Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8047,2,Mod(1,8047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8047, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8047 = 13 \cdot 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8047.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: | \(64.2556185065\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8047.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.618034 | −0.437016 | −0.218508 | − | 0.975835i | \(-0.570119\pi\) | ||||
−0.218508 | + | 0.975835i | \(0.570119\pi\) | |||||||
\(3\) | −0.381966 | −0.220528 | −0.110264 | − | 0.993902i | \(-0.535170\pi\) | ||||
−0.110264 | + | 0.993902i | \(0.535170\pi\) | |||||||
\(4\) | −1.61803 | −0.809017 | ||||||||
\(5\) | 3.23607 | 1.44721 | 0.723607 | − | 0.690212i | \(-0.242483\pi\) | ||||
0.723607 | + | 0.690212i | \(0.242483\pi\) | |||||||
\(6\) | 0.236068 | 0.0963743 | ||||||||
\(7\) | −2.61803 | −0.989524 | −0.494762 | − | 0.869029i | \(-0.664745\pi\) | ||||
−0.494762 | + | 0.869029i | \(0.664745\pi\) | |||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | −2.85410 | −0.951367 | ||||||||
\(10\) | −2.00000 | −0.632456 | ||||||||
\(11\) | 5.00000 | 1.50756 | 0.753778 | − | 0.657129i | \(-0.228229\pi\) | ||||
0.753778 | + | 0.657129i | \(0.228229\pi\) | |||||||
\(12\) | 0.618034 | 0.178411 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 1.61803 | 0.432438 | ||||||||
\(15\) | −1.23607 | −0.319151 | ||||||||
\(16\) | 1.85410 | 0.463525 | ||||||||
\(17\) | 4.23607 | 1.02740 | 0.513699 | − | 0.857971i | \(-0.328275\pi\) | ||||
0.513699 | + | 0.857971i | \(0.328275\pi\) | |||||||
\(18\) | 1.76393 | 0.415763 | ||||||||
\(19\) | −8.23607 | −1.88948 | −0.944742 | − | 0.327815i | \(-0.893688\pi\) | ||||
−0.944742 | + | 0.327815i | \(0.893688\pi\) | |||||||
\(20\) | −5.23607 | −1.17082 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −3.09017 | −0.658826 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | −0.854102 | −0.174343 | ||||||||
\(25\) | 5.47214 | 1.09443 | ||||||||
\(26\) | 0.618034 | 0.121206 | ||||||||
\(27\) | 2.23607 | 0.430331 | ||||||||
\(28\) | 4.23607 | 0.800542 | ||||||||
\(29\) | 7.23607 | 1.34370 | 0.671852 | − | 0.740685i | \(-0.265499\pi\) | ||||
0.671852 | + | 0.740685i | \(0.265499\pi\) | |||||||
\(30\) | 0.763932 | 0.139474 | ||||||||
\(31\) | −6.23607 | −1.12003 | −0.560015 | − | 0.828482i | \(-0.689205\pi\) | ||||
−0.560015 | + | 0.828482i | \(0.689205\pi\) | |||||||
\(32\) | −5.61803 | −0.993137 | ||||||||
\(33\) | −1.90983 | −0.332459 | ||||||||
\(34\) | −2.61803 | −0.448989 | ||||||||
\(35\) | −8.47214 | −1.43205 | ||||||||
\(36\) | 4.61803 | 0.769672 | ||||||||
\(37\) | −2.47214 | −0.406417 | −0.203208 | − | 0.979136i | \(-0.565137\pi\) | ||||
−0.203208 | + | 0.979136i | \(0.565137\pi\) | |||||||
\(38\) | 5.09017 | 0.825735 | ||||||||
\(39\) | 0.381966 | 0.0611635 | ||||||||
\(40\) | 7.23607 | 1.14412 | ||||||||
\(41\) | 4.23607 | 0.661563 | 0.330781 | − | 0.943707i | \(-0.392688\pi\) | ||||
0.330781 | + | 0.943707i | \(0.392688\pi\) | |||||||
\(42\) | −0.618034 | −0.0953647 | ||||||||
\(43\) | −9.23607 | −1.40849 | −0.704244 | − | 0.709958i | \(-0.748714\pi\) | ||||
−0.704244 | + | 0.709958i | \(0.748714\pi\) | |||||||
\(44\) | −8.09017 | −1.21964 | ||||||||
\(45\) | −9.23607 | −1.37683 | ||||||||
\(46\) | 2.47214 | 0.364497 | ||||||||
\(47\) | 5.14590 | 0.750606 | 0.375303 | − | 0.926902i | \(-0.377539\pi\) | ||||
0.375303 | + | 0.926902i | \(0.377539\pi\) | |||||||
\(48\) | −0.708204 | −0.102220 | ||||||||
\(49\) | −0.145898 | −0.0208426 | ||||||||
\(50\) | −3.38197 | −0.478282 | ||||||||
\(51\) | −1.61803 | −0.226570 | ||||||||
\(52\) | 1.61803 | 0.224381 | ||||||||
\(53\) | 5.70820 | 0.784082 | 0.392041 | − | 0.919948i | \(-0.371769\pi\) | ||||
0.392041 | + | 0.919948i | \(0.371769\pi\) | |||||||
\(54\) | −1.38197 | −0.188062 | ||||||||
\(55\) | 16.1803 | 2.18176 | ||||||||
\(56\) | −5.85410 | −0.782287 | ||||||||
\(57\) | 3.14590 | 0.416684 | ||||||||
\(58\) | −4.47214 | −0.587220 | ||||||||
\(59\) | 11.0902 | 1.44382 | 0.721909 | − | 0.691988i | \(-0.243265\pi\) | ||||
0.721909 | + | 0.691988i | \(0.243265\pi\) | |||||||
\(60\) | 2.00000 | 0.258199 | ||||||||
\(61\) | 11.9443 | 1.52931 | 0.764654 | − | 0.644441i | \(-0.222910\pi\) | ||||
0.764654 | + | 0.644441i | \(0.222910\pi\) | |||||||
\(62\) | 3.85410 | 0.489471 | ||||||||
\(63\) | 7.47214 | 0.941401 | ||||||||
\(64\) | −0.236068 | −0.0295085 | ||||||||
\(65\) | −3.23607 | −0.401385 | ||||||||
\(66\) | 1.18034 | 0.145290 | ||||||||
\(67\) | −6.70820 | −0.819538 | −0.409769 | − | 0.912189i | \(-0.634391\pi\) | ||||
−0.409769 | + | 0.912189i | \(0.634391\pi\) | |||||||
\(68\) | −6.85410 | −0.831182 | ||||||||
\(69\) | 1.52786 | 0.183933 | ||||||||
\(70\) | 5.23607 | 0.625830 | ||||||||
\(71\) | 9.18034 | 1.08951 | 0.544753 | − | 0.838597i | \(-0.316623\pi\) | ||||
0.544753 | + | 0.838597i | \(0.316623\pi\) | |||||||
\(72\) | −6.38197 | −0.752122 | ||||||||
\(73\) | 13.4164 | 1.57027 | 0.785136 | − | 0.619324i | \(-0.212593\pi\) | ||||
0.785136 | + | 0.619324i | \(0.212593\pi\) | |||||||
\(74\) | 1.52786 | 0.177611 | ||||||||
\(75\) | −2.09017 | −0.241352 | ||||||||
\(76\) | 13.3262 | 1.52862 | ||||||||
\(77\) | −13.0902 | −1.49176 | ||||||||
\(78\) | −0.236068 | −0.0267294 | ||||||||
\(79\) | −9.47214 | −1.06570 | −0.532849 | − | 0.846210i | \(-0.678879\pi\) | ||||
−0.532849 | + | 0.846210i | \(0.678879\pi\) | |||||||
\(80\) | 6.00000 | 0.670820 | ||||||||
\(81\) | 7.70820 | 0.856467 | ||||||||
\(82\) | −2.61803 | −0.289113 | ||||||||
\(83\) | −1.76393 | −0.193617 | −0.0968083 | − | 0.995303i | \(-0.530863\pi\) | ||||
−0.0968083 | + | 0.995303i | \(0.530863\pi\) | |||||||
\(84\) | −1.61803 | −0.176542 | ||||||||
\(85\) | 13.7082 | 1.48686 | ||||||||
\(86\) | 5.70820 | 0.615531 | ||||||||
\(87\) | −2.76393 | −0.296325 | ||||||||
\(88\) | 11.1803 | 1.19183 | ||||||||
\(89\) | 0.145898 | 0.0154652 | 0.00773258 | − | 0.999970i | \(-0.497539\pi\) | ||||
0.00773258 | + | 0.999970i | \(0.497539\pi\) | |||||||
\(90\) | 5.70820 | 0.601698 | ||||||||
\(91\) | 2.61803 | 0.274445 | ||||||||
\(92\) | 6.47214 | 0.674767 | ||||||||
\(93\) | 2.38197 | 0.246998 | ||||||||
\(94\) | −3.18034 | −0.328027 | ||||||||
\(95\) | −26.6525 | −2.73449 | ||||||||
\(96\) | 2.14590 | 0.219015 | ||||||||
\(97\) | 3.90983 | 0.396983 | 0.198492 | − | 0.980103i | \(-0.436396\pi\) | ||||
0.198492 | + | 0.980103i | \(0.436396\pi\) | |||||||
\(98\) | 0.0901699 | 0.00910854 | ||||||||
\(99\) | −14.2705 | −1.43424 | ||||||||
\(100\) | −8.85410 | −0.885410 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | −13.7984 | −1.35959 | −0.679797 | − | 0.733400i | \(-0.737932\pi\) | ||||
−0.679797 | + | 0.733400i | \(0.737932\pi\) | |||||||
\(104\) | −2.23607 | −0.219265 | ||||||||
\(105\) | 3.23607 | 0.315808 | ||||||||
\(106\) | −3.52786 | −0.342656 | ||||||||
\(107\) | −11.0000 | −1.06341 | −0.531705 | − | 0.846930i | \(-0.678449\pi\) | ||||
−0.531705 | + | 0.846930i | \(0.678449\pi\) | |||||||
\(108\) | −3.61803 | −0.348145 | ||||||||
\(109\) | −18.7082 | −1.79192 | −0.895960 | − | 0.444134i | \(-0.853511\pi\) | ||||
−0.895960 | + | 0.444134i | \(0.853511\pi\) | |||||||
\(110\) | −10.0000 | −0.953463 | ||||||||
\(111\) | 0.944272 | 0.0896263 | ||||||||
\(112\) | −4.85410 | −0.458670 | ||||||||
\(113\) | 6.09017 | 0.572915 | 0.286457 | − | 0.958093i | \(-0.407522\pi\) | ||||
0.286457 | + | 0.958093i | \(0.407522\pi\) | |||||||
\(114\) | −1.94427 | −0.182098 | ||||||||
\(115\) | −12.9443 | −1.20706 | ||||||||
\(116\) | −11.7082 | −1.08708 | ||||||||
\(117\) | 2.85410 | 0.263862 | ||||||||
\(118\) | −6.85410 | −0.630971 | ||||||||
\(119\) | −11.0902 | −1.01663 | ||||||||
\(120\) | −2.76393 | −0.252311 | ||||||||
\(121\) | 14.0000 | 1.27273 | ||||||||
\(122\) | −7.38197 | −0.668332 | ||||||||
\(123\) | −1.61803 | −0.145893 | ||||||||
\(124\) | 10.0902 | 0.906124 | ||||||||
\(125\) | 1.52786 | 0.136656 | ||||||||
\(126\) | −4.61803 | −0.411407 | ||||||||
\(127\) | 19.7984 | 1.75682 | 0.878411 | − | 0.477906i | \(-0.158604\pi\) | ||||
0.878411 | + | 0.477906i | \(0.158604\pi\) | |||||||
\(128\) | 11.3820 | 1.00603 | ||||||||
\(129\) | 3.52786 | 0.310611 | ||||||||
\(130\) | 2.00000 | 0.175412 | ||||||||
\(131\) | −16.4164 | −1.43431 | −0.717154 | − | 0.696915i | \(-0.754556\pi\) | ||||
−0.717154 | + | 0.696915i | \(0.754556\pi\) | |||||||
\(132\) | 3.09017 | 0.268965 | ||||||||
\(133\) | 21.5623 | 1.86969 | ||||||||
\(134\) | 4.14590 | 0.358151 | ||||||||
\(135\) | 7.23607 | 0.622782 | ||||||||
\(136\) | 9.47214 | 0.812229 | ||||||||
\(137\) | 13.7082 | 1.17117 | 0.585585 | − | 0.810611i | \(-0.300865\pi\) | ||||
0.585585 | + | 0.810611i | \(0.300865\pi\) | |||||||
\(138\) | −0.944272 | −0.0803818 | ||||||||
\(139\) | 3.23607 | 0.274480 | 0.137240 | − | 0.990538i | \(-0.456177\pi\) | ||||
0.137240 | + | 0.990538i | \(0.456177\pi\) | |||||||
\(140\) | 13.7082 | 1.15855 | ||||||||
\(141\) | −1.96556 | −0.165530 | ||||||||
\(142\) | −5.67376 | −0.476132 | ||||||||
\(143\) | −5.00000 | −0.418121 | ||||||||
\(144\) | −5.29180 | −0.440983 | ||||||||
\(145\) | 23.4164 | 1.94463 | ||||||||
\(146\) | −8.29180 | −0.686234 | ||||||||
\(147\) | 0.0557281 | 0.00459638 | ||||||||
\(148\) | 4.00000 | 0.328798 | ||||||||
\(149\) | −16.6180 | −1.36140 | −0.680701 | − | 0.732561i | \(-0.738325\pi\) | ||||
−0.680701 | + | 0.732561i | \(0.738325\pi\) | |||||||
\(150\) | 1.29180 | 0.105475 | ||||||||
\(151\) | 3.05573 | 0.248672 | 0.124336 | − | 0.992240i | \(-0.460320\pi\) | ||||
0.124336 | + | 0.992240i | \(0.460320\pi\) | |||||||
\(152\) | −18.4164 | −1.49377 | ||||||||
\(153\) | −12.0902 | −0.977432 | ||||||||
\(154\) | 8.09017 | 0.651924 | ||||||||
\(155\) | −20.1803 | −1.62092 | ||||||||
\(156\) | −0.618034 | −0.0494823 | ||||||||
\(157\) | −0.944272 | −0.0753611 | −0.0376806 | − | 0.999290i | \(-0.511997\pi\) | ||||
−0.0376806 | + | 0.999290i | \(0.511997\pi\) | |||||||
\(158\) | 5.85410 | 0.465727 | ||||||||
\(159\) | −2.18034 | −0.172912 | ||||||||
\(160\) | −18.1803 | −1.43728 | ||||||||
\(161\) | 10.4721 | 0.825320 | ||||||||
\(162\) | −4.76393 | −0.374290 | ||||||||
\(163\) | 0.708204 | 0.0554708 | 0.0277354 | − | 0.999615i | \(-0.491170\pi\) | ||||
0.0277354 | + | 0.999615i | \(0.491170\pi\) | |||||||
\(164\) | −6.85410 | −0.535215 | ||||||||
\(165\) | −6.18034 | −0.481139 | ||||||||
\(166\) | 1.09017 | 0.0846136 | ||||||||
\(167\) | 20.9443 | 1.62072 | 0.810358 | − | 0.585935i | \(-0.199273\pi\) | ||||
0.810358 | + | 0.585935i | \(0.199273\pi\) | |||||||
\(168\) | 2.23607 | 0.172516 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −8.47214 | −0.649783 | ||||||||
\(171\) | 23.5066 | 1.79759 | ||||||||
\(172\) | 14.9443 | 1.13949 | ||||||||
\(173\) | 3.29180 | 0.250271 | 0.125135 | − | 0.992140i | \(-0.460064\pi\) | ||||
0.125135 | + | 0.992140i | \(0.460064\pi\) | |||||||
\(174\) | 1.70820 | 0.129499 | ||||||||
\(175\) | −14.3262 | −1.08296 | ||||||||
\(176\) | 9.27051 | 0.698791 | ||||||||
\(177\) | −4.23607 | −0.318402 | ||||||||
\(178\) | −0.0901699 | −0.00675852 | ||||||||
\(179\) | 22.7082 | 1.69729 | 0.848645 | − | 0.528962i | \(-0.177419\pi\) | ||||
0.848645 | + | 0.528962i | \(0.177419\pi\) | |||||||
\(180\) | 14.9443 | 1.11388 | ||||||||
\(181\) | 18.2361 | 1.35548 | 0.677738 | − | 0.735303i | \(-0.262960\pi\) | ||||
0.677738 | + | 0.735303i | \(0.262960\pi\) | |||||||
\(182\) | −1.61803 | −0.119937 | ||||||||
\(183\) | −4.56231 | −0.337255 | ||||||||
\(184\) | −8.94427 | −0.659380 | ||||||||
\(185\) | −8.00000 | −0.588172 | ||||||||
\(186\) | −1.47214 | −0.107942 | ||||||||
\(187\) | 21.1803 | 1.54886 | ||||||||
\(188\) | −8.32624 | −0.607253 | ||||||||
\(189\) | −5.85410 | −0.425823 | ||||||||
\(190\) | 16.4721 | 1.19501 | ||||||||
\(191\) | 1.79837 | 0.130126 | 0.0650629 | − | 0.997881i | \(-0.479275\pi\) | ||||
0.0650629 | + | 0.997881i | \(0.479275\pi\) | |||||||
\(192\) | 0.0901699 | 0.00650746 | ||||||||
\(193\) | 6.00000 | 0.431889 | 0.215945 | − | 0.976406i | \(-0.430717\pi\) | ||||
0.215945 | + | 0.976406i | \(0.430717\pi\) | |||||||
\(194\) | −2.41641 | −0.173488 | ||||||||
\(195\) | 1.23607 | 0.0885167 | ||||||||
\(196\) | 0.236068 | 0.0168620 | ||||||||
\(197\) | 12.5623 | 0.895027 | 0.447514 | − | 0.894277i | \(-0.352310\pi\) | ||||
0.447514 | + | 0.894277i | \(0.352310\pi\) | |||||||
\(198\) | 8.81966 | 0.626786 | ||||||||
\(199\) | −2.61803 | −0.185588 | −0.0927938 | − | 0.995685i | \(-0.529580\pi\) | ||||
−0.0927938 | + | 0.995685i | \(0.529580\pi\) | |||||||
\(200\) | 12.2361 | 0.865221 | ||||||||
\(201\) | 2.56231 | 0.180731 | ||||||||
\(202\) | 3.70820 | 0.260908 | ||||||||
\(203\) | −18.9443 | −1.32963 | ||||||||
\(204\) | 2.61803 | 0.183299 | ||||||||
\(205\) | 13.7082 | 0.957422 | ||||||||
\(206\) | 8.52786 | 0.594164 | ||||||||
\(207\) | 11.4164 | 0.793495 | ||||||||
\(208\) | −1.85410 | −0.128559 | ||||||||
\(209\) | −41.1803 | −2.84850 | ||||||||
\(210\) | −2.00000 | −0.138013 | ||||||||
\(211\) | −19.2705 | −1.32664 | −0.663318 | − | 0.748337i | \(-0.730852\pi\) | ||||
−0.663318 | + | 0.748337i | \(0.730852\pi\) | |||||||
\(212\) | −9.23607 | −0.634336 | ||||||||
\(213\) | −3.50658 | −0.240267 | ||||||||
\(214\) | 6.79837 | 0.464727 | ||||||||
\(215\) | −29.8885 | −2.03838 | ||||||||
\(216\) | 5.00000 | 0.340207 | ||||||||
\(217\) | 16.3262 | 1.10830 | ||||||||
\(218\) | 11.5623 | 0.783098 | ||||||||
\(219\) | −5.12461 | −0.346289 | ||||||||
\(220\) | −26.1803 | −1.76508 | ||||||||
\(221\) | −4.23607 | −0.284949 | ||||||||
\(222\) | −0.583592 | −0.0391681 | ||||||||
\(223\) | 19.0902 | 1.27837 | 0.639186 | − | 0.769052i | \(-0.279271\pi\) | ||||
0.639186 | + | 0.769052i | \(0.279271\pi\) | |||||||
\(224\) | 14.7082 | 0.982733 | ||||||||
\(225\) | −15.6180 | −1.04120 | ||||||||
\(226\) | −3.76393 | −0.250373 | ||||||||
\(227\) | −20.4164 | −1.35508 | −0.677542 | − | 0.735484i | \(-0.736955\pi\) | ||||
−0.677542 | + | 0.735484i | \(0.736955\pi\) | |||||||
\(228\) | −5.09017 | −0.337105 | ||||||||
\(229\) | −9.41641 | −0.622254 | −0.311127 | − | 0.950368i | \(-0.600706\pi\) | ||||
−0.311127 | + | 0.950368i | \(0.600706\pi\) | |||||||
\(230\) | 8.00000 | 0.527504 | ||||||||
\(231\) | 5.00000 | 0.328976 | ||||||||
\(232\) | 16.1803 | 1.06229 | ||||||||
\(233\) | −4.56231 | −0.298887 | −0.149443 | − | 0.988770i | \(-0.547748\pi\) | ||||
−0.149443 | + | 0.988770i | \(0.547748\pi\) | |||||||
\(234\) | −1.76393 | −0.115312 | ||||||||
\(235\) | 16.6525 | 1.08629 | ||||||||
\(236\) | −17.9443 | −1.16807 | ||||||||
\(237\) | 3.61803 | 0.235017 | ||||||||
\(238\) | 6.85410 | 0.444285 | ||||||||
\(239\) | 15.7082 | 1.01608 | 0.508040 | − | 0.861334i | \(-0.330370\pi\) | ||||
0.508040 | + | 0.861334i | \(0.330370\pi\) | |||||||
\(240\) | −2.29180 | −0.147935 | ||||||||
\(241\) | −10.8885 | −0.701393 | −0.350696 | − | 0.936489i | \(-0.614055\pi\) | ||||
−0.350696 | + | 0.936489i | \(0.614055\pi\) | |||||||
\(242\) | −8.65248 | −0.556202 | ||||||||
\(243\) | −9.65248 | −0.619207 | ||||||||
\(244\) | −19.3262 | −1.23724 | ||||||||
\(245\) | −0.472136 | −0.0301637 | ||||||||
\(246\) | 1.00000 | 0.0637577 | ||||||||
\(247\) | 8.23607 | 0.524048 | ||||||||
\(248\) | −13.9443 | −0.885462 | ||||||||
\(249\) | 0.673762 | 0.0426979 | ||||||||
\(250\) | −0.944272 | −0.0597210 | ||||||||
\(251\) | 19.4721 | 1.22907 | 0.614535 | − | 0.788889i | \(-0.289344\pi\) | ||||
0.614535 | + | 0.788889i | \(0.289344\pi\) | |||||||
\(252\) | −12.0902 | −0.761609 | ||||||||
\(253\) | −20.0000 | −1.25739 | ||||||||
\(254\) | −12.2361 | −0.767759 | ||||||||
\(255\) | −5.23607 | −0.327895 | ||||||||
\(256\) | −6.56231 | −0.410144 | ||||||||
\(257\) | 0.819660 | 0.0511290 | 0.0255645 | − | 0.999673i | \(-0.491862\pi\) | ||||
0.0255645 | + | 0.999673i | \(0.491862\pi\) | |||||||
\(258\) | −2.18034 | −0.135742 | ||||||||
\(259\) | 6.47214 | 0.402159 | ||||||||
\(260\) | 5.23607 | 0.324727 | ||||||||
\(261\) | −20.6525 | −1.27836 | ||||||||
\(262\) | 10.1459 | 0.626816 | ||||||||
\(263\) | 18.2361 | 1.12448 | 0.562242 | − | 0.826973i | \(-0.309939\pi\) | ||||
0.562242 | + | 0.826973i | \(0.309939\pi\) | |||||||
\(264\) | −4.27051 | −0.262832 | ||||||||
\(265\) | 18.4721 | 1.13473 | ||||||||
\(266\) | −13.3262 | −0.817084 | ||||||||
\(267\) | −0.0557281 | −0.00341050 | ||||||||
\(268\) | 10.8541 | 0.663020 | ||||||||
\(269\) | 15.2361 | 0.928959 | 0.464480 | − | 0.885584i | \(-0.346241\pi\) | ||||
0.464480 | + | 0.885584i | \(0.346241\pi\) | |||||||
\(270\) | −4.47214 | −0.272166 | ||||||||
\(271\) | −13.0000 | −0.789694 | −0.394847 | − | 0.918747i | \(-0.629202\pi\) | ||||
−0.394847 | + | 0.918747i | \(0.629202\pi\) | |||||||
\(272\) | 7.85410 | 0.476225 | ||||||||
\(273\) | −1.00000 | −0.0605228 | ||||||||
\(274\) | −8.47214 | −0.511820 | ||||||||
\(275\) | 27.3607 | 1.64991 | ||||||||
\(276\) | −2.47214 | −0.148805 | ||||||||
\(277\) | −22.0344 | −1.32392 | −0.661961 | − | 0.749539i | \(-0.730275\pi\) | ||||
−0.661961 | + | 0.749539i | \(0.730275\pi\) | |||||||
\(278\) | −2.00000 | −0.119952 | ||||||||
\(279\) | 17.7984 | 1.06556 | ||||||||
\(280\) | −18.9443 | −1.13214 | ||||||||
\(281\) | 26.7082 | 1.59328 | 0.796639 | − | 0.604455i | \(-0.206609\pi\) | ||||
0.796639 | + | 0.604455i | \(0.206609\pi\) | |||||||
\(282\) | 1.21478 | 0.0723392 | ||||||||
\(283\) | 7.29180 | 0.433452 | 0.216726 | − | 0.976232i | \(-0.430462\pi\) | ||||
0.216726 | + | 0.976232i | \(0.430462\pi\) | |||||||
\(284\) | −14.8541 | −0.881429 | ||||||||
\(285\) | 10.1803 | 0.603031 | ||||||||
\(286\) | 3.09017 | 0.182726 | ||||||||
\(287\) | −11.0902 | −0.654632 | ||||||||
\(288\) | 16.0344 | 0.944839 | ||||||||
\(289\) | 0.944272 | 0.0555454 | ||||||||
\(290\) | −14.4721 | −0.849833 | ||||||||
\(291\) | −1.49342 | −0.0875460 | ||||||||
\(292\) | −21.7082 | −1.27038 | ||||||||
\(293\) | −22.7426 | −1.32864 | −0.664320 | − | 0.747448i | \(-0.731279\pi\) | ||||
−0.664320 | + | 0.747448i | \(0.731279\pi\) | |||||||
\(294\) | −0.0344419 | −0.00200869 | ||||||||
\(295\) | 35.8885 | 2.08951 | ||||||||
\(296\) | −5.52786 | −0.321301 | ||||||||
\(297\) | 11.1803 | 0.648749 | ||||||||
\(298\) | 10.2705 | 0.594955 | ||||||||
\(299\) | 4.00000 | 0.231326 | ||||||||
\(300\) | 3.38197 | 0.195258 | ||||||||
\(301\) | 24.1803 | 1.39373 | ||||||||
\(302\) | −1.88854 | −0.108673 | ||||||||
\(303\) | 2.29180 | 0.131660 | ||||||||
\(304\) | −15.2705 | −0.875824 | ||||||||
\(305\) | 38.6525 | 2.21323 | ||||||||
\(306\) | 7.47214 | 0.427154 | ||||||||
\(307\) | 4.14590 | 0.236619 | 0.118309 | − | 0.992977i | \(-0.462253\pi\) | ||||
0.118309 | + | 0.992977i | \(0.462253\pi\) | |||||||
\(308\) | 21.1803 | 1.20686 | ||||||||
\(309\) | 5.27051 | 0.299829 | ||||||||
\(310\) | 12.4721 | 0.708370 | ||||||||
\(311\) | −11.2918 | −0.640299 | −0.320150 | − | 0.947367i | \(-0.603733\pi\) | ||||
−0.320150 | + | 0.947367i | \(0.603733\pi\) | |||||||
\(312\) | 0.854102 | 0.0483540 | ||||||||
\(313\) | 18.0000 | 1.01742 | 0.508710 | − | 0.860938i | \(-0.330123\pi\) | ||||
0.508710 | + | 0.860938i | \(0.330123\pi\) | |||||||
\(314\) | 0.583592 | 0.0329340 | ||||||||
\(315\) | 24.1803 | 1.36241 | ||||||||
\(316\) | 15.3262 | 0.862168 | ||||||||
\(317\) | 14.8885 | 0.836224 | 0.418112 | − | 0.908395i | \(-0.362692\pi\) | ||||
0.418112 | + | 0.908395i | \(0.362692\pi\) | |||||||
\(318\) | 1.34752 | 0.0755654 | ||||||||
\(319\) | 36.1803 | 2.02571 | ||||||||
\(320\) | −0.763932 | −0.0427051 | ||||||||
\(321\) | 4.20163 | 0.234512 | ||||||||
\(322\) | −6.47214 | −0.360678 | ||||||||
\(323\) | −34.8885 | −1.94125 | ||||||||
\(324\) | −12.4721 | −0.692896 | ||||||||
\(325\) | −5.47214 | −0.303539 | ||||||||
\(326\) | −0.437694 | −0.0242416 | ||||||||
\(327\) | 7.14590 | 0.395169 | ||||||||
\(328\) | 9.47214 | 0.523011 | ||||||||
\(329\) | −13.4721 | −0.742743 | ||||||||
\(330\) | 3.81966 | 0.210265 | ||||||||
\(331\) | −7.03444 | −0.386648 | −0.193324 | − | 0.981135i | \(-0.561927\pi\) | ||||
−0.193324 | + | 0.981135i | \(0.561927\pi\) | |||||||
\(332\) | 2.85410 | 0.156639 | ||||||||
\(333\) | 7.05573 | 0.386652 | ||||||||
\(334\) | −12.9443 | −0.708279 | ||||||||
\(335\) | −21.7082 | −1.18605 | ||||||||
\(336\) | 1.85410 | 0.101150 | ||||||||
\(337\) | 8.67376 | 0.472490 | 0.236245 | − | 0.971694i | \(-0.424083\pi\) | ||||
0.236245 | + | 0.971694i | \(0.424083\pi\) | |||||||
\(338\) | −0.618034 | −0.0336166 | ||||||||
\(339\) | −2.32624 | −0.126344 | ||||||||
\(340\) | −22.1803 | −1.20290 | ||||||||
\(341\) | −31.1803 | −1.68851 | ||||||||
\(342\) | −14.5279 | −0.785577 | ||||||||
\(343\) | 18.7082 | 1.01015 | ||||||||
\(344\) | −20.6525 | −1.11351 | ||||||||
\(345\) | 4.94427 | 0.266191 | ||||||||
\(346\) | −2.03444 | −0.109372 | ||||||||
\(347\) | −5.23607 | −0.281087 | −0.140543 | − | 0.990075i | \(-0.544885\pi\) | ||||
−0.140543 | + | 0.990075i | \(0.544885\pi\) | |||||||
\(348\) | 4.47214 | 0.239732 | ||||||||
\(349\) | −2.52786 | −0.135313 | −0.0676567 | − | 0.997709i | \(-0.521552\pi\) | ||||
−0.0676567 | + | 0.997709i | \(0.521552\pi\) | |||||||
\(350\) | 8.85410 | 0.473272 | ||||||||
\(351\) | −2.23607 | −0.119352 | ||||||||
\(352\) | −28.0902 | −1.49721 | ||||||||
\(353\) | 11.6525 | 0.620199 | 0.310099 | − | 0.950704i | \(-0.399638\pi\) | ||||
0.310099 | + | 0.950704i | \(0.399638\pi\) | |||||||
\(354\) | 2.61803 | 0.139147 | ||||||||
\(355\) | 29.7082 | 1.57675 | ||||||||
\(356\) | −0.236068 | −0.0125116 | ||||||||
\(357\) | 4.23607 | 0.224196 | ||||||||
\(358\) | −14.0344 | −0.741743 | ||||||||
\(359\) | −5.47214 | −0.288808 | −0.144404 | − | 0.989519i | \(-0.546127\pi\) | ||||
−0.144404 | + | 0.989519i | \(0.546127\pi\) | |||||||
\(360\) | −20.6525 | −1.08848 | ||||||||
\(361\) | 48.8328 | 2.57015 | ||||||||
\(362\) | −11.2705 | −0.592365 | ||||||||
\(363\) | −5.34752 | −0.280672 | ||||||||
\(364\) | −4.23607 | −0.222030 | ||||||||
\(365\) | 43.4164 | 2.27252 | ||||||||
\(366\) | 2.81966 | 0.147386 | ||||||||
\(367\) | 1.43769 | 0.0750470 | 0.0375235 | − | 0.999296i | \(-0.488053\pi\) | ||||
0.0375235 | + | 0.999296i | \(0.488053\pi\) | |||||||
\(368\) | −7.41641 | −0.386607 | ||||||||
\(369\) | −12.0902 | −0.629389 | ||||||||
\(370\) | 4.94427 | 0.257040 | ||||||||
\(371\) | −14.9443 | −0.775868 | ||||||||
\(372\) | −3.85410 | −0.199826 | ||||||||
\(373\) | 4.85410 | 0.251336 | 0.125668 | − | 0.992072i | \(-0.459893\pi\) | ||||
0.125668 | + | 0.992072i | \(0.459893\pi\) | |||||||
\(374\) | −13.0902 | −0.676877 | ||||||||
\(375\) | −0.583592 | −0.0301366 | ||||||||
\(376\) | 11.5066 | 0.593406 | ||||||||
\(377\) | −7.23607 | −0.372676 | ||||||||
\(378\) | 3.61803 | 0.186092 | ||||||||
\(379\) | 13.1246 | 0.674166 | 0.337083 | − | 0.941475i | \(-0.390560\pi\) | ||||
0.337083 | + | 0.941475i | \(0.390560\pi\) | |||||||
\(380\) | 43.1246 | 2.21225 | ||||||||
\(381\) | −7.56231 | −0.387429 | ||||||||
\(382\) | −1.11146 | −0.0568670 | ||||||||
\(383\) | −12.2918 | −0.628081 | −0.314041 | − | 0.949410i | \(-0.601683\pi\) | ||||
−0.314041 | + | 0.949410i | \(0.601683\pi\) | |||||||
\(384\) | −4.34752 | −0.221859 | ||||||||
\(385\) | −42.3607 | −2.15890 | ||||||||
\(386\) | −3.70820 | −0.188743 | ||||||||
\(387\) | 26.3607 | 1.33999 | ||||||||
\(388\) | −6.32624 | −0.321166 | ||||||||
\(389\) | −1.41641 | −0.0718147 | −0.0359074 | − | 0.999355i | \(-0.511432\pi\) | ||||
−0.0359074 | + | 0.999355i | \(0.511432\pi\) | |||||||
\(390\) | −0.763932 | −0.0386832 | ||||||||
\(391\) | −16.9443 | −0.856909 | ||||||||
\(392\) | −0.326238 | −0.0164775 | ||||||||
\(393\) | 6.27051 | 0.316305 | ||||||||
\(394\) | −7.76393 | −0.391141 | ||||||||
\(395\) | −30.6525 | −1.54229 | ||||||||
\(396\) | 23.0902 | 1.16032 | ||||||||
\(397\) | −8.05573 | −0.404305 | −0.202153 | − | 0.979354i | \(-0.564794\pi\) | ||||
−0.202153 | + | 0.979354i | \(0.564794\pi\) | |||||||
\(398\) | 1.61803 | 0.0811047 | ||||||||
\(399\) | −8.23607 | −0.412319 | ||||||||
\(400\) | 10.1459 | 0.507295 | ||||||||
\(401\) | 6.52786 | 0.325986 | 0.162993 | − | 0.986627i | \(-0.447885\pi\) | ||||
0.162993 | + | 0.986627i | \(0.447885\pi\) | |||||||
\(402\) | −1.58359 | −0.0789824 | ||||||||
\(403\) | 6.23607 | 0.310641 | ||||||||
\(404\) | 9.70820 | 0.483001 | ||||||||
\(405\) | 24.9443 | 1.23949 | ||||||||
\(406\) | 11.7082 | 0.581068 | ||||||||
\(407\) | −12.3607 | −0.612696 | ||||||||
\(408\) | −3.61803 | −0.179119 | ||||||||
\(409\) | −29.2705 | −1.44733 | −0.723667 | − | 0.690150i | \(-0.757545\pi\) | ||||
−0.723667 | + | 0.690150i | \(0.757545\pi\) | |||||||
\(410\) | −8.47214 | −0.418409 | ||||||||
\(411\) | −5.23607 | −0.258276 | ||||||||
\(412\) | 22.3262 | 1.09993 | ||||||||
\(413\) | −29.0344 | −1.42869 | ||||||||
\(414\) | −7.05573 | −0.346770 | ||||||||
\(415\) | −5.70820 | −0.280205 | ||||||||
\(416\) | 5.61803 | 0.275447 | ||||||||
\(417\) | −1.23607 | −0.0605305 | ||||||||
\(418\) | 25.4508 | 1.24484 | ||||||||
\(419\) | −15.6525 | −0.764673 | −0.382337 | − | 0.924023i | \(-0.624881\pi\) | ||||
−0.382337 | + | 0.924023i | \(0.624881\pi\) | |||||||
\(420\) | −5.23607 | −0.255494 | ||||||||
\(421\) | 17.5279 | 0.854256 | 0.427128 | − | 0.904191i | \(-0.359525\pi\) | ||||
0.427128 | + | 0.904191i | \(0.359525\pi\) | |||||||
\(422\) | 11.9098 | 0.579761 | ||||||||
\(423\) | −14.6869 | −0.714102 | ||||||||
\(424\) | 12.7639 | 0.619871 | ||||||||
\(425\) | 23.1803 | 1.12441 | ||||||||
\(426\) | 2.16718 | 0.105000 | ||||||||
\(427\) | −31.2705 | −1.51329 | ||||||||
\(428\) | 17.7984 | 0.860317 | ||||||||
\(429\) | 1.90983 | 0.0922075 | ||||||||
\(430\) | 18.4721 | 0.890805 | ||||||||
\(431\) | −0.416408 | −0.0200577 | −0.0100288 | − | 0.999950i | \(-0.503192\pi\) | ||||
−0.0100288 | + | 0.999950i | \(0.503192\pi\) | |||||||
\(432\) | 4.14590 | 0.199470 | ||||||||
\(433\) | 25.5623 | 1.22845 | 0.614223 | − | 0.789132i | \(-0.289470\pi\) | ||||
0.614223 | + | 0.789132i | \(0.289470\pi\) | |||||||
\(434\) | −10.0902 | −0.484344 | ||||||||
\(435\) | −8.94427 | −0.428845 | ||||||||
\(436\) | 30.2705 | 1.44969 | ||||||||
\(437\) | 32.9443 | 1.57594 | ||||||||
\(438\) | 3.16718 | 0.151334 | ||||||||
\(439\) | 40.9443 | 1.95416 | 0.977082 | − | 0.212864i | \(-0.0682793\pi\) | ||||
0.977082 | + | 0.212864i | \(0.0682793\pi\) | |||||||
\(440\) | 36.1803 | 1.72483 | ||||||||
\(441\) | 0.416408 | 0.0198289 | ||||||||
\(442\) | 2.61803 | 0.124527 | ||||||||
\(443\) | −21.8541 | −1.03832 | −0.519160 | − | 0.854677i | \(-0.673755\pi\) | ||||
−0.519160 | + | 0.854677i | \(0.673755\pi\) | |||||||
\(444\) | −1.52786 | −0.0725092 | ||||||||
\(445\) | 0.472136 | 0.0223814 | ||||||||
\(446\) | −11.7984 | −0.558669 | ||||||||
\(447\) | 6.34752 | 0.300228 | ||||||||
\(448\) | 0.618034 | 0.0291994 | ||||||||
\(449\) | 34.1246 | 1.61044 | 0.805220 | − | 0.592976i | \(-0.202047\pi\) | ||||
0.805220 | + | 0.592976i | \(0.202047\pi\) | |||||||
\(450\) | 9.65248 | 0.455022 | ||||||||
\(451\) | 21.1803 | 0.997343 | ||||||||
\(452\) | −9.85410 | −0.463498 | ||||||||
\(453\) | −1.16718 | −0.0548391 | ||||||||
\(454\) | 12.6180 | 0.592194 | ||||||||
\(455\) | 8.47214 | 0.397180 | ||||||||
\(456\) | 7.03444 | 0.329418 | ||||||||
\(457\) | 8.23607 | 0.385267 | 0.192634 | − | 0.981271i | \(-0.438297\pi\) | ||||
0.192634 | + | 0.981271i | \(0.438297\pi\) | |||||||
\(458\) | 5.81966 | 0.271935 | ||||||||
\(459\) | 9.47214 | 0.442121 | ||||||||
\(460\) | 20.9443 | 0.976532 | ||||||||
\(461\) | 11.0902 | 0.516521 | 0.258260 | − | 0.966075i | \(-0.416851\pi\) | ||||
0.258260 | + | 0.966075i | \(0.416851\pi\) | |||||||
\(462\) | −3.09017 | −0.143768 | ||||||||
\(463\) | 6.12461 | 0.284635 | 0.142317 | − | 0.989821i | \(-0.454545\pi\) | ||||
0.142317 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(464\) | 13.4164 | 0.622841 | ||||||||
\(465\) | 7.70820 | 0.357459 | ||||||||
\(466\) | 2.81966 | 0.130618 | ||||||||
\(467\) | 8.29180 | 0.383699 | 0.191849 | − | 0.981424i | \(-0.438552\pi\) | ||||
0.191849 | + | 0.981424i | \(0.438552\pi\) | |||||||
\(468\) | −4.61803 | −0.213469 | ||||||||
\(469\) | 17.5623 | 0.810952 | ||||||||
\(470\) | −10.2918 | −0.474725 | ||||||||
\(471\) | 0.360680 | 0.0166192 | ||||||||
\(472\) | 24.7984 | 1.14144 | ||||||||
\(473\) | −46.1803 | −2.12337 | ||||||||
\(474\) | −2.23607 | −0.102706 | ||||||||
\(475\) | −45.0689 | −2.06790 | ||||||||
\(476\) | 17.9443 | 0.822474 | ||||||||
\(477\) | −16.2918 | −0.745950 | ||||||||
\(478\) | −9.70820 | −0.444043 | ||||||||
\(479\) | 19.3607 | 0.884612 | 0.442306 | − | 0.896864i | \(-0.354161\pi\) | ||||
0.442306 | + | 0.896864i | \(0.354161\pi\) | |||||||
\(480\) | 6.94427 | 0.316961 | ||||||||
\(481\) | 2.47214 | 0.112720 | ||||||||
\(482\) | 6.72949 | 0.306520 | ||||||||
\(483\) | −4.00000 | −0.182006 | ||||||||
\(484\) | −22.6525 | −1.02966 | ||||||||
\(485\) | 12.6525 | 0.574519 | ||||||||
\(486\) | 5.96556 | 0.270603 | ||||||||
\(487\) | 43.6869 | 1.97964 | 0.989822 | − | 0.142314i | \(-0.0454542\pi\) | ||||
0.989822 | + | 0.142314i | \(0.0454542\pi\) | |||||||
\(488\) | 26.7082 | 1.20902 | ||||||||
\(489\) | −0.270510 | −0.0122329 | ||||||||
\(490\) | 0.291796 | 0.0131820 | ||||||||
\(491\) | 2.76393 | 0.124735 | 0.0623673 | − | 0.998053i | \(-0.480135\pi\) | ||||
0.0623673 | + | 0.998053i | \(0.480135\pi\) | |||||||
\(492\) | 2.61803 | 0.118030 | ||||||||
\(493\) | 30.6525 | 1.38052 | ||||||||
\(494\) | −5.09017 | −0.229018 | ||||||||
\(495\) | −46.1803 | −2.07565 | ||||||||
\(496\) | −11.5623 | −0.519163 | ||||||||
\(497\) | −24.0344 | −1.07809 | ||||||||
\(498\) | −0.416408 | −0.0186597 | ||||||||
\(499\) | 19.9787 | 0.894370 | 0.447185 | − | 0.894441i | \(-0.352427\pi\) | ||||
0.447185 | + | 0.894441i | \(0.352427\pi\) | |||||||
\(500\) | −2.47214 | −0.110557 | ||||||||
\(501\) | −8.00000 | −0.357414 | ||||||||
\(502\) | −12.0344 | −0.537123 | ||||||||
\(503\) | 32.5410 | 1.45093 | 0.725466 | − | 0.688258i | \(-0.241624\pi\) | ||||
0.725466 | + | 0.688258i | \(0.241624\pi\) | |||||||
\(504\) | 16.7082 | 0.744243 | ||||||||
\(505\) | −19.4164 | −0.864019 | ||||||||
\(506\) | 12.3607 | 0.549499 | ||||||||
\(507\) | −0.381966 | −0.0169637 | ||||||||
\(508\) | −32.0344 | −1.42130 | ||||||||
\(509\) | −4.85410 | −0.215154 | −0.107577 | − | 0.994197i | \(-0.534309\pi\) | ||||
−0.107577 | + | 0.994197i | \(0.534309\pi\) | |||||||
\(510\) | 3.23607 | 0.143295 | ||||||||
\(511\) | −35.1246 | −1.55382 | ||||||||
\(512\) | −18.7082 | −0.826794 | ||||||||
\(513\) | −18.4164 | −0.813104 | ||||||||
\(514\) | −0.506578 | −0.0223442 | ||||||||
\(515\) | −44.6525 | −1.96762 | ||||||||
\(516\) | −5.70820 | −0.251290 | ||||||||
\(517\) | 25.7295 | 1.13158 | ||||||||
\(518\) | −4.00000 | −0.175750 | ||||||||
\(519\) | −1.25735 | −0.0551917 | ||||||||
\(520\) | −7.23607 | −0.317323 | ||||||||
\(521\) | 13.2148 | 0.578950 | 0.289475 | − | 0.957186i | \(-0.406519\pi\) | ||||
0.289475 | + | 0.957186i | \(0.406519\pi\) | |||||||
\(522\) | 12.7639 | 0.558662 | ||||||||
\(523\) | 11.3475 | 0.496193 | 0.248096 | − | 0.968735i | \(-0.420195\pi\) | ||||
0.248096 | + | 0.968735i | \(0.420195\pi\) | |||||||
\(524\) | 26.5623 | 1.16038 | ||||||||
\(525\) | 5.47214 | 0.238824 | ||||||||
\(526\) | −11.2705 | −0.491418 | ||||||||
\(527\) | −26.4164 | −1.15072 | ||||||||
\(528\) | −3.54102 | −0.154103 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | −11.4164 | −0.495897 | ||||||||
\(531\) | −31.6525 | −1.37360 | ||||||||
\(532\) | −34.8885 | −1.51261 | ||||||||
\(533\) | −4.23607 | −0.183484 | ||||||||
\(534\) | 0.0344419 | 0.00149044 | ||||||||
\(535\) | −35.5967 | −1.53898 | ||||||||
\(536\) | −15.0000 | −0.647901 | ||||||||
\(537\) | −8.67376 | −0.374300 | ||||||||
\(538\) | −9.41641 | −0.405970 | ||||||||
\(539\) | −0.729490 | −0.0314214 | ||||||||
\(540\) | −11.7082 | −0.503841 | ||||||||
\(541\) | 11.9443 | 0.513524 | 0.256762 | − | 0.966475i | \(-0.417344\pi\) | ||||
0.256762 | + | 0.966475i | \(0.417344\pi\) | |||||||
\(542\) | 8.03444 | 0.345109 | ||||||||
\(543\) | −6.96556 | −0.298921 | ||||||||
\(544\) | −23.7984 | −1.02035 | ||||||||
\(545\) | −60.5410 | −2.59329 | ||||||||
\(546\) | 0.618034 | 0.0264494 | ||||||||
\(547\) | 13.8197 | 0.590886 | 0.295443 | − | 0.955360i | \(-0.404533\pi\) | ||||
0.295443 | + | 0.955360i | \(0.404533\pi\) | |||||||
\(548\) | −22.1803 | −0.947497 | ||||||||
\(549\) | −34.0902 | −1.45493 | ||||||||
\(550\) | −16.9098 | −0.721038 | ||||||||
\(551\) | −59.5967 | −2.53891 | ||||||||
\(552\) | 3.41641 | 0.145412 | ||||||||
\(553\) | 24.7984 | 1.05453 | ||||||||
\(554\) | 13.6180 | 0.578575 | ||||||||
\(555\) | 3.05573 | 0.129708 | ||||||||
\(556\) | −5.23607 | −0.222059 | ||||||||
\(557\) | −9.38197 | −0.397527 | −0.198763 | − | 0.980048i | \(-0.563693\pi\) | ||||
−0.198763 | + | 0.980048i | \(0.563693\pi\) | |||||||
\(558\) | −11.0000 | −0.465667 | ||||||||
\(559\) | 9.23607 | 0.390644 | ||||||||
\(560\) | −15.7082 | −0.663793 | ||||||||
\(561\) | −8.09017 | −0.341567 | ||||||||
\(562\) | −16.5066 | −0.696288 | ||||||||
\(563\) | 9.09017 | 0.383105 | 0.191552 | − | 0.981482i | \(-0.438648\pi\) | ||||
0.191552 | + | 0.981482i | \(0.438648\pi\) | |||||||
\(564\) | 3.18034 | 0.133916 | ||||||||
\(565\) | 19.7082 | 0.829130 | ||||||||
\(566\) | −4.50658 | −0.189426 | ||||||||
\(567\) | −20.1803 | −0.847495 | ||||||||
\(568\) | 20.5279 | 0.861330 | ||||||||
\(569\) | 17.9098 | 0.750819 | 0.375410 | − | 0.926859i | \(-0.377502\pi\) | ||||
0.375410 | + | 0.926859i | \(0.377502\pi\) | |||||||
\(570\) | −6.29180 | −0.263534 | ||||||||
\(571\) | 32.7771 | 1.37168 | 0.685839 | − | 0.727753i | \(-0.259435\pi\) | ||||
0.685839 | + | 0.727753i | \(0.259435\pi\) | |||||||
\(572\) | 8.09017 | 0.338267 | ||||||||
\(573\) | −0.686918 | −0.0286964 | ||||||||
\(574\) | 6.85410 | 0.286085 | ||||||||
\(575\) | −21.8885 | −0.912815 | ||||||||
\(576\) | 0.673762 | 0.0280734 | ||||||||
\(577\) | −23.1246 | −0.962690 | −0.481345 | − | 0.876531i | \(-0.659852\pi\) | ||||
−0.481345 | + | 0.876531i | \(0.659852\pi\) | |||||||
\(578\) | −0.583592 | −0.0242742 | ||||||||
\(579\) | −2.29180 | −0.0952438 | ||||||||
\(580\) | −37.8885 | −1.57324 | ||||||||
\(581\) | 4.61803 | 0.191588 | ||||||||
\(582\) | 0.922986 | 0.0382590 | ||||||||
\(583\) | 28.5410 | 1.18205 | ||||||||
\(584\) | 30.0000 | 1.24141 | ||||||||
\(585\) | 9.23607 | 0.381864 | ||||||||
\(586\) | 14.0557 | 0.580637 | ||||||||
\(587\) | −36.7984 | −1.51883 | −0.759416 | − | 0.650606i | \(-0.774515\pi\) | ||||
−0.759416 | + | 0.650606i | \(0.774515\pi\) | |||||||
\(588\) | −0.0901699 | −0.00371855 | ||||||||
\(589\) | 51.3607 | 2.11628 | ||||||||
\(590\) | −22.1803 | −0.913150 | ||||||||
\(591\) | −4.79837 | −0.197379 | ||||||||
\(592\) | −4.58359 | −0.188384 | ||||||||
\(593\) | 21.0344 | 0.863781 | 0.431890 | − | 0.901926i | \(-0.357847\pi\) | ||||
0.431890 | + | 0.901926i | \(0.357847\pi\) | |||||||
\(594\) | −6.90983 | −0.283514 | ||||||||
\(595\) | −35.8885 | −1.47129 | ||||||||
\(596\) | 26.8885 | 1.10140 | ||||||||
\(597\) | 1.00000 | 0.0409273 | ||||||||
\(598\) | −2.47214 | −0.101093 | ||||||||
\(599\) | −2.12461 | −0.0868093 | −0.0434046 | − | 0.999058i | \(-0.513820\pi\) | ||||
−0.0434046 | + | 0.999058i | \(0.513820\pi\) | |||||||
\(600\) | −4.67376 | −0.190806 | ||||||||
\(601\) | 38.2705 | 1.56109 | 0.780543 | − | 0.625102i | \(-0.214943\pi\) | ||||
0.780543 | + | 0.625102i | \(0.214943\pi\) | |||||||
\(602\) | −14.9443 | −0.609083 | ||||||||
\(603\) | 19.1459 | 0.779681 | ||||||||
\(604\) | −4.94427 | −0.201180 | ||||||||
\(605\) | 45.3050 | 1.84191 | ||||||||
\(606\) | −1.41641 | −0.0575376 | ||||||||
\(607\) | 19.3607 | 0.785826 | 0.392913 | − | 0.919576i | \(-0.371467\pi\) | ||||
0.392913 | + | 0.919576i | \(0.371467\pi\) | |||||||
\(608\) | 46.2705 | 1.87652 | ||||||||
\(609\) | 7.23607 | 0.293220 | ||||||||
\(610\) | −23.8885 | −0.967219 | ||||||||
\(611\) | −5.14590 | −0.208181 | ||||||||
\(612\) | 19.5623 | 0.790759 | ||||||||
\(613\) | 12.0344 | 0.486067 | 0.243033 | − | 0.970018i | \(-0.421858\pi\) | ||||
0.243033 | + | 0.970018i | \(0.421858\pi\) | |||||||
\(614\) | −2.56231 | −0.103406 | ||||||||
\(615\) | −5.23607 | −0.211139 | ||||||||
\(616\) | −29.2705 | −1.17934 | ||||||||
\(617\) | 38.6525 | 1.55609 | 0.778045 | − | 0.628208i | \(-0.216212\pi\) | ||||
0.778045 | + | 0.628208i | \(0.216212\pi\) | |||||||
\(618\) | −3.25735 | −0.131030 | ||||||||
\(619\) | 1.00000 | 0.0401934 | ||||||||
\(620\) | 32.6525 | 1.31135 | ||||||||
\(621\) | −8.94427 | −0.358921 | ||||||||
\(622\) | 6.97871 | 0.279821 | ||||||||
\(623\) | −0.381966 | −0.0153031 | ||||||||
\(624\) | 0.708204 | 0.0283508 | ||||||||
\(625\) | −22.4164 | −0.896656 | ||||||||
\(626\) | −11.1246 | −0.444629 | ||||||||
\(627\) | 15.7295 | 0.628175 | ||||||||
\(628\) | 1.52786 | 0.0609684 | ||||||||
\(629\) | −10.4721 | −0.417551 | ||||||||
\(630\) | −14.9443 | −0.595394 | ||||||||
\(631\) | −30.2148 | −1.20283 | −0.601416 | − | 0.798936i | \(-0.705396\pi\) | ||||
−0.601416 | + | 0.798936i | \(0.705396\pi\) | |||||||
\(632\) | −21.1803 | −0.842509 | ||||||||
\(633\) | 7.36068 | 0.292561 | ||||||||
\(634\) | −9.20163 | −0.365443 | ||||||||
\(635\) | 64.0689 | 2.54250 | ||||||||
\(636\) | 3.52786 | 0.139889 | ||||||||
\(637\) | 0.145898 | 0.00578069 | ||||||||
\(638\) | −22.3607 | −0.885268 | ||||||||
\(639\) | −26.2016 | −1.03652 | ||||||||
\(640\) | 36.8328 | 1.45594 | ||||||||
\(641\) | 24.0000 | 0.947943 | 0.473972 | − | 0.880540i | \(-0.342820\pi\) | ||||
0.473972 | + | 0.880540i | \(0.342820\pi\) | |||||||
\(642\) | −2.59675 | −0.102485 | ||||||||
\(643\) | 12.4164 | 0.489655 | 0.244828 | − | 0.969567i | \(-0.421269\pi\) | ||||
0.244828 | + | 0.969567i | \(0.421269\pi\) | |||||||
\(644\) | −16.9443 | −0.667698 | ||||||||
\(645\) | 11.4164 | 0.449521 | ||||||||
\(646\) | 21.5623 | 0.848358 | ||||||||
\(647\) | −4.87539 | −0.191671 | −0.0958356 | − | 0.995397i | \(-0.530552\pi\) | ||||
−0.0958356 | + | 0.995397i | \(0.530552\pi\) | |||||||
\(648\) | 17.2361 | 0.677097 | ||||||||
\(649\) | 55.4508 | 2.17664 | ||||||||
\(650\) | 3.38197 | 0.132652 | ||||||||
\(651\) | −6.23607 | −0.244411 | ||||||||
\(652\) | −1.14590 | −0.0448768 | ||||||||
\(653\) | 1.00000 | 0.0391330 | 0.0195665 | − | 0.999809i | \(-0.493771\pi\) | ||||
0.0195665 | + | 0.999809i | \(0.493771\pi\) | |||||||
\(654\) | −4.41641 | −0.172695 | ||||||||
\(655\) | −53.1246 | −2.07575 | ||||||||
\(656\) | 7.85410 | 0.306651 | ||||||||
\(657\) | −38.2918 | −1.49391 | ||||||||
\(658\) | 8.32624 | 0.324591 | ||||||||
\(659\) | −22.0000 | −0.856998 | −0.428499 | − | 0.903542i | \(-0.640958\pi\) | ||||
−0.428499 | + | 0.903542i | \(0.640958\pi\) | |||||||
\(660\) | 10.0000 | 0.389249 | ||||||||
\(661\) | −20.7082 | −0.805456 | −0.402728 | − | 0.915320i | \(-0.631938\pi\) | ||||
−0.402728 | + | 0.915320i | \(0.631938\pi\) | |||||||
\(662\) | 4.34752 | 0.168971 | ||||||||
\(663\) | 1.61803 | 0.0628392 | ||||||||
\(664\) | −3.94427 | −0.153067 | ||||||||
\(665\) | 69.7771 | 2.70584 | ||||||||
\(666\) | −4.36068 | −0.168973 | ||||||||
\(667\) | −28.9443 | −1.12073 | ||||||||
\(668\) | −33.8885 | −1.31119 | ||||||||
\(669\) | −7.29180 | −0.281917 | ||||||||
\(670\) | 13.4164 | 0.518321 | ||||||||
\(671\) | 59.7214 | 2.30552 | ||||||||
\(672\) | −5.61803 | −0.216720 | ||||||||
\(673\) | −26.5623 | −1.02390 | −0.511951 | − | 0.859015i | \(-0.671077\pi\) | ||||
−0.511951 | + | 0.859015i | \(0.671077\pi\) | |||||||
\(674\) | −5.36068 | −0.206486 | ||||||||
\(675\) | 12.2361 | 0.470966 | ||||||||
\(676\) | −1.61803 | −0.0622321 | ||||||||
\(677\) | −11.2918 | −0.433979 | −0.216989 | − | 0.976174i | \(-0.569624\pi\) | ||||
−0.216989 | + | 0.976174i | \(0.569624\pi\) | |||||||
\(678\) | 1.43769 | 0.0552143 | ||||||||
\(679\) | −10.2361 | −0.392824 | ||||||||
\(680\) | 30.6525 | 1.17547 | ||||||||
\(681\) | 7.79837 | 0.298834 | ||||||||
\(682\) | 19.2705 | 0.737906 | ||||||||
\(683\) | −29.5623 | −1.13117 | −0.565585 | − | 0.824690i | \(-0.691350\pi\) | ||||
−0.565585 | + | 0.824690i | \(0.691350\pi\) | |||||||
\(684\) | −38.0344 | −1.45428 | ||||||||
\(685\) | 44.3607 | 1.69493 | ||||||||
\(686\) | −11.5623 | −0.441451 | ||||||||
\(687\) | 3.59675 | 0.137224 | ||||||||
\(688\) | −17.1246 | −0.652870 | ||||||||
\(689\) | −5.70820 | −0.217465 | ||||||||
\(690\) | −3.05573 | −0.116330 | ||||||||
\(691\) | 35.8328 | 1.36314 | 0.681572 | − | 0.731751i | \(-0.261297\pi\) | ||||
0.681572 | + | 0.731751i | \(0.261297\pi\) | |||||||
\(692\) | −5.32624 | −0.202473 | ||||||||
\(693\) | 37.3607 | 1.41921 | ||||||||
\(694\) | 3.23607 | 0.122839 | ||||||||
\(695\) | 10.4721 | 0.397231 | ||||||||
\(696\) | −6.18034 | −0.234265 | ||||||||
\(697\) | 17.9443 | 0.679688 | ||||||||
\(698\) | 1.56231 | 0.0591342 | ||||||||
\(699\) | 1.74265 | 0.0659129 | ||||||||
\(700\) | 23.1803 | 0.876134 | ||||||||
\(701\) | 30.2361 | 1.14200 | 0.571000 | − | 0.820950i | \(-0.306556\pi\) | ||||
0.571000 | + | 0.820950i | \(0.306556\pi\) | |||||||
\(702\) | 1.38197 | 0.0521589 | ||||||||
\(703\) | 20.3607 | 0.767918 | ||||||||
\(704\) | −1.18034 | −0.0444857 | ||||||||
\(705\) | −6.36068 | −0.239557 | ||||||||
\(706\) | −7.20163 | −0.271037 | ||||||||
\(707\) | 15.7082 | 0.590768 | ||||||||
\(708\) | 6.85410 | 0.257593 | ||||||||
\(709\) | −47.1246 | −1.76980 | −0.884901 | − | 0.465779i | \(-0.845774\pi\) | ||||
−0.884901 | + | 0.465779i | \(0.845774\pi\) | |||||||
\(710\) | −18.3607 | −0.689064 | ||||||||
\(711\) | 27.0344 | 1.01387 | ||||||||
\(712\) | 0.326238 | 0.0122263 | ||||||||
\(713\) | 24.9443 | 0.934170 | ||||||||
\(714\) | −2.61803 | −0.0979775 | ||||||||
\(715\) | −16.1803 | −0.605110 | ||||||||
\(716\) | −36.7426 | −1.37314 | ||||||||
\(717\) | −6.00000 | −0.224074 | ||||||||
\(718\) | 3.38197 | 0.126214 | ||||||||
\(719\) | 32.2918 | 1.20428 | 0.602140 | − | 0.798390i | \(-0.294315\pi\) | ||||
0.602140 | + | 0.798390i | \(0.294315\pi\) | |||||||
\(720\) | −17.1246 | −0.638197 | ||||||||
\(721\) | 36.1246 | 1.34535 | ||||||||
\(722\) | −30.1803 | −1.12320 | ||||||||
\(723\) | 4.15905 | 0.154677 | ||||||||
\(724\) | −29.5066 | −1.09660 | ||||||||
\(725\) | 39.5967 | 1.47059 | ||||||||
\(726\) | 3.30495 | 0.122658 | ||||||||
\(727\) | 44.1803 | 1.63856 | 0.819279 | − | 0.573395i | \(-0.194374\pi\) | ||||
0.819279 | + | 0.573395i | \(0.194374\pi\) | |||||||
\(728\) | 5.85410 | 0.216967 | ||||||||
\(729\) | −19.4377 | −0.719915 | ||||||||
\(730\) | −26.8328 | −0.993127 | ||||||||
\(731\) | −39.1246 | −1.44708 | ||||||||
\(732\) | 7.38197 | 0.272845 | ||||||||
\(733\) | 20.5836 | 0.760272 | 0.380136 | − | 0.924931i | \(-0.375877\pi\) | ||||
0.380136 | + | 0.924931i | \(0.375877\pi\) | |||||||
\(734\) | −0.888544 | −0.0327968 | ||||||||
\(735\) | 0.180340 | 0.00665194 | ||||||||
\(736\) | 22.4721 | 0.828334 | ||||||||
\(737\) | −33.5410 | −1.23550 | ||||||||
\(738\) | 7.47214 | 0.275053 | ||||||||
\(739\) | 18.1803 | 0.668775 | 0.334387 | − | 0.942436i | \(-0.391471\pi\) | ||||
0.334387 | + | 0.942436i | \(0.391471\pi\) | |||||||
\(740\) | 12.9443 | 0.475841 | ||||||||
\(741\) | −3.14590 | −0.115567 | ||||||||
\(742\) | 9.23607 | 0.339067 | ||||||||
\(743\) | −10.8541 | −0.398198 | −0.199099 | − | 0.979979i | \(-0.563802\pi\) | ||||
−0.199099 | + | 0.979979i | \(0.563802\pi\) | |||||||
\(744\) | 5.32624 | 0.195269 | ||||||||
\(745\) | −53.7771 | −1.97024 | ||||||||
\(746\) | −3.00000 | −0.109838 | ||||||||
\(747\) | 5.03444 | 0.184201 | ||||||||
\(748\) | −34.2705 | −1.25305 | ||||||||
\(749\) | 28.7984 | 1.05227 | ||||||||
\(750\) | 0.360680 | 0.0131702 | ||||||||
\(751\) | 44.2148 | 1.61342 | 0.806710 | − | 0.590947i | \(-0.201246\pi\) | ||||
0.806710 | + | 0.590947i | \(0.201246\pi\) | |||||||
\(752\) | 9.54102 | 0.347925 | ||||||||
\(753\) | −7.43769 | −0.271045 | ||||||||
\(754\) | 4.47214 | 0.162866 | ||||||||
\(755\) | 9.88854 | 0.359881 | ||||||||
\(756\) | 9.47214 | 0.344498 | ||||||||
\(757\) | −21.3820 | −0.777141 | −0.388570 | − | 0.921419i | \(-0.627031\pi\) | ||||
−0.388570 | + | 0.921419i | \(0.627031\pi\) | |||||||
\(758\) | −8.11146 | −0.294621 | ||||||||
\(759\) | 7.63932 | 0.277290 | ||||||||
\(760\) | −59.5967 | −2.16180 | ||||||||
\(761\) | −12.9098 | −0.467981 | −0.233990 | − | 0.972239i | \(-0.575178\pi\) | ||||
−0.233990 | + | 0.972239i | \(0.575178\pi\) | |||||||
\(762\) | 4.67376 | 0.169313 | ||||||||
\(763\) | 48.9787 | 1.77315 | ||||||||
\(764\) | −2.90983 | −0.105274 | ||||||||
\(765\) | −39.1246 | −1.41455 | ||||||||
\(766\) | 7.59675 | 0.274482 | ||||||||
\(767\) | −11.0902 | −0.400443 | ||||||||
\(768\) | 2.50658 | 0.0904483 | ||||||||
\(769\) | −4.02129 | −0.145011 | −0.0725056 | − | 0.997368i | \(-0.523100\pi\) | ||||
−0.0725056 | + | 0.997368i | \(0.523100\pi\) | |||||||
\(770\) | 26.1803 | 0.943474 | ||||||||
\(771\) | −0.313082 | −0.0112754 | ||||||||
\(772\) | −9.70820 | −0.349406 | ||||||||
\(773\) | −29.7426 | −1.06977 | −0.534884 | − | 0.844925i | \(-0.679645\pi\) | ||||
−0.534884 | + | 0.844925i | \(0.679645\pi\) | |||||||
\(774\) | −16.2918 | −0.585597 | ||||||||
\(775\) | −34.1246 | −1.22579 | ||||||||
\(776\) | 8.74265 | 0.313843 | ||||||||
\(777\) | −2.47214 | −0.0886874 | ||||||||
\(778\) | 0.875388 | 0.0313842 | ||||||||
\(779\) | −34.8885 | −1.25001 | ||||||||
\(780\) | −2.00000 | −0.0716115 | ||||||||
\(781\) | 45.9017 | 1.64249 | ||||||||
\(782\) | 10.4721 | 0.374483 | ||||||||
\(783\) | 16.1803 | 0.578238 | ||||||||
\(784\) | −0.270510 | −0.00966107 | ||||||||
\(785\) | −3.05573 | −0.109064 | ||||||||
\(786\) | −3.87539 | −0.138231 | ||||||||
\(787\) | 43.0000 | 1.53278 | 0.766392 | − | 0.642373i | \(-0.222050\pi\) | ||||
0.766392 | + | 0.642373i | \(0.222050\pi\) | |||||||
\(788\) | −20.3262 | −0.724092 | ||||||||
\(789\) | −6.96556 | −0.247980 | ||||||||
\(790\) | 18.9443 | 0.674007 | ||||||||
\(791\) | −15.9443 | −0.566913 | ||||||||
\(792\) | −31.9098 | −1.13387 | ||||||||
\(793\) | −11.9443 | −0.424154 | ||||||||
\(794\) | 4.97871 | 0.176688 | ||||||||
\(795\) | −7.05573 | −0.250241 | ||||||||
\(796\) | 4.23607 | 0.150143 | ||||||||
\(797\) | −44.8328 | −1.58806 | −0.794030 | − | 0.607879i | \(-0.792021\pi\) | ||||
−0.794030 | + | 0.607879i | \(0.792021\pi\) | |||||||
\(798\) | 5.09017 | 0.180190 | ||||||||
\(799\) | 21.7984 | 0.771171 | ||||||||
\(800\) | −30.7426 | −1.08692 | ||||||||
\(801\) | −0.416408 | −0.0147130 | ||||||||
\(802\) | −4.03444 | −0.142461 | ||||||||
\(803\) | 67.0820 | 2.36727 | ||||||||
\(804\) | −4.14590 | −0.146215 | ||||||||
\(805\) | 33.8885 | 1.19441 | ||||||||
\(806\) | −3.85410 | −0.135755 | ||||||||
\(807\) | −5.81966 | −0.204862 | ||||||||
\(808\) | −13.4164 | −0.471988 | ||||||||
\(809\) | 38.7426 | 1.36212 | 0.681059 | − | 0.732228i | \(-0.261520\pi\) | ||||
0.681059 | + | 0.732228i | \(0.261520\pi\) | |||||||
\(810\) | −15.4164 | −0.541677 | ||||||||
\(811\) | −37.9443 | −1.33240 | −0.666202 | − | 0.745772i | \(-0.732081\pi\) | ||||
−0.666202 | + | 0.745772i | \(0.732081\pi\) | |||||||
\(812\) | 30.6525 | 1.07569 | ||||||||
\(813\) | 4.96556 | 0.174150 | ||||||||
\(814\) | 7.63932 | 0.267758 | ||||||||
\(815\) | 2.29180 | 0.0802781 | ||||||||
\(816\) | −3.00000 | −0.105021 | ||||||||
\(817\) | 76.0689 | 2.66131 | ||||||||
\(818\) | 18.0902 | 0.632508 | ||||||||
\(819\) | −7.47214 | −0.261098 | ||||||||
\(820\) | −22.1803 | −0.774571 | ||||||||
\(821\) | 7.76393 | 0.270963 | 0.135482 | − | 0.990780i | \(-0.456742\pi\) | ||||
0.135482 | + | 0.990780i | \(0.456742\pi\) | |||||||
\(822\) | 3.23607 | 0.112871 | ||||||||
\(823\) | 21.7639 | 0.758643 | 0.379321 | − | 0.925265i | \(-0.376157\pi\) | ||||
0.379321 | + | 0.925265i | \(0.376157\pi\) | |||||||
\(824\) | −30.8541 | −1.07485 | ||||||||
\(825\) | −10.4508 | −0.363852 | ||||||||
\(826\) | 17.9443 | 0.624361 | ||||||||
\(827\) | 39.9574 | 1.38946 | 0.694728 | − | 0.719273i | \(-0.255525\pi\) | ||||
0.694728 | + | 0.719273i | \(0.255525\pi\) | |||||||
\(828\) | −18.4721 | −0.641951 | ||||||||
\(829\) | −29.7984 | −1.03494 | −0.517470 | − | 0.855701i | \(-0.673126\pi\) | ||||
−0.517470 | + | 0.855701i | \(0.673126\pi\) | |||||||
\(830\) | 3.52786 | 0.122454 | ||||||||
\(831\) | 8.41641 | 0.291962 | ||||||||
\(832\) | 0.236068 | 0.00818418 | ||||||||
\(833\) | −0.618034 | −0.0214136 | ||||||||
\(834\) | 0.763932 | 0.0264528 | ||||||||
\(835\) | 67.7771 | 2.34552 | ||||||||
\(836\) | 66.6312 | 2.30449 | ||||||||
\(837\) | −13.9443 | −0.481985 | ||||||||
\(838\) | 9.67376 | 0.334175 | ||||||||
\(839\) | 12.0344 | 0.415475 | 0.207738 | − | 0.978185i | \(-0.433390\pi\) | ||||
0.207738 | + | 0.978185i | \(0.433390\pi\) | |||||||
\(840\) | 7.23607 | 0.249668 | ||||||||
\(841\) | 23.3607 | 0.805541 | ||||||||
\(842\) | −10.8328 | −0.373323 | ||||||||
\(843\) | −10.2016 | −0.351363 | ||||||||
\(844\) | 31.1803 | 1.07327 | ||||||||
\(845\) | 3.23607 | 0.111324 | ||||||||
\(846\) | 9.07701 | 0.312074 | ||||||||
\(847\) | −36.6525 | −1.25939 | ||||||||
\(848\) | 10.5836 | 0.363442 | ||||||||
\(849\) | −2.78522 | −0.0955884 | ||||||||
\(850\) | −14.3262 | −0.491386 | ||||||||
\(851\) | 9.88854 | 0.338975 | ||||||||
\(852\) | 5.67376 | 0.194380 | ||||||||
\(853\) | 16.5279 | 0.565903 | 0.282952 | − | 0.959134i | \(-0.408686\pi\) | ||||
0.282952 | + | 0.959134i | \(0.408686\pi\) | |||||||
\(854\) | 19.3262 | 0.661330 | ||||||||
\(855\) | 76.0689 | 2.60150 | ||||||||
\(856\) | −24.5967 | −0.840700 | ||||||||
\(857\) | 36.9230 | 1.26127 | 0.630633 | − | 0.776082i | \(-0.282796\pi\) | ||||
0.630633 | + | 0.776082i | \(0.282796\pi\) | |||||||
\(858\) | −1.18034 | −0.0402961 | ||||||||
\(859\) | 5.45085 | 0.185981 | 0.0929903 | − | 0.995667i | \(-0.470357\pi\) | ||||
0.0929903 | + | 0.995667i | \(0.470357\pi\) | |||||||
\(860\) | 48.3607 | 1.64909 | ||||||||
\(861\) | 4.23607 | 0.144365 | ||||||||
\(862\) | 0.257354 | 0.00876552 | ||||||||
\(863\) | −5.21478 | −0.177513 | −0.0887566 | − | 0.996053i | \(-0.528289\pi\) | ||||
−0.0887566 | + | 0.996053i | \(0.528289\pi\) | |||||||
\(864\) | −12.5623 | −0.427378 | ||||||||
\(865\) | 10.6525 | 0.362195 | ||||||||
\(866\) | −15.7984 | −0.536851 | ||||||||
\(867\) | −0.360680 | −0.0122493 | ||||||||
\(868\) | −26.4164 | −0.896631 | ||||||||
\(869\) | −47.3607 | −1.60660 | ||||||||
\(870\) | 5.52786 | 0.187412 | ||||||||
\(871\) | 6.70820 | 0.227299 | ||||||||
\(872\) | −41.8328 | −1.41664 | ||||||||
\(873\) | −11.1591 | −0.377677 | ||||||||
\(874\) | −20.3607 | −0.688710 | ||||||||
\(875\) | −4.00000 | −0.135225 | ||||||||
\(876\) | 8.29180 | 0.280154 | ||||||||
\(877\) | −17.8328 | −0.602171 | −0.301086 | − | 0.953597i | \(-0.597349\pi\) | ||||
−0.301086 | + | 0.953597i | \(0.597349\pi\) | |||||||
\(878\) | −25.3050 | −0.854001 | ||||||||
\(879\) | 8.68692 | 0.293002 | ||||||||
\(880\) | 30.0000 | 1.01130 | ||||||||
\(881\) | −30.2148 | −1.01796 | −0.508981 | − | 0.860778i | \(-0.669978\pi\) | ||||
−0.508981 | + | 0.860778i | \(0.669978\pi\) | |||||||
\(882\) | −0.257354 | −0.00866557 | ||||||||
\(883\) | 7.21478 | 0.242797 | 0.121398 | − | 0.992604i | \(-0.461262\pi\) | ||||
0.121398 | + | 0.992604i | \(0.461262\pi\) | |||||||
\(884\) | 6.85410 | 0.230528 | ||||||||
\(885\) | −13.7082 | −0.460796 | ||||||||
\(886\) | 13.5066 | 0.453762 | ||||||||
\(887\) | 3.67376 | 0.123353 | 0.0616764 | − | 0.998096i | \(-0.480355\pi\) | ||||
0.0616764 | + | 0.998096i | \(0.480355\pi\) | |||||||
\(888\) | 2.11146 | 0.0708558 | ||||||||
\(889\) | −51.8328 | −1.73842 | ||||||||
\(890\) | −0.291796 | −0.00978103 | ||||||||
\(891\) | 38.5410 | 1.29117 | ||||||||
\(892\) | −30.8885 | −1.03422 | ||||||||
\(893\) | −42.3820 | −1.41826 | ||||||||
\(894\) | −3.92299 | −0.131204 | ||||||||
\(895\) | 73.4853 | 2.45634 | ||||||||
\(896\) | −29.7984 | −0.995494 | ||||||||
\(897\) | −1.52786 | −0.0510139 | ||||||||
\(898\) | −21.0902 | −0.703788 | ||||||||
\(899\) | −45.1246 | −1.50499 | ||||||||
\(900\) | 25.2705 | 0.842350 | ||||||||
\(901\) | 24.1803 | 0.805564 | ||||||||
\(902\) | −13.0902 | −0.435855 | ||||||||
\(903\) | −9.23607 | −0.307357 | ||||||||
\(904\) | 13.6180 | 0.452929 | ||||||||
\(905\) | 59.0132 | 1.96166 | ||||||||
\(906\) | 0.721360 | 0.0239656 | ||||||||
\(907\) | −40.9230 | −1.35883 | −0.679413 | − | 0.733756i | \(-0.737765\pi\) | ||||
−0.679413 | + | 0.733756i | \(0.737765\pi\) | |||||||
\(908\) | 33.0344 | 1.09629 | ||||||||
\(909\) | 17.1246 | 0.567988 | ||||||||
\(910\) | −5.23607 | −0.173574 | ||||||||
\(911\) | 48.5623 | 1.60894 | 0.804470 | − | 0.593993i | \(-0.202449\pi\) | ||||
0.804470 | + | 0.593993i | \(0.202449\pi\) | |||||||
\(912\) | 5.83282 | 0.193144 | ||||||||
\(913\) | −8.81966 | −0.291888 | ||||||||
\(914\) | −5.09017 | −0.168368 | ||||||||
\(915\) | −14.7639 | −0.488081 | ||||||||
\(916\) | 15.2361 | 0.503414 | ||||||||
\(917\) | 42.9787 | 1.41928 | ||||||||
\(918\) | −5.85410 | −0.193214 | ||||||||
\(919\) | 22.4164 | 0.739449 | 0.369725 | − | 0.929141i | \(-0.379452\pi\) | ||||
0.369725 | + | 0.929141i | \(0.379452\pi\) | |||||||
\(920\) | −28.9443 | −0.954264 | ||||||||
\(921\) | −1.58359 | −0.0521811 | ||||||||
\(922\) | −6.85410 | −0.225728 | ||||||||
\(923\) | −9.18034 | −0.302175 | ||||||||
\(924\) | −8.09017 | −0.266147 | ||||||||
\(925\) | −13.5279 | −0.444793 | ||||||||
\(926\) | −3.78522 | −0.124390 | ||||||||
\(927\) | 39.3820 | 1.29347 | ||||||||
\(928\) | −40.6525 | −1.33448 | ||||||||
\(929\) | 29.3607 | 0.963293 | 0.481646 | − | 0.876366i | \(-0.340039\pi\) | ||||
0.481646 | + | 0.876366i | \(0.340039\pi\) | |||||||
\(930\) | −4.76393 | −0.156215 | ||||||||
\(931\) | 1.20163 | 0.0393817 | ||||||||
\(932\) | 7.38197 | 0.241804 | ||||||||
\(933\) | 4.31308 | 0.141204 | ||||||||
\(934\) | −5.12461 | −0.167682 | ||||||||
\(935\) | 68.5410 | 2.24153 | ||||||||
\(936\) | 6.38197 | 0.208601 | ||||||||
\(937\) | 13.3475 | 0.436045 | 0.218022 | − | 0.975944i | \(-0.430039\pi\) | ||||
0.218022 | + | 0.975944i | \(0.430039\pi\) | |||||||
\(938\) | −10.8541 | −0.354399 | ||||||||
\(939\) | −6.87539 | −0.224370 | ||||||||
\(940\) | −26.9443 | −0.878825 | ||||||||
\(941\) | 36.2705 | 1.18238 | 0.591192 | − | 0.806531i | \(-0.298657\pi\) | ||||
0.591192 | + | 0.806531i | \(0.298657\pi\) | |||||||
\(942\) | −0.222912 | −0.00726288 | ||||||||
\(943\) | −16.9443 | −0.551781 | ||||||||
\(944\) | 20.5623 | 0.669246 | ||||||||
\(945\) | −18.9443 | −0.616257 | ||||||||
\(946\) | 28.5410 | 0.927949 | ||||||||
\(947\) | −25.5410 | −0.829972 | −0.414986 | − | 0.909828i | \(-0.636213\pi\) | ||||
−0.414986 | + | 0.909828i | \(0.636213\pi\) | |||||||
\(948\) | −5.85410 | −0.190132 | ||||||||
\(949\) | −13.4164 | −0.435515 | ||||||||
\(950\) | 27.8541 | 0.903706 | ||||||||
\(951\) | −5.68692 | −0.184411 | ||||||||
\(952\) | −24.7984 | −0.803720 | ||||||||
\(953\) | −26.7771 | −0.867395 | −0.433697 | − | 0.901059i | \(-0.642791\pi\) | ||||
−0.433697 | + | 0.901059i | \(0.642791\pi\) | |||||||
\(954\) | 10.0689 | 0.325992 | ||||||||
\(955\) | 5.81966 | 0.188320 | ||||||||
\(956\) | −25.4164 | −0.822025 | ||||||||
\(957\) | −13.8197 | −0.446726 | ||||||||
\(958\) | −11.9656 | −0.386590 | ||||||||
\(959\) | −35.8885 | −1.15890 | ||||||||
\(960\) | 0.291796 | 0.00941768 | ||||||||
\(961\) | 7.88854 | 0.254469 | ||||||||
\(962\) | −1.52786 | −0.0492603 | ||||||||
\(963\) | 31.3951 | 1.01169 | ||||||||
\(964\) | 17.6180 | 0.567439 | ||||||||
\(965\) | 19.4164 | 0.625036 | ||||||||
\(966\) | 2.47214 | 0.0795397 | ||||||||
\(967\) | −16.3951 | −0.527232 | −0.263616 | − | 0.964628i | \(-0.584915\pi\) | ||||
−0.263616 | + | 0.964628i | \(0.584915\pi\) | |||||||
\(968\) | 31.3050 | 1.00618 | ||||||||
\(969\) | 13.3262 | 0.428100 | ||||||||
\(970\) | −7.81966 | −0.251074 | ||||||||
\(971\) | −18.1246 | −0.581646 | −0.290823 | − | 0.956777i | \(-0.593929\pi\) | ||||
−0.290823 | + | 0.956777i | \(0.593929\pi\) | |||||||
\(972\) | 15.6180 | 0.500949 | ||||||||
\(973\) | −8.47214 | −0.271604 | ||||||||
\(974\) | −27.0000 | −0.865136 | ||||||||
\(975\) | 2.09017 | 0.0669390 | ||||||||
\(976\) | 22.1459 | 0.708873 | ||||||||
\(977\) | 32.6738 | 1.04533 | 0.522663 | − | 0.852539i | \(-0.324939\pi\) | ||||
0.522663 | + | 0.852539i | \(0.324939\pi\) | |||||||
\(978\) | 0.167184 | 0.00534596 | ||||||||
\(979\) | 0.729490 | 0.0233146 | ||||||||
\(980\) | 0.763932 | 0.0244029 | ||||||||
\(981\) | 53.3951 | 1.70478 | ||||||||
\(982\) | −1.70820 | −0.0545110 | ||||||||
\(983\) | −54.7771 | −1.74712 | −0.873559 | − | 0.486718i | \(-0.838194\pi\) | ||||
−0.873559 | + | 0.486718i | \(0.838194\pi\) | |||||||
\(984\) | −3.61803 | −0.115339 | ||||||||
\(985\) | 40.6525 | 1.29530 | ||||||||
\(986\) | −18.9443 | −0.603309 | ||||||||
\(987\) | 5.14590 | 0.163796 | ||||||||
\(988\) | −13.3262 | −0.423964 | ||||||||
\(989\) | 36.9443 | 1.17476 | ||||||||
\(990\) | 28.5410 | 0.907093 | ||||||||
\(991\) | 49.3050 | 1.56622 | 0.783112 | − | 0.621881i | \(-0.213631\pi\) | ||||
0.783112 | + | 0.621881i | \(0.213631\pi\) | |||||||
\(992\) | 35.0344 | 1.11234 | ||||||||
\(993\) | 2.68692 | 0.0852668 | ||||||||
\(994\) | 14.8541 | 0.471144 | ||||||||
\(995\) | −8.47214 | −0.268585 | ||||||||
\(996\) | −1.09017 | −0.0345434 | ||||||||
\(997\) | −23.4508 | −0.742696 | −0.371348 | − | 0.928494i | \(-0.621104\pi\) | ||||
−0.371348 | + | 0.928494i | \(0.621104\pi\) | |||||||
\(998\) | −12.3475 | −0.390854 | ||||||||
\(999\) | −5.52786 | −0.174894 |
(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 | 8047.2.a.a.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8047.2.a.a.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial |