Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4015,2,Mod(1,4015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4015 = 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4015.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0599364115\) |
Analytic rank: | \(1\) |
Dimension: | \(23\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 4015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.09501 | −0.774292 | −0.387146 | − | 0.922018i | \(-0.626539\pi\) | ||||
−0.387146 | + | 0.922018i | \(0.626539\pi\) | |||||||
\(3\) | −2.94583 | −1.70078 | −0.850389 | − | 0.526154i | \(-0.823634\pi\) | ||||
−0.850389 | + | 0.526154i | \(0.823634\pi\) | |||||||
\(4\) | −0.800943 | −0.400472 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 3.22573 | 1.31690 | ||||||||
\(7\) | 2.47152 | 0.934147 | 0.467074 | − | 0.884218i | \(-0.345308\pi\) | ||||
0.467074 | + | 0.884218i | \(0.345308\pi\) | |||||||
\(8\) | 3.06707 | 1.08437 | ||||||||
\(9\) | 5.67794 | 1.89265 | ||||||||
\(10\) | −1.09501 | −0.346274 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 2.35945 | 0.681113 | ||||||||
\(13\) | 0.870712 | 0.241492 | 0.120746 | − | 0.992683i | \(-0.461471\pi\) | ||||
0.120746 | + | 0.992683i | \(0.461471\pi\) | |||||||
\(14\) | −2.70635 | −0.723303 | ||||||||
\(15\) | −2.94583 | −0.760611 | ||||||||
\(16\) | −1.75660 | −0.439151 | ||||||||
\(17\) | 5.55777 | 1.34796 | 0.673979 | − | 0.738750i | \(-0.264584\pi\) | ||||
0.673979 | + | 0.738750i | \(0.264584\pi\) | |||||||
\(18\) | −6.21743 | −1.46546 | ||||||||
\(19\) | 0.757543 | 0.173792 | 0.0868962 | − | 0.996217i | \(-0.472305\pi\) | ||||
0.0868962 | + | 0.996217i | \(0.472305\pi\) | |||||||
\(20\) | −0.800943 | −0.179096 | ||||||||
\(21\) | −7.28069 | −1.58878 | ||||||||
\(22\) | −1.09501 | −0.233458 | ||||||||
\(23\) | −7.95898 | −1.65956 | −0.829781 | − | 0.558089i | \(-0.811535\pi\) | ||||
−0.829781 | + | 0.558089i | \(0.811535\pi\) | |||||||
\(24\) | −9.03509 | −1.84428 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.953443 | −0.186986 | ||||||||
\(27\) | −7.88878 | −1.51820 | ||||||||
\(28\) | −1.97955 | −0.374099 | ||||||||
\(29\) | −7.07445 | −1.31369 | −0.656846 | − | 0.754024i | \(-0.728110\pi\) | ||||
−0.656846 | + | 0.754024i | \(0.728110\pi\) | |||||||
\(30\) | 3.22573 | 0.588935 | ||||||||
\(31\) | 6.68841 | 1.20127 | 0.600637 | − | 0.799522i | \(-0.294914\pi\) | ||||
0.600637 | + | 0.799522i | \(0.294914\pi\) | |||||||
\(32\) | −4.21064 | −0.744343 | ||||||||
\(33\) | −2.94583 | −0.512804 | ||||||||
\(34\) | −6.08584 | −1.04371 | ||||||||
\(35\) | 2.47152 | 0.417763 | ||||||||
\(36\) | −4.54771 | −0.757952 | ||||||||
\(37\) | −5.46020 | −0.897652 | −0.448826 | − | 0.893619i | \(-0.648158\pi\) | ||||
−0.448826 | + | 0.893619i | \(0.648158\pi\) | |||||||
\(38\) | −0.829521 | −0.134566 | ||||||||
\(39\) | −2.56497 | −0.410725 | ||||||||
\(40\) | 3.06707 | 0.484947 | ||||||||
\(41\) | −10.2168 | −1.59559 | −0.797796 | − | 0.602928i | \(-0.794001\pi\) | ||||
−0.797796 | + | 0.602928i | \(0.794001\pi\) | |||||||
\(42\) | 7.97247 | 1.23018 | ||||||||
\(43\) | −5.63905 | −0.859946 | −0.429973 | − | 0.902842i | \(-0.641477\pi\) | ||||
−0.429973 | + | 0.902842i | \(0.641477\pi\) | |||||||
\(44\) | −0.800943 | −0.120747 | ||||||||
\(45\) | 5.67794 | 0.846418 | ||||||||
\(46\) | 8.71520 | 1.28499 | ||||||||
\(47\) | 7.07320 | 1.03173 | 0.515866 | − | 0.856669i | \(-0.327470\pi\) | ||||
0.515866 | + | 0.856669i | \(0.327470\pi\) | |||||||
\(48\) | 5.17466 | 0.746899 | ||||||||
\(49\) | −0.891581 | −0.127369 | ||||||||
\(50\) | −1.09501 | −0.154858 | ||||||||
\(51\) | −16.3723 | −2.29258 | ||||||||
\(52\) | −0.697391 | −0.0967107 | ||||||||
\(53\) | −5.43075 | −0.745970 | −0.372985 | − | 0.927837i | \(-0.621666\pi\) | ||||
−0.372985 | + | 0.927837i | \(0.621666\pi\) | |||||||
\(54\) | 8.63833 | 1.17553 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 7.58034 | 1.01297 | ||||||||
\(57\) | −2.23160 | −0.295582 | ||||||||
\(58\) | 7.74663 | 1.01718 | ||||||||
\(59\) | 6.03850 | 0.786145 | 0.393073 | − | 0.919507i | \(-0.371412\pi\) | ||||
0.393073 | + | 0.919507i | \(0.371412\pi\) | |||||||
\(60\) | 2.35945 | 0.304603 | ||||||||
\(61\) | 3.86324 | 0.494637 | 0.247319 | − | 0.968934i | \(-0.420451\pi\) | ||||
0.247319 | + | 0.968934i | \(0.420451\pi\) | |||||||
\(62\) | −7.32391 | −0.930137 | ||||||||
\(63\) | 14.0332 | 1.76801 | ||||||||
\(64\) | 8.12392 | 1.01549 | ||||||||
\(65\) | 0.870712 | 0.107999 | ||||||||
\(66\) | 3.22573 | 0.397060 | ||||||||
\(67\) | 1.40262 | 0.171357 | 0.0856785 | − | 0.996323i | \(-0.472694\pi\) | ||||
0.0856785 | + | 0.996323i | \(0.472694\pi\) | |||||||
\(68\) | −4.45146 | −0.539819 | ||||||||
\(69\) | 23.4458 | 2.82255 | ||||||||
\(70\) | −2.70635 | −0.323471 | ||||||||
\(71\) | −12.8543 | −1.52552 | −0.762760 | − | 0.646682i | \(-0.776156\pi\) | ||||
−0.762760 | + | 0.646682i | \(0.776156\pi\) | |||||||
\(72\) | 17.4147 | 2.05234 | ||||||||
\(73\) | −1.00000 | −0.117041 | ||||||||
\(74\) | 5.97900 | 0.695045 | ||||||||
\(75\) | −2.94583 | −0.340156 | ||||||||
\(76\) | −0.606749 | −0.0695989 | ||||||||
\(77\) | 2.47152 | 0.281656 | ||||||||
\(78\) | 2.80868 | 0.318021 | ||||||||
\(79\) | −11.9602 | −1.34563 | −0.672814 | − | 0.739812i | \(-0.734914\pi\) | ||||
−0.672814 | + | 0.739812i | \(0.734914\pi\) | |||||||
\(80\) | −1.75660 | −0.196394 | ||||||||
\(81\) | 6.20521 | 0.689468 | ||||||||
\(82\) | 11.1875 | 1.23545 | ||||||||
\(83\) | 13.3277 | 1.46291 | 0.731455 | − | 0.681890i | \(-0.238842\pi\) | ||||
0.731455 | + | 0.681890i | \(0.238842\pi\) | |||||||
\(84\) | 5.83142 | 0.636260 | ||||||||
\(85\) | 5.55777 | 0.602825 | ||||||||
\(86\) | 6.17484 | 0.665850 | ||||||||
\(87\) | 20.8402 | 2.23430 | ||||||||
\(88\) | 3.06707 | 0.326951 | ||||||||
\(89\) | −15.7768 | −1.67234 | −0.836171 | − | 0.548469i | \(-0.815211\pi\) | ||||
−0.836171 | + | 0.548469i | \(0.815211\pi\) | |||||||
\(90\) | −6.21743 | −0.655375 | ||||||||
\(91\) | 2.15198 | 0.225589 | ||||||||
\(92\) | 6.37469 | 0.664607 | ||||||||
\(93\) | −19.7030 | −2.04310 | ||||||||
\(94\) | −7.74525 | −0.798862 | ||||||||
\(95\) | 0.757543 | 0.0777223 | ||||||||
\(96\) | 12.4039 | 1.26596 | ||||||||
\(97\) | 7.91533 | 0.803680 | 0.401840 | − | 0.915710i | \(-0.368371\pi\) | ||||
0.401840 | + | 0.915710i | \(0.368371\pi\) | |||||||
\(98\) | 0.976294 | 0.0986206 | ||||||||
\(99\) | 5.67794 | 0.570655 | ||||||||
\(100\) | −0.800943 | −0.0800943 | ||||||||
\(101\) | 2.19475 | 0.218385 | 0.109193 | − | 0.994021i | \(-0.465173\pi\) | ||||
0.109193 | + | 0.994021i | \(0.465173\pi\) | |||||||
\(102\) | 17.9279 | 1.77513 | ||||||||
\(103\) | −4.26799 | −0.420537 | −0.210269 | − | 0.977644i | \(-0.567434\pi\) | ||||
−0.210269 | + | 0.977644i | \(0.567434\pi\) | |||||||
\(104\) | 2.67054 | 0.261868 | ||||||||
\(105\) | −7.28069 | −0.710523 | ||||||||
\(106\) | 5.94675 | 0.577599 | ||||||||
\(107\) | 15.1153 | 1.46125 | 0.730624 | − | 0.682780i | \(-0.239229\pi\) | ||||
0.730624 | + | 0.682780i | \(0.239229\pi\) | |||||||
\(108\) | 6.31846 | 0.607995 | ||||||||
\(109\) | −12.6267 | −1.20942 | −0.604711 | − | 0.796445i | \(-0.706712\pi\) | ||||
−0.604711 | + | 0.796445i | \(0.706712\pi\) | |||||||
\(110\) | −1.09501 | −0.104406 | ||||||||
\(111\) | 16.0849 | 1.52671 | ||||||||
\(112\) | −4.34148 | −0.410232 | ||||||||
\(113\) | −7.20649 | −0.677929 | −0.338965 | − | 0.940799i | \(-0.610077\pi\) | ||||
−0.338965 | + | 0.940799i | \(0.610077\pi\) | |||||||
\(114\) | 2.44363 | 0.228867 | ||||||||
\(115\) | −7.95898 | −0.742179 | ||||||||
\(116\) | 5.66623 | 0.526097 | ||||||||
\(117\) | 4.94386 | 0.457060 | ||||||||
\(118\) | −6.61224 | −0.608706 | ||||||||
\(119\) | 13.7362 | 1.25919 | ||||||||
\(120\) | −9.03509 | −0.824787 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −4.23030 | −0.382994 | ||||||||
\(123\) | 30.0969 | 2.71375 | ||||||||
\(124\) | −5.35704 | −0.481076 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −15.3665 | −1.36896 | ||||||||
\(127\) | −4.51562 | −0.400696 | −0.200348 | − | 0.979725i | \(-0.564207\pi\) | ||||
−0.200348 | + | 0.979725i | \(0.564207\pi\) | |||||||
\(128\) | −0.474530 | −0.0419429 | ||||||||
\(129\) | 16.6117 | 1.46258 | ||||||||
\(130\) | −0.953443 | −0.0836225 | ||||||||
\(131\) | 1.88324 | 0.164540 | 0.0822698 | − | 0.996610i | \(-0.473783\pi\) | ||||
0.0822698 | + | 0.996610i | \(0.473783\pi\) | |||||||
\(132\) | 2.35945 | 0.205363 | ||||||||
\(133\) | 1.87229 | 0.162348 | ||||||||
\(134\) | −1.53589 | −0.132680 | ||||||||
\(135\) | −7.88878 | −0.678958 | ||||||||
\(136\) | 17.0461 | 1.46169 | ||||||||
\(137\) | −20.4924 | −1.75078 | −0.875392 | − | 0.483414i | \(-0.839397\pi\) | ||||
−0.875392 | + | 0.483414i | \(0.839397\pi\) | |||||||
\(138\) | −25.6735 | −2.18548 | ||||||||
\(139\) | 8.93621 | 0.757959 | 0.378980 | − | 0.925405i | \(-0.376275\pi\) | ||||
0.378980 | + | 0.925405i | \(0.376275\pi\) | |||||||
\(140\) | −1.97955 | −0.167302 | ||||||||
\(141\) | −20.8365 | −1.75475 | ||||||||
\(142\) | 14.0756 | 1.18120 | ||||||||
\(143\) | 0.870712 | 0.0728126 | ||||||||
\(144\) | −9.97390 | −0.831158 | ||||||||
\(145\) | −7.07445 | −0.587501 | ||||||||
\(146\) | 1.09501 | 0.0906240 | ||||||||
\(147\) | 2.62645 | 0.216626 | ||||||||
\(148\) | 4.37331 | 0.359484 | ||||||||
\(149\) | −1.90995 | −0.156470 | −0.0782348 | − | 0.996935i | \(-0.524928\pi\) | ||||
−0.0782348 | + | 0.996935i | \(0.524928\pi\) | |||||||
\(150\) | 3.22573 | 0.263380 | ||||||||
\(151\) | −18.6127 | −1.51468 | −0.757340 | − | 0.653021i | \(-0.773501\pi\) | ||||
−0.757340 | + | 0.653021i | \(0.773501\pi\) | |||||||
\(152\) | 2.32344 | 0.188456 | ||||||||
\(153\) | 31.5567 | 2.55121 | ||||||||
\(154\) | −2.70635 | −0.218084 | ||||||||
\(155\) | 6.68841 | 0.537226 | ||||||||
\(156\) | 2.05440 | 0.164484 | ||||||||
\(157\) | −1.00577 | −0.0802695 | −0.0401347 | − | 0.999194i | \(-0.512779\pi\) | ||||
−0.0401347 | + | 0.999194i | \(0.512779\pi\) | |||||||
\(158\) | 13.0966 | 1.04191 | ||||||||
\(159\) | 15.9981 | 1.26873 | ||||||||
\(160\) | −4.21064 | −0.332880 | ||||||||
\(161\) | −19.6708 | −1.55028 | ||||||||
\(162\) | −6.79480 | −0.533850 | ||||||||
\(163\) | 6.91444 | 0.541580 | 0.270790 | − | 0.962638i | \(-0.412715\pi\) | ||||
0.270790 | + | 0.962638i | \(0.412715\pi\) | |||||||
\(164\) | 8.18305 | 0.638989 | ||||||||
\(165\) | −2.94583 | −0.229333 | ||||||||
\(166\) | −14.5941 | −1.13272 | ||||||||
\(167\) | 12.2339 | 0.946685 | 0.473342 | − | 0.880879i | \(-0.343047\pi\) | ||||
0.473342 | + | 0.880879i | \(0.343047\pi\) | |||||||
\(168\) | −22.3304 | −1.72283 | ||||||||
\(169\) | −12.2419 | −0.941682 | ||||||||
\(170\) | −6.08584 | −0.466763 | ||||||||
\(171\) | 4.30129 | 0.328928 | ||||||||
\(172\) | 4.51655 | 0.344384 | ||||||||
\(173\) | 3.10000 | 0.235689 | 0.117844 | − | 0.993032i | \(-0.462402\pi\) | ||||
0.117844 | + | 0.993032i | \(0.462402\pi\) | |||||||
\(174\) | −22.8203 | −1.73000 | ||||||||
\(175\) | 2.47152 | 0.186829 | ||||||||
\(176\) | −1.75660 | −0.132409 | ||||||||
\(177\) | −17.7884 | −1.33706 | ||||||||
\(178\) | 17.2759 | 1.29488 | ||||||||
\(179\) | −5.92443 | −0.442813 | −0.221406 | − | 0.975182i | \(-0.571065\pi\) | ||||
−0.221406 | + | 0.975182i | \(0.571065\pi\) | |||||||
\(180\) | −4.54771 | −0.338966 | ||||||||
\(181\) | −9.28992 | −0.690514 | −0.345257 | − | 0.938508i | \(-0.612208\pi\) | ||||
−0.345257 | + | 0.938508i | \(0.612208\pi\) | |||||||
\(182\) | −2.35645 | −0.174672 | ||||||||
\(183\) | −11.3805 | −0.841268 | ||||||||
\(184\) | −24.4108 | −1.79959 | ||||||||
\(185\) | −5.46020 | −0.401442 | ||||||||
\(186\) | 21.5750 | 1.58196 | ||||||||
\(187\) | 5.55777 | 0.406425 | ||||||||
\(188\) | −5.66523 | −0.413179 | ||||||||
\(189\) | −19.4973 | −1.41822 | ||||||||
\(190\) | −0.829521 | −0.0601798 | ||||||||
\(191\) | 12.0638 | 0.872908 | 0.436454 | − | 0.899727i | \(-0.356234\pi\) | ||||
0.436454 | + | 0.899727i | \(0.356234\pi\) | |||||||
\(192\) | −23.9317 | −1.72712 | ||||||||
\(193\) | 10.2839 | 0.740248 | 0.370124 | − | 0.928982i | \(-0.379315\pi\) | ||||
0.370124 | + | 0.928982i | \(0.379315\pi\) | |||||||
\(194\) | −8.66740 | −0.622283 | ||||||||
\(195\) | −2.56497 | −0.183682 | ||||||||
\(196\) | 0.714105 | 0.0510075 | ||||||||
\(197\) | 6.06425 | 0.432060 | 0.216030 | − | 0.976387i | \(-0.430689\pi\) | ||||
0.216030 | + | 0.976387i | \(0.430689\pi\) | |||||||
\(198\) | −6.21743 | −0.441854 | ||||||||
\(199\) | −11.5157 | −0.816327 | −0.408164 | − | 0.912909i | \(-0.633831\pi\) | ||||
−0.408164 | + | 0.912909i | \(0.633831\pi\) | |||||||
\(200\) | 3.06707 | 0.216875 | ||||||||
\(201\) | −4.13188 | −0.291440 | ||||||||
\(202\) | −2.40328 | −0.169094 | ||||||||
\(203\) | −17.4847 | −1.22718 | ||||||||
\(204\) | 13.1133 | 0.918113 | ||||||||
\(205\) | −10.2168 | −0.713570 | ||||||||
\(206\) | 4.67351 | 0.325619 | ||||||||
\(207\) | −45.1906 | −3.14097 | ||||||||
\(208\) | −1.52950 | −0.106052 | ||||||||
\(209\) | 0.757543 | 0.0524004 | ||||||||
\(210\) | 7.97247 | 0.550152 | ||||||||
\(211\) | −7.92338 | −0.545468 | −0.272734 | − | 0.962089i | \(-0.587928\pi\) | ||||
−0.272734 | + | 0.962089i | \(0.587928\pi\) | |||||||
\(212\) | 4.34972 | 0.298740 | ||||||||
\(213\) | 37.8665 | 2.59457 | ||||||||
\(214\) | −16.5514 | −1.13143 | ||||||||
\(215\) | −5.63905 | −0.384580 | ||||||||
\(216\) | −24.1955 | −1.64629 | ||||||||
\(217\) | 16.5306 | 1.12217 | ||||||||
\(218\) | 13.8265 | 0.936447 | ||||||||
\(219\) | 2.94583 | 0.199061 | ||||||||
\(220\) | −0.800943 | −0.0539996 | ||||||||
\(221\) | 4.83922 | 0.325521 | ||||||||
\(222\) | −17.6132 | −1.18212 | ||||||||
\(223\) | 9.00137 | 0.602776 | 0.301388 | − | 0.953502i | \(-0.402550\pi\) | ||||
0.301388 | + | 0.953502i | \(0.402550\pi\) | |||||||
\(224\) | −10.4067 | −0.695326 | ||||||||
\(225\) | 5.67794 | 0.378530 | ||||||||
\(226\) | 7.89121 | 0.524915 | ||||||||
\(227\) | 1.98190 | 0.131544 | 0.0657718 | − | 0.997835i | \(-0.479049\pi\) | ||||
0.0657718 | + | 0.997835i | \(0.479049\pi\) | |||||||
\(228\) | 1.78738 | 0.118372 | ||||||||
\(229\) | 14.2877 | 0.944160 | 0.472080 | − | 0.881556i | \(-0.343503\pi\) | ||||
0.472080 | + | 0.881556i | \(0.343503\pi\) | |||||||
\(230\) | 8.71520 | 0.574663 | ||||||||
\(231\) | −7.28069 | −0.479035 | ||||||||
\(232\) | −21.6979 | −1.42453 | ||||||||
\(233\) | −12.9620 | −0.849168 | −0.424584 | − | 0.905388i | \(-0.639580\pi\) | ||||
−0.424584 | + | 0.905388i | \(0.639580\pi\) | |||||||
\(234\) | −5.41359 | −0.353898 | ||||||||
\(235\) | 7.07320 | 0.461404 | ||||||||
\(236\) | −4.83649 | −0.314829 | ||||||||
\(237\) | 35.2328 | 2.28861 | ||||||||
\(238\) | −15.0413 | −0.974982 | ||||||||
\(239\) | 15.7979 | 1.02188 | 0.510942 | − | 0.859615i | \(-0.329297\pi\) | ||||
0.510942 | + | 0.859615i | \(0.329297\pi\) | |||||||
\(240\) | 5.17466 | 0.334023 | ||||||||
\(241\) | −17.6872 | −1.13933 | −0.569665 | − | 0.821877i | \(-0.692927\pi\) | ||||
−0.569665 | + | 0.821877i | \(0.692927\pi\) | |||||||
\(242\) | −1.09501 | −0.0703902 | ||||||||
\(243\) | 5.38680 | 0.345564 | ||||||||
\(244\) | −3.09424 | −0.198088 | ||||||||
\(245\) | −0.891581 | −0.0569610 | ||||||||
\(246\) | −32.9566 | −2.10123 | ||||||||
\(247\) | 0.659602 | 0.0419695 | ||||||||
\(248\) | 20.5139 | 1.30263 | ||||||||
\(249\) | −39.2613 | −2.48808 | ||||||||
\(250\) | −1.09501 | −0.0692548 | ||||||||
\(251\) | −12.5130 | −0.789815 | −0.394907 | − | 0.918721i | \(-0.629223\pi\) | ||||
−0.394907 | + | 0.918721i | \(0.629223\pi\) | |||||||
\(252\) | −11.2398 | −0.708039 | ||||||||
\(253\) | −7.95898 | −0.500377 | ||||||||
\(254\) | 4.94467 | 0.310256 | ||||||||
\(255\) | −16.3723 | −1.02527 | ||||||||
\(256\) | −15.7282 | −0.983014 | ||||||||
\(257\) | −3.00200 | −0.187260 | −0.0936299 | − | 0.995607i | \(-0.529847\pi\) | ||||
−0.0936299 | + | 0.995607i | \(0.529847\pi\) | |||||||
\(258\) | −18.1900 | −1.13246 | ||||||||
\(259\) | −13.4950 | −0.838539 | ||||||||
\(260\) | −0.697391 | −0.0432504 | ||||||||
\(261\) | −40.1683 | −2.48636 | ||||||||
\(262\) | −2.06218 | −0.127402 | ||||||||
\(263\) | −30.8707 | −1.90357 | −0.951784 | − | 0.306767i | \(-0.900753\pi\) | ||||
−0.951784 | + | 0.306767i | \(0.900753\pi\) | |||||||
\(264\) | −9.03509 | −0.556071 | ||||||||
\(265\) | −5.43075 | −0.333608 | ||||||||
\(266\) | −2.05018 | −0.125705 | ||||||||
\(267\) | 46.4760 | 2.84428 | ||||||||
\(268\) | −1.12342 | −0.0686236 | ||||||||
\(269\) | −19.9040 | −1.21357 | −0.606786 | − | 0.794866i | \(-0.707541\pi\) | ||||
−0.606786 | + | 0.794866i | \(0.707541\pi\) | |||||||
\(270\) | 8.63833 | 0.525712 | ||||||||
\(271\) | 8.34396 | 0.506860 | 0.253430 | − | 0.967354i | \(-0.418441\pi\) | ||||
0.253430 | + | 0.967354i | \(0.418441\pi\) | |||||||
\(272\) | −9.76281 | −0.591957 | ||||||||
\(273\) | −6.33939 | −0.383677 | ||||||||
\(274\) | 22.4395 | 1.35562 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −18.7788 | −1.13035 | ||||||||
\(277\) | 14.3377 | 0.861471 | 0.430735 | − | 0.902478i | \(-0.358254\pi\) | ||||
0.430735 | + | 0.902478i | \(0.358254\pi\) | |||||||
\(278\) | −9.78528 | −0.586882 | ||||||||
\(279\) | 37.9764 | 2.27359 | ||||||||
\(280\) | 7.58034 | 0.453012 | ||||||||
\(281\) | 6.41640 | 0.382770 | 0.191385 | − | 0.981515i | \(-0.438702\pi\) | ||||
0.191385 | + | 0.981515i | \(0.438702\pi\) | |||||||
\(282\) | 22.8162 | 1.35869 | ||||||||
\(283\) | 9.77983 | 0.581351 | 0.290675 | − | 0.956822i | \(-0.406120\pi\) | ||||
0.290675 | + | 0.956822i | \(0.406120\pi\) | |||||||
\(284\) | 10.2955 | 0.610927 | ||||||||
\(285\) | −2.23160 | −0.132188 | ||||||||
\(286\) | −0.953443 | −0.0563782 | ||||||||
\(287\) | −25.2510 | −1.49052 | ||||||||
\(288\) | −23.9078 | −1.40878 | ||||||||
\(289\) | 13.8889 | 0.816992 | ||||||||
\(290\) | 7.74663 | 0.454898 | ||||||||
\(291\) | −23.3172 | −1.36688 | ||||||||
\(292\) | 0.800943 | 0.0468717 | ||||||||
\(293\) | 0.807120 | 0.0471524 | 0.0235762 | − | 0.999722i | \(-0.492495\pi\) | ||||
0.0235762 | + | 0.999722i | \(0.492495\pi\) | |||||||
\(294\) | −2.87600 | −0.167732 | ||||||||
\(295\) | 6.03850 | 0.351575 | ||||||||
\(296\) | −16.7468 | −0.973390 | ||||||||
\(297\) | −7.88878 | −0.457753 | ||||||||
\(298\) | 2.09143 | 0.121153 | ||||||||
\(299\) | −6.92998 | −0.400771 | ||||||||
\(300\) | 2.35945 | 0.136223 | ||||||||
\(301\) | −13.9370 | −0.803317 | ||||||||
\(302\) | 20.3812 | 1.17280 | ||||||||
\(303\) | −6.46536 | −0.371425 | ||||||||
\(304\) | −1.33070 | −0.0763211 | ||||||||
\(305\) | 3.86324 | 0.221208 | ||||||||
\(306\) | −34.5551 | −1.97538 | ||||||||
\(307\) | −19.8361 | −1.13211 | −0.566054 | − | 0.824368i | \(-0.691531\pi\) | ||||
−0.566054 | + | 0.824368i | \(0.691531\pi\) | |||||||
\(308\) | −1.97955 | −0.112795 | ||||||||
\(309\) | 12.5728 | 0.715241 | ||||||||
\(310\) | −7.32391 | −0.415970 | ||||||||
\(311\) | −21.9230 | −1.24314 | −0.621571 | − | 0.783358i | \(-0.713505\pi\) | ||||
−0.621571 | + | 0.783358i | \(0.713505\pi\) | |||||||
\(312\) | −7.86697 | −0.445379 | ||||||||
\(313\) | −9.06793 | −0.512550 | −0.256275 | − | 0.966604i | \(-0.582495\pi\) | ||||
−0.256275 | + | 0.966604i | \(0.582495\pi\) | |||||||
\(314\) | 1.10134 | 0.0621520 | ||||||||
\(315\) | 14.0332 | 0.790679 | ||||||||
\(316\) | 9.57944 | 0.538885 | ||||||||
\(317\) | −8.58224 | −0.482027 | −0.241013 | − | 0.970522i | \(-0.577480\pi\) | ||||
−0.241013 | + | 0.970522i | \(0.577480\pi\) | |||||||
\(318\) | −17.5181 | −0.982368 | ||||||||
\(319\) | −7.07445 | −0.396093 | ||||||||
\(320\) | 8.12392 | 0.454141 | ||||||||
\(321\) | −44.5271 | −2.48526 | ||||||||
\(322\) | 21.5398 | 1.20037 | ||||||||
\(323\) | 4.21026 | 0.234265 | ||||||||
\(324\) | −4.97002 | −0.276112 | ||||||||
\(325\) | 0.870712 | 0.0482984 | ||||||||
\(326\) | −7.57141 | −0.419342 | ||||||||
\(327\) | 37.1963 | 2.05696 | ||||||||
\(328\) | −31.3356 | −1.73022 | ||||||||
\(329\) | 17.4816 | 0.963790 | ||||||||
\(330\) | 3.22573 | 0.177571 | ||||||||
\(331\) | −18.5141 | −1.01762 | −0.508812 | − | 0.860878i | \(-0.669915\pi\) | ||||
−0.508812 | + | 0.860878i | \(0.669915\pi\) | |||||||
\(332\) | −10.6748 | −0.585854 | ||||||||
\(333\) | −31.0027 | −1.69894 | ||||||||
\(334\) | −13.3963 | −0.733011 | ||||||||
\(335\) | 1.40262 | 0.0766332 | ||||||||
\(336\) | 12.7893 | 0.697713 | ||||||||
\(337\) | 34.1933 | 1.86263 | 0.931315 | − | 0.364216i | \(-0.118663\pi\) | ||||
0.931315 | + | 0.364216i | \(0.118663\pi\) | |||||||
\(338\) | 13.4050 | 0.729137 | ||||||||
\(339\) | 21.2291 | 1.15301 | ||||||||
\(340\) | −4.45146 | −0.241414 | ||||||||
\(341\) | 6.68841 | 0.362198 | ||||||||
\(342\) | −4.70997 | −0.254686 | ||||||||
\(343\) | −19.5042 | −1.05313 | ||||||||
\(344\) | −17.2954 | −0.932504 | ||||||||
\(345\) | 23.4458 | 1.26228 | ||||||||
\(346\) | −3.39454 | −0.182492 | ||||||||
\(347\) | −0.224774 | −0.0120665 | −0.00603325 | − | 0.999982i | \(-0.501920\pi\) | ||||
−0.00603325 | + | 0.999982i | \(0.501920\pi\) | |||||||
\(348\) | −16.6918 | −0.894774 | ||||||||
\(349\) | −4.33673 | −0.232140 | −0.116070 | − | 0.993241i | \(-0.537030\pi\) | ||||
−0.116070 | + | 0.993241i | \(0.537030\pi\) | |||||||
\(350\) | −2.70635 | −0.144661 | ||||||||
\(351\) | −6.86886 | −0.366633 | ||||||||
\(352\) | −4.21064 | −0.224428 | ||||||||
\(353\) | −26.8758 | −1.43045 | −0.715227 | − | 0.698892i | \(-0.753677\pi\) | ||||
−0.715227 | + | 0.698892i | \(0.753677\pi\) | |||||||
\(354\) | 19.4786 | 1.03527 | ||||||||
\(355\) | −12.8543 | −0.682233 | ||||||||
\(356\) | 12.6363 | 0.669725 | ||||||||
\(357\) | −40.4645 | −2.14161 | ||||||||
\(358\) | 6.48734 | 0.342866 | ||||||||
\(359\) | −0.0594923 | −0.00313988 | −0.00156994 | − | 0.999999i | \(-0.500500\pi\) | ||||
−0.00156994 | + | 0.999999i | \(0.500500\pi\) | |||||||
\(360\) | 17.4147 | 0.917834 | ||||||||
\(361\) | −18.4261 | −0.969796 | ||||||||
\(362\) | 10.1726 | 0.534660 | ||||||||
\(363\) | −2.94583 | −0.154616 | ||||||||
\(364\) | −1.72362 | −0.0903421 | ||||||||
\(365\) | −1.00000 | −0.0523424 | ||||||||
\(366\) | 12.4618 | 0.651387 | ||||||||
\(367\) | 16.0978 | 0.840298 | 0.420149 | − | 0.907455i | \(-0.361978\pi\) | ||||
0.420149 | + | 0.907455i | \(0.361978\pi\) | |||||||
\(368\) | 13.9808 | 0.728798 | ||||||||
\(369\) | −58.0102 | −3.01989 | ||||||||
\(370\) | 5.97900 | 0.310833 | ||||||||
\(371\) | −13.4222 | −0.696846 | ||||||||
\(372\) | 15.7810 | 0.818204 | ||||||||
\(373\) | 27.9783 | 1.44866 | 0.724331 | − | 0.689452i | \(-0.242149\pi\) | ||||
0.724331 | + | 0.689452i | \(0.242149\pi\) | |||||||
\(374\) | −6.08584 | −0.314692 | ||||||||
\(375\) | −2.94583 | −0.152122 | ||||||||
\(376\) | 21.6940 | 1.11878 | ||||||||
\(377\) | −6.15981 | −0.317246 | ||||||||
\(378\) | 21.3498 | 1.09812 | ||||||||
\(379\) | 32.4329 | 1.66597 | 0.832983 | − | 0.553298i | \(-0.186631\pi\) | ||||
0.832983 | + | 0.553298i | \(0.186631\pi\) | |||||||
\(380\) | −0.606749 | −0.0311256 | ||||||||
\(381\) | 13.3023 | 0.681495 | ||||||||
\(382\) | −13.2101 | −0.675886 | ||||||||
\(383\) | −27.2576 | −1.39280 | −0.696400 | − | 0.717654i | \(-0.745216\pi\) | ||||
−0.696400 | + | 0.717654i | \(0.745216\pi\) | |||||||
\(384\) | 1.39789 | 0.0713356 | ||||||||
\(385\) | 2.47152 | 0.125960 | ||||||||
\(386\) | −11.2610 | −0.573168 | ||||||||
\(387\) | −32.0182 | −1.62758 | ||||||||
\(388\) | −6.33973 | −0.321851 | ||||||||
\(389\) | −37.2600 | −1.88916 | −0.944578 | − | 0.328288i | \(-0.893528\pi\) | ||||
−0.944578 | + | 0.328288i | \(0.893528\pi\) | |||||||
\(390\) | 2.80868 | 0.142223 | ||||||||
\(391\) | −44.2342 | −2.23702 | ||||||||
\(392\) | −2.73454 | −0.138115 | ||||||||
\(393\) | −5.54772 | −0.279846 | ||||||||
\(394\) | −6.64045 | −0.334541 | ||||||||
\(395\) | −11.9602 | −0.601783 | ||||||||
\(396\) | −4.54771 | −0.228531 | ||||||||
\(397\) | 24.5578 | 1.23252 | 0.616259 | − | 0.787543i | \(-0.288647\pi\) | ||||
0.616259 | + | 0.787543i | \(0.288647\pi\) | |||||||
\(398\) | 12.6099 | 0.632076 | ||||||||
\(399\) | −5.51544 | −0.276118 | ||||||||
\(400\) | −1.75660 | −0.0878302 | ||||||||
\(401\) | −13.0718 | −0.652775 | −0.326388 | − | 0.945236i | \(-0.605831\pi\) | ||||
−0.326388 | + | 0.945236i | \(0.605831\pi\) | |||||||
\(402\) | 4.52447 | 0.225660 | ||||||||
\(403\) | 5.82368 | 0.290098 | ||||||||
\(404\) | −1.75787 | −0.0874572 | ||||||||
\(405\) | 6.20521 | 0.308340 | ||||||||
\(406\) | 19.1460 | 0.950198 | ||||||||
\(407\) | −5.46020 | −0.270652 | ||||||||
\(408\) | −50.2150 | −2.48601 | ||||||||
\(409\) | 13.2276 | 0.654063 | 0.327031 | − | 0.945014i | \(-0.393952\pi\) | ||||
0.327031 | + | 0.945014i | \(0.393952\pi\) | |||||||
\(410\) | 11.1875 | 0.552512 | ||||||||
\(411\) | 60.3672 | 2.97770 | ||||||||
\(412\) | 3.41842 | 0.168413 | ||||||||
\(413\) | 14.9243 | 0.734376 | ||||||||
\(414\) | 49.4844 | 2.43203 | ||||||||
\(415\) | 13.3277 | 0.654233 | ||||||||
\(416\) | −3.66626 | −0.179753 | ||||||||
\(417\) | −26.3246 | −1.28912 | ||||||||
\(418\) | −0.829521 | −0.0405732 | ||||||||
\(419\) | 25.4228 | 1.24199 | 0.620993 | − | 0.783816i | \(-0.286729\pi\) | ||||
0.620993 | + | 0.783816i | \(0.286729\pi\) | |||||||
\(420\) | 5.83142 | 0.284544 | ||||||||
\(421\) | −14.2837 | −0.696144 | −0.348072 | − | 0.937468i | \(-0.613163\pi\) | ||||
−0.348072 | + | 0.937468i | \(0.613163\pi\) | |||||||
\(422\) | 8.67622 | 0.422352 | ||||||||
\(423\) | 40.1612 | 1.95270 | ||||||||
\(424\) | −16.6565 | −0.808911 | ||||||||
\(425\) | 5.55777 | 0.269592 | ||||||||
\(426\) | −41.4644 | −2.00896 | ||||||||
\(427\) | 9.54808 | 0.462064 | ||||||||
\(428\) | −12.1065 | −0.585189 | ||||||||
\(429\) | −2.56497 | −0.123838 | ||||||||
\(430\) | 6.17484 | 0.297777 | ||||||||
\(431\) | −4.69541 | −0.226170 | −0.113085 | − | 0.993585i | \(-0.536073\pi\) | ||||
−0.113085 | + | 0.993585i | \(0.536073\pi\) | |||||||
\(432\) | 13.8575 | 0.666717 | ||||||||
\(433\) | 26.9266 | 1.29401 | 0.647005 | − | 0.762486i | \(-0.276021\pi\) | ||||
0.647005 | + | 0.762486i | \(0.276021\pi\) | |||||||
\(434\) | −18.1012 | −0.868885 | ||||||||
\(435\) | 20.8402 | 0.999209 | ||||||||
\(436\) | 10.1133 | 0.484339 | ||||||||
\(437\) | −6.02927 | −0.288419 | ||||||||
\(438\) | −3.22573 | −0.154131 | ||||||||
\(439\) | −24.6259 | −1.17533 | −0.587664 | − | 0.809105i | \(-0.699952\pi\) | ||||
−0.587664 | + | 0.809105i | \(0.699952\pi\) | |||||||
\(440\) | 3.06707 | 0.146217 | ||||||||
\(441\) | −5.06235 | −0.241064 | ||||||||
\(442\) | −5.29902 | −0.252049 | ||||||||
\(443\) | 26.0494 | 1.23765 | 0.618823 | − | 0.785530i | \(-0.287610\pi\) | ||||
0.618823 | + | 0.785530i | \(0.287610\pi\) | |||||||
\(444\) | −12.8831 | −0.611403 | ||||||||
\(445\) | −15.7768 | −0.747894 | ||||||||
\(446\) | −9.85663 | −0.466725 | ||||||||
\(447\) | 5.62641 | 0.266120 | ||||||||
\(448\) | 20.0784 | 0.948617 | ||||||||
\(449\) | −12.9213 | −0.609795 | −0.304897 | − | 0.952385i | \(-0.598622\pi\) | ||||
−0.304897 | + | 0.952385i | \(0.598622\pi\) | |||||||
\(450\) | −6.21743 | −0.293093 | ||||||||
\(451\) | −10.2168 | −0.481089 | ||||||||
\(452\) | 5.77199 | 0.271491 | ||||||||
\(453\) | 54.8299 | 2.57613 | ||||||||
\(454\) | −2.17021 | −0.101853 | ||||||||
\(455\) | 2.15198 | 0.100887 | ||||||||
\(456\) | −6.84448 | −0.320522 | ||||||||
\(457\) | −37.2398 | −1.74200 | −0.871002 | − | 0.491279i | \(-0.836529\pi\) | ||||
−0.871002 | + | 0.491279i | \(0.836529\pi\) | |||||||
\(458\) | −15.6453 | −0.731056 | ||||||||
\(459\) | −43.8441 | −2.04647 | ||||||||
\(460\) | 6.37469 | 0.297221 | ||||||||
\(461\) | 23.9723 | 1.11650 | 0.558251 | − | 0.829672i | \(-0.311473\pi\) | ||||
0.558251 | + | 0.829672i | \(0.311473\pi\) | |||||||
\(462\) | 7.97247 | 0.370913 | ||||||||
\(463\) | 0.494605 | 0.0229863 | 0.0114931 | − | 0.999934i | \(-0.496342\pi\) | ||||
0.0114931 | + | 0.999934i | \(0.496342\pi\) | |||||||
\(464\) | 12.4270 | 0.576909 | ||||||||
\(465\) | −19.7030 | −0.913703 | ||||||||
\(466\) | 14.1936 | 0.657504 | ||||||||
\(467\) | 10.7787 | 0.498777 | 0.249389 | − | 0.968404i | \(-0.419770\pi\) | ||||
0.249389 | + | 0.968404i | \(0.419770\pi\) | |||||||
\(468\) | −3.95975 | −0.183039 | ||||||||
\(469\) | 3.46660 | 0.160073 | ||||||||
\(470\) | −7.74525 | −0.357262 | ||||||||
\(471\) | 2.96284 | 0.136521 | ||||||||
\(472\) | 18.5205 | 0.852476 | ||||||||
\(473\) | −5.63905 | −0.259284 | ||||||||
\(474\) | −38.5804 | −1.77206 | ||||||||
\(475\) | 0.757543 | 0.0347585 | ||||||||
\(476\) | −11.0019 | −0.504271 | ||||||||
\(477\) | −30.8355 | −1.41186 | ||||||||
\(478\) | −17.2990 | −0.791237 | ||||||||
\(479\) | 15.3091 | 0.699490 | 0.349745 | − | 0.936845i | \(-0.386268\pi\) | ||||
0.349745 | + | 0.936845i | \(0.386268\pi\) | |||||||
\(480\) | 12.4039 | 0.566156 | ||||||||
\(481\) | −4.75427 | −0.216776 | ||||||||
\(482\) | 19.3677 | 0.882175 | ||||||||
\(483\) | 57.9469 | 2.63668 | ||||||||
\(484\) | −0.800943 | −0.0364065 | ||||||||
\(485\) | 7.91533 | 0.359417 | ||||||||
\(486\) | −5.89863 | −0.267567 | ||||||||
\(487\) | 35.3315 | 1.60102 | 0.800512 | − | 0.599317i | \(-0.204561\pi\) | ||||
0.800512 | + | 0.599317i | \(0.204561\pi\) | |||||||
\(488\) | 11.8488 | 0.536372 | ||||||||
\(489\) | −20.3688 | −0.921109 | ||||||||
\(490\) | 0.976294 | 0.0441045 | ||||||||
\(491\) | −1.24511 | −0.0561909 | −0.0280955 | − | 0.999605i | \(-0.508944\pi\) | ||||
−0.0280955 | + | 0.999605i | \(0.508944\pi\) | |||||||
\(492\) | −24.1059 | −1.08678 | ||||||||
\(493\) | −39.3182 | −1.77080 | ||||||||
\(494\) | −0.722274 | −0.0324967 | ||||||||
\(495\) | 5.67794 | 0.255205 | ||||||||
\(496\) | −11.7489 | −0.527541 | ||||||||
\(497\) | −31.7696 | −1.42506 | ||||||||
\(498\) | 42.9917 | 1.92650 | ||||||||
\(499\) | 37.9293 | 1.69795 | 0.848974 | − | 0.528434i | \(-0.177221\pi\) | ||||
0.848974 | + | 0.528434i | \(0.177221\pi\) | |||||||
\(500\) | −0.800943 | −0.0358193 | ||||||||
\(501\) | −36.0389 | −1.61010 | ||||||||
\(502\) | 13.7019 | 0.611547 | ||||||||
\(503\) | 27.9846 | 1.24777 | 0.623885 | − | 0.781516i | \(-0.285553\pi\) | ||||
0.623885 | + | 0.781516i | \(0.285553\pi\) | |||||||
\(504\) | 43.0407 | 1.91719 | ||||||||
\(505\) | 2.19475 | 0.0976649 | ||||||||
\(506\) | 8.71520 | 0.387438 | ||||||||
\(507\) | 36.0625 | 1.60159 | ||||||||
\(508\) | 3.61675 | 0.160467 | ||||||||
\(509\) | 0.0577389 | 0.00255923 | 0.00127962 | − | 0.999999i | \(-0.499593\pi\) | ||||
0.00127962 | + | 0.999999i | \(0.499593\pi\) | |||||||
\(510\) | 17.9279 | 0.793860 | ||||||||
\(511\) | −2.47152 | −0.109334 | ||||||||
\(512\) | 18.1717 | 0.803083 | ||||||||
\(513\) | −5.97609 | −0.263851 | ||||||||
\(514\) | 3.28724 | 0.144994 | ||||||||
\(515\) | −4.26799 | −0.188070 | ||||||||
\(516\) | −13.3050 | −0.585721 | ||||||||
\(517\) | 7.07320 | 0.311079 | ||||||||
\(518\) | 14.7772 | 0.649274 | ||||||||
\(519\) | −9.13209 | −0.400854 | ||||||||
\(520\) | 2.67054 | 0.117111 | ||||||||
\(521\) | −14.8885 | −0.652275 | −0.326138 | − | 0.945322i | \(-0.605747\pi\) | ||||
−0.326138 | + | 0.945322i | \(0.605747\pi\) | |||||||
\(522\) | 43.9849 | 1.92517 | ||||||||
\(523\) | 18.5362 | 0.810533 | 0.405266 | − | 0.914199i | \(-0.367179\pi\) | ||||
0.405266 | + | 0.914199i | \(0.367179\pi\) | |||||||
\(524\) | −1.50837 | −0.0658935 | ||||||||
\(525\) | −7.28069 | −0.317756 | ||||||||
\(526\) | 33.8039 | 1.47392 | ||||||||
\(527\) | 37.1727 | 1.61927 | ||||||||
\(528\) | 5.17466 | 0.225198 | ||||||||
\(529\) | 40.3454 | 1.75415 | ||||||||
\(530\) | 5.94675 | 0.258310 | ||||||||
\(531\) | 34.2862 | 1.48790 | ||||||||
\(532\) | −1.49959 | −0.0650156 | ||||||||
\(533\) | −8.89587 | −0.385323 | ||||||||
\(534\) | −50.8918 | −2.20231 | ||||||||
\(535\) | 15.1153 | 0.653490 | ||||||||
\(536\) | 4.30193 | 0.185815 | ||||||||
\(537\) | 17.4524 | 0.753127 | ||||||||
\(538\) | 21.7952 | 0.939659 | ||||||||
\(539\) | −0.891581 | −0.0384031 | ||||||||
\(540\) | 6.31846 | 0.271903 | ||||||||
\(541\) | 2.55332 | 0.109776 | 0.0548878 | − | 0.998493i | \(-0.482520\pi\) | ||||
0.0548878 | + | 0.998493i | \(0.482520\pi\) | |||||||
\(542\) | −9.13676 | −0.392457 | ||||||||
\(543\) | 27.3666 | 1.17441 | ||||||||
\(544\) | −23.4018 | −1.00334 | ||||||||
\(545\) | −12.6267 | −0.540870 | ||||||||
\(546\) | 6.94173 | 0.297078 | ||||||||
\(547\) | −38.4112 | −1.64234 | −0.821172 | − | 0.570680i | \(-0.806680\pi\) | ||||
−0.821172 | + | 0.570680i | \(0.806680\pi\) | |||||||
\(548\) | 16.4132 | 0.701139 | ||||||||
\(549\) | 21.9353 | 0.936174 | ||||||||
\(550\) | −1.09501 | −0.0466916 | ||||||||
\(551\) | −5.35920 | −0.228310 | ||||||||
\(552\) | 71.9101 | 3.06070 | ||||||||
\(553\) | −29.5599 | −1.25701 | ||||||||
\(554\) | −15.7000 | −0.667030 | ||||||||
\(555\) | 16.0849 | 0.682764 | ||||||||
\(556\) | −7.15739 | −0.303541 | ||||||||
\(557\) | 6.71479 | 0.284515 | 0.142257 | − | 0.989830i | \(-0.454564\pi\) | ||||
0.142257 | + | 0.989830i | \(0.454564\pi\) | |||||||
\(558\) | −41.5847 | −1.76042 | ||||||||
\(559\) | −4.90999 | −0.207670 | ||||||||
\(560\) | −4.34148 | −0.183461 | ||||||||
\(561\) | −16.3723 | −0.691239 | ||||||||
\(562\) | −7.02605 | −0.296376 | ||||||||
\(563\) | 7.27771 | 0.306719 | 0.153360 | − | 0.988170i | \(-0.450991\pi\) | ||||
0.153360 | + | 0.988170i | \(0.450991\pi\) | |||||||
\(564\) | 16.6888 | 0.702726 | ||||||||
\(565\) | −7.20649 | −0.303179 | ||||||||
\(566\) | −10.7091 | −0.450135 | ||||||||
\(567\) | 15.3363 | 0.644065 | ||||||||
\(568\) | −39.4249 | −1.65423 | ||||||||
\(569\) | 30.3294 | 1.27147 | 0.635736 | − | 0.771906i | \(-0.280697\pi\) | ||||
0.635736 | + | 0.771906i | \(0.280697\pi\) | |||||||
\(570\) | 2.44363 | 0.102352 | ||||||||
\(571\) | −4.43487 | −0.185593 | −0.0927967 | − | 0.995685i | \(-0.529581\pi\) | ||||
−0.0927967 | + | 0.995685i | \(0.529581\pi\) | |||||||
\(572\) | −0.697391 | −0.0291594 | ||||||||
\(573\) | −35.5380 | −1.48462 | ||||||||
\(574\) | 27.6502 | 1.15410 | ||||||||
\(575\) | −7.95898 | −0.331912 | ||||||||
\(576\) | 46.1272 | 1.92196 | ||||||||
\(577\) | −24.8176 | −1.03317 | −0.516586 | − | 0.856235i | \(-0.672797\pi\) | ||||
−0.516586 | + | 0.856235i | \(0.672797\pi\) | |||||||
\(578\) | −15.2085 | −0.632590 | ||||||||
\(579\) | −30.2945 | −1.25900 | ||||||||
\(580\) | 5.66623 | 0.235278 | ||||||||
\(581\) | 32.9398 | 1.36657 | ||||||||
\(582\) | 25.5327 | 1.05837 | ||||||||
\(583\) | −5.43075 | −0.224919 | ||||||||
\(584\) | −3.06707 | −0.126916 | ||||||||
\(585\) | 4.94386 | 0.204403 | ||||||||
\(586\) | −0.883808 | −0.0365098 | ||||||||
\(587\) | −9.03596 | −0.372954 | −0.186477 | − | 0.982459i | \(-0.559707\pi\) | ||||
−0.186477 | + | 0.982459i | \(0.559707\pi\) | |||||||
\(588\) | −2.10364 | −0.0867525 | ||||||||
\(589\) | 5.06676 | 0.208772 | ||||||||
\(590\) | −6.61224 | −0.272222 | ||||||||
\(591\) | −17.8643 | −0.734839 | ||||||||
\(592\) | 9.59141 | 0.394205 | ||||||||
\(593\) | −30.8139 | −1.26538 | −0.632688 | − | 0.774407i | \(-0.718048\pi\) | ||||
−0.632688 | + | 0.774407i | \(0.718048\pi\) | |||||||
\(594\) | 8.63833 | 0.354435 | ||||||||
\(595\) | 13.7362 | 0.563128 | ||||||||
\(596\) | 1.52977 | 0.0626616 | ||||||||
\(597\) | 33.9234 | 1.38839 | ||||||||
\(598\) | 7.58843 | 0.310314 | ||||||||
\(599\) | 34.8634 | 1.42448 | 0.712241 | − | 0.701935i | \(-0.247680\pi\) | ||||
0.712241 | + | 0.701935i | \(0.247680\pi\) | |||||||
\(600\) | −9.03509 | −0.368856 | ||||||||
\(601\) | 26.0001 | 1.06057 | 0.530283 | − | 0.847821i | \(-0.322086\pi\) | ||||
0.530283 | + | 0.847821i | \(0.322086\pi\) | |||||||
\(602\) | 15.2612 | 0.622002 | ||||||||
\(603\) | 7.96399 | 0.324319 | ||||||||
\(604\) | 14.9077 | 0.606586 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 7.07966 | 0.287592 | ||||||||
\(607\) | 10.3793 | 0.421284 | 0.210642 | − | 0.977563i | \(-0.432445\pi\) | ||||
0.210642 | + | 0.977563i | \(0.432445\pi\) | |||||||
\(608\) | −3.18974 | −0.129361 | ||||||||
\(609\) | 51.5069 | 2.08717 | ||||||||
\(610\) | −4.23030 | −0.171280 | ||||||||
\(611\) | 6.15872 | 0.249155 | ||||||||
\(612\) | −25.2751 | −1.02169 | ||||||||
\(613\) | 22.2019 | 0.896726 | 0.448363 | − | 0.893851i | \(-0.352007\pi\) | ||||
0.448363 | + | 0.893851i | \(0.352007\pi\) | |||||||
\(614\) | 21.7209 | 0.876583 | ||||||||
\(615\) | 30.0969 | 1.21362 | ||||||||
\(616\) | 7.58034 | 0.305421 | ||||||||
\(617\) | −23.0135 | −0.926490 | −0.463245 | − | 0.886230i | \(-0.653315\pi\) | ||||
−0.463245 | + | 0.886230i | \(0.653315\pi\) | |||||||
\(618\) | −13.7674 | −0.553805 | ||||||||
\(619\) | −17.4912 | −0.703031 | −0.351515 | − | 0.936182i | \(-0.614334\pi\) | ||||
−0.351515 | + | 0.936182i | \(0.614334\pi\) | |||||||
\(620\) | −5.35704 | −0.215144 | ||||||||
\(621\) | 62.7866 | 2.51954 | ||||||||
\(622\) | 24.0060 | 0.962555 | ||||||||
\(623\) | −38.9928 | −1.56221 | ||||||||
\(624\) | 4.50564 | 0.180370 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 9.92951 | 0.396863 | ||||||||
\(627\) | −2.23160 | −0.0891214 | ||||||||
\(628\) | 0.805567 | 0.0321456 | ||||||||
\(629\) | −30.3466 | −1.21000 | ||||||||
\(630\) | −15.3665 | −0.612217 | ||||||||
\(631\) | 1.27512 | 0.0507618 | 0.0253809 | − | 0.999678i | \(-0.491920\pi\) | ||||
0.0253809 | + | 0.999678i | \(0.491920\pi\) | |||||||
\(632\) | −36.6828 | −1.45916 | ||||||||
\(633\) | 23.3410 | 0.927721 | ||||||||
\(634\) | 9.39768 | 0.373230 | ||||||||
\(635\) | −4.51562 | −0.179197 | ||||||||
\(636\) | −12.8136 | −0.508090 | ||||||||
\(637\) | −0.776310 | −0.0307585 | ||||||||
\(638\) | 7.74663 | 0.306692 | ||||||||
\(639\) | −72.9857 | −2.88727 | ||||||||
\(640\) | −0.474530 | −0.0187574 | ||||||||
\(641\) | −25.5304 | −1.00839 | −0.504195 | − | 0.863590i | \(-0.668211\pi\) | ||||
−0.504195 | + | 0.863590i | \(0.668211\pi\) | |||||||
\(642\) | 48.7578 | 1.92432 | ||||||||
\(643\) | −32.1027 | −1.26601 | −0.633003 | − | 0.774149i | \(-0.718178\pi\) | ||||
−0.633003 | + | 0.774149i | \(0.718178\pi\) | |||||||
\(644\) | 15.7552 | 0.620841 | ||||||||
\(645\) | 16.6117 | 0.654085 | ||||||||
\(646\) | −4.61029 | −0.181389 | ||||||||
\(647\) | −35.2256 | −1.38486 | −0.692431 | − | 0.721484i | \(-0.743460\pi\) | ||||
−0.692431 | + | 0.721484i | \(0.743460\pi\) | |||||||
\(648\) | 19.0318 | 0.747642 | ||||||||
\(649\) | 6.03850 | 0.237032 | ||||||||
\(650\) | −0.953443 | −0.0373971 | ||||||||
\(651\) | −48.6963 | −1.90856 | ||||||||
\(652\) | −5.53807 | −0.216888 | ||||||||
\(653\) | −44.1898 | −1.72928 | −0.864640 | − | 0.502393i | \(-0.832453\pi\) | ||||
−0.864640 | + | 0.502393i | \(0.832453\pi\) | |||||||
\(654\) | −40.7305 | −1.59269 | ||||||||
\(655\) | 1.88324 | 0.0735844 | ||||||||
\(656\) | 17.9468 | 0.700705 | ||||||||
\(657\) | −5.67794 | −0.221518 | ||||||||
\(658\) | −19.1426 | −0.746255 | ||||||||
\(659\) | −44.6080 | −1.73768 | −0.868841 | − | 0.495091i | \(-0.835135\pi\) | ||||
−0.868841 | + | 0.495091i | \(0.835135\pi\) | |||||||
\(660\) | 2.35945 | 0.0918413 | ||||||||
\(661\) | 25.8795 | 1.00659 | 0.503297 | − | 0.864113i | \(-0.332120\pi\) | ||||
0.503297 | + | 0.864113i | \(0.332120\pi\) | |||||||
\(662\) | 20.2732 | 0.787939 | ||||||||
\(663\) | −14.2556 | −0.553640 | ||||||||
\(664\) | 40.8772 | 1.58634 | ||||||||
\(665\) | 1.87229 | 0.0726041 | ||||||||
\(666\) | 33.9484 | 1.31548 | ||||||||
\(667\) | 56.3054 | 2.18015 | ||||||||
\(668\) | −9.79863 | −0.379120 | ||||||||
\(669\) | −26.5165 | −1.02519 | ||||||||
\(670\) | −1.53589 | −0.0593365 | ||||||||
\(671\) | 3.86324 | 0.149139 | ||||||||
\(672\) | 30.6564 | 1.18260 | ||||||||
\(673\) | 9.19811 | 0.354561 | 0.177281 | − | 0.984160i | \(-0.443270\pi\) | ||||
0.177281 | + | 0.984160i | \(0.443270\pi\) | |||||||
\(674\) | −37.4422 | −1.44222 | ||||||||
\(675\) | −7.88878 | −0.303639 | ||||||||
\(676\) | 9.80503 | 0.377117 | ||||||||
\(677\) | −45.8043 | −1.76040 | −0.880201 | − | 0.474602i | \(-0.842592\pi\) | ||||
−0.880201 | + | 0.474602i | \(0.842592\pi\) | |||||||
\(678\) | −23.2462 | −0.892765 | ||||||||
\(679\) | 19.5629 | 0.750755 | ||||||||
\(680\) | 17.0461 | 0.653688 | ||||||||
\(681\) | −5.83836 | −0.223726 | ||||||||
\(682\) | −7.32391 | −0.280447 | ||||||||
\(683\) | −25.2811 | −0.967356 | −0.483678 | − | 0.875246i | \(-0.660699\pi\) | ||||
−0.483678 | + | 0.875246i | \(0.660699\pi\) | |||||||
\(684\) | −3.44509 | −0.131726 | ||||||||
\(685\) | −20.4924 | −0.782974 | ||||||||
\(686\) | 21.3574 | 0.815429 | ||||||||
\(687\) | −42.0893 | −1.60581 | ||||||||
\(688\) | 9.90557 | 0.377646 | ||||||||
\(689\) | −4.72862 | −0.180146 | ||||||||
\(690\) | −25.6735 | −0.977375 | ||||||||
\(691\) | −33.3171 | −1.26744 | −0.633721 | − | 0.773562i | \(-0.718473\pi\) | ||||
−0.633721 | + | 0.773562i | \(0.718473\pi\) | |||||||
\(692\) | −2.48292 | −0.0943866 | ||||||||
\(693\) | 14.0332 | 0.533076 | ||||||||
\(694\) | 0.246131 | 0.00934299 | ||||||||
\(695\) | 8.93621 | 0.338970 | ||||||||
\(696\) | 63.9183 | 2.42282 | ||||||||
\(697\) | −56.7825 | −2.15079 | ||||||||
\(698\) | 4.74878 | 0.179744 | ||||||||
\(699\) | 38.1839 | 1.44425 | ||||||||
\(700\) | −1.97955 | −0.0748199 | ||||||||
\(701\) | 31.3586 | 1.18440 | 0.592198 | − | 0.805792i | \(-0.298260\pi\) | ||||
0.592198 | + | 0.805792i | \(0.298260\pi\) | |||||||
\(702\) | 7.52150 | 0.283881 | ||||||||
\(703\) | −4.13634 | −0.156005 | ||||||||
\(704\) | 8.12392 | 0.306182 | ||||||||
\(705\) | −20.8365 | −0.784747 | ||||||||
\(706\) | 29.4294 | 1.10759 | ||||||||
\(707\) | 5.42436 | 0.204004 | ||||||||
\(708\) | 14.2475 | 0.535454 | ||||||||
\(709\) | 21.0375 | 0.790078 | 0.395039 | − | 0.918664i | \(-0.370731\pi\) | ||||
0.395039 | + | 0.918664i | \(0.370731\pi\) | |||||||
\(710\) | 14.0756 | 0.528248 | ||||||||
\(711\) | −67.9093 | −2.54680 | ||||||||
\(712\) | −48.3887 | −1.81344 | ||||||||
\(713\) | −53.2329 | −1.99359 | ||||||||
\(714\) | 44.3092 | 1.65823 | ||||||||
\(715\) | 0.870712 | 0.0325628 | ||||||||
\(716\) | 4.74513 | 0.177334 | ||||||||
\(717\) | −46.5381 | −1.73800 | ||||||||
\(718\) | 0.0651449 | 0.00243119 | ||||||||
\(719\) | 31.2347 | 1.16486 | 0.582428 | − | 0.812882i | \(-0.302103\pi\) | ||||
0.582428 | + | 0.812882i | \(0.302103\pi\) | |||||||
\(720\) | −9.97390 | −0.371705 | ||||||||
\(721\) | −10.5484 | −0.392844 | ||||||||
\(722\) | 20.1769 | 0.750906 | ||||||||
\(723\) | 52.1035 | 1.93775 | ||||||||
\(724\) | 7.44070 | 0.276531 | ||||||||
\(725\) | −7.07445 | −0.262739 | ||||||||
\(726\) | 3.22573 | 0.119718 | ||||||||
\(727\) | 41.2639 | 1.53039 | 0.765196 | − | 0.643798i | \(-0.222642\pi\) | ||||
0.765196 | + | 0.643798i | \(0.222642\pi\) | |||||||
\(728\) | 6.60029 | 0.244623 | ||||||||
\(729\) | −34.4843 | −1.27720 | ||||||||
\(730\) | 1.09501 | 0.0405283 | ||||||||
\(731\) | −31.3405 | −1.15917 | ||||||||
\(732\) | 9.11511 | 0.336904 | ||||||||
\(733\) | 36.2052 | 1.33727 | 0.668636 | − | 0.743590i | \(-0.266879\pi\) | ||||
0.668636 | + | 0.743590i | \(0.266879\pi\) | |||||||
\(734\) | −17.6273 | −0.650636 | ||||||||
\(735\) | 2.62645 | 0.0968781 | ||||||||
\(736\) | 33.5124 | 1.23528 | ||||||||
\(737\) | 1.40262 | 0.0516661 | ||||||||
\(738\) | 63.5221 | 2.33828 | ||||||||
\(739\) | −2.45772 | −0.0904085 | −0.0452043 | − | 0.998978i | \(-0.514394\pi\) | ||||
−0.0452043 | + | 0.998978i | \(0.514394\pi\) | |||||||
\(740\) | 4.37331 | 0.160766 | ||||||||
\(741\) | −1.94308 | −0.0713808 | ||||||||
\(742\) | 14.6975 | 0.539563 | ||||||||
\(743\) | −49.8334 | −1.82821 | −0.914104 | − | 0.405479i | \(-0.867105\pi\) | ||||
−0.914104 | + | 0.405479i | \(0.867105\pi\) | |||||||
\(744\) | −60.4304 | −2.21549 | ||||||||
\(745\) | −1.90995 | −0.0699753 | ||||||||
\(746\) | −30.6367 | −1.12169 | ||||||||
\(747\) | 75.6741 | 2.76877 | ||||||||
\(748\) | −4.45146 | −0.162762 | ||||||||
\(749\) | 37.3577 | 1.36502 | ||||||||
\(750\) | 3.22573 | 0.117787 | ||||||||
\(751\) | −14.9540 | −0.545679 | −0.272840 | − | 0.962059i | \(-0.587963\pi\) | ||||
−0.272840 | + | 0.962059i | \(0.587963\pi\) | |||||||
\(752\) | −12.4248 | −0.453086 | ||||||||
\(753\) | 36.8613 | 1.34330 | ||||||||
\(754\) | 6.74508 | 0.245641 | ||||||||
\(755\) | −18.6127 | −0.677385 | ||||||||
\(756\) | 15.6162 | 0.567957 | ||||||||
\(757\) | 5.93691 | 0.215781 | 0.107890 | − | 0.994163i | \(-0.465590\pi\) | ||||
0.107890 | + | 0.994163i | \(0.465590\pi\) | |||||||
\(758\) | −35.5145 | −1.28995 | ||||||||
\(759\) | 23.4458 | 0.851030 | ||||||||
\(760\) | 2.32344 | 0.0842801 | ||||||||
\(761\) | 18.3124 | 0.663824 | 0.331912 | − | 0.943310i | \(-0.392306\pi\) | ||||
0.331912 | + | 0.943310i | \(0.392306\pi\) | |||||||
\(762\) | −14.5662 | −0.527677 | ||||||||
\(763\) | −31.2073 | −1.12978 | ||||||||
\(764\) | −9.66244 | −0.349575 | ||||||||
\(765\) | 31.5567 | 1.14094 | ||||||||
\(766\) | 29.8475 | 1.07843 | ||||||||
\(767\) | 5.25779 | 0.189848 | ||||||||
\(768\) | 46.3327 | 1.67189 | ||||||||
\(769\) | −6.43575 | −0.232079 | −0.116039 | − | 0.993245i | \(-0.537020\pi\) | ||||
−0.116039 | + | 0.993245i | \(0.537020\pi\) | |||||||
\(770\) | −2.70635 | −0.0975302 | ||||||||
\(771\) | 8.84341 | 0.318488 | ||||||||
\(772\) | −8.23678 | −0.296448 | ||||||||
\(773\) | 38.7052 | 1.39213 | 0.696065 | − | 0.717978i | \(-0.254932\pi\) | ||||
0.696065 | + | 0.717978i | \(0.254932\pi\) | |||||||
\(774\) | 35.0604 | 1.26022 | ||||||||
\(775\) | 6.68841 | 0.240255 | ||||||||
\(776\) | 24.2769 | 0.871490 | ||||||||
\(777\) | 39.7541 | 1.42617 | ||||||||
\(778\) | 40.8002 | 1.46276 | ||||||||
\(779\) | −7.73965 | −0.277302 | ||||||||
\(780\) | 2.05440 | 0.0735593 | ||||||||
\(781\) | −12.8543 | −0.459961 | ||||||||
\(782\) | 48.4371 | 1.73211 | ||||||||
\(783\) | 55.8088 | 1.99444 | ||||||||
\(784\) | 1.56615 | 0.0559341 | ||||||||
\(785\) | −1.00577 | −0.0358976 | ||||||||
\(786\) | 6.07484 | 0.216682 | ||||||||
\(787\) | −9.41304 | −0.335539 | −0.167769 | − | 0.985826i | \(-0.553656\pi\) | ||||
−0.167769 | + | 0.985826i | \(0.553656\pi\) | |||||||
\(788\) | −4.85712 | −0.173028 | ||||||||
\(789\) | 90.9400 | 3.23755 | ||||||||
\(790\) | 13.0966 | 0.465956 | ||||||||
\(791\) | −17.8110 | −0.633286 | ||||||||
\(792\) | 17.4147 | 0.618803 | ||||||||
\(793\) | 3.36377 | 0.119451 | ||||||||
\(794\) | −26.8911 | −0.954330 | ||||||||
\(795\) | 15.9981 | 0.567394 | ||||||||
\(796\) | 9.22343 | 0.326916 | ||||||||
\(797\) | 12.4775 | 0.441977 | 0.220988 | − | 0.975276i | \(-0.429072\pi\) | ||||
0.220988 | + | 0.975276i | \(0.429072\pi\) | |||||||
\(798\) | 6.03949 | 0.213796 | ||||||||
\(799\) | 39.3112 | 1.39073 | ||||||||
\(800\) | −4.21064 | −0.148869 | ||||||||
\(801\) | −89.5800 | −3.16515 | ||||||||
\(802\) | 14.3138 | 0.505439 | ||||||||
\(803\) | −1.00000 | −0.0352892 | ||||||||
\(804\) | 3.30940 | 0.116714 | ||||||||
\(805\) | −19.6708 | −0.693304 | ||||||||
\(806\) | −6.37702 | −0.224621 | ||||||||
\(807\) | 58.6340 | 2.06402 | ||||||||
\(808\) | 6.73145 | 0.236812 | ||||||||
\(809\) | −13.4837 | −0.474062 | −0.237031 | − | 0.971502i | \(-0.576174\pi\) | ||||
−0.237031 | + | 0.971502i | \(0.576174\pi\) | |||||||
\(810\) | −6.79480 | −0.238745 | ||||||||
\(811\) | 39.3284 | 1.38101 | 0.690504 | − | 0.723329i | \(-0.257389\pi\) | ||||
0.690504 | + | 0.723329i | \(0.257389\pi\) | |||||||
\(812\) | 14.0042 | 0.491452 | ||||||||
\(813\) | −24.5799 | −0.862056 | ||||||||
\(814\) | 5.97900 | 0.209564 | ||||||||
\(815\) | 6.91444 | 0.242202 | ||||||||
\(816\) | 28.7596 | 1.00679 | ||||||||
\(817\) | −4.27182 | −0.149452 | ||||||||
\(818\) | −14.4844 | −0.506436 | ||||||||
\(819\) | 12.2188 | 0.426961 | ||||||||
\(820\) | 8.18305 | 0.285765 | ||||||||
\(821\) | 29.3360 | 1.02383 | 0.511917 | − | 0.859035i | \(-0.328936\pi\) | ||||
0.511917 | + | 0.859035i | \(0.328936\pi\) | |||||||
\(822\) | −66.1030 | −2.30561 | ||||||||
\(823\) | −28.2826 | −0.985868 | −0.492934 | − | 0.870067i | \(-0.664076\pi\) | ||||
−0.492934 | + | 0.870067i | \(0.664076\pi\) | |||||||
\(824\) | −13.0902 | −0.456020 | ||||||||
\(825\) | −2.94583 | −0.102561 | ||||||||
\(826\) | −16.3423 | −0.568621 | ||||||||
\(827\) | 8.63406 | 0.300236 | 0.150118 | − | 0.988668i | \(-0.452035\pi\) | ||||
0.150118 | + | 0.988668i | \(0.452035\pi\) | |||||||
\(828\) | 36.1951 | 1.25787 | ||||||||
\(829\) | 40.3031 | 1.39979 | 0.699893 | − | 0.714248i | \(-0.253231\pi\) | ||||
0.699893 | + | 0.714248i | \(0.253231\pi\) | |||||||
\(830\) | −14.5941 | −0.506567 | ||||||||
\(831\) | −42.2366 | −1.46517 | ||||||||
\(832\) | 7.07360 | 0.245233 | ||||||||
\(833\) | −4.95520 | −0.171688 | ||||||||
\(834\) | 28.8258 | 0.998156 | ||||||||
\(835\) | 12.2339 | 0.423370 | ||||||||
\(836\) | −0.606749 | −0.0209849 | ||||||||
\(837\) | −52.7634 | −1.82377 | ||||||||
\(838\) | −27.8384 | −0.961661 | ||||||||
\(839\) | −28.7110 | −0.991215 | −0.495607 | − | 0.868547i | \(-0.665055\pi\) | ||||
−0.495607 | + | 0.868547i | \(0.665055\pi\) | |||||||
\(840\) | −22.3304 | −0.770473 | ||||||||
\(841\) | 21.0479 | 0.725788 | ||||||||
\(842\) | 15.6408 | 0.539019 | ||||||||
\(843\) | −18.9016 | −0.651007 | ||||||||
\(844\) | 6.34618 | 0.218445 | ||||||||
\(845\) | −12.2419 | −0.421133 | ||||||||
\(846\) | −43.9771 | −1.51196 | ||||||||
\(847\) | 2.47152 | 0.0849225 | ||||||||
\(848\) | 9.53967 | 0.327594 | ||||||||
\(849\) | −28.8098 | −0.988749 | ||||||||
\(850\) | −6.08584 | −0.208743 | ||||||||
\(851\) | 43.4576 | 1.48971 | ||||||||
\(852\) | −30.3289 | −1.03905 | ||||||||
\(853\) | −13.4424 | −0.460258 | −0.230129 | − | 0.973160i | \(-0.573915\pi\) | ||||
−0.230129 | + | 0.973160i | \(0.573915\pi\) | |||||||
\(854\) | −10.4553 | −0.357773 | ||||||||
\(855\) | 4.30129 | 0.147101 | ||||||||
\(856\) | 46.3597 | 1.58454 | ||||||||
\(857\) | 2.90205 | 0.0991322 | 0.0495661 | − | 0.998771i | \(-0.484216\pi\) | ||||
0.0495661 | + | 0.998771i | \(0.484216\pi\) | |||||||
\(858\) | 2.80868 | 0.0958869 | ||||||||
\(859\) | −8.61521 | −0.293947 | −0.146974 | − | 0.989140i | \(-0.546953\pi\) | ||||
−0.146974 | + | 0.989140i | \(0.546953\pi\) | |||||||
\(860\) | 4.51655 | 0.154013 | ||||||||
\(861\) | 74.3852 | 2.53504 | ||||||||
\(862\) | 5.14154 | 0.175121 | ||||||||
\(863\) | 20.5742 | 0.700353 | 0.350177 | − | 0.936684i | \(-0.386122\pi\) | ||||
0.350177 | + | 0.936684i | \(0.386122\pi\) | |||||||
\(864\) | 33.2168 | 1.13006 | ||||||||
\(865\) | 3.10000 | 0.105403 | ||||||||
\(866\) | −29.4850 | −1.00194 | ||||||||
\(867\) | −40.9143 | −1.38952 | ||||||||
\(868\) | −13.2400 | −0.449396 | ||||||||
\(869\) | −11.9602 | −0.405722 | ||||||||
\(870\) | −22.8203 | −0.773680 | ||||||||
\(871\) | 1.22128 | 0.0413814 | ||||||||
\(872\) | −38.7272 | −1.31147 | ||||||||
\(873\) | 44.9428 | 1.52108 | ||||||||
\(874\) | 6.60214 | 0.223321 | ||||||||
\(875\) | 2.47152 | 0.0835527 | ||||||||
\(876\) | −2.35945 | −0.0797183 | ||||||||
\(877\) | −21.8467 | −0.737711 | −0.368856 | − | 0.929487i | \(-0.620250\pi\) | ||||
−0.368856 | + | 0.929487i | \(0.620250\pi\) | |||||||
\(878\) | 26.9657 | 0.910048 | ||||||||
\(879\) | −2.37764 | −0.0801958 | ||||||||
\(880\) | −1.75660 | −0.0592151 | ||||||||
\(881\) | −10.7521 | −0.362247 | −0.181124 | − | 0.983460i | \(-0.557973\pi\) | ||||
−0.181124 | + | 0.983460i | \(0.557973\pi\) | |||||||
\(882\) | 5.54334 | 0.186654 | ||||||||
\(883\) | −21.1124 | −0.710489 | −0.355244 | − | 0.934773i | \(-0.615602\pi\) | ||||
−0.355244 | + | 0.934773i | \(0.615602\pi\) | |||||||
\(884\) | −3.87594 | −0.130362 | ||||||||
\(885\) | −17.7884 | −0.597951 | ||||||||
\(886\) | −28.5245 | −0.958300 | ||||||||
\(887\) | 18.2536 | 0.612896 | 0.306448 | − | 0.951887i | \(-0.400859\pi\) | ||||
0.306448 | + | 0.951887i | \(0.400859\pi\) | |||||||
\(888\) | 49.3334 | 1.65552 | ||||||||
\(889\) | −11.1604 | −0.374309 | ||||||||
\(890\) | 17.2759 | 0.579088 | ||||||||
\(891\) | 6.20521 | 0.207882 | ||||||||
\(892\) | −7.20958 | −0.241395 | ||||||||
\(893\) | 5.35825 | 0.179307 | ||||||||
\(894\) | −6.16100 | −0.206055 | ||||||||
\(895\) | −5.92443 | −0.198032 | ||||||||
\(896\) | −1.17281 | −0.0391808 | ||||||||
\(897\) | 20.4146 | 0.681623 | ||||||||
\(898\) | 14.1490 | 0.472159 | ||||||||
\(899\) | −47.3168 | −1.57811 | ||||||||
\(900\) | −4.54771 | −0.151590 | ||||||||
\(901\) | −30.1829 | −1.00554 | ||||||||
\(902\) | 11.1875 | 0.372503 | ||||||||
\(903\) | 41.0562 | 1.36626 | ||||||||
\(904\) | −22.1028 | −0.735129 | ||||||||
\(905\) | −9.28992 | −0.308807 | ||||||||
\(906\) | −60.0396 | −1.99468 | ||||||||
\(907\) | −18.5536 | −0.616061 | −0.308031 | − | 0.951376i | \(-0.599670\pi\) | ||||
−0.308031 | + | 0.951376i | \(0.599670\pi\) | |||||||
\(908\) | −1.58739 | −0.0526794 | ||||||||
\(909\) | 12.4616 | 0.413327 | ||||||||
\(910\) | −2.35645 | −0.0781157 | ||||||||
\(911\) | −44.2680 | −1.46666 | −0.733332 | − | 0.679871i | \(-0.762036\pi\) | ||||
−0.733332 | + | 0.679871i | \(0.762036\pi\) | |||||||
\(912\) | 3.92003 | 0.129805 | ||||||||
\(913\) | 13.3277 | 0.441084 | ||||||||
\(914\) | 40.7781 | 1.34882 | ||||||||
\(915\) | −11.3805 | −0.376227 | ||||||||
\(916\) | −11.4437 | −0.378109 | ||||||||
\(917\) | 4.65447 | 0.153704 | ||||||||
\(918\) | 48.0099 | 1.58456 | ||||||||
\(919\) | 9.35309 | 0.308530 | 0.154265 | − | 0.988030i | \(-0.450699\pi\) | ||||
0.154265 | + | 0.988030i | \(0.450699\pi\) | |||||||
\(920\) | −24.4108 | −0.804799 | ||||||||
\(921\) | 58.4340 | 1.92547 | ||||||||
\(922\) | −26.2500 | −0.864498 | ||||||||
\(923\) | −11.1924 | −0.368401 | ||||||||
\(924\) | 5.83142 | 0.191840 | ||||||||
\(925\) | −5.46020 | −0.179530 | ||||||||
\(926\) | −0.541600 | −0.0177981 | ||||||||
\(927\) | −24.2334 | −0.795929 | ||||||||
\(928\) | 29.7880 | 0.977838 | ||||||||
\(929\) | −13.5633 | −0.444999 | −0.222499 | − | 0.974933i | \(-0.571422\pi\) | ||||
−0.222499 | + | 0.974933i | \(0.571422\pi\) | |||||||
\(930\) | 21.5750 | 0.707473 | ||||||||
\(931\) | −0.675411 | −0.0221357 | ||||||||
\(932\) | 10.3818 | 0.340068 | ||||||||
\(933\) | 64.5816 | 2.11431 | ||||||||
\(934\) | −11.8028 | −0.386199 | ||||||||
\(935\) | 5.55777 | 0.181759 | ||||||||
\(936\) | 15.1632 | 0.495624 | ||||||||
\(937\) | −48.3686 | −1.58013 | −0.790067 | − | 0.613020i | \(-0.789954\pi\) | ||||
−0.790067 | + | 0.613020i | \(0.789954\pi\) | |||||||
\(938\) | −3.79598 | −0.123943 | ||||||||
\(939\) | 26.7126 | 0.871734 | ||||||||
\(940\) | −5.66523 | −0.184779 | ||||||||
\(941\) | 37.4129 | 1.21963 | 0.609813 | − | 0.792545i | \(-0.291245\pi\) | ||||
0.609813 | + | 0.792545i | \(0.291245\pi\) | |||||||
\(942\) | −3.24436 | −0.105707 | ||||||||
\(943\) | 81.3151 | 2.64798 | ||||||||
\(944\) | −10.6072 | −0.345236 | ||||||||
\(945\) | −19.4973 | −0.634247 | ||||||||
\(946\) | 6.17484 | 0.200761 | ||||||||
\(947\) | −36.0948 | −1.17292 | −0.586461 | − | 0.809977i | \(-0.699479\pi\) | ||||
−0.586461 | + | 0.809977i | \(0.699479\pi\) | |||||||
\(948\) | −28.2194 | −0.916525 | ||||||||
\(949\) | −0.870712 | −0.0282645 | ||||||||
\(950\) | −0.829521 | −0.0269132 | ||||||||
\(951\) | 25.2819 | 0.819821 | ||||||||
\(952\) | 42.1298 | 1.36544 | ||||||||
\(953\) | −32.6936 | −1.05905 | −0.529525 | − | 0.848294i | \(-0.677630\pi\) | ||||
−0.529525 | + | 0.848294i | \(0.677630\pi\) | |||||||
\(954\) | 33.7653 | 1.09319 | ||||||||
\(955\) | 12.0638 | 0.390376 | ||||||||
\(956\) | −12.6533 | −0.409235 | ||||||||
\(957\) | 20.8402 | 0.673667 | ||||||||
\(958\) | −16.7637 | −0.541610 | ||||||||
\(959\) | −50.6474 | −1.63549 | ||||||||
\(960\) | −23.9317 | −0.772393 | ||||||||
\(961\) | 13.7349 | 0.443060 | ||||||||
\(962\) | 5.20599 | 0.167848 | ||||||||
\(963\) | 85.8237 | 2.76563 | ||||||||
\(964\) | 14.1664 | 0.456269 | ||||||||
\(965\) | 10.2839 | 0.331049 | ||||||||
\(966\) | −63.4527 | −2.04156 | ||||||||
\(967\) | 49.8269 | 1.60233 | 0.801163 | − | 0.598447i | \(-0.204215\pi\) | ||||
0.801163 | + | 0.598447i | \(0.204215\pi\) | |||||||
\(968\) | 3.06707 | 0.0985795 | ||||||||
\(969\) | −12.4027 | −0.398433 | ||||||||
\(970\) | −8.66740 | −0.278293 | ||||||||
\(971\) | −51.0389 | −1.63792 | −0.818958 | − | 0.573853i | \(-0.805448\pi\) | ||||
−0.818958 | + | 0.573853i | \(0.805448\pi\) | |||||||
\(972\) | −4.31452 | −0.138388 | ||||||||
\(973\) | 22.0860 | 0.708046 | ||||||||
\(974\) | −38.6885 | −1.23966 | ||||||||
\(975\) | −2.56497 | −0.0821449 | ||||||||
\(976\) | −6.78618 | −0.217220 | ||||||||
\(977\) | 3.92220 | 0.125482 | 0.0627412 | − | 0.998030i | \(-0.480016\pi\) | ||||
0.0627412 | + | 0.998030i | \(0.480016\pi\) | |||||||
\(978\) | 22.3041 | 0.713207 | ||||||||
\(979\) | −15.7768 | −0.504230 | ||||||||
\(980\) | 0.714105 | 0.0228113 | ||||||||
\(981\) | −71.6939 | −2.28901 | ||||||||
\(982\) | 1.36341 | 0.0435082 | ||||||||
\(983\) | −47.4469 | −1.51332 | −0.756660 | − | 0.653808i | \(-0.773170\pi\) | ||||
−0.756660 | + | 0.653808i | \(0.773170\pi\) | |||||||
\(984\) | 92.3094 | 2.94272 | ||||||||
\(985\) | 6.06425 | 0.193223 | ||||||||
\(986\) | 43.0540 | 1.37112 | ||||||||
\(987\) | −51.4978 | −1.63919 | ||||||||
\(988\) | −0.528304 | −0.0168076 | ||||||||
\(989\) | 44.8810 | 1.42713 | ||||||||
\(990\) | −6.21743 | −0.197603 | ||||||||
\(991\) | −55.2816 | −1.75608 | −0.878039 | − | 0.478588i | \(-0.841149\pi\) | ||||
−0.878039 | + | 0.478588i | \(0.841149\pi\) | |||||||
\(992\) | −28.1625 | −0.894160 | ||||||||
\(993\) | 54.5393 | 1.73075 | ||||||||
\(994\) | 34.7881 | 1.10341 | ||||||||
\(995\) | −11.5157 | −0.365073 | ||||||||
\(996\) | 31.4461 | 0.996407 | ||||||||
\(997\) | −31.4861 | −0.997176 | −0.498588 | − | 0.866839i | \(-0.666148\pi\) | ||||
−0.498588 | + | 0.866839i | \(0.666148\pi\) | |||||||
\(998\) | −41.5331 | −1.31471 | ||||||||
\(999\) | 43.0743 | 1.36281 |
(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 | 4015.2.a.b.1.9 | ✓ | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4015.2.a.b.1.9 | ✓ | 23 | 1.1 | even | 1 | trivial |