Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4010,2,Mod(1,4010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4010, 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("4010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4010 = 2 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4010.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0200112105\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 7 x^{14} - 7 x^{13} + 133 x^{12} - 99 x^{11} - 941 x^{10} + 1290 x^{9} + 3031 x^{8} - 5452 x^{7} - 4098 x^{6} + 9986 x^{5} + 850 x^{4} - 7216 x^{3} + 1688 x^{2} + \cdots - 512 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Root | \(0.495927\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4010.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 3.15350 | 1.82067 | 0.910337 | − | 0.413868i | \(-0.135823\pi\) | ||||
0.910337 | + | 0.413868i | \(0.135823\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −3.15350 | −1.28741 | ||||||||
\(7\) | −0.474552 | −0.179364 | −0.0896820 | − | 0.995970i | \(-0.528585\pi\) | ||||
−0.0896820 | + | 0.995970i | \(0.528585\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 6.94456 | 2.31485 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −1.05395 | −0.317777 | −0.158888 | − | 0.987297i | \(-0.550791\pi\) | ||||
−0.158888 | + | 0.987297i | \(0.550791\pi\) | |||||||
\(12\) | 3.15350 | 0.910337 | ||||||||
\(13\) | −3.43732 | −0.953340 | −0.476670 | − | 0.879082i | \(-0.658156\pi\) | ||||
−0.476670 | + | 0.879082i | \(0.658156\pi\) | |||||||
\(14\) | 0.474552 | 0.126829 | ||||||||
\(15\) | −3.15350 | −0.814230 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.69477 | −1.13865 | −0.569325 | − | 0.822113i | \(-0.692795\pi\) | ||||
−0.569325 | + | 0.822113i | \(0.692795\pi\) | |||||||
\(18\) | −6.94456 | −1.63685 | ||||||||
\(19\) | −6.53467 | −1.49916 | −0.749578 | − | 0.661916i | \(-0.769744\pi\) | ||||
−0.749578 | + | 0.661916i | \(0.769744\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −1.49650 | −0.326563 | ||||||||
\(22\) | 1.05395 | 0.224702 | ||||||||
\(23\) | −6.00037 | −1.25116 | −0.625582 | − | 0.780159i | \(-0.715138\pi\) | ||||
−0.625582 | + | 0.780159i | \(0.715138\pi\) | |||||||
\(24\) | −3.15350 | −0.643705 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.43732 | 0.674113 | ||||||||
\(27\) | 12.4392 | 2.39392 | ||||||||
\(28\) | −0.474552 | −0.0896820 | ||||||||
\(29\) | 8.30861 | 1.54287 | 0.771435 | − | 0.636309i | \(-0.219539\pi\) | ||||
0.771435 | + | 0.636309i | \(0.219539\pi\) | |||||||
\(30\) | 3.15350 | 0.575748 | ||||||||
\(31\) | 0.592756 | 0.106462 | 0.0532311 | − | 0.998582i | \(-0.483048\pi\) | ||||
0.0532311 | + | 0.998582i | \(0.483048\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −3.32362 | −0.578568 | ||||||||
\(34\) | 4.69477 | 0.805147 | ||||||||
\(35\) | 0.474552 | 0.0802140 | ||||||||
\(36\) | 6.94456 | 1.15743 | ||||||||
\(37\) | 0.575428 | 0.0945998 | 0.0472999 | − | 0.998881i | \(-0.484938\pi\) | ||||
0.0472999 | + | 0.998881i | \(0.484938\pi\) | |||||||
\(38\) | 6.53467 | 1.06006 | ||||||||
\(39\) | −10.8396 | −1.73572 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 2.13638 | 0.333646 | 0.166823 | − | 0.985987i | \(-0.446649\pi\) | ||||
0.166823 | + | 0.985987i | \(0.446649\pi\) | |||||||
\(42\) | 1.49650 | 0.230915 | ||||||||
\(43\) | −3.03439 | −0.462740 | −0.231370 | − | 0.972866i | \(-0.574321\pi\) | ||||
−0.231370 | + | 0.972866i | \(0.574321\pi\) | |||||||
\(44\) | −1.05395 | −0.158888 | ||||||||
\(45\) | −6.94456 | −1.03523 | ||||||||
\(46\) | 6.00037 | 0.884706 | ||||||||
\(47\) | −1.96294 | −0.286325 | −0.143162 | − | 0.989699i | \(-0.545727\pi\) | ||||
−0.143162 | + | 0.989699i | \(0.545727\pi\) | |||||||
\(48\) | 3.15350 | 0.455168 | ||||||||
\(49\) | −6.77480 | −0.967829 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −14.8050 | −2.07311 | ||||||||
\(52\) | −3.43732 | −0.476670 | ||||||||
\(53\) | −6.30721 | −0.866362 | −0.433181 | − | 0.901307i | \(-0.642609\pi\) | ||||
−0.433181 | + | 0.901307i | \(0.642609\pi\) | |||||||
\(54\) | −12.4392 | −1.69275 | ||||||||
\(55\) | 1.05395 | 0.142114 | ||||||||
\(56\) | 0.474552 | 0.0634147 | ||||||||
\(57\) | −20.6071 | −2.72948 | ||||||||
\(58\) | −8.30861 | −1.09097 | ||||||||
\(59\) | −4.62666 | −0.602340 | −0.301170 | − | 0.953571i | \(-0.597377\pi\) | ||||
−0.301170 | + | 0.953571i | \(0.597377\pi\) | |||||||
\(60\) | −3.15350 | −0.407115 | ||||||||
\(61\) | 13.0715 | 1.67364 | 0.836819 | − | 0.547480i | \(-0.184413\pi\) | ||||
0.836819 | + | 0.547480i | \(0.184413\pi\) | |||||||
\(62\) | −0.592756 | −0.0752801 | ||||||||
\(63\) | −3.29555 | −0.415201 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.43732 | 0.426347 | ||||||||
\(66\) | 3.32362 | 0.409109 | ||||||||
\(67\) | −14.9844 | −1.83063 | −0.915316 | − | 0.402737i | \(-0.868059\pi\) | ||||
−0.915316 | + | 0.402737i | \(0.868059\pi\) | |||||||
\(68\) | −4.69477 | −0.569325 | ||||||||
\(69\) | −18.9222 | −2.27796 | ||||||||
\(70\) | −0.474552 | −0.0567198 | ||||||||
\(71\) | −10.7215 | −1.27240 | −0.636201 | − | 0.771523i | \(-0.719495\pi\) | ||||
−0.636201 | + | 0.771523i | \(0.719495\pi\) | |||||||
\(72\) | −6.94456 | −0.818424 | ||||||||
\(73\) | −6.62649 | −0.775572 | −0.387786 | − | 0.921749i | \(-0.626760\pi\) | ||||
−0.387786 | + | 0.921749i | \(0.626760\pi\) | |||||||
\(74\) | −0.575428 | −0.0668922 | ||||||||
\(75\) | 3.15350 | 0.364135 | ||||||||
\(76\) | −6.53467 | −0.749578 | ||||||||
\(77\) | 0.500153 | 0.0569977 | ||||||||
\(78\) | 10.8396 | 1.22734 | ||||||||
\(79\) | −10.7602 | −1.21062 | −0.605308 | − | 0.795991i | \(-0.706950\pi\) | ||||
−0.605308 | + | 0.795991i | \(0.706950\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 18.3932 | 2.04369 | ||||||||
\(82\) | −2.13638 | −0.235923 | ||||||||
\(83\) | 12.6166 | 1.38485 | 0.692427 | − | 0.721488i | \(-0.256542\pi\) | ||||
0.692427 | + | 0.721488i | \(0.256542\pi\) | |||||||
\(84\) | −1.49650 | −0.163282 | ||||||||
\(85\) | 4.69477 | 0.509220 | ||||||||
\(86\) | 3.03439 | 0.327207 | ||||||||
\(87\) | 26.2012 | 2.80906 | ||||||||
\(88\) | 1.05395 | 0.112351 | ||||||||
\(89\) | 2.47205 | 0.262037 | 0.131018 | − | 0.991380i | \(-0.458175\pi\) | ||||
0.131018 | + | 0.991380i | \(0.458175\pi\) | |||||||
\(90\) | 6.94456 | 0.732020 | ||||||||
\(91\) | 1.63119 | 0.170995 | ||||||||
\(92\) | −6.00037 | −0.625582 | ||||||||
\(93\) | 1.86926 | 0.193833 | ||||||||
\(94\) | 1.96294 | 0.202462 | ||||||||
\(95\) | 6.53467 | 0.670443 | ||||||||
\(96\) | −3.15350 | −0.321853 | ||||||||
\(97\) | −7.44033 | −0.755451 | −0.377725 | − | 0.925918i | \(-0.623294\pi\) | ||||
−0.377725 | + | 0.925918i | \(0.623294\pi\) | |||||||
\(98\) | 6.77480 | 0.684358 | ||||||||
\(99\) | −7.31919 | −0.735606 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 17.3668 | 1.72806 | 0.864032 | − | 0.503437i | \(-0.167931\pi\) | ||||
0.864032 | + | 0.503437i | \(0.167931\pi\) | |||||||
\(102\) | 14.8050 | 1.46591 | ||||||||
\(103\) | −18.4129 | −1.81428 | −0.907138 | − | 0.420833i | \(-0.861738\pi\) | ||||
−0.907138 | + | 0.420833i | \(0.861738\pi\) | |||||||
\(104\) | 3.43732 | 0.337057 | ||||||||
\(105\) | 1.49650 | 0.146043 | ||||||||
\(106\) | 6.30721 | 0.612611 | ||||||||
\(107\) | −12.0183 | −1.16185 | −0.580927 | − | 0.813956i | \(-0.697310\pi\) | ||||
−0.580927 | + | 0.813956i | \(0.697310\pi\) | |||||||
\(108\) | 12.4392 | 1.19696 | ||||||||
\(109\) | 13.1575 | 1.26026 | 0.630132 | − | 0.776488i | \(-0.283001\pi\) | ||||
0.630132 | + | 0.776488i | \(0.283001\pi\) | |||||||
\(110\) | −1.05395 | −0.100490 | ||||||||
\(111\) | 1.81461 | 0.172235 | ||||||||
\(112\) | −0.474552 | −0.0448410 | ||||||||
\(113\) | 3.81072 | 0.358482 | 0.179241 | − | 0.983805i | \(-0.442636\pi\) | ||||
0.179241 | + | 0.983805i | \(0.442636\pi\) | |||||||
\(114\) | 20.6071 | 1.93003 | ||||||||
\(115\) | 6.00037 | 0.559537 | ||||||||
\(116\) | 8.30861 | 0.771435 | ||||||||
\(117\) | −23.8706 | −2.20684 | ||||||||
\(118\) | 4.62666 | 0.425918 | ||||||||
\(119\) | 2.22792 | 0.204233 | ||||||||
\(120\) | 3.15350 | 0.287874 | ||||||||
\(121\) | −9.88920 | −0.899018 | ||||||||
\(122\) | −13.0715 | −1.18344 | ||||||||
\(123\) | 6.73706 | 0.607460 | ||||||||
\(124\) | 0.592756 | 0.0532311 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 3.29555 | 0.293591 | ||||||||
\(127\) | 13.1465 | 1.16656 | 0.583281 | − | 0.812271i | \(-0.301769\pi\) | ||||
0.583281 | + | 0.812271i | \(0.301769\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −9.56895 | −0.842499 | ||||||||
\(130\) | −3.43732 | −0.301473 | ||||||||
\(131\) | −0.566335 | −0.0494809 | −0.0247405 | − | 0.999694i | \(-0.507876\pi\) | ||||
−0.0247405 | + | 0.999694i | \(0.507876\pi\) | |||||||
\(132\) | −3.32362 | −0.289284 | ||||||||
\(133\) | 3.10104 | 0.268895 | ||||||||
\(134\) | 14.9844 | 1.29445 | ||||||||
\(135\) | −12.4392 | −1.07059 | ||||||||
\(136\) | 4.69477 | 0.402573 | ||||||||
\(137\) | −1.40749 | −0.120250 | −0.0601251 | − | 0.998191i | \(-0.519150\pi\) | ||||
−0.0601251 | + | 0.998191i | \(0.519150\pi\) | |||||||
\(138\) | 18.9222 | 1.61076 | ||||||||
\(139\) | 10.3966 | 0.881827 | 0.440913 | − | 0.897550i | \(-0.354655\pi\) | ||||
0.440913 | + | 0.897550i | \(0.354655\pi\) | |||||||
\(140\) | 0.474552 | 0.0401070 | ||||||||
\(141\) | −6.19014 | −0.521304 | ||||||||
\(142\) | 10.7215 | 0.899725 | ||||||||
\(143\) | 3.62275 | 0.302949 | ||||||||
\(144\) | 6.94456 | 0.578713 | ||||||||
\(145\) | −8.30861 | −0.689992 | ||||||||
\(146\) | 6.62649 | 0.548412 | ||||||||
\(147\) | −21.3643 | −1.76210 | ||||||||
\(148\) | 0.575428 | 0.0472999 | ||||||||
\(149\) | −22.1535 | −1.81489 | −0.907445 | − | 0.420172i | \(-0.861970\pi\) | ||||
−0.907445 | + | 0.420172i | \(0.861970\pi\) | |||||||
\(150\) | −3.15350 | −0.257482 | ||||||||
\(151\) | −9.77674 | −0.795620 | −0.397810 | − | 0.917468i | \(-0.630230\pi\) | ||||
−0.397810 | + | 0.917468i | \(0.630230\pi\) | |||||||
\(152\) | 6.53467 | 0.530032 | ||||||||
\(153\) | −32.6031 | −2.63581 | ||||||||
\(154\) | −0.500153 | −0.0403034 | ||||||||
\(155\) | −0.592756 | −0.0476113 | ||||||||
\(156\) | −10.8396 | −0.867861 | ||||||||
\(157\) | −3.67323 | −0.293156 | −0.146578 | − | 0.989199i | \(-0.546826\pi\) | ||||
−0.146578 | + | 0.989199i | \(0.546826\pi\) | |||||||
\(158\) | 10.7602 | 0.856035 | ||||||||
\(159\) | −19.8898 | −1.57736 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 2.84749 | 0.224414 | ||||||||
\(162\) | −18.3932 | −1.44511 | ||||||||
\(163\) | 4.65548 | 0.364646 | 0.182323 | − | 0.983239i | \(-0.441638\pi\) | ||||
0.182323 | + | 0.983239i | \(0.441638\pi\) | |||||||
\(164\) | 2.13638 | 0.166823 | ||||||||
\(165\) | 3.32362 | 0.258743 | ||||||||
\(166\) | −12.6166 | −0.979239 | ||||||||
\(167\) | −4.29110 | −0.332055 | −0.166028 | − | 0.986121i | \(-0.553094\pi\) | ||||
−0.166028 | + | 0.986121i | \(0.553094\pi\) | |||||||
\(168\) | 1.49650 | 0.115457 | ||||||||
\(169\) | −1.18486 | −0.0911427 | ||||||||
\(170\) | −4.69477 | −0.360073 | ||||||||
\(171\) | −45.3804 | −3.47033 | ||||||||
\(172\) | −3.03439 | −0.231370 | ||||||||
\(173\) | 23.3544 | 1.77561 | 0.887803 | − | 0.460224i | \(-0.152231\pi\) | ||||
0.887803 | + | 0.460224i | \(0.152231\pi\) | |||||||
\(174\) | −26.2012 | −1.98631 | ||||||||
\(175\) | −0.474552 | −0.0358728 | ||||||||
\(176\) | −1.05395 | −0.0794442 | ||||||||
\(177\) | −14.5902 | −1.09666 | ||||||||
\(178\) | −2.47205 | −0.185288 | ||||||||
\(179\) | 11.9470 | 0.892963 | 0.446481 | − | 0.894793i | \(-0.352677\pi\) | ||||
0.446481 | + | 0.894793i | \(0.352677\pi\) | |||||||
\(180\) | −6.94456 | −0.517617 | ||||||||
\(181\) | 16.2940 | 1.21112 | 0.605560 | − | 0.795799i | \(-0.292949\pi\) | ||||
0.605560 | + | 0.795799i | \(0.292949\pi\) | |||||||
\(182\) | −1.63119 | −0.120912 | ||||||||
\(183\) | 41.2211 | 3.04715 | ||||||||
\(184\) | 6.00037 | 0.442353 | ||||||||
\(185\) | −0.575428 | −0.0423063 | ||||||||
\(186\) | −1.86926 | −0.137061 | ||||||||
\(187\) | 4.94804 | 0.361836 | ||||||||
\(188\) | −1.96294 | −0.143162 | ||||||||
\(189\) | −5.90303 | −0.429382 | ||||||||
\(190\) | −6.53467 | −0.474075 | ||||||||
\(191\) | 13.0588 | 0.944902 | 0.472451 | − | 0.881357i | \(-0.343369\pi\) | ||||
0.472451 | + | 0.881357i | \(0.343369\pi\) | |||||||
\(192\) | 3.15350 | 0.227584 | ||||||||
\(193\) | 19.6904 | 1.41734 | 0.708672 | − | 0.705538i | \(-0.249295\pi\) | ||||
0.708672 | + | 0.705538i | \(0.249295\pi\) | |||||||
\(194\) | 7.44033 | 0.534185 | ||||||||
\(195\) | 10.8396 | 0.776238 | ||||||||
\(196\) | −6.77480 | −0.483914 | ||||||||
\(197\) | 16.9507 | 1.20769 | 0.603844 | − | 0.797102i | \(-0.293635\pi\) | ||||
0.603844 | + | 0.797102i | \(0.293635\pi\) | |||||||
\(198\) | 7.31919 | 0.520152 | ||||||||
\(199\) | −9.47071 | −0.671361 | −0.335680 | − | 0.941976i | \(-0.608966\pi\) | ||||
−0.335680 | + | 0.941976i | \(0.608966\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −47.2532 | −3.33298 | ||||||||
\(202\) | −17.3668 | −1.22193 | ||||||||
\(203\) | −3.94287 | −0.276735 | ||||||||
\(204\) | −14.8050 | −1.03655 | ||||||||
\(205\) | −2.13638 | −0.149211 | ||||||||
\(206\) | 18.4129 | 1.28289 | ||||||||
\(207\) | −41.6699 | −2.89626 | ||||||||
\(208\) | −3.43732 | −0.238335 | ||||||||
\(209\) | 6.88719 | 0.476397 | ||||||||
\(210\) | −1.49650 | −0.103268 | ||||||||
\(211\) | −22.7837 | −1.56850 | −0.784248 | − | 0.620447i | \(-0.786951\pi\) | ||||
−0.784248 | + | 0.620447i | \(0.786951\pi\) | |||||||
\(212\) | −6.30721 | −0.433181 | ||||||||
\(213\) | −33.8101 | −2.31663 | ||||||||
\(214\) | 12.0183 | 0.821555 | ||||||||
\(215\) | 3.03439 | 0.206944 | ||||||||
\(216\) | −12.4392 | −0.846377 | ||||||||
\(217\) | −0.281294 | −0.0190955 | ||||||||
\(218\) | −13.1575 | −0.891141 | ||||||||
\(219\) | −20.8966 | −1.41206 | ||||||||
\(220\) | 1.05395 | 0.0710570 | ||||||||
\(221\) | 16.1374 | 1.08552 | ||||||||
\(222\) | −1.81461 | −0.121789 | ||||||||
\(223\) | −3.34891 | −0.224259 | −0.112130 | − | 0.993694i | \(-0.535767\pi\) | ||||
−0.112130 | + | 0.993694i | \(0.535767\pi\) | |||||||
\(224\) | 0.474552 | 0.0317074 | ||||||||
\(225\) | 6.94456 | 0.462970 | ||||||||
\(226\) | −3.81072 | −0.253485 | ||||||||
\(227\) | −26.0852 | −1.73133 | −0.865667 | − | 0.500621i | \(-0.833105\pi\) | ||||
−0.865667 | + | 0.500621i | \(0.833105\pi\) | |||||||
\(228\) | −20.6071 | −1.36474 | ||||||||
\(229\) | 11.1271 | 0.735303 | 0.367651 | − | 0.929964i | \(-0.380162\pi\) | ||||
0.367651 | + | 0.929964i | \(0.380162\pi\) | |||||||
\(230\) | −6.00037 | −0.395653 | ||||||||
\(231\) | 1.57723 | 0.103774 | ||||||||
\(232\) | −8.30861 | −0.545487 | ||||||||
\(233\) | 17.6495 | 1.15625 | 0.578127 | − | 0.815947i | \(-0.303784\pi\) | ||||
0.578127 | + | 0.815947i | \(0.303784\pi\) | |||||||
\(234\) | 23.8706 | 1.56047 | ||||||||
\(235\) | 1.96294 | 0.128048 | ||||||||
\(236\) | −4.62666 | −0.301170 | ||||||||
\(237\) | −33.9323 | −2.20414 | ||||||||
\(238\) | −2.22792 | −0.144414 | ||||||||
\(239\) | −22.4986 | −1.45532 | −0.727658 | − | 0.685940i | \(-0.759391\pi\) | ||||
−0.727658 | + | 0.685940i | \(0.759391\pi\) | |||||||
\(240\) | −3.15350 | −0.203557 | ||||||||
\(241\) | −17.8502 | −1.14983 | −0.574916 | − | 0.818212i | \(-0.694965\pi\) | ||||
−0.574916 | + | 0.818212i | \(0.694965\pi\) | |||||||
\(242\) | 9.88920 | 0.635702 | ||||||||
\(243\) | 20.6854 | 1.32697 | ||||||||
\(244\) | 13.0715 | 0.836819 | ||||||||
\(245\) | 6.77480 | 0.432826 | ||||||||
\(246\) | −6.73706 | −0.429539 | ||||||||
\(247\) | 22.4617 | 1.42921 | ||||||||
\(248\) | −0.592756 | −0.0376401 | ||||||||
\(249\) | 39.7865 | 2.52137 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 12.9427 | 0.816934 | 0.408467 | − | 0.912773i | \(-0.366064\pi\) | ||||
0.408467 | + | 0.912773i | \(0.366064\pi\) | |||||||
\(252\) | −3.29555 | −0.207600 | ||||||||
\(253\) | 6.32407 | 0.397591 | ||||||||
\(254\) | −13.1465 | −0.824883 | ||||||||
\(255\) | 14.8050 | 0.927123 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −17.4206 | −1.08667 | −0.543333 | − | 0.839517i | \(-0.682838\pi\) | ||||
−0.543333 | + | 0.839517i | \(0.682838\pi\) | |||||||
\(258\) | 9.56895 | 0.595737 | ||||||||
\(259\) | −0.273071 | −0.0169678 | ||||||||
\(260\) | 3.43732 | 0.213173 | ||||||||
\(261\) | 57.6996 | 3.57151 | ||||||||
\(262\) | 0.566335 | 0.0349883 | ||||||||
\(263\) | 10.9851 | 0.677373 | 0.338687 | − | 0.940899i | \(-0.390017\pi\) | ||||
0.338687 | + | 0.940899i | \(0.390017\pi\) | |||||||
\(264\) | 3.32362 | 0.204555 | ||||||||
\(265\) | 6.30721 | 0.387449 | ||||||||
\(266\) | −3.10104 | −0.190137 | ||||||||
\(267\) | 7.79561 | 0.477083 | ||||||||
\(268\) | −14.9844 | −0.915316 | ||||||||
\(269\) | −10.8695 | −0.662724 | −0.331362 | − | 0.943504i | \(-0.607508\pi\) | ||||
−0.331362 | + | 0.943504i | \(0.607508\pi\) | |||||||
\(270\) | 12.4392 | 0.757023 | ||||||||
\(271\) | 12.3201 | 0.748394 | 0.374197 | − | 0.927349i | \(-0.377918\pi\) | ||||
0.374197 | + | 0.927349i | \(0.377918\pi\) | |||||||
\(272\) | −4.69477 | −0.284662 | ||||||||
\(273\) | 5.14394 | 0.311326 | ||||||||
\(274\) | 1.40749 | 0.0850297 | ||||||||
\(275\) | −1.05395 | −0.0635554 | ||||||||
\(276\) | −18.9222 | −1.13898 | ||||||||
\(277\) | −6.25679 | −0.375934 | −0.187967 | − | 0.982175i | \(-0.560190\pi\) | ||||
−0.187967 | + | 0.982175i | \(0.560190\pi\) | |||||||
\(278\) | −10.3966 | −0.623546 | ||||||||
\(279\) | 4.11643 | 0.246444 | ||||||||
\(280\) | −0.474552 | −0.0283599 | ||||||||
\(281\) | 23.2116 | 1.38469 | 0.692345 | − | 0.721567i | \(-0.256578\pi\) | ||||
0.692345 | + | 0.721567i | \(0.256578\pi\) | |||||||
\(282\) | 6.19014 | 0.368617 | ||||||||
\(283\) | 10.4175 | 0.619253 | 0.309627 | − | 0.950858i | \(-0.399796\pi\) | ||||
0.309627 | + | 0.950858i | \(0.399796\pi\) | |||||||
\(284\) | −10.7215 | −0.636201 | ||||||||
\(285\) | 20.6071 | 1.22066 | ||||||||
\(286\) | −3.62275 | −0.214218 | ||||||||
\(287\) | −1.01382 | −0.0598440 | ||||||||
\(288\) | −6.94456 | −0.409212 | ||||||||
\(289\) | 5.04089 | 0.296523 | ||||||||
\(290\) | 8.30861 | 0.487898 | ||||||||
\(291\) | −23.4631 | −1.37543 | ||||||||
\(292\) | −6.62649 | −0.387786 | ||||||||
\(293\) | −1.15574 | −0.0675189 | −0.0337595 | − | 0.999430i | \(-0.510748\pi\) | ||||
−0.0337595 | + | 0.999430i | \(0.510748\pi\) | |||||||
\(294\) | 21.3643 | 1.24599 | ||||||||
\(295\) | 4.62666 | 0.269374 | ||||||||
\(296\) | −0.575428 | −0.0334461 | ||||||||
\(297\) | −13.1102 | −0.760731 | ||||||||
\(298\) | 22.1535 | 1.28332 | ||||||||
\(299\) | 20.6252 | 1.19278 | ||||||||
\(300\) | 3.15350 | 0.182067 | ||||||||
\(301\) | 1.43998 | 0.0829989 | ||||||||
\(302\) | 9.77674 | 0.562588 | ||||||||
\(303\) | 54.7663 | 3.14624 | ||||||||
\(304\) | −6.53467 | −0.374789 | ||||||||
\(305\) | −13.0715 | −0.748474 | ||||||||
\(306\) | 32.6031 | 1.86380 | ||||||||
\(307\) | −3.59248 | −0.205034 | −0.102517 | − | 0.994731i | \(-0.532690\pi\) | ||||
−0.102517 | + | 0.994731i | \(0.532690\pi\) | |||||||
\(308\) | 0.500153 | 0.0284988 | ||||||||
\(309\) | −58.0651 | −3.30321 | ||||||||
\(310\) | 0.592756 | 0.0336663 | ||||||||
\(311\) | −16.7427 | −0.949391 | −0.474696 | − | 0.880150i | \(-0.657442\pi\) | ||||
−0.474696 | + | 0.880150i | \(0.657442\pi\) | |||||||
\(312\) | 10.8396 | 0.613670 | ||||||||
\(313\) | −27.9220 | −1.57824 | −0.789122 | − | 0.614236i | \(-0.789464\pi\) | ||||
−0.789122 | + | 0.614236i | \(0.789464\pi\) | |||||||
\(314\) | 3.67323 | 0.207292 | ||||||||
\(315\) | 3.29555 | 0.185683 | ||||||||
\(316\) | −10.7602 | −0.605308 | ||||||||
\(317\) | 24.5975 | 1.38153 | 0.690766 | − | 0.723078i | \(-0.257274\pi\) | ||||
0.690766 | + | 0.723078i | \(0.257274\pi\) | |||||||
\(318\) | 19.8898 | 1.11536 | ||||||||
\(319\) | −8.75682 | −0.490288 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −37.8997 | −2.11536 | ||||||||
\(322\) | −2.84749 | −0.158684 | ||||||||
\(323\) | 30.6788 | 1.70701 | ||||||||
\(324\) | 18.3932 | 1.02184 | ||||||||
\(325\) | −3.43732 | −0.190668 | ||||||||
\(326\) | −4.65548 | −0.257843 | ||||||||
\(327\) | 41.4923 | 2.29453 | ||||||||
\(328\) | −2.13638 | −0.117962 | ||||||||
\(329\) | 0.931519 | 0.0513563 | ||||||||
\(330\) | −3.32362 | −0.182959 | ||||||||
\(331\) | −0.197429 | −0.0108517 | −0.00542583 | − | 0.999985i | \(-0.501727\pi\) | ||||
−0.00542583 | + | 0.999985i | \(0.501727\pi\) | |||||||
\(332\) | 12.6166 | 0.692427 | ||||||||
\(333\) | 3.99609 | 0.218985 | ||||||||
\(334\) | 4.29110 | 0.234799 | ||||||||
\(335\) | 14.9844 | 0.818683 | ||||||||
\(336\) | −1.49650 | −0.0816408 | ||||||||
\(337\) | 1.92974 | 0.105119 | 0.0525597 | − | 0.998618i | \(-0.483262\pi\) | ||||
0.0525597 | + | 0.998618i | \(0.483262\pi\) | |||||||
\(338\) | 1.18486 | 0.0644476 | ||||||||
\(339\) | 12.0171 | 0.652679 | ||||||||
\(340\) | 4.69477 | 0.254610 | ||||||||
\(341\) | −0.624733 | −0.0338312 | ||||||||
\(342\) | 45.3804 | 2.45389 | ||||||||
\(343\) | 6.53686 | 0.352957 | ||||||||
\(344\) | 3.03439 | 0.163603 | ||||||||
\(345\) | 18.9222 | 1.01874 | ||||||||
\(346\) | −23.3544 | −1.25554 | ||||||||
\(347\) | 9.84709 | 0.528620 | 0.264310 | − | 0.964438i | \(-0.414856\pi\) | ||||
0.264310 | + | 0.964438i | \(0.414856\pi\) | |||||||
\(348\) | 26.2012 | 1.40453 | ||||||||
\(349\) | 20.8401 | 1.11554 | 0.557772 | − | 0.829994i | \(-0.311656\pi\) | ||||
0.557772 | + | 0.829994i | \(0.311656\pi\) | |||||||
\(350\) | 0.474552 | 0.0253659 | ||||||||
\(351\) | −42.7573 | −2.28222 | ||||||||
\(352\) | 1.05395 | 0.0561755 | ||||||||
\(353\) | 0.766412 | 0.0407920 | 0.0203960 | − | 0.999792i | \(-0.493507\pi\) | ||||
0.0203960 | + | 0.999792i | \(0.493507\pi\) | |||||||
\(354\) | 14.5902 | 0.775458 | ||||||||
\(355\) | 10.7215 | 0.569036 | ||||||||
\(356\) | 2.47205 | 0.131018 | ||||||||
\(357\) | 7.02573 | 0.371841 | ||||||||
\(358\) | −11.9470 | −0.631420 | ||||||||
\(359\) | 28.3525 | 1.49639 | 0.748195 | − | 0.663479i | \(-0.230921\pi\) | ||||
0.748195 | + | 0.663479i | \(0.230921\pi\) | |||||||
\(360\) | 6.94456 | 0.366010 | ||||||||
\(361\) | 23.7020 | 1.24747 | ||||||||
\(362\) | −16.2940 | −0.856392 | ||||||||
\(363\) | −31.1856 | −1.63682 | ||||||||
\(364\) | 1.63119 | 0.0854974 | ||||||||
\(365\) | 6.62649 | 0.346846 | ||||||||
\(366\) | −41.2211 | −2.15466 | ||||||||
\(367\) | −16.1601 | −0.843549 | −0.421774 | − | 0.906701i | \(-0.638593\pi\) | ||||
−0.421774 | + | 0.906701i | \(0.638593\pi\) | |||||||
\(368\) | −6.00037 | −0.312791 | ||||||||
\(369\) | 14.8362 | 0.772341 | ||||||||
\(370\) | 0.575428 | 0.0299151 | ||||||||
\(371\) | 2.99310 | 0.155394 | ||||||||
\(372\) | 1.86926 | 0.0969165 | ||||||||
\(373\) | −15.0275 | −0.778096 | −0.389048 | − | 0.921217i | \(-0.627196\pi\) | ||||
−0.389048 | + | 0.921217i | \(0.627196\pi\) | |||||||
\(374\) | −4.94804 | −0.255857 | ||||||||
\(375\) | −3.15350 | −0.162846 | ||||||||
\(376\) | 1.96294 | 0.101231 | ||||||||
\(377\) | −28.5593 | −1.47088 | ||||||||
\(378\) | 5.90303 | 0.303619 | ||||||||
\(379\) | −14.6512 | −0.752581 | −0.376291 | − | 0.926502i | \(-0.622801\pi\) | ||||
−0.376291 | + | 0.926502i | \(0.622801\pi\) | |||||||
\(380\) | 6.53467 | 0.335222 | ||||||||
\(381\) | 41.4574 | 2.12393 | ||||||||
\(382\) | −13.0588 | −0.668146 | ||||||||
\(383\) | 13.9724 | 0.713956 | 0.356978 | − | 0.934113i | \(-0.383807\pi\) | ||||
0.356978 | + | 0.934113i | \(0.383807\pi\) | |||||||
\(384\) | −3.15350 | −0.160926 | ||||||||
\(385\) | −0.500153 | −0.0254901 | ||||||||
\(386\) | −19.6904 | −1.00221 | ||||||||
\(387\) | −21.0725 | −1.07118 | ||||||||
\(388\) | −7.44033 | −0.377725 | ||||||||
\(389\) | 3.34407 | 0.169551 | 0.0847755 | − | 0.996400i | \(-0.472983\pi\) | ||||
0.0847755 | + | 0.996400i | \(0.472983\pi\) | |||||||
\(390\) | −10.8396 | −0.548883 | ||||||||
\(391\) | 28.1704 | 1.42464 | ||||||||
\(392\) | 6.77480 | 0.342179 | ||||||||
\(393\) | −1.78594 | −0.0900886 | ||||||||
\(394\) | −16.9507 | −0.853964 | ||||||||
\(395\) | 10.7602 | 0.541404 | ||||||||
\(396\) | −7.31919 | −0.367803 | ||||||||
\(397\) | 4.05193 | 0.203360 | 0.101680 | − | 0.994817i | \(-0.467578\pi\) | ||||
0.101680 | + | 0.994817i | \(0.467578\pi\) | |||||||
\(398\) | 9.47071 | 0.474724 | ||||||||
\(399\) | 9.77914 | 0.489569 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | 47.2532 | 2.35677 | ||||||||
\(403\) | −2.03749 | −0.101495 | ||||||||
\(404\) | 17.3668 | 0.864032 | ||||||||
\(405\) | −18.3932 | −0.913965 | ||||||||
\(406\) | 3.94287 | 0.195681 | ||||||||
\(407\) | −0.606470 | −0.0300616 | ||||||||
\(408\) | 14.8050 | 0.732955 | ||||||||
\(409\) | −35.2075 | −1.74090 | −0.870449 | − | 0.492259i | \(-0.836171\pi\) | ||||
−0.870449 | + | 0.492259i | \(0.836171\pi\) | |||||||
\(410\) | 2.13638 | 0.105508 | ||||||||
\(411\) | −4.43853 | −0.218936 | ||||||||
\(412\) | −18.4129 | −0.907138 | ||||||||
\(413\) | 2.19559 | 0.108038 | ||||||||
\(414\) | 41.6699 | 2.04796 | ||||||||
\(415\) | −12.6166 | −0.619325 | ||||||||
\(416\) | 3.43732 | 0.168528 | ||||||||
\(417\) | 32.7856 | 1.60552 | ||||||||
\(418\) | −6.88719 | −0.336864 | ||||||||
\(419\) | 12.9090 | 0.630645 | 0.315322 | − | 0.948985i | \(-0.397887\pi\) | ||||
0.315322 | + | 0.948985i | \(0.397887\pi\) | |||||||
\(420\) | 1.49650 | 0.0730217 | ||||||||
\(421\) | −25.0552 | −1.22112 | −0.610559 | − | 0.791971i | \(-0.709055\pi\) | ||||
−0.610559 | + | 0.791971i | \(0.709055\pi\) | |||||||
\(422\) | 22.7837 | 1.10909 | ||||||||
\(423\) | −13.6318 | −0.662799 | ||||||||
\(424\) | 6.30721 | 0.306305 | ||||||||
\(425\) | −4.69477 | −0.227730 | ||||||||
\(426\) | 33.8101 | 1.63810 | ||||||||
\(427\) | −6.20312 | −0.300190 | ||||||||
\(428\) | −12.0183 | −0.580927 | ||||||||
\(429\) | 11.4243 | 0.551572 | ||||||||
\(430\) | −3.03439 | −0.146331 | ||||||||
\(431\) | −18.2753 | −0.880289 | −0.440145 | − | 0.897927i | \(-0.645073\pi\) | ||||
−0.440145 | + | 0.897927i | \(0.645073\pi\) | |||||||
\(432\) | 12.4392 | 0.598479 | ||||||||
\(433\) | −24.2793 | −1.16679 | −0.583394 | − | 0.812189i | \(-0.698276\pi\) | ||||
−0.583394 | + | 0.812189i | \(0.698276\pi\) | |||||||
\(434\) | 0.281294 | 0.0135025 | ||||||||
\(435\) | −26.2012 | −1.25625 | ||||||||
\(436\) | 13.1575 | 0.630132 | ||||||||
\(437\) | 39.2105 | 1.87569 | ||||||||
\(438\) | 20.8966 | 0.998480 | ||||||||
\(439\) | 39.0419 | 1.86337 | 0.931683 | − | 0.363272i | \(-0.118340\pi\) | ||||
0.931683 | + | 0.363272i | \(0.118340\pi\) | |||||||
\(440\) | −1.05395 | −0.0502449 | ||||||||
\(441\) | −47.0480 | −2.24038 | ||||||||
\(442\) | −16.1374 | −0.767579 | ||||||||
\(443\) | 28.5384 | 1.35590 | 0.677951 | − | 0.735107i | \(-0.262868\pi\) | ||||
0.677951 | + | 0.735107i | \(0.262868\pi\) | |||||||
\(444\) | 1.81461 | 0.0861177 | ||||||||
\(445\) | −2.47205 | −0.117186 | ||||||||
\(446\) | 3.34891 | 0.158575 | ||||||||
\(447\) | −69.8612 | −3.30432 | ||||||||
\(448\) | −0.474552 | −0.0224205 | ||||||||
\(449\) | −6.91622 | −0.326396 | −0.163198 | − | 0.986593i | \(-0.552181\pi\) | ||||
−0.163198 | + | 0.986593i | \(0.552181\pi\) | |||||||
\(450\) | −6.94456 | −0.327370 | ||||||||
\(451\) | −2.25163 | −0.106025 | ||||||||
\(452\) | 3.81072 | 0.179241 | ||||||||
\(453\) | −30.8309 | −1.44856 | ||||||||
\(454\) | 26.0852 | 1.22424 | ||||||||
\(455\) | −1.63119 | −0.0764712 | ||||||||
\(456\) | 20.6071 | 0.965015 | ||||||||
\(457\) | −3.94501 | −0.184540 | −0.0922698 | − | 0.995734i | \(-0.529412\pi\) | ||||
−0.0922698 | + | 0.995734i | \(0.529412\pi\) | |||||||
\(458\) | −11.1271 | −0.519937 | ||||||||
\(459\) | −58.3990 | −2.72583 | ||||||||
\(460\) | 6.00037 | 0.279769 | ||||||||
\(461\) | −12.2147 | −0.568894 | −0.284447 | − | 0.958692i | \(-0.591810\pi\) | ||||
−0.284447 | + | 0.958692i | \(0.591810\pi\) | |||||||
\(462\) | −1.57723 | −0.0733794 | ||||||||
\(463\) | 0.135978 | 0.00631943 | 0.00315972 | − | 0.999995i | \(-0.498994\pi\) | ||||
0.00315972 | + | 0.999995i | \(0.498994\pi\) | |||||||
\(464\) | 8.30861 | 0.385717 | ||||||||
\(465\) | −1.86926 | −0.0866847 | ||||||||
\(466\) | −17.6495 | −0.817595 | ||||||||
\(467\) | −19.1532 | −0.886305 | −0.443152 | − | 0.896446i | \(-0.646140\pi\) | ||||
−0.443152 | + | 0.896446i | \(0.646140\pi\) | |||||||
\(468\) | −23.8706 | −1.10342 | ||||||||
\(469\) | 7.11086 | 0.328349 | ||||||||
\(470\) | −1.96294 | −0.0905438 | ||||||||
\(471\) | −11.5835 | −0.533741 | ||||||||
\(472\) | 4.62666 | 0.212959 | ||||||||
\(473\) | 3.19808 | 0.147048 | ||||||||
\(474\) | 33.9323 | 1.55856 | ||||||||
\(475\) | −6.53467 | −0.299831 | ||||||||
\(476\) | 2.22792 | 0.102116 | ||||||||
\(477\) | −43.8008 | −2.00550 | ||||||||
\(478\) | 22.4986 | 1.02906 | ||||||||
\(479\) | −24.0010 | −1.09663 | −0.548317 | − | 0.836271i | \(-0.684731\pi\) | ||||
−0.548317 | + | 0.836271i | \(0.684731\pi\) | |||||||
\(480\) | 3.15350 | 0.143937 | ||||||||
\(481\) | −1.97793 | −0.0901858 | ||||||||
\(482\) | 17.8502 | 0.813055 | ||||||||
\(483\) | 8.97956 | 0.408584 | ||||||||
\(484\) | −9.88920 | −0.449509 | ||||||||
\(485\) | 7.44033 | 0.337848 | ||||||||
\(486\) | −20.6854 | −0.938311 | ||||||||
\(487\) | −29.9631 | −1.35776 | −0.678878 | − | 0.734251i | \(-0.737534\pi\) | ||||
−0.678878 | + | 0.734251i | \(0.737534\pi\) | |||||||
\(488\) | −13.0715 | −0.591720 | ||||||||
\(489\) | 14.6811 | 0.663900 | ||||||||
\(490\) | −6.77480 | −0.306054 | ||||||||
\(491\) | 20.9770 | 0.946677 | 0.473338 | − | 0.880881i | \(-0.343049\pi\) | ||||
0.473338 | + | 0.880881i | \(0.343049\pi\) | |||||||
\(492\) | 6.73706 | 0.303730 | ||||||||
\(493\) | −39.0070 | −1.75679 | ||||||||
\(494\) | −22.4617 | −1.01060 | ||||||||
\(495\) | 7.31919 | 0.328973 | ||||||||
\(496\) | 0.592756 | 0.0266156 | ||||||||
\(497\) | 5.08789 | 0.228223 | ||||||||
\(498\) | −39.7865 | −1.78288 | ||||||||
\(499\) | −37.4023 | −1.67436 | −0.837178 | − | 0.546930i | \(-0.815796\pi\) | ||||
−0.837178 | + | 0.546930i | \(0.815796\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −13.5320 | −0.604564 | ||||||||
\(502\) | −12.9427 | −0.577659 | ||||||||
\(503\) | 37.6096 | 1.67693 | 0.838464 | − | 0.544958i | \(-0.183454\pi\) | ||||
0.838464 | + | 0.544958i | \(0.183454\pi\) | |||||||
\(504\) | 3.29555 | 0.146796 | ||||||||
\(505\) | −17.3668 | −0.772814 | ||||||||
\(506\) | −6.32407 | −0.281139 | ||||||||
\(507\) | −3.73644 | −0.165941 | ||||||||
\(508\) | 13.1465 | 0.583281 | ||||||||
\(509\) | 0.111220 | 0.00492972 | 0.00246486 | − | 0.999997i | \(-0.499215\pi\) | ||||
0.00246486 | + | 0.999997i | \(0.499215\pi\) | |||||||
\(510\) | −14.8050 | −0.655575 | ||||||||
\(511\) | 3.14462 | 0.139110 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −81.2858 | −3.58886 | ||||||||
\(514\) | 17.4206 | 0.768390 | ||||||||
\(515\) | 18.4129 | 0.811369 | ||||||||
\(516\) | −9.56895 | −0.421249 | ||||||||
\(517\) | 2.06884 | 0.0909873 | ||||||||
\(518\) | 0.273071 | 0.0119980 | ||||||||
\(519\) | 73.6482 | 3.23280 | ||||||||
\(520\) | −3.43732 | −0.150736 | ||||||||
\(521\) | −29.9013 | −1.31000 | −0.655000 | − | 0.755628i | \(-0.727332\pi\) | ||||
−0.655000 | + | 0.755628i | \(0.727332\pi\) | |||||||
\(522\) | −57.6996 | −2.52544 | ||||||||
\(523\) | 18.6140 | 0.813933 | 0.406967 | − | 0.913443i | \(-0.366587\pi\) | ||||
0.406967 | + | 0.913443i | \(0.366587\pi\) | |||||||
\(524\) | −0.566335 | −0.0247405 | ||||||||
\(525\) | −1.49650 | −0.0653126 | ||||||||
\(526\) | −10.9851 | −0.478975 | ||||||||
\(527\) | −2.78286 | −0.121223 | ||||||||
\(528\) | −3.32362 | −0.144642 | ||||||||
\(529\) | 13.0044 | 0.565411 | ||||||||
\(530\) | −6.30721 | −0.273968 | ||||||||
\(531\) | −32.1301 | −1.39433 | ||||||||
\(532\) | 3.10104 | 0.134447 | ||||||||
\(533\) | −7.34340 | −0.318078 | ||||||||
\(534\) | −7.79561 | −0.337349 | ||||||||
\(535\) | 12.0183 | 0.519597 | ||||||||
\(536\) | 14.9844 | 0.647226 | ||||||||
\(537\) | 37.6749 | 1.62579 | ||||||||
\(538\) | 10.8695 | 0.468616 | ||||||||
\(539\) | 7.14028 | 0.307553 | ||||||||
\(540\) | −12.4392 | −0.535296 | ||||||||
\(541\) | 6.61840 | 0.284547 | 0.142274 | − | 0.989827i | \(-0.454559\pi\) | ||||
0.142274 | + | 0.989827i | \(0.454559\pi\) | |||||||
\(542\) | −12.3201 | −0.529195 | ||||||||
\(543\) | 51.3830 | 2.20506 | ||||||||
\(544\) | 4.69477 | 0.201287 | ||||||||
\(545\) | −13.1575 | −0.563607 | ||||||||
\(546\) | −5.14394 | −0.220141 | ||||||||
\(547\) | 14.0053 | 0.598824 | 0.299412 | − | 0.954124i | \(-0.403209\pi\) | ||||
0.299412 | + | 0.954124i | \(0.403209\pi\) | |||||||
\(548\) | −1.40749 | −0.0601251 | ||||||||
\(549\) | 90.7760 | 3.87422 | ||||||||
\(550\) | 1.05395 | 0.0449404 | ||||||||
\(551\) | −54.2940 | −2.31300 | ||||||||
\(552\) | 18.9222 | 0.805381 | ||||||||
\(553\) | 5.10627 | 0.217141 | ||||||||
\(554\) | 6.25679 | 0.265826 | ||||||||
\(555\) | −1.81461 | −0.0770260 | ||||||||
\(556\) | 10.3966 | 0.440913 | ||||||||
\(557\) | 13.1509 | 0.557222 | 0.278611 | − | 0.960404i | \(-0.410126\pi\) | ||||
0.278611 | + | 0.960404i | \(0.410126\pi\) | |||||||
\(558\) | −4.11643 | −0.174262 | ||||||||
\(559\) | 10.4302 | 0.441149 | ||||||||
\(560\) | 0.474552 | 0.0200535 | ||||||||
\(561\) | 15.6036 | 0.658786 | ||||||||
\(562\) | −23.2116 | −0.979123 | ||||||||
\(563\) | −31.6543 | −1.33407 | −0.667035 | − | 0.745026i | \(-0.732437\pi\) | ||||
−0.667035 | + | 0.745026i | \(0.732437\pi\) | |||||||
\(564\) | −6.19014 | −0.260652 | ||||||||
\(565\) | −3.81072 | −0.160318 | ||||||||
\(566\) | −10.4175 | −0.437878 | ||||||||
\(567\) | −8.72853 | −0.366564 | ||||||||
\(568\) | 10.7215 | 0.449862 | ||||||||
\(569\) | −12.1707 | −0.510222 | −0.255111 | − | 0.966912i | \(-0.582112\pi\) | ||||
−0.255111 | + | 0.966912i | \(0.582112\pi\) | |||||||
\(570\) | −20.6071 | −0.863136 | ||||||||
\(571\) | 15.1041 | 0.632085 | 0.316043 | − | 0.948745i | \(-0.397646\pi\) | ||||
0.316043 | + | 0.948745i | \(0.397646\pi\) | |||||||
\(572\) | 3.62275 | 0.151475 | ||||||||
\(573\) | 41.1809 | 1.72036 | ||||||||
\(574\) | 1.01382 | 0.0423161 | ||||||||
\(575\) | −6.00037 | −0.250233 | ||||||||
\(576\) | 6.94456 | 0.289357 | ||||||||
\(577\) | 32.8633 | 1.36812 | 0.684059 | − | 0.729427i | \(-0.260213\pi\) | ||||
0.684059 | + | 0.729427i | \(0.260213\pi\) | |||||||
\(578\) | −5.04089 | −0.209673 | ||||||||
\(579\) | 62.0935 | 2.58052 | ||||||||
\(580\) | −8.30861 | −0.344996 | ||||||||
\(581\) | −5.98724 | −0.248393 | ||||||||
\(582\) | 23.4631 | 0.972576 | ||||||||
\(583\) | 6.64746 | 0.275310 | ||||||||
\(584\) | 6.62649 | 0.274206 | ||||||||
\(585\) | 23.8706 | 0.986929 | ||||||||
\(586\) | 1.15574 | 0.0477431 | ||||||||
\(587\) | −23.0518 | −0.951448 | −0.475724 | − | 0.879594i | \(-0.657814\pi\) | ||||
−0.475724 | + | 0.879594i | \(0.657814\pi\) | |||||||
\(588\) | −21.3643 | −0.881050 | ||||||||
\(589\) | −3.87347 | −0.159604 | ||||||||
\(590\) | −4.62666 | −0.190477 | ||||||||
\(591\) | 53.4541 | 2.19881 | ||||||||
\(592\) | 0.575428 | 0.0236500 | ||||||||
\(593\) | 29.0499 | 1.19294 | 0.596469 | − | 0.802636i | \(-0.296570\pi\) | ||||
0.596469 | + | 0.802636i | \(0.296570\pi\) | |||||||
\(594\) | 13.1102 | 0.537918 | ||||||||
\(595\) | −2.22792 | −0.0913356 | ||||||||
\(596\) | −22.1535 | −0.907445 | ||||||||
\(597\) | −29.8659 | −1.22233 | ||||||||
\(598\) | −20.6252 | −0.843426 | ||||||||
\(599\) | 7.22925 | 0.295379 | 0.147689 | − | 0.989034i | \(-0.452816\pi\) | ||||
0.147689 | + | 0.989034i | \(0.452816\pi\) | |||||||
\(600\) | −3.15350 | −0.128741 | ||||||||
\(601\) | 8.42647 | 0.343723 | 0.171862 | − | 0.985121i | \(-0.445022\pi\) | ||||
0.171862 | + | 0.985121i | \(0.445022\pi\) | |||||||
\(602\) | −1.43998 | −0.0586891 | ||||||||
\(603\) | −104.060 | −4.23764 | ||||||||
\(604\) | −9.77674 | −0.397810 | ||||||||
\(605\) | 9.88920 | 0.402053 | ||||||||
\(606\) | −54.7663 | −2.22473 | ||||||||
\(607\) | 12.1519 | 0.493230 | 0.246615 | − | 0.969114i | \(-0.420682\pi\) | ||||
0.246615 | + | 0.969114i | \(0.420682\pi\) | |||||||
\(608\) | 6.53467 | 0.265016 | ||||||||
\(609\) | −12.4338 | −0.503844 | ||||||||
\(610\) | 13.0715 | 0.529251 | ||||||||
\(611\) | 6.74725 | 0.272965 | ||||||||
\(612\) | −32.6031 | −1.31790 | ||||||||
\(613\) | −3.31433 | −0.133865 | −0.0669323 | − | 0.997758i | \(-0.521321\pi\) | ||||
−0.0669323 | + | 0.997758i | \(0.521321\pi\) | |||||||
\(614\) | 3.59248 | 0.144981 | ||||||||
\(615\) | −6.73706 | −0.271665 | ||||||||
\(616\) | −0.500153 | −0.0201517 | ||||||||
\(617\) | −23.3807 | −0.941273 | −0.470637 | − | 0.882327i | \(-0.655976\pi\) | ||||
−0.470637 | + | 0.882327i | \(0.655976\pi\) | |||||||
\(618\) | 58.0651 | 2.33572 | ||||||||
\(619\) | 31.8826 | 1.28147 | 0.640736 | − | 0.767762i | \(-0.278630\pi\) | ||||
0.640736 | + | 0.767762i | \(0.278630\pi\) | |||||||
\(620\) | −0.592756 | −0.0238057 | ||||||||
\(621\) | −74.6395 | −2.99518 | ||||||||
\(622\) | 16.7427 | 0.671321 | ||||||||
\(623\) | −1.17312 | −0.0469999 | ||||||||
\(624\) | −10.8396 | −0.433930 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 27.9220 | 1.11599 | ||||||||
\(627\) | 21.7188 | 0.867364 | ||||||||
\(628\) | −3.67323 | −0.146578 | ||||||||
\(629\) | −2.70150 | −0.107716 | ||||||||
\(630\) | −3.29555 | −0.131298 | ||||||||
\(631\) | 13.7124 | 0.545881 | 0.272941 | − | 0.962031i | \(-0.412004\pi\) | ||||
0.272941 | + | 0.962031i | \(0.412004\pi\) | |||||||
\(632\) | 10.7602 | 0.428018 | ||||||||
\(633\) | −71.8485 | −2.85572 | ||||||||
\(634\) | −24.5975 | −0.976890 | ||||||||
\(635\) | −13.1465 | −0.521702 | ||||||||
\(636\) | −19.8898 | −0.788681 | ||||||||
\(637\) | 23.2871 | 0.922670 | ||||||||
\(638\) | 8.75682 | 0.346686 | ||||||||
\(639\) | −74.4558 | −2.94542 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 35.4099 | 1.39861 | 0.699304 | − | 0.714825i | \(-0.253494\pi\) | ||||
0.699304 | + | 0.714825i | \(0.253494\pi\) | |||||||
\(642\) | 37.8997 | 1.49578 | ||||||||
\(643\) | −45.3047 | −1.78664 | −0.893321 | − | 0.449420i | \(-0.851631\pi\) | ||||
−0.893321 | + | 0.449420i | \(0.851631\pi\) | |||||||
\(644\) | 2.84749 | 0.112207 | ||||||||
\(645\) | 9.56895 | 0.376777 | ||||||||
\(646\) | −30.6788 | −1.20704 | ||||||||
\(647\) | 24.7742 | 0.973974 | 0.486987 | − | 0.873409i | \(-0.338096\pi\) | ||||
0.486987 | + | 0.873409i | \(0.338096\pi\) | |||||||
\(648\) | −18.3932 | −0.722553 | ||||||||
\(649\) | 4.87625 | 0.191410 | ||||||||
\(650\) | 3.43732 | 0.134823 | ||||||||
\(651\) | −0.887060 | −0.0347666 | ||||||||
\(652\) | 4.65548 | 0.182323 | ||||||||
\(653\) | 8.37484 | 0.327733 | 0.163866 | − | 0.986483i | \(-0.447603\pi\) | ||||
0.163866 | + | 0.986483i | \(0.447603\pi\) | |||||||
\(654\) | −41.4923 | −1.62248 | ||||||||
\(655\) | 0.566335 | 0.0221285 | ||||||||
\(656\) | 2.13638 | 0.0834115 | ||||||||
\(657\) | −46.0180 | −1.79533 | ||||||||
\(658\) | −0.931519 | −0.0363144 | ||||||||
\(659\) | 2.31861 | 0.0903201 | 0.0451601 | − | 0.998980i | \(-0.485620\pi\) | ||||
0.0451601 | + | 0.998980i | \(0.485620\pi\) | |||||||
\(660\) | 3.32362 | 0.129372 | ||||||||
\(661\) | −7.46012 | −0.290165 | −0.145082 | − | 0.989420i | \(-0.546345\pi\) | ||||
−0.145082 | + | 0.989420i | \(0.546345\pi\) | |||||||
\(662\) | 0.197429 | 0.00767328 | ||||||||
\(663\) | 50.8893 | 1.97638 | ||||||||
\(664\) | −12.6166 | −0.489620 | ||||||||
\(665\) | −3.10104 | −0.120253 | ||||||||
\(666\) | −3.99609 | −0.154845 | ||||||||
\(667\) | −49.8547 | −1.93038 | ||||||||
\(668\) | −4.29110 | −0.166028 | ||||||||
\(669\) | −10.5608 | −0.408303 | ||||||||
\(670\) | −14.9844 | −0.578896 | ||||||||
\(671\) | −13.7767 | −0.531843 | ||||||||
\(672\) | 1.49650 | 0.0577287 | ||||||||
\(673\) | 9.18273 | 0.353968 | 0.176984 | − | 0.984214i | \(-0.443366\pi\) | ||||
0.176984 | + | 0.984214i | \(0.443366\pi\) | |||||||
\(674\) | −1.92974 | −0.0743307 | ||||||||
\(675\) | 12.4392 | 0.478783 | ||||||||
\(676\) | −1.18486 | −0.0455714 | ||||||||
\(677\) | −27.6474 | −1.06258 | −0.531288 | − | 0.847191i | \(-0.678292\pi\) | ||||
−0.531288 | + | 0.847191i | \(0.678292\pi\) | |||||||
\(678\) | −12.0171 | −0.461514 | ||||||||
\(679\) | 3.53083 | 0.135501 | ||||||||
\(680\) | −4.69477 | −0.180036 | ||||||||
\(681\) | −82.2596 | −3.15219 | ||||||||
\(682\) | 0.624733 | 0.0239223 | ||||||||
\(683\) | −2.41739 | −0.0924988 | −0.0462494 | − | 0.998930i | \(-0.514727\pi\) | ||||
−0.0462494 | + | 0.998930i | \(0.514727\pi\) | |||||||
\(684\) | −45.3804 | −1.73516 | ||||||||
\(685\) | 1.40749 | 0.0537775 | ||||||||
\(686\) | −6.53686 | −0.249579 | ||||||||
\(687\) | 35.0894 | 1.33875 | ||||||||
\(688\) | −3.03439 | −0.115685 | ||||||||
\(689\) | 21.6799 | 0.825938 | ||||||||
\(690\) | −18.9222 | −0.720354 | ||||||||
\(691\) | −41.2899 | −1.57074 | −0.785370 | − | 0.619026i | \(-0.787528\pi\) | ||||
−0.785370 | + | 0.619026i | \(0.787528\pi\) | |||||||
\(692\) | 23.3544 | 0.887803 | ||||||||
\(693\) | 3.47334 | 0.131941 | ||||||||
\(694\) | −9.84709 | −0.373791 | ||||||||
\(695\) | −10.3966 | −0.394365 | ||||||||
\(696\) | −26.2012 | −0.993153 | ||||||||
\(697\) | −10.0298 | −0.379906 | ||||||||
\(698\) | −20.8401 | −0.788808 | ||||||||
\(699\) | 55.6575 | 2.10516 | ||||||||
\(700\) | −0.474552 | −0.0179364 | ||||||||
\(701\) | −15.7272 | −0.594009 | −0.297005 | − | 0.954876i | \(-0.595988\pi\) | ||||
−0.297005 | + | 0.954876i | \(0.595988\pi\) | |||||||
\(702\) | 42.7573 | 1.61377 | ||||||||
\(703\) | −3.76024 | −0.141820 | ||||||||
\(704\) | −1.05395 | −0.0397221 | ||||||||
\(705\) | 6.19014 | 0.233134 | ||||||||
\(706\) | −0.766412 | −0.0288443 | ||||||||
\(707\) | −8.24147 | −0.309952 | ||||||||
\(708\) | −14.5902 | −0.548332 | ||||||||
\(709\) | 42.7621 | 1.60596 | 0.802982 | − | 0.596003i | \(-0.203246\pi\) | ||||
0.802982 | + | 0.596003i | \(0.203246\pi\) | |||||||
\(710\) | −10.7215 | −0.402369 | ||||||||
\(711\) | −74.7248 | −2.80240 | ||||||||
\(712\) | −2.47205 | −0.0926440 | ||||||||
\(713\) | −3.55676 | −0.133202 | ||||||||
\(714\) | −7.02573 | −0.262931 | ||||||||
\(715\) | −3.62275 | −0.135483 | ||||||||
\(716\) | 11.9470 | 0.446481 | ||||||||
\(717\) | −70.9495 | −2.64966 | ||||||||
\(718\) | −28.3525 | −1.05811 | ||||||||
\(719\) | 45.7972 | 1.70795 | 0.853974 | − | 0.520316i | \(-0.174186\pi\) | ||||
0.853974 | + | 0.520316i | \(0.174186\pi\) | |||||||
\(720\) | −6.94456 | −0.258808 | ||||||||
\(721\) | 8.73788 | 0.325416 | ||||||||
\(722\) | −23.7020 | −0.882095 | ||||||||
\(723\) | −56.2906 | −2.09347 | ||||||||
\(724\) | 16.2940 | 0.605560 | ||||||||
\(725\) | 8.30861 | 0.308574 | ||||||||
\(726\) | 31.1856 | 1.15741 | ||||||||
\(727\) | 15.9640 | 0.592072 | 0.296036 | − | 0.955177i | \(-0.404335\pi\) | ||||
0.296036 | + | 0.955177i | \(0.404335\pi\) | |||||||
\(728\) | −1.63119 | −0.0604558 | ||||||||
\(729\) | 10.0520 | 0.372295 | ||||||||
\(730\) | −6.62649 | −0.245257 | ||||||||
\(731\) | 14.2458 | 0.526899 | ||||||||
\(732\) | 41.2211 | 1.52357 | ||||||||
\(733\) | −29.8776 | −1.10356 | −0.551778 | − | 0.833991i | \(-0.686050\pi\) | ||||
−0.551778 | + | 0.833991i | \(0.686050\pi\) | |||||||
\(734\) | 16.1601 | 0.596479 | ||||||||
\(735\) | 21.3643 | 0.788035 | ||||||||
\(736\) | 6.00037 | 0.221177 | ||||||||
\(737\) | 15.7927 | 0.581732 | ||||||||
\(738\) | −14.8362 | −0.546128 | ||||||||
\(739\) | −1.45055 | −0.0533593 | −0.0266797 | − | 0.999644i | \(-0.508493\pi\) | ||||
−0.0266797 | + | 0.999644i | \(0.508493\pi\) | |||||||
\(740\) | −0.575428 | −0.0211532 | ||||||||
\(741\) | 70.8331 | 2.60212 | ||||||||
\(742\) | −2.99310 | −0.109880 | ||||||||
\(743\) | 39.9782 | 1.46666 | 0.733328 | − | 0.679875i | \(-0.237966\pi\) | ||||
0.733328 | + | 0.679875i | \(0.237966\pi\) | |||||||
\(744\) | −1.86926 | −0.0685303 | ||||||||
\(745\) | 22.1535 | 0.811643 | ||||||||
\(746\) | 15.0275 | 0.550197 | ||||||||
\(747\) | 87.6168 | 3.20573 | ||||||||
\(748\) | 4.94804 | 0.180918 | ||||||||
\(749\) | 5.70332 | 0.208395 | ||||||||
\(750\) | 3.15350 | 0.115150 | ||||||||
\(751\) | 46.4906 | 1.69647 | 0.848233 | − | 0.529624i | \(-0.177667\pi\) | ||||
0.848233 | + | 0.529624i | \(0.177667\pi\) | |||||||
\(752\) | −1.96294 | −0.0715811 | ||||||||
\(753\) | 40.8147 | 1.48737 | ||||||||
\(754\) | 28.5593 | 1.04007 | ||||||||
\(755\) | 9.77674 | 0.355812 | ||||||||
\(756\) | −5.90303 | −0.214691 | ||||||||
\(757\) | −29.8235 | −1.08395 | −0.541977 | − | 0.840393i | \(-0.682324\pi\) | ||||
−0.541977 | + | 0.840393i | \(0.682324\pi\) | |||||||
\(758\) | 14.6512 | 0.532155 | ||||||||
\(759\) | 19.9429 | 0.723883 | ||||||||
\(760\) | −6.53467 | −0.237038 | ||||||||
\(761\) | −4.20554 | −0.152451 | −0.0762253 | − | 0.997091i | \(-0.524287\pi\) | ||||
−0.0762253 | + | 0.997091i | \(0.524287\pi\) | |||||||
\(762\) | −41.4574 | −1.50184 | ||||||||
\(763\) | −6.24394 | −0.226046 | ||||||||
\(764\) | 13.0588 | 0.472451 | ||||||||
\(765\) | 32.6031 | 1.17877 | ||||||||
\(766\) | −13.9724 | −0.504843 | ||||||||
\(767\) | 15.9033 | 0.574235 | ||||||||
\(768\) | 3.15350 | 0.113792 | ||||||||
\(769\) | −11.5511 | −0.416544 | −0.208272 | − | 0.978071i | \(-0.566784\pi\) | ||||
−0.208272 | + | 0.978071i | \(0.566784\pi\) | |||||||
\(770\) | 0.500153 | 0.0180242 | ||||||||
\(771\) | −54.9358 | −1.97847 | ||||||||
\(772\) | 19.6904 | 0.708672 | ||||||||
\(773\) | −48.2056 | −1.73383 | −0.866917 | − | 0.498453i | \(-0.833902\pi\) | ||||
−0.866917 | + | 0.498453i | \(0.833902\pi\) | |||||||
\(774\) | 21.0725 | 0.757435 | ||||||||
\(775\) | 0.592756 | 0.0212924 | ||||||||
\(776\) | 7.44033 | 0.267092 | ||||||||
\(777\) | −0.861129 | −0.0308928 | ||||||||
\(778\) | −3.34407 | −0.119891 | ||||||||
\(779\) | −13.9605 | −0.500188 | ||||||||
\(780\) | 10.8396 | 0.388119 | ||||||||
\(781\) | 11.2998 | 0.404340 | ||||||||
\(782\) | −28.1704 | −1.00737 | ||||||||
\(783\) | 103.352 | 3.69350 | ||||||||
\(784\) | −6.77480 | −0.241957 | ||||||||
\(785\) | 3.67323 | 0.131103 | ||||||||
\(786\) | 1.78594 | 0.0637023 | ||||||||
\(787\) | −39.1121 | −1.39420 | −0.697099 | − | 0.716975i | \(-0.745526\pi\) | ||||
−0.697099 | + | 0.716975i | \(0.745526\pi\) | |||||||
\(788\) | 16.9507 | 0.603844 | ||||||||
\(789\) | 34.6417 | 1.23328 | ||||||||
\(790\) | −10.7602 | −0.382831 | ||||||||
\(791\) | −1.80838 | −0.0642987 | ||||||||
\(792\) | 7.31919 | 0.260076 | ||||||||
\(793\) | −44.9310 | −1.59555 | ||||||||
\(794\) | −4.05193 | −0.143797 | ||||||||
\(795\) | 19.8898 | 0.705418 | ||||||||
\(796\) | −9.47071 | −0.335680 | ||||||||
\(797\) | −33.1920 | −1.17572 | −0.587861 | − | 0.808962i | \(-0.700030\pi\) | ||||
−0.587861 | + | 0.808962i | \(0.700030\pi\) | |||||||
\(798\) | −9.77914 | −0.346178 | ||||||||
\(799\) | 9.21557 | 0.326023 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 17.1673 | 0.606576 | ||||||||
\(802\) | 1.00000 | 0.0353112 | ||||||||
\(803\) | 6.98397 | 0.246459 | ||||||||
\(804\) | −47.2532 | −1.66649 | ||||||||
\(805\) | −2.84749 | −0.100361 | ||||||||
\(806\) | 2.03749 | 0.0717676 | ||||||||
\(807\) | −34.2769 | −1.20660 | ||||||||
\(808\) | −17.3668 | −0.610963 | ||||||||
\(809\) | −34.7471 | −1.22164 | −0.610822 | − | 0.791768i | \(-0.709161\pi\) | ||||
−0.610822 | + | 0.791768i | \(0.709161\pi\) | |||||||
\(810\) | 18.3932 | 0.646271 | ||||||||
\(811\) | −25.4546 | −0.893831 | −0.446915 | − | 0.894576i | \(-0.647477\pi\) | ||||
−0.446915 | + | 0.894576i | \(0.647477\pi\) | |||||||
\(812\) | −3.94287 | −0.138368 | ||||||||
\(813\) | 38.8515 | 1.36258 | ||||||||
\(814\) | 0.606470 | 0.0212568 | ||||||||
\(815\) | −4.65548 | −0.163074 | ||||||||
\(816\) | −14.8050 | −0.518277 | ||||||||
\(817\) | 19.8288 | 0.693720 | ||||||||
\(818\) | 35.2075 | 1.23100 | ||||||||
\(819\) | 11.3279 | 0.395828 | ||||||||
\(820\) | −2.13638 | −0.0746055 | ||||||||
\(821\) | −3.61530 | −0.126175 | −0.0630875 | − | 0.998008i | \(-0.520095\pi\) | ||||
−0.0630875 | + | 0.998008i | \(0.520095\pi\) | |||||||
\(822\) | 4.43853 | 0.154811 | ||||||||
\(823\) | −22.2385 | −0.775186 | −0.387593 | − | 0.921831i | \(-0.626693\pi\) | ||||
−0.387593 | + | 0.921831i | \(0.626693\pi\) | |||||||
\(824\) | 18.4129 | 0.641444 | ||||||||
\(825\) | −3.32362 | −0.115714 | ||||||||
\(826\) | −2.19559 | −0.0763944 | ||||||||
\(827\) | −35.1752 | −1.22316 | −0.611582 | − | 0.791181i | \(-0.709466\pi\) | ||||
−0.611582 | + | 0.791181i | \(0.709466\pi\) | |||||||
\(828\) | −41.6699 | −1.44813 | ||||||||
\(829\) | −34.8087 | −1.20896 | −0.604478 | − | 0.796622i | \(-0.706618\pi\) | ||||
−0.604478 | + | 0.796622i | \(0.706618\pi\) | |||||||
\(830\) | 12.6166 | 0.437929 | ||||||||
\(831\) | −19.7308 | −0.684454 | ||||||||
\(832\) | −3.43732 | −0.119168 | ||||||||
\(833\) | 31.8061 | 1.10202 | ||||||||
\(834\) | −32.7856 | −1.13527 | ||||||||
\(835\) | 4.29110 | 0.148500 | ||||||||
\(836\) | 6.88719 | 0.238199 | ||||||||
\(837\) | 7.37339 | 0.254862 | ||||||||
\(838\) | −12.9090 | −0.445933 | ||||||||
\(839\) | 10.2957 | 0.355446 | 0.177723 | − | 0.984081i | \(-0.443127\pi\) | ||||
0.177723 | + | 0.984081i | \(0.443127\pi\) | |||||||
\(840\) | −1.49650 | −0.0516342 | ||||||||
\(841\) | 40.0329 | 1.38045 | ||||||||
\(842\) | 25.0552 | 0.863461 | ||||||||
\(843\) | 73.1978 | 2.52107 | ||||||||
\(844\) | −22.7837 | −0.784248 | ||||||||
\(845\) | 1.18486 | 0.0407603 | ||||||||
\(846\) | 13.6318 | 0.468670 | ||||||||
\(847\) | 4.69294 | 0.161251 | ||||||||
\(848\) | −6.30721 | −0.216591 | ||||||||
\(849\) | 32.8514 | 1.12746 | ||||||||
\(850\) | 4.69477 | 0.161029 | ||||||||
\(851\) | −3.45278 | −0.118360 | ||||||||
\(852\) | −33.8101 | −1.15832 | ||||||||
\(853\) | 17.2745 | 0.591466 | 0.295733 | − | 0.955271i | \(-0.404436\pi\) | ||||
0.295733 | + | 0.955271i | \(0.404436\pi\) | |||||||
\(854\) | 6.20312 | 0.212267 | ||||||||
\(855\) | 45.3804 | 1.55198 | ||||||||
\(856\) | 12.0183 | 0.410777 | ||||||||
\(857\) | −14.6672 | −0.501024 | −0.250512 | − | 0.968114i | \(-0.580599\pi\) | ||||
−0.250512 | + | 0.968114i | \(0.580599\pi\) | |||||||
\(858\) | −11.4243 | −0.390020 | ||||||||
\(859\) | 52.3161 | 1.78500 | 0.892501 | − | 0.451045i | \(-0.148949\pi\) | ||||
0.892501 | + | 0.451045i | \(0.148949\pi\) | |||||||
\(860\) | 3.03439 | 0.103472 | ||||||||
\(861\) | −3.19709 | −0.108956 | ||||||||
\(862\) | 18.2753 | 0.622459 | ||||||||
\(863\) | −17.3127 | −0.589332 | −0.294666 | − | 0.955600i | \(-0.595208\pi\) | ||||
−0.294666 | + | 0.955600i | \(0.595208\pi\) | |||||||
\(864\) | −12.4392 | −0.423189 | ||||||||
\(865\) | −23.3544 | −0.794075 | ||||||||
\(866\) | 24.2793 | 0.825044 | ||||||||
\(867\) | 15.8964 | 0.539871 | ||||||||
\(868\) | −0.281294 | −0.00954774 | ||||||||
\(869\) | 11.3407 | 0.384706 | ||||||||
\(870\) | 26.2012 | 0.888303 | ||||||||
\(871\) | 51.5060 | 1.74521 | ||||||||
\(872\) | −13.1575 | −0.445571 | ||||||||
\(873\) | −51.6698 | −1.74876 | ||||||||
\(874\) | −39.2105 | −1.32631 | ||||||||
\(875\) | 0.474552 | 0.0160428 | ||||||||
\(876\) | −20.8966 | −0.706032 | ||||||||
\(877\) | −11.1664 | −0.377063 | −0.188532 | − | 0.982067i | \(-0.560373\pi\) | ||||
−0.188532 | + | 0.982067i | \(0.560373\pi\) | |||||||
\(878\) | −39.0419 | −1.31760 | ||||||||
\(879\) | −3.64462 | −0.122930 | ||||||||
\(880\) | 1.05395 | 0.0355285 | ||||||||
\(881\) | 36.1158 | 1.21677 | 0.608387 | − | 0.793641i | \(-0.291817\pi\) | ||||
0.608387 | + | 0.793641i | \(0.291817\pi\) | |||||||
\(882\) | 47.0480 | 1.58419 | ||||||||
\(883\) | −15.1612 | −0.510215 | −0.255108 | − | 0.966913i | \(-0.582111\pi\) | ||||
−0.255108 | + | 0.966913i | \(0.582111\pi\) | |||||||
\(884\) | 16.1374 | 0.542760 | ||||||||
\(885\) | 14.5902 | 0.490443 | ||||||||
\(886\) | −28.5384 | −0.958767 | ||||||||
\(887\) | 24.2627 | 0.814662 | 0.407331 | − | 0.913281i | \(-0.366460\pi\) | ||||
0.407331 | + | 0.913281i | \(0.366460\pi\) | |||||||
\(888\) | −1.81461 | −0.0608944 | ||||||||
\(889\) | −6.23869 | −0.209239 | ||||||||
\(890\) | 2.47205 | 0.0828633 | ||||||||
\(891\) | −19.3854 | −0.649437 | ||||||||
\(892\) | −3.34891 | −0.112130 | ||||||||
\(893\) | 12.8272 | 0.429245 | ||||||||
\(894\) | 69.8612 | 2.33651 | ||||||||
\(895\) | −11.9470 | −0.399345 | ||||||||
\(896\) | 0.474552 | 0.0158537 | ||||||||
\(897\) | 65.0415 | 2.17167 | ||||||||
\(898\) | 6.91622 | 0.230797 | ||||||||
\(899\) | 4.92498 | 0.164257 | ||||||||
\(900\) | 6.94456 | 0.231485 | ||||||||
\(901\) | 29.6109 | 0.986483 | ||||||||
\(902\) | 2.25163 | 0.0749709 | ||||||||
\(903\) | 4.54097 | 0.151114 | ||||||||
\(904\) | −3.81072 | −0.126743 | ||||||||
\(905\) | −16.2940 | −0.541630 | ||||||||
\(906\) | 30.8309 | 1.02429 | ||||||||
\(907\) | −32.4651 | −1.07799 | −0.538994 | − | 0.842310i | \(-0.681195\pi\) | ||||
−0.538994 | + | 0.842310i | \(0.681195\pi\) | |||||||
\(908\) | −26.0852 | −0.865667 | ||||||||
\(909\) | 120.605 | 4.00021 | ||||||||
\(910\) | 1.63119 | 0.0540733 | ||||||||
\(911\) | 58.8363 | 1.94933 | 0.974667 | − | 0.223660i | \(-0.0718006\pi\) | ||||
0.974667 | + | 0.223660i | \(0.0718006\pi\) | |||||||
\(912\) | −20.6071 | −0.682369 | ||||||||
\(913\) | −13.2972 | −0.440074 | ||||||||
\(914\) | 3.94501 | 0.130489 | ||||||||
\(915\) | −41.2211 | −1.36273 | ||||||||
\(916\) | 11.1271 | 0.367651 | ||||||||
\(917\) | 0.268756 | 0.00887509 | ||||||||
\(918\) | 58.3990 | 1.92745 | ||||||||
\(919\) | 19.4972 | 0.643155 | 0.321577 | − | 0.946883i | \(-0.395787\pi\) | ||||
0.321577 | + | 0.946883i | \(0.395787\pi\) | |||||||
\(920\) | −6.00037 | −0.197826 | ||||||||
\(921\) | −11.3289 | −0.373300 | ||||||||
\(922\) | 12.2147 | 0.402269 | ||||||||
\(923\) | 36.8530 | 1.21303 | ||||||||
\(924\) | 1.57723 | 0.0518871 | ||||||||
\(925\) | 0.575428 | 0.0189200 | ||||||||
\(926\) | −0.135978 | −0.00446851 | ||||||||
\(927\) | −127.869 | −4.19978 | ||||||||
\(928\) | −8.30861 | −0.272743 | ||||||||
\(929\) | 24.6678 | 0.809325 | 0.404663 | − | 0.914466i | \(-0.367389\pi\) | ||||
0.404663 | + | 0.914466i | \(0.367389\pi\) | |||||||
\(930\) | 1.86926 | 0.0612954 | ||||||||
\(931\) | 44.2711 | 1.45093 | ||||||||
\(932\) | 17.6495 | 0.578127 | ||||||||
\(933\) | −52.7981 | −1.72853 | ||||||||
\(934\) | 19.1532 | 0.626712 | ||||||||
\(935\) | −4.94804 | −0.161818 | ||||||||
\(936\) | 23.8706 | 0.780236 | ||||||||
\(937\) | −8.19286 | −0.267649 | −0.133825 | − | 0.991005i | \(-0.542726\pi\) | ||||
−0.133825 | + | 0.991005i | \(0.542726\pi\) | |||||||
\(938\) | −7.11086 | −0.232178 | ||||||||
\(939\) | −88.0520 | −2.87347 | ||||||||
\(940\) | 1.96294 | 0.0640241 | ||||||||
\(941\) | −3.17998 | −0.103664 | −0.0518321 | − | 0.998656i | \(-0.516506\pi\) | ||||
−0.0518321 | + | 0.998656i | \(0.516506\pi\) | |||||||
\(942\) | 11.5835 | 0.377412 | ||||||||
\(943\) | −12.8191 | −0.417446 | ||||||||
\(944\) | −4.62666 | −0.150585 | ||||||||
\(945\) | 5.90303 | 0.192026 | ||||||||
\(946\) | −3.19808 | −0.103979 | ||||||||
\(947\) | −2.37096 | −0.0770459 | −0.0385230 | − | 0.999258i | \(-0.512265\pi\) | ||||
−0.0385230 | + | 0.999258i | \(0.512265\pi\) | |||||||
\(948\) | −33.9323 | −1.10207 | ||||||||
\(949\) | 22.7773 | 0.739384 | ||||||||
\(950\) | 6.53467 | 0.212013 | ||||||||
\(951\) | 77.5681 | 2.51532 | ||||||||
\(952\) | −2.22792 | −0.0722071 | ||||||||
\(953\) | 34.3615 | 1.11308 | 0.556539 | − | 0.830821i | \(-0.312129\pi\) | ||||
0.556539 | + | 0.830821i | \(0.312129\pi\) | |||||||
\(954\) | 43.8008 | 1.41810 | ||||||||
\(955\) | −13.0588 | −0.422573 | ||||||||
\(956\) | −22.4986 | −0.727658 | ||||||||
\(957\) | −27.6146 | −0.892654 | ||||||||
\(958\) | 24.0010 | 0.775437 | ||||||||
\(959\) | 0.667929 | 0.0215685 | ||||||||
\(960\) | −3.15350 | −0.101779 | ||||||||
\(961\) | −30.6486 | −0.988666 | ||||||||
\(962\) | 1.97793 | 0.0637710 | ||||||||
\(963\) | −83.4619 | −2.68952 | ||||||||
\(964\) | −17.8502 | −0.574916 | ||||||||
\(965\) | −19.6904 | −0.633855 | ||||||||
\(966\) | −8.97956 | −0.288912 | ||||||||
\(967\) | 37.4377 | 1.20392 | 0.601958 | − | 0.798528i | \(-0.294388\pi\) | ||||
0.601958 | + | 0.798528i | \(0.294388\pi\) | |||||||
\(968\) | 9.88920 | 0.317851 | ||||||||
\(969\) | 96.7456 | 3.10792 | ||||||||
\(970\) | −7.44033 | −0.238895 | ||||||||
\(971\) | 37.8384 | 1.21429 | 0.607146 | − | 0.794590i | \(-0.292314\pi\) | ||||
0.607146 | + | 0.794590i | \(0.292314\pi\) | |||||||
\(972\) | 20.6854 | 0.663486 | ||||||||
\(973\) | −4.93372 | −0.158168 | ||||||||
\(974\) | 29.9631 | 0.960079 | ||||||||
\(975\) | −10.8396 | −0.347144 | ||||||||
\(976\) | 13.0715 | 0.418409 | ||||||||
\(977\) | 40.0521 | 1.28138 | 0.640690 | − | 0.767800i | \(-0.278649\pi\) | ||||
0.640690 | + | 0.767800i | \(0.278649\pi\) | |||||||
\(978\) | −14.6811 | −0.469449 | ||||||||
\(979\) | −2.60541 | −0.0832692 | ||||||||
\(980\) | 6.77480 | 0.216413 | ||||||||
\(981\) | 91.3733 | 2.91732 | ||||||||
\(982\) | −20.9770 | −0.669402 | ||||||||
\(983\) | −12.7989 | −0.408220 | −0.204110 | − | 0.978948i | \(-0.565430\pi\) | ||||
−0.204110 | + | 0.978948i | \(0.565430\pi\) | |||||||
\(984\) | −6.73706 | −0.214770 | ||||||||
\(985\) | −16.9507 | −0.540095 | ||||||||
\(986\) | 39.0070 | 1.24224 | ||||||||
\(987\) | 2.93754 | 0.0935030 | ||||||||
\(988\) | 22.4617 | 0.714603 | ||||||||
\(989\) | 18.2075 | 0.578964 | ||||||||
\(990\) | −7.31919 | −0.232619 | ||||||||
\(991\) | 38.3312 | 1.21763 | 0.608816 | − | 0.793312i | \(-0.291645\pi\) | ||||
0.608816 | + | 0.793312i | \(0.291645\pi\) | |||||||
\(992\) | −0.592756 | −0.0188200 | ||||||||
\(993\) | −0.622591 | −0.0197573 | ||||||||
\(994\) | −5.08789 | −0.161378 | ||||||||
\(995\) | 9.47071 | 0.300242 | ||||||||
\(996\) | 39.7865 | 1.26068 | ||||||||
\(997\) | −11.4733 | −0.363362 | −0.181681 | − | 0.983357i | \(-0.558154\pi\) | ||||
−0.181681 | + | 0.983357i | \(0.558154\pi\) | |||||||
\(998\) | 37.4023 | 1.18395 | ||||||||
\(999\) | 7.15784 | 0.226464 |
(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 | 4010.2.a.k.1.15 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4010.2.a.k.1.15 | ✓ | 15 | 1.1 | even | 1 | trivial |