Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.5225.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 8x^{2} + x + 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.88301\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 3.04678 | 1.75906 | 0.879528 | − | 0.475846i | \(-0.157858\pi\) | ||||
0.879528 | + | 0.475846i | \(0.157858\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 3.04678 | 1.24384 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 6.28284 | 2.09428 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 3.04678 | 0.879528 | ||||||||
\(13\) | 0.353057 | 0.0979204 | 0.0489602 | − | 0.998801i | \(-0.484409\pi\) | ||||
0.0489602 | + | 0.998801i | \(0.484409\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −3.04678 | −0.786674 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.810708 | 0.196626 | 0.0983128 | − | 0.995156i | \(-0.468655\pi\) | ||||
0.0983128 | + | 0.995156i | \(0.468655\pi\) | |||||||
\(18\) | 6.28284 | 1.48088 | ||||||||
\(19\) | −2.59251 | −0.594762 | −0.297381 | − | 0.954759i | \(-0.596113\pi\) | ||||
−0.297381 | + | 0.954759i | \(0.596113\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 3.04678 | 0.664861 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.00000 | −0.417029 | −0.208514 | − | 0.978019i | \(-0.566863\pi\) | ||||
−0.208514 | + | 0.978019i | \(0.566863\pi\) | |||||||
\(24\) | 3.04678 | 0.621921 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.353057 | 0.0692401 | ||||||||
\(27\) | 10.0021 | 1.92490 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 9.54782 | 1.77299 | 0.886493 | − | 0.462742i | \(-0.153134\pi\) | ||||
0.886493 | + | 0.462742i | \(0.153134\pi\) | |||||||
\(30\) | −3.04678 | −0.556263 | ||||||||
\(31\) | −5.70820 | −1.02522 | −0.512612 | − | 0.858620i | \(-0.671322\pi\) | ||||
−0.512612 | + | 0.858620i | \(0.671322\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.810708 | 0.139035 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 6.28284 | 1.04714 | ||||||||
\(37\) | 3.56360 | 0.585852 | 0.292926 | − | 0.956135i | \(-0.405371\pi\) | ||||
0.292926 | + | 0.956135i | \(0.405371\pi\) | |||||||
\(38\) | −2.59251 | −0.420560 | ||||||||
\(39\) | 1.07569 | 0.172247 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 8.25732 | 1.28958 | 0.644788 | − | 0.764361i | \(-0.276946\pi\) | ||||
0.644788 | + | 0.764361i | \(0.276946\pi\) | |||||||
\(42\) | 3.04678 | 0.470128 | ||||||||
\(43\) | 9.49338 | 1.44773 | 0.723864 | − | 0.689943i | \(-0.242364\pi\) | ||||
0.723864 | + | 0.689943i | \(0.242364\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.28284 | −0.936591 | ||||||||
\(46\) | −2.00000 | −0.294884 | ||||||||
\(47\) | −8.60773 | −1.25557 | −0.627783 | − | 0.778388i | \(-0.716038\pi\) | ||||
−0.627783 | + | 0.778388i | \(0.716038\pi\) | |||||||
\(48\) | 3.04678 | 0.439764 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 2.47005 | 0.345876 | ||||||||
\(52\) | 0.353057 | 0.0489602 | ||||||||
\(53\) | −2.79967 | −0.384564 | −0.192282 | − | 0.981340i | \(-0.561589\pi\) | ||||
−0.192282 | + | 0.981340i | \(0.561589\pi\) | |||||||
\(54\) | 10.0021 | 1.36111 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −7.89879 | −1.04622 | ||||||||
\(58\) | 9.54782 | 1.25369 | ||||||||
\(59\) | 13.2092 | 1.71970 | 0.859849 | − | 0.510549i | \(-0.170558\pi\) | ||||
0.859849 | + | 0.510549i | \(0.170558\pi\) | |||||||
\(60\) | −3.04678 | −0.393337 | ||||||||
\(61\) | 6.70611 | 0.858630 | 0.429315 | − | 0.903155i | \(-0.358755\pi\) | ||||
0.429315 | + | 0.903155i | \(0.358755\pi\) | |||||||
\(62\) | −5.70820 | −0.724943 | ||||||||
\(63\) | 6.28284 | 0.791564 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.353057 | −0.0437913 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.40749 | −0.171953 | −0.0859763 | − | 0.996297i | \(-0.527401\pi\) | ||||
−0.0859763 | + | 0.996297i | \(0.527401\pi\) | |||||||
\(68\) | 0.810708 | 0.0983128 | ||||||||
\(69\) | −6.09355 | −0.733577 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −12.9187 | −1.53317 | −0.766586 | − | 0.642141i | \(-0.778046\pi\) | ||||
−0.766586 | + | 0.642141i | \(0.778046\pi\) | |||||||
\(72\) | 6.28284 | 0.740440 | ||||||||
\(73\) | 5.15008 | 0.602771 | 0.301386 | − | 0.953502i | \(-0.402551\pi\) | ||||
0.301386 | + | 0.953502i | \(0.402551\pi\) | |||||||
\(74\) | 3.56360 | 0.414260 | ||||||||
\(75\) | 3.04678 | 0.351811 | ||||||||
\(76\) | −2.59251 | −0.297381 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.07569 | 0.121797 | ||||||||
\(79\) | 3.64694 | 0.410313 | 0.205157 | − | 0.978729i | \(-0.434230\pi\) | ||||
0.205157 | + | 0.978729i | \(0.434230\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 11.6256 | 1.29173 | ||||||||
\(82\) | 8.25732 | 0.911868 | ||||||||
\(83\) | 2.66819 | 0.292872 | 0.146436 | − | 0.989220i | \(-0.453220\pi\) | ||||
0.146436 | + | 0.989220i | \(0.453220\pi\) | |||||||
\(84\) | 3.04678 | 0.332431 | ||||||||
\(85\) | −0.810708 | −0.0879336 | ||||||||
\(86\) | 9.49338 | 1.02370 | ||||||||
\(87\) | 29.0901 | 3.11878 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.63799 | 1.02163 | 0.510813 | − | 0.859692i | \(-0.329345\pi\) | ||||
0.510813 | + | 0.859692i | \(0.329345\pi\) | |||||||
\(90\) | −6.28284 | −0.662270 | ||||||||
\(91\) | 0.353057 | 0.0370104 | ||||||||
\(92\) | −2.00000 | −0.208514 | ||||||||
\(93\) | −17.3916 | −1.80343 | ||||||||
\(94\) | −8.60773 | −0.887820 | ||||||||
\(95\) | 2.59251 | 0.265986 | ||||||||
\(96\) | 3.04678 | 0.310960 | ||||||||
\(97\) | −9.79837 | −0.994874 | −0.497437 | − | 0.867500i | \(-0.665725\pi\) | ||||
−0.497437 | + | 0.867500i | \(0.665725\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 0.904358 | 0.0899870 | 0.0449935 | − | 0.998987i | \(-0.485673\pi\) | ||||
0.0449935 | + | 0.998987i | \(0.485673\pi\) | |||||||
\(102\) | 2.47005 | 0.244571 | ||||||||
\(103\) | 11.2203 | 1.10557 | 0.552784 | − | 0.833325i | \(-0.313565\pi\) | ||||
0.552784 | + | 0.833325i | \(0.313565\pi\) | |||||||
\(104\) | 0.353057 | 0.0346201 | ||||||||
\(105\) | −3.04678 | −0.297335 | ||||||||
\(106\) | −2.79967 | −0.271928 | ||||||||
\(107\) | −8.89614 | −0.860023 | −0.430011 | − | 0.902823i | \(-0.641490\pi\) | ||||
−0.430011 | + | 0.902823i | \(0.641490\pi\) | |||||||
\(108\) | 10.0021 | 0.962452 | ||||||||
\(109\) | −18.4763 | −1.76971 | −0.884855 | − | 0.465866i | \(-0.845743\pi\) | ||||
−0.884855 | + | 0.465866i | \(0.845743\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.8575 | 1.03055 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −12.6902 | −1.19380 | −0.596899 | − | 0.802317i | \(-0.703601\pi\) | ||||
−0.596899 | + | 0.802317i | \(0.703601\pi\) | |||||||
\(114\) | −7.89879 | −0.739789 | ||||||||
\(115\) | 2.00000 | 0.186501 | ||||||||
\(116\) | 9.54782 | 0.886493 | ||||||||
\(117\) | 2.21820 | 0.205073 | ||||||||
\(118\) | 13.2092 | 1.21601 | ||||||||
\(119\) | 0.810708 | 0.0743175 | ||||||||
\(120\) | −3.04678 | −0.278131 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 6.70611 | 0.607143 | ||||||||
\(123\) | 25.1582 | 2.26844 | ||||||||
\(124\) | −5.70820 | −0.512612 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 6.28284 | 0.559720 | ||||||||
\(127\) | −16.2382 | −1.44090 | −0.720452 | − | 0.693505i | \(-0.756066\pi\) | ||||
−0.720452 | + | 0.693505i | \(0.756066\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 28.9242 | 2.54664 | ||||||||
\(130\) | −0.353057 | −0.0309651 | ||||||||
\(131\) | 8.08882 | 0.706723 | 0.353362 | − | 0.935487i | \(-0.385039\pi\) | ||||
0.353362 | + | 0.935487i | \(0.385039\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.59251 | −0.224799 | ||||||||
\(134\) | −1.40749 | −0.121589 | ||||||||
\(135\) | −10.0021 | −0.860843 | ||||||||
\(136\) | 0.810708 | 0.0695176 | ||||||||
\(137\) | 10.4019 | 0.888696 | 0.444348 | − | 0.895854i | \(-0.353435\pi\) | ||||
0.444348 | + | 0.895854i | \(0.353435\pi\) | |||||||
\(138\) | −6.09355 | −0.518718 | ||||||||
\(139\) | −0.757168 | −0.0642221 | −0.0321111 | − | 0.999484i | \(-0.510223\pi\) | ||||
−0.0321111 | + | 0.999484i | \(0.510223\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | −26.2258 | −2.20861 | ||||||||
\(142\) | −12.9187 | −1.08412 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 6.28284 | 0.523570 | ||||||||
\(145\) | −9.54782 | −0.792903 | ||||||||
\(146\) | 5.15008 | 0.426224 | ||||||||
\(147\) | 3.04678 | 0.251294 | ||||||||
\(148\) | 3.56360 | 0.292926 | ||||||||
\(149\) | 8.96980 | 0.734835 | 0.367417 | − | 0.930056i | \(-0.380242\pi\) | ||||
0.367417 | + | 0.930056i | \(0.380242\pi\) | |||||||
\(150\) | 3.04678 | 0.248768 | ||||||||
\(151\) | 21.9731 | 1.78814 | 0.894072 | − | 0.447923i | \(-0.147836\pi\) | ||||
0.894072 | + | 0.447923i | \(0.147836\pi\) | |||||||
\(152\) | −2.59251 | −0.210280 | ||||||||
\(153\) | 5.09355 | 0.411789 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.70820 | 0.458494 | ||||||||
\(156\) | 1.07569 | 0.0861237 | ||||||||
\(157\) | 0.0668308 | 0.00533368 | 0.00266684 | − | 0.999996i | \(-0.499151\pi\) | ||||
0.00266684 | + | 0.999996i | \(0.499151\pi\) | |||||||
\(158\) | 3.64694 | 0.290135 | ||||||||
\(159\) | −8.52995 | −0.676469 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −2.00000 | −0.157622 | ||||||||
\(162\) | 11.6256 | 0.913393 | ||||||||
\(163\) | 22.2692 | 1.74426 | 0.872128 | − | 0.489279i | \(-0.162740\pi\) | ||||
0.872128 | + | 0.489279i | \(0.162740\pi\) | |||||||
\(164\) | 8.25732 | 0.644788 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.66819 | 0.207092 | ||||||||
\(167\) | 12.0000 | 0.928588 | 0.464294 | − | 0.885681i | \(-0.346308\pi\) | ||||
0.464294 | + | 0.885681i | \(0.346308\pi\) | |||||||
\(168\) | 3.04678 | 0.235064 | ||||||||
\(169\) | −12.8754 | −0.990412 | ||||||||
\(170\) | −0.810708 | −0.0621785 | ||||||||
\(171\) | −16.2883 | −1.24560 | ||||||||
\(172\) | 9.49338 | 0.723864 | ||||||||
\(173\) | −19.8698 | −1.51067 | −0.755336 | − | 0.655338i | \(-0.772526\pi\) | ||||
−0.755336 | + | 0.655338i | \(0.772526\pi\) | |||||||
\(174\) | 29.0901 | 2.20531 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 40.2456 | 3.02505 | ||||||||
\(178\) | 9.63799 | 0.722398 | ||||||||
\(179\) | −8.61246 | −0.643726 | −0.321863 | − | 0.946786i | \(-0.604309\pi\) | ||||
−0.321863 | + | 0.946786i | \(0.604309\pi\) | |||||||
\(180\) | −6.28284 | −0.468296 | ||||||||
\(181\) | 11.7345 | 0.872216 | 0.436108 | − | 0.899894i | \(-0.356357\pi\) | ||||
0.436108 | + | 0.899894i | \(0.356357\pi\) | |||||||
\(182\) | 0.353057 | 0.0261703 | ||||||||
\(183\) | 20.4320 | 1.51038 | ||||||||
\(184\) | −2.00000 | −0.147442 | ||||||||
\(185\) | −3.56360 | −0.262001 | ||||||||
\(186\) | −17.3916 | −1.27522 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −8.60773 | −0.627783 | ||||||||
\(189\) | 10.0021 | 0.727545 | ||||||||
\(190\) | 2.59251 | 0.188080 | ||||||||
\(191\) | −8.15063 | −0.589759 | −0.294880 | − | 0.955534i | \(-0.595280\pi\) | ||||
−0.294880 | + | 0.955534i | \(0.595280\pi\) | |||||||
\(192\) | 3.04678 | 0.219882 | ||||||||
\(193\) | −8.74185 | −0.629252 | −0.314626 | − | 0.949216i | \(-0.601879\pi\) | ||||
−0.314626 | + | 0.949216i | \(0.601879\pi\) | |||||||
\(194\) | −9.79837 | −0.703482 | ||||||||
\(195\) | −1.07569 | −0.0770314 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −14.4568 | −1.03001 | −0.515003 | − | 0.857189i | \(-0.672209\pi\) | ||||
−0.515003 | + | 0.857189i | \(0.672209\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.0446 | −0.782930 | −0.391465 | − | 0.920193i | \(-0.628032\pi\) | ||||
−0.391465 | + | 0.920193i | \(0.628032\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −4.28832 | −0.302475 | ||||||||
\(202\) | 0.904358 | 0.0636304 | ||||||||
\(203\) | 9.54782 | 0.670126 | ||||||||
\(204\) | 2.47005 | 0.172938 | ||||||||
\(205\) | −8.25732 | −0.576716 | ||||||||
\(206\) | 11.2203 | 0.781755 | ||||||||
\(207\) | −12.5657 | −0.873376 | ||||||||
\(208\) | 0.353057 | 0.0244801 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −3.04678 | −0.210248 | ||||||||
\(211\) | −23.7102 | −1.63228 | −0.816139 | − | 0.577856i | \(-0.803889\pi\) | ||||
−0.816139 | + | 0.577856i | \(0.803889\pi\) | |||||||
\(212\) | −2.79967 | −0.192282 | ||||||||
\(213\) | −39.3605 | −2.69694 | ||||||||
\(214\) | −8.89614 | −0.608128 | ||||||||
\(215\) | −9.49338 | −0.647443 | ||||||||
\(216\) | 10.0021 | 0.680556 | ||||||||
\(217\) | −5.70820 | −0.387498 | ||||||||
\(218\) | −18.4763 | −1.25137 | ||||||||
\(219\) | 15.6911 | 1.06031 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.286226 | 0.0192536 | ||||||||
\(222\) | 10.8575 | 0.728707 | ||||||||
\(223\) | −5.58986 | −0.374325 | −0.187162 | − | 0.982329i | \(-0.559929\pi\) | ||||
−0.187162 | + | 0.982329i | \(0.559929\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 6.28284 | 0.418856 | ||||||||
\(226\) | −12.6902 | −0.844142 | ||||||||
\(227\) | 6.32206 | 0.419610 | 0.209805 | − | 0.977743i | \(-0.432717\pi\) | ||||
0.209805 | + | 0.977743i | \(0.432717\pi\) | |||||||
\(228\) | −7.89879 | −0.523110 | ||||||||
\(229\) | −3.89113 | −0.257133 | −0.128566 | − | 0.991701i | \(-0.541038\pi\) | ||||
−0.128566 | + | 0.991701i | \(0.541038\pi\) | |||||||
\(230\) | 2.00000 | 0.131876 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.54782 | 0.626845 | ||||||||
\(233\) | −15.1659 | −0.993548 | −0.496774 | − | 0.867880i | \(-0.665482\pi\) | ||||
−0.496774 | + | 0.867880i | \(0.665482\pi\) | |||||||
\(234\) | 2.21820 | 0.145008 | ||||||||
\(235\) | 8.60773 | 0.561506 | ||||||||
\(236\) | 13.2092 | 0.859849 | ||||||||
\(237\) | 11.1114 | 0.721764 | ||||||||
\(238\) | 0.810708 | 0.0525504 | ||||||||
\(239\) | 21.0949 | 1.36452 | 0.682258 | − | 0.731112i | \(-0.260998\pi\) | ||||
0.682258 | + | 0.731112i | \(0.260998\pi\) | |||||||
\(240\) | −3.04678 | −0.196669 | ||||||||
\(241\) | 11.9416 | 0.769228 | 0.384614 | − | 0.923078i | \(-0.374335\pi\) | ||||
0.384614 | + | 0.923078i | \(0.374335\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.41432 | 0.347329 | ||||||||
\(244\) | 6.70611 | 0.429315 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 25.1582 | 1.60403 | ||||||||
\(247\) | −0.915302 | −0.0582393 | ||||||||
\(248\) | −5.70820 | −0.362471 | ||||||||
\(249\) | 8.12938 | 0.515179 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 2.11834 | 0.133709 | 0.0668543 | − | 0.997763i | \(-0.478704\pi\) | ||||
0.0668543 | + | 0.997763i | \(0.478704\pi\) | |||||||
\(252\) | 6.28284 | 0.395782 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −16.2382 | −1.01887 | ||||||||
\(255\) | −2.47005 | −0.154680 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −20.7137 | −1.29208 | −0.646042 | − | 0.763302i | \(-0.723577\pi\) | ||||
−0.646042 | + | 0.763302i | \(0.723577\pi\) | |||||||
\(258\) | 28.9242 | 1.80074 | ||||||||
\(259\) | 3.56360 | 0.221431 | ||||||||
\(260\) | −0.353057 | −0.0218957 | ||||||||
\(261\) | 59.9875 | 3.71313 | ||||||||
\(262\) | 8.08882 | 0.499729 | ||||||||
\(263\) | −3.89531 | −0.240195 | −0.120097 | − | 0.992762i | \(-0.538321\pi\) | ||||
−0.120097 | + | 0.992762i | \(0.538321\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.79967 | 0.171982 | ||||||||
\(266\) | −2.59251 | −0.158957 | ||||||||
\(267\) | 29.3648 | 1.79710 | ||||||||
\(268\) | −1.40749 | −0.0859763 | ||||||||
\(269\) | −22.8684 | −1.39431 | −0.697156 | − | 0.716919i | \(-0.745552\pi\) | ||||
−0.697156 | + | 0.716919i | \(0.745552\pi\) | |||||||
\(270\) | −10.0021 | −0.608708 | ||||||||
\(271\) | −20.6082 | −1.25186 | −0.625929 | − | 0.779880i | \(-0.715280\pi\) | ||||
−0.625929 | + | 0.779880i | \(0.715280\pi\) | |||||||
\(272\) | 0.810708 | 0.0491564 | ||||||||
\(273\) | 1.07569 | 0.0651034 | ||||||||
\(274\) | 10.4019 | 0.628403 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.09355 | −0.366789 | ||||||||
\(277\) | −17.2045 | −1.03372 | −0.516860 | − | 0.856070i | \(-0.672899\pi\) | ||||
−0.516860 | + | 0.856070i | \(0.672899\pi\) | |||||||
\(278\) | −0.757168 | −0.0454119 | ||||||||
\(279\) | −35.8638 | −2.14711 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | −30.4444 | −1.81616 | −0.908081 | − | 0.418795i | \(-0.862453\pi\) | ||||
−0.908081 | + | 0.418795i | \(0.862453\pi\) | |||||||
\(282\) | −26.2258 | −1.56173 | ||||||||
\(283\) | −9.99517 | −0.594151 | −0.297076 | − | 0.954854i | \(-0.596011\pi\) | ||||
−0.297076 | + | 0.954854i | \(0.596011\pi\) | |||||||
\(284\) | −12.9187 | −0.766586 | ||||||||
\(285\) | 7.89879 | 0.467884 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.25732 | 0.487414 | ||||||||
\(288\) | 6.28284 | 0.370220 | ||||||||
\(289\) | −16.3428 | −0.961338 | ||||||||
\(290\) | −9.54782 | −0.560667 | ||||||||
\(291\) | −29.8535 | −1.75004 | ||||||||
\(292\) | 5.15008 | 0.301386 | ||||||||
\(293\) | 6.46796 | 0.377862 | 0.188931 | − | 0.981990i | \(-0.439498\pi\) | ||||
0.188931 | + | 0.981990i | \(0.439498\pi\) | |||||||
\(294\) | 3.04678 | 0.177692 | ||||||||
\(295\) | −13.2092 | −0.769072 | ||||||||
\(296\) | 3.56360 | 0.207130 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.96980 | 0.519607 | ||||||||
\(299\) | −0.706114 | −0.0408356 | ||||||||
\(300\) | 3.04678 | 0.175906 | ||||||||
\(301\) | 9.49338 | 0.547190 | ||||||||
\(302\) | 21.9731 | 1.26441 | ||||||||
\(303\) | 2.75538 | 0.158292 | ||||||||
\(304\) | −2.59251 | −0.148690 | ||||||||
\(305\) | −6.70611 | −0.383991 | ||||||||
\(306\) | 5.09355 | 0.291179 | ||||||||
\(307\) | 20.6473 | 1.17840 | 0.589202 | − | 0.807986i | \(-0.299442\pi\) | ||||
0.589202 | + | 0.807986i | \(0.299442\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 34.1857 | 1.94476 | ||||||||
\(310\) | 5.70820 | 0.324204 | ||||||||
\(311\) | 23.4385 | 1.32907 | 0.664537 | − | 0.747255i | \(-0.268629\pi\) | ||||
0.664537 | + | 0.747255i | \(0.268629\pi\) | |||||||
\(312\) | 1.07569 | 0.0608987 | ||||||||
\(313\) | 11.9059 | 0.672961 | 0.336480 | − | 0.941690i | \(-0.390763\pi\) | ||||
0.336480 | + | 0.941690i | \(0.390763\pi\) | |||||||
\(314\) | 0.0668308 | 0.00377148 | ||||||||
\(315\) | −6.28284 | −0.353998 | ||||||||
\(316\) | 3.64694 | 0.205157 | ||||||||
\(317\) | −34.4185 | −1.93314 | −0.966568 | − | 0.256411i | \(-0.917460\pi\) | ||||
−0.966568 | + | 0.256411i | \(0.917460\pi\) | |||||||
\(318\) | −8.52995 | −0.478336 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −27.1046 | −1.51283 | ||||||||
\(322\) | −2.00000 | −0.111456 | ||||||||
\(323\) | −2.10177 | −0.116945 | ||||||||
\(324\) | 11.6256 | 0.645866 | ||||||||
\(325\) | 0.353057 | 0.0195841 | ||||||||
\(326\) | 22.2692 | 1.23337 | ||||||||
\(327\) | −56.2932 | −3.11302 | ||||||||
\(328\) | 8.25732 | 0.455934 | ||||||||
\(329\) | −8.60773 | −0.474559 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.6770 | −0.641829 | −0.320914 | − | 0.947108i | \(-0.603990\pi\) | ||||
−0.320914 | + | 0.947108i | \(0.603990\pi\) | |||||||
\(332\) | 2.66819 | 0.146436 | ||||||||
\(333\) | 22.3895 | 1.22694 | ||||||||
\(334\) | 12.0000 | 0.656611 | ||||||||
\(335\) | 1.40749 | 0.0768996 | ||||||||
\(336\) | 3.04678 | 0.166215 | ||||||||
\(337\) | 10.3337 | 0.562915 | 0.281457 | − | 0.959574i | \(-0.409182\pi\) | ||||
0.281457 | + | 0.959574i | \(0.409182\pi\) | |||||||
\(338\) | −12.8754 | −0.700327 | ||||||||
\(339\) | −38.6643 | −2.09996 | ||||||||
\(340\) | −0.810708 | −0.0439668 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −16.2883 | −0.880771 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 9.49338 | 0.511849 | ||||||||
\(345\) | 6.09355 | 0.328066 | ||||||||
\(346\) | −19.8698 | −1.06821 | ||||||||
\(347\) | 18.3202 | 0.983480 | 0.491740 | − | 0.870742i | \(-0.336361\pi\) | ||||
0.491740 | + | 0.870742i | \(0.336361\pi\) | |||||||
\(348\) | 29.0901 | 1.55939 | ||||||||
\(349\) | 29.9216 | 1.60167 | 0.800833 | − | 0.598888i | \(-0.204391\pi\) | ||||
0.800833 | + | 0.598888i | \(0.204391\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | 3.53131 | 0.188487 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.93024 | −0.475309 | −0.237654 | − | 0.971350i | \(-0.576379\pi\) | ||||
−0.237654 | + | 0.971350i | \(0.576379\pi\) | |||||||
\(354\) | 40.2456 | 2.13903 | ||||||||
\(355\) | 12.9187 | 0.685656 | ||||||||
\(356\) | 9.63799 | 0.510813 | ||||||||
\(357\) | 2.47005 | 0.130729 | ||||||||
\(358\) | −8.61246 | −0.455183 | ||||||||
\(359\) | 29.7915 | 1.57234 | 0.786169 | − | 0.618012i | \(-0.212062\pi\) | ||||
0.786169 | + | 0.618012i | \(0.212062\pi\) | |||||||
\(360\) | −6.28284 | −0.331135 | ||||||||
\(361\) | −12.2789 | −0.646258 | ||||||||
\(362\) | 11.7345 | 0.616750 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.353057 | 0.0185052 | ||||||||
\(365\) | −5.15008 | −0.269567 | ||||||||
\(366\) | 20.4320 | 1.06800 | ||||||||
\(367\) | −24.7535 | −1.29212 | −0.646062 | − | 0.763285i | \(-0.723585\pi\) | ||||
−0.646062 | + | 0.763285i | \(0.723585\pi\) | |||||||
\(368\) | −2.00000 | −0.104257 | ||||||||
\(369\) | 51.8794 | 2.70074 | ||||||||
\(370\) | −3.56360 | −0.185263 | ||||||||
\(371\) | −2.79967 | −0.145351 | ||||||||
\(372\) | −17.3916 | −0.901713 | ||||||||
\(373\) | 9.75070 | 0.504872 | 0.252436 | − | 0.967614i | \(-0.418768\pi\) | ||||
0.252436 | + | 0.967614i | \(0.418768\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.04678 | −0.157335 | ||||||||
\(376\) | −8.60773 | −0.443910 | ||||||||
\(377\) | 3.37092 | 0.173611 | ||||||||
\(378\) | 10.0021 | 0.514452 | ||||||||
\(379\) | 21.0454 | 1.08103 | 0.540514 | − | 0.841335i | \(-0.318230\pi\) | ||||
0.540514 | + | 0.841335i | \(0.318230\pi\) | |||||||
\(380\) | 2.59251 | 0.132993 | ||||||||
\(381\) | −49.4740 | −2.53463 | ||||||||
\(382\) | −8.15063 | −0.417023 | ||||||||
\(383\) | −34.8828 | −1.78243 | −0.891214 | − | 0.453582i | \(-0.850146\pi\) | ||||
−0.891214 | + | 0.453582i | \(0.850146\pi\) | |||||||
\(384\) | 3.04678 | 0.155480 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.74185 | −0.444948 | ||||||||
\(387\) | 59.6455 | 3.03195 | ||||||||
\(388\) | −9.79837 | −0.497437 | ||||||||
\(389\) | −12.7069 | −0.644263 | −0.322131 | − | 0.946695i | \(-0.604399\pi\) | ||||
−0.322131 | + | 0.946695i | \(0.604399\pi\) | |||||||
\(390\) | −1.07569 | −0.0544694 | ||||||||
\(391\) | −1.62142 | −0.0819985 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 24.6448 | 1.24317 | ||||||||
\(394\) | −14.4568 | −0.728324 | ||||||||
\(395\) | −3.64694 | −0.183498 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.33036 | 0.167146 | 0.0835729 | − | 0.996502i | \(-0.473367\pi\) | ||||
0.0835729 | + | 0.996502i | \(0.473367\pi\) | |||||||
\(398\) | −11.0446 | −0.553615 | ||||||||
\(399\) | −7.89879 | −0.395434 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −9.27248 | −0.463046 | −0.231523 | − | 0.972829i | \(-0.574371\pi\) | ||||
−0.231523 | + | 0.972829i | \(0.574371\pi\) | |||||||
\(402\) | −4.28832 | −0.213882 | ||||||||
\(403\) | −2.01532 | −0.100390 | ||||||||
\(404\) | 0.904358 | 0.0449935 | ||||||||
\(405\) | −11.6256 | −0.577681 | ||||||||
\(406\) | 9.54782 | 0.473850 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 2.47005 | 0.122285 | ||||||||
\(409\) | 0.349614 | 0.0172873 | 0.00864366 | − | 0.999963i | \(-0.497249\pi\) | ||||
0.00864366 | + | 0.999963i | \(0.497249\pi\) | |||||||
\(410\) | −8.25732 | −0.407800 | ||||||||
\(411\) | 31.6923 | 1.56327 | ||||||||
\(412\) | 11.2203 | 0.552784 | ||||||||
\(413\) | 13.2092 | 0.649985 | ||||||||
\(414\) | −12.5657 | −0.617570 | ||||||||
\(415\) | −2.66819 | −0.130976 | ||||||||
\(416\) | 0.353057 | 0.0173100 | ||||||||
\(417\) | −2.30692 | −0.112970 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.9340 | 1.36466 | 0.682332 | − | 0.731043i | \(-0.260966\pi\) | ||||
0.682332 | + | 0.731043i | \(0.260966\pi\) | |||||||
\(420\) | −3.04678 | −0.148667 | ||||||||
\(421\) | 8.07221 | 0.393415 | 0.196708 | − | 0.980462i | \(-0.436975\pi\) | ||||
0.196708 | + | 0.980462i | \(0.436975\pi\) | |||||||
\(422\) | −23.7102 | −1.15419 | ||||||||
\(423\) | −54.0810 | −2.62951 | ||||||||
\(424\) | −2.79967 | −0.135964 | ||||||||
\(425\) | 0.810708 | 0.0393251 | ||||||||
\(426\) | −39.3605 | −1.90702 | ||||||||
\(427\) | 6.70611 | 0.324532 | ||||||||
\(428\) | −8.89614 | −0.430011 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.49338 | −0.457812 | ||||||||
\(431\) | −20.0088 | −0.963791 | −0.481895 | − | 0.876229i | \(-0.660051\pi\) | ||||
−0.481895 | + | 0.876229i | \(0.660051\pi\) | |||||||
\(432\) | 10.0021 | 0.481226 | ||||||||
\(433\) | −38.7447 | −1.86195 | −0.930977 | − | 0.365079i | \(-0.881042\pi\) | ||||
−0.930977 | + | 0.365079i | \(0.881042\pi\) | |||||||
\(434\) | −5.70820 | −0.274003 | ||||||||
\(435\) | −29.0901 | −1.39476 | ||||||||
\(436\) | −18.4763 | −0.884855 | ||||||||
\(437\) | 5.18501 | 0.248033 | ||||||||
\(438\) | 15.6911 | 0.749751 | ||||||||
\(439\) | −5.62560 | −0.268495 | −0.134248 | − | 0.990948i | \(-0.542862\pi\) | ||||
−0.134248 | + | 0.990948i | \(0.542862\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.28284 | 0.299183 | ||||||||
\(442\) | 0.286226 | 0.0136144 | ||||||||
\(443\) | −15.6763 | −0.744804 | −0.372402 | − | 0.928072i | \(-0.621466\pi\) | ||||
−0.372402 | + | 0.928072i | \(0.621466\pi\) | |||||||
\(444\) | 10.8575 | 0.515273 | ||||||||
\(445\) | −9.63799 | −0.456885 | ||||||||
\(446\) | −5.58986 | −0.264688 | ||||||||
\(447\) | 27.3290 | 1.29262 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −26.1032 | −1.23189 | −0.615943 | − | 0.787791i | \(-0.711225\pi\) | ||||
−0.615943 | + | 0.787791i | \(0.711225\pi\) | |||||||
\(450\) | 6.28284 | 0.296176 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −12.6902 | −0.596899 | ||||||||
\(453\) | 66.9471 | 3.14545 | ||||||||
\(454\) | 6.32206 | 0.296709 | ||||||||
\(455\) | −0.353057 | −0.0165516 | ||||||||
\(456\) | −7.89879 | −0.369895 | ||||||||
\(457\) | 35.5911 | 1.66488 | 0.832441 | − | 0.554114i | \(-0.186943\pi\) | ||||
0.832441 | + | 0.554114i | \(0.186943\pi\) | |||||||
\(458\) | −3.89113 | −0.181820 | ||||||||
\(459\) | 8.10877 | 0.378485 | ||||||||
\(460\) | 2.00000 | 0.0932505 | ||||||||
\(461\) | 9.66571 | 0.450177 | 0.225088 | − | 0.974338i | \(-0.427733\pi\) | ||||
0.225088 | + | 0.974338i | \(0.427733\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.9726 | −1.39295 | −0.696473 | − | 0.717583i | \(-0.745248\pi\) | ||||
−0.696473 | + | 0.717583i | \(0.745248\pi\) | |||||||
\(464\) | 9.54782 | 0.443246 | ||||||||
\(465\) | 17.3916 | 0.806517 | ||||||||
\(466\) | −15.1659 | −0.702545 | ||||||||
\(467\) | 30.5086 | 1.41177 | 0.705885 | − | 0.708326i | \(-0.250550\pi\) | ||||
0.705885 | + | 0.708326i | \(0.250550\pi\) | |||||||
\(468\) | 2.21820 | 0.102536 | ||||||||
\(469\) | −1.40749 | −0.0649920 | ||||||||
\(470\) | 8.60773 | 0.397045 | ||||||||
\(471\) | 0.203619 | 0.00938225 | ||||||||
\(472\) | 13.2092 | 0.608005 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 11.1114 | 0.510364 | ||||||||
\(475\) | −2.59251 | −0.118952 | ||||||||
\(476\) | 0.810708 | 0.0371587 | ||||||||
\(477\) | −17.5899 | −0.805384 | ||||||||
\(478\) | 21.0949 | 0.964858 | ||||||||
\(479\) | 38.7127 | 1.76883 | 0.884414 | − | 0.466704i | \(-0.154559\pi\) | ||||
0.884414 | + | 0.466704i | \(0.154559\pi\) | |||||||
\(480\) | −3.04678 | −0.139066 | ||||||||
\(481\) | 1.25815 | 0.0573668 | ||||||||
\(482\) | 11.9416 | 0.543926 | ||||||||
\(483\) | −6.09355 | −0.277266 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.79837 | 0.444921 | ||||||||
\(486\) | 5.41432 | 0.245598 | ||||||||
\(487\) | 33.8375 | 1.53332 | 0.766662 | − | 0.642052i | \(-0.221916\pi\) | ||||
0.766662 | + | 0.642052i | \(0.221916\pi\) | |||||||
\(488\) | 6.70611 | 0.303572 | ||||||||
\(489\) | 67.8491 | 3.06824 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | 18.5755 | 0.838301 | 0.419150 | − | 0.907917i | \(-0.362328\pi\) | ||||
0.419150 | + | 0.907917i | \(0.362328\pi\) | |||||||
\(492\) | 25.1582 | 1.13422 | ||||||||
\(493\) | 7.74050 | 0.348614 | ||||||||
\(494\) | −0.915302 | −0.0411814 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.70820 | −0.256306 | ||||||||
\(497\) | −12.9187 | −0.579485 | ||||||||
\(498\) | 8.12938 | 0.364286 | ||||||||
\(499\) | −14.7069 | −0.658372 | −0.329186 | − | 0.944265i | \(-0.606774\pi\) | ||||
−0.329186 | + | 0.944265i | \(0.606774\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 36.5613 | 1.63344 | ||||||||
\(502\) | 2.11834 | 0.0945462 | ||||||||
\(503\) | −5.50234 | −0.245337 | −0.122669 | − | 0.992448i | \(-0.539145\pi\) | ||||
−0.122669 | + | 0.992448i | \(0.539145\pi\) | |||||||
\(504\) | 6.28284 | 0.279860 | ||||||||
\(505\) | −0.904358 | −0.0402434 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −39.2283 | −1.74219 | ||||||||
\(508\) | −16.2382 | −0.720452 | ||||||||
\(509\) | 24.1045 | 1.06841 | 0.534207 | − | 0.845354i | \(-0.320610\pi\) | ||||
0.534207 | + | 0.845354i | \(0.320610\pi\) | |||||||
\(510\) | −2.47005 | −0.109375 | ||||||||
\(511\) | 5.15008 | 0.227826 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −25.9305 | −1.14486 | ||||||||
\(514\) | −20.7137 | −0.913641 | ||||||||
\(515\) | −11.2203 | −0.494425 | ||||||||
\(516\) | 28.9242 | 1.27332 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 3.56360 | 0.156575 | ||||||||
\(519\) | −60.5388 | −2.65736 | ||||||||
\(520\) | −0.353057 | −0.0154826 | ||||||||
\(521\) | 8.73293 | 0.382597 | 0.191298 | − | 0.981532i | \(-0.438730\pi\) | ||||
0.191298 | + | 0.981532i | \(0.438730\pi\) | |||||||
\(522\) | 59.9875 | 2.62558 | ||||||||
\(523\) | −44.2475 | −1.93481 | −0.967405 | − | 0.253235i | \(-0.918505\pi\) | ||||
−0.967405 | + | 0.253235i | \(0.918505\pi\) | |||||||
\(524\) | 8.08882 | 0.353362 | ||||||||
\(525\) | 3.04678 | 0.132972 | ||||||||
\(526\) | −3.89531 | −0.169843 | ||||||||
\(527\) | −4.62769 | −0.201585 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.0000 | −0.826087 | ||||||||
\(530\) | 2.79967 | 0.121610 | ||||||||
\(531\) | 82.9917 | 3.60153 | ||||||||
\(532\) | −2.59251 | −0.112399 | ||||||||
\(533\) | 2.91530 | 0.126276 | ||||||||
\(534\) | 29.3648 | 1.27074 | ||||||||
\(535\) | 8.89614 | 0.384614 | ||||||||
\(536\) | −1.40749 | −0.0607944 | ||||||||
\(537\) | −26.2402 | −1.13235 | ||||||||
\(538\) | −22.8684 | −0.985928 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −10.0021 | −0.430421 | ||||||||
\(541\) | −14.0407 | −0.603655 | −0.301827 | − | 0.953363i | \(-0.597597\pi\) | ||||
−0.301827 | + | 0.953363i | \(0.597597\pi\) | |||||||
\(542\) | −20.6082 | −0.885197 | ||||||||
\(543\) | 35.7523 | 1.53428 | ||||||||
\(544\) | 0.810708 | 0.0347588 | ||||||||
\(545\) | 18.4763 | 0.791438 | ||||||||
\(546\) | 1.07569 | 0.0460351 | ||||||||
\(547\) | −6.48093 | −0.277105 | −0.138552 | − | 0.990355i | \(-0.544245\pi\) | ||||
−0.138552 | + | 0.990355i | \(0.544245\pi\) | |||||||
\(548\) | 10.4019 | 0.444348 | ||||||||
\(549\) | 42.1335 | 1.79821 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24.7528 | −1.05450 | ||||||||
\(552\) | −6.09355 | −0.259359 | ||||||||
\(553\) | 3.64694 | 0.155084 | ||||||||
\(554\) | −17.2045 | −0.730950 | ||||||||
\(555\) | −10.8575 | −0.460875 | ||||||||
\(556\) | −0.757168 | −0.0321111 | ||||||||
\(557\) | −10.0109 | −0.424177 | −0.212089 | − | 0.977250i | \(-0.568027\pi\) | ||||
−0.212089 | + | 0.977250i | \(0.568027\pi\) | |||||||
\(558\) | −35.8638 | −1.51823 | ||||||||
\(559\) | 3.35170 | 0.141762 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −30.4444 | −1.28422 | ||||||||
\(563\) | −3.32206 | −0.140008 | −0.0700040 | − | 0.997547i | \(-0.522301\pi\) | ||||
−0.0700040 | + | 0.997547i | \(0.522301\pi\) | |||||||
\(564\) | −26.2258 | −1.10431 | ||||||||
\(565\) | 12.6902 | 0.533882 | ||||||||
\(566\) | −9.99517 | −0.420128 | ||||||||
\(567\) | 11.6256 | 0.488229 | ||||||||
\(568\) | −12.9187 | −0.542058 | ||||||||
\(569\) | −30.5120 | −1.27913 | −0.639564 | − | 0.768738i | \(-0.720885\pi\) | ||||
−0.639564 | + | 0.768738i | \(0.720885\pi\) | |||||||
\(570\) | 7.89879 | 0.330844 | ||||||||
\(571\) | −2.37904 | −0.0995597 | −0.0497799 | − | 0.998760i | \(-0.515852\pi\) | ||||
−0.0497799 | + | 0.998760i | \(0.515852\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −24.8332 | −1.03742 | ||||||||
\(574\) | 8.25732 | 0.344654 | ||||||||
\(575\) | −2.00000 | −0.0834058 | ||||||||
\(576\) | 6.28284 | 0.261785 | ||||||||
\(577\) | −12.5384 | −0.521981 | −0.260990 | − | 0.965341i | \(-0.584049\pi\) | ||||
−0.260990 | + | 0.965341i | \(0.584049\pi\) | |||||||
\(578\) | −16.3428 | −0.679769 | ||||||||
\(579\) | −26.6345 | −1.10689 | ||||||||
\(580\) | −9.54782 | −0.396452 | ||||||||
\(581\) | 2.66819 | 0.110695 | ||||||||
\(582\) | −29.8535 | −1.23747 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 5.15008 | 0.213112 | ||||||||
\(585\) | −2.21820 | −0.0917113 | ||||||||
\(586\) | 6.46796 | 0.267189 | ||||||||
\(587\) | 43.5800 | 1.79874 | 0.899370 | − | 0.437189i | \(-0.144026\pi\) | ||||
0.899370 | + | 0.437189i | \(0.144026\pi\) | |||||||
\(588\) | 3.04678 | 0.125647 | ||||||||
\(589\) | 14.7986 | 0.609764 | ||||||||
\(590\) | −13.2092 | −0.543816 | ||||||||
\(591\) | −44.0467 | −1.81184 | ||||||||
\(592\) | 3.56360 | 0.146463 | ||||||||
\(593\) | −0.0535401 | −0.00219863 | −0.00109931 | − | 0.999999i | \(-0.500350\pi\) | ||||
−0.00109931 | + | 0.999999i | \(0.500350\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.810708 | −0.0332358 | ||||||||
\(596\) | 8.96980 | 0.367417 | ||||||||
\(597\) | −33.6504 | −1.37722 | ||||||||
\(598\) | −0.706114 | −0.0288751 | ||||||||
\(599\) | 28.9504 | 1.18288 | 0.591440 | − | 0.806349i | \(-0.298560\pi\) | ||||
0.591440 | + | 0.806349i | \(0.298560\pi\) | |||||||
\(600\) | 3.04678 | 0.124384 | ||||||||
\(601\) | −31.0406 | −1.26617 | −0.633085 | − | 0.774082i | \(-0.718212\pi\) | ||||
−0.633085 | + | 0.774082i | \(0.718212\pi\) | |||||||
\(602\) | 9.49338 | 0.386921 | ||||||||
\(603\) | −8.84306 | −0.360117 | ||||||||
\(604\) | 21.9731 | 0.894072 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.75538 | 0.111929 | ||||||||
\(607\) | −8.20288 | −0.332945 | −0.166472 | − | 0.986046i | \(-0.553238\pi\) | ||||
−0.166472 | + | 0.986046i | \(0.553238\pi\) | |||||||
\(608\) | −2.59251 | −0.105140 | ||||||||
\(609\) | 29.0901 | 1.17879 | ||||||||
\(610\) | −6.70611 | −0.271523 | ||||||||
\(611\) | −3.03902 | −0.122946 | ||||||||
\(612\) | 5.09355 | 0.205895 | ||||||||
\(613\) | 21.6035 | 0.872558 | 0.436279 | − | 0.899812i | \(-0.356296\pi\) | ||||
0.436279 | + | 0.899812i | \(0.356296\pi\) | |||||||
\(614\) | 20.6473 | 0.833257 | ||||||||
\(615\) | −25.1582 | −1.01448 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.5772 | 0.667372 | 0.333686 | − | 0.942684i | \(-0.391707\pi\) | ||||
0.333686 | + | 0.942684i | \(0.391707\pi\) | |||||||
\(618\) | 34.1857 | 1.37515 | ||||||||
\(619\) | −17.8133 | −0.715975 | −0.357988 | − | 0.933726i | \(-0.616537\pi\) | ||||
−0.357988 | + | 0.933726i | \(0.616537\pi\) | |||||||
\(620\) | 5.70820 | 0.229247 | ||||||||
\(621\) | −20.0042 | −0.802740 | ||||||||
\(622\) | 23.4385 | 0.939798 | ||||||||
\(623\) | 9.63799 | 0.386138 | ||||||||
\(624\) | 1.07569 | 0.0430619 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 11.9059 | 0.475855 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.0668308 | 0.00266684 | ||||||||
\(629\) | 2.88904 | 0.115193 | ||||||||
\(630\) | −6.28284 | −0.250314 | ||||||||
\(631\) | 13.5121 | 0.537908 | 0.268954 | − | 0.963153i | \(-0.413322\pi\) | ||||
0.268954 | + | 0.963153i | \(0.413322\pi\) | |||||||
\(632\) | 3.64694 | 0.145068 | ||||||||
\(633\) | −72.2397 | −2.87127 | ||||||||
\(634\) | −34.4185 | −1.36693 | ||||||||
\(635\) | 16.2382 | 0.644392 | ||||||||
\(636\) | −8.52995 | −0.338235 | ||||||||
\(637\) | 0.353057 | 0.0139886 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −81.1665 | −3.21090 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 44.3116 | 1.75020 | 0.875102 | − | 0.483939i | \(-0.160794\pi\) | ||||
0.875102 | + | 0.483939i | \(0.160794\pi\) | |||||||
\(642\) | −27.1046 | −1.06973 | ||||||||
\(643\) | 34.2852 | 1.35208 | 0.676039 | − | 0.736866i | \(-0.263695\pi\) | ||||
0.676039 | + | 0.736866i | \(0.263695\pi\) | |||||||
\(644\) | −2.00000 | −0.0788110 | ||||||||
\(645\) | −28.9242 | −1.13889 | ||||||||
\(646\) | −2.10177 | −0.0826929 | ||||||||
\(647\) | 27.8742 | 1.09585 | 0.547925 | − | 0.836528i | \(-0.315418\pi\) | ||||
0.547925 | + | 0.836528i | \(0.315418\pi\) | |||||||
\(648\) | 11.6256 | 0.456697 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0.353057 | 0.0138480 | ||||||||
\(651\) | −17.3916 | −0.681631 | ||||||||
\(652\) | 22.2692 | 0.872128 | ||||||||
\(653\) | −27.5831 | −1.07941 | −0.539705 | − | 0.841854i | \(-0.681464\pi\) | ||||
−0.539705 | + | 0.841854i | \(0.681464\pi\) | |||||||
\(654\) | −56.2932 | −2.20124 | ||||||||
\(655\) | −8.08882 | −0.316056 | ||||||||
\(656\) | 8.25732 | 0.322394 | ||||||||
\(657\) | 32.3571 | 1.26237 | ||||||||
\(658\) | −8.60773 | −0.335564 | ||||||||
\(659\) | −2.49969 | −0.0973742 | −0.0486871 | − | 0.998814i | \(-0.515504\pi\) | ||||
−0.0486871 | + | 0.998814i | \(0.515504\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.1499 | 0.394785 | 0.197393 | − | 0.980325i | \(-0.436753\pi\) | ||||
0.197393 | + | 0.980325i | \(0.436753\pi\) | |||||||
\(662\) | −11.6770 | −0.453841 | ||||||||
\(663\) | 0.872067 | 0.0338683 | ||||||||
\(664\) | 2.66819 | 0.103546 | ||||||||
\(665\) | 2.59251 | 0.100533 | ||||||||
\(666\) | 22.3895 | 0.867577 | ||||||||
\(667\) | −19.0956 | −0.739386 | ||||||||
\(668\) | 12.0000 | 0.464294 | ||||||||
\(669\) | −17.0311 | −0.658459 | ||||||||
\(670\) | 1.40749 | 0.0543762 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 3.04678 | 0.117532 | ||||||||
\(673\) | −36.9488 | −1.42427 | −0.712136 | − | 0.702042i | \(-0.752272\pi\) | ||||
−0.712136 | + | 0.702042i | \(0.752272\pi\) | |||||||
\(674\) | 10.3337 | 0.398041 | ||||||||
\(675\) | 10.0021 | 0.384981 | ||||||||
\(676\) | −12.8754 | −0.495206 | ||||||||
\(677\) | −8.83753 | −0.339654 | −0.169827 | − | 0.985474i | \(-0.554321\pi\) | ||||
−0.169827 | + | 0.985474i | \(0.554321\pi\) | |||||||
\(678\) | −38.6643 | −1.48489 | ||||||||
\(679\) | −9.79837 | −0.376027 | ||||||||
\(680\) | −0.810708 | −0.0310892 | ||||||||
\(681\) | 19.2619 | 0.738117 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.0803 | 1.26578 | 0.632892 | − | 0.774240i | \(-0.281868\pi\) | ||||
0.632892 | + | 0.774240i | \(0.281868\pi\) | |||||||
\(684\) | −16.2883 | −0.622799 | ||||||||
\(685\) | −10.4019 | −0.397437 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −11.8554 | −0.452311 | ||||||||
\(688\) | 9.49338 | 0.361932 | ||||||||
\(689\) | −0.988441 | −0.0376566 | ||||||||
\(690\) | 6.09355 | 0.231978 | ||||||||
\(691\) | −9.22130 | −0.350795 | −0.175397 | − | 0.984498i | \(-0.556121\pi\) | ||||
−0.175397 | + | 0.984498i | \(0.556121\pi\) | |||||||
\(692\) | −19.8698 | −0.755336 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.3202 | 0.695426 | ||||||||
\(695\) | 0.757168 | 0.0287210 | ||||||||
\(696\) | 29.0901 | 1.10266 | ||||||||
\(697\) | 6.69427 | 0.253564 | ||||||||
\(698\) | 29.9216 | 1.13255 | ||||||||
\(699\) | −46.2070 | −1.74771 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | −26.2969 | −0.993220 | −0.496610 | − | 0.867974i | \(-0.665422\pi\) | ||||
−0.496610 | + | 0.867974i | \(0.665422\pi\) | |||||||
\(702\) | 3.53131 | 0.133281 | ||||||||
\(703\) | −9.23865 | −0.348442 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 26.2258 | 0.987722 | ||||||||
\(706\) | −8.93024 | −0.336094 | ||||||||
\(707\) | 0.904358 | 0.0340119 | ||||||||
\(708\) | 40.2456 | 1.51252 | ||||||||
\(709\) | −34.6228 | −1.30029 | −0.650143 | − | 0.759812i | \(-0.725291\pi\) | ||||
−0.650143 | + | 0.759812i | \(0.725291\pi\) | |||||||
\(710\) | 12.9187 | 0.484832 | ||||||||
\(711\) | 22.9132 | 0.859311 | ||||||||
\(712\) | 9.63799 | 0.361199 | ||||||||
\(713\) | 11.4164 | 0.427548 | ||||||||
\(714\) | 2.47005 | 0.0924391 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.61246 | −0.321863 | ||||||||
\(717\) | 64.2714 | 2.40026 | ||||||||
\(718\) | 29.7915 | 1.11181 | ||||||||
\(719\) | −37.1839 | −1.38673 | −0.693363 | − | 0.720589i | \(-0.743872\pi\) | ||||
−0.693363 | + | 0.720589i | \(0.743872\pi\) | |||||||
\(720\) | −6.28284 | −0.234148 | ||||||||
\(721\) | 11.2203 | 0.417865 | ||||||||
\(722\) | −12.2789 | −0.456974 | ||||||||
\(723\) | 36.3835 | 1.35312 | ||||||||
\(724\) | 11.7345 | 0.436108 | ||||||||
\(725\) | 9.54782 | 0.354597 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.8666 | 0.625547 | 0.312773 | − | 0.949828i | \(-0.398742\pi\) | ||||
0.312773 | + | 0.949828i | \(0.398742\pi\) | |||||||
\(728\) | 0.353057 | 0.0130852 | ||||||||
\(729\) | −18.3806 | −0.680762 | ||||||||
\(730\) | −5.15008 | −0.190613 | ||||||||
\(731\) | 7.69636 | 0.284660 | ||||||||
\(732\) | 20.4320 | 0.755189 | ||||||||
\(733\) | −35.0947 | −1.29625 | −0.648126 | − | 0.761533i | \(-0.724447\pi\) | ||||
−0.648126 | + | 0.761533i | \(0.724447\pi\) | |||||||
\(734\) | −24.7535 | −0.913669 | ||||||||
\(735\) | −3.04678 | −0.112382 | ||||||||
\(736\) | −2.00000 | −0.0737210 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 51.8794 | 1.90971 | ||||||||
\(739\) | 8.98641 | 0.330570 | 0.165285 | − | 0.986246i | \(-0.447146\pi\) | ||||
0.165285 | + | 0.986246i | \(0.447146\pi\) | |||||||
\(740\) | −3.56360 | −0.131000 | ||||||||
\(741\) | −2.78872 | −0.102446 | ||||||||
\(742\) | −2.79967 | −0.102779 | ||||||||
\(743\) | 9.59663 | 0.352066 | 0.176033 | − | 0.984384i | \(-0.443673\pi\) | ||||
0.176033 | + | 0.984384i | \(0.443673\pi\) | |||||||
\(744\) | −17.3916 | −0.637608 | ||||||||
\(745\) | −8.96980 | −0.328628 | ||||||||
\(746\) | 9.75070 | 0.356999 | ||||||||
\(747\) | 16.7638 | 0.613357 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.89614 | −0.325058 | ||||||||
\(750\) | −3.04678 | −0.111253 | ||||||||
\(751\) | −14.1491 | −0.516309 | −0.258154 | − | 0.966104i | \(-0.583114\pi\) | ||||
−0.258154 | + | 0.966104i | \(0.583114\pi\) | |||||||
\(752\) | −8.60773 | −0.313892 | ||||||||
\(753\) | 6.45411 | 0.235201 | ||||||||
\(754\) | 3.37092 | 0.122762 | ||||||||
\(755\) | −21.9731 | −0.799682 | ||||||||
\(756\) | 10.0021 | 0.363773 | ||||||||
\(757\) | 45.6765 | 1.66014 | 0.830070 | − | 0.557660i | \(-0.188301\pi\) | ||||
0.830070 | + | 0.557660i | \(0.188301\pi\) | |||||||
\(758\) | 21.0454 | 0.764403 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.59251 | 0.0940401 | ||||||||
\(761\) | 16.5237 | 0.598985 | 0.299493 | − | 0.954099i | \(-0.403183\pi\) | ||||
0.299493 | + | 0.954099i | \(0.403183\pi\) | |||||||
\(762\) | −49.4740 | −1.79226 | ||||||||
\(763\) | −18.4763 | −0.668888 | ||||||||
\(764\) | −8.15063 | −0.294880 | ||||||||
\(765\) | −5.09355 | −0.184158 | ||||||||
\(766\) | −34.8828 | −1.26037 | ||||||||
\(767\) | 4.66362 | 0.168393 | ||||||||
\(768\) | 3.04678 | 0.109941 | ||||||||
\(769\) | −26.5929 | −0.958963 | −0.479482 | − | 0.877552i | \(-0.659175\pi\) | ||||
−0.479482 | + | 0.877552i | \(0.659175\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −63.1099 | −2.27285 | ||||||||
\(772\) | −8.74185 | −0.314626 | ||||||||
\(773\) | 35.4777 | 1.27604 | 0.638022 | − | 0.770019i | \(-0.279753\pi\) | ||||
0.638022 | + | 0.770019i | \(0.279753\pi\) | |||||||
\(774\) | 59.6455 | 2.14391 | ||||||||
\(775\) | −5.70820 | −0.205045 | ||||||||
\(776\) | −9.79837 | −0.351741 | ||||||||
\(777\) | 10.8575 | 0.389510 | ||||||||
\(778\) | −12.7069 | −0.455563 | ||||||||
\(779\) | −21.4072 | −0.766991 | ||||||||
\(780\) | −1.07569 | −0.0385157 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −1.62142 | −0.0579817 | ||||||||
\(783\) | 95.4982 | 3.41283 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −0.0668308 | −0.00238529 | ||||||||
\(786\) | 24.6448 | 0.879051 | ||||||||
\(787\) | 16.0990 | 0.573868 | 0.286934 | − | 0.957950i | \(-0.407364\pi\) | ||||
0.286934 | + | 0.957950i | \(0.407364\pi\) | |||||||
\(788\) | −14.4568 | −0.515003 | ||||||||
\(789\) | −11.8681 | −0.422517 | ||||||||
\(790\) | −3.64694 | −0.129752 | ||||||||
\(791\) | −12.6902 | −0.451213 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.36764 | 0.0840773 | ||||||||
\(794\) | 3.33036 | 0.118190 | ||||||||
\(795\) | 8.52995 | 0.302526 | ||||||||
\(796\) | −11.0446 | −0.391465 | ||||||||
\(797\) | 38.0457 | 1.34765 | 0.673825 | − | 0.738891i | \(-0.264650\pi\) | ||||
0.673825 | + | 0.738891i | \(0.264650\pi\) | |||||||
\(798\) | −7.89879 | −0.279614 | ||||||||
\(799\) | −6.97836 | −0.246876 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 60.5540 | 2.13957 | ||||||||
\(802\) | −9.27248 | −0.327423 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −4.28832 | −0.151237 | ||||||||
\(805\) | 2.00000 | 0.0704907 | ||||||||
\(806\) | −2.01532 | −0.0709866 | ||||||||
\(807\) | −69.6750 | −2.45268 | ||||||||
\(808\) | 0.904358 | 0.0318152 | ||||||||
\(809\) | −14.7984 | −0.520283 | −0.260142 | − | 0.965570i | \(-0.583769\pi\) | ||||
−0.260142 | + | 0.965570i | \(0.583769\pi\) | |||||||
\(810\) | −11.6256 | −0.408482 | ||||||||
\(811\) | 0.702276 | 0.0246602 | 0.0123301 | − | 0.999924i | \(-0.496075\pi\) | ||||
0.0123301 | + | 0.999924i | \(0.496075\pi\) | |||||||
\(812\) | 9.54782 | 0.335063 | ||||||||
\(813\) | −62.7885 | −2.20209 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.2692 | −0.780055 | ||||||||
\(816\) | 2.47005 | 0.0864689 | ||||||||
\(817\) | −24.6117 | −0.861053 | ||||||||
\(818\) | 0.349614 | 0.0122240 | ||||||||
\(819\) | 2.21820 | 0.0775102 | ||||||||
\(820\) | −8.25732 | −0.288358 | ||||||||
\(821\) | 1.50680 | 0.0525877 | 0.0262938 | − | 0.999654i | \(-0.491629\pi\) | ||||
0.0262938 | + | 0.999654i | \(0.491629\pi\) | |||||||
\(822\) | 31.6923 | 1.10540 | ||||||||
\(823\) | −30.8989 | −1.07707 | −0.538534 | − | 0.842604i | \(-0.681021\pi\) | ||||
−0.538534 | + | 0.842604i | \(0.681021\pi\) | |||||||
\(824\) | 11.2203 | 0.390877 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.2092 | 0.459609 | ||||||||
\(827\) | 52.7658 | 1.83485 | 0.917423 | − | 0.397914i | \(-0.130266\pi\) | ||||
0.917423 | + | 0.397914i | \(0.130266\pi\) | |||||||
\(828\) | −12.5657 | −0.436688 | ||||||||
\(829\) | −27.7575 | −0.964057 | −0.482028 | − | 0.876156i | \(-0.660100\pi\) | ||||
−0.482028 | + | 0.876156i | \(0.660100\pi\) | |||||||
\(830\) | −2.66819 | −0.0926143 | ||||||||
\(831\) | −52.4183 | −1.81837 | ||||||||
\(832\) | 0.353057 | 0.0122400 | ||||||||
\(833\) | 0.810708 | 0.0280894 | ||||||||
\(834\) | −2.30692 | −0.0798821 | ||||||||
\(835\) | −12.0000 | −0.415277 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −57.0940 | −1.97346 | ||||||||
\(838\) | 27.9340 | 0.964963 | ||||||||
\(839\) | −48.0237 | −1.65796 | −0.828981 | − | 0.559277i | \(-0.811079\pi\) | ||||
−0.828981 | + | 0.559277i | \(0.811079\pi\) | |||||||
\(840\) | −3.04678 | −0.105124 | ||||||||
\(841\) | 62.1609 | 2.14348 | ||||||||
\(842\) | 8.07221 | 0.278187 | ||||||||
\(843\) | −92.7573 | −3.19473 | ||||||||
\(844\) | −23.7102 | −0.816139 | ||||||||
\(845\) | 12.8754 | 0.442926 | ||||||||
\(846\) | −54.0810 | −1.85934 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.79967 | −0.0961409 | ||||||||
\(849\) | −30.4530 | −1.04515 | ||||||||
\(850\) | 0.810708 | 0.0278071 | ||||||||
\(851\) | −7.12720 | −0.244317 | ||||||||
\(852\) | −39.3605 | −1.34847 | ||||||||
\(853\) | −36.0186 | −1.23325 | −0.616626 | − | 0.787256i | \(-0.711501\pi\) | ||||
−0.616626 | + | 0.787256i | \(0.711501\pi\) | |||||||
\(854\) | 6.70611 | 0.229478 | ||||||||
\(855\) | 16.2883 | 0.557049 | ||||||||
\(856\) | −8.89614 | −0.304064 | ||||||||
\(857\) | 5.73142 | 0.195782 | 0.0978908 | − | 0.995197i | \(-0.468790\pi\) | ||||
0.0978908 | + | 0.995197i | \(0.468790\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.4569 | 1.14153 | 0.570767 | − | 0.821112i | \(-0.306646\pi\) | ||||
0.570767 | + | 0.821112i | \(0.306646\pi\) | |||||||
\(860\) | −9.49338 | −0.323722 | ||||||||
\(861\) | 25.1582 | 0.857389 | ||||||||
\(862\) | −20.0088 | −0.681503 | ||||||||
\(863\) | 10.8522 | 0.369413 | 0.184707 | − | 0.982794i | \(-0.440867\pi\) | ||||
0.184707 | + | 0.982794i | \(0.440867\pi\) | |||||||
\(864\) | 10.0021 | 0.340278 | ||||||||
\(865\) | 19.8698 | 0.675593 | ||||||||
\(866\) | −38.7447 | −1.31660 | ||||||||
\(867\) | −49.7927 | −1.69105 | ||||||||
\(868\) | −5.70820 | −0.193749 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −29.0901 | −0.986246 | ||||||||
\(871\) | −0.496925 | −0.0168377 | ||||||||
\(872\) | −18.4763 | −0.625687 | ||||||||
\(873\) | −61.5617 | −2.08355 | ||||||||
\(874\) | 5.18501 | 0.175386 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 15.6911 | 0.530154 | ||||||||
\(877\) | −21.1287 | −0.713465 | −0.356732 | − | 0.934207i | \(-0.616109\pi\) | ||||
−0.356732 | + | 0.934207i | \(0.616109\pi\) | |||||||
\(878\) | −5.62560 | −0.189855 | ||||||||
\(879\) | 19.7064 | 0.664681 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.5805 | 0.828137 | 0.414069 | − | 0.910246i | \(-0.364107\pi\) | ||||
0.414069 | + | 0.910246i | \(0.364107\pi\) | |||||||
\(882\) | 6.28284 | 0.211554 | ||||||||
\(883\) | −15.4728 | −0.520700 | −0.260350 | − | 0.965514i | \(-0.583838\pi\) | ||||
−0.260350 | + | 0.965514i | \(0.583838\pi\) | |||||||
\(884\) | 0.286226 | 0.00962682 | ||||||||
\(885\) | −40.2456 | −1.35284 | ||||||||
\(886\) | −15.6763 | −0.526656 | ||||||||
\(887\) | −20.4358 | −0.686165 | −0.343083 | − | 0.939305i | \(-0.611471\pi\) | ||||
−0.343083 | + | 0.939305i | \(0.611471\pi\) | |||||||
\(888\) | 10.8575 | 0.364353 | ||||||||
\(889\) | −16.2382 | −0.544610 | ||||||||
\(890\) | −9.63799 | −0.323066 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.58986 | −0.187162 | ||||||||
\(893\) | 22.3156 | 0.746763 | ||||||||
\(894\) | 27.3290 | 0.914017 | ||||||||
\(895\) | 8.61246 | 0.287883 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −2.15137 | −0.0718322 | ||||||||
\(898\) | −26.1032 | −0.871075 | ||||||||
\(899\) | −54.5009 | −1.81771 | ||||||||
\(900\) | 6.28284 | 0.209428 | ||||||||
\(901\) | −2.26971 | −0.0756151 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 28.9242 | 0.962538 | ||||||||
\(904\) | −12.6902 | −0.422071 | ||||||||
\(905\) | −11.7345 | −0.390067 | ||||||||
\(906\) | 66.9471 | 2.22417 | ||||||||
\(907\) | 30.9777 | 1.02860 | 0.514298 | − | 0.857611i | \(-0.328052\pi\) | ||||
0.514298 | + | 0.857611i | \(0.328052\pi\) | |||||||
\(908\) | 6.32206 | 0.209805 | ||||||||
\(909\) | 5.68194 | 0.188458 | ||||||||
\(910\) | −0.353057 | −0.0117037 | ||||||||
\(911\) | −29.0687 | −0.963090 | −0.481545 | − | 0.876421i | \(-0.659924\pi\) | ||||
−0.481545 | + | 0.876421i | \(0.659924\pi\) | |||||||
\(912\) | −7.89879 | −0.261555 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 35.5911 | 1.17725 | ||||||||
\(915\) | −20.4320 | −0.675462 | ||||||||
\(916\) | −3.89113 | −0.128566 | ||||||||
\(917\) | 8.08882 | 0.267116 | ||||||||
\(918\) | 8.10877 | 0.267629 | ||||||||
\(919\) | −38.2375 | −1.26134 | −0.630669 | − | 0.776052i | \(-0.717220\pi\) | ||||
−0.630669 | + | 0.776052i | \(0.717220\pi\) | |||||||
\(920\) | 2.00000 | 0.0659380 | ||||||||
\(921\) | 62.9077 | 2.07288 | ||||||||
\(922\) | 9.66571 | 0.318323 | ||||||||
\(923\) | −4.56105 | −0.150129 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.56360 | 0.117170 | ||||||||
\(926\) | −29.9726 | −0.984962 | ||||||||
\(927\) | 70.4953 | 2.31537 | ||||||||
\(928\) | 9.54782 | 0.313423 | ||||||||
\(929\) | 38.7575 | 1.27159 | 0.635797 | − | 0.771857i | \(-0.280672\pi\) | ||||
0.635797 | + | 0.771857i | \(0.280672\pi\) | |||||||
\(930\) | 17.3916 | 0.570294 | ||||||||
\(931\) | −2.59251 | −0.0849660 | ||||||||
\(932\) | −15.1659 | −0.496774 | ||||||||
\(933\) | 71.4118 | 2.33792 | ||||||||
\(934\) | 30.5086 | 0.998272 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.21820 | 0.0725042 | ||||||||
\(937\) | −10.4997 | −0.343010 | −0.171505 | − | 0.985183i | \(-0.554863\pi\) | ||||
−0.171505 | + | 0.985183i | \(0.554863\pi\) | |||||||
\(938\) | −1.40749 | −0.0459563 | ||||||||
\(939\) | 36.2746 | 1.18378 | ||||||||
\(940\) | 8.60773 | 0.280753 | ||||||||
\(941\) | 10.1957 | 0.332369 | 0.166185 | − | 0.986095i | \(-0.446855\pi\) | ||||
0.166185 | + | 0.986095i | \(0.446855\pi\) | |||||||
\(942\) | 0.203619 | 0.00663425 | ||||||||
\(943\) | −16.5146 | −0.537790 | ||||||||
\(944\) | 13.2092 | 0.429924 | ||||||||
\(945\) | −10.0021 | −0.325368 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −47.2023 | −1.53387 | −0.766934 | − | 0.641726i | \(-0.778219\pi\) | ||||
−0.766934 | + | 0.641726i | \(0.778219\pi\) | |||||||
\(948\) | 11.1114 | 0.360882 | ||||||||
\(949\) | 1.81827 | 0.0590236 | ||||||||
\(950\) | −2.59251 | −0.0841120 | ||||||||
\(951\) | −104.865 | −3.40050 | ||||||||
\(952\) | 0.810708 | 0.0262752 | ||||||||
\(953\) | −5.18794 | −0.168054 | −0.0840269 | − | 0.996463i | \(-0.526778\pi\) | ||||
−0.0840269 | + | 0.996463i | \(0.526778\pi\) | |||||||
\(954\) | −17.5899 | −0.569493 | ||||||||
\(955\) | 8.15063 | 0.263748 | ||||||||
\(956\) | 21.0949 | 0.682258 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 38.7127 | 1.25075 | ||||||||
\(959\) | 10.4019 | 0.335896 | ||||||||
\(960\) | −3.04678 | −0.0983343 | ||||||||
\(961\) | 1.58359 | 0.0510836 | ||||||||
\(962\) | 1.25815 | 0.0405645 | ||||||||
\(963\) | −55.8931 | −1.80113 | ||||||||
\(964\) | 11.9416 | 0.384614 | ||||||||
\(965\) | 8.74185 | 0.281410 | ||||||||
\(966\) | −6.09355 | −0.196057 | ||||||||
\(967\) | −18.9841 | −0.610486 | −0.305243 | − | 0.952274i | \(-0.598738\pi\) | ||||
−0.305243 | + | 0.952274i | \(0.598738\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.40361 | −0.205714 | ||||||||
\(970\) | 9.79837 | 0.314607 | ||||||||
\(971\) | −41.9080 | −1.34489 | −0.672447 | − | 0.740146i | \(-0.734757\pi\) | ||||
−0.672447 | + | 0.740146i | \(0.734757\pi\) | |||||||
\(972\) | 5.41432 | 0.173664 | ||||||||
\(973\) | −0.757168 | −0.0242737 | ||||||||
\(974\) | 33.8375 | 1.08422 | ||||||||
\(975\) | 1.07569 | 0.0344495 | ||||||||
\(976\) | 6.70611 | 0.214657 | ||||||||
\(977\) | 8.12073 | 0.259805 | 0.129903 | − | 0.991527i | \(-0.458534\pi\) | ||||
0.129903 | + | 0.991527i | \(0.458534\pi\) | |||||||
\(978\) | 67.8491 | 2.16958 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −116.084 | −3.70627 | ||||||||
\(982\) | 18.5755 | 0.592768 | ||||||||
\(983\) | −38.8143 | −1.23799 | −0.618993 | − | 0.785397i | \(-0.712459\pi\) | ||||
−0.618993 | + | 0.785397i | \(0.712459\pi\) | |||||||
\(984\) | 25.1582 | 0.802014 | ||||||||
\(985\) | 14.4568 | 0.460632 | ||||||||
\(986\) | 7.74050 | 0.246508 | ||||||||
\(987\) | −26.2258 | −0.834777 | ||||||||
\(988\) | −0.915302 | −0.0291196 | ||||||||
\(989\) | −18.9868 | −0.603744 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.30139 | 0.0413400 | 0.0206700 | − | 0.999786i | \(-0.493420\pi\) | ||||
0.0206700 | + | 0.999786i | \(0.493420\pi\) | |||||||
\(992\) | −5.70820 | −0.181236 | ||||||||
\(993\) | −35.5773 | −1.12901 | ||||||||
\(994\) | −12.9187 | −0.409758 | ||||||||
\(995\) | 11.0446 | 0.350137 | ||||||||
\(996\) | 8.12938 | 0.257589 | ||||||||
\(997\) | −14.8018 | −0.468777 | −0.234389 | − | 0.972143i | \(-0.575309\pi\) | ||||
−0.234389 | + | 0.972143i | \(0.575309\pi\) | |||||||
\(998\) | −14.7069 | −0.465539 | ||||||||
\(999\) | 35.6434 | 1.12771 |
(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 | 8470.2.a.ct.1.4 | 4 | ||
11.2 | odd | 10 | 770.2.n.e.631.2 | yes | 8 | ||
11.6 | odd | 10 | 770.2.n.e.421.2 | ✓ | 8 | ||
11.10 | odd | 2 | 8470.2.a.cq.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.e.421.2 | ✓ | 8 | 11.6 | odd | 10 | ||
770.2.n.e.631.2 | yes | 8 | 11.2 | odd | 10 | ||
8470.2.a.cq.1.4 | 4 | 11.10 | odd | 2 | |||
8470.2.a.ct.1.4 | 4 | 1.1 | even | 1 | trivial |