 | −0.487160 | − | 0.873313i | \(-0.661967\pi\) | ||||
−0.487160 | + | 0.873313i | \(0.661967\pi\) | |||||||
\(422\) | −2.08320 | −0.101409 | ||||||||
\(423\) | −30.6190 | −1.48875 | ||||||||
\(424\) | 6.95715 | 0.337869 | ||||||||
\(425\) | 15.0589 | 0.730466 | ||||||||
\(426\) | 54.0212 | 2.61734 | ||||||||
\(427\) | 1.63057 | 0.0789090 | ||||||||
\(428\) | −15.5205 | −0.750211 | ||||||||
\(429\) | −2.44638 | −0.118112 | ||||||||
\(430\) | 82.6420 | 3.98535 | ||||||||
\(431\) | −3.35013 | −0.161370 | −0.0806850 | − | 0.996740i | \(-0.525711\pi\) | ||||
−0.0806850 | + | 0.996740i | \(0.525711\pi\) | |||||||
\(432\) | −2.18426 | −0.105090 | ||||||||
\(433\) | 21.6782 | 1.04179 | 0.520895 | − | 0.853621i | \(-0.325598\pi\) | ||||
0.520895 | + | 0.853621i | \(0.325598\pi\) | |||||||
\(434\) | −11.1076 | −0.533180 | ||||||||
\(435\) | −91.9303 | −4.40772 | ||||||||
\(436\) | −5.50596 | −0.263687 | ||||||||
\(437\) | 3.32840 | 0.159219 | ||||||||
\(438\) | −57.7348 | −2.75867 | ||||||||
\(439\) | −33.0035 | −1.57517 | −0.787585 | − | 0.616206i | \(-0.788669\pi\) | ||||
−0.787585 | + | 0.616206i | \(0.788669\pi\) | |||||||
\(440\) | −2.16722 | −0.103318 | ||||||||
\(441\) | 26.7307 | 1.27289 | ||||||||
\(442\) | −3.23469 | −0.153858 | ||||||||
\(443\) | −27.9772 | −1.32924 | −0.664619 | − | 0.747183i | \(-0.731406\pi\) | ||||
−0.664619 | + | 0.747183i | \(0.731406\pi\) | |||||||
\(444\) | −2.03979 | −0.0968040 | ||||||||
\(445\) | −47.4976 | −2.25160 | ||||||||
\(446\) | −21.0702 | −0.997701 | ||||||||
\(447\) | −7.70464 | −0.364417 | ||||||||
\(448\) | 40.6915 | 1.92249 | ||||||||
\(449\) | 3.53561 | 0.166856 | 0.0834279 | − | 0.996514i | \(-0.473413\pi\) | ||||
0.0834279 | + | 0.996514i | \(0.473413\pi\) | |||||||
\(450\) | −89.9500 | −4.24028 | ||||||||
\(451\) | 2.29528 | 0.108080 | ||||||||
\(452\) | 10.3545 | 0.487036 | ||||||||
\(453\) | 16.6786 | 0.783628 | ||||||||
\(454\) | 58.9213 | 2.76531 | ||||||||
\(455\) | 22.6058 | 1.05977 | ||||||||
\(456\) | −1.77237 | −0.0829989 | ||||||||
\(457\) | 11.9057 | 0.556926 | 0.278463 | − | 0.960447i | \(-0.410175\pi\) | ||||
0.278463 | + | 0.960447i | \(0.410175\pi\) | |||||||
\(458\) | −15.8740 | −0.741745 | ||||||||
\(459\) | 0.777690 | 0.0362995 | ||||||||
\(460\) | −33.2190 | −1.54884 | ||||||||
\(461\) | 17.7625 | 0.827284 | 0.413642 | − | 0.910440i | \(-0.364257\pi\) | ||||
0.413642 | + | 0.910440i | \(0.364257\pi\) | |||||||
\(462\) | −14.5877 | −0.678682 | ||||||||
\(463\) | −7.23358 | −0.336173 | −0.168086 | − | 0.985772i | \(-0.553759\pi\) | ||||
−0.168086 | + | 0.985772i | \(0.553759\pi\) | |||||||
\(464\) | −27.5812 | −1.28042 | ||||||||
\(465\) | 14.6252 | 0.678226 | ||||||||
\(466\) | 46.7268 | 2.16458 | ||||||||
\(467\) | 16.7818 | 0.776569 | 0.388285 | − | 0.921540i | \(-0.373068\pi\) | ||||
0.388285 | + | 0.921540i | \(0.373068\pi\) | |||||||
\(468\) | 10.4170 | 0.481524 | ||||||||
\(469\) | −22.8903 | −1.05698 | ||||||||
\(470\) | −83.1536 | −3.83559 | ||||||||
\(471\) | 29.2216 | 1.34646 | ||||||||
\(472\) | 0.786610 | 0.0362067 | ||||||||
\(473\) | −6.67652 | −0.306987 | ||||||||
\(474\) | −52.2780 | −2.40121 | ||||||||
\(475\) | 13.1960 | 0.605474 | ||||||||
\(476\) | −10.3991 | −0.476644 | ||||||||
\(477\) | −32.1671 | −1.47283 | ||||||||
\(478\) | 18.1246 | 0.829000 | ||||||||
\(479\) | 3.34578 | 0.152873 | 0.0764363 | − | 0.997074i | \(-0.475646\pi\) | ||||
0.0764363 | + | 0.997074i | \(0.475646\pi\) | |||||||
\(480\) | −86.4512 | −3.94594 | ||||||||
\(481\) | −0.473657 | −0.0215969 | ||||||||
\(482\) | 27.9681 | 1.27391 | ||||||||
\(483\) | −32.4656 | −1.47724 | ||||||||
\(484\) | −24.5310 | −1.11505 | ||||||||
\(485\) | 21.3692 | 0.970325 | ||||||||
\(486\) | 46.5685 | 2.11239 | ||||||||
\(487\) | −0.173122 | −0.00784489 | −0.00392244 | − | 0.999992i | \(-0.501249\pi\) | ||||
−0.00392244 | + | 0.999992i | \(0.501249\pi\) | |||||||
\(488\) | 0.296283 | 0.0134121 | ||||||||
\(489\) | −32.4268 | −1.46639 | ||||||||
\(490\) | 72.5939 | 3.27946 | ||||||||
\(491\) | −3.39523 | −0.153224 | −0.0766122 | − | 0.997061i | \(-0.524410\pi\) | ||||
−0.0766122 | + | 0.997061i | \(0.524410\pi\) | |||||||
\(492\) | −18.7343 | −0.844609 | ||||||||
\(493\) | 9.82010 | 0.442275 | ||||||||
\(494\) | −2.83452 | −0.127531 | ||||||||
\(495\) | 10.0204 | 0.450382 | ||||||||
\(496\) | 4.38789 | 0.197022 | ||||||||
\(497\) | 40.3282 | 1.80897 | ||||||||
\(498\) | −6.74879 | −0.302420 | ||||||||
\(499\) | −10.9801 | −0.491537 | −0.245768 | − | 0.969329i | \(-0.579040\pi\) | ||||
−0.245768 | + | 0.969329i | \(0.579040\pi\) | |||||||
\(500\) | −81.8000 | −3.65821 | ||||||||
\(501\) | −24.5261 | −1.09575 | ||||||||
\(502\) | 45.5637 | 2.03361 | ||||||||
\(503\) | −14.7808 | −0.659044 | −0.329522 | − | 0.944148i | \(-0.606888\pi\) | ||||
−0.329522 | + | 0.944148i | \(0.606888\pi\) | |||||||
\(504\) | 9.01899 | 0.401738 | ||||||||
\(505\) | 21.1087 | 0.939326 | ||||||||
\(506\) | 4.97776 | 0.221288 | ||||||||
\(507\) | −27.9208 | −1.24001 | ||||||||
\(508\) | −39.7572 | −1.76394 | ||||||||
\(509\) | 0.220794 | 0.00978650 | 0.00489325 | − | 0.999988i | \(-0.498442\pi\) | ||||
0.00489325 | + | 0.999988i | \(0.498442\pi\) | |||||||
\(510\) | 25.3967 | 1.12459 | ||||||||
\(511\) | −43.1004 | −1.90665 | ||||||||
\(512\) | −30.4739 | −1.34677 | ||||||||
\(513\) | 0.681482 | 0.0300882 | ||||||||
\(514\) | 6.05691 | 0.267159 | ||||||||
\(515\) | 20.0477 | 0.883409 | ||||||||
\(516\) | 54.4945 | 2.39899 | ||||||||
\(517\) | 6.71785 | 0.295451 | ||||||||
\(518\) | −2.82441 | −0.124097 | ||||||||
\(519\) | 27.5242 | 1.20818 | ||||||||
\(520\) | 4.10757 | 0.180129 | ||||||||
\(521\) | −14.6300 | −0.640954 | −0.320477 | − | 0.947256i | \(-0.603843\pi\) | ||||
−0.320477 | + | 0.947256i | \(0.603843\pi\) | |||||||
\(522\) | −58.6574 | −2.56736 | ||||||||
\(523\) | 23.2970 | 1.01871 | 0.509353 | − | 0.860558i | \(-0.329885\pi\) | ||||
0.509353 | + | 0.860558i | \(0.329885\pi\) | |||||||
\(524\) | 6.41741 | 0.280346 | ||||||||
\(525\) | −128.716 | −5.61761 | ||||||||
\(526\) | 37.6460 | 1.64144 | ||||||||
\(527\) | −1.56228 | −0.0680539 | ||||||||
\(528\) | 5.76268 | 0.250788 | ||||||||
\(529\) | −11.9218 | −0.518338 | ||||||||
\(530\) | −87.3579 | −3.79459 | ||||||||
\(531\) | −3.63697 | −0.157831 | ||||||||
\(532\) | −9.11266 | −0.395084 | ||||||||
\(533\) | −4.35028 | −0.188431 | ||||||||
\(534\) | −58.0927 | −2.51392 | ||||||||
\(535\) | 28.2963 | 1.22336 | ||||||||
\(536\) | −4.15928 | −0.179653 | ||||||||
\(537\) | −20.2014 | −0.871755 | ||||||||
\(538\) | −0.888050 | −0.0382865 | ||||||||
\(539\) | −5.86475 | −0.252613 | ||||||||
\(540\) | −6.80151 | −0.292691 | ||||||||
\(541\) | −27.5243 | −1.18336 | −0.591681 | − | 0.806172i | \(-0.701535\pi\) | ||||
−0.591681 | + | 0.806172i | \(0.701535\pi\) | |||||||
\(542\) | 48.2173 | 2.07111 | ||||||||
\(543\) | −13.2004 | −0.566483 | ||||||||
\(544\) | 9.23482 | 0.395940 | ||||||||
\(545\) | 10.0382 | 0.429991 | ||||||||
\(546\) | 27.6483 | 1.18324 | ||||||||
\(547\) | −36.1302 | −1.54482 | −0.772408 | − | 0.635126i | \(-0.780948\pi\) | ||||
−0.772408 | + | 0.635126i | \(0.780948\pi\) | |||||||
\(548\) | −7.55608 | −0.322780 | ||||||||
\(549\) | −1.36989 | −0.0584656 | ||||||||
\(550\) | 19.7352 | 0.841510 | ||||||||
\(551\) | 8.60525 | 0.366596 | ||||||||
\(552\) | −5.89916 | −0.251085 | ||||||||
\(553\) | −39.0268 | −1.65959 | ||||||||
\(554\) | −28.6562 | −1.21748 | ||||||||
\(555\) | 3.71886 | 0.157857 | ||||||||
\(556\) | −29.0977 | −1.23402 | ||||||||
\(557\) | −39.2333 | −1.66237 | −0.831184 | − | 0.555997i | \(-0.812337\pi\) | ||||
−0.831184 | + | 0.555997i | \(0.812337\pi\) | |||||||
\(558\) | 9.33180 | 0.395046 | ||||||||
\(559\) | 12.6541 | 0.535212 | ||||||||
\(560\) | −53.2500 | −2.25022 | ||||||||
\(561\) | −2.05176 | −0.0866254 | ||||||||
\(562\) | −55.0489 | −2.32210 | ||||||||
\(563\) | 15.1668 | 0.639206 | 0.319603 | − | 0.947552i | \(-0.396451\pi\) | ||||
0.319603 | + | 0.947552i | \(0.396451\pi\) | |||||||
\(564\) | −54.8318 | −2.30884 | ||||||||
\(565\) | −18.8780 | −0.794202 | ||||||||
\(566\) | −38.9555 | −1.63742 | ||||||||
\(567\) | 31.5851 | 1.32645 | ||||||||
\(568\) | 7.32781 | 0.307468 | ||||||||
\(569\) | −38.4545 | −1.61210 | −0.806049 | − | 0.591849i | \(-0.798398\pi\) | ||||
−0.806049 | + | 0.591849i | \(0.798398\pi\) | |||||||
\(570\) | 22.2549 | 0.932155 | ||||||||
\(571\) | −36.8816 | −1.54345 | −0.771723 | − | 0.635959i | \(-0.780605\pi\) | ||||
−0.771723 | + | 0.635959i | \(0.780605\pi\) | |||||||
\(572\) | −2.28549 | −0.0955613 | ||||||||
\(573\) | −53.2953 | −2.22645 | ||||||||
\(574\) | −25.9406 | −1.08274 | ||||||||
\(575\) | 43.9215 | 1.83165 | ||||||||
\(576\) | −34.1861 | −1.42442 | ||||||||
\(577\) | −27.1309 | −1.12947 | −0.564736 | − | 0.825272i | \(-0.691022\pi\) | ||||
−0.564736 | + | 0.825272i | \(0.691022\pi\) | |||||||
\(578\) | 32.7015 | 1.36020 | ||||||||
\(579\) | 54.2348 | 2.25392 | ||||||||
\(580\) | −85.8845 | −3.56616 | ||||||||
\(581\) | −5.03814 | −0.209017 | ||||||||
\(582\) | 26.1359 | 1.08337 | ||||||||
\(583\) | 7.05751 | 0.292292 | ||||||||
\(584\) | −7.83155 | −0.324072 | ||||||||
\(585\) | −18.9918 | −0.785213 | ||||||||
\(586\) | 60.3247 | 2.49199 | ||||||||
\(587\) | 21.0774 | 0.869958 | 0.434979 | − | 0.900441i | \(-0.356756\pi\) | ||||
0.434979 | + | 0.900441i | \(0.356756\pi\) | |||||||
\(588\) | 47.8687 | 1.97407 | ||||||||
\(589\) | −1.36901 | −0.0564090 | ||||||||
\(590\) | −9.87712 | −0.406634 | ||||||||
\(591\) | −11.5030 | −0.473171 | ||||||||
\(592\) | 1.11574 | 0.0458567 | ||||||||
\(593\) | 39.6201 | 1.62700 | 0.813502 | − | 0.581562i | \(-0.197558\pi\) | ||||
0.813502 | + | 0.581562i | \(0.197558\pi\) | |||||||
\(594\) | 1.01918 | 0.0418176 | ||||||||
\(595\) | 18.9593 | 0.777255 | ||||||||
\(596\) | −7.19795 | −0.294840 | ||||||||
\(597\) | 68.5560 | 2.80581 | ||||||||
\(598\) | −9.43441 | −0.385802 | ||||||||
\(599\) | −45.4804 | −1.85828 | −0.929139 | − | 0.369731i | \(-0.879450\pi\) | ||||
−0.929139 | + | 0.369731i | \(0.879450\pi\) | |||||||
\(600\) | −23.3882 | −0.954820 | ||||||||
\(601\) | 4.90388 | 0.200034 | 0.100017 | − | 0.994986i | \(-0.468110\pi\) | ||||
0.100017 | + | 0.994986i | \(0.468110\pi\) | |||||||
\(602\) | 75.4562 | 3.07537 | ||||||||
\(603\) | 19.2308 | 0.783140 | ||||||||
\(604\) | 15.5817 | 0.634012 | ||||||||
\(605\) | 44.7240 | 1.81829 | ||||||||
\(606\) | 25.8174 | 1.04876 | ||||||||
\(607\) | 5.95518 | 0.241713 | 0.120857 | − | 0.992670i | \(-0.461436\pi\) | ||||
0.120857 | + | 0.992670i | \(0.461436\pi\) | |||||||
\(608\) | 8.09238 | 0.328189 | ||||||||
\(609\) | −83.9368 | −3.40129 | ||||||||
\(610\) | −3.72030 | −0.150630 | ||||||||
\(611\) | −12.7324 | −0.515100 | ||||||||
\(612\) | 8.73662 | 0.353157 | ||||||||
\(613\) | −19.2455 | −0.777320 | −0.388660 | − | 0.921381i | \(-0.627062\pi\) | ||||
−0.388660 | + | 0.921381i | \(0.627062\pi\) | |||||||
\(614\) | 0.171467 | 0.00691984 | ||||||||
\(615\) | 34.1557 | 1.37729 | ||||||||
\(616\) | −1.97878 | −0.0797273 | ||||||||
\(617\) | 18.8192 | 0.757633 | 0.378816 | − | 0.925472i | \(-0.376331\pi\) | ||||
0.378816 | + | 0.925472i | \(0.376331\pi\) | |||||||
\(618\) | 24.5197 | 0.986327 | ||||||||
\(619\) | −1.82633 | −0.0734064 | −0.0367032 | − | 0.999326i | \(-0.511686\pi\) | ||||
−0.0367032 | + | 0.999326i | \(0.511686\pi\) | |||||||
\(620\) | 13.6634 | 0.548734 | ||||||||
\(621\) | 2.26824 | 0.0910214 | ||||||||
\(622\) | −32.5417 | −1.30480 | ||||||||
\(623\) | −43.3677 | −1.73749 | ||||||||
\(624\) | −10.9221 | −0.437233 | ||||||||
\(625\) | 83.1544 | 3.32618 | ||||||||
\(626\) | 29.0896 | 1.16265 | ||||||||
\(627\) | −1.79794 | −0.0718027 | ||||||||
\(628\) | 27.2998 | 1.08938 | ||||||||
\(629\) | −0.397252 | −0.0158395 | ||||||||
\(630\) | −113.248 | −4.51189 | ||||||||
\(631\) | 8.07679 | 0.321532 | 0.160766 | − | 0.986993i | \(-0.448604\pi\) | ||||
0.160766 | + | 0.986993i | \(0.448604\pi\) | |||||||
\(632\) | −7.09136 | −0.282079 | ||||||||
\(633\) | 2.50442 | 0.0995417 | ||||||||
\(634\) | 42.1465 | 1.67385 | ||||||||
\(635\) | 72.4837 | 2.87643 | ||||||||
\(636\) | −57.6042 | −2.28415 | ||||||||
\(637\) | 11.1155 | 0.440414 | ||||||||
\(638\) | 12.8695 | 0.509509 | ||||||||
\(639\) | −33.8809 | −1.34031 | ||||||||
\(640\) | −23.8021 | −0.940860 | ||||||||
\(641\) | −45.9378 | −1.81443 | −0.907216 | − | 0.420664i | \(-0.861797\pi\) | ||||
−0.907216 | + | 0.420664i | \(0.861797\pi\) | |||||||
\(642\) | 34.6083 | 1.36588 | ||||||||
\(643\) | 32.1642 | 1.26843 | 0.634216 | − | 0.773156i | \(-0.281323\pi\) | ||||
0.634216 | + | 0.773156i | \(0.281323\pi\) | |||||||
\(644\) | −30.3306 | −1.19519 | ||||||||
\(645\) | −99.3521 | −3.91199 | ||||||||
\(646\) | −2.37729 | −0.0935334 | ||||||||
\(647\) | 45.2590 | 1.77931 | 0.889657 | − | 0.456630i | \(-0.150944\pi\) | ||||
0.889657 | + | 0.456630i | \(0.150944\pi\) | |||||||
\(648\) | 5.73916 | 0.225456 | ||||||||
\(649\) | 0.797957 | 0.0313225 | ||||||||
\(650\) | −37.4044 | −1.46712 | ||||||||
\(651\) | 13.3535 | 0.523365 | ||||||||
\(652\) | −30.2943 | −1.18642 | ||||||||
\(653\) | 28.9430 | 1.13263 | 0.566314 | − | 0.824190i | \(-0.308369\pi\) | ||||
0.566314 | + | 0.824190i | \(0.308369\pi\) | |||||||
\(654\) | 12.2774 | 0.480085 | ||||||||
\(655\) | −11.7000 | −0.457155 | ||||||||
\(656\) | 10.2475 | 0.400097 | ||||||||
\(657\) | 36.2099 | 1.41268 | ||||||||
\(658\) | −75.9233 | −2.95980 | ||||||||
\(659\) | −18.1301 | −0.706248 | −0.353124 | − | 0.935577i | \(-0.614881\pi\) | ||||
−0.353124 | + | 0.935577i | \(0.614881\pi\) | |||||||
\(660\) | 17.9443 | 0.698480 | ||||||||
\(661\) | 4.80886 | 0.187043 | 0.0935215 | − | 0.995617i | \(-0.470188\pi\) | ||||
0.0935215 | + | 0.995617i | \(0.470188\pi\) | |||||||
\(662\) | −3.38574 | −0.131590 | ||||||||
\(663\) | 3.88873 | 0.151026 | ||||||||
\(664\) | −0.915453 | −0.0355265 | ||||||||
\(665\) | 16.6138 | 0.644257 | ||||||||
\(666\) | 2.37287 | 0.0919467 | ||||||||
\(667\) | 28.6417 | 1.10901 | ||||||||
\(668\) | −22.9132 | −0.886538 | ||||||||
\(669\) | 25.3305 | 0.979334 | ||||||||
\(670\) | 52.2262 | 2.01767 | ||||||||
\(671\) | 0.300557 | 0.0116029 | ||||||||
\(672\) | −78.9342 | −3.04495 | ||||||||
\(673\) | −45.6346 | −1.75909 | −0.879543 | − | 0.475820i | \(-0.842152\pi\) | ||||
−0.879543 | + | 0.475820i | \(0.842152\pi\) | |||||||
\(674\) | −21.6693 | −0.834669 | ||||||||
\(675\) | 8.99283 | 0.346134 | ||||||||
\(676\) | −26.0846 | −1.00325 | ||||||||
\(677\) | −17.6007 | −0.676451 | −0.338225 | − | 0.941065i | \(-0.609827\pi\) | ||||
−0.338225 | + | 0.941065i | \(0.609827\pi\) | |||||||
\(678\) | −23.0890 | −0.886727 | ||||||||
\(679\) | 19.5111 | 0.748767 | ||||||||
\(680\) | 3.44499 | 0.132109 | ||||||||
\(681\) | −70.8351 | −2.71441 | ||||||||
\(682\) | −2.04741 | −0.0783994 | ||||||||
\(683\) | 8.30785 | 0.317891 | 0.158946 | − | 0.987287i | \(-0.449191\pi\) | ||||
0.158946 | + | 0.987287i | \(0.449191\pi\) | |||||||
\(684\) | 7.65582 | 0.292727 | ||||||||
\(685\) | 13.7759 | 0.526352 | ||||||||
\(686\) | 9.48674 | 0.362205 | ||||||||
\(687\) | 19.0837 | 0.728090 | ||||||||
\(688\) | −29.8079 | −1.13642 | ||||||||
\(689\) | −13.3762 | −0.509593 | ||||||||
\(690\) | 74.0731 | 2.81992 | ||||||||
\(691\) | 22.4090 | 0.852477 | 0.426238 | − | 0.904611i | \(-0.359838\pi\) | ||||
0.426238 | + | 0.904611i | \(0.359838\pi\) | |||||||
\(692\) | 25.7140 | 0.977501 | ||||||||
\(693\) | 9.14909 | 0.347545 | ||||||||
\(694\) | 27.9555 | 1.06118 | ||||||||
\(695\) | 53.0497 | 2.01229 | ||||||||
\(696\) | −15.2517 | −0.578114 | ||||||||
\(697\) | −3.64855 | −0.138199 | ||||||||
\(698\) | 60.1642 | 2.27725 | ||||||||
\(699\) | −56.1750 | −2.12473 | ||||||||
\(700\) | −120.251 | −4.54505 | ||||||||
\(701\) | 11.7052 | 0.442100 | 0.221050 | − | 0.975262i | \(-0.429052\pi\) | ||||
0.221050 | + | 0.975262i | \(0.429052\pi\) | |||||||
\(702\) | −1.93168 | −0.0729064 | ||||||||
\(703\) | −0.348108 | −0.0131292 | ||||||||
\(704\) | 7.50048 | 0.282685 | ||||||||
\(705\) | 99.9672 | 3.76498 | ||||||||
\(706\) | −46.2367 | −1.74014 | ||||||||
\(707\) | 19.2733 | 0.724847 | ||||||||
\(708\) | −6.51301 | −0.244774 | ||||||||
\(709\) | −35.8423 | −1.34609 | −0.673043 | − | 0.739603i | \(-0.735013\pi\) | ||||
−0.673043 | + | 0.739603i | \(0.735013\pi\) | |||||||
\(710\) | −92.0122 | −3.45315 | ||||||||
\(711\) | 32.7876 | 1.22963 | ||||||||
\(712\) | −7.88011 | −0.295319 | ||||||||
\(713\) | −4.55661 | −0.170646 | ||||||||
\(714\) | 23.1884 | 0.867806 | ||||||||
\(715\) | 4.16682 | 0.155830 | ||||||||
\(716\) | −18.8729 | −0.705313 | ||||||||
\(717\) | −21.7894 | −0.813739 | ||||||||
\(718\) | 47.0560 | 1.75612 | ||||||||
\(719\) | −51.6705 | −1.92698 | −0.963492 | − | 0.267737i | \(-0.913724\pi\) | ||||
−0.963492 | + | 0.267737i | \(0.913724\pi\) | |||||||
\(720\) | 44.7369 | 1.66724 | ||||||||
\(721\) | 18.3046 | 0.681698 | ||||||||
\(722\) | −2.08320 | −0.0775286 | ||||||||
\(723\) | −33.6232 | −1.25046 | ||||||||
\(724\) | −12.3323 | −0.458326 | ||||||||
\(725\) | 113.555 | 4.21732 | ||||||||
\(726\) | 54.7003 | 2.03012 | ||||||||
\(727\) | −12.9863 | −0.481634 | −0.240817 | − | 0.970571i | \(-0.577415\pi\) | ||||
−0.240817 | + | 0.970571i | \(0.577415\pi\) | |||||||
\(728\) | 3.75041 | 0.139000 | ||||||||
\(729\) | −31.6557 | −1.17243 | ||||||||
\(730\) | 98.3373 | 3.63963 | ||||||||
\(731\) | 10.6129 | 0.392533 | ||||||||
\(732\) | −2.45318 | −0.0906721 | ||||||||
\(733\) | −10.8703 | −0.401505 | −0.200753 | − | 0.979642i | \(-0.564339\pi\) | ||||
−0.200753 | + | 0.979642i | \(0.564339\pi\) | |||||||
\(734\) | −23.6767 | −0.873923 | ||||||||
\(735\) | −87.2723 | −3.21909 | ||||||||
\(736\) | 26.9346 | 0.992824 | ||||||||
\(737\) | −4.21927 | −0.155419 | ||||||||
\(738\) | 21.7935 | 0.802229 | ||||||||
\(739\) | −33.7667 | −1.24213 | −0.621063 | − | 0.783760i | \(-0.713299\pi\) | ||||
−0.621063 | + | 0.783760i | \(0.713299\pi\) | |||||||
\(740\) | 3.47429 | 0.127717 | ||||||||
\(741\) | 3.40766 | 0.125183 | ||||||||
\(742\) | −79.7620 | −2.92816 | ||||||||
\(743\) | 7.36333 | 0.270135 | 0.135067 | − | 0.990836i | \(-0.456875\pi\) | ||||
0.135067 | + | 0.990836i | \(0.456875\pi\) | |||||||
\(744\) | 2.42639 | 0.0889559 | ||||||||
\(745\) | 13.1230 | 0.480790 | ||||||||
\(746\) | −72.4987 | −2.65436 | ||||||||
\(747\) | 4.23269 | 0.154866 | ||||||||
\(748\) | −1.91683 | −0.0700862 | ||||||||
\(749\) | 25.8359 | 0.944024 | ||||||||
\(750\) | 182.401 | 6.66035 | ||||||||
\(751\) | −8.65055 | −0.315663 | −0.157832 | − | 0.987466i | \(-0.550450\pi\) | ||||
−0.157832 | + | 0.987466i | \(0.550450\pi\) | |||||||
\(752\) | 29.9925 | 1.09371 | ||||||||
\(753\) | −54.7766 | −1.99617 | ||||||||
\(754\) | −24.3918 | −0.888296 | ||||||||
\(755\) | −28.4080 | −1.03387 | ||||||||
\(756\) | −6.21011 | −0.225860 | ||||||||
\(757\) | −23.9176 | −0.869299 | −0.434650 | − | 0.900600i | \(-0.643128\pi\) | ||||
−0.434650 | + | 0.900600i | \(0.643128\pi\) | |||||||
\(758\) | −60.9724 | −2.21462 | ||||||||
\(759\) | −5.98425 | −0.217215 | ||||||||
\(760\) | 3.01881 | 0.109504 | ||||||||
\(761\) | 2.80990 | 0.101859 | 0.0509294 | − | 0.998702i | \(-0.483782\pi\) | ||||
0.0509294 | + | 0.998702i | \(0.483782\pi\) | |||||||
\(762\) | 88.6523 | 3.21153 | ||||||||
\(763\) | 9.16540 | 0.331810 | ||||||||
\(764\) | −49.7904 | −1.80135 | ||||||||
\(765\) | −15.9283 | −0.575887 | ||||||||
\(766\) | −32.5517 | −1.17614 | ||||||||
\(767\) | −1.51238 | −0.0546088 | ||||||||
\(768\) | 23.2194 | 0.837857 | ||||||||
\(769\) | −13.8811 | −0.500564 | −0.250282 | − | 0.968173i | \(-0.580523\pi\) | ||||
−0.250282 | + | 0.968173i | \(0.580523\pi\) | |||||||
\(770\) | 24.8467 | 0.895412 | ||||||||
\(771\) | −7.28161 | −0.262241 | ||||||||
\(772\) | 50.6681 | 1.82358 | ||||||||
\(773\) | 24.3274 | 0.874994 | 0.437497 | − | 0.899220i | \(-0.355865\pi\) | ||||
0.437497 | + | 0.899220i | \(0.355865\pi\) | |||||||
\(774\) | −63.3930 | −2.27861 | ||||||||
\(775\) | −18.0654 | −0.648930 | ||||||||
\(776\) | 3.54526 | 0.127267 | ||||||||
\(777\) | 3.39550 | 0.121813 | ||||||||
\(778\) | −74.6270 | −2.67551 | ||||||||
\(779\) | −3.19719 | −0.114551 | ||||||||
\(780\) | −34.0101 | −1.21776 | ||||||||
\(781\) | 7.43352 | 0.265992 | ||||||||
\(782\) | −7.91258 | −0.282953 | ||||||||
\(783\) | 5.86432 | 0.209574 | ||||||||
\(784\) | −26.1837 | −0.935133 | ||||||||
\(785\) | −49.7719 | −1.77644 | ||||||||
\(786\) | −14.3098 | −0.510414 | ||||||||
\(787\) | 21.8086 | 0.777392 | 0.388696 | − | 0.921366i | \(-0.372926\pi\) | ||||
0.388696 | + | 0.921366i | \(0.372926\pi\) | |||||||
\(788\) | −10.7465 | −0.382829 | ||||||||
\(789\) | −45.2580 | −1.61123 | ||||||||
\(790\) | 89.0431 | 3.16801 | ||||||||
\(791\) | −17.2365 | −0.612859 | ||||||||
\(792\) | 1.66243 | 0.0590719 | ||||||||
\(793\) | −0.569650 | −0.0202289 | ||||||||
\(794\) | 46.2739 | 1.64220 | ||||||||
\(795\) | 105.022 | 3.72473 | ||||||||
\(796\) | 64.0475 | 2.27010 | ||||||||
\(797\) | −31.3673 | −1.11109 | −0.555544 | − | 0.831487i | \(-0.687490\pi\) | ||||
−0.555544 | + | 0.831487i | \(0.687490\pi\) | |||||||
\(798\) | 20.3198 | 0.719313 | ||||||||
\(799\) | −10.6786 | −0.377782 | ||||||||
\(800\) | 106.787 | 3.77549 | ||||||||
\(801\) | 36.4344 | 1.28735 | ||||||||
\(802\) | −64.2429 | −2.26850 | ||||||||
\(803\) | −7.94452 | −0.280356 | ||||||||
\(804\) | 34.4382 | 1.21454 | ||||||||
\(805\) | 55.2974 | 1.94898 | ||||||||
\(806\) | 3.88049 | 0.136684 | ||||||||
\(807\) | 1.06761 | 0.0375817 | ||||||||
\(808\) | 3.50205 | 0.123202 | ||||||||
\(809\) | −7.49622 | −0.263553 | −0.131776 | − | 0.991279i | \(-0.542068\pi\) | ||||
−0.131776 | + | 0.991279i | \(0.542068\pi\) | |||||||
\(810\) | −72.0641 | −2.53208 | ||||||||
\(811\) | −8.05207 | −0.282746 | −0.141373 | − | 0.989956i | \(-0.545152\pi\) | ||||
−0.141373 | + | 0.989956i | \(0.545152\pi\) | |||||||
\(812\) | −78.4168 | −2.75189 | ||||||||
\(813\) | −57.9668 | −2.03298 | ||||||||
\(814\) | −0.520610 | −0.0182474 | ||||||||
\(815\) | 55.2313 | 1.93467 | ||||||||
\(816\) | −9.16028 | −0.320674 | ||||||||
\(817\) | 9.29999 | 0.325365 | ||||||||
\(818\) | −74.2180 | −2.59497 | ||||||||
\(819\) | −17.3404 | −0.605923 | ||||||||
\(820\) | 31.9094 | 1.11433 | ||||||||
\(821\) | 3.45632 | 0.120627 | 0.0603133 | − | 0.998179i | \(-0.480790\pi\) | ||||
0.0603133 | + | 0.998179i | \(0.480790\pi\) | |||||||
\(822\) | 16.8489 | 0.587672 | ||||||||
\(823\) | 14.6503 | 0.510678 | 0.255339 | − | 0.966852i | \(-0.417813\pi\) | ||||
0.255339 | + | 0.966852i | \(0.417813\pi\) | |||||||
\(824\) | 3.32602 | 0.115868 | ||||||||
\(825\) | −23.7256 | −0.826019 | ||||||||
\(826\) | −9.01829 | −0.313786 | ||||||||
\(827\) | −9.58314 | −0.333239 | −0.166619 | − | 0.986021i | \(-0.553285\pi\) | ||||
−0.166619 | + | 0.986021i | \(0.553285\pi\) | |||||||
\(828\) | 25.4816 | 0.885546 | ||||||||
\(829\) | −21.4262 | −0.744162 | −0.372081 | − | 0.928200i | \(-0.621356\pi\) | ||||
−0.372081 | + | 0.928200i | \(0.621356\pi\) | |||||||
\(830\) | 11.4949 | 0.398995 | ||||||||
\(831\) | 34.4504 | 1.19507 | ||||||||
\(832\) | −14.2158 | −0.492843 | ||||||||
\(833\) | 9.32253 | 0.323007 | ||||||||
\(834\) | 64.8833 | 2.24672 | ||||||||
\(835\) | 41.7744 | 1.44566 | ||||||||
\(836\) | −1.67970 | −0.0580936 | ||||||||
\(837\) | −0.932955 | −0.0322476 | ||||||||
\(838\) | 35.2978 | 1.21934 | ||||||||
\(839\) | 28.6087 | 0.987681 | 0.493841 | − | 0.869552i | \(-0.335593\pi\) | ||||
0.493841 | + | 0.869552i | \(0.335593\pi\) | |||||||
\(840\) | −29.4459 | −1.01598 | ||||||||
\(841\) | 45.0504 | 1.55346 | ||||||||
\(842\) | 41.6460 | 1.43522 | ||||||||
\(843\) | 66.1797 | 2.27935 | ||||||||
\(844\) | 2.33972 | 0.0805364 | ||||||||
\(845\) | 47.5564 | 1.63599 | ||||||||
\(846\) | 63.7854 | 2.19299 | ||||||||
\(847\) | 40.8352 | 1.40311 | ||||||||
\(848\) | 31.5089 | 1.08202 | ||||||||
\(849\) | 46.8322 | 1.60728 | ||||||||
\(850\) | −31.3708 | −1.07601 | ||||||||
\(851\) | −1.15864 | −0.0397178 | ||||||||
\(852\) | −60.6732 | −2.07863 | ||||||||
\(853\) | −3.10834 | −0.106428 | −0.0532138 | − | 0.998583i | \(-0.516946\pi\) | ||||
−0.0532138 | + | 0.998583i | \(0.516946\pi\) | |||||||
\(854\) | −3.39681 | −0.116236 | ||||||||
\(855\) | −13.9578 | −0.477346 | ||||||||
\(856\) | 4.69451 | 0.160455 | ||||||||
\(857\) | −14.0270 | −0.479152 | −0.239576 | − | 0.970878i | \(-0.577008\pi\) | ||||
−0.239576 | + | 0.970878i | \(0.577008\pi\) | |||||||
\(858\) | 5.09629 | 0.173985 | ||||||||
\(859\) | 38.5787 | 1.31629 | 0.658144 | − | 0.752892i | \(-0.271342\pi\) | ||||
0.658144 | + | 0.752892i | \(0.271342\pi\) | |||||||
\(860\) | −92.8183 | −3.16508 | ||||||||
\(861\) | 31.1858 | 1.06281 | ||||||||
\(862\) | 6.97899 | 0.237705 | ||||||||
\(863\) | 21.8286 | 0.743053 | 0.371527 | − | 0.928422i | \(-0.378834\pi\) | ||||
0.371527 | + | 0.928422i | \(0.378834\pi\) | |||||||
\(864\) | 5.51481 | 0.187618 | ||||||||
\(865\) | −46.8808 | −1.59400 | ||||||||
\(866\) | −45.1601 | −1.53460 | ||||||||
\(867\) | −39.3137 | −1.33516 | ||||||||
\(868\) | 12.4753 | 0.423440 | ||||||||
\(869\) | −7.19365 | −0.244028 | ||||||||
\(870\) | 191.509 | 6.49276 | ||||||||
\(871\) | 7.99685 | 0.270963 | ||||||||
\(872\) | 1.66540 | 0.0563974 | ||||||||
\(873\) | −16.3919 | −0.554780 | ||||||||
\(874\) | −6.93371 | −0.234536 | ||||||||
\(875\) | 136.167 | 4.60328 | ||||||||
\(876\) | 64.8440 | 2.19088 | ||||||||
\(877\) | 21.8967 | 0.739400 | 0.369700 | − | 0.929151i | \(-0.379460\pi\) | ||||
0.369700 | + | 0.929151i | \(0.379460\pi\) | |||||||
\(878\) | 68.7528 | 2.32029 | ||||||||
\(879\) | −72.5222 | −2.44611 | ||||||||
\(880\) | −9.81534 | −0.330875 | ||||||||
\(881\) | 1.27404 | 0.0429234 | 0.0214617 | − | 0.999770i | \(-0.493168\pi\) | ||||
0.0214617 | + | 0.999770i | \(0.493168\pi\) | |||||||
\(882\) | −55.6853 | −1.87502 | ||||||||
\(883\) | −38.9964 | −1.31233 | −0.656166 | − | 0.754616i | \(-0.727823\pi\) | ||||
−0.656166 | + | 0.754616i | \(0.727823\pi\) | |||||||
\(884\) | 3.63299 | 0.122191 | ||||||||
\(885\) | 11.8743 | 0.399149 | ||||||||
\(886\) | 58.2821 | 1.95803 | ||||||||
\(887\) | 41.6509 | 1.39850 | 0.699251 | − | 0.714877i | \(-0.253517\pi\) | ||||
0.699251 | + | 0.714877i | \(0.253517\pi\) | |||||||
\(888\) | 0.616977 | 0.0207044 | ||||||||
\(889\) | 66.1812 | 2.21964 | ||||||||
\(890\) | 98.9470 | 3.31671 | ||||||||
\(891\) | 5.82195 | 0.195043 | ||||||||
\(892\) | 23.6647 | 0.792351 | ||||||||
\(893\) | −9.35756 | −0.313139 | ||||||||
\(894\) | 16.0503 | 0.536802 | ||||||||
\(895\) | 34.4083 | 1.15014 | ||||||||
\(896\) | −21.7325 | −0.726031 | ||||||||
\(897\) | 11.3420 | 0.378700 | ||||||||
\(898\) | −7.36538 | −0.245786 | ||||||||
\(899\) | −11.7807 | −0.392907 | ||||||||
\(900\) | 101.026 | 3.36754 | ||||||||
\(901\) | −11.2185 | −0.373743 | ||||||||
\(902\) | −4.78152 | −0.159207 | ||||||||
\(903\) | −90.7134 | −3.01875 | ||||||||
\(904\) | −3.13195 | −0.104167 | ||||||||
\(905\) | 22.4837 | 0.747384 | ||||||||
\(906\) | −34.7448 | −1.15432 | ||||||||
\(907\) | 34.8756 | 1.15802 | 0.579012 | − | 0.815319i | \(-0.303438\pi\) | ||||
0.579012 | + | 0.815319i | \(0.303438\pi\) | |||||||
\(908\) | −66.1767 | −2.19615 | ||||||||
\(909\) | −16.1921 | −0.537057 | ||||||||
\(910\) | −47.0923 | −1.56109 | ||||||||
\(911\) | 6.34470 | 0.210209 | 0.105105 | − | 0.994461i | \(-0.466482\pi\) | ||||
0.105105 | + | 0.994461i | \(0.466482\pi\) | |||||||
\(912\) | −8.02706 | −0.265802 | ||||||||
\(913\) | −0.928658 | −0.0307341 | ||||||||
\(914\) | −24.8020 | −0.820376 | ||||||||
\(915\) | 4.47253 | 0.147857 | ||||||||
\(916\) | 17.8287 | 0.589077 | ||||||||
\(917\) | −10.6826 | −0.352772 | ||||||||
\(918\) | −1.62008 | −0.0534707 | ||||||||
\(919\) | 56.4297 | 1.86144 | 0.930721 | − | 0.365729i | \(-0.119180\pi\) | ||||
0.930721 | + | 0.365729i | \(0.119180\pi\) | |||||||
\(920\) | 10.0478 | 0.331266 | ||||||||
\(921\) | −0.206137 | −0.00679245 | ||||||||
\(922\) | −37.0029 | −1.21863 | ||||||||
\(923\) | −14.0889 | −0.463740 | ||||||||
\(924\) | 16.3840 | 0.538994 | ||||||||
\(925\) | −4.59364 | −0.151038 | ||||||||
\(926\) | 15.0690 | 0.495198 | ||||||||
\(927\) | −15.3782 | −0.505086 | ||||||||
\(928\) | 69.6370 | 2.28595 | ||||||||
\(929\) | 9.73990 | 0.319556 | 0.159778 | − | 0.987153i | \(-0.448922\pi\) | ||||
0.159778 | + | 0.987153i | \(0.448922\pi\) | |||||||
\(930\) | −30.4672 | −0.999057 | ||||||||
\(931\) | 8.16924 | 0.267736 | ||||||||
\(932\) | −52.4806 | −1.71906 | ||||||||
\(933\) | 39.1216 | 1.28078 | ||||||||
\(934\) | −34.9598 | −1.14392 | ||||||||
\(935\) | 3.49468 | 0.114288 | ||||||||
\(936\) | −3.15083 | −0.102988 | ||||||||
\(937\) | −60.6415 | −1.98107 | −0.990536 | − | 0.137252i | \(-0.956173\pi\) | ||||
−0.990536 | + | 0.137252i | \(0.956173\pi\) | |||||||
\(938\) | 47.6851 | 1.55697 | ||||||||
\(939\) | −34.9715 | −1.14125 | ||||||||
\(940\) | 93.3929 | 3.04614 | ||||||||
\(941\) | 4.68933 | 0.152868 | 0.0764339 | − | 0.997075i | \(-0.475647\pi\) | ||||
0.0764339 | + | 0.997075i | \(0.475647\pi\) | |||||||
\(942\) | −60.8743 | −1.98339 | ||||||||
\(943\) | −10.6415 | −0.346535 | ||||||||
\(944\) | 3.56255 | 0.115951 | ||||||||
\(945\) | 11.3220 | 0.368306 | ||||||||
\(946\) | 13.9085 | 0.452205 | ||||||||
\(947\) | −51.8828 | −1.68597 | −0.842983 | − | 0.537941i | \(-0.819202\pi\) | ||||
−0.842983 | + | 0.537941i | \(0.819202\pi\) | |||||||
\(948\) | 58.7153 | 1.90699 | ||||||||
\(949\) | 15.0574 | 0.488783 | ||||||||
\(950\) | −27.4899 | −0.891890 | ||||||||
\(951\) | −50.6685 | −1.64304 | ||||||||
\(952\) | 3.14544 | 0.101944 | ||||||||
\(953\) | −6.58417 | −0.213282 | −0.106641 | − | 0.994298i | \(-0.534010\pi\) | ||||
−0.106641 | + | 0.994298i | \(0.534010\pi\) | |||||||
\(954\) | 67.0104 | 2.16954 | ||||||||
\(955\) | 90.7759 | 2.93744 | ||||||||
\(956\) | −20.3564 | −0.658373 | ||||||||
\(957\) | −15.4717 | −0.500129 | ||||||||
\(958\) | −6.96993 | −0.225188 | ||||||||
\(959\) | 12.5781 | 0.406168 | ||||||||
\(960\) | 111.613 | 3.60231 | ||||||||
\(961\) | −29.1258 | −0.939542 | ||||||||
\(962\) | 0.986721 | 0.0318132 | ||||||||
\(963\) | −21.7055 | −0.699451 | ||||||||
\(964\) | −31.4120 | −1.01171 | ||||||||
\(965\) | −92.3760 | −2.97369 | ||||||||
\(966\) | 67.6324 | 2.17604 | ||||||||
\(967\) | −3.91548 | −0.125913 | −0.0629566 | − | 0.998016i | \(-0.520053\pi\) | ||||
−0.0629566 | + | 0.998016i | \(0.520053\pi\) | |||||||
\(968\) | 7.41994 | 0.238486 | ||||||||
\(969\) | 2.85798 | 0.0918115 | ||||||||
\(970\) | −44.5163 | −1.42933 | ||||||||
\(971\) | 54.9374 | 1.76302 | 0.881512 | − | 0.472161i | \(-0.156526\pi\) | ||||
0.881512 | + | 0.472161i | \(0.156526\pi\) | |||||||
\(972\) | −52.3028 | −1.67761 | ||||||||
\(973\) | 48.4370 | 1.55282 | ||||||||
\(974\) | 0.360647 | 0.0115559 | ||||||||
\(975\) | 44.9675 | 1.44011 | ||||||||
\(976\) | 1.34186 | 0.0429520 | ||||||||
\(977\) | −5.10472 | −0.163314 | −0.0816572 | − | 0.996660i | \(-0.526021\pi\) | ||||
−0.0816572 | + | 0.996660i | \(0.526021\pi\) | |||||||
\(978\) | 67.5515 | 2.16006 | ||||||||
\(979\) | −7.99377 | −0.255482 | ||||||||
\(980\) | −81.5329 | −2.60447 | ||||||||
\(981\) | −7.70012 | −0.245846 | ||||||||
\(982\) | 7.07293 | 0.225706 | ||||||||
\(983\) | −7.36642 | −0.234952 | −0.117476 | − | 0.993076i | \(-0.537480\pi\) | ||||
−0.117476 | + | 0.993076i | \(0.537480\pi\) | |||||||
\(984\) | 5.66660 | 0.180645 | ||||||||
\(985\) | 19.5926 | 0.624273 | ||||||||
\(986\) | −20.4572 | −0.651490 | ||||||||
\(987\) | 91.2749 | 2.90531 | ||||||||
\(988\) | 3.18356 | 0.101282 | ||||||||
\(989\) | 30.9540 | 0.984281 | ||||||||
\(990\) | −20.8744 | −0.663433 | ||||||||
\(991\) | −36.8773 | −1.17145 | −0.585723 | − | 0.810512i | \(-0.699189\pi\) | ||||
−0.585723 | + | 0.810512i | \(0.699189\pi\) | |||||||
\(992\) | −11.0785 | −0.351744 | ||||||||
\(993\) | 4.07033 | 0.129168 | ||||||||
\(994\) | −84.0116 | −2.66469 | ||||||||
\(995\) | −116.769 | −3.70182 | ||||||||
\(996\) | 7.57981 | 0.240176 | ||||||||
\(997\) | 31.3387 | 0.992508 | 0.496254 | − | 0.868178i | \(-0.334709\pi\) | ||||
0.496254 | + | 0.868178i | \(0.334709\pi\) | |||||||
\(998\) | 22.8737 | 0.724055 | ||||||||
\(999\) | −0.237230 | −0.00750561 |
(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 | 4009.2.a.c.1.14 | ✓ | 71 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4009.2.a.c.1.14 | ✓ | 71 | 1.1 | even | 1 | trivial |