Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8031,2,Mod(1,8031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8031, 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("8031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8031 = 3 \cdot 2677 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8031.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: | \(64.1278578633\) |
Analytic rank: | \(0\) |
Dimension: | \(121\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 8031.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.74757 | −1.94282 | −0.971412 | − | 0.237400i | \(-0.923705\pi\) | ||||
−0.971412 | + | 0.237400i | \(0.923705\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.54913 | 2.77456 | ||||||||
\(5\) | 2.21252 | 0.989468 | 0.494734 | − | 0.869045i | \(-0.335266\pi\) | ||||
0.494734 | + | 0.869045i | \(0.335266\pi\) | |||||||
\(6\) | 2.74757 | 1.12169 | ||||||||
\(7\) | −1.55769 | −0.588752 | −0.294376 | − | 0.955690i | \(-0.595112\pi\) | ||||
−0.294376 | + | 0.955690i | \(0.595112\pi\) | |||||||
\(8\) | −9.75147 | −3.44767 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −6.07904 | −1.92236 | ||||||||
\(11\) | 6.00610 | 1.81091 | 0.905453 | − | 0.424446i | \(-0.139531\pi\) | ||||
0.905453 | + | 0.424446i | \(0.139531\pi\) | |||||||
\(12\) | −5.54913 | −1.60190 | ||||||||
\(13\) | 6.05867 | 1.68037 | 0.840186 | − | 0.542299i | \(-0.182446\pi\) | ||||
0.840186 | + | 0.542299i | \(0.182446\pi\) | |||||||
\(14\) | 4.27986 | 1.14384 | ||||||||
\(15\) | −2.21252 | −0.571270 | ||||||||
\(16\) | 15.6946 | 3.92364 | ||||||||
\(17\) | 4.46030 | 1.08178 | 0.540890 | − | 0.841093i | \(-0.318087\pi\) | ||||
0.540890 | + | 0.841093i | \(0.318087\pi\) | |||||||
\(18\) | −2.74757 | −0.647608 | ||||||||
\(19\) | −4.53083 | −1.03944 | −0.519722 | − | 0.854336i | \(-0.673964\pi\) | ||||
−0.519722 | + | 0.854336i | \(0.673964\pi\) | |||||||
\(20\) | 12.2775 | 2.74534 | ||||||||
\(21\) | 1.55769 | 0.339916 | ||||||||
\(22\) | −16.5022 | −3.51827 | ||||||||
\(23\) | −3.96954 | −0.827706 | −0.413853 | − | 0.910344i | \(-0.635817\pi\) | ||||
−0.413853 | + | 0.910344i | \(0.635817\pi\) | |||||||
\(24\) | 9.75147 | 1.99051 | ||||||||
\(25\) | −0.104767 | −0.0209535 | ||||||||
\(26\) | −16.6466 | −3.26467 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −8.64382 | −1.63353 | ||||||||
\(29\) | −6.62434 | −1.23011 | −0.615055 | − | 0.788484i | \(-0.710866\pi\) | ||||
−0.615055 | + | 0.788484i | \(0.710866\pi\) | |||||||
\(30\) | 6.07904 | 1.10988 | ||||||||
\(31\) | 1.30598 | 0.234560 | 0.117280 | − | 0.993099i | \(-0.462582\pi\) | ||||
0.117280 | + | 0.993099i | \(0.462582\pi\) | |||||||
\(32\) | −23.6190 | −4.17528 | ||||||||
\(33\) | −6.00610 | −1.04553 | ||||||||
\(34\) | −12.2550 | −2.10171 | ||||||||
\(35\) | −3.44642 | −0.582551 | ||||||||
\(36\) | 5.54913 | 0.924855 | ||||||||
\(37\) | 8.30005 | 1.36452 | 0.682260 | − | 0.731110i | \(-0.260997\pi\) | ||||
0.682260 | + | 0.731110i | \(0.260997\pi\) | |||||||
\(38\) | 12.4488 | 2.01946 | ||||||||
\(39\) | −6.05867 | −0.970163 | ||||||||
\(40\) | −21.5753 | −3.41135 | ||||||||
\(41\) | 8.28247 | 1.29350 | 0.646752 | − | 0.762700i | \(-0.276127\pi\) | ||||
0.646752 | + | 0.762700i | \(0.276127\pi\) | |||||||
\(42\) | −4.27986 | −0.660397 | ||||||||
\(43\) | −7.55710 | −1.15245 | −0.576223 | − | 0.817292i | \(-0.695474\pi\) | ||||
−0.576223 | + | 0.817292i | \(0.695474\pi\) | |||||||
\(44\) | 33.3286 | 5.02448 | ||||||||
\(45\) | 2.21252 | 0.329823 | ||||||||
\(46\) | 10.9066 | 1.60809 | ||||||||
\(47\) | −6.00883 | −0.876477 | −0.438239 | − | 0.898859i | \(-0.644398\pi\) | ||||
−0.438239 | + | 0.898859i | \(0.644398\pi\) | |||||||
\(48\) | −15.6946 | −2.26532 | ||||||||
\(49\) | −4.57360 | −0.653371 | ||||||||
\(50\) | 0.287855 | 0.0407089 | ||||||||
\(51\) | −4.46030 | −0.624566 | ||||||||
\(52\) | 33.6203 | 4.66230 | ||||||||
\(53\) | −5.93758 | −0.815589 | −0.407795 | − | 0.913074i | \(-0.633702\pi\) | ||||
−0.407795 | + | 0.913074i | \(0.633702\pi\) | |||||||
\(54\) | 2.74757 | 0.373897 | ||||||||
\(55\) | 13.2886 | 1.79183 | ||||||||
\(56\) | 15.1898 | 2.02982 | ||||||||
\(57\) | 4.53083 | 0.600123 | ||||||||
\(58\) | 18.2008 | 2.38989 | ||||||||
\(59\) | 10.4522 | 1.36076 | 0.680378 | − | 0.732861i | \(-0.261816\pi\) | ||||
0.680378 | + | 0.732861i | \(0.261816\pi\) | |||||||
\(60\) | −12.2775 | −1.58502 | ||||||||
\(61\) | 12.7662 | 1.63454 | 0.817271 | − | 0.576254i | \(-0.195486\pi\) | ||||
0.817271 | + | 0.576254i | \(0.195486\pi\) | |||||||
\(62\) | −3.58826 | −0.455709 | ||||||||
\(63\) | −1.55769 | −0.196251 | ||||||||
\(64\) | 33.5055 | 4.18819 | ||||||||
\(65\) | 13.4049 | 1.66267 | ||||||||
\(66\) | 16.5022 | 2.03128 | ||||||||
\(67\) | −1.73062 | −0.211429 | −0.105715 | − | 0.994397i | \(-0.533713\pi\) | ||||
−0.105715 | + | 0.994397i | \(0.533713\pi\) | |||||||
\(68\) | 24.7508 | 3.00147 | ||||||||
\(69\) | 3.96954 | 0.477876 | ||||||||
\(70\) | 9.46926 | 1.13179 | ||||||||
\(71\) | 8.40701 | 0.997729 | 0.498864 | − | 0.866680i | \(-0.333751\pi\) | ||||
0.498864 | + | 0.866680i | \(0.333751\pi\) | |||||||
\(72\) | −9.75147 | −1.14922 | ||||||||
\(73\) | −0.502247 | −0.0587836 | −0.0293918 | − | 0.999568i | \(-0.509357\pi\) | ||||
−0.0293918 | + | 0.999568i | \(0.509357\pi\) | |||||||
\(74\) | −22.8050 | −2.65102 | ||||||||
\(75\) | 0.104767 | 0.0120975 | ||||||||
\(76\) | −25.1422 | −2.88400 | ||||||||
\(77\) | −9.35564 | −1.06617 | ||||||||
\(78\) | 16.6466 | 1.88486 | ||||||||
\(79\) | −16.1915 | −1.82168 | −0.910840 | − | 0.412759i | \(-0.864565\pi\) | ||||
−0.910840 | + | 0.412759i | \(0.864565\pi\) | |||||||
\(80\) | 34.7245 | 3.88232 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −22.7566 | −2.51305 | ||||||||
\(83\) | 3.50690 | 0.384932 | 0.192466 | − | 0.981304i | \(-0.438352\pi\) | ||||
0.192466 | + | 0.981304i | \(0.438352\pi\) | |||||||
\(84\) | 8.64382 | 0.943119 | ||||||||
\(85\) | 9.86848 | 1.07039 | ||||||||
\(86\) | 20.7636 | 2.23900 | ||||||||
\(87\) | 6.62434 | 0.710204 | ||||||||
\(88\) | −58.5683 | −6.24340 | ||||||||
\(89\) | 3.54616 | 0.375892 | 0.187946 | − | 0.982179i | \(-0.439817\pi\) | ||||
0.187946 | + | 0.982179i | \(0.439817\pi\) | |||||||
\(90\) | −6.07904 | −0.640787 | ||||||||
\(91\) | −9.43753 | −0.989322 | ||||||||
\(92\) | −22.0275 | −2.29652 | ||||||||
\(93\) | −1.30598 | −0.135423 | ||||||||
\(94\) | 16.5097 | 1.70284 | ||||||||
\(95\) | −10.0245 | −1.02850 | ||||||||
\(96\) | 23.6190 | 2.41060 | ||||||||
\(97\) | 4.69477 | 0.476682 | 0.238341 | − | 0.971182i | \(-0.423396\pi\) | ||||
0.238341 | + | 0.971182i | \(0.423396\pi\) | |||||||
\(98\) | 12.5663 | 1.26939 | ||||||||
\(99\) | 6.00610 | 0.603636 | ||||||||
\(100\) | −0.581367 | −0.0581367 | ||||||||
\(101\) | 3.25149 | 0.323535 | 0.161767 | − | 0.986829i | \(-0.448281\pi\) | ||||
0.161767 | + | 0.986829i | \(0.448281\pi\) | |||||||
\(102\) | 12.2550 | 1.21342 | ||||||||
\(103\) | −15.1892 | −1.49664 | −0.748319 | − | 0.663339i | \(-0.769139\pi\) | ||||
−0.748319 | + | 0.663339i | \(0.769139\pi\) | |||||||
\(104\) | −59.0809 | −5.79336 | ||||||||
\(105\) | 3.44642 | 0.336336 | ||||||||
\(106\) | 16.3139 | 1.58455 | ||||||||
\(107\) | 19.3046 | 1.86624 | 0.933121 | − | 0.359562i | \(-0.117074\pi\) | ||||
0.933121 | + | 0.359562i | \(0.117074\pi\) | |||||||
\(108\) | −5.54913 | −0.533965 | ||||||||
\(109\) | −2.16302 | −0.207179 | −0.103590 | − | 0.994620i | \(-0.533033\pi\) | ||||
−0.103590 | + | 0.994620i | \(0.533033\pi\) | |||||||
\(110\) | −36.5113 | −3.48122 | ||||||||
\(111\) | −8.30005 | −0.787806 | ||||||||
\(112\) | −24.4473 | −2.31005 | ||||||||
\(113\) | 17.6074 | 1.65636 | 0.828181 | − | 0.560461i | \(-0.189376\pi\) | ||||
0.828181 | + | 0.560461i | \(0.189376\pi\) | |||||||
\(114\) | −12.4488 | −1.16593 | ||||||||
\(115\) | −8.78267 | −0.818988 | ||||||||
\(116\) | −36.7593 | −3.41302 | ||||||||
\(117\) | 6.05867 | 0.560124 | ||||||||
\(118\) | −28.7180 | −2.64371 | ||||||||
\(119\) | −6.94776 | −0.636900 | ||||||||
\(120\) | 21.5753 | 1.96955 | ||||||||
\(121\) | 25.0732 | 2.27938 | ||||||||
\(122\) | −35.0759 | −3.17563 | ||||||||
\(123\) | −8.28247 | −0.746805 | ||||||||
\(124\) | 7.24703 | 0.650803 | ||||||||
\(125\) | −11.2944 | −1.01020 | ||||||||
\(126\) | 4.27986 | 0.381280 | ||||||||
\(127\) | −15.7505 | −1.39763 | −0.698816 | − | 0.715301i | \(-0.746289\pi\) | ||||
−0.698816 | + | 0.715301i | \(0.746289\pi\) | |||||||
\(128\) | −44.8208 | −3.96164 | ||||||||
\(129\) | 7.55710 | 0.665365 | ||||||||
\(130\) | −36.8309 | −3.23028 | ||||||||
\(131\) | 11.3099 | 0.988150 | 0.494075 | − | 0.869419i | \(-0.335507\pi\) | ||||
0.494075 | + | 0.869419i | \(0.335507\pi\) | |||||||
\(132\) | −33.3286 | −2.90088 | ||||||||
\(133\) | 7.05763 | 0.611974 | ||||||||
\(134\) | 4.75500 | 0.410770 | ||||||||
\(135\) | −2.21252 | −0.190423 | ||||||||
\(136\) | −43.4944 | −3.72962 | ||||||||
\(137\) | 4.38239 | 0.374413 | 0.187207 | − | 0.982321i | \(-0.440057\pi\) | ||||
0.187207 | + | 0.982321i | \(0.440057\pi\) | |||||||
\(138\) | −10.9066 | −0.928429 | ||||||||
\(139\) | 23.4390 | 1.98807 | 0.994035 | − | 0.109063i | \(-0.0347850\pi\) | ||||
0.994035 | + | 0.109063i | \(0.0347850\pi\) | |||||||
\(140\) | −19.1246 | −1.61632 | ||||||||
\(141\) | 6.00883 | 0.506034 | ||||||||
\(142\) | −23.0988 | −1.93841 | ||||||||
\(143\) | 36.3889 | 3.04300 | ||||||||
\(144\) | 15.6946 | 1.30788 | ||||||||
\(145\) | −14.6565 | −1.21715 | ||||||||
\(146\) | 1.37996 | 0.114206 | ||||||||
\(147\) | 4.57360 | 0.377224 | ||||||||
\(148\) | 46.0581 | 3.78595 | ||||||||
\(149\) | 19.2293 | 1.57533 | 0.787663 | − | 0.616106i | \(-0.211291\pi\) | ||||
0.787663 | + | 0.616106i | \(0.211291\pi\) | |||||||
\(150\) | −0.287855 | −0.0235033 | ||||||||
\(151\) | −4.55171 | −0.370413 | −0.185206 | − | 0.982700i | \(-0.559295\pi\) | ||||
−0.185206 | + | 0.982700i | \(0.559295\pi\) | |||||||
\(152\) | 44.1823 | 3.58365 | ||||||||
\(153\) | 4.46030 | 0.360594 | ||||||||
\(154\) | 25.7053 | 2.07139 | ||||||||
\(155\) | 2.88950 | 0.232090 | ||||||||
\(156\) | −33.6203 | −2.69178 | ||||||||
\(157\) | −2.77945 | −0.221824 | −0.110912 | − | 0.993830i | \(-0.535377\pi\) | ||||
−0.110912 | + | 0.993830i | \(0.535377\pi\) | |||||||
\(158\) | 44.4871 | 3.53920 | ||||||||
\(159\) | 5.93758 | 0.470881 | ||||||||
\(160\) | −52.2573 | −4.13131 | ||||||||
\(161\) | 6.18331 | 0.487313 | ||||||||
\(162\) | −2.74757 | −0.215869 | ||||||||
\(163\) | 1.21163 | 0.0949018 | 0.0474509 | − | 0.998874i | \(-0.484890\pi\) | ||||
0.0474509 | + | 0.998874i | \(0.484890\pi\) | |||||||
\(164\) | 45.9605 | 3.58891 | ||||||||
\(165\) | −13.2886 | −1.03452 | ||||||||
\(166\) | −9.63543 | −0.747855 | ||||||||
\(167\) | 4.46349 | 0.345396 | 0.172698 | − | 0.984975i | \(-0.444752\pi\) | ||||
0.172698 | + | 0.984975i | \(0.444752\pi\) | |||||||
\(168\) | −15.1898 | −1.17192 | ||||||||
\(169\) | 23.7074 | 1.82365 | ||||||||
\(170\) | −27.1143 | −2.07957 | ||||||||
\(171\) | −4.53083 | −0.346481 | ||||||||
\(172\) | −41.9353 | −3.19754 | ||||||||
\(173\) | −18.7613 | −1.42640 | −0.713198 | − | 0.700963i | \(-0.752754\pi\) | ||||
−0.713198 | + | 0.700963i | \(0.752754\pi\) | |||||||
\(174\) | −18.2008 | −1.37980 | ||||||||
\(175\) | 0.163195 | 0.0123364 | ||||||||
\(176\) | 94.2631 | 7.10535 | ||||||||
\(177\) | −10.4522 | −0.785633 | ||||||||
\(178\) | −9.74331 | −0.730292 | ||||||||
\(179\) | 0.436788 | 0.0326471 | 0.0163235 | − | 0.999867i | \(-0.494804\pi\) | ||||
0.0163235 | + | 0.999867i | \(0.494804\pi\) | |||||||
\(180\) | 12.2775 | 0.915114 | ||||||||
\(181\) | 4.76246 | 0.353991 | 0.176995 | − | 0.984212i | \(-0.443362\pi\) | ||||
0.176995 | + | 0.984212i | \(0.443362\pi\) | |||||||
\(182\) | 25.9302 | 1.92208 | ||||||||
\(183\) | −12.7662 | −0.943703 | ||||||||
\(184\) | 38.7088 | 2.85365 | ||||||||
\(185\) | 18.3640 | 1.35015 | ||||||||
\(186\) | 3.58826 | 0.263104 | ||||||||
\(187\) | 26.7890 | 1.95900 | ||||||||
\(188\) | −33.3437 | −2.43184 | ||||||||
\(189\) | 1.55769 | 0.113305 | ||||||||
\(190\) | 27.5431 | 1.99819 | ||||||||
\(191\) | 0.772465 | 0.0558936 | 0.0279468 | − | 0.999609i | \(-0.491103\pi\) | ||||
0.0279468 | + | 0.999609i | \(0.491103\pi\) | |||||||
\(192\) | −33.5055 | −2.41805 | ||||||||
\(193\) | 10.0741 | 0.725152 | 0.362576 | − | 0.931954i | \(-0.381897\pi\) | ||||
0.362576 | + | 0.931954i | \(0.381897\pi\) | |||||||
\(194\) | −12.8992 | −0.926109 | ||||||||
\(195\) | −13.4049 | −0.959945 | ||||||||
\(196\) | −25.3795 | −1.81282 | ||||||||
\(197\) | −16.5714 | −1.18066 | −0.590331 | − | 0.807161i | \(-0.701003\pi\) | ||||
−0.590331 | + | 0.807161i | \(0.701003\pi\) | |||||||
\(198\) | −16.5022 | −1.17276 | ||||||||
\(199\) | −11.8970 | −0.843355 | −0.421677 | − | 0.906746i | \(-0.638559\pi\) | ||||
−0.421677 | + | 0.906746i | \(0.638559\pi\) | |||||||
\(200\) | 1.02164 | 0.0722405 | ||||||||
\(201\) | 1.73062 | 0.122069 | ||||||||
\(202\) | −8.93368 | −0.628571 | ||||||||
\(203\) | 10.3187 | 0.724229 | ||||||||
\(204\) | −24.7508 | −1.73290 | ||||||||
\(205\) | 18.3251 | 1.27988 | ||||||||
\(206\) | 41.7334 | 2.90770 | ||||||||
\(207\) | −3.96954 | −0.275902 | ||||||||
\(208\) | 95.0882 | 6.59318 | ||||||||
\(209\) | −27.2126 | −1.88234 | ||||||||
\(210\) | −9.46926 | −0.653441 | ||||||||
\(211\) | −5.38451 | −0.370685 | −0.185343 | − | 0.982674i | \(-0.559339\pi\) | ||||
−0.185343 | + | 0.982674i | \(0.559339\pi\) | |||||||
\(212\) | −32.9484 | −2.26290 | ||||||||
\(213\) | −8.40701 | −0.576039 | ||||||||
\(214\) | −53.0406 | −3.62578 | ||||||||
\(215\) | −16.7202 | −1.14031 | ||||||||
\(216\) | 9.75147 | 0.663504 | ||||||||
\(217\) | −2.03431 | −0.138098 | ||||||||
\(218\) | 5.94303 | 0.402513 | ||||||||
\(219\) | 0.502247 | 0.0339387 | ||||||||
\(220\) | 73.7401 | 4.97156 | ||||||||
\(221\) | 27.0234 | 1.81779 | ||||||||
\(222\) | 22.8050 | 1.53057 | ||||||||
\(223\) | −18.7497 | −1.25557 | −0.627786 | − | 0.778386i | \(-0.716039\pi\) | ||||
−0.627786 | + | 0.778386i | \(0.716039\pi\) | |||||||
\(224\) | 36.7910 | 2.45820 | ||||||||
\(225\) | −0.104767 | −0.00698449 | ||||||||
\(226\) | −48.3774 | −3.21802 | ||||||||
\(227\) | −0.0521256 | −0.00345970 | −0.00172985 | − | 0.999999i | \(-0.500551\pi\) | ||||
−0.00172985 | + | 0.999999i | \(0.500551\pi\) | |||||||
\(228\) | 25.1422 | 1.66508 | ||||||||
\(229\) | 4.20753 | 0.278041 | 0.139021 | − | 0.990289i | \(-0.455605\pi\) | ||||
0.139021 | + | 0.990289i | \(0.455605\pi\) | |||||||
\(230\) | 24.1310 | 1.59115 | ||||||||
\(231\) | 9.35564 | 0.615556 | ||||||||
\(232\) | 64.5971 | 4.24101 | ||||||||
\(233\) | 28.7006 | 1.88024 | 0.940119 | − | 0.340846i | \(-0.110713\pi\) | ||||
0.940119 | + | 0.340846i | \(0.110713\pi\) | |||||||
\(234\) | −16.6466 | −1.08822 | ||||||||
\(235\) | −13.2946 | −0.867246 | ||||||||
\(236\) | 58.0004 | 3.77551 | ||||||||
\(237\) | 16.1915 | 1.05175 | ||||||||
\(238\) | 19.0894 | 1.23738 | ||||||||
\(239\) | 25.1940 | 1.62967 | 0.814833 | − | 0.579696i | \(-0.196829\pi\) | ||||
0.814833 | + | 0.579696i | \(0.196829\pi\) | |||||||
\(240\) | −34.7245 | −2.24146 | ||||||||
\(241\) | 18.6150 | 1.19910 | 0.599549 | − | 0.800338i | \(-0.295347\pi\) | ||||
0.599549 | + | 0.800338i | \(0.295347\pi\) | |||||||
\(242\) | −68.8903 | −4.42844 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 70.8411 | 4.53514 | ||||||||
\(245\) | −10.1192 | −0.646490 | ||||||||
\(246\) | 22.7566 | 1.45091 | ||||||||
\(247\) | −27.4508 | −1.74665 | ||||||||
\(248\) | −12.7352 | −0.808686 | ||||||||
\(249\) | −3.50690 | −0.222240 | ||||||||
\(250\) | 31.0321 | 1.96264 | ||||||||
\(251\) | 23.3464 | 1.47361 | 0.736807 | − | 0.676103i | \(-0.236333\pi\) | ||||
0.736807 | + | 0.676103i | \(0.236333\pi\) | |||||||
\(252\) | −8.64382 | −0.544510 | ||||||||
\(253\) | −23.8414 | −1.49890 | ||||||||
\(254\) | 43.2756 | 2.71535 | ||||||||
\(255\) | −9.86848 | −0.617988 | ||||||||
\(256\) | 56.1371 | 3.50857 | ||||||||
\(257\) | −13.6295 | −0.850183 | −0.425092 | − | 0.905150i | \(-0.639758\pi\) | ||||
−0.425092 | + | 0.905150i | \(0.639758\pi\) | |||||||
\(258\) | −20.7636 | −1.29269 | ||||||||
\(259\) | −12.9289 | −0.803363 | ||||||||
\(260\) | 74.3855 | 4.61319 | ||||||||
\(261\) | −6.62434 | −0.410036 | ||||||||
\(262\) | −31.0747 | −1.91980 | ||||||||
\(263\) | 23.1750 | 1.42903 | 0.714515 | − | 0.699620i | \(-0.246647\pi\) | ||||
0.714515 | + | 0.699620i | \(0.246647\pi\) | |||||||
\(264\) | 58.5683 | 3.60463 | ||||||||
\(265\) | −13.1370 | −0.806999 | ||||||||
\(266\) | −19.3913 | −1.18896 | ||||||||
\(267\) | −3.54616 | −0.217021 | ||||||||
\(268\) | −9.60345 | −0.586624 | ||||||||
\(269\) | −22.1242 | −1.34893 | −0.674467 | − | 0.738305i | \(-0.735627\pi\) | ||||
−0.674467 | + | 0.738305i | \(0.735627\pi\) | |||||||
\(270\) | 6.07904 | 0.369959 | ||||||||
\(271\) | −28.9996 | −1.76160 | −0.880799 | − | 0.473490i | \(-0.842994\pi\) | ||||
−0.880799 | + | 0.473490i | \(0.842994\pi\) | |||||||
\(272\) | 70.0024 | 4.24452 | ||||||||
\(273\) | 9.43753 | 0.571185 | ||||||||
\(274\) | −12.0409 | −0.727419 | ||||||||
\(275\) | −0.629243 | −0.0379448 | ||||||||
\(276\) | 22.0275 | 1.32590 | ||||||||
\(277\) | −31.0328 | −1.86458 | −0.932290 | − | 0.361711i | \(-0.882193\pi\) | ||||
−0.932290 | + | 0.361711i | \(0.882193\pi\) | |||||||
\(278\) | −64.4002 | −3.86247 | ||||||||
\(279\) | 1.30598 | 0.0781868 | ||||||||
\(280\) | 33.6076 | 2.00844 | ||||||||
\(281\) | 26.9054 | 1.60504 | 0.802519 | − | 0.596626i | \(-0.203492\pi\) | ||||
0.802519 | + | 0.596626i | \(0.203492\pi\) | |||||||
\(282\) | −16.5097 | −0.983136 | ||||||||
\(283\) | 6.18102 | 0.367424 | 0.183712 | − | 0.982980i | \(-0.441189\pi\) | ||||
0.183712 | + | 0.982980i | \(0.441189\pi\) | |||||||
\(284\) | 46.6516 | 2.76826 | ||||||||
\(285\) | 10.0245 | 0.593802 | ||||||||
\(286\) | −99.9811 | −5.91201 | ||||||||
\(287\) | −12.9015 | −0.761553 | ||||||||
\(288\) | −23.6190 | −1.39176 | ||||||||
\(289\) | 2.89423 | 0.170249 | ||||||||
\(290\) | 40.2696 | 2.36471 | ||||||||
\(291\) | −4.69477 | −0.275212 | ||||||||
\(292\) | −2.78703 | −0.163099 | ||||||||
\(293\) | 6.45950 | 0.377368 | 0.188684 | − | 0.982038i | \(-0.439578\pi\) | ||||
0.188684 | + | 0.982038i | \(0.439578\pi\) | |||||||
\(294\) | −12.5663 | −0.732880 | ||||||||
\(295\) | 23.1256 | 1.34642 | ||||||||
\(296\) | −80.9377 | −4.70441 | ||||||||
\(297\) | −6.00610 | −0.348509 | ||||||||
\(298\) | −52.8338 | −3.06058 | ||||||||
\(299\) | −24.0501 | −1.39085 | ||||||||
\(300\) | 0.581367 | 0.0335653 | ||||||||
\(301\) | 11.7716 | 0.678505 | ||||||||
\(302\) | 12.5061 | 0.719647 | ||||||||
\(303\) | −3.25149 | −0.186793 | ||||||||
\(304\) | −71.1094 | −4.07841 | ||||||||
\(305\) | 28.2454 | 1.61733 | ||||||||
\(306\) | −12.2550 | −0.700570 | ||||||||
\(307\) | 31.6904 | 1.80867 | 0.904333 | − | 0.426829i | \(-0.140369\pi\) | ||||
0.904333 | + | 0.426829i | \(0.140369\pi\) | |||||||
\(308\) | −51.9157 | −2.95817 | ||||||||
\(309\) | 15.1892 | 0.864084 | ||||||||
\(310\) | −7.93909 | −0.450910 | ||||||||
\(311\) | 1.83262 | 0.103918 | 0.0519592 | − | 0.998649i | \(-0.483453\pi\) | ||||
0.0519592 | + | 0.998649i | \(0.483453\pi\) | |||||||
\(312\) | 59.0809 | 3.34480 | ||||||||
\(313\) | −7.97844 | −0.450968 | −0.225484 | − | 0.974247i | \(-0.572396\pi\) | ||||
−0.225484 | + | 0.974247i | \(0.572396\pi\) | |||||||
\(314\) | 7.63672 | 0.430965 | ||||||||
\(315\) | −3.44642 | −0.194184 | ||||||||
\(316\) | −89.8484 | −5.05437 | ||||||||
\(317\) | −18.8827 | −1.06056 | −0.530279 | − | 0.847823i | \(-0.677913\pi\) | ||||
−0.530279 | + | 0.847823i | \(0.677913\pi\) | |||||||
\(318\) | −16.3139 | −0.914838 | ||||||||
\(319\) | −39.7864 | −2.22761 | ||||||||
\(320\) | 74.1316 | 4.14408 | ||||||||
\(321\) | −19.3046 | −1.07748 | ||||||||
\(322\) | −16.9891 | −0.946763 | ||||||||
\(323\) | −20.2088 | −1.12445 | ||||||||
\(324\) | 5.54913 | 0.308285 | ||||||||
\(325\) | −0.634750 | −0.0352096 | ||||||||
\(326\) | −3.32902 | −0.184378 | ||||||||
\(327\) | 2.16302 | 0.119615 | ||||||||
\(328\) | −80.7662 | −4.45957 | ||||||||
\(329\) | 9.35989 | 0.516027 | ||||||||
\(330\) | 36.5113 | 2.00988 | ||||||||
\(331\) | −3.82207 | −0.210080 | −0.105040 | − | 0.994468i | \(-0.533497\pi\) | ||||
−0.105040 | + | 0.994468i | \(0.533497\pi\) | |||||||
\(332\) | 19.4602 | 1.06802 | ||||||||
\(333\) | 8.30005 | 0.454840 | ||||||||
\(334\) | −12.2638 | −0.671043 | ||||||||
\(335\) | −3.82903 | −0.209202 | ||||||||
\(336\) | 24.4473 | 1.33371 | ||||||||
\(337\) | 11.2743 | 0.614150 | 0.307075 | − | 0.951685i | \(-0.400650\pi\) | ||||
0.307075 | + | 0.951685i | \(0.400650\pi\) | |||||||
\(338\) | −65.1378 | −3.54303 | ||||||||
\(339\) | −17.6074 | −0.956301 | ||||||||
\(340\) | 54.7615 | 2.96986 | ||||||||
\(341\) | 7.84383 | 0.424767 | ||||||||
\(342\) | 12.4488 | 0.673152 | ||||||||
\(343\) | 18.0281 | 0.973425 | ||||||||
\(344\) | 73.6928 | 3.97325 | ||||||||
\(345\) | 8.78267 | 0.472843 | ||||||||
\(346\) | 51.5479 | 2.77123 | ||||||||
\(347\) | 20.0963 | 1.07883 | 0.539413 | − | 0.842041i | \(-0.318646\pi\) | ||||
0.539413 | + | 0.842041i | \(0.318646\pi\) | |||||||
\(348\) | 36.7593 | 1.97051 | ||||||||
\(349\) | 4.54278 | 0.243169 | 0.121585 | − | 0.992581i | \(-0.461202\pi\) | ||||
0.121585 | + | 0.992581i | \(0.461202\pi\) | |||||||
\(350\) | −0.448389 | −0.0239674 | ||||||||
\(351\) | −6.05867 | −0.323388 | ||||||||
\(352\) | −141.858 | −7.56104 | ||||||||
\(353\) | 15.6005 | 0.830329 | 0.415164 | − | 0.909746i | \(-0.363724\pi\) | ||||
0.415164 | + | 0.909746i | \(0.363724\pi\) | |||||||
\(354\) | 28.7180 | 1.52635 | ||||||||
\(355\) | 18.6007 | 0.987220 | ||||||||
\(356\) | 19.6781 | 1.04294 | ||||||||
\(357\) | 6.94776 | 0.367714 | ||||||||
\(358\) | −1.20011 | −0.0634276 | ||||||||
\(359\) | 0.108663 | 0.00573500 | 0.00286750 | − | 0.999996i | \(-0.499087\pi\) | ||||
0.00286750 | + | 0.999996i | \(0.499087\pi\) | |||||||
\(360\) | −21.5753 | −1.13712 | ||||||||
\(361\) | 1.52842 | 0.0804432 | ||||||||
\(362\) | −13.0852 | −0.687741 | ||||||||
\(363\) | −25.0732 | −1.31600 | ||||||||
\(364\) | −52.3700 | −2.74494 | ||||||||
\(365\) | −1.11123 | −0.0581644 | ||||||||
\(366\) | 35.0759 | 1.83345 | ||||||||
\(367\) | −2.93528 | −0.153221 | −0.0766103 | − | 0.997061i | \(-0.524410\pi\) | ||||
−0.0766103 | + | 0.997061i | \(0.524410\pi\) | |||||||
\(368\) | −62.3002 | −3.24762 | ||||||||
\(369\) | 8.28247 | 0.431168 | ||||||||
\(370\) | −50.4564 | −2.62310 | ||||||||
\(371\) | 9.24891 | 0.480179 | ||||||||
\(372\) | −7.24703 | −0.375741 | ||||||||
\(373\) | −11.3967 | −0.590099 | −0.295050 | − | 0.955482i | \(-0.595336\pi\) | ||||
−0.295050 | + | 0.955482i | \(0.595336\pi\) | |||||||
\(374\) | −73.6045 | −3.80600 | ||||||||
\(375\) | 11.2944 | 0.583240 | ||||||||
\(376\) | 58.5949 | 3.02180 | ||||||||
\(377\) | −40.1347 | −2.06704 | ||||||||
\(378\) | −4.27986 | −0.220132 | ||||||||
\(379\) | 2.70586 | 0.138991 | 0.0694953 | − | 0.997582i | \(-0.477861\pi\) | ||||
0.0694953 | + | 0.997582i | \(0.477861\pi\) | |||||||
\(380\) | −55.6275 | −2.85363 | ||||||||
\(381\) | 15.7505 | 0.806923 | ||||||||
\(382\) | −2.12240 | −0.108591 | ||||||||
\(383\) | −10.6807 | −0.545758 | −0.272879 | − | 0.962048i | \(-0.587976\pi\) | ||||
−0.272879 | + | 0.962048i | \(0.587976\pi\) | |||||||
\(384\) | 44.8208 | 2.28725 | ||||||||
\(385\) | −20.6995 | −1.05495 | ||||||||
\(386\) | −27.6794 | −1.40884 | ||||||||
\(387\) | −7.55710 | −0.384149 | ||||||||
\(388\) | 26.0519 | 1.32258 | ||||||||
\(389\) | −12.6876 | −0.643288 | −0.321644 | − | 0.946861i | \(-0.604235\pi\) | ||||
−0.321644 | + | 0.946861i | \(0.604235\pi\) | |||||||
\(390\) | 36.8309 | 1.86500 | ||||||||
\(391\) | −17.7053 | −0.895396 | ||||||||
\(392\) | 44.5993 | 2.25261 | ||||||||
\(393\) | −11.3099 | −0.570508 | ||||||||
\(394\) | 45.5310 | 2.29382 | ||||||||
\(395\) | −35.8239 | −1.80249 | ||||||||
\(396\) | 33.3286 | 1.67483 | ||||||||
\(397\) | 25.4445 | 1.27702 | 0.638512 | − | 0.769612i | \(-0.279550\pi\) | ||||
0.638512 | + | 0.769612i | \(0.279550\pi\) | |||||||
\(398\) | 32.6878 | 1.63849 | ||||||||
\(399\) | −7.05763 | −0.353323 | ||||||||
\(400\) | −1.64428 | −0.0822139 | ||||||||
\(401\) | −18.5924 | −0.928458 | −0.464229 | − | 0.885715i | \(-0.653669\pi\) | ||||
−0.464229 | + | 0.885715i | \(0.653669\pi\) | |||||||
\(402\) | −4.75500 | −0.237158 | ||||||||
\(403\) | 7.91248 | 0.394149 | ||||||||
\(404\) | 18.0429 | 0.897668 | ||||||||
\(405\) | 2.21252 | 0.109941 | ||||||||
\(406\) | −28.3513 | −1.40705 | ||||||||
\(407\) | 49.8509 | 2.47102 | ||||||||
\(408\) | 43.4944 | 2.15330 | ||||||||
\(409\) | −17.5494 | −0.867763 | −0.433882 | − | 0.900970i | \(-0.642856\pi\) | ||||
−0.433882 | + | 0.900970i | \(0.642856\pi\) | |||||||
\(410\) | −50.3495 | −2.48658 | ||||||||
\(411\) | −4.38239 | −0.216168 | ||||||||
\(412\) | −84.2869 | −4.15252 | ||||||||
\(413\) | −16.2812 | −0.801148 | ||||||||
\(414\) | 10.9066 | 0.536029 | ||||||||
\(415\) | 7.75907 | 0.380878 | ||||||||
\(416\) | −143.099 | −7.01602 | ||||||||
\(417\) | −23.4390 | −1.14781 | ||||||||
\(418\) | 74.7685 | 3.65705 | ||||||||
\(419\) | 1.68013 | 0.0820798 | 0.0410399 | − | 0.999158i | \(-0.486933\pi\) | ||||
0.0410399 | + | 0.999158i | \(0.486933\pi\) | |||||||
\(420\) | 19.1246 | 0.933185 | ||||||||
\(421\) | 1.72155 | 0.0839033 | 0.0419517 | − | 0.999120i | \(-0.486642\pi\) | ||||
0.0419517 | + | 0.999120i | \(0.486642\pi\) | |||||||
\(422\) | 14.7943 | 0.720176 | ||||||||
\(423\) | −6.00883 | −0.292159 | ||||||||
\(424\) | 57.9001 | 2.81188 | ||||||||
\(425\) | −0.467293 | −0.0226670 | ||||||||
\(426\) | 23.0988 | 1.11914 | ||||||||
\(427\) | −19.8857 | −0.962339 | ||||||||
\(428\) | 107.124 | 5.17801 | ||||||||
\(429\) | −36.3889 | −1.75687 | ||||||||
\(430\) | 45.9399 | 2.21542 | ||||||||
\(431\) | −34.5959 | −1.66643 | −0.833214 | − | 0.552951i | \(-0.813502\pi\) | ||||
−0.833214 | + | 0.552951i | \(0.813502\pi\) | |||||||
\(432\) | −15.6946 | −0.755105 | ||||||||
\(433\) | 38.3222 | 1.84165 | 0.920825 | − | 0.389977i | \(-0.127517\pi\) | ||||
0.920825 | + | 0.389977i | \(0.127517\pi\) | |||||||
\(434\) | 5.58940 | 0.268300 | ||||||||
\(435\) | 14.6565 | 0.702724 | ||||||||
\(436\) | −12.0029 | −0.574832 | ||||||||
\(437\) | 17.9853 | 0.860353 | ||||||||
\(438\) | −1.37996 | −0.0659369 | ||||||||
\(439\) | −11.1961 | −0.534359 | −0.267180 | − | 0.963647i | \(-0.586092\pi\) | ||||
−0.267180 | + | 0.963647i | \(0.586092\pi\) | |||||||
\(440\) | −129.583 | −6.17764 | ||||||||
\(441\) | −4.57360 | −0.217790 | ||||||||
\(442\) | −74.2487 | −3.53165 | ||||||||
\(443\) | −19.8137 | −0.941378 | −0.470689 | − | 0.882299i | \(-0.655995\pi\) | ||||
−0.470689 | + | 0.882299i | \(0.655995\pi\) | |||||||
\(444\) | −46.0581 | −2.18582 | ||||||||
\(445\) | 7.84594 | 0.371933 | ||||||||
\(446\) | 51.5161 | 2.43936 | ||||||||
\(447\) | −19.2293 | −0.909515 | ||||||||
\(448\) | −52.1912 | −2.46580 | ||||||||
\(449\) | −37.6608 | −1.77732 | −0.888662 | − | 0.458563i | \(-0.848364\pi\) | ||||
−0.888662 | + | 0.458563i | \(0.848364\pi\) | |||||||
\(450\) | 0.287855 | 0.0135696 | ||||||||
\(451\) | 49.7453 | 2.34241 | ||||||||
\(452\) | 97.7055 | 4.59568 | ||||||||
\(453\) | 4.55171 | 0.213858 | ||||||||
\(454\) | 0.143219 | 0.00672158 | ||||||||
\(455\) | −20.8807 | −0.978902 | ||||||||
\(456\) | −44.1823 | −2.06902 | ||||||||
\(457\) | −23.2165 | −1.08602 | −0.543012 | − | 0.839725i | \(-0.682716\pi\) | ||||
−0.543012 | + | 0.839725i | \(0.682716\pi\) | |||||||
\(458\) | −11.5605 | −0.540185 | ||||||||
\(459\) | −4.46030 | −0.208189 | ||||||||
\(460\) | −48.7362 | −2.27234 | ||||||||
\(461\) | 37.7809 | 1.75963 | 0.879816 | − | 0.475314i | \(-0.157666\pi\) | ||||
0.879816 | + | 0.475314i | \(0.157666\pi\) | |||||||
\(462\) | −25.7053 | −1.19592 | ||||||||
\(463\) | 42.0857 | 1.95589 | 0.977945 | − | 0.208863i | \(-0.0669762\pi\) | ||||
0.977945 | + | 0.208863i | \(0.0669762\pi\) | |||||||
\(464\) | −103.966 | −4.82651 | ||||||||
\(465\) | −2.88950 | −0.133997 | ||||||||
\(466\) | −78.8568 | −3.65297 | ||||||||
\(467\) | −36.7484 | −1.70052 | −0.850258 | − | 0.526367i | \(-0.823554\pi\) | ||||
−0.850258 | + | 0.526367i | \(0.823554\pi\) | |||||||
\(468\) | 33.6203 | 1.55410 | ||||||||
\(469\) | 2.69577 | 0.124479 | ||||||||
\(470\) | 36.5279 | 1.68491 | ||||||||
\(471\) | 2.77945 | 0.128070 | ||||||||
\(472\) | −101.924 | −4.69143 | ||||||||
\(473\) | −45.3887 | −2.08697 | ||||||||
\(474\) | −44.4871 | −2.04336 | ||||||||
\(475\) | 0.474683 | 0.0217799 | ||||||||
\(476\) | −38.5540 | −1.76712 | ||||||||
\(477\) | −5.93758 | −0.271863 | ||||||||
\(478\) | −69.2223 | −3.16615 | ||||||||
\(479\) | 9.37331 | 0.428277 | 0.214139 | − | 0.976803i | \(-0.431306\pi\) | ||||
0.214139 | + | 0.976803i | \(0.431306\pi\) | |||||||
\(480\) | 52.2573 | 2.38521 | ||||||||
\(481\) | 50.2872 | 2.29290 | ||||||||
\(482\) | −51.1460 | −2.32963 | ||||||||
\(483\) | −6.18331 | −0.281350 | ||||||||
\(484\) | 139.134 | 6.32429 | ||||||||
\(485\) | 10.3873 | 0.471661 | ||||||||
\(486\) | 2.74757 | 0.124632 | ||||||||
\(487\) | −13.3452 | −0.604727 | −0.302363 | − | 0.953193i | \(-0.597776\pi\) | ||||
−0.302363 | + | 0.953193i | \(0.597776\pi\) | |||||||
\(488\) | −124.489 | −5.63535 | ||||||||
\(489\) | −1.21163 | −0.0547916 | ||||||||
\(490\) | 27.8031 | 1.25602 | ||||||||
\(491\) | 7.91585 | 0.357238 | 0.178619 | − | 0.983918i | \(-0.442837\pi\) | ||||
0.178619 | + | 0.983918i | \(0.442837\pi\) | |||||||
\(492\) | −45.9605 | −2.07206 | ||||||||
\(493\) | −29.5465 | −1.33071 | ||||||||
\(494\) | 75.4229 | 3.39344 | ||||||||
\(495\) | 13.2886 | 0.597278 | ||||||||
\(496\) | 20.4967 | 0.920331 | ||||||||
\(497\) | −13.0955 | −0.587414 | ||||||||
\(498\) | 9.63543 | 0.431774 | ||||||||
\(499\) | 31.8490 | 1.42576 | 0.712879 | − | 0.701287i | \(-0.247391\pi\) | ||||
0.712879 | + | 0.701287i | \(0.247391\pi\) | |||||||
\(500\) | −62.6740 | −2.80287 | ||||||||
\(501\) | −4.46349 | −0.199414 | ||||||||
\(502\) | −64.1459 | −2.86297 | ||||||||
\(503\) | −9.28352 | −0.413932 | −0.206966 | − | 0.978348i | \(-0.566359\pi\) | ||||
−0.206966 | + | 0.978348i | \(0.566359\pi\) | |||||||
\(504\) | 15.1898 | 0.676606 | ||||||||
\(505\) | 7.19397 | 0.320127 | ||||||||
\(506\) | 65.5059 | 2.91209 | ||||||||
\(507\) | −23.7074 | −1.05288 | ||||||||
\(508\) | −87.4016 | −3.87782 | ||||||||
\(509\) | −13.2090 | −0.585478 | −0.292739 | − | 0.956192i | \(-0.594567\pi\) | ||||
−0.292739 | + | 0.956192i | \(0.594567\pi\) | |||||||
\(510\) | 27.1143 | 1.20064 | ||||||||
\(511\) | 0.782345 | 0.0346089 | ||||||||
\(512\) | −64.5990 | −2.85490 | ||||||||
\(513\) | 4.53083 | 0.200041 | ||||||||
\(514\) | 37.4479 | 1.65176 | ||||||||
\(515\) | −33.6064 | −1.48087 | ||||||||
\(516\) | 41.9353 | 1.84610 | ||||||||
\(517\) | −36.0896 | −1.58722 | ||||||||
\(518\) | 35.5231 | 1.56079 | ||||||||
\(519\) | 18.7613 | 0.823530 | ||||||||
\(520\) | −130.718 | −5.73234 | ||||||||
\(521\) | −16.7692 | −0.734670 | −0.367335 | − | 0.930089i | \(-0.619730\pi\) | ||||
−0.367335 | + | 0.930089i | \(0.619730\pi\) | |||||||
\(522\) | 18.2008 | 0.796629 | ||||||||
\(523\) | 4.20465 | 0.183856 | 0.0919282 | − | 0.995766i | \(-0.470697\pi\) | ||||
0.0919282 | + | 0.995766i | \(0.470697\pi\) | |||||||
\(524\) | 62.7600 | 2.74168 | ||||||||
\(525\) | −0.163195 | −0.00712242 | ||||||||
\(526\) | −63.6748 | −2.77635 | ||||||||
\(527\) | 5.82504 | 0.253743 | ||||||||
\(528\) | −94.2631 | −4.10228 | ||||||||
\(529\) | −7.24278 | −0.314903 | ||||||||
\(530\) | 36.0948 | 1.56786 | ||||||||
\(531\) | 10.4522 | 0.453585 | ||||||||
\(532\) | 39.1637 | 1.69796 | ||||||||
\(533\) | 50.1807 | 2.17357 | ||||||||
\(534\) | 9.74331 | 0.421634 | ||||||||
\(535\) | 42.7117 | 1.84659 | ||||||||
\(536\) | 16.8761 | 0.728937 | ||||||||
\(537\) | −0.436788 | −0.0188488 | ||||||||
\(538\) | 60.7877 | 2.62074 | ||||||||
\(539\) | −27.4695 | −1.18319 | ||||||||
\(540\) | −12.2775 | −0.528341 | ||||||||
\(541\) | 7.46536 | 0.320961 | 0.160480 | − | 0.987039i | \(-0.448696\pi\) | ||||
0.160480 | + | 0.987039i | \(0.448696\pi\) | |||||||
\(542\) | 79.6783 | 3.42248 | ||||||||
\(543\) | −4.76246 | −0.204377 | ||||||||
\(544\) | −105.347 | −4.51674 | ||||||||
\(545\) | −4.78571 | −0.204997 | ||||||||
\(546\) | −25.9302 | −1.10971 | ||||||||
\(547\) | 2.12491 | 0.0908548 | 0.0454274 | − | 0.998968i | \(-0.485535\pi\) | ||||
0.0454274 | + | 0.998968i | \(0.485535\pi\) | |||||||
\(548\) | 24.3185 | 1.03883 | ||||||||
\(549\) | 12.7662 | 0.544847 | ||||||||
\(550\) | 1.72889 | 0.0737200 | ||||||||
\(551\) | 30.0138 | 1.27863 | ||||||||
\(552\) | −38.7088 | −1.64756 | ||||||||
\(553\) | 25.2213 | 1.07252 | ||||||||
\(554\) | 85.2647 | 3.62255 | ||||||||
\(555\) | −18.3640 | −0.779509 | ||||||||
\(556\) | 130.066 | 5.51603 | ||||||||
\(557\) | 28.6682 | 1.21471 | 0.607355 | − | 0.794430i | \(-0.292230\pi\) | ||||
0.607355 | + | 0.794430i | \(0.292230\pi\) | |||||||
\(558\) | −3.58826 | −0.151903 | ||||||||
\(559\) | −45.7859 | −1.93654 | ||||||||
\(560\) | −54.0900 | −2.28572 | ||||||||
\(561\) | −26.7890 | −1.13103 | ||||||||
\(562\) | −73.9243 | −3.11831 | ||||||||
\(563\) | −11.0213 | −0.464493 | −0.232247 | − | 0.972657i | \(-0.574608\pi\) | ||||
−0.232247 | + | 0.972657i | \(0.574608\pi\) | |||||||
\(564\) | 33.3437 | 1.40402 | ||||||||
\(565\) | 38.9566 | 1.63892 | ||||||||
\(566\) | −16.9828 | −0.713840 | ||||||||
\(567\) | −1.55769 | −0.0654169 | ||||||||
\(568\) | −81.9807 | −3.43983 | ||||||||
\(569\) | 22.1356 | 0.927974 | 0.463987 | − | 0.885842i | \(-0.346418\pi\) | ||||
0.463987 | + | 0.885842i | \(0.346418\pi\) | |||||||
\(570\) | −27.5431 | −1.15365 | ||||||||
\(571\) | −17.1742 | −0.718718 | −0.359359 | − | 0.933199i | \(-0.617005\pi\) | ||||
−0.359359 | + | 0.933199i | \(0.617005\pi\) | |||||||
\(572\) | 201.927 | 8.44299 | ||||||||
\(573\) | −0.772465 | −0.0322702 | ||||||||
\(574\) | 35.4478 | 1.47956 | ||||||||
\(575\) | 0.415878 | 0.0173433 | ||||||||
\(576\) | 33.5055 | 1.39606 | ||||||||
\(577\) | −36.2145 | −1.50763 | −0.753816 | − | 0.657086i | \(-0.771789\pi\) | ||||
−0.753816 | + | 0.657086i | \(0.771789\pi\) | |||||||
\(578\) | −7.95210 | −0.330764 | ||||||||
\(579\) | −10.0741 | −0.418667 | ||||||||
\(580\) | −81.3306 | −3.37707 | ||||||||
\(581\) | −5.46266 | −0.226629 | ||||||||
\(582\) | 12.8992 | 0.534689 | ||||||||
\(583\) | −35.6617 | −1.47696 | ||||||||
\(584\) | 4.89765 | 0.202666 | ||||||||
\(585\) | 13.4049 | 0.554225 | ||||||||
\(586\) | −17.7479 | −0.733159 | ||||||||
\(587\) | −9.70486 | −0.400562 | −0.200281 | − | 0.979738i | \(-0.564186\pi\) | ||||
−0.200281 | + | 0.979738i | \(0.564186\pi\) | |||||||
\(588\) | 25.3795 | 1.04663 | ||||||||
\(589\) | −5.91716 | −0.243812 | ||||||||
\(590\) | −63.5392 | −2.61587 | ||||||||
\(591\) | 16.5714 | 0.681655 | ||||||||
\(592\) | 130.266 | 5.35389 | ||||||||
\(593\) | 6.66096 | 0.273533 | 0.136767 | − | 0.990603i | \(-0.456329\pi\) | ||||
0.136767 | + | 0.990603i | \(0.456329\pi\) | |||||||
\(594\) | 16.5022 | 0.677092 | ||||||||
\(595\) | −15.3720 | −0.630192 | ||||||||
\(596\) | 106.706 | 4.37084 | ||||||||
\(597\) | 11.8970 | 0.486911 | ||||||||
\(598\) | 66.0793 | 2.70218 | ||||||||
\(599\) | −3.19469 | −0.130532 | −0.0652658 | − | 0.997868i | \(-0.520790\pi\) | ||||
−0.0652658 | + | 0.997868i | \(0.520790\pi\) | |||||||
\(600\) | −1.02164 | −0.0417081 | ||||||||
\(601\) | −15.9699 | −0.651426 | −0.325713 | − | 0.945469i | \(-0.605604\pi\) | ||||
−0.325713 | + | 0.945469i | \(0.605604\pi\) | |||||||
\(602\) | −32.3433 | −1.31822 | ||||||||
\(603\) | −1.73062 | −0.0704764 | ||||||||
\(604\) | −25.2580 | −1.02773 | ||||||||
\(605\) | 55.4749 | 2.25538 | ||||||||
\(606\) | 8.93368 | 0.362906 | ||||||||
\(607\) | −27.1464 | −1.10184 | −0.550919 | − | 0.834559i | \(-0.685723\pi\) | ||||
−0.550919 | + | 0.834559i | \(0.685723\pi\) | |||||||
\(608\) | 107.013 | 4.33997 | ||||||||
\(609\) | −10.3187 | −0.418134 | ||||||||
\(610\) | −77.6061 | −3.14218 | ||||||||
\(611\) | −36.4055 | −1.47281 | ||||||||
\(612\) | 24.7508 | 1.00049 | ||||||||
\(613\) | 37.5344 | 1.51600 | 0.757999 | − | 0.652256i | \(-0.226177\pi\) | ||||
0.757999 | + | 0.652256i | \(0.226177\pi\) | |||||||
\(614\) | −87.0714 | −3.51392 | ||||||||
\(615\) | −18.3251 | −0.738939 | ||||||||
\(616\) | 91.2313 | 3.67581 | ||||||||
\(617\) | −16.3640 | −0.658788 | −0.329394 | − | 0.944193i | \(-0.606844\pi\) | ||||
−0.329394 | + | 0.944193i | \(0.606844\pi\) | |||||||
\(618\) | −41.7334 | −1.67876 | ||||||||
\(619\) | −7.16607 | −0.288029 | −0.144014 | − | 0.989576i | \(-0.546001\pi\) | ||||
−0.144014 | + | 0.989576i | \(0.546001\pi\) | |||||||
\(620\) | 16.0342 | 0.643948 | ||||||||
\(621\) | 3.96954 | 0.159292 | ||||||||
\(622\) | −5.03525 | −0.201895 | ||||||||
\(623\) | −5.52382 | −0.221307 | ||||||||
\(624\) | −95.0882 | −3.80657 | ||||||||
\(625\) | −24.4652 | −0.978607 | ||||||||
\(626\) | 21.9213 | 0.876152 | ||||||||
\(627\) | 27.2126 | 1.08677 | ||||||||
\(628\) | −15.4235 | −0.615465 | ||||||||
\(629\) | 37.0207 | 1.47611 | ||||||||
\(630\) | 9.46926 | 0.377265 | ||||||||
\(631\) | −5.30805 | −0.211310 | −0.105655 | − | 0.994403i | \(-0.533694\pi\) | ||||
−0.105655 | + | 0.994403i | \(0.533694\pi\) | |||||||
\(632\) | 157.890 | 6.28055 | ||||||||
\(633\) | 5.38451 | 0.214015 | ||||||||
\(634\) | 51.8815 | 2.06048 | ||||||||
\(635\) | −34.8483 | −1.38291 | ||||||||
\(636\) | 32.9484 | 1.30649 | ||||||||
\(637\) | −27.7099 | −1.09791 | ||||||||
\(638\) | 109.316 | 4.32786 | ||||||||
\(639\) | 8.40701 | 0.332576 | ||||||||
\(640\) | −99.1668 | −3.91991 | ||||||||
\(641\) | 22.5211 | 0.889530 | 0.444765 | − | 0.895647i | \(-0.353287\pi\) | ||||
0.444765 | + | 0.895647i | \(0.353287\pi\) | |||||||
\(642\) | 53.0406 | 2.09335 | ||||||||
\(643\) | 6.32161 | 0.249300 | 0.124650 | − | 0.992201i | \(-0.460219\pi\) | ||||
0.124650 | + | 0.992201i | \(0.460219\pi\) | |||||||
\(644\) | 34.3120 | 1.35208 | ||||||||
\(645\) | 16.7202 | 0.658358 | ||||||||
\(646\) | 55.5252 | 2.18461 | ||||||||
\(647\) | −35.8582 | −1.40973 | −0.704865 | − | 0.709341i | \(-0.748993\pi\) | ||||
−0.704865 | + | 0.709341i | \(0.748993\pi\) | |||||||
\(648\) | −9.75147 | −0.383074 | ||||||||
\(649\) | 62.7767 | 2.46420 | ||||||||
\(650\) | 1.74402 | 0.0684061 | ||||||||
\(651\) | 2.03431 | 0.0797308 | ||||||||
\(652\) | 6.72346 | 0.263311 | ||||||||
\(653\) | 26.1548 | 1.02351 | 0.511757 | − | 0.859130i | \(-0.328995\pi\) | ||||
0.511757 | + | 0.859130i | \(0.328995\pi\) | |||||||
\(654\) | −5.94303 | −0.232391 | ||||||||
\(655\) | 25.0233 | 0.977742 | ||||||||
\(656\) | 129.990 | 5.07525 | ||||||||
\(657\) | −0.502247 | −0.0195945 | ||||||||
\(658\) | −25.7169 | −1.00255 | ||||||||
\(659\) | 27.4431 | 1.06903 | 0.534516 | − | 0.845158i | \(-0.320494\pi\) | ||||
0.534516 | + | 0.845158i | \(0.320494\pi\) | |||||||
\(660\) | −73.7401 | −2.87033 | ||||||||
\(661\) | 34.9362 | 1.35886 | 0.679430 | − | 0.733741i | \(-0.262227\pi\) | ||||
0.679430 | + | 0.733741i | \(0.262227\pi\) | |||||||
\(662\) | 10.5014 | 0.408148 | ||||||||
\(663\) | −27.0234 | −1.04950 | ||||||||
\(664\) | −34.1974 | −1.32712 | ||||||||
\(665\) | 15.6151 | 0.605529 | ||||||||
\(666\) | −22.8050 | −0.883674 | ||||||||
\(667\) | 26.2956 | 1.01817 | ||||||||
\(668\) | 24.7685 | 0.958322 | ||||||||
\(669\) | 18.7497 | 0.724905 | ||||||||
\(670\) | 10.5205 | 0.406443 | ||||||||
\(671\) | 76.6749 | 2.96000 | ||||||||
\(672\) | −36.7910 | −1.41924 | ||||||||
\(673\) | −13.8123 | −0.532426 | −0.266213 | − | 0.963914i | \(-0.585772\pi\) | ||||
−0.266213 | + | 0.963914i | \(0.585772\pi\) | |||||||
\(674\) | −30.9769 | −1.19318 | ||||||||
\(675\) | 0.104767 | 0.00403250 | ||||||||
\(676\) | 131.556 | 5.05983 | ||||||||
\(677\) | −45.5712 | −1.75144 | −0.875722 | − | 0.482815i | \(-0.839614\pi\) | ||||
−0.875722 | + | 0.482815i | \(0.839614\pi\) | |||||||
\(678\) | 48.3774 | 1.85792 | ||||||||
\(679\) | −7.31300 | −0.280647 | ||||||||
\(680\) | −96.2322 | −3.69034 | ||||||||
\(681\) | 0.0521256 | 0.00199746 | ||||||||
\(682\) | −21.5514 | −0.825247 | ||||||||
\(683\) | 47.1810 | 1.80533 | 0.902666 | − | 0.430342i | \(-0.141607\pi\) | ||||
0.902666 | + | 0.430342i | \(0.141607\pi\) | |||||||
\(684\) | −25.1422 | −0.961334 | ||||||||
\(685\) | 9.69612 | 0.370470 | ||||||||
\(686\) | −49.5334 | −1.89119 | ||||||||
\(687\) | −4.20753 | −0.160527 | ||||||||
\(688\) | −118.605 | −4.52179 | ||||||||
\(689\) | −35.9738 | −1.37049 | ||||||||
\(690\) | −24.1310 | −0.918651 | ||||||||
\(691\) | 16.2660 | 0.618788 | 0.309394 | − | 0.950934i | \(-0.399874\pi\) | ||||
0.309394 | + | 0.950934i | \(0.399874\pi\) | |||||||
\(692\) | −104.109 | −3.95763 | ||||||||
\(693\) | −9.35564 | −0.355391 | ||||||||
\(694\) | −55.2160 | −2.09597 | ||||||||
\(695\) | 51.8592 | 1.96713 | ||||||||
\(696\) | −64.5971 | −2.44855 | ||||||||
\(697\) | 36.9422 | 1.39929 | ||||||||
\(698\) | −12.4816 | −0.472435 | ||||||||
\(699\) | −28.7006 | −1.08556 | ||||||||
\(700\) | 0.905590 | 0.0342281 | ||||||||
\(701\) | 5.78202 | 0.218384 | 0.109192 | − | 0.994021i | \(-0.465174\pi\) | ||||
0.109192 | + | 0.994021i | \(0.465174\pi\) | |||||||
\(702\) | 16.6466 | 0.628285 | ||||||||
\(703\) | −37.6061 | −1.41834 | ||||||||
\(704\) | 201.237 | 7.58442 | ||||||||
\(705\) | 13.2946 | 0.500705 | ||||||||
\(706\) | −42.8633 | −1.61318 | ||||||||
\(707\) | −5.06481 | −0.190482 | ||||||||
\(708\) | −58.0004 | −2.17979 | ||||||||
\(709\) | 39.1600 | 1.47069 | 0.735343 | − | 0.677695i | \(-0.237021\pi\) | ||||
0.735343 | + | 0.677695i | \(0.237021\pi\) | |||||||
\(710\) | −51.1066 | −1.91800 | ||||||||
\(711\) | −16.1915 | −0.607227 | ||||||||
\(712\) | −34.5803 | −1.29595 | ||||||||
\(713\) | −5.18412 | −0.194147 | ||||||||
\(714\) | −19.0894 | −0.714404 | ||||||||
\(715\) | 80.5112 | 3.01095 | ||||||||
\(716\) | 2.42379 | 0.0905815 | ||||||||
\(717\) | −25.1940 | −0.940888 | ||||||||
\(718\) | −0.298558 | −0.0111421 | ||||||||
\(719\) | −22.9261 | −0.854997 | −0.427499 | − | 0.904016i | \(-0.640605\pi\) | ||||
−0.427499 | + | 0.904016i | \(0.640605\pi\) | |||||||
\(720\) | 34.7245 | 1.29411 | ||||||||
\(721\) | 23.6601 | 0.881148 | ||||||||
\(722\) | −4.19944 | −0.156287 | ||||||||
\(723\) | −18.6150 | −0.692299 | ||||||||
\(724\) | 26.4275 | 0.982170 | ||||||||
\(725\) | 0.694014 | 0.0257751 | ||||||||
\(726\) | 68.8903 | 2.55676 | ||||||||
\(727\) | 30.4660 | 1.12992 | 0.564961 | − | 0.825118i | \(-0.308891\pi\) | ||||
0.564961 | + | 0.825118i | \(0.308891\pi\) | |||||||
\(728\) | 92.0298 | 3.41085 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.05318 | 0.113003 | ||||||||
\(731\) | −33.7069 | −1.24669 | ||||||||
\(732\) | −70.8411 | −2.61836 | ||||||||
\(733\) | −3.38895 | −0.125174 | −0.0625868 | − | 0.998040i | \(-0.519935\pi\) | ||||
−0.0625868 | + | 0.998040i | \(0.519935\pi\) | |||||||
\(734\) | 8.06489 | 0.297681 | ||||||||
\(735\) | 10.1192 | 0.373251 | ||||||||
\(736\) | 93.7563 | 3.45590 | ||||||||
\(737\) | −10.3943 | −0.382879 | ||||||||
\(738\) | −22.7566 | −0.837683 | ||||||||
\(739\) | 4.48104 | 0.164838 | 0.0824189 | − | 0.996598i | \(-0.473735\pi\) | ||||
0.0824189 | + | 0.996598i | \(0.473735\pi\) | |||||||
\(740\) | 101.904 | 3.74607 | ||||||||
\(741\) | 27.4508 | 1.00843 | ||||||||
\(742\) | −25.4120 | −0.932904 | ||||||||
\(743\) | −19.8126 | −0.726852 | −0.363426 | − | 0.931623i | \(-0.618393\pi\) | ||||
−0.363426 | + | 0.931623i | \(0.618393\pi\) | |||||||
\(744\) | 12.7352 | 0.466895 | ||||||||
\(745\) | 42.5452 | 1.55873 | ||||||||
\(746\) | 31.3132 | 1.14646 | ||||||||
\(747\) | 3.50690 | 0.128311 | ||||||||
\(748\) | 148.655 | 5.43538 | ||||||||
\(749\) | −30.0705 | −1.09875 | ||||||||
\(750\) | −31.0321 | −1.13313 | ||||||||
\(751\) | 36.9001 | 1.34650 | 0.673252 | − | 0.739414i | \(-0.264897\pi\) | ||||
0.673252 | + | 0.739414i | \(0.264897\pi\) | |||||||
\(752\) | −94.3059 | −3.43898 | ||||||||
\(753\) | −23.3464 | −0.850792 | ||||||||
\(754\) | 110.273 | 4.01590 | ||||||||
\(755\) | −10.0707 | −0.366512 | ||||||||
\(756\) | 8.64382 | 0.314373 | ||||||||
\(757\) | 10.5912 | 0.384943 | 0.192472 | − | 0.981303i | \(-0.438350\pi\) | ||||
0.192472 | + | 0.981303i | \(0.438350\pi\) | |||||||
\(758\) | −7.43453 | −0.270034 | ||||||||
\(759\) | 23.8414 | 0.865389 | ||||||||
\(760\) | 97.7540 | 3.54591 | ||||||||
\(761\) | 7.96614 | 0.288773 | 0.144386 | − | 0.989521i | \(-0.453879\pi\) | ||||
0.144386 | + | 0.989521i | \(0.453879\pi\) | |||||||
\(762\) | −43.2756 | −1.56771 | ||||||||
\(763\) | 3.36931 | 0.121977 | ||||||||
\(764\) | 4.28651 | 0.155080 | ||||||||
\(765\) | 9.86848 | 0.356796 | ||||||||
\(766\) | 29.3460 | 1.06031 | ||||||||
\(767\) | 63.3262 | 2.28658 | ||||||||
\(768\) | −56.1371 | −2.02567 | ||||||||
\(769\) | −1.77309 | −0.0639394 | −0.0319697 | − | 0.999489i | \(-0.510178\pi\) | ||||
−0.0319697 | + | 0.999489i | \(0.510178\pi\) | |||||||
\(770\) | 56.8733 | 2.04957 | ||||||||
\(771\) | 13.6295 | 0.490854 | ||||||||
\(772\) | 55.9026 | 2.01198 | ||||||||
\(773\) | −30.4558 | −1.09542 | −0.547710 | − | 0.836668i | \(-0.684500\pi\) | ||||
−0.547710 | + | 0.836668i | \(0.684500\pi\) | |||||||
\(774\) | 20.7636 | 0.746334 | ||||||||
\(775\) | −0.136824 | −0.00491485 | ||||||||
\(776\) | −45.7809 | −1.64344 | ||||||||
\(777\) | 12.9289 | 0.463822 | ||||||||
\(778\) | 34.8601 | 1.24980 | ||||||||
\(779\) | −37.5264 | −1.34452 | ||||||||
\(780\) | −74.3855 | −2.66343 | ||||||||
\(781\) | 50.4933 | 1.80679 | ||||||||
\(782\) | 48.6465 | 1.73960 | ||||||||
\(783\) | 6.62434 | 0.236735 | ||||||||
\(784\) | −71.7807 | −2.56360 | ||||||||
\(785\) | −6.14957 | −0.219488 | ||||||||
\(786\) | 31.0747 | 1.10840 | ||||||||
\(787\) | −29.2173 | −1.04148 | −0.520741 | − | 0.853715i | \(-0.674344\pi\) | ||||
−0.520741 | + | 0.853715i | \(0.674344\pi\) | |||||||
\(788\) | −91.9567 | −3.27582 | ||||||||
\(789\) | −23.1750 | −0.825051 | ||||||||
\(790\) | 98.4285 | 3.50193 | ||||||||
\(791\) | −27.4268 | −0.975186 | ||||||||
\(792\) | −58.5683 | −2.08113 | ||||||||
\(793\) | 77.3460 | 2.74664 | ||||||||
\(794\) | −69.9105 | −2.48103 | ||||||||
\(795\) | 13.1370 | 0.465921 | ||||||||
\(796\) | −66.0179 | −2.33994 | ||||||||
\(797\) | −14.1708 | −0.501955 | −0.250978 | − | 0.967993i | \(-0.580752\pi\) | ||||
−0.250978 | + | 0.967993i | \(0.580752\pi\) | |||||||
\(798\) | 19.3913 | 0.686445 | ||||||||
\(799\) | −26.8011 | −0.948156 | ||||||||
\(800\) | 2.47449 | 0.0874866 | ||||||||
\(801\) | 3.54616 | 0.125297 | ||||||||
\(802\) | 51.0838 | 1.80383 | ||||||||
\(803\) | −3.01654 | −0.106452 | ||||||||
\(804\) | 9.60345 | 0.338688 | ||||||||
\(805\) | 13.6807 | 0.482181 | ||||||||
\(806\) | −21.7401 | −0.765761 | ||||||||
\(807\) | 22.1242 | 0.778808 | ||||||||
\(808\) | −31.7068 | −1.11544 | ||||||||
\(809\) | 46.7791 | 1.64467 | 0.822333 | − | 0.569006i | \(-0.192672\pi\) | ||||
0.822333 | + | 0.569006i | \(0.192672\pi\) | |||||||
\(810\) | −6.07904 | −0.213596 | ||||||||
\(811\) | 27.3604 | 0.960755 | 0.480378 | − | 0.877062i | \(-0.340500\pi\) | ||||
0.480378 | + | 0.877062i | \(0.340500\pi\) | |||||||
\(812\) | 57.2596 | 2.00942 | ||||||||
\(813\) | 28.9996 | 1.01706 | ||||||||
\(814\) | −136.969 | −4.80075 | ||||||||
\(815\) | 2.68074 | 0.0939023 | ||||||||
\(816\) | −70.0024 | −2.45057 | ||||||||
\(817\) | 34.2399 | 1.19790 | ||||||||
\(818\) | 48.2182 | 1.68591 | ||||||||
\(819\) | −9.43753 | −0.329774 | ||||||||
\(820\) | 101.688 | 3.55111 | ||||||||
\(821\) | 48.9465 | 1.70824 | 0.854122 | − | 0.520073i | \(-0.174095\pi\) | ||||
0.854122 | + | 0.520073i | \(0.174095\pi\) | |||||||
\(822\) | 12.0409 | 0.419975 | ||||||||
\(823\) | 28.3115 | 0.986877 | 0.493439 | − | 0.869781i | \(-0.335740\pi\) | ||||
0.493439 | + | 0.869781i | \(0.335740\pi\) | |||||||
\(824\) | 148.117 | 5.15990 | ||||||||
\(825\) | 0.629243 | 0.0219074 | ||||||||
\(826\) | 44.7338 | 1.55649 | ||||||||
\(827\) | 53.5224 | 1.86116 | 0.930579 | − | 0.366092i | \(-0.119305\pi\) | ||||
0.930579 | + | 0.366092i | \(0.119305\pi\) | |||||||
\(828\) | −22.0275 | −0.765508 | ||||||||
\(829\) | −32.0943 | −1.11468 | −0.557340 | − | 0.830284i | \(-0.688178\pi\) | ||||
−0.557340 | + | 0.830284i | \(0.688178\pi\) | |||||||
\(830\) | −21.3186 | −0.739978 | ||||||||
\(831\) | 31.0328 | 1.07652 | ||||||||
\(832\) | 202.999 | 7.03772 | ||||||||
\(833\) | −20.3996 | −0.706805 | ||||||||
\(834\) | 64.4002 | 2.23000 | ||||||||
\(835\) | 9.87556 | 0.341758 | ||||||||
\(836\) | −151.006 | −5.22266 | ||||||||
\(837\) | −1.30598 | −0.0451412 | ||||||||
\(838\) | −4.61627 | −0.159467 | ||||||||
\(839\) | −2.16030 | −0.0745819 | −0.0372909 | − | 0.999304i | \(-0.511873\pi\) | ||||
−0.0372909 | + | 0.999304i | \(0.511873\pi\) | |||||||
\(840\) | −33.6076 | −1.15957 | ||||||||
\(841\) | 14.8819 | 0.513169 | ||||||||
\(842\) | −4.73008 | −0.163009 | ||||||||
\(843\) | −26.9054 | −0.926670 | ||||||||
\(844\) | −29.8793 | −1.02849 | ||||||||
\(845\) | 52.4531 | 1.80444 | ||||||||
\(846\) | 16.5097 | 0.567614 | ||||||||
\(847\) | −39.0563 | −1.34199 | ||||||||
\(848\) | −93.1877 | −3.20008 | ||||||||
\(849\) | −6.18102 | −0.212132 | ||||||||
\(850\) | 1.28392 | 0.0440381 | ||||||||
\(851\) | −32.9474 | −1.12942 | ||||||||
\(852\) | −46.6516 | −1.59826 | ||||||||
\(853\) | −29.1123 | −0.996785 | −0.498392 | − | 0.866952i | \(-0.666076\pi\) | ||||
−0.498392 | + | 0.866952i | \(0.666076\pi\) | |||||||
\(854\) | 54.6374 | 1.86965 | ||||||||
\(855\) | −10.0245 | −0.342832 | ||||||||
\(856\) | −188.248 | −6.43418 | ||||||||
\(857\) | −41.9008 | −1.43130 | −0.715652 | − | 0.698457i | \(-0.753870\pi\) | ||||
−0.715652 | + | 0.698457i | \(0.753870\pi\) | |||||||
\(858\) | 99.9811 | 3.41330 | ||||||||
\(859\) | 14.8808 | 0.507727 | 0.253863 | − | 0.967240i | \(-0.418299\pi\) | ||||
0.253863 | + | 0.967240i | \(0.418299\pi\) | |||||||
\(860\) | −92.7826 | −3.16386 | ||||||||
\(861\) | 12.9015 | 0.439683 | ||||||||
\(862\) | 95.0547 | 3.23758 | ||||||||
\(863\) | −5.73504 | −0.195223 | −0.0976115 | − | 0.995225i | \(-0.531120\pi\) | ||||
−0.0976115 | + | 0.995225i | \(0.531120\pi\) | |||||||
\(864\) | 23.6190 | 0.803533 | ||||||||
\(865\) | −41.5097 | −1.41137 | ||||||||
\(866\) | −105.293 | −3.57800 | ||||||||
\(867\) | −2.89423 | −0.0982933 | ||||||||
\(868\) | −11.2886 | −0.383161 | ||||||||
\(869\) | −97.2474 | −3.29889 | ||||||||
\(870\) | −40.2696 | −1.36527 | ||||||||
\(871\) | −10.4853 | −0.355280 | ||||||||
\(872\) | 21.0926 | 0.714285 | ||||||||
\(873\) | 4.69477 | 0.158894 | ||||||||
\(874\) | −49.4158 | −1.67152 | ||||||||
\(875\) | 17.5932 | 0.594757 | ||||||||
\(876\) | 2.78703 | 0.0941651 | ||||||||
\(877\) | 16.4626 | 0.555902 | 0.277951 | − | 0.960595i | \(-0.410345\pi\) | ||||
0.277951 | + | 0.960595i | \(0.410345\pi\) | |||||||
\(878\) | 30.7619 | 1.03817 | ||||||||
\(879\) | −6.45950 | −0.217873 | ||||||||
\(880\) | 208.559 | 7.03052 | ||||||||
\(881\) | 18.1854 | 0.612683 | 0.306341 | − | 0.951922i | \(-0.400895\pi\) | ||||
0.306341 | + | 0.951922i | \(0.400895\pi\) | |||||||
\(882\) | 12.5663 | 0.423129 | ||||||||
\(883\) | −18.0335 | −0.606876 | −0.303438 | − | 0.952851i | \(-0.598135\pi\) | ||||
−0.303438 | + | 0.952851i | \(0.598135\pi\) | |||||||
\(884\) | 149.957 | 5.04358 | ||||||||
\(885\) | −23.1256 | −0.777359 | ||||||||
\(886\) | 54.4395 | 1.82893 | ||||||||
\(887\) | 0.865135 | 0.0290484 | 0.0145242 | − | 0.999895i | \(-0.495377\pi\) | ||||
0.0145242 | + | 0.999895i | \(0.495377\pi\) | |||||||
\(888\) | 80.9377 | 2.71609 | ||||||||
\(889\) | 24.5344 | 0.822858 | ||||||||
\(890\) | −21.5572 | −0.722600 | ||||||||
\(891\) | 6.00610 | 0.201212 | ||||||||
\(892\) | −104.044 | −3.48367 | ||||||||
\(893\) | 27.2250 | 0.911049 | ||||||||
\(894\) | 52.8338 | 1.76703 | ||||||||
\(895\) | 0.966402 | 0.0323033 | ||||||||
\(896\) | 69.8169 | 2.33242 | ||||||||
\(897\) | 24.0501 | 0.803009 | ||||||||
\(898\) | 103.476 | 3.45303 | ||||||||
\(899\) | −8.65124 | −0.288535 | ||||||||
\(900\) | −0.581367 | −0.0193789 | ||||||||
\(901\) | −26.4833 | −0.882288 | ||||||||
\(902\) | −136.679 | −4.55090 | ||||||||
\(903\) | −11.7716 | −0.391735 | ||||||||
\(904\) | −171.698 | −5.71058 | ||||||||
\(905\) | 10.5370 | 0.350262 | ||||||||
\(906\) | −12.5061 | −0.415488 | ||||||||
\(907\) | 59.5470 | 1.97723 | 0.988614 | − | 0.150476i | \(-0.0480806\pi\) | ||||
0.988614 | + | 0.150476i | \(0.0480806\pi\) | |||||||
\(908\) | −0.289252 | −0.00959915 | ||||||||
\(909\) | 3.25149 | 0.107845 | ||||||||
\(910\) | 57.3711 | 1.90183 | ||||||||
\(911\) | −21.0274 | −0.696669 | −0.348335 | − | 0.937370i | \(-0.613253\pi\) | ||||
−0.348335 | + | 0.937370i | \(0.613253\pi\) | |||||||
\(912\) | 71.1094 | 2.35467 | ||||||||
\(913\) | 21.0628 | 0.697076 | ||||||||
\(914\) | 63.7890 | 2.10995 | ||||||||
\(915\) | −28.2454 | −0.933764 | ||||||||
\(916\) | 23.3481 | 0.771444 | ||||||||
\(917\) | −17.6173 | −0.581775 | ||||||||
\(918\) | 12.2550 | 0.404474 | ||||||||
\(919\) | −22.4420 | −0.740292 | −0.370146 | − | 0.928974i | \(-0.620692\pi\) | ||||
−0.370146 | + | 0.928974i | \(0.620692\pi\) | |||||||
\(920\) | 85.6439 | 2.82360 | ||||||||
\(921\) | −31.6904 | −1.04423 | ||||||||
\(922\) | −103.806 | −3.41866 | ||||||||
\(923\) | 50.9353 | 1.67655 | ||||||||
\(924\) | 51.9157 | 1.70790 | ||||||||
\(925\) | −0.869574 | −0.0285914 | ||||||||
\(926\) | −115.633 | −3.79995 | ||||||||
\(927\) | −15.1892 | −0.498879 | ||||||||
\(928\) | 156.460 | 5.13605 | ||||||||
\(929\) | 22.2913 | 0.731355 | 0.365678 | − | 0.930742i | \(-0.380837\pi\) | ||||
0.365678 | + | 0.930742i | \(0.380837\pi\) | |||||||
\(930\) | 7.93909 | 0.260333 | ||||||||
\(931\) | 20.7222 | 0.679143 | ||||||||
\(932\) | 159.263 | 5.21684 | ||||||||
\(933\) | −1.83262 | −0.0599973 | ||||||||
\(934\) | 100.969 | 3.30380 | ||||||||
\(935\) | 59.2711 | 1.93837 | ||||||||
\(936\) | −59.0809 | −1.93112 | ||||||||
\(937\) | −49.6565 | −1.62221 | −0.811103 | − | 0.584903i | \(-0.801133\pi\) | ||||
−0.811103 | + | 0.584903i | \(0.801133\pi\) | |||||||
\(938\) | −7.40682 | −0.241841 | ||||||||
\(939\) | 7.97844 | 0.260367 | ||||||||
\(940\) | −73.7736 | −2.40623 | ||||||||
\(941\) | 19.5649 | 0.637798 | 0.318899 | − | 0.947789i | \(-0.396687\pi\) | ||||
0.318899 | + | 0.947789i | \(0.396687\pi\) | |||||||
\(942\) | −7.63672 | −0.248818 | ||||||||
\(943\) | −32.8776 | −1.07064 | ||||||||
\(944\) | 164.042 | 5.33912 | ||||||||
\(945\) | 3.44642 | 0.112112 | ||||||||
\(946\) | 124.708 | 4.05462 | ||||||||
\(947\) | −1.24093 | −0.0403248 | −0.0201624 | − | 0.999797i | \(-0.506418\pi\) | ||||
−0.0201624 | + | 0.999797i | \(0.506418\pi\) | |||||||
\(948\) | 89.8484 | 2.91814 | ||||||||
\(949\) | −3.04295 | −0.0987782 | ||||||||
\(950\) | −1.30422 | −0.0423146 | ||||||||
\(951\) | 18.8827 | 0.612313 | ||||||||
\(952\) | 67.7509 | 2.19582 | ||||||||
\(953\) | −13.7099 | −0.444108 | −0.222054 | − | 0.975034i | \(-0.571276\pi\) | ||||
−0.222054 | + | 0.975034i | \(0.571276\pi\) | |||||||
\(954\) | 16.3139 | 0.528182 | ||||||||
\(955\) | 1.70909 | 0.0553049 | ||||||||
\(956\) | 139.805 | 4.52161 | ||||||||
\(957\) | 39.7864 | 1.28611 | ||||||||
\(958\) | −25.7538 | −0.832067 | ||||||||
\(959\) | −6.82641 | −0.220436 | ||||||||
\(960\) | −74.1316 | −2.39259 | ||||||||
\(961\) | −29.2944 | −0.944981 | ||||||||
\(962\) | −138.168 | −4.45470 | ||||||||
\(963\) | 19.3046 | 0.622081 | ||||||||
\(964\) | 103.297 | 3.32697 | ||||||||
\(965\) | 22.2892 | 0.717514 | ||||||||
\(966\) | 16.9891 | 0.546614 | ||||||||
\(967\) | 25.0489 | 0.805517 | 0.402759 | − | 0.915306i | \(-0.368051\pi\) | ||||
0.402759 | + | 0.915306i | \(0.368051\pi\) | |||||||
\(968\) | −244.501 | −7.85855 | ||||||||
\(969\) | 20.2088 | 0.649201 | ||||||||
\(970\) | −28.5397 | −0.916355 | ||||||||
\(971\) | −18.0040 | −0.577776 | −0.288888 | − | 0.957363i | \(-0.593286\pi\) | ||||
−0.288888 | + | 0.957363i | \(0.593286\pi\) | |||||||
\(972\) | −5.54913 | −0.177988 | ||||||||
\(973\) | −36.5107 | −1.17048 | ||||||||
\(974\) | 36.6667 | 1.17488 | ||||||||
\(975\) | 0.634750 | 0.0203283 | ||||||||
\(976\) | 200.360 | 6.41336 | ||||||||
\(977\) | −23.3256 | −0.746252 | −0.373126 | − | 0.927781i | \(-0.621714\pi\) | ||||
−0.373126 | + | 0.927781i | \(0.621714\pi\) | |||||||
\(978\) | 3.32902 | 0.106450 | ||||||||
\(979\) | 21.2986 | 0.680705 | ||||||||
\(980\) | −56.1526 | −1.79373 | ||||||||
\(981\) | −2.16302 | −0.0690598 | ||||||||
\(982\) | −21.7493 | −0.694050 | ||||||||
\(983\) | 3.95871 | 0.126263 | 0.0631316 | − | 0.998005i | \(-0.479891\pi\) | ||||
0.0631316 | + | 0.998005i | \(0.479891\pi\) | |||||||
\(984\) | 80.7662 | 2.57473 | ||||||||
\(985\) | −36.6645 | −1.16823 | ||||||||
\(986\) | 81.1811 | 2.58533 | ||||||||
\(987\) | −9.35989 | −0.297929 | ||||||||
\(988\) | −152.328 | −4.84620 | ||||||||
\(989\) | 29.9982 | 0.953887 | ||||||||
\(990\) | −36.5113 | −1.16041 | ||||||||
\(991\) | −4.88474 | −0.155169 | −0.0775845 | − | 0.996986i | \(-0.524721\pi\) | ||||
−0.0775845 | + | 0.996986i | \(0.524721\pi\) | |||||||
\(992\) | −30.8458 | −0.979355 | ||||||||
\(993\) | 3.82207 | 0.121290 | ||||||||
\(994\) | 35.9808 | 1.14124 | ||||||||
\(995\) | −26.3223 | −0.834473 | ||||||||
\(996\) | −19.4602 | −0.616620 | ||||||||
\(997\) | 56.5284 | 1.79027 | 0.895136 | − | 0.445793i | \(-0.147078\pi\) | ||||
0.895136 | + | 0.445793i | \(0.147078\pi\) | |||||||
\(998\) | −87.5073 | −2.77000 | ||||||||
\(999\) | −8.30005 | −0.262602 |
(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 | 8031.2.a.c.1.2 | ✓ | 121 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8031.2.a.c.1.2 | ✓ | 121 | 1.1 | even | 1 | trivial |