Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1925,2,Mod(1,1925)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1925, 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("1925.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1925 = 5^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1925.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: | \(15.3712023891\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.9921856.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 7x^{4} + 11x^{2} - 2x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 385) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.226645\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1925.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.226645 | −0.160262 | −0.0801310 | − | 0.996784i | \(-0.525534\pi\) | ||||
−0.0801310 | + | 0.996784i | \(0.525534\pi\) | |||||||
\(3\) | 1.89494 | 1.09404 | 0.547021 | − | 0.837119i | \(-0.315762\pi\) | ||||
0.547021 | + | 0.837119i | \(0.315762\pi\) | |||||||
\(4\) | −1.94863 | −0.974316 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.429477 | −0.175333 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0.894936 | 0.316408 | ||||||||
\(9\) | 0.590784 | 0.196928 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −3.69253 | −1.06594 | ||||||||
\(13\) | −2.71469 | −0.752920 | −0.376460 | − | 0.926433i | \(-0.622859\pi\) | ||||
−0.376460 | + | 0.926433i | \(0.622859\pi\) | |||||||
\(14\) | 0.226645 | 0.0605733 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.69443 | 0.923608 | ||||||||
\(17\) | 6.92945 | 1.68064 | 0.840319 | − | 0.542092i | \(-0.182367\pi\) | ||||
0.840319 | + | 0.542092i | \(0.182367\pi\) | |||||||
\(18\) | −0.133898 | −0.0315601 | ||||||||
\(19\) | 6.38464 | 1.46474 | 0.732368 | − | 0.680909i | \(-0.238415\pi\) | ||||
0.732368 | + | 0.680909i | \(0.238415\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.89494 | −0.413509 | ||||||||
\(22\) | 0.226645 | 0.0483208 | ||||||||
\(23\) | −2.82331 | −0.588700 | −0.294350 | − | 0.955698i | \(-0.595103\pi\) | ||||
−0.294350 | + | 0.955698i | \(0.595103\pi\) | |||||||
\(24\) | 1.69585 | 0.346163 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.615271 | 0.120664 | ||||||||
\(27\) | −4.56531 | −0.878595 | ||||||||
\(28\) | 1.94863 | 0.368257 | ||||||||
\(29\) | 4.88997 | 0.908045 | 0.454022 | − | 0.890990i | \(-0.349989\pi\) | ||||
0.454022 | + | 0.890990i | \(0.349989\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.04479 | −1.26528 | −0.632640 | − | 0.774446i | \(-0.718029\pi\) | ||||
−0.632640 | + | 0.774446i | \(0.718029\pi\) | |||||||
\(32\) | −2.62720 | −0.464427 | ||||||||
\(33\) | −1.89494 | −0.329866 | ||||||||
\(34\) | −1.57052 | −0.269342 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.15122 | −0.191870 | ||||||||
\(37\) | −1.27517 | −0.209637 | −0.104819 | − | 0.994491i | \(-0.533426\pi\) | ||||
−0.104819 | + | 0.994491i | \(0.533426\pi\) | |||||||
\(38\) | −1.44704 | −0.234742 | ||||||||
\(39\) | −5.14417 | −0.823726 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.34306 | 0.834446 | 0.417223 | − | 0.908804i | \(-0.363003\pi\) | ||||
0.417223 | + | 0.908804i | \(0.363003\pi\) | |||||||
\(42\) | 0.429477 | 0.0662698 | ||||||||
\(43\) | 9.92780 | 1.51397 | 0.756987 | − | 0.653429i | \(-0.226670\pi\) | ||||
0.756987 | + | 0.653429i | \(0.226670\pi\) | |||||||
\(44\) | 1.94863 | 0.293767 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.639888 | 0.0943463 | ||||||||
\(47\) | 7.64491 | 1.11512 | 0.557562 | − | 0.830135i | \(-0.311737\pi\) | ||||
0.557562 | + | 0.830135i | \(0.311737\pi\) | |||||||
\(48\) | 7.00071 | 1.01047 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13.1309 | 1.83869 | ||||||||
\(52\) | 5.28994 | 0.733582 | ||||||||
\(53\) | 2.16500 | 0.297386 | 0.148693 | − | 0.988883i | \(-0.452493\pi\) | ||||
0.148693 | + | 0.988883i | \(0.452493\pi\) | |||||||
\(54\) | 1.03470 | 0.140805 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.894936 | −0.119591 | ||||||||
\(57\) | 12.0985 | 1.60248 | ||||||||
\(58\) | −1.10829 | −0.145525 | ||||||||
\(59\) | 12.0226 | 1.56521 | 0.782606 | − | 0.622517i | \(-0.213890\pi\) | ||||
0.782606 | + | 0.622517i | \(0.213890\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.513231 | −0.0657124 | −0.0328562 | − | 0.999460i | \(-0.510460\pi\) | ||||
−0.0328562 | + | 0.999460i | \(0.510460\pi\) | |||||||
\(62\) | 1.59666 | 0.202776 | ||||||||
\(63\) | −0.590784 | −0.0744317 | ||||||||
\(64\) | −6.79342 | −0.849178 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.429477 | 0.0528650 | ||||||||
\(67\) | 13.7761 | 1.68302 | 0.841509 | − | 0.540244i | \(-0.181668\pi\) | ||||
0.841509 | + | 0.540244i | \(0.181668\pi\) | |||||||
\(68\) | −13.5030 | −1.63747 | ||||||||
\(69\) | −5.34999 | −0.644063 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.96893 | 1.06442 | 0.532208 | − | 0.846614i | \(-0.321362\pi\) | ||||
0.532208 | + | 0.846614i | \(0.321362\pi\) | |||||||
\(72\) | 0.528714 | 0.0623095 | ||||||||
\(73\) | 6.93424 | 0.811592 | 0.405796 | − | 0.913964i | \(-0.366994\pi\) | ||||
0.405796 | + | 0.913964i | \(0.366994\pi\) | |||||||
\(74\) | 0.289011 | 0.0335969 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −12.4413 | −1.42712 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 1.16590 | 0.132012 | ||||||||
\(79\) | −10.8414 | −1.21975 | −0.609875 | − | 0.792497i | \(-0.708780\pi\) | ||||
−0.609875 | + | 0.792497i | \(0.708780\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.4233 | −1.15815 | ||||||||
\(82\) | −1.21098 | −0.133730 | ||||||||
\(83\) | −9.07907 | −0.996557 | −0.498279 | − | 0.867017i | \(-0.666034\pi\) | ||||
−0.498279 | + | 0.867017i | \(0.666034\pi\) | |||||||
\(84\) | 3.69253 | 0.402888 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.25008 | −0.242633 | ||||||||
\(87\) | 9.26618 | 0.993439 | ||||||||
\(88\) | −0.894936 | −0.0954005 | ||||||||
\(89\) | −5.69209 | −0.603360 | −0.301680 | − | 0.953409i | \(-0.597547\pi\) | ||||
−0.301680 | + | 0.953409i | \(0.597547\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.71469 | 0.284577 | ||||||||
\(92\) | 5.50159 | 0.573580 | ||||||||
\(93\) | −13.3494 | −1.38427 | ||||||||
\(94\) | −1.73268 | −0.178712 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.97837 | −0.508103 | ||||||||
\(97\) | 6.05204 | 0.614492 | 0.307246 | − | 0.951630i | \(-0.400593\pi\) | ||||
0.307246 | + | 0.951630i | \(0.400593\pi\) | |||||||
\(98\) | −0.226645 | −0.0228946 | ||||||||
\(99\) | −0.590784 | −0.0593760 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.71518 | −0.867192 | −0.433596 | − | 0.901107i | \(-0.642756\pi\) | ||||
−0.433596 | + | 0.901107i | \(0.642756\pi\) | |||||||
\(102\) | −2.97604 | −0.294672 | ||||||||
\(103\) | 19.7813 | 1.94911 | 0.974553 | − | 0.224156i | \(-0.0719625\pi\) | ||||
0.974553 | + | 0.224156i | \(0.0719625\pi\) | |||||||
\(104\) | −2.42948 | −0.238230 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.490687 | −0.0476597 | ||||||||
\(107\) | 10.0523 | 0.971791 | 0.485895 | − | 0.874017i | \(-0.338494\pi\) | ||||
0.485895 | + | 0.874017i | \(0.338494\pi\) | |||||||
\(108\) | 8.89611 | 0.856029 | ||||||||
\(109\) | 2.52611 | 0.241958 | 0.120979 | − | 0.992655i | \(-0.461397\pi\) | ||||
0.120979 | + | 0.992655i | \(0.461397\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.41637 | −0.229352 | ||||||||
\(112\) | −3.69443 | −0.349091 | ||||||||
\(113\) | 3.09105 | 0.290781 | 0.145391 | − | 0.989374i | \(-0.453556\pi\) | ||||
0.145391 | + | 0.989374i | \(0.453556\pi\) | |||||||
\(114\) | −2.74206 | −0.256817 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.52875 | −0.884722 | ||||||||
\(117\) | −1.60380 | −0.148271 | ||||||||
\(118\) | −2.72486 | −0.250844 | ||||||||
\(119\) | −6.92945 | −0.635222 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0.116321 | 0.0105312 | ||||||||
\(123\) | 10.1248 | 0.912919 | ||||||||
\(124\) | 13.7277 | 1.23278 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.133898 | 0.0119286 | ||||||||
\(127\) | −13.1184 | −1.16407 | −0.582035 | − | 0.813164i | \(-0.697743\pi\) | ||||
−0.582035 | + | 0.813164i | \(0.697743\pi\) | |||||||
\(128\) | 6.79408 | 0.600518 | ||||||||
\(129\) | 18.8125 | 1.65635 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.919423 | 0.0803304 | 0.0401652 | − | 0.999193i | \(-0.487212\pi\) | ||||
0.0401652 | + | 0.999193i | \(0.487212\pi\) | |||||||
\(132\) | 3.69253 | 0.321394 | ||||||||
\(133\) | −6.38464 | −0.553618 | ||||||||
\(134\) | −3.12228 | −0.269724 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.20142 | 0.531767 | ||||||||
\(137\) | 13.1365 | 1.12233 | 0.561164 | − | 0.827704i | \(-0.310354\pi\) | ||||
0.561164 | + | 0.827704i | \(0.310354\pi\) | |||||||
\(138\) | 1.21255 | 0.103219 | ||||||||
\(139\) | −19.8836 | −1.68651 | −0.843254 | − | 0.537515i | \(-0.819363\pi\) | ||||
−0.843254 | + | 0.537515i | \(0.819363\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14.4866 | 1.21999 | ||||||||
\(142\) | −2.03276 | −0.170585 | ||||||||
\(143\) | 2.71469 | 0.227014 | ||||||||
\(144\) | 2.18261 | 0.181884 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.57161 | −0.130067 | ||||||||
\(147\) | 1.89494 | 0.156292 | ||||||||
\(148\) | 2.48485 | 0.204253 | ||||||||
\(149\) | −7.23587 | −0.592785 | −0.296393 | − | 0.955066i | \(-0.595784\pi\) | ||||
−0.296393 | + | 0.955066i | \(0.595784\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.43840 | −0.605329 | −0.302664 | − | 0.953097i | \(-0.597876\pi\) | ||||
−0.302664 | + | 0.953097i | \(0.597876\pi\) | |||||||
\(152\) | 5.71384 | 0.463454 | ||||||||
\(153\) | 4.09381 | 0.330965 | ||||||||
\(154\) | −0.226645 | −0.0182635 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 10.0241 | 0.802570 | ||||||||
\(157\) | −14.8104 | −1.18200 | −0.590999 | − | 0.806672i | \(-0.701266\pi\) | ||||
−0.590999 | + | 0.806672i | \(0.701266\pi\) | |||||||
\(158\) | 2.45714 | 0.195480 | ||||||||
\(159\) | 4.10255 | 0.325353 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.82331 | 0.222508 | ||||||||
\(162\) | 2.36239 | 0.185607 | ||||||||
\(163\) | 12.0213 | 0.941585 | 0.470792 | − | 0.882244i | \(-0.343968\pi\) | ||||
0.470792 | + | 0.882244i | \(0.343968\pi\) | |||||||
\(164\) | −10.4117 | −0.813014 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.05772 | 0.159710 | ||||||||
\(167\) | 2.24124 | 0.173432 | 0.0867162 | − | 0.996233i | \(-0.472363\pi\) | ||||
0.0867162 | + | 0.996233i | \(0.472363\pi\) | |||||||
\(168\) | −1.69585 | −0.130837 | ||||||||
\(169\) | −5.63044 | −0.433111 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.77194 | 0.288447 | ||||||||
\(172\) | −19.3456 | −1.47509 | ||||||||
\(173\) | −5.43476 | −0.413197 | −0.206598 | − | 0.978426i | \(-0.566239\pi\) | ||||
−0.206598 | + | 0.978426i | \(0.566239\pi\) | |||||||
\(174\) | −2.10013 | −0.159210 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.69443 | −0.278478 | ||||||||
\(177\) | 22.7821 | 1.71241 | ||||||||
\(178\) | 1.29008 | 0.0966957 | ||||||||
\(179\) | 8.92059 | 0.666756 | 0.333378 | − | 0.942793i | \(-0.391811\pi\) | ||||
0.333378 | + | 0.942793i | \(0.391811\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.84320 | −0.434322 | −0.217161 | − | 0.976136i | \(-0.569680\pi\) | ||||
−0.217161 | + | 0.976136i | \(0.569680\pi\) | |||||||
\(182\) | −0.615271 | −0.0456069 | ||||||||
\(183\) | −0.972539 | −0.0718922 | ||||||||
\(184\) | −2.52668 | −0.186269 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.02557 | 0.221846 | ||||||||
\(187\) | −6.92945 | −0.506732 | ||||||||
\(188\) | −14.8971 | −1.08648 | ||||||||
\(189\) | 4.56531 | 0.332078 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.5949 | 1.27312 | 0.636560 | − | 0.771227i | \(-0.280357\pi\) | ||||
0.636560 | + | 0.771227i | \(0.280357\pi\) | |||||||
\(192\) | −12.8731 | −0.929036 | ||||||||
\(193\) | 8.04491 | 0.579085 | 0.289543 | − | 0.957165i | \(-0.406497\pi\) | ||||
0.289543 | + | 0.957165i | \(0.406497\pi\) | |||||||
\(194\) | −1.37166 | −0.0984797 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.94863 | −0.139188 | ||||||||
\(197\) | 11.0440 | 0.786856 | 0.393428 | − | 0.919356i | \(-0.371289\pi\) | ||||
0.393428 | + | 0.919356i | \(0.371289\pi\) | |||||||
\(198\) | 0.133898 | 0.00951571 | ||||||||
\(199\) | 7.87899 | 0.558527 | 0.279264 | − | 0.960215i | \(-0.409910\pi\) | ||||
0.279264 | + | 0.960215i | \(0.409910\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 26.1048 | 1.84129 | ||||||||
\(202\) | 1.97525 | 0.138978 | ||||||||
\(203\) | −4.88997 | −0.343209 | ||||||||
\(204\) | −25.5872 | −1.79146 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.48332 | −0.312368 | ||||||||
\(207\) | −1.66796 | −0.115932 | ||||||||
\(208\) | −10.0292 | −0.695403 | ||||||||
\(209\) | −6.38464 | −0.441635 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.0258 | −1.44748 | −0.723738 | − | 0.690074i | \(-0.757578\pi\) | ||||
−0.723738 | + | 0.690074i | \(0.757578\pi\) | |||||||
\(212\) | −4.21880 | −0.289748 | ||||||||
\(213\) | 16.9956 | 1.16452 | ||||||||
\(214\) | −2.27830 | −0.155741 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.08566 | −0.277994 | ||||||||
\(217\) | 7.04479 | 0.478231 | ||||||||
\(218\) | −0.572530 | −0.0387766 | ||||||||
\(219\) | 13.1399 | 0.887915 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.8113 | −1.26539 | ||||||||
\(222\) | 0.547658 | 0.0367564 | ||||||||
\(223\) | −3.27301 | −0.219177 | −0.109588 | − | 0.993977i | \(-0.534953\pi\) | ||||
−0.109588 | + | 0.993977i | \(0.534953\pi\) | |||||||
\(224\) | 2.62720 | 0.175537 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.700570 | −0.0466012 | ||||||||
\(227\) | −22.3224 | −1.48159 | −0.740794 | − | 0.671732i | \(-0.765551\pi\) | ||||
−0.740794 | + | 0.671732i | \(0.765551\pi\) | |||||||
\(228\) | −23.5755 | −1.56133 | ||||||||
\(229\) | −2.14092 | −0.141476 | −0.0707378 | − | 0.997495i | \(-0.522535\pi\) | ||||
−0.0707378 | + | 0.997495i | \(0.522535\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.89494 | 0.124678 | ||||||||
\(232\) | 4.37621 | 0.287312 | ||||||||
\(233\) | 10.3046 | 0.675075 | 0.337538 | − | 0.941312i | \(-0.390406\pi\) | ||||
0.337538 | + | 0.941312i | \(0.390406\pi\) | |||||||
\(234\) | 0.363492 | 0.0237622 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −23.4277 | −1.52501 | ||||||||
\(237\) | −20.5437 | −1.33446 | ||||||||
\(238\) | 1.57052 | 0.101802 | ||||||||
\(239\) | −10.4572 | −0.676422 | −0.338211 | − | 0.941070i | \(-0.609822\pi\) | ||||
−0.338211 | + | 0.941070i | \(0.609822\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.4618 | 1.51131 | 0.755653 | − | 0.654973i | \(-0.227320\pi\) | ||||
0.755653 | + | 0.654973i | \(0.227320\pi\) | |||||||
\(242\) | −0.226645 | −0.0145693 | ||||||||
\(243\) | −6.05560 | −0.388467 | ||||||||
\(244\) | 1.00010 | 0.0640247 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.29472 | −0.146306 | ||||||||
\(247\) | −17.3323 | −1.10283 | ||||||||
\(248\) | −6.30464 | −0.400345 | ||||||||
\(249\) | −17.2043 | −1.09028 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.37954 | −0.465793 | −0.232896 | − | 0.972502i | \(-0.574820\pi\) | ||||
−0.232896 | + | 0.972502i | \(0.574820\pi\) | |||||||
\(252\) | 1.15122 | 0.0725201 | ||||||||
\(253\) | 2.82331 | 0.177500 | ||||||||
\(254\) | 2.97322 | 0.186556 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.0470 | 0.752938 | ||||||||
\(257\) | −29.3675 | −1.83189 | −0.915947 | − | 0.401300i | \(-0.868559\pi\) | ||||
−0.915947 | + | 0.401300i | \(0.868559\pi\) | |||||||
\(258\) | −4.26376 | −0.265450 | ||||||||
\(259\) | 1.27517 | 0.0792355 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.88891 | 0.178819 | ||||||||
\(262\) | −0.208382 | −0.0128739 | ||||||||
\(263\) | 15.2412 | 0.939814 | 0.469907 | − | 0.882716i | \(-0.344287\pi\) | ||||
0.469907 | + | 0.882716i | \(0.344287\pi\) | |||||||
\(264\) | −1.69585 | −0.104372 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.44704 | 0.0887240 | ||||||||
\(267\) | −10.7861 | −0.660102 | ||||||||
\(268\) | −26.8445 | −1.63979 | ||||||||
\(269\) | 26.2583 | 1.60099 | 0.800497 | − | 0.599336i | \(-0.204569\pi\) | ||||
0.800497 | + | 0.599336i | \(0.204569\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.5816 | −0.885771 | −0.442886 | − | 0.896578i | \(-0.646045\pi\) | ||||
−0.442886 | + | 0.896578i | \(0.646045\pi\) | |||||||
\(272\) | 25.6004 | 1.55225 | ||||||||
\(273\) | 5.14417 | 0.311339 | ||||||||
\(274\) | −2.97732 | −0.179867 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 10.4252 | 0.627521 | ||||||||
\(277\) | 7.25963 | 0.436189 | 0.218095 | − | 0.975928i | \(-0.430016\pi\) | ||||
0.218095 | + | 0.975928i | \(0.430016\pi\) | |||||||
\(278\) | 4.50652 | 0.270283 | ||||||||
\(279\) | −4.16194 | −0.249169 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.68302 | −0.577640 | −0.288820 | − | 0.957383i | \(-0.593263\pi\) | ||||
−0.288820 | + | 0.957383i | \(0.593263\pi\) | |||||||
\(282\) | −3.28331 | −0.195519 | ||||||||
\(283\) | 3.97480 | 0.236277 | 0.118139 | − | 0.992997i | \(-0.462307\pi\) | ||||
0.118139 | + | 0.992997i | \(0.462307\pi\) | |||||||
\(284\) | −17.4771 | −1.03708 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.615271 | −0.0363817 | ||||||||
\(287\) | −5.34306 | −0.315391 | ||||||||
\(288\) | −1.55210 | −0.0914586 | ||||||||
\(289\) | 31.0173 | 1.82455 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.4682 | 0.672280 | ||||||||
\(292\) | −13.5123 | −0.790747 | ||||||||
\(293\) | −18.9865 | −1.10920 | −0.554602 | − | 0.832116i | \(-0.687130\pi\) | ||||
−0.554602 | + | 0.832116i | \(0.687130\pi\) | |||||||
\(294\) | −0.429477 | −0.0250476 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.14120 | −0.0663309 | ||||||||
\(297\) | 4.56531 | 0.264906 | ||||||||
\(298\) | 1.63997 | 0.0950009 | ||||||||
\(299\) | 7.66441 | 0.443244 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.92780 | −0.572229 | ||||||||
\(302\) | 1.68587 | 0.0970112 | ||||||||
\(303\) | −16.5147 | −0.948745 | ||||||||
\(304\) | 23.5876 | 1.35284 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.927839 | −0.0530410 | ||||||||
\(307\) | 2.29041 | 0.130721 | 0.0653604 | − | 0.997862i | \(-0.479180\pi\) | ||||
0.0653604 | + | 0.997862i | \(0.479180\pi\) | |||||||
\(308\) | −1.94863 | −0.111034 | ||||||||
\(309\) | 37.4843 | 2.13240 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.70629 | −0.210165 | −0.105082 | − | 0.994464i | \(-0.533511\pi\) | ||||
−0.105082 | + | 0.994464i | \(0.533511\pi\) | |||||||
\(312\) | −4.60370 | −0.260633 | ||||||||
\(313\) | −10.4251 | −0.589263 | −0.294631 | − | 0.955611i | \(-0.595197\pi\) | ||||
−0.294631 | + | 0.955611i | \(0.595197\pi\) | |||||||
\(314\) | 3.35670 | 0.189429 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 21.1259 | 1.18842 | ||||||||
\(317\) | −8.16477 | −0.458579 | −0.229289 | − | 0.973358i | \(-0.573640\pi\) | ||||
−0.229289 | + | 0.973358i | \(0.573640\pi\) | |||||||
\(318\) | −0.929820 | −0.0521417 | ||||||||
\(319\) | −4.88997 | −0.273786 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.0484 | 1.06318 | ||||||||
\(322\) | −0.639888 | −0.0356595 | ||||||||
\(323\) | 44.2420 | 2.46169 | ||||||||
\(324\) | 20.3112 | 1.12840 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.72457 | −0.150900 | ||||||||
\(327\) | 4.78682 | 0.264712 | ||||||||
\(328\) | 4.78170 | 0.264025 | ||||||||
\(329\) | −7.64491 | −0.421478 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.2519 | 0.618459 | 0.309230 | − | 0.950987i | \(-0.399929\pi\) | ||||
0.309230 | + | 0.950987i | \(0.399929\pi\) | |||||||
\(332\) | 17.6918 | 0.970962 | ||||||||
\(333\) | −0.753352 | −0.0412834 | ||||||||
\(334\) | −0.507965 | −0.0277946 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −7.00071 | −0.381920 | ||||||||
\(337\) | −23.5677 | −1.28381 | −0.641907 | − | 0.766782i | \(-0.721857\pi\) | ||||
−0.641907 | + | 0.766782i | \(0.721857\pi\) | |||||||
\(338\) | 1.27611 | 0.0694112 | ||||||||
\(339\) | 5.85734 | 0.318127 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.04479 | 0.381497 | ||||||||
\(342\) | −0.854890 | −0.0462272 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 8.88475 | 0.479033 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.23176 | 0.0662197 | ||||||||
\(347\) | 26.8229 | 1.43993 | 0.719965 | − | 0.694011i | \(-0.244158\pi\) | ||||
0.719965 | + | 0.694011i | \(0.244158\pi\) | |||||||
\(348\) | −18.0564 | −0.967924 | ||||||||
\(349\) | 20.5516 | 1.10010 | 0.550052 | − | 0.835131i | \(-0.314608\pi\) | ||||
0.550052 | + | 0.835131i | \(0.314608\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.3934 | 0.661512 | ||||||||
\(352\) | 2.62720 | 0.140030 | ||||||||
\(353\) | −34.1433 | −1.81726 | −0.908631 | − | 0.417599i | \(-0.862872\pi\) | ||||
−0.908631 | + | 0.417599i | \(0.862872\pi\) | |||||||
\(354\) | −5.16344 | −0.274434 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 11.0918 | 0.587864 | ||||||||
\(357\) | −13.1309 | −0.694959 | ||||||||
\(358\) | −2.02180 | −0.106856 | ||||||||
\(359\) | −21.2017 | −1.11898 | −0.559491 | − | 0.828836i | \(-0.689003\pi\) | ||||
−0.559491 | + | 0.828836i | \(0.689003\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.7636 | 1.14545 | ||||||||
\(362\) | 1.32433 | 0.0696053 | ||||||||
\(363\) | 1.89494 | 0.0994584 | ||||||||
\(364\) | −5.28994 | −0.277268 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.220421 | 0.0115216 | ||||||||
\(367\) | 32.1138 | 1.67633 | 0.838163 | − | 0.545421i | \(-0.183630\pi\) | ||||
0.838163 | + | 0.545421i | \(0.183630\pi\) | |||||||
\(368\) | −10.4305 | −0.543728 | ||||||||
\(369\) | 3.15659 | 0.164326 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.16500 | −0.112401 | ||||||||
\(372\) | 26.0131 | 1.34872 | ||||||||
\(373\) | 10.5291 | 0.545177 | 0.272589 | − | 0.962131i | \(-0.412120\pi\) | ||||
0.272589 | + | 0.962131i | \(0.412120\pi\) | |||||||
\(374\) | 1.57052 | 0.0812098 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.84171 | 0.352834 | ||||||||
\(377\) | −13.2748 | −0.683685 | ||||||||
\(378\) | −1.03470 | −0.0532194 | ||||||||
\(379\) | −25.1566 | −1.29221 | −0.646105 | − | 0.763249i | \(-0.723603\pi\) | ||||
−0.646105 | + | 0.763249i | \(0.723603\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −24.8585 | −1.27354 | ||||||||
\(382\) | −3.98778 | −0.204033 | ||||||||
\(383\) | −20.8031 | −1.06299 | −0.531494 | − | 0.847062i | \(-0.678369\pi\) | ||||
−0.531494 | + | 0.847062i | \(0.678369\pi\) | |||||||
\(384\) | 12.8744 | 0.656992 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.82334 | −0.0928053 | ||||||||
\(387\) | 5.86518 | 0.298144 | ||||||||
\(388\) | −11.7932 | −0.598709 | ||||||||
\(389\) | 4.17853 | 0.211860 | 0.105930 | − | 0.994374i | \(-0.466218\pi\) | ||||
0.105930 | + | 0.994374i | \(0.466218\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.5640 | −0.989393 | ||||||||
\(392\) | 0.894936 | 0.0452011 | ||||||||
\(393\) | 1.74225 | 0.0878848 | ||||||||
\(394\) | −2.50307 | −0.126103 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.15122 | 0.0578510 | ||||||||
\(397\) | 20.1701 | 1.01231 | 0.506155 | − | 0.862442i | \(-0.331066\pi\) | ||||
0.506155 | + | 0.862442i | \(0.331066\pi\) | |||||||
\(398\) | −1.78573 | −0.0895106 | ||||||||
\(399\) | −12.0985 | −0.605682 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.05971 | −0.452421 | −0.226210 | − | 0.974078i | \(-0.572634\pi\) | ||||
−0.226210 | + | 0.974078i | \(0.572634\pi\) | |||||||
\(402\) | −5.91652 | −0.295089 | ||||||||
\(403\) | 19.1244 | 0.952656 | ||||||||
\(404\) | 16.9827 | 0.844919 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.10829 | 0.0550033 | ||||||||
\(407\) | 1.27517 | 0.0632080 | ||||||||
\(408\) | 11.7513 | 0.581776 | ||||||||
\(409\) | 5.19698 | 0.256974 | 0.128487 | − | 0.991711i | \(-0.458988\pi\) | ||||
0.128487 | + | 0.991711i | \(0.458988\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.8929 | 1.22787 | ||||||||
\(412\) | −38.5464 | −1.89905 | ||||||||
\(413\) | −12.0226 | −0.591595 | ||||||||
\(414\) | 0.378035 | 0.0185794 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 7.13203 | 0.349677 | ||||||||
\(417\) | −37.6782 | −1.84511 | ||||||||
\(418\) | 1.44704 | 0.0707772 | ||||||||
\(419\) | −34.0187 | −1.66192 | −0.830962 | − | 0.556329i | \(-0.812210\pi\) | ||||
−0.830962 | + | 0.556329i | \(0.812210\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.3577 | −1.67449 | −0.837245 | − | 0.546828i | \(-0.815835\pi\) | ||||
−0.837245 | + | 0.546828i | \(0.815835\pi\) | |||||||
\(422\) | 4.76539 | 0.231975 | ||||||||
\(423\) | 4.51649 | 0.219599 | ||||||||
\(424\) | 1.93754 | 0.0940953 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.85195 | −0.186628 | ||||||||
\(427\) | 0.513231 | 0.0248370 | ||||||||
\(428\) | −19.5882 | −0.946831 | ||||||||
\(429\) | 5.14417 | 0.248363 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.5131 | −1.22892 | −0.614462 | − | 0.788947i | \(-0.710627\pi\) | ||||
−0.614462 | + | 0.788947i | \(0.710627\pi\) | |||||||
\(432\) | −16.8662 | −0.811477 | ||||||||
\(433\) | −1.07504 | −0.0516629 | −0.0258315 | − | 0.999666i | \(-0.508223\pi\) | ||||
−0.0258315 | + | 0.999666i | \(0.508223\pi\) | |||||||
\(434\) | −1.59666 | −0.0766423 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.92247 | −0.235743 | ||||||||
\(437\) | −18.0258 | −0.862291 | ||||||||
\(438\) | −2.97810 | −0.142299 | ||||||||
\(439\) | −11.6914 | −0.558002 | −0.279001 | − | 0.960291i | \(-0.590003\pi\) | ||||
−0.279001 | + | 0.960291i | \(0.590003\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.590784 | 0.0281326 | ||||||||
\(442\) | 4.26349 | 0.202793 | ||||||||
\(443\) | 6.92747 | 0.329134 | 0.164567 | − | 0.986366i | \(-0.447377\pi\) | ||||
0.164567 | + | 0.986366i | \(0.447377\pi\) | |||||||
\(444\) | 4.70862 | 0.223461 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.741809 | 0.0351257 | ||||||||
\(447\) | −13.7115 | −0.648532 | ||||||||
\(448\) | 6.79342 | 0.320959 | ||||||||
\(449\) | −6.65819 | −0.314220 | −0.157110 | − | 0.987581i | \(-0.550218\pi\) | ||||
−0.157110 | + | 0.987581i | \(0.550218\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.34306 | −0.251595 | ||||||||
\(452\) | −6.02332 | −0.283313 | ||||||||
\(453\) | −14.0953 | −0.662255 | ||||||||
\(454\) | 5.05925 | 0.237442 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10.8274 | 0.507038 | ||||||||
\(457\) | 9.78442 | 0.457696 | 0.228848 | − | 0.973462i | \(-0.426504\pi\) | ||||
0.228848 | + | 0.973462i | \(0.426504\pi\) | |||||||
\(458\) | 0.485227 | 0.0226732 | ||||||||
\(459\) | −31.6351 | −1.47660 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.87760 | −0.460046 | −0.230023 | − | 0.973185i | \(-0.573880\pi\) | ||||
−0.230023 | + | 0.973185i | \(0.573880\pi\) | |||||||
\(462\) | −0.429477 | −0.0199811 | ||||||||
\(463\) | 14.5142 | 0.674531 | 0.337266 | − | 0.941410i | \(-0.390498\pi\) | ||||
0.337266 | + | 0.941410i | \(0.390498\pi\) | |||||||
\(464\) | 18.0657 | 0.838677 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.33548 | −0.108189 | ||||||||
\(467\) | −24.3690 | −1.12766 | −0.563832 | − | 0.825889i | \(-0.690674\pi\) | ||||
−0.563832 | + | 0.825889i | \(0.690674\pi\) | |||||||
\(468\) | 3.12521 | 0.144463 | ||||||||
\(469\) | −13.7761 | −0.636121 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −28.0647 | −1.29316 | ||||||||
\(472\) | 10.7595 | 0.495245 | ||||||||
\(473\) | −9.92780 | −0.456481 | ||||||||
\(474\) | 4.65612 | 0.213863 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 13.5030 | 0.618907 | ||||||||
\(477\) | 1.27905 | 0.0585637 | ||||||||
\(478\) | 2.37007 | 0.108405 | ||||||||
\(479\) | −6.49628 | −0.296823 | −0.148411 | − | 0.988926i | \(-0.547416\pi\) | ||||
−0.148411 | + | 0.988926i | \(0.547416\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.46171 | 0.157840 | ||||||||
\(482\) | −5.31748 | −0.242205 | ||||||||
\(483\) | 5.34999 | 0.243433 | ||||||||
\(484\) | −1.94863 | −0.0885742 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.37247 | 0.0622565 | ||||||||
\(487\) | 30.2243 | 1.36960 | 0.684798 | − | 0.728733i | \(-0.259891\pi\) | ||||
0.684798 | + | 0.728733i | \(0.259891\pi\) | |||||||
\(488\) | −0.459309 | −0.0207919 | ||||||||
\(489\) | 22.7797 | 1.03013 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.3260 | −0.691653 | −0.345826 | − | 0.938298i | \(-0.612401\pi\) | ||||
−0.345826 | + | 0.938298i | \(0.612401\pi\) | |||||||
\(492\) | −19.7294 | −0.889471 | ||||||||
\(493\) | 33.8848 | 1.52609 | ||||||||
\(494\) | 3.92828 | 0.176742 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −26.0265 | −1.16862 | ||||||||
\(497\) | −8.96893 | −0.402312 | ||||||||
\(498\) | 3.89925 | 0.174730 | ||||||||
\(499\) | 23.5020 | 1.05209 | 0.526046 | − | 0.850456i | \(-0.323674\pi\) | ||||
0.526046 | + | 0.850456i | \(0.323674\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.24701 | 0.189742 | ||||||||
\(502\) | 1.67253 | 0.0746488 | ||||||||
\(503\) | 36.5297 | 1.62878 | 0.814390 | − | 0.580318i | \(-0.197072\pi\) | ||||
0.814390 | + | 0.580318i | \(0.197072\pi\) | |||||||
\(504\) | −0.528714 | −0.0235508 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.639888 | −0.0284465 | ||||||||
\(507\) | −10.6693 | −0.473842 | ||||||||
\(508\) | 25.5629 | 1.13417 | ||||||||
\(509\) | −9.57002 | −0.424184 | −0.212092 | − | 0.977250i | \(-0.568028\pi\) | ||||
−0.212092 | + | 0.977250i | \(0.568028\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.93424 | −0.306753 | ||||||||
\(512\) | −16.3186 | −0.721185 | ||||||||
\(513\) | −29.1479 | −1.28691 | ||||||||
\(514\) | 6.65598 | 0.293583 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −36.6587 | −1.61381 | ||||||||
\(517\) | −7.64491 | −0.336223 | ||||||||
\(518\) | −0.289011 | −0.0126984 | ||||||||
\(519\) | −10.2985 | −0.452055 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.6884 | 0.774943 | 0.387471 | − | 0.921882i | \(-0.373349\pi\) | ||||
0.387471 | + | 0.921882i | \(0.373349\pi\) | |||||||
\(522\) | −0.654757 | −0.0286579 | ||||||||
\(523\) | 37.8115 | 1.65338 | 0.826691 | − | 0.562656i | \(-0.190220\pi\) | ||||
0.826691 | + | 0.562656i | \(0.190220\pi\) | |||||||
\(524\) | −1.79162 | −0.0782672 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.45434 | −0.150616 | ||||||||
\(527\) | −48.8165 | −2.12648 | ||||||||
\(528\) | −7.00071 | −0.304667 | ||||||||
\(529\) | −15.0289 | −0.653432 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.10277 | 0.308234 | ||||||||
\(532\) | 12.4413 | 0.539399 | ||||||||
\(533\) | −14.5048 | −0.628271 | ||||||||
\(534\) | 2.44462 | 0.105789 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12.3287 | 0.532520 | ||||||||
\(537\) | 16.9039 | 0.729459 | ||||||||
\(538\) | −5.95129 | −0.256579 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.25551 | −0.182959 | −0.0914794 | − | 0.995807i | \(-0.529160\pi\) | ||||
−0.0914794 | + | 0.995807i | \(0.529160\pi\) | |||||||
\(542\) | 3.30485 | 0.141955 | ||||||||
\(543\) | −11.0725 | −0.475166 | ||||||||
\(544\) | −18.2050 | −0.780534 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.16590 | −0.0498959 | ||||||||
\(547\) | 0.773105 | 0.0330556 | 0.0165278 | − | 0.999863i | \(-0.494739\pi\) | ||||
0.0165278 | + | 0.999863i | \(0.494739\pi\) | |||||||
\(548\) | −25.5982 | −1.09350 | ||||||||
\(549\) | −0.303208 | −0.0129406 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 31.2207 | 1.33005 | ||||||||
\(552\) | −4.78790 | −0.203787 | ||||||||
\(553\) | 10.8414 | 0.461022 | ||||||||
\(554\) | −1.64536 | −0.0699045 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 38.7459 | 1.64319 | ||||||||
\(557\) | −24.5625 | −1.04074 | −0.520372 | − | 0.853940i | \(-0.674207\pi\) | ||||
−0.520372 | + | 0.853940i | \(0.674207\pi\) | |||||||
\(558\) | 0.943282 | 0.0399323 | ||||||||
\(559\) | −26.9509 | −1.13990 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.1309 | −0.554386 | ||||||||
\(562\) | 2.19460 | 0.0925738 | ||||||||
\(563\) | −3.70616 | −0.156196 | −0.0780981 | − | 0.996946i | \(-0.524885\pi\) | ||||
−0.0780981 | + | 0.996946i | \(0.524885\pi\) | |||||||
\(564\) | −28.2291 | −1.18866 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.900867 | −0.0378663 | ||||||||
\(567\) | 10.4233 | 0.437739 | ||||||||
\(568\) | 8.02662 | 0.336790 | ||||||||
\(569\) | 14.2498 | 0.597381 | 0.298691 | − | 0.954350i | \(-0.403450\pi\) | ||||
0.298691 | + | 0.954350i | \(0.403450\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.31485 | 0.347966 | 0.173983 | − | 0.984749i | \(-0.444336\pi\) | ||||
0.173983 | + | 0.984749i | \(0.444336\pi\) | |||||||
\(572\) | −5.28994 | −0.221183 | ||||||||
\(573\) | 33.3412 | 1.39285 | ||||||||
\(574\) | 1.21098 | 0.0505452 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.01344 | −0.167227 | ||||||||
\(577\) | 9.01917 | 0.375473 | 0.187736 | − | 0.982219i | \(-0.439885\pi\) | ||||
0.187736 | + | 0.982219i | \(0.439885\pi\) | |||||||
\(578\) | −7.02990 | −0.292405 | ||||||||
\(579\) | 15.2446 | 0.633543 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.07907 | 0.376663 | ||||||||
\(582\) | −2.59921 | −0.107741 | ||||||||
\(583\) | −2.16500 | −0.0896653 | ||||||||
\(584\) | 6.20571 | 0.256794 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.30319 | 0.177763 | ||||||||
\(587\) | 5.17843 | 0.213737 | 0.106868 | − | 0.994273i | \(-0.465918\pi\) | ||||
0.106868 | + | 0.994273i | \(0.465918\pi\) | |||||||
\(588\) | −3.69253 | −0.152278 | ||||||||
\(589\) | −44.9784 | −1.85330 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.9278 | 0.860853 | ||||||||
\(592\) | −4.71104 | −0.193623 | ||||||||
\(593\) | 17.3248 | 0.711443 | 0.355722 | − | 0.934592i | \(-0.384235\pi\) | ||||
0.355722 | + | 0.934592i | \(0.384235\pi\) | |||||||
\(594\) | −1.03470 | −0.0424544 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14.1000 | 0.577560 | ||||||||
\(597\) | 14.9302 | 0.611052 | ||||||||
\(598\) | −1.73710 | −0.0710352 | ||||||||
\(599\) | 24.7227 | 1.01014 | 0.505070 | − | 0.863078i | \(-0.331467\pi\) | ||||
0.505070 | + | 0.863078i | \(0.331467\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 46.3237 | 1.88958 | 0.944792 | − | 0.327670i | \(-0.106263\pi\) | ||||
0.944792 | + | 0.327670i | \(0.106263\pi\) | |||||||
\(602\) | 2.25008 | 0.0917065 | ||||||||
\(603\) | 8.13869 | 0.331433 | ||||||||
\(604\) | 14.4947 | 0.589782 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.74297 | 0.152048 | ||||||||
\(607\) | 32.6404 | 1.32483 | 0.662416 | − | 0.749136i | \(-0.269531\pi\) | ||||
0.662416 | + | 0.749136i | \(0.269531\pi\) | |||||||
\(608\) | −16.7737 | −0.680263 | ||||||||
\(609\) | −9.26618 | −0.375485 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.7536 | −0.839600 | ||||||||
\(612\) | −7.97732 | −0.322464 | ||||||||
\(613\) | −17.5678 | −0.709555 | −0.354778 | − | 0.934951i | \(-0.615443\pi\) | ||||
−0.354778 | + | 0.934951i | \(0.615443\pi\) | |||||||
\(614\) | −0.519110 | −0.0209496 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.894936 | 0.0360580 | ||||||||
\(617\) | −41.9900 | −1.69045 | −0.845226 | − | 0.534409i | \(-0.820534\pi\) | ||||
−0.845226 | + | 0.534409i | \(0.820534\pi\) | |||||||
\(618\) | −8.49560 | −0.341743 | ||||||||
\(619\) | 9.54044 | 0.383463 | 0.191731 | − | 0.981447i | \(-0.438590\pi\) | ||||
0.191731 | + | 0.981447i | \(0.438590\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.8893 | 0.517229 | ||||||||
\(622\) | 0.840011 | 0.0336814 | ||||||||
\(623\) | 5.69209 | 0.228049 | ||||||||
\(624\) | −19.0048 | −0.760800 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.36280 | 0.0944364 | ||||||||
\(627\) | −12.0985 | −0.483167 | ||||||||
\(628\) | 28.8600 | 1.15164 | ||||||||
\(629\) | −8.83626 | −0.352325 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.9289 | −1.19145 | −0.595726 | − | 0.803188i | \(-0.703135\pi\) | ||||
−0.595726 | + | 0.803188i | \(0.703135\pi\) | |||||||
\(632\) | −9.70234 | −0.385939 | ||||||||
\(633\) | −39.8426 | −1.58360 | ||||||||
\(634\) | 1.85050 | 0.0734928 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7.99435 | −0.316997 | ||||||||
\(637\) | −2.71469 | −0.107560 | ||||||||
\(638\) | 1.10829 | 0.0438774 | ||||||||
\(639\) | 5.29870 | 0.209613 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.4319 | −1.16249 | −0.581246 | − | 0.813728i | \(-0.697434\pi\) | ||||
−0.581246 | + | 0.813728i | \(0.697434\pi\) | |||||||
\(642\) | −4.31722 | −0.170387 | ||||||||
\(643\) | −13.3683 | −0.527196 | −0.263598 | − | 0.964633i | \(-0.584909\pi\) | ||||
−0.263598 | + | 0.964633i | \(0.584909\pi\) | |||||||
\(644\) | −5.50159 | −0.216793 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.0272 | −0.394516 | ||||||||
\(647\) | 39.5103 | 1.55331 | 0.776655 | − | 0.629926i | \(-0.216915\pi\) | ||||
0.776655 | + | 0.629926i | \(0.216915\pi\) | |||||||
\(648\) | −9.32821 | −0.366447 | ||||||||
\(649\) | −12.0226 | −0.471929 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.3494 | 0.523205 | ||||||||
\(652\) | −23.4252 | −0.917401 | ||||||||
\(653\) | 12.4194 | 0.486009 | 0.243004 | − | 0.970025i | \(-0.421867\pi\) | ||||
0.243004 | + | 0.970025i | \(0.421867\pi\) | |||||||
\(654\) | −1.08491 | −0.0424233 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 19.7396 | 0.770701 | ||||||||
\(657\) | 4.09664 | 0.159825 | ||||||||
\(658\) | 1.73268 | 0.0675468 | ||||||||
\(659\) | −22.6922 | −0.883962 | −0.441981 | − | 0.897024i | \(-0.645724\pi\) | ||||
−0.441981 | + | 0.897024i | \(0.645724\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.980639 | 0.0381424 | 0.0190712 | − | 0.999818i | \(-0.493929\pi\) | ||||
0.0190712 | + | 0.999818i | \(0.493929\pi\) | |||||||
\(662\) | −2.55018 | −0.0991155 | ||||||||
\(663\) | −35.6463 | −1.38439 | ||||||||
\(664\) | −8.12519 | −0.315318 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.170743 | 0.00661617 | ||||||||
\(667\) | −13.8059 | −0.534566 | ||||||||
\(668\) | −4.36736 | −0.168978 | ||||||||
\(669\) | −6.20214 | −0.239789 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.513231 | 0.0198130 | ||||||||
\(672\) | 4.97837 | 0.192045 | ||||||||
\(673\) | −14.7455 | −0.568397 | −0.284199 | − | 0.958765i | \(-0.591728\pi\) | ||||
−0.284199 | + | 0.958765i | \(0.591728\pi\) | |||||||
\(674\) | 5.34149 | 0.205747 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.9717 | 0.421987 | ||||||||
\(677\) | 9.42359 | 0.362178 | 0.181089 | − | 0.983467i | \(-0.442038\pi\) | ||||
0.181089 | + | 0.983467i | \(0.442038\pi\) | |||||||
\(678\) | −1.32753 | −0.0509837 | ||||||||
\(679\) | −6.05204 | −0.232256 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −42.2995 | −1.62092 | ||||||||
\(682\) | −1.59666 | −0.0611394 | ||||||||
\(683\) | 8.86005 | 0.339020 | 0.169510 | − | 0.985528i | \(-0.445781\pi\) | ||||
0.169510 | + | 0.985528i | \(0.445781\pi\) | |||||||
\(684\) | −7.35012 | −0.281039 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.226645 | 0.00865333 | ||||||||
\(687\) | −4.05690 | −0.154780 | ||||||||
\(688\) | 36.6776 | 1.39832 | ||||||||
\(689\) | −5.87732 | −0.223908 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.69667 | −0.292795 | −0.146398 | − | 0.989226i | \(-0.546768\pi\) | ||||
−0.146398 | + | 0.989226i | \(0.546768\pi\) | |||||||
\(692\) | 10.5903 | 0.402584 | ||||||||
\(693\) | 0.590784 | 0.0224420 | ||||||||
\(694\) | −6.07927 | −0.230766 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.29264 | 0.314332 | ||||||||
\(697\) | 37.0245 | 1.40240 | ||||||||
\(698\) | −4.65792 | −0.176305 | ||||||||
\(699\) | 19.5265 | 0.738561 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.21711 | −0.310356 | −0.155178 | − | 0.987887i | \(-0.549595\pi\) | ||||
−0.155178 | + | 0.987887i | \(0.549595\pi\) | |||||||
\(702\) | −2.80890 | −0.106015 | ||||||||
\(703\) | −8.14153 | −0.307063 | ||||||||
\(704\) | 6.79342 | 0.256037 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.73839 | 0.291238 | ||||||||
\(707\) | 8.71518 | 0.327768 | ||||||||
\(708\) | −44.3940 | −1.66843 | ||||||||
\(709\) | −8.20752 | −0.308240 | −0.154120 | − | 0.988052i | \(-0.549254\pi\) | ||||
−0.154120 | + | 0.988052i | \(0.549254\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.40491 | −0.240203 | ||||||||
\(712\) | −5.09406 | −0.190908 | ||||||||
\(713\) | 19.8896 | 0.744871 | ||||||||
\(714\) | 2.97604 | 0.111376 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −17.3829 | −0.649631 | ||||||||
\(717\) | −19.8158 | −0.740034 | ||||||||
\(718\) | 4.80525 | 0.179330 | ||||||||
\(719\) | 2.38303 | 0.0888720 | 0.0444360 | − | 0.999012i | \(-0.485851\pi\) | ||||
0.0444360 | + | 0.999012i | \(0.485851\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.7813 | −0.736693 | ||||||||
\(722\) | −4.93260 | −0.183572 | ||||||||
\(723\) | 44.4585 | 1.65343 | ||||||||
\(724\) | 11.3863 | 0.423167 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.429477 | −0.0159394 | ||||||||
\(727\) | 24.8734 | 0.922504 | 0.461252 | − | 0.887269i | \(-0.347400\pi\) | ||||
0.461252 | + | 0.887269i | \(0.347400\pi\) | |||||||
\(728\) | 2.42948 | 0.0900424 | ||||||||
\(729\) | 19.7950 | 0.733148 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 68.7942 | 2.54444 | ||||||||
\(732\) | 1.89512 | 0.0700457 | ||||||||
\(733\) | 3.23427 | 0.119461 | 0.0597303 | − | 0.998215i | \(-0.480976\pi\) | ||||
0.0597303 | + | 0.998215i | \(0.480976\pi\) | |||||||
\(734\) | −7.27841 | −0.268651 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.41738 | 0.273408 | ||||||||
\(737\) | −13.7761 | −0.507449 | ||||||||
\(738\) | −0.715425 | −0.0263351 | ||||||||
\(739\) | 2.59092 | 0.0953084 | 0.0476542 | − | 0.998864i | \(-0.484825\pi\) | ||||
0.0476542 | + | 0.998864i | \(0.484825\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −32.8437 | −1.20654 | ||||||||
\(742\) | 0.490687 | 0.0180137 | ||||||||
\(743\) | −35.2841 | −1.29445 | −0.647225 | − | 0.762299i | \(-0.724070\pi\) | ||||
−0.647225 | + | 0.762299i | \(0.724070\pi\) | |||||||
\(744\) | −11.9469 | −0.437994 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.38637 | −0.0873712 | ||||||||
\(747\) | −5.36377 | −0.196250 | ||||||||
\(748\) | 13.5030 | 0.493717 | ||||||||
\(749\) | −10.0523 | −0.367302 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.09221 | −0.258798 | −0.129399 | − | 0.991593i | \(-0.541305\pi\) | ||||
−0.129399 | + | 0.991593i | \(0.541305\pi\) | |||||||
\(752\) | 28.2436 | 1.02994 | ||||||||
\(753\) | −13.9838 | −0.509597 | ||||||||
\(754\) | 3.00865 | 0.109569 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8.89611 | −0.323549 | ||||||||
\(757\) | 35.6937 | 1.29731 | 0.648654 | − | 0.761083i | \(-0.275332\pi\) | ||||
0.648654 | + | 0.761083i | \(0.275332\pi\) | |||||||
\(758\) | 5.70162 | 0.207092 | ||||||||
\(759\) | 5.34999 | 0.194192 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.8388 | −1.22666 | −0.613328 | − | 0.789828i | \(-0.710170\pi\) | ||||
−0.613328 | + | 0.789828i | \(0.710170\pi\) | |||||||
\(762\) | 5.63406 | 0.204100 | ||||||||
\(763\) | −2.52611 | −0.0914515 | ||||||||
\(764\) | −34.2859 | −1.24042 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.71491 | 0.170356 | ||||||||
\(767\) | −32.6377 | −1.17848 | ||||||||
\(768\) | 22.8283 | 0.823746 | ||||||||
\(769\) | 33.1746 | 1.19631 | 0.598153 | − | 0.801382i | \(-0.295902\pi\) | ||||
0.598153 | + | 0.801382i | \(0.295902\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −55.6495 | −2.00417 | ||||||||
\(772\) | −15.6766 | −0.564212 | ||||||||
\(773\) | 38.6688 | 1.39082 | 0.695411 | − | 0.718613i | \(-0.255223\pi\) | ||||
0.695411 | + | 0.718613i | \(0.255223\pi\) | |||||||
\(774\) | −1.32931 | −0.0477811 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.41619 | 0.194430 | ||||||||
\(777\) | 2.41637 | 0.0866869 | ||||||||
\(778\) | −0.947041 | −0.0339531 | ||||||||
\(779\) | 34.1135 | 1.22224 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.96893 | −0.320934 | ||||||||
\(782\) | 4.43407 | 0.158562 | ||||||||
\(783\) | −22.3242 | −0.797803 | ||||||||
\(784\) | 3.69443 | 0.131944 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.394871 | −0.0140846 | ||||||||
\(787\) | −35.4748 | −1.26454 | −0.632269 | − | 0.774749i | \(-0.717876\pi\) | ||||
−0.632269 | + | 0.774749i | \(0.717876\pi\) | |||||||
\(788\) | −21.5208 | −0.766646 | ||||||||
\(789\) | 28.8812 | 1.02820 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.09105 | −0.109905 | ||||||||
\(792\) | −0.528714 | −0.0187870 | ||||||||
\(793\) | 1.39326 | 0.0494762 | ||||||||
\(794\) | −4.57146 | −0.162235 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −15.3533 | −0.544182 | ||||||||
\(797\) | −10.5336 | −0.373120 | −0.186560 | − | 0.982444i | \(-0.559734\pi\) | ||||
−0.186560 | + | 0.982444i | \(0.559734\pi\) | |||||||
\(798\) | 2.74206 | 0.0970677 | ||||||||
\(799\) | 52.9750 | 1.87412 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.36279 | −0.118818 | ||||||||
\(802\) | 2.05334 | 0.0725058 | ||||||||
\(803\) | −6.93424 | −0.244704 | ||||||||
\(804\) | −50.8687 | −1.79400 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.33445 | −0.152674 | ||||||||
\(807\) | 49.7577 | 1.75156 | ||||||||
\(808\) | −7.79953 | −0.274386 | ||||||||
\(809\) | −51.6743 | −1.81677 | −0.908385 | − | 0.418135i | \(-0.862684\pi\) | ||||
−0.908385 | + | 0.418135i | \(0.862684\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.1386 | 0.707161 | 0.353581 | − | 0.935404i | \(-0.384964\pi\) | ||||
0.353581 | + | 0.935404i | \(0.384964\pi\) | |||||||
\(812\) | 9.52875 | 0.334394 | ||||||||
\(813\) | −27.6313 | −0.969071 | ||||||||
\(814\) | −0.289011 | −0.0101298 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 48.5111 | 1.69823 | ||||||||
\(817\) | 63.3854 | 2.21757 | ||||||||
\(818\) | −1.17787 | −0.0411832 | ||||||||
\(819\) | 1.60380 | 0.0560412 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.72653 | −0.130057 | −0.0650284 | − | 0.997883i | \(-0.520714\pi\) | ||||
−0.0650284 | + | 0.997883i | \(0.520714\pi\) | |||||||
\(822\) | −5.64184 | −0.196782 | ||||||||
\(823\) | −45.3334 | −1.58022 | −0.790111 | − | 0.612964i | \(-0.789977\pi\) | ||||
−0.790111 | + | 0.612964i | \(0.789977\pi\) | |||||||
\(824\) | 17.7030 | 0.616712 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.72486 | 0.0948101 | ||||||||
\(827\) | 23.2710 | 0.809214 | 0.404607 | − | 0.914491i | \(-0.367408\pi\) | ||||
0.404607 | + | 0.914491i | \(0.367408\pi\) | |||||||
\(828\) | 3.25025 | 0.112954 | ||||||||
\(829\) | 49.0037 | 1.70197 | 0.850985 | − | 0.525190i | \(-0.176006\pi\) | ||||
0.850985 | + | 0.525190i | \(0.176006\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.7565 | 0.477209 | ||||||||
\(832\) | 18.4421 | 0.639363 | ||||||||
\(833\) | 6.92945 | 0.240091 | ||||||||
\(834\) | 8.53957 | 0.295701 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.4413 | 0.430292 | ||||||||
\(837\) | 32.1616 | 1.11167 | ||||||||
\(838\) | 7.71017 | 0.266343 | ||||||||
\(839\) | −6.44771 | −0.222600 | −0.111300 | − | 0.993787i | \(-0.535501\pi\) | ||||
−0.111300 | + | 0.993787i | \(0.535501\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.08820 | −0.175455 | ||||||||
\(842\) | 7.78698 | 0.268357 | ||||||||
\(843\) | −18.3487 | −0.631963 | ||||||||
\(844\) | 40.9716 | 1.41030 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.02364 | −0.0351934 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 7.99846 | 0.274668 | ||||||||
\(849\) | 7.53199 | 0.258497 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.60021 | 0.123414 | ||||||||
\(852\) | −33.1181 | −1.13461 | ||||||||
\(853\) | 3.55016 | 0.121555 | 0.0607777 | − | 0.998151i | \(-0.480642\pi\) | ||||
0.0607777 | + | 0.998151i | \(0.480642\pi\) | |||||||
\(854\) | −0.116321 | −0.00398042 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.99615 | 0.307482 | ||||||||
\(857\) | −51.9633 | −1.77503 | −0.887516 | − | 0.460777i | \(-0.847571\pi\) | ||||
−0.887516 | + | 0.460777i | \(0.847571\pi\) | |||||||
\(858\) | −1.16590 | −0.0398031 | ||||||||
\(859\) | −36.2287 | −1.23611 | −0.618054 | − | 0.786136i | \(-0.712079\pi\) | ||||
−0.618054 | + | 0.786136i | \(0.712079\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.1248 | −0.345051 | ||||||||
\(862\) | 5.78241 | 0.196950 | ||||||||
\(863\) | −1.69567 | −0.0577213 | −0.0288607 | − | 0.999583i | \(-0.509188\pi\) | ||||
−0.0288607 | + | 0.999583i | \(0.509188\pi\) | |||||||
\(864\) | 11.9940 | 0.408043 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.243651 | 0.00827960 | ||||||||
\(867\) | 58.7758 | 1.99613 | ||||||||
\(868\) | −13.7277 | −0.465948 | ||||||||
\(869\) | 10.8414 | 0.367769 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37.3978 | −1.26718 | ||||||||
\(872\) | 2.26071 | 0.0765573 | ||||||||
\(873\) | 3.57545 | 0.121011 | ||||||||
\(874\) | 4.08545 | 0.138192 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −25.6049 | −0.865110 | ||||||||
\(877\) | 22.4861 | 0.759303 | 0.379652 | − | 0.925130i | \(-0.376044\pi\) | ||||
0.379652 | + | 0.925130i | \(0.376044\pi\) | |||||||
\(878\) | 2.64980 | 0.0894265 | ||||||||
\(879\) | −35.9783 | −1.21352 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 54.4829 | 1.83558 | 0.917788 | − | 0.397071i | \(-0.129973\pi\) | ||||
0.917788 | + | 0.397071i | \(0.129973\pi\) | |||||||
\(882\) | −0.133898 | −0.00450858 | ||||||||
\(883\) | −48.5342 | −1.63331 | −0.816654 | − | 0.577128i | \(-0.804173\pi\) | ||||
−0.816654 | + | 0.577128i | \(0.804173\pi\) | |||||||
\(884\) | 36.6564 | 1.23289 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.57007 | −0.0527476 | ||||||||
\(887\) | 5.91327 | 0.198548 | 0.0992742 | − | 0.995060i | \(-0.468348\pi\) | ||||
0.0992742 | + | 0.995060i | \(0.468348\pi\) | |||||||
\(888\) | −2.16250 | −0.0725688 | ||||||||
\(889\) | 13.1184 | 0.439977 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.4233 | 0.349195 | ||||||||
\(892\) | 6.37789 | 0.213547 | ||||||||
\(893\) | 48.8100 | 1.63336 | ||||||||
\(894\) | 3.10764 | 0.103935 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −6.79408 | −0.226974 | ||||||||
\(897\) | 14.5236 | 0.484928 | ||||||||
\(898\) | 1.50904 | 0.0503574 | ||||||||
\(899\) | −34.4488 | −1.14893 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.0023 | 0.499799 | ||||||||
\(902\) | 1.21098 | 0.0403211 | ||||||||
\(903\) | −18.8125 | −0.626042 | ||||||||
\(904\) | 2.76629 | 0.0920055 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.19462 | 0.106134 | ||||||||
\(907\) | 18.1745 | 0.603474 | 0.301737 | − | 0.953391i | \(-0.402434\pi\) | ||||
0.301737 | + | 0.953391i | \(0.402434\pi\) | |||||||
\(908\) | 43.4981 | 1.44354 | ||||||||
\(909\) | −5.14878 | −0.170774 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.9701 | 1.09235 | 0.546174 | − | 0.837671i | \(-0.316084\pi\) | ||||
0.546174 | + | 0.837671i | \(0.316084\pi\) | |||||||
\(912\) | 44.6970 | 1.48007 | ||||||||
\(913\) | 9.07907 | 0.300473 | ||||||||
\(914\) | −2.21759 | −0.0733512 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.17186 | 0.137842 | ||||||||
\(917\) | −0.919423 | −0.0303620 | ||||||||
\(918\) | 7.16993 | 0.236643 | ||||||||
\(919\) | 32.4023 | 1.06885 | 0.534426 | − | 0.845215i | \(-0.320528\pi\) | ||||
0.534426 | + | 0.845215i | \(0.320528\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.34019 | 0.143014 | ||||||||
\(922\) | 2.23871 | 0.0737279 | ||||||||
\(923\) | −24.3479 | −0.801421 | ||||||||
\(924\) | −3.69253 | −0.121475 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.28956 | −0.108102 | ||||||||
\(927\) | 11.6865 | 0.383833 | ||||||||
\(928\) | −12.8469 | −0.421720 | ||||||||
\(929\) | 15.6805 | 0.514462 | 0.257231 | − | 0.966350i | \(-0.417190\pi\) | ||||
0.257231 | + | 0.966350i | \(0.417190\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.38464 | 0.209248 | ||||||||
\(932\) | −20.0798 | −0.657737 | ||||||||
\(933\) | −7.02319 | −0.229929 | ||||||||
\(934\) | 5.52311 | 0.180722 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.43530 | −0.0469141 | ||||||||
\(937\) | 13.6128 | 0.444710 | 0.222355 | − | 0.974966i | \(-0.428626\pi\) | ||||
0.222355 | + | 0.974966i | \(0.428626\pi\) | |||||||
\(938\) | 3.12228 | 0.101946 | ||||||||
\(939\) | −19.7549 | −0.644678 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.5175 | 0.929644 | 0.464822 | − | 0.885404i | \(-0.346118\pi\) | ||||
0.464822 | + | 0.885404i | \(0.346118\pi\) | |||||||
\(942\) | 6.36072 | 0.207244 | ||||||||
\(943\) | −15.0851 | −0.491238 | ||||||||
\(944\) | 44.4168 | 1.44564 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.25008 | 0.0731565 | ||||||||
\(947\) | 4.38617 | 0.142531 | 0.0712657 | − | 0.997457i | \(-0.477296\pi\) | ||||
0.0712657 | + | 0.997457i | \(0.477296\pi\) | |||||||
\(948\) | 40.0322 | 1.30018 | ||||||||
\(949\) | −18.8243 | −0.611064 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.4717 | −0.501705 | ||||||||
\(952\) | −6.20142 | −0.200989 | ||||||||
\(953\) | −56.7069 | −1.83692 | −0.918458 | − | 0.395519i | \(-0.870565\pi\) | ||||
−0.918458 | + | 0.395519i | \(0.870565\pi\) | |||||||
\(954\) | −0.289890 | −0.00938553 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 20.3773 | 0.659048 | ||||||||
\(957\) | −9.26618 | −0.299533 | ||||||||
\(958\) | 1.47235 | 0.0475694 | ||||||||
\(959\) | −13.1365 | −0.424200 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.6290 | 0.600936 | ||||||||
\(962\) | −0.784577 | −0.0252958 | ||||||||
\(963\) | 5.93872 | 0.191373 | ||||||||
\(964\) | −45.7183 | −1.47249 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.21255 | −0.0390130 | ||||||||
\(967\) | −23.3022 | −0.749349 | −0.374675 | − | 0.927156i | \(-0.622246\pi\) | ||||
−0.374675 | + | 0.927156i | \(0.622246\pi\) | |||||||
\(968\) | 0.894936 | 0.0287643 | ||||||||
\(969\) | 83.8358 | 2.69319 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.11862 | 0.164264 | 0.0821322 | − | 0.996621i | \(-0.473827\pi\) | ||||
0.0821322 | + | 0.996621i | \(0.473827\pi\) | |||||||
\(972\) | 11.8001 | 0.378490 | ||||||||
\(973\) | 19.8836 | 0.637440 | ||||||||
\(974\) | −6.85018 | −0.219494 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.89610 | −0.0606925 | ||||||||
\(977\) | 0.477556 | 0.0152784 | 0.00763918 | − | 0.999971i | \(-0.497568\pi\) | ||||
0.00763918 | + | 0.999971i | \(0.497568\pi\) | |||||||
\(978\) | −5.16289 | −0.165091 | ||||||||
\(979\) | 5.69209 | 0.181920 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.49239 | 0.0476482 | ||||||||
\(982\) | 3.47356 | 0.110846 | ||||||||
\(983\) | −35.0509 | −1.11795 | −0.558975 | − | 0.829185i | \(-0.688805\pi\) | ||||
−0.558975 | + | 0.829185i | \(0.688805\pi\) | |||||||
\(984\) | 9.06101 | 0.288855 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.67981 | −0.244575 | ||||||||
\(987\) | −14.4866 | −0.461114 | ||||||||
\(988\) | 33.7743 | 1.07450 | ||||||||
\(989\) | −28.0292 | −0.891278 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.7459 | −0.404887 | −0.202443 | − | 0.979294i | \(-0.564888\pi\) | ||||
−0.202443 | + | 0.979294i | \(0.564888\pi\) | |||||||
\(992\) | 18.5080 | 0.587631 | ||||||||
\(993\) | 21.3216 | 0.676621 | ||||||||
\(994\) | 2.03276 | 0.0644752 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 33.5248 | 1.06227 | ||||||||
\(997\) | −0.547098 | −0.0173268 | −0.00866338 | − | 0.999962i | \(-0.502758\pi\) | ||||
−0.00866338 | + | 0.999962i | \(0.502758\pi\) | |||||||
\(998\) | −5.32659 | −0.168610 | ||||||||
\(999\) | 5.82157 | 0.184186 |
(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 | 1925.2.a.z.1.3 | 6 | ||
5.2 | odd | 4 | 385.2.b.c.309.6 | ✓ | 12 | ||
5.3 | odd | 4 | 385.2.b.c.309.7 | yes | 12 | ||
5.4 | even | 2 | 1925.2.a.y.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
385.2.b.c.309.6 | ✓ | 12 | 5.2 | odd | 4 | ||
385.2.b.c.309.7 | yes | 12 | 5.3 | odd | 4 | ||
1925.2.a.y.1.4 | 6 | 5.4 | even | 2 | |||
1925.2.a.z.1.3 | 6 | 1.1 | even | 1 | trivial |