Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4019,2,Mod(1,4019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4019, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4019.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: | \(32.0918765724\) |
Analytic rank: | \(0\) |
Dimension: | \(186\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 4019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.71067 | −1.91674 | −0.958368 | − | 0.285536i | \(-0.907828\pi\) | ||||
−0.958368 | + | 0.285536i | \(0.907828\pi\) | |||||||
\(3\) | −2.48956 | −1.43735 | −0.718673 | − | 0.695348i | \(-0.755250\pi\) | ||||
−0.718673 | + | 0.695348i | \(0.755250\pi\) | |||||||
\(4\) | 5.34775 | 2.67388 | ||||||||
\(5\) | −1.96358 | −0.878140 | −0.439070 | − | 0.898453i | \(-0.644692\pi\) | ||||
−0.439070 | + | 0.898453i | \(0.644692\pi\) | |||||||
\(6\) | 6.74838 | 2.75501 | ||||||||
\(7\) | 3.14635 | 1.18921 | 0.594604 | − | 0.804018i | \(-0.297309\pi\) | ||||
0.594604 | + | 0.804018i | \(0.297309\pi\) | |||||||
\(8\) | −9.07467 | −3.20838 | ||||||||
\(9\) | 3.19790 | 1.06597 | ||||||||
\(10\) | 5.32263 | 1.68316 | ||||||||
\(11\) | −0.760163 | −0.229198 | −0.114599 | − | 0.993412i | \(-0.536558\pi\) | ||||
−0.114599 | + | 0.993412i | \(0.536558\pi\) | |||||||
\(12\) | −13.3135 | −3.84329 | ||||||||
\(13\) | −3.23629 | −0.897587 | −0.448793 | − | 0.893636i | \(-0.648146\pi\) | ||||
−0.448793 | + | 0.893636i | \(0.648146\pi\) | |||||||
\(14\) | −8.52873 | −2.27940 | ||||||||
\(15\) | 4.88845 | 1.26219 | ||||||||
\(16\) | 13.9030 | 3.47574 | ||||||||
\(17\) | −6.89437 | −1.67213 | −0.836065 | − | 0.548630i | \(-0.815150\pi\) | ||||
−0.836065 | + | 0.548630i | \(0.815150\pi\) | |||||||
\(18\) | −8.66846 | −2.04318 | ||||||||
\(19\) | 5.80103 | 1.33085 | 0.665424 | − | 0.746465i | \(-0.268251\pi\) | ||||
0.665424 | + | 0.746465i | \(0.268251\pi\) | |||||||
\(20\) | −10.5007 | −2.34804 | ||||||||
\(21\) | −7.83302 | −1.70931 | ||||||||
\(22\) | 2.06055 | 0.439311 | ||||||||
\(23\) | −2.00733 | −0.418556 | −0.209278 | − | 0.977856i | \(-0.567111\pi\) | ||||
−0.209278 | + | 0.977856i | \(0.567111\pi\) | |||||||
\(24\) | 22.5919 | 4.61155 | ||||||||
\(25\) | −1.14435 | −0.228870 | ||||||||
\(26\) | 8.77254 | 1.72044 | ||||||||
\(27\) | −0.492681 | −0.0948166 | ||||||||
\(28\) | 16.8259 | 3.17980 | ||||||||
\(29\) | −3.67543 | −0.682510 | −0.341255 | − | 0.939971i | \(-0.610852\pi\) | ||||
−0.341255 | + | 0.939971i | \(0.610852\pi\) | |||||||
\(30\) | −13.2510 | −2.41929 | ||||||||
\(31\) | −6.53081 | −1.17297 | −0.586484 | − | 0.809961i | \(-0.699488\pi\) | ||||
−0.586484 | + | 0.809961i | \(0.699488\pi\) | |||||||
\(32\) | −19.5371 | −3.45370 | ||||||||
\(33\) | 1.89247 | 0.329437 | ||||||||
\(34\) | 18.6884 | 3.20503 | ||||||||
\(35\) | −6.17812 | −1.04429 | ||||||||
\(36\) | 17.1016 | 2.85026 | ||||||||
\(37\) | −8.82183 | −1.45030 | −0.725150 | − | 0.688591i | \(-0.758230\pi\) | ||||
−0.725150 | + | 0.688591i | \(0.758230\pi\) | |||||||
\(38\) | −15.7247 | −2.55089 | ||||||||
\(39\) | 8.05694 | 1.29014 | ||||||||
\(40\) | 17.8188 | 2.81741 | ||||||||
\(41\) | −3.43051 | −0.535755 | −0.267878 | − | 0.963453i | \(-0.586322\pi\) | ||||
−0.267878 | + | 0.963453i | \(0.586322\pi\) | |||||||
\(42\) | 21.2328 | 3.27629 | ||||||||
\(43\) | 0.759370 | 0.115803 | 0.0579014 | − | 0.998322i | \(-0.481559\pi\) | ||||
0.0579014 | + | 0.998322i | \(0.481559\pi\) | |||||||
\(44\) | −4.06516 | −0.612846 | ||||||||
\(45\) | −6.27933 | −0.936068 | ||||||||
\(46\) | 5.44120 | 0.802262 | ||||||||
\(47\) | 0.514988 | 0.0751188 | 0.0375594 | − | 0.999294i | \(-0.488042\pi\) | ||||
0.0375594 | + | 0.999294i | \(0.488042\pi\) | |||||||
\(48\) | −34.6122 | −4.99584 | ||||||||
\(49\) | 2.89952 | 0.414218 | ||||||||
\(50\) | 3.10196 | 0.438683 | ||||||||
\(51\) | 17.1639 | 2.40343 | ||||||||
\(52\) | −17.3069 | −2.40004 | ||||||||
\(53\) | 0.447477 | 0.0614657 | 0.0307328 | − | 0.999528i | \(-0.490216\pi\) | ||||
0.0307328 | + | 0.999528i | \(0.490216\pi\) | |||||||
\(54\) | 1.33550 | 0.181738 | ||||||||
\(55\) | 1.49264 | 0.201268 | ||||||||
\(56\) | −28.5521 | −3.81543 | ||||||||
\(57\) | −14.4420 | −1.91289 | ||||||||
\(58\) | 9.96289 | 1.30819 | ||||||||
\(59\) | 7.42963 | 0.967256 | 0.483628 | − | 0.875274i | \(-0.339319\pi\) | ||||
0.483628 | + | 0.875274i | \(0.339319\pi\) | |||||||
\(60\) | 26.1422 | 3.37495 | ||||||||
\(61\) | 6.72321 | 0.860819 | 0.430410 | − | 0.902634i | \(-0.358369\pi\) | ||||
0.430410 | + | 0.902634i | \(0.358369\pi\) | |||||||
\(62\) | 17.7029 | 2.24827 | ||||||||
\(63\) | 10.0617 | 1.26766 | ||||||||
\(64\) | 25.1527 | 3.14408 | ||||||||
\(65\) | 6.35473 | 0.788207 | ||||||||
\(66\) | −5.12987 | −0.631443 | ||||||||
\(67\) | −7.29726 | −0.891502 | −0.445751 | − | 0.895157i | \(-0.647063\pi\) | ||||
−0.445751 | + | 0.895157i | \(0.647063\pi\) | |||||||
\(68\) | −36.8694 | −4.47107 | ||||||||
\(69\) | 4.99735 | 0.601611 | ||||||||
\(70\) | 16.7469 | 2.00163 | ||||||||
\(71\) | 9.64369 | 1.14450 | 0.572248 | − | 0.820081i | \(-0.306071\pi\) | ||||
0.572248 | + | 0.820081i | \(0.306071\pi\) | |||||||
\(72\) | −29.0199 | −3.42002 | ||||||||
\(73\) | 9.23105 | 1.08041 | 0.540206 | − | 0.841533i | \(-0.318346\pi\) | ||||
0.540206 | + | 0.841533i | \(0.318346\pi\) | |||||||
\(74\) | 23.9131 | 2.77984 | ||||||||
\(75\) | 2.84892 | 0.328965 | ||||||||
\(76\) | 31.0225 | 3.55852 | ||||||||
\(77\) | −2.39174 | −0.272564 | ||||||||
\(78\) | −21.8397 | −2.47286 | ||||||||
\(79\) | 8.16355 | 0.918471 | 0.459236 | − | 0.888315i | \(-0.348123\pi\) | ||||
0.459236 | + | 0.888315i | \(0.348123\pi\) | |||||||
\(80\) | −27.2996 | −3.05219 | ||||||||
\(81\) | −8.36714 | −0.929682 | ||||||||
\(82\) | 9.29899 | 1.02690 | ||||||||
\(83\) | 5.79023 | 0.635560 | 0.317780 | − | 0.948164i | \(-0.397063\pi\) | ||||
0.317780 | + | 0.948164i | \(0.397063\pi\) | |||||||
\(84\) | −41.8891 | −4.57047 | ||||||||
\(85\) | 13.5377 | 1.46837 | ||||||||
\(86\) | −2.05841 | −0.221964 | ||||||||
\(87\) | 9.15019 | 0.981004 | ||||||||
\(88\) | 6.89822 | 0.735353 | ||||||||
\(89\) | −4.81803 | −0.510711 | −0.255355 | − | 0.966847i | \(-0.582192\pi\) | ||||
−0.255355 | + | 0.966847i | \(0.582192\pi\) | |||||||
\(90\) | 17.0212 | 1.79420 | ||||||||
\(91\) | −10.1825 | −1.06742 | ||||||||
\(92\) | −10.7347 | −1.11917 | ||||||||
\(93\) | 16.2588 | 1.68596 | ||||||||
\(94\) | −1.39597 | −0.143983 | ||||||||
\(95\) | −11.3908 | −1.16867 | ||||||||
\(96\) | 48.6386 | 4.96416 | ||||||||
\(97\) | −16.2672 | −1.65168 | −0.825840 | − | 0.563904i | \(-0.809299\pi\) | ||||
−0.825840 | + | 0.563904i | \(0.809299\pi\) | |||||||
\(98\) | −7.85966 | −0.793946 | ||||||||
\(99\) | −2.43092 | −0.244317 | ||||||||
\(100\) | −6.11969 | −0.611969 | ||||||||
\(101\) | −15.7220 | −1.56440 | −0.782199 | − | 0.623028i | \(-0.785902\pi\) | ||||
−0.782199 | + | 0.623028i | \(0.785902\pi\) | |||||||
\(102\) | −46.5258 | −4.60674 | ||||||||
\(103\) | −3.71893 | −0.366437 | −0.183219 | − | 0.983072i | \(-0.558652\pi\) | ||||
−0.183219 | + | 0.983072i | \(0.558652\pi\) | |||||||
\(104\) | 29.3683 | 2.87980 | ||||||||
\(105\) | 15.3808 | 1.50101 | ||||||||
\(106\) | −1.21296 | −0.117814 | ||||||||
\(107\) | −9.49161 | −0.917588 | −0.458794 | − | 0.888543i | \(-0.651718\pi\) | ||||
−0.458794 | + | 0.888543i | \(0.651718\pi\) | |||||||
\(108\) | −2.63474 | −0.253528 | ||||||||
\(109\) | −8.64832 | −0.828359 | −0.414180 | − | 0.910195i | \(-0.635931\pi\) | ||||
−0.414180 | + | 0.910195i | \(0.635931\pi\) | |||||||
\(110\) | −4.04606 | −0.385777 | ||||||||
\(111\) | 21.9625 | 2.08458 | ||||||||
\(112\) | 43.7436 | 4.13338 | ||||||||
\(113\) | 6.24207 | 0.587205 | 0.293602 | − | 0.955928i | \(-0.405146\pi\) | ||||
0.293602 | + | 0.955928i | \(0.405146\pi\) | |||||||
\(114\) | 39.1476 | 3.66651 | ||||||||
\(115\) | 3.94155 | 0.367551 | ||||||||
\(116\) | −19.6553 | −1.82495 | ||||||||
\(117\) | −10.3493 | −0.956797 | ||||||||
\(118\) | −20.1393 | −1.85397 | ||||||||
\(119\) | −21.6921 | −1.98851 | ||||||||
\(120\) | −44.3611 | −4.04959 | ||||||||
\(121\) | −10.4222 | −0.947468 | ||||||||
\(122\) | −18.2244 | −1.64996 | ||||||||
\(123\) | 8.54045 | 0.770066 | ||||||||
\(124\) | −34.9252 | −3.13637 | ||||||||
\(125\) | 12.0649 | 1.07912 | ||||||||
\(126\) | −27.2740 | −2.42976 | ||||||||
\(127\) | −4.13447 | −0.366875 | −0.183437 | − | 0.983031i | \(-0.558722\pi\) | ||||
−0.183437 | + | 0.983031i | \(0.558722\pi\) | |||||||
\(128\) | −29.1066 | −2.57268 | ||||||||
\(129\) | −1.89050 | −0.166449 | ||||||||
\(130\) | −17.2256 | −1.51078 | ||||||||
\(131\) | 9.10277 | 0.795313 | 0.397657 | − | 0.917534i | \(-0.369824\pi\) | ||||
0.397657 | + | 0.917534i | \(0.369824\pi\) | |||||||
\(132\) | 10.1205 | 0.880873 | ||||||||
\(133\) | 18.2521 | 1.58266 | ||||||||
\(134\) | 19.7805 | 1.70877 | ||||||||
\(135\) | 0.967420 | 0.0832622 | ||||||||
\(136\) | 62.5641 | 5.36483 | ||||||||
\(137\) | −5.28083 | −0.451172 | −0.225586 | − | 0.974223i | \(-0.572430\pi\) | ||||
−0.225586 | + | 0.974223i | \(0.572430\pi\) | |||||||
\(138\) | −13.5462 | −1.15313 | ||||||||
\(139\) | −14.4174 | −1.22287 | −0.611434 | − | 0.791296i | \(-0.709407\pi\) | ||||
−0.611434 | + | 0.791296i | \(0.709407\pi\) | |||||||
\(140\) | −33.0390 | −2.79231 | ||||||||
\(141\) | −1.28209 | −0.107972 | ||||||||
\(142\) | −26.1409 | −2.19370 | ||||||||
\(143\) | 2.46011 | 0.205725 | ||||||||
\(144\) | 44.4603 | 3.70502 | ||||||||
\(145\) | 7.21700 | 0.599339 | ||||||||
\(146\) | −25.0224 | −2.07087 | ||||||||
\(147\) | −7.21853 | −0.595374 | ||||||||
\(148\) | −47.1770 | −3.87792 | ||||||||
\(149\) | −22.1086 | −1.81120 | −0.905602 | − | 0.424128i | \(-0.860581\pi\) | ||||
−0.905602 | + | 0.424128i | \(0.860581\pi\) | |||||||
\(150\) | −7.72250 | −0.630539 | ||||||||
\(151\) | −1.78018 | −0.144869 | −0.0724346 | − | 0.997373i | \(-0.523077\pi\) | ||||
−0.0724346 | + | 0.997373i | \(0.523077\pi\) | |||||||
\(152\) | −52.6425 | −4.26987 | ||||||||
\(153\) | −22.0475 | −1.78244 | ||||||||
\(154\) | 6.48322 | 0.522433 | ||||||||
\(155\) | 12.8238 | 1.03003 | ||||||||
\(156\) | 43.0865 | 3.44968 | ||||||||
\(157\) | 2.24791 | 0.179402 | 0.0897012 | − | 0.995969i | \(-0.471409\pi\) | ||||
0.0897012 | + | 0.995969i | \(0.471409\pi\) | |||||||
\(158\) | −22.1287 | −1.76047 | ||||||||
\(159\) | −1.11402 | −0.0883475 | ||||||||
\(160\) | 38.3626 | 3.03283 | ||||||||
\(161\) | −6.31575 | −0.497751 | ||||||||
\(162\) | 22.6806 | 1.78196 | ||||||||
\(163\) | 17.8027 | 1.39442 | 0.697208 | − | 0.716869i | \(-0.254426\pi\) | ||||
0.697208 | + | 0.716869i | \(0.254426\pi\) | |||||||
\(164\) | −18.3455 | −1.43254 | ||||||||
\(165\) | −3.71602 | −0.289292 | ||||||||
\(166\) | −15.6954 | −1.21820 | ||||||||
\(167\) | 1.98721 | 0.153775 | 0.0768874 | − | 0.997040i | \(-0.475502\pi\) | ||||
0.0768874 | + | 0.997040i | \(0.475502\pi\) | |||||||
\(168\) | 71.0821 | 5.48410 | ||||||||
\(169\) | −2.52640 | −0.194338 | ||||||||
\(170\) | −36.6962 | −2.81447 | ||||||||
\(171\) | 18.5511 | 1.41864 | ||||||||
\(172\) | 4.06093 | 0.309643 | ||||||||
\(173\) | −11.9449 | −0.908155 | −0.454077 | − | 0.890962i | \(-0.650031\pi\) | ||||
−0.454077 | + | 0.890962i | \(0.650031\pi\) | |||||||
\(174\) | −24.8032 | −1.88032 | ||||||||
\(175\) | −3.60052 | −0.272174 | ||||||||
\(176\) | −10.5685 | −0.796632 | ||||||||
\(177\) | −18.4965 | −1.39028 | ||||||||
\(178\) | 13.0601 | 0.978898 | ||||||||
\(179\) | 8.79944 | 0.657701 | 0.328850 | − | 0.944382i | \(-0.393339\pi\) | ||||
0.328850 | + | 0.944382i | \(0.393339\pi\) | |||||||
\(180\) | −33.5803 | −2.50293 | ||||||||
\(181\) | −14.8249 | −1.10193 | −0.550964 | − | 0.834529i | \(-0.685740\pi\) | ||||
−0.550964 | + | 0.834529i | \(0.685740\pi\) | |||||||
\(182\) | 27.6015 | 2.04596 | ||||||||
\(183\) | −16.7378 | −1.23730 | ||||||||
\(184\) | 18.2158 | 1.34289 | ||||||||
\(185\) | 17.3224 | 1.27357 | ||||||||
\(186\) | −44.0724 | −3.23155 | ||||||||
\(187\) | 5.24084 | 0.383249 | ||||||||
\(188\) | 2.75403 | 0.200858 | ||||||||
\(189\) | −1.55015 | −0.112757 | ||||||||
\(190\) | 30.8767 | 2.24003 | ||||||||
\(191\) | 24.8645 | 1.79913 | 0.899567 | − | 0.436784i | \(-0.143883\pi\) | ||||
0.899567 | + | 0.436784i | \(0.143883\pi\) | |||||||
\(192\) | −62.6190 | −4.51914 | ||||||||
\(193\) | −7.78597 | −0.560447 | −0.280223 | − | 0.959935i | \(-0.590409\pi\) | ||||
−0.280223 | + | 0.959935i | \(0.590409\pi\) | |||||||
\(194\) | 44.0950 | 3.16584 | ||||||||
\(195\) | −15.8205 | −1.13293 | ||||||||
\(196\) | 15.5059 | 1.10757 | ||||||||
\(197\) | −9.63954 | −0.686789 | −0.343394 | − | 0.939191i | \(-0.611577\pi\) | ||||
−0.343394 | + | 0.939191i | \(0.611577\pi\) | |||||||
\(198\) | 6.58944 | 0.468291 | ||||||||
\(199\) | 4.71053 | 0.333920 | 0.166960 | − | 0.985964i | \(-0.446605\pi\) | ||||
0.166960 | + | 0.985964i | \(0.446605\pi\) | |||||||
\(200\) | 10.3846 | 0.734301 | ||||||||
\(201\) | 18.1669 | 1.28140 | ||||||||
\(202\) | 42.6172 | 2.99854 | ||||||||
\(203\) | −11.5642 | −0.811647 | ||||||||
\(204\) | 91.7885 | 6.42648 | ||||||||
\(205\) | 6.73608 | 0.470468 | ||||||||
\(206\) | 10.0808 | 0.702364 | ||||||||
\(207\) | −6.41922 | −0.446167 | ||||||||
\(208\) | −44.9941 | −3.11978 | ||||||||
\(209\) | −4.40973 | −0.305027 | ||||||||
\(210\) | −41.6923 | −2.87704 | ||||||||
\(211\) | 18.0847 | 1.24500 | 0.622500 | − | 0.782620i | \(-0.286117\pi\) | ||||
0.622500 | + | 0.782620i | \(0.286117\pi\) | |||||||
\(212\) | 2.39300 | 0.164352 | ||||||||
\(213\) | −24.0085 | −1.64504 | ||||||||
\(214\) | 25.7286 | 1.75877 | ||||||||
\(215\) | −1.49109 | −0.101691 | ||||||||
\(216\) | 4.47092 | 0.304208 | ||||||||
\(217\) | −20.5482 | −1.39490 | ||||||||
\(218\) | 23.4428 | 1.58775 | ||||||||
\(219\) | −22.9812 | −1.55293 | ||||||||
\(220\) | 7.98228 | 0.538165 | ||||||||
\(221\) | 22.3122 | 1.50088 | ||||||||
\(222\) | −59.5331 | −3.99560 | ||||||||
\(223\) | −25.4753 | −1.70595 | −0.852975 | − | 0.521952i | \(-0.825204\pi\) | ||||
−0.852975 | + | 0.521952i | \(0.825204\pi\) | |||||||
\(224\) | −61.4704 | −4.10717 | ||||||||
\(225\) | −3.65951 | −0.243967 | ||||||||
\(226\) | −16.9202 | −1.12552 | ||||||||
\(227\) | −0.233345 | −0.0154876 | −0.00774381 | − | 0.999970i | \(-0.502465\pi\) | ||||
−0.00774381 | + | 0.999970i | \(0.502465\pi\) | |||||||
\(228\) | −77.2323 | −5.11483 | ||||||||
\(229\) | 8.60966 | 0.568943 | 0.284471 | − | 0.958685i | \(-0.408182\pi\) | ||||
0.284471 | + | 0.958685i | \(0.408182\pi\) | |||||||
\(230\) | −10.6842 | −0.704498 | ||||||||
\(231\) | 5.95437 | 0.391769 | ||||||||
\(232\) | 33.3533 | 2.18975 | ||||||||
\(233\) | −12.5073 | −0.819379 | −0.409690 | − | 0.912225i | \(-0.634363\pi\) | ||||
−0.409690 | + | 0.912225i | \(0.634363\pi\) | |||||||
\(234\) | 28.0537 | 1.83393 | ||||||||
\(235\) | −1.01122 | −0.0659648 | ||||||||
\(236\) | 39.7318 | 2.58632 | ||||||||
\(237\) | −20.3236 | −1.32016 | ||||||||
\(238\) | 58.8002 | 3.81145 | ||||||||
\(239\) | −23.1892 | −1.49999 | −0.749993 | − | 0.661446i | \(-0.769943\pi\) | ||||
−0.749993 | + | 0.661446i | \(0.769943\pi\) | |||||||
\(240\) | 67.9639 | 4.38705 | ||||||||
\(241\) | −26.2160 | −1.68872 | −0.844360 | − | 0.535777i | \(-0.820019\pi\) | ||||
−0.844360 | + | 0.535777i | \(0.820019\pi\) | |||||||
\(242\) | 28.2511 | 1.81605 | ||||||||
\(243\) | 22.3085 | 1.43109 | ||||||||
\(244\) | 35.9541 | 2.30172 | ||||||||
\(245\) | −5.69345 | −0.363741 | ||||||||
\(246\) | −23.1504 | −1.47601 | ||||||||
\(247\) | −18.7739 | −1.19455 | ||||||||
\(248\) | 59.2650 | 3.76333 | ||||||||
\(249\) | −14.4151 | −0.913521 | ||||||||
\(250\) | −32.7041 | −2.06839 | ||||||||
\(251\) | 19.6395 | 1.23964 | 0.619818 | − | 0.784745i | \(-0.287206\pi\) | ||||
0.619818 | + | 0.784745i | \(0.287206\pi\) | |||||||
\(252\) | 53.8076 | 3.38956 | ||||||||
\(253\) | 1.52589 | 0.0959321 | ||||||||
\(254\) | 11.2072 | 0.703202 | ||||||||
\(255\) | −33.7028 | −2.11055 | ||||||||
\(256\) | 28.5931 | 1.78707 | ||||||||
\(257\) | −3.96992 | −0.247637 | −0.123818 | − | 0.992305i | \(-0.539514\pi\) | ||||
−0.123818 | + | 0.992305i | \(0.539514\pi\) | |||||||
\(258\) | 5.12452 | 0.319039 | ||||||||
\(259\) | −27.7566 | −1.72471 | ||||||||
\(260\) | 33.9835 | 2.10757 | ||||||||
\(261\) | −11.7536 | −0.727533 | ||||||||
\(262\) | −24.6747 | −1.52441 | ||||||||
\(263\) | −18.7296 | −1.15492 | −0.577459 | − | 0.816420i | \(-0.695956\pi\) | ||||
−0.577459 | + | 0.816420i | \(0.695956\pi\) | |||||||
\(264\) | −17.1735 | −1.05696 | ||||||||
\(265\) | −0.878657 | −0.0539755 | ||||||||
\(266\) | −49.4755 | −3.03353 | ||||||||
\(267\) | 11.9948 | 0.734068 | ||||||||
\(268\) | −39.0239 | −2.38377 | ||||||||
\(269\) | 25.4097 | 1.54926 | 0.774628 | − | 0.632417i | \(-0.217937\pi\) | ||||
0.774628 | + | 0.632417i | \(0.217937\pi\) | |||||||
\(270\) | −2.62236 | −0.159592 | ||||||||
\(271\) | −0.902749 | −0.0548381 | −0.0274191 | − | 0.999624i | \(-0.508729\pi\) | ||||
−0.0274191 | + | 0.999624i | \(0.508729\pi\) | |||||||
\(272\) | −95.8522 | −5.81189 | ||||||||
\(273\) | 25.3500 | 1.53425 | ||||||||
\(274\) | 14.3146 | 0.864777 | ||||||||
\(275\) | 0.869891 | 0.0524564 | ||||||||
\(276\) | 26.7246 | 1.60863 | ||||||||
\(277\) | 29.4004 | 1.76650 | 0.883251 | − | 0.468901i | \(-0.155350\pi\) | ||||
0.883251 | + | 0.468901i | \(0.155350\pi\) | |||||||
\(278\) | 39.0809 | 2.34391 | ||||||||
\(279\) | −20.8849 | −1.25035 | ||||||||
\(280\) | 56.0643 | 3.35049 | ||||||||
\(281\) | 15.6373 | 0.932842 | 0.466421 | − | 0.884563i | \(-0.345543\pi\) | ||||
0.466421 | + | 0.884563i | \(0.345543\pi\) | |||||||
\(282\) | 3.47534 | 0.206953 | ||||||||
\(283\) | 1.67109 | 0.0993358 | 0.0496679 | − | 0.998766i | \(-0.484184\pi\) | ||||
0.0496679 | + | 0.998766i | \(0.484184\pi\) | |||||||
\(284\) | 51.5721 | 3.06024 | ||||||||
\(285\) | 28.3581 | 1.67979 | ||||||||
\(286\) | −6.66856 | −0.394320 | ||||||||
\(287\) | −10.7936 | −0.637125 | ||||||||
\(288\) | −62.4775 | −3.68152 | ||||||||
\(289\) | 30.5324 | 1.79602 | ||||||||
\(290\) | −19.5629 | −1.14878 | ||||||||
\(291\) | 40.4981 | 2.37404 | ||||||||
\(292\) | 49.3654 | 2.88889 | ||||||||
\(293\) | 11.3596 | 0.663634 | 0.331817 | − | 0.943344i | \(-0.392338\pi\) | ||||
0.331817 | + | 0.943344i | \(0.392338\pi\) | |||||||
\(294\) | 19.5671 | 1.14118 | ||||||||
\(295\) | −14.5887 | −0.849386 | ||||||||
\(296\) | 80.0552 | 4.65311 | ||||||||
\(297\) | 0.374518 | 0.0217317 | ||||||||
\(298\) | 59.9291 | 3.47160 | ||||||||
\(299\) | 6.49629 | 0.375690 | ||||||||
\(300\) | 15.2353 | 0.879612 | ||||||||
\(301\) | 2.38925 | 0.137714 | ||||||||
\(302\) | 4.82550 | 0.277676 | ||||||||
\(303\) | 39.1409 | 2.24858 | ||||||||
\(304\) | 80.6515 | 4.62568 | ||||||||
\(305\) | −13.2016 | −0.755920 | ||||||||
\(306\) | 59.7636 | 3.41646 | ||||||||
\(307\) | 31.5720 | 1.80191 | 0.900954 | − | 0.433915i | \(-0.142868\pi\) | ||||
0.900954 | + | 0.433915i | \(0.142868\pi\) | |||||||
\(308\) | −12.7904 | −0.728802 | ||||||||
\(309\) | 9.25850 | 0.526698 | ||||||||
\(310\) | −34.7611 | −1.97430 | ||||||||
\(311\) | −2.50240 | −0.141898 | −0.0709491 | − | 0.997480i | \(-0.522603\pi\) | ||||
−0.0709491 | + | 0.997480i | \(0.522603\pi\) | |||||||
\(312\) | −73.1141 | −4.13927 | ||||||||
\(313\) | −25.0610 | −1.41653 | −0.708266 | − | 0.705945i | \(-0.750522\pi\) | ||||
−0.708266 | + | 0.705945i | \(0.750522\pi\) | |||||||
\(314\) | −6.09334 | −0.343867 | ||||||||
\(315\) | −19.7570 | −1.11318 | ||||||||
\(316\) | 43.6566 | 2.45588 | ||||||||
\(317\) | −2.84292 | −0.159675 | −0.0798373 | − | 0.996808i | \(-0.525440\pi\) | ||||
−0.0798373 | + | 0.996808i | \(0.525440\pi\) | |||||||
\(318\) | 3.01974 | 0.169339 | ||||||||
\(319\) | 2.79392 | 0.156430 | ||||||||
\(320\) | −49.3893 | −2.76095 | ||||||||
\(321\) | 23.6299 | 1.31889 | ||||||||
\(322\) | 17.1199 | 0.954057 | ||||||||
\(323\) | −39.9945 | −2.22535 | ||||||||
\(324\) | −44.7454 | −2.48586 | ||||||||
\(325\) | 3.70345 | 0.205430 | ||||||||
\(326\) | −48.2573 | −2.67273 | ||||||||
\(327\) | 21.5305 | 1.19064 | ||||||||
\(328\) | 31.1307 | 1.71891 | ||||||||
\(329\) | 1.62033 | 0.0893319 | ||||||||
\(330\) | 10.0729 | 0.554496 | ||||||||
\(331\) | −23.8977 | −1.31354 | −0.656769 | − | 0.754092i | \(-0.728077\pi\) | ||||
−0.656769 | + | 0.754092i | \(0.728077\pi\) | |||||||
\(332\) | 30.9647 | 1.69941 | ||||||||
\(333\) | −28.2113 | −1.54597 | ||||||||
\(334\) | −5.38667 | −0.294746 | ||||||||
\(335\) | 14.3288 | 0.782864 | ||||||||
\(336\) | −108.902 | −5.94110 | ||||||||
\(337\) | −21.7396 | −1.18423 | −0.592116 | − | 0.805853i | \(-0.701707\pi\) | ||||
−0.592116 | + | 0.805853i | \(0.701707\pi\) | |||||||
\(338\) | 6.84824 | 0.372495 | ||||||||
\(339\) | −15.5400 | −0.844017 | ||||||||
\(340\) | 72.3961 | 3.92623 | ||||||||
\(341\) | 4.96448 | 0.268842 | ||||||||
\(342\) | −50.2860 | −2.71916 | ||||||||
\(343\) | −12.9015 | −0.696618 | ||||||||
\(344\) | −6.89103 | −0.371540 | ||||||||
\(345\) | −9.81271 | −0.528298 | ||||||||
\(346\) | 32.3788 | 1.74069 | ||||||||
\(347\) | 25.5731 | 1.37284 | 0.686418 | − | 0.727207i | \(-0.259182\pi\) | ||||
0.686418 | + | 0.727207i | \(0.259182\pi\) | |||||||
\(348\) | 48.9330 | 2.62308 | ||||||||
\(349\) | −9.36695 | −0.501401 | −0.250701 | − | 0.968065i | \(-0.580661\pi\) | ||||
−0.250701 | + | 0.968065i | \(0.580661\pi\) | |||||||
\(350\) | 9.75984 | 0.521685 | ||||||||
\(351\) | 1.59446 | 0.0851061 | ||||||||
\(352\) | 14.8513 | 0.791579 | ||||||||
\(353\) | −13.2181 | −0.703529 | −0.351764 | − | 0.936089i | \(-0.614418\pi\) | ||||
−0.351764 | + | 0.936089i | \(0.614418\pi\) | |||||||
\(354\) | 50.1380 | 2.66480 | ||||||||
\(355\) | −18.9362 | −1.00503 | ||||||||
\(356\) | −25.7657 | −1.36558 | ||||||||
\(357\) | 54.0038 | 2.85818 | ||||||||
\(358\) | −23.8524 | −1.26064 | ||||||||
\(359\) | 17.0003 | 0.897241 | 0.448620 | − | 0.893722i | \(-0.351916\pi\) | ||||
0.448620 | + | 0.893722i | \(0.351916\pi\) | |||||||
\(360\) | 56.9829 | 3.00326 | ||||||||
\(361\) | 14.6520 | 0.771158 | ||||||||
\(362\) | 40.1855 | 2.11211 | ||||||||
\(363\) | 25.9466 | 1.36184 | ||||||||
\(364\) | −54.4536 | −2.85414 | ||||||||
\(365\) | −18.1259 | −0.948754 | ||||||||
\(366\) | 45.3708 | 2.37157 | ||||||||
\(367\) | 6.73353 | 0.351487 | 0.175744 | − | 0.984436i | \(-0.443767\pi\) | ||||
0.175744 | + | 0.984436i | \(0.443767\pi\) | |||||||
\(368\) | −27.9078 | −1.45479 | ||||||||
\(369\) | −10.9704 | −0.571097 | ||||||||
\(370\) | −46.9553 | −2.44109 | ||||||||
\(371\) | 1.40792 | 0.0730955 | ||||||||
\(372\) | 86.9483 | 4.50806 | ||||||||
\(373\) | 25.9401 | 1.34313 | 0.671564 | − | 0.740947i | \(-0.265623\pi\) | ||||
0.671564 | + | 0.740947i | \(0.265623\pi\) | |||||||
\(374\) | −14.2062 | −0.734586 | ||||||||
\(375\) | −30.0363 | −1.55107 | ||||||||
\(376\) | −4.67335 | −0.241010 | ||||||||
\(377\) | 11.8948 | 0.612612 | ||||||||
\(378\) | 4.20195 | 0.216125 | ||||||||
\(379\) | −19.9717 | −1.02588 | −0.512940 | − | 0.858425i | \(-0.671444\pi\) | ||||
−0.512940 | + | 0.858425i | \(0.671444\pi\) | |||||||
\(380\) | −60.9152 | −3.12488 | ||||||||
\(381\) | 10.2930 | 0.527326 | ||||||||
\(382\) | −67.3996 | −3.44846 | ||||||||
\(383\) | −4.81142 | −0.245852 | −0.122926 | − | 0.992416i | \(-0.539228\pi\) | ||||
−0.122926 | + | 0.992416i | \(0.539228\pi\) | |||||||
\(384\) | 72.4625 | 3.69784 | ||||||||
\(385\) | 4.69637 | 0.239349 | ||||||||
\(386\) | 21.1052 | 1.07423 | ||||||||
\(387\) | 2.42839 | 0.123442 | ||||||||
\(388\) | −86.9928 | −4.41639 | ||||||||
\(389\) | 19.0592 | 0.966342 | 0.483171 | − | 0.875526i | \(-0.339485\pi\) | ||||
0.483171 | + | 0.875526i | \(0.339485\pi\) | |||||||
\(390\) | 42.8841 | 2.17152 | ||||||||
\(391\) | 13.8392 | 0.699881 | ||||||||
\(392\) | −26.3122 | −1.32897 | ||||||||
\(393\) | −22.6619 | −1.14314 | ||||||||
\(394\) | 26.1297 | 1.31639 | ||||||||
\(395\) | −16.0298 | −0.806546 | ||||||||
\(396\) | −13.0000 | −0.653274 | ||||||||
\(397\) | 19.8208 | 0.994775 | 0.497388 | − | 0.867528i | \(-0.334293\pi\) | ||||
0.497388 | + | 0.867528i | \(0.334293\pi\) | |||||||
\(398\) | −12.7687 | −0.640037 | ||||||||
\(399\) | −45.4396 | −2.27483 | ||||||||
\(400\) | −15.9098 | −0.795492 | ||||||||
\(401\) | 10.1980 | 0.509265 | 0.254633 | − | 0.967038i | \(-0.418045\pi\) | ||||
0.254633 | + | 0.967038i | \(0.418045\pi\) | |||||||
\(402\) | −49.2447 | −2.45610 | ||||||||
\(403\) | 21.1356 | 1.05284 | ||||||||
\(404\) | −84.0774 | −4.18301 | ||||||||
\(405\) | 16.4296 | 0.816391 | ||||||||
\(406\) | 31.3467 | 1.55571 | ||||||||
\(407\) | 6.70603 | 0.332405 | ||||||||
\(408\) | −155.757 | −7.71112 | ||||||||
\(409\) | 38.2717 | 1.89241 | 0.946206 | − | 0.323566i | \(-0.104882\pi\) | ||||
0.946206 | + | 0.323566i | \(0.104882\pi\) | |||||||
\(410\) | −18.2593 | −0.901763 | ||||||||
\(411\) | 13.1469 | 0.648490 | ||||||||
\(412\) | −19.8879 | −0.979808 | ||||||||
\(413\) | 23.3762 | 1.15027 | ||||||||
\(414\) | 17.4004 | 0.855184 | ||||||||
\(415\) | −11.3696 | −0.558111 | ||||||||
\(416\) | 63.2277 | 3.09999 | ||||||||
\(417\) | 35.8929 | 1.75768 | ||||||||
\(418\) | 11.9533 | 0.584657 | ||||||||
\(419\) | 6.96572 | 0.340298 | 0.170149 | − | 0.985418i | \(-0.445575\pi\) | ||||
0.170149 | + | 0.985418i | \(0.445575\pi\) | |||||||
\(420\) | 82.2526 | 4.01352 | ||||||||
\(421\) | −27.2935 | −1.33020 | −0.665101 | − | 0.746753i | \(-0.731612\pi\) | ||||
−0.665101 | + | 0.746753i | \(0.731612\pi\) | |||||||
\(422\) | −49.0216 | −2.38634 | ||||||||
\(423\) | 1.64688 | 0.0800741 | ||||||||
\(424\) | −4.06071 | −0.197205 | ||||||||
\(425\) | 7.88956 | 0.382700 | ||||||||
\(426\) | 65.0793 | 3.15310 | ||||||||
\(427\) | 21.1536 | 1.02369 | ||||||||
\(428\) | −50.7588 | −2.45352 | ||||||||
\(429\) | −6.12459 | −0.295698 | ||||||||
\(430\) | 4.04185 | 0.194915 | ||||||||
\(431\) | −2.24443 | −0.108111 | −0.0540553 | − | 0.998538i | \(-0.517215\pi\) | ||||
−0.0540553 | + | 0.998538i | \(0.517215\pi\) | |||||||
\(432\) | −6.84973 | −0.329558 | ||||||||
\(433\) | 31.4301 | 1.51044 | 0.755218 | − | 0.655474i | \(-0.227531\pi\) | ||||
0.755218 | + | 0.655474i | \(0.227531\pi\) | |||||||
\(434\) | 55.6995 | 2.67366 | ||||||||
\(435\) | −17.9671 | −0.861459 | ||||||||
\(436\) | −46.2491 | −2.21493 | ||||||||
\(437\) | −11.6446 | −0.557035 | ||||||||
\(438\) | 62.2946 | 2.97655 | ||||||||
\(439\) | −8.44635 | −0.403122 | −0.201561 | − | 0.979476i | \(-0.564601\pi\) | ||||
−0.201561 | + | 0.979476i | \(0.564601\pi\) | |||||||
\(440\) | −13.5452 | −0.645743 | ||||||||
\(441\) | 9.27238 | 0.441542 | ||||||||
\(442\) | −60.4811 | −2.87679 | ||||||||
\(443\) | −5.82437 | −0.276724 | −0.138362 | − | 0.990382i | \(-0.544184\pi\) | ||||
−0.138362 | + | 0.990382i | \(0.544184\pi\) | |||||||
\(444\) | 117.450 | 5.57392 | ||||||||
\(445\) | 9.46060 | 0.448476 | ||||||||
\(446\) | 69.0551 | 3.26985 | ||||||||
\(447\) | 55.0406 | 2.60333 | ||||||||
\(448\) | 79.1391 | 3.73897 | ||||||||
\(449\) | −8.16761 | −0.385453 | −0.192727 | − | 0.981252i | \(-0.561733\pi\) | ||||
−0.192727 | + | 0.981252i | \(0.561733\pi\) | |||||||
\(450\) | 9.91974 | 0.467621 | ||||||||
\(451\) | 2.60774 | 0.122794 | ||||||||
\(452\) | 33.3811 | 1.57011 | ||||||||
\(453\) | 4.43187 | 0.208227 | ||||||||
\(454\) | 0.632521 | 0.0296857 | ||||||||
\(455\) | 19.9942 | 0.937343 | ||||||||
\(456\) | 131.056 | 6.13728 | ||||||||
\(457\) | −1.13934 | −0.0532962 | −0.0266481 | − | 0.999645i | \(-0.508483\pi\) | ||||
−0.0266481 | + | 0.999645i | \(0.508483\pi\) | |||||||
\(458\) | −23.3380 | −1.09051 | ||||||||
\(459\) | 3.39673 | 0.158546 | ||||||||
\(460\) | 21.0784 | 0.982786 | ||||||||
\(461\) | 40.5258 | 1.88748 | 0.943738 | − | 0.330693i | \(-0.107283\pi\) | ||||
0.943738 | + | 0.330693i | \(0.107283\pi\) | |||||||
\(462\) | −16.1404 | −0.750918 | ||||||||
\(463\) | 7.51253 | 0.349137 | 0.174568 | − | 0.984645i | \(-0.444147\pi\) | ||||
0.174568 | + | 0.984645i | \(0.444147\pi\) | |||||||
\(464\) | −51.0993 | −2.37223 | ||||||||
\(465\) | −31.9255 | −1.48051 | ||||||||
\(466\) | 33.9032 | 1.57053 | ||||||||
\(467\) | 41.5412 | 1.92230 | 0.961148 | − | 0.276033i | \(-0.0890198\pi\) | ||||
0.961148 | + | 0.276033i | \(0.0890198\pi\) | |||||||
\(468\) | −55.3457 | −2.55836 | ||||||||
\(469\) | −22.9597 | −1.06018 | ||||||||
\(470\) | 2.74109 | 0.126437 | ||||||||
\(471\) | −5.59629 | −0.257864 | ||||||||
\(472\) | −67.4214 | −3.10332 | ||||||||
\(473\) | −0.577245 | −0.0265418 | ||||||||
\(474\) | 55.0907 | 2.53040 | ||||||||
\(475\) | −6.63841 | −0.304591 | ||||||||
\(476\) | −116.004 | −5.31704 | ||||||||
\(477\) | 1.43099 | 0.0655204 | ||||||||
\(478\) | 62.8584 | 2.87508 | ||||||||
\(479\) | 9.40166 | 0.429573 | 0.214786 | − | 0.976661i | \(-0.431094\pi\) | ||||
0.214786 | + | 0.976661i | \(0.431094\pi\) | |||||||
\(480\) | −95.5059 | −4.35923 | ||||||||
\(481\) | 28.5500 | 1.30177 | ||||||||
\(482\) | 71.0630 | 3.23683 | ||||||||
\(483\) | 15.7234 | 0.715440 | ||||||||
\(484\) | −55.7351 | −2.53341 | ||||||||
\(485\) | 31.9419 | 1.45041 | ||||||||
\(486\) | −60.4711 | −2.74303 | ||||||||
\(487\) | 27.4134 | 1.24222 | 0.621110 | − | 0.783723i | \(-0.286682\pi\) | ||||
0.621110 | + | 0.783723i | \(0.286682\pi\) | |||||||
\(488\) | −61.0109 | −2.76183 | ||||||||
\(489\) | −44.3209 | −2.00426 | ||||||||
\(490\) | 15.4331 | 0.697196 | ||||||||
\(491\) | −14.0153 | −0.632502 | −0.316251 | − | 0.948676i | \(-0.602424\pi\) | ||||
−0.316251 | + | 0.948676i | \(0.602424\pi\) | |||||||
\(492\) | 45.6722 | 2.05906 | ||||||||
\(493\) | 25.3398 | 1.14125 | ||||||||
\(494\) | 50.8898 | 2.28964 | ||||||||
\(495\) | 4.77332 | 0.214545 | ||||||||
\(496\) | −90.7976 | −4.07693 | ||||||||
\(497\) | 30.3424 | 1.36104 | ||||||||
\(498\) | 39.0747 | 1.75098 | ||||||||
\(499\) | −21.9365 | −0.982013 | −0.491006 | − | 0.871156i | \(-0.663371\pi\) | ||||
−0.491006 | + | 0.871156i | \(0.663371\pi\) | |||||||
\(500\) | 64.5203 | 2.88543 | ||||||||
\(501\) | −4.94727 | −0.221028 | ||||||||
\(502\) | −53.2364 | −2.37606 | ||||||||
\(503\) | −22.6862 | −1.01153 | −0.505764 | − | 0.862672i | \(-0.668789\pi\) | ||||
−0.505764 | + | 0.862672i | \(0.668789\pi\) | |||||||
\(504\) | −91.3067 | −4.06712 | ||||||||
\(505\) | 30.8714 | 1.37376 | ||||||||
\(506\) | −4.13620 | −0.183877 | ||||||||
\(507\) | 6.28962 | 0.279332 | ||||||||
\(508\) | −22.1101 | −0.980977 | ||||||||
\(509\) | 2.58248 | 0.114467 | 0.0572333 | − | 0.998361i | \(-0.481772\pi\) | ||||
0.0572333 | + | 0.998361i | \(0.481772\pi\) | |||||||
\(510\) | 91.3573 | 4.04537 | ||||||||
\(511\) | 29.0441 | 1.28484 | ||||||||
\(512\) | −19.2934 | −0.852655 | ||||||||
\(513\) | −2.85806 | −0.126186 | ||||||||
\(514\) | 10.7612 | 0.474655 | ||||||||
\(515\) | 7.30243 | 0.321783 | ||||||||
\(516\) | −10.1099 | −0.445064 | ||||||||
\(517\) | −0.391475 | −0.0172171 | ||||||||
\(518\) | 75.2390 | 3.30581 | ||||||||
\(519\) | 29.7376 | 1.30533 | ||||||||
\(520\) | −57.6670 | −2.52887 | ||||||||
\(521\) | −29.8975 | −1.30983 | −0.654916 | − | 0.755701i | \(-0.727296\pi\) | ||||
−0.654916 | + | 0.755701i | \(0.727296\pi\) | |||||||
\(522\) | 31.8603 | 1.39449 | ||||||||
\(523\) | 3.66846 | 0.160411 | 0.0802053 | − | 0.996778i | \(-0.474442\pi\) | ||||
0.0802053 | + | 0.996778i | \(0.474442\pi\) | |||||||
\(524\) | 48.6794 | 2.12657 | ||||||||
\(525\) | 8.96371 | 0.391208 | ||||||||
\(526\) | 50.7699 | 2.21367 | ||||||||
\(527\) | 45.0258 | 1.96136 | ||||||||
\(528\) | 26.3109 | 1.14504 | ||||||||
\(529\) | −18.9706 | −0.824811 | ||||||||
\(530\) | 2.38175 | 0.103457 | ||||||||
\(531\) | 23.7592 | 1.03106 | ||||||||
\(532\) | 97.6077 | 4.23183 | ||||||||
\(533\) | 11.1021 | 0.480887 | ||||||||
\(534\) | −32.5139 | −1.40702 | ||||||||
\(535\) | 18.6375 | 0.805771 | ||||||||
\(536\) | 66.2202 | 2.86028 | ||||||||
\(537\) | −21.9067 | −0.945345 | ||||||||
\(538\) | −68.8774 | −2.96952 | ||||||||
\(539\) | −2.20411 | −0.0949377 | ||||||||
\(540\) | 5.17352 | 0.222633 | ||||||||
\(541\) | 33.8529 | 1.45545 | 0.727724 | − | 0.685870i | \(-0.240578\pi\) | ||||
0.727724 | + | 0.685870i | \(0.240578\pi\) | |||||||
\(542\) | 2.44706 | 0.105110 | ||||||||
\(543\) | 36.9075 | 1.58385 | ||||||||
\(544\) | 134.696 | 5.77503 | ||||||||
\(545\) | 16.9817 | 0.727416 | ||||||||
\(546\) | −68.7155 | −2.94075 | ||||||||
\(547\) | −20.4548 | −0.874583 | −0.437292 | − | 0.899320i | \(-0.644062\pi\) | ||||
−0.437292 | + | 0.899320i | \(0.644062\pi\) | |||||||
\(548\) | −28.2406 | −1.20638 | ||||||||
\(549\) | 21.5002 | 0.917604 | ||||||||
\(550\) | −2.35799 | −0.100545 | ||||||||
\(551\) | −21.3213 | −0.908317 | ||||||||
\(552\) | −45.3493 | −1.93019 | ||||||||
\(553\) | 25.6854 | 1.09225 | ||||||||
\(554\) | −79.6950 | −3.38592 | ||||||||
\(555\) | −43.1251 | −1.83056 | ||||||||
\(556\) | −77.1007 | −3.26980 | ||||||||
\(557\) | 9.30087 | 0.394091 | 0.197045 | − | 0.980394i | \(-0.436865\pi\) | ||||
0.197045 | + | 0.980394i | \(0.436865\pi\) | |||||||
\(558\) | 56.6121 | 2.39658 | ||||||||
\(559\) | −2.45755 | −0.103943 | ||||||||
\(560\) | −85.8941 | −3.62969 | ||||||||
\(561\) | −13.0474 | −0.550861 | ||||||||
\(562\) | −42.3876 | −1.78801 | ||||||||
\(563\) | −41.2380 | −1.73797 | −0.868987 | − | 0.494834i | \(-0.835229\pi\) | ||||
−0.868987 | + | 0.494834i | \(0.835229\pi\) | |||||||
\(564\) | −6.85632 | −0.288703 | ||||||||
\(565\) | −12.2568 | −0.515648 | ||||||||
\(566\) | −4.52977 | −0.190400 | ||||||||
\(567\) | −26.3260 | −1.10559 | ||||||||
\(568\) | −87.5133 | −3.67198 | ||||||||
\(569\) | 4.76017 | 0.199557 | 0.0997784 | − | 0.995010i | \(-0.468187\pi\) | ||||
0.0997784 | + | 0.995010i | \(0.468187\pi\) | |||||||
\(570\) | −76.8695 | −3.21971 | ||||||||
\(571\) | 7.05451 | 0.295222 | 0.147611 | − | 0.989045i | \(-0.452842\pi\) | ||||
0.147611 | + | 0.989045i | \(0.452842\pi\) | |||||||
\(572\) | 13.1561 | 0.550083 | ||||||||
\(573\) | −61.9016 | −2.58598 | ||||||||
\(574\) | 29.2579 | 1.22120 | ||||||||
\(575\) | 2.29708 | 0.0957948 | ||||||||
\(576\) | 80.4357 | 3.35149 | ||||||||
\(577\) | 16.8988 | 0.703507 | 0.351754 | − | 0.936093i | \(-0.385586\pi\) | ||||
0.351754 | + | 0.936093i | \(0.385586\pi\) | |||||||
\(578\) | −82.7633 | −3.44250 | ||||||||
\(579\) | 19.3836 | 0.805556 | ||||||||
\(580\) | 38.5947 | 1.60256 | ||||||||
\(581\) | 18.2181 | 0.755814 | ||||||||
\(582\) | −109.777 | −4.55040 | ||||||||
\(583\) | −0.340155 | −0.0140878 | ||||||||
\(584\) | −83.7687 | −3.46637 | ||||||||
\(585\) | 20.3218 | 0.840202 | ||||||||
\(586\) | −30.7921 | −1.27201 | ||||||||
\(587\) | 19.2572 | 0.794829 | 0.397415 | − | 0.917639i | \(-0.369908\pi\) | ||||
0.397415 | + | 0.917639i | \(0.369908\pi\) | |||||||
\(588\) | −38.6029 | −1.59196 | ||||||||
\(589\) | −37.8855 | −1.56104 | ||||||||
\(590\) | 39.5452 | 1.62805 | ||||||||
\(591\) | 23.9982 | 0.987154 | ||||||||
\(592\) | −122.650 | −5.04087 | ||||||||
\(593\) | −6.81249 | −0.279756 | −0.139878 | − | 0.990169i | \(-0.544671\pi\) | ||||
−0.139878 | + | 0.990169i | \(0.544671\pi\) | |||||||
\(594\) | −1.01520 | −0.0416540 | ||||||||
\(595\) | 42.5942 | 1.74619 | ||||||||
\(596\) | −118.231 | −4.84294 | ||||||||
\(597\) | −11.7271 | −0.479960 | ||||||||
\(598\) | −17.6093 | −0.720099 | ||||||||
\(599\) | −10.6354 | −0.434551 | −0.217276 | − | 0.976110i | \(-0.569717\pi\) | ||||
−0.217276 | + | 0.976110i | \(0.569717\pi\) | |||||||
\(600\) | −25.8530 | −1.05545 | ||||||||
\(601\) | 8.95573 | 0.365312 | 0.182656 | − | 0.983177i | \(-0.441531\pi\) | ||||
0.182656 | + | 0.983177i | \(0.441531\pi\) | |||||||
\(602\) | −6.47646 | −0.263961 | ||||||||
\(603\) | −23.3359 | −0.950311 | ||||||||
\(604\) | −9.51998 | −0.387363 | ||||||||
\(605\) | 20.4647 | 0.832010 | ||||||||
\(606\) | −106.098 | −4.30994 | ||||||||
\(607\) | 32.7248 | 1.32826 | 0.664129 | − | 0.747618i | \(-0.268803\pi\) | ||||
0.664129 | + | 0.747618i | \(0.268803\pi\) | |||||||
\(608\) | −113.335 | −4.59635 | ||||||||
\(609\) | 28.7897 | 1.16662 | ||||||||
\(610\) | 35.7852 | 1.44890 | ||||||||
\(611\) | −1.66665 | −0.0674256 | ||||||||
\(612\) | −117.905 | −4.76601 | ||||||||
\(613\) | 4.47171 | 0.180611 | 0.0903053 | − | 0.995914i | \(-0.471216\pi\) | ||||
0.0903053 | + | 0.995914i | \(0.471216\pi\) | |||||||
\(614\) | −85.5813 | −3.45378 | ||||||||
\(615\) | −16.7699 | −0.676226 | ||||||||
\(616\) | 21.7042 | 0.874489 | ||||||||
\(617\) | −43.3472 | −1.74509 | −0.872546 | − | 0.488533i | \(-0.837532\pi\) | ||||
−0.872546 | + | 0.488533i | \(0.837532\pi\) | |||||||
\(618\) | −25.0968 | −1.00954 | ||||||||
\(619\) | 20.4229 | 0.820865 | 0.410433 | − | 0.911891i | \(-0.365378\pi\) | ||||
0.410433 | + | 0.911891i | \(0.365378\pi\) | |||||||
\(620\) | 68.5784 | 2.75418 | ||||||||
\(621\) | 0.988972 | 0.0396861 | ||||||||
\(622\) | 6.78320 | 0.271982 | ||||||||
\(623\) | −15.1592 | −0.607342 | ||||||||
\(624\) | 112.015 | 4.48420 | ||||||||
\(625\) | −17.9687 | −0.718749 | ||||||||
\(626\) | 67.9323 | 2.71512 | ||||||||
\(627\) | 10.9783 | 0.438430 | ||||||||
\(628\) | 12.0212 | 0.479700 | ||||||||
\(629\) | 60.8210 | 2.42509 | ||||||||
\(630\) | 53.5548 | 2.13367 | ||||||||
\(631\) | 41.5432 | 1.65381 | 0.826905 | − | 0.562342i | \(-0.190100\pi\) | ||||
0.826905 | + | 0.562342i | \(0.190100\pi\) | |||||||
\(632\) | −74.0815 | −2.94680 | ||||||||
\(633\) | −45.0228 | −1.78950 | ||||||||
\(634\) | 7.70624 | 0.306054 | ||||||||
\(635\) | 8.11836 | 0.322167 | ||||||||
\(636\) | −5.95750 | −0.236230 | ||||||||
\(637\) | −9.38371 | −0.371796 | ||||||||
\(638\) | −7.57342 | −0.299834 | ||||||||
\(639\) | 30.8396 | 1.21999 | ||||||||
\(640\) | 57.1531 | 2.25917 | ||||||||
\(641\) | −14.9749 | −0.591472 | −0.295736 | − | 0.955270i | \(-0.595565\pi\) | ||||
−0.295736 | + | 0.955270i | \(0.595565\pi\) | |||||||
\(642\) | −64.0530 | −2.52797 | ||||||||
\(643\) | −30.8154 | −1.21524 | −0.607620 | − | 0.794228i | \(-0.707876\pi\) | ||||
−0.607620 | + | 0.794228i | \(0.707876\pi\) | |||||||
\(644\) | −33.7751 | −1.33092 | ||||||||
\(645\) | 3.71214 | 0.146166 | ||||||||
\(646\) | 108.412 | 4.26541 | ||||||||
\(647\) | 16.6102 | 0.653016 | 0.326508 | − | 0.945195i | \(-0.394128\pi\) | ||||
0.326508 | + | 0.945195i | \(0.394128\pi\) | |||||||
\(648\) | 75.9290 | 2.98277 | ||||||||
\(649\) | −5.64773 | −0.221693 | ||||||||
\(650\) | −10.0388 | −0.393756 | ||||||||
\(651\) | 51.1560 | 2.00496 | ||||||||
\(652\) | 95.2044 | 3.72849 | ||||||||
\(653\) | 37.4975 | 1.46739 | 0.733695 | − | 0.679479i | \(-0.237794\pi\) | ||||
0.733695 | + | 0.679479i | \(0.237794\pi\) | |||||||
\(654\) | −58.3622 | −2.28214 | ||||||||
\(655\) | −17.8740 | −0.698396 | ||||||||
\(656\) | −47.6942 | −1.86215 | ||||||||
\(657\) | 29.5200 | 1.15168 | ||||||||
\(658\) | −4.39220 | −0.171226 | ||||||||
\(659\) | −35.3137 | −1.37563 | −0.687814 | − | 0.725887i | \(-0.741429\pi\) | ||||
−0.687814 | + | 0.725887i | \(0.741429\pi\) | |||||||
\(660\) | −19.8723 | −0.773530 | ||||||||
\(661\) | −36.2937 | −1.41166 | −0.705830 | − | 0.708381i | \(-0.749426\pi\) | ||||
−0.705830 | + | 0.708381i | \(0.749426\pi\) | |||||||
\(662\) | 64.7789 | 2.51770 | ||||||||
\(663\) | −55.5476 | −2.15729 | ||||||||
\(664\) | −52.5444 | −2.03912 | ||||||||
\(665\) | −35.8395 | −1.38979 | ||||||||
\(666\) | 76.4717 | 2.96322 | ||||||||
\(667\) | 7.37778 | 0.285669 | ||||||||
\(668\) | 10.6271 | 0.411175 | ||||||||
\(669\) | 63.4221 | 2.45204 | ||||||||
\(670\) | −38.8406 | −1.50054 | ||||||||
\(671\) | −5.11074 | −0.197298 | ||||||||
\(672\) | 153.034 | 5.90342 | ||||||||
\(673\) | 40.6468 | 1.56682 | 0.783409 | − | 0.621507i | \(-0.213479\pi\) | ||||
0.783409 | + | 0.621507i | \(0.213479\pi\) | |||||||
\(674\) | 58.9290 | 2.26986 | ||||||||
\(675\) | 0.563799 | 0.0217006 | ||||||||
\(676\) | −13.5106 | −0.519637 | ||||||||
\(677\) | 17.3927 | 0.668455 | 0.334227 | − | 0.942492i | \(-0.391525\pi\) | ||||
0.334227 | + | 0.942492i | \(0.391525\pi\) | |||||||
\(678\) | 42.1239 | 1.61776 | ||||||||
\(679\) | −51.1822 | −1.96419 | ||||||||
\(680\) | −122.850 | −4.71107 | ||||||||
\(681\) | 0.580925 | 0.0222611 | ||||||||
\(682\) | −13.4571 | −0.515299 | ||||||||
\(683\) | −33.4432 | −1.27967 | −0.639834 | − | 0.768513i | \(-0.720997\pi\) | ||||
−0.639834 | + | 0.768513i | \(0.720997\pi\) | |||||||
\(684\) | 99.2068 | 3.79327 | ||||||||
\(685\) | 10.3693 | 0.396192 | ||||||||
\(686\) | 34.9719 | 1.33523 | ||||||||
\(687\) | −21.4343 | −0.817768 | ||||||||
\(688\) | 10.5575 | 0.402501 | ||||||||
\(689\) | −1.44817 | −0.0551708 | ||||||||
\(690\) | 26.5990 | 1.01261 | ||||||||
\(691\) | −1.05092 | −0.0399787 | −0.0199894 | − | 0.999800i | \(-0.506363\pi\) | ||||
−0.0199894 | + | 0.999800i | \(0.506363\pi\) | |||||||
\(692\) | −63.8784 | −2.42829 | ||||||||
\(693\) | −7.64854 | −0.290544 | ||||||||
\(694\) | −69.3203 | −2.63136 | ||||||||
\(695\) | 28.3097 | 1.07385 | ||||||||
\(696\) | −83.0350 | −3.14743 | ||||||||
\(697\) | 23.6512 | 0.895853 | ||||||||
\(698\) | 25.3907 | 0.961054 | ||||||||
\(699\) | 31.1376 | 1.17773 | ||||||||
\(700\) | −19.2547 | −0.727759 | ||||||||
\(701\) | −35.0393 | −1.32342 | −0.661709 | − | 0.749761i | \(-0.730168\pi\) | ||||
−0.661709 | + | 0.749761i | \(0.730168\pi\) | |||||||
\(702\) | −4.32207 | −0.163126 | ||||||||
\(703\) | −51.1757 | −1.93013 | ||||||||
\(704\) | −19.1201 | −0.720617 | ||||||||
\(705\) | 2.51749 | 0.0948143 | ||||||||
\(706\) | 35.8300 | 1.34848 | ||||||||
\(707\) | −49.4670 | −1.86040 | ||||||||
\(708\) | −98.9147 | −3.71744 | ||||||||
\(709\) | 15.5934 | 0.585624 | 0.292812 | − | 0.956170i | \(-0.405409\pi\) | ||||
0.292812 | + | 0.956170i | \(0.405409\pi\) | |||||||
\(710\) | 51.3298 | 1.92637 | ||||||||
\(711\) | 26.1062 | 0.979059 | ||||||||
\(712\) | 43.7221 | 1.63855 | ||||||||
\(713\) | 13.1095 | 0.490953 | ||||||||
\(714\) | −146.387 | −5.47838 | ||||||||
\(715\) | −4.83063 | −0.180655 | ||||||||
\(716\) | 47.0572 | 1.75861 | ||||||||
\(717\) | 57.7309 | 2.15600 | ||||||||
\(718\) | −46.0822 | −1.71977 | ||||||||
\(719\) | 44.5927 | 1.66303 | 0.831513 | − | 0.555505i | \(-0.187475\pi\) | ||||
0.831513 | + | 0.555505i | \(0.187475\pi\) | |||||||
\(720\) | −87.3013 | −3.25353 | ||||||||
\(721\) | −11.7011 | −0.435770 | ||||||||
\(722\) | −39.7168 | −1.47811 | ||||||||
\(723\) | 65.2662 | 2.42728 | ||||||||
\(724\) | −79.2800 | −2.94642 | ||||||||
\(725\) | 4.20597 | 0.156206 | ||||||||
\(726\) | −70.3326 | −2.61029 | ||||||||
\(727\) | −43.3424 | −1.60748 | −0.803741 | − | 0.594980i | \(-0.797160\pi\) | ||||
−0.803741 | + | 0.594980i | \(0.797160\pi\) | |||||||
\(728\) | 92.4030 | 3.42468 | ||||||||
\(729\) | −30.4369 | −1.12729 | ||||||||
\(730\) | 49.1335 | 1.81851 | ||||||||
\(731\) | −5.23538 | −0.193638 | ||||||||
\(732\) | −89.5098 | −3.30838 | ||||||||
\(733\) | 32.9733 | 1.21790 | 0.608949 | − | 0.793209i | \(-0.291591\pi\) | ||||
0.608949 | + | 0.793209i | \(0.291591\pi\) | |||||||
\(734\) | −18.2524 | −0.673708 | ||||||||
\(735\) | 14.1742 | 0.522822 | ||||||||
\(736\) | 39.2172 | 1.44557 | ||||||||
\(737\) | 5.54710 | 0.204330 | ||||||||
\(738\) | 29.7372 | 1.09464 | ||||||||
\(739\) | 33.4101 | 1.22901 | 0.614505 | − | 0.788913i | \(-0.289356\pi\) | ||||
0.614505 | + | 0.788913i | \(0.289356\pi\) | |||||||
\(740\) | 92.6358 | 3.40536 | ||||||||
\(741\) | 46.7386 | 1.71699 | ||||||||
\(742\) | −3.81641 | −0.140105 | ||||||||
\(743\) | −14.4451 | −0.529940 | −0.264970 | − | 0.964257i | \(-0.585362\pi\) | ||||
−0.264970 | + | 0.964257i | \(0.585362\pi\) | |||||||
\(744\) | −147.544 | −5.40921 | ||||||||
\(745\) | 43.4120 | 1.59049 | ||||||||
\(746\) | −70.3152 | −2.57442 | ||||||||
\(747\) | 18.5166 | 0.677486 | ||||||||
\(748\) | 28.0267 | 1.02476 | ||||||||
\(749\) | −29.8639 | −1.09120 | ||||||||
\(750\) | 81.4187 | 2.97299 | ||||||||
\(751\) | 13.2742 | 0.484383 | 0.242191 | − | 0.970229i | \(-0.422134\pi\) | ||||
0.242191 | + | 0.970229i | \(0.422134\pi\) | |||||||
\(752\) | 7.15986 | 0.261093 | ||||||||
\(753\) | −48.8938 | −1.78179 | ||||||||
\(754\) | −32.2428 | −1.17421 | ||||||||
\(755\) | 3.49554 | 0.127216 | ||||||||
\(756\) | −8.28981 | −0.301497 | ||||||||
\(757\) | −8.48669 | −0.308454 | −0.154227 | − | 0.988035i | \(-0.549289\pi\) | ||||
−0.154227 | + | 0.988035i | \(0.549289\pi\) | |||||||
\(758\) | 54.1369 | 1.96634 | ||||||||
\(759\) | −3.79880 | −0.137888 | ||||||||
\(760\) | 103.368 | 3.74954 | ||||||||
\(761\) | −5.90542 | −0.214071 | −0.107036 | − | 0.994255i | \(-0.534136\pi\) | ||||
−0.107036 | + | 0.994255i | \(0.534136\pi\) | |||||||
\(762\) | −27.9010 | −1.01074 | ||||||||
\(763\) | −27.2107 | −0.985092 | ||||||||
\(764\) | 132.969 | 4.81066 | ||||||||
\(765\) | 43.2921 | 1.56523 | ||||||||
\(766\) | 13.0422 | 0.471234 | ||||||||
\(767\) | −24.0445 | −0.868196 | ||||||||
\(768\) | −71.1841 | −2.56864 | ||||||||
\(769\) | 17.0472 | 0.614736 | 0.307368 | − | 0.951591i | \(-0.400552\pi\) | ||||
0.307368 | + | 0.951591i | \(0.400552\pi\) | |||||||
\(770\) | −12.7303 | −0.458770 | ||||||||
\(771\) | 9.88335 | 0.355940 | ||||||||
\(772\) | −41.6375 | −1.49857 | ||||||||
\(773\) | −39.5804 | −1.42361 | −0.711804 | − | 0.702378i | \(-0.752122\pi\) | ||||
−0.711804 | + | 0.702378i | \(0.752122\pi\) | |||||||
\(774\) | −6.58257 | −0.236606 | ||||||||
\(775\) | 7.47353 | 0.268457 | ||||||||
\(776\) | 147.619 | 5.29922 | ||||||||
\(777\) | 69.1016 | 2.47901 | ||||||||
\(778\) | −51.6634 | −1.85222 | ||||||||
\(779\) | −19.9005 | −0.713009 | ||||||||
\(780\) | −84.6039 | −3.02931 | ||||||||
\(781\) | −7.33078 | −0.262316 | ||||||||
\(782\) | −37.5137 | −1.34149 | ||||||||
\(783\) | 1.81081 | 0.0647132 | ||||||||
\(784\) | 40.3119 | 1.43971 | ||||||||
\(785\) | −4.41395 | −0.157541 | ||||||||
\(786\) | 61.4290 | 2.19110 | ||||||||
\(787\) | −8.89384 | −0.317031 | −0.158516 | − | 0.987356i | \(-0.550671\pi\) | ||||
−0.158516 | + | 0.987356i | \(0.550671\pi\) | |||||||
\(788\) | −51.5499 | −1.83639 | ||||||||
\(789\) | 46.6285 | 1.66002 | ||||||||
\(790\) | 43.4515 | 1.54594 | ||||||||
\(791\) | 19.6397 | 0.698309 | ||||||||
\(792\) | 22.0598 | 0.783862 | ||||||||
\(793\) | −21.7583 | −0.772660 | ||||||||
\(794\) | −53.7276 | −1.90672 | ||||||||
\(795\) | 2.18747 | 0.0775815 | ||||||||
\(796\) | 25.1907 | 0.892862 | ||||||||
\(797\) | 42.4359 | 1.50316 | 0.751579 | − | 0.659644i | \(-0.229293\pi\) | ||||
0.751579 | + | 0.659644i | \(0.229293\pi\) | |||||||
\(798\) | 123.172 | 4.36024 | ||||||||
\(799\) | −3.55052 | −0.125608 | ||||||||
\(800\) | 22.3572 | 0.790446 | ||||||||
\(801\) | −15.4076 | −0.544400 | ||||||||
\(802\) | −27.6435 | −0.976127 | ||||||||
\(803\) | −7.01710 | −0.247628 | ||||||||
\(804\) | 97.1523 | 3.42630 | ||||||||
\(805\) | 12.4015 | 0.437095 | ||||||||
\(806\) | −57.2918 | −2.01802 | ||||||||
\(807\) | −63.2589 | −2.22682 | ||||||||
\(808\) | 142.672 | 5.01918 | ||||||||
\(809\) | 16.8759 | 0.593325 | 0.296663 | − | 0.954982i | \(-0.404126\pi\) | ||||
0.296663 | + | 0.954982i | \(0.404126\pi\) | |||||||
\(810\) | −44.5352 | −1.56481 | ||||||||
\(811\) | 17.6841 | 0.620974 | 0.310487 | − | 0.950578i | \(-0.399508\pi\) | ||||
0.310487 | + | 0.950578i | \(0.399508\pi\) | |||||||
\(812\) | −61.8424 | −2.17024 | ||||||||
\(813\) | 2.24745 | 0.0788214 | ||||||||
\(814\) | −18.1779 | −0.637134 | ||||||||
\(815\) | −34.9570 | −1.22449 | ||||||||
\(816\) | 238.630 | 8.35370 | ||||||||
\(817\) | 4.40513 | 0.154116 | ||||||||
\(818\) | −103.742 | −3.62725 | ||||||||
\(819\) | −32.5627 | −1.13783 | ||||||||
\(820\) | 36.0229 | 1.25797 | ||||||||
\(821\) | 46.9484 | 1.63851 | 0.819255 | − | 0.573429i | \(-0.194387\pi\) | ||||
0.819255 | + | 0.573429i | \(0.194387\pi\) | |||||||
\(822\) | −35.6370 | −1.24298 | ||||||||
\(823\) | 37.9695 | 1.32354 | 0.661768 | − | 0.749709i | \(-0.269807\pi\) | ||||
0.661768 | + | 0.749709i | \(0.269807\pi\) | |||||||
\(824\) | 33.7481 | 1.17567 | ||||||||
\(825\) | −2.16564 | −0.0753981 | ||||||||
\(826\) | −63.3653 | −2.20476 | ||||||||
\(827\) | −3.82507 | −0.133011 | −0.0665053 | − | 0.997786i | \(-0.521185\pi\) | ||||
−0.0665053 | + | 0.997786i | \(0.521185\pi\) | |||||||
\(828\) | −34.3284 | −1.19300 | ||||||||
\(829\) | 29.6152 | 1.02858 | 0.514290 | − | 0.857616i | \(-0.328056\pi\) | ||||
0.514290 | + | 0.857616i | \(0.328056\pi\) | |||||||
\(830\) | 30.8192 | 1.06975 | ||||||||
\(831\) | −73.1941 | −2.53908 | ||||||||
\(832\) | −81.4014 | −2.82209 | ||||||||
\(833\) | −19.9904 | −0.692626 | ||||||||
\(834\) | −97.2941 | −3.36902 | ||||||||
\(835\) | −3.90204 | −0.135036 | ||||||||
\(836\) | −23.5821 | −0.815606 | ||||||||
\(837\) | 3.21761 | 0.111217 | ||||||||
\(838\) | −18.8818 | −0.652261 | ||||||||
\(839\) | 0.643477 | 0.0222153 | 0.0111076 | − | 0.999938i | \(-0.496464\pi\) | ||||
0.0111076 | + | 0.999938i | \(0.496464\pi\) | |||||||
\(840\) | −139.575 | −4.81581 | ||||||||
\(841\) | −15.4912 | −0.534180 | ||||||||
\(842\) | 73.9837 | 2.54965 | ||||||||
\(843\) | −38.9299 | −1.34082 | ||||||||
\(844\) | 96.7123 | 3.32898 | ||||||||
\(845\) | 4.96079 | 0.170656 | ||||||||
\(846\) | −4.46416 | −0.153481 | ||||||||
\(847\) | −32.7917 | −1.12674 | ||||||||
\(848\) | 6.22125 | 0.213639 | ||||||||
\(849\) | −4.16027 | −0.142780 | ||||||||
\(850\) | −21.3860 | −0.733535 | ||||||||
\(851\) | 17.7083 | 0.607032 | ||||||||
\(852\) | −128.392 | −4.39863 | ||||||||
\(853\) | 42.4084 | 1.45204 | 0.726018 | − | 0.687676i | \(-0.241369\pi\) | ||||
0.726018 | + | 0.687676i | \(0.241369\pi\) | |||||||
\(854\) | −57.3405 | −1.96215 | ||||||||
\(855\) | −36.4266 | −1.24576 | ||||||||
\(856\) | 86.1332 | 2.94397 | ||||||||
\(857\) | −4.59827 | −0.157074 | −0.0785370 | − | 0.996911i | \(-0.525025\pi\) | ||||
−0.0785370 | + | 0.996911i | \(0.525025\pi\) | |||||||
\(858\) | 16.6018 | 0.566775 | ||||||||
\(859\) | 2.47609 | 0.0844831 | 0.0422415 | − | 0.999107i | \(-0.486550\pi\) | ||||
0.0422415 | + | 0.999107i | \(0.486550\pi\) | |||||||
\(860\) | −7.97396 | −0.271910 | ||||||||
\(861\) | 26.8712 | 0.915769 | ||||||||
\(862\) | 6.08392 | 0.207219 | ||||||||
\(863\) | 28.8473 | 0.981972 | 0.490986 | − | 0.871167i | \(-0.336637\pi\) | ||||
0.490986 | + | 0.871167i | \(0.336637\pi\) | |||||||
\(864\) | 9.62554 | 0.327468 | ||||||||
\(865\) | 23.4548 | 0.797487 | ||||||||
\(866\) | −85.1969 | −2.89511 | ||||||||
\(867\) | −76.0121 | −2.58151 | ||||||||
\(868\) | −109.887 | −3.72980 | ||||||||
\(869\) | −6.20563 | −0.210511 | ||||||||
\(870\) | 48.7031 | 1.65119 | ||||||||
\(871\) | 23.6161 | 0.800200 | ||||||||
\(872\) | 78.4807 | 2.65769 | ||||||||
\(873\) | −52.0208 | −1.76064 | ||||||||
\(874\) | 31.5646 | 1.06769 | ||||||||
\(875\) | 37.9605 | 1.28330 | ||||||||
\(876\) | −122.898 | −4.15234 | ||||||||
\(877\) | −28.1144 | −0.949355 | −0.474678 | − | 0.880160i | \(-0.657435\pi\) | ||||
−0.474678 | + | 0.880160i | \(0.657435\pi\) | |||||||
\(878\) | 22.8953 | 0.772679 | ||||||||
\(879\) | −28.2803 | −0.953872 | ||||||||
\(880\) | 20.7521 | 0.699554 | ||||||||
\(881\) | −25.4031 | −0.855853 | −0.427927 | − | 0.903814i | \(-0.640756\pi\) | ||||
−0.427927 | + | 0.903814i | \(0.640756\pi\) | |||||||
\(882\) | −25.1344 | −0.846319 | ||||||||
\(883\) | 18.6923 | 0.629046 | 0.314523 | − | 0.949250i | \(-0.398155\pi\) | ||||
0.314523 | + | 0.949250i | \(0.398155\pi\) | |||||||
\(884\) | 119.320 | 4.01317 | ||||||||
\(885\) | 36.3194 | 1.22086 | ||||||||
\(886\) | 15.7880 | 0.530407 | ||||||||
\(887\) | 1.33166 | 0.0447129 | 0.0223565 | − | 0.999750i | \(-0.492883\pi\) | ||||
0.0223565 | + | 0.999750i | \(0.492883\pi\) | |||||||
\(888\) | −199.302 | −6.68814 | ||||||||
\(889\) | −13.0085 | −0.436290 | ||||||||
\(890\) | −25.6446 | −0.859609 | ||||||||
\(891\) | 6.36039 | 0.213081 | ||||||||
\(892\) | −136.235 | −4.56150 | ||||||||
\(893\) | 2.98747 | 0.0999717 | ||||||||
\(894\) | −149.197 | −4.98990 | ||||||||
\(895\) | −17.2784 | −0.577554 | ||||||||
\(896\) | −91.5794 | −3.05945 | ||||||||
\(897\) | −16.1729 | −0.539998 | ||||||||
\(898\) | 22.1397 | 0.738812 | ||||||||
\(899\) | 24.0035 | 0.800563 | ||||||||
\(900\) | −19.5702 | −0.652339 | ||||||||
\(901\) | −3.08507 | −0.102779 | ||||||||
\(902\) | −7.06874 | −0.235363 | ||||||||
\(903\) | −5.94816 | −0.197943 | ||||||||
\(904\) | −56.6447 | −1.88398 | ||||||||
\(905\) | 29.1099 | 0.967647 | ||||||||
\(906\) | −12.0134 | −0.399117 | ||||||||
\(907\) | −2.78524 | −0.0924825 | −0.0462412 | − | 0.998930i | \(-0.514724\pi\) | ||||
−0.0462412 | + | 0.998930i | \(0.514724\pi\) | |||||||
\(908\) | −1.24787 | −0.0414120 | ||||||||
\(909\) | −50.2774 | −1.66760 | ||||||||
\(910\) | −54.1978 | −1.79664 | ||||||||
\(911\) | −6.16899 | −0.204388 | −0.102194 | − | 0.994765i | \(-0.532586\pi\) | ||||
−0.102194 | + | 0.994765i | \(0.532586\pi\) | |||||||
\(912\) | −200.787 | −6.64871 | ||||||||
\(913\) | −4.40152 | −0.145669 | ||||||||
\(914\) | 3.08839 | 0.102155 | ||||||||
\(915\) | 32.8661 | 1.08652 | ||||||||
\(916\) | 46.0424 | 1.52128 | ||||||||
\(917\) | 28.6405 | 0.945793 | ||||||||
\(918\) | −9.20742 | −0.303890 | ||||||||
\(919\) | −16.8411 | −0.555536 | −0.277768 | − | 0.960648i | \(-0.589595\pi\) | ||||
−0.277768 | + | 0.960648i | \(0.589595\pi\) | |||||||
\(920\) | −35.7682 | −1.17924 | ||||||||
\(921\) | −78.6003 | −2.58997 | ||||||||
\(922\) | −109.852 | −3.61779 | ||||||||
\(923\) | −31.2098 | −1.02728 | ||||||||
\(924\) | 31.8425 | 1.04754 | ||||||||
\(925\) | 10.0953 | 0.331930 | ||||||||
\(926\) | −20.3640 | −0.669203 | ||||||||
\(927\) | −11.8928 | −0.390610 | ||||||||
\(928\) | 71.8070 | 2.35718 | ||||||||
\(929\) | −15.4258 | −0.506104 | −0.253052 | − | 0.967453i | \(-0.581434\pi\) | ||||
−0.253052 | + | 0.967453i | \(0.581434\pi\) | |||||||
\(930\) | 86.5398 | 2.83775 | ||||||||
\(931\) | 16.8202 | 0.551261 | ||||||||
\(932\) | −66.8858 | −2.19092 | ||||||||
\(933\) | 6.22988 | 0.203957 | ||||||||
\(934\) | −112.605 | −3.68453 | ||||||||
\(935\) | −10.2908 | −0.336546 | ||||||||
\(936\) | 93.9168 | 3.06977 | ||||||||
\(937\) | 12.0587 | 0.393939 | 0.196969 | − | 0.980410i | \(-0.436890\pi\) | ||||
0.196969 | + | 0.980410i | \(0.436890\pi\) | |||||||
\(938\) | 62.2363 | 2.03209 | ||||||||
\(939\) | 62.3909 | 2.03605 | ||||||||
\(940\) | −5.40776 | −0.176382 | ||||||||
\(941\) | 53.9637 | 1.75917 | 0.879583 | − | 0.475745i | \(-0.157821\pi\) | ||||
0.879583 | + | 0.475745i | \(0.157821\pi\) | |||||||
\(942\) | 15.1697 | 0.494256 | ||||||||
\(943\) | 6.88614 | 0.224244 | ||||||||
\(944\) | 103.294 | 3.36193 | ||||||||
\(945\) | 3.04384 | 0.0990162 | ||||||||
\(946\) | 1.56472 | 0.0508735 | ||||||||
\(947\) | 23.6666 | 0.769060 | 0.384530 | − | 0.923112i | \(-0.374364\pi\) | ||||
0.384530 | + | 0.923112i | \(0.374364\pi\) | |||||||
\(948\) | −108.686 | −3.52995 | ||||||||
\(949\) | −29.8744 | −0.969764 | ||||||||
\(950\) | 17.9946 | 0.583820 | ||||||||
\(951\) | 7.07763 | 0.229508 | ||||||||
\(952\) | 196.849 | 6.37990 | ||||||||
\(953\) | 0.431503 | 0.0139777 | 0.00698887 | − | 0.999976i | \(-0.497775\pi\) | ||||
0.00698887 | + | 0.999976i | \(0.497775\pi\) | |||||||
\(954\) | −3.87894 | −0.125585 | ||||||||
\(955\) | −48.8235 | −1.57989 | ||||||||
\(956\) | −124.010 | −4.01078 | ||||||||
\(957\) | −6.95564 | −0.224844 | ||||||||
\(958\) | −25.4848 | −0.823378 | ||||||||
\(959\) | −16.6153 | −0.536537 | ||||||||
\(960\) | 122.958 | 3.96844 | ||||||||
\(961\) | 11.6515 | 0.375855 | ||||||||
\(962\) | −77.3899 | −2.49515 | ||||||||
\(963\) | −30.3532 | −0.978118 | ||||||||
\(964\) | −140.197 | −4.51543 | ||||||||
\(965\) | 15.2884 | 0.492151 | ||||||||
\(966\) | −42.6211 | −1.37131 | ||||||||
\(967\) | −17.6874 | −0.568787 | −0.284394 | − | 0.958708i | \(-0.591792\pi\) | ||||
−0.284394 | + | 0.958708i | \(0.591792\pi\) | |||||||
\(968\) | 94.5776 | 3.03984 | ||||||||
\(969\) | 99.5686 | 3.19860 | ||||||||
\(970\) | −86.5841 | −2.78005 | ||||||||
\(971\) | −59.2061 | −1.90001 | −0.950007 | − | 0.312227i | \(-0.898925\pi\) | ||||
−0.950007 | + | 0.312227i | \(0.898925\pi\) | |||||||
\(972\) | 119.300 | 3.82656 | ||||||||
\(973\) | −45.3622 | −1.45424 | ||||||||
\(974\) | −74.3088 | −2.38101 | ||||||||
\(975\) | −9.21995 | −0.295275 | ||||||||
\(976\) | 93.4726 | 2.99198 | ||||||||
\(977\) | 10.2612 | 0.328284 | 0.164142 | − | 0.986437i | \(-0.447514\pi\) | ||||
0.164142 | + | 0.986437i | \(0.447514\pi\) | |||||||
\(978\) | 120.139 | 3.84163 | ||||||||
\(979\) | 3.66249 | 0.117054 | ||||||||
\(980\) | −30.4472 | −0.972599 | ||||||||
\(981\) | −27.6565 | −0.883003 | ||||||||
\(982\) | 37.9909 | 1.21234 | ||||||||
\(983\) | 42.1307 | 1.34376 | 0.671881 | − | 0.740659i | \(-0.265487\pi\) | ||||
0.671881 | + | 0.740659i | \(0.265487\pi\) | |||||||
\(984\) | −77.5017 | −2.47066 | ||||||||
\(985\) | 18.9280 | 0.603097 | ||||||||
\(986\) | −68.6878 | −2.18747 | ||||||||
\(987\) | −4.03392 | −0.128401 | ||||||||
\(988\) | −100.398 | −3.19408 | ||||||||
\(989\) | −1.52430 | −0.0484700 | ||||||||
\(990\) | −12.9389 | −0.411225 | ||||||||
\(991\) | 26.1634 | 0.831109 | 0.415555 | − | 0.909568i | \(-0.363588\pi\) | ||||
0.415555 | + | 0.909568i | \(0.363588\pi\) | |||||||
\(992\) | 127.593 | 4.05108 | ||||||||
\(993\) | 59.4948 | 1.88801 | ||||||||
\(994\) | −82.2485 | −2.60876 | ||||||||
\(995\) | −9.24950 | −0.293229 | ||||||||
\(996\) | −77.0885 | −2.44264 | ||||||||
\(997\) | −7.02785 | −0.222574 | −0.111287 | − | 0.993788i | \(-0.535497\pi\) | ||||
−0.111287 | + | 0.993788i | \(0.535497\pi\) | |||||||
\(998\) | 59.4627 | 1.88226 | ||||||||
\(999\) | 4.34635 | 0.137512 |
(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 | 4019.2.a.b.1.6 | ✓ | 186 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4019.2.a.b.1.6 | ✓ | 186 | 1.1 | even | 1 | trivial |