Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,2,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, 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("1859.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.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: | \(14.8441897358\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.14442 | 1.51634 | 0.758169 | − | 0.652058i | \(-0.226094\pi\) | ||||
0.758169 | + | 0.652058i | \(0.226094\pi\) | |||||||
\(3\) | −1.72478 | −0.995801 | −0.497900 | − | 0.867234i | \(-0.665895\pi\) | ||||
−0.497900 | + | 0.867234i | \(0.665895\pi\) | |||||||
\(4\) | 2.59856 | 1.29928 | ||||||||
\(5\) | −3.54668 | −1.58612 | −0.793061 | − | 0.609142i | \(-0.791514\pi\) | ||||
−0.793061 | + | 0.609142i | \(0.791514\pi\) | |||||||
\(6\) | −3.69866 | −1.50997 | ||||||||
\(7\) | −2.57025 | −0.971462 | −0.485731 | − | 0.874108i | \(-0.661447\pi\) | ||||
−0.485731 | + | 0.874108i | \(0.661447\pi\) | |||||||
\(8\) | 1.28356 | 0.453808 | ||||||||
\(9\) | −0.0251423 | −0.00838075 | ||||||||
\(10\) | −7.60558 | −2.40510 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −4.48193 | −1.29382 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −5.51170 | −1.47306 | ||||||||
\(15\) | 6.11723 | 1.57946 | ||||||||
\(16\) | −2.44461 | −0.611153 | ||||||||
\(17\) | 4.72512 | 1.14601 | 0.573005 | − | 0.819552i | \(-0.305778\pi\) | ||||
0.573005 | + | 0.819552i | \(0.305778\pi\) | |||||||
\(18\) | −0.0539157 | −0.0127080 | ||||||||
\(19\) | 4.99317 | 1.14551 | 0.572756 | − | 0.819726i | \(-0.305874\pi\) | ||||
0.572756 | + | 0.819726i | \(0.305874\pi\) | |||||||
\(20\) | −9.21624 | −2.06082 | ||||||||
\(21\) | 4.43311 | 0.967383 | ||||||||
\(22\) | 2.14442 | 0.457193 | ||||||||
\(23\) | 4.05972 | 0.846510 | 0.423255 | − | 0.906011i | \(-0.360887\pi\) | ||||
0.423255 | + | 0.906011i | \(0.360887\pi\) | |||||||
\(24\) | −2.21386 | −0.451902 | ||||||||
\(25\) | 7.57891 | 1.51578 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.21770 | 1.00415 | ||||||||
\(28\) | −6.67894 | −1.26220 | ||||||||
\(29\) | 7.00199 | 1.30024 | 0.650118 | − | 0.759833i | \(-0.274719\pi\) | ||||
0.650118 | + | 0.759833i | \(0.274719\pi\) | |||||||
\(30\) | 13.1179 | 2.39500 | ||||||||
\(31\) | −5.08275 | −0.912889 | −0.456445 | − | 0.889752i | \(-0.650877\pi\) | ||||
−0.456445 | + | 0.889752i | \(0.650877\pi\) | |||||||
\(32\) | −7.80941 | −1.38052 | ||||||||
\(33\) | −1.72478 | −0.300245 | ||||||||
\(34\) | 10.1327 | 1.73774 | ||||||||
\(35\) | 9.11584 | 1.54086 | ||||||||
\(36\) | −0.0653336 | −0.0108889 | ||||||||
\(37\) | −5.18091 | −0.851737 | −0.425868 | − | 0.904785i | \(-0.640031\pi\) | ||||
−0.425868 | + | 0.904785i | \(0.640031\pi\) | |||||||
\(38\) | 10.7075 | 1.73698 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.55238 | −0.719795 | ||||||||
\(41\) | 1.93123 | 0.301608 | 0.150804 | − | 0.988564i | \(-0.451814\pi\) | ||||
0.150804 | + | 0.988564i | \(0.451814\pi\) | |||||||
\(42\) | 9.50646 | 1.46688 | ||||||||
\(43\) | −6.58494 | −1.00419 | −0.502097 | − | 0.864811i | \(-0.667438\pi\) | ||||
−0.502097 | + | 0.864811i | \(0.667438\pi\) | |||||||
\(44\) | 2.59856 | 0.391747 | ||||||||
\(45\) | 0.0891714 | 0.0132929 | ||||||||
\(46\) | 8.70576 | 1.28359 | ||||||||
\(47\) | 12.6416 | 1.84397 | 0.921983 | − | 0.387231i | \(-0.126568\pi\) | ||||
0.921983 | + | 0.387231i | \(0.126568\pi\) | |||||||
\(48\) | 4.21641 | 0.608587 | ||||||||
\(49\) | −0.393826 | −0.0562608 | ||||||||
\(50\) | 16.2524 | 2.29844 | ||||||||
\(51\) | −8.14978 | −1.14120 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.48415 | −0.615945 | −0.307972 | − | 0.951395i | \(-0.599650\pi\) | ||||
−0.307972 | + | 0.951395i | \(0.599650\pi\) | |||||||
\(54\) | 11.1890 | 1.52262 | ||||||||
\(55\) | −3.54668 | −0.478234 | ||||||||
\(56\) | −3.29908 | −0.440857 | ||||||||
\(57\) | −8.61211 | −1.14070 | ||||||||
\(58\) | 15.0152 | 1.97160 | ||||||||
\(59\) | 9.21857 | 1.20016 | 0.600078 | − | 0.799941i | \(-0.295136\pi\) | ||||
0.600078 | + | 0.799941i | \(0.295136\pi\) | |||||||
\(60\) | 15.8960 | 2.05216 | ||||||||
\(61\) | 14.7423 | 1.88756 | 0.943778 | − | 0.330580i | \(-0.107244\pi\) | ||||
0.943778 | + | 0.330580i | \(0.107244\pi\) | |||||||
\(62\) | −10.8996 | −1.38425 | ||||||||
\(63\) | 0.0646218 | 0.00814159 | ||||||||
\(64\) | −11.8575 | −1.48218 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.69866 | −0.455273 | ||||||||
\(67\) | −13.2163 | −1.61463 | −0.807315 | − | 0.590121i | \(-0.799080\pi\) | ||||
−0.807315 | + | 0.590121i | \(0.799080\pi\) | |||||||
\(68\) | 12.2785 | 1.48899 | ||||||||
\(69\) | −7.00211 | −0.842955 | ||||||||
\(70\) | 19.5482 | 2.33646 | ||||||||
\(71\) | −4.22483 | −0.501395 | −0.250697 | − | 0.968065i | \(-0.580660\pi\) | ||||
−0.250697 | + | 0.968065i | \(0.580660\pi\) | |||||||
\(72\) | −0.0322717 | −0.00380325 | ||||||||
\(73\) | −0.634771 | −0.0742943 | −0.0371472 | − | 0.999310i | \(-0.511827\pi\) | ||||
−0.0371472 | + | 0.999310i | \(0.511827\pi\) | |||||||
\(74\) | −11.1101 | −1.29152 | ||||||||
\(75\) | −13.0719 | −1.50942 | ||||||||
\(76\) | 12.9750 | 1.48834 | ||||||||
\(77\) | −2.57025 | −0.292907 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.2751 | 1.71859 | 0.859293 | − | 0.511484i | \(-0.170904\pi\) | ||||
0.859293 | + | 0.511484i | \(0.170904\pi\) | |||||||
\(80\) | 8.67025 | 0.969363 | ||||||||
\(81\) | −8.92394 | −0.991549 | ||||||||
\(82\) | 4.14139 | 0.457340 | ||||||||
\(83\) | 2.96049 | 0.324956 | 0.162478 | − | 0.986712i | \(-0.448051\pi\) | ||||
0.162478 | + | 0.986712i | \(0.448051\pi\) | |||||||
\(84\) | 11.5197 | 1.25690 | ||||||||
\(85\) | −16.7585 | −1.81771 | ||||||||
\(86\) | −14.1209 | −1.52270 | ||||||||
\(87\) | −12.0769 | −1.29478 | ||||||||
\(88\) | 1.28356 | 0.136828 | ||||||||
\(89\) | −11.2939 | −1.19715 | −0.598576 | − | 0.801066i | \(-0.704266\pi\) | ||||
−0.598576 | + | 0.801066i | \(0.704266\pi\) | |||||||
\(90\) | 0.191221 | 0.0201565 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 10.5494 | 1.09985 | ||||||||
\(93\) | 8.76662 | 0.909056 | ||||||||
\(94\) | 27.1089 | 2.79607 | ||||||||
\(95\) | −17.7092 | −1.81692 | ||||||||
\(96\) | 13.4695 | 1.37473 | ||||||||
\(97\) | 1.28597 | 0.130571 | 0.0652854 | − | 0.997867i | \(-0.479204\pi\) | ||||
0.0652854 | + | 0.997867i | \(0.479204\pi\) | |||||||
\(98\) | −0.844529 | −0.0853103 | ||||||||
\(99\) | −0.0251423 | −0.00252689 | ||||||||
\(100\) | 19.6942 | 1.96942 | ||||||||
\(101\) | −0.669816 | −0.0666492 | −0.0333246 | − | 0.999445i | \(-0.510610\pi\) | ||||
−0.0333246 | + | 0.999445i | \(0.510610\pi\) | |||||||
\(102\) | −17.4766 | −1.73044 | ||||||||
\(103\) | −8.63085 | −0.850423 | −0.425212 | − | 0.905094i | \(-0.639800\pi\) | ||||
−0.425212 | + | 0.905094i | \(0.639800\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −15.7228 | −1.53439 | ||||||||
\(106\) | −9.61592 | −0.933980 | ||||||||
\(107\) | −11.1760 | −1.08043 | −0.540214 | − | 0.841528i | \(-0.681657\pi\) | ||||
−0.540214 | + | 0.841528i | \(0.681657\pi\) | |||||||
\(108\) | 13.5585 | 1.30467 | ||||||||
\(109\) | 13.3313 | 1.27690 | 0.638452 | − | 0.769662i | \(-0.279575\pi\) | ||||
0.638452 | + | 0.769662i | \(0.279575\pi\) | |||||||
\(110\) | −7.60558 | −0.725164 | ||||||||
\(111\) | 8.93592 | 0.848160 | ||||||||
\(112\) | 6.28326 | 0.593712 | ||||||||
\(113\) | −2.50302 | −0.235464 | −0.117732 | − | 0.993045i | \(-0.537562\pi\) | ||||
−0.117732 | + | 0.993045i | \(0.537562\pi\) | |||||||
\(114\) | −18.4680 | −1.72969 | ||||||||
\(115\) | −14.3985 | −1.34267 | ||||||||
\(116\) | 18.1951 | 1.68937 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 19.7685 | 1.81984 | ||||||||
\(119\) | −12.1447 | −1.11330 | ||||||||
\(120\) | 7.85185 | 0.716772 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 31.6137 | 2.86217 | ||||||||
\(123\) | −3.33095 | −0.300342 | ||||||||
\(124\) | −13.2078 | −1.18610 | ||||||||
\(125\) | −9.14657 | −0.818094 | ||||||||
\(126\) | 0.138577 | 0.0123454 | ||||||||
\(127\) | 4.54101 | 0.402949 | 0.201475 | − | 0.979494i | \(-0.435427\pi\) | ||||
0.201475 | + | 0.979494i | \(0.435427\pi\) | |||||||
\(128\) | −9.80864 | −0.866969 | ||||||||
\(129\) | 11.3576 | 0.999978 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.7762 | 1.29100 | 0.645501 | − | 0.763759i | \(-0.276649\pi\) | ||||
0.645501 | + | 0.763759i | \(0.276649\pi\) | |||||||
\(132\) | −4.48193 | −0.390102 | ||||||||
\(133\) | −12.8337 | −1.11282 | ||||||||
\(134\) | −28.3414 | −2.44832 | ||||||||
\(135\) | −18.5055 | −1.59270 | ||||||||
\(136\) | 6.06499 | 0.520068 | ||||||||
\(137\) | 21.8110 | 1.86344 | 0.931719 | − | 0.363181i | \(-0.118309\pi\) | ||||
0.931719 | + | 0.363181i | \(0.118309\pi\) | |||||||
\(138\) | −15.0155 | −1.27820 | ||||||||
\(139\) | 9.65198 | 0.818671 | 0.409335 | − | 0.912384i | \(-0.365761\pi\) | ||||
0.409335 | + | 0.912384i | \(0.365761\pi\) | |||||||
\(140\) | 23.6880 | 2.00200 | ||||||||
\(141\) | −21.8039 | −1.83622 | ||||||||
\(142\) | −9.05983 | −0.760284 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.0614631 | 0.00512192 | ||||||||
\(145\) | −24.8338 | −2.06233 | ||||||||
\(146\) | −1.36122 | −0.112655 | ||||||||
\(147\) | 0.679262 | 0.0560245 | ||||||||
\(148\) | −13.4629 | −1.10664 | ||||||||
\(149\) | −0.517117 | −0.0423639 | −0.0211820 | − | 0.999776i | \(-0.506743\pi\) | ||||
−0.0211820 | + | 0.999776i | \(0.506743\pi\) | |||||||
\(150\) | −28.0318 | −2.28879 | ||||||||
\(151\) | 7.42259 | 0.604042 | 0.302021 | − | 0.953301i | \(-0.402339\pi\) | ||||
0.302021 | + | 0.953301i | \(0.402339\pi\) | |||||||
\(152\) | 6.40905 | 0.519843 | ||||||||
\(153\) | −0.118800 | −0.00960442 | ||||||||
\(154\) | −5.51170 | −0.444146 | ||||||||
\(155\) | 18.0269 | 1.44795 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.9738 | 1.59409 | 0.797043 | − | 0.603923i | \(-0.206396\pi\) | ||||
0.797043 | + | 0.603923i | \(0.206396\pi\) | |||||||
\(158\) | 32.7564 | 2.60596 | ||||||||
\(159\) | 7.73416 | 0.613359 | ||||||||
\(160\) | 27.6975 | 2.18968 | ||||||||
\(161\) | −10.4345 | −0.822353 | ||||||||
\(162\) | −19.1367 | −1.50352 | ||||||||
\(163\) | 11.3102 | 0.885884 | 0.442942 | − | 0.896550i | \(-0.353935\pi\) | ||||
0.442942 | + | 0.896550i | \(0.353935\pi\) | |||||||
\(164\) | 5.01842 | 0.391873 | ||||||||
\(165\) | 6.11723 | 0.476226 | ||||||||
\(166\) | 6.34854 | 0.492742 | ||||||||
\(167\) | 0.366013 | 0.0283230 | 0.0141615 | − | 0.999900i | \(-0.495492\pi\) | ||||
0.0141615 | + | 0.999900i | \(0.495492\pi\) | |||||||
\(168\) | 5.69017 | 0.439006 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −35.9373 | −2.75626 | ||||||||
\(171\) | −0.125540 | −0.00960025 | ||||||||
\(172\) | −17.1114 | −1.30473 | ||||||||
\(173\) | 17.3822 | 1.32154 | 0.660771 | − | 0.750587i | \(-0.270229\pi\) | ||||
0.660771 | + | 0.750587i | \(0.270229\pi\) | |||||||
\(174\) | −25.8980 | −1.96332 | ||||||||
\(175\) | −19.4797 | −1.47253 | ||||||||
\(176\) | −2.44461 | −0.184270 | ||||||||
\(177\) | −15.9000 | −1.19512 | ||||||||
\(178\) | −24.2189 | −1.81528 | ||||||||
\(179\) | −5.97206 | −0.446373 | −0.223187 | − | 0.974776i | \(-0.571646\pi\) | ||||
−0.223187 | + | 0.974776i | \(0.571646\pi\) | |||||||
\(180\) | 0.231717 | 0.0172712 | ||||||||
\(181\) | 15.3470 | 1.14073 | 0.570366 | − | 0.821391i | \(-0.306801\pi\) | ||||
0.570366 | + | 0.821391i | \(0.306801\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −25.4272 | −1.87963 | ||||||||
\(184\) | 5.21091 | 0.384153 | ||||||||
\(185\) | 18.3750 | 1.35096 | ||||||||
\(186\) | 18.7994 | 1.37844 | ||||||||
\(187\) | 4.72512 | 0.345535 | ||||||||
\(188\) | 32.8499 | 2.39583 | ||||||||
\(189\) | −13.4108 | −0.975490 | ||||||||
\(190\) | −37.9760 | −2.75507 | ||||||||
\(191\) | −7.43795 | −0.538191 | −0.269095 | − | 0.963114i | \(-0.586725\pi\) | ||||
−0.269095 | + | 0.963114i | \(0.586725\pi\) | |||||||
\(192\) | 20.4515 | 1.47596 | ||||||||
\(193\) | 10.1737 | 0.732316 | 0.366158 | − | 0.930553i | \(-0.380673\pi\) | ||||
0.366158 | + | 0.930553i | \(0.380673\pi\) | |||||||
\(194\) | 2.75767 | 0.197989 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.02338 | −0.0730985 | ||||||||
\(197\) | −8.87640 | −0.632417 | −0.316209 | − | 0.948690i | \(-0.602410\pi\) | ||||
−0.316209 | + | 0.948690i | \(0.602410\pi\) | |||||||
\(198\) | −0.0539157 | −0.00383162 | ||||||||
\(199\) | 3.08077 | 0.218390 | 0.109195 | − | 0.994020i | \(-0.465173\pi\) | ||||
0.109195 | + | 0.994020i | \(0.465173\pi\) | |||||||
\(200\) | 9.72801 | 0.687874 | ||||||||
\(201\) | 22.7952 | 1.60785 | ||||||||
\(202\) | −1.43637 | −0.101063 | ||||||||
\(203\) | −17.9969 | −1.26313 | ||||||||
\(204\) | −21.1777 | −1.48273 | ||||||||
\(205\) | −6.84946 | −0.478387 | ||||||||
\(206\) | −18.5082 | −1.28953 | ||||||||
\(207\) | −0.102071 | −0.00709439 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.99317 | 0.345385 | ||||||||
\(210\) | −33.7163 | −2.32665 | ||||||||
\(211\) | 16.3487 | 1.12549 | 0.562744 | − | 0.826631i | \(-0.309746\pi\) | ||||
0.562744 | + | 0.826631i | \(0.309746\pi\) | |||||||
\(212\) | −11.6523 | −0.800284 | ||||||||
\(213\) | 7.28689 | 0.499289 | ||||||||
\(214\) | −23.9662 | −1.63829 | ||||||||
\(215\) | 23.3547 | 1.59278 | ||||||||
\(216\) | 6.69724 | 0.455690 | ||||||||
\(217\) | 13.0639 | 0.886838 | ||||||||
\(218\) | 28.5879 | 1.93622 | ||||||||
\(219\) | 1.09484 | 0.0739823 | ||||||||
\(220\) | −9.21624 | −0.621359 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 19.1624 | 1.28610 | ||||||||
\(223\) | 9.12661 | 0.611163 | 0.305581 | − | 0.952166i | \(-0.401149\pi\) | ||||
0.305581 | + | 0.952166i | \(0.401149\pi\) | |||||||
\(224\) | 20.0721 | 1.34113 | ||||||||
\(225\) | −0.190551 | −0.0127034 | ||||||||
\(226\) | −5.36754 | −0.357044 | ||||||||
\(227\) | −11.6168 | −0.771032 | −0.385516 | − | 0.922701i | \(-0.625977\pi\) | ||||
−0.385516 | + | 0.922701i | \(0.625977\pi\) | |||||||
\(228\) | −22.3791 | −1.48209 | ||||||||
\(229\) | −1.87102 | −0.123640 | −0.0618202 | − | 0.998087i | \(-0.519691\pi\) | ||||
−0.0618202 | + | 0.998087i | \(0.519691\pi\) | |||||||
\(230\) | −30.8765 | −2.03594 | ||||||||
\(231\) | 4.43311 | 0.291677 | ||||||||
\(232\) | 8.98750 | 0.590058 | ||||||||
\(233\) | −10.2911 | −0.674189 | −0.337095 | − | 0.941471i | \(-0.609444\pi\) | ||||
−0.337095 | + | 0.941471i | \(0.609444\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −44.8356 | −2.92475 | ||||||||
\(236\) | 23.9550 | 1.55934 | ||||||||
\(237\) | −26.3462 | −1.71137 | ||||||||
\(238\) | −26.0434 | −1.68815 | ||||||||
\(239\) | −9.03038 | −0.584127 | −0.292063 | − | 0.956399i | \(-0.594342\pi\) | ||||
−0.292063 | + | 0.956399i | \(0.594342\pi\) | |||||||
\(240\) | −14.9542 | −0.965292 | ||||||||
\(241\) | −17.6595 | −1.13755 | −0.568773 | − | 0.822494i | \(-0.692582\pi\) | ||||
−0.568773 | + | 0.822494i | \(0.692582\pi\) | |||||||
\(242\) | 2.14442 | 0.137849 | ||||||||
\(243\) | −0.261279 | −0.0167611 | ||||||||
\(244\) | 38.3087 | 2.45246 | ||||||||
\(245\) | 1.39677 | 0.0892365 | ||||||||
\(246\) | −7.14297 | −0.455419 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.52403 | −0.414277 | ||||||||
\(249\) | −5.10618 | −0.323591 | ||||||||
\(250\) | −19.6141 | −1.24051 | ||||||||
\(251\) | −20.3256 | −1.28294 | −0.641471 | − | 0.767148i | \(-0.721675\pi\) | ||||
−0.641471 | + | 0.767148i | \(0.721675\pi\) | |||||||
\(252\) | 0.167924 | 0.0105782 | ||||||||
\(253\) | 4.05972 | 0.255232 | ||||||||
\(254\) | 9.73784 | 0.611007 | ||||||||
\(255\) | 28.9046 | 1.81008 | ||||||||
\(256\) | 2.68106 | 0.167566 | ||||||||
\(257\) | −25.0044 | −1.55973 | −0.779866 | − | 0.625947i | \(-0.784713\pi\) | ||||
−0.779866 | + | 0.625947i | \(0.784713\pi\) | |||||||
\(258\) | 24.3554 | 1.51630 | ||||||||
\(259\) | 13.3162 | 0.827430 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.176046 | −0.0108970 | ||||||||
\(262\) | 31.6864 | 1.95760 | ||||||||
\(263\) | 16.8372 | 1.03822 | 0.519112 | − | 0.854706i | \(-0.326263\pi\) | ||||
0.519112 | + | 0.854706i | \(0.326263\pi\) | |||||||
\(264\) | −2.21386 | −0.136254 | ||||||||
\(265\) | 15.9038 | 0.976964 | ||||||||
\(266\) | −27.5209 | −1.68741 | ||||||||
\(267\) | 19.4795 | 1.19212 | ||||||||
\(268\) | −34.3434 | −2.09785 | ||||||||
\(269\) | 26.1626 | 1.59516 | 0.797580 | − | 0.603213i | \(-0.206113\pi\) | ||||
0.797580 | + | 0.603213i | \(0.206113\pi\) | |||||||
\(270\) | −39.6836 | −2.41507 | ||||||||
\(271\) | −5.03791 | −0.306031 | −0.153016 | − | 0.988224i | \(-0.548898\pi\) | ||||
−0.153016 | + | 0.988224i | \(0.548898\pi\) | |||||||
\(272\) | −11.5511 | −0.700387 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 46.7720 | 2.82560 | ||||||||
\(275\) | 7.57891 | 0.457026 | ||||||||
\(276\) | −18.1954 | −1.09523 | ||||||||
\(277\) | 26.2874 | 1.57946 | 0.789729 | − | 0.613456i | \(-0.210221\pi\) | ||||
0.789729 | + | 0.613456i | \(0.210221\pi\) | |||||||
\(278\) | 20.6980 | 1.24138 | ||||||||
\(279\) | 0.127792 | 0.00765070 | ||||||||
\(280\) | 11.7008 | 0.699254 | ||||||||
\(281\) | −21.5484 | −1.28547 | −0.642734 | − | 0.766089i | \(-0.722200\pi\) | ||||
−0.642734 | + | 0.766089i | \(0.722200\pi\) | |||||||
\(282\) | −46.7569 | −2.78433 | ||||||||
\(283\) | 18.1673 | 1.07994 | 0.539968 | − | 0.841685i | \(-0.318436\pi\) | ||||
0.539968 | + | 0.841685i | \(0.318436\pi\) | |||||||
\(284\) | −10.9785 | −0.651452 | ||||||||
\(285\) | 30.5444 | 1.80929 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.96375 | −0.293001 | ||||||||
\(288\) | 0.196346 | 0.0115698 | ||||||||
\(289\) | 5.32673 | 0.313337 | ||||||||
\(290\) | −53.2542 | −3.12719 | ||||||||
\(291\) | −2.21802 | −0.130022 | ||||||||
\(292\) | −1.64949 | −0.0965291 | ||||||||
\(293\) | −3.61441 | −0.211156 | −0.105578 | − | 0.994411i | \(-0.533669\pi\) | ||||
−0.105578 | + | 0.994411i | \(0.533669\pi\) | |||||||
\(294\) | 1.45663 | 0.0849521 | ||||||||
\(295\) | −32.6953 | −1.90359 | ||||||||
\(296\) | −6.65003 | −0.386525 | ||||||||
\(297\) | 5.21770 | 0.302762 | ||||||||
\(298\) | −1.10892 | −0.0642380 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −33.9682 | −1.96115 | ||||||||
\(301\) | 16.9249 | 0.975537 | ||||||||
\(302\) | 15.9172 | 0.915931 | ||||||||
\(303\) | 1.15528 | 0.0663693 | ||||||||
\(304\) | −12.2064 | −0.700083 | ||||||||
\(305\) | −52.2861 | −2.99389 | ||||||||
\(306\) | −0.254758 | −0.0145635 | ||||||||
\(307\) | −6.00757 | −0.342870 | −0.171435 | − | 0.985195i | \(-0.554840\pi\) | ||||
−0.171435 | + | 0.985195i | \(0.554840\pi\) | |||||||
\(308\) | −6.67894 | −0.380568 | ||||||||
\(309\) | 14.8863 | 0.846852 | ||||||||
\(310\) | 38.6573 | 2.19559 | ||||||||
\(311\) | −9.64155 | −0.546722 | −0.273361 | − | 0.961911i | \(-0.588135\pi\) | ||||
−0.273361 | + | 0.961911i | \(0.588135\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.62146 | 0.0916503 | 0.0458251 | − | 0.998949i | \(-0.485408\pi\) | ||||
0.0458251 | + | 0.998949i | \(0.485408\pi\) | |||||||
\(314\) | 42.8324 | 2.41717 | ||||||||
\(315\) | −0.229193 | −0.0129135 | ||||||||
\(316\) | 39.6933 | 2.23292 | ||||||||
\(317\) | −2.66354 | −0.149599 | −0.0747997 | − | 0.997199i | \(-0.523832\pi\) | ||||
−0.0747997 | + | 0.997199i | \(0.523832\pi\) | |||||||
\(318\) | 16.5853 | 0.930058 | ||||||||
\(319\) | 7.00199 | 0.392036 | ||||||||
\(320\) | 42.0546 | 2.35093 | ||||||||
\(321\) | 19.2762 | 1.07589 | ||||||||
\(322\) | −22.3760 | −1.24696 | ||||||||
\(323\) | 23.5933 | 1.31277 | ||||||||
\(324\) | −23.1894 | −1.28830 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 24.2539 | 1.34330 | ||||||||
\(327\) | −22.9935 | −1.27154 | ||||||||
\(328\) | 2.47886 | 0.136872 | ||||||||
\(329\) | −32.4920 | −1.79134 | ||||||||
\(330\) | 13.1179 | 0.722119 | ||||||||
\(331\) | −5.98410 | −0.328916 | −0.164458 | − | 0.986384i | \(-0.552587\pi\) | ||||
−0.164458 | + | 0.986384i | \(0.552587\pi\) | |||||||
\(332\) | 7.69300 | 0.422208 | ||||||||
\(333\) | 0.130260 | 0.00713819 | ||||||||
\(334\) | 0.784888 | 0.0429472 | ||||||||
\(335\) | 46.8740 | 2.56100 | ||||||||
\(336\) | −10.8372 | −0.591219 | ||||||||
\(337\) | 21.3322 | 1.16204 | 0.581018 | − | 0.813890i | \(-0.302654\pi\) | ||||
0.581018 | + | 0.813890i | \(0.302654\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.31716 | 0.234476 | ||||||||
\(340\) | −43.5478 | −2.36171 | ||||||||
\(341\) | −5.08275 | −0.275247 | ||||||||
\(342\) | −0.269210 | −0.0145572 | ||||||||
\(343\) | 19.0040 | 1.02612 | ||||||||
\(344\) | −8.45219 | −0.455712 | ||||||||
\(345\) | 24.8342 | 1.33703 | ||||||||
\(346\) | 37.2748 | 2.00390 | ||||||||
\(347\) | 2.65792 | 0.142685 | 0.0713423 | − | 0.997452i | \(-0.477272\pi\) | ||||
0.0713423 | + | 0.997452i | \(0.477272\pi\) | |||||||
\(348\) | −31.3825 | −1.68228 | ||||||||
\(349\) | 27.0398 | 1.44741 | 0.723703 | − | 0.690111i | \(-0.242438\pi\) | ||||
0.723703 | + | 0.690111i | \(0.242438\pi\) | |||||||
\(350\) | −41.7727 | −2.23285 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7.80941 | −0.416243 | ||||||||
\(353\) | −21.3343 | −1.13551 | −0.567754 | − | 0.823198i | \(-0.692187\pi\) | ||||
−0.567754 | + | 0.823198i | \(0.692187\pi\) | |||||||
\(354\) | −34.0963 | −1.81220 | ||||||||
\(355\) | 14.9841 | 0.795273 | ||||||||
\(356\) | −29.3479 | −1.55543 | ||||||||
\(357\) | 20.9469 | 1.10863 | ||||||||
\(358\) | −12.8066 | −0.676852 | ||||||||
\(359\) | −4.54231 | −0.239734 | −0.119867 | − | 0.992790i | \(-0.538247\pi\) | ||||
−0.119867 | + | 0.992790i | \(0.538247\pi\) | |||||||
\(360\) | 0.114457 | 0.00603242 | ||||||||
\(361\) | 5.93175 | 0.312197 | ||||||||
\(362\) | 32.9104 | 1.72973 | ||||||||
\(363\) | −1.72478 | −0.0905273 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.25133 | 0.117840 | ||||||||
\(366\) | −54.5266 | −2.85015 | ||||||||
\(367\) | −1.89674 | −0.0990091 | −0.0495045 | − | 0.998774i | \(-0.515764\pi\) | ||||
−0.0495045 | + | 0.998774i | \(0.515764\pi\) | |||||||
\(368\) | −9.92444 | −0.517347 | ||||||||
\(369\) | −0.0485556 | −0.00252770 | ||||||||
\(370\) | 39.4039 | 2.04851 | ||||||||
\(371\) | 11.5254 | 0.598367 | ||||||||
\(372\) | 22.7806 | 1.18112 | ||||||||
\(373\) | 13.4499 | 0.696409 | 0.348204 | − | 0.937419i | \(-0.386792\pi\) | ||||
0.348204 | + | 0.937419i | \(0.386792\pi\) | |||||||
\(374\) | 10.1327 | 0.523947 | ||||||||
\(375\) | 15.7758 | 0.814659 | ||||||||
\(376\) | 16.2263 | 0.836806 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −28.7584 | −1.47917 | ||||||||
\(379\) | −12.3262 | −0.633155 | −0.316578 | − | 0.948567i | \(-0.602534\pi\) | ||||
−0.316578 | + | 0.948567i | \(0.602534\pi\) | |||||||
\(380\) | −46.0183 | −2.36069 | ||||||||
\(381\) | −7.83222 | −0.401257 | ||||||||
\(382\) | −15.9501 | −0.816079 | ||||||||
\(383\) | 20.1380 | 1.02900 | 0.514501 | − | 0.857490i | \(-0.327977\pi\) | ||||
0.514501 | + | 0.857490i | \(0.327977\pi\) | |||||||
\(384\) | 16.9177 | 0.863329 | ||||||||
\(385\) | 9.11584 | 0.464586 | ||||||||
\(386\) | 21.8166 | 1.11044 | ||||||||
\(387\) | 0.165560 | 0.00841591 | ||||||||
\(388\) | 3.34167 | 0.169648 | ||||||||
\(389\) | −3.79806 | −0.192569 | −0.0962846 | − | 0.995354i | \(-0.530696\pi\) | ||||
−0.0962846 | + | 0.995354i | \(0.530696\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.1827 | 0.970108 | ||||||||
\(392\) | −0.505500 | −0.0255316 | ||||||||
\(393\) | −25.4857 | −1.28558 | ||||||||
\(394\) | −19.0348 | −0.958958 | ||||||||
\(395\) | −54.1759 | −2.72589 | ||||||||
\(396\) | −0.0653336 | −0.00328314 | ||||||||
\(397\) | −6.34245 | −0.318319 | −0.159159 | − | 0.987253i | \(-0.550878\pi\) | ||||
−0.159159 | + | 0.987253i | \(0.550878\pi\) | |||||||
\(398\) | 6.60648 | 0.331153 | ||||||||
\(399\) | 22.1353 | 1.10815 | ||||||||
\(400\) | −18.5275 | −0.926375 | ||||||||
\(401\) | 23.4516 | 1.17112 | 0.585558 | − | 0.810630i | \(-0.300875\pi\) | ||||
0.585558 | + | 0.810630i | \(0.300875\pi\) | |||||||
\(402\) | 48.8826 | 2.43804 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1.74056 | −0.0865959 | ||||||||
\(405\) | 31.6503 | 1.57272 | ||||||||
\(406\) | −38.5929 | −1.91533 | ||||||||
\(407\) | −5.18091 | −0.256808 | ||||||||
\(408\) | −10.4608 | −0.517884 | ||||||||
\(409\) | 23.9114 | 1.18234 | 0.591171 | − | 0.806546i | \(-0.298666\pi\) | ||||
0.591171 | + | 0.806546i | \(0.298666\pi\) | |||||||
\(410\) | −14.6882 | −0.725396 | ||||||||
\(411\) | −37.6191 | −1.85561 | ||||||||
\(412\) | −22.4278 | −1.10494 | ||||||||
\(413\) | −23.6940 | −1.16591 | ||||||||
\(414\) | −0.218883 | −0.0107575 | ||||||||
\(415\) | −10.4999 | −0.515419 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.6475 | −0.815233 | ||||||||
\(418\) | 10.7075 | 0.523720 | ||||||||
\(419\) | −25.7815 | −1.25951 | −0.629755 | − | 0.776794i | \(-0.716845\pi\) | ||||
−0.629755 | + | 0.776794i | \(0.716845\pi\) | |||||||
\(420\) | −40.8566 | −1.99360 | ||||||||
\(421\) | −35.1936 | −1.71523 | −0.857616 | − | 0.514290i | \(-0.828055\pi\) | ||||
−0.857616 | + | 0.514290i | \(0.828055\pi\) | |||||||
\(422\) | 35.0585 | 1.70662 | ||||||||
\(423\) | −0.317838 | −0.0154538 | ||||||||
\(424\) | −5.75569 | −0.279521 | ||||||||
\(425\) | 35.8113 | 1.73710 | ||||||||
\(426\) | 15.6262 | 0.757091 | ||||||||
\(427\) | −37.8913 | −1.83369 | ||||||||
\(428\) | −29.0416 | −1.40378 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 50.0823 | 2.41518 | ||||||||
\(431\) | −1.23727 | −0.0595973 | −0.0297987 | − | 0.999556i | \(-0.509487\pi\) | ||||
−0.0297987 | + | 0.999556i | \(0.509487\pi\) | |||||||
\(432\) | −12.7552 | −0.613687 | ||||||||
\(433\) | 28.2869 | 1.35938 | 0.679691 | − | 0.733499i | \(-0.262114\pi\) | ||||
0.679691 | + | 0.733499i | \(0.262114\pi\) | |||||||
\(434\) | 28.0146 | 1.34475 | ||||||||
\(435\) | 42.8328 | 2.05367 | ||||||||
\(436\) | 34.6421 | 1.65905 | ||||||||
\(437\) | 20.2709 | 0.969687 | ||||||||
\(438\) | 2.34780 | 0.112182 | ||||||||
\(439\) | −4.72129 | −0.225335 | −0.112668 | − | 0.993633i | \(-0.535940\pi\) | ||||
−0.112668 | + | 0.993633i | \(0.535940\pi\) | |||||||
\(440\) | −4.55238 | −0.217026 | ||||||||
\(441\) | 0.00990166 | 0.000471508 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −30.7146 | −1.45930 | −0.729648 | − | 0.683823i | \(-0.760316\pi\) | ||||
−0.729648 | + | 0.683823i | \(0.760316\pi\) | |||||||
\(444\) | 23.2205 | 1.10200 | ||||||||
\(445\) | 40.0558 | 1.89883 | ||||||||
\(446\) | 19.5713 | 0.926729 | ||||||||
\(447\) | 0.891912 | 0.0421860 | ||||||||
\(448\) | 30.4767 | 1.43989 | ||||||||
\(449\) | −27.6456 | −1.30468 | −0.652338 | − | 0.757928i | \(-0.726212\pi\) | ||||
−0.652338 | + | 0.757928i | \(0.726212\pi\) | |||||||
\(450\) | −0.408622 | −0.0192626 | ||||||||
\(451\) | 1.93123 | 0.0909383 | ||||||||
\(452\) | −6.50425 | −0.305934 | ||||||||
\(453\) | −12.8023 | −0.601505 | ||||||||
\(454\) | −24.9113 | −1.16915 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −11.0542 | −0.517660 | ||||||||
\(457\) | −3.15166 | −0.147428 | −0.0737142 | − | 0.997279i | \(-0.523485\pi\) | ||||
−0.0737142 | + | 0.997279i | \(0.523485\pi\) | |||||||
\(458\) | −4.01226 | −0.187481 | ||||||||
\(459\) | 24.6542 | 1.15076 | ||||||||
\(460\) | −37.4154 | −1.74450 | ||||||||
\(461\) | −5.36574 | −0.249908 | −0.124954 | − | 0.992163i | \(-0.539878\pi\) | ||||
−0.124954 | + | 0.992163i | \(0.539878\pi\) | |||||||
\(462\) | 9.50646 | 0.442281 | ||||||||
\(463\) | −16.3015 | −0.757594 | −0.378797 | − | 0.925480i | \(-0.623662\pi\) | ||||
−0.378797 | + | 0.925480i | \(0.623662\pi\) | |||||||
\(464\) | −17.1171 | −0.794644 | ||||||||
\(465\) | −31.0924 | −1.44187 | ||||||||
\(466\) | −22.0684 | −1.02230 | ||||||||
\(467\) | −38.1313 | −1.76450 | −0.882252 | − | 0.470777i | \(-0.843973\pi\) | ||||
−0.882252 | + | 0.470777i | \(0.843973\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 33.9692 | 1.56855 | ||||||||
\(470\) | −96.1466 | −4.43491 | ||||||||
\(471\) | −34.4504 | −1.58739 | ||||||||
\(472\) | 11.8326 | 0.544641 | ||||||||
\(473\) | −6.58494 | −0.302776 | ||||||||
\(474\) | −56.4974 | −2.59501 | ||||||||
\(475\) | 37.8428 | 1.73635 | ||||||||
\(476\) | −31.5588 | −1.44649 | ||||||||
\(477\) | 0.112742 | 0.00516208 | ||||||||
\(478\) | −19.3650 | −0.885733 | ||||||||
\(479\) | 7.24692 | 0.331120 | 0.165560 | − | 0.986200i | \(-0.447057\pi\) | ||||
0.165560 | + | 0.986200i | \(0.447057\pi\) | |||||||
\(480\) | −47.7720 | −2.18048 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −37.8694 | −1.72490 | ||||||||
\(483\) | 17.9972 | 0.818899 | ||||||||
\(484\) | 2.59856 | 0.118116 | ||||||||
\(485\) | −4.56093 | −0.207101 | ||||||||
\(486\) | −0.560293 | −0.0254154 | ||||||||
\(487\) | −19.5823 | −0.887361 | −0.443680 | − | 0.896185i | \(-0.646327\pi\) | ||||
−0.443680 | + | 0.896185i | \(0.646327\pi\) | |||||||
\(488\) | 18.9227 | 0.856588 | ||||||||
\(489\) | −19.5076 | −0.882164 | ||||||||
\(490\) | 2.99527 | 0.135313 | ||||||||
\(491\) | −0.556479 | −0.0251136 | −0.0125568 | − | 0.999921i | \(-0.503997\pi\) | ||||
−0.0125568 | + | 0.999921i | \(0.503997\pi\) | |||||||
\(492\) | −8.65567 | −0.390228 | ||||||||
\(493\) | 33.0852 | 1.49008 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.0891714 | 0.00400796 | ||||||||
\(496\) | 12.4254 | 0.557915 | ||||||||
\(497\) | 10.8589 | 0.487086 | ||||||||
\(498\) | −10.9498 | −0.490673 | ||||||||
\(499\) | −22.5020 | −1.00733 | −0.503664 | − | 0.863900i | \(-0.668015\pi\) | ||||
−0.503664 | + | 0.863900i | \(0.668015\pi\) | |||||||
\(500\) | −23.7679 | −1.06293 | ||||||||
\(501\) | −0.631292 | −0.0282040 | ||||||||
\(502\) | −43.5867 | −1.94537 | ||||||||
\(503\) | 9.61297 | 0.428621 | 0.214310 | − | 0.976766i | \(-0.431250\pi\) | ||||
0.214310 | + | 0.976766i | \(0.431250\pi\) | |||||||
\(504\) | 0.0829462 | 0.00369472 | ||||||||
\(505\) | 2.37562 | 0.105714 | ||||||||
\(506\) | 8.70576 | 0.387018 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.8001 | 0.523543 | ||||||||
\(509\) | 15.0569 | 0.667384 | 0.333692 | − | 0.942682i | \(-0.391705\pi\) | ||||
0.333692 | + | 0.942682i | \(0.391705\pi\) | |||||||
\(510\) | 61.9838 | 2.74469 | ||||||||
\(511\) | 1.63152 | 0.0721741 | ||||||||
\(512\) | 25.3666 | 1.12106 | ||||||||
\(513\) | 26.0529 | 1.15026 | ||||||||
\(514\) | −53.6200 | −2.36508 | ||||||||
\(515\) | 30.6108 | 1.34888 | ||||||||
\(516\) | 29.5133 | 1.29925 | ||||||||
\(517\) | 12.6416 | 0.555976 | ||||||||
\(518\) | 28.5557 | 1.25466 | ||||||||
\(519\) | −29.9804 | −1.31599 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.3300 | −0.496375 | −0.248188 | − | 0.968712i | \(-0.579835\pi\) | ||||
−0.248188 | + | 0.968712i | \(0.579835\pi\) | |||||||
\(522\) | −0.377517 | −0.0165235 | ||||||||
\(523\) | −11.1265 | −0.486527 | −0.243264 | − | 0.969960i | \(-0.578218\pi\) | ||||
−0.243264 | + | 0.969960i | \(0.578218\pi\) | |||||||
\(524\) | 38.3968 | 1.67737 | ||||||||
\(525\) | 33.5981 | 1.46634 | ||||||||
\(526\) | 36.1060 | 1.57430 | ||||||||
\(527\) | −24.0166 | −1.04618 | ||||||||
\(528\) | 4.21641 | 0.183496 | ||||||||
\(529\) | −6.51868 | −0.283421 | ||||||||
\(530\) | 34.1045 | 1.48141 | ||||||||
\(531\) | −0.231776 | −0.0100582 | ||||||||
\(532\) | −33.3491 | −1.44587 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 41.7723 | 1.80766 | ||||||||
\(535\) | 39.6378 | 1.71369 | ||||||||
\(536\) | −16.9640 | −0.732732 | ||||||||
\(537\) | 10.3005 | 0.444499 | ||||||||
\(538\) | 56.1037 | 2.41880 | ||||||||
\(539\) | −0.393826 | −0.0169633 | ||||||||
\(540\) | −48.0876 | −2.06936 | ||||||||
\(541\) | 45.0049 | 1.93491 | 0.967455 | − | 0.253044i | \(-0.0814316\pi\) | ||||
0.967455 | + | 0.253044i | \(0.0814316\pi\) | |||||||
\(542\) | −10.8034 | −0.464047 | ||||||||
\(543\) | −26.4701 | −1.13594 | ||||||||
\(544\) | −36.9004 | −1.58209 | ||||||||
\(545\) | −47.2817 | −2.02533 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.30701 | −0.141397 | −0.0706987 | − | 0.997498i | \(-0.522523\pi\) | ||||
−0.0706987 | + | 0.997498i | \(0.522523\pi\) | |||||||
\(548\) | 56.6771 | 2.42113 | ||||||||
\(549\) | −0.370654 | −0.0158191 | ||||||||
\(550\) | 16.2524 | 0.693005 | ||||||||
\(551\) | 34.9621 | 1.48944 | ||||||||
\(552\) | −8.98765 | −0.382540 | ||||||||
\(553\) | −39.2609 | −1.66954 | ||||||||
\(554\) | 56.3714 | 2.39499 | ||||||||
\(555\) | −31.6928 | −1.34529 | ||||||||
\(556\) | 25.0812 | 1.06368 | ||||||||
\(557\) | −7.28456 | −0.308657 | −0.154328 | − | 0.988020i | \(-0.549321\pi\) | ||||
−0.154328 | + | 0.988020i | \(0.549321\pi\) | |||||||
\(558\) | 0.274040 | 0.0116010 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −22.2847 | −0.941700 | ||||||||
\(561\) | −8.14978 | −0.344084 | ||||||||
\(562\) | −46.2089 | −1.94920 | ||||||||
\(563\) | 21.4623 | 0.904527 | 0.452263 | − | 0.891884i | \(-0.350617\pi\) | ||||
0.452263 | + | 0.891884i | \(0.350617\pi\) | |||||||
\(564\) | −56.6588 | −2.38576 | ||||||||
\(565\) | 8.87741 | 0.373475 | ||||||||
\(566\) | 38.9585 | 1.63755 | ||||||||
\(567\) | 22.9367 | 0.963253 | ||||||||
\(568\) | −5.42283 | −0.227537 | ||||||||
\(569\) | 29.8261 | 1.25037 | 0.625187 | − | 0.780475i | \(-0.285023\pi\) | ||||
0.625187 | + | 0.780475i | \(0.285023\pi\) | |||||||
\(570\) | 65.5001 | 2.74350 | ||||||||
\(571\) | 23.2173 | 0.971615 | 0.485807 | − | 0.874066i | \(-0.338526\pi\) | ||||
0.485807 | + | 0.874066i | \(0.338526\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.8288 | 0.535931 | ||||||||
\(574\) | −10.6444 | −0.444288 | ||||||||
\(575\) | 30.7683 | 1.28313 | ||||||||
\(576\) | 0.298124 | 0.0124218 | ||||||||
\(577\) | 11.5542 | 0.481007 | 0.240503 | − | 0.970648i | \(-0.422687\pi\) | ||||
0.240503 | + | 0.970648i | \(0.422687\pi\) | |||||||
\(578\) | 11.4228 | 0.475125 | ||||||||
\(579\) | −17.5473 | −0.729241 | ||||||||
\(580\) | −64.5321 | −2.67955 | ||||||||
\(581\) | −7.60919 | −0.315682 | ||||||||
\(582\) | −4.75637 | −0.197158 | ||||||||
\(583\) | −4.48415 | −0.185714 | ||||||||
\(584\) | −0.814769 | −0.0337154 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.75082 | −0.320183 | ||||||||
\(587\) | −29.3693 | −1.21220 | −0.606101 | − | 0.795388i | \(-0.707267\pi\) | ||||
−0.606101 | + | 0.795388i | \(0.707267\pi\) | |||||||
\(588\) | 1.76510 | 0.0727915 | ||||||||
\(589\) | −25.3791 | −1.04573 | ||||||||
\(590\) | −70.1126 | −2.88649 | ||||||||
\(591\) | 15.3098 | 0.629761 | ||||||||
\(592\) | 12.6653 | 0.520541 | ||||||||
\(593\) | 27.8117 | 1.14209 | 0.571045 | − | 0.820919i | \(-0.306538\pi\) | ||||
0.571045 | + | 0.820919i | \(0.306538\pi\) | |||||||
\(594\) | 11.1890 | 0.459089 | ||||||||
\(595\) | 43.0734 | 1.76584 | ||||||||
\(596\) | −1.34376 | −0.0550425 | ||||||||
\(597\) | −5.31364 | −0.217473 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.9070 | 1.09939 | 0.549695 | − | 0.835366i | \(-0.314744\pi\) | ||||
0.549695 | + | 0.835366i | \(0.314744\pi\) | |||||||
\(600\) | −16.7787 | −0.684986 | ||||||||
\(601\) | 24.9122 | 1.01619 | 0.508095 | − | 0.861301i | \(-0.330350\pi\) | ||||
0.508095 | + | 0.861301i | \(0.330350\pi\) | |||||||
\(602\) | 36.2943 | 1.47924 | ||||||||
\(603\) | 0.332288 | 0.0135318 | ||||||||
\(604\) | 19.2880 | 0.784819 | ||||||||
\(605\) | −3.54668 | −0.144193 | ||||||||
\(606\) | 2.47742 | 0.100638 | ||||||||
\(607\) | −29.8024 | −1.20964 | −0.604821 | − | 0.796361i | \(-0.706755\pi\) | ||||
−0.604821 | + | 0.796361i | \(0.706755\pi\) | |||||||
\(608\) | −38.9937 | −1.58140 | ||||||||
\(609\) | 31.0406 | 1.25783 | ||||||||
\(610\) | −112.124 | −4.53975 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.308709 | −0.0124788 | ||||||||
\(613\) | 12.7050 | 0.513151 | 0.256575 | − | 0.966524i | \(-0.417406\pi\) | ||||
0.256575 | + | 0.966524i | \(0.417406\pi\) | |||||||
\(614\) | −12.8828 | −0.519907 | ||||||||
\(615\) | 11.8138 | 0.476378 | ||||||||
\(616\) | −3.29908 | −0.132924 | ||||||||
\(617\) | −14.3958 | −0.579552 | −0.289776 | − | 0.957095i | \(-0.593581\pi\) | ||||
−0.289776 | + | 0.957095i | \(0.593581\pi\) | |||||||
\(618\) | 31.9226 | 1.28411 | ||||||||
\(619\) | 11.0835 | 0.445485 | 0.222742 | − | 0.974877i | \(-0.428499\pi\) | ||||
0.222742 | + | 0.974877i | \(0.428499\pi\) | |||||||
\(620\) | 46.8439 | 1.88130 | ||||||||
\(621\) | 21.1824 | 0.850020 | ||||||||
\(622\) | −20.6756 | −0.829015 | ||||||||
\(623\) | 29.0281 | 1.16299 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.45464 | −0.218186 | ||||||||
\(626\) | 3.47710 | 0.138973 | ||||||||
\(627\) | −8.61211 | −0.343934 | ||||||||
\(628\) | 51.9032 | 2.07116 | ||||||||
\(629\) | −24.4804 | −0.976098 | ||||||||
\(630\) | −0.491487 | −0.0195813 | ||||||||
\(631\) | 31.1311 | 1.23931 | 0.619655 | − | 0.784874i | \(-0.287273\pi\) | ||||
0.619655 | + | 0.784874i | \(0.287273\pi\) | |||||||
\(632\) | 19.6066 | 0.779908 | ||||||||
\(633\) | −28.1978 | −1.12076 | ||||||||
\(634\) | −5.71176 | −0.226843 | ||||||||
\(635\) | −16.1055 | −0.639126 | ||||||||
\(636\) | 20.0977 | 0.796924 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 15.0152 | 0.594459 | ||||||||
\(639\) | 0.106222 | 0.00420207 | ||||||||
\(640\) | 34.7881 | 1.37512 | ||||||||
\(641\) | 32.0469 | 1.26578 | 0.632889 | − | 0.774243i | \(-0.281869\pi\) | ||||
0.632889 | + | 0.774243i | \(0.281869\pi\) | |||||||
\(642\) | 41.3363 | 1.63141 | ||||||||
\(643\) | −6.56917 | −0.259063 | −0.129531 | − | 0.991575i | \(-0.541347\pi\) | ||||
−0.129531 | + | 0.991575i | \(0.541347\pi\) | |||||||
\(644\) | −27.1146 | −1.06847 | ||||||||
\(645\) | −40.2816 | −1.58609 | ||||||||
\(646\) | 50.5941 | 1.99060 | ||||||||
\(647\) | −11.1001 | −0.436391 | −0.218195 | − | 0.975905i | \(-0.570017\pi\) | ||||
−0.218195 | + | 0.975905i | \(0.570017\pi\) | |||||||
\(648\) | −11.4544 | −0.449973 | ||||||||
\(649\) | 9.21857 | 0.361861 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −22.5324 | −0.883114 | ||||||||
\(652\) | 29.3902 | 1.15101 | ||||||||
\(653\) | −22.5719 | −0.883307 | −0.441653 | − | 0.897186i | \(-0.645608\pi\) | ||||
−0.441653 | + | 0.897186i | \(0.645608\pi\) | |||||||
\(654\) | −49.3078 | −1.92809 | ||||||||
\(655\) | −52.4064 | −2.04769 | ||||||||
\(656\) | −4.72112 | −0.184329 | ||||||||
\(657\) | 0.0159596 | 0.000622642 0 | ||||||||
\(658\) | −69.6767 | −2.71628 | ||||||||
\(659\) | −1.18788 | −0.0462734 | −0.0231367 | − | 0.999732i | \(-0.507365\pi\) | ||||
−0.0231367 | + | 0.999732i | \(0.507365\pi\) | |||||||
\(660\) | 15.8960 | 0.618750 | ||||||||
\(661\) | −8.66908 | −0.337188 | −0.168594 | − | 0.985686i | \(-0.553923\pi\) | ||||
−0.168594 | + | 0.985686i | \(0.553923\pi\) | |||||||
\(662\) | −12.8325 | −0.498748 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.79997 | 0.147468 | ||||||||
\(665\) | 45.5169 | 1.76507 | ||||||||
\(666\) | 0.279332 | 0.0108239 | ||||||||
\(667\) | 28.4261 | 1.10066 | ||||||||
\(668\) | 0.951107 | 0.0367994 | ||||||||
\(669\) | −15.7414 | −0.608597 | ||||||||
\(670\) | 100.518 | 3.88334 | ||||||||
\(671\) | 14.7423 | 0.569120 | ||||||||
\(672\) | −34.6200 | −1.33549 | ||||||||
\(673\) | −12.2403 | −0.471828 | −0.235914 | − | 0.971774i | \(-0.575808\pi\) | ||||
−0.235914 | + | 0.971774i | \(0.575808\pi\) | |||||||
\(674\) | 45.7452 | 1.76204 | ||||||||
\(675\) | 39.5445 | 1.52207 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.83784 | 0.301233 | 0.150616 | − | 0.988592i | \(-0.451874\pi\) | ||||
0.150616 | + | 0.988592i | \(0.451874\pi\) | |||||||
\(678\) | 9.25782 | 0.355544 | ||||||||
\(679\) | −3.30527 | −0.126845 | ||||||||
\(680\) | −21.5105 | −0.824892 | ||||||||
\(681\) | 20.0364 | 0.767795 | ||||||||
\(682\) | −10.8996 | −0.417367 | ||||||||
\(683\) | 38.2481 | 1.46352 | 0.731761 | − | 0.681561i | \(-0.238699\pi\) | ||||
0.731761 | + | 0.681561i | \(0.238699\pi\) | |||||||
\(684\) | −0.326222 | −0.0124734 | ||||||||
\(685\) | −77.3565 | −2.95564 | ||||||||
\(686\) | 40.7526 | 1.55594 | ||||||||
\(687\) | 3.22709 | 0.123121 | ||||||||
\(688\) | 16.0976 | 0.613717 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 53.2551 | 2.02739 | ||||||||
\(691\) | −15.0173 | −0.571284 | −0.285642 | − | 0.958336i | \(-0.592207\pi\) | ||||
−0.285642 | + | 0.958336i | \(0.592207\pi\) | |||||||
\(692\) | 45.1686 | 1.71705 | ||||||||
\(693\) | 0.0646218 | 0.00245478 | ||||||||
\(694\) | 5.69971 | 0.216358 | ||||||||
\(695\) | −34.2325 | −1.29851 | ||||||||
\(696\) | −15.5014 | −0.587580 | ||||||||
\(697\) | 9.12531 | 0.345646 | ||||||||
\(698\) | 57.9848 | 2.19476 | ||||||||
\(699\) | 17.7498 | 0.671358 | ||||||||
\(700\) | −50.6191 | −1.91322 | ||||||||
\(701\) | 45.1498 | 1.70528 | 0.852641 | − | 0.522497i | \(-0.174999\pi\) | ||||
0.852641 | + | 0.522497i | \(0.174999\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.8692 | −0.975675 | ||||||||
\(704\) | −11.8575 | −0.446895 | ||||||||
\(705\) | 77.3315 | 2.91247 | ||||||||
\(706\) | −45.7497 | −1.72181 | ||||||||
\(707\) | 1.72159 | 0.0647472 | ||||||||
\(708\) | −41.3170 | −1.55279 | ||||||||
\(709\) | −4.75440 | −0.178555 | −0.0892777 | − | 0.996007i | \(-0.528456\pi\) | ||||
−0.0892777 | + | 0.996007i | \(0.528456\pi\) | |||||||
\(710\) | 32.1323 | 1.20590 | ||||||||
\(711\) | −0.384051 | −0.0144030 | ||||||||
\(712\) | −14.4964 | −0.543277 | ||||||||
\(713\) | −20.6346 | −0.772770 | ||||||||
\(714\) | 44.9192 | 1.68106 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −15.5188 | −0.579963 | ||||||||
\(717\) | 15.5754 | 0.581674 | ||||||||
\(718\) | −9.74065 | −0.363518 | ||||||||
\(719\) | −48.1031 | −1.79394 | −0.896971 | − | 0.442090i | \(-0.854237\pi\) | ||||
−0.896971 | + | 0.442090i | \(0.854237\pi\) | |||||||
\(720\) | −0.217990 | −0.00812399 | ||||||||
\(721\) | 22.1834 | 0.826154 | ||||||||
\(722\) | 12.7202 | 0.473397 | ||||||||
\(723\) | 30.4587 | 1.13277 | ||||||||
\(724\) | 39.8800 | 1.48213 | ||||||||
\(725\) | 53.0675 | 1.97088 | ||||||||
\(726\) | −3.69866 | −0.137270 | ||||||||
\(727\) | −29.3876 | −1.08993 | −0.544963 | − | 0.838460i | \(-0.683456\pi\) | ||||
−0.544963 | + | 0.838460i | \(0.683456\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.2225 | 1.00824 | ||||||||
\(730\) | 4.82780 | 0.178685 | ||||||||
\(731\) | −31.1146 | −1.15082 | ||||||||
\(732\) | −66.0740 | −2.44216 | ||||||||
\(733\) | 30.8866 | 1.14082 | 0.570411 | − | 0.821360i | \(-0.306784\pi\) | ||||
0.570411 | + | 0.821360i | \(0.306784\pi\) | |||||||
\(734\) | −4.06742 | −0.150131 | ||||||||
\(735\) | −2.40912 | −0.0888618 | ||||||||
\(736\) | −31.7040 | −1.16863 | ||||||||
\(737\) | −13.2163 | −0.486829 | ||||||||
\(738\) | −0.104124 | −0.00383285 | ||||||||
\(739\) | 1.22732 | 0.0451475 | 0.0225738 | − | 0.999745i | \(-0.492814\pi\) | ||||
0.0225738 | + | 0.999745i | \(0.492814\pi\) | |||||||
\(740\) | 47.7486 | 1.75527 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 24.7153 | 0.907327 | ||||||||
\(743\) | −28.2751 | −1.03731 | −0.518656 | − | 0.854983i | \(-0.673567\pi\) | ||||
−0.518656 | + | 0.854983i | \(0.673567\pi\) | |||||||
\(744\) | 11.2525 | 0.412537 | ||||||||
\(745\) | 1.83405 | 0.0671943 | ||||||||
\(746\) | 28.8423 | 1.05599 | ||||||||
\(747\) | −0.0744333 | −0.00272337 | ||||||||
\(748\) | 12.2785 | 0.448946 | ||||||||
\(749\) | 28.7252 | 1.04960 | ||||||||
\(750\) | 33.8300 | 1.23530 | ||||||||
\(751\) | −17.1244 | −0.624879 | −0.312439 | − | 0.949938i | \(-0.601146\pi\) | ||||
−0.312439 | + | 0.949938i | \(0.601146\pi\) | |||||||
\(752\) | −30.9038 | −1.12694 | ||||||||
\(753\) | 35.0572 | 1.27755 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −26.3255 | −0.958084 | ||||||||
\(756\) | −34.8487 | −1.26743 | ||||||||
\(757\) | 30.5788 | 1.11141 | 0.555703 | − | 0.831381i | \(-0.312449\pi\) | ||||
0.555703 | + | 0.831381i | \(0.312449\pi\) | |||||||
\(758\) | −26.4327 | −0.960077 | ||||||||
\(759\) | −7.00211 | −0.254161 | ||||||||
\(760\) | −22.7308 | −0.824534 | ||||||||
\(761\) | 35.0432 | 1.27031 | 0.635157 | − | 0.772383i | \(-0.280935\pi\) | ||||
0.635157 | + | 0.772383i | \(0.280935\pi\) | |||||||
\(762\) | −16.7956 | −0.608441 | ||||||||
\(763\) | −34.2647 | −1.24046 | ||||||||
\(764\) | −19.3279 | −0.699260 | ||||||||
\(765\) | 0.421346 | 0.0152338 | ||||||||
\(766\) | 43.1843 | 1.56031 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −4.62423 | −0.166862 | ||||||||
\(769\) | −21.7812 | −0.785451 | −0.392725 | − | 0.919656i | \(-0.628468\pi\) | ||||
−0.392725 | + | 0.919656i | \(0.628468\pi\) | |||||||
\(770\) | 19.5482 | 0.704469 | ||||||||
\(771\) | 43.1270 | 1.55318 | ||||||||
\(772\) | 26.4368 | 0.951483 | ||||||||
\(773\) | 43.4039 | 1.56113 | 0.780565 | − | 0.625075i | \(-0.214932\pi\) | ||||
0.780565 | + | 0.625075i | \(0.214932\pi\) | |||||||
\(774\) | 0.355032 | 0.0127614 | ||||||||
\(775\) | −38.5217 | −1.38374 | ||||||||
\(776\) | 1.65063 | 0.0592540 | ||||||||
\(777\) | −22.9675 | −0.823956 | ||||||||
\(778\) | −8.14465 | −0.292000 | ||||||||
\(779\) | 9.64298 | 0.345496 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.22483 | −0.151176 | ||||||||
\(782\) | 41.1358 | 1.47101 | ||||||||
\(783\) | 36.5343 | 1.30563 | ||||||||
\(784\) | 0.962751 | 0.0343840 | ||||||||
\(785\) | −70.8407 | −2.52841 | ||||||||
\(786\) | −54.6521 | −1.94937 | ||||||||
\(787\) | −18.9269 | −0.674670 | −0.337335 | − | 0.941385i | \(-0.609525\pi\) | ||||
−0.337335 | + | 0.941385i | \(0.609525\pi\) | |||||||
\(788\) | −23.0658 | −0.821686 | ||||||||
\(789\) | −29.0404 | −1.03386 | ||||||||
\(790\) | −116.176 | −4.13336 | ||||||||
\(791\) | 6.43339 | 0.228745 | ||||||||
\(792\) | −0.0322717 | −0.00114672 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −13.6009 | −0.482678 | ||||||||
\(795\) | −27.4306 | −0.972861 | ||||||||
\(796\) | 8.00556 | 0.283749 | ||||||||
\(797\) | 1.81101 | 0.0641492 | 0.0320746 | − | 0.999485i | \(-0.489789\pi\) | ||||
0.0320746 | + | 0.999485i | \(0.489789\pi\) | |||||||
\(798\) | 47.4674 | 1.68033 | ||||||||
\(799\) | 59.7330 | 2.11320 | ||||||||
\(800\) | −59.1869 | −2.09257 | ||||||||
\(801\) | 0.283954 | 0.0100330 | ||||||||
\(802\) | 50.2902 | 1.77581 | ||||||||
\(803\) | −0.634771 | −0.0224006 | ||||||||
\(804\) | 59.2346 | 2.08904 | ||||||||
\(805\) | 37.0077 | 1.30435 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −45.1246 | −1.58846 | ||||||||
\(808\) | −0.859751 | −0.0302459 | ||||||||
\(809\) | 38.2291 | 1.34407 | 0.672033 | − | 0.740522i | \(-0.265421\pi\) | ||||
0.672033 | + | 0.740522i | \(0.265421\pi\) | |||||||
\(810\) | 67.8718 | 2.38477 | ||||||||
\(811\) | 22.0319 | 0.773644 | 0.386822 | − | 0.922154i | \(-0.373573\pi\) | ||||
0.386822 | + | 0.922154i | \(0.373573\pi\) | |||||||
\(812\) | −46.7659 | −1.64116 | ||||||||
\(813\) | 8.68927 | 0.304746 | ||||||||
\(814\) | −11.1101 | −0.389408 | ||||||||
\(815\) | −40.1136 | −1.40512 | ||||||||
\(816\) | 19.9230 | 0.697446 | ||||||||
\(817\) | −32.8798 | −1.15032 | ||||||||
\(818\) | 51.2762 | 1.79283 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −17.7987 | −0.621559 | ||||||||
\(821\) | 24.0571 | 0.839599 | 0.419800 | − | 0.907617i | \(-0.362100\pi\) | ||||
0.419800 | + | 0.907617i | \(0.362100\pi\) | |||||||
\(822\) | −80.6713 | −2.81373 | ||||||||
\(823\) | −31.3858 | −1.09404 | −0.547019 | − | 0.837120i | \(-0.684238\pi\) | ||||
−0.547019 | + | 0.837120i | \(0.684238\pi\) | |||||||
\(824\) | −11.0782 | −0.385929 | ||||||||
\(825\) | −13.0719 | −0.455107 | ||||||||
\(826\) | −50.8100 | −1.76791 | ||||||||
\(827\) | 1.22049 | 0.0424407 | 0.0212203 | − | 0.999775i | \(-0.493245\pi\) | ||||
0.0212203 | + | 0.999775i | \(0.493245\pi\) | |||||||
\(828\) | −0.265236 | −0.00921759 | ||||||||
\(829\) | 53.2052 | 1.84789 | 0.923947 | − | 0.382520i | \(-0.124944\pi\) | ||||
0.923947 | + | 0.382520i | \(0.124944\pi\) | |||||||
\(830\) | −22.5162 | −0.781550 | ||||||||
\(831\) | −45.3399 | −1.57283 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.86087 | −0.0644754 | ||||||||
\(834\) | −35.6994 | −1.23617 | ||||||||
\(835\) | −1.29813 | −0.0449237 | ||||||||
\(836\) | 12.9750 | 0.448751 | ||||||||
\(837\) | −26.5203 | −0.916675 | ||||||||
\(838\) | −55.2865 | −1.90984 | ||||||||
\(839\) | −8.59689 | −0.296798 | −0.148399 | − | 0.988928i | \(-0.547412\pi\) | ||||
−0.148399 | + | 0.988928i | \(0.547412\pi\) | |||||||
\(840\) | −20.1812 | −0.696317 | ||||||||
\(841\) | 20.0279 | 0.690616 | ||||||||
\(842\) | −75.4701 | −2.60087 | ||||||||
\(843\) | 37.1662 | 1.28007 | ||||||||
\(844\) | 42.4830 | 1.46232 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.681580 | −0.0234332 | ||||||||
\(847\) | −2.57025 | −0.0883148 | ||||||||
\(848\) | 10.9620 | 0.376437 | ||||||||
\(849\) | −31.3346 | −1.07540 | ||||||||
\(850\) | 76.7945 | 2.63403 | ||||||||
\(851\) | −21.0331 | −0.721004 | ||||||||
\(852\) | 18.9354 | 0.648716 | ||||||||
\(853\) | −34.7749 | −1.19067 | −0.595335 | − | 0.803477i | \(-0.702981\pi\) | ||||
−0.595335 | + | 0.803477i | \(0.702981\pi\) | |||||||
\(854\) | −81.2551 | −2.78049 | ||||||||
\(855\) | 0.445248 | 0.0152272 | ||||||||
\(856\) | −14.3452 | −0.490307 | ||||||||
\(857\) | −25.7161 | −0.878446 | −0.439223 | − | 0.898378i | \(-0.644746\pi\) | ||||
−0.439223 | + | 0.898378i | \(0.644746\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.7344 | 1.28748 | 0.643740 | − | 0.765244i | \(-0.277382\pi\) | ||||
0.643740 | + | 0.765244i | \(0.277382\pi\) | |||||||
\(860\) | 60.6885 | 2.06946 | ||||||||
\(861\) | 8.56137 | 0.291771 | ||||||||
\(862\) | −2.65324 | −0.0903696 | ||||||||
\(863\) | 43.3135 | 1.47441 | 0.737204 | − | 0.675671i | \(-0.236146\pi\) | ||||
0.737204 | + | 0.675671i | \(0.236146\pi\) | |||||||
\(864\) | −40.7472 | −1.38625 | ||||||||
\(865\) | −61.6490 | −2.09613 | ||||||||
\(866\) | 60.6591 | 2.06128 | ||||||||
\(867\) | −9.18743 | −0.312022 | ||||||||
\(868\) | 33.9474 | 1.15225 | ||||||||
\(869\) | 15.2751 | 0.518173 | ||||||||
\(870\) | 91.8517 | 3.11406 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 17.1115 | 0.579469 | ||||||||
\(873\) | −0.0323322 | −0.00109428 | ||||||||
\(874\) | 43.4694 | 1.47037 | ||||||||
\(875\) | 23.5090 | 0.794748 | ||||||||
\(876\) | 2.84500 | 0.0961237 | ||||||||
\(877\) | 29.9138 | 1.01012 | 0.505058 | − | 0.863085i | \(-0.331471\pi\) | ||||
0.505058 | + | 0.863085i | \(0.331471\pi\) | |||||||
\(878\) | −10.1245 | −0.341684 | ||||||||
\(879\) | 6.23404 | 0.210269 | ||||||||
\(880\) | 8.67025 | 0.292274 | ||||||||
\(881\) | −6.35670 | −0.214163 | −0.107081 | − | 0.994250i | \(-0.534151\pi\) | ||||
−0.107081 | + | 0.994250i | \(0.534151\pi\) | |||||||
\(882\) | 0.0212334 | 0.000714965 0 | ||||||||
\(883\) | −7.65280 | −0.257537 | −0.128769 | − | 0.991675i | \(-0.541102\pi\) | ||||
−0.128769 | + | 0.991675i | \(0.541102\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 56.3921 | 1.89560 | ||||||||
\(886\) | −65.8652 | −2.21279 | ||||||||
\(887\) | −8.90168 | −0.298889 | −0.149445 | − | 0.988770i | \(-0.547749\pi\) | ||||
−0.149445 | + | 0.988770i | \(0.547749\pi\) | |||||||
\(888\) | 11.4698 | 0.384902 | ||||||||
\(889\) | −11.6715 | −0.391450 | ||||||||
\(890\) | 85.8967 | 2.87926 | ||||||||
\(891\) | −8.92394 | −0.298963 | ||||||||
\(892\) | 23.7160 | 0.794071 | ||||||||
\(893\) | 63.1216 | 2.11228 | ||||||||
\(894\) | 1.91264 | 0.0639682 | ||||||||
\(895\) | 21.1810 | 0.708002 | ||||||||
\(896\) | 25.2106 | 0.842228 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −59.2839 | −1.97833 | ||||||||
\(899\) | −35.5894 | −1.18697 | ||||||||
\(900\) | −0.495158 | −0.0165053 | ||||||||
\(901\) | −21.1881 | −0.705879 | ||||||||
\(902\) | 4.14139 | 0.137893 | ||||||||
\(903\) | −29.1918 | −0.971441 | ||||||||
\(904\) | −3.21279 | −0.106856 | ||||||||
\(905\) | −54.4308 | −1.80934 | ||||||||
\(906\) | −27.4536 | −0.912085 | ||||||||
\(907\) | −34.8690 | −1.15781 | −0.578903 | − | 0.815396i | \(-0.696519\pi\) | ||||
−0.578903 | + | 0.815396i | \(0.696519\pi\) | |||||||
\(908\) | −30.1869 | −1.00179 | ||||||||
\(909\) | 0.0168407 | 0.000558570 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.8230 | −0.457976 | −0.228988 | − | 0.973429i | \(-0.573542\pi\) | ||||
−0.228988 | + | 0.973429i | \(0.573542\pi\) | |||||||
\(912\) | 21.0533 | 0.697143 | ||||||||
\(913\) | 2.96049 | 0.0979778 | ||||||||
\(914\) | −6.75849 | −0.223551 | ||||||||
\(915\) | 90.1819 | 2.98132 | ||||||||
\(916\) | −4.86195 | −0.160644 | ||||||||
\(917\) | −37.9785 | −1.25416 | ||||||||
\(918\) | 52.8692 | 1.74494 | ||||||||
\(919\) | −18.7389 | −0.618139 | −0.309070 | − | 0.951039i | \(-0.600018\pi\) | ||||
−0.309070 | + | 0.951039i | \(0.600018\pi\) | |||||||
\(920\) | −18.4814 | −0.609314 | ||||||||
\(921\) | 10.3617 | 0.341430 | ||||||||
\(922\) | −11.5064 | −0.378944 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 11.5197 | 0.378970 | ||||||||
\(925\) | −39.2657 | −1.29105 | ||||||||
\(926\) | −34.9573 | −1.14877 | ||||||||
\(927\) | 0.216999 | 0.00712719 | ||||||||
\(928\) | −54.6814 | −1.79501 | ||||||||
\(929\) | −10.8192 | −0.354966 | −0.177483 | − | 0.984124i | \(-0.556795\pi\) | ||||
−0.177483 | + | 0.984124i | \(0.556795\pi\) | |||||||
\(930\) | −66.6752 | −2.18637 | ||||||||
\(931\) | −1.96644 | −0.0644474 | ||||||||
\(932\) | −26.7419 | −0.875960 | ||||||||
\(933\) | 16.6295 | 0.544426 | ||||||||
\(934\) | −81.7696 | −2.67558 | ||||||||
\(935\) | −16.7585 | −0.548060 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50.1230 | −1.63745 | −0.818724 | − | 0.574187i | \(-0.805318\pi\) | ||||
−0.818724 | + | 0.574187i | \(0.805318\pi\) | |||||||
\(938\) | 72.8444 | 2.37845 | ||||||||
\(939\) | −2.79666 | −0.0912654 | ||||||||
\(940\) | −116.508 | −3.80007 | ||||||||
\(941\) | 54.8886 | 1.78932 | 0.894659 | − | 0.446749i | \(-0.147418\pi\) | ||||
0.894659 | + | 0.446749i | \(0.147418\pi\) | |||||||
\(942\) | −73.8764 | −2.40702 | ||||||||
\(943\) | 7.84027 | 0.255314 | ||||||||
\(944\) | −22.5358 | −0.733479 | ||||||||
\(945\) | 47.5637 | 1.54725 | ||||||||
\(946\) | −14.1209 | −0.459111 | ||||||||
\(947\) | −0.903664 | −0.0293651 | −0.0146826 | − | 0.999892i | \(-0.504674\pi\) | ||||
−0.0146826 | + | 0.999892i | \(0.504674\pi\) | |||||||
\(948\) | −68.4621 | −2.22355 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 81.1511 | 2.63289 | ||||||||
\(951\) | 4.59402 | 0.148971 | ||||||||
\(952\) | −15.5885 | −0.505227 | ||||||||
\(953\) | −33.0470 | −1.07050 | −0.535248 | − | 0.844695i | \(-0.679782\pi\) | ||||
−0.535248 | + | 0.844695i | \(0.679782\pi\) | |||||||
\(954\) | 0.241766 | 0.00782746 | ||||||||
\(955\) | 26.3800 | 0.853636 | ||||||||
\(956\) | −23.4660 | −0.758944 | ||||||||
\(957\) | −12.0769 | −0.390390 | ||||||||
\(958\) | 15.5405 | 0.502090 | ||||||||
\(959\) | −56.0596 | −1.81026 | ||||||||
\(960\) | −72.5349 | −2.34105 | ||||||||
\(961\) | −5.16562 | −0.166633 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.280991 | 0.00905480 | ||||||||
\(964\) | −45.8892 | −1.47799 | ||||||||
\(965\) | −36.0827 | −1.16154 | ||||||||
\(966\) | 38.5936 | 1.24173 | ||||||||
\(967\) | 12.7841 | 0.411108 | 0.205554 | − | 0.978646i | \(-0.434100\pi\) | ||||
0.205554 | + | 0.978646i | \(0.434100\pi\) | |||||||
\(968\) | 1.28356 | 0.0412553 | ||||||||
\(969\) | −40.6932 | −1.30725 | ||||||||
\(970\) | −9.78057 | −0.314035 | ||||||||
\(971\) | 8.74157 | 0.280530 | 0.140265 | − | 0.990114i | \(-0.455204\pi\) | ||||
0.140265 | + | 0.990114i | \(0.455204\pi\) | |||||||
\(972\) | −0.678949 | −0.0217773 | ||||||||
\(973\) | −24.8080 | −0.795308 | ||||||||
\(974\) | −41.9929 | −1.34554 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −36.0392 | −1.15359 | ||||||||
\(977\) | −28.2808 | −0.904784 | −0.452392 | − | 0.891819i | \(-0.649429\pi\) | ||||
−0.452392 | + | 0.891819i | \(0.649429\pi\) | |||||||
\(978\) | −41.8326 | −1.33766 | ||||||||
\(979\) | −11.2939 | −0.360955 | ||||||||
\(980\) | 3.62959 | 0.115943 | ||||||||
\(981\) | −0.335178 | −0.0107014 | ||||||||
\(982\) | −1.19333 | −0.0380806 | ||||||||
\(983\) | 37.8496 | 1.20722 | 0.603608 | − | 0.797281i | \(-0.293729\pi\) | ||||
0.603608 | + | 0.797281i | \(0.293729\pi\) | |||||||
\(984\) | −4.27548 | −0.136297 | ||||||||
\(985\) | 31.4817 | 1.00309 | ||||||||
\(986\) | 70.9488 | 2.25947 | ||||||||
\(987\) | 56.0415 | 1.78382 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −26.7330 | −0.850061 | ||||||||
\(990\) | 0.191221 | 0.00607742 | ||||||||
\(991\) | 0.282659 | 0.00897896 | 0.00448948 | − | 0.999990i | \(-0.498571\pi\) | ||||
0.00448948 | + | 0.999990i | \(0.498571\pi\) | |||||||
\(992\) | 39.6933 | 1.26026 | ||||||||
\(993\) | 10.3212 | 0.327535 | ||||||||
\(994\) | 23.2860 | 0.738587 | ||||||||
\(995\) | −10.9265 | −0.346393 | ||||||||
\(996\) | −13.2687 | −0.420435 | ||||||||
\(997\) | 9.47402 | 0.300045 | 0.150023 | − | 0.988683i | \(-0.452065\pi\) | ||||
0.150023 | + | 0.988683i | \(0.452065\pi\) | |||||||
\(998\) | −48.2539 | −1.52745 | ||||||||
\(999\) | −27.0324 | −0.855268 |
(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 | 1859.2.a.t.1.17 | yes | 21 | |
13.12 | even | 2 | 1859.2.a.s.1.5 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1859.2.a.s.1.5 | ✓ | 21 | 13.12 | even | 2 | ||
1859.2.a.t.1.17 | yes | 21 | 1.1 | even | 1 | trivial |