Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{9} - 15x^{8} + 72x^{7} - 27x^{6} - 115x^{5} + 54x^{4} + 68x^{3} - 15x^{2} - 15x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-4.04714\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.30484 | 1.92518 | 0.962591 | − | 0.270959i | \(-0.0873407\pi\) | ||||
0.962591 | + | 0.270959i | \(0.0873407\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −3.32584 | −1.25705 | −0.628524 | − | 0.777790i | \(-0.716341\pi\) | ||||
−0.628524 | + | 0.777790i | \(0.716341\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −4.30484 | −1.36131 | ||||||||
\(11\) | −2.99032 | −0.901616 | −0.450808 | − | 0.892621i | \(-0.648864\pi\) | ||||
−0.450808 | + | 0.892621i | \(0.648864\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 3.32584 | 0.888868 | ||||||||
\(15\) | −4.30484 | −1.11150 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.37298 | 1.78821 | 0.894105 | − | 0.447858i | \(-0.147813\pi\) | ||||
0.894105 | + | 0.447858i | \(0.147813\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 1.56088 | 0.358090 | 0.179045 | − | 0.983841i | \(-0.442699\pi\) | ||||
0.179045 | + | 0.983841i | \(0.442699\pi\) | |||||||
\(20\) | 4.30484 | 0.962591 | ||||||||
\(21\) | 3.32584 | 0.725757 | ||||||||
\(22\) | 2.99032 | 0.637539 | ||||||||
\(23\) | −3.98856 | −0.831673 | −0.415836 | − | 0.909439i | \(-0.636511\pi\) | ||||
−0.415836 | + | 0.909439i | \(0.636511\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 13.5316 | 2.70633 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −3.32584 | −0.628524 | ||||||||
\(29\) | −5.10669 | −0.948289 | −0.474144 | − | 0.880447i | \(-0.657243\pi\) | ||||
−0.474144 | + | 0.880447i | \(0.657243\pi\) | |||||||
\(30\) | 4.30484 | 0.785952 | ||||||||
\(31\) | −6.12120 | −1.09940 | −0.549700 | − | 0.835362i | \(-0.685258\pi\) | ||||
−0.549700 | + | 0.835362i | \(0.685258\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.99032 | 0.520549 | ||||||||
\(34\) | −7.37298 | −1.26446 | ||||||||
\(35\) | −14.3172 | −2.42005 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −5.21790 | −0.857818 | −0.428909 | − | 0.903348i | \(-0.641102\pi\) | ||||
−0.428909 | + | 0.903348i | \(0.641102\pi\) | |||||||
\(38\) | −1.56088 | −0.253208 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −4.30484 | −0.680655 | ||||||||
\(41\) | −1.29895 | −0.202863 | −0.101431 | − | 0.994843i | \(-0.532342\pi\) | ||||
−0.101431 | + | 0.994843i | \(0.532342\pi\) | |||||||
\(42\) | −3.32584 | −0.513188 | ||||||||
\(43\) | −2.11927 | −0.323185 | −0.161593 | − | 0.986858i | \(-0.551663\pi\) | ||||
−0.161593 | + | 0.986858i | \(0.551663\pi\) | |||||||
\(44\) | −2.99032 | −0.450808 | ||||||||
\(45\) | 4.30484 | 0.641727 | ||||||||
\(46\) | 3.98856 | 0.588081 | ||||||||
\(47\) | 10.0352 | 1.46379 | 0.731893 | − | 0.681419i | \(-0.238637\pi\) | ||||
0.731893 | + | 0.681419i | \(0.238637\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 4.06120 | 0.580171 | ||||||||
\(50\) | −13.5316 | −1.91366 | ||||||||
\(51\) | −7.37298 | −1.03242 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | −8.84758 | −1.21531 | −0.607654 | − | 0.794202i | \(-0.707889\pi\) | ||||
−0.607654 | + | 0.794202i | \(0.707889\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −12.8729 | −1.73578 | ||||||||
\(56\) | 3.32584 | 0.444434 | ||||||||
\(57\) | −1.56088 | −0.206743 | ||||||||
\(58\) | 5.10669 | 0.670541 | ||||||||
\(59\) | 3.83269 | 0.498973 | 0.249487 | − | 0.968378i | \(-0.419738\pi\) | ||||
0.249487 | + | 0.968378i | \(0.419738\pi\) | |||||||
\(60\) | −4.30484 | −0.555752 | ||||||||
\(61\) | 4.47557 | 0.573039 | 0.286519 | − | 0.958074i | \(-0.407502\pi\) | ||||
0.286519 | + | 0.958074i | \(0.407502\pi\) | |||||||
\(62\) | 6.12120 | 0.777393 | ||||||||
\(63\) | −3.32584 | −0.419016 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.30484 | −0.533949 | ||||||||
\(66\) | −2.99032 | −0.368083 | ||||||||
\(67\) | 1.76088 | 0.215125 | 0.107563 | − | 0.994198i | \(-0.465695\pi\) | ||||
0.107563 | + | 0.994198i | \(0.465695\pi\) | |||||||
\(68\) | 7.37298 | 0.894105 | ||||||||
\(69\) | 3.98856 | 0.480166 | ||||||||
\(70\) | 14.3172 | 1.71123 | ||||||||
\(71\) | −10.4599 | −1.24136 | −0.620682 | − | 0.784062i | \(-0.713144\pi\) | ||||
−0.620682 | + | 0.784062i | \(0.713144\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 9.29221 | 1.08757 | 0.543785 | − | 0.839224i | \(-0.316991\pi\) | ||||
0.543785 | + | 0.839224i | \(0.316991\pi\) | |||||||
\(74\) | 5.21790 | 0.606569 | ||||||||
\(75\) | −13.5316 | −1.56250 | ||||||||
\(76\) | 1.56088 | 0.179045 | ||||||||
\(77\) | 9.94533 | 1.13338 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | 12.4331 | 1.39884 | 0.699418 | − | 0.714713i | \(-0.253442\pi\) | ||||
0.699418 | + | 0.714713i | \(0.253442\pi\) | |||||||
\(80\) | 4.30484 | 0.481295 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.29895 | 0.143445 | ||||||||
\(83\) | −7.29642 | −0.800886 | −0.400443 | − | 0.916322i | \(-0.631144\pi\) | ||||
−0.400443 | + | 0.916322i | \(0.631144\pi\) | |||||||
\(84\) | 3.32584 | 0.362879 | ||||||||
\(85\) | 31.7395 | 3.44263 | ||||||||
\(86\) | 2.11927 | 0.228526 | ||||||||
\(87\) | 5.10669 | 0.547495 | ||||||||
\(88\) | 2.99032 | 0.318770 | ||||||||
\(89\) | 0.220099 | 0.0233304 | 0.0116652 | − | 0.999932i | \(-0.496287\pi\) | ||||
0.0116652 | + | 0.999932i | \(0.496287\pi\) | |||||||
\(90\) | −4.30484 | −0.453770 | ||||||||
\(91\) | 3.32584 | 0.348643 | ||||||||
\(92\) | −3.98856 | −0.415836 | ||||||||
\(93\) | 6.12120 | 0.634739 | ||||||||
\(94\) | −10.0352 | −1.03505 | ||||||||
\(95\) | 6.71933 | 0.689389 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −10.6956 | −1.08597 | −0.542985 | − | 0.839742i | \(-0.682706\pi\) | ||||
−0.542985 | + | 0.839742i | \(0.682706\pi\) | |||||||
\(98\) | −4.06120 | −0.410243 | ||||||||
\(99\) | −2.99032 | −0.300539 | ||||||||
\(100\) | 13.5316 | 1.35316 | ||||||||
\(101\) | −19.7975 | −1.96992 | −0.984961 | − | 0.172776i | \(-0.944726\pi\) | ||||
−0.984961 | + | 0.172776i | \(0.944726\pi\) | |||||||
\(102\) | 7.37298 | 0.730034 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 14.3172 | 1.39721 | ||||||||
\(106\) | 8.84758 | 0.859353 | ||||||||
\(107\) | 7.21479 | 0.697481 | 0.348740 | − | 0.937219i | \(-0.386610\pi\) | ||||
0.348740 | + | 0.937219i | \(0.386610\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −4.48414 | −0.429503 | −0.214751 | − | 0.976669i | \(-0.568894\pi\) | ||||
−0.214751 | + | 0.976669i | \(0.568894\pi\) | |||||||
\(110\) | 12.8729 | 1.22738 | ||||||||
\(111\) | 5.21790 | 0.495261 | ||||||||
\(112\) | −3.32584 | −0.314262 | ||||||||
\(113\) | −13.7149 | −1.29018 | −0.645092 | − | 0.764105i | \(-0.723181\pi\) | ||||
−0.645092 | + | 0.764105i | \(0.723181\pi\) | |||||||
\(114\) | 1.56088 | 0.146190 | ||||||||
\(115\) | −17.1701 | −1.60112 | ||||||||
\(116\) | −5.10669 | −0.474144 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −3.83269 | −0.352827 | ||||||||
\(119\) | −24.5213 | −2.24787 | ||||||||
\(120\) | 4.30484 | 0.392976 | ||||||||
\(121\) | −2.05796 | −0.187088 | ||||||||
\(122\) | −4.47557 | −0.405200 | ||||||||
\(123\) | 1.29895 | 0.117123 | ||||||||
\(124\) | −6.12120 | −0.549700 | ||||||||
\(125\) | 36.7273 | 3.28499 | ||||||||
\(126\) | 3.32584 | 0.296289 | ||||||||
\(127\) | 6.88336 | 0.610800 | 0.305400 | − | 0.952224i | \(-0.401210\pi\) | ||||
0.305400 | + | 0.952224i | \(0.401210\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.11927 | 0.186591 | ||||||||
\(130\) | 4.30484 | 0.377559 | ||||||||
\(131\) | −4.41826 | −0.386025 | −0.193013 | − | 0.981196i | \(-0.561826\pi\) | ||||
−0.193013 | + | 0.981196i | \(0.561826\pi\) | |||||||
\(132\) | 2.99032 | 0.260274 | ||||||||
\(133\) | −5.19123 | −0.450137 | ||||||||
\(134\) | −1.76088 | −0.152116 | ||||||||
\(135\) | −4.30484 | −0.370501 | ||||||||
\(136\) | −7.37298 | −0.632228 | ||||||||
\(137\) | 1.04246 | 0.0890637 | 0.0445318 | − | 0.999008i | \(-0.485820\pi\) | ||||
0.0445318 | + | 0.999008i | \(0.485820\pi\) | |||||||
\(138\) | −3.98856 | −0.339529 | ||||||||
\(139\) | 2.48271 | 0.210581 | 0.105290 | − | 0.994442i | \(-0.466423\pi\) | ||||
0.105290 | + | 0.994442i | \(0.466423\pi\) | |||||||
\(140\) | −14.3172 | −1.21002 | ||||||||
\(141\) | −10.0352 | −0.845117 | ||||||||
\(142\) | 10.4599 | 0.877777 | ||||||||
\(143\) | 2.99032 | 0.250063 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −21.9835 | −1.82563 | ||||||||
\(146\) | −9.29221 | −0.769028 | ||||||||
\(147\) | −4.06120 | −0.334962 | ||||||||
\(148\) | −5.21790 | −0.428909 | ||||||||
\(149\) | 11.6489 | 0.954316 | 0.477158 | − | 0.878818i | \(-0.341667\pi\) | ||||
0.477158 | + | 0.878818i | \(0.341667\pi\) | |||||||
\(150\) | 13.5316 | 1.10485 | ||||||||
\(151\) | −9.39427 | −0.764495 | −0.382247 | − | 0.924060i | \(-0.624850\pi\) | ||||
−0.382247 | + | 0.924060i | \(0.624850\pi\) | |||||||
\(152\) | −1.56088 | −0.126604 | ||||||||
\(153\) | 7.37298 | 0.596070 | ||||||||
\(154\) | −9.94533 | −0.801418 | ||||||||
\(155\) | −26.3508 | −2.11655 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | 7.98927 | 0.637613 | 0.318806 | − | 0.947820i | \(-0.396718\pi\) | ||||
0.318806 | + | 0.947820i | \(0.396718\pi\) | |||||||
\(158\) | −12.4331 | −0.989127 | ||||||||
\(159\) | 8.84758 | 0.701658 | ||||||||
\(160\) | −4.30484 | −0.340327 | ||||||||
\(161\) | 13.2653 | 1.04545 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −22.6367 | −1.77304 | −0.886522 | − | 0.462686i | \(-0.846886\pi\) | ||||
−0.886522 | + | 0.462686i | \(0.846886\pi\) | |||||||
\(164\) | −1.29895 | −0.101431 | ||||||||
\(165\) | 12.8729 | 1.00215 | ||||||||
\(166\) | 7.29642 | 0.566312 | ||||||||
\(167\) | −10.0191 | −0.775298 | −0.387649 | − | 0.921807i | \(-0.626713\pi\) | ||||
−0.387649 | + | 0.921807i | \(0.626713\pi\) | |||||||
\(168\) | −3.32584 | −0.256594 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −31.7395 | −2.43431 | ||||||||
\(171\) | 1.56088 | 0.119363 | ||||||||
\(172\) | −2.11927 | −0.161593 | ||||||||
\(173\) | −6.74785 | −0.513030 | −0.256515 | − | 0.966540i | \(-0.582574\pi\) | ||||
−0.256515 | + | 0.966540i | \(0.582574\pi\) | |||||||
\(174\) | −5.10669 | −0.387137 | ||||||||
\(175\) | −45.0040 | −3.40198 | ||||||||
\(176\) | −2.99032 | −0.225404 | ||||||||
\(177\) | −3.83269 | −0.288082 | ||||||||
\(178\) | −0.220099 | −0.0164971 | ||||||||
\(179\) | 7.52216 | 0.562232 | 0.281116 | − | 0.959674i | \(-0.409295\pi\) | ||||
0.281116 | + | 0.959674i | \(0.409295\pi\) | |||||||
\(180\) | 4.30484 | 0.320864 | ||||||||
\(181\) | 2.55602 | 0.189987 | 0.0949936 | − | 0.995478i | \(-0.469717\pi\) | ||||
0.0949936 | + | 0.995478i | \(0.469717\pi\) | |||||||
\(182\) | −3.32584 | −0.246528 | ||||||||
\(183\) | −4.47557 | −0.330844 | ||||||||
\(184\) | 3.98856 | 0.294041 | ||||||||
\(185\) | −22.4622 | −1.65146 | ||||||||
\(186\) | −6.12120 | −0.448828 | ||||||||
\(187\) | −22.0476 | −1.61228 | ||||||||
\(188\) | 10.0352 | 0.731893 | ||||||||
\(189\) | 3.32584 | 0.241919 | ||||||||
\(190\) | −6.71933 | −0.487471 | ||||||||
\(191\) | −8.59420 | −0.621855 | −0.310927 | − | 0.950434i | \(-0.600640\pi\) | ||||
−0.310927 | + | 0.950434i | \(0.600640\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 12.7715 | 0.919313 | 0.459656 | − | 0.888097i | \(-0.347973\pi\) | ||||
0.459656 | + | 0.888097i | \(0.347973\pi\) | |||||||
\(194\) | 10.6956 | 0.767897 | ||||||||
\(195\) | 4.30484 | 0.308276 | ||||||||
\(196\) | 4.06120 | 0.290086 | ||||||||
\(197\) | −5.83763 | −0.415914 | −0.207957 | − | 0.978138i | \(-0.566681\pi\) | ||||
−0.207957 | + | 0.978138i | \(0.566681\pi\) | |||||||
\(198\) | 2.99032 | 0.212513 | ||||||||
\(199\) | 7.01930 | 0.497585 | 0.248792 | − | 0.968557i | \(-0.419966\pi\) | ||||
0.248792 | + | 0.968557i | \(0.419966\pi\) | |||||||
\(200\) | −13.5316 | −0.956830 | ||||||||
\(201\) | −1.76088 | −0.124203 | ||||||||
\(202\) | 19.7975 | 1.39295 | ||||||||
\(203\) | 16.9840 | 1.19204 | ||||||||
\(204\) | −7.37298 | −0.516212 | ||||||||
\(205\) | −5.59179 | −0.390547 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | −3.98856 | −0.277224 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −4.66753 | −0.322860 | ||||||||
\(210\) | −14.3172 | −0.987980 | ||||||||
\(211\) | −26.6852 | −1.83709 | −0.918543 | − | 0.395320i | \(-0.870634\pi\) | ||||
−0.918543 | + | 0.395320i | \(0.870634\pi\) | |||||||
\(212\) | −8.84758 | −0.607654 | ||||||||
\(213\) | 10.4599 | 0.716702 | ||||||||
\(214\) | −7.21479 | −0.493193 | ||||||||
\(215\) | −9.12310 | −0.622190 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 20.3581 | 1.38200 | ||||||||
\(218\) | 4.48414 | 0.303704 | ||||||||
\(219\) | −9.29221 | −0.627909 | ||||||||
\(220\) | −12.8729 | −0.867888 | ||||||||
\(221\) | −7.37298 | −0.495960 | ||||||||
\(222\) | −5.21790 | −0.350203 | ||||||||
\(223\) | −18.5806 | −1.24425 | −0.622125 | − | 0.782918i | \(-0.713731\pi\) | ||||
−0.622125 | + | 0.782918i | \(0.713731\pi\) | |||||||
\(224\) | 3.32584 | 0.222217 | ||||||||
\(225\) | 13.5316 | 0.902108 | ||||||||
\(226\) | 13.7149 | 0.912298 | ||||||||
\(227\) | 1.22947 | 0.0816030 | 0.0408015 | − | 0.999167i | \(-0.487009\pi\) | ||||
0.0408015 | + | 0.999167i | \(0.487009\pi\) | |||||||
\(228\) | −1.56088 | −0.103372 | ||||||||
\(229\) | 22.9718 | 1.51802 | 0.759008 | − | 0.651081i | \(-0.225684\pi\) | ||||
0.759008 | + | 0.651081i | \(0.225684\pi\) | |||||||
\(230\) | 17.1701 | 1.13216 | ||||||||
\(231\) | −9.94533 | −0.654355 | ||||||||
\(232\) | 5.10669 | 0.335271 | ||||||||
\(233\) | −0.967978 | −0.0634144 | −0.0317072 | − | 0.999497i | \(-0.510094\pi\) | ||||
−0.0317072 | + | 0.999497i | \(0.510094\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | 43.2000 | 2.81806 | ||||||||
\(236\) | 3.83269 | 0.249487 | ||||||||
\(237\) | −12.4331 | −0.807619 | ||||||||
\(238\) | 24.5213 | 1.58948 | ||||||||
\(239\) | −23.9676 | −1.55033 | −0.775166 | − | 0.631757i | \(-0.782334\pi\) | ||||
−0.775166 | + | 0.631757i | \(0.782334\pi\) | |||||||
\(240\) | −4.30484 | −0.277876 | ||||||||
\(241\) | −22.4990 | −1.44929 | −0.724645 | − | 0.689123i | \(-0.757996\pi\) | ||||
−0.724645 | + | 0.689123i | \(0.757996\pi\) | |||||||
\(242\) | 2.05796 | 0.132291 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 4.47557 | 0.286519 | ||||||||
\(245\) | 17.4828 | 1.11694 | ||||||||
\(246\) | −1.29895 | −0.0828183 | ||||||||
\(247\) | −1.56088 | −0.0993163 | ||||||||
\(248\) | 6.12120 | 0.388697 | ||||||||
\(249\) | 7.29642 | 0.462392 | ||||||||
\(250\) | −36.7273 | −2.32284 | ||||||||
\(251\) | 25.7307 | 1.62411 | 0.812055 | − | 0.583581i | \(-0.198349\pi\) | ||||
0.812055 | + | 0.583581i | \(0.198349\pi\) | |||||||
\(252\) | −3.32584 | −0.209508 | ||||||||
\(253\) | 11.9271 | 0.749850 | ||||||||
\(254\) | −6.88336 | −0.431901 | ||||||||
\(255\) | −31.7395 | −1.98760 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.1726 | 1.25833 | 0.629165 | − | 0.777272i | \(-0.283397\pi\) | ||||
0.629165 | + | 0.777272i | \(0.283397\pi\) | |||||||
\(258\) | −2.11927 | −0.131940 | ||||||||
\(259\) | 17.3539 | 1.07832 | ||||||||
\(260\) | −4.30484 | −0.266975 | ||||||||
\(261\) | −5.10669 | −0.316096 | ||||||||
\(262\) | 4.41826 | 0.272961 | ||||||||
\(263\) | −22.0673 | −1.36073 | −0.680364 | − | 0.732875i | \(-0.738178\pi\) | ||||
−0.680364 | + | 0.732875i | \(0.738178\pi\) | |||||||
\(264\) | −2.99032 | −0.184042 | ||||||||
\(265\) | −38.0874 | −2.33969 | ||||||||
\(266\) | 5.19123 | 0.318295 | ||||||||
\(267\) | −0.220099 | −0.0134698 | ||||||||
\(268\) | 1.76088 | 0.107563 | ||||||||
\(269\) | 10.9730 | 0.669038 | 0.334519 | − | 0.942389i | \(-0.391426\pi\) | ||||
0.334519 | + | 0.942389i | \(0.391426\pi\) | |||||||
\(270\) | 4.30484 | 0.261984 | ||||||||
\(271\) | −18.4643 | −1.12163 | −0.560813 | − | 0.827942i | \(-0.689512\pi\) | ||||
−0.560813 | + | 0.827942i | \(0.689512\pi\) | |||||||
\(272\) | 7.37298 | 0.447052 | ||||||||
\(273\) | −3.32584 | −0.201289 | ||||||||
\(274\) | −1.04246 | −0.0629775 | ||||||||
\(275\) | −40.4639 | −2.44007 | ||||||||
\(276\) | 3.98856 | 0.240083 | ||||||||
\(277\) | −14.5293 | −0.872984 | −0.436492 | − | 0.899708i | \(-0.643779\pi\) | ||||
−0.436492 | + | 0.899708i | \(0.643779\pi\) | |||||||
\(278\) | −2.48271 | −0.148903 | ||||||||
\(279\) | −6.12120 | −0.366467 | ||||||||
\(280\) | 14.3172 | 0.855616 | ||||||||
\(281\) | −15.7883 | −0.941854 | −0.470927 | − | 0.882172i | \(-0.656080\pi\) | ||||
−0.470927 | + | 0.882172i | \(0.656080\pi\) | |||||||
\(282\) | 10.0352 | 0.597588 | ||||||||
\(283\) | 18.1693 | 1.08005 | 0.540026 | − | 0.841649i | \(-0.318415\pi\) | ||||
0.540026 | + | 0.841649i | \(0.318415\pi\) | |||||||
\(284\) | −10.4599 | −0.620682 | ||||||||
\(285\) | −6.71933 | −0.398019 | ||||||||
\(286\) | −2.99032 | −0.176822 | ||||||||
\(287\) | 4.32011 | 0.255008 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 37.3608 | 2.19769 | ||||||||
\(290\) | 21.9835 | 1.29091 | ||||||||
\(291\) | 10.6956 | 0.626986 | ||||||||
\(292\) | 9.29221 | 0.543785 | ||||||||
\(293\) | −3.82927 | −0.223708 | −0.111854 | − | 0.993725i | \(-0.535679\pi\) | ||||
−0.111854 | + | 0.993725i | \(0.535679\pi\) | |||||||
\(294\) | 4.06120 | 0.236854 | ||||||||
\(295\) | 16.4991 | 0.960614 | ||||||||
\(296\) | 5.21790 | 0.303284 | ||||||||
\(297\) | 2.99032 | 0.173516 | ||||||||
\(298\) | −11.6489 | −0.674803 | ||||||||
\(299\) | 3.98856 | 0.230664 | ||||||||
\(300\) | −13.5316 | −0.781249 | ||||||||
\(301\) | 7.04834 | 0.406259 | ||||||||
\(302\) | 9.39427 | 0.540579 | ||||||||
\(303\) | 19.7975 | 1.13734 | ||||||||
\(304\) | 1.56088 | 0.0895225 | ||||||||
\(305\) | 19.2666 | 1.10320 | ||||||||
\(306\) | −7.37298 | −0.421485 | ||||||||
\(307\) | −16.8905 | −0.963992 | −0.481996 | − | 0.876173i | \(-0.660088\pi\) | ||||
−0.481996 | + | 0.876173i | \(0.660088\pi\) | |||||||
\(308\) | 9.94533 | 0.566688 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 26.3508 | 1.49662 | ||||||||
\(311\) | 2.23173 | 0.126550 | 0.0632748 | − | 0.997996i | \(-0.479846\pi\) | ||||
0.0632748 | + | 0.997996i | \(0.479846\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | −5.72536 | −0.323616 | −0.161808 | − | 0.986822i | \(-0.551733\pi\) | ||||
−0.161808 | + | 0.986822i | \(0.551733\pi\) | |||||||
\(314\) | −7.98927 | −0.450860 | ||||||||
\(315\) | −14.3172 | −0.806682 | ||||||||
\(316\) | 12.4331 | 0.699418 | ||||||||
\(317\) | 4.04068 | 0.226947 | 0.113474 | − | 0.993541i | \(-0.463802\pi\) | ||||
0.113474 | + | 0.993541i | \(0.463802\pi\) | |||||||
\(318\) | −8.84758 | −0.496147 | ||||||||
\(319\) | 15.2707 | 0.854993 | ||||||||
\(320\) | 4.30484 | 0.240648 | ||||||||
\(321\) | −7.21479 | −0.402691 | ||||||||
\(322\) | −13.2653 | −0.739247 | ||||||||
\(323\) | 11.5083 | 0.640340 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −13.5316 | −0.750600 | ||||||||
\(326\) | 22.6367 | 1.25373 | ||||||||
\(327\) | 4.48414 | 0.247974 | ||||||||
\(328\) | 1.29895 | 0.0717227 | ||||||||
\(329\) | −33.3755 | −1.84005 | ||||||||
\(330\) | −12.8729 | −0.708627 | ||||||||
\(331\) | 11.2057 | 0.615922 | 0.307961 | − | 0.951399i | \(-0.400353\pi\) | ||||
0.307961 | + | 0.951399i | \(0.400353\pi\) | |||||||
\(332\) | −7.29642 | −0.400443 | ||||||||
\(333\) | −5.21790 | −0.285939 | ||||||||
\(334\) | 10.0191 | 0.548219 | ||||||||
\(335\) | 7.58028 | 0.414155 | ||||||||
\(336\) | 3.32584 | 0.181439 | ||||||||
\(337\) | −15.9410 | −0.868363 | −0.434182 | − | 0.900825i | \(-0.642962\pi\) | ||||
−0.434182 | + | 0.900825i | \(0.642962\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 13.7149 | 0.744888 | ||||||||
\(340\) | 31.7395 | 1.72131 | ||||||||
\(341\) | 18.3044 | 0.991237 | ||||||||
\(342\) | −1.56088 | −0.0844027 | ||||||||
\(343\) | 9.77398 | 0.527745 | ||||||||
\(344\) | 2.11927 | 0.114263 | ||||||||
\(345\) | 17.1701 | 0.924408 | ||||||||
\(346\) | 6.74785 | 0.362767 | ||||||||
\(347\) | 24.4975 | 1.31510 | 0.657548 | − | 0.753413i | \(-0.271594\pi\) | ||||
0.657548 | + | 0.753413i | \(0.271594\pi\) | |||||||
\(348\) | 5.10669 | 0.273747 | ||||||||
\(349\) | −4.60506 | −0.246503 | −0.123252 | − | 0.992375i | \(-0.539332\pi\) | ||||
−0.123252 | + | 0.992375i | \(0.539332\pi\) | |||||||
\(350\) | 45.0040 | 2.40556 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 2.99032 | 0.159385 | ||||||||
\(353\) | 7.92700 | 0.421912 | 0.210956 | − | 0.977496i | \(-0.432342\pi\) | ||||
0.210956 | + | 0.977496i | \(0.432342\pi\) | |||||||
\(354\) | 3.83269 | 0.203705 | ||||||||
\(355\) | −45.0283 | −2.38985 | ||||||||
\(356\) | 0.220099 | 0.0116652 | ||||||||
\(357\) | 24.5213 | 1.29781 | ||||||||
\(358\) | −7.52216 | −0.397558 | ||||||||
\(359\) | −16.5493 | −0.873438 | −0.436719 | − | 0.899598i | \(-0.643860\pi\) | ||||
−0.436719 | + | 0.899598i | \(0.643860\pi\) | |||||||
\(360\) | −4.30484 | −0.226885 | ||||||||
\(361\) | −16.5637 | −0.871771 | ||||||||
\(362\) | −2.55602 | −0.134341 | ||||||||
\(363\) | 2.05796 | 0.108015 | ||||||||
\(364\) | 3.32584 | 0.174321 | ||||||||
\(365\) | 40.0014 | 2.09377 | ||||||||
\(366\) | 4.47557 | 0.233942 | ||||||||
\(367\) | 2.43300 | 0.127002 | 0.0635009 | − | 0.997982i | \(-0.479773\pi\) | ||||
0.0635009 | + | 0.997982i | \(0.479773\pi\) | |||||||
\(368\) | −3.98856 | −0.207918 | ||||||||
\(369\) | −1.29895 | −0.0676208 | ||||||||
\(370\) | 22.4622 | 1.16776 | ||||||||
\(371\) | 29.4256 | 1.52770 | ||||||||
\(372\) | 6.12120 | 0.317370 | ||||||||
\(373\) | 18.4891 | 0.957330 | 0.478665 | − | 0.877998i | \(-0.341121\pi\) | ||||
0.478665 | + | 0.877998i | \(0.341121\pi\) | |||||||
\(374\) | 22.0476 | 1.14005 | ||||||||
\(375\) | −36.7273 | −1.89659 | ||||||||
\(376\) | −10.0352 | −0.517527 | ||||||||
\(377\) | 5.10669 | 0.263008 | ||||||||
\(378\) | −3.32584 | −0.171063 | ||||||||
\(379\) | 8.19688 | 0.421046 | 0.210523 | − | 0.977589i | \(-0.432483\pi\) | ||||
0.210523 | + | 0.977589i | \(0.432483\pi\) | |||||||
\(380\) | 6.71933 | 0.344694 | ||||||||
\(381\) | −6.88336 | −0.352645 | ||||||||
\(382\) | 8.59420 | 0.439718 | ||||||||
\(383\) | 1.76663 | 0.0902704 | 0.0451352 | − | 0.998981i | \(-0.485628\pi\) | ||||
0.0451352 | + | 0.998981i | \(0.485628\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 42.8130 | 2.18195 | ||||||||
\(386\) | −12.7715 | −0.650052 | ||||||||
\(387\) | −2.11927 | −0.107728 | ||||||||
\(388\) | −10.6956 | −0.542985 | ||||||||
\(389\) | −13.1999 | −0.669260 | −0.334630 | − | 0.942350i | \(-0.608611\pi\) | ||||
−0.334630 | + | 0.942350i | \(0.608611\pi\) | |||||||
\(390\) | −4.30484 | −0.217984 | ||||||||
\(391\) | −29.4076 | −1.48721 | ||||||||
\(392\) | −4.06120 | −0.205122 | ||||||||
\(393\) | 4.41826 | 0.222872 | ||||||||
\(394\) | 5.83763 | 0.294095 | ||||||||
\(395\) | 53.5226 | 2.69301 | ||||||||
\(396\) | −2.99032 | −0.150269 | ||||||||
\(397\) | 7.07627 | 0.355148 | 0.177574 | − | 0.984107i | \(-0.443175\pi\) | ||||
0.177574 | + | 0.984107i | \(0.443175\pi\) | |||||||
\(398\) | −7.01930 | −0.351846 | ||||||||
\(399\) | 5.19123 | 0.259887 | ||||||||
\(400\) | 13.5316 | 0.676581 | ||||||||
\(401\) | 33.5184 | 1.67383 | 0.836914 | − | 0.547334i | \(-0.184357\pi\) | ||||
0.836914 | + | 0.547334i | \(0.184357\pi\) | |||||||
\(402\) | 1.76088 | 0.0878245 | ||||||||
\(403\) | 6.12120 | 0.304919 | ||||||||
\(404\) | −19.7975 | −0.984961 | ||||||||
\(405\) | 4.30484 | 0.213909 | ||||||||
\(406\) | −16.9840 | −0.842903 | ||||||||
\(407\) | 15.6032 | 0.773423 | ||||||||
\(408\) | 7.37298 | 0.365017 | ||||||||
\(409\) | −26.8161 | −1.32597 | −0.662986 | − | 0.748632i | \(-0.730711\pi\) | ||||
−0.662986 | + | 0.748632i | \(0.730711\pi\) | |||||||
\(410\) | 5.59179 | 0.276159 | ||||||||
\(411\) | −1.04246 | −0.0514209 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | −12.7469 | −0.627234 | ||||||||
\(414\) | 3.98856 | 0.196027 | ||||||||
\(415\) | −31.4099 | −1.54185 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | −2.48271 | −0.121579 | ||||||||
\(418\) | 4.66753 | 0.228296 | ||||||||
\(419\) | −29.2983 | −1.43131 | −0.715657 | − | 0.698452i | \(-0.753872\pi\) | ||||
−0.715657 | + | 0.698452i | \(0.753872\pi\) | |||||||
\(420\) | 14.3172 | 0.698607 | ||||||||
\(421\) | −34.2832 | −1.67086 | −0.835429 | − | 0.549598i | \(-0.814781\pi\) | ||||
−0.835429 | + | 0.549598i | \(0.814781\pi\) | |||||||
\(422\) | 26.6852 | 1.29902 | ||||||||
\(423\) | 10.0352 | 0.487929 | ||||||||
\(424\) | 8.84758 | 0.429676 | ||||||||
\(425\) | 99.7684 | 4.83948 | ||||||||
\(426\) | −10.4599 | −0.506785 | ||||||||
\(427\) | −14.8850 | −0.720337 | ||||||||
\(428\) | 7.21479 | 0.348740 | ||||||||
\(429\) | −2.99032 | −0.144374 | ||||||||
\(430\) | 9.12310 | 0.439955 | ||||||||
\(431\) | 7.96742 | 0.383777 | 0.191889 | − | 0.981417i | \(-0.438539\pi\) | ||||
0.191889 | + | 0.981417i | \(0.438539\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 4.95655 | 0.238196 | 0.119098 | − | 0.992882i | \(-0.462000\pi\) | ||||
0.119098 | + | 0.992882i | \(0.462000\pi\) | |||||||
\(434\) | −20.3581 | −0.977221 | ||||||||
\(435\) | 21.9835 | 1.05403 | ||||||||
\(436\) | −4.48414 | −0.214751 | ||||||||
\(437\) | −6.22566 | −0.297814 | ||||||||
\(438\) | 9.29221 | 0.443999 | ||||||||
\(439\) | −31.5089 | −1.50384 | −0.751918 | − | 0.659256i | \(-0.770871\pi\) | ||||
−0.751918 | + | 0.659256i | \(0.770871\pi\) | |||||||
\(440\) | 12.8729 | 0.613689 | ||||||||
\(441\) | 4.06120 | 0.193390 | ||||||||
\(442\) | 7.37298 | 0.350697 | ||||||||
\(443\) | 31.4030 | 1.49200 | 0.746000 | − | 0.665946i | \(-0.231972\pi\) | ||||
0.746000 | + | 0.665946i | \(0.231972\pi\) | |||||||
\(444\) | 5.21790 | 0.247631 | ||||||||
\(445\) | 0.947490 | 0.0449154 | ||||||||
\(446\) | 18.5806 | 0.879818 | ||||||||
\(447\) | −11.6489 | −0.550975 | ||||||||
\(448\) | −3.32584 | −0.157131 | ||||||||
\(449\) | −28.1392 | −1.32797 | −0.663985 | − | 0.747746i | \(-0.731136\pi\) | ||||
−0.663985 | + | 0.747746i | \(0.731136\pi\) | |||||||
\(450\) | −13.5316 | −0.637887 | ||||||||
\(451\) | 3.88429 | 0.182904 | ||||||||
\(452\) | −13.7149 | −0.645092 | ||||||||
\(453\) | 9.39427 | 0.441381 | ||||||||
\(454\) | −1.22947 | −0.0577021 | ||||||||
\(455\) | 14.3172 | 0.671200 | ||||||||
\(456\) | 1.56088 | 0.0730948 | ||||||||
\(457\) | 27.3601 | 1.27985 | 0.639925 | − | 0.768437i | \(-0.278965\pi\) | ||||
0.639925 | + | 0.768437i | \(0.278965\pi\) | |||||||
\(458\) | −22.9718 | −1.07340 | ||||||||
\(459\) | −7.37298 | −0.344141 | ||||||||
\(460\) | −17.1701 | −0.800561 | ||||||||
\(461\) | −14.1704 | −0.659983 | −0.329992 | − | 0.943984i | \(-0.607046\pi\) | ||||
−0.329992 | + | 0.943984i | \(0.607046\pi\) | |||||||
\(462\) | 9.94533 | 0.462699 | ||||||||
\(463\) | −42.2795 | −1.96490 | −0.982448 | − | 0.186535i | \(-0.940274\pi\) | ||||
−0.982448 | + | 0.186535i | \(0.940274\pi\) | |||||||
\(464\) | −5.10669 | −0.237072 | ||||||||
\(465\) | 26.3508 | 1.22199 | ||||||||
\(466\) | 0.967978 | 0.0448407 | ||||||||
\(467\) | −2.38852 | −0.110528 | −0.0552638 | − | 0.998472i | \(-0.517600\pi\) | ||||
−0.0552638 | + | 0.998472i | \(0.517600\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | −5.85639 | −0.270423 | ||||||||
\(470\) | −43.2000 | −1.99267 | ||||||||
\(471\) | −7.98927 | −0.368126 | ||||||||
\(472\) | −3.83269 | −0.176414 | ||||||||
\(473\) | 6.33729 | 0.291389 | ||||||||
\(474\) | 12.4331 | 0.571073 | ||||||||
\(475\) | 21.1212 | 0.969108 | ||||||||
\(476\) | −24.5213 | −1.12393 | ||||||||
\(477\) | −8.84758 | −0.405103 | ||||||||
\(478\) | 23.9676 | 1.09625 | ||||||||
\(479\) | −31.2618 | −1.42839 | −0.714195 | − | 0.699947i | \(-0.753207\pi\) | ||||
−0.714195 | + | 0.699947i | \(0.753207\pi\) | |||||||
\(480\) | 4.30484 | 0.196488 | ||||||||
\(481\) | 5.21790 | 0.237916 | ||||||||
\(482\) | 22.4990 | 1.02480 | ||||||||
\(483\) | −13.2653 | −0.603593 | ||||||||
\(484\) | −2.05796 | −0.0935439 | ||||||||
\(485\) | −46.0427 | −2.09069 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 9.37604 | 0.424869 | 0.212434 | − | 0.977175i | \(-0.431861\pi\) | ||||
0.212434 | + | 0.977175i | \(0.431861\pi\) | |||||||
\(488\) | −4.47557 | −0.202600 | ||||||||
\(489\) | 22.6367 | 1.02367 | ||||||||
\(490\) | −17.4828 | −0.789793 | ||||||||
\(491\) | −27.2778 | −1.23103 | −0.615515 | − | 0.788125i | \(-0.711052\pi\) | ||||
−0.615515 | + | 0.788125i | \(0.711052\pi\) | |||||||
\(492\) | 1.29895 | 0.0585614 | ||||||||
\(493\) | −37.6515 | −1.69574 | ||||||||
\(494\) | 1.56088 | 0.0702273 | ||||||||
\(495\) | −12.8729 | −0.578592 | ||||||||
\(496\) | −6.12120 | −0.274850 | ||||||||
\(497\) | 34.7880 | 1.56046 | ||||||||
\(498\) | −7.29642 | −0.326961 | ||||||||
\(499\) | −6.22981 | −0.278885 | −0.139442 | − | 0.990230i | \(-0.544531\pi\) | ||||
−0.139442 | + | 0.990230i | \(0.544531\pi\) | |||||||
\(500\) | 36.7273 | 1.64249 | ||||||||
\(501\) | 10.0191 | 0.447619 | ||||||||
\(502\) | −25.7307 | −1.14842 | ||||||||
\(503\) | 29.8429 | 1.33063 | 0.665314 | − | 0.746564i | \(-0.268298\pi\) | ||||
0.665314 | + | 0.746564i | \(0.268298\pi\) | |||||||
\(504\) | 3.32584 | 0.148145 | ||||||||
\(505\) | −85.2249 | −3.79246 | ||||||||
\(506\) | −11.9271 | −0.530224 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 6.88336 | 0.305400 | ||||||||
\(509\) | 3.79641 | 0.168273 | 0.0841365 | − | 0.996454i | \(-0.473187\pi\) | ||||
0.0841365 | + | 0.996454i | \(0.473187\pi\) | |||||||
\(510\) | 31.7395 | 1.40545 | ||||||||
\(511\) | −30.9044 | −1.36713 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.56088 | −0.0689145 | ||||||||
\(514\) | −20.1726 | −0.889773 | ||||||||
\(515\) | −4.30484 | −0.189694 | ||||||||
\(516\) | 2.11927 | 0.0932955 | ||||||||
\(517\) | −30.0085 | −1.31977 | ||||||||
\(518\) | −17.3539 | −0.762486 | ||||||||
\(519\) | 6.74785 | 0.296198 | ||||||||
\(520\) | 4.30484 | 0.188780 | ||||||||
\(521\) | 3.96799 | 0.173841 | 0.0869203 | − | 0.996215i | \(-0.472297\pi\) | ||||
0.0869203 | + | 0.996215i | \(0.472297\pi\) | |||||||
\(522\) | 5.10669 | 0.223514 | ||||||||
\(523\) | −38.8836 | −1.70026 | −0.850130 | − | 0.526573i | \(-0.823477\pi\) | ||||
−0.850130 | + | 0.526573i | \(0.823477\pi\) | |||||||
\(524\) | −4.41826 | −0.193013 | ||||||||
\(525\) | 45.0040 | 1.96414 | ||||||||
\(526\) | 22.0673 | 0.962180 | ||||||||
\(527\) | −45.1315 | −1.96596 | ||||||||
\(528\) | 2.99032 | 0.130137 | ||||||||
\(529\) | −7.09137 | −0.308321 | ||||||||
\(530\) | 38.0874 | 1.65441 | ||||||||
\(531\) | 3.83269 | 0.166324 | ||||||||
\(532\) | −5.19123 | −0.225068 | ||||||||
\(533\) | 1.29895 | 0.0562639 | ||||||||
\(534\) | 0.220099 | 0.00952461 | ||||||||
\(535\) | 31.0585 | 1.34278 | ||||||||
\(536\) | −1.76088 | −0.0760582 | ||||||||
\(537\) | −7.52216 | −0.324605 | ||||||||
\(538\) | −10.9730 | −0.473082 | ||||||||
\(539\) | −12.1443 | −0.523092 | ||||||||
\(540\) | −4.30484 | −0.185251 | ||||||||
\(541\) | −8.71614 | −0.374736 | −0.187368 | − | 0.982290i | \(-0.559996\pi\) | ||||
−0.187368 | + | 0.982290i | \(0.559996\pi\) | |||||||
\(542\) | 18.4643 | 0.793110 | ||||||||
\(543\) | −2.55602 | −0.109689 | ||||||||
\(544\) | −7.37298 | −0.316114 | ||||||||
\(545\) | −19.3035 | −0.826871 | ||||||||
\(546\) | 3.32584 | 0.142333 | ||||||||
\(547\) | −5.82757 | −0.249169 | −0.124584 | − | 0.992209i | \(-0.539760\pi\) | ||||
−0.124584 | + | 0.992209i | \(0.539760\pi\) | |||||||
\(548\) | 1.04246 | 0.0445318 | ||||||||
\(549\) | 4.47557 | 0.191013 | ||||||||
\(550\) | 40.4639 | 1.72539 | ||||||||
\(551\) | −7.97092 | −0.339573 | ||||||||
\(552\) | −3.98856 | −0.169764 | ||||||||
\(553\) | −41.3506 | −1.75841 | ||||||||
\(554\) | 14.5293 | 0.617293 | ||||||||
\(555\) | 22.4622 | 0.953468 | ||||||||
\(556\) | 2.48271 | 0.105290 | ||||||||
\(557\) | 27.4278 | 1.16215 | 0.581077 | − | 0.813848i | \(-0.302631\pi\) | ||||
0.581077 | + | 0.813848i | \(0.302631\pi\) | |||||||
\(558\) | 6.12120 | 0.259131 | ||||||||
\(559\) | 2.11927 | 0.0896354 | ||||||||
\(560\) | −14.3172 | −0.605012 | ||||||||
\(561\) | 22.0476 | 0.930850 | ||||||||
\(562\) | 15.7883 | 0.665991 | ||||||||
\(563\) | 14.8220 | 0.624674 | 0.312337 | − | 0.949971i | \(-0.398888\pi\) | ||||
0.312337 | + | 0.949971i | \(0.398888\pi\) | |||||||
\(564\) | −10.0352 | −0.422559 | ||||||||
\(565\) | −59.0402 | −2.48384 | ||||||||
\(566\) | −18.1693 | −0.763712 | ||||||||
\(567\) | −3.32584 | −0.139672 | ||||||||
\(568\) | 10.4599 | 0.438889 | ||||||||
\(569\) | 19.0046 | 0.796714 | 0.398357 | − | 0.917230i | \(-0.369581\pi\) | ||||
0.398357 | + | 0.917230i | \(0.369581\pi\) | |||||||
\(570\) | 6.71933 | 0.281442 | ||||||||
\(571\) | −4.68766 | −0.196173 | −0.0980863 | − | 0.995178i | \(-0.531272\pi\) | ||||
−0.0980863 | + | 0.995178i | \(0.531272\pi\) | |||||||
\(572\) | 2.99032 | 0.125032 | ||||||||
\(573\) | 8.59420 | 0.359028 | ||||||||
\(574\) | −4.32011 | −0.180318 | ||||||||
\(575\) | −53.9717 | −2.25078 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −34.3823 | −1.43135 | −0.715676 | − | 0.698433i | \(-0.753881\pi\) | ||||
−0.715676 | + | 0.698433i | \(0.753881\pi\) | |||||||
\(578\) | −37.3608 | −1.55400 | ||||||||
\(579\) | −12.7715 | −0.530765 | ||||||||
\(580\) | −21.9835 | −0.912814 | ||||||||
\(581\) | 24.2667 | 1.00675 | ||||||||
\(582\) | −10.6956 | −0.443346 | ||||||||
\(583\) | 26.4571 | 1.09574 | ||||||||
\(584\) | −9.29221 | −0.384514 | ||||||||
\(585\) | −4.30484 | −0.177983 | ||||||||
\(586\) | 3.82927 | 0.158185 | ||||||||
\(587\) | −35.2121 | −1.45336 | −0.726680 | − | 0.686976i | \(-0.758938\pi\) | ||||
−0.726680 | + | 0.686976i | \(0.758938\pi\) | |||||||
\(588\) | −4.06120 | −0.167481 | ||||||||
\(589\) | −9.55445 | −0.393684 | ||||||||
\(590\) | −16.4991 | −0.679257 | ||||||||
\(591\) | 5.83763 | 0.240128 | ||||||||
\(592\) | −5.21790 | −0.214454 | ||||||||
\(593\) | 10.1964 | 0.418717 | 0.209358 | − | 0.977839i | \(-0.432862\pi\) | ||||
0.209358 | + | 0.977839i | \(0.432862\pi\) | |||||||
\(594\) | −2.99032 | −0.122694 | ||||||||
\(595\) | −105.560 | −4.32755 | ||||||||
\(596\) | 11.6489 | 0.477158 | ||||||||
\(597\) | −7.01930 | −0.287281 | ||||||||
\(598\) | −3.98856 | −0.163104 | ||||||||
\(599\) | −10.1752 | −0.415746 | −0.207873 | − | 0.978156i | \(-0.566654\pi\) | ||||
−0.207873 | + | 0.978156i | \(0.566654\pi\) | |||||||
\(600\) | 13.5316 | 0.552426 | ||||||||
\(601\) | −32.2687 | −1.31627 | −0.658133 | − | 0.752902i | \(-0.728654\pi\) | ||||
−0.658133 | + | 0.752902i | \(0.728654\pi\) | |||||||
\(602\) | −7.04834 | −0.287269 | ||||||||
\(603\) | 1.76088 | 0.0717084 | ||||||||
\(604\) | −9.39427 | −0.382247 | ||||||||
\(605\) | −8.85920 | −0.360178 | ||||||||
\(606\) | −19.7975 | −0.804217 | ||||||||
\(607\) | 21.8134 | 0.885380 | 0.442690 | − | 0.896675i | \(-0.354024\pi\) | ||||
0.442690 | + | 0.896675i | \(0.354024\pi\) | |||||||
\(608\) | −1.56088 | −0.0633020 | ||||||||
\(609\) | −16.9840 | −0.688227 | ||||||||
\(610\) | −19.2666 | −0.780083 | ||||||||
\(611\) | −10.0352 | −0.405981 | ||||||||
\(612\) | 7.37298 | 0.298035 | ||||||||
\(613\) | 12.3559 | 0.499049 | 0.249524 | − | 0.968369i | \(-0.419726\pi\) | ||||
0.249524 | + | 0.968369i | \(0.419726\pi\) | |||||||
\(614\) | 16.8905 | 0.681645 | ||||||||
\(615\) | 5.59179 | 0.225483 | ||||||||
\(616\) | −9.94533 | −0.400709 | ||||||||
\(617\) | 39.8625 | 1.60480 | 0.802401 | − | 0.596785i | \(-0.203556\pi\) | ||||
0.802401 | + | 0.596785i | \(0.203556\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | 24.8162 | 0.997448 | 0.498724 | − | 0.866761i | \(-0.333802\pi\) | ||||
0.498724 | + | 0.866761i | \(0.333802\pi\) | |||||||
\(620\) | −26.3508 | −1.05827 | ||||||||
\(621\) | 3.98856 | 0.160055 | ||||||||
\(622\) | −2.23173 | −0.0894840 | ||||||||
\(623\) | −0.732014 | −0.0293275 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | 90.4468 | 3.61787 | ||||||||
\(626\) | 5.72536 | 0.228831 | ||||||||
\(627\) | 4.66753 | 0.186403 | ||||||||
\(628\) | 7.98927 | 0.318806 | ||||||||
\(629\) | −38.4715 | −1.53396 | ||||||||
\(630\) | 14.3172 | 0.570411 | ||||||||
\(631\) | −33.5627 | −1.33611 | −0.668055 | − | 0.744112i | \(-0.732873\pi\) | ||||
−0.668055 | + | 0.744112i | \(0.732873\pi\) | |||||||
\(632\) | −12.4331 | −0.494563 | ||||||||
\(633\) | 26.6852 | 1.06064 | ||||||||
\(634\) | −4.04068 | −0.160476 | ||||||||
\(635\) | 29.6318 | 1.17590 | ||||||||
\(636\) | 8.84758 | 0.350829 | ||||||||
\(637\) | −4.06120 | −0.160911 | ||||||||
\(638\) | −15.2707 | −0.604571 | ||||||||
\(639\) | −10.4599 | −0.413788 | ||||||||
\(640\) | −4.30484 | −0.170164 | ||||||||
\(641\) | −28.5203 | −1.12649 | −0.563243 | − | 0.826291i | \(-0.690447\pi\) | ||||
−0.563243 | + | 0.826291i | \(0.690447\pi\) | |||||||
\(642\) | 7.21479 | 0.284745 | ||||||||
\(643\) | 30.9929 | 1.22224 | 0.611120 | − | 0.791538i | \(-0.290719\pi\) | ||||
0.611120 | + | 0.791538i | \(0.290719\pi\) | |||||||
\(644\) | 13.2653 | 0.522726 | ||||||||
\(645\) | 9.12310 | 0.359222 | ||||||||
\(646\) | −11.5083 | −0.452789 | ||||||||
\(647\) | −8.18516 | −0.321792 | −0.160896 | − | 0.986971i | \(-0.551438\pi\) | ||||
−0.160896 | + | 0.986971i | \(0.551438\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −11.4610 | −0.449883 | ||||||||
\(650\) | 13.5316 | 0.530754 | ||||||||
\(651\) | −20.3581 | −0.797898 | ||||||||
\(652\) | −22.6367 | −0.886522 | ||||||||
\(653\) | −21.0639 | −0.824294 | −0.412147 | − | 0.911117i | \(-0.635221\pi\) | ||||
−0.412147 | + | 0.911117i | \(0.635221\pi\) | |||||||
\(654\) | −4.48414 | −0.175344 | ||||||||
\(655\) | −19.0199 | −0.743169 | ||||||||
\(656\) | −1.29895 | −0.0507156 | ||||||||
\(657\) | 9.29221 | 0.362524 | ||||||||
\(658\) | 33.3755 | 1.30111 | ||||||||
\(659\) | 42.0600 | 1.63842 | 0.819212 | − | 0.573490i | \(-0.194411\pi\) | ||||
0.819212 | + | 0.573490i | \(0.194411\pi\) | |||||||
\(660\) | 12.8729 | 0.501075 | ||||||||
\(661\) | −13.7964 | −0.536619 | −0.268310 | − | 0.963333i | \(-0.586465\pi\) | ||||
−0.268310 | + | 0.963333i | \(0.586465\pi\) | |||||||
\(662\) | −11.2057 | −0.435523 | ||||||||
\(663\) | 7.37298 | 0.286343 | ||||||||
\(664\) | 7.29642 | 0.283156 | ||||||||
\(665\) | −22.3474 | −0.866595 | ||||||||
\(666\) | 5.21790 | 0.202190 | ||||||||
\(667\) | 20.3684 | 0.788666 | ||||||||
\(668\) | −10.0191 | −0.387649 | ||||||||
\(669\) | 18.5806 | 0.718368 | ||||||||
\(670\) | −7.58028 | −0.292852 | ||||||||
\(671\) | −13.3834 | −0.516661 | ||||||||
\(672\) | −3.32584 | −0.128297 | ||||||||
\(673\) | −14.6214 | −0.563615 | −0.281807 | − | 0.959471i | \(-0.590934\pi\) | ||||
−0.281807 | + | 0.959471i | \(0.590934\pi\) | |||||||
\(674\) | 15.9410 | 0.614026 | ||||||||
\(675\) | −13.5316 | −0.520833 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −6.64862 | −0.255527 | −0.127764 | − | 0.991805i | \(-0.540780\pi\) | ||||
−0.127764 | + | 0.991805i | \(0.540780\pi\) | |||||||
\(678\) | −13.7149 | −0.526716 | ||||||||
\(679\) | 35.5717 | 1.36512 | ||||||||
\(680\) | −31.7395 | −1.21715 | ||||||||
\(681\) | −1.22947 | −0.0471135 | ||||||||
\(682\) | −18.3044 | −0.700911 | ||||||||
\(683\) | 42.8630 | 1.64011 | 0.820053 | − | 0.572288i | \(-0.193944\pi\) | ||||
0.820053 | + | 0.572288i | \(0.193944\pi\) | |||||||
\(684\) | 1.56088 | 0.0596817 | ||||||||
\(685\) | 4.48764 | 0.171464 | ||||||||
\(686\) | −9.77398 | −0.373172 | ||||||||
\(687\) | −22.9718 | −0.876427 | ||||||||
\(688\) | −2.11927 | −0.0807963 | ||||||||
\(689\) | 8.84758 | 0.337066 | ||||||||
\(690\) | −17.1701 | −0.653655 | ||||||||
\(691\) | 17.9411 | 0.682511 | 0.341256 | − | 0.939971i | \(-0.389148\pi\) | ||||
0.341256 | + | 0.939971i | \(0.389148\pi\) | |||||||
\(692\) | −6.74785 | −0.256515 | ||||||||
\(693\) | 9.94533 | 0.377792 | ||||||||
\(694\) | −24.4975 | −0.929913 | ||||||||
\(695\) | 10.6877 | 0.405406 | ||||||||
\(696\) | −5.10669 | −0.193569 | ||||||||
\(697\) | −9.57716 | −0.362761 | ||||||||
\(698\) | 4.60506 | 0.174304 | ||||||||
\(699\) | 0.967978 | 0.0366123 | ||||||||
\(700\) | −45.0040 | −1.70099 | ||||||||
\(701\) | 37.7810 | 1.42697 | 0.713485 | − | 0.700671i | \(-0.247116\pi\) | ||||
0.713485 | + | 0.700671i | \(0.247116\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | −8.14451 | −0.307176 | ||||||||
\(704\) | −2.99032 | −0.112702 | ||||||||
\(705\) | −43.2000 | −1.62700 | ||||||||
\(706\) | −7.92700 | −0.298337 | ||||||||
\(707\) | 65.8432 | 2.47629 | ||||||||
\(708\) | −3.83269 | −0.144041 | ||||||||
\(709\) | −20.9024 | −0.785007 | −0.392504 | − | 0.919750i | \(-0.628391\pi\) | ||||
−0.392504 | + | 0.919750i | \(0.628391\pi\) | |||||||
\(710\) | 45.0283 | 1.68988 | ||||||||
\(711\) | 12.4331 | 0.466279 | ||||||||
\(712\) | −0.220099 | −0.00824856 | ||||||||
\(713\) | 24.4148 | 0.914341 | ||||||||
\(714\) | −24.5213 | −0.917688 | ||||||||
\(715\) | 12.8729 | 0.481418 | ||||||||
\(716\) | 7.52216 | 0.281116 | ||||||||
\(717\) | 23.9676 | 0.895085 | ||||||||
\(718\) | 16.5493 | 0.617614 | ||||||||
\(719\) | 25.2877 | 0.943071 | 0.471536 | − | 0.881847i | \(-0.343700\pi\) | ||||
0.471536 | + | 0.881847i | \(0.343700\pi\) | |||||||
\(720\) | 4.30484 | 0.160432 | ||||||||
\(721\) | 3.32584 | 0.123861 | ||||||||
\(722\) | 16.5637 | 0.616436 | ||||||||
\(723\) | 22.4990 | 0.836748 | ||||||||
\(724\) | 2.55602 | 0.0949936 | ||||||||
\(725\) | −69.1018 | −2.56638 | ||||||||
\(726\) | −2.05796 | −0.0763782 | ||||||||
\(727\) | 27.9994 | 1.03844 | 0.519220 | − | 0.854641i | \(-0.326223\pi\) | ||||
0.519220 | + | 0.854641i | \(0.326223\pi\) | |||||||
\(728\) | −3.32584 | −0.123264 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −40.0014 | −1.48052 | ||||||||
\(731\) | −15.6253 | −0.577923 | ||||||||
\(732\) | −4.47557 | −0.165422 | ||||||||
\(733\) | −47.3618 | −1.74935 | −0.874674 | − | 0.484712i | \(-0.838924\pi\) | ||||
−0.874674 | + | 0.484712i | \(0.838924\pi\) | |||||||
\(734\) | −2.43300 | −0.0898038 | ||||||||
\(735\) | −17.4828 | −0.644863 | ||||||||
\(736\) | 3.98856 | 0.147020 | ||||||||
\(737\) | −5.26559 | −0.193960 | ||||||||
\(738\) | 1.29895 | 0.0478152 | ||||||||
\(739\) | −13.5407 | −0.498103 | −0.249051 | − | 0.968490i | \(-0.580119\pi\) | ||||
−0.249051 | + | 0.968490i | \(0.580119\pi\) | |||||||
\(740\) | −22.4622 | −0.825728 | ||||||||
\(741\) | 1.56088 | 0.0573403 | ||||||||
\(742\) | −29.4256 | −1.08025 | ||||||||
\(743\) | −23.4603 | −0.860676 | −0.430338 | − | 0.902668i | \(-0.641606\pi\) | ||||
−0.430338 | + | 0.902668i | \(0.641606\pi\) | |||||||
\(744\) | −6.12120 | −0.224414 | ||||||||
\(745\) | 50.1467 | 1.83723 | ||||||||
\(746\) | −18.4891 | −0.676935 | ||||||||
\(747\) | −7.29642 | −0.266962 | ||||||||
\(748\) | −22.0476 | −0.806140 | ||||||||
\(749\) | −23.9952 | −0.876767 | ||||||||
\(750\) | 36.7273 | 1.34109 | ||||||||
\(751\) | −21.3600 | −0.779436 | −0.389718 | − | 0.920934i | \(-0.627428\pi\) | ||||
−0.389718 | + | 0.920934i | \(0.627428\pi\) | |||||||
\(752\) | 10.0352 | 0.365947 | ||||||||
\(753\) | −25.7307 | −0.937680 | ||||||||
\(754\) | −5.10669 | −0.185975 | ||||||||
\(755\) | −40.4408 | −1.47179 | ||||||||
\(756\) | 3.32584 | 0.120960 | ||||||||
\(757\) | −23.0970 | −0.839475 | −0.419737 | − | 0.907646i | \(-0.637878\pi\) | ||||
−0.419737 | + | 0.907646i | \(0.637878\pi\) | |||||||
\(758\) | −8.19688 | −0.297724 | ||||||||
\(759\) | −11.9271 | −0.432926 | ||||||||
\(760\) | −6.71933 | −0.243736 | ||||||||
\(761\) | −36.3536 | −1.31782 | −0.658909 | − | 0.752222i | \(-0.728982\pi\) | ||||
−0.658909 | + | 0.752222i | \(0.728982\pi\) | |||||||
\(762\) | 6.88336 | 0.249358 | ||||||||
\(763\) | 14.9135 | 0.539906 | ||||||||
\(764\) | −8.59420 | −0.310927 | ||||||||
\(765\) | 31.7395 | 1.14754 | ||||||||
\(766\) | −1.76663 | −0.0638308 | ||||||||
\(767\) | −3.83269 | −0.138390 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 30.5206 | 1.10060 | 0.550301 | − | 0.834966i | \(-0.314513\pi\) | ||||
0.550301 | + | 0.834966i | \(0.314513\pi\) | |||||||
\(770\) | −42.8130 | −1.54287 | ||||||||
\(771\) | −20.1726 | −0.726497 | ||||||||
\(772\) | 12.7715 | 0.459656 | ||||||||
\(773\) | −36.6077 | −1.31669 | −0.658344 | − | 0.752717i | \(-0.728743\pi\) | ||||
−0.658344 | + | 0.752717i | \(0.728743\pi\) | |||||||
\(774\) | 2.11927 | 0.0761754 | ||||||||
\(775\) | −82.8298 | −2.97533 | ||||||||
\(776\) | 10.6956 | 0.383949 | ||||||||
\(777\) | −17.3539 | −0.622568 | ||||||||
\(778\) | 13.1999 | 0.473238 | ||||||||
\(779\) | −2.02751 | −0.0726431 | ||||||||
\(780\) | 4.30484 | 0.154138 | ||||||||
\(781\) | 31.2786 | 1.11923 | ||||||||
\(782\) | 29.4076 | 1.05161 | ||||||||
\(783\) | 5.10669 | 0.182498 | ||||||||
\(784\) | 4.06120 | 0.145043 | ||||||||
\(785\) | 34.3925 | 1.22752 | ||||||||
\(786\) | −4.41826 | −0.157594 | ||||||||
\(787\) | 1.66558 | 0.0593714 | 0.0296857 | − | 0.999559i | \(-0.490549\pi\) | ||||
0.0296857 | + | 0.999559i | \(0.490549\pi\) | |||||||
\(788\) | −5.83763 | −0.207957 | ||||||||
\(789\) | 22.0673 | 0.785616 | ||||||||
\(790\) | −53.5226 | −1.90425 | ||||||||
\(791\) | 45.6134 | 1.62182 | ||||||||
\(792\) | 2.99032 | 0.106257 | ||||||||
\(793\) | −4.47557 | −0.158932 | ||||||||
\(794\) | −7.07627 | −0.251128 | ||||||||
\(795\) | 38.0874 | 1.35082 | ||||||||
\(796\) | 7.01930 | 0.248792 | ||||||||
\(797\) | 42.0267 | 1.48866 | 0.744331 | − | 0.667811i | \(-0.232768\pi\) | ||||
0.744331 | + | 0.667811i | \(0.232768\pi\) | |||||||
\(798\) | −5.19123 | −0.183768 | ||||||||
\(799\) | 73.9894 | 2.61756 | ||||||||
\(800\) | −13.5316 | −0.478415 | ||||||||
\(801\) | 0.220099 | 0.00777682 | ||||||||
\(802\) | −33.5184 | −1.18358 | ||||||||
\(803\) | −27.7867 | −0.980572 | ||||||||
\(804\) | −1.76088 | −0.0621013 | ||||||||
\(805\) | 57.1050 | 2.01269 | ||||||||
\(806\) | −6.12120 | −0.215610 | ||||||||
\(807\) | −10.9730 | −0.386270 | ||||||||
\(808\) | 19.7975 | 0.696473 | ||||||||
\(809\) | 38.2429 | 1.34455 | 0.672275 | − | 0.740302i | \(-0.265317\pi\) | ||||
0.672275 | + | 0.740302i | \(0.265317\pi\) | |||||||
\(810\) | −4.30484 | −0.151257 | ||||||||
\(811\) | −10.4223 | −0.365978 | −0.182989 | − | 0.983115i | \(-0.558577\pi\) | ||||
−0.182989 | + | 0.983115i | \(0.558577\pi\) | |||||||
\(812\) | 16.9840 | 0.596022 | ||||||||
\(813\) | 18.4643 | 0.647572 | ||||||||
\(814\) | −15.6032 | −0.546892 | ||||||||
\(815\) | −97.4474 | −3.41343 | ||||||||
\(816\) | −7.37298 | −0.258106 | ||||||||
\(817\) | −3.30792 | −0.115729 | ||||||||
\(818\) | 26.8161 | 0.937603 | ||||||||
\(819\) | 3.32584 | 0.116214 | ||||||||
\(820\) | −5.59179 | −0.195274 | ||||||||
\(821\) | 14.6432 | 0.511052 | 0.255526 | − | 0.966802i | \(-0.417751\pi\) | ||||
0.255526 | + | 0.966802i | \(0.417751\pi\) | |||||||
\(822\) | 1.04246 | 0.0363601 | ||||||||
\(823\) | −27.0111 | −0.941547 | −0.470774 | − | 0.882254i | \(-0.656025\pi\) | ||||
−0.470774 | + | 0.882254i | \(0.656025\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | 40.4639 | 1.40877 | ||||||||
\(826\) | 12.7469 | 0.443521 | ||||||||
\(827\) | 8.35498 | 0.290531 | 0.145266 | − | 0.989393i | \(-0.453596\pi\) | ||||
0.145266 | + | 0.989393i | \(0.453596\pi\) | |||||||
\(828\) | −3.98856 | −0.138612 | ||||||||
\(829\) | −32.0899 | −1.11453 | −0.557264 | − | 0.830335i | \(-0.688149\pi\) | ||||
−0.557264 | + | 0.830335i | \(0.688149\pi\) | |||||||
\(830\) | 31.4099 | 1.09025 | ||||||||
\(831\) | 14.5293 | 0.504017 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 29.9431 | 1.03747 | ||||||||
\(834\) | 2.48271 | 0.0859692 | ||||||||
\(835\) | −43.1304 | −1.49259 | ||||||||
\(836\) | −4.66753 | −0.161430 | ||||||||
\(837\) | 6.12120 | 0.211580 | ||||||||
\(838\) | 29.2983 | 1.01209 | ||||||||
\(839\) | −25.5252 | −0.881229 | −0.440615 | − | 0.897696i | \(-0.645239\pi\) | ||||
−0.440615 | + | 0.897696i | \(0.645239\pi\) | |||||||
\(840\) | −14.3172 | −0.493990 | ||||||||
\(841\) | −2.92171 | −0.100749 | ||||||||
\(842\) | 34.2832 | 1.18148 | ||||||||
\(843\) | 15.7883 | 0.543780 | ||||||||
\(844\) | −26.6852 | −0.918543 | ||||||||
\(845\) | 4.30484 | 0.148091 | ||||||||
\(846\) | −10.0352 | −0.345018 | ||||||||
\(847\) | 6.84446 | 0.235178 | ||||||||
\(848\) | −8.84758 | −0.303827 | ||||||||
\(849\) | −18.1693 | −0.623568 | ||||||||
\(850\) | −99.7684 | −3.42203 | ||||||||
\(851\) | 20.8119 | 0.713424 | ||||||||
\(852\) | 10.4599 | 0.358351 | ||||||||
\(853\) | −39.7735 | −1.36182 | −0.680910 | − | 0.732367i | \(-0.738416\pi\) | ||||
−0.680910 | + | 0.732367i | \(0.738416\pi\) | |||||||
\(854\) | 14.8850 | 0.509355 | ||||||||
\(855\) | 6.71933 | 0.229796 | ||||||||
\(856\) | −7.21479 | −0.246597 | ||||||||
\(857\) | −20.8272 | −0.711445 | −0.355723 | − | 0.934592i | \(-0.615765\pi\) | ||||
−0.355723 | + | 0.934592i | \(0.615765\pi\) | |||||||
\(858\) | 2.99032 | 0.102088 | ||||||||
\(859\) | 28.1578 | 0.960733 | 0.480367 | − | 0.877068i | \(-0.340504\pi\) | ||||
0.480367 | + | 0.877068i | \(0.340504\pi\) | |||||||
\(860\) | −9.12310 | −0.311095 | ||||||||
\(861\) | −4.32011 | −0.147229 | ||||||||
\(862\) | −7.96742 | −0.271371 | ||||||||
\(863\) | 34.1892 | 1.16382 | 0.581908 | − | 0.813255i | \(-0.302307\pi\) | ||||
0.581908 | + | 0.813255i | \(0.302307\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −29.0484 | −0.987675 | ||||||||
\(866\) | −4.95655 | −0.168430 | ||||||||
\(867\) | −37.3608 | −1.26884 | ||||||||
\(868\) | 20.3581 | 0.691000 | ||||||||
\(869\) | −37.1791 | −1.26121 | ||||||||
\(870\) | −21.9835 | −0.745310 | ||||||||
\(871\) | −1.76088 | −0.0596650 | ||||||||
\(872\) | 4.48414 | 0.151852 | ||||||||
\(873\) | −10.6956 | −0.361990 | ||||||||
\(874\) | 6.22566 | 0.210586 | ||||||||
\(875\) | −122.149 | −4.12939 | ||||||||
\(876\) | −9.29221 | −0.313955 | ||||||||
\(877\) | −22.8923 | −0.773017 | −0.386509 | − | 0.922286i | \(-0.626319\pi\) | ||||
−0.386509 | + | 0.922286i | \(0.626319\pi\) | |||||||
\(878\) | 31.5089 | 1.06337 | ||||||||
\(879\) | 3.82927 | 0.129158 | ||||||||
\(880\) | −12.8729 | −0.433944 | ||||||||
\(881\) | −41.5807 | −1.40089 | −0.700444 | − | 0.713707i | \(-0.747015\pi\) | ||||
−0.700444 | + | 0.713707i | \(0.747015\pi\) | |||||||
\(882\) | −4.06120 | −0.136748 | ||||||||
\(883\) | 8.47194 | 0.285103 | 0.142552 | − | 0.989787i | \(-0.454469\pi\) | ||||
0.142552 | + | 0.989787i | \(0.454469\pi\) | |||||||
\(884\) | −7.37298 | −0.247980 | ||||||||
\(885\) | −16.4991 | −0.554611 | ||||||||
\(886\) | −31.4030 | −1.05500 | ||||||||
\(887\) | 28.3749 | 0.952735 | 0.476368 | − | 0.879246i | \(-0.341953\pi\) | ||||
0.476368 | + | 0.879246i | \(0.341953\pi\) | |||||||
\(888\) | −5.21790 | −0.175101 | ||||||||
\(889\) | −22.8929 | −0.767805 | ||||||||
\(890\) | −0.947490 | −0.0317599 | ||||||||
\(891\) | −2.99032 | −0.100180 | ||||||||
\(892\) | −18.5806 | −0.622125 | ||||||||
\(893\) | 15.6638 | 0.524167 | ||||||||
\(894\) | 11.6489 | 0.389598 | ||||||||
\(895\) | 32.3817 | 1.08240 | ||||||||
\(896\) | 3.32584 | 0.111108 | ||||||||
\(897\) | −3.98856 | −0.133174 | ||||||||
\(898\) | 28.1392 | 0.939016 | ||||||||
\(899\) | 31.2591 | 1.04255 | ||||||||
\(900\) | 13.5316 | 0.451054 | ||||||||
\(901\) | −65.2330 | −2.17323 | ||||||||
\(902\) | −3.88429 | −0.129333 | ||||||||
\(903\) | −7.04834 | −0.234554 | ||||||||
\(904\) | 13.7149 | 0.456149 | ||||||||
\(905\) | 11.0032 | 0.365760 | ||||||||
\(906\) | −9.39427 | −0.312104 | ||||||||
\(907\) | −7.70609 | −0.255877 | −0.127938 | − | 0.991782i | \(-0.540836\pi\) | ||||
−0.127938 | + | 0.991782i | \(0.540836\pi\) | |||||||
\(908\) | 1.22947 | 0.0408015 | ||||||||
\(909\) | −19.7975 | −0.656641 | ||||||||
\(910\) | −14.3172 | −0.474610 | ||||||||
\(911\) | −38.2938 | −1.26873 | −0.634364 | − | 0.773034i | \(-0.718738\pi\) | ||||
−0.634364 | + | 0.773034i | \(0.718738\pi\) | |||||||
\(912\) | −1.56088 | −0.0516859 | ||||||||
\(913\) | 21.8187 | 0.722092 | ||||||||
\(914\) | −27.3601 | −0.904991 | ||||||||
\(915\) | −19.2666 | −0.636935 | ||||||||
\(916\) | 22.9718 | 0.759008 | ||||||||
\(917\) | 14.6944 | 0.485253 | ||||||||
\(918\) | 7.37298 | 0.243345 | ||||||||
\(919\) | 12.2865 | 0.405294 | 0.202647 | − | 0.979252i | \(-0.435046\pi\) | ||||
0.202647 | + | 0.979252i | \(0.435046\pi\) | |||||||
\(920\) | 17.1701 | 0.566082 | ||||||||
\(921\) | 16.8905 | 0.556561 | ||||||||
\(922\) | 14.1704 | 0.466679 | ||||||||
\(923\) | 10.4599 | 0.344293 | ||||||||
\(924\) | −9.94533 | −0.327177 | ||||||||
\(925\) | −70.6067 | −2.32153 | ||||||||
\(926\) | 42.2795 | 1.38939 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 5.10669 | 0.167635 | ||||||||
\(929\) | −16.9963 | −0.557629 | −0.278815 | − | 0.960345i | \(-0.589942\pi\) | ||||
−0.278815 | + | 0.960345i | \(0.589942\pi\) | |||||||
\(930\) | −26.3508 | −0.864076 | ||||||||
\(931\) | 6.33904 | 0.207754 | ||||||||
\(932\) | −0.967978 | −0.0317072 | ||||||||
\(933\) | −2.23173 | −0.0730634 | ||||||||
\(934\) | 2.38852 | 0.0781548 | ||||||||
\(935\) | −94.9113 | −3.10393 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | −48.7121 | −1.59135 | −0.795677 | − | 0.605721i | \(-0.792885\pi\) | ||||
−0.795677 | + | 0.605721i | \(0.792885\pi\) | |||||||
\(938\) | 5.85639 | 0.191218 | ||||||||
\(939\) | 5.72536 | 0.186840 | ||||||||
\(940\) | 43.2000 | 1.40903 | ||||||||
\(941\) | −55.2320 | −1.80051 | −0.900255 | − | 0.435362i | \(-0.856620\pi\) | ||||
−0.900255 | + | 0.435362i | \(0.856620\pi\) | |||||||
\(942\) | 7.98927 | 0.260304 | ||||||||
\(943\) | 5.18096 | 0.168715 | ||||||||
\(944\) | 3.83269 | 0.124743 | ||||||||
\(945\) | 14.3172 | 0.465738 | ||||||||
\(946\) | −6.33729 | −0.206043 | ||||||||
\(947\) | 54.4116 | 1.76814 | 0.884070 | − | 0.467354i | \(-0.154793\pi\) | ||||
0.884070 | + | 0.467354i | \(0.154793\pi\) | |||||||
\(948\) | −12.4331 | −0.403809 | ||||||||
\(949\) | −9.29221 | −0.301638 | ||||||||
\(950\) | −21.1212 | −0.685263 | ||||||||
\(951\) | −4.04068 | −0.131028 | ||||||||
\(952\) | 24.5213 | 0.794741 | ||||||||
\(953\) | −40.6163 | −1.31569 | −0.657846 | − | 0.753153i | \(-0.728532\pi\) | ||||
−0.657846 | + | 0.753153i | \(0.728532\pi\) | |||||||
\(954\) | 8.84758 | 0.286451 | ||||||||
\(955\) | −36.9966 | −1.19718 | ||||||||
\(956\) | −23.9676 | −0.775166 | ||||||||
\(957\) | −15.2707 | −0.493630 | ||||||||
\(958\) | 31.2618 | 1.01002 | ||||||||
\(959\) | −3.46707 | −0.111957 | ||||||||
\(960\) | −4.30484 | −0.138938 | ||||||||
\(961\) | 6.46911 | 0.208681 | ||||||||
\(962\) | −5.21790 | −0.168232 | ||||||||
\(963\) | 7.21479 | 0.232494 | ||||||||
\(964\) | −22.4990 | −0.724645 | ||||||||
\(965\) | 54.9792 | 1.76984 | ||||||||
\(966\) | 13.2653 | 0.426804 | ||||||||
\(967\) | −16.5401 | −0.531894 | −0.265947 | − | 0.963988i | \(-0.585685\pi\) | ||||
−0.265947 | + | 0.963988i | \(0.585685\pi\) | |||||||
\(968\) | 2.05796 | 0.0661455 | ||||||||
\(969\) | −11.5083 | −0.369701 | ||||||||
\(970\) | 46.0427 | 1.47834 | ||||||||
\(971\) | −41.7009 | −1.33825 | −0.669123 | − | 0.743152i | \(-0.733330\pi\) | ||||
−0.669123 | + | 0.743152i | \(0.733330\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −8.25709 | −0.264710 | ||||||||
\(974\) | −9.37604 | −0.300428 | ||||||||
\(975\) | 13.5316 | 0.433359 | ||||||||
\(976\) | 4.47557 | 0.143260 | ||||||||
\(977\) | 4.78150 | 0.152974 | 0.0764868 | − | 0.997071i | \(-0.475630\pi\) | ||||
0.0764868 | + | 0.997071i | \(0.475630\pi\) | |||||||
\(978\) | −22.6367 | −0.723842 | ||||||||
\(979\) | −0.658167 | −0.0210351 | ||||||||
\(980\) | 17.4828 | 0.558468 | ||||||||
\(981\) | −4.48414 | −0.143168 | ||||||||
\(982\) | 27.2778 | 0.870470 | ||||||||
\(983\) | −40.8081 | −1.30158 | −0.650788 | − | 0.759260i | \(-0.725561\pi\) | ||||
−0.650788 | + | 0.759260i | \(0.725561\pi\) | |||||||
\(984\) | −1.29895 | −0.0414091 | ||||||||
\(985\) | −25.1300 | −0.800710 | ||||||||
\(986\) | 37.6515 | 1.19907 | ||||||||
\(987\) | 33.3755 | 1.06235 | ||||||||
\(988\) | −1.56088 | −0.0496582 | ||||||||
\(989\) | 8.45282 | 0.268784 | ||||||||
\(990\) | 12.8729 | 0.409126 | ||||||||
\(991\) | 58.8569 | 1.86965 | 0.934826 | − | 0.355106i | \(-0.115555\pi\) | ||||
0.934826 | + | 0.355106i | \(0.115555\pi\) | |||||||
\(992\) | 6.12120 | 0.194348 | ||||||||
\(993\) | −11.2057 | −0.355603 | ||||||||
\(994\) | −34.7880 | −1.10341 | ||||||||
\(995\) | 30.2169 | 0.957941 | ||||||||
\(996\) | 7.29642 | 0.231196 | ||||||||
\(997\) | −18.7423 | −0.593574 | −0.296787 | − | 0.954944i | \(-0.595915\pi\) | ||||
−0.296787 | + | 0.954944i | \(0.595915\pi\) | |||||||
\(998\) | 6.22981 | 0.197201 | ||||||||
\(999\) | 5.21790 | 0.165087 |
(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 | 8034.2.a.s.1.10 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.s.1.10 | ✓ | 10 | 1.1 | even | 1 | trivial |