Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, 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("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(1\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 | ||||||||
\(3\) | −3.31570 | −1.91432 | −0.957160 | − | 0.289558i | \(-0.906492\pi\) | ||||
−0.957160 | + | 0.289558i | \(0.906492\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.532224 | −0.238018 | −0.119009 | − | 0.992893i | \(-0.537972\pi\) | ||||
−0.119009 | + | 0.992893i | \(0.537972\pi\) | |||||||
\(6\) | 3.31570 | 1.35363 | ||||||||
\(7\) | −2.51205 | −0.949467 | −0.474733 | − | 0.880130i | \(-0.657455\pi\) | ||||
−0.474733 | + | 0.880130i | \(0.657455\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 7.99387 | 2.66462 | ||||||||
\(10\) | 0.532224 | 0.168304 | ||||||||
\(11\) | 6.00144 | 1.80950 | 0.904752 | − | 0.425940i | \(-0.140056\pi\) | ||||
0.904752 | + | 0.425940i | \(0.140056\pi\) | |||||||
\(12\) | −3.31570 | −0.957160 | ||||||||
\(13\) | 4.31378 | 1.19643 | 0.598213 | − | 0.801337i | \(-0.295878\pi\) | ||||
0.598213 | + | 0.801337i | \(0.295878\pi\) | |||||||
\(14\) | 2.51205 | 0.671374 | ||||||||
\(15\) | 1.76470 | 0.455643 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.00033 | 0.485150 | 0.242575 | − | 0.970133i | \(-0.422008\pi\) | ||||
0.242575 | + | 0.970133i | \(0.422008\pi\) | |||||||
\(18\) | −7.99387 | −1.88417 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −0.532224 | −0.119009 | ||||||||
\(21\) | 8.32922 | 1.81758 | ||||||||
\(22\) | −6.00144 | −1.27951 | ||||||||
\(23\) | −2.59430 | −0.540948 | −0.270474 | − | 0.962727i | \(-0.587180\pi\) | ||||
−0.270474 | + | 0.962727i | \(0.587180\pi\) | |||||||
\(24\) | 3.31570 | 0.676815 | ||||||||
\(25\) | −4.71674 | −0.943348 | ||||||||
\(26\) | −4.31378 | −0.846001 | ||||||||
\(27\) | −16.5582 | −3.18663 | ||||||||
\(28\) | −2.51205 | −0.474733 | ||||||||
\(29\) | 10.1254 | 1.88025 | 0.940124 | − | 0.340832i | \(-0.110709\pi\) | ||||
0.940124 | + | 0.340832i | \(0.110709\pi\) | |||||||
\(30\) | −1.76470 | −0.322188 | ||||||||
\(31\) | 5.47223 | 0.982841 | 0.491420 | − | 0.870923i | \(-0.336478\pi\) | ||||
0.491420 | + | 0.870923i | \(0.336478\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −19.8990 | −3.46397 | ||||||||
\(34\) | −2.00033 | −0.343053 | ||||||||
\(35\) | 1.33697 | 0.225990 | ||||||||
\(36\) | 7.99387 | 1.33231 | ||||||||
\(37\) | −9.44633 | −1.55297 | −0.776484 | − | 0.630138i | \(-0.782998\pi\) | ||||
−0.776484 | + | 0.630138i | \(0.782998\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −14.3032 | −2.29034 | ||||||||
\(40\) | 0.532224 | 0.0841520 | ||||||||
\(41\) | 0.879606 | 0.137371 | 0.0686857 | − | 0.997638i | \(-0.478119\pi\) | ||||
0.0686857 | + | 0.997638i | \(0.478119\pi\) | |||||||
\(42\) | −8.32922 | −1.28523 | ||||||||
\(43\) | 2.40635 | 0.366965 | 0.183482 | − | 0.983023i | \(-0.441263\pi\) | ||||
0.183482 | + | 0.983023i | \(0.441263\pi\) | |||||||
\(44\) | 6.00144 | 0.904752 | ||||||||
\(45\) | −4.25453 | −0.634228 | ||||||||
\(46\) | 2.59430 | 0.382508 | ||||||||
\(47\) | −2.58783 | −0.377474 | −0.188737 | − | 0.982028i | \(-0.560439\pi\) | ||||
−0.188737 | + | 0.982028i | \(0.560439\pi\) | |||||||
\(48\) | −3.31570 | −0.478580 | ||||||||
\(49\) | −0.689592 | −0.0985131 | ||||||||
\(50\) | 4.71674 | 0.667047 | ||||||||
\(51\) | −6.63248 | −0.928733 | ||||||||
\(52\) | 4.31378 | 0.598213 | ||||||||
\(53\) | −11.7756 | −1.61750 | −0.808750 | − | 0.588153i | \(-0.799855\pi\) | ||||
−0.808750 | + | 0.588153i | \(0.799855\pi\) | |||||||
\(54\) | 16.5582 | 2.25328 | ||||||||
\(55\) | −3.19411 | −0.430694 | ||||||||
\(56\) | 2.51205 | 0.335687 | ||||||||
\(57\) | 3.31570 | 0.439175 | ||||||||
\(58\) | −10.1254 | −1.32954 | ||||||||
\(59\) | −14.3370 | −1.86652 | −0.933259 | − | 0.359203i | \(-0.883049\pi\) | ||||
−0.933259 | + | 0.359203i | \(0.883049\pi\) | |||||||
\(60\) | 1.76470 | 0.227821 | ||||||||
\(61\) | 15.3249 | 1.96215 | 0.981074 | − | 0.193636i | \(-0.0620280\pi\) | ||||
0.981074 | + | 0.193636i | \(0.0620280\pi\) | |||||||
\(62\) | −5.47223 | −0.694973 | ||||||||
\(63\) | −20.0810 | −2.52997 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.29590 | −0.284771 | ||||||||
\(66\) | 19.8990 | 2.44940 | ||||||||
\(67\) | −9.80986 | −1.19847 | −0.599233 | − | 0.800575i | \(-0.704528\pi\) | ||||
−0.599233 | + | 0.800575i | \(0.704528\pi\) | |||||||
\(68\) | 2.00033 | 0.242575 | ||||||||
\(69\) | 8.60191 | 1.03555 | ||||||||
\(70\) | −1.33697 | −0.159799 | ||||||||
\(71\) | −2.81792 | −0.334426 | −0.167213 | − | 0.985921i | \(-0.553477\pi\) | ||||
−0.167213 | + | 0.985921i | \(0.553477\pi\) | |||||||
\(72\) | −7.99387 | −0.942087 | ||||||||
\(73\) | 3.87418 | 0.453438 | 0.226719 | − | 0.973960i | \(-0.427200\pi\) | ||||
0.226719 | + | 0.973960i | \(0.427200\pi\) | |||||||
\(74\) | 9.44633 | 1.09811 | ||||||||
\(75\) | 15.6393 | 1.80587 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −15.0759 | −1.71806 | ||||||||
\(78\) | 14.3032 | 1.61952 | ||||||||
\(79\) | −1.12586 | −0.126669 | −0.0633345 | − | 0.997992i | \(-0.520174\pi\) | ||||
−0.0633345 | + | 0.997992i | \(0.520174\pi\) | |||||||
\(80\) | −0.532224 | −0.0595045 | ||||||||
\(81\) | 30.9204 | 3.43560 | ||||||||
\(82\) | −0.879606 | −0.0971363 | ||||||||
\(83\) | −13.8218 | −1.51714 | −0.758571 | − | 0.651591i | \(-0.774102\pi\) | ||||
−0.758571 | + | 0.651591i | \(0.774102\pi\) | |||||||
\(84\) | 8.32922 | 0.908792 | ||||||||
\(85\) | −1.06462 | −0.115474 | ||||||||
\(86\) | −2.40635 | −0.259483 | ||||||||
\(87\) | −33.5730 | −3.59940 | ||||||||
\(88\) | −6.00144 | −0.639756 | ||||||||
\(89\) | −10.7320 | −1.13759 | −0.568795 | − | 0.822480i | \(-0.692590\pi\) | ||||
−0.568795 | + | 0.822480i | \(0.692590\pi\) | |||||||
\(90\) | 4.25453 | 0.448467 | ||||||||
\(91\) | −10.8364 | −1.13597 | ||||||||
\(92\) | −2.59430 | −0.270474 | ||||||||
\(93\) | −18.1443 | −1.88147 | ||||||||
\(94\) | 2.58783 | 0.266915 | ||||||||
\(95\) | 0.532224 | 0.0546050 | ||||||||
\(96\) | 3.31570 | 0.338407 | ||||||||
\(97\) | 7.84668 | 0.796710 | 0.398355 | − | 0.917231i | \(-0.369581\pi\) | ||||
0.398355 | + | 0.917231i | \(0.369581\pi\) | |||||||
\(98\) | 0.689592 | 0.0696593 | ||||||||
\(99\) | 47.9748 | 4.82165 | ||||||||
\(100\) | −4.71674 | −0.471674 | ||||||||
\(101\) | −6.15584 | −0.612529 | −0.306264 | − | 0.951947i | \(-0.599079\pi\) | ||||
−0.306264 | + | 0.951947i | \(0.599079\pi\) | |||||||
\(102\) | 6.63248 | 0.656714 | ||||||||
\(103\) | 16.6328 | 1.63888 | 0.819439 | − | 0.573166i | \(-0.194285\pi\) | ||||
0.819439 | + | 0.573166i | \(0.194285\pi\) | |||||||
\(104\) | −4.31378 | −0.423001 | ||||||||
\(105\) | −4.43301 | −0.432617 | ||||||||
\(106\) | 11.7756 | 1.14375 | ||||||||
\(107\) | 5.65780 | 0.546960 | 0.273480 | − | 0.961878i | \(-0.411825\pi\) | ||||
0.273480 | + | 0.961878i | \(0.411825\pi\) | |||||||
\(108\) | −16.5582 | −1.59331 | ||||||||
\(109\) | −6.51313 | −0.623844 | −0.311922 | − | 0.950108i | \(-0.600973\pi\) | ||||
−0.311922 | + | 0.950108i | \(0.600973\pi\) | |||||||
\(110\) | 3.19411 | 0.304547 | ||||||||
\(111\) | 31.3212 | 2.97288 | ||||||||
\(112\) | −2.51205 | −0.237367 | ||||||||
\(113\) | 1.07069 | 0.100722 | 0.0503609 | − | 0.998731i | \(-0.483963\pi\) | ||||
0.0503609 | + | 0.998731i | \(0.483963\pi\) | |||||||
\(114\) | −3.31570 | −0.310544 | ||||||||
\(115\) | 1.38075 | 0.128755 | ||||||||
\(116\) | 10.1254 | 0.940124 | ||||||||
\(117\) | 34.4838 | 3.18803 | ||||||||
\(118\) | 14.3370 | 1.31983 | ||||||||
\(119\) | −5.02492 | −0.460634 | ||||||||
\(120\) | −1.76470 | −0.161094 | ||||||||
\(121\) | 25.0173 | 2.27430 | ||||||||
\(122\) | −15.3249 | −1.38745 | ||||||||
\(123\) | −2.91651 | −0.262973 | ||||||||
\(124\) | 5.47223 | 0.491420 | ||||||||
\(125\) | 5.17148 | 0.462551 | ||||||||
\(126\) | 20.0810 | 1.78896 | ||||||||
\(127\) | −19.5247 | −1.73254 | −0.866271 | − | 0.499575i | \(-0.833489\pi\) | ||||
−0.866271 | + | 0.499575i | \(0.833489\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −7.97874 | −0.702489 | ||||||||
\(130\) | 2.29590 | 0.201363 | ||||||||
\(131\) | 9.05590 | 0.791218 | 0.395609 | − | 0.918419i | \(-0.370534\pi\) | ||||
0.395609 | + | 0.918419i | \(0.370534\pi\) | |||||||
\(132\) | −19.8990 | −1.73198 | ||||||||
\(133\) | 2.51205 | 0.217823 | ||||||||
\(134\) | 9.80986 | 0.847443 | ||||||||
\(135\) | 8.81267 | 0.758474 | ||||||||
\(136\) | −2.00033 | −0.171527 | ||||||||
\(137\) | 6.02022 | 0.514342 | 0.257171 | − | 0.966366i | \(-0.417210\pi\) | ||||
0.257171 | + | 0.966366i | \(0.417210\pi\) | |||||||
\(138\) | −8.60191 | −0.732243 | ||||||||
\(139\) | −7.63928 | −0.647955 | −0.323978 | − | 0.946065i | \(-0.605020\pi\) | ||||
−0.323978 | + | 0.946065i | \(0.605020\pi\) | |||||||
\(140\) | 1.33697 | 0.112995 | ||||||||
\(141\) | 8.58048 | 0.722607 | ||||||||
\(142\) | 2.81792 | 0.236475 | ||||||||
\(143\) | 25.8889 | 2.16494 | ||||||||
\(144\) | 7.99387 | 0.666156 | ||||||||
\(145\) | −5.38901 | −0.447533 | ||||||||
\(146\) | −3.87418 | −0.320629 | ||||||||
\(147\) | 2.28648 | 0.188586 | ||||||||
\(148\) | −9.44633 | −0.776484 | ||||||||
\(149\) | −5.91544 | −0.484612 | −0.242306 | − | 0.970200i | \(-0.577904\pi\) | ||||
−0.242306 | + | 0.970200i | \(0.577904\pi\) | |||||||
\(150\) | −15.6393 | −1.27694 | ||||||||
\(151\) | −5.07937 | −0.413353 | −0.206676 | − | 0.978409i | \(-0.566265\pi\) | ||||
−0.206676 | + | 0.978409i | \(0.566265\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 15.9903 | 1.29274 | ||||||||
\(154\) | 15.0759 | 1.21485 | ||||||||
\(155\) | −2.91245 | −0.233934 | ||||||||
\(156\) | −14.3032 | −1.14517 | ||||||||
\(157\) | 19.3190 | 1.54182 | 0.770911 | − | 0.636943i | \(-0.219801\pi\) | ||||
0.770911 | + | 0.636943i | \(0.219801\pi\) | |||||||
\(158\) | 1.12586 | 0.0895685 | ||||||||
\(159\) | 39.0443 | 3.09641 | ||||||||
\(160\) | 0.532224 | 0.0420760 | ||||||||
\(161\) | 6.51701 | 0.513612 | ||||||||
\(162\) | −30.9204 | −2.42934 | ||||||||
\(163\) | −0.564810 | −0.0442393 | −0.0221197 | − | 0.999755i | \(-0.507041\pi\) | ||||
−0.0221197 | + | 0.999755i | \(0.507041\pi\) | |||||||
\(164\) | 0.879606 | 0.0686857 | ||||||||
\(165\) | 10.5907 | 0.824487 | ||||||||
\(166\) | 13.8218 | 1.07278 | ||||||||
\(167\) | −16.6926 | −1.29171 | −0.645856 | − | 0.763460i | \(-0.723499\pi\) | ||||
−0.645856 | + | 0.763460i | \(0.723499\pi\) | |||||||
\(168\) | −8.32922 | −0.642613 | ||||||||
\(169\) | 5.60868 | 0.431437 | ||||||||
\(170\) | 1.06462 | 0.0816527 | ||||||||
\(171\) | −7.99387 | −0.611307 | ||||||||
\(172\) | 2.40635 | 0.183482 | ||||||||
\(173\) | −8.32146 | −0.632669 | −0.316335 | − | 0.948648i | \(-0.602452\pi\) | ||||
−0.316335 | + | 0.948648i | \(0.602452\pi\) | |||||||
\(174\) | 33.5730 | 2.54516 | ||||||||
\(175\) | 11.8487 | 0.895677 | ||||||||
\(176\) | 6.00144 | 0.452376 | ||||||||
\(177\) | 47.5372 | 3.57312 | ||||||||
\(178\) | 10.7320 | 0.804397 | ||||||||
\(179\) | −0.372786 | −0.0278634 | −0.0139317 | − | 0.999903i | \(-0.504435\pi\) | ||||
−0.0139317 | + | 0.999903i | \(0.504435\pi\) | |||||||
\(180\) | −4.25453 | −0.317114 | ||||||||
\(181\) | −13.6576 | −1.01516 | −0.507580 | − | 0.861605i | \(-0.669460\pi\) | ||||
−0.507580 | + | 0.861605i | \(0.669460\pi\) | |||||||
\(182\) | 10.8364 | 0.803250 | ||||||||
\(183\) | −50.8126 | −3.75618 | ||||||||
\(184\) | 2.59430 | 0.191254 | ||||||||
\(185\) | 5.02756 | 0.369634 | ||||||||
\(186\) | 18.1443 | 1.33040 | ||||||||
\(187\) | 12.0048 | 0.877881 | ||||||||
\(188\) | −2.58783 | −0.188737 | ||||||||
\(189\) | 41.5950 | 3.02559 | ||||||||
\(190\) | −0.532224 | −0.0386116 | ||||||||
\(191\) | 6.08193 | 0.440073 | 0.220036 | − | 0.975492i | \(-0.429382\pi\) | ||||
0.220036 | + | 0.975492i | \(0.429382\pi\) | |||||||
\(192\) | −3.31570 | −0.239290 | ||||||||
\(193\) | 22.0638 | 1.58819 | 0.794094 | − | 0.607795i | \(-0.207946\pi\) | ||||
0.794094 | + | 0.607795i | \(0.207946\pi\) | |||||||
\(194\) | −7.84668 | −0.563359 | ||||||||
\(195\) | 7.61251 | 0.545143 | ||||||||
\(196\) | −0.689592 | −0.0492565 | ||||||||
\(197\) | −13.8017 | −0.983330 | −0.491665 | − | 0.870785i | \(-0.663611\pi\) | ||||
−0.491665 | + | 0.870785i | \(0.663611\pi\) | |||||||
\(198\) | −47.9748 | −3.40942 | ||||||||
\(199\) | −22.9043 | −1.62364 | −0.811822 | − | 0.583905i | \(-0.801524\pi\) | ||||
−0.811822 | + | 0.583905i | \(0.801524\pi\) | |||||||
\(200\) | 4.71674 | 0.333524 | ||||||||
\(201\) | 32.5266 | 2.29425 | ||||||||
\(202\) | 6.15584 | 0.433123 | ||||||||
\(203\) | −25.4357 | −1.78523 | ||||||||
\(204\) | −6.63248 | −0.464367 | ||||||||
\(205\) | −0.468148 | −0.0326969 | ||||||||
\(206\) | −16.6328 | −1.15886 | ||||||||
\(207\) | −20.7385 | −1.44142 | ||||||||
\(208\) | 4.31378 | 0.299107 | ||||||||
\(209\) | −6.00144 | −0.415128 | ||||||||
\(210\) | 4.43301 | 0.305907 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | −11.7756 | −0.808750 | ||||||||
\(213\) | 9.34339 | 0.640199 | ||||||||
\(214\) | −5.65780 | −0.386759 | ||||||||
\(215\) | −1.28072 | −0.0873442 | ||||||||
\(216\) | 16.5582 | 1.12664 | ||||||||
\(217\) | −13.7465 | −0.933174 | ||||||||
\(218\) | 6.51313 | 0.441125 | ||||||||
\(219\) | −12.8456 | −0.868026 | ||||||||
\(220\) | −3.19411 | −0.215347 | ||||||||
\(221\) | 8.62896 | 0.580447 | ||||||||
\(222\) | −31.3212 | −2.10214 | ||||||||
\(223\) | 19.7312 | 1.32130 | 0.660651 | − | 0.750693i | \(-0.270280\pi\) | ||||
0.660651 | + | 0.750693i | \(0.270280\pi\) | |||||||
\(224\) | 2.51205 | 0.167844 | ||||||||
\(225\) | −37.7050 | −2.51367 | ||||||||
\(226\) | −1.07069 | −0.0712211 | ||||||||
\(227\) | 28.4902 | 1.89096 | 0.945481 | − | 0.325677i | \(-0.105592\pi\) | ||||
0.945481 | + | 0.325677i | \(0.105592\pi\) | |||||||
\(228\) | 3.31570 | 0.219588 | ||||||||
\(229\) | −22.2398 | −1.46965 | −0.734823 | − | 0.678259i | \(-0.762735\pi\) | ||||
−0.734823 | + | 0.678259i | \(0.762735\pi\) | |||||||
\(230\) | −1.38075 | −0.0910438 | ||||||||
\(231\) | 49.9873 | 3.28892 | ||||||||
\(232\) | −10.1254 | −0.664768 | ||||||||
\(233\) | 8.79219 | 0.575996 | 0.287998 | − | 0.957631i | \(-0.407010\pi\) | ||||
0.287998 | + | 0.957631i | \(0.407010\pi\) | |||||||
\(234\) | −34.4838 | −2.25428 | ||||||||
\(235\) | 1.37731 | 0.0898456 | ||||||||
\(236\) | −14.3370 | −0.933259 | ||||||||
\(237\) | 3.73301 | 0.242485 | ||||||||
\(238\) | 5.02492 | 0.325717 | ||||||||
\(239\) | −20.9718 | −1.35655 | −0.678277 | − | 0.734806i | \(-0.737273\pi\) | ||||
−0.678277 | + | 0.734806i | \(0.737273\pi\) | |||||||
\(240\) | 1.76470 | 0.113911 | ||||||||
\(241\) | −24.3204 | −1.56661 | −0.783306 | − | 0.621636i | \(-0.786468\pi\) | ||||
−0.783306 | + | 0.621636i | \(0.786468\pi\) | |||||||
\(242\) | −25.0173 | −1.60817 | ||||||||
\(243\) | −52.8482 | −3.39021 | ||||||||
\(244\) | 15.3249 | 0.981074 | ||||||||
\(245\) | 0.367017 | 0.0234479 | ||||||||
\(246\) | 2.91651 | 0.185950 | ||||||||
\(247\) | −4.31378 | −0.274479 | ||||||||
\(248\) | −5.47223 | −0.347487 | ||||||||
\(249\) | 45.8290 | 2.90430 | ||||||||
\(250\) | −5.17148 | −0.327073 | ||||||||
\(251\) | 6.35992 | 0.401435 | 0.200717 | − | 0.979649i | \(-0.435673\pi\) | ||||
0.200717 | + | 0.979649i | \(0.435673\pi\) | |||||||
\(252\) | −20.0810 | −1.26499 | ||||||||
\(253\) | −15.5695 | −0.978847 | ||||||||
\(254\) | 19.5247 | 1.22509 | ||||||||
\(255\) | 3.52997 | 0.221055 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.7714 | 0.734280 | 0.367140 | − | 0.930166i | \(-0.380337\pi\) | ||||
0.367140 | + | 0.930166i | \(0.380337\pi\) | |||||||
\(258\) | 7.97874 | 0.496734 | ||||||||
\(259\) | 23.7297 | 1.47449 | ||||||||
\(260\) | −2.29590 | −0.142385 | ||||||||
\(261\) | 80.9416 | 5.01016 | ||||||||
\(262\) | −9.05590 | −0.559475 | ||||||||
\(263\) | −2.03361 | −0.125397 | −0.0626987 | − | 0.998032i | \(-0.519971\pi\) | ||||
−0.0626987 | + | 0.998032i | \(0.519971\pi\) | |||||||
\(264\) | 19.8990 | 1.22470 | ||||||||
\(265\) | 6.26725 | 0.384994 | ||||||||
\(266\) | −2.51205 | −0.154024 | ||||||||
\(267\) | 35.5841 | 2.17771 | ||||||||
\(268\) | −9.80986 | −0.599233 | ||||||||
\(269\) | −1.11148 | −0.0677684 | −0.0338842 | − | 0.999426i | \(-0.510788\pi\) | ||||
−0.0338842 | + | 0.999426i | \(0.510788\pi\) | |||||||
\(270\) | −8.81267 | −0.536322 | ||||||||
\(271\) | −1.29913 | −0.0789168 | −0.0394584 | − | 0.999221i | \(-0.512563\pi\) | ||||
−0.0394584 | + | 0.999221i | \(0.512563\pi\) | |||||||
\(272\) | 2.00033 | 0.121288 | ||||||||
\(273\) | 35.9304 | 2.17461 | ||||||||
\(274\) | −6.02022 | −0.363695 | ||||||||
\(275\) | −28.3072 | −1.70699 | ||||||||
\(276\) | 8.60191 | 0.517774 | ||||||||
\(277\) | −7.79030 | −0.468074 | −0.234037 | − | 0.972228i | \(-0.575194\pi\) | ||||
−0.234037 | + | 0.972228i | \(0.575194\pi\) | |||||||
\(278\) | 7.63928 | 0.458174 | ||||||||
\(279\) | 43.7443 | 2.61890 | ||||||||
\(280\) | −1.33697 | −0.0798995 | ||||||||
\(281\) | −1.41989 | −0.0847037 | −0.0423519 | − | 0.999103i | \(-0.513485\pi\) | ||||
−0.0423519 | + | 0.999103i | \(0.513485\pi\) | |||||||
\(282\) | −8.58048 | −0.510960 | ||||||||
\(283\) | 24.0398 | 1.42902 | 0.714510 | − | 0.699625i | \(-0.246650\pi\) | ||||
0.714510 | + | 0.699625i | \(0.246650\pi\) | |||||||
\(284\) | −2.81792 | −0.167213 | ||||||||
\(285\) | −1.76470 | −0.104532 | ||||||||
\(286\) | −25.8889 | −1.53084 | ||||||||
\(287\) | −2.20962 | −0.130430 | ||||||||
\(288\) | −7.99387 | −0.471043 | ||||||||
\(289\) | −12.9987 | −0.764629 | ||||||||
\(290\) | 5.38901 | 0.316453 | ||||||||
\(291\) | −26.0172 | −1.52516 | ||||||||
\(292\) | 3.87418 | 0.226719 | ||||||||
\(293\) | 1.14275 | 0.0667601 | 0.0333801 | − | 0.999443i | \(-0.489373\pi\) | ||||
0.0333801 | + | 0.999443i | \(0.489373\pi\) | |||||||
\(294\) | −2.28648 | −0.133350 | ||||||||
\(295\) | 7.63050 | 0.444265 | ||||||||
\(296\) | 9.44633 | 0.549057 | ||||||||
\(297\) | −99.3730 | −5.76621 | ||||||||
\(298\) | 5.91544 | 0.342672 | ||||||||
\(299\) | −11.1912 | −0.647205 | ||||||||
\(300\) | 15.6393 | 0.902935 | ||||||||
\(301\) | −6.04488 | −0.348421 | ||||||||
\(302\) | 5.07937 | 0.292285 | ||||||||
\(303\) | 20.4109 | 1.17258 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −8.15626 | −0.467026 | ||||||||
\(306\) | −15.9903 | −0.914107 | ||||||||
\(307\) | −26.4911 | −1.51193 | −0.755965 | − | 0.654612i | \(-0.772832\pi\) | ||||
−0.755965 | + | 0.654612i | \(0.772832\pi\) | |||||||
\(308\) | −15.0759 | −0.859031 | ||||||||
\(309\) | −55.1494 | −3.13734 | ||||||||
\(310\) | 2.91245 | 0.165416 | ||||||||
\(311\) | −16.7266 | −0.948477 | −0.474238 | − | 0.880397i | \(-0.657276\pi\) | ||||
−0.474238 | + | 0.880397i | \(0.657276\pi\) | |||||||
\(312\) | 14.3032 | 0.809759 | ||||||||
\(313\) | −2.36264 | −0.133544 | −0.0667722 | − | 0.997768i | \(-0.521270\pi\) | ||||
−0.0667722 | + | 0.997768i | \(0.521270\pi\) | |||||||
\(314\) | −19.3190 | −1.09023 | ||||||||
\(315\) | 10.6876 | 0.602179 | ||||||||
\(316\) | −1.12586 | −0.0633345 | ||||||||
\(317\) | 26.0184 | 1.46134 | 0.730670 | − | 0.682731i | \(-0.239208\pi\) | ||||
0.730670 | + | 0.682731i | \(0.239208\pi\) | |||||||
\(318\) | −39.0443 | −2.18950 | ||||||||
\(319\) | 60.7673 | 3.40232 | ||||||||
\(320\) | −0.532224 | −0.0297522 | ||||||||
\(321\) | −18.7596 | −1.04706 | ||||||||
\(322\) | −6.51701 | −0.363179 | ||||||||
\(323\) | −2.00033 | −0.111301 | ||||||||
\(324\) | 30.9204 | 1.71780 | ||||||||
\(325\) | −20.3470 | −1.12865 | ||||||||
\(326\) | 0.564810 | 0.0312819 | ||||||||
\(327\) | 21.5956 | 1.19424 | ||||||||
\(328\) | −0.879606 | −0.0485681 | ||||||||
\(329\) | 6.50077 | 0.358399 | ||||||||
\(330\) | −10.5907 | −0.583000 | ||||||||
\(331\) | −19.2136 | −1.05607 | −0.528037 | − | 0.849221i | \(-0.677072\pi\) | ||||
−0.528037 | + | 0.849221i | \(0.677072\pi\) | |||||||
\(332\) | −13.8218 | −0.758571 | ||||||||
\(333\) | −75.5128 | −4.13807 | ||||||||
\(334\) | 16.6926 | 0.913378 | ||||||||
\(335\) | 5.22104 | 0.285256 | ||||||||
\(336\) | 8.32922 | 0.454396 | ||||||||
\(337\) | −5.71500 | −0.311316 | −0.155658 | − | 0.987811i | \(-0.549750\pi\) | ||||
−0.155658 | + | 0.987811i | \(0.549750\pi\) | |||||||
\(338\) | −5.60868 | −0.305072 | ||||||||
\(339\) | −3.55008 | −0.192814 | ||||||||
\(340\) | −1.06462 | −0.0577372 | ||||||||
\(341\) | 32.8412 | 1.77845 | ||||||||
\(342\) | 7.99387 | 0.432259 | ||||||||
\(343\) | 19.3167 | 1.04300 | ||||||||
\(344\) | −2.40635 | −0.129742 | ||||||||
\(345\) | −4.57814 | −0.246479 | ||||||||
\(346\) | 8.32146 | 0.447365 | ||||||||
\(347\) | −11.0469 | −0.593031 | −0.296516 | − | 0.955028i | \(-0.595825\pi\) | ||||
−0.296516 | + | 0.955028i | \(0.595825\pi\) | |||||||
\(348\) | −33.5730 | −1.79970 | ||||||||
\(349\) | 5.41033 | 0.289608 | 0.144804 | − | 0.989460i | \(-0.453745\pi\) | ||||
0.144804 | + | 0.989460i | \(0.453745\pi\) | |||||||
\(350\) | −11.8487 | −0.633339 | ||||||||
\(351\) | −71.4284 | −3.81256 | ||||||||
\(352\) | −6.00144 | −0.319878 | ||||||||
\(353\) | 8.21985 | 0.437499 | 0.218749 | − | 0.975781i | \(-0.429802\pi\) | ||||
0.218749 | + | 0.975781i | \(0.429802\pi\) | |||||||
\(354\) | −47.5372 | −2.52657 | ||||||||
\(355\) | 1.49977 | 0.0795994 | ||||||||
\(356\) | −10.7320 | −0.568795 | ||||||||
\(357\) | 16.6611 | 0.881801 | ||||||||
\(358\) | 0.372786 | 0.0197024 | ||||||||
\(359\) | 27.5741 | 1.45531 | 0.727653 | − | 0.685945i | \(-0.240611\pi\) | ||||
0.727653 | + | 0.685945i | \(0.240611\pi\) | |||||||
\(360\) | 4.25453 | 0.224234 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 13.6576 | 0.717826 | ||||||||
\(363\) | −82.9499 | −4.35374 | ||||||||
\(364\) | −10.8364 | −0.567984 | ||||||||
\(365\) | −2.06193 | −0.107926 | ||||||||
\(366\) | 50.8126 | 2.65602 | ||||||||
\(367\) | −35.1518 | −1.83491 | −0.917453 | − | 0.397843i | \(-0.869759\pi\) | ||||
−0.917453 | + | 0.397843i | \(0.869759\pi\) | |||||||
\(368\) | −2.59430 | −0.135237 | ||||||||
\(369\) | 7.03146 | 0.366043 | ||||||||
\(370\) | −5.02756 | −0.261371 | ||||||||
\(371\) | 29.5809 | 1.53576 | ||||||||
\(372\) | −18.1443 | −0.940736 | ||||||||
\(373\) | −21.9794 | −1.13805 | −0.569025 | − | 0.822320i | \(-0.692679\pi\) | ||||
−0.569025 | + | 0.822320i | \(0.692679\pi\) | |||||||
\(374\) | −12.0048 | −0.620755 | ||||||||
\(375\) | −17.1471 | −0.885472 | ||||||||
\(376\) | 2.58783 | 0.133457 | ||||||||
\(377\) | 43.6789 | 2.24958 | ||||||||
\(378\) | −41.5950 | −2.13942 | ||||||||
\(379\) | −5.41110 | −0.277950 | −0.138975 | − | 0.990296i | \(-0.544381\pi\) | ||||
−0.138975 | + | 0.990296i | \(0.544381\pi\) | |||||||
\(380\) | 0.532224 | 0.0273025 | ||||||||
\(381\) | 64.7382 | 3.31664 | ||||||||
\(382\) | −6.08193 | −0.311178 | ||||||||
\(383\) | 3.51955 | 0.179841 | 0.0899204 | − | 0.995949i | \(-0.471339\pi\) | ||||
0.0899204 | + | 0.995949i | \(0.471339\pi\) | |||||||
\(384\) | 3.31570 | 0.169204 | ||||||||
\(385\) | 8.02378 | 0.408930 | ||||||||
\(386\) | −22.0638 | −1.12302 | ||||||||
\(387\) | 19.2361 | 0.977824 | ||||||||
\(388\) | 7.84668 | 0.398355 | ||||||||
\(389\) | 9.79046 | 0.496396 | 0.248198 | − | 0.968709i | \(-0.420162\pi\) | ||||
0.248198 | + | 0.968709i | \(0.420162\pi\) | |||||||
\(390\) | −7.61251 | −0.385474 | ||||||||
\(391\) | −5.18944 | −0.262441 | ||||||||
\(392\) | 0.689592 | 0.0348296 | ||||||||
\(393\) | −30.0267 | −1.51464 | ||||||||
\(394\) | 13.8017 | 0.695319 | ||||||||
\(395\) | 0.599209 | 0.0301495 | ||||||||
\(396\) | 47.9748 | 2.41082 | ||||||||
\(397\) | 13.4179 | 0.673424 | 0.336712 | − | 0.941608i | \(-0.390685\pi\) | ||||
0.336712 | + | 0.941608i | \(0.390685\pi\) | |||||||
\(398\) | 22.9043 | 1.14809 | ||||||||
\(399\) | −8.32922 | −0.416982 | ||||||||
\(400\) | −4.71674 | −0.235837 | ||||||||
\(401\) | 36.6623 | 1.83083 | 0.915413 | − | 0.402516i | \(-0.131864\pi\) | ||||
0.915413 | + | 0.402516i | \(0.131864\pi\) | |||||||
\(402\) | −32.5266 | −1.62228 | ||||||||
\(403\) | 23.6060 | 1.17590 | ||||||||
\(404\) | −6.15584 | −0.306264 | ||||||||
\(405\) | −16.4566 | −0.817734 | ||||||||
\(406\) | 25.4357 | 1.26235 | ||||||||
\(407\) | −56.6916 | −2.81010 | ||||||||
\(408\) | 6.63248 | 0.328357 | ||||||||
\(409\) | −23.9115 | −1.18235 | −0.591175 | − | 0.806544i | \(-0.701336\pi\) | ||||
−0.591175 | + | 0.806544i | \(0.701336\pi\) | |||||||
\(410\) | 0.468148 | 0.0231202 | ||||||||
\(411\) | −19.9613 | −0.984616 | ||||||||
\(412\) | 16.6328 | 0.819439 | ||||||||
\(413\) | 36.0153 | 1.77220 | ||||||||
\(414\) | 20.7385 | 1.01924 | ||||||||
\(415\) | 7.35631 | 0.361107 | ||||||||
\(416\) | −4.31378 | −0.211500 | ||||||||
\(417\) | 25.3296 | 1.24039 | ||||||||
\(418\) | 6.00144 | 0.293540 | ||||||||
\(419\) | −14.7038 | −0.718329 | −0.359164 | − | 0.933274i | \(-0.616938\pi\) | ||||
−0.359164 | + | 0.933274i | \(0.616938\pi\) | |||||||
\(420\) | −4.43301 | −0.216309 | ||||||||
\(421\) | 11.7662 | 0.573448 | 0.286724 | − | 0.958013i | \(-0.407434\pi\) | ||||
0.286724 | + | 0.958013i | \(0.407434\pi\) | |||||||
\(422\) | 1.00000 | 0.0486792 | ||||||||
\(423\) | −20.6868 | −1.00583 | ||||||||
\(424\) | 11.7756 | 0.571873 | ||||||||
\(425\) | −9.43501 | −0.457665 | ||||||||
\(426\) | −9.34339 | −0.452689 | ||||||||
\(427\) | −38.4969 | −1.86299 | ||||||||
\(428\) | 5.65780 | 0.273480 | ||||||||
\(429\) | −85.8398 | −4.14439 | ||||||||
\(430\) | 1.28072 | 0.0617617 | ||||||||
\(431\) | −34.5868 | −1.66599 | −0.832993 | − | 0.553283i | \(-0.813375\pi\) | ||||
−0.832993 | + | 0.553283i | \(0.813375\pi\) | |||||||
\(432\) | −16.5582 | −0.796656 | ||||||||
\(433\) | −25.8068 | −1.24020 | −0.620098 | − | 0.784524i | \(-0.712907\pi\) | ||||
−0.620098 | + | 0.784524i | \(0.712907\pi\) | |||||||
\(434\) | 13.7465 | 0.659854 | ||||||||
\(435\) | 17.8683 | 0.856721 | ||||||||
\(436\) | −6.51313 | −0.311922 | ||||||||
\(437\) | 2.59430 | 0.124102 | ||||||||
\(438\) | 12.8456 | 0.613787 | ||||||||
\(439\) | −15.6198 | −0.745491 | −0.372745 | − | 0.927934i | \(-0.621584\pi\) | ||||
−0.372745 | + | 0.927934i | \(0.621584\pi\) | |||||||
\(440\) | 3.19411 | 0.152273 | ||||||||
\(441\) | −5.51251 | −0.262500 | ||||||||
\(442\) | −8.62896 | −0.410438 | ||||||||
\(443\) | 6.69100 | 0.317899 | 0.158949 | − | 0.987287i | \(-0.449189\pi\) | ||||
0.158949 | + | 0.987287i | \(0.449189\pi\) | |||||||
\(444\) | 31.3212 | 1.48644 | ||||||||
\(445\) | 5.71183 | 0.270767 | ||||||||
\(446\) | −19.7312 | −0.934301 | ||||||||
\(447\) | 19.6138 | 0.927702 | ||||||||
\(448\) | −2.51205 | −0.118683 | ||||||||
\(449\) | 10.4379 | 0.492595 | 0.246297 | − | 0.969194i | \(-0.420786\pi\) | ||||
0.246297 | + | 0.969194i | \(0.420786\pi\) | |||||||
\(450\) | 37.7050 | 1.77743 | ||||||||
\(451\) | 5.27891 | 0.248574 | ||||||||
\(452\) | 1.07069 | 0.0503609 | ||||||||
\(453\) | 16.8417 | 0.791290 | ||||||||
\(454\) | −28.4902 | −1.33711 | ||||||||
\(455\) | 5.76741 | 0.270381 | ||||||||
\(456\) | −3.31570 | −0.155272 | ||||||||
\(457\) | 21.5202 | 1.00667 | 0.503336 | − | 0.864091i | \(-0.332106\pi\) | ||||
0.503336 | + | 0.864091i | \(0.332106\pi\) | |||||||
\(458\) | 22.2398 | 1.03920 | ||||||||
\(459\) | −33.1218 | −1.54599 | ||||||||
\(460\) | 1.38075 | 0.0643777 | ||||||||
\(461\) | 38.6757 | 1.80131 | 0.900654 | − | 0.434538i | \(-0.143088\pi\) | ||||
0.900654 | + | 0.434538i | \(0.143088\pi\) | |||||||
\(462\) | −49.9873 | −2.32562 | ||||||||
\(463\) | −3.68622 | −0.171313 | −0.0856566 | − | 0.996325i | \(-0.527299\pi\) | ||||
−0.0856566 | + | 0.996325i | \(0.527299\pi\) | |||||||
\(464\) | 10.1254 | 0.470062 | ||||||||
\(465\) | 9.65681 | 0.447824 | ||||||||
\(466\) | −8.79219 | −0.407290 | ||||||||
\(467\) | 7.66542 | 0.354713 | 0.177357 | − | 0.984147i | \(-0.443245\pi\) | ||||
0.177357 | + | 0.984147i | \(0.443245\pi\) | |||||||
\(468\) | 34.4838 | 1.59401 | ||||||||
\(469\) | 24.6429 | 1.13790 | ||||||||
\(470\) | −1.37731 | −0.0635304 | ||||||||
\(471\) | −64.0560 | −2.95154 | ||||||||
\(472\) | 14.3370 | 0.659914 | ||||||||
\(473\) | 14.4416 | 0.664024 | ||||||||
\(474\) | −3.73301 | −0.171463 | ||||||||
\(475\) | 4.71674 | 0.216419 | ||||||||
\(476\) | −5.02492 | −0.230317 | ||||||||
\(477\) | −94.1325 | −4.31003 | ||||||||
\(478\) | 20.9718 | 0.959229 | ||||||||
\(479\) | 12.8827 | 0.588625 | 0.294313 | − | 0.955709i | \(-0.404909\pi\) | ||||
0.294313 | + | 0.955709i | \(0.404909\pi\) | |||||||
\(480\) | −1.76470 | −0.0805470 | ||||||||
\(481\) | −40.7494 | −1.85801 | ||||||||
\(482\) | 24.3204 | 1.10776 | ||||||||
\(483\) | −21.6085 | −0.983219 | ||||||||
\(484\) | 25.0173 | 1.13715 | ||||||||
\(485\) | −4.17619 | −0.189631 | ||||||||
\(486\) | 52.8482 | 2.39724 | ||||||||
\(487\) | −36.9578 | −1.67472 | −0.837359 | − | 0.546654i | \(-0.815901\pi\) | ||||
−0.837359 | + | 0.546654i | \(0.815901\pi\) | |||||||
\(488\) | −15.3249 | −0.693724 | ||||||||
\(489\) | 1.87274 | 0.0846883 | ||||||||
\(490\) | −0.367017 | −0.0165802 | ||||||||
\(491\) | −12.0707 | −0.544743 | −0.272371 | − | 0.962192i | \(-0.587808\pi\) | ||||
−0.272371 | + | 0.962192i | \(0.587808\pi\) | |||||||
\(492\) | −2.91651 | −0.131487 | ||||||||
\(493\) | 20.2542 | 0.912203 | ||||||||
\(494\) | 4.31378 | 0.194086 | ||||||||
\(495\) | −25.5333 | −1.14764 | ||||||||
\(496\) | 5.47223 | 0.245710 | ||||||||
\(497\) | 7.07877 | 0.317526 | ||||||||
\(498\) | −45.8290 | −2.05365 | ||||||||
\(499\) | −21.9071 | −0.980697 | −0.490349 | − | 0.871526i | \(-0.663131\pi\) | ||||
−0.490349 | + | 0.871526i | \(0.663131\pi\) | |||||||
\(500\) | 5.17148 | 0.231276 | ||||||||
\(501\) | 55.3476 | 2.47275 | ||||||||
\(502\) | −6.35992 | −0.283857 | ||||||||
\(503\) | 24.4459 | 1.08999 | 0.544994 | − | 0.838440i | \(-0.316532\pi\) | ||||
0.544994 | + | 0.838440i | \(0.316532\pi\) | |||||||
\(504\) | 20.0810 | 0.894480 | ||||||||
\(505\) | 3.27628 | 0.145793 | ||||||||
\(506\) | 15.5695 | 0.692150 | ||||||||
\(507\) | −18.5967 | −0.825909 | ||||||||
\(508\) | −19.5247 | −0.866271 | ||||||||
\(509\) | 33.3226 | 1.47700 | 0.738499 | − | 0.674254i | \(-0.235535\pi\) | ||||
0.738499 | + | 0.674254i | \(0.235535\pi\) | |||||||
\(510\) | −3.52997 | −0.156310 | ||||||||
\(511\) | −9.73214 | −0.430524 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 16.5582 | 0.731062 | ||||||||
\(514\) | −11.7714 | −0.519214 | ||||||||
\(515\) | −8.85238 | −0.390082 | ||||||||
\(516\) | −7.97874 | −0.351244 | ||||||||
\(517\) | −15.5307 | −0.683041 | ||||||||
\(518\) | −23.7297 | −1.04262 | ||||||||
\(519\) | 27.5915 | 1.21113 | ||||||||
\(520\) | 2.29590 | 0.100682 | ||||||||
\(521\) | −20.9988 | −0.919975 | −0.459987 | − | 0.887925i | \(-0.652146\pi\) | ||||
−0.459987 | + | 0.887925i | \(0.652146\pi\) | |||||||
\(522\) | −80.9416 | −3.54272 | ||||||||
\(523\) | −5.03035 | −0.219962 | −0.109981 | − | 0.993934i | \(-0.535079\pi\) | ||||
−0.109981 | + | 0.993934i | \(0.535079\pi\) | |||||||
\(524\) | 9.05590 | 0.395609 | ||||||||
\(525\) | −39.2867 | −1.71461 | ||||||||
\(526\) | 2.03361 | 0.0886694 | ||||||||
\(527\) | 10.9462 | 0.476825 | ||||||||
\(528\) | −19.8990 | −0.865992 | ||||||||
\(529\) | −16.2696 | −0.707375 | ||||||||
\(530\) | −6.26725 | −0.272232 | ||||||||
\(531\) | −114.608 | −4.97357 | ||||||||
\(532\) | 2.51205 | 0.108911 | ||||||||
\(533\) | 3.79443 | 0.164355 | ||||||||
\(534\) | −35.5841 | −1.53987 | ||||||||
\(535\) | −3.01122 | −0.130186 | ||||||||
\(536\) | 9.80986 | 0.423721 | ||||||||
\(537\) | 1.23605 | 0.0533394 | ||||||||
\(538\) | 1.11148 | 0.0479195 | ||||||||
\(539\) | −4.13854 | −0.178260 | ||||||||
\(540\) | 8.81267 | 0.379237 | ||||||||
\(541\) | −25.3594 | −1.09028 | −0.545142 | − | 0.838344i | \(-0.683524\pi\) | ||||
−0.545142 | + | 0.838344i | \(0.683524\pi\) | |||||||
\(542\) | 1.29913 | 0.0558026 | ||||||||
\(543\) | 45.2844 | 1.94334 | ||||||||
\(544\) | −2.00033 | −0.0857633 | ||||||||
\(545\) | 3.46644 | 0.148486 | ||||||||
\(546\) | −35.9304 | −1.53768 | ||||||||
\(547\) | 13.5467 | 0.579213 | 0.289607 | − | 0.957146i | \(-0.406476\pi\) | ||||
0.289607 | + | 0.957146i | \(0.406476\pi\) | |||||||
\(548\) | 6.02022 | 0.257171 | ||||||||
\(549\) | 122.505 | 5.22838 | ||||||||
\(550\) | 28.3072 | 1.20702 | ||||||||
\(551\) | −10.1254 | −0.431359 | ||||||||
\(552\) | −8.60191 | −0.366122 | ||||||||
\(553\) | 2.82822 | 0.120268 | ||||||||
\(554\) | 7.79030 | 0.330978 | ||||||||
\(555\) | −16.6699 | −0.707598 | ||||||||
\(556\) | −7.63928 | −0.323978 | ||||||||
\(557\) | −10.8735 | −0.460725 | −0.230363 | − | 0.973105i | \(-0.573991\pi\) | ||||
−0.230363 | + | 0.973105i | \(0.573991\pi\) | |||||||
\(558\) | −43.7443 | −1.85184 | ||||||||
\(559\) | 10.3805 | 0.439047 | ||||||||
\(560\) | 1.33697 | 0.0564975 | ||||||||
\(561\) | −39.8045 | −1.68055 | ||||||||
\(562\) | 1.41989 | 0.0598946 | ||||||||
\(563\) | −27.5105 | −1.15943 | −0.579714 | − | 0.814820i | \(-0.696836\pi\) | ||||
−0.579714 | + | 0.814820i | \(0.696836\pi\) | |||||||
\(564\) | 8.58048 | 0.361303 | ||||||||
\(565\) | −0.569846 | −0.0239736 | ||||||||
\(566\) | −24.0398 | −1.01047 | ||||||||
\(567\) | −77.6736 | −3.26199 | ||||||||
\(568\) | 2.81792 | 0.118237 | ||||||||
\(569\) | −24.9055 | −1.04409 | −0.522047 | − | 0.852916i | \(-0.674832\pi\) | ||||
−0.522047 | + | 0.852916i | \(0.674832\pi\) | |||||||
\(570\) | 1.76470 | 0.0739150 | ||||||||
\(571\) | −5.55007 | −0.232263 | −0.116132 | − | 0.993234i | \(-0.537049\pi\) | ||||
−0.116132 | + | 0.993234i | \(0.537049\pi\) | |||||||
\(572\) | 25.8889 | 1.08247 | ||||||||
\(573\) | −20.1659 | −0.842441 | ||||||||
\(574\) | 2.20962 | 0.0922277 | ||||||||
\(575\) | 12.2366 | 0.510302 | ||||||||
\(576\) | 7.99387 | 0.333078 | ||||||||
\(577\) | 18.4253 | 0.767057 | 0.383528 | − | 0.923529i | \(-0.374709\pi\) | ||||
0.383528 | + | 0.923529i | \(0.374709\pi\) | |||||||
\(578\) | 12.9987 | 0.540675 | ||||||||
\(579\) | −73.1570 | −3.04030 | ||||||||
\(580\) | −5.38901 | −0.223766 | ||||||||
\(581\) | 34.7211 | 1.44048 | ||||||||
\(582\) | 26.0172 | 1.07845 | ||||||||
\(583\) | −70.6705 | −2.92687 | ||||||||
\(584\) | −3.87418 | −0.160315 | ||||||||
\(585\) | −18.3531 | −0.758808 | ||||||||
\(586\) | −1.14275 | −0.0472065 | ||||||||
\(587\) | 31.6993 | 1.30837 | 0.654185 | − | 0.756334i | \(-0.273012\pi\) | ||||
0.654185 | + | 0.756334i | \(0.273012\pi\) | |||||||
\(588\) | 2.28648 | 0.0942928 | ||||||||
\(589\) | −5.47223 | −0.225479 | ||||||||
\(590\) | −7.63050 | −0.314143 | ||||||||
\(591\) | 45.7623 | 1.88241 | ||||||||
\(592\) | −9.44633 | −0.388242 | ||||||||
\(593\) | −5.01929 | −0.206118 | −0.103059 | − | 0.994675i | \(-0.532863\pi\) | ||||
−0.103059 | + | 0.994675i | \(0.532863\pi\) | |||||||
\(594\) | 99.3730 | 4.07732 | ||||||||
\(595\) | 2.67439 | 0.109639 | ||||||||
\(596\) | −5.91544 | −0.242306 | ||||||||
\(597\) | 75.9439 | 3.10818 | ||||||||
\(598\) | 11.1912 | 0.457643 | ||||||||
\(599\) | 18.2729 | 0.746609 | 0.373305 | − | 0.927709i | \(-0.378225\pi\) | ||||
0.373305 | + | 0.927709i | \(0.378225\pi\) | |||||||
\(600\) | −15.6393 | −0.638471 | ||||||||
\(601\) | −21.3508 | −0.870919 | −0.435460 | − | 0.900208i | \(-0.643414\pi\) | ||||
−0.435460 | + | 0.900208i | \(0.643414\pi\) | |||||||
\(602\) | 6.04488 | 0.246371 | ||||||||
\(603\) | −78.4188 | −3.19346 | ||||||||
\(604\) | −5.07937 | −0.206676 | ||||||||
\(605\) | −13.3148 | −0.541324 | ||||||||
\(606\) | −20.4109 | −0.829137 | ||||||||
\(607\) | −22.7582 | −0.923728 | −0.461864 | − | 0.886951i | \(-0.652819\pi\) | ||||
−0.461864 | + | 0.886951i | \(0.652819\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 84.3370 | 3.41751 | ||||||||
\(610\) | 8.15626 | 0.330237 | ||||||||
\(611\) | −11.1633 | −0.451620 | ||||||||
\(612\) | 15.9903 | 0.646372 | ||||||||
\(613\) | 0.0618928 | 0.00249983 | 0.00124991 | − | 0.999999i | \(-0.499602\pi\) | ||||
0.00124991 | + | 0.999999i | \(0.499602\pi\) | |||||||
\(614\) | 26.4911 | 1.06910 | ||||||||
\(615\) | 1.55224 | 0.0625923 | ||||||||
\(616\) | 15.0759 | 0.607427 | ||||||||
\(617\) | 14.1077 | 0.567953 | 0.283977 | − | 0.958831i | \(-0.408346\pi\) | ||||
0.283977 | + | 0.958831i | \(0.408346\pi\) | |||||||
\(618\) | 55.1494 | 2.21843 | ||||||||
\(619\) | 22.2558 | 0.894535 | 0.447268 | − | 0.894400i | \(-0.352397\pi\) | ||||
0.447268 | + | 0.894400i | \(0.352397\pi\) | |||||||
\(620\) | −2.91245 | −0.116967 | ||||||||
\(621\) | 42.9569 | 1.72380 | ||||||||
\(622\) | 16.7266 | 0.670674 | ||||||||
\(623\) | 26.9593 | 1.08010 | ||||||||
\(624\) | −14.3032 | −0.572586 | ||||||||
\(625\) | 20.8313 | 0.833252 | ||||||||
\(626\) | 2.36264 | 0.0944301 | ||||||||
\(627\) | 19.8990 | 0.794689 | ||||||||
\(628\) | 19.3190 | 0.770911 | ||||||||
\(629\) | −18.8957 | −0.753422 | ||||||||
\(630\) | −10.6876 | −0.425805 | ||||||||
\(631\) | 3.89365 | 0.155004 | 0.0775019 | − | 0.996992i | \(-0.475306\pi\) | ||||
0.0775019 | + | 0.996992i | \(0.475306\pi\) | |||||||
\(632\) | 1.12586 | 0.0447843 | ||||||||
\(633\) | 3.31570 | 0.131787 | ||||||||
\(634\) | −26.0184 | −1.03332 | ||||||||
\(635\) | 10.3915 | 0.412376 | ||||||||
\(636\) | 39.0443 | 1.54821 | ||||||||
\(637\) | −2.97475 | −0.117864 | ||||||||
\(638\) | −60.7673 | −2.40580 | ||||||||
\(639\) | −22.5261 | −0.891120 | ||||||||
\(640\) | 0.532224 | 0.0210380 | ||||||||
\(641\) | −21.4135 | −0.845781 | −0.422891 | − | 0.906181i | \(-0.638985\pi\) | ||||
−0.422891 | + | 0.906181i | \(0.638985\pi\) | |||||||
\(642\) | 18.7596 | 0.740381 | ||||||||
\(643\) | −28.1090 | −1.10851 | −0.554256 | − | 0.832347i | \(-0.686997\pi\) | ||||
−0.554256 | + | 0.832347i | \(0.686997\pi\) | |||||||
\(644\) | 6.51701 | 0.256806 | ||||||||
\(645\) | 4.24648 | 0.167205 | ||||||||
\(646\) | 2.00033 | 0.0787018 | ||||||||
\(647\) | −18.1515 | −0.713610 | −0.356805 | − | 0.934179i | \(-0.616134\pi\) | ||||
−0.356805 | + | 0.934179i | \(0.616134\pi\) | |||||||
\(648\) | −30.9204 | −1.21467 | ||||||||
\(649\) | −86.0427 | −3.37747 | ||||||||
\(650\) | 20.3470 | 0.798073 | ||||||||
\(651\) | 45.5793 | 1.78640 | ||||||||
\(652\) | −0.564810 | −0.0221197 | ||||||||
\(653\) | 5.18457 | 0.202888 | 0.101444 | − | 0.994841i | \(-0.467654\pi\) | ||||
0.101444 | + | 0.994841i | \(0.467654\pi\) | |||||||
\(654\) | −21.5956 | −0.844454 | ||||||||
\(655\) | −4.81977 | −0.188324 | ||||||||
\(656\) | 0.879606 | 0.0343429 | ||||||||
\(657\) | 30.9697 | 1.20824 | ||||||||
\(658\) | −6.50077 | −0.253426 | ||||||||
\(659\) | −33.7893 | −1.31624 | −0.658122 | − | 0.752911i | \(-0.728649\pi\) | ||||
−0.658122 | + | 0.752911i | \(0.728649\pi\) | |||||||
\(660\) | 10.5907 | 0.412243 | ||||||||
\(661\) | −39.7254 | −1.54514 | −0.772569 | − | 0.634930i | \(-0.781029\pi\) | ||||
−0.772569 | + | 0.634930i | \(0.781029\pi\) | |||||||
\(662\) | 19.2136 | 0.746757 | ||||||||
\(663\) | −28.6111 | −1.11116 | ||||||||
\(664\) | 13.8218 | 0.536391 | ||||||||
\(665\) | −1.33697 | −0.0518457 | ||||||||
\(666\) | 75.5128 | 2.92606 | ||||||||
\(667\) | −26.2684 | −1.01712 | ||||||||
\(668\) | −16.6926 | −0.645856 | ||||||||
\(669\) | −65.4229 | −2.52939 | ||||||||
\(670\) | −5.22104 | −0.201707 | ||||||||
\(671\) | 91.9713 | 3.55051 | ||||||||
\(672\) | −8.32922 | −0.321306 | ||||||||
\(673\) | −25.0815 | −0.966821 | −0.483410 | − | 0.875394i | \(-0.660602\pi\) | ||||
−0.483410 | + | 0.875394i | \(0.660602\pi\) | |||||||
\(674\) | 5.71500 | 0.220133 | ||||||||
\(675\) | 78.1006 | 3.00609 | ||||||||
\(676\) | 5.60868 | 0.215719 | ||||||||
\(677\) | 31.4916 | 1.21032 | 0.605161 | − | 0.796103i | \(-0.293109\pi\) | ||||
0.605161 | + | 0.796103i | \(0.293109\pi\) | |||||||
\(678\) | 3.55008 | 0.136340 | ||||||||
\(679\) | −19.7113 | −0.756449 | ||||||||
\(680\) | 1.06462 | 0.0408264 | ||||||||
\(681\) | −94.4650 | −3.61991 | ||||||||
\(682\) | −32.8412 | −1.25756 | ||||||||
\(683\) | 10.2390 | 0.391786 | 0.195893 | − | 0.980625i | \(-0.437239\pi\) | ||||
0.195893 | + | 0.980625i | \(0.437239\pi\) | |||||||
\(684\) | −7.99387 | −0.305653 | ||||||||
\(685\) | −3.20411 | −0.122423 | ||||||||
\(686\) | −19.3167 | −0.737513 | ||||||||
\(687\) | 73.7404 | 2.81337 | ||||||||
\(688\) | 2.40635 | 0.0917412 | ||||||||
\(689\) | −50.7972 | −1.93522 | ||||||||
\(690\) | 4.57814 | 0.174287 | ||||||||
\(691\) | 35.4416 | 1.34826 | 0.674131 | − | 0.738612i | \(-0.264518\pi\) | ||||
0.674131 | + | 0.738612i | \(0.264518\pi\) | |||||||
\(692\) | −8.32146 | −0.316335 | ||||||||
\(693\) | −120.515 | −4.57799 | ||||||||
\(694\) | 11.0469 | 0.419336 | ||||||||
\(695\) | 4.06581 | 0.154225 | ||||||||
\(696\) | 33.5730 | 1.27258 | ||||||||
\(697\) | 1.75950 | 0.0666458 | ||||||||
\(698\) | −5.41033 | −0.204784 | ||||||||
\(699\) | −29.1523 | −1.10264 | ||||||||
\(700\) | 11.8487 | 0.447838 | ||||||||
\(701\) | −47.9520 | −1.81112 | −0.905561 | − | 0.424216i | \(-0.860550\pi\) | ||||
−0.905561 | + | 0.424216i | \(0.860550\pi\) | |||||||
\(702\) | 71.4284 | 2.69589 | ||||||||
\(703\) | 9.44633 | 0.356275 | ||||||||
\(704\) | 6.00144 | 0.226188 | ||||||||
\(705\) | −4.56674 | −0.171993 | ||||||||
\(706\) | −8.21985 | −0.309358 | ||||||||
\(707\) | 15.4638 | 0.581575 | ||||||||
\(708\) | 47.5372 | 1.78656 | ||||||||
\(709\) | 24.7691 | 0.930224 | 0.465112 | − | 0.885252i | \(-0.346014\pi\) | ||||
0.465112 | + | 0.885252i | \(0.346014\pi\) | |||||||
\(710\) | −1.49977 | −0.0562853 | ||||||||
\(711\) | −8.99997 | −0.337525 | ||||||||
\(712\) | 10.7320 | 0.402198 | ||||||||
\(713\) | −14.1966 | −0.531666 | ||||||||
\(714\) | −16.6611 | −0.623528 | ||||||||
\(715\) | −13.7787 | −0.515294 | ||||||||
\(716\) | −0.372786 | −0.0139317 | ||||||||
\(717\) | 69.5363 | 2.59688 | ||||||||
\(718\) | −27.5741 | −1.02906 | ||||||||
\(719\) | −0.289733 | −0.0108052 | −0.00540262 | − | 0.999985i | \(-0.501720\pi\) | ||||
−0.00540262 | + | 0.999985i | \(0.501720\pi\) | |||||||
\(720\) | −4.25453 | −0.158557 | ||||||||
\(721\) | −41.7825 | −1.55606 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 80.6390 | 2.99900 | ||||||||
\(724\) | −13.6576 | −0.507580 | ||||||||
\(725\) | −47.7591 | −1.77373 | ||||||||
\(726\) | 82.9499 | 3.07856 | ||||||||
\(727\) | 51.4476 | 1.90808 | 0.954042 | − | 0.299673i | \(-0.0968775\pi\) | ||||
0.954042 | + | 0.299673i | \(0.0968775\pi\) | |||||||
\(728\) | 10.8364 | 0.401625 | ||||||||
\(729\) | 82.4676 | 3.05436 | ||||||||
\(730\) | 2.06193 | 0.0763155 | ||||||||
\(731\) | 4.81348 | 0.178033 | ||||||||
\(732\) | −50.8126 | −1.87809 | ||||||||
\(733\) | 27.8290 | 1.02789 | 0.513943 | − | 0.857824i | \(-0.328184\pi\) | ||||
0.513943 | + | 0.857824i | \(0.328184\pi\) | |||||||
\(734\) | 35.1518 | 1.29747 | ||||||||
\(735\) | −1.21692 | −0.0448868 | ||||||||
\(736\) | 2.59430 | 0.0956270 | ||||||||
\(737\) | −58.8733 | −2.16863 | ||||||||
\(738\) | −7.03146 | −0.258832 | ||||||||
\(739\) | −29.1854 | −1.07360 | −0.536802 | − | 0.843709i | \(-0.680368\pi\) | ||||
−0.536802 | + | 0.843709i | \(0.680368\pi\) | |||||||
\(740\) | 5.02756 | 0.184817 | ||||||||
\(741\) | 14.3032 | 0.525441 | ||||||||
\(742\) | −29.5809 | −1.08595 | ||||||||
\(743\) | 34.3759 | 1.26113 | 0.630564 | − | 0.776137i | \(-0.282824\pi\) | ||||
0.630564 | + | 0.776137i | \(0.282824\pi\) | |||||||
\(744\) | 18.1443 | 0.665201 | ||||||||
\(745\) | 3.14834 | 0.115346 | ||||||||
\(746\) | 21.9794 | 0.804723 | ||||||||
\(747\) | −110.490 | −4.04261 | ||||||||
\(748\) | 12.0048 | 0.438940 | ||||||||
\(749\) | −14.2127 | −0.519320 | ||||||||
\(750\) | 17.1471 | 0.626123 | ||||||||
\(751\) | −21.7340 | −0.793085 | −0.396542 | − | 0.918016i | \(-0.629790\pi\) | ||||
−0.396542 | + | 0.918016i | \(0.629790\pi\) | |||||||
\(752\) | −2.58783 | −0.0943685 | ||||||||
\(753\) | −21.0876 | −0.768475 | ||||||||
\(754\) | −43.6789 | −1.59069 | ||||||||
\(755\) | 2.70336 | 0.0983854 | ||||||||
\(756\) | 41.5950 | 1.51280 | ||||||||
\(757\) | 23.7135 | 0.861881 | 0.430941 | − | 0.902380i | \(-0.358182\pi\) | ||||
0.430941 | + | 0.902380i | \(0.358182\pi\) | |||||||
\(758\) | 5.41110 | 0.196540 | ||||||||
\(759\) | 51.6239 | 1.87383 | ||||||||
\(760\) | −0.532224 | −0.0193058 | ||||||||
\(761\) | 39.4330 | 1.42945 | 0.714723 | − | 0.699408i | \(-0.246553\pi\) | ||||
0.714723 | + | 0.699408i | \(0.246553\pi\) | |||||||
\(762\) | −64.7382 | −2.34522 | ||||||||
\(763\) | 16.3613 | 0.592319 | ||||||||
\(764\) | 6.08193 | 0.220036 | ||||||||
\(765\) | −8.51045 | −0.307696 | ||||||||
\(766\) | −3.51955 | −0.127167 | ||||||||
\(767\) | −61.8467 | −2.23315 | ||||||||
\(768\) | −3.31570 | −0.119645 | ||||||||
\(769\) | 16.5387 | 0.596401 | 0.298200 | − | 0.954503i | \(-0.403614\pi\) | ||||
0.298200 | + | 0.954503i | \(0.403614\pi\) | |||||||
\(770\) | −8.02378 | −0.289157 | ||||||||
\(771\) | −39.0304 | −1.40565 | ||||||||
\(772\) | 22.0638 | 0.794094 | ||||||||
\(773\) | 10.4349 | 0.375319 | 0.187659 | − | 0.982234i | \(-0.439910\pi\) | ||||
0.187659 | + | 0.982234i | \(0.439910\pi\) | |||||||
\(774\) | −19.2361 | −0.691426 | ||||||||
\(775\) | −25.8110 | −0.927160 | ||||||||
\(776\) | −7.84668 | −0.281679 | ||||||||
\(777\) | −78.6805 | −2.82265 | ||||||||
\(778\) | −9.79046 | −0.351005 | ||||||||
\(779\) | −0.879606 | −0.0315152 | ||||||||
\(780\) | 7.61251 | 0.272571 | ||||||||
\(781\) | −16.9116 | −0.605145 | ||||||||
\(782\) | 5.18944 | 0.185574 | ||||||||
\(783\) | −167.659 | −5.99165 | ||||||||
\(784\) | −0.689592 | −0.0246283 | ||||||||
\(785\) | −10.2820 | −0.366981 | ||||||||
\(786\) | 30.0267 | 1.07102 | ||||||||
\(787\) | 15.4677 | 0.551362 | 0.275681 | − | 0.961249i | \(-0.411097\pi\) | ||||
0.275681 | + | 0.961249i | \(0.411097\pi\) | |||||||
\(788\) | −13.8017 | −0.491665 | ||||||||
\(789\) | 6.74283 | 0.240051 | ||||||||
\(790\) | −0.599209 | −0.0213189 | ||||||||
\(791\) | −2.68962 | −0.0956320 | ||||||||
\(792\) | −47.9748 | −1.70471 | ||||||||
\(793\) | 66.1080 | 2.34757 | ||||||||
\(794\) | −13.4179 | −0.476182 | ||||||||
\(795\) | −20.7803 | −0.737002 | ||||||||
\(796\) | −22.9043 | −0.811822 | ||||||||
\(797\) | 5.17864 | 0.183437 | 0.0917184 | − | 0.995785i | \(-0.470764\pi\) | ||||
0.0917184 | + | 0.995785i | \(0.470764\pi\) | |||||||
\(798\) | 8.32922 | 0.294851 | ||||||||
\(799\) | −5.17651 | −0.183132 | ||||||||
\(800\) | 4.71674 | 0.166762 | ||||||||
\(801\) | −85.7902 | −3.03125 | ||||||||
\(802\) | −36.6623 | −1.29459 | ||||||||
\(803\) | 23.2506 | 0.820498 | ||||||||
\(804\) | 32.5266 | 1.14712 | ||||||||
\(805\) | −3.46851 | −0.122249 | ||||||||
\(806\) | −23.6060 | −0.831485 | ||||||||
\(807\) | 3.68535 | 0.129730 | ||||||||
\(808\) | 6.15584 | 0.216562 | ||||||||
\(809\) | −2.47229 | −0.0869211 | −0.0434605 | − | 0.999055i | \(-0.513838\pi\) | ||||
−0.0434605 | + | 0.999055i | \(0.513838\pi\) | |||||||
\(810\) | 16.4566 | 0.578225 | ||||||||
\(811\) | −44.9503 | −1.57842 | −0.789209 | − | 0.614124i | \(-0.789509\pi\) | ||||
−0.789209 | + | 0.614124i | \(0.789509\pi\) | |||||||
\(812\) | −25.4357 | −0.892617 | ||||||||
\(813\) | 4.30754 | 0.151072 | ||||||||
\(814\) | 56.6916 | 1.98704 | ||||||||
\(815\) | 0.300606 | 0.0105298 | ||||||||
\(816\) | −6.63248 | −0.232183 | ||||||||
\(817\) | −2.40635 | −0.0841875 | ||||||||
\(818\) | 23.9115 | 0.836047 | ||||||||
\(819\) | −86.6251 | −3.02693 | ||||||||
\(820\) | −0.468148 | −0.0163484 | ||||||||
\(821\) | 0.446654 | 0.0155883 | 0.00779417 | − | 0.999970i | \(-0.497519\pi\) | ||||
0.00779417 | + | 0.999970i | \(0.497519\pi\) | |||||||
\(822\) | 19.9613 | 0.696229 | ||||||||
\(823\) | −39.7433 | −1.38536 | −0.692681 | − | 0.721244i | \(-0.743571\pi\) | ||||
−0.692681 | + | 0.721244i | \(0.743571\pi\) | |||||||
\(824\) | −16.6328 | −0.579431 | ||||||||
\(825\) | 93.8583 | 3.26773 | ||||||||
\(826\) | −36.0153 | −1.25313 | ||||||||
\(827\) | −33.8125 | −1.17578 | −0.587888 | − | 0.808942i | \(-0.700040\pi\) | ||||
−0.587888 | + | 0.808942i | \(0.700040\pi\) | |||||||
\(828\) | −20.7385 | −0.720712 | ||||||||
\(829\) | −11.4591 | −0.397990 | −0.198995 | − | 0.980001i | \(-0.563768\pi\) | ||||
−0.198995 | + | 0.980001i | \(0.563768\pi\) | |||||||
\(830\) | −7.35631 | −0.255341 | ||||||||
\(831\) | 25.8303 | 0.896043 | ||||||||
\(832\) | 4.31378 | 0.149553 | ||||||||
\(833\) | −1.37941 | −0.0477937 | ||||||||
\(834\) | −25.3296 | −0.877091 | ||||||||
\(835\) | 8.88420 | 0.307450 | ||||||||
\(836\) | −6.00144 | −0.207564 | ||||||||
\(837\) | −90.6101 | −3.13194 | ||||||||
\(838\) | 14.7038 | 0.507935 | ||||||||
\(839\) | 17.5795 | 0.606913 | 0.303456 | − | 0.952845i | \(-0.401859\pi\) | ||||
0.303456 | + | 0.952845i | \(0.401859\pi\) | |||||||
\(840\) | 4.43301 | 0.152953 | ||||||||
\(841\) | 73.5247 | 2.53534 | ||||||||
\(842\) | −11.7662 | −0.405489 | ||||||||
\(843\) | 4.70794 | 0.162150 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | −2.98508 | −0.102690 | ||||||||
\(846\) | 20.6868 | 0.711227 | ||||||||
\(847\) | −62.8448 | −2.15937 | ||||||||
\(848\) | −11.7756 | −0.404375 | ||||||||
\(849\) | −79.7089 | −2.73560 | ||||||||
\(850\) | 9.43501 | 0.323618 | ||||||||
\(851\) | 24.5066 | 0.840075 | ||||||||
\(852\) | 9.34339 | 0.320099 | ||||||||
\(853\) | 27.7700 | 0.950827 | 0.475414 | − | 0.879762i | \(-0.342298\pi\) | ||||
0.475414 | + | 0.879762i | \(0.342298\pi\) | |||||||
\(854\) | 38.4969 | 1.31734 | ||||||||
\(855\) | 4.25453 | 0.145502 | ||||||||
\(856\) | −5.65780 | −0.193380 | ||||||||
\(857\) | 26.3289 | 0.899379 | 0.449689 | − | 0.893185i | \(-0.351535\pi\) | ||||
0.449689 | + | 0.893185i | \(0.351535\pi\) | |||||||
\(858\) | 85.8398 | 2.93052 | ||||||||
\(859\) | 38.2165 | 1.30393 | 0.651965 | − | 0.758249i | \(-0.273945\pi\) | ||||
0.651965 | + | 0.758249i | \(0.273945\pi\) | |||||||
\(860\) | −1.28072 | −0.0436721 | ||||||||
\(861\) | 7.32643 | 0.249684 | ||||||||
\(862\) | 34.5868 | 1.17803 | ||||||||
\(863\) | −44.0262 | −1.49867 | −0.749335 | − | 0.662191i | \(-0.769627\pi\) | ||||
−0.749335 | + | 0.662191i | \(0.769627\pi\) | |||||||
\(864\) | 16.5582 | 0.563321 | ||||||||
\(865\) | 4.42888 | 0.150587 | ||||||||
\(866\) | 25.8068 | 0.876951 | ||||||||
\(867\) | 43.0998 | 1.46375 | ||||||||
\(868\) | −13.7465 | −0.466587 | ||||||||
\(869\) | −6.75678 | −0.229208 | ||||||||
\(870\) | −17.8683 | −0.605793 | ||||||||
\(871\) | −42.3176 | −1.43388 | ||||||||
\(872\) | 6.51313 | 0.220562 | ||||||||
\(873\) | 62.7254 | 2.12293 | ||||||||
\(874\) | −2.59430 | −0.0877534 | ||||||||
\(875\) | −12.9910 | −0.439177 | ||||||||
\(876\) | −12.8456 | −0.434013 | ||||||||
\(877\) | 12.6840 | 0.428307 | 0.214154 | − | 0.976800i | \(-0.431301\pi\) | ||||
0.214154 | + | 0.976800i | \(0.431301\pi\) | |||||||
\(878\) | 15.6198 | 0.527142 | ||||||||
\(879\) | −3.78901 | −0.127800 | ||||||||
\(880\) | −3.19411 | −0.107674 | ||||||||
\(881\) | −39.1519 | −1.31906 | −0.659530 | − | 0.751678i | \(-0.729245\pi\) | ||||
−0.659530 | + | 0.751678i | \(0.729245\pi\) | |||||||
\(882\) | 5.51251 | 0.185616 | ||||||||
\(883\) | 29.2904 | 0.985701 | 0.492851 | − | 0.870114i | \(-0.335955\pi\) | ||||
0.492851 | + | 0.870114i | \(0.335955\pi\) | |||||||
\(884\) | 8.62896 | 0.290223 | ||||||||
\(885\) | −25.3005 | −0.850465 | ||||||||
\(886\) | −6.69100 | −0.224788 | ||||||||
\(887\) | −32.2916 | −1.08425 | −0.542123 | − | 0.840299i | \(-0.682379\pi\) | ||||
−0.542123 | + | 0.840299i | \(0.682379\pi\) | |||||||
\(888\) | −31.3212 | −1.05107 | ||||||||
\(889\) | 49.0472 | 1.64499 | ||||||||
\(890\) | −5.71183 | −0.191461 | ||||||||
\(891\) | 185.567 | 6.21673 | ||||||||
\(892\) | 19.7312 | 0.660651 | ||||||||
\(893\) | 2.58783 | 0.0865985 | ||||||||
\(894\) | −19.6138 | −0.655984 | ||||||||
\(895\) | 0.198406 | 0.00663198 | ||||||||
\(896\) | 2.51205 | 0.0839218 | ||||||||
\(897\) | 37.1067 | 1.23896 | ||||||||
\(898\) | −10.4379 | −0.348317 | ||||||||
\(899\) | 55.4087 | 1.84798 | ||||||||
\(900\) | −37.7050 | −1.25683 | ||||||||
\(901\) | −23.5550 | −0.784730 | ||||||||
\(902\) | −5.27891 | −0.175768 | ||||||||
\(903\) | 20.0430 | 0.666990 | ||||||||
\(904\) | −1.07069 | −0.0356105 | ||||||||
\(905\) | 7.26889 | 0.241626 | ||||||||
\(906\) | −16.8417 | −0.559527 | ||||||||
\(907\) | −11.0212 | −0.365954 | −0.182977 | − | 0.983117i | \(-0.558573\pi\) | ||||
−0.182977 | + | 0.983117i | \(0.558573\pi\) | |||||||
\(908\) | 28.4902 | 0.945481 | ||||||||
\(909\) | −49.2090 | −1.63216 | ||||||||
\(910\) | −5.76741 | −0.191188 | ||||||||
\(911\) | 12.8298 | 0.425072 | 0.212536 | − | 0.977153i | \(-0.431828\pi\) | ||||
0.212536 | + | 0.977153i | \(0.431828\pi\) | |||||||
\(912\) | 3.31570 | 0.109794 | ||||||||
\(913\) | −82.9509 | −2.74527 | ||||||||
\(914\) | −21.5202 | −0.711825 | ||||||||
\(915\) | 27.0437 | 0.894038 | ||||||||
\(916\) | −22.2398 | −0.734823 | ||||||||
\(917\) | −22.7489 | −0.751235 | ||||||||
\(918\) | 33.1218 | 1.09318 | ||||||||
\(919\) | 13.1128 | 0.432550 | 0.216275 | − | 0.976333i | \(-0.430609\pi\) | ||||
0.216275 | + | 0.976333i | \(0.430609\pi\) | |||||||
\(920\) | −1.38075 | −0.0455219 | ||||||||
\(921\) | 87.8367 | 2.89432 | ||||||||
\(922\) | −38.6757 | −1.27372 | ||||||||
\(923\) | −12.1559 | −0.400116 | ||||||||
\(924\) | 49.9873 | 1.64446 | ||||||||
\(925\) | 44.5559 | 1.46499 | ||||||||
\(926\) | 3.68622 | 0.121137 | ||||||||
\(927\) | 132.960 | 4.36700 | ||||||||
\(928\) | −10.1254 | −0.332384 | ||||||||
\(929\) | −31.7158 | −1.04056 | −0.520281 | − | 0.853995i | \(-0.674173\pi\) | ||||
−0.520281 | + | 0.853995i | \(0.674173\pi\) | |||||||
\(930\) | −9.65681 | −0.316659 | ||||||||
\(931\) | 0.689592 | 0.0226005 | ||||||||
\(932\) | 8.79219 | 0.287998 | ||||||||
\(933\) | 55.4603 | 1.81569 | ||||||||
\(934\) | −7.66542 | −0.250820 | ||||||||
\(935\) | −6.38926 | −0.208951 | ||||||||
\(936\) | −34.4838 | −1.12714 | ||||||||
\(937\) | −40.8118 | −1.33326 | −0.666631 | − | 0.745388i | \(-0.732264\pi\) | ||||
−0.666631 | + | 0.745388i | \(0.732264\pi\) | |||||||
\(938\) | −24.6429 | −0.804619 | ||||||||
\(939\) | 7.83381 | 0.255647 | ||||||||
\(940\) | 1.37731 | 0.0449228 | ||||||||
\(941\) | 41.1901 | 1.34276 | 0.671379 | − | 0.741114i | \(-0.265702\pi\) | ||||
0.671379 | + | 0.741114i | \(0.265702\pi\) | |||||||
\(942\) | 64.0560 | 2.08706 | ||||||||
\(943\) | −2.28196 | −0.0743108 | ||||||||
\(944\) | −14.3370 | −0.466630 | ||||||||
\(945\) | −22.1379 | −0.720145 | ||||||||
\(946\) | −14.4416 | −0.469536 | ||||||||
\(947\) | −11.1139 | −0.361154 | −0.180577 | − | 0.983561i | \(-0.557796\pi\) | ||||
−0.180577 | + | 0.983561i | \(0.557796\pi\) | |||||||
\(948\) | 3.73301 | 0.121243 | ||||||||
\(949\) | 16.7123 | 0.542505 | ||||||||
\(950\) | −4.71674 | −0.153031 | ||||||||
\(951\) | −86.2692 | −2.79747 | ||||||||
\(952\) | 5.02492 | 0.162859 | ||||||||
\(953\) | −52.8313 | −1.71137 | −0.855687 | − | 0.517493i | \(-0.826865\pi\) | ||||
−0.855687 | + | 0.517493i | \(0.826865\pi\) | |||||||
\(954\) | 94.1325 | 3.04765 | ||||||||
\(955\) | −3.23695 | −0.104745 | ||||||||
\(956\) | −20.9718 | −0.678277 | ||||||||
\(957\) | −201.486 | −6.51312 | ||||||||
\(958\) | −12.8827 | −0.416221 | ||||||||
\(959\) | −15.1231 | −0.488351 | ||||||||
\(960\) | 1.76470 | 0.0569553 | ||||||||
\(961\) | −1.05475 | −0.0340242 | ||||||||
\(962\) | 40.7494 | 1.31381 | ||||||||
\(963\) | 45.2277 | 1.45744 | ||||||||
\(964\) | −24.3204 | −0.783306 | ||||||||
\(965\) | −11.7429 | −0.378017 | ||||||||
\(966\) | 21.6085 | 0.695241 | ||||||||
\(967\) | 35.4337 | 1.13947 | 0.569735 | − | 0.821829i | \(-0.307046\pi\) | ||||
0.569735 | + | 0.821829i | \(0.307046\pi\) | |||||||
\(968\) | −25.0173 | −0.804087 | ||||||||
\(969\) | 6.63248 | 0.213066 | ||||||||
\(970\) | 4.17619 | 0.134089 | ||||||||
\(971\) | 27.7189 | 0.889541 | 0.444771 | − | 0.895644i | \(-0.353285\pi\) | ||||
0.444771 | + | 0.895644i | \(0.353285\pi\) | |||||||
\(972\) | −52.8482 | −1.69511 | ||||||||
\(973\) | 19.1903 | 0.615212 | ||||||||
\(974\) | 36.9578 | 1.18420 | ||||||||
\(975\) | 67.4644 | 2.16059 | ||||||||
\(976\) | 15.3249 | 0.490537 | ||||||||
\(977\) | 0.472769 | 0.0151252 | 0.00756261 | − | 0.999971i | \(-0.497593\pi\) | ||||
0.00756261 | + | 0.999971i | \(0.497593\pi\) | |||||||
\(978\) | −1.87274 | −0.0598837 | ||||||||
\(979\) | −64.4074 | −2.05847 | ||||||||
\(980\) | 0.367017 | 0.0117239 | ||||||||
\(981\) | −52.0651 | −1.66231 | ||||||||
\(982\) | 12.0707 | 0.385191 | ||||||||
\(983\) | 37.5753 | 1.19847 | 0.599234 | − | 0.800574i | \(-0.295472\pi\) | ||||
0.599234 | + | 0.800574i | \(0.295472\pi\) | |||||||
\(984\) | 2.91651 | 0.0929750 | ||||||||
\(985\) | 7.34559 | 0.234050 | ||||||||
\(986\) | −20.2542 | −0.645025 | ||||||||
\(987\) | −21.5546 | −0.686091 | ||||||||
\(988\) | −4.31378 | −0.137240 | ||||||||
\(989\) | −6.24279 | −0.198509 | ||||||||
\(990\) | 25.5333 | 0.811502 | ||||||||
\(991\) | −22.5540 | −0.716451 | −0.358226 | − | 0.933635i | \(-0.616618\pi\) | ||||
−0.358226 | + | 0.933635i | \(0.616618\pi\) | |||||||
\(992\) | −5.47223 | −0.173743 | ||||||||
\(993\) | 63.7065 | 2.02166 | ||||||||
\(994\) | −7.07877 | −0.224525 | ||||||||
\(995\) | 12.1902 | 0.386456 | ||||||||
\(996\) | 45.8290 | 1.45215 | ||||||||
\(997\) | −10.3390 | −0.327440 | −0.163720 | − | 0.986507i | \(-0.552349\pi\) | ||||
−0.163720 | + | 0.986507i | \(0.552349\pi\) | |||||||
\(998\) | 21.9071 | 0.693458 | ||||||||
\(999\) | 156.414 | 4.94872 |
(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 | 8018.2.a.f.1.1 | ✓ | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.f.1.1 | ✓ | 34 | 1.1 | even | 1 | trivial |