Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8006,2,Mod(1,8006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8006, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8006 = 2 \cdot 4003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8006.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: | \(63.9282318582\) |
Analytic rank: | \(1\) |
Dimension: | \(75\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 8006.1 |
$q$-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 | ||||||||
\(3\) | −2.34883 | −1.35610 | −0.678048 | − | 0.735017i | \(-0.737174\pi\) | ||||
−0.678048 | + | 0.735017i | \(0.737174\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.23352 | 0.998863 | 0.499431 | − | 0.866353i | \(-0.333542\pi\) | ||||
0.499431 | + | 0.866353i | \(0.333542\pi\) | |||||||
\(6\) | 2.34883 | 0.958905 | ||||||||
\(7\) | 0.995037 | 0.376089 | 0.188044 | − | 0.982161i | \(-0.439785\pi\) | ||||
0.188044 | + | 0.982161i | \(0.439785\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.51700 | 0.838999 | ||||||||
\(10\) | −2.23352 | −0.706303 | ||||||||
\(11\) | 5.14516 | 1.55133 | 0.775663 | − | 0.631148i | \(-0.217416\pi\) | ||||
0.775663 | + | 0.631148i | \(0.217416\pi\) | |||||||
\(12\) | −2.34883 | −0.678048 | ||||||||
\(13\) | −3.84886 | −1.06748 | −0.533741 | − | 0.845648i | \(-0.679214\pi\) | ||||
−0.533741 | + | 0.845648i | \(0.679214\pi\) | |||||||
\(14\) | −0.995037 | −0.265935 | ||||||||
\(15\) | −5.24617 | −1.35455 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.71393 | 0.415689 | 0.207844 | − | 0.978162i | \(-0.433355\pi\) | ||||
0.207844 | + | 0.978162i | \(0.433355\pi\) | |||||||
\(18\) | −2.51700 | −0.593262 | ||||||||
\(19\) | −7.38779 | −1.69487 | −0.847437 | − | 0.530895i | \(-0.821856\pi\) | ||||
−0.847437 | + | 0.530895i | \(0.821856\pi\) | |||||||
\(20\) | 2.23352 | 0.499431 | ||||||||
\(21\) | −2.33717 | −0.510013 | ||||||||
\(22\) | −5.14516 | −1.09695 | ||||||||
\(23\) | −2.20233 | −0.459217 | −0.229609 | − | 0.973283i | \(-0.573745\pi\) | ||||
−0.229609 | + | 0.973283i | \(0.573745\pi\) | |||||||
\(24\) | 2.34883 | 0.479453 | ||||||||
\(25\) | −0.0113665 | −0.00227330 | ||||||||
\(26\) | 3.84886 | 0.754824 | ||||||||
\(27\) | 1.13449 | 0.218334 | ||||||||
\(28\) | 0.995037 | 0.188044 | ||||||||
\(29\) | −3.74508 | −0.695443 | −0.347722 | − | 0.937598i | \(-0.613045\pi\) | ||||
−0.347722 | + | 0.937598i | \(0.613045\pi\) | |||||||
\(30\) | 5.24617 | 0.957815 | ||||||||
\(31\) | 8.09676 | 1.45422 | 0.727111 | − | 0.686520i | \(-0.240863\pi\) | ||||
0.727111 | + | 0.686520i | \(0.240863\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −12.0851 | −2.10375 | ||||||||
\(34\) | −1.71393 | −0.293936 | ||||||||
\(35\) | 2.22244 | 0.375661 | ||||||||
\(36\) | 2.51700 | 0.419499 | ||||||||
\(37\) | 7.24334 | 1.19080 | 0.595399 | − | 0.803430i | \(-0.296994\pi\) | ||||
0.595399 | + | 0.803430i | \(0.296994\pi\) | |||||||
\(38\) | 7.38779 | 1.19846 | ||||||||
\(39\) | 9.04032 | 1.44761 | ||||||||
\(40\) | −2.23352 | −0.353151 | ||||||||
\(41\) | 11.4099 | 1.78193 | 0.890964 | − | 0.454074i | \(-0.150030\pi\) | ||||
0.890964 | + | 0.454074i | \(0.150030\pi\) | |||||||
\(42\) | 2.33717 | 0.360633 | ||||||||
\(43\) | 8.01588 | 1.22241 | 0.611205 | − | 0.791472i | \(-0.290685\pi\) | ||||
0.611205 | + | 0.791472i | \(0.290685\pi\) | |||||||
\(44\) | 5.14516 | 0.775663 | ||||||||
\(45\) | 5.62177 | 0.838044 | ||||||||
\(46\) | 2.20233 | 0.324716 | ||||||||
\(47\) | −10.9483 | −1.59697 | −0.798484 | − | 0.602017i | \(-0.794364\pi\) | ||||
−0.798484 | + | 0.602017i | \(0.794364\pi\) | |||||||
\(48\) | −2.34883 | −0.339024 | ||||||||
\(49\) | −6.00990 | −0.858557 | ||||||||
\(50\) | 0.0113665 | 0.00160747 | ||||||||
\(51\) | −4.02573 | −0.563714 | ||||||||
\(52\) | −3.84886 | −0.533741 | ||||||||
\(53\) | −8.67445 | −1.19153 | −0.595763 | − | 0.803160i | \(-0.703150\pi\) | ||||
−0.595763 | + | 0.803160i | \(0.703150\pi\) | |||||||
\(54\) | −1.13449 | −0.154385 | ||||||||
\(55\) | 11.4919 | 1.54956 | ||||||||
\(56\) | −0.995037 | −0.132967 | ||||||||
\(57\) | 17.3526 | 2.29841 | ||||||||
\(58\) | 3.74508 | 0.491753 | ||||||||
\(59\) | −9.49865 | −1.23662 | −0.618310 | − | 0.785935i | \(-0.712182\pi\) | ||||
−0.618310 | + | 0.785935i | \(0.712182\pi\) | |||||||
\(60\) | −5.24617 | −0.677277 | ||||||||
\(61\) | −8.32675 | −1.06613 | −0.533066 | − | 0.846074i | \(-0.678960\pi\) | ||||
−0.533066 | + | 0.846074i | \(0.678960\pi\) | |||||||
\(62\) | −8.09676 | −1.02829 | ||||||||
\(63\) | 2.50450 | 0.315538 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −8.59653 | −1.06627 | ||||||||
\(66\) | 12.0851 | 1.48757 | ||||||||
\(67\) | −3.71549 | −0.453919 | −0.226960 | − | 0.973904i | \(-0.572879\pi\) | ||||
−0.226960 | + | 0.973904i | \(0.572879\pi\) | |||||||
\(68\) | 1.71393 | 0.207844 | ||||||||
\(69\) | 5.17289 | 0.622743 | ||||||||
\(70\) | −2.22244 | −0.265632 | ||||||||
\(71\) | −6.29825 | −0.747465 | −0.373733 | − | 0.927537i | \(-0.621922\pi\) | ||||
−0.373733 | + | 0.927537i | \(0.621922\pi\) | |||||||
\(72\) | −2.51700 | −0.296631 | ||||||||
\(73\) | 8.73715 | 1.02261 | 0.511303 | − | 0.859400i | \(-0.329163\pi\) | ||||
0.511303 | + | 0.859400i | \(0.329163\pi\) | |||||||
\(74\) | −7.24334 | −0.842021 | ||||||||
\(75\) | 0.0266980 | 0.00308282 | ||||||||
\(76\) | −7.38779 | −0.847437 | ||||||||
\(77\) | 5.11963 | 0.583436 | ||||||||
\(78\) | −9.04032 | −1.02361 | ||||||||
\(79\) | −13.0345 | −1.46649 | −0.733247 | − | 0.679963i | \(-0.761996\pi\) | ||||
−0.733247 | + | 0.679963i | \(0.761996\pi\) | |||||||
\(80\) | 2.23352 | 0.249716 | ||||||||
\(81\) | −10.2157 | −1.13508 | ||||||||
\(82\) | −11.4099 | −1.26001 | ||||||||
\(83\) | 3.23651 | 0.355253 | 0.177627 | − | 0.984098i | \(-0.443158\pi\) | ||||
0.177627 | + | 0.984098i | \(0.443158\pi\) | |||||||
\(84\) | −2.33717 | −0.255006 | ||||||||
\(85\) | 3.82810 | 0.415216 | ||||||||
\(86\) | −8.01588 | −0.864375 | ||||||||
\(87\) | 8.79654 | 0.943088 | ||||||||
\(88\) | −5.14516 | −0.548476 | ||||||||
\(89\) | −7.51185 | −0.796254 | −0.398127 | − | 0.917330i | \(-0.630340\pi\) | ||||
−0.398127 | + | 0.917330i | \(0.630340\pi\) | |||||||
\(90\) | −5.62177 | −0.592587 | ||||||||
\(91\) | −3.82976 | −0.401468 | ||||||||
\(92\) | −2.20233 | −0.229609 | ||||||||
\(93\) | −19.0179 | −1.97207 | ||||||||
\(94\) | 10.9483 | 1.12923 | ||||||||
\(95\) | −16.5008 | −1.69295 | ||||||||
\(96\) | 2.34883 | 0.239726 | ||||||||
\(97\) | −9.27019 | −0.941245 | −0.470623 | − | 0.882335i | \(-0.655971\pi\) | ||||
−0.470623 | + | 0.882335i | \(0.655971\pi\) | |||||||
\(98\) | 6.00990 | 0.607092 | ||||||||
\(99\) | 12.9504 | 1.30156 | ||||||||
\(100\) | −0.0113665 | −0.00113665 | ||||||||
\(101\) | −9.58731 | −0.953973 | −0.476987 | − | 0.878911i | \(-0.658271\pi\) | ||||
−0.476987 | + | 0.878911i | \(0.658271\pi\) | |||||||
\(102\) | 4.02573 | 0.398606 | ||||||||
\(103\) | 9.85484 | 0.971027 | 0.485513 | − | 0.874229i | \(-0.338633\pi\) | ||||
0.485513 | + | 0.874229i | \(0.338633\pi\) | |||||||
\(104\) | 3.84886 | 0.377412 | ||||||||
\(105\) | −5.22013 | −0.509433 | ||||||||
\(106\) | 8.67445 | 0.842537 | ||||||||
\(107\) | 8.30423 | 0.802800 | 0.401400 | − | 0.915903i | \(-0.368524\pi\) | ||||
0.401400 | + | 0.915903i | \(0.368524\pi\) | |||||||
\(108\) | 1.13449 | 0.109167 | ||||||||
\(109\) | −8.73192 | −0.836366 | −0.418183 | − | 0.908363i | \(-0.637333\pi\) | ||||
−0.418183 | + | 0.908363i | \(0.637333\pi\) | |||||||
\(110\) | −11.4919 | −1.09570 | ||||||||
\(111\) | −17.0134 | −1.61484 | ||||||||
\(112\) | 0.995037 | 0.0940221 | ||||||||
\(113\) | 20.4964 | 1.92814 | 0.964071 | − | 0.265643i | \(-0.0855843\pi\) | ||||
0.964071 | + | 0.265643i | \(0.0855843\pi\) | |||||||
\(114\) | −17.3526 | −1.62522 | ||||||||
\(115\) | −4.91896 | −0.458695 | ||||||||
\(116\) | −3.74508 | −0.347722 | ||||||||
\(117\) | −9.68757 | −0.895616 | ||||||||
\(118\) | 9.49865 | 0.874422 | ||||||||
\(119\) | 1.70542 | 0.156336 | ||||||||
\(120\) | 5.24617 | 0.478907 | ||||||||
\(121\) | 15.4727 | 1.40661 | ||||||||
\(122\) | 8.32675 | 0.753869 | ||||||||
\(123\) | −26.7999 | −2.41647 | ||||||||
\(124\) | 8.09676 | 0.727111 | ||||||||
\(125\) | −11.1930 | −1.00113 | ||||||||
\(126\) | −2.50450 | −0.223119 | ||||||||
\(127\) | −11.6925 | −1.03754 | −0.518770 | − | 0.854914i | \(-0.673610\pi\) | ||||
−0.518770 | + | 0.854914i | \(0.673610\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −18.8279 | −1.65771 | ||||||||
\(130\) | 8.59653 | 0.753966 | ||||||||
\(131\) | −1.34288 | −0.117328 | −0.0586639 | − | 0.998278i | \(-0.518684\pi\) | ||||
−0.0586639 | + | 0.998278i | \(0.518684\pi\) | |||||||
\(132\) | −12.0851 | −1.05187 | ||||||||
\(133\) | −7.35112 | −0.637423 | ||||||||
\(134\) | 3.71549 | 0.320970 | ||||||||
\(135\) | 2.53392 | 0.218085 | ||||||||
\(136\) | −1.71393 | −0.146968 | ||||||||
\(137\) | −5.22331 | −0.446257 | −0.223129 | − | 0.974789i | \(-0.571627\pi\) | ||||
−0.223129 | + | 0.974789i | \(0.571627\pi\) | |||||||
\(138\) | −5.17289 | −0.440346 | ||||||||
\(139\) | 12.6423 | 1.07230 | 0.536151 | − | 0.844122i | \(-0.319878\pi\) | ||||
0.536151 | + | 0.844122i | \(0.319878\pi\) | |||||||
\(140\) | 2.22244 | 0.187830 | ||||||||
\(141\) | 25.7156 | 2.16564 | ||||||||
\(142\) | 6.29825 | 0.528538 | ||||||||
\(143\) | −19.8030 | −1.65601 | ||||||||
\(144\) | 2.51700 | 0.209750 | ||||||||
\(145\) | −8.36472 | −0.694652 | ||||||||
\(146\) | −8.73715 | −0.723092 | ||||||||
\(147\) | 14.1162 | 1.16429 | ||||||||
\(148\) | 7.24334 | 0.595399 | ||||||||
\(149\) | −7.49216 | −0.613782 | −0.306891 | − | 0.951745i | \(-0.599289\pi\) | ||||
−0.306891 | + | 0.951745i | \(0.599289\pi\) | |||||||
\(150\) | −0.0266980 | −0.00217988 | ||||||||
\(151\) | −10.8580 | −0.883608 | −0.441804 | − | 0.897112i | \(-0.645661\pi\) | ||||
−0.441804 | + | 0.897112i | \(0.645661\pi\) | |||||||
\(152\) | 7.38779 | 0.599229 | ||||||||
\(153\) | 4.31395 | 0.348762 | ||||||||
\(154\) | −5.11963 | −0.412551 | ||||||||
\(155\) | 18.0843 | 1.45257 | ||||||||
\(156\) | 9.04032 | 0.723805 | ||||||||
\(157\) | 10.8927 | 0.869332 | 0.434666 | − | 0.900592i | \(-0.356866\pi\) | ||||
0.434666 | + | 0.900592i | \(0.356866\pi\) | |||||||
\(158\) | 13.0345 | 1.03697 | ||||||||
\(159\) | 20.3748 | 1.61583 | ||||||||
\(160\) | −2.23352 | −0.176576 | ||||||||
\(161\) | −2.19140 | −0.172706 | ||||||||
\(162\) | 10.2157 | 0.802623 | ||||||||
\(163\) | −1.51117 | −0.118364 | −0.0591819 | − | 0.998247i | \(-0.518849\pi\) | ||||
−0.0591819 | + | 0.998247i | \(0.518849\pi\) | |||||||
\(164\) | 11.4099 | 0.890964 | ||||||||
\(165\) | −26.9924 | −2.10135 | ||||||||
\(166\) | −3.23651 | −0.251202 | ||||||||
\(167\) | 9.36815 | 0.724929 | 0.362465 | − | 0.931998i | \(-0.381935\pi\) | ||||
0.362465 | + | 0.931998i | \(0.381935\pi\) | |||||||
\(168\) | 2.33717 | 0.180317 | ||||||||
\(169\) | 1.81375 | 0.139519 | ||||||||
\(170\) | −3.82810 | −0.293602 | ||||||||
\(171\) | −18.5950 | −1.42200 | ||||||||
\(172\) | 8.01588 | 0.611205 | ||||||||
\(173\) | 0.294859 | 0.0224177 | 0.0112089 | − | 0.999937i | \(-0.496432\pi\) | ||||
0.0112089 | + | 0.999937i | \(0.496432\pi\) | |||||||
\(174\) | −8.79654 | −0.666864 | ||||||||
\(175\) | −0.0113101 | −0.000854962 0 | ||||||||
\(176\) | 5.14516 | 0.387831 | ||||||||
\(177\) | 22.3107 | 1.67698 | ||||||||
\(178\) | 7.51185 | 0.563037 | ||||||||
\(179\) | −12.7957 | −0.956392 | −0.478196 | − | 0.878253i | \(-0.658709\pi\) | ||||
−0.478196 | + | 0.878253i | \(0.658709\pi\) | |||||||
\(180\) | 5.62177 | 0.419022 | ||||||||
\(181\) | −9.17056 | −0.681642 | −0.340821 | − | 0.940128i | \(-0.610705\pi\) | ||||
−0.340821 | + | 0.940128i | \(0.610705\pi\) | |||||||
\(182\) | 3.82976 | 0.283881 | ||||||||
\(183\) | 19.5581 | 1.44578 | ||||||||
\(184\) | 2.20233 | 0.162358 | ||||||||
\(185\) | 16.1782 | 1.18944 | ||||||||
\(186\) | 19.0179 | 1.39446 | ||||||||
\(187\) | 8.81845 | 0.644869 | ||||||||
\(188\) | −10.9483 | −0.798484 | ||||||||
\(189\) | 1.12886 | 0.0821128 | ||||||||
\(190\) | 16.5008 | 1.19709 | ||||||||
\(191\) | −10.0537 | −0.727462 | −0.363731 | − | 0.931504i | \(-0.618497\pi\) | ||||
−0.363731 | + | 0.931504i | \(0.618497\pi\) | |||||||
\(192\) | −2.34883 | −0.169512 | ||||||||
\(193\) | 16.0777 | 1.15730 | 0.578651 | − | 0.815576i | \(-0.303580\pi\) | ||||
0.578651 | + | 0.815576i | \(0.303580\pi\) | |||||||
\(194\) | 9.27019 | 0.665561 | ||||||||
\(195\) | 20.1918 | 1.44596 | ||||||||
\(196\) | −6.00990 | −0.429279 | ||||||||
\(197\) | 2.71892 | 0.193715 | 0.0968575 | − | 0.995298i | \(-0.469121\pi\) | ||||
0.0968575 | + | 0.995298i | \(0.469121\pi\) | |||||||
\(198\) | −12.9504 | −0.920342 | ||||||||
\(199\) | 20.9881 | 1.48781 | 0.743903 | − | 0.668288i | \(-0.232973\pi\) | ||||
0.743903 | + | 0.668288i | \(0.232973\pi\) | |||||||
\(200\) | 0.0113665 | 0.000803733 0 | ||||||||
\(201\) | 8.72705 | 0.615559 | ||||||||
\(202\) | 9.58731 | 0.674561 | ||||||||
\(203\) | −3.72649 | −0.261548 | ||||||||
\(204\) | −4.02573 | −0.281857 | ||||||||
\(205\) | 25.4843 | 1.77990 | ||||||||
\(206\) | −9.85484 | −0.686619 | ||||||||
\(207\) | −5.54325 | −0.385283 | ||||||||
\(208\) | −3.84886 | −0.266871 | ||||||||
\(209\) | −38.0114 | −2.62930 | ||||||||
\(210\) | 5.22013 | 0.360223 | ||||||||
\(211\) | 13.5100 | 0.930064 | 0.465032 | − | 0.885294i | \(-0.346043\pi\) | ||||
0.465032 | + | 0.885294i | \(0.346043\pi\) | |||||||
\(212\) | −8.67445 | −0.595763 | ||||||||
\(213\) | 14.7935 | 1.01364 | ||||||||
\(214\) | −8.30423 | −0.567665 | ||||||||
\(215\) | 17.9037 | 1.22102 | ||||||||
\(216\) | −1.13449 | −0.0771926 | ||||||||
\(217\) | 8.05658 | 0.546916 | ||||||||
\(218\) | 8.73192 | 0.591400 | ||||||||
\(219\) | −20.5221 | −1.38675 | ||||||||
\(220\) | 11.4919 | 0.774780 | ||||||||
\(221\) | −6.59668 | −0.443741 | ||||||||
\(222\) | 17.0134 | 1.14186 | ||||||||
\(223\) | −6.63393 | −0.444241 | −0.222120 | − | 0.975019i | \(-0.571298\pi\) | ||||
−0.222120 | + | 0.975019i | \(0.571298\pi\) | |||||||
\(224\) | −0.995037 | −0.0664837 | ||||||||
\(225\) | −0.0286094 | −0.00190730 | ||||||||
\(226\) | −20.4964 | −1.36340 | ||||||||
\(227\) | −19.1777 | −1.27287 | −0.636435 | − | 0.771330i | \(-0.719592\pi\) | ||||
−0.636435 | + | 0.771330i | \(0.719592\pi\) | |||||||
\(228\) | 17.3526 | 1.14921 | ||||||||
\(229\) | −17.8995 | −1.18283 | −0.591417 | − | 0.806366i | \(-0.701431\pi\) | ||||
−0.591417 | + | 0.806366i | \(0.701431\pi\) | |||||||
\(230\) | 4.91896 | 0.324346 | ||||||||
\(231\) | −12.0251 | −0.791195 | ||||||||
\(232\) | 3.74508 | 0.245876 | ||||||||
\(233\) | 15.5094 | 1.01606 | 0.508029 | − | 0.861340i | \(-0.330374\pi\) | ||||
0.508029 | + | 0.861340i | \(0.330374\pi\) | |||||||
\(234\) | 9.68757 | 0.633296 | ||||||||
\(235\) | −24.4532 | −1.59515 | ||||||||
\(236\) | −9.49865 | −0.618310 | ||||||||
\(237\) | 30.6158 | 1.98871 | ||||||||
\(238\) | −1.70542 | −0.110546 | ||||||||
\(239\) | −2.07421 | −0.134170 | −0.0670849 | − | 0.997747i | \(-0.521370\pi\) | ||||
−0.0670849 | + | 0.997747i | \(0.521370\pi\) | |||||||
\(240\) | −5.24617 | −0.338639 | ||||||||
\(241\) | −11.8031 | −0.760306 | −0.380153 | − | 0.924924i | \(-0.624129\pi\) | ||||
−0.380153 | + | 0.924924i | \(0.624129\pi\) | |||||||
\(242\) | −15.4727 | −0.994623 | ||||||||
\(243\) | 20.5915 | 1.32094 | ||||||||
\(244\) | −8.32675 | −0.533066 | ||||||||
\(245\) | −13.4233 | −0.857581 | ||||||||
\(246\) | 26.7999 | 1.70870 | ||||||||
\(247\) | 28.4346 | 1.80925 | ||||||||
\(248\) | −8.09676 | −0.514145 | ||||||||
\(249\) | −7.60201 | −0.481758 | ||||||||
\(250\) | 11.1930 | 0.707908 | ||||||||
\(251\) | 28.9777 | 1.82906 | 0.914528 | − | 0.404523i | \(-0.132563\pi\) | ||||
0.914528 | + | 0.404523i | \(0.132563\pi\) | |||||||
\(252\) | 2.50450 | 0.157769 | ||||||||
\(253\) | −11.3313 | −0.712395 | ||||||||
\(254\) | 11.6925 | 0.733652 | ||||||||
\(255\) | −8.99156 | −0.563073 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.1050 | 1.25412 | 0.627059 | − | 0.778972i | \(-0.284259\pi\) | ||||
0.627059 | + | 0.778972i | \(0.284259\pi\) | |||||||
\(258\) | 18.8279 | 1.17218 | ||||||||
\(259\) | 7.20739 | 0.447845 | ||||||||
\(260\) | −8.59653 | −0.533134 | ||||||||
\(261\) | −9.42634 | −0.583476 | ||||||||
\(262\) | 1.34288 | 0.0829632 | ||||||||
\(263\) | −0.370427 | −0.0228415 | −0.0114208 | − | 0.999935i | \(-0.503635\pi\) | ||||
−0.0114208 | + | 0.999935i | \(0.503635\pi\) | |||||||
\(264\) | 12.0851 | 0.743787 | ||||||||
\(265\) | −19.3746 | −1.19017 | ||||||||
\(266\) | 7.35112 | 0.450726 | ||||||||
\(267\) | 17.6440 | 1.07980 | ||||||||
\(268\) | −3.71549 | −0.226960 | ||||||||
\(269\) | −27.3825 | −1.66954 | −0.834770 | − | 0.550598i | \(-0.814400\pi\) | ||||
−0.834770 | + | 0.550598i | \(0.814400\pi\) | |||||||
\(270\) | −2.53392 | −0.154210 | ||||||||
\(271\) | 19.0234 | 1.15559 | 0.577794 | − | 0.816183i | \(-0.303914\pi\) | ||||
0.577794 | + | 0.816183i | \(0.303914\pi\) | |||||||
\(272\) | 1.71393 | 0.103922 | ||||||||
\(273\) | 8.99545 | 0.544430 | ||||||||
\(274\) | 5.22331 | 0.315551 | ||||||||
\(275\) | −0.0584825 | −0.00352663 | ||||||||
\(276\) | 5.17289 | 0.311372 | ||||||||
\(277\) | −18.3627 | −1.10331 | −0.551653 | − | 0.834074i | \(-0.686003\pi\) | ||||
−0.551653 | + | 0.834074i | \(0.686003\pi\) | |||||||
\(278\) | −12.6423 | −0.758232 | ||||||||
\(279\) | 20.3795 | 1.22009 | ||||||||
\(280\) | −2.22244 | −0.132816 | ||||||||
\(281\) | −27.6749 | −1.65095 | −0.825473 | − | 0.564442i | \(-0.809091\pi\) | ||||
−0.825473 | + | 0.564442i | \(0.809091\pi\) | |||||||
\(282\) | −25.7156 | −1.53134 | ||||||||
\(283\) | 21.1856 | 1.25935 | 0.629677 | − | 0.776857i | \(-0.283187\pi\) | ||||
0.629677 | + | 0.776857i | \(0.283187\pi\) | |||||||
\(284\) | −6.29825 | −0.373733 | ||||||||
\(285\) | 38.7576 | 2.29580 | ||||||||
\(286\) | 19.8030 | 1.17098 | ||||||||
\(287\) | 11.3533 | 0.670163 | ||||||||
\(288\) | −2.51700 | −0.148315 | ||||||||
\(289\) | −14.0624 | −0.827203 | ||||||||
\(290\) | 8.36472 | 0.491193 | ||||||||
\(291\) | 21.7741 | 1.27642 | ||||||||
\(292\) | 8.73715 | 0.511303 | ||||||||
\(293\) | −13.1598 | −0.768806 | −0.384403 | − | 0.923165i | \(-0.625593\pi\) | ||||
−0.384403 | + | 0.923165i | \(0.625593\pi\) | |||||||
\(294\) | −14.1162 | −0.823275 | ||||||||
\(295\) | −21.2155 | −1.23521 | ||||||||
\(296\) | −7.24334 | −0.421010 | ||||||||
\(297\) | 5.83716 | 0.338706 | ||||||||
\(298\) | 7.49216 | 0.434009 | ||||||||
\(299\) | 8.47646 | 0.490206 | ||||||||
\(300\) | 0.0266980 | 0.00154141 | ||||||||
\(301\) | 7.97610 | 0.459735 | ||||||||
\(302\) | 10.8580 | 0.624805 | ||||||||
\(303\) | 22.5189 | 1.29368 | ||||||||
\(304\) | −7.38779 | −0.423719 | ||||||||
\(305\) | −18.5980 | −1.06492 | ||||||||
\(306\) | −4.31395 | −0.246612 | ||||||||
\(307\) | 2.80861 | 0.160296 | 0.0801480 | − | 0.996783i | \(-0.474461\pi\) | ||||
0.0801480 | + | 0.996783i | \(0.474461\pi\) | |||||||
\(308\) | 5.11963 | 0.291718 | ||||||||
\(309\) | −23.1473 | −1.31681 | ||||||||
\(310\) | −18.0843 | −1.02712 | ||||||||
\(311\) | −13.4142 | −0.760648 | −0.380324 | − | 0.924853i | \(-0.624187\pi\) | ||||
−0.380324 | + | 0.924853i | \(0.624187\pi\) | |||||||
\(312\) | −9.04032 | −0.511807 | ||||||||
\(313\) | 7.26667 | 0.410737 | 0.205368 | − | 0.978685i | \(-0.434161\pi\) | ||||
0.205368 | + | 0.978685i | \(0.434161\pi\) | |||||||
\(314\) | −10.8927 | −0.614711 | ||||||||
\(315\) | 5.59387 | 0.315179 | ||||||||
\(316\) | −13.0345 | −0.733247 | ||||||||
\(317\) | 2.98249 | 0.167513 | 0.0837567 | − | 0.996486i | \(-0.473308\pi\) | ||||
0.0837567 | + | 0.996486i | \(0.473308\pi\) | |||||||
\(318\) | −20.3748 | −1.14256 | ||||||||
\(319\) | −19.2690 | −1.07886 | ||||||||
\(320\) | 2.23352 | 0.124858 | ||||||||
\(321\) | −19.5052 | −1.08867 | ||||||||
\(322\) | 2.19140 | 0.122122 | ||||||||
\(323\) | −12.6621 | −0.704541 | ||||||||
\(324\) | −10.2157 | −0.567540 | ||||||||
\(325\) | 0.0437481 | 0.00242671 | ||||||||
\(326\) | 1.51117 | 0.0836958 | ||||||||
\(327\) | 20.5098 | 1.13419 | ||||||||
\(328\) | −11.4099 | −0.630007 | ||||||||
\(329\) | −10.8939 | −0.600601 | ||||||||
\(330\) | 26.9924 | 1.48588 | ||||||||
\(331\) | 24.7285 | 1.35920 | 0.679600 | − | 0.733583i | \(-0.262153\pi\) | ||||
0.679600 | + | 0.733583i | \(0.262153\pi\) | |||||||
\(332\) | 3.23651 | 0.177627 | ||||||||
\(333\) | 18.2314 | 0.999077 | ||||||||
\(334\) | −9.36815 | −0.512602 | ||||||||
\(335\) | −8.29864 | −0.453403 | ||||||||
\(336\) | −2.33717 | −0.127503 | ||||||||
\(337\) | 24.8604 | 1.35423 | 0.677117 | − | 0.735875i | \(-0.263229\pi\) | ||||
0.677117 | + | 0.735875i | \(0.263229\pi\) | |||||||
\(338\) | −1.81375 | −0.0986551 | ||||||||
\(339\) | −48.1426 | −2.61475 | ||||||||
\(340\) | 3.82810 | 0.207608 | ||||||||
\(341\) | 41.6592 | 2.25597 | ||||||||
\(342\) | 18.5950 | 1.00550 | ||||||||
\(343\) | −12.9453 | −0.698982 | ||||||||
\(344\) | −8.01588 | −0.432187 | ||||||||
\(345\) | 11.5538 | 0.622035 | ||||||||
\(346\) | −0.294859 | −0.0158517 | ||||||||
\(347\) | −16.1853 | −0.868872 | −0.434436 | − | 0.900703i | \(-0.643052\pi\) | ||||
−0.434436 | + | 0.900703i | \(0.643052\pi\) | |||||||
\(348\) | 8.79654 | 0.471544 | ||||||||
\(349\) | −18.0334 | −0.965308 | −0.482654 | − | 0.875811i | \(-0.660327\pi\) | ||||
−0.482654 | + | 0.875811i | \(0.660327\pi\) | |||||||
\(350\) | 0.0113101 | 0.000604550 0 | ||||||||
\(351\) | −4.36651 | −0.233067 | ||||||||
\(352\) | −5.14516 | −0.274238 | ||||||||
\(353\) | −24.7218 | −1.31581 | −0.657904 | − | 0.753102i | \(-0.728557\pi\) | ||||
−0.657904 | + | 0.753102i | \(0.728557\pi\) | |||||||
\(354\) | −22.3107 | −1.18580 | ||||||||
\(355\) | −14.0673 | −0.746615 | ||||||||
\(356\) | −7.51185 | −0.398127 | ||||||||
\(357\) | −4.00575 | −0.212007 | ||||||||
\(358\) | 12.7957 | 0.676271 | ||||||||
\(359\) | 22.6756 | 1.19677 | 0.598385 | − | 0.801209i | \(-0.295809\pi\) | ||||
0.598385 | + | 0.801209i | \(0.295809\pi\) | |||||||
\(360\) | −5.62177 | −0.296293 | ||||||||
\(361\) | 35.5794 | 1.87260 | ||||||||
\(362\) | 9.17056 | 0.481994 | ||||||||
\(363\) | −36.3427 | −1.90750 | ||||||||
\(364\) | −3.82976 | −0.200734 | ||||||||
\(365\) | 19.5147 | 1.02144 | ||||||||
\(366\) | −19.5581 | −1.02232 | ||||||||
\(367\) | 9.01555 | 0.470608 | 0.235304 | − | 0.971922i | \(-0.424391\pi\) | ||||
0.235304 | + | 0.971922i | \(0.424391\pi\) | |||||||
\(368\) | −2.20233 | −0.114804 | ||||||||
\(369\) | 28.7187 | 1.49503 | ||||||||
\(370\) | −16.1782 | −0.841063 | ||||||||
\(371\) | −8.63139 | −0.448120 | ||||||||
\(372\) | −19.0179 | −0.986033 | ||||||||
\(373\) | −21.3928 | −1.10768 | −0.553838 | − | 0.832624i | \(-0.686837\pi\) | ||||
−0.553838 | + | 0.832624i | \(0.686837\pi\) | |||||||
\(374\) | −8.81845 | −0.455991 | ||||||||
\(375\) | 26.2905 | 1.35763 | ||||||||
\(376\) | 10.9483 | 0.564613 | ||||||||
\(377\) | 14.4143 | 0.742374 | ||||||||
\(378\) | −1.12886 | −0.0580625 | ||||||||
\(379\) | −11.9165 | −0.612107 | −0.306054 | − | 0.952014i | \(-0.599009\pi\) | ||||
−0.306054 | + | 0.952014i | \(0.599009\pi\) | |||||||
\(380\) | −16.5008 | −0.846474 | ||||||||
\(381\) | 27.4636 | 1.40700 | ||||||||
\(382\) | 10.0537 | 0.514393 | ||||||||
\(383\) | −37.7910 | −1.93103 | −0.965515 | − | 0.260346i | \(-0.916163\pi\) | ||||
−0.965515 | + | 0.260346i | \(0.916163\pi\) | |||||||
\(384\) | 2.34883 | 0.119863 | ||||||||
\(385\) | 11.4348 | 0.582772 | ||||||||
\(386\) | −16.0777 | −0.818335 | ||||||||
\(387\) | 20.1759 | 1.02560 | ||||||||
\(388\) | −9.27019 | −0.470623 | ||||||||
\(389\) | −9.45255 | −0.479263 | −0.239632 | − | 0.970864i | \(-0.577027\pi\) | ||||
−0.239632 | + | 0.970864i | \(0.577027\pi\) | |||||||
\(390\) | −20.1918 | −1.02245 | ||||||||
\(391\) | −3.77464 | −0.190892 | ||||||||
\(392\) | 6.00990 | 0.303546 | ||||||||
\(393\) | 3.15419 | 0.159108 | ||||||||
\(394\) | −2.71892 | −0.136977 | ||||||||
\(395\) | −29.1128 | −1.46483 | ||||||||
\(396\) | 12.9504 | 0.650780 | ||||||||
\(397\) | 1.57937 | 0.0792663 | 0.0396332 | − | 0.999214i | \(-0.487381\pi\) | ||||
0.0396332 | + | 0.999214i | \(0.487381\pi\) | |||||||
\(398\) | −20.9881 | −1.05204 | ||||||||
\(399\) | 17.2665 | 0.864407 | ||||||||
\(400\) | −0.0113665 | −0.000568325 0 | ||||||||
\(401\) | 4.35142 | 0.217300 | 0.108650 | − | 0.994080i | \(-0.465347\pi\) | ||||
0.108650 | + | 0.994080i | \(0.465347\pi\) | |||||||
\(402\) | −8.72705 | −0.435266 | ||||||||
\(403\) | −31.1633 | −1.55236 | ||||||||
\(404\) | −9.58731 | −0.476987 | ||||||||
\(405\) | −22.8171 | −1.13379 | ||||||||
\(406\) | 3.72649 | 0.184943 | ||||||||
\(407\) | 37.2682 | 1.84731 | ||||||||
\(408\) | 4.02573 | 0.199303 | ||||||||
\(409\) | −30.4919 | −1.50773 | −0.753863 | − | 0.657031i | \(-0.771812\pi\) | ||||
−0.753863 | + | 0.657031i | \(0.771812\pi\) | |||||||
\(410\) | −25.4843 | −1.25858 | ||||||||
\(411\) | 12.2687 | 0.605168 | ||||||||
\(412\) | 9.85484 | 0.485513 | ||||||||
\(413\) | −9.45151 | −0.465078 | ||||||||
\(414\) | 5.54325 | 0.272436 | ||||||||
\(415\) | 7.22883 | 0.354849 | ||||||||
\(416\) | 3.84886 | 0.188706 | ||||||||
\(417\) | −29.6945 | −1.45414 | ||||||||
\(418\) | 38.0114 | 1.85920 | ||||||||
\(419\) | 31.0210 | 1.51547 | 0.757736 | − | 0.652561i | \(-0.226305\pi\) | ||||
0.757736 | + | 0.652561i | \(0.226305\pi\) | |||||||
\(420\) | −5.22013 | −0.254716 | ||||||||
\(421\) | −18.6987 | −0.911317 | −0.455659 | − | 0.890155i | \(-0.650596\pi\) | ||||
−0.455659 | + | 0.890155i | \(0.650596\pi\) | |||||||
\(422\) | −13.5100 | −0.657654 | ||||||||
\(423\) | −27.5567 | −1.33985 | ||||||||
\(424\) | 8.67445 | 0.421268 | ||||||||
\(425\) | −0.0194814 | −0.000944986 0 | ||||||||
\(426\) | −14.7935 | −0.716748 | ||||||||
\(427\) | −8.28543 | −0.400960 | ||||||||
\(428\) | 8.30423 | 0.401400 | ||||||||
\(429\) | 46.5139 | 2.24571 | ||||||||
\(430\) | −17.9037 | −0.863392 | ||||||||
\(431\) | −11.7880 | −0.567806 | −0.283903 | − | 0.958853i | \(-0.591629\pi\) | ||||
−0.283903 | + | 0.958853i | \(0.591629\pi\) | |||||||
\(432\) | 1.13449 | 0.0545834 | ||||||||
\(433\) | 6.35407 | 0.305357 | 0.152679 | − | 0.988276i | \(-0.451210\pi\) | ||||
0.152679 | + | 0.988276i | \(0.451210\pi\) | |||||||
\(434\) | −8.05658 | −0.386728 | ||||||||
\(435\) | 19.6473 | 0.942016 | ||||||||
\(436\) | −8.73192 | −0.418183 | ||||||||
\(437\) | 16.2703 | 0.778316 | ||||||||
\(438\) | 20.5221 | 0.980583 | ||||||||
\(439\) | 2.15788 | 0.102990 | 0.0514951 | − | 0.998673i | \(-0.483601\pi\) | ||||
0.0514951 | + | 0.998673i | \(0.483601\pi\) | |||||||
\(440\) | −11.4919 | −0.547852 | ||||||||
\(441\) | −15.1269 | −0.720328 | ||||||||
\(442\) | 6.59668 | 0.313772 | ||||||||
\(443\) | −31.7447 | −1.50824 | −0.754118 | − | 0.656739i | \(-0.771935\pi\) | ||||
−0.754118 | + | 0.656739i | \(0.771935\pi\) | |||||||
\(444\) | −17.0134 | −0.807418 | ||||||||
\(445\) | −16.7779 | −0.795349 | ||||||||
\(446\) | 6.63393 | 0.314126 | ||||||||
\(447\) | 17.5978 | 0.832347 | ||||||||
\(448\) | 0.995037 | 0.0470111 | ||||||||
\(449\) | −21.0383 | −0.992859 | −0.496430 | − | 0.868077i | \(-0.665356\pi\) | ||||
−0.496430 | + | 0.868077i | \(0.665356\pi\) | |||||||
\(450\) | 0.0286094 | 0.00134866 | ||||||||
\(451\) | 58.7058 | 2.76435 | ||||||||
\(452\) | 20.4964 | 0.964071 | ||||||||
\(453\) | 25.5035 | 1.19826 | ||||||||
\(454\) | 19.1777 | 0.900056 | ||||||||
\(455\) | −8.55387 | −0.401011 | ||||||||
\(456\) | −17.3526 | −0.812612 | ||||||||
\(457\) | −33.2982 | −1.55762 | −0.778811 | − | 0.627258i | \(-0.784177\pi\) | ||||
−0.778811 | + | 0.627258i | \(0.784177\pi\) | |||||||
\(458\) | 17.8995 | 0.836390 | ||||||||
\(459\) | 1.94444 | 0.0907588 | ||||||||
\(460\) | −4.91896 | −0.229347 | ||||||||
\(461\) | 27.2173 | 1.26764 | 0.633818 | − | 0.773482i | \(-0.281487\pi\) | ||||
0.633818 | + | 0.773482i | \(0.281487\pi\) | |||||||
\(462\) | 12.0251 | 0.559460 | ||||||||
\(463\) | −17.4002 | −0.808655 | −0.404328 | − | 0.914614i | \(-0.632494\pi\) | ||||
−0.404328 | + | 0.914614i | \(0.632494\pi\) | |||||||
\(464\) | −3.74508 | −0.173861 | ||||||||
\(465\) | −42.4770 | −1.96982 | ||||||||
\(466\) | −15.5094 | −0.718461 | ||||||||
\(467\) | 37.5732 | 1.73868 | 0.869341 | − | 0.494212i | \(-0.164543\pi\) | ||||
0.869341 | + | 0.494212i | \(0.164543\pi\) | |||||||
\(468\) | −9.68757 | −0.447808 | ||||||||
\(469\) | −3.69705 | −0.170714 | ||||||||
\(470\) | 24.4532 | 1.12794 | ||||||||
\(471\) | −25.5851 | −1.17890 | ||||||||
\(472\) | 9.49865 | 0.437211 | ||||||||
\(473\) | 41.2430 | 1.89636 | ||||||||
\(474\) | −30.6158 | −1.40623 | ||||||||
\(475\) | 0.0839733 | 0.00385296 | ||||||||
\(476\) | 1.70542 | 0.0781679 | ||||||||
\(477\) | −21.8335 | −0.999689 | ||||||||
\(478\) | 2.07421 | 0.0948723 | ||||||||
\(479\) | 42.7897 | 1.95511 | 0.977555 | − | 0.210680i | \(-0.0675678\pi\) | ||||
0.977555 | + | 0.210680i | \(0.0675678\pi\) | |||||||
\(480\) | 5.24617 | 0.239454 | ||||||||
\(481\) | −27.8786 | −1.27116 | ||||||||
\(482\) | 11.8031 | 0.537618 | ||||||||
\(483\) | 5.14722 | 0.234207 | ||||||||
\(484\) | 15.4727 | 0.703305 | ||||||||
\(485\) | −20.7052 | −0.940175 | ||||||||
\(486\) | −20.5915 | −0.934049 | ||||||||
\(487\) | 40.1808 | 1.82077 | 0.910384 | − | 0.413764i | \(-0.135786\pi\) | ||||
0.910384 | + | 0.413764i | \(0.135786\pi\) | |||||||
\(488\) | 8.32675 | 0.376934 | ||||||||
\(489\) | 3.54947 | 0.160513 | ||||||||
\(490\) | 13.4233 | 0.606401 | ||||||||
\(491\) | 19.8522 | 0.895915 | 0.447958 | − | 0.894055i | \(-0.352152\pi\) | ||||
0.447958 | + | 0.894055i | \(0.352152\pi\) | |||||||
\(492\) | −26.7999 | −1.20823 | ||||||||
\(493\) | −6.41880 | −0.289088 | ||||||||
\(494\) | −28.4346 | −1.27933 | ||||||||
\(495\) | 28.9249 | 1.30008 | ||||||||
\(496\) | 8.09676 | 0.363555 | ||||||||
\(497\) | −6.26699 | −0.281113 | ||||||||
\(498\) | 7.60201 | 0.340654 | ||||||||
\(499\) | 28.0755 | 1.25683 | 0.628416 | − | 0.777878i | \(-0.283704\pi\) | ||||
0.628416 | + | 0.777878i | \(0.283704\pi\) | |||||||
\(500\) | −11.1930 | −0.500567 | ||||||||
\(501\) | −22.0042 | −0.983074 | ||||||||
\(502\) | −28.9777 | −1.29334 | ||||||||
\(503\) | 38.4524 | 1.71451 | 0.857253 | − | 0.514895i | \(-0.172169\pi\) | ||||
0.857253 | + | 0.514895i | \(0.172169\pi\) | |||||||
\(504\) | −2.50450 | −0.111559 | ||||||||
\(505\) | −21.4135 | −0.952888 | ||||||||
\(506\) | 11.3313 | 0.503739 | ||||||||
\(507\) | −4.26019 | −0.189202 | ||||||||
\(508\) | −11.6925 | −0.518770 | ||||||||
\(509\) | −29.3003 | −1.29871 | −0.649357 | − | 0.760483i | \(-0.724962\pi\) | ||||
−0.649357 | + | 0.760483i | \(0.724962\pi\) | |||||||
\(510\) | 8.99156 | 0.398153 | ||||||||
\(511\) | 8.69379 | 0.384591 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −8.38140 | −0.370048 | ||||||||
\(514\) | −20.1050 | −0.886795 | ||||||||
\(515\) | 22.0110 | 0.969922 | ||||||||
\(516\) | −18.8279 | −0.828854 | ||||||||
\(517\) | −56.3306 | −2.47742 | ||||||||
\(518\) | −7.20739 | −0.316674 | ||||||||
\(519\) | −0.692573 | −0.0304006 | ||||||||
\(520\) | 8.59653 | 0.376983 | ||||||||
\(521\) | −18.7152 | −0.819929 | −0.409965 | − | 0.912101i | \(-0.634459\pi\) | ||||
−0.409965 | + | 0.912101i | \(0.634459\pi\) | |||||||
\(522\) | 9.42634 | 0.412580 | ||||||||
\(523\) | 0.595583 | 0.0260430 | 0.0130215 | − | 0.999915i | \(-0.495855\pi\) | ||||
0.0130215 | + | 0.999915i | \(0.495855\pi\) | |||||||
\(524\) | −1.34288 | −0.0586639 | ||||||||
\(525\) | 0.0265655 | 0.00115941 | ||||||||
\(526\) | 0.370427 | 0.0161514 | ||||||||
\(527\) | 13.8773 | 0.604504 | ||||||||
\(528\) | −12.0851 | −0.525937 | ||||||||
\(529\) | −18.1497 | −0.789120 | ||||||||
\(530\) | 19.3746 | 0.841578 | ||||||||
\(531\) | −23.9081 | −1.03752 | ||||||||
\(532\) | −7.35112 | −0.318712 | ||||||||
\(533\) | −43.9152 | −1.90218 | ||||||||
\(534\) | −17.6440 | −0.763533 | ||||||||
\(535\) | 18.5477 | 0.801887 | ||||||||
\(536\) | 3.71549 | 0.160485 | ||||||||
\(537\) | 30.0548 | 1.29696 | ||||||||
\(538\) | 27.3825 | 1.18054 | ||||||||
\(539\) | −30.9219 | −1.33190 | ||||||||
\(540\) | 2.53392 | 0.109043 | ||||||||
\(541\) | −29.3256 | −1.26080 | −0.630402 | − | 0.776269i | \(-0.717110\pi\) | ||||
−0.630402 | + | 0.776269i | \(0.717110\pi\) | |||||||
\(542\) | −19.0234 | −0.817124 | ||||||||
\(543\) | 21.5401 | 0.924373 | ||||||||
\(544\) | −1.71393 | −0.0734841 | ||||||||
\(545\) | −19.5030 | −0.835415 | ||||||||
\(546\) | −8.99545 | −0.384970 | ||||||||
\(547\) | −11.7341 | −0.501714 | −0.250857 | − | 0.968024i | \(-0.580712\pi\) | ||||
−0.250857 | + | 0.968024i | \(0.580712\pi\) | |||||||
\(548\) | −5.22331 | −0.223129 | ||||||||
\(549\) | −20.9584 | −0.894483 | ||||||||
\(550\) | 0.0584825 | 0.00249370 | ||||||||
\(551\) | 27.6678 | 1.17869 | ||||||||
\(552\) | −5.17289 | −0.220173 | ||||||||
\(553\) | −12.9698 | −0.551532 | ||||||||
\(554\) | 18.3627 | 0.780155 | ||||||||
\(555\) | −37.9998 | −1.61300 | ||||||||
\(556\) | 12.6423 | 0.536151 | ||||||||
\(557\) | −24.2803 | −1.02879 | −0.514395 | − | 0.857554i | \(-0.671983\pi\) | ||||
−0.514395 | + | 0.857554i | \(0.671983\pi\) | |||||||
\(558\) | −20.3795 | −0.862734 | ||||||||
\(559\) | −30.8520 | −1.30490 | ||||||||
\(560\) | 2.22244 | 0.0939152 | ||||||||
\(561\) | −20.7130 | −0.874504 | ||||||||
\(562\) | 27.6749 | 1.16740 | ||||||||
\(563\) | −41.4899 | −1.74859 | −0.874295 | − | 0.485396i | \(-0.838676\pi\) | ||||
−0.874295 | + | 0.485396i | \(0.838676\pi\) | |||||||
\(564\) | 25.7156 | 1.08282 | ||||||||
\(565\) | 45.7793 | 1.92595 | ||||||||
\(566\) | −21.1856 | −0.890497 | ||||||||
\(567\) | −10.1650 | −0.426891 | ||||||||
\(568\) | 6.29825 | 0.264269 | ||||||||
\(569\) | 16.5791 | 0.695033 | 0.347517 | − | 0.937674i | \(-0.387025\pi\) | ||||
0.347517 | + | 0.937674i | \(0.387025\pi\) | |||||||
\(570\) | −38.7576 | −1.62338 | ||||||||
\(571\) | −0.865552 | −0.0362222 | −0.0181111 | − | 0.999836i | \(-0.505765\pi\) | ||||
−0.0181111 | + | 0.999836i | \(0.505765\pi\) | |||||||
\(572\) | −19.8030 | −0.828006 | ||||||||
\(573\) | 23.6145 | 0.986508 | ||||||||
\(574\) | −11.3533 | −0.473877 | ||||||||
\(575\) | 0.0250328 | 0.00104394 | ||||||||
\(576\) | 2.51700 | 0.104875 | ||||||||
\(577\) | −6.50059 | −0.270623 | −0.135312 | − | 0.990803i | \(-0.543204\pi\) | ||||
−0.135312 | + | 0.990803i | \(0.543204\pi\) | |||||||
\(578\) | 14.0624 | 0.584921 | ||||||||
\(579\) | −37.7639 | −1.56941 | ||||||||
\(580\) | −8.36472 | −0.347326 | ||||||||
\(581\) | 3.22045 | 0.133607 | ||||||||
\(582\) | −21.7741 | −0.902565 | ||||||||
\(583\) | −44.6314 | −1.84845 | ||||||||
\(584\) | −8.73715 | −0.361546 | ||||||||
\(585\) | −21.6374 | −0.894598 | ||||||||
\(586\) | 13.1598 | 0.543628 | ||||||||
\(587\) | −37.3417 | −1.54126 | −0.770628 | − | 0.637285i | \(-0.780057\pi\) | ||||
−0.770628 | + | 0.637285i | \(0.780057\pi\) | |||||||
\(588\) | 14.1162 | 0.582143 | ||||||||
\(589\) | −59.8172 | −2.46472 | ||||||||
\(590\) | 21.2155 | 0.873427 | ||||||||
\(591\) | −6.38627 | −0.262696 | ||||||||
\(592\) | 7.24334 | 0.297699 | ||||||||
\(593\) | 30.1915 | 1.23981 | 0.619907 | − | 0.784675i | \(-0.287170\pi\) | ||||
0.619907 | + | 0.784675i | \(0.287170\pi\) | |||||||
\(594\) | −5.83716 | −0.239502 | ||||||||
\(595\) | 3.80910 | 0.156158 | ||||||||
\(596\) | −7.49216 | −0.306891 | ||||||||
\(597\) | −49.2974 | −2.01761 | ||||||||
\(598\) | −8.47646 | −0.346628 | ||||||||
\(599\) | −0.494951 | −0.0202231 | −0.0101116 | − | 0.999949i | \(-0.503219\pi\) | ||||
−0.0101116 | + | 0.999949i | \(0.503219\pi\) | |||||||
\(600\) | −0.0266980 | −0.00108994 | ||||||||
\(601\) | −19.9566 | −0.814048 | −0.407024 | − | 0.913418i | \(-0.633433\pi\) | ||||
−0.407024 | + | 0.913418i | \(0.633433\pi\) | |||||||
\(602\) | −7.97610 | −0.325082 | ||||||||
\(603\) | −9.35187 | −0.380838 | ||||||||
\(604\) | −10.8580 | −0.441804 | ||||||||
\(605\) | 34.5587 | 1.40501 | ||||||||
\(606\) | −22.5189 | −0.914770 | ||||||||
\(607\) | −45.0130 | −1.82702 | −0.913510 | − | 0.406815i | \(-0.866639\pi\) | ||||
−0.913510 | + | 0.406815i | \(0.866639\pi\) | |||||||
\(608\) | 7.38779 | 0.299614 | ||||||||
\(609\) | 8.75288 | 0.354685 | ||||||||
\(610\) | 18.5980 | 0.753011 | ||||||||
\(611\) | 42.1383 | 1.70473 | ||||||||
\(612\) | 4.31395 | 0.174381 | ||||||||
\(613\) | −9.66995 | −0.390566 | −0.195283 | − | 0.980747i | \(-0.562562\pi\) | ||||
−0.195283 | + | 0.980747i | \(0.562562\pi\) | |||||||
\(614\) | −2.80861 | −0.113346 | ||||||||
\(615\) | −59.8583 | −2.41372 | ||||||||
\(616\) | −5.11963 | −0.206276 | ||||||||
\(617\) | 24.0775 | 0.969323 | 0.484662 | − | 0.874702i | \(-0.338943\pi\) | ||||
0.484662 | + | 0.874702i | \(0.338943\pi\) | |||||||
\(618\) | 23.1473 | 0.931122 | ||||||||
\(619\) | 11.0834 | 0.445480 | 0.222740 | − | 0.974878i | \(-0.428500\pi\) | ||||
0.222740 | + | 0.974878i | \(0.428500\pi\) | |||||||
\(620\) | 18.0843 | 0.726284 | ||||||||
\(621\) | −2.49853 | −0.100263 | ||||||||
\(622\) | 13.4142 | 0.537859 | ||||||||
\(623\) | −7.47457 | −0.299462 | ||||||||
\(624\) | 9.04032 | 0.361902 | ||||||||
\(625\) | −24.9430 | −0.997722 | ||||||||
\(626\) | −7.26667 | −0.290435 | ||||||||
\(627\) | 89.2822 | 3.56559 | ||||||||
\(628\) | 10.8927 | 0.434666 | ||||||||
\(629\) | 12.4146 | 0.495001 | ||||||||
\(630\) | −5.59387 | −0.222865 | ||||||||
\(631\) | −20.6835 | −0.823396 | −0.411698 | − | 0.911320i | \(-0.635064\pi\) | ||||
−0.411698 | + | 0.911320i | \(0.635064\pi\) | |||||||
\(632\) | 13.0345 | 0.518484 | ||||||||
\(633\) | −31.7326 | −1.26126 | ||||||||
\(634\) | −2.98249 | −0.118450 | ||||||||
\(635\) | −26.1155 | −1.03636 | ||||||||
\(636\) | 20.3748 | 0.807913 | ||||||||
\(637\) | 23.1313 | 0.916495 | ||||||||
\(638\) | 19.2690 | 0.762868 | ||||||||
\(639\) | −15.8527 | −0.627122 | ||||||||
\(640\) | −2.23352 | −0.0882878 | ||||||||
\(641\) | 25.4843 | 1.00657 | 0.503285 | − | 0.864121i | \(-0.332125\pi\) | ||||
0.503285 | + | 0.864121i | \(0.332125\pi\) | |||||||
\(642\) | 19.5052 | 0.769809 | ||||||||
\(643\) | 26.7173 | 1.05363 | 0.526813 | − | 0.849981i | \(-0.323387\pi\) | ||||
0.526813 | + | 0.849981i | \(0.323387\pi\) | |||||||
\(644\) | −2.19140 | −0.0863532 | ||||||||
\(645\) | −42.0527 | −1.65582 | ||||||||
\(646\) | 12.6621 | 0.498185 | ||||||||
\(647\) | −14.1580 | −0.556610 | −0.278305 | − | 0.960493i | \(-0.589773\pi\) | ||||
−0.278305 | + | 0.960493i | \(0.589773\pi\) | |||||||
\(648\) | 10.2157 | 0.401311 | ||||||||
\(649\) | −48.8721 | −1.91840 | ||||||||
\(650\) | −0.0437481 | −0.00171594 | ||||||||
\(651\) | −18.9235 | −0.741671 | ||||||||
\(652\) | −1.51117 | −0.0591819 | ||||||||
\(653\) | −4.20829 | −0.164683 | −0.0823415 | − | 0.996604i | \(-0.526240\pi\) | ||||
−0.0823415 | + | 0.996604i | \(0.526240\pi\) | |||||||
\(654\) | −20.5098 | −0.801996 | ||||||||
\(655\) | −2.99935 | −0.117194 | ||||||||
\(656\) | 11.4099 | 0.445482 | ||||||||
\(657\) | 21.9914 | 0.857965 | ||||||||
\(658\) | 10.8939 | 0.424689 | ||||||||
\(659\) | 10.1760 | 0.396400 | 0.198200 | − | 0.980162i | \(-0.436490\pi\) | ||||
0.198200 | + | 0.980162i | \(0.436490\pi\) | |||||||
\(660\) | −26.9924 | −1.05068 | ||||||||
\(661\) | −17.6388 | −0.686068 | −0.343034 | − | 0.939323i | \(-0.611455\pi\) | ||||
−0.343034 | + | 0.939323i | \(0.611455\pi\) | |||||||
\(662\) | −24.7285 | −0.961100 | ||||||||
\(663\) | 15.4945 | 0.601755 | ||||||||
\(664\) | −3.23651 | −0.125601 | ||||||||
\(665\) | −16.4189 | −0.636698 | ||||||||
\(666\) | −18.2314 | −0.706454 | ||||||||
\(667\) | 8.24789 | 0.319360 | ||||||||
\(668\) | 9.36815 | 0.362465 | ||||||||
\(669\) | 15.5820 | 0.602434 | ||||||||
\(670\) | 8.29864 | 0.320604 | ||||||||
\(671\) | −42.8425 | −1.65392 | ||||||||
\(672\) | 2.33717 | 0.0901583 | ||||||||
\(673\) | −1.96373 | −0.0756964 | −0.0378482 | − | 0.999284i | \(-0.512050\pi\) | ||||
−0.0378482 | + | 0.999284i | \(0.512050\pi\) | |||||||
\(674\) | −24.8604 | −0.957588 | ||||||||
\(675\) | −0.0128952 | −0.000496338 0 | ||||||||
\(676\) | 1.81375 | 0.0697597 | ||||||||
\(677\) | 29.2002 | 1.12225 | 0.561126 | − | 0.827730i | \(-0.310368\pi\) | ||||
0.561126 | + | 0.827730i | \(0.310368\pi\) | |||||||
\(678\) | 48.1426 | 1.84891 | ||||||||
\(679\) | −9.22418 | −0.353992 | ||||||||
\(680\) | −3.82810 | −0.146801 | ||||||||
\(681\) | 45.0452 | 1.72614 | ||||||||
\(682\) | −41.6592 | −1.59521 | ||||||||
\(683\) | 23.9120 | 0.914966 | 0.457483 | − | 0.889218i | \(-0.348751\pi\) | ||||
0.457483 | + | 0.889218i | \(0.348751\pi\) | |||||||
\(684\) | −18.5950 | −0.710999 | ||||||||
\(685\) | −11.6664 | −0.445750 | ||||||||
\(686\) | 12.9453 | 0.494255 | ||||||||
\(687\) | 42.0429 | 1.60404 | ||||||||
\(688\) | 8.01588 | 0.305603 | ||||||||
\(689\) | 33.3868 | 1.27193 | ||||||||
\(690\) | −11.5538 | −0.439845 | ||||||||
\(691\) | −15.6254 | −0.594417 | −0.297209 | − | 0.954813i | \(-0.596056\pi\) | ||||
−0.297209 | + | 0.954813i | \(0.596056\pi\) | |||||||
\(692\) | 0.294859 | 0.0112089 | ||||||||
\(693\) | 12.8861 | 0.489502 | ||||||||
\(694\) | 16.1853 | 0.614385 | ||||||||
\(695\) | 28.2368 | 1.07108 | ||||||||
\(696\) | −8.79654 | −0.333432 | ||||||||
\(697\) | 19.5558 | 0.740728 | ||||||||
\(698\) | 18.0334 | 0.682576 | ||||||||
\(699\) | −36.4290 | −1.37787 | ||||||||
\(700\) | −0.0113101 | −0.000427481 0 | ||||||||
\(701\) | −34.3225 | −1.29634 | −0.648172 | − | 0.761494i | \(-0.724466\pi\) | ||||
−0.648172 | + | 0.761494i | \(0.724466\pi\) | |||||||
\(702\) | 4.36651 | 0.164803 | ||||||||
\(703\) | −53.5122 | −2.01825 | ||||||||
\(704\) | 5.14516 | 0.193916 | ||||||||
\(705\) | 57.4364 | 2.16318 | ||||||||
\(706\) | 24.7218 | 0.930416 | ||||||||
\(707\) | −9.53973 | −0.358778 | ||||||||
\(708\) | 22.3107 | 0.838488 | ||||||||
\(709\) | 2.78977 | 0.104772 | 0.0523859 | − | 0.998627i | \(-0.483317\pi\) | ||||
0.0523859 | + | 0.998627i | \(0.483317\pi\) | |||||||
\(710\) | 14.0673 | 0.527937 | ||||||||
\(711\) | −32.8077 | −1.23039 | ||||||||
\(712\) | 7.51185 | 0.281518 | ||||||||
\(713\) | −17.8317 | −0.667804 | ||||||||
\(714\) | 4.00575 | 0.149911 | ||||||||
\(715\) | −44.2306 | −1.65413 | ||||||||
\(716\) | −12.7957 | −0.478196 | ||||||||
\(717\) | 4.87197 | 0.181947 | ||||||||
\(718\) | −22.6756 | −0.846244 | ||||||||
\(719\) | −32.8736 | −1.22598 | −0.612989 | − | 0.790091i | \(-0.710033\pi\) | ||||
−0.612989 | + | 0.790091i | \(0.710033\pi\) | |||||||
\(720\) | 5.62177 | 0.209511 | ||||||||
\(721\) | 9.80593 | 0.365192 | ||||||||
\(722\) | −35.5794 | −1.32413 | ||||||||
\(723\) | 27.7235 | 1.03105 | ||||||||
\(724\) | −9.17056 | −0.340821 | ||||||||
\(725\) | 0.0425684 | 0.00158095 | ||||||||
\(726\) | 36.3427 | 1.34881 | ||||||||
\(727\) | −13.7935 | −0.511572 | −0.255786 | − | 0.966733i | \(-0.582334\pi\) | ||||
−0.255786 | + | 0.966733i | \(0.582334\pi\) | |||||||
\(728\) | 3.82976 | 0.141940 | ||||||||
\(729\) | −17.7187 | −0.656249 | ||||||||
\(730\) | −19.5147 | −0.722270 | ||||||||
\(731\) | 13.7387 | 0.508142 | ||||||||
\(732\) | 19.5581 | 0.722889 | ||||||||
\(733\) | 27.5268 | 1.01673 | 0.508363 | − | 0.861143i | \(-0.330251\pi\) | ||||
0.508363 | + | 0.861143i | \(0.330251\pi\) | |||||||
\(734\) | −9.01555 | −0.332770 | ||||||||
\(735\) | 31.5289 | 1.16296 | ||||||||
\(736\) | 2.20233 | 0.0811789 | ||||||||
\(737\) | −19.1168 | −0.704177 | ||||||||
\(738\) | −28.7187 | −1.05715 | ||||||||
\(739\) | 16.5669 | 0.609422 | 0.304711 | − | 0.952445i | \(-0.401440\pi\) | ||||
0.304711 | + | 0.952445i | \(0.401440\pi\) | |||||||
\(740\) | 16.1782 | 0.594721 | ||||||||
\(741\) | −66.7880 | −2.45352 | ||||||||
\(742\) | 8.63139 | 0.316868 | ||||||||
\(743\) | 21.4188 | 0.785781 | 0.392890 | − | 0.919585i | \(-0.371475\pi\) | ||||
0.392890 | + | 0.919585i | \(0.371475\pi\) | |||||||
\(744\) | 19.0179 | 0.697230 | ||||||||
\(745\) | −16.7339 | −0.613084 | ||||||||
\(746\) | 21.3928 | 0.783246 | ||||||||
\(747\) | 8.14628 | 0.298057 | ||||||||
\(748\) | 8.81845 | 0.322434 | ||||||||
\(749\) | 8.26301 | 0.301924 | ||||||||
\(750\) | −26.2905 | −0.959992 | ||||||||
\(751\) | −10.3607 | −0.378068 | −0.189034 | − | 0.981971i | \(-0.560536\pi\) | ||||
−0.189034 | + | 0.981971i | \(0.560536\pi\) | |||||||
\(752\) | −10.9483 | −0.399242 | ||||||||
\(753\) | −68.0636 | −2.48038 | ||||||||
\(754\) | −14.4143 | −0.524937 | ||||||||
\(755\) | −24.2515 | −0.882603 | ||||||||
\(756\) | 1.12886 | 0.0410564 | ||||||||
\(757\) | 16.3663 | 0.594845 | 0.297422 | − | 0.954746i | \(-0.403873\pi\) | ||||
0.297422 | + | 0.954746i | \(0.403873\pi\) | |||||||
\(758\) | 11.9165 | 0.432825 | ||||||||
\(759\) | 26.6154 | 0.966077 | ||||||||
\(760\) | 16.5008 | 0.598547 | ||||||||
\(761\) | 26.4737 | 0.959669 | 0.479835 | − | 0.877359i | \(-0.340697\pi\) | ||||
0.479835 | + | 0.877359i | \(0.340697\pi\) | |||||||
\(762\) | −27.4636 | −0.994903 | ||||||||
\(763\) | −8.68858 | −0.314548 | ||||||||
\(764\) | −10.0537 | −0.363731 | ||||||||
\(765\) | 9.63532 | 0.348366 | ||||||||
\(766\) | 37.7910 | 1.36544 | ||||||||
\(767\) | 36.5590 | 1.32007 | ||||||||
\(768\) | −2.34883 | −0.0847561 | ||||||||
\(769\) | −12.8384 | −0.462965 | −0.231482 | − | 0.972839i | \(-0.574358\pi\) | ||||
−0.231482 | + | 0.972839i | \(0.574358\pi\) | |||||||
\(770\) | −11.4348 | −0.412082 | ||||||||
\(771\) | −47.2233 | −1.70070 | ||||||||
\(772\) | 16.0777 | 0.578651 | ||||||||
\(773\) | −19.2624 | −0.692819 | −0.346410 | − | 0.938083i | \(-0.612599\pi\) | ||||
−0.346410 | + | 0.938083i | \(0.612599\pi\) | |||||||
\(774\) | −20.1759 | −0.725209 | ||||||||
\(775\) | −0.0920319 | −0.00330588 | ||||||||
\(776\) | 9.27019 | 0.332781 | ||||||||
\(777\) | −16.9289 | −0.607322 | ||||||||
\(778\) | 9.45255 | 0.338890 | ||||||||
\(779\) | −84.2940 | −3.02014 | ||||||||
\(780\) | 20.1918 | 0.722982 | ||||||||
\(781\) | −32.4055 | −1.15956 | ||||||||
\(782\) | 3.77464 | 0.134981 | ||||||||
\(783\) | −4.24877 | −0.151839 | ||||||||
\(784\) | −6.00990 | −0.214639 | ||||||||
\(785\) | 24.3291 | 0.868344 | ||||||||
\(786\) | −3.15419 | −0.112506 | ||||||||
\(787\) | 4.71235 | 0.167977 | 0.0839885 | − | 0.996467i | \(-0.473234\pi\) | ||||
0.0839885 | + | 0.996467i | \(0.473234\pi\) | |||||||
\(788\) | 2.71892 | 0.0968575 | ||||||||
\(789\) | 0.870071 | 0.0309753 | ||||||||
\(790\) | 29.1128 | 1.03579 | ||||||||
\(791\) | 20.3947 | 0.725153 | ||||||||
\(792\) | −12.9504 | −0.460171 | ||||||||
\(793\) | 32.0485 | 1.13808 | ||||||||
\(794\) | −1.57937 | −0.0560498 | ||||||||
\(795\) | 45.5076 | 1.61399 | ||||||||
\(796\) | 20.9881 | 0.743903 | ||||||||
\(797\) | 1.43465 | 0.0508181 | 0.0254090 | − | 0.999677i | \(-0.491911\pi\) | ||||
0.0254090 | + | 0.999677i | \(0.491911\pi\) | |||||||
\(798\) | −17.2665 | −0.611228 | ||||||||
\(799\) | −18.7645 | −0.663841 | ||||||||
\(800\) | 0.0113665 | 0.000401867 0 | ||||||||
\(801\) | −18.9073 | −0.668056 | ||||||||
\(802\) | −4.35142 | −0.153654 | ||||||||
\(803\) | 44.9541 | 1.58640 | ||||||||
\(804\) | 8.72705 | 0.307779 | ||||||||
\(805\) | −4.89454 | −0.172510 | ||||||||
\(806\) | 31.1633 | 1.09768 | ||||||||
\(807\) | 64.3168 | 2.26406 | ||||||||
\(808\) | 9.58731 | 0.337280 | ||||||||
\(809\) | 46.9252 | 1.64980 | 0.824901 | − | 0.565277i | \(-0.191231\pi\) | ||||
0.824901 | + | 0.565277i | \(0.191231\pi\) | |||||||
\(810\) | 22.8171 | 0.801710 | ||||||||
\(811\) | −23.8180 | −0.836362 | −0.418181 | − | 0.908364i | \(-0.637332\pi\) | ||||
−0.418181 | + | 0.908364i | \(0.637332\pi\) | |||||||
\(812\) | −3.72649 | −0.130774 | ||||||||
\(813\) | −44.6826 | −1.56709 | ||||||||
\(814\) | −37.2682 | −1.30625 | ||||||||
\(815\) | −3.37523 | −0.118229 | ||||||||
\(816\) | −4.02573 | −0.140929 | ||||||||
\(817\) | −59.2196 | −2.07183 | ||||||||
\(818\) | 30.4919 | 1.06612 | ||||||||
\(819\) | −9.63949 | −0.336831 | ||||||||
\(820\) | 25.4843 | 0.889951 | ||||||||
\(821\) | 1.20419 | 0.0420266 | 0.0210133 | − | 0.999779i | \(-0.493311\pi\) | ||||
0.0210133 | + | 0.999779i | \(0.493311\pi\) | |||||||
\(822\) | −12.2687 | −0.427918 | ||||||||
\(823\) | 18.5327 | 0.646011 | 0.323006 | − | 0.946397i | \(-0.395307\pi\) | ||||
0.323006 | + | 0.946397i | \(0.395307\pi\) | |||||||
\(824\) | −9.85484 | −0.343310 | ||||||||
\(825\) | 0.137365 | 0.00478245 | ||||||||
\(826\) | 9.45151 | 0.328860 | ||||||||
\(827\) | −9.34430 | −0.324933 | −0.162467 | − | 0.986714i | \(-0.551945\pi\) | ||||
−0.162467 | + | 0.986714i | \(0.551945\pi\) | |||||||
\(828\) | −5.54325 | −0.192641 | ||||||||
\(829\) | −24.0958 | −0.836883 | −0.418441 | − | 0.908244i | \(-0.637423\pi\) | ||||
−0.418441 | + | 0.908244i | \(0.637423\pi\) | |||||||
\(830\) | −7.22883 | −0.250916 | ||||||||
\(831\) | 43.1308 | 1.49619 | ||||||||
\(832\) | −3.84886 | −0.133435 | ||||||||
\(833\) | −10.3005 | −0.356893 | ||||||||
\(834\) | 29.6945 | 1.02824 | ||||||||
\(835\) | 20.9240 | 0.724105 | ||||||||
\(836\) | −38.0114 | −1.31465 | ||||||||
\(837\) | 9.18573 | 0.317505 | ||||||||
\(838\) | −31.0210 | −1.07160 | ||||||||
\(839\) | 12.9542 | 0.447230 | 0.223615 | − | 0.974678i | \(-0.428214\pi\) | ||||
0.223615 | + | 0.974678i | \(0.428214\pi\) | |||||||
\(840\) | 5.22013 | 0.180112 | ||||||||
\(841\) | −14.9744 | −0.516359 | ||||||||
\(842\) | 18.6987 | 0.644399 | ||||||||
\(843\) | 65.0036 | 2.23884 | ||||||||
\(844\) | 13.5100 | 0.465032 | ||||||||
\(845\) | 4.05106 | 0.139361 | ||||||||
\(846\) | 27.5567 | 0.947419 | ||||||||
\(847\) | 15.3959 | 0.529010 | ||||||||
\(848\) | −8.67445 | −0.297882 | ||||||||
\(849\) | −49.7613 | −1.70781 | ||||||||
\(850\) | 0.0194814 | 0.000668206 0 | ||||||||
\(851\) | −15.9522 | −0.546835 | ||||||||
\(852\) | 14.7935 | 0.506818 | ||||||||
\(853\) | −2.81402 | −0.0963503 | −0.0481751 | − | 0.998839i | \(-0.515341\pi\) | ||||
−0.0481751 | + | 0.998839i | \(0.515341\pi\) | |||||||
\(854\) | 8.28543 | 0.283521 | ||||||||
\(855\) | −41.5325 | −1.42038 | ||||||||
\(856\) | −8.30423 | −0.283833 | ||||||||
\(857\) | 2.63164 | 0.0898949 | 0.0449475 | − | 0.998989i | \(-0.485688\pi\) | ||||
0.0449475 | + | 0.998989i | \(0.485688\pi\) | |||||||
\(858\) | −46.5139 | −1.58796 | ||||||||
\(859\) | −24.0385 | −0.820183 | −0.410091 | − | 0.912044i | \(-0.634503\pi\) | ||||
−0.410091 | + | 0.912044i | \(0.634503\pi\) | |||||||
\(860\) | 17.9037 | 0.610510 | ||||||||
\(861\) | −26.6669 | −0.908805 | ||||||||
\(862\) | 11.7880 | 0.401499 | ||||||||
\(863\) | −1.06568 | −0.0362762 | −0.0181381 | − | 0.999835i | \(-0.505774\pi\) | ||||
−0.0181381 | + | 0.999835i | \(0.505774\pi\) | |||||||
\(864\) | −1.13449 | −0.0385963 | ||||||||
\(865\) | 0.658575 | 0.0223922 | ||||||||
\(866\) | −6.35407 | −0.215920 | ||||||||
\(867\) | 33.0303 | 1.12177 | ||||||||
\(868\) | 8.05658 | 0.273458 | ||||||||
\(869\) | −67.0645 | −2.27501 | ||||||||
\(870\) | −19.6473 | −0.666106 | ||||||||
\(871\) | 14.3004 | 0.484551 | ||||||||
\(872\) | 8.73192 | 0.295700 | ||||||||
\(873\) | −23.3330 | −0.789704 | ||||||||
\(874\) | −16.2703 | −0.550352 | ||||||||
\(875\) | −11.1375 | −0.376515 | ||||||||
\(876\) | −20.5221 | −0.693377 | ||||||||
\(877\) | −39.3923 | −1.33018 | −0.665091 | − | 0.746762i | \(-0.731607\pi\) | ||||
−0.665091 | + | 0.746762i | \(0.731607\pi\) | |||||||
\(878\) | −2.15788 | −0.0728250 | ||||||||
\(879\) | 30.9102 | 1.04258 | ||||||||
\(880\) | 11.4919 | 0.387390 | ||||||||
\(881\) | 56.7603 | 1.91230 | 0.956152 | − | 0.292870i | \(-0.0946105\pi\) | ||||
0.956152 | + | 0.292870i | \(0.0946105\pi\) | |||||||
\(882\) | 15.1269 | 0.509349 | ||||||||
\(883\) | −32.0198 | −1.07755 | −0.538775 | − | 0.842450i | \(-0.681113\pi\) | ||||
−0.538775 | + | 0.842450i | \(0.681113\pi\) | |||||||
\(884\) | −6.59668 | −0.221870 | ||||||||
\(885\) | 49.8315 | 1.67507 | ||||||||
\(886\) | 31.7447 | 1.06648 | ||||||||
\(887\) | −50.0266 | −1.67973 | −0.839864 | − | 0.542797i | \(-0.817365\pi\) | ||||
−0.839864 | + | 0.542797i | \(0.817365\pi\) | |||||||
\(888\) | 17.0134 | 0.570931 | ||||||||
\(889\) | −11.6345 | −0.390207 | ||||||||
\(890\) | 16.7779 | 0.562397 | ||||||||
\(891\) | −52.5615 | −1.76088 | ||||||||
\(892\) | −6.63393 | −0.222120 | ||||||||
\(893\) | 80.8834 | 2.70666 | ||||||||
\(894\) | −17.5978 | −0.588558 | ||||||||
\(895\) | −28.5794 | −0.955304 | ||||||||
\(896\) | −0.995037 | −0.0332418 | ||||||||
\(897\) | −19.9098 | −0.664767 | ||||||||
\(898\) | 21.0383 | 0.702057 | ||||||||
\(899\) | −30.3230 | −1.01133 | ||||||||
\(900\) | −0.0286094 | −0.000953648 0 | ||||||||
\(901\) | −14.8674 | −0.495304 | ||||||||
\(902\) | −58.7058 | −1.95469 | ||||||||
\(903\) | −18.7345 | −0.623445 | ||||||||
\(904\) | −20.4964 | −0.681701 | ||||||||
\(905\) | −20.4827 | −0.680867 | ||||||||
\(906\) | −25.5035 | −0.847297 | ||||||||
\(907\) | −28.7556 | −0.954814 | −0.477407 | − | 0.878682i | \(-0.658423\pi\) | ||||
−0.477407 | + | 0.878682i | \(0.658423\pi\) | |||||||
\(908\) | −19.1777 | −0.636435 | ||||||||
\(909\) | −24.1312 | −0.800382 | ||||||||
\(910\) | 8.55387 | 0.283558 | ||||||||
\(911\) | 38.9709 | 1.29116 | 0.645582 | − | 0.763691i | \(-0.276615\pi\) | ||||
0.645582 | + | 0.763691i | \(0.276615\pi\) | |||||||
\(912\) | 17.3526 | 0.574604 | ||||||||
\(913\) | 16.6524 | 0.551113 | ||||||||
\(914\) | 33.2982 | 1.10141 | ||||||||
\(915\) | 43.6835 | 1.44413 | ||||||||
\(916\) | −17.8995 | −0.591417 | ||||||||
\(917\) | −1.33621 | −0.0441256 | ||||||||
\(918\) | −1.94444 | −0.0641762 | ||||||||
\(919\) | −36.0484 | −1.18913 | −0.594563 | − | 0.804049i | \(-0.702675\pi\) | ||||
−0.594563 | + | 0.804049i | \(0.702675\pi\) | |||||||
\(920\) | 4.91896 | 0.162173 | ||||||||
\(921\) | −6.59695 | −0.217377 | ||||||||
\(922\) | −27.2173 | −0.896354 | ||||||||
\(923\) | 24.2411 | 0.797906 | ||||||||
\(924\) | −12.0251 | −0.395598 | ||||||||
\(925\) | −0.0823314 | −0.00270704 | ||||||||
\(926\) | 17.4002 | 0.571805 | ||||||||
\(927\) | 24.8046 | 0.814690 | ||||||||
\(928\) | 3.74508 | 0.122938 | ||||||||
\(929\) | −33.7157 | −1.10618 | −0.553088 | − | 0.833123i | \(-0.686551\pi\) | ||||
−0.553088 | + | 0.833123i | \(0.686551\pi\) | |||||||
\(930\) | 42.4770 | 1.39288 | ||||||||
\(931\) | 44.3999 | 1.45515 | ||||||||
\(932\) | 15.5094 | 0.508029 | ||||||||
\(933\) | 31.5076 | 1.03151 | ||||||||
\(934\) | −37.5732 | −1.22943 | ||||||||
\(935\) | 19.6962 | 0.644135 | ||||||||
\(936\) | 9.68757 | 0.316648 | ||||||||
\(937\) | −41.2182 | −1.34654 | −0.673270 | − | 0.739397i | \(-0.735111\pi\) | ||||
−0.673270 | + | 0.739397i | \(0.735111\pi\) | |||||||
\(938\) | 3.69705 | 0.120713 | ||||||||
\(939\) | −17.0682 | −0.556999 | ||||||||
\(940\) | −24.4532 | −0.797575 | ||||||||
\(941\) | −57.3203 | −1.86859 | −0.934293 | − | 0.356505i | \(-0.883968\pi\) | ||||
−0.934293 | + | 0.356505i | \(0.883968\pi\) | |||||||
\(942\) | 25.5851 | 0.833607 | ||||||||
\(943\) | −25.1284 | −0.818292 | ||||||||
\(944\) | −9.49865 | −0.309155 | ||||||||
\(945\) | 2.52135 | 0.0820194 | ||||||||
\(946\) | −41.2430 | −1.34093 | ||||||||
\(947\) | −20.6235 | −0.670173 | −0.335086 | − | 0.942187i | \(-0.608765\pi\) | ||||
−0.335086 | + | 0.942187i | \(0.608765\pi\) | |||||||
\(948\) | 30.6158 | 0.994354 | ||||||||
\(949\) | −33.6281 | −1.09161 | ||||||||
\(950\) | −0.0839733 | −0.00272445 | ||||||||
\(951\) | −7.00536 | −0.227164 | ||||||||
\(952\) | −1.70542 | −0.0552731 | ||||||||
\(953\) | −17.5106 | −0.567225 | −0.283613 | − | 0.958939i | \(-0.591533\pi\) | ||||
−0.283613 | + | 0.958939i | \(0.591533\pi\) | |||||||
\(954\) | 21.8335 | 0.706887 | ||||||||
\(955\) | −22.4552 | −0.726634 | ||||||||
\(956\) | −2.07421 | −0.0670849 | ||||||||
\(957\) | 45.2596 | 1.46304 | ||||||||
\(958\) | −42.7897 | −1.38247 | ||||||||
\(959\) | −5.19738 | −0.167832 | ||||||||
\(960\) | −5.24617 | −0.169319 | ||||||||
\(961\) | 34.5576 | 1.11476 | ||||||||
\(962\) | 27.8786 | 0.898843 | ||||||||
\(963\) | 20.9017 | 0.673548 | ||||||||
\(964\) | −11.8031 | −0.380153 | ||||||||
\(965\) | 35.9100 | 1.15598 | ||||||||
\(966\) | −5.14722 | −0.165609 | ||||||||
\(967\) | −55.9622 | −1.79962 | −0.899812 | − | 0.436278i | \(-0.856296\pi\) | ||||
−0.899812 | + | 0.436278i | \(0.856296\pi\) | |||||||
\(968\) | −15.4727 | −0.497312 | ||||||||
\(969\) | 29.7412 | 0.955425 | ||||||||
\(970\) | 20.7052 | 0.664804 | ||||||||
\(971\) | 10.0573 | 0.322755 | 0.161378 | − | 0.986893i | \(-0.448406\pi\) | ||||
0.161378 | + | 0.986893i | \(0.448406\pi\) | |||||||
\(972\) | 20.5915 | 0.660472 | ||||||||
\(973\) | 12.5795 | 0.403280 | ||||||||
\(974\) | −40.1808 | −1.28748 | ||||||||
\(975\) | −0.102757 | −0.00329085 | ||||||||
\(976\) | −8.32675 | −0.266533 | ||||||||
\(977\) | −46.0128 | −1.47208 | −0.736040 | − | 0.676938i | \(-0.763307\pi\) | ||||
−0.736040 | + | 0.676938i | \(0.763307\pi\) | |||||||
\(978\) | −3.54947 | −0.113500 | ||||||||
\(979\) | −38.6497 | −1.23525 | ||||||||
\(980\) | −13.4233 | −0.428790 | ||||||||
\(981\) | −21.9782 | −0.701710 | ||||||||
\(982\) | −19.8522 | −0.633508 | ||||||||
\(983\) | −10.1921 | −0.325079 | −0.162539 | − | 0.986702i | \(-0.551968\pi\) | ||||
−0.162539 | + | 0.986702i | \(0.551968\pi\) | |||||||
\(984\) | 26.7999 | 0.854350 | ||||||||
\(985\) | 6.07277 | 0.193495 | ||||||||
\(986\) | 6.41880 | 0.204416 | ||||||||
\(987\) | 25.5879 | 0.814473 | ||||||||
\(988\) | 28.4346 | 0.904625 | ||||||||
\(989\) | −17.6536 | −0.561352 | ||||||||
\(990\) | −28.9249 | −0.919295 | ||||||||
\(991\) | −28.2206 | −0.896458 | −0.448229 | − | 0.893919i | \(-0.647945\pi\) | ||||
−0.448229 | + | 0.893919i | \(0.647945\pi\) | |||||||
\(992\) | −8.09676 | −0.257073 | ||||||||
\(993\) | −58.0830 | −1.84321 | ||||||||
\(994\) | 6.26699 | 0.198777 | ||||||||
\(995\) | 46.8774 | 1.48611 | ||||||||
\(996\) | −7.60201 | −0.240879 | ||||||||
\(997\) | 24.5981 | 0.779030 | 0.389515 | − | 0.921020i | \(-0.372643\pi\) | ||||
0.389515 | + | 0.921020i | \(0.372643\pi\) | |||||||
\(998\) | −28.0755 | −0.888714 | ||||||||
\(999\) | 8.21753 | 0.259991 |
(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 | 8006.2.a.b.1.12 | ✓ | 75 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8006.2.a.b.1.12 | ✓ | 75 | 1.1 | even | 1 | trivial |