Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6724,2,Mod(1,6724)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6724, 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("6724.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6724 = 2^{2} \cdot 41^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6724.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: | \(53.6914103191\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.25808.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 10x^{2} - 6x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 164) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.31526\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6724.1 |
$q$-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 | 0 | ||||||||
\(3\) | −0.0950939 | −0.0549025 | −0.0274513 | − | 0.999623i | \(-0.508739\pi\) | ||||
−0.0274513 | + | 0.999623i | \(0.508739\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.17025 | 0.523350 | 0.261675 | − | 0.965156i | \(-0.415725\pi\) | ||||
0.261675 | + | 0.965156i | \(0.415725\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.14501 | −1.18870 | −0.594352 | − | 0.804205i | \(-0.702591\pi\) | ||||
−0.594352 | + | 0.804205i | \(0.702591\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.99096 | −0.996986 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.67570 | 0.505241 | 0.252621 | − | 0.967565i | \(-0.418708\pi\) | ||||
0.252621 | + | 0.967565i | \(0.418708\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.63052 | −1.83898 | −0.919488 | − | 0.393118i | \(-0.871396\pi\) | ||||
−0.919488 | + | 0.393118i | \(0.871396\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.111283 | −0.0287332 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.16120 | −1.25178 | −0.625888 | − | 0.779913i | \(-0.715263\pi\) | ||||
−0.625888 | + | 0.779913i | \(0.715263\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.72562 | 1.08413 | 0.542065 | − | 0.840336i | \(-0.317643\pi\) | ||||
0.542065 | + | 0.840336i | \(0.317643\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.299072 | 0.0652628 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.82071 | −1.83925 | −0.919623 | − | 0.392803i | \(-0.871505\pi\) | ||||
−0.919623 | + | 0.392803i | \(0.871505\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.63052 | −0.726104 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.569704 | 0.109640 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.80981 | 0.336074 | 0.168037 | − | 0.985781i | \(-0.446257\pi\) | ||||
0.168037 | + | 0.985781i | \(0.446257\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.65951 | −0.298056 | −0.149028 | − | 0.988833i | \(-0.547614\pi\) | ||||
−0.149028 | + | 0.988833i | \(0.547614\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.159349 | −0.0277390 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.68044 | −0.622108 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.99096 | −0.327311 | −0.163656 | − | 0.986518i | \(-0.552329\pi\) | ||||
−0.163656 | + | 0.986518i | \(0.552329\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.630522 | 0.100964 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.46932 | 0.224069 | 0.112034 | − | 0.993704i | \(-0.464263\pi\) | ||||
0.112034 | + | 0.993704i | \(0.464263\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.50016 | −0.521773 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.53543 | 1.24502 | 0.622510 | − | 0.782612i | \(-0.286113\pi\) | ||||
0.622510 | + | 0.782612i | \(0.286113\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.89112 | 0.413017 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.490799 | 0.0687256 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.35139 | 1.28451 | 0.642256 | − | 0.766490i | \(-0.277999\pi\) | ||||
0.642256 | + | 0.766490i | \(0.277999\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.96098 | 0.264418 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.449377 | −0.0595215 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.82071 | 1.14836 | 0.574179 | − | 0.818730i | \(-0.305321\pi\) | ||||
0.574179 | + | 0.818730i | \(0.305321\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.6305 | 1.61717 | 0.808586 | − | 0.588378i | \(-0.200233\pi\) | ||||
0.808586 | + | 0.588378i | \(0.200233\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.40660 | 1.18512 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.75935 | −0.962429 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.67570 | −1.18207 | −0.591037 | − | 0.806644i | \(-0.701281\pi\) | ||||
−0.591037 | + | 0.806644i | \(0.701281\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.838796 | 0.100979 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.776081 | 0.0921039 | 0.0460519 | − | 0.998939i | \(-0.485336\pi\) | ||||
0.0460519 | + | 0.998939i | \(0.485336\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.33145 | 0.975123 | 0.487561 | − | 0.873089i | \(-0.337887\pi\) | ||||
0.487561 | + | 0.873089i | \(0.337887\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.345241 | 0.0398650 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.27009 | −0.600582 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.915804 | −0.103036 | −0.0515180 | − | 0.998672i | \(-0.516406\pi\) | ||||
−0.0515180 | + | 0.998672i | \(0.516406\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.91870 | 0.990966 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.0998 | −1.10860 | −0.554301 | − | 0.832316i | \(-0.687014\pi\) | ||||
−0.554301 | + | 0.832316i | \(0.687014\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.03988 | −0.655117 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.172102 | −0.0184513 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.44033 | 0.682674 | 0.341337 | − | 0.939941i | \(-0.389120\pi\) | ||||
0.341337 | + | 0.939941i | \(0.389120\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.8531 | 2.18600 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.157809 | 0.0163640 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.53014 | 0.567380 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.32241 | 0.845012 | 0.422506 | − | 0.906360i | \(-0.361150\pi\) | ||||
0.422506 | + | 0.906360i | \(0.361150\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.01193 | −0.503718 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.79173 | −0.974313 | −0.487157 | − | 0.873315i | \(-0.661966\pi\) | ||||
−0.487157 | + | 0.873315i | \(0.661966\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.648608 | −0.0639093 | −0.0319546 | − | 0.999489i | \(-0.510173\pi\) | ||||
−0.0319546 | + | 0.999489i | \(0.510173\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.349988 | 0.0341553 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.8026 | 1.62437 | 0.812186 | − | 0.583399i | \(-0.198278\pi\) | ||||
0.812186 | + | 0.583399i | \(0.198278\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.84969 | −0.368734 | −0.184367 | − | 0.982857i | \(-0.559023\pi\) | ||||
−0.184367 | + | 0.982857i | \(0.559023\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.189328 | 0.0179702 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.65046 | −0.719695 | −0.359848 | − | 0.933011i | \(-0.617171\pi\) | ||||
−0.359848 | + | 0.933011i | \(0.617171\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.3224 | −0.962569 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 19.8316 | 1.83343 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.2321 | 1.48799 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.19204 | −0.744731 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.0998 | −0.903357 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.9206 | 1.32398 | 0.661992 | − | 0.749511i | \(-0.269711\pi\) | ||||
0.661992 | + | 0.749511i | \(0.269711\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.139723 | −0.0123019 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.19019 | 0.366098 | 0.183049 | − | 0.983104i | \(-0.441403\pi\) | ||||
0.183049 | + | 0.983104i | \(0.441403\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.8621 | −1.28871 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.666694 | 0.0573799 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.09984 | −0.350273 | −0.175137 | − | 0.984544i | \(-0.556037\pi\) | ||||
−0.175137 | + | 0.984544i | \(0.556037\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.9819 | −1.01629 | −0.508146 | − | 0.861271i | \(-0.669669\pi\) | ||||
−0.508146 | + | 0.861271i | \(0.669669\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.811668 | −0.0683547 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.1107 | −0.929127 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.11793 | 0.175884 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.274928 | −0.0226756 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.80981 | 0.148266 | 0.0741328 | − | 0.997248i | \(-0.476381\pi\) | ||||
0.0741328 | + | 0.997248i | \(0.476381\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.3561 | 1.73794 | 0.868969 | − | 0.494867i | \(-0.164783\pi\) | ||||
0.868969 | + | 0.494867i | \(0.164783\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15.4369 | 1.24800 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.94203 | −0.155988 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.1107 | −1.04635 | −0.523175 | − | 0.852225i | \(-0.675253\pi\) | ||||
−0.523175 | + | 0.852225i | \(0.675253\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.889261 | −0.0705230 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 27.7413 | 2.18632 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.7808 | 0.844420 | 0.422210 | − | 0.906498i | \(-0.361255\pi\) | ||||
0.422210 | + | 0.906498i | \(0.361255\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.186477 | −0.0145172 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.6757 | −1.05826 | −0.529129 | − | 0.848542i | \(-0.677481\pi\) | ||||
−0.529129 | + | 0.848542i | \(0.677481\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 30.9638 | 2.38183 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.1341 | −1.08086 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.5801 | 0.804387 | 0.402193 | − | 0.915555i | \(-0.368248\pi\) | ||||
0.402193 | + | 0.915555i | \(0.368248\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.4180 | 0.863123 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.838796 | −0.0630478 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.23536 | 0.0923352 | 0.0461676 | − | 0.998934i | \(-0.485299\pi\) | ||||
0.0461676 | + | 0.998934i | \(0.485299\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.90965 | 0.290602 | 0.145301 | − | 0.989387i | \(-0.453585\pi\) | ||||
0.145301 | + | 0.989387i | \(0.453585\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.20109 | −0.0887868 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.32991 | −0.171298 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.64861 | −0.632449 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.79173 | −0.130329 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.31712 | 0.529448 | 0.264724 | − | 0.964324i | \(-0.414719\pi\) | ||||
0.264724 | + | 0.964324i | \(0.414719\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.3009 | 0.957422 | 0.478711 | − | 0.877973i | \(-0.341104\pi\) | ||||
0.478711 | + | 0.877973i | \(0.341104\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.737867 | 0.0528397 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.5692 | −1.10926 | −0.554628 | − | 0.832098i | \(-0.687140\pi\) | ||||
−0.554628 | + | 0.832098i | \(0.687140\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 27.8972 | 1.97758 | 0.988789 | − | 0.149319i | \(-0.0477080\pi\) | ||||
0.988789 | + | 0.149319i | \(0.0477080\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.920100 | 0.0648989 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.69189 | −0.399492 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 26.3824 | 1.83370 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.91870 | 0.547748 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.1484 | −1.24939 | −0.624694 | − | 0.780870i | \(-0.714776\pi\) | ||||
−0.624694 | + | 0.780870i | \(0.714776\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.0738006 | −0.00505673 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.71947 | 0.117267 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.21917 | 0.354300 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.792270 | −0.0535367 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 34.2215 | 2.30199 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.55826 | −0.439174 | −0.219587 | − | 0.975593i | \(-0.570471\pi\) | ||||
−0.219587 | + | 0.975593i | \(0.570471\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.8587 | 0.723916 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.4884 | −1.55898 | −0.779489 | − | 0.626416i | \(-0.784521\pi\) | ||||
−0.779489 | + | 0.626416i | \(0.784521\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.1503 | −0.802915 | −0.401457 | − | 0.915878i | \(-0.631496\pi\) | ||||
−0.401457 | + | 0.915878i | \(0.631496\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.501153 | 0.0329735 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.8422 | 1.43093 | 0.715465 | − | 0.698649i | \(-0.246215\pi\) | ||||
0.715465 | + | 0.698649i | \(0.246215\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.98856 | 0.651582 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.0870874 | 0.00565694 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.5968 | −1.39698 | −0.698490 | − | 0.715620i | \(-0.746144\pi\) | ||||
−0.698490 | + | 0.715620i | \(0.746144\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.6305 | 0.813603 | 0.406802 | − | 0.913516i | \(-0.366644\pi\) | ||||
0.406802 | + | 0.913516i | \(0.366644\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.55723 | −0.164046 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.38332 | 0.216152 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −31.3333 | −1.99369 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.960434 | 0.0608650 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.7702 | 1.31101 | 0.655503 | − | 0.755192i | \(-0.272457\pi\) | ||||
0.655503 | + | 0.755192i | \(0.272457\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.7808 | −0.929263 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.574356 | 0.0359676 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.8207 | −0.924491 | −0.462245 | − | 0.886752i | \(-0.652956\pi\) | ||||
−0.462245 | + | 0.886752i | \(0.652956\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.26159 | 0.389076 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.41307 | −0.335061 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.4175 | −1.13567 | −0.567836 | − | 0.823142i | \(-0.692219\pi\) | ||||
−0.567836 | + | 0.823142i | \(0.692219\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.9434 | 0.672250 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.612437 | −0.0374805 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.8916 | −1.57864 | −0.789318 | − | 0.613984i | \(-0.789566\pi\) | ||||
−0.789318 | + | 0.613984i | \(0.789566\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.5017 | −1.06315 | −0.531576 | − | 0.847010i | \(-0.678400\pi\) | ||||
−0.531576 | + | 0.847010i | \(0.678400\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.98300 | −0.120017 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.08365 | −0.366858 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.77179 | 0.527045 | 0.263523 | − | 0.964653i | \(-0.415116\pi\) | ||||
0.263523 | + | 0.964653i | \(0.415116\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.96351 | 0.297158 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.2215 | −0.967692 | −0.483846 | − | 0.875153i | \(-0.660761\pi\) | ||||
−0.483846 | + | 0.875153i | \(0.660761\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.9819 | −0.712251 | −0.356125 | − | 0.934438i | \(-0.615902\pi\) | ||||
−0.356125 | + | 0.934438i | \(0.615902\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.525883 | −0.0311506 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.63803 | 0.566943 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.791411 | −0.0463933 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.2516 | 0.657323 | 0.328661 | − | 0.944448i | \(-0.393403\pi\) | ||||
0.328661 | + | 0.944448i | \(0.393403\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.3224 | 0.600994 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.954650 | 0.0553944 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 58.4859 | 3.38233 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.62103 | −0.266352 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.931134 | 0.0534922 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.7808 | 0.846348 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.61244 | 0.491538 | 0.245769 | − | 0.969328i | \(-0.420960\pi\) | ||||
0.245769 | + | 0.969328i | \(0.420960\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.0616787 | 0.00350878 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.7575 | −1.80080 | −0.900400 | − | 0.435063i | \(-0.856726\pi\) | ||||
−0.900400 | + | 0.435063i | \(0.856726\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.21777 | −0.125356 | −0.0626778 | − | 0.998034i | \(-0.519964\pi\) | ||||
−0.0626778 | + | 0.998034i | \(0.519964\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 11.0080 | 0.620233 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.3947 | 1.03315 | 0.516574 | − | 0.856243i | \(-0.327207\pi\) | ||||
0.516574 | + | 0.856243i | \(0.327207\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.03269 | 0.169798 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.59783 | −0.0891820 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −24.3899 | −1.35709 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 24.0723 | 1.33529 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.366083 | 0.0202444 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −26.8440 | −1.47996 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.1160 | −0.556027 | −0.278014 | − | 0.960577i | \(-0.589676\pi\) | ||||
−0.278014 | + | 0.960577i | \(0.589676\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.95487 | 0.326325 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.3230 | −0.618639 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.81135 | 0.425511 | 0.212756 | − | 0.977105i | \(-0.431756\pi\) | ||||
0.212756 | + | 0.977105i | \(0.431756\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.727513 | 0.0395131 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.78083 | −0.150590 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.9225 | 0.697749 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.981598 | 0.0528475 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.6281 | 0.838959 | 0.419480 | − | 0.907765i | \(-0.362213\pi\) | ||||
0.419480 | + | 0.907765i | \(0.362213\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.49265 | 0.401073 | 0.200536 | − | 0.979686i | \(-0.435732\pi\) | ||||
0.200536 | + | 0.979686i | \(0.435732\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.77743 | −0.201624 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.4313 | 1.19390 | 0.596949 | − | 0.802279i | \(-0.296380\pi\) | ||||
0.596949 | + | 0.802279i | \(0.296380\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.908206 | 0.0482026 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.54357 | −0.0816944 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.6196 | −0.824372 | −0.412186 | − | 0.911100i | \(-0.635235\pi\) | ||||
−0.412186 | + | 0.911100i | \(0.635235\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.33145 | 0.175340 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.779014 | 0.0408876 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.74985 | 0.510331 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.82790 | −0.199815 | −0.0999073 | − | 0.994997i | \(-0.531855\pi\) | ||||
−0.0999073 | + | 0.994997i | \(0.531855\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −29.4103 | −1.52690 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.1997 | −0.942344 | −0.471172 | − | 0.882041i | \(-0.656169\pi\) | ||||
−0.471172 | + | 0.882041i | \(0.656169\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.960434 | 0.0495966 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.7627 | −0.758311 | −0.379156 | − | 0.925333i | \(-0.623785\pi\) | ||||
−0.379156 | + | 0.925333i | \(0.623785\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.41885 | −0.0726901 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.75406 | −0.242921 | −0.121460 | − | 0.992596i | \(-0.538758\pi\) | ||||
−0.121460 | + | 0.992596i | \(0.538758\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.16730 | −0.314315 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.39467 | −0.223394 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.3804 | 0.729114 | 0.364557 | − | 0.931181i | \(-0.381220\pi\) | ||||
0.364557 | + | 0.931181i | \(0.381220\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 45.5255 | 2.30232 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.398461 | −0.0200997 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.07172 | −0.0539239 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.9311 | 0.548618 | 0.274309 | − | 0.961642i | \(-0.411551\pi\) | ||||
0.274309 | + | 0.961642i | \(0.411551\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.41330 | 0.0707534 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.4132 | 1.51876 | 0.759382 | − | 0.650646i | \(-0.225502\pi\) | ||||
0.759382 | + | 0.650646i | \(0.225502\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.0034 | 0.548118 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.4371 | 0.518622 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.33624 | −0.165371 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.3100 | 0.658136 | 0.329068 | − | 0.944306i | \(-0.393266\pi\) | ||||
0.329068 | + | 0.944306i | \(0.393266\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.389870 | 0.0192309 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −27.7413 | −1.36506 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.8193 | −0.580187 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.13941 | 0.0557970 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.7917 | 0.771476 | 0.385738 | − | 0.922608i | \(-0.373947\pi\) | ||||
0.385738 | + | 0.922608i | \(0.373947\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.4317 | 1.67810 | 0.839050 | − | 0.544054i | \(-0.183111\pi\) | ||||
0.839050 | + | 0.544054i | \(0.183111\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −25.5291 | −1.24127 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 18.7379 | 0.908920 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −39.7232 | −1.92234 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.05656 | 0.0510114 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.69189 | 0.274168 | 0.137084 | − | 0.990559i | \(-0.456227\pi\) | ||||
0.137084 | + | 0.990559i | \(0.456227\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.0034 | −0.624903 | −0.312452 | − | 0.949934i | \(-0.601150\pi\) | ||||
−0.312452 | + | 0.949934i | \(0.601150\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.201402 | −0.00965649 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −41.6833 | −1.99398 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.59593 | −0.457989 | −0.228994 | − | 0.973428i | \(-0.573544\pi\) | ||||
−0.228994 | + | 0.973428i | \(0.573544\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.64720 | −0.411772 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.47072 | −0.117388 | −0.0586938 | − | 0.998276i | \(-0.518694\pi\) | ||||
−0.0586938 | + | 0.998276i | \(0.518694\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.53678 | 0.357278 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.172102 | −0.00814015 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.2324 | 1.66272 | 0.831359 | − | 0.555735i | \(-0.187563\pi\) | ||||
0.831359 | + | 0.555735i | \(0.187563\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.03084 | −0.0954172 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 24.4033 | 1.14404 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.0241 | 1.73191 | 0.865957 | − | 0.500118i | \(-0.166710\pi\) | ||||
0.865957 | + | 0.500118i | \(0.166710\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.94036 | −0.137244 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.6324 | −1.28697 | −0.643484 | − | 0.765460i | \(-0.722512\pi\) | ||||
−0.643484 | + | 0.765460i | \(0.722512\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.1877 | −1.07763 | −0.538813 | − | 0.842425i | \(-0.681127\pi\) | ||||
−0.538813 | + | 0.842425i | \(0.681127\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.184675 | 0.00856412 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.5235 | −1.27364 | −0.636818 | − | 0.771014i | \(-0.719750\pi\) | ||||
−0.636818 | + | 0.771014i | \(0.719750\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 30.4302 | 1.40514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.24675 | 0.0574473 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.46213 | 0.113209 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.1565 | −0.787192 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −27.9696 | −1.28064 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.1088 | −0.507576 | −0.253788 | − | 0.967260i | \(-0.581677\pi\) | ||||
−0.253788 | + | 0.967260i | \(0.581677\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.2011 | 0.601918 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.63803 | −0.120034 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.73927 | 0.442238 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.3933 | −1.42256 | −0.711282 | − | 0.702906i | \(-0.751885\pi\) | ||||
−0.711282 | + | 0.702906i | \(0.751885\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.02519 | −0.0463608 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.9590 | 1.80333 | 0.901663 | − | 0.432440i | \(-0.142347\pi\) | ||||
0.901663 | + | 0.432440i | \(0.142347\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.34081 | −0.420689 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.86520 | −0.263621 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.44079 | −0.109484 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.0951 | −0.720515 | −0.360258 | − | 0.932853i | \(-0.617311\pi\) | ||||
−0.360258 | + | 0.932853i | \(0.617311\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.30048 | 0.0581010 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.97717 | −0.266509 | −0.133254 | − | 0.991082i | \(-0.542543\pi\) | ||||
−0.133254 | + | 0.991082i | \(0.542543\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.4587 | −0.509907 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.94447 | −0.130769 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.5726 | 0.557269 | 0.278634 | − | 0.960397i | \(-0.410118\pi\) | ||||
0.278634 | + | 0.960397i | \(0.410118\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −26.2025 | −1.15913 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.69220 | 0.118864 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.759032 | −0.0334469 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.3028 | 0.629036 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.00610 | −0.0441629 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.6233 | 1.38544 | 0.692722 | − | 0.721205i | \(-0.256411\pi\) | ||||
0.692722 | + | 0.721205i | \(0.256411\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.5405 | −0.941900 | −0.470950 | − | 0.882160i | \(-0.656089\pi\) | ||||
−0.470950 | + | 0.882160i | \(0.656089\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.08579 | −0.0473876 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.56505 | 0.373099 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 54.8049 | 2.38282 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −26.3824 | −1.14490 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.6632 | 0.850115 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.117475 | −0.00506944 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.84463 | 0.208673 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.4927 | 1.35397 | 0.676987 | − | 0.735995i | \(-0.263285\pi\) | ||||
0.676987 | + | 0.735995i | \(0.263285\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.371784 | −0.0159548 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.50509 | −0.192977 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.6861 | 0.756201 | 0.378100 | − | 0.925765i | \(-0.376577\pi\) | ||||
0.378100 | + | 0.925765i | \(0.376577\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −37.7774 | −1.61230 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.55248 | 0.364348 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.88022 | 0.122479 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.221560 | 0.00940472 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.3296 | 0.819021 | 0.409511 | − | 0.912305i | \(-0.365699\pi\) | ||||
0.409511 | + | 0.912305i | \(0.365699\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.74235 | −0.412057 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.822430 | 0.0347230 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −35.7299 | −1.50583 | −0.752917 | − | 0.658115i | \(-0.771354\pi\) | ||||
−0.752917 | + | 0.658115i | \(0.771354\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.95293 | −0.376653 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −28.0494 | −1.17797 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.65187 | 0.195016 | 0.0975082 | − | 0.995235i | \(-0.468913\pi\) | ||||
0.0975082 | + | 0.995235i | \(0.468913\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.6791 | 0.865393 | 0.432697 | − | 0.901540i | \(-0.357562\pi\) | ||||
0.432697 | + | 0.901540i | \(0.357562\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.695813 | −0.0290680 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 32.0238 | 1.33548 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.7808 | 1.03164 | 0.515820 | − | 0.856697i | \(-0.327487\pi\) | ||||
0.515820 | + | 0.856697i | \(0.327487\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.26484 | −0.0525649 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 31.7641 | 1.31780 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.6701 | 0.648989 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 23.2079 | 0.959528 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.4027 | 0.553187 | 0.276594 | − | 0.960987i | \(-0.410794\pi\) | ||||
0.276594 | + | 0.960987i | \(0.410794\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.84219 | −0.323132 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.48053 | 0.0609010 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.83911 | 0.0755233 | 0.0377616 | − | 0.999287i | \(-0.487977\pi\) | ||||
0.0377616 | + | 0.999287i | \(0.487977\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.9955 | 0.778740 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.65285 | −0.108574 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −35.9457 | −1.46870 | −0.734352 | − | 0.678769i | \(-0.762514\pi\) | ||||
−0.734352 | + | 0.678769i | \(0.762514\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.8858 | 1.21907 | 0.609533 | − | 0.792760i | \(-0.291357\pi\) | ||||
0.609533 | + | 0.792760i | \(0.291357\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 28.9396 | 1.17851 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.58671 | −0.389755 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.25015 | 0.172508 | 0.0862541 | − | 0.996273i | \(-0.472510\pi\) | ||||
0.0862541 | + | 0.996273i | \(0.472510\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.541264 | 0.0219331 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −56.5944 | −2.28956 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.35184 | −0.377717 | −0.188859 | − | 0.982004i | \(-0.560479\pi\) | ||||
−0.188859 | + | 0.982004i | \(0.560479\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.6019 | 0.507332 | 0.253666 | − | 0.967292i | \(-0.418364\pi\) | ||||
0.253666 | + | 0.967292i | \(0.418364\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.54018 | −0.102098 | −0.0510491 | − | 0.998696i | \(-0.516257\pi\) | ||||
−0.0510491 | + | 0.998696i | \(0.516257\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.02519 | −0.201654 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −20.2549 | −0.811497 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.33331 | 0.253332 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.753020 | −0.0300727 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.2757 | 0.409720 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 48.0057 | 1.91108 | 0.955538 | − | 0.294867i | \(-0.0952752\pi\) | ||||
0.955538 | + | 0.294867i | \(0.0952752\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.72580 | 0.0685945 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17.4607 | 0.692908 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.1696 | −0.759528 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.32123 | −0.0918262 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.02148 | −0.0403461 | −0.0201730 | − | 0.999797i | \(-0.506422\pi\) | ||||
−0.0201730 | + | 0.999797i | \(0.506422\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.40606 | 0.331503 | 0.165751 | − | 0.986168i | \(-0.446995\pi\) | ||||
0.165751 | + | 0.986168i | \(0.446995\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.163511 | −0.00643823 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.86778 | 0.230686 | 0.115343 | − | 0.993326i | \(-0.463203\pi\) | ||||
0.115343 | + | 0.993326i | \(0.463203\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.7808 | 0.580198 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.496312 | −0.0194520 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −37.5749 | −1.47042 | −0.735209 | − | 0.677841i | \(-0.762916\pi\) | ||||
−0.735209 | + | 0.677841i | \(0.762916\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.90355 | 0.191598 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −24.9190 | −0.972183 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.8360 | 0.655839 | 0.327919 | − | 0.944706i | \(-0.393653\pi\) | ||||
0.327919 | + | 0.944706i | \(0.393653\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.84983 | 0.188637 | 0.0943183 | − | 0.995542i | \(-0.469933\pi\) | ||||
0.0943183 | + | 0.995542i | \(0.469933\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.25426 | −0.126385 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −17.3924 | −0.674447 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.9638 | −0.618122 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.623651 | 0.0241117 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.1649 | 0.817062 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.24065 | −0.240559 | −0.120280 | − | 0.992740i | \(-0.538379\pi\) | ||||
−0.120280 | + | 0.992740i | \(0.538379\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.06832 | −0.0796098 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.3566 | −1.12827 | −0.564134 | − | 0.825683i | \(-0.690790\pi\) | ||||
−0.564134 | + | 0.825683i | \(0.690790\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26.1741 | −1.00447 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.23360 | 0.0855918 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.6861 | 0.982849 | 0.491425 | − | 0.870920i | \(-0.336476\pi\) | ||||
0.491425 | + | 0.870920i | \(0.336476\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.79783 | −0.183316 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.15542 | 0.0440820 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −62.0046 | −2.36219 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.77128 | −0.333675 | −0.166838 | − | 0.985984i | \(-0.553356\pi\) | ||||
−0.166838 | + | 0.985984i | \(0.553356\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.7626 | 0.598772 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.0218 | −0.531877 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.07706 | −0.0785616 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.1075 | −0.570602 | −0.285301 | − | 0.958438i | \(-0.592094\pi\) | ||||
−0.285301 | + | 0.958438i | \(0.592094\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.40850 | −0.354848 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.949851 | −0.0357735 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 30.7951 | 1.15817 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.0132 | 0.451165 | 0.225583 | − | 0.974224i | \(-0.427571\pi\) | ||||
0.225583 | + | 0.974224i | \(0.427571\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.73913 | 0.102725 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.6380 | 0.548198 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.0023 | −0.486259 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.05372 | 0.0766977 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.27778 | 0.0849468 | 0.0424734 | − | 0.999098i | \(-0.486476\pi\) | ||||
0.0424734 | + | 0.999098i | \(0.486476\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.03988 | 0.0759692 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.20109 | −0.0446689 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.57056 | −0.244025 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.71952 | −0.286301 | −0.143151 | − | 0.989701i | \(-0.545723\pi\) | ||||
−0.143151 | + | 0.989701i | \(0.545723\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.5129 | −0.981960 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.58345 | −0.280484 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.2753 | 1.22905 | 0.614526 | − | 0.788896i | \(-0.289347\pi\) | ||||
0.614526 | + | 0.788896i | \(0.289347\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.321733 | −0.0118673 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.2135 | −0.597233 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 48.0057 | 1.76592 | 0.882959 | − | 0.469450i | \(-0.155548\pi\) | ||||
0.882959 | + | 0.469450i | \(0.155548\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.97961 | 0.109459 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 43.1345 | 1.58245 | 0.791226 | − | 0.611524i | \(-0.209443\pi\) | ||||
0.791226 | + | 0.611524i | \(0.209443\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.11793 | 0.0775948 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 30.2082 | 1.10526 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −52.8445 | −1.93090 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.46883 | 0.236051 | 0.118025 | − | 0.993011i | \(-0.462344\pi\) | ||||
0.118025 | + | 0.993011i | \(0.462344\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.97512 | −0.0719775 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.9920 | 0.909550 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.5531 | 1.43758 | 0.718790 | − | 0.695227i | \(-0.244696\pi\) | ||||
0.718790 | + | 0.695227i | \(0.244696\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.40557 | 0.0510189 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.5130 | 1.03360 | 0.516799 | − | 0.856107i | \(-0.327124\pi\) | ||||
0.516799 | + | 0.856107i | \(0.327124\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.1073 | 0.438315 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 18.0650 | 0.653142 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −58.4859 | −2.11180 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 49.7184 | 1.79289 | 0.896445 | − | 0.443154i | \(-0.146141\pi\) | ||||
0.896445 | + | 0.443154i | \(0.146141\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.40936 | 0.0507569 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.2539 | 0.872351 | 0.436175 | − | 0.899862i | \(-0.356333\pi\) | ||||
0.436175 | + | 0.899862i | \(0.356333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.02488 | 0.216420 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.595439 | −0.0213613 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.30048 | 0.0465347 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.03106 | 0.0368470 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.3428 | −0.547608 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.907346 | 0.0323434 | 0.0161717 | − | 0.999869i | \(-0.494852\pi\) | ||||
0.0161717 | + | 0.999869i | \(0.494852\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.75139 | 0.0623512 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.0608 | 0.855504 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −83.7470 | −2.97394 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.04065 | −0.0369082 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32.4934 | −1.15098 | −0.575488 | − | 0.817810i | \(-0.695188\pi\) | ||||
−0.575488 | + | 0.817810i | \(0.695188\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −44.0531 | −1.55849 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.2628 | −0.680616 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.9610 | 0.492672 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 32.4641 | 1.14421 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.46213 | 0.0866711 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.07804 | 0.0730602 | 0.0365301 | − | 0.999333i | \(-0.488370\pi\) | ||||
0.0365301 | + | 0.999333i | \(0.488370\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.7518 | −0.482893 | −0.241446 | − | 0.970414i | \(-0.577622\pi\) | ||||
−0.241446 | + | 0.970414i | \(0.577622\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.66431 | 0.0583697 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.6162 | 0.441927 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.94344 | 0.242920 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −62.3707 | −2.17941 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.76979 | 0.236267 | 0.118134 | − | 0.992998i | \(-0.462309\pi\) | ||||
0.118134 | + | 0.992998i | \(0.462309\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.3575 | −0.779335 | −0.389667 | − | 0.920956i | \(-0.627410\pi\) | ||||
−0.389667 | + | 0.920956i | \(0.627410\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.578518 | 0.0201414 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.1160 | −0.908143 | −0.454072 | − | 0.890965i | \(-0.650029\pi\) | ||||
−0.454072 | + | 0.890965i | \(0.650029\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.7540 | −0.686085 | −0.343043 | − | 0.939320i | \(-0.611458\pi\) | ||||
−0.343043 | + | 0.939320i | \(0.611458\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.834144 | −0.0289361 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.9216 | −0.517004 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.0039 | −0.553839 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.945427 | −0.0326787 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.8188 | −0.718745 | −0.359373 | − | 0.933194i | \(-0.617009\pi\) | ||||
−0.359373 | + | 0.933194i | \(0.617009\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.7246 | −0.887054 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.54256 | 0.0531287 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 36.2353 | 1.24653 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.7641 | 0.885265 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.13941 | 0.0391044 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.5617 | 0.602006 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.6666 | 1.66631 | 0.833157 | − | 0.553037i | \(-0.186531\pi\) | ||||
0.833157 | + | 0.553037i | \(0.186531\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.5404 | −0.565670 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.8515 | −0.439001 | −0.219500 | − | 0.975612i | \(-0.570443\pi\) | ||||
−0.219500 | + | 0.975612i | \(0.570443\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.60904 | −0.0548998 | −0.0274499 | − | 0.999623i | \(-0.508739\pi\) | ||||
−0.0274499 | + | 0.999623i | \(0.508739\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46.0494 | −1.56754 | −0.783770 | − | 0.621052i | \(-0.786706\pi\) | ||||
−0.783770 | + | 0.621052i | \(0.786706\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.3813 | 0.420976 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.916518 | −0.0311266 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.53461 | −0.0520581 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 64.1549 | 2.17381 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −24.8920 | −0.842465 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 31.7641 | 1.07382 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.63392 | 0.122709 | 0.0613543 | − | 0.998116i | \(-0.480458\pi\) | ||||
0.0613543 | + | 0.998116i | \(0.480458\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.06995 | −0.0360887 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.2426 | 0.951519 | 0.475759 | − | 0.879575i | \(-0.342173\pi\) | ||||
0.475759 | + | 0.879575i | \(0.342173\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.23962 | 0.142674 | 0.0713372 | − | 0.997452i | \(-0.477273\pi\) | ||||
0.0713372 | + | 0.997452i | \(0.477273\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.981598 | −0.0329961 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 46.4003 | 1.55797 | 0.778984 | − | 0.627043i | \(-0.215735\pi\) | ||||
0.778984 | + | 0.627043i | \(0.215735\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −46.9254 | −1.57383 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14.9450 | 0.500677 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 40.3352 | 1.34976 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.44568 | 0.0483237 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.56166 | −0.185698 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.00339 | −0.100169 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −48.2644 | −1.60792 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.439432 | 0.0146234 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.57526 | 0.152087 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.0358 | −0.897708 | −0.448854 | − | 0.893605i | \(-0.648168\pi\) | ||||
−0.448854 | + | 0.893605i | \(0.648168\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 29.2866 | 0.971376 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.3500 | −1.40312 | −0.701559 | − | 0.712612i | \(-0.747512\pi\) | ||||
−0.701559 | + | 0.712612i | \(0.747512\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.9243 | −0.560111 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.40557 | −0.0464666 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.1782 | −0.435183 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.17400 | −0.269635 | −0.134818 | − | 0.990870i | \(-0.543045\pi\) | ||||
−0.134818 | + | 0.990870i | \(0.543045\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.818991 | −0.0269867 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.14582 | −0.169377 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.22821 | 0.237662 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.93996 | 0.0637166 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −42.2596 | −1.38649 | −0.693247 | − | 0.720700i | \(-0.743820\pi\) | ||||
−0.693247 | + | 0.720700i | \(0.743820\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.6623 | 0.447764 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.01994 | 0.0988684 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.1210 | −0.330992 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.16600 | −0.0380917 | −0.0190458 | − | 0.999819i | \(-0.506063\pi\) | ||||
−0.0190458 | + | 0.999819i | \(0.506063\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.210896 | 0.00688234 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.93864 | 0.160995 | 0.0804975 | − | 0.996755i | \(-0.474349\pi\) | ||||
0.0804975 | + | 0.996755i | \(0.474349\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.09676 | −0.0682077 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.3210 | 0.822822 | 0.411411 | − | 0.911450i | \(-0.365036\pi\) | ||||
0.411411 | + | 0.911450i | \(0.365036\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −55.2419 | −1.79323 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.74922 | −0.0567224 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −47.6143 | −1.54238 | −0.771189 | − | 0.636606i | \(-0.780338\pi\) | ||||
−0.771189 | + | 0.636606i | \(0.780338\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.56283 | 0.277087 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.288391 | −0.00932235 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.8941 | 0.416371 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.2460 | −0.911163 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −50.2559 | −1.61947 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.5654 | 0.501067 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.9763 | 0.835342 | 0.417671 | − | 0.908598i | \(-0.362847\pi\) | ||||
0.417671 | + | 0.908598i | \(0.362847\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.31933 | 0.0745076 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 55.8687 | 1.79291 | 0.896457 | − | 0.443132i | \(-0.146133\pi\) | ||||
0.896457 | + | 0.443132i | \(0.146133\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 37.6833 | 1.20807 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.28913 | −0.0733107 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42.5241 | 1.36047 | 0.680233 | − | 0.732996i | \(-0.261879\pi\) | ||||
0.680233 | + | 0.732996i | \(0.261879\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.7920 | 0.344915 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.5143 | 0.367622 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 50.8977 | 1.62338 | 0.811692 | − | 0.584086i | \(-0.198547\pi\) | ||||
0.811692 | + | 0.584086i | \(0.198547\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.2198 | −0.580530 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.55271 | 0.0812535 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.9604 | −0.412118 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.7147 | 0.880387 | 0.440194 | − | 0.897903i | \(-0.354910\pi\) | ||||
0.440194 | + | 0.897903i | \(0.354910\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.961973 | 0.0305273 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 32.6466 | 1.03497 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.3480 | 0.707768 | 0.353884 | − | 0.935289i | \(-0.384861\pi\) | ||||
0.353884 | + | 0.935289i | \(0.384861\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.13426 | −0.0358863 |
(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 | 6724.2.a.c.1.3 | 4 | ||
41.40 | even | 2 | 164.2.a.a.1.2 | ✓ | 4 | ||
123.122 | odd | 2 | 1476.2.a.g.1.3 | 4 | |||
164.163 | odd | 2 | 656.2.a.i.1.3 | 4 | |||
205.122 | odd | 4 | 4100.2.d.c.1149.4 | 8 | |||
205.163 | odd | 4 | 4100.2.d.c.1149.5 | 8 | |||
205.204 | even | 2 | 4100.2.a.c.1.3 | 4 | |||
287.286 | odd | 2 | 8036.2.a.i.1.3 | 4 | |||
328.163 | odd | 2 | 2624.2.a.y.1.2 | 4 | |||
328.245 | even | 2 | 2624.2.a.v.1.3 | 4 | |||
492.491 | even | 2 | 5904.2.a.bp.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
164.2.a.a.1.2 | ✓ | 4 | 41.40 | even | 2 | ||
656.2.a.i.1.3 | 4 | 164.163 | odd | 2 | |||
1476.2.a.g.1.3 | 4 | 123.122 | odd | 2 | |||
2624.2.a.v.1.3 | 4 | 328.245 | even | 2 | |||
2624.2.a.y.1.2 | 4 | 328.163 | odd | 2 | |||
4100.2.a.c.1.3 | 4 | 205.204 | even | 2 | |||
4100.2.d.c.1149.4 | 8 | 205.122 | odd | 4 | |||
4100.2.d.c.1149.5 | 8 | 205.163 | odd | 4 | |||
5904.2.a.bp.1.3 | 4 | 492.491 | even | 2 | |||
6724.2.a.c.1.3 | 4 | 1.1 | even | 1 | trivial | ||
8036.2.a.i.1.3 | 4 | 287.286 | odd | 2 |