Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,4,Mod(55,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("84.55");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(4.95616044048\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} - 2x^{10} - 6x^{9} + 56x^{7} - 448x^{6} + 448x^{5} - 3072x^{3} - 8192x^{2} - 32768x + 262144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{13} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.12 | ||
Root | \(2.82801 + 0.0488466i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 84.55 |
Dual form | 84.4.b.a.55.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.82801 | + | 0.0488466i | 0.999851 | + | 0.0172699i | ||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 7.99523 | + | 0.276277i | 0.999404 | + | 0.0345346i | ||||
\(5\) | − | 16.6517i | − | 1.48938i | −0.667412 | − | 0.744689i | \(-0.732598\pi\) | ||
0.667412 | − | 0.744689i | \(-0.267402\pi\) | |||||||
\(6\) | −8.48402 | − | 0.146540i | −0.577264 | − | 0.00997076i | ||||
\(7\) | 15.0420 | + | 10.8045i | 0.812194 | + | 0.583387i | ||||
\(8\) | 22.5971 | + | 1.17185i | 0.998658 | + | 0.0517890i | ||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0.813380 | − | 47.0912i | 0.0257213 | − | 1.48916i | ||||
\(11\) | − | 64.0450i | − | 1.75548i | −0.479136 | − | 0.877741i | \(-0.659050\pi\) | ||
0.479136 | − | 0.877741i | \(-0.340950\pi\) | |||||||
\(12\) | −23.9857 | − | 0.828830i | −0.577006 | − | 0.0199385i | ||||
\(13\) | 28.6879i | 0.612046i | 0.952024 | + | 0.306023i | \(0.0989985\pi\) | ||||
−0.952024 | + | 0.306023i | \(0.901002\pi\) | |||||||
\(14\) | 42.0112 | + | 31.2899i | 0.801998 | + | 0.597327i | ||||
\(15\) | 49.9552i | 0.859892i | ||||||||
\(16\) | 63.8473 | + | 4.41779i | 0.997615 | + | 0.0690280i | ||||
\(17\) | 82.9041i | 1.18278i | 0.806387 | + | 0.591388i | \(0.201420\pi\) | ||||
−0.806387 | + | 0.591388i | \(0.798580\pi\) | |||||||
\(18\) | 25.4520 | + | 0.439619i | 0.333284 | + | 0.00575662i | ||||
\(19\) | −17.1236 | −0.206759 | −0.103379 | − | 0.994642i | \(-0.532966\pi\) | ||||
−0.103379 | + | 0.994642i | \(0.532966\pi\) | |||||||
\(20\) | 4.60049 | − | 133.134i | 0.0514350 | − | 1.48849i | ||||
\(21\) | −45.1261 | − | 32.4134i | −0.468921 | − | 0.336819i | ||||
\(22\) | 3.12838 | − | 181.120i | 0.0303169 | − | 1.75522i | ||||
\(23\) | 95.0501i | 0.861710i | 0.902421 | + | 0.430855i | \(0.141788\pi\) | ||||
−0.902421 | + | 0.430855i | \(0.858212\pi\) | |||||||
\(24\) | −67.7912 | − | 3.51555i | −0.576575 | − | 0.0299004i | ||||
\(25\) | −152.281 | −1.21824 | ||||||||
\(26\) | −1.40131 | + | 81.1296i | −0.0105700 | + | 0.611955i | ||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 117.280 | + | 90.5401i | 0.791563 | + | 0.611088i | ||||
\(29\) | −197.365 | −1.26378 | −0.631892 | − | 0.775056i | \(-0.717722\pi\) | ||||
−0.631892 | + | 0.775056i | \(0.717722\pi\) | |||||||
\(30\) | −2.44014 | + | 141.274i | −0.0148502 | + | 0.859764i | ||||
\(31\) | −153.515 | −0.889422 | −0.444711 | − | 0.895674i | \(-0.646694\pi\) | ||||
−0.444711 | + | 0.895674i | \(0.646694\pi\) | |||||||
\(32\) | 180.345 | + | 15.6123i | 0.996274 | + | 0.0862463i | ||||
\(33\) | 192.135i | 1.01353i | ||||||||
\(34\) | −4.04958 | + | 234.453i | −0.0204264 | + | 1.18260i | ||||
\(35\) | 179.913 | − | 250.476i | 0.868883 | − | 1.20966i | ||||
\(36\) | 71.9571 | + | 2.48649i | 0.333135 | + | 0.0115115i | ||||
\(37\) | 10.7262 | 0.0476589 | 0.0238294 | − | 0.999716i | \(-0.492414\pi\) | ||||
0.0238294 | + | 0.999716i | \(0.492414\pi\) | |||||||
\(38\) | −48.4255 | − | 0.836427i | −0.206728 | − | 0.00357069i | ||||
\(39\) | − | 86.0638i | − | 0.353365i | ||||||
\(40\) | 19.5134 | − | 376.280i | 0.0771333 | − | 1.48738i | ||||
\(41\) | 41.1342i | 0.156685i | 0.996927 | + | 0.0783425i | \(0.0249628\pi\) | ||||
−0.996927 | + | 0.0783425i | \(0.975037\pi\) | |||||||
\(42\) | −126.034 | − | 93.8696i | −0.463034 | − | 0.344867i | ||||
\(43\) | 412.497i | 1.46291i | 0.681890 | + | 0.731455i | \(0.261158\pi\) | ||||
−0.681890 | + | 0.731455i | \(0.738842\pi\) | |||||||
\(44\) | 17.6941 | − | 512.055i | 0.0606248 | − | 1.75443i | ||||
\(45\) | − | 149.866i | − | 0.496459i | ||||||
\(46\) | −4.64287 | + | 268.802i | −0.0148816 | + | 0.861581i | ||||
\(47\) | 477.704 | 1.48256 | 0.741280 | − | 0.671196i | \(-0.234219\pi\) | ||||
0.741280 | + | 0.671196i | \(0.234219\pi\) | |||||||
\(48\) | −191.542 | − | 13.2534i | −0.575973 | − | 0.0398533i | ||||
\(49\) | 109.526 | + | 325.043i | 0.319319 | + | 0.947647i | ||||
\(50\) | −430.650 | − | 7.43838i | −1.21806 | − | 0.0210389i | ||||
\(51\) | − | 248.712i | − | 0.682877i | ||||||
\(52\) | −7.92580 | + | 229.367i | −0.0211368 | + | 0.611681i | ||||
\(53\) | −35.2304 | −0.0913069 | −0.0456534 | − | 0.998957i | \(-0.514537\pi\) | ||||
−0.0456534 | + | 0.998957i | \(0.514537\pi\) | |||||||
\(54\) | −76.3561 | − | 1.31886i | −0.192421 | − | 0.00332359i | ||||
\(55\) | −1066.46 | −2.61457 | ||||||||
\(56\) | 327.245 | + | 261.776i | 0.780891 | + | 0.624667i | ||||
\(57\) | 51.3707 | 0.119372 | ||||||||
\(58\) | −558.149 | − | 9.64060i | −1.26360 | − | 0.0218254i | ||||
\(59\) | 494.608 | 1.09140 | 0.545699 | − | 0.837981i | \(-0.316264\pi\) | ||||
0.545699 | + | 0.837981i | \(0.316264\pi\) | |||||||
\(60\) | −13.8015 | + | 399.403i | −0.0296960 | + | 0.859379i | ||||
\(61\) | − | 294.084i | − | 0.617273i | −0.951180 | − | 0.308636i | \(-0.900127\pi\) | ||
0.951180 | − | 0.308636i | \(-0.0998727\pi\) | |||||||
\(62\) | −434.141 | − | 7.49867i | −0.889289 | − | 0.0153602i | ||||
\(63\) | 135.378 | + | 97.2403i | 0.270731 | + | 0.194462i | ||||
\(64\) | 509.254 | + | 52.9608i | 0.994636 | + | 0.103439i | ||||
\(65\) | 477.704 | 0.911567 | ||||||||
\(66\) | −9.38514 | + | 543.359i | −0.0175035 | + | 1.01338i | ||||
\(67\) | 207.870i | 0.379036i | 0.981877 | + | 0.189518i | \(0.0606926\pi\) | ||||
−0.981877 | + | 0.189518i | \(0.939307\pi\) | |||||||
\(68\) | −22.9045 | + | 662.837i | −0.0408467 | + | 1.18207i | ||||
\(69\) | − | 285.150i | − | 0.497508i | ||||||
\(70\) | 521.031 | − | 699.560i | 0.889645 | − | 1.19448i | ||||
\(71\) | − | 534.040i | − | 0.892660i | −0.894869 | − | 0.446330i | \(-0.852731\pi\) | ||
0.894869 | − | 0.446330i | \(-0.147269\pi\) | |||||||
\(72\) | 203.373 | + | 10.5467i | 0.332886 | + | 0.0172630i | ||||
\(73\) | − | 582.270i | − | 0.933555i | −0.884375 | − | 0.466778i | \(-0.845415\pi\) | ||
0.884375 | − | 0.466778i | \(-0.154585\pi\) | |||||||
\(74\) | 30.3338 | + | 0.523939i | 0.0476518 | + | 0.000823063i | ||||
\(75\) | 456.842 | 0.703354 | ||||||||
\(76\) | −136.907 | − | 4.73084i | −0.206635 | − | 0.00714032i | ||||
\(77\) | 691.973 | − | 963.368i | 1.02413 | − | 1.42579i | ||||
\(78\) | 4.20392 | − | 243.389i | 0.00610257 | − | 0.353312i | ||||
\(79\) | 311.277i | 0.443309i | 0.975125 | + | 0.221654i | \(0.0711457\pi\) | ||||
−0.975125 | + | 0.221654i | \(0.928854\pi\) | |||||||
\(80\) | 73.5639 | − | 1063.17i | 0.102809 | − | 1.48582i | ||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −2.00926 | + | 116.328i | −0.00270593 | + | 0.156662i | ||||
\(83\) | −1319.63 | −1.74515 | −0.872577 | − | 0.488477i | \(-0.837553\pi\) | ||||
−0.872577 | + | 0.488477i | \(0.837553\pi\) | |||||||
\(84\) | −351.839 | − | 271.620i | −0.457009 | − | 0.352812i | ||||
\(85\) | 1380.50 | 1.76160 | ||||||||
\(86\) | −20.1490 | + | 1166.54i | −0.0252643 | + | 1.46269i | ||||
\(87\) | 592.095 | 0.729646 | ||||||||
\(88\) | 75.0512 | − | 1447.23i | 0.0909146 | − | 1.75313i | ||||
\(89\) | − | 616.091i | − | 0.733770i | −0.930266 | − | 0.366885i | \(-0.880424\pi\) | ||
0.930266 | − | 0.366885i | \(-0.119576\pi\) | |||||||
\(90\) | 7.32042 | − | 423.821i | 0.00857378 | − | 0.496385i | ||||
\(91\) | −309.958 | + | 431.525i | −0.357060 | + | 0.497100i | ||||
\(92\) | −26.2601 | + | 759.948i | −0.0297588 | + | 0.861196i | ||||
\(93\) | 460.545 | 0.513508 | ||||||||
\(94\) | 1350.95 | + | 23.3342i | 1.48234 | + | 0.0256036i | ||||
\(95\) | 285.137i | 0.307941i | ||||||||
\(96\) | −541.034 | − | 46.8368i | −0.575199 | − | 0.0497943i | ||||
\(97\) | 104.076i | 0.108941i | 0.998515 | + | 0.0544706i | \(0.0173471\pi\) | ||||
−0.998515 | + | 0.0544706i | \(0.982653\pi\) | |||||||
\(98\) | 293.864 | + | 924.573i | 0.302906 | + | 0.953021i | ||||
\(99\) | − | 576.405i | − | 0.585161i | ||||||
\(100\) | −1217.52 | − | 42.0716i | −1.21752 | − | 0.0420716i | ||||
\(101\) | 1754.34i | 1.72835i | 0.503196 | + | 0.864173i | \(0.332158\pi\) | ||||
−0.503196 | + | 0.864173i | \(0.667842\pi\) | |||||||
\(102\) | 12.1487 | − | 703.360i | 0.0117932 | − | 0.682775i | ||||
\(103\) | 310.370 | 0.296910 | 0.148455 | − | 0.988919i | \(-0.452570\pi\) | ||||
0.148455 | + | 0.988919i | \(0.452570\pi\) | |||||||
\(104\) | −33.6180 | + | 648.263i | −0.0316973 | + | 0.611225i | ||||
\(105\) | −539.740 | + | 751.429i | −0.501650 | + | 0.698400i | ||||
\(106\) | −99.6317 | − | 1.72088i | −0.0912932 | − | 0.00157686i | ||||
\(107\) | − | 482.444i | − | 0.435884i | −0.975962 | − | 0.217942i | \(-0.930066\pi\) | ||
0.975962 | − | 0.217942i | \(-0.0699344\pi\) | |||||||
\(108\) | −215.871 | − | 7.45947i | −0.192335 | − | 0.00664618i | ||||
\(109\) | −72.5584 | −0.0637600 | −0.0318800 | − | 0.999492i | \(-0.510149\pi\) | ||||
−0.0318800 | + | 0.999492i | \(0.510149\pi\) | |||||||
\(110\) | −3015.96 | − | 52.0930i | −2.61418 | − | 0.0451533i | ||||
\(111\) | −32.1786 | −0.0275159 | ||||||||
\(112\) | 912.663 | + | 756.290i | 0.769987 | + | 0.638060i | ||||
\(113\) | −1545.99 | −1.28703 | −0.643514 | − | 0.765434i | \(-0.722524\pi\) | ||||
−0.643514 | + | 0.765434i | \(0.722524\pi\) | |||||||
\(114\) | 145.276 | + | 2.50928i | 0.119354 | + | 0.00206154i | ||||
\(115\) | 1582.75 | 1.28341 | ||||||||
\(116\) | −1577.98 | − | 54.5273i | −1.26303 | − | 0.0436443i | ||||
\(117\) | 258.191i | 0.204015i | ||||||||
\(118\) | 1398.75 | + | 24.1599i | 1.09124 | + | 0.0188483i | ||||
\(119\) | −895.736 | + | 1247.05i | −0.690017 | + | 0.960645i | ||||
\(120\) | −58.5401 | + | 1128.84i | −0.0445330 | + | 0.858738i | ||||
\(121\) | −2770.76 | −2.08172 | ||||||||
\(122\) | 14.3650 | − | 831.672i | 0.0106602 | − | 0.617181i | ||||
\(123\) | − | 123.403i | − | 0.0904621i | ||||||
\(124\) | −1227.39 | − | 42.4126i | −0.888892 | − | 0.0307158i | ||||
\(125\) | 454.269i | 0.325048i | ||||||||
\(126\) | 378.101 | + | 281.609i | 0.267333 | + | 0.199109i | ||||
\(127\) | − | 1982.75i | − | 1.38536i | −0.721246 | − | 0.692679i | \(-0.756430\pi\) | ||
0.721246 | − | 0.692679i | \(-0.243570\pi\) | |||||||
\(128\) | 1437.58 | + | 174.649i | 0.992701 | + | 0.120601i | ||||
\(129\) | − | 1237.49i | − | 0.844612i | ||||||
\(130\) | 1350.95 | + | 23.3342i | 0.911432 | + | 0.0157426i | ||||
\(131\) | 403.984 | 0.269437 | 0.134719 | − | 0.990884i | \(-0.456987\pi\) | ||||
0.134719 | + | 0.990884i | \(0.456987\pi\) | |||||||
\(132\) | −53.0824 | + | 1536.16i | −0.0350018 | + | 1.01292i | ||||
\(133\) | −257.573 | − | 185.011i | −0.167928 | − | 0.120620i | ||||
\(134\) | −10.1538 | + | 587.859i | −0.00654590 | + | 0.378980i | ||||
\(135\) | 449.597i | 0.286631i | ||||||||
\(136\) | −97.1513 | + | 1873.39i | −0.0612548 | + | 1.18119i | ||||
\(137\) | −1366.78 | −0.852350 | −0.426175 | − | 0.904641i | \(-0.640139\pi\) | ||||
−0.426175 | + | 0.904641i | \(0.640139\pi\) | |||||||
\(138\) | 13.9286 | − | 806.407i | 0.00859190 | − | 0.497434i | ||||
\(139\) | −1770.10 | −1.08013 | −0.540065 | − | 0.841623i | \(-0.681600\pi\) | ||||
−0.540065 | + | 0.841623i | \(0.681600\pi\) | |||||||
\(140\) | 1507.65 | − | 1952.91i | 0.910140 | − | 1.17894i | ||||
\(141\) | −1433.11 | −0.855956 | ||||||||
\(142\) | 26.0860 | − | 1510.27i | 0.0154161 | − | 0.892527i | ||||
\(143\) | 1837.32 | 1.07444 | ||||||||
\(144\) | 574.626 | + | 39.7601i | 0.332538 | + | 0.0230093i | ||||
\(145\) | 3286.47i | 1.88225i | ||||||||
\(146\) | 28.4419 | − | 1646.66i | 0.0161224 | − | 0.933416i | ||||
\(147\) | −328.579 | − | 975.129i | −0.184359 | − | 0.547124i | ||||
\(148\) | 85.7585 | + | 2.96340i | 0.0476305 | + | 0.00164588i | ||||
\(149\) | 1991.97 | 1.09522 | 0.547612 | − | 0.836732i | \(-0.315537\pi\) | ||||
0.547612 | + | 0.836732i | \(0.315537\pi\) | |||||||
\(150\) | 1291.95 | + | 22.3151i | 0.703249 | + | 0.0121468i | ||||
\(151\) | 1117.45i | 0.602229i | 0.953588 | + | 0.301115i | \(0.0973586\pi\) | ||||
−0.953588 | + | 0.301115i | \(0.902641\pi\) | |||||||
\(152\) | −386.942 | − | 20.0663i | −0.206481 | − | 0.0107078i | ||||
\(153\) | 746.137i | 0.394259i | ||||||||
\(154\) | 2003.96 | − | 2690.61i | 1.04860 | − | 1.40789i | ||||
\(155\) | 2556.29i | 1.32468i | ||||||||
\(156\) | 23.7774 | − | 688.100i | 0.0122033 | − | 0.353154i | ||||
\(157\) | − | 758.016i | − | 0.385327i | −0.981265 | − | 0.192663i | \(-0.938287\pi\) | ||
0.981265 | − | 0.192663i | \(-0.0617125\pi\) | |||||||
\(158\) | −15.2048 | + | 880.293i | −0.00765588 | + | 0.443243i | ||||
\(159\) | 105.691 | 0.0527160 | ||||||||
\(160\) | 259.971 | − | 3003.06i | 0.128453 | − | 1.48383i | ||||
\(161\) | −1026.97 | + | 1429.75i | −0.502710 | + | 0.699876i | ||||
\(162\) | 229.068 | + | 3.95657i | 0.111095 | + | 0.00191887i | ||||
\(163\) | 147.846i | 0.0710443i | 0.999369 | + | 0.0355222i | \(0.0113094\pi\) | ||||
−0.999369 | + | 0.0355222i | \(0.988691\pi\) | |||||||
\(164\) | −11.3644 | + | 328.877i | −0.00541105 | + | 0.156591i | ||||
\(165\) | 3199.38 | 1.50953 | ||||||||
\(166\) | −3731.91 | − | 64.4592i | −1.74489 | − | 0.0301386i | ||||
\(167\) | −1741.92 | −0.807148 | −0.403574 | − | 0.914947i | \(-0.632232\pi\) | ||||
−0.403574 | + | 0.914947i | \(0.632232\pi\) | |||||||
\(168\) | −981.734 | − | 785.329i | −0.450848 | − | 0.360652i | ||||
\(169\) | 1374.00 | 0.625400 | ||||||||
\(170\) | 3904.06 | + | 67.4326i | 1.76134 | + | 0.0304226i | ||||
\(171\) | −154.112 | −0.0689195 | ||||||||
\(172\) | −113.963 | + | 3298.00i | −0.0505210 | + | 1.46204i | ||||
\(173\) | − | 2686.73i | − | 1.18074i | −0.807131 | − | 0.590372i | \(-0.798981\pi\) | ||
0.807131 | − | 0.590372i | \(-0.201019\pi\) | |||||||
\(174\) | 1674.45 | + | 28.9218i | 0.729538 | + | 0.0126009i | ||||
\(175\) | −2290.61 | − | 1645.31i | −0.989451 | − | 0.710708i | ||||
\(176\) | 282.937 | − | 4089.10i | 0.121177 | − | 1.75129i | ||||
\(177\) | −1483.82 | −0.630119 | ||||||||
\(178\) | 30.0939 | − | 1742.31i | 0.0126721 | − | 0.733661i | ||||
\(179\) | − | 1032.53i | − | 0.431146i | −0.976488 | − | 0.215573i | \(-0.930838\pi\) | ||
0.976488 | − | 0.215573i | \(-0.0691619\pi\) | |||||||
\(180\) | 41.4044 | − | 1198.21i | 0.0171450 | − | 0.496163i | ||||
\(181\) | − | 1608.53i | − | 0.660558i | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||
0.943883 | − | 0.330279i | \(-0.107143\pi\) | |||||||
\(182\) | −897.642 | + | 1205.22i | −0.365591 | + | 0.490860i | ||||
\(183\) | 882.253i | 0.356383i | ||||||||
\(184\) | −111.385 | + | 2147.85i | −0.0446271 | + | 0.860553i | ||||
\(185\) | − | 178.610i | − | 0.0709821i | ||||||
\(186\) | 1302.42 | + | 22.4960i | 0.513431 | + | 0.00886821i | ||||
\(187\) | 5309.60 | 2.07634 | ||||||||
\(188\) | 3819.35 | + | 131.978i | 1.48167 | + | 0.0511996i | ||||
\(189\) | −406.135 | − | 291.721i | −0.156307 | − | 0.112273i | ||||
\(190\) | −13.9280 | + | 806.369i | −0.00531811 | + | 0.307896i | ||||
\(191\) | − | 1970.43i | − | 0.746469i | −0.927737 | − | 0.373235i | \(-0.878249\pi\) | ||
0.927737 | − | 0.373235i | \(-0.121751\pi\) | |||||||
\(192\) | −1527.76 | − | 158.882i | −0.574253 | − | 0.0597205i | ||||
\(193\) | 966.622 | 0.360513 | 0.180256 | − | 0.983620i | \(-0.442307\pi\) | ||||
0.180256 | + | 0.983620i | \(0.442307\pi\) | |||||||
\(194\) | −5.08374 | + | 294.327i | −0.00188140 | + | 0.108925i | ||||
\(195\) | −1433.11 | −0.526294 | ||||||||
\(196\) | 785.887 | + | 2629.05i | 0.286402 | + | 0.958110i | ||||
\(197\) | 1068.53 | 0.386443 | 0.193222 | − | 0.981155i | \(-0.438106\pi\) | ||||
0.193222 | + | 0.981155i | \(0.438106\pi\) | |||||||
\(198\) | 28.1554 | − | 1630.08i | 0.0101056 | − | 0.585073i | ||||
\(199\) | 252.660 | 0.0900029 | 0.0450015 | − | 0.998987i | \(-0.485671\pi\) | ||||
0.0450015 | + | 0.998987i | \(0.485671\pi\) | |||||||
\(200\) | −3441.09 | − | 178.450i | −1.21661 | − | 0.0630916i | ||||
\(201\) | − | 623.611i | − | 0.218837i | ||||||
\(202\) | −85.6932 | + | 4961.27i | −0.0298483 | + | 1.72809i | ||||
\(203\) | −2968.77 | − | 2132.43i | −1.02644 | − | 0.737276i | ||||
\(204\) | 68.7134 | − | 1988.51i | 0.0235829 | − | 0.682469i | ||||
\(205\) | 684.956 | 0.233363 | ||||||||
\(206\) | 877.728 | + | 15.1605i | 0.296865 | + | 0.00512759i | ||||
\(207\) | 855.451i | 0.287237i | ||||||||
\(208\) | −126.737 | + | 1831.65i | −0.0422483 | + | 0.610586i | ||||
\(209\) | 1096.68i | 0.362961i | ||||||||
\(210\) | −1563.09 | + | 2098.68i | −0.513637 | + | 0.689632i | ||||
\(211\) | 4606.20i | 1.50286i | 0.659811 | + | 0.751432i | \(0.270636\pi\) | ||||
−0.659811 | + | 0.751432i | \(0.729364\pi\) | |||||||
\(212\) | −281.675 | − | 9.73333i | −0.0912524 | − | 0.00315324i | ||||
\(213\) | 1602.12i | 0.515377i | ||||||||
\(214\) | 23.5657 | − | 1364.35i | 0.00752766 | − | 0.435819i | ||||
\(215\) | 6868.79 | 2.17883 | ||||||||
\(216\) | −610.120 | − | 31.6400i | −0.192192 | − | 0.00996680i | ||||
\(217\) | −2309.18 | − | 1658.65i | −0.722383 | − | 0.518877i | ||||
\(218\) | −205.196 | − | 3.54423i | −0.0637505 | − | 0.00110113i | ||||
\(219\) | 1746.81i | 0.538988i | ||||||||
\(220\) | −8526.60 | − | 294.638i | −2.61301 | − | 0.0902932i | ||||
\(221\) | −2378.35 | −0.723914 | ||||||||
\(222\) | −91.0014 | − | 1.57182i | −0.0275118 | − | 0.000475195i | ||||
\(223\) | 1927.65 | 0.578857 | 0.289428 | − | 0.957200i | \(-0.406535\pi\) | ||||
0.289428 | + | 0.957200i | \(0.406535\pi\) | |||||||
\(224\) | 2544.07 | + | 2183.37i | 0.758853 | + | 0.651262i | ||||
\(225\) | −1370.52 | −0.406081 | ||||||||
\(226\) | −4372.06 | − | 75.5161i | −1.28684 | − | 0.0222268i | ||||
\(227\) | −4063.72 | −1.18819 | −0.594093 | − | 0.804396i | \(-0.702489\pi\) | ||||
−0.594093 | + | 0.804396i | \(0.702489\pi\) | |||||||
\(228\) | 410.720 | + | 14.1925i | 0.119301 | + | 0.00412247i | ||||
\(229\) | − | 4096.49i | − | 1.18211i | −0.806631 | − | 0.591056i | \(-0.798711\pi\) | ||
0.806631 | − | 0.591056i | \(-0.201289\pi\) | |||||||
\(230\) | 4476.03 | + | 77.3119i | 1.28322 | + | 0.0221643i | ||||
\(231\) | −2075.92 | + | 2890.10i | −0.591279 | + | 0.823181i | ||||
\(232\) | −4459.87 | − | 231.282i | −1.26209 | − | 0.0654501i | ||||
\(233\) | 1950.08 | 0.548301 | 0.274150 | − | 0.961687i | \(-0.411603\pi\) | ||||
0.274150 | + | 0.961687i | \(0.411603\pi\) | |||||||
\(234\) | −12.6118 | + | 730.166i | −0.00352332 | + | 0.203985i | ||||
\(235\) | − | 7954.60i | − | 2.20809i | ||||||
\(236\) | 3954.51 | + | 136.649i | 1.09075 | + | 0.0376910i | ||||
\(237\) | − | 933.831i | − | 0.255944i | ||||||
\(238\) | −2594.06 | + | 3482.90i | −0.706504 | + | 0.948585i | ||||
\(239\) | − | 2861.53i | − | 0.774465i | −0.921982 | − | 0.387232i | \(-0.873431\pi\) | ||
0.921982 | − | 0.387232i | \(-0.126569\pi\) | |||||||
\(240\) | −220.692 | + | 3189.51i | −0.0593566 | + | 0.857841i | ||||
\(241\) | 4320.12i | 1.15470i | 0.816496 | + | 0.577351i | \(0.195914\pi\) | ||||
−0.816496 | + | 0.577351i | \(0.804086\pi\) | |||||||
\(242\) | −7835.74 | − | 135.342i | −2.08141 | − | 0.0359510i | ||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 81.2487 | − | 2351.27i | 0.0213173 | − | 0.616905i | ||||
\(245\) | 5412.53 | − | 1823.81i | 1.41140 | − | 0.475586i | ||||
\(246\) | 6.02779 | − | 348.983i | 0.00156227 | − | 0.0904486i | ||||
\(247\) | − | 491.239i | − | 0.126546i | ||||||
\(248\) | −3468.98 | − | 179.897i | −0.888229 | − | 0.0460623i | ||||
\(249\) | 3958.88 | 1.00756 | ||||||||
\(250\) | −22.1895 | + | 1284.67i | −0.00561354 | + | 0.325000i | ||||
\(251\) | 1366.74 | 0.343698 | 0.171849 | − | 0.985123i | \(-0.445026\pi\) | ||||
0.171849 | + | 0.985123i | \(0.445026\pi\) | |||||||
\(252\) | 1055.52 | + | 814.860i | 0.263854 | + | 0.203696i | ||||
\(253\) | 6087.49 | 1.51272 | ||||||||
\(254\) | 96.8504 | − | 5607.22i | 0.0239249 | − | 1.38515i | ||||
\(255\) | −4141.50 | −1.01706 | ||||||||
\(256\) | 4056.97 | + | 564.128i | 0.990470 | + | 0.137727i | ||||
\(257\) | 5993.21i | 1.45465i | 0.686291 | + | 0.727327i | \(0.259238\pi\) | ||||
−0.686291 | + | 0.727327i | \(0.740762\pi\) | |||||||
\(258\) | 60.4471 | − | 3499.63i | 0.0145863 | − | 0.844486i | ||||
\(259\) | 161.344 | + | 115.891i | 0.0387083 | + | 0.0278036i | ||||
\(260\) | 3819.35 | + | 131.978i | 0.911024 | + | 0.0314806i | ||||
\(261\) | −1776.28 | −0.421262 | ||||||||
\(262\) | 1142.47 | + | 19.7332i | 0.269397 | + | 0.00465314i | ||||
\(263\) | 1636.95i | 0.383798i | 0.981415 | + | 0.191899i | \(0.0614646\pi\) | ||||
−0.981415 | + | 0.191899i | \(0.938535\pi\) | |||||||
\(264\) | −225.154 | + | 4341.69i | −0.0524896 | + | 1.01217i | ||||
\(265\) | 586.647i | 0.135990i | ||||||||
\(266\) | −719.381 | − | 535.794i | −0.165820 | − | 0.123502i | ||||
\(267\) | 1848.27i | 0.423642i | ||||||||
\(268\) | −57.4298 | + | 1661.97i | −0.0130899 | + | 0.378810i | ||||
\(269\) | − | 7442.41i | − | 1.68688i | −0.537220 | − | 0.843442i | \(-0.680526\pi\) | ||
0.537220 | − | 0.843442i | \(-0.319474\pi\) | |||||||
\(270\) | −21.9613 | + | 1271.46i | −0.00495007 | + | 0.286588i | ||||
\(271\) | 5619.33 | 1.25959 | 0.629797 | − | 0.776760i | \(-0.283138\pi\) | ||||
0.629797 | + | 0.776760i | \(0.283138\pi\) | |||||||
\(272\) | −366.253 | + | 5293.21i | −0.0816447 | + | 1.17996i | ||||
\(273\) | 929.874 | − | 1294.58i | 0.206149 | − | 0.287001i | ||||
\(274\) | −3865.26 | − | 66.7625i | −0.852223 | − | 0.0147200i | ||||
\(275\) | 9752.81i | 2.13861i | ||||||||
\(276\) | 78.7804 | − | 2279.84i | 0.0171812 | − | 0.497212i | ||||
\(277\) | −698.240 | −0.151456 | −0.0757278 | − | 0.997129i | \(-0.524128\pi\) | ||||
−0.0757278 | + | 0.997129i | \(0.524128\pi\) | |||||||
\(278\) | −5005.86 | − | 86.4634i | −1.07997 | − | 0.0186537i | ||||
\(279\) | −1381.63 | −0.296474 | ||||||||
\(280\) | 4359.03 | − | 5449.19i | 0.930365 | − | 1.16304i | ||||
\(281\) | −5026.99 | −1.06721 | −0.533604 | − | 0.845735i | \(-0.679163\pi\) | ||||
−0.533604 | + | 0.845735i | \(0.679163\pi\) | |||||||
\(282\) | −4052.85 | − | 70.0026i | −0.855828 | − | 0.0147822i | ||||
\(283\) | −3596.17 | −0.755371 | −0.377686 | − | 0.925934i | \(-0.623280\pi\) | ||||
−0.377686 | + | 0.925934i | \(0.623280\pi\) | |||||||
\(284\) | 147.543 | − | 4269.77i | 0.0308276 | − | 0.892127i | ||||
\(285\) | − | 855.411i | − | 0.177790i | ||||||
\(286\) | 5195.95 | + | 89.7467i | 1.07428 | + | 0.0185554i | ||||
\(287\) | −444.434 | + | 618.743i | −0.0914080 | + | 0.127259i | ||||
\(288\) | 1623.10 | + | 140.510i | 0.332091 | + | 0.0287488i | ||||
\(289\) | −1960.10 | −0.398961 | ||||||||
\(290\) | −160.533 | + | 9294.16i | −0.0325062 | + | 1.88197i | ||||
\(291\) | − | 312.227i | − | 0.0628972i | ||||||
\(292\) | 160.868 | − | 4655.38i | 0.0322399 | − | 0.932999i | ||||
\(293\) | − | 4095.02i | − | 0.816497i | −0.912871 | − | 0.408248i | \(-0.866140\pi\) | ||
0.912871 | − | 0.408248i | \(-0.133860\pi\) | |||||||
\(294\) | −881.592 | − | 2773.72i | −0.174883 | − | 0.550227i | ||||
\(295\) | − | 8236.09i | − | 1.62550i | ||||||
\(296\) | 242.381 | + | 12.5695i | 0.0475949 | + | 0.00246821i | ||||
\(297\) | 1729.22i | 0.337843i | ||||||||
\(298\) | 5633.30 | + | 97.3008i | 1.09506 | + | 0.0189144i | ||||
\(299\) | −2726.79 | −0.527406 | ||||||||
\(300\) | 3652.55 | + | 126.215i | 0.702934 | + | 0.0242900i | ||||
\(301\) | −4456.81 | + | 6204.79i | −0.853443 | + | 1.18817i | ||||
\(302\) | −54.5835 | + | 3160.15i | −0.0104004 | + | 0.602139i | ||||
\(303\) | − | 5263.01i | − | 0.997861i | ||||||
\(304\) | −1093.29 | − | 75.6482i | −0.206265 | − | 0.0142721i | ||||
\(305\) | −4897.02 | −0.919352 | ||||||||
\(306\) | −36.4462 | + | 2110.08i | −0.00680880 | + | 0.394200i | ||||
\(307\) | 6214.27 | 1.15527 | 0.577633 | − | 0.816296i | \(-0.303976\pi\) | ||||
0.577633 | + | 0.816296i | \(0.303976\pi\) | |||||||
\(308\) | 5798.64 | − | 7511.17i | 1.07275 | − | 1.38957i | ||||
\(309\) | −931.110 | −0.171421 | ||||||||
\(310\) | −124.866 | + | 7229.20i | −0.0228771 | + | 1.32449i | ||||
\(311\) | −4044.93 | −0.737514 | −0.368757 | − | 0.929526i | \(-0.620216\pi\) | ||||
−0.368757 | + | 0.929526i | \(0.620216\pi\) | |||||||
\(312\) | 100.854 | − | 1944.79i | 0.0183004 | − | 0.352891i | ||||
\(313\) | − | 6931.84i | − | 1.25179i | −0.779907 | − | 0.625896i | \(-0.784734\pi\) | ||
0.779907 | − | 0.625896i | \(-0.215266\pi\) | |||||||
\(314\) | 37.0265 | − | 2143.67i | 0.00665454 | − | 0.385269i | ||||
\(315\) | 1619.22 | − | 2254.29i | 0.289628 | − | 0.403221i | ||||
\(316\) | −85.9986 | + | 2488.73i | −0.0153095 | + | 0.443044i | ||||
\(317\) | 3966.39 | 0.702759 | 0.351379 | − | 0.936233i | \(-0.385713\pi\) | ||||
0.351379 | + | 0.936233i | \(0.385713\pi\) | |||||||
\(318\) | 298.895 | + | 5.16265i | 0.0527082 | + | 0.000910399i | ||||
\(319\) | 12640.2i | 2.21855i | ||||||||
\(320\) | 881.889 | − | 8479.96i | 0.154060 | − | 1.48139i | ||||
\(321\) | 1447.33i | 0.251658i | ||||||||
\(322\) | −2974.11 | + | 3993.17i | −0.514722 | + | 0.691090i | ||||
\(323\) | − | 1419.61i | − | 0.244549i | ||||||
\(324\) | 647.613 | + | 22.3784i | 0.111045 | + | 0.00383718i | ||||
\(325\) | − | 4368.61i | − | 0.745622i | ||||||
\(326\) | −7.22179 | + | 418.110i | −0.00122693 | + | 0.0710337i | ||||
\(327\) | 217.675 | 0.0368118 | ||||||||
\(328\) | −48.2032 | + | 929.512i | −0.00811455 | + | 0.156475i | ||||
\(329\) | 7185.65 | + | 5161.34i | 1.20413 | + | 0.864906i | ||||
\(330\) | 9047.87 | + | 156.279i | 1.50930 | + | 0.0260693i | ||||
\(331\) | − | 9949.84i | − | 1.65224i | −0.563491 | − | 0.826122i | \(-0.690542\pi\) | ||
0.563491 | − | 0.826122i | \(-0.309458\pi\) | |||||||
\(332\) | −10550.7 | − | 364.582i | −1.74411 | − | 0.0602681i | ||||
\(333\) | 96.5359 | 0.0158863 | ||||||||
\(334\) | −4926.15 | − | 85.0867i | −0.807027 | − | 0.0139393i | ||||
\(335\) | 3461.41 | 0.564528 | ||||||||
\(336\) | −2737.99 | − | 2268.87i | −0.444552 | − | 0.368384i | ||||
\(337\) | 4947.26 | 0.799686 | 0.399843 | − | 0.916584i | \(-0.369065\pi\) | ||||
0.399843 | + | 0.916584i | \(0.369065\pi\) | |||||||
\(338\) | 3885.69 | + | 67.1153i | 0.625306 | + | 0.0108006i | ||||
\(339\) | 4637.96 | 0.743066 | ||||||||
\(340\) | 11037.4 | + | 381.399i | 1.76055 | + | 0.0608361i | ||||
\(341\) | 9831.86i | 1.56136i | ||||||||
\(342\) | −435.829 | − | 7.52784i | −0.0689092 | − | 0.00119023i | ||||
\(343\) | −1864.42 | + | 6072.69i | −0.293496 | + | 0.955960i | ||||
\(344\) | −483.385 | + | 9321.21i | −0.0757627 | + | 1.46095i | ||||
\(345\) | −4748.25 | −0.740978 | ||||||||
\(346\) | 131.238 | − | 7598.10i | 0.0203913 | − | 1.18057i | ||||
\(347\) | 5246.44i | 0.811653i | 0.913950 | + | 0.405826i | \(0.133016\pi\) | ||||
−0.913950 | + | 0.405826i | \(0.866984\pi\) | |||||||
\(348\) | 4733.93 | + | 163.582i | 0.729211 | + | 0.0251980i | ||||
\(349\) | 8703.25i | 1.33488i | 0.744662 | + | 0.667442i | \(0.232611\pi\) | ||||
−0.744662 | + | 0.667442i | \(0.767389\pi\) | |||||||
\(350\) | −6397.49 | − | 4764.84i | −0.977030 | − | 0.727690i | ||||
\(351\) | − | 774.574i | − | 0.117788i | ||||||
\(352\) | 999.887 | − | 11550.2i | 0.151404 | − | 1.74894i | ||||
\(353\) | 1402.85i | 0.211519i | 0.994392 | + | 0.105760i | \(0.0337274\pi\) | ||||
−0.994392 | + | 0.105760i | \(0.966273\pi\) | |||||||
\(354\) | −4196.26 | − | 72.4797i | −0.630025 | − | 0.0108821i | ||||
\(355\) | −8892.69 | −1.32951 | ||||||||
\(356\) | 170.212 | − | 4925.79i | 0.0253404 | − | 0.733332i | ||||
\(357\) | 2687.21 | − | 3741.14i | 0.398381 | − | 0.554628i | ||||
\(358\) | 50.4356 | − | 2920.01i | 0.00744583 | − | 0.431081i | ||||
\(359\) | − | 9556.07i | − | 1.40487i | −0.711746 | − | 0.702437i | \(-0.752095\pi\) | ||
0.711746 | − | 0.702437i | \(-0.247905\pi\) | |||||||
\(360\) | 175.620 | − | 3386.52i | 0.0257111 | − | 0.495793i | ||||
\(361\) | −6565.78 | −0.957251 | ||||||||
\(362\) | 78.5711 | − | 4548.93i | 0.0114077 | − | 0.660459i | ||||
\(363\) | 8312.29 | 1.20188 | ||||||||
\(364\) | −2597.41 | + | 3364.51i | −0.374014 | + | 0.484473i | ||||
\(365\) | −9695.81 | −1.39042 | ||||||||
\(366\) | −43.0950 | + | 2495.02i | −0.00615468 | + | 0.356330i | ||||
\(367\) | 1036.73 | 0.147458 | 0.0737289 | − | 0.997278i | \(-0.476510\pi\) | ||||
0.0737289 | + | 0.997278i | \(0.476510\pi\) | |||||||
\(368\) | −419.912 | + | 6068.70i | −0.0594821 | + | 0.859654i | ||||
\(369\) | 370.208i | 0.0522283i | ||||||||
\(370\) | 8.72449 | − | 505.111i | 0.00122585 | − | 0.0709715i | ||||
\(371\) | −529.937 | − | 380.646i | −0.0741589 | − | 0.0532672i | ||||
\(372\) | 3682.16 | + | 127.238i | 0.513202 | + | 0.0177338i | ||||
\(373\) | 10769.4 | 1.49496 | 0.747481 | − | 0.664283i | \(-0.231263\pi\) | ||||
0.747481 | + | 0.664283i | \(0.231263\pi\) | |||||||
\(374\) | 15015.6 | + | 259.356i | 2.07603 | + | 0.0358582i | ||||
\(375\) | − | 1362.81i | − | 0.187667i | ||||||
\(376\) | 10794.7 | + | 559.798i | 1.48057 | + | 0.0767803i | ||||
\(377\) | − | 5661.99i | − | 0.773494i | ||||||
\(378\) | −1134.30 | − | 844.827i | −0.154345 | − | 0.114956i | ||||
\(379\) | 3268.34i | 0.442963i | 0.975165 | + | 0.221482i | \(0.0710893\pi\) | ||||
−0.975165 | + | 0.221482i | \(0.928911\pi\) | |||||||
\(380\) | −78.7767 | + | 2279.74i | −0.0106346 | + | 0.307758i | ||||
\(381\) | 5948.25i | 0.799837i | ||||||||
\(382\) | 96.2489 | − | 5572.40i | 0.0128914 | − | 0.746358i | ||||
\(383\) | −5143.39 | −0.686201 | −0.343101 | − | 0.939299i | \(-0.611477\pi\) | ||||
−0.343101 | + | 0.939299i | \(0.611477\pi\) | |||||||
\(384\) | −4312.75 | − | 523.946i | −0.573136 | − | 0.0696289i | ||||
\(385\) | −16041.8 | − | 11522.6i | −2.12354 | − | 1.52531i | ||||
\(386\) | 2733.61 | + | 47.2161i | 0.360459 | + | 0.00622601i | ||||
\(387\) | 3712.47i | 0.487637i | ||||||||
\(388\) | −28.7537 | + | 832.109i | −0.00376224 | + | 0.108876i | ||||
\(389\) | −5140.27 | −0.669979 | −0.334990 | − | 0.942222i | \(-0.608733\pi\) | ||||
−0.334990 | + | 0.942222i | \(0.608733\pi\) | |||||||
\(390\) | −4052.85 | − | 70.0026i | −0.526215 | − | 0.00908902i | ||||
\(391\) | −7880.05 | −1.01921 | ||||||||
\(392\) | 2094.07 | + | 7473.36i | 0.269813 | + | 0.962913i | ||||
\(393\) | −1211.95 | −0.155560 | ||||||||
\(394\) | 3021.80 | + | 52.1938i | 0.386386 | + | 0.00667382i | ||||
\(395\) | 5183.30 | 0.660254 | ||||||||
\(396\) | 159.247 | − | 4608.49i | 0.0202083 | − | 0.584812i | ||||
\(397\) | 6774.24i | 0.856396i | 0.903685 | + | 0.428198i | \(0.140851\pi\) | ||||
−0.903685 | + | 0.428198i | \(0.859149\pi\) | |||||||
\(398\) | 714.523 | + | 12.3416i | 0.0899895 | + | 0.00155434i | ||||
\(399\) | 772.720 | + | 555.033i | 0.0969533 | + | 0.0696401i | ||||
\(400\) | −9722.71 | − | 672.743i | −1.21534 | − | 0.0840929i | ||||
\(401\) | −8827.27 | −1.09928 | −0.549642 | − | 0.835401i | \(-0.685236\pi\) | ||||
−0.549642 | + | 0.835401i | \(0.685236\pi\) | |||||||
\(402\) | 30.4613 | − | 1763.58i | 0.00377928 | − | 0.218804i | ||||
\(403\) | − | 4404.02i | − | 0.544367i | ||||||
\(404\) | −484.682 | + | 14026.3i | −0.0596877 | + | 1.72731i | ||||
\(405\) | − | 1348.79i | − | 0.165486i | ||||||
\(406\) | −8291.54 | − | 6175.53i | −1.01355 | − | 0.754892i | ||||
\(407\) | − | 686.961i | − | 0.0836643i | ||||||
\(408\) | 291.454 | − | 5620.17i | 0.0353655 | − | 0.681960i | ||||
\(409\) | 11986.2i | 1.44910i | 0.689223 | + | 0.724549i | \(0.257952\pi\) | ||||
−0.689223 | + | 0.724549i | \(0.742048\pi\) | |||||||
\(410\) | 1937.06 | + | 33.4577i | 0.233328 | + | 0.00403015i | ||||
\(411\) | 4100.34 | 0.492105 | ||||||||
\(412\) | 2481.48 | + | 85.7480i | 0.296732 | + | 0.0102536i | ||||
\(413\) | 7439.92 | + | 5343.98i | 0.886427 | + | 0.636708i | ||||
\(414\) | −41.7858 | + | 2419.22i | −0.00496054 | + | 0.287194i | ||||
\(415\) | 21974.1i | 2.59919i | ||||||||
\(416\) | −447.883 | + | 5173.72i | −0.0527867 | + | 0.609766i | ||||
\(417\) | 5310.31 | 0.623614 | ||||||||
\(418\) | −53.5690 | + | 3101.41i | −0.00626828 | + | 0.362907i | ||||
\(419\) | −4098.42 | −0.477854 | −0.238927 | − | 0.971038i | \(-0.576796\pi\) | ||||
−0.238927 | + | 0.971038i | \(0.576796\pi\) | |||||||
\(420\) | −4522.95 | + | 5858.73i | −0.525470 | + | 0.680659i | ||||
\(421\) | 318.996 | 0.0369285 | 0.0184643 | − | 0.999830i | \(-0.494122\pi\) | ||||
0.0184643 | + | 0.999830i | \(0.494122\pi\) | |||||||
\(422\) | −224.997 | + | 13026.4i | −0.0259542 | + | 1.50264i | ||||
\(423\) | 4299.34 | 0.494186 | ||||||||
\(424\) | −796.102 | − | 41.2847i | −0.0911843 | − | 0.00472869i | ||||
\(425\) | − | 12624.7i | − | 1.44091i | ||||||
\(426\) | −78.2580 | + | 4530.80i | −0.00890050 | + | 0.515300i | ||||
\(427\) | 3177.43 | − | 4423.63i | 0.360109 | − | 0.501346i | ||||
\(428\) | 133.288 | − | 3857.25i | 0.0150531 | − | 0.435624i | ||||
\(429\) | −5511.96 | −0.620326 | ||||||||
\(430\) | 19425.0 | + | 335.517i | 2.17850 | + | 0.0376280i | ||||
\(431\) | − | 9939.59i | − | 1.11084i | −0.831569 | − | 0.555422i | \(-0.812557\pi\) | ||
0.831569 | − | 0.555422i | \(-0.187443\pi\) | |||||||
\(432\) | −1723.88 | − | 119.280i | −0.191991 | − | 0.0132844i | ||||
\(433\) | − | 1254.43i | − | 0.139225i | −0.997574 | − | 0.0696123i | \(-0.977824\pi\) | ||
0.997574 | − | 0.0696123i | \(-0.0221762\pi\) | |||||||
\(434\) | −6449.35 | − | 4803.46i | −0.713315 | − | 0.531275i | ||||
\(435\) | − | 9859.41i | − | 1.08672i | ||||||
\(436\) | −580.121 | − | 20.0462i | −0.0637220 | − | 0.00220192i | ||||
\(437\) | − | 1627.60i | − | 0.178166i | ||||||
\(438\) | −85.3256 | + | 4939.99i | −0.00930826 | + | 0.538908i | ||||
\(439\) | −12933.4 | −1.40610 | −0.703049 | − | 0.711141i | \(-0.748179\pi\) | ||||
−0.703049 | + | 0.711141i | \(0.748179\pi\) | |||||||
\(440\) | −24098.9 | − | 1249.73i | −2.61107 | − | 0.135406i | ||||
\(441\) | 985.738 | + | 2925.39i | 0.106440 | + | 0.315882i | ||||
\(442\) | −6725.98 | − | 116.174i | −0.723806 | − | 0.0125019i | ||||
\(443\) | − | 596.175i | − | 0.0639394i | −0.999489 | − | 0.0319697i | \(-0.989822\pi\) | ||
0.999489 | − | 0.0319697i | \(-0.0101780\pi\) | |||||||
\(444\) | −257.276 | − | 8.89021i | −0.0274995 | − | 0.000950249i | ||||
\(445\) | −10259.0 | −1.09286 | ||||||||
\(446\) | 5451.41 | + | 94.1591i | 0.578770 | + | 0.00999677i | ||||
\(447\) | −5975.91 | −0.632328 | ||||||||
\(448\) | 7088.00 | + | 6298.86i | 0.747492 | + | 0.664270i | ||||
\(449\) | −3428.69 | −0.360378 | −0.180189 | − | 0.983632i | \(-0.557671\pi\) | ||||
−0.180189 | + | 0.983632i | \(0.557671\pi\) | |||||||
\(450\) | −3875.85 | − | 66.9454i | −0.406021 | − | 0.00701297i | ||||
\(451\) | 2634.44 | 0.275058 | ||||||||
\(452\) | −12360.5 | − | 427.120i | −1.28626 | − | 0.0444470i | ||||
\(453\) | − | 3352.34i | − | 0.347697i | ||||||
\(454\) | −11492.2 | − | 198.499i | −1.18801 | − | 0.0205198i | ||||
\(455\) | 7185.65 | + | 5161.34i | 0.740370 | + | 0.531797i | ||||
\(456\) | 1160.83 | + | 60.1988i | 0.119212 | + | 0.00618216i | ||||
\(457\) | 19011.5 | 1.94600 | 0.973000 | − | 0.230807i | \(-0.0741367\pi\) | ||||
0.973000 | + | 0.230807i | \(0.0741367\pi\) | |||||||
\(458\) | 200.099 | − | 11584.9i | 0.0204149 | − | 1.18194i | ||||
\(459\) | − | 2238.41i | − | 0.227626i | ||||||
\(460\) | 12654.5 | + | 437.277i | 1.28265 | + | 0.0443221i | ||||
\(461\) | 13187.0i | 1.33227i | 0.745830 | + | 0.666137i | \(0.232053\pi\) | ||||
−0.745830 | + | 0.666137i | \(0.767947\pi\) | |||||||
\(462\) | −6011.88 | + | 8071.83i | −0.605407 | + | 0.812847i | ||||
\(463\) | 7425.75i | 0.745364i | 0.927959 | + | 0.372682i | \(0.121562\pi\) | ||||
−0.927959 | + | 0.372682i | \(0.878438\pi\) | |||||||
\(464\) | −12601.2 | − | 871.917i | −1.26077 | − | 0.0872365i | ||||
\(465\) | − | 7668.87i | − | 0.764807i | ||||||
\(466\) | 5514.84 | + | 95.2548i | 0.548219 | + | 0.00946908i | ||||
\(467\) | −11474.1 | −1.13695 | −0.568476 | − | 0.822700i | \(-0.692467\pi\) | ||||
−0.568476 | + | 0.822700i | \(0.692467\pi\) | |||||||
\(468\) | −71.3322 | + | 2064.30i | −0.00704558 | + | 0.203894i | ||||
\(469\) | −2245.93 | + | 3126.80i | −0.221125 | + | 0.307851i | ||||
\(470\) | 388.555 | − | 22495.7i | 0.0381334 | − | 2.20776i | ||||
\(471\) | 2274.05i | 0.222468i | ||||||||
\(472\) | 11176.7 | + | 579.607i | 1.08993 | + | 0.0565224i | ||||
\(473\) | 26418.4 | 2.56811 | ||||||||
\(474\) | 45.6144 | − | 2640.88i | 0.00442013 | − | 0.255906i | ||||
\(475\) | 2607.58 | 0.251882 | ||||||||
\(476\) | −7506.15 | + | 9722.96i | −0.722781 | + | 0.936242i | ||||
\(477\) | −317.073 | −0.0304356 | ||||||||
\(478\) | 139.776 | − | 8092.42i | 0.0133749 | − | 0.774349i | ||||
\(479\) | 17924.0 | 1.70975 | 0.854873 | − | 0.518837i | \(-0.173635\pi\) | ||||
0.854873 | + | 0.518837i | \(0.173635\pi\) | |||||||
\(480\) | −779.914 | + | 9009.17i | −0.0741626 | + | 0.856688i | ||||
\(481\) | 307.713i | 0.0291694i | ||||||||
\(482\) | −211.023 | + | 12217.3i | −0.0199415 | + | 1.15453i | ||||
\(483\) | 3080.90 | − | 4289.25i | 0.290240 | − | 0.404073i | ||||
\(484\) | −22152.9 | − | 765.497i | −2.08047 | − | 0.0718912i | ||||
\(485\) | 1733.04 | 0.162254 | ||||||||
\(486\) | −687.205 | − | 11.8697i | −0.0641405 | − | 0.00110786i | ||||
\(487\) | − | 8161.93i | − | 0.759450i | −0.925099 | − | 0.379725i | \(-0.876019\pi\) | ||
0.925099 | − | 0.379725i | \(-0.123981\pi\) | |||||||
\(488\) | 344.623 | − | 6645.44i | 0.0319679 | − | 0.616445i | ||||
\(489\) | − | 443.539i | − | 0.0410174i | ||||||
\(490\) | 15395.8 | − | 4893.35i | 1.41941 | − | 0.451141i | ||||
\(491\) | 17622.4i | 1.61973i | 0.586616 | + | 0.809865i | \(0.300460\pi\) | ||||
−0.586616 | + | 0.809865i | \(0.699540\pi\) | |||||||
\(492\) | 34.0933 | − | 986.632i | 0.00312407 | − | 0.0904081i | ||||
\(493\) | − | 16362.4i | − | 1.49478i | ||||||
\(494\) | 23.9953 | − | 1389.23i | 0.00218543 | − | 0.126527i | ||||
\(495\) | −9598.15 | −0.871525 | ||||||||
\(496\) | −9801.52 | − | 678.196i | −0.887301 | − | 0.0613950i | ||||
\(497\) | 5770.02 | − | 8033.05i | 0.520766 | − | 0.725013i | ||||
\(498\) | 11195.7 | + | 193.378i | 1.00741 | + | 0.0174005i | ||||
\(499\) | − | 6772.04i | − | 0.607531i | −0.952747 | − | 0.303766i | \(-0.901756\pi\) | ||
0.952747 | − | 0.303766i | \(-0.0982440\pi\) | |||||||
\(500\) | −125.504 | + | 3631.98i | −0.0112254 | + | 0.324854i | ||||
\(501\) | 5225.75 | 0.466007 | ||||||||
\(502\) | 3865.16 | + | 66.7608i | 0.343647 | + | 0.00593561i | ||||
\(503\) | 15340.8 | 1.35987 | 0.679935 | − | 0.733273i | \(-0.262008\pi\) | ||||
0.679935 | + | 0.733273i | \(0.262008\pi\) | |||||||
\(504\) | 2945.20 | + | 2355.99i | 0.260297 | + | 0.208222i | ||||
\(505\) | 29212.7 | 2.57416 | ||||||||
\(506\) | 17215.4 | + | 297.353i | 1.51249 | + | 0.0261244i | ||||
\(507\) | −4122.01 | −0.361075 | ||||||||
\(508\) | 547.787 | − | 15852.5i | 0.0478428 | − | 1.38453i | ||||
\(509\) | − | 7729.91i | − | 0.673128i | −0.941661 | − | 0.336564i | \(-0.890735\pi\) | ||
0.941661 | − | 0.336564i | \(-0.109265\pi\) | |||||||
\(510\) | −11712.2 | − | 202.298i | −1.01691 | − | 0.0175645i | ||||
\(511\) | 6291.12 | − | 8758.53i | 0.544624 | − | 0.758228i | ||||
\(512\) | 11445.6 | + | 1793.53i | 0.987944 | + | 0.154811i | ||||
\(513\) | 462.336 | 0.0397907 | ||||||||
\(514\) | −292.748 | + | 16948.8i | −0.0251217 | + | 1.45444i | ||||
\(515\) | − | 5168.20i | − | 0.442210i | ||||||
\(516\) | 341.890 | − | 9894.01i | 0.0291683 | − | 0.844108i | ||||
\(517\) | − | 30594.6i | − | 2.60261i | ||||||
\(518\) | 450.621 | + | 335.622i | 0.0382223 | + | 0.0284679i | ||||
\(519\) | 8060.20i | 0.681703i | ||||||||
\(520\) | 10794.7 | + | 559.798i | 0.910344 | + | 0.0472092i | ||||
\(521\) | − | 9454.94i | − | 0.795064i | −0.917588 | − | 0.397532i | \(-0.869867\pi\) | ||
0.917588 | − | 0.397532i | \(-0.130133\pi\) | |||||||
\(522\) | −5023.34 | − | 86.7654i | −0.421199 | − | 0.00727513i | ||||
\(523\) | −20468.5 | −1.71133 | −0.855665 | − | 0.517531i | \(-0.826851\pi\) | ||||
−0.855665 | + | 0.517531i | \(0.826851\pi\) | |||||||
\(524\) | 3229.95 | + | 111.611i | 0.269276 | + | 0.00930490i | ||||
\(525\) | 6871.83 | + | 4935.94i | 0.571260 | + | 0.410327i | ||||
\(526\) | −79.9596 | + | 4629.32i | −0.00662814 | + | 0.383741i | ||||
\(527\) | − | 12727.0i | − | 1.05199i | ||||||
\(528\) | −848.812 | + | 12267.3i | −0.0699618 | + | 1.01111i | ||||
\(529\) | 3132.47 | 0.257456 | ||||||||
\(530\) | −28.6557 | + | 1659.04i | −0.00234853 | + | 0.135970i | ||||
\(531\) | 4451.47 | 0.363799 | ||||||||
\(532\) | −2008.24 | − | 1550.37i | −0.163662 | − | 0.126348i | ||||
\(533\) | −1180.05 | −0.0958984 | ||||||||
\(534\) | −90.2818 | + | 5226.93i | −0.00731625 | + | 0.423579i | ||||
\(535\) | −8033.53 | −0.649196 | ||||||||
\(536\) | −243.593 | + | 4697.26i | −0.0196299 | + | 0.378528i | ||||
\(537\) | 3097.60i | 0.248922i | ||||||||
\(538\) | 363.536 | − | 21047.2i | 0.0291323 | − | 1.68663i | ||||
\(539\) | 20817.4 | − | 7014.62i | 1.66358 | − | 0.560559i | ||||
\(540\) | −124.213 | + | 3594.63i | −0.00989867 | + | 0.286460i | ||||
\(541\) | −14593.7 | −1.15976 | −0.579882 | − | 0.814700i | \(-0.696901\pi\) | ||||
−0.579882 | + | 0.814700i | \(0.696901\pi\) | |||||||
\(542\) | 15891.5 | + | 274.485i | 1.25941 | + | 0.0217530i | ||||
\(543\) | 4825.58i | 0.381373i | ||||||||
\(544\) | −1294.32 | + | 14951.3i | −0.102010 | + | 1.17837i | ||||
\(545\) | 1208.22i | 0.0949627i | ||||||||
\(546\) | 2692.93 | − | 3615.65i | 0.211074 | − | 0.283398i | ||||
\(547\) | 8758.57i | 0.684624i | 0.939586 | + | 0.342312i | \(0.111210\pi\) | ||||
−0.939586 | + | 0.342312i | \(0.888790\pi\) | |||||||
\(548\) | −10927.7 | − | 377.610i | −0.851842 | − | 0.0294356i | ||||
\(549\) | − | 2646.76i | − | 0.205758i | ||||||
\(550\) | −476.391 | + | 27581.0i | −0.0369334 | + | 2.13829i | ||||
\(551\) | 3379.59 | 0.261298 | ||||||||
\(552\) | 334.154 | − | 6443.56i | 0.0257655 | − | 0.496841i | ||||
\(553\) | −3363.19 | + | 4682.24i | −0.258621 | + | 0.360053i | ||||
\(554\) | −1974.63 | − | 34.1066i | −0.151433 | − | 0.00261562i | ||||
\(555\) | 535.831i | 0.0409815i | ||||||||
\(556\) | −14152.4 | − | 489.038i | −1.07949 | − | 0.0373019i | ||||
\(557\) | −3314.26 | −0.252118 | −0.126059 | − | 0.992023i | \(-0.540233\pi\) | ||||
−0.126059 | + | 0.992023i | \(0.540233\pi\) | |||||||
\(558\) | −3907.27 | − | 67.4880i | −0.296430 | − | 0.00512007i | ||||
\(559\) | −11833.7 | −0.895369 | ||||||||
\(560\) | 12593.5 | − | 15197.4i | 0.950312 | − | 1.14680i | ||||
\(561\) | −15928.8 | −1.19878 | ||||||||
\(562\) | −14216.4 | − | 245.551i | −1.06705 | − | 0.0184305i | ||||
\(563\) | −21115.0 | −1.58062 | −0.790310 | − | 0.612707i | \(-0.790081\pi\) | ||||
−0.790310 | + | 0.612707i | \(0.790081\pi\) | |||||||
\(564\) | −11458.1 | − | 395.935i | −0.855445 | − | 0.0295601i | ||||
\(565\) | 25743.4i | 1.91687i | ||||||||
\(566\) | −10170.0 | − | 175.660i | −0.755259 | − | 0.0130452i | ||||
\(567\) | 1218.41 | + | 875.163i | 0.0902438 | + | 0.0648208i | ||||
\(568\) | 625.815 | − | 12067.7i | 0.0462299 | − | 0.891462i | ||||
\(569\) | −8726.10 | −0.642912 | −0.321456 | − | 0.946924i | \(-0.604172\pi\) | ||||
−0.321456 | + | 0.946924i | \(0.604172\pi\) | |||||||
\(570\) | 41.7839 | − | 2419.11i | 0.00307041 | − | 0.177764i | ||||
\(571\) | 19948.3i | 1.46202i | 0.682369 | + | 0.731008i | \(0.260950\pi\) | ||||
−0.682369 | + | 0.731008i | \(0.739050\pi\) | |||||||
\(572\) | 14689.8 | + | 507.608i | 1.07379 | + | 0.0371052i | ||||
\(573\) | 5911.30i | 0.430974i | ||||||||
\(574\) | −1287.08 | + | 1728.10i | −0.0935921 | + | 0.125661i | ||||
\(575\) | − | 14474.3i | − | 1.04977i | ||||||
\(576\) | 4583.28 | + | 476.647i | 0.331545 | + | 0.0344797i | ||||
\(577\) | 4516.90i | 0.325894i | 0.986635 | + | 0.162947i | \(0.0521000\pi\) | ||||
−0.986635 | + | 0.162947i | \(0.947900\pi\) | |||||||
\(578\) | −5543.16 | − | 95.7439i | −0.398902 | − | 0.00689001i | ||||
\(579\) | −2899.87 | −0.208142 | ||||||||
\(580\) | −907.975 | + | 26276.1i | −0.0650028 | + | 1.88113i | ||||
\(581\) | −19849.9 | − | 14257.9i | −1.41740 | − | 1.01810i | ||||
\(582\) | 15.2512 | − | 882.980i | 0.00108623 | − | 0.0628878i | ||||
\(583\) | 2256.33i | 0.160288i | ||||||||
\(584\) | 682.334 | − | 13157.6i | 0.0483479 | − | 0.932303i | ||||
\(585\) | 4299.34 | 0.303856 | ||||||||
\(586\) | 200.028 | − | 11580.7i | 0.0141008 | − | 0.816375i | ||||
\(587\) | −1629.66 | −0.114588 | −0.0572942 | − | 0.998357i | \(-0.518247\pi\) | ||||
−0.0572942 | + | 0.998357i | \(0.518247\pi\) | |||||||
\(588\) | −2357.66 | − | 7887.16i | −0.165354 | − | 0.553165i | ||||
\(589\) | 2628.72 | 0.183896 | ||||||||
\(590\) | 402.305 | − | 23291.7i | 0.0280722 | − | 1.62526i | ||||
\(591\) | −3205.58 | −0.223113 | ||||||||
\(592\) | 684.840 | + | 47.3862i | 0.0475452 | + | 0.00328980i | ||||
\(593\) | 6205.32i | 0.429717i | 0.976645 | + | 0.214858i | \(0.0689290\pi\) | ||||
−0.976645 | + | 0.214858i | \(0.931071\pi\) | |||||||
\(594\) | −84.4662 | + | 4890.23i | −0.00583450 | + | 0.337792i | ||||
\(595\) | 20765.5 | + | 14915.6i | 1.43076 | + | 1.02770i | ||||
\(596\) | 15926.2 | + | 550.334i | 1.09457 | + | 0.0378231i | ||||
\(597\) | −757.980 | −0.0519632 | ||||||||
\(598\) | −7711.38 | − | 133.194i | −0.527327 | − | 0.00910823i | ||||
\(599\) | 752.600i | 0.0513362i | 0.999671 | + | 0.0256681i | \(0.00817131\pi\) | ||||
−0.999671 | + | 0.0256681i | \(0.991829\pi\) | |||||||
\(600\) | 10323.3 | + | 535.350i | 0.702410 | + | 0.0364260i | ||||
\(601\) | 21945.7i | 1.48949i | 0.667348 | + | 0.744746i | \(0.267430\pi\) | ||||
−0.667348 | + | 0.744746i | \(0.732570\pi\) | |||||||
\(602\) | −12907.0 | + | 17329.5i | −0.873835 | + | 1.17325i | ||||
\(603\) | 1870.83i | 0.126345i | ||||||||
\(604\) | −308.725 | + | 8934.25i | −0.0207977 | + | 0.601870i | ||||
\(605\) | 46138.1i | 3.10046i | ||||||||
\(606\) | 257.080 | − | 14883.8i | 0.0172329 | − | 0.997712i | ||||
\(607\) | 1770.10 | 0.118363 | 0.0591815 | − | 0.998247i | \(-0.481151\pi\) | ||||
0.0591815 | + | 0.998247i | \(0.481151\pi\) | |||||||
\(608\) | −3088.14 | − | 267.337i | −0.205988 | − | 0.0178322i | ||||
\(609\) | 8906.32 | + | 6397.28i | 0.592615 | + | 0.425666i | ||||
\(610\) | −13848.8 | − | 239.202i | −0.919215 | − | 0.0158771i | ||||
\(611\) | 13704.3i | 0.907395i | ||||||||
\(612\) | −206.140 | + | 5965.54i | −0.0136156 | + | 0.394024i | ||||
\(613\) | −22582.9 | −1.48795 | −0.743977 | − | 0.668205i | \(-0.767063\pi\) | ||||
−0.743977 | + | 0.668205i | \(0.767063\pi\) | |||||||
\(614\) | 17574.0 | + | 303.546i | 1.15509 | + | 0.0199513i | ||||
\(615\) | −2054.87 | −0.134732 | ||||||||
\(616\) | 16765.5 | − | 20958.4i | 1.09659 | − | 1.37084i | ||||
\(617\) | 12035.2 | 0.785279 | 0.392639 | − | 0.919692i | \(-0.371562\pi\) | ||||
0.392639 | + | 0.919692i | \(0.371562\pi\) | |||||||
\(618\) | −2633.19 | − | 45.4815i | −0.171395 | − | 0.00296041i | ||||
\(619\) | 875.313 | 0.0568365 | 0.0284183 | − | 0.999596i | \(-0.490953\pi\) | ||||
0.0284183 | + | 0.999596i | \(0.490953\pi\) | |||||||
\(620\) | −706.243 | + | 20438.1i | −0.0457474 | + | 1.32389i | ||||
\(621\) | − | 2566.35i | − | 0.165836i | ||||||
\(622\) | −11439.1 | − | 197.581i | −0.737404 | − | 0.0127368i | ||||
\(623\) | 6656.54 | − | 9267.27i | 0.428072 | − | 0.595964i | ||||
\(624\) | 380.212 | − | 5494.94i | 0.0243921 | − | 0.352522i | ||||
\(625\) | −11470.7 | −0.734125 | ||||||||
\(626\) | 338.596 | − | 19603.3i | 0.0216183 | − | 1.25160i | ||||
\(627\) | − | 3290.03i | − | 0.209556i | ||||||
\(628\) | 209.422 | − | 6060.51i | 0.0133071 | − | 0.385097i | ||||
\(629\) | 889.248i | 0.0563698i | ||||||||
\(630\) | 4689.28 | − | 6296.04i | 0.296548 | − | 0.398159i | ||||
\(631\) | − | 18162.8i | − | 1.14588i | −0.819597 | − | 0.572940i | \(-0.805803\pi\) | ||
0.819597 | − | 0.572940i | \(-0.194197\pi\) | |||||||
\(632\) | −364.770 | + | 7033.94i | −0.0229585 | + | 0.442714i | ||||
\(633\) | − | 13818.6i | − | 0.867679i | ||||||
\(634\) | 11217.0 | + | 193.744i | 0.702654 | + | 0.0121365i | ||||
\(635\) | −33016.2 | −2.06332 | ||||||||
\(636\) | 845.024 | + | 29.2000i | 0.0526846 | + | 0.00182053i | ||||
\(637\) | −9324.81 | + | 3142.09i | −0.580004 | + | 0.195438i | ||||
\(638\) | −617.432 | + | 35746.7i | −0.0383141 | + | 2.21822i | ||||
\(639\) | − | 4806.36i | − | 0.297553i | ||||||
\(640\) | 2908.20 | − | 23938.3i | 0.179620 | − | 1.47851i | ||||
\(641\) | 2528.87 | 0.155826 | 0.0779128 | − | 0.996960i | \(-0.475174\pi\) | ||||
0.0779128 | + | 0.996960i | \(0.475174\pi\) | |||||||
\(642\) | −70.6972 | + | 4093.06i | −0.00434610 | + | 0.251620i | ||||
\(643\) | 22947.8 | 1.40742 | 0.703712 | − | 0.710485i | \(-0.251524\pi\) | ||||
0.703712 | + | 0.710485i | \(0.251524\pi\) | |||||||
\(644\) | −8605.85 | + | 11147.4i | −0.526580 | + | 0.682097i | ||||
\(645\) | −20606.4 | −1.25795 | ||||||||
\(646\) | 69.3432 | − | 4014.67i | 0.00422333 | − | 0.244513i | ||||
\(647\) | 8556.53 | 0.519926 | 0.259963 | − | 0.965619i | \(-0.416290\pi\) | ||||
0.259963 | + | 0.965619i | \(0.416290\pi\) | |||||||
\(648\) | 1830.36 | + | 94.9199i | 0.110962 | + | 0.00575433i | ||||
\(649\) | − | 31677.2i | − | 1.91593i | ||||||
\(650\) | 213.392 | − | 12354.5i | 0.0128768 | − | 0.745510i | ||||
\(651\) | 6927.53 | + | 4975.95i | 0.417068 | + | 0.299574i | ||||
\(652\) | −40.8465 | + | 1182.07i | −0.00245349 | + | 0.0710019i | ||||
\(653\) | −18532.9 | −1.11064 | −0.555319 | − | 0.831637i | \(-0.687404\pi\) | ||||
−0.555319 | + | 0.831637i | \(0.687404\pi\) | |||||||
\(654\) | 615.587 | + | 10.6327i | 0.0368064 | + | 0.000635736i | ||||
\(655\) | − | 6727.04i | − | 0.401293i | ||||||
\(656\) | −181.722 | + | 2626.31i | −0.0108156 | + | 0.156311i | ||||
\(657\) | − | 5240.43i | − | 0.311185i | ||||||
\(658\) | 20068.9 | + | 14947.3i | 1.18901 | + | 0.885572i | ||||
\(659\) | − | 20893.8i | − | 1.23506i | −0.786546 | − | 0.617532i | \(-0.788133\pi\) | ||
0.786546 | − | 0.617532i | \(-0.211867\pi\) | |||||||
\(660\) | 25579.8 | + | 883.915i | 1.50862 | + | 0.0521308i | ||||
\(661\) | 5459.18i | 0.321237i | 0.987017 | + | 0.160618i | \(0.0513488\pi\) | ||||
−0.987017 | + | 0.160618i | \(0.948651\pi\) | |||||||
\(662\) | 486.015 | − | 28138.2i | 0.0285340 | − | 1.65200i | ||||
\(663\) | 7135.04 | 0.417952 | ||||||||
\(664\) | −29819.7 | − | 1546.40i | −1.74281 | − | 0.0903797i | ||||
\(665\) | −3080.76 | + | 4289.04i | −0.179649 | + | 0.250108i | ||||
\(666\) | 273.004 | + | 4.71545i | 0.0158839 | + | 0.000274354i | ||||
\(667\) | − | 18759.6i | − | 1.08902i | ||||||
\(668\) | −13927.0 | − | 481.251i | −0.806666 | − | 0.0278745i | ||||
\(669\) | −5782.95 | −0.334203 | ||||||||
\(670\) | 9788.87 | + | 169.078i | 0.564444 | + | 0.00974932i | ||||
\(671\) | −18834.6 | −1.08361 | ||||||||
\(672\) | −7632.22 | − | 6550.12i | −0.438124 | − | 0.376006i | ||||
\(673\) | 1716.03 | 0.0982882 | 0.0491441 | − | 0.998792i | \(-0.484351\pi\) | ||||
0.0491441 | + | 0.998792i | \(0.484351\pi\) | |||||||
\(674\) | 13990.9 | + | 241.656i | 0.799567 | + | 0.0138105i | ||||
\(675\) | 4111.57 | 0.234451 | ||||||||
\(676\) | 10985.5 | + | 379.605i | 0.625027 | + | 0.0215979i | ||||
\(677\) | − | 17235.8i | − | 0.978474i | −0.872151 | − | 0.489237i | \(-0.837275\pi\) | ||
0.872151 | − | 0.489237i | \(-0.162725\pi\) | |||||||
\(678\) | 13116.2 | + | 226.548i | 0.742955 | + | 0.0128326i | ||||
\(679\) | −1124.48 | + | 1565.51i | −0.0635548 | + | 0.0884813i | ||||
\(680\) | 31195.2 | + | 1617.74i | 1.75924 | + | 0.0912315i | ||||
\(681\) | 12191.1 | 0.686000 | ||||||||
\(682\) | −480.253 | + | 27804.6i | −0.0269645 | + | 1.56113i | ||||
\(683\) | 19454.4i | 1.08990i | 0.838468 | + | 0.544951i | \(0.183452\pi\) | ||||
−0.838468 | + | 0.544951i | \(0.816548\pi\) | |||||||
\(684\) | −1232.16 | − | 42.5775i | −0.0688784 | − | 0.00238011i | ||||
\(685\) | 22759.3i | 1.26947i | ||||||||
\(686\) | −5569.22 | + | 17082.5i | −0.309962 | + | 0.950749i | ||||
\(687\) | 12289.5i | 0.682492i | ||||||||
\(688\) | −1822.32 | + | 26336.8i | −0.100982 | + | 1.45942i | ||||
\(689\) | − | 1010.69i | − | 0.0558840i | ||||||
\(690\) | −13428.1 | − | 231.936i | −0.740867 | − | 0.0127966i | ||||
\(691\) | 17230.7 | 0.948604 | 0.474302 | − | 0.880362i | \(-0.342700\pi\) | ||||
0.474302 | + | 0.880362i | \(0.342700\pi\) | |||||||
\(692\) | 742.282 | − | 21481.1i | 0.0407765 | − | 1.18004i | ||||
\(693\) | 6227.76 | − | 8670.31i | 0.341375 | − | 0.475264i | ||||
\(694\) | −256.270 | + | 14837.0i | −0.0140171 | + | 0.811532i | ||||
\(695\) | 29475.3i | 1.60872i | ||||||||
\(696\) | 13379.6 | + | 693.847i | 0.728667 | + | 0.0377877i | ||||
\(697\) | −3410.20 | −0.185323 | ||||||||
\(698\) | −425.124 | + | 24612.8i | −0.0230533 | + | 1.33468i | ||||
\(699\) | −5850.25 | −0.316562 | ||||||||
\(700\) | −17859.4 | − | 13787.5i | −0.964317 | − | 0.744454i | ||||
\(701\) | −22169.2 | −1.19447 | −0.597233 | − | 0.802068i | \(-0.703733\pi\) | ||||
−0.597233 | + | 0.802068i | \(0.703733\pi\) | |||||||
\(702\) | 37.8353 | − | 2190.50i | 0.00203419 | − | 0.117771i | ||||
\(703\) | −183.671 | −0.00985388 | ||||||||
\(704\) | 3391.87 | − | 32615.2i | 0.181585 | − | 1.74607i | ||||
\(705\) | 23863.8i | 1.27484i | ||||||||
\(706\) | −68.5245 | + | 3967.27i | −0.00365291 | + | 0.211488i | ||||
\(707\) | −18954.7 | + | 26388.8i | −1.00829 | + | 1.40375i | ||||
\(708\) | −11863.5 | − | 409.946i | −0.629743 | − | 0.0217609i | ||||
\(709\) | 15665.5 | 0.829800 | 0.414900 | − | 0.909867i | \(-0.363817\pi\) | ||||
0.414900 | + | 0.909867i | \(0.363817\pi\) | |||||||
\(710\) | −25148.6 | − | 434.377i | −1.32931 | − | 0.0229604i | ||||
\(711\) | 2801.49i | 0.147770i | ||||||||
\(712\) | 721.967 | − | 13921.8i | 0.0380012 | − | 0.732785i | ||||
\(713\) | − | 14591.6i | − | 0.766424i | ||||||
\(714\) | 7782.18 | − | 10448.7i | 0.407900 | − | 0.547666i | ||||
\(715\) | − | 30594.6i | − | 1.60024i | ||||||
\(716\) | 285.265 | − | 8255.33i | 0.0148894 | − | 0.430889i | ||||
\(717\) | 8584.59i | 0.447137i | ||||||||
\(718\) | 466.781 | − | 27024.6i | 0.0242620 | − | 1.40466i | ||||
\(719\) | 35225.3 | 1.82709 | 0.913547 | − | 0.406733i | \(-0.133332\pi\) | ||||
0.913547 | + | 0.406733i | \(0.133332\pi\) | |||||||
\(720\) | 662.075 | − | 9568.53i | 0.0342696 | − | 0.495275i | ||||
\(721\) | 4668.60 | + | 3353.39i | 0.241148 | + | 0.173213i | ||||
\(722\) | −18568.1 | − | 320.716i | −0.957108 | − | 0.0165316i | ||||
\(723\) | − | 12960.3i | − | 0.666667i | ||||||
\(724\) | 444.399 | − | 12860.5i | 0.0228121 | − | 0.660164i | ||||
\(725\) | 30054.8 | 1.53960 | ||||||||
\(726\) | 23507.2 | + | 406.027i | 1.20170 | + | 0.0207563i | ||||
\(727\) | 12778.0 | 0.651872 | 0.325936 | − | 0.945392i | \(-0.394321\pi\) | ||||
0.325936 | + | 0.945392i | \(0.394321\pi\) | |||||||
\(728\) | −7509.82 | + | 9387.97i | −0.382325 | + | 0.477941i | ||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −27419.8 | − | 473.607i | −1.39021 | − | 0.0240123i | ||||
\(731\) | −34197.7 | −1.73030 | ||||||||
\(732\) | −243.746 | + | 7053.82i | −0.0123075 | + | 0.356170i | ||||
\(733\) | 9725.54i | 0.490069i | 0.969514 | + | 0.245035i | \(0.0787994\pi\) | ||||
−0.969514 | + | 0.245035i | \(0.921201\pi\) | |||||||
\(734\) | 2931.88 | + | 50.6408i | 0.147436 | + | 0.00254658i | ||||
\(735\) | −16237.6 | + | 5471.42i | −0.814875 | + | 0.274580i | ||||
\(736\) | −1483.95 | + | 17141.8i | −0.0743193 | + | 0.858499i | ||||
\(737\) | 13313.1 | 0.665391 | ||||||||
\(738\) | −18.0834 | + | 1046.95i | −0.000901976 | + | 0.0522205i | ||||
\(739\) | − | 18977.4i | − | 0.944648i | −0.881425 | − | 0.472324i | \(-0.843415\pi\) | ||
0.881425 | − | 0.472324i | \(-0.156585\pi\) | |||||||
\(740\) | 49.3458 | − | 1428.03i | 0.00245134 | − | 0.0709397i | ||||
\(741\) | 1473.72i | 0.0730612i | ||||||||
\(742\) | −1480.07 | − | 1102.35i | −0.0732279 | − | 0.0545400i | ||||
\(743\) | 18688.2i | 0.922752i | 0.887205 | + | 0.461376i | \(0.152644\pi\) | ||||
−0.887205 | + | 0.461376i | \(0.847356\pi\) | |||||||
\(744\) | 10407.0 | + | 539.690i | 0.512819 | + | 0.0265941i | ||||
\(745\) | − | 33169.7i | − | 1.63120i | ||||||
\(746\) | 30456.1 | + | 526.051i | 1.49474 | + | 0.0258178i | ||||
\(747\) | −11876.6 | −0.581718 | ||||||||
\(748\) | 42451.4 | + | 1466.92i | 2.07510 | + | 0.0717056i | ||||
\(749\) | 5212.56 | − | 7256.95i | 0.254289 | − | 0.354023i | ||||
\(750\) | 66.5684 | − | 3854.02i | 0.00324098 | − | 0.187639i | ||||
\(751\) | − | 19229.5i | − | 0.934345i | −0.884166 | − | 0.467173i | \(-0.845273\pi\) | ||
0.884166 | − | 0.467173i | \(-0.154727\pi\) | |||||||
\(752\) | 30500.1 | + | 2110.40i | 1.47902 | + | 0.102338i | ||||
\(753\) | −4100.23 | −0.198434 | ||||||||
\(754\) | 276.569 | − | 16012.1i | 0.0133581 | − | 0.773379i | ||||
\(755\) | 18607.4 | 0.896946 | ||||||||
\(756\) | −3166.55 | − | 2444.58i | −0.152336 | − | 0.117604i | ||||
\(757\) | 35890.6 | 1.72321 | 0.861603 | − | 0.507584i | \(-0.169461\pi\) | ||||
0.861603 | + | 0.507584i | \(0.169461\pi\) | |||||||
\(758\) | −159.647 | + | 9242.87i | −0.00764992 | + | 0.442897i | ||||
\(759\) | −18262.5 | −0.873367 | ||||||||
\(760\) | −334.138 | + | 6443.26i | −0.0159480 | + | 0.307528i | ||||
\(761\) | 16455.3i | 0.783843i | 0.919999 | + | 0.391922i | \(0.128190\pi\) | ||||
−0.919999 | + | 0.391922i | \(0.871810\pi\) | |||||||
\(762\) | −290.551 | + | 16821.7i | −0.0138131 | + | 0.799718i | ||||
\(763\) | −1091.43 | − | 783.956i | −0.0517855 | − | 0.0371968i | ||||
\(764\) | 544.385 | − | 15754.1i | 0.0257790 | − | 0.746024i | ||||
\(765\) | 12424.5 | 0.587200 | ||||||||
\(766\) | −14545.5 | − | 251.237i | −0.686099 | − | 0.0118506i | ||||
\(767\) | 14189.3i | 0.667986i | ||||||||
\(768\) | −12170.9 | − | 1692.38i | −0.571848 | − | 0.0795165i | ||||
\(769\) | − | 32125.7i | − | 1.50648i | −0.657746 | − | 0.753240i | \(-0.728490\pi\) | ||
0.657746 | − | 0.753240i | \(-0.271510\pi\) | |||||||
\(770\) | −44803.3 | − | 33369.4i | −2.09688 | − | 1.56175i | ||||
\(771\) | − | 17979.6i | − | 0.839845i | ||||||
\(772\) | 7728.36 | + | 267.055i | 0.360298 | + | 0.0124502i | ||||
\(773\) | − | 302.967i | − | 0.0140970i | −0.999975 | − | 0.00704850i | \(-0.997756\pi\) | ||
0.999975 | − | 0.00704850i | \(-0.00224363\pi\) | |||||||
\(774\) | −181.341 | + | 10498.9i | −0.00842142 | + | 0.487564i | ||||
\(775\) | 23377.3 | 1.08353 | ||||||||
\(776\) | −121.961 | + | 2351.80i | −0.00564195 | + | 0.108795i | ||||
\(777\) | −484.033 | − | 347.674i | −0.0223482 | − | 0.0160524i | ||||
\(778\) | −14536.7 | − | 251.084i | −0.669879 | − | 0.0115704i | ||||
\(779\) | − | 704.364i | − | 0.0323959i | ||||||
\(780\) | −11458.1 | − | 395.935i | −0.525980 | − | 0.0181753i | ||||
\(781\) | −34202.6 | −1.56705 | ||||||||
\(782\) | −22284.8 | − | 384.913i | −1.01906 | − | 0.0176016i | ||||
\(783\) | 5328.85 | 0.243215 | ||||||||
\(784\) | 5557.00 | + | 21237.0i | 0.253143 | + | 0.967429i | ||||
\(785\) | −12622.3 | −0.573897 | ||||||||
\(786\) | −3427.41 | − | 59.1997i | −0.155536 | − | 0.00268649i | ||||
\(787\) | 23519.9 | 1.06531 | 0.532653 | − | 0.846334i | \(-0.321195\pi\) | ||||
0.532653 | + | 0.846334i | \(0.321195\pi\) | |||||||
\(788\) | 8543.11 | + | 295.209i | 0.386213 | + | 0.0133457i | ||||
\(789\) | − | 4910.86i | − | 0.221586i | ||||||
\(790\) | 14658.4 | + | 253.187i | 0.660156 | + | 0.0114025i | ||||
\(791\) | −23254.8 | − | 16703.6i | −1.04532 | − | 0.750835i | ||||
\(792\) | 675.461 | − | 13025.1i | 0.0303049 | − | 0.584375i | ||||
\(793\) | 8436.67 | 0.377800 | ||||||||
\(794\) | −330.898 | + | 19157.6i | −0.0147898 | + | 0.856269i | ||||
\(795\) | − | 1759.94i | − | 0.0785141i | ||||||
\(796\) | 2020.07 | + | 69.8040i | 0.0899492 | + | 0.00310821i | ||||
\(797\) | 7210.03i | 0.320442i | 0.987081 | + | 0.160221i | \(0.0512207\pi\) | ||||
−0.987081 | + | 0.160221i | \(0.948779\pi\) | |||||||
\(798\) | 2158.14 | + | 1607.38i | 0.0957362 | + | 0.0713041i | ||||
\(799\) | 39603.6i | 1.75354i | ||||||||
\(800\) | −27463.0 | − | 2377.44i | −1.21370 | − | 0.105069i | ||||
\(801\) | − | 5544.82i | − | 0.244590i | ||||||
\(802\) | −24963.6 | − | 431.181i | −1.09912 | − | 0.0189845i | ||||
\(803\) | −37291.5 | −1.63884 | ||||||||
\(804\) | 172.289 | − | 4985.92i | 0.00755743 | − | 0.218706i | ||||
\(805\) | 23807.8 | + | 17100.8i | 1.04238 | + | 0.748725i | ||||
\(806\) | 215.121 | − | 12454.6i | 0.00940115 | − | 0.544286i | ||||
\(807\) | 22327.2i | 0.973923i | ||||||||
\(808\) | −2055.82 | + | 39642.8i | −0.0895093 | + | 1.72603i | ||||
\(809\) | 40393.4 | 1.75544 | 0.877722 | − | 0.479170i | \(-0.159062\pi\) | ||||
0.877722 | + | 0.479170i | \(0.159062\pi\) | |||||||
\(810\) | 65.8838 | − | 3814.39i | 0.00285793 | − | 0.165462i | ||||
\(811\) | 29435.6 | 1.27450 | 0.637252 | − | 0.770655i | \(-0.280071\pi\) | ||||
0.637252 | + | 0.770655i | \(0.280071\pi\) | |||||||
\(812\) | −23146.9 | − | 17869.4i | −1.00036 | − | 0.772284i | ||||
\(813\) | −16858.0 | −0.727227 | ||||||||
\(814\) | 33.5557 | − | 1942.73i | 0.00144487 | − | 0.0836518i | ||||
\(815\) | 2461.90 | 0.105812 | ||||||||
\(816\) | 1098.76 | − | 15879.6i | 0.0471376 | − | 0.681248i | ||||
\(817\) | − | 7063.41i | − | 0.302469i | ||||||
\(818\) | −585.486 | + | 33897.1i | −0.0250257 | + | 1.44888i | ||||
\(819\) | −2789.62 | + | 3883.73i | −0.119020 | + | 0.165700i | ||||
\(820\) | 5476.38 | + | 189.237i | 0.233224 | + | 0.00805909i | ||||
\(821\) | 12341.4 | 0.524624 | 0.262312 | − | 0.964983i | \(-0.415515\pi\) | ||||
0.262312 | + | 0.964983i | \(0.415515\pi\) | |||||||
\(822\) | 11595.8 | + | 200.288i | 0.492031 | + | 0.00849858i | ||||
\(823\) | − | 22102.8i | − | 0.936153i | −0.883688 | − | 0.468077i | \(-0.844947\pi\) | ||
0.883688 | − | 0.468077i | \(-0.155053\pi\) | |||||||
\(824\) | 7013.45 | + | 363.708i | 0.296511 | + | 0.0153766i | ||||
\(825\) | − | 29258.4i | − | 1.23472i | ||||||
\(826\) | 20779.1 | + | 15476.2i | 0.875299 | + | 0.651921i | ||||
\(827\) | − | 3867.63i | − | 0.162625i | −0.996689 | − | 0.0813124i | \(-0.974089\pi\) | ||
0.996689 | − | 0.0813124i | \(-0.0259111\pi\) | |||||||
\(828\) | −236.341 | + | 6839.53i | −0.00991959 | + | 0.287065i | ||||
\(829\) | − | 11642.7i | − | 0.487778i | −0.969803 | − | 0.243889i | \(-0.921577\pi\) | ||
0.969803 | − | 0.243889i | \(-0.0784233\pi\) | |||||||
\(830\) | −1073.36 | + | 62142.8i | −0.0448877 | + | 2.59880i | ||||
\(831\) | 2094.72 | 0.0874429 | ||||||||
\(832\) | −1519.33 | + | 14609.4i | −0.0633094 | + | 0.608763i | ||||
\(833\) | −26947.4 | + | 9080.19i | −1.12086 | + | 0.377683i | ||||
\(834\) | 15017.6 | + | 259.390i | 0.623521 | + | 0.0107697i | ||||
\(835\) | 29006.0i | 1.20215i | ||||||||
\(836\) | −302.987 | + | 8768.19i | −0.0125347 | + | 0.362744i | ||||
\(837\) | 4144.90 | 0.171169 | ||||||||
\(838\) | −11590.3 | − | 200.193i | −0.477782 | − | 0.00825247i | ||||
\(839\) | 1522.64 | 0.0626546 | 0.0313273 | − | 0.999509i | \(-0.490027\pi\) | ||||
0.0313273 | + | 0.999509i | \(0.490027\pi\) | |||||||
\(840\) | −13077.1 | + | 16347.6i | −0.537146 | + | 0.671482i | ||||
\(841\) | 14563.9 | 0.597152 | ||||||||
\(842\) | 902.122 | + | 15.5819i | 0.0369230 | + | 0.000637751i | ||||
\(843\) | 15081.0 | 0.616152 | ||||||||
\(844\) | −1272.59 | + | 36827.7i | −0.0519008 | + | 1.50197i | ||||
\(845\) | − | 22879.5i | − | 0.931456i | ||||||
\(846\) | 12158.5 | + | 210.008i | 0.494113 | + | 0.00853453i | ||||
\(847\) | −41678.0 | − | 29936.7i | −1.69076 | − | 1.21445i | ||||
\(848\) | −2249.37 | − | 155.640i | −0.0910891 | − | 0.00630273i | ||||
\(849\) | 10788.5 | 0.436114 | ||||||||
\(850\) | 616.672 | − | 35702.7i | 0.0248843 | − | 1.44070i | ||||
\(851\) | 1019.53i | 0.0410681i | ||||||||
\(852\) | −442.628 | + | 12809.3i | −0.0177983 | + | 0.515070i | ||||
\(853\) | 16334.5i | 0.655664i | 0.944736 | + | 0.327832i | \(0.106318\pi\) | ||||
−0.944736 | + | 0.327832i | \(0.893682\pi\) | |||||||
\(854\) | 9201.87 | − | 12354.8i | 0.368714 | − | 0.495052i | ||||
\(855\) | 2566.23i | 0.102647i | ||||||||
\(856\) | 565.353 | − | 10901.8i | 0.0225740 | − | 0.435299i | ||||
\(857\) | − | 40489.7i | − | 1.61389i | −0.590627 | − | 0.806945i | \(-0.701120\pi\) | ||
0.590627 | − | 0.806945i | \(-0.298880\pi\) | |||||||
\(858\) | −15587.8 | − | 269.240i | −0.620233 | − | 0.0107129i | ||||
\(859\) | −3963.14 | −0.157416 | −0.0787080 | − | 0.996898i | \(-0.525079\pi\) | ||||
−0.0787080 | + | 0.996898i | \(0.525079\pi\) | |||||||
\(860\) | 54917.5 | + | 1897.69i | 2.17753 | + | 0.0752448i | ||||
\(861\) | 1333.30 | − | 1856.23i | 0.0527744 | − | 0.0734728i | ||||
\(862\) | 485.515 | − | 28109.2i | 0.0191841 | − | 1.11068i | ||||
\(863\) | − | 38486.3i | − | 1.51806i | −0.651054 | − | 0.759031i | \(-0.725673\pi\) | ||
0.651054 | − | 0.759031i | \(-0.274327\pi\) | |||||||
\(864\) | −4869.31 | − | 421.531i | −0.191733 | − | 0.0165981i | ||||
\(865\) | −44738.8 | −1.75857 | ||||||||
\(866\) | 61.2748 | − | 3547.55i | 0.00240439 | − | 0.139204i | ||||
\(867\) | 5880.29 | 0.230340 | ||||||||
\(868\) | −18004.2 | − | 13899.2i | −0.704033 | − | 0.543515i | ||||
\(869\) | 19935.7 | 0.778221 | ||||||||
\(870\) | 481.598 | − | 27882.5i | 0.0187675 | − | 1.08656i | ||||
\(871\) | −5963.37 | −0.231988 | ||||||||
\(872\) | −1639.61 | − | 85.0277i | −0.0636744 | − | 0.00330207i | ||||
\(873\) | 936.681i | 0.0363137i | ||||||||
\(874\) | 79.5025 | − | 4602.85i | 0.00307690 | − | 0.178139i | ||||
\(875\) | −4908.14 | + | 6833.13i | −0.189629 | + | 0.264002i | ||||
\(876\) | −482.603 | + | 13966.1i | −0.0186137 | + | 0.538667i | ||||
\(877\) | −7715.19 | −0.297062 | −0.148531 | − | 0.988908i | \(-0.547454\pi\) | ||||
−0.148531 | + | 0.988908i | \(0.547454\pi\) | |||||||
\(878\) | −36575.7 | − | 631.752i | −1.40589 | − | 0.0242831i | ||||
\(879\) | 12285.1i | 0.471405i | ||||||||
\(880\) | −68090.7 | − | 4711.40i | −2.60834 | − | 0.180479i | ||||
\(881\) | 10746.0i | 0.410946i | 0.978663 | + | 0.205473i | \(0.0658732\pi\) | ||||
−0.978663 | + | 0.205473i | \(0.934127\pi\) | |||||||
\(882\) | 2644.78 | + | 8321.16i | 0.100969 | + | 0.317674i | ||||
\(883\) | − | 3332.31i | − | 0.127000i | −0.997982 | − | 0.0635000i | \(-0.979774\pi\) | ||
0.997982 | − | 0.0635000i | \(-0.0202263\pi\) | |||||||
\(884\) | −19015.4 | − | 657.082i | −0.723482 | − | 0.0250001i | ||||
\(885\) | 24708.3i | 0.938485i | ||||||||
\(886\) | 29.1211 | − | 1685.99i | 0.00110422 | − | 0.0639298i | ||||
\(887\) | 29194.6 | 1.10514 | 0.552569 | − | 0.833467i | \(-0.313647\pi\) | ||||
0.552569 | + | 0.833467i | \(0.313647\pi\) | |||||||
\(888\) | −727.143 | − | 37.7086i | −0.0274789 | − | 0.00142502i | ||||
\(889\) | 21422.6 | − | 29824.6i | 0.808200 | − | 1.12518i | ||||
\(890\) | −29012.5 | − | 501.116i | −1.09270 | − | 0.0188735i | ||||
\(891\) | − | 5187.65i | − | 0.195054i | ||||||
\(892\) | 15412.0 | + | 532.565i | 0.578511 | + | 0.0199906i | ||||
\(893\) | −8179.99 | −0.306532 | ||||||||
\(894\) | −16899.9 | − | 291.902i | −0.632234 | − | 0.0109202i | ||||
\(895\) | −17193.5 | −0.642139 | ||||||||
\(896\) | 19737.2 | + | 18159.4i | 0.735909 | + | 0.677080i | ||||
\(897\) | 8180.37 | 0.304498 | ||||||||
\(898\) | −9696.35 | − | 167.480i | −0.360324 | − | 0.00622368i | ||||
\(899\) | 30298.5 | 1.12404 | ||||||||
\(900\) | −10957.7 | − | 378.644i | −0.405839 | − | 0.0140239i | ||||
\(901\) | − | 2920.74i | − | 0.107996i | ||||||
\(902\) | 7450.21 | + | 128.683i | 0.275017 | + | 0.00475021i | ||||
\(903\) | 13370.4 | − | 18614.4i | 0.492736 | − | 0.685989i | ||||
\(904\) | −34934.7 | − | 1811.67i | −1.28530 | − | 0.0666539i | ||||
\(905\) | −26784.8 | −0.983820 | ||||||||
\(906\) | 163.750 | − | 9480.44i | 0.00600468 | − | 0.347645i | ||||
\(907\) | 42775.0i | 1.56595i | 0.622051 | + | 0.782976i | \(0.286299\pi\) | ||||
−0.622051 | + | 0.782976i | \(0.713701\pi\) | |||||||
\(908\) | −32490.3 | − | 1122.71i | −1.18748 | − | 0.0410335i | ||||
\(909\) | 15789.0i | 0.576115i | ||||||||
\(910\) | 20068.9 | + | 14947.3i | 0.731075 | + | 0.544504i | ||||
\(911\) | 43757.7i | 1.59139i | 0.605697 | + | 0.795696i | \(0.292895\pi\) | ||||
−0.605697 | + | 0.795696i | \(0.707105\pi\) | |||||||
\(912\) | 3279.88 | + | 226.945i | 0.119087 | + | 0.00824001i | ||||
\(913\) | 84515.5i | 3.06359i | ||||||||
\(914\) | 53764.7 | + | 928.647i | 1.94571 | + | 0.0336071i | ||||
\(915\) | 14691.1 | 0.530788 | ||||||||
\(916\) | 1131.76 | − | 32752.3i | 0.0408237 | − | 1.18141i | ||||
\(917\) | 6076.75 | + | 4364.84i | 0.218835 | + | 0.157186i | ||||
\(918\) | 109.339 | − | 6330.24i | 0.00393106 | − | 0.227592i | ||||
\(919\) | 2327.16i | 0.0835322i | 0.999127 | + | 0.0417661i | \(0.0132984\pi\) | ||||
−0.999127 | + | 0.0417661i | \(0.986702\pi\) | |||||||
\(920\) | 35765.5 | + | 1854.75i | 1.28169 | + | 0.0664666i | ||||
\(921\) | −18642.8 | −0.666994 | ||||||||
\(922\) | −644.138 | + | 37292.8i | −0.0230082 | + | 1.33207i | ||||
\(923\) | 15320.5 | 0.546349 | ||||||||
\(924\) | −17395.9 | + | 22533.5i | −0.619355 | + | 0.802271i | ||||
\(925\) | −1633.39 | −0.0580602 | ||||||||
\(926\) | −362.722 | + | 21000.0i | −0.0128723 | + | 0.745253i | ||||
\(927\) | 2793.33 | 0.0989698 | ||||||||
\(928\) | −35593.8 | − | 3081.31i | −1.25908 | − | 0.108997i | ||||
\(929\) | 44503.1i | 1.57169i | 0.618423 | + | 0.785845i | \(0.287772\pi\) | ||||
−0.618423 | + | 0.785845i | \(0.712228\pi\) | |||||||
\(930\) | 374.598 | − | 21687.6i | 0.0132081 | − | 0.764693i | ||||
\(931\) | −1875.48 | − | 5565.89i | −0.0660219 | − | 0.195934i | ||||
\(932\) | 15591.3 | + | 538.762i | 0.547974 | + | 0.0189353i | ||||
\(933\) | 12134.8 | 0.425804 | ||||||||
\(934\) | −32448.7 | − | 560.469i | −1.13678 | − | 0.0196350i | ||||
\(935\) | − | 88414.0i | − | 3.09246i | ||||||
\(936\) | −302.562 | + | 5834.36i | −0.0105658 | + | 0.203742i | ||||
\(937\) | 19995.0i | 0.697128i | 0.937285 | + | 0.348564i | \(0.113331\pi\) | ||||
−0.937285 | + | 0.348564i | \(0.886669\pi\) | |||||||
\(938\) | −6504.24 | + | 8732.89i | −0.226408 | + | 0.303986i | ||||
\(939\) | 20795.5i | 0.722722i | ||||||||
\(940\) | 2197.67 | − | 63598.9i | 0.0762555 | − | 2.20677i | ||||
\(941\) | − | 5492.38i | − | 0.190272i | −0.995464 | − | 0.0951362i | \(-0.969671\pi\) | ||
0.995464 | − | 0.0951362i | \(-0.0303287\pi\) | |||||||
\(942\) | −111.079 | + | 6431.02i | −0.00384200 | + | 0.222435i | ||||
\(943\) | −3909.81 | −0.135017 | ||||||||
\(944\) | 31579.4 | + | 2185.07i | 1.08880 | + | 0.0753370i | ||||
\(945\) | −4857.66 | + | 6762.86i | −0.167217 | + | 0.232800i | ||||
\(946\) | 74711.2 | + | 1290.45i | 2.56773 | + | 0.0443510i | ||||
\(947\) | − | 25553.9i | − | 0.876863i | −0.898765 | − | 0.438432i | \(-0.855534\pi\) | ||
0.898765 | − | 0.438432i | \(-0.144466\pi\) | |||||||
\(948\) | 257.996 | − | 7466.19i | 0.00883894 | − | 0.255792i | ||||
\(949\) | 16704.1 | 0.571379 | ||||||||
\(950\) | 7374.26 | + | 127.371i | 0.251845 | + | 0.00434998i | ||||
\(951\) | −11899.2 | −0.405738 | ||||||||
\(952\) | −21702.4 | + | 27129.9i | −0.738842 | + | 0.923620i | ||||
\(953\) | −39066.4 | −1.32790 | −0.663948 | − | 0.747779i | \(-0.731120\pi\) | ||||
−0.663948 | + | 0.747779i | \(0.731120\pi\) | |||||||
\(954\) | −896.685 | − | 15.4879i | −0.0304311 | − | 0.000525619i | ||||
\(955\) | −32811.2 | −1.11177 | ||||||||
\(956\) | 790.574 | − | 22878.6i | 0.0267458 | − | 0.774003i | ||||
\(957\) | − | 37920.7i | − | 1.28088i | ||||||
\(958\) | 50689.2 | + | 875.526i | 1.70949 | + | 0.0295271i | ||||
\(959\) | −20559.2 | − | 14767.4i | −0.692274 | − | 0.497250i | ||||
\(960\) | −2645.67 | + | 25439.9i | −0.0889464 | + | 0.855280i | ||||
\(961\) | −6224.19 | −0.208928 | ||||||||
\(962\) | −15.0307 | + | 870.214i | −0.000503752 | + | 0.0291651i | ||||
\(963\) | − | 4342.00i | − | 0.145295i | ||||||
\(964\) | −1193.55 | + | 34540.3i | −0.0398771 | + | 1.15401i | ||||
\(965\) | − | 16095.9i | − | 0.536939i | ||||||
\(966\) | 8922.32 | − | 11979.5i | 0.297175 | − | 0.399001i | ||||
\(967\) | 17718.4i | 0.589229i | 0.955616 | + | 0.294614i | \(0.0951912\pi\) | ||||
−0.955616 | + | 0.294614i | \(0.904809\pi\) | |||||||
\(968\) | −62611.1 | − | 3246.92i | −2.07892 | − | 0.107810i | ||||
\(969\) | 4258.84i | 0.141191i | ||||||||
\(970\) | 4901.05 | + | 84.6531i | 0.162230 | + | 0.00280211i | ||||
\(971\) | 48730.8 | 1.61055 | 0.805276 | − | 0.592900i | \(-0.202017\pi\) | ||||
0.805276 | + | 0.592900i | \(0.202017\pi\) | |||||||
\(972\) | −1942.84 | − | 67.1352i | −0.0641118 | − | 0.00221539i | ||||
\(973\) | −26626.0 | − | 19125.0i | −0.877276 | − | 0.630134i | ||||
\(974\) | 398.682 | − | 23082.0i | 0.0131156 | − | 0.759337i | ||||
\(975\) | 13105.8i | 0.430485i | ||||||||
\(976\) | 1299.20 | − | 18776.5i | 0.0426091 | − | 0.615801i | ||||
\(977\) | 18189.4 | 0.595629 | 0.297815 | − | 0.954624i | \(-0.403742\pi\) | ||||
0.297815 | + | 0.954624i | \(0.403742\pi\) | |||||||
\(978\) | 21.6654 | − | 1254.33i | 0.000708366 | − | 0.0410113i | ||||
\(979\) | −39457.6 | −1.28812 | ||||||||
\(980\) | 43778.3 | − | 13086.4i | 1.42699 | − | 0.426560i | ||||
\(981\) | −653.026 | −0.0212533 | ||||||||
\(982\) | −860.793 | + | 49836.2i | −0.0279725 | + | 1.61949i | ||||
\(983\) | 8921.53 | 0.289474 | 0.144737 | − | 0.989470i | \(-0.453766\pi\) | ||||
0.144737 | + | 0.989470i | \(0.453766\pi\) | |||||||
\(984\) | 144.609 | − | 2788.53i | 0.00468494 | − | 0.0903407i | ||||
\(985\) | − | 17792.8i | − | 0.575560i | ||||||
\(986\) | 799.245 | − | 46272.9i | 0.0258146 | − | 1.49455i | ||||
\(987\) | −21556.9 | − | 15484.0i | −0.695203 | − | 0.499354i | ||||
\(988\) | 135.718 | − | 3927.57i | 0.00437020 | − | 0.126470i | ||||
\(989\) | −39207.9 | −1.26060 | ||||||||
\(990\) | −27143.6 | − | 468.837i | −0.871395 | − | 0.0150511i | ||||
\(991\) | 38882.1i | 1.24635i | 0.782083 | + | 0.623174i | \(0.214157\pi\) | ||||
−0.782083 | + | 0.623174i | \(0.785843\pi\) | |||||||
\(992\) | −27685.6 | − | 2396.71i | −0.886108 | − | 0.0767094i | ||||
\(993\) | 29849.5i | 0.953924i | ||||||||
\(994\) | 16710.0 | − | 22435.7i | 0.533209 | − | 0.715911i | ||||
\(995\) | − | 4207.23i | − | 0.134048i | ||||||
\(996\) | 31652.1 | + | 1093.75i | 1.00696 | + | 0.0347958i | ||||
\(997\) | − | 37847.7i | − | 1.20225i | −0.799153 | − | 0.601127i | \(-0.794719\pi\) | ||
0.799153 | − | 0.601127i | \(-0.205281\pi\) | |||||||
\(998\) | 330.791 | − | 19151.4i | 0.0104920 | − | 0.607441i | ||||
\(999\) | −289.608 | −0.00917196 |
(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 | 84.4.b.a.55.12 | yes | 12 | |
3.2 | odd | 2 | 252.4.b.f.55.1 | 12 | |||
4.3 | odd | 2 | 84.4.b.b.55.11 | yes | 12 | ||
7.6 | odd | 2 | 84.4.b.b.55.12 | yes | 12 | ||
8.3 | odd | 2 | 1344.4.b.g.895.11 | 12 | |||
8.5 | even | 2 | 1344.4.b.h.895.11 | 12 | |||
12.11 | even | 2 | 252.4.b.e.55.2 | 12 | |||
21.20 | even | 2 | 252.4.b.e.55.1 | 12 | |||
28.27 | even | 2 | inner | 84.4.b.a.55.11 | ✓ | 12 | |
56.13 | odd | 2 | 1344.4.b.g.895.2 | 12 | |||
56.27 | even | 2 | 1344.4.b.h.895.2 | 12 | |||
84.83 | odd | 2 | 252.4.b.f.55.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.b.a.55.11 | ✓ | 12 | 28.27 | even | 2 | inner | |
84.4.b.a.55.12 | yes | 12 | 1.1 | even | 1 | trivial | |
84.4.b.b.55.11 | yes | 12 | 4.3 | odd | 2 | ||
84.4.b.b.55.12 | yes | 12 | 7.6 | odd | 2 | ||
252.4.b.e.55.1 | 12 | 21.20 | even | 2 | |||
252.4.b.e.55.2 | 12 | 12.11 | even | 2 | |||
252.4.b.f.55.1 | 12 | 3.2 | odd | 2 | |||
252.4.b.f.55.2 | 12 | 84.83 | odd | 2 | |||
1344.4.b.g.895.2 | 12 | 56.13 | odd | 2 | |||
1344.4.b.g.895.11 | 12 | 8.3 | odd | 2 | |||
1344.4.b.h.895.2 | 12 | 56.27 | even | 2 | |||
1344.4.b.h.895.11 | 12 | 8.5 | even | 2 |