Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2873,2,Mod(1,2873)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2873, 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("2873.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2873 = 13^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2873.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: | \(22.9410205007\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.28134208.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 9x^{4} + 6x^{3} + 23x^{2} - 7x - 11 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 221) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.37245\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2873.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.301567 | 0.213240 | 0.106620 | − | 0.994300i | \(-0.465997\pi\) | ||||
0.106620 | + | 0.994300i | \(0.465997\pi\) | |||||||
\(3\) | 2.62851 | 1.51757 | 0.758785 | − | 0.651341i | \(-0.225793\pi\) | ||||
0.758785 | + | 0.651341i | \(0.225793\pi\) | |||||||
\(4\) | −1.90906 | −0.954529 | ||||||||
\(5\) | −0.792671 | −0.354493 | −0.177247 | − | 0.984166i | \(-0.556719\pi\) | ||||
−0.177247 | + | 0.984166i | \(0.556719\pi\) | |||||||
\(6\) | 0.792671 | 0.323606 | ||||||||
\(7\) | −0.519592 | −0.196387 | −0.0981936 | − | 0.995167i | \(-0.531306\pi\) | ||||
−0.0981936 | + | 0.995167i | \(0.531306\pi\) | |||||||
\(8\) | −1.17884 | −0.416783 | ||||||||
\(9\) | 3.90906 | 1.30302 | ||||||||
\(10\) | −0.239043 | −0.0755920 | ||||||||
\(11\) | −2.90906 | −0.877114 | −0.438557 | − | 0.898703i | \(-0.644510\pi\) | ||||
−0.438557 | + | 0.898703i | \(0.644510\pi\) | |||||||
\(12\) | −5.01797 | −1.44856 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.156692 | −0.0418776 | ||||||||
\(15\) | −2.08354 | −0.537968 | ||||||||
\(16\) | 3.46262 | 0.865654 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 1.17884 | 0.277856 | ||||||||
\(19\) | 4.16607 | 0.955763 | 0.477882 | − | 0.878424i | \(-0.341405\pi\) | ||||
0.477882 | + | 0.878424i | \(0.341405\pi\) | |||||||
\(20\) | 1.51325 | 0.338374 | ||||||||
\(21\) | −1.36575 | −0.298031 | ||||||||
\(22\) | −0.877275 | −0.187036 | ||||||||
\(23\) | −2.16589 | −0.451620 | −0.225810 | − | 0.974171i | \(-0.572503\pi\) | ||||
−0.225810 | + | 0.974171i | \(0.572503\pi\) | |||||||
\(24\) | −3.09859 | −0.632498 | ||||||||
\(25\) | −4.37167 | −0.874335 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.38947 | 0.459853 | ||||||||
\(28\) | 0.991931 | 0.187457 | ||||||||
\(29\) | −4.38947 | −0.815103 | −0.407552 | − | 0.913182i | \(-0.633617\pi\) | ||||
−0.407552 | + | 0.913182i | \(0.633617\pi\) | |||||||
\(30\) | −0.628327 | −0.114716 | ||||||||
\(31\) | −1.17448 | −0.210944 | −0.105472 | − | 0.994422i | \(-0.533635\pi\) | ||||
−0.105472 | + | 0.994422i | \(0.533635\pi\) | |||||||
\(32\) | 3.40189 | 0.601375 | ||||||||
\(33\) | −7.64648 | −1.33108 | ||||||||
\(34\) | −0.301567 | −0.0517183 | ||||||||
\(35\) | 0.411865 | 0.0696179 | ||||||||
\(36\) | −7.46262 | −1.24377 | ||||||||
\(37\) | −4.46435 | −0.733934 | −0.366967 | − | 0.930234i | \(-0.619604\pi\) | ||||
−0.366967 | + | 0.930234i | \(0.619604\pi\) | |||||||
\(38\) | 1.25635 | 0.203807 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.934433 | 0.147747 | ||||||||
\(41\) | −6.85381 | −1.07039 | −0.535193 | − | 0.844730i | \(-0.679761\pi\) | ||||
−0.535193 | + | 0.844730i | \(0.679761\pi\) | |||||||
\(42\) | −0.411865 | −0.0635522 | ||||||||
\(43\) | 1.84331 | 0.281102 | 0.140551 | − | 0.990073i | \(-0.455113\pi\) | ||||
0.140551 | + | 0.990073i | \(0.455113\pi\) | |||||||
\(44\) | 5.55356 | 0.837230 | ||||||||
\(45\) | −3.09859 | −0.461911 | ||||||||
\(46\) | −0.653161 | −0.0963033 | ||||||||
\(47\) | 9.38206 | 1.36851 | 0.684257 | − | 0.729241i | \(-0.260126\pi\) | ||||
0.684257 | + | 0.729241i | \(0.260126\pi\) | |||||||
\(48\) | 9.10152 | 1.31369 | ||||||||
\(49\) | −6.73002 | −0.961432 | ||||||||
\(50\) | −1.31835 | −0.186443 | ||||||||
\(51\) | −2.62851 | −0.368065 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.3228 | −1.69266 | −0.846331 | − | 0.532657i | \(-0.821194\pi\) | ||||
−0.846331 | + | 0.532657i | \(0.821194\pi\) | |||||||
\(54\) | 0.720583 | 0.0980589 | ||||||||
\(55\) | 2.30592 | 0.310931 | ||||||||
\(56\) | 0.612516 | 0.0818510 | ||||||||
\(57\) | 10.9506 | 1.45044 | ||||||||
\(58\) | −1.32372 | −0.173812 | ||||||||
\(59\) | 4.01684 | 0.522948 | 0.261474 | − | 0.965210i | \(-0.415791\pi\) | ||||
0.261474 | + | 0.965210i | \(0.415791\pi\) | |||||||
\(60\) | 3.97760 | 0.513506 | ||||||||
\(61\) | −0.548951 | −0.0702860 | −0.0351430 | − | 0.999382i | \(-0.511189\pi\) | ||||
−0.0351430 | + | 0.999382i | \(0.511189\pi\) | |||||||
\(62\) | −0.354185 | −0.0449816 | ||||||||
\(63\) | −2.03111 | −0.255896 | ||||||||
\(64\) | −5.89933 | −0.737417 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.30592 | −0.283840 | ||||||||
\(67\) | −11.7611 | −1.43685 | −0.718426 | − | 0.695603i | \(-0.755137\pi\) | ||||
−0.718426 | + | 0.695603i | \(0.755137\pi\) | |||||||
\(68\) | 1.90906 | 0.231507 | ||||||||
\(69\) | −5.69307 | −0.685365 | ||||||||
\(70\) | 0.124205 | 0.0148453 | ||||||||
\(71\) | 5.59406 | 0.663892 | 0.331946 | − | 0.943298i | \(-0.392295\pi\) | ||||
0.331946 | + | 0.943298i | \(0.392295\pi\) | |||||||
\(72\) | −4.60816 | −0.543077 | ||||||||
\(73\) | −13.6224 | −1.59438 | −0.797188 | − | 0.603731i | \(-0.793680\pi\) | ||||
−0.797188 | + | 0.603731i | \(0.793680\pi\) | |||||||
\(74\) | −1.34630 | −0.156504 | ||||||||
\(75\) | −11.4910 | −1.32686 | ||||||||
\(76\) | −7.95328 | −0.912303 | ||||||||
\(77\) | 1.51152 | 0.172254 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.34909 | −0.376802 | −0.188401 | − | 0.982092i | \(-0.560331\pi\) | ||||
−0.188401 | + | 0.982092i | \(0.560331\pi\) | |||||||
\(80\) | −2.74471 | −0.306868 | ||||||||
\(81\) | −5.44644 | −0.605160 | ||||||||
\(82\) | −2.06688 | −0.228249 | ||||||||
\(83\) | 2.31185 | 0.253758 | 0.126879 | − | 0.991918i | \(-0.459504\pi\) | ||||
0.126879 | + | 0.991918i | \(0.459504\pi\) | |||||||
\(84\) | 2.60730 | 0.284480 | ||||||||
\(85\) | 0.792671 | 0.0859772 | ||||||||
\(86\) | 0.555880 | 0.0599421 | ||||||||
\(87\) | −11.5377 | −1.23698 | ||||||||
\(88\) | 3.42932 | 0.365566 | ||||||||
\(89\) | −2.00972 | −0.213030 | −0.106515 | − | 0.994311i | \(-0.533969\pi\) | ||||
−0.106515 | + | 0.994311i | \(0.533969\pi\) | |||||||
\(90\) | −0.934433 | −0.0984979 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.13481 | 0.431084 | ||||||||
\(93\) | −3.08714 | −0.320122 | ||||||||
\(94\) | 2.82932 | 0.291822 | ||||||||
\(95\) | −3.30232 | −0.338811 | ||||||||
\(96\) | 8.94190 | 0.912629 | ||||||||
\(97\) | −12.5884 | −1.27816 | −0.639078 | − | 0.769142i | \(-0.720684\pi\) | ||||
−0.639078 | + | 0.769142i | \(0.720684\pi\) | |||||||
\(98\) | −2.02955 | −0.205016 | ||||||||
\(99\) | −11.3717 | −1.14290 | ||||||||
\(100\) | 8.34578 | 0.834578 | ||||||||
\(101\) | −5.37167 | −0.534501 | −0.267251 | − | 0.963627i | \(-0.586115\pi\) | ||||
−0.267251 | + | 0.963627i | \(0.586115\pi\) | |||||||
\(102\) | −0.792671 | −0.0784861 | ||||||||
\(103\) | 12.0463 | 1.18696 | 0.593481 | − | 0.804848i | \(-0.297753\pi\) | ||||
0.593481 | + | 0.804848i | \(0.297753\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.08259 | 0.105650 | ||||||||
\(106\) | −3.71614 | −0.360943 | ||||||||
\(107\) | 9.23581 | 0.892859 | 0.446430 | − | 0.894819i | \(-0.352695\pi\) | ||||
0.446430 | + | 0.894819i | \(0.352695\pi\) | |||||||
\(108\) | −4.56163 | −0.438943 | ||||||||
\(109\) | −1.68034 | −0.160947 | −0.0804735 | − | 0.996757i | \(-0.525643\pi\) | ||||
−0.0804735 | + | 0.996757i | \(0.525643\pi\) | |||||||
\(110\) | 0.695390 | 0.0663028 | ||||||||
\(111\) | −11.7346 | −1.11380 | ||||||||
\(112\) | −1.79915 | −0.170003 | ||||||||
\(113\) | 12.4513 | 1.17132 | 0.585659 | − | 0.810558i | \(-0.300836\pi\) | ||||
0.585659 | + | 0.810558i | \(0.300836\pi\) | |||||||
\(114\) | 3.30232 | 0.309291 | ||||||||
\(115\) | 1.71684 | 0.160096 | ||||||||
\(116\) | 8.37974 | 0.778040 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.21135 | 0.111513 | ||||||||
\(119\) | 0.519592 | 0.0476309 | ||||||||
\(120\) | 2.45616 | 0.224216 | ||||||||
\(121\) | −2.53738 | −0.230671 | ||||||||
\(122\) | −0.165545 | −0.0149878 | ||||||||
\(123\) | −18.0153 | −1.62439 | ||||||||
\(124\) | 2.24216 | 0.201352 | ||||||||
\(125\) | 7.42865 | 0.664439 | ||||||||
\(126\) | −0.612516 | −0.0545673 | ||||||||
\(127\) | 3.23116 | 0.286719 | 0.143359 | − | 0.989671i | \(-0.454210\pi\) | ||||
0.143359 | + | 0.989671i | \(0.454210\pi\) | |||||||
\(128\) | −8.58283 | −0.758622 | ||||||||
\(129\) | 4.84515 | 0.426592 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.555358 | −0.0485219 | −0.0242609 | − | 0.999706i | \(-0.507723\pi\) | ||||
−0.0242609 | + | 0.999706i | \(0.507723\pi\) | |||||||
\(132\) | 14.5976 | 1.27056 | ||||||||
\(133\) | −2.16466 | −0.187700 | ||||||||
\(134\) | −3.54677 | −0.306394 | ||||||||
\(135\) | −1.89406 | −0.163015 | ||||||||
\(136\) | 1.17884 | 0.101085 | ||||||||
\(137\) | 7.82784 | 0.668777 | 0.334389 | − | 0.942435i | \(-0.391470\pi\) | ||||
0.334389 | + | 0.942435i | \(0.391470\pi\) | |||||||
\(138\) | −1.71684 | −0.146147 | ||||||||
\(139\) | 18.1176 | 1.53672 | 0.768359 | − | 0.640019i | \(-0.221074\pi\) | ||||
0.768359 | + | 0.640019i | \(0.221074\pi\) | |||||||
\(140\) | −0.786274 | −0.0664523 | ||||||||
\(141\) | 24.6608 | 2.07682 | ||||||||
\(142\) | 1.68698 | 0.141568 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 13.5356 | 1.12796 | ||||||||
\(145\) | 3.47940 | 0.288948 | ||||||||
\(146\) | −4.10805 | −0.339984 | ||||||||
\(147\) | −17.6899 | −1.45904 | ||||||||
\(148\) | 8.52269 | 0.700561 | ||||||||
\(149\) | −17.5126 | −1.43468 | −0.717342 | − | 0.696721i | \(-0.754642\pi\) | ||||
−0.717342 | + | 0.696721i | \(0.754642\pi\) | |||||||
\(150\) | −3.46530 | −0.282940 | ||||||||
\(151\) | −23.3974 | −1.90405 | −0.952025 | − | 0.306019i | \(-0.901003\pi\) | ||||
−0.952025 | + | 0.306019i | \(0.901003\pi\) | |||||||
\(152\) | −4.91114 | −0.398346 | ||||||||
\(153\) | −3.90906 | −0.316029 | ||||||||
\(154\) | 0.455825 | 0.0367314 | ||||||||
\(155\) | 0.930979 | 0.0747780 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.2591 | −1.69666 | −0.848329 | − | 0.529470i | \(-0.822391\pi\) | ||||
−0.848329 | + | 0.529470i | \(0.822391\pi\) | |||||||
\(158\) | −1.00997 | −0.0803492 | ||||||||
\(159\) | −32.3905 | −2.56873 | ||||||||
\(160\) | −2.69658 | −0.213183 | ||||||||
\(161\) | 1.12538 | 0.0886924 | ||||||||
\(162\) | −1.64247 | −0.129044 | ||||||||
\(163\) | 2.71678 | 0.212795 | 0.106397 | − | 0.994324i | \(-0.466068\pi\) | ||||
0.106397 | + | 0.994324i | \(0.466068\pi\) | |||||||
\(164\) | 13.0843 | 1.02171 | ||||||||
\(165\) | 6.06114 | 0.471859 | ||||||||
\(166\) | 0.697176 | 0.0541113 | ||||||||
\(167\) | 15.3119 | 1.18487 | 0.592436 | − | 0.805617i | \(-0.298166\pi\) | ||||
0.592436 | + | 0.805617i | \(0.298166\pi\) | |||||||
\(168\) | 1.61000 | 0.124215 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0.239043 | 0.0183338 | ||||||||
\(171\) | 16.2854 | 1.24538 | ||||||||
\(172\) | −3.51898 | −0.268320 | ||||||||
\(173\) | −19.5601 | −1.48713 | −0.743565 | − | 0.668663i | \(-0.766867\pi\) | ||||
−0.743565 | + | 0.668663i | \(0.766867\pi\) | |||||||
\(174\) | −3.47940 | −0.263773 | ||||||||
\(175\) | 2.27149 | 0.171708 | ||||||||
\(176\) | −10.0729 | −0.759277 | ||||||||
\(177\) | 10.5583 | 0.793611 | ||||||||
\(178\) | −0.606065 | −0.0454265 | ||||||||
\(179\) | 18.2790 | 1.36623 | 0.683117 | − | 0.730309i | \(-0.260624\pi\) | ||||
0.683117 | + | 0.730309i | \(0.260624\pi\) | |||||||
\(180\) | 5.91540 | 0.440908 | ||||||||
\(181\) | 5.58255 | 0.414947 | 0.207474 | − | 0.978241i | \(-0.433476\pi\) | ||||
0.207474 | + | 0.978241i | \(0.433476\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.44292 | −0.106664 | ||||||||
\(184\) | 2.55324 | 0.188228 | ||||||||
\(185\) | 3.53876 | 0.260175 | ||||||||
\(186\) | −0.930979 | −0.0682627 | ||||||||
\(187\) | 2.90906 | 0.212731 | ||||||||
\(188\) | −17.9109 | −1.30629 | ||||||||
\(189\) | −1.24155 | −0.0903093 | ||||||||
\(190\) | −0.995871 | −0.0722481 | ||||||||
\(191\) | −9.02196 | −0.652806 | −0.326403 | − | 0.945231i | \(-0.605837\pi\) | ||||
−0.326403 | + | 0.945231i | \(0.605837\pi\) | |||||||
\(192\) | −15.5065 | −1.11908 | ||||||||
\(193\) | 5.92858 | 0.426749 | 0.213374 | − | 0.976971i | \(-0.431555\pi\) | ||||
0.213374 | + | 0.976971i | \(0.431555\pi\) | |||||||
\(194\) | −3.79624 | −0.272554 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.8480 | 0.917715 | ||||||||
\(197\) | 18.1075 | 1.29011 | 0.645053 | − | 0.764138i | \(-0.276835\pi\) | ||||
0.645053 | + | 0.764138i | \(0.276835\pi\) | |||||||
\(198\) | −3.42932 | −0.243711 | ||||||||
\(199\) | 4.91949 | 0.348734 | 0.174367 | − | 0.984681i | \(-0.444212\pi\) | ||||
0.174367 | + | 0.984681i | \(0.444212\pi\) | |||||||
\(200\) | 5.15351 | 0.364408 | ||||||||
\(201\) | −30.9143 | −2.18052 | ||||||||
\(202\) | −1.61992 | −0.113977 | ||||||||
\(203\) | 2.28073 | 0.160076 | ||||||||
\(204\) | 5.01797 | 0.351328 | ||||||||
\(205\) | 5.43282 | 0.379444 | ||||||||
\(206\) | 3.63277 | 0.253107 | ||||||||
\(207\) | −8.46660 | −0.588469 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.1194 | −0.838313 | ||||||||
\(210\) | 0.326473 | 0.0225288 | ||||||||
\(211\) | 10.1407 | 0.698115 | 0.349057 | − | 0.937101i | \(-0.386502\pi\) | ||||
0.349057 | + | 0.937101i | \(0.386502\pi\) | |||||||
\(212\) | 23.5249 | 1.61569 | ||||||||
\(213\) | 14.7040 | 1.00750 | ||||||||
\(214\) | 2.78521 | 0.190393 | ||||||||
\(215\) | −1.46114 | −0.0996487 | ||||||||
\(216\) | −2.81680 | −0.191659 | ||||||||
\(217\) | 0.610252 | 0.0414266 | ||||||||
\(218\) | −0.506733 | −0.0343203 | ||||||||
\(219\) | −35.8065 | −2.41958 | ||||||||
\(220\) | −4.40214 | −0.296792 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.53876 | −0.237506 | ||||||||
\(223\) | −12.8238 | −0.858743 | −0.429371 | − | 0.903128i | \(-0.641265\pi\) | ||||
−0.429371 | + | 0.903128i | \(0.641265\pi\) | |||||||
\(224\) | −1.76760 | −0.118102 | ||||||||
\(225\) | −17.0891 | −1.13927 | ||||||||
\(226\) | 3.75489 | 0.249772 | ||||||||
\(227\) | −9.59990 | −0.637168 | −0.318584 | − | 0.947895i | \(-0.603207\pi\) | ||||
−0.318584 | + | 0.947895i | \(0.603207\pi\) | |||||||
\(228\) | −20.9053 | −1.38448 | ||||||||
\(229\) | 24.4739 | 1.61728 | 0.808640 | − | 0.588303i | \(-0.200204\pi\) | ||||
0.808640 | + | 0.588303i | \(0.200204\pi\) | |||||||
\(230\) | 0.517742 | 0.0341389 | ||||||||
\(231\) | 3.97305 | 0.261408 | ||||||||
\(232\) | 5.17448 | 0.339722 | ||||||||
\(233\) | 24.2241 | 1.58697 | 0.793486 | − | 0.608588i | \(-0.208264\pi\) | ||||
0.793486 | + | 0.608588i | \(0.208264\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.43689 | −0.485129 | ||||||||
\(236\) | −7.66838 | −0.499169 | ||||||||
\(237\) | −8.80312 | −0.571824 | ||||||||
\(238\) | 0.156692 | 0.0101568 | ||||||||
\(239\) | −20.9735 | −1.35666 | −0.678332 | − | 0.734756i | \(-0.737297\pi\) | ||||
−0.678332 | + | 0.734756i | \(0.737297\pi\) | |||||||
\(240\) | −7.21450 | −0.465694 | ||||||||
\(241\) | 25.3068 | 1.63016 | 0.815079 | − | 0.579350i | \(-0.196694\pi\) | ||||
0.815079 | + | 0.579350i | \(0.196694\pi\) | |||||||
\(242\) | −0.765190 | −0.0491883 | ||||||||
\(243\) | −21.4844 | −1.37823 | ||||||||
\(244\) | 1.04798 | 0.0670900 | ||||||||
\(245\) | 5.33469 | 0.340821 | ||||||||
\(246\) | −5.43282 | −0.346384 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.38453 | 0.0879178 | ||||||||
\(249\) | 6.07671 | 0.385096 | ||||||||
\(250\) | 2.24023 | 0.141685 | ||||||||
\(251\) | 21.5150 | 1.35801 | 0.679007 | − | 0.734132i | \(-0.262411\pi\) | ||||
0.679007 | + | 0.734132i | \(0.262411\pi\) | |||||||
\(252\) | 3.87752 | 0.244260 | ||||||||
\(253\) | 6.30071 | 0.396122 | ||||||||
\(254\) | 0.974409 | 0.0611399 | ||||||||
\(255\) | 2.08354 | 0.130476 | ||||||||
\(256\) | 9.21037 | 0.575648 | ||||||||
\(257\) | −2.02556 | −0.126351 | −0.0631754 | − | 0.998002i | \(-0.520123\pi\) | ||||
−0.0631754 | + | 0.998002i | \(0.520123\pi\) | |||||||
\(258\) | 1.46114 | 0.0909664 | ||||||||
\(259\) | 2.31964 | 0.144135 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −17.1587 | −1.06210 | ||||||||
\(262\) | −0.167478 | −0.0103468 | ||||||||
\(263\) | −12.6626 | −0.780809 | −0.390405 | − | 0.920643i | \(-0.627665\pi\) | ||||
−0.390405 | + | 0.920643i | \(0.627665\pi\) | |||||||
\(264\) | 9.01399 | 0.554773 | ||||||||
\(265\) | 9.76789 | 0.600037 | ||||||||
\(266\) | −0.652789 | −0.0400251 | ||||||||
\(267\) | −5.28257 | −0.323288 | ||||||||
\(268\) | 22.4527 | 1.37152 | ||||||||
\(269\) | 4.81840 | 0.293783 | 0.146891 | − | 0.989153i | \(-0.453073\pi\) | ||||
0.146891 | + | 0.989153i | \(0.453073\pi\) | |||||||
\(270\) | −0.571185 | −0.0347612 | ||||||||
\(271\) | −5.76144 | −0.349983 | −0.174991 | − | 0.984570i | \(-0.555990\pi\) | ||||
−0.174991 | + | 0.984570i | \(0.555990\pi\) | |||||||
\(272\) | −3.46262 | −0.209952 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.36061 | 0.142610 | ||||||||
\(275\) | 12.7174 | 0.766891 | ||||||||
\(276\) | 10.8684 | 0.654200 | ||||||||
\(277\) | −0.445963 | −0.0267953 | −0.0133977 | − | 0.999910i | \(-0.504265\pi\) | ||||
−0.0133977 | + | 0.999910i | \(0.504265\pi\) | |||||||
\(278\) | 5.46367 | 0.327689 | ||||||||
\(279\) | −4.59112 | −0.274863 | ||||||||
\(280\) | −0.485524 | −0.0290156 | ||||||||
\(281\) | 17.2730 | 1.03042 | 0.515210 | − | 0.857064i | \(-0.327714\pi\) | ||||
0.515210 | + | 0.857064i | \(0.327714\pi\) | |||||||
\(282\) | 7.43689 | 0.442860 | ||||||||
\(283\) | −21.5692 | −1.28215 | −0.641077 | − | 0.767476i | \(-0.721512\pi\) | ||||
−0.641077 | + | 0.767476i | \(0.721512\pi\) | |||||||
\(284\) | −10.6794 | −0.633704 | ||||||||
\(285\) | −8.68019 | −0.514170 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.56119 | 0.210210 | ||||||||
\(288\) | 13.2982 | 0.783604 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 1.04927 | 0.0616153 | ||||||||
\(291\) | −33.0887 | −1.93969 | ||||||||
\(292\) | 26.0059 | 1.52188 | ||||||||
\(293\) | 3.41879 | 0.199728 | 0.0998639 | − | 0.995001i | \(-0.468159\pi\) | ||||
0.0998639 | + | 0.995001i | \(0.468159\pi\) | |||||||
\(294\) | −5.33469 | −0.311126 | ||||||||
\(295\) | −3.18403 | −0.185382 | ||||||||
\(296\) | 5.26276 | 0.305892 | ||||||||
\(297\) | −6.95109 | −0.403343 | ||||||||
\(298\) | −5.28120 | −0.305932 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 21.9369 | 1.26653 | ||||||||
\(301\) | −0.957768 | −0.0552048 | ||||||||
\(302\) | −7.05587 | −0.406019 | ||||||||
\(303\) | −14.1195 | −0.811143 | ||||||||
\(304\) | 14.4255 | 0.827360 | ||||||||
\(305\) | 0.435137 | 0.0249159 | ||||||||
\(306\) | −1.17884 | −0.0673899 | ||||||||
\(307\) | −25.3012 | −1.44401 | −0.722007 | − | 0.691886i | \(-0.756780\pi\) | ||||
−0.722007 | + | 0.691886i | \(0.756780\pi\) | |||||||
\(308\) | −2.88558 | −0.164421 | ||||||||
\(309\) | 31.6639 | 1.80130 | ||||||||
\(310\) | 0.280752 | 0.0159457 | ||||||||
\(311\) | 28.2726 | 1.60319 | 0.801595 | − | 0.597867i | \(-0.203985\pi\) | ||||
0.801595 | + | 0.597867i | \(0.203985\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −29.5305 | −1.66916 | −0.834582 | − | 0.550884i | \(-0.814291\pi\) | ||||
−0.834582 | + | 0.550884i | \(0.814291\pi\) | |||||||
\(314\) | −6.41102 | −0.361795 | ||||||||
\(315\) | 1.61000 | 0.0907135 | ||||||||
\(316\) | 6.39361 | 0.359669 | ||||||||
\(317\) | 34.6807 | 1.94786 | 0.973930 | − | 0.226848i | \(-0.0728421\pi\) | ||||
0.973930 | + | 0.226848i | \(0.0728421\pi\) | |||||||
\(318\) | −9.76789 | −0.547756 | ||||||||
\(319\) | 12.7692 | 0.714938 | ||||||||
\(320\) | 4.67623 | 0.261409 | ||||||||
\(321\) | 24.2764 | 1.35498 | ||||||||
\(322\) | 0.339377 | 0.0189128 | ||||||||
\(323\) | −4.16607 | −0.231807 | ||||||||
\(324\) | 10.3976 | 0.577643 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.819291 | 0.0453763 | ||||||||
\(327\) | −4.41678 | −0.244248 | ||||||||
\(328\) | 8.07956 | 0.446119 | ||||||||
\(329\) | −4.87485 | −0.268759 | ||||||||
\(330\) | 1.82784 | 0.100619 | ||||||||
\(331\) | 34.3851 | 1.88997 | 0.944987 | − | 0.327107i | \(-0.106074\pi\) | ||||
0.944987 | + | 0.327107i | \(0.106074\pi\) | |||||||
\(332\) | −4.41345 | −0.242219 | ||||||||
\(333\) | −17.4514 | −0.956330 | ||||||||
\(334\) | 4.61757 | 0.252662 | ||||||||
\(335\) | 9.32271 | 0.509354 | ||||||||
\(336\) | −4.72907 | −0.257992 | ||||||||
\(337\) | 23.9307 | 1.30359 | 0.651793 | − | 0.758397i | \(-0.274017\pi\) | ||||
0.651793 | + | 0.758397i | \(0.274017\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 32.7283 | 1.77756 | ||||||||
\(340\) | −1.51325 | −0.0820677 | ||||||||
\(341\) | 3.41664 | 0.185021 | ||||||||
\(342\) | 4.91114 | 0.265564 | ||||||||
\(343\) | 7.13401 | 0.385200 | ||||||||
\(344\) | −2.17297 | −0.117159 | ||||||||
\(345\) | 4.51273 | 0.242957 | ||||||||
\(346\) | −5.89869 | −0.317115 | ||||||||
\(347\) | −6.95161 | −0.373182 | −0.186591 | − | 0.982438i | \(-0.559744\pi\) | ||||
−0.186591 | + | 0.982438i | \(0.559744\pi\) | |||||||
\(348\) | 22.0262 | 1.18073 | ||||||||
\(349\) | −32.3434 | −1.73130 | −0.865652 | − | 0.500646i | \(-0.833096\pi\) | ||||
−0.865652 | + | 0.500646i | \(0.833096\pi\) | |||||||
\(350\) | 0.685005 | 0.0366150 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −9.89630 | −0.527475 | ||||||||
\(353\) | −28.5522 | −1.51968 | −0.759841 | − | 0.650109i | \(-0.774723\pi\) | ||||
−0.759841 | + | 0.650109i | \(0.774723\pi\) | |||||||
\(354\) | 3.18403 | 0.169229 | ||||||||
\(355\) | −4.43424 | −0.235345 | ||||||||
\(356\) | 3.83668 | 0.203343 | ||||||||
\(357\) | 1.36575 | 0.0722833 | ||||||||
\(358\) | 5.51233 | 0.291336 | ||||||||
\(359\) | −10.6546 | −0.562326 | −0.281163 | − | 0.959660i | \(-0.590720\pi\) | ||||
−0.281163 | + | 0.959660i | \(0.590720\pi\) | |||||||
\(360\) | 3.65275 | 0.192517 | ||||||||
\(361\) | −1.64382 | −0.0865169 | ||||||||
\(362\) | 1.68351 | 0.0884833 | ||||||||
\(363\) | −6.66954 | −0.350060 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.7980 | 0.565195 | ||||||||
\(366\) | −0.435137 | −0.0227450 | ||||||||
\(367\) | 30.7661 | 1.60598 | 0.802989 | − | 0.595994i | \(-0.203242\pi\) | ||||
0.802989 | + | 0.595994i | \(0.203242\pi\) | |||||||
\(368\) | −7.49965 | −0.390947 | ||||||||
\(369\) | −26.7919 | −1.39473 | ||||||||
\(370\) | 1.06717 | 0.0554796 | ||||||||
\(371\) | 6.40281 | 0.332417 | ||||||||
\(372\) | 5.89353 | 0.305565 | ||||||||
\(373\) | 4.59135 | 0.237731 | 0.118866 | − | 0.992910i | \(-0.462074\pi\) | ||||
0.118866 | + | 0.992910i | \(0.462074\pi\) | |||||||
\(374\) | 0.877275 | 0.0453628 | ||||||||
\(375\) | 19.5263 | 1.00833 | ||||||||
\(376\) | −11.0600 | −0.570374 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.374409 | −0.0192575 | ||||||||
\(379\) | −5.44535 | −0.279709 | −0.139855 | − | 0.990172i | \(-0.544663\pi\) | ||||
−0.139855 | + | 0.990172i | \(0.544663\pi\) | |||||||
\(380\) | 6.30433 | 0.323405 | ||||||||
\(381\) | 8.49312 | 0.435116 | ||||||||
\(382\) | −2.72072 | −0.139204 | ||||||||
\(383\) | 13.7016 | 0.700117 | 0.350058 | − | 0.936728i | \(-0.386162\pi\) | ||||
0.350058 | + | 0.936728i | \(0.386162\pi\) | |||||||
\(384\) | −22.5600 | −1.15126 | ||||||||
\(385\) | −1.19814 | −0.0610629 | ||||||||
\(386\) | 1.78786 | 0.0909998 | ||||||||
\(387\) | 7.20560 | 0.366281 | ||||||||
\(388\) | 24.0320 | 1.22004 | ||||||||
\(389\) | −24.9817 | −1.26662 | −0.633311 | − | 0.773897i | \(-0.718305\pi\) | ||||
−0.633311 | + | 0.773897i | \(0.718305\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.16589 | 0.109534 | ||||||||
\(392\) | 7.93363 | 0.400709 | ||||||||
\(393\) | −1.45976 | −0.0736354 | ||||||||
\(394\) | 5.46062 | 0.275102 | ||||||||
\(395\) | 2.65473 | 0.133574 | ||||||||
\(396\) | 21.7092 | 1.09093 | ||||||||
\(397\) | −3.54176 | −0.177756 | −0.0888780 | − | 0.996043i | \(-0.528328\pi\) | ||||
−0.0888780 | + | 0.996043i | \(0.528328\pi\) | |||||||
\(398\) | 1.48355 | 0.0743639 | ||||||||
\(399\) | −5.68982 | −0.284848 | ||||||||
\(400\) | −15.1374 | −0.756871 | ||||||||
\(401\) | 28.1841 | 1.40745 | 0.703724 | − | 0.710474i | \(-0.251519\pi\) | ||||
0.703724 | + | 0.710474i | \(0.251519\pi\) | |||||||
\(402\) | −9.32271 | −0.464974 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 10.2548 | 0.510197 | ||||||||
\(405\) | 4.31723 | 0.214525 | ||||||||
\(406\) | 0.687792 | 0.0341346 | ||||||||
\(407\) | 12.9870 | 0.643744 | ||||||||
\(408\) | 3.09859 | 0.153403 | ||||||||
\(409\) | 22.6445 | 1.11970 | 0.559849 | − | 0.828595i | \(-0.310859\pi\) | ||||
0.559849 | + | 0.828595i | \(0.310859\pi\) | |||||||
\(410\) | 1.63836 | 0.0809126 | ||||||||
\(411\) | 20.5755 | 1.01492 | ||||||||
\(412\) | −22.9972 | −1.13299 | ||||||||
\(413\) | −2.08712 | −0.102700 | ||||||||
\(414\) | −2.55324 | −0.125485 | ||||||||
\(415\) | −1.83253 | −0.0899555 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 47.6224 | 2.33208 | ||||||||
\(418\) | −3.65479 | −0.178762 | ||||||||
\(419\) | 6.16414 | 0.301138 | 0.150569 | − | 0.988600i | \(-0.451889\pi\) | ||||
0.150569 | + | 0.988600i | \(0.451889\pi\) | |||||||
\(420\) | −2.06673 | −0.100846 | ||||||||
\(421\) | −11.3636 | −0.553829 | −0.276915 | − | 0.960895i | \(-0.589312\pi\) | ||||
−0.276915 | + | 0.960895i | \(0.589312\pi\) | |||||||
\(422\) | 3.05810 | 0.148866 | ||||||||
\(423\) | 36.6750 | 1.78320 | ||||||||
\(424\) | 14.5266 | 0.705473 | ||||||||
\(425\) | 4.37167 | 0.212057 | ||||||||
\(426\) | 4.43424 | 0.214840 | ||||||||
\(427\) | 0.285230 | 0.0138033 | ||||||||
\(428\) | −17.6317 | −0.852260 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.440630 | −0.0212491 | ||||||||
\(431\) | −2.35318 | −0.113349 | −0.0566743 | − | 0.998393i | \(-0.518050\pi\) | ||||
−0.0566743 | + | 0.998393i | \(0.518050\pi\) | |||||||
\(432\) | 8.27380 | 0.398073 | ||||||||
\(433\) | −1.83217 | −0.0880484 | −0.0440242 | − | 0.999030i | \(-0.514018\pi\) | ||||
−0.0440242 | + | 0.999030i | \(0.514018\pi\) | |||||||
\(434\) | 0.184032 | 0.00883381 | ||||||||
\(435\) | 9.14563 | 0.438500 | ||||||||
\(436\) | 3.20786 | 0.153629 | ||||||||
\(437\) | −9.02327 | −0.431642 | ||||||||
\(438\) | −10.7980 | −0.515950 | ||||||||
\(439\) | −11.0770 | −0.528676 | −0.264338 | − | 0.964430i | \(-0.585153\pi\) | ||||
−0.264338 | + | 0.964430i | \(0.585153\pi\) | |||||||
\(440\) | −2.71832 | −0.129591 | ||||||||
\(441\) | −26.3081 | −1.25276 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −33.0939 | −1.57234 | −0.786168 | − | 0.618013i | \(-0.787938\pi\) | ||||
−0.786168 | + | 0.618013i | \(0.787938\pi\) | |||||||
\(444\) | 22.4020 | 1.06315 | ||||||||
\(445\) | 1.59305 | 0.0755177 | ||||||||
\(446\) | −3.86722 | −0.183118 | ||||||||
\(447\) | −46.0319 | −2.17723 | ||||||||
\(448\) | 3.06525 | 0.144819 | ||||||||
\(449\) | −23.8928 | −1.12757 | −0.563786 | − | 0.825921i | \(-0.690656\pi\) | ||||
−0.563786 | + | 0.825921i | \(0.690656\pi\) | |||||||
\(450\) | −5.15351 | −0.242939 | ||||||||
\(451\) | 19.9381 | 0.938850 | ||||||||
\(452\) | −23.7702 | −1.11806 | ||||||||
\(453\) | −61.5002 | −2.88953 | ||||||||
\(454\) | −2.89501 | −0.135870 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.9090 | −0.604518 | ||||||||
\(457\) | −3.88289 | −0.181634 | −0.0908170 | − | 0.995868i | \(-0.528948\pi\) | ||||
−0.0908170 | + | 0.995868i | \(0.528948\pi\) | |||||||
\(458\) | 7.38051 | 0.344869 | ||||||||
\(459\) | −2.38947 | −0.111531 | ||||||||
\(460\) | −3.27755 | −0.152816 | ||||||||
\(461\) | 12.7192 | 0.592394 | 0.296197 | − | 0.955127i | \(-0.404282\pi\) | ||||
0.296197 | + | 0.955127i | \(0.404282\pi\) | |||||||
\(462\) | 1.19814 | 0.0557425 | ||||||||
\(463\) | −11.4030 | −0.529941 | −0.264971 | − | 0.964256i | \(-0.585362\pi\) | ||||
−0.264971 | + | 0.964256i | \(0.585362\pi\) | |||||||
\(464\) | −15.1990 | −0.705597 | ||||||||
\(465\) | 2.44709 | 0.113481 | ||||||||
\(466\) | 7.30518 | 0.338406 | ||||||||
\(467\) | −12.1805 | −0.563648 | −0.281824 | − | 0.959466i | \(-0.590939\pi\) | ||||
−0.281824 | + | 0.959466i | \(0.590939\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.11099 | 0.282179 | ||||||||
\(470\) | −2.24272 | −0.103449 | ||||||||
\(471\) | −55.8796 | −2.57480 | ||||||||
\(472\) | −4.73522 | −0.217956 | ||||||||
\(473\) | −5.36229 | −0.246558 | ||||||||
\(474\) | −2.65473 | −0.121936 | ||||||||
\(475\) | −18.2127 | −0.835657 | ||||||||
\(476\) | −0.991931 | −0.0454651 | ||||||||
\(477\) | −48.1704 | −2.20557 | ||||||||
\(478\) | −6.32491 | −0.289295 | ||||||||
\(479\) | −25.8162 | −1.17957 | −0.589787 | − | 0.807559i | \(-0.700788\pi\) | ||||
−0.589787 | + | 0.807559i | \(0.700788\pi\) | |||||||
\(480\) | −7.08798 | −0.323521 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 7.63170 | 0.347614 | ||||||||
\(483\) | 2.95807 | 0.134597 | ||||||||
\(484\) | 4.84401 | 0.220182 | ||||||||
\(485\) | 9.97844 | 0.453098 | ||||||||
\(486\) | −6.47898 | −0.293893 | ||||||||
\(487\) | 15.8984 | 0.720425 | 0.360212 | − | 0.932870i | \(-0.382704\pi\) | ||||
0.360212 | + | 0.932870i | \(0.382704\pi\) | |||||||
\(488\) | 0.647126 | 0.0292940 | ||||||||
\(489\) | 7.14108 | 0.322931 | ||||||||
\(490\) | 1.60877 | 0.0726766 | ||||||||
\(491\) | 15.9982 | 0.721991 | 0.360995 | − | 0.932568i | \(-0.382437\pi\) | ||||
0.360995 | + | 0.932568i | \(0.382437\pi\) | |||||||
\(492\) | 34.3923 | 1.55052 | ||||||||
\(493\) | 4.38947 | 0.197692 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.01399 | 0.405149 | ||||||||
\(496\) | −4.06679 | −0.182604 | ||||||||
\(497\) | −2.90663 | −0.130380 | ||||||||
\(498\) | 1.83253 | 0.0821177 | ||||||||
\(499\) | −9.15142 | −0.409674 | −0.204837 | − | 0.978796i | \(-0.565666\pi\) | ||||
−0.204837 | + | 0.978796i | \(0.565666\pi\) | |||||||
\(500\) | −14.1817 | −0.634226 | ||||||||
\(501\) | 40.2475 | 1.79813 | ||||||||
\(502\) | 6.48820 | 0.289583 | ||||||||
\(503\) | −28.0587 | −1.25108 | −0.625538 | − | 0.780194i | \(-0.715121\pi\) | ||||
−0.625538 | + | 0.780194i | \(0.715121\pi\) | |||||||
\(504\) | 2.39436 | 0.106653 | ||||||||
\(505\) | 4.25797 | 0.189477 | ||||||||
\(506\) | 1.90008 | 0.0844690 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.16846 | −0.273681 | ||||||||
\(509\) | −28.8738 | −1.27981 | −0.639903 | − | 0.768455i | \(-0.721026\pi\) | ||||
−0.639903 | + | 0.768455i | \(0.721026\pi\) | |||||||
\(510\) | 0.628327 | 0.0278228 | ||||||||
\(511\) | 7.07806 | 0.313115 | ||||||||
\(512\) | 19.9432 | 0.881373 | ||||||||
\(513\) | 9.95469 | 0.439510 | ||||||||
\(514\) | −0.610841 | −0.0269430 | ||||||||
\(515\) | −9.54878 | −0.420769 | ||||||||
\(516\) | −9.24967 | −0.407194 | ||||||||
\(517\) | −27.2930 | −1.20034 | ||||||||
\(518\) | 0.699526 | 0.0307354 | ||||||||
\(519\) | −51.4140 | −2.25682 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.5970 | 0.551882 | 0.275941 | − | 0.961175i | \(-0.411010\pi\) | ||||
0.275941 | + | 0.961175i | \(0.411010\pi\) | |||||||
\(522\) | −5.17448 | −0.226481 | ||||||||
\(523\) | 6.65716 | 0.291097 | 0.145549 | − | 0.989351i | \(-0.453505\pi\) | ||||
0.145549 | + | 0.989351i | \(0.453505\pi\) | |||||||
\(524\) | 1.06021 | 0.0463155 | ||||||||
\(525\) | 5.97062 | 0.260579 | ||||||||
\(526\) | −3.81862 | −0.166500 | ||||||||
\(527\) | 1.17448 | 0.0511613 | ||||||||
\(528\) | −26.4768 | −1.15226 | ||||||||
\(529\) | −18.3089 | −0.796040 | ||||||||
\(530\) | 2.94567 | 0.127952 | ||||||||
\(531\) | 15.7021 | 0.681412 | ||||||||
\(532\) | 4.13246 | 0.179165 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −1.59305 | −0.0689379 | ||||||||
\(535\) | −7.32095 | −0.316512 | ||||||||
\(536\) | 13.8645 | 0.598856 | ||||||||
\(537\) | 48.0464 | 2.07336 | ||||||||
\(538\) | 1.45307 | 0.0626462 | ||||||||
\(539\) | 19.5780 | 0.843285 | ||||||||
\(540\) | 3.61587 | 0.155602 | ||||||||
\(541\) | −28.9363 | −1.24407 | −0.622034 | − | 0.782991i | \(-0.713693\pi\) | ||||
−0.622034 | + | 0.782991i | \(0.713693\pi\) | |||||||
\(542\) | −1.73746 | −0.0746303 | ||||||||
\(543\) | 14.6738 | 0.629712 | ||||||||
\(544\) | −3.40189 | −0.145855 | ||||||||
\(545\) | 1.33195 | 0.0570546 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.2571 | 1.46473 | 0.732364 | − | 0.680914i | \(-0.238417\pi\) | ||||
0.732364 | + | 0.680914i | \(0.238417\pi\) | |||||||
\(548\) | −14.9438 | −0.638367 | ||||||||
\(549\) | −2.14588 | −0.0915840 | ||||||||
\(550\) | 3.83516 | 0.163532 | ||||||||
\(551\) | −18.2868 | −0.779046 | ||||||||
\(552\) | 6.71122 | 0.285649 | ||||||||
\(553\) | 1.74016 | 0.0739992 | ||||||||
\(554\) | −0.134488 | −0.00571383 | ||||||||
\(555\) | 9.30165 | 0.394833 | ||||||||
\(556\) | −34.5876 | −1.46684 | ||||||||
\(557\) | −38.4162 | −1.62775 | −0.813874 | − | 0.581042i | \(-0.802645\pi\) | ||||
−0.813874 | + | 0.581042i | \(0.802645\pi\) | |||||||
\(558\) | −1.38453 | −0.0586118 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.42613 | 0.0602650 | ||||||||
\(561\) | 7.64648 | 0.322835 | ||||||||
\(562\) | 5.20896 | 0.219727 | ||||||||
\(563\) | 40.0488 | 1.68786 | 0.843928 | − | 0.536456i | \(-0.180237\pi\) | ||||
0.843928 | + | 0.536456i | \(0.180237\pi\) | |||||||
\(564\) | −47.0790 | −1.98238 | ||||||||
\(565\) | −9.86976 | −0.415224 | ||||||||
\(566\) | −6.50455 | −0.273406 | ||||||||
\(567\) | 2.82993 | 0.118846 | ||||||||
\(568\) | −6.59451 | −0.276699 | ||||||||
\(569\) | 12.4612 | 0.522401 | 0.261201 | − | 0.965285i | \(-0.415882\pi\) | ||||
0.261201 | + | 0.965285i | \(0.415882\pi\) | |||||||
\(570\) | −2.61766 | −0.109642 | ||||||||
\(571\) | −8.66499 | −0.362618 | −0.181309 | − | 0.983426i | \(-0.558033\pi\) | ||||
−0.181309 | + | 0.983426i | \(0.558033\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −23.7143 | −0.990679 | ||||||||
\(574\) | 1.07393 | 0.0448252 | ||||||||
\(575\) | 9.46858 | 0.394867 | ||||||||
\(576\) | −23.0608 | −0.960868 | ||||||||
\(577\) | 25.4123 | 1.05793 | 0.528964 | − | 0.848644i | \(-0.322581\pi\) | ||||
0.528964 | + | 0.848644i | \(0.322581\pi\) | |||||||
\(578\) | 0.301567 | 0.0125435 | ||||||||
\(579\) | 15.5833 | 0.647621 | ||||||||
\(580\) | −6.64238 | −0.275810 | ||||||||
\(581\) | −1.20122 | −0.0498349 | ||||||||
\(582\) | −9.97844 | −0.413620 | ||||||||
\(583\) | 35.8476 | 1.48466 | ||||||||
\(584\) | 16.0586 | 0.664509 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.03099 | 0.0425899 | ||||||||
\(587\) | 24.9726 | 1.03073 | 0.515364 | − | 0.856971i | \(-0.327657\pi\) | ||||
0.515364 | + | 0.856971i | \(0.327657\pi\) | |||||||
\(588\) | 33.7711 | 1.39270 | ||||||||
\(589\) | −4.89299 | −0.201612 | ||||||||
\(590\) | −0.960198 | −0.0395307 | ||||||||
\(591\) | 47.5957 | 1.95783 | ||||||||
\(592\) | −15.4583 | −0.635333 | ||||||||
\(593\) | 35.3802 | 1.45289 | 0.726445 | − | 0.687224i | \(-0.241171\pi\) | ||||
0.726445 | + | 0.687224i | \(0.241171\pi\) | |||||||
\(594\) | −2.09622 | −0.0860089 | ||||||||
\(595\) | −0.411865 | −0.0168848 | ||||||||
\(596\) | 33.4325 | 1.36945 | ||||||||
\(597\) | 12.9309 | 0.529228 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.6743 | −1.08988 | −0.544942 | − | 0.838474i | \(-0.683448\pi\) | ||||
−0.544942 | + | 0.838474i | \(0.683448\pi\) | |||||||
\(600\) | 13.5460 | 0.553015 | ||||||||
\(601\) | 32.9492 | 1.34402 | 0.672012 | − | 0.740540i | \(-0.265430\pi\) | ||||
0.672012 | + | 0.740540i | \(0.265430\pi\) | |||||||
\(602\) | −0.288831 | −0.0117719 | ||||||||
\(603\) | −45.9750 | −1.87225 | ||||||||
\(604\) | 44.6669 | 1.81747 | ||||||||
\(605\) | 2.01131 | 0.0817714 | ||||||||
\(606\) | −4.25797 | −0.172968 | ||||||||
\(607\) | −39.2161 | −1.59173 | −0.795865 | − | 0.605474i | \(-0.792984\pi\) | ||||
−0.795865 | + | 0.605474i | \(0.792984\pi\) | |||||||
\(608\) | 14.1725 | 0.574772 | ||||||||
\(609\) | 5.99492 | 0.242926 | ||||||||
\(610\) | 0.131223 | 0.00531306 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 7.46262 | 0.301658 | ||||||||
\(613\) | −43.7946 | −1.76885 | −0.884424 | − | 0.466684i | \(-0.845448\pi\) | ||||
−0.884424 | + | 0.466684i | \(0.845448\pi\) | |||||||
\(614\) | −7.62999 | −0.307921 | ||||||||
\(615\) | 14.2802 | 0.575833 | ||||||||
\(616\) | −1.78185 | −0.0717926 | ||||||||
\(617\) | −24.2054 | −0.974474 | −0.487237 | − | 0.873270i | \(-0.661995\pi\) | ||||
−0.487237 | + | 0.873270i | \(0.661995\pi\) | |||||||
\(618\) | 9.54878 | 0.384108 | ||||||||
\(619\) | −35.1257 | −1.41182 | −0.705910 | − | 0.708302i | \(-0.749462\pi\) | ||||
−0.705910 | + | 0.708302i | \(0.749462\pi\) | |||||||
\(620\) | −1.77729 | −0.0713778 | ||||||||
\(621\) | −5.17533 | −0.207679 | ||||||||
\(622\) | 8.52606 | 0.341864 | ||||||||
\(623\) | 1.04424 | 0.0418364 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.9699 | 0.638796 | ||||||||
\(626\) | −8.90542 | −0.355932 | ||||||||
\(627\) | −31.8558 | −1.27220 | ||||||||
\(628\) | 40.5848 | 1.61951 | ||||||||
\(629\) | 4.46435 | 0.178005 | ||||||||
\(630\) | 0.485524 | 0.0193437 | ||||||||
\(631\) | 26.7154 | 1.06352 | 0.531761 | − | 0.846894i | \(-0.321530\pi\) | ||||
0.531761 | + | 0.846894i | \(0.321530\pi\) | |||||||
\(632\) | 3.94805 | 0.157045 | ||||||||
\(633\) | 26.6549 | 1.05944 | ||||||||
\(634\) | 10.4585 | 0.415361 | ||||||||
\(635\) | −2.56124 | −0.101640 | ||||||||
\(636\) | 61.8353 | 2.45193 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.85077 | 0.152453 | ||||||||
\(639\) | 21.8675 | 0.865064 | ||||||||
\(640\) | 6.80335 | 0.268926 | ||||||||
\(641\) | −25.9752 | −1.02596 | −0.512979 | − | 0.858401i | \(-0.671458\pi\) | ||||
−0.512979 | + | 0.858401i | \(0.671458\pi\) | |||||||
\(642\) | 7.32095 | 0.288935 | ||||||||
\(643\) | 18.8467 | 0.743240 | 0.371620 | − | 0.928385i | \(-0.378802\pi\) | ||||
0.371620 | + | 0.928385i | \(0.378802\pi\) | |||||||
\(644\) | −2.14842 | −0.0846595 | ||||||||
\(645\) | −3.84061 | −0.151224 | ||||||||
\(646\) | −1.25635 | −0.0494304 | ||||||||
\(647\) | −7.79836 | −0.306585 | −0.153293 | − | 0.988181i | \(-0.548988\pi\) | ||||
−0.153293 | + | 0.988181i | \(0.548988\pi\) | |||||||
\(648\) | 6.42049 | 0.252221 | ||||||||
\(649\) | −11.6852 | −0.458685 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.60405 | 0.0628678 | ||||||||
\(652\) | −5.18649 | −0.203119 | ||||||||
\(653\) | −17.3230 | −0.677902 | −0.338951 | − | 0.940804i | \(-0.610072\pi\) | ||||
−0.338951 | + | 0.940804i | \(0.610072\pi\) | |||||||
\(654\) | −1.33195 | −0.0520835 | ||||||||
\(655\) | 0.440216 | 0.0172007 | ||||||||
\(656\) | −23.7321 | −0.926584 | ||||||||
\(657\) | −53.2506 | −2.07750 | ||||||||
\(658\) | −1.47009 | −0.0573101 | ||||||||
\(659\) | 19.0325 | 0.741401 | 0.370701 | − | 0.928752i | \(-0.379118\pi\) | ||||
0.370701 | + | 0.928752i | \(0.379118\pi\) | |||||||
\(660\) | −11.5711 | −0.450403 | ||||||||
\(661\) | −21.9959 | −0.855540 | −0.427770 | − | 0.903888i | \(-0.640701\pi\) | ||||
−0.427770 | + | 0.903888i | \(0.640701\pi\) | |||||||
\(662\) | 10.3694 | 0.403018 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.72530 | −0.105762 | ||||||||
\(665\) | 1.71586 | 0.0665382 | ||||||||
\(666\) | −5.26276 | −0.203928 | ||||||||
\(667\) | 9.50711 | 0.368117 | ||||||||
\(668\) | −29.2314 | −1.13100 | ||||||||
\(669\) | −33.7074 | −1.30320 | ||||||||
\(670\) | 2.81142 | 0.108615 | ||||||||
\(671\) | 1.59693 | 0.0616488 | ||||||||
\(672\) | −4.64614 | −0.179229 | ||||||||
\(673\) | −16.7076 | −0.644032 | −0.322016 | − | 0.946734i | \(-0.604361\pi\) | ||||
−0.322016 | + | 0.946734i | \(0.604361\pi\) | |||||||
\(674\) | 7.21669 | 0.277977 | ||||||||
\(675\) | −10.4460 | −0.402065 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.9976 | −0.461105 | −0.230552 | − | 0.973060i | \(-0.574053\pi\) | ||||
−0.230552 | + | 0.973060i | \(0.574053\pi\) | |||||||
\(678\) | 9.86976 | 0.379046 | ||||||||
\(679\) | 6.54082 | 0.251014 | ||||||||
\(680\) | −0.934433 | −0.0358339 | ||||||||
\(681\) | −25.2334 | −0.966947 | ||||||||
\(682\) | 1.03034 | 0.0394539 | ||||||||
\(683\) | 31.9597 | 1.22290 | 0.611451 | − | 0.791282i | \(-0.290586\pi\) | ||||
0.611451 | + | 0.791282i | \(0.290586\pi\) | |||||||
\(684\) | −31.0898 | −1.18875 | ||||||||
\(685\) | −6.20490 | −0.237077 | ||||||||
\(686\) | 2.15138 | 0.0821401 | ||||||||
\(687\) | 64.3299 | 2.45434 | ||||||||
\(688\) | 6.38267 | 0.243337 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 1.36089 | 0.0518081 | ||||||||
\(691\) | −22.0953 | −0.840546 | −0.420273 | − | 0.907398i | \(-0.638066\pi\) | ||||
−0.420273 | + | 0.907398i | \(0.638066\pi\) | |||||||
\(692\) | 37.3414 | 1.41951 | ||||||||
\(693\) | 5.90863 | 0.224450 | ||||||||
\(694\) | −2.09638 | −0.0795773 | ||||||||
\(695\) | −14.3613 | −0.544756 | ||||||||
\(696\) | 13.6012 | 0.515551 | ||||||||
\(697\) | 6.85381 | 0.259607 | ||||||||
\(698\) | −9.75370 | −0.369183 | ||||||||
\(699\) | 63.6732 | 2.40834 | ||||||||
\(700\) | −4.33640 | −0.163900 | ||||||||
\(701\) | 45.9236 | 1.73451 | 0.867256 | − | 0.497863i | \(-0.165882\pi\) | ||||
0.867256 | + | 0.497863i | \(0.165882\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.5988 | −0.701467 | ||||||||
\(704\) | 17.1615 | 0.646798 | ||||||||
\(705\) | −19.5479 | −0.736217 | ||||||||
\(706\) | −8.61041 | −0.324057 | ||||||||
\(707\) | 2.79108 | 0.104969 | ||||||||
\(708\) | −20.1564 | −0.757524 | ||||||||
\(709\) | 52.0600 | 1.95516 | 0.977578 | − | 0.210575i | \(-0.0675338\pi\) | ||||
0.977578 | + | 0.210575i | \(0.0675338\pi\) | |||||||
\(710\) | −1.33722 | −0.0501850 | ||||||||
\(711\) | −13.0918 | −0.490981 | ||||||||
\(712\) | 2.36914 | 0.0887875 | ||||||||
\(713\) | 2.54381 | 0.0952663 | ||||||||
\(714\) | 0.411865 | 0.0154137 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −34.8956 | −1.30411 | ||||||||
\(717\) | −55.1291 | −2.05883 | ||||||||
\(718\) | −3.21306 | −0.119910 | ||||||||
\(719\) | 16.7262 | 0.623781 | 0.311890 | − | 0.950118i | \(-0.399038\pi\) | ||||
0.311890 | + | 0.950118i | \(0.399038\pi\) | |||||||
\(720\) | −10.7292 | −0.399855 | ||||||||
\(721\) | −6.25918 | −0.233104 | ||||||||
\(722\) | −0.495722 | −0.0184488 | ||||||||
\(723\) | 66.5193 | 2.47388 | ||||||||
\(724\) | −10.6574 | −0.396079 | ||||||||
\(725\) | 19.1893 | 0.712673 | ||||||||
\(726\) | −2.01131 | −0.0746467 | ||||||||
\(727\) | −30.3497 | −1.12561 | −0.562804 | − | 0.826590i | \(-0.690277\pi\) | ||||
−0.562804 | + | 0.826590i | \(0.690277\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −40.1326 | −1.48639 | ||||||||
\(730\) | 3.25633 | 0.120522 | ||||||||
\(731\) | −1.84331 | −0.0681772 | ||||||||
\(732\) | 2.75462 | 0.101814 | ||||||||
\(733\) | −19.0800 | −0.704738 | −0.352369 | − | 0.935861i | \(-0.614624\pi\) | ||||
−0.352369 | + | 0.935861i | \(0.614624\pi\) | |||||||
\(734\) | 9.27803 | 0.342458 | ||||||||
\(735\) | 14.0223 | 0.517220 | ||||||||
\(736\) | −7.36813 | −0.271593 | ||||||||
\(737\) | 34.2138 | 1.26028 | ||||||||
\(738\) | −8.07956 | −0.297413 | ||||||||
\(739\) | −23.6616 | −0.870407 | −0.435203 | − | 0.900332i | \(-0.643323\pi\) | ||||
−0.435203 | + | 0.900332i | \(0.643323\pi\) | |||||||
\(740\) | −6.75569 | −0.248344 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.93087 | 0.0708846 | ||||||||
\(743\) | 21.2932 | 0.781172 | 0.390586 | − | 0.920566i | \(-0.372272\pi\) | ||||
0.390586 | + | 0.920566i | \(0.372272\pi\) | |||||||
\(744\) | 3.63925 | 0.133421 | ||||||||
\(745\) | 13.8817 | 0.508586 | ||||||||
\(746\) | 1.38460 | 0.0506937 | ||||||||
\(747\) | 9.03714 | 0.330652 | ||||||||
\(748\) | −5.55356 | −0.203058 | ||||||||
\(749\) | −4.79885 | −0.175346 | ||||||||
\(750\) | 5.88847 | 0.215017 | ||||||||
\(751\) | 36.9916 | 1.34984 | 0.674921 | − | 0.737890i | \(-0.264178\pi\) | ||||
0.674921 | + | 0.737890i | \(0.264178\pi\) | |||||||
\(752\) | 32.4865 | 1.18466 | ||||||||
\(753\) | 56.5523 | 2.06088 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.5464 | 0.674973 | ||||||||
\(756\) | 2.37018 | 0.0862028 | ||||||||
\(757\) | 8.17425 | 0.297098 | 0.148549 | − | 0.988905i | \(-0.452540\pi\) | ||||
0.148549 | + | 0.988905i | \(0.452540\pi\) | |||||||
\(758\) | −1.64214 | −0.0596451 | ||||||||
\(759\) | 16.5615 | 0.601143 | ||||||||
\(760\) | 3.89292 | 0.141211 | ||||||||
\(761\) | −4.61076 | −0.167140 | −0.0835700 | − | 0.996502i | \(-0.526632\pi\) | ||||
−0.0835700 | + | 0.996502i | \(0.526632\pi\) | |||||||
\(762\) | 2.56124 | 0.0927840 | ||||||||
\(763\) | 0.873089 | 0.0316080 | ||||||||
\(764\) | 17.2234 | 0.623122 | ||||||||
\(765\) | 3.09859 | 0.112030 | ||||||||
\(766\) | 4.13193 | 0.149293 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 24.2095 | 0.873587 | ||||||||
\(769\) | 2.88794 | 0.104142 | 0.0520708 | − | 0.998643i | \(-0.483418\pi\) | ||||
0.0520708 | + | 0.998643i | \(0.483418\pi\) | |||||||
\(770\) | −0.361319 | −0.0130210 | ||||||||
\(771\) | −5.32419 | −0.191746 | ||||||||
\(772\) | −11.3180 | −0.407344 | ||||||||
\(773\) | −9.36385 | −0.336794 | −0.168397 | − | 0.985719i | \(-0.553859\pi\) | ||||
−0.168397 | + | 0.985719i | \(0.553859\pi\) | |||||||
\(774\) | 2.17297 | 0.0781057 | ||||||||
\(775\) | 5.13446 | 0.184435 | ||||||||
\(776\) | 14.8397 | 0.532715 | ||||||||
\(777\) | 6.09719 | 0.218735 | ||||||||
\(778\) | −7.53365 | −0.270094 | ||||||||
\(779\) | −28.5535 | −1.02304 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.2734 | −0.582309 | ||||||||
\(782\) | 0.653161 | 0.0233570 | ||||||||
\(783\) | −10.4885 | −0.374828 | ||||||||
\(784\) | −23.3035 | −0.832267 | ||||||||
\(785\) | 16.8514 | 0.601453 | ||||||||
\(786\) | −0.440216 | −0.0157020 | ||||||||
\(787\) | −45.6682 | −1.62790 | −0.813948 | − | 0.580937i | \(-0.802686\pi\) | ||||
−0.813948 | + | 0.580937i | \(0.802686\pi\) | |||||||
\(788\) | −34.5683 | −1.23144 | ||||||||
\(789\) | −33.2838 | −1.18493 | ||||||||
\(790\) | 0.800577 | 0.0284832 | ||||||||
\(791\) | −6.46958 | −0.230032 | ||||||||
\(792\) | 13.4054 | 0.476340 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −1.06808 | −0.0379047 | ||||||||
\(795\) | 25.6750 | 0.910598 | ||||||||
\(796\) | −9.39159 | −0.332876 | ||||||||
\(797\) | −4.61369 | −0.163425 | −0.0817127 | − | 0.996656i | \(-0.526039\pi\) | ||||
−0.0817127 | + | 0.996656i | \(0.526039\pi\) | |||||||
\(798\) | −1.71586 | −0.0607408 | ||||||||
\(799\) | −9.38206 | −0.331914 | ||||||||
\(800\) | −14.8720 | −0.525803 | ||||||||
\(801\) | −7.85612 | −0.277582 | ||||||||
\(802\) | 8.49939 | 0.300124 | ||||||||
\(803\) | 39.6282 | 1.39845 | ||||||||
\(804\) | 59.0171 | 2.08137 | ||||||||
\(805\) | −0.892056 | −0.0314408 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.6652 | 0.445836 | ||||||||
\(808\) | 6.33235 | 0.222771 | ||||||||
\(809\) | −10.3148 | −0.362650 | −0.181325 | − | 0.983423i | \(-0.558039\pi\) | ||||
−0.181325 | + | 0.983423i | \(0.558039\pi\) | |||||||
\(810\) | 1.30193 | 0.0457453 | ||||||||
\(811\) | −17.7710 | −0.624025 | −0.312013 | − | 0.950078i | \(-0.601003\pi\) | ||||
−0.312013 | + | 0.950078i | \(0.601003\pi\) | |||||||
\(812\) | −4.35405 | −0.152797 | ||||||||
\(813\) | −15.1440 | −0.531123 | ||||||||
\(814\) | 3.91646 | 0.137272 | ||||||||
\(815\) | −2.15351 | −0.0754343 | ||||||||
\(816\) | −9.10152 | −0.318617 | ||||||||
\(817\) | 7.67936 | 0.268667 | ||||||||
\(818\) | 6.82882 | 0.238764 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.3716 | −0.362190 | ||||||||
\(821\) | 40.1933 | 1.40275 | 0.701377 | − | 0.712790i | \(-0.252569\pi\) | ||||
0.701377 | + | 0.712790i | \(0.252569\pi\) | |||||||
\(822\) | 6.20490 | 0.216421 | ||||||||
\(823\) | −38.5083 | −1.34231 | −0.671157 | − | 0.741315i | \(-0.734203\pi\) | ||||
−0.671157 | + | 0.741315i | \(0.734203\pi\) | |||||||
\(824\) | −14.2007 | −0.494706 | ||||||||
\(825\) | 33.4279 | 1.16381 | ||||||||
\(826\) | −0.629405 | −0.0218998 | ||||||||
\(827\) | 44.6381 | 1.55222 | 0.776109 | − | 0.630598i | \(-0.217190\pi\) | ||||
0.776109 | + | 0.630598i | \(0.217190\pi\) | |||||||
\(828\) | 16.1632 | 0.561711 | ||||||||
\(829\) | −7.29204 | −0.253263 | −0.126632 | − | 0.991950i | \(-0.540417\pi\) | ||||
−0.126632 | + | 0.991950i | \(0.540417\pi\) | |||||||
\(830\) | −0.552631 | −0.0191821 | ||||||||
\(831\) | −1.17222 | −0.0406638 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.73002 | 0.233182 | ||||||||
\(834\) | 14.3613 | 0.497292 | ||||||||
\(835\) | −12.1373 | −0.420029 | ||||||||
\(836\) | 23.1365 | 0.800194 | ||||||||
\(837\) | −2.80639 | −0.0970030 | ||||||||
\(838\) | 1.85890 | 0.0642146 | ||||||||
\(839\) | 12.5000 | 0.431547 | 0.215774 | − | 0.976443i | \(-0.430773\pi\) | ||||
0.215774 | + | 0.976443i | \(0.430773\pi\) | |||||||
\(840\) | −1.27620 | −0.0440332 | ||||||||
\(841\) | −9.73259 | −0.335607 | ||||||||
\(842\) | −3.42689 | −0.118098 | ||||||||
\(843\) | 45.4022 | 1.56373 | ||||||||
\(844\) | −19.3592 | −0.666370 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 11.0600 | 0.380249 | ||||||||
\(847\) | 1.31840 | 0.0453009 | ||||||||
\(848\) | −42.6690 | −1.46526 | ||||||||
\(849\) | −56.6948 | −1.94576 | ||||||||
\(850\) | 1.31835 | 0.0452191 | ||||||||
\(851\) | 9.66930 | 0.331459 | ||||||||
\(852\) | −28.0708 | −0.961691 | ||||||||
\(853\) | 26.1387 | 0.894970 | 0.447485 | − | 0.894291i | \(-0.352320\pi\) | ||||
0.447485 | + | 0.894291i | \(0.352320\pi\) | |||||||
\(854\) | 0.0860160 | 0.00294341 | ||||||||
\(855\) | −12.9090 | −0.441478 | ||||||||
\(856\) | −10.8876 | −0.372129 | ||||||||
\(857\) | 6.85700 | 0.234231 | 0.117115 | − | 0.993118i | \(-0.462635\pi\) | ||||
0.117115 | + | 0.993118i | \(0.462635\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.1004 | 1.67528 | 0.837642 | − | 0.546220i | \(-0.183934\pi\) | ||||
0.837642 | + | 0.546220i | \(0.183934\pi\) | |||||||
\(860\) | 2.78939 | 0.0951175 | ||||||||
\(861\) | 9.36061 | 0.319009 | ||||||||
\(862\) | −0.709640 | −0.0241704 | ||||||||
\(863\) | −18.0088 | −0.613027 | −0.306514 | − | 0.951866i | \(-0.599162\pi\) | ||||
−0.306514 | + | 0.951866i | \(0.599162\pi\) | |||||||
\(864\) | 8.12870 | 0.276544 | ||||||||
\(865\) | 15.5048 | 0.527177 | ||||||||
\(866\) | −0.552521 | −0.0187754 | ||||||||
\(867\) | 2.62851 | 0.0892688 | ||||||||
\(868\) | −1.16501 | −0.0395429 | ||||||||
\(869\) | 9.74270 | 0.330498 | ||||||||
\(870\) | 2.75802 | 0.0935056 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 1.98085 | 0.0670801 | ||||||||
\(873\) | −49.2087 | −1.66546 | ||||||||
\(874\) | −2.72112 | −0.0920432 | ||||||||
\(875\) | −3.85987 | −0.130487 | ||||||||
\(876\) | 68.3566 | 2.30956 | ||||||||
\(877\) | 1.09058 | 0.0368264 | 0.0184132 | − | 0.999830i | \(-0.494139\pi\) | ||||
0.0184132 | + | 0.999830i | \(0.494139\pi\) | |||||||
\(878\) | −3.34045 | −0.112735 | ||||||||
\(879\) | 8.98631 | 0.303101 | ||||||||
\(880\) | 7.98453 | 0.269158 | ||||||||
\(881\) | −44.5730 | −1.50170 | −0.750852 | − | 0.660471i | \(-0.770357\pi\) | ||||
−0.750852 | + | 0.660471i | \(0.770357\pi\) | |||||||
\(882\) | −7.93363 | −0.267139 | ||||||||
\(883\) | −5.83736 | −0.196443 | −0.0982214 | − | 0.995165i | \(-0.531315\pi\) | ||||
−0.0982214 | + | 0.995165i | \(0.531315\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.36926 | −0.281329 | ||||||||
\(886\) | −9.98000 | −0.335285 | ||||||||
\(887\) | −34.4008 | −1.15507 | −0.577533 | − | 0.816368i | \(-0.695984\pi\) | ||||
−0.577533 | + | 0.816368i | \(0.695984\pi\) | |||||||
\(888\) | 13.8332 | 0.464212 | ||||||||
\(889\) | −1.67888 | −0.0563079 | ||||||||
\(890\) | 0.480410 | 0.0161034 | ||||||||
\(891\) | 15.8440 | 0.530794 | ||||||||
\(892\) | 24.4813 | 0.819694 | ||||||||
\(893\) | 39.0864 | 1.30798 | ||||||||
\(894\) | −13.8817 | −0.464273 | ||||||||
\(895\) | −14.4892 | −0.484321 | ||||||||
\(896\) | 4.45957 | 0.148984 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.20528 | −0.240443 | ||||||||
\(899\) | 5.15536 | 0.171941 | ||||||||
\(900\) | 32.6241 | 1.08747 | ||||||||
\(901\) | 12.3228 | 0.410531 | ||||||||
\(902\) | 6.01268 | 0.200200 | ||||||||
\(903\) | −2.51750 | −0.0837772 | ||||||||
\(904\) | −14.6781 | −0.488186 | ||||||||
\(905\) | −4.42512 | −0.147096 | ||||||||
\(906\) | −18.5464 | −0.616163 | ||||||||
\(907\) | 11.8364 | 0.393020 | 0.196510 | − | 0.980502i | \(-0.437039\pi\) | ||||
0.196510 | + | 0.980502i | \(0.437039\pi\) | |||||||
\(908\) | 18.3268 | 0.608195 | ||||||||
\(909\) | −20.9982 | −0.696466 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.55788 | −0.217272 | −0.108636 | − | 0.994082i | \(-0.534648\pi\) | ||||
−0.108636 | + | 0.994082i | \(0.534648\pi\) | |||||||
\(912\) | 37.9176 | 1.25558 | ||||||||
\(913\) | −6.72529 | −0.222575 | ||||||||
\(914\) | −1.17095 | −0.0387316 | ||||||||
\(915\) | 1.14376 | 0.0378116 | ||||||||
\(916\) | −46.7221 | −1.54374 | ||||||||
\(917\) | 0.288560 | 0.00952908 | ||||||||
\(918\) | −0.720583 | −0.0237828 | ||||||||
\(919\) | −43.1171 | −1.42230 | −0.711150 | − | 0.703040i | \(-0.751825\pi\) | ||||
−0.711150 | + | 0.703040i | \(0.751825\pi\) | |||||||
\(920\) | −2.02388 | −0.0667254 | ||||||||
\(921\) | −66.5044 | −2.19139 | ||||||||
\(922\) | 3.83570 | 0.126322 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −7.58478 | −0.249521 | ||||||||
\(925\) | 19.5167 | 0.641704 | ||||||||
\(926\) | −3.43876 | −0.113005 | ||||||||
\(927\) | 47.0898 | 1.54663 | ||||||||
\(928\) | −14.9325 | −0.490183 | ||||||||
\(929\) | 2.64916 | 0.0869162 | 0.0434581 | − | 0.999055i | \(-0.486162\pi\) | ||||
0.0434581 | + | 0.999055i | \(0.486162\pi\) | |||||||
\(930\) | 0.737959 | 0.0241986 | ||||||||
\(931\) | −28.0378 | −0.918901 | ||||||||
\(932\) | −46.2452 | −1.51481 | ||||||||
\(933\) | 74.3147 | 2.43295 | ||||||||
\(934\) | −3.67324 | −0.120192 | ||||||||
\(935\) | −2.30592 | −0.0754118 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.4947 | 0.571527 | 0.285764 | − | 0.958300i | \(-0.407753\pi\) | ||||
0.285764 | + | 0.958300i | \(0.407753\pi\) | |||||||
\(938\) | 1.84287 | 0.0601719 | ||||||||
\(939\) | −77.6212 | −2.53307 | ||||||||
\(940\) | 14.1974 | 0.463070 | ||||||||
\(941\) | −16.8686 | −0.549901 | −0.274950 | − | 0.961458i | \(-0.588661\pi\) | ||||
−0.274950 | + | 0.961458i | \(0.588661\pi\) | |||||||
\(942\) | −16.8514 | −0.549049 | ||||||||
\(943\) | 14.8446 | 0.483407 | ||||||||
\(944\) | 13.9088 | 0.452692 | ||||||||
\(945\) | 0.984138 | 0.0320140 | ||||||||
\(946\) | −1.61709 | −0.0525761 | ||||||||
\(947\) | 4.43747 | 0.144199 | 0.0720993 | − | 0.997397i | \(-0.477030\pi\) | ||||
0.0720993 | + | 0.997397i | \(0.477030\pi\) | |||||||
\(948\) | 16.8057 | 0.545822 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −5.49235 | −0.178195 | ||||||||
\(951\) | 91.1584 | 2.95601 | ||||||||
\(952\) | −0.612516 | −0.0198518 | ||||||||
\(953\) | 22.6220 | 0.732798 | 0.366399 | − | 0.930458i | \(-0.380591\pi\) | ||||
0.366399 | + | 0.930458i | \(0.380591\pi\) | |||||||
\(954\) | −14.5266 | −0.470316 | ||||||||
\(955\) | 7.15144 | 0.231415 | ||||||||
\(956\) | 40.0397 | 1.29497 | ||||||||
\(957\) | 33.5640 | 1.08497 | ||||||||
\(958\) | −7.78532 | −0.251532 | ||||||||
\(959\) | −4.06728 | −0.131339 | ||||||||
\(960\) | 12.2915 | 0.396707 | ||||||||
\(961\) | −29.6206 | −0.955503 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 36.1033 | 1.16341 | ||||||||
\(964\) | −48.3122 | −1.55603 | ||||||||
\(965\) | −4.69941 | −0.151279 | ||||||||
\(966\) | 0.892056 | 0.0287014 | ||||||||
\(967\) | −19.9189 | −0.640549 | −0.320275 | − | 0.947325i | \(-0.603775\pi\) | ||||
−0.320275 | + | 0.947325i | \(0.603775\pi\) | |||||||
\(968\) | 2.99117 | 0.0961400 | ||||||||
\(969\) | −10.9506 | −0.351783 | ||||||||
\(970\) | 3.00917 | 0.0966185 | ||||||||
\(971\) | 17.4305 | 0.559373 | 0.279686 | − | 0.960091i | \(-0.409770\pi\) | ||||
0.279686 | + | 0.960091i | \(0.409770\pi\) | |||||||
\(972\) | 41.0150 | 1.31556 | ||||||||
\(973\) | −9.41378 | −0.301792 | ||||||||
\(974\) | 4.79442 | 0.153623 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.90081 | −0.0608433 | ||||||||
\(977\) | 31.9242 | 1.02135 | 0.510673 | − | 0.859775i | \(-0.329396\pi\) | ||||
0.510673 | + | 0.859775i | \(0.329396\pi\) | |||||||
\(978\) | 2.15351 | 0.0688617 | ||||||||
\(979\) | 5.84640 | 0.186852 | ||||||||
\(980\) | −10.1842 | −0.325323 | ||||||||
\(981\) | −6.56853 | −0.209717 | ||||||||
\(982\) | 4.82454 | 0.153957 | ||||||||
\(983\) | 25.7807 | 0.822278 | 0.411139 | − | 0.911573i | \(-0.365131\pi\) | ||||
0.411139 | + | 0.911573i | \(0.365131\pi\) | |||||||
\(984\) | 21.2372 | 0.677017 | ||||||||
\(985\) | −14.3533 | −0.457334 | ||||||||
\(986\) | 1.32372 | 0.0421557 | ||||||||
\(987\) | −12.8136 | −0.407861 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.99241 | −0.126951 | ||||||||
\(990\) | 2.71832 | 0.0863938 | ||||||||
\(991\) | 16.2633 | 0.516620 | 0.258310 | − | 0.966062i | \(-0.416834\pi\) | ||||
0.258310 | + | 0.966062i | \(0.416834\pi\) | |||||||
\(992\) | −3.99547 | −0.126856 | ||||||||
\(993\) | 90.3815 | 2.86817 | ||||||||
\(994\) | −0.876542 | −0.0278022 | ||||||||
\(995\) | −3.89954 | −0.123624 | ||||||||
\(996\) | −11.6008 | −0.367585 | ||||||||
\(997\) | 48.0580 | 1.52201 | 0.761006 | − | 0.648745i | \(-0.224706\pi\) | ||||
0.761006 | + | 0.648745i | \(0.224706\pi\) | |||||||
\(998\) | −2.75976 | −0.0873587 | ||||||||
\(999\) | −10.6674 | −0.337502 |
(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 | 2873.2.a.n.1.4 | 6 | ||
13.12 | even | 2 | 221.2.a.g.1.3 | ✓ | 6 | ||
39.38 | odd | 2 | 1989.2.a.p.1.4 | 6 | |||
52.51 | odd | 2 | 3536.2.a.bh.1.1 | 6 | |||
65.64 | even | 2 | 5525.2.a.bb.1.4 | 6 | |||
221.220 | even | 2 | 3757.2.a.w.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
221.2.a.g.1.3 | ✓ | 6 | 13.12 | even | 2 | ||
1989.2.a.p.1.4 | 6 | 39.38 | odd | 2 | |||
2873.2.a.n.1.4 | 6 | 1.1 | even | 1 | trivial | ||
3536.2.a.bh.1.1 | 6 | 52.51 | odd | 2 | |||
3757.2.a.w.1.3 | 6 | 221.220 | even | 2 | |||
5525.2.a.bb.1.4 | 6 | 65.64 | even | 2 |