Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8005,2,Mod(1,8005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8005, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8005.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8005 = 5 \cdot 1601 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8005.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: | \(63.9202468180\) |
Analytic rank: | \(1\) |
Dimension: | \(126\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 8005.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.60227 | −1.84008 | −0.920040 | − | 0.391825i | \(-0.871844\pi\) | ||||
−0.920040 | + | 0.391825i | \(0.871844\pi\) | |||||||
\(3\) | −2.65544 | −1.53312 | −0.766560 | − | 0.642173i | \(-0.778033\pi\) | ||||
−0.766560 | + | 0.642173i | \(0.778033\pi\) | |||||||
\(4\) | 4.77178 | 2.38589 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 6.91016 | 2.82106 | ||||||||
\(7\) | 2.75161 | 1.04001 | 0.520006 | − | 0.854163i | \(-0.325930\pi\) | ||||
0.520006 | + | 0.854163i | \(0.325930\pi\) | |||||||
\(8\) | −7.21291 | −2.55015 | ||||||||
\(9\) | 4.05137 | 1.35046 | ||||||||
\(10\) | −2.60227 | −0.822908 | ||||||||
\(11\) | −0.255242 | −0.0769584 | −0.0384792 | − | 0.999259i | \(-0.512251\pi\) | ||||
−0.0384792 | + | 0.999259i | \(0.512251\pi\) | |||||||
\(12\) | −12.6712 | −3.65786 | ||||||||
\(13\) | 2.04832 | 0.568102 | 0.284051 | − | 0.958809i | \(-0.408321\pi\) | ||||
0.284051 | + | 0.958809i | \(0.408321\pi\) | |||||||
\(14\) | −7.16043 | −1.91370 | ||||||||
\(15\) | −2.65544 | −0.685632 | ||||||||
\(16\) | 9.22635 | 2.30659 | ||||||||
\(17\) | −7.65192 | −1.85586 | −0.927931 | − | 0.372752i | \(-0.878414\pi\) | ||||
−0.927931 | + | 0.372752i | \(0.878414\pi\) | |||||||
\(18\) | −10.5427 | −2.48495 | ||||||||
\(19\) | −3.20945 | −0.736299 | −0.368150 | − | 0.929767i | \(-0.620009\pi\) | ||||
−0.368150 | + | 0.929767i | \(0.620009\pi\) | |||||||
\(20\) | 4.77178 | 1.06700 | ||||||||
\(21\) | −7.30675 | −1.59446 | ||||||||
\(22\) | 0.664208 | 0.141610 | ||||||||
\(23\) | −1.51464 | −0.315824 | −0.157912 | − | 0.987453i | \(-0.550476\pi\) | ||||
−0.157912 | + | 0.987453i | \(0.550476\pi\) | |||||||
\(24\) | 19.1535 | 3.90969 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.33028 | −1.04535 | ||||||||
\(27\) | −2.79186 | −0.537294 | ||||||||
\(28\) | 13.1301 | 2.48136 | ||||||||
\(29\) | −7.77707 | −1.44417 | −0.722083 | − | 0.691806i | \(-0.756815\pi\) | ||||
−0.722083 | + | 0.691806i | \(0.756815\pi\) | |||||||
\(30\) | 6.91016 | 1.26162 | ||||||||
\(31\) | 9.40876 | 1.68986 | 0.844932 | − | 0.534874i | \(-0.179641\pi\) | ||||
0.844932 | + | 0.534874i | \(0.179641\pi\) | |||||||
\(32\) | −9.58357 | −1.69415 | ||||||||
\(33\) | 0.677781 | 0.117987 | ||||||||
\(34\) | 19.9123 | 3.41493 | ||||||||
\(35\) | 2.75161 | 0.465107 | ||||||||
\(36\) | 19.3323 | 3.22205 | ||||||||
\(37\) | −10.9863 | −1.80613 | −0.903066 | − | 0.429502i | \(-0.858689\pi\) | ||||
−0.903066 | + | 0.429502i | \(0.858689\pi\) | |||||||
\(38\) | 8.35185 | 1.35485 | ||||||||
\(39\) | −5.43920 | −0.870969 | ||||||||
\(40\) | −7.21291 | −1.14046 | ||||||||
\(41\) | 12.1796 | 1.90214 | 0.951071 | − | 0.308974i | \(-0.0999855\pi\) | ||||
0.951071 | + | 0.308974i | \(0.0999855\pi\) | |||||||
\(42\) | 19.0141 | 2.93394 | ||||||||
\(43\) | 1.81152 | 0.276254 | 0.138127 | − | 0.990415i | \(-0.455892\pi\) | ||||
0.138127 | + | 0.990415i | \(0.455892\pi\) | |||||||
\(44\) | −1.21796 | −0.183614 | ||||||||
\(45\) | 4.05137 | 0.603943 | ||||||||
\(46\) | 3.94149 | 0.581142 | ||||||||
\(47\) | 5.19390 | 0.757608 | 0.378804 | − | 0.925477i | \(-0.376335\pi\) | ||||
0.378804 | + | 0.925477i | \(0.376335\pi\) | |||||||
\(48\) | −24.5000 | −3.53628 | ||||||||
\(49\) | 0.571374 | 0.0816249 | ||||||||
\(50\) | −2.60227 | −0.368016 | ||||||||
\(51\) | 20.3192 | 2.84526 | ||||||||
\(52\) | 9.77415 | 1.35543 | ||||||||
\(53\) | −8.31779 | −1.14254 | −0.571268 | − | 0.820764i | \(-0.693548\pi\) | ||||
−0.571268 | + | 0.820764i | \(0.693548\pi\) | |||||||
\(54\) | 7.26516 | 0.988663 | ||||||||
\(55\) | −0.255242 | −0.0344169 | ||||||||
\(56\) | −19.8471 | −2.65219 | ||||||||
\(57\) | 8.52252 | 1.12883 | ||||||||
\(58\) | 20.2380 | 2.65738 | ||||||||
\(59\) | 6.33586 | 0.824859 | 0.412430 | − | 0.910990i | \(-0.364680\pi\) | ||||
0.412430 | + | 0.910990i | \(0.364680\pi\) | |||||||
\(60\) | −12.6712 | −1.63584 | ||||||||
\(61\) | 10.4139 | 1.33336 | 0.666681 | − | 0.745343i | \(-0.267714\pi\) | ||||
0.666681 | + | 0.745343i | \(0.267714\pi\) | |||||||
\(62\) | −24.4841 | −3.10948 | ||||||||
\(63\) | 11.1478 | 1.40449 | ||||||||
\(64\) | 6.48630 | 0.810788 | ||||||||
\(65\) | 2.04832 | 0.254063 | ||||||||
\(66\) | −1.76377 | −0.217105 | ||||||||
\(67\) | −0.920885 | −0.112504 | −0.0562520 | − | 0.998417i | \(-0.517915\pi\) | ||||
−0.0562520 | + | 0.998417i | \(0.517915\pi\) | |||||||
\(68\) | −36.5133 | −4.42789 | ||||||||
\(69\) | 4.02204 | 0.484197 | ||||||||
\(70\) | −7.16043 | −0.855835 | ||||||||
\(71\) | −5.84286 | −0.693420 | −0.346710 | − | 0.937972i | \(-0.612701\pi\) | ||||
−0.346710 | + | 0.937972i | \(0.612701\pi\) | |||||||
\(72\) | −29.2222 | −3.44387 | ||||||||
\(73\) | 13.3537 | 1.56294 | 0.781469 | − | 0.623944i | \(-0.214471\pi\) | ||||
0.781469 | + | 0.623944i | \(0.214471\pi\) | |||||||
\(74\) | 28.5892 | 3.32343 | ||||||||
\(75\) | −2.65544 | −0.306624 | ||||||||
\(76\) | −15.3148 | −1.75673 | ||||||||
\(77\) | −0.702328 | −0.0800377 | ||||||||
\(78\) | 14.1542 | 1.60265 | ||||||||
\(79\) | 0.662656 | 0.0745546 | 0.0372773 | − | 0.999305i | \(-0.488132\pi\) | ||||
0.0372773 | + | 0.999305i | \(0.488132\pi\) | |||||||
\(80\) | 9.22635 | 1.03154 | ||||||||
\(81\) | −4.74049 | −0.526722 | ||||||||
\(82\) | −31.6947 | −3.50009 | ||||||||
\(83\) | −5.01500 | −0.550468 | −0.275234 | − | 0.961377i | \(-0.588755\pi\) | ||||
−0.275234 | + | 0.961377i | \(0.588755\pi\) | |||||||
\(84\) | −34.8662 | −3.80422 | ||||||||
\(85\) | −7.65192 | −0.829967 | ||||||||
\(86\) | −4.71405 | −0.508329 | ||||||||
\(87\) | 20.6516 | 2.21408 | ||||||||
\(88\) | 1.84104 | 0.196256 | ||||||||
\(89\) | 8.04409 | 0.852672 | 0.426336 | − | 0.904565i | \(-0.359804\pi\) | ||||
0.426336 | + | 0.904565i | \(0.359804\pi\) | |||||||
\(90\) | −10.5427 | −1.11130 | ||||||||
\(91\) | 5.63619 | 0.590833 | ||||||||
\(92\) | −7.22753 | −0.753523 | ||||||||
\(93\) | −24.9844 | −2.59076 | ||||||||
\(94\) | −13.5159 | −1.39406 | ||||||||
\(95\) | −3.20945 | −0.329283 | ||||||||
\(96\) | 25.4486 | 2.59734 | ||||||||
\(97\) | −3.17274 | −0.322143 | −0.161072 | − | 0.986943i | \(-0.551495\pi\) | ||||
−0.161072 | + | 0.986943i | \(0.551495\pi\) | |||||||
\(98\) | −1.48687 | −0.150196 | ||||||||
\(99\) | −1.03408 | −0.103929 | ||||||||
\(100\) | 4.77178 | 0.477178 | ||||||||
\(101\) | 8.90088 | 0.885670 | 0.442835 | − | 0.896603i | \(-0.353973\pi\) | ||||
0.442835 | + | 0.896603i | \(0.353973\pi\) | |||||||
\(102\) | −52.8760 | −5.23550 | ||||||||
\(103\) | 4.31504 | 0.425174 | 0.212587 | − | 0.977142i | \(-0.431811\pi\) | ||||
0.212587 | + | 0.977142i | \(0.431811\pi\) | |||||||
\(104\) | −14.7744 | −1.44875 | ||||||||
\(105\) | −7.30675 | −0.713066 | ||||||||
\(106\) | 21.6451 | 2.10236 | ||||||||
\(107\) | −16.3847 | −1.58396 | −0.791982 | − | 0.610544i | \(-0.790951\pi\) | ||||
−0.791982 | + | 0.610544i | \(0.790951\pi\) | |||||||
\(108\) | −13.3222 | −1.28193 | ||||||||
\(109\) | −3.94538 | −0.377899 | −0.188950 | − | 0.981987i | \(-0.560508\pi\) | ||||
−0.188950 | + | 0.981987i | \(0.560508\pi\) | |||||||
\(110\) | 0.664208 | 0.0633297 | ||||||||
\(111\) | 29.1734 | 2.76902 | ||||||||
\(112\) | 25.3873 | 2.39888 | ||||||||
\(113\) | 2.76272 | 0.259895 | 0.129948 | − | 0.991521i | \(-0.458519\pi\) | ||||
0.129948 | + | 0.991521i | \(0.458519\pi\) | |||||||
\(114\) | −22.1778 | −2.07715 | ||||||||
\(115\) | −1.51464 | −0.141241 | ||||||||
\(116\) | −37.1105 | −3.44562 | ||||||||
\(117\) | 8.29852 | 0.767198 | ||||||||
\(118\) | −16.4876 | −1.51781 | ||||||||
\(119\) | −21.0551 | −1.93012 | ||||||||
\(120\) | 19.1535 | 1.74847 | ||||||||
\(121\) | −10.9349 | −0.994077 | ||||||||
\(122\) | −27.0997 | −2.45349 | ||||||||
\(123\) | −32.3423 | −2.91621 | ||||||||
\(124\) | 44.8966 | 4.03183 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −29.0096 | −2.58438 | ||||||||
\(127\) | 10.1331 | 0.899164 | 0.449582 | − | 0.893239i | \(-0.351573\pi\) | ||||
0.449582 | + | 0.893239i | \(0.351573\pi\) | |||||||
\(128\) | 2.28807 | 0.202238 | ||||||||
\(129\) | −4.81038 | −0.423531 | ||||||||
\(130\) | −5.33028 | −0.467496 | ||||||||
\(131\) | 0.749989 | 0.0655268 | 0.0327634 | − | 0.999463i | \(-0.489569\pi\) | ||||
0.0327634 | + | 0.999463i | \(0.489569\pi\) | |||||||
\(132\) | 3.23422 | 0.281503 | ||||||||
\(133\) | −8.83117 | −0.765760 | ||||||||
\(134\) | 2.39639 | 0.207016 | ||||||||
\(135\) | −2.79186 | −0.240285 | ||||||||
\(136\) | 55.1926 | 4.73273 | ||||||||
\(137\) | −0.947492 | −0.0809497 | −0.0404748 | − | 0.999181i | \(-0.512887\pi\) | ||||
−0.0404748 | + | 0.999181i | \(0.512887\pi\) | |||||||
\(138\) | −10.4664 | −0.890960 | ||||||||
\(139\) | 1.53935 | 0.130566 | 0.0652829 | − | 0.997867i | \(-0.479205\pi\) | ||||
0.0652829 | + | 0.997867i | \(0.479205\pi\) | |||||||
\(140\) | 13.1301 | 1.10970 | ||||||||
\(141\) | −13.7921 | −1.16150 | ||||||||
\(142\) | 15.2047 | 1.27595 | ||||||||
\(143\) | −0.522818 | −0.0437202 | ||||||||
\(144\) | 37.3794 | 3.11495 | ||||||||
\(145\) | −7.77707 | −0.645851 | ||||||||
\(146\) | −34.7500 | −2.87593 | ||||||||
\(147\) | −1.51725 | −0.125141 | ||||||||
\(148\) | −52.4241 | −4.30923 | ||||||||
\(149\) | −16.2503 | −1.33128 | −0.665639 | − | 0.746274i | \(-0.731841\pi\) | ||||
−0.665639 | + | 0.746274i | \(0.731841\pi\) | |||||||
\(150\) | 6.91016 | 0.564213 | ||||||||
\(151\) | 4.29802 | 0.349768 | 0.174884 | − | 0.984589i | \(-0.444045\pi\) | ||||
0.174884 | + | 0.984589i | \(0.444045\pi\) | |||||||
\(152\) | 23.1495 | 1.87767 | ||||||||
\(153\) | −31.0008 | −2.50626 | ||||||||
\(154\) | 1.82764 | 0.147276 | ||||||||
\(155\) | 9.40876 | 0.755730 | ||||||||
\(156\) | −25.9547 | −2.07804 | ||||||||
\(157\) | −10.2831 | −0.820683 | −0.410342 | − | 0.911932i | \(-0.634591\pi\) | ||||
−0.410342 | + | 0.911932i | \(0.634591\pi\) | |||||||
\(158\) | −1.72441 | −0.137186 | ||||||||
\(159\) | 22.0874 | 1.75164 | ||||||||
\(160\) | −9.58357 | −0.757648 | ||||||||
\(161\) | −4.16770 | −0.328461 | ||||||||
\(162\) | 12.3360 | 0.969209 | ||||||||
\(163\) | 8.35764 | 0.654621 | 0.327310 | − | 0.944917i | \(-0.393858\pi\) | ||||
0.327310 | + | 0.944917i | \(0.393858\pi\) | |||||||
\(164\) | 58.1186 | 4.53830 | ||||||||
\(165\) | 0.677781 | 0.0527652 | ||||||||
\(166\) | 13.0504 | 1.01290 | ||||||||
\(167\) | −20.9145 | −1.61841 | −0.809206 | − | 0.587525i | \(-0.800102\pi\) | ||||
−0.809206 | + | 0.587525i | \(0.800102\pi\) | |||||||
\(168\) | 52.7030 | 4.06612 | ||||||||
\(169\) | −8.80438 | −0.677260 | ||||||||
\(170\) | 19.9123 | 1.52720 | ||||||||
\(171\) | −13.0027 | −0.994341 | ||||||||
\(172\) | 8.64417 | 0.659112 | ||||||||
\(173\) | 0.973306 | 0.0739991 | 0.0369995 | − | 0.999315i | \(-0.488220\pi\) | ||||
0.0369995 | + | 0.999315i | \(0.488220\pi\) | |||||||
\(174\) | −53.7408 | −4.07408 | ||||||||
\(175\) | 2.75161 | 0.208002 | ||||||||
\(176\) | −2.35495 | −0.177511 | ||||||||
\(177\) | −16.8245 | −1.26461 | ||||||||
\(178\) | −20.9329 | −1.56898 | ||||||||
\(179\) | 13.5387 | 1.01193 | 0.505965 | − | 0.862554i | \(-0.331136\pi\) | ||||
0.505965 | + | 0.862554i | \(0.331136\pi\) | |||||||
\(180\) | 19.3323 | 1.44094 | ||||||||
\(181\) | 5.29939 | 0.393901 | 0.196950 | − | 0.980413i | \(-0.436896\pi\) | ||||
0.196950 | + | 0.980413i | \(0.436896\pi\) | |||||||
\(182\) | −14.6669 | −1.08718 | ||||||||
\(183\) | −27.6535 | −2.04421 | ||||||||
\(184\) | 10.9250 | 0.805399 | ||||||||
\(185\) | −10.9863 | −0.807727 | ||||||||
\(186\) | 65.0161 | 4.76721 | ||||||||
\(187\) | 1.95309 | 0.142824 | ||||||||
\(188\) | 24.7842 | 1.80757 | ||||||||
\(189\) | −7.68212 | −0.558792 | ||||||||
\(190\) | 8.35185 | 0.605907 | ||||||||
\(191\) | −9.65146 | −0.698355 | −0.349177 | − | 0.937057i | \(-0.613539\pi\) | ||||
−0.349177 | + | 0.937057i | \(0.613539\pi\) | |||||||
\(192\) | −17.2240 | −1.24304 | ||||||||
\(193\) | 16.5722 | 1.19289 | 0.596445 | − | 0.802654i | \(-0.296579\pi\) | ||||
0.596445 | + | 0.802654i | \(0.296579\pi\) | |||||||
\(194\) | 8.25632 | 0.592769 | ||||||||
\(195\) | −5.43920 | −0.389509 | ||||||||
\(196\) | 2.72647 | 0.194748 | ||||||||
\(197\) | −3.54848 | −0.252819 | −0.126409 | − | 0.991978i | \(-0.540345\pi\) | ||||
−0.126409 | + | 0.991978i | \(0.540345\pi\) | |||||||
\(198\) | 2.69095 | 0.191238 | ||||||||
\(199\) | 9.54313 | 0.676495 | 0.338247 | − | 0.941057i | \(-0.390166\pi\) | ||||
0.338247 | + | 0.941057i | \(0.390166\pi\) | |||||||
\(200\) | −7.21291 | −0.510030 | ||||||||
\(201\) | 2.44536 | 0.172482 | ||||||||
\(202\) | −23.1624 | −1.62970 | ||||||||
\(203\) | −21.3995 | −1.50195 | ||||||||
\(204\) | 96.9589 | 6.78848 | ||||||||
\(205\) | 12.1796 | 0.850663 | ||||||||
\(206\) | −11.2289 | −0.782354 | ||||||||
\(207\) | −6.13637 | −0.426507 | ||||||||
\(208\) | 18.8985 | 1.31038 | ||||||||
\(209\) | 0.819188 | 0.0566644 | ||||||||
\(210\) | 19.0141 | 1.31210 | ||||||||
\(211\) | −16.4839 | −1.13480 | −0.567401 | − | 0.823442i | \(-0.692051\pi\) | ||||
−0.567401 | + | 0.823442i | \(0.692051\pi\) | |||||||
\(212\) | −39.6907 | −2.72597 | ||||||||
\(213\) | 15.5154 | 1.06310 | ||||||||
\(214\) | 42.6372 | 2.91462 | ||||||||
\(215\) | 1.81152 | 0.123545 | ||||||||
\(216\) | 20.1375 | 1.37018 | ||||||||
\(217\) | 25.8893 | 1.75748 | ||||||||
\(218\) | 10.2669 | 0.695365 | ||||||||
\(219\) | −35.4601 | −2.39617 | ||||||||
\(220\) | −1.21796 | −0.0821149 | ||||||||
\(221\) | −15.6736 | −1.05432 | ||||||||
\(222\) | −75.9169 | −5.09521 | ||||||||
\(223\) | −17.3492 | −1.16179 | −0.580894 | − | 0.813979i | \(-0.697297\pi\) | ||||
−0.580894 | + | 0.813979i | \(0.697297\pi\) | |||||||
\(224\) | −26.3703 | −1.76194 | ||||||||
\(225\) | 4.05137 | 0.270092 | ||||||||
\(226\) | −7.18934 | −0.478227 | ||||||||
\(227\) | −11.4398 | −0.759286 | −0.379643 | − | 0.925133i | \(-0.623953\pi\) | ||||
−0.379643 | + | 0.925133i | \(0.623953\pi\) | |||||||
\(228\) | 40.6676 | 2.69328 | ||||||||
\(229\) | 27.3345 | 1.80631 | 0.903157 | − | 0.429309i | \(-0.141243\pi\) | ||||
0.903157 | + | 0.429309i | \(0.141243\pi\) | |||||||
\(230\) | 3.94149 | 0.259894 | ||||||||
\(231\) | 1.86499 | 0.122707 | ||||||||
\(232\) | 56.0954 | 3.68284 | ||||||||
\(233\) | 15.3749 | 1.00724 | 0.503621 | − | 0.863925i | \(-0.332001\pi\) | ||||
0.503621 | + | 0.863925i | \(0.332001\pi\) | |||||||
\(234\) | −21.5949 | −1.41171 | ||||||||
\(235\) | 5.19390 | 0.338813 | ||||||||
\(236\) | 30.2334 | 1.96802 | ||||||||
\(237\) | −1.75964 | −0.114301 | ||||||||
\(238\) | 54.7910 | 3.55157 | ||||||||
\(239\) | −8.38075 | −0.542106 | −0.271053 | − | 0.962564i | \(-0.587372\pi\) | ||||
−0.271053 | + | 0.962564i | \(0.587372\pi\) | |||||||
\(240\) | −24.5000 | −1.58147 | ||||||||
\(241\) | 12.6311 | 0.813643 | 0.406822 | − | 0.913508i | \(-0.366637\pi\) | ||||
0.406822 | + | 0.913508i | \(0.366637\pi\) | |||||||
\(242\) | 28.4554 | 1.82918 | ||||||||
\(243\) | 20.9637 | 1.34482 | ||||||||
\(244\) | 49.6929 | 3.18126 | ||||||||
\(245\) | 0.571374 | 0.0365037 | ||||||||
\(246\) | 84.1634 | 5.36606 | ||||||||
\(247\) | −6.57399 | −0.418293 | ||||||||
\(248\) | −67.8646 | −4.30941 | ||||||||
\(249\) | 13.3170 | 0.843933 | ||||||||
\(250\) | −2.60227 | −0.164582 | ||||||||
\(251\) | −10.3834 | −0.655394 | −0.327697 | − | 0.944783i | \(-0.606272\pi\) | ||||
−0.327697 | + | 0.944783i | \(0.606272\pi\) | |||||||
\(252\) | 53.1949 | 3.35097 | ||||||||
\(253\) | 0.386600 | 0.0243053 | ||||||||
\(254\) | −26.3689 | −1.65453 | ||||||||
\(255\) | 20.3192 | 1.27244 | ||||||||
\(256\) | −18.9268 | −1.18292 | ||||||||
\(257\) | −9.71540 | −0.606030 | −0.303015 | − | 0.952986i | \(-0.597993\pi\) | ||||
−0.303015 | + | 0.952986i | \(0.597993\pi\) | |||||||
\(258\) | 12.5179 | 0.779330 | ||||||||
\(259\) | −30.2300 | −1.87840 | ||||||||
\(260\) | 9.77415 | 0.606167 | ||||||||
\(261\) | −31.5078 | −1.95029 | ||||||||
\(262\) | −1.95167 | −0.120575 | ||||||||
\(263\) | 14.4204 | 0.889202 | 0.444601 | − | 0.895729i | \(-0.353345\pi\) | ||||
0.444601 | + | 0.895729i | \(0.353345\pi\) | |||||||
\(264\) | −4.88878 | −0.300883 | ||||||||
\(265\) | −8.31779 | −0.510958 | ||||||||
\(266\) | 22.9811 | 1.40906 | ||||||||
\(267\) | −21.3606 | −1.30725 | ||||||||
\(268\) | −4.39426 | −0.268422 | ||||||||
\(269\) | −10.0265 | −0.611324 | −0.305662 | − | 0.952140i | \(-0.598878\pi\) | ||||
−0.305662 | + | 0.952140i | \(0.598878\pi\) | |||||||
\(270\) | 7.26516 | 0.442144 | ||||||||
\(271\) | −22.7416 | −1.38145 | −0.690727 | − | 0.723116i | \(-0.742709\pi\) | ||||
−0.690727 | + | 0.723116i | \(0.742709\pi\) | |||||||
\(272\) | −70.5992 | −4.28071 | ||||||||
\(273\) | −14.9666 | −0.905818 | ||||||||
\(274\) | 2.46562 | 0.148954 | ||||||||
\(275\) | −0.255242 | −0.0153917 | ||||||||
\(276\) | 19.1923 | 1.15524 | ||||||||
\(277\) | −15.9153 | −0.956256 | −0.478128 | − | 0.878290i | \(-0.658685\pi\) | ||||
−0.478128 | + | 0.878290i | \(0.658685\pi\) | |||||||
\(278\) | −4.00579 | −0.240251 | ||||||||
\(279\) | 38.1184 | 2.28209 | ||||||||
\(280\) | −19.8471 | −1.18609 | ||||||||
\(281\) | 22.4614 | 1.33994 | 0.669969 | − | 0.742389i | \(-0.266308\pi\) | ||||
0.669969 | + | 0.742389i | \(0.266308\pi\) | |||||||
\(282\) | 35.8907 | 2.13726 | ||||||||
\(283\) | −14.0120 | −0.832924 | −0.416462 | − | 0.909153i | \(-0.636730\pi\) | ||||
−0.416462 | + | 0.909153i | \(0.636730\pi\) | |||||||
\(284\) | −27.8809 | −1.65443 | ||||||||
\(285\) | 8.52252 | 0.504830 | ||||||||
\(286\) | 1.36051 | 0.0804487 | ||||||||
\(287\) | 33.5137 | 1.97825 | ||||||||
\(288\) | −38.8266 | −2.28788 | ||||||||
\(289\) | 41.5518 | 2.44422 | ||||||||
\(290\) | 20.2380 | 1.18842 | ||||||||
\(291\) | 8.42504 | 0.493885 | ||||||||
\(292\) | 63.7212 | 3.72900 | ||||||||
\(293\) | 6.43164 | 0.375741 | 0.187870 | − | 0.982194i | \(-0.439842\pi\) | ||||
0.187870 | + | 0.982194i | \(0.439842\pi\) | |||||||
\(294\) | 3.94829 | 0.230269 | ||||||||
\(295\) | 6.33586 | 0.368888 | ||||||||
\(296\) | 79.2430 | 4.60591 | ||||||||
\(297\) | 0.712601 | 0.0413493 | ||||||||
\(298\) | 42.2876 | 2.44966 | ||||||||
\(299\) | −3.10247 | −0.179420 | ||||||||
\(300\) | −12.6712 | −0.731572 | ||||||||
\(301\) | 4.98460 | 0.287307 | ||||||||
\(302\) | −11.1846 | −0.643600 | ||||||||
\(303\) | −23.6358 | −1.35784 | ||||||||
\(304\) | −29.6115 | −1.69834 | ||||||||
\(305\) | 10.4139 | 0.596298 | ||||||||
\(306\) | 80.6722 | 4.61172 | ||||||||
\(307\) | −12.7754 | −0.729132 | −0.364566 | − | 0.931178i | \(-0.618783\pi\) | ||||
−0.364566 | + | 0.931178i | \(0.618783\pi\) | |||||||
\(308\) | −3.35136 | −0.190961 | ||||||||
\(309\) | −11.4584 | −0.651843 | ||||||||
\(310\) | −24.4841 | −1.39060 | ||||||||
\(311\) | 18.2371 | 1.03413 | 0.517066 | − | 0.855945i | \(-0.327024\pi\) | ||||
0.517066 | + | 0.855945i | \(0.327024\pi\) | |||||||
\(312\) | 39.2325 | 2.22110 | ||||||||
\(313\) | 20.9210 | 1.18252 | 0.591261 | − | 0.806480i | \(-0.298630\pi\) | ||||
0.591261 | + | 0.806480i | \(0.298630\pi\) | |||||||
\(314\) | 26.7594 | 1.51012 | ||||||||
\(315\) | 11.1478 | 0.628108 | ||||||||
\(316\) | 3.16205 | 0.177879 | ||||||||
\(317\) | −3.75276 | −0.210776 | −0.105388 | − | 0.994431i | \(-0.533608\pi\) | ||||
−0.105388 | + | 0.994431i | \(0.533608\pi\) | |||||||
\(318\) | −57.4773 | −3.22317 | ||||||||
\(319\) | 1.98504 | 0.111141 | ||||||||
\(320\) | 6.48630 | 0.362595 | ||||||||
\(321\) | 43.5085 | 2.42841 | ||||||||
\(322\) | 10.8455 | 0.604394 | ||||||||
\(323\) | 24.5585 | 1.36647 | ||||||||
\(324\) | −22.6206 | −1.25670 | ||||||||
\(325\) | 2.04832 | 0.113620 | ||||||||
\(326\) | −21.7488 | −1.20455 | ||||||||
\(327\) | 10.4767 | 0.579365 | ||||||||
\(328\) | −87.8507 | −4.85075 | ||||||||
\(329\) | 14.2916 | 0.787922 | ||||||||
\(330\) | −1.76377 | −0.0970921 | ||||||||
\(331\) | −21.8059 | −1.19856 | −0.599279 | − | 0.800540i | \(-0.704546\pi\) | ||||
−0.599279 | + | 0.800540i | \(0.704546\pi\) | |||||||
\(332\) | −23.9305 | −1.31336 | ||||||||
\(333\) | −44.5095 | −2.43910 | ||||||||
\(334\) | 54.4250 | 2.97801 | ||||||||
\(335\) | −0.920885 | −0.0503133 | ||||||||
\(336\) | −67.4146 | −3.67777 | ||||||||
\(337\) | −8.72009 | −0.475014 | −0.237507 | − | 0.971386i | \(-0.576330\pi\) | ||||
−0.237507 | + | 0.971386i | \(0.576330\pi\) | |||||||
\(338\) | 22.9113 | 1.24621 | ||||||||
\(339\) | −7.33625 | −0.398450 | ||||||||
\(340\) | −36.5133 | −1.98021 | ||||||||
\(341\) | −2.40151 | −0.130049 | ||||||||
\(342\) | 33.8365 | 1.82967 | ||||||||
\(343\) | −17.6891 | −0.955121 | ||||||||
\(344\) | −13.0663 | −0.704489 | ||||||||
\(345\) | 4.02204 | 0.216539 | ||||||||
\(346\) | −2.53280 | −0.136164 | ||||||||
\(347\) | −17.1834 | −0.922452 | −0.461226 | − | 0.887283i | \(-0.652590\pi\) | ||||
−0.461226 | + | 0.887283i | \(0.652590\pi\) | |||||||
\(348\) | 98.5448 | 5.28256 | ||||||||
\(349\) | 12.0183 | 0.643324 | 0.321662 | − | 0.946855i | \(-0.395759\pi\) | ||||
0.321662 | + | 0.946855i | \(0.395759\pi\) | |||||||
\(350\) | −7.16043 | −0.382741 | ||||||||
\(351\) | −5.71863 | −0.305238 | ||||||||
\(352\) | 2.44613 | 0.130379 | ||||||||
\(353\) | 8.78586 | 0.467624 | 0.233812 | − | 0.972282i | \(-0.424880\pi\) | ||||
0.233812 | + | 0.972282i | \(0.424880\pi\) | |||||||
\(354\) | 43.7819 | 2.32698 | ||||||||
\(355\) | −5.84286 | −0.310107 | ||||||||
\(356\) | 38.3846 | 2.03438 | ||||||||
\(357\) | 55.9106 | 2.95910 | ||||||||
\(358\) | −35.2313 | −1.86203 | ||||||||
\(359\) | −1.78811 | −0.0943729 | −0.0471865 | − | 0.998886i | \(-0.515025\pi\) | ||||
−0.0471865 | + | 0.998886i | \(0.515025\pi\) | |||||||
\(360\) | −29.2222 | −1.54015 | ||||||||
\(361\) | −8.69941 | −0.457864 | ||||||||
\(362\) | −13.7904 | −0.724809 | ||||||||
\(363\) | 29.0369 | 1.52404 | ||||||||
\(364\) | 26.8947 | 1.40966 | ||||||||
\(365\) | 13.3537 | 0.698967 | ||||||||
\(366\) | 71.9617 | 3.76150 | ||||||||
\(367\) | 6.46016 | 0.337218 | 0.168609 | − | 0.985683i | \(-0.446073\pi\) | ||||
0.168609 | + | 0.985683i | \(0.446073\pi\) | |||||||
\(368\) | −13.9746 | −0.728476 | ||||||||
\(369\) | 49.3443 | 2.56876 | ||||||||
\(370\) | 28.5892 | 1.48628 | ||||||||
\(371\) | −22.8873 | −1.18825 | ||||||||
\(372\) | −119.220 | −6.18128 | ||||||||
\(373\) | −7.28401 | −0.377152 | −0.188576 | − | 0.982059i | \(-0.560387\pi\) | ||||
−0.188576 | + | 0.982059i | \(0.560387\pi\) | |||||||
\(374\) | −5.08246 | −0.262808 | ||||||||
\(375\) | −2.65544 | −0.137126 | ||||||||
\(376\) | −37.4632 | −1.93202 | ||||||||
\(377\) | −15.9299 | −0.820434 | ||||||||
\(378\) | 19.9909 | 1.02822 | ||||||||
\(379\) | −20.3956 | −1.04765 | −0.523826 | − | 0.851825i | \(-0.675496\pi\) | ||||
−0.523826 | + | 0.851825i | \(0.675496\pi\) | |||||||
\(380\) | −15.3148 | −0.785633 | ||||||||
\(381\) | −26.9078 | −1.37853 | ||||||||
\(382\) | 25.1156 | 1.28503 | ||||||||
\(383\) | 19.8690 | 1.01526 | 0.507630 | − | 0.861575i | \(-0.330522\pi\) | ||||
0.507630 | + | 0.861575i | \(0.330522\pi\) | |||||||
\(384\) | −6.07583 | −0.310056 | ||||||||
\(385\) | −0.702328 | −0.0357939 | ||||||||
\(386\) | −43.1251 | −2.19501 | ||||||||
\(387\) | 7.33914 | 0.373069 | ||||||||
\(388\) | −15.1396 | −0.768599 | ||||||||
\(389\) | 28.5665 | 1.44838 | 0.724189 | − | 0.689602i | \(-0.242214\pi\) | ||||
0.724189 | + | 0.689602i | \(0.242214\pi\) | |||||||
\(390\) | 14.1542 | 0.716728 | ||||||||
\(391\) | 11.5899 | 0.586126 | ||||||||
\(392\) | −4.12127 | −0.208156 | ||||||||
\(393\) | −1.99155 | −0.100460 | ||||||||
\(394\) | 9.23408 | 0.465206 | ||||||||
\(395\) | 0.662656 | 0.0333418 | ||||||||
\(396\) | −4.93441 | −0.247964 | ||||||||
\(397\) | 25.9083 | 1.30030 | 0.650150 | − | 0.759806i | \(-0.274706\pi\) | ||||
0.650150 | + | 0.759806i | \(0.274706\pi\) | |||||||
\(398\) | −24.8338 | −1.24480 | ||||||||
\(399\) | 23.4507 | 1.17400 | ||||||||
\(400\) | 9.22635 | 0.461317 | ||||||||
\(401\) | −27.5549 | −1.37603 | −0.688013 | − | 0.725698i | \(-0.741517\pi\) | ||||
−0.688013 | + | 0.725698i | \(0.741517\pi\) | |||||||
\(402\) | −6.36347 | −0.317381 | ||||||||
\(403\) | 19.2722 | 0.960015 | ||||||||
\(404\) | 42.4731 | 2.11311 | ||||||||
\(405\) | −4.74049 | −0.235557 | ||||||||
\(406\) | 55.6871 | 2.76371 | ||||||||
\(407\) | 2.80416 | 0.138997 | ||||||||
\(408\) | −146.561 | −7.25584 | ||||||||
\(409\) | −11.6625 | −0.576671 | −0.288336 | − | 0.957529i | \(-0.593102\pi\) | ||||
−0.288336 | + | 0.957529i | \(0.593102\pi\) | |||||||
\(410\) | −31.6947 | −1.56529 | ||||||||
\(411\) | 2.51601 | 0.124106 | ||||||||
\(412\) | 20.5905 | 1.01442 | ||||||||
\(413\) | 17.4338 | 0.857863 | ||||||||
\(414\) | 15.9685 | 0.784807 | ||||||||
\(415\) | −5.01500 | −0.246177 | ||||||||
\(416\) | −19.6302 | −0.962452 | ||||||||
\(417\) | −4.08765 | −0.200173 | ||||||||
\(418\) | −2.13174 | −0.104267 | ||||||||
\(419\) | 8.70010 | 0.425028 | 0.212514 | − | 0.977158i | \(-0.431835\pi\) | ||||
0.212514 | + | 0.977158i | \(0.431835\pi\) | |||||||
\(420\) | −34.8662 | −1.70130 | ||||||||
\(421\) | −30.6168 | −1.49217 | −0.746086 | − | 0.665849i | \(-0.768069\pi\) | ||||
−0.746086 | + | 0.665849i | \(0.768069\pi\) | |||||||
\(422\) | 42.8956 | 2.08813 | ||||||||
\(423\) | 21.0424 | 1.02312 | ||||||||
\(424\) | 59.9955 | 2.91364 | ||||||||
\(425\) | −7.65192 | −0.371172 | ||||||||
\(426\) | −40.3752 | −1.95618 | ||||||||
\(427\) | 28.6550 | 1.38671 | ||||||||
\(428\) | −78.1840 | −3.77917 | ||||||||
\(429\) | 1.38831 | 0.0670284 | ||||||||
\(430\) | −4.71405 | −0.227332 | ||||||||
\(431\) | −39.6091 | −1.90790 | −0.953952 | − | 0.299961i | \(-0.903026\pi\) | ||||
−0.953952 | + | 0.299961i | \(0.903026\pi\) | |||||||
\(432\) | −25.7587 | −1.23932 | ||||||||
\(433\) | −31.3493 | −1.50655 | −0.753276 | − | 0.657704i | \(-0.771528\pi\) | ||||
−0.753276 | + | 0.657704i | \(0.771528\pi\) | |||||||
\(434\) | −67.3708 | −3.23390 | ||||||||
\(435\) | 20.6516 | 0.990167 | ||||||||
\(436\) | −18.8265 | −0.901627 | ||||||||
\(437\) | 4.86117 | 0.232541 | ||||||||
\(438\) | 92.2766 | 4.40914 | ||||||||
\(439\) | 13.5850 | 0.648376 | 0.324188 | − | 0.945993i | \(-0.394909\pi\) | ||||
0.324188 | + | 0.945993i | \(0.394909\pi\) | |||||||
\(440\) | 1.84104 | 0.0877681 | ||||||||
\(441\) | 2.31485 | 0.110231 | ||||||||
\(442\) | 40.7868 | 1.94003 | ||||||||
\(443\) | 1.66550 | 0.0791302 | 0.0395651 | − | 0.999217i | \(-0.487403\pi\) | ||||
0.0395651 | + | 0.999217i | \(0.487403\pi\) | |||||||
\(444\) | 139.209 | 6.60657 | ||||||||
\(445\) | 8.04409 | 0.381326 | ||||||||
\(446\) | 45.1472 | 2.13778 | ||||||||
\(447\) | 43.1518 | 2.04101 | ||||||||
\(448\) | 17.8478 | 0.843229 | ||||||||
\(449\) | 5.36062 | 0.252983 | 0.126492 | − | 0.991968i | \(-0.459628\pi\) | ||||
0.126492 | + | 0.991968i | \(0.459628\pi\) | |||||||
\(450\) | −10.5427 | −0.496990 | ||||||||
\(451\) | −3.10876 | −0.146386 | ||||||||
\(452\) | 13.1831 | 0.620081 | ||||||||
\(453\) | −11.4131 | −0.536236 | ||||||||
\(454\) | 29.7694 | 1.39715 | ||||||||
\(455\) | 5.63619 | 0.264229 | ||||||||
\(456\) | −61.4722 | −2.87870 | ||||||||
\(457\) | 15.7380 | 0.736192 | 0.368096 | − | 0.929788i | \(-0.380010\pi\) | ||||
0.368096 | + | 0.929788i | \(0.380010\pi\) | |||||||
\(458\) | −71.1316 | −3.32376 | ||||||||
\(459\) | 21.3631 | 0.997144 | ||||||||
\(460\) | −7.22753 | −0.336986 | ||||||||
\(461\) | −5.74844 | −0.267732 | −0.133866 | − | 0.990999i | \(-0.542739\pi\) | ||||
−0.133866 | + | 0.990999i | \(0.542739\pi\) | |||||||
\(462\) | −4.85320 | −0.225791 | ||||||||
\(463\) | −35.5404 | −1.65170 | −0.825851 | − | 0.563889i | \(-0.809305\pi\) | ||||
−0.825851 | + | 0.563889i | \(0.809305\pi\) | |||||||
\(464\) | −71.7540 | −3.33109 | ||||||||
\(465\) | −24.9844 | −1.15863 | ||||||||
\(466\) | −40.0095 | −1.85341 | ||||||||
\(467\) | 26.4982 | 1.22619 | 0.613096 | − | 0.790009i | \(-0.289924\pi\) | ||||
0.613096 | + | 0.790009i | \(0.289924\pi\) | |||||||
\(468\) | 39.5987 | 1.83045 | ||||||||
\(469\) | −2.53392 | −0.117006 | ||||||||
\(470\) | −13.5159 | −0.623442 | ||||||||
\(471\) | 27.3063 | 1.25821 | ||||||||
\(472\) | −45.7000 | −2.10351 | ||||||||
\(473\) | −0.462376 | −0.0212601 | ||||||||
\(474\) | 4.57906 | 0.210323 | ||||||||
\(475\) | −3.20945 | −0.147260 | ||||||||
\(476\) | −100.470 | −4.60505 | ||||||||
\(477\) | −33.6985 | −1.54295 | ||||||||
\(478\) | 21.8089 | 0.997518 | ||||||||
\(479\) | 22.8888 | 1.04582 | 0.522908 | − | 0.852389i | \(-0.324847\pi\) | ||||
0.522908 | + | 0.852389i | \(0.324847\pi\) | |||||||
\(480\) | 25.4486 | 1.16157 | ||||||||
\(481\) | −22.5034 | −1.02607 | ||||||||
\(482\) | −32.8696 | −1.49717 | ||||||||
\(483\) | 11.0671 | 0.503570 | ||||||||
\(484\) | −52.1787 | −2.37176 | ||||||||
\(485\) | −3.17274 | −0.144067 | ||||||||
\(486\) | −54.5531 | −2.47458 | ||||||||
\(487\) | −37.7392 | −1.71013 | −0.855063 | − | 0.518524i | \(-0.826482\pi\) | ||||
−0.855063 | + | 0.518524i | \(0.826482\pi\) | |||||||
\(488\) | −75.1146 | −3.40028 | ||||||||
\(489\) | −22.1932 | −1.00361 | ||||||||
\(490\) | −1.48687 | −0.0671698 | ||||||||
\(491\) | 31.7506 | 1.43288 | 0.716442 | − | 0.697646i | \(-0.245769\pi\) | ||||
0.716442 | + | 0.697646i | \(0.245769\pi\) | |||||||
\(492\) | −154.331 | −6.95776 | ||||||||
\(493\) | 59.5095 | 2.68017 | ||||||||
\(494\) | 17.1073 | 0.769692 | ||||||||
\(495\) | −1.03408 | −0.0464785 | ||||||||
\(496\) | 86.8085 | 3.89782 | ||||||||
\(497\) | −16.0773 | −0.721166 | ||||||||
\(498\) | −34.6545 | −1.55290 | ||||||||
\(499\) | 21.8588 | 0.978536 | 0.489268 | − | 0.872134i | \(-0.337264\pi\) | ||||
0.489268 | + | 0.872134i | \(0.337264\pi\) | |||||||
\(500\) | 4.77178 | 0.213401 | ||||||||
\(501\) | 55.5372 | 2.48122 | ||||||||
\(502\) | 27.0203 | 1.20598 | ||||||||
\(503\) | −9.43807 | −0.420823 | −0.210411 | − | 0.977613i | \(-0.567480\pi\) | ||||
−0.210411 | + | 0.977613i | \(0.567480\pi\) | |||||||
\(504\) | −80.4082 | −3.58167 | ||||||||
\(505\) | 8.90088 | 0.396084 | ||||||||
\(506\) | −1.00604 | −0.0447237 | ||||||||
\(507\) | 23.3795 | 1.03832 | ||||||||
\(508\) | 48.3528 | 2.14531 | ||||||||
\(509\) | 21.3682 | 0.947131 | 0.473565 | − | 0.880759i | \(-0.342967\pi\) | ||||
0.473565 | + | 0.880759i | \(0.342967\pi\) | |||||||
\(510\) | −52.8760 | −2.34139 | ||||||||
\(511\) | 36.7443 | 1.62547 | ||||||||
\(512\) | 44.6763 | 1.97443 | ||||||||
\(513\) | 8.96035 | 0.395609 | ||||||||
\(514\) | 25.2821 | 1.11514 | ||||||||
\(515\) | 4.31504 | 0.190144 | ||||||||
\(516\) | −22.9541 | −1.01050 | ||||||||
\(517\) | −1.32570 | −0.0583043 | ||||||||
\(518\) | 78.6664 | 3.45640 | ||||||||
\(519\) | −2.58456 | −0.113450 | ||||||||
\(520\) | −14.7744 | −0.647899 | ||||||||
\(521\) | −18.5818 | −0.814083 | −0.407041 | − | 0.913410i | \(-0.633440\pi\) | ||||
−0.407041 | + | 0.913410i | \(0.633440\pi\) | |||||||
\(522\) | 81.9917 | 3.58868 | ||||||||
\(523\) | −26.9576 | −1.17877 | −0.589386 | − | 0.807852i | \(-0.700630\pi\) | ||||
−0.589386 | + | 0.807852i | \(0.700630\pi\) | |||||||
\(524\) | 3.57878 | 0.156340 | ||||||||
\(525\) | −7.30675 | −0.318893 | ||||||||
\(526\) | −37.5258 | −1.63620 | ||||||||
\(527\) | −71.9951 | −3.13615 | ||||||||
\(528\) | 6.25344 | 0.272146 | ||||||||
\(529\) | −20.7059 | −0.900255 | ||||||||
\(530\) | 21.6451 | 0.940202 | ||||||||
\(531\) | 25.6689 | 1.11394 | ||||||||
\(532\) | −42.1404 | −1.82702 | ||||||||
\(533\) | 24.9478 | 1.08061 | ||||||||
\(534\) | 55.5860 | 2.40544 | ||||||||
\(535\) | −16.3847 | −0.708371 | ||||||||
\(536\) | 6.64227 | 0.286902 | ||||||||
\(537\) | −35.9513 | −1.55141 | ||||||||
\(538\) | 26.0915 | 1.12489 | ||||||||
\(539\) | −0.145839 | −0.00628172 | ||||||||
\(540\) | −13.3222 | −0.573294 | ||||||||
\(541\) | 9.03487 | 0.388440 | 0.194220 | − | 0.980958i | \(-0.437783\pi\) | ||||
0.194220 | + | 0.980958i | \(0.437783\pi\) | |||||||
\(542\) | 59.1797 | 2.54198 | ||||||||
\(543\) | −14.0722 | −0.603897 | ||||||||
\(544\) | 73.3327 | 3.14411 | ||||||||
\(545\) | −3.94538 | −0.169002 | ||||||||
\(546\) | 38.9470 | 1.66678 | ||||||||
\(547\) | 34.3299 | 1.46784 | 0.733920 | − | 0.679236i | \(-0.237689\pi\) | ||||
0.733920 | + | 0.679236i | \(0.237689\pi\) | |||||||
\(548\) | −4.52123 | −0.193137 | ||||||||
\(549\) | 42.1906 | 1.80065 | ||||||||
\(550\) | 0.664208 | 0.0283219 | ||||||||
\(551\) | 24.9601 | 1.06334 | ||||||||
\(552\) | −29.0106 | −1.23477 | ||||||||
\(553\) | 1.82337 | 0.0775377 | ||||||||
\(554\) | 41.4158 | 1.75959 | ||||||||
\(555\) | 29.1734 | 1.23834 | ||||||||
\(556\) | 7.34543 | 0.311516 | ||||||||
\(557\) | 17.9907 | 0.762290 | 0.381145 | − | 0.924515i | \(-0.375530\pi\) | ||||
0.381145 | + | 0.924515i | \(0.375530\pi\) | |||||||
\(558\) | −99.1942 | −4.19923 | ||||||||
\(559\) | 3.71057 | 0.156941 | ||||||||
\(560\) | 25.3873 | 1.07281 | ||||||||
\(561\) | −5.18632 | −0.218967 | ||||||||
\(562\) | −58.4506 | −2.46559 | ||||||||
\(563\) | −25.7960 | −1.08717 | −0.543587 | − | 0.839353i | \(-0.682934\pi\) | ||||
−0.543587 | + | 0.839353i | \(0.682934\pi\) | |||||||
\(564\) | −65.8129 | −2.77122 | ||||||||
\(565\) | 2.76272 | 0.116229 | ||||||||
\(566\) | 36.4628 | 1.53265 | ||||||||
\(567\) | −13.0440 | −0.547797 | ||||||||
\(568\) | 42.1441 | 1.76833 | ||||||||
\(569\) | −20.9667 | −0.878971 | −0.439486 | − | 0.898250i | \(-0.644839\pi\) | ||||
−0.439486 | + | 0.898250i | \(0.644839\pi\) | |||||||
\(570\) | −22.1778 | −0.928928 | ||||||||
\(571\) | −16.9091 | −0.707624 | −0.353812 | − | 0.935317i | \(-0.615115\pi\) | ||||
−0.353812 | + | 0.935317i | \(0.615115\pi\) | |||||||
\(572\) | −2.49477 | −0.104312 | ||||||||
\(573\) | 25.6289 | 1.07066 | ||||||||
\(574\) | −87.2115 | −3.64014 | ||||||||
\(575\) | −1.51464 | −0.0631649 | ||||||||
\(576\) | 26.2784 | 1.09494 | ||||||||
\(577\) | 30.8871 | 1.28585 | 0.642924 | − | 0.765930i | \(-0.277721\pi\) | ||||
0.642924 | + | 0.765930i | \(0.277721\pi\) | |||||||
\(578\) | −108.129 | −4.49757 | ||||||||
\(579\) | −44.0064 | −1.82884 | ||||||||
\(580\) | −37.1105 | −1.54093 | ||||||||
\(581\) | −13.7993 | −0.572493 | ||||||||
\(582\) | −21.9242 | −0.908787 | ||||||||
\(583\) | 2.12305 | 0.0879277 | ||||||||
\(584\) | −96.3194 | −3.98573 | ||||||||
\(585\) | 8.29852 | 0.343101 | ||||||||
\(586\) | −16.7368 | −0.691392 | ||||||||
\(587\) | −42.3565 | −1.74824 | −0.874119 | − | 0.485711i | \(-0.838561\pi\) | ||||
−0.874119 | + | 0.485711i | \(0.838561\pi\) | |||||||
\(588\) | −7.23999 | −0.298572 | ||||||||
\(589\) | −30.1970 | −1.24425 | ||||||||
\(590\) | −16.4876 | −0.678783 | ||||||||
\(591\) | 9.42278 | 0.387601 | ||||||||
\(592\) | −101.363 | −4.16600 | ||||||||
\(593\) | 29.4538 | 1.20952 | 0.604760 | − | 0.796408i | \(-0.293269\pi\) | ||||
0.604760 | + | 0.796408i | \(0.293269\pi\) | |||||||
\(594\) | −1.85438 | −0.0760860 | ||||||||
\(595\) | −21.0551 | −0.863175 | ||||||||
\(596\) | −77.5430 | −3.17628 | ||||||||
\(597\) | −25.3412 | −1.03715 | ||||||||
\(598\) | 8.07345 | 0.330148 | ||||||||
\(599\) | 22.9344 | 0.937073 | 0.468537 | − | 0.883444i | \(-0.344781\pi\) | ||||
0.468537 | + | 0.883444i | \(0.344781\pi\) | |||||||
\(600\) | 19.1535 | 0.781937 | ||||||||
\(601\) | −11.7080 | −0.477579 | −0.238789 | − | 0.971071i | \(-0.576751\pi\) | ||||
−0.238789 | + | 0.971071i | \(0.576751\pi\) | |||||||
\(602\) | −12.9712 | −0.528668 | ||||||||
\(603\) | −3.73085 | −0.151932 | ||||||||
\(604\) | 20.5092 | 0.834508 | ||||||||
\(605\) | −10.9349 | −0.444565 | ||||||||
\(606\) | 61.5065 | 2.49853 | ||||||||
\(607\) | 26.3800 | 1.07073 | 0.535366 | − | 0.844620i | \(-0.320174\pi\) | ||||
0.535366 | + | 0.844620i | \(0.320174\pi\) | |||||||
\(608\) | 30.7580 | 1.24740 | ||||||||
\(609\) | 56.8251 | 2.30267 | ||||||||
\(610\) | −27.0997 | −1.09724 | ||||||||
\(611\) | 10.6388 | 0.430399 | ||||||||
\(612\) | −147.929 | −5.97967 | ||||||||
\(613\) | 38.1142 | 1.53942 | 0.769709 | − | 0.638395i | \(-0.220401\pi\) | ||||
0.769709 | + | 0.638395i | \(0.220401\pi\) | |||||||
\(614\) | 33.2450 | 1.34166 | ||||||||
\(615\) | −32.3423 | −1.30417 | ||||||||
\(616\) | 5.06583 | 0.204108 | ||||||||
\(617\) | 6.51019 | 0.262090 | 0.131045 | − | 0.991376i | \(-0.458167\pi\) | ||||
0.131045 | + | 0.991376i | \(0.458167\pi\) | |||||||
\(618\) | 29.8177 | 1.19944 | ||||||||
\(619\) | −43.3005 | −1.74039 | −0.870197 | − | 0.492703i | \(-0.836009\pi\) | ||||
−0.870197 | + | 0.492703i | \(0.836009\pi\) | |||||||
\(620\) | 44.8966 | 1.80309 | ||||||||
\(621\) | 4.22867 | 0.169690 | ||||||||
\(622\) | −47.4579 | −1.90289 | ||||||||
\(623\) | 22.1342 | 0.886789 | ||||||||
\(624\) | −50.1840 | −2.00897 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −54.4419 | −2.17594 | ||||||||
\(627\) | −2.17531 | −0.0868734 | ||||||||
\(628\) | −49.0689 | −1.95806 | ||||||||
\(629\) | 84.0660 | 3.35193 | ||||||||
\(630\) | −29.0096 | −1.15577 | ||||||||
\(631\) | −32.2621 | −1.28433 | −0.642166 | − | 0.766565i | \(-0.721964\pi\) | ||||
−0.642166 | + | 0.766565i | \(0.721964\pi\) | |||||||
\(632\) | −4.77968 | −0.190125 | ||||||||
\(633\) | 43.7722 | 1.73979 | ||||||||
\(634\) | 9.76567 | 0.387844 | ||||||||
\(635\) | 10.1331 | 0.402118 | ||||||||
\(636\) | 105.396 | 4.17923 | ||||||||
\(637\) | 1.17036 | 0.0463713 | ||||||||
\(638\) | −5.16559 | −0.204508 | ||||||||
\(639\) | −23.6716 | −0.936435 | ||||||||
\(640\) | 2.28807 | 0.0904437 | ||||||||
\(641\) | −25.5128 | −1.00769 | −0.503847 | − | 0.863793i | \(-0.668082\pi\) | ||||
−0.503847 | + | 0.863793i | \(0.668082\pi\) | |||||||
\(642\) | −113.221 | −4.46846 | ||||||||
\(643\) | 9.84898 | 0.388406 | 0.194203 | − | 0.980961i | \(-0.437788\pi\) | ||||
0.194203 | + | 0.980961i | \(0.437788\pi\) | |||||||
\(644\) | −19.8874 | −0.783672 | ||||||||
\(645\) | −4.81038 | −0.189409 | ||||||||
\(646\) | −63.9076 | −2.51441 | ||||||||
\(647\) | 6.48902 | 0.255110 | 0.127555 | − | 0.991832i | \(-0.459287\pi\) | ||||
0.127555 | + | 0.991832i | \(0.459287\pi\) | |||||||
\(648\) | 34.1928 | 1.34322 | ||||||||
\(649\) | −1.61718 | −0.0634798 | ||||||||
\(650\) | −5.33028 | −0.209071 | ||||||||
\(651\) | −68.7475 | −2.69443 | ||||||||
\(652\) | 39.8809 | 1.56185 | ||||||||
\(653\) | −38.9254 | −1.52327 | −0.761634 | − | 0.648008i | \(-0.775603\pi\) | ||||
−0.761634 | + | 0.648008i | \(0.775603\pi\) | |||||||
\(654\) | −27.2633 | −1.06608 | ||||||||
\(655\) | 0.749989 | 0.0293045 | ||||||||
\(656\) | 112.374 | 4.38745 | ||||||||
\(657\) | 54.1010 | 2.11068 | ||||||||
\(658\) | −37.1905 | −1.44984 | ||||||||
\(659\) | −35.0037 | −1.36355 | −0.681775 | − | 0.731562i | \(-0.738792\pi\) | ||||
−0.681775 | + | 0.731562i | \(0.738792\pi\) | |||||||
\(660\) | 3.23422 | 0.125892 | ||||||||
\(661\) | −13.6897 | −0.532469 | −0.266235 | − | 0.963908i | \(-0.585780\pi\) | ||||
−0.266235 | + | 0.963908i | \(0.585780\pi\) | |||||||
\(662\) | 56.7446 | 2.20544 | ||||||||
\(663\) | 41.6203 | 1.61640 | ||||||||
\(664\) | 36.1728 | 1.40378 | ||||||||
\(665\) | −8.83117 | −0.342458 | ||||||||
\(666\) | 115.825 | 4.48815 | ||||||||
\(667\) | 11.7795 | 0.456103 | ||||||||
\(668\) | −99.7994 | −3.86135 | ||||||||
\(669\) | 46.0698 | 1.78116 | ||||||||
\(670\) | 2.39639 | 0.0925805 | ||||||||
\(671\) | −2.65807 | −0.102614 | ||||||||
\(672\) | 70.0248 | 2.70126 | ||||||||
\(673\) | 29.4839 | 1.13652 | 0.568261 | − | 0.822848i | \(-0.307616\pi\) | ||||
0.568261 | + | 0.822848i | \(0.307616\pi\) | |||||||
\(674\) | 22.6920 | 0.874063 | ||||||||
\(675\) | −2.79186 | −0.107459 | ||||||||
\(676\) | −42.0126 | −1.61587 | ||||||||
\(677\) | −0.0362667 | −0.00139384 | −0.000696921 | − | 1.00000i | \(-0.500222\pi\) | ||||
−0.000696921 | 1.00000i | \(0.500222\pi\) | ||||||||
\(678\) | 19.0909 | 0.733180 | ||||||||
\(679\) | −8.73016 | −0.335033 | ||||||||
\(680\) | 55.1926 | 2.11654 | ||||||||
\(681\) | 30.3777 | 1.16408 | ||||||||
\(682\) | 6.24938 | 0.239301 | ||||||||
\(683\) | −39.8114 | −1.52334 | −0.761670 | − | 0.647965i | \(-0.775620\pi\) | ||||
−0.761670 | + | 0.647965i | \(0.775620\pi\) | |||||||
\(684\) | −62.0460 | −2.37239 | ||||||||
\(685\) | −0.947492 | −0.0362018 | ||||||||
\(686\) | 46.0317 | 1.75750 | ||||||||
\(687\) | −72.5852 | −2.76930 | ||||||||
\(688\) | 16.7137 | 0.637204 | ||||||||
\(689\) | −17.0375 | −0.649077 | ||||||||
\(690\) | −10.4664 | −0.398450 | ||||||||
\(691\) | 23.4142 | 0.890718 | 0.445359 | − | 0.895352i | \(-0.353076\pi\) | ||||
0.445359 | + | 0.895352i | \(0.353076\pi\) | |||||||
\(692\) | 4.64441 | 0.176554 | ||||||||
\(693\) | −2.84539 | −0.108087 | ||||||||
\(694\) | 44.7157 | 1.69738 | ||||||||
\(695\) | 1.53935 | 0.0583908 | ||||||||
\(696\) | −148.958 | −5.64624 | ||||||||
\(697\) | −93.1976 | −3.53011 | ||||||||
\(698\) | −31.2748 | −1.18377 | ||||||||
\(699\) | −40.8271 | −1.54422 | ||||||||
\(700\) | 13.1301 | 0.496271 | ||||||||
\(701\) | 4.48116 | 0.169251 | 0.0846255 | − | 0.996413i | \(-0.473031\pi\) | ||||
0.0846255 | + | 0.996413i | \(0.473031\pi\) | |||||||
\(702\) | 14.8814 | 0.561662 | ||||||||
\(703\) | 35.2599 | 1.32985 | ||||||||
\(704\) | −1.65558 | −0.0623970 | ||||||||
\(705\) | −13.7921 | −0.519441 | ||||||||
\(706\) | −22.8631 | −0.860466 | ||||||||
\(707\) | 24.4918 | 0.921108 | ||||||||
\(708\) | −80.2829 | −3.01722 | ||||||||
\(709\) | −24.2229 | −0.909712 | −0.454856 | − | 0.890565i | \(-0.650309\pi\) | ||||
−0.454856 | + | 0.890565i | \(0.650309\pi\) | |||||||
\(710\) | 15.2047 | 0.570622 | ||||||||
\(711\) | 2.68467 | 0.100683 | ||||||||
\(712\) | −58.0213 | −2.17444 | ||||||||
\(713\) | −14.2509 | −0.533700 | ||||||||
\(714\) | −145.494 | −5.44499 | ||||||||
\(715\) | −0.522818 | −0.0195523 | ||||||||
\(716\) | 64.6038 | 2.41436 | ||||||||
\(717\) | 22.2546 | 0.831113 | ||||||||
\(718\) | 4.65314 | 0.173654 | ||||||||
\(719\) | −27.3429 | −1.01972 | −0.509859 | − | 0.860258i | \(-0.670302\pi\) | ||||
−0.509859 | + | 0.860258i | \(0.670302\pi\) | |||||||
\(720\) | 37.3794 | 1.39305 | ||||||||
\(721\) | 11.8733 | 0.442186 | ||||||||
\(722\) | 22.6382 | 0.842506 | ||||||||
\(723\) | −33.5413 | −1.24741 | ||||||||
\(724\) | 25.2876 | 0.939805 | ||||||||
\(725\) | −7.77707 | −0.288833 | ||||||||
\(726\) | −75.5616 | −2.80435 | ||||||||
\(727\) | −21.7008 | −0.804839 | −0.402420 | − | 0.915455i | \(-0.631831\pi\) | ||||
−0.402420 | + | 0.915455i | \(0.631831\pi\) | |||||||
\(728\) | −40.6533 | −1.50671 | ||||||||
\(729\) | −41.4464 | −1.53505 | ||||||||
\(730\) | −34.7500 | −1.28615 | ||||||||
\(731\) | −13.8616 | −0.512689 | ||||||||
\(732\) | −131.957 | −4.87725 | ||||||||
\(733\) | 34.5377 | 1.27568 | 0.637840 | − | 0.770169i | \(-0.279828\pi\) | ||||
0.637840 | + | 0.770169i | \(0.279828\pi\) | |||||||
\(734\) | −16.8111 | −0.620507 | ||||||||
\(735\) | −1.51725 | −0.0559646 | ||||||||
\(736\) | 14.5157 | 0.535055 | ||||||||
\(737\) | 0.235049 | 0.00865813 | ||||||||
\(738\) | −128.407 | −4.72672 | ||||||||
\(739\) | 5.65559 | 0.208044 | 0.104022 | − | 0.994575i | \(-0.466829\pi\) | ||||
0.104022 | + | 0.994575i | \(0.466829\pi\) | |||||||
\(740\) | −52.4241 | −1.92715 | ||||||||
\(741\) | 17.4569 | 0.641294 | ||||||||
\(742\) | 59.5589 | 2.18648 | ||||||||
\(743\) | −12.1078 | −0.444193 | −0.222096 | − | 0.975025i | \(-0.571290\pi\) | ||||
−0.222096 | + | 0.975025i | \(0.571290\pi\) | |||||||
\(744\) | 180.211 | 6.60684 | ||||||||
\(745\) | −16.2503 | −0.595365 | ||||||||
\(746\) | 18.9549 | 0.693989 | ||||||||
\(747\) | −20.3176 | −0.743384 | ||||||||
\(748\) | 9.31973 | 0.340763 | ||||||||
\(749\) | −45.0842 | −1.64734 | ||||||||
\(750\) | 6.91016 | 0.252324 | ||||||||
\(751\) | 8.66996 | 0.316371 | 0.158186 | − | 0.987409i | \(-0.449436\pi\) | ||||
0.158186 | + | 0.987409i | \(0.449436\pi\) | |||||||
\(752\) | 47.9207 | 1.74749 | ||||||||
\(753\) | 27.5725 | 1.00480 | ||||||||
\(754\) | 41.4539 | 1.50966 | ||||||||
\(755\) | 4.29802 | 0.156421 | ||||||||
\(756\) | −36.6574 | −1.33322 | ||||||||
\(757\) | 9.77857 | 0.355408 | 0.177704 | − | 0.984084i | \(-0.443133\pi\) | ||||
0.177704 | + | 0.984084i | \(0.443133\pi\) | |||||||
\(758\) | 53.0748 | 1.92776 | ||||||||
\(759\) | −1.02659 | −0.0372630 | ||||||||
\(760\) | 23.1495 | 0.839721 | ||||||||
\(761\) | 9.95003 | 0.360688 | 0.180344 | − | 0.983604i | \(-0.442279\pi\) | ||||
0.180344 | + | 0.983604i | \(0.442279\pi\) | |||||||
\(762\) | 70.0211 | 2.53660 | ||||||||
\(763\) | −10.8562 | −0.393020 | ||||||||
\(764\) | −46.0547 | −1.66620 | ||||||||
\(765\) | −31.0008 | −1.12084 | ||||||||
\(766\) | −51.7045 | −1.86816 | ||||||||
\(767\) | 12.9779 | 0.468604 | ||||||||
\(768\) | 50.2589 | 1.81356 | ||||||||
\(769\) | −48.2482 | −1.73988 | −0.869938 | − | 0.493161i | \(-0.835841\pi\) | ||||
−0.869938 | + | 0.493161i | \(0.835841\pi\) | |||||||
\(770\) | 1.82764 | 0.0658637 | ||||||||
\(771\) | 25.7987 | 0.929117 | ||||||||
\(772\) | 79.0787 | 2.84611 | ||||||||
\(773\) | −44.4332 | −1.59815 | −0.799076 | − | 0.601230i | \(-0.794678\pi\) | ||||
−0.799076 | + | 0.601230i | \(0.794678\pi\) | |||||||
\(774\) | −19.0984 | −0.686477 | ||||||||
\(775\) | 9.40876 | 0.337973 | ||||||||
\(776\) | 22.8847 | 0.821514 | ||||||||
\(777\) | 80.2739 | 2.87981 | ||||||||
\(778\) | −74.3375 | −2.66513 | ||||||||
\(779\) | −39.0900 | −1.40054 | ||||||||
\(780\) | −25.9547 | −0.929327 | ||||||||
\(781\) | 1.49135 | 0.0533645 | ||||||||
\(782\) | −30.1600 | −1.07852 | ||||||||
\(783\) | 21.7125 | 0.775942 | ||||||||
\(784\) | 5.27170 | 0.188275 | ||||||||
\(785\) | −10.2831 | −0.367021 | ||||||||
\(786\) | 5.18255 | 0.184855 | ||||||||
\(787\) | −48.6166 | −1.73299 | −0.866497 | − | 0.499183i | \(-0.833634\pi\) | ||||
−0.866497 | + | 0.499183i | \(0.833634\pi\) | |||||||
\(788\) | −16.9326 | −0.603198 | ||||||||
\(789\) | −38.2926 | −1.36325 | ||||||||
\(790\) | −1.72441 | −0.0613516 | ||||||||
\(791\) | 7.60194 | 0.270294 | ||||||||
\(792\) | 7.45874 | 0.265035 | ||||||||
\(793\) | 21.3310 | 0.757486 | ||||||||
\(794\) | −67.4203 | −2.39266 | ||||||||
\(795\) | 22.0874 | 0.783359 | ||||||||
\(796\) | 45.5378 | 1.61404 | ||||||||
\(797\) | −53.0582 | −1.87942 | −0.939709 | − | 0.341975i | \(-0.888904\pi\) | ||||
−0.939709 | + | 0.341975i | \(0.888904\pi\) | |||||||
\(798\) | −61.0249 | −2.16026 | ||||||||
\(799\) | −39.7433 | −1.40602 | ||||||||
\(800\) | −9.58357 | −0.338831 | ||||||||
\(801\) | 32.5896 | 1.15150 | ||||||||
\(802\) | 71.7052 | 2.53200 | ||||||||
\(803\) | −3.40844 | −0.120281 | ||||||||
\(804\) | 11.6687 | 0.411524 | ||||||||
\(805\) | −4.16770 | −0.146892 | ||||||||
\(806\) | −50.1513 | −1.76650 | ||||||||
\(807\) | 26.6247 | 0.937234 | ||||||||
\(808\) | −64.2013 | −2.25859 | ||||||||
\(809\) | −16.0781 | −0.565278 | −0.282639 | − | 0.959226i | \(-0.591210\pi\) | ||||
−0.282639 | + | 0.959226i | \(0.591210\pi\) | |||||||
\(810\) | 12.3360 | 0.433444 | ||||||||
\(811\) | −34.8349 | −1.22322 | −0.611609 | − | 0.791160i | \(-0.709478\pi\) | ||||
−0.611609 | + | 0.791160i | \(0.709478\pi\) | |||||||
\(812\) | −102.114 | −3.58349 | ||||||||
\(813\) | 60.3890 | 2.11793 | ||||||||
\(814\) | −7.29717 | −0.255766 | ||||||||
\(815\) | 8.35764 | 0.292755 | ||||||||
\(816\) | 187.472 | 6.56284 | ||||||||
\(817\) | −5.81398 | −0.203406 | ||||||||
\(818\) | 30.3488 | 1.06112 | ||||||||
\(819\) | 22.8343 | 0.797895 | ||||||||
\(820\) | 58.1186 | 2.02959 | ||||||||
\(821\) | −33.0689 | −1.15411 | −0.577056 | − | 0.816705i | \(-0.695798\pi\) | ||||
−0.577056 | + | 0.816705i | \(0.695798\pi\) | |||||||
\(822\) | −6.54732 | −0.228364 | ||||||||
\(823\) | 53.3234 | 1.85874 | 0.929368 | − | 0.369154i | \(-0.120353\pi\) | ||||
0.929368 | + | 0.369154i | \(0.120353\pi\) | |||||||
\(824\) | −31.1240 | −1.08426 | ||||||||
\(825\) | 0.677781 | 0.0235973 | ||||||||
\(826\) | −45.3675 | −1.57854 | ||||||||
\(827\) | −4.73099 | −0.164512 | −0.0822562 | − | 0.996611i | \(-0.526213\pi\) | ||||
−0.0822562 | + | 0.996611i | \(0.526213\pi\) | |||||||
\(828\) | −29.2814 | −1.01760 | ||||||||
\(829\) | 18.2801 | 0.634894 | 0.317447 | − | 0.948276i | \(-0.397174\pi\) | ||||
0.317447 | + | 0.948276i | \(0.397174\pi\) | |||||||
\(830\) | 13.0504 | 0.452985 | ||||||||
\(831\) | 42.2621 | 1.46606 | ||||||||
\(832\) | 13.2860 | 0.460610 | ||||||||
\(833\) | −4.37211 | −0.151484 | ||||||||
\(834\) | 10.6371 | 0.368334 | ||||||||
\(835\) | −20.9145 | −0.723776 | ||||||||
\(836\) | 3.90899 | 0.135195 | ||||||||
\(837\) | −26.2680 | −0.907954 | ||||||||
\(838\) | −22.6400 | −0.782085 | ||||||||
\(839\) | −14.9349 | −0.515609 | −0.257805 | − | 0.966197i | \(-0.582999\pi\) | ||||
−0.257805 | + | 0.966197i | \(0.582999\pi\) | |||||||
\(840\) | 52.7030 | 1.81842 | ||||||||
\(841\) | 31.4828 | 1.08562 | ||||||||
\(842\) | 79.6731 | 2.74572 | ||||||||
\(843\) | −59.6451 | −2.05428 | ||||||||
\(844\) | −78.6578 | −2.70751 | ||||||||
\(845\) | −8.80438 | −0.302880 | ||||||||
\(846\) | −54.7580 | −1.88262 | ||||||||
\(847\) | −30.0885 | −1.03385 | ||||||||
\(848\) | −76.7428 | −2.63536 | ||||||||
\(849\) | 37.2079 | 1.27697 | ||||||||
\(850\) | 19.9123 | 0.682987 | ||||||||
\(851\) | 16.6402 | 0.570420 | ||||||||
\(852\) | 74.0361 | 2.53643 | ||||||||
\(853\) | 10.8532 | 0.371607 | 0.185804 | − | 0.982587i | \(-0.440511\pi\) | ||||
0.185804 | + | 0.982587i | \(0.440511\pi\) | |||||||
\(854\) | −74.5679 | −2.55166 | ||||||||
\(855\) | −13.0027 | −0.444683 | ||||||||
\(856\) | 118.181 | 4.03935 | ||||||||
\(857\) | 17.9480 | 0.613091 | 0.306545 | − | 0.951856i | \(-0.400827\pi\) | ||||
0.306545 | + | 0.951856i | \(0.400827\pi\) | |||||||
\(858\) | −3.61276 | −0.123338 | ||||||||
\(859\) | −41.9916 | −1.43273 | −0.716367 | − | 0.697723i | \(-0.754196\pi\) | ||||
−0.716367 | + | 0.697723i | \(0.754196\pi\) | |||||||
\(860\) | 8.64417 | 0.294764 | ||||||||
\(861\) | −88.9936 | −3.03289 | ||||||||
\(862\) | 103.073 | 3.51069 | ||||||||
\(863\) | −22.9489 | −0.781189 | −0.390594 | − | 0.920563i | \(-0.627730\pi\) | ||||
−0.390594 | + | 0.920563i | \(0.627730\pi\) | |||||||
\(864\) | 26.7560 | 0.910258 | ||||||||
\(865\) | 0.973306 | 0.0330934 | ||||||||
\(866\) | 81.5793 | 2.77218 | ||||||||
\(867\) | −110.338 | −3.74729 | ||||||||
\(868\) | 123.538 | 4.19315 | ||||||||
\(869\) | −0.169138 | −0.00573761 | ||||||||
\(870\) | −53.7408 | −1.82199 | ||||||||
\(871\) | −1.88627 | −0.0639138 | ||||||||
\(872\) | 28.4577 | 0.963700 | ||||||||
\(873\) | −12.8540 | −0.435041 | ||||||||
\(874\) | −12.6500 | −0.427894 | ||||||||
\(875\) | 2.75161 | 0.0930215 | ||||||||
\(876\) | −169.208 | −5.71700 | ||||||||
\(877\) | 24.3636 | 0.822700 | 0.411350 | − | 0.911477i | \(-0.365057\pi\) | ||||
0.411350 | + | 0.911477i | \(0.365057\pi\) | |||||||
\(878\) | −35.3517 | −1.19306 | ||||||||
\(879\) | −17.0789 | −0.576055 | ||||||||
\(880\) | −2.35495 | −0.0793855 | ||||||||
\(881\) | −28.2722 | −0.952514 | −0.476257 | − | 0.879306i | \(-0.658007\pi\) | ||||
−0.476257 | + | 0.879306i | \(0.658007\pi\) | |||||||
\(882\) | −6.02385 | −0.202834 | ||||||||
\(883\) | 51.2260 | 1.72389 | 0.861947 | − | 0.506999i | \(-0.169245\pi\) | ||||
0.861947 | + | 0.506999i | \(0.169245\pi\) | |||||||
\(884\) | −74.7909 | −2.51549 | ||||||||
\(885\) | −16.8245 | −0.565550 | ||||||||
\(886\) | −4.33407 | −0.145606 | ||||||||
\(887\) | 25.7314 | 0.863977 | 0.431989 | − | 0.901879i | \(-0.357812\pi\) | ||||
0.431989 | + | 0.901879i | \(0.357812\pi\) | |||||||
\(888\) | −210.425 | −7.06141 | ||||||||
\(889\) | 27.8823 | 0.935141 | ||||||||
\(890\) | −20.9329 | −0.701671 | ||||||||
\(891\) | 1.20997 | 0.0405357 | ||||||||
\(892\) | −82.7865 | −2.77190 | ||||||||
\(893\) | −16.6696 | −0.557826 | ||||||||
\(894\) | −112.292 | −3.75562 | ||||||||
\(895\) | 13.5387 | 0.452549 | ||||||||
\(896\) | 6.29587 | 0.210330 | ||||||||
\(897\) | 8.23843 | 0.275073 | ||||||||
\(898\) | −13.9498 | −0.465509 | ||||||||
\(899\) | −73.1726 | −2.44044 | ||||||||
\(900\) | 19.3323 | 0.644409 | ||||||||
\(901\) | 63.6470 | 2.12039 | ||||||||
\(902\) | 8.08982 | 0.269361 | ||||||||
\(903\) | −13.2363 | −0.440477 | ||||||||
\(904\) | −19.9273 | −0.662771 | ||||||||
\(905\) | 5.29939 | 0.176158 | ||||||||
\(906\) | 29.7000 | 0.986717 | ||||||||
\(907\) | −18.8636 | −0.626356 | −0.313178 | − | 0.949695i | \(-0.601394\pi\) | ||||
−0.313178 | + | 0.949695i | \(0.601394\pi\) | |||||||
\(908\) | −54.5883 | −1.81157 | ||||||||
\(909\) | 36.0608 | 1.19606 | ||||||||
\(910\) | −14.6669 | −0.486202 | ||||||||
\(911\) | −7.87007 | −0.260747 | −0.130373 | − | 0.991465i | \(-0.541618\pi\) | ||||
−0.130373 | + | 0.991465i | \(0.541618\pi\) | |||||||
\(912\) | 78.6317 | 2.60376 | ||||||||
\(913\) | 1.28004 | 0.0423631 | ||||||||
\(914\) | −40.9544 | −1.35465 | ||||||||
\(915\) | −27.6535 | −0.914197 | ||||||||
\(916\) | 130.434 | 4.30967 | ||||||||
\(917\) | 2.06368 | 0.0681487 | ||||||||
\(918\) | −55.5924 | −1.83482 | ||||||||
\(919\) | 24.8253 | 0.818910 | 0.409455 | − | 0.912330i | \(-0.365719\pi\) | ||||
0.409455 | + | 0.912330i | \(0.365719\pi\) | |||||||
\(920\) | 10.9250 | 0.360186 | ||||||||
\(921\) | 33.9244 | 1.11785 | ||||||||
\(922\) | 14.9590 | 0.492648 | ||||||||
\(923\) | −11.9681 | −0.393934 | ||||||||
\(924\) | 8.89933 | 0.292767 | ||||||||
\(925\) | −10.9863 | −0.361226 | ||||||||
\(926\) | 92.4855 | 3.03926 | ||||||||
\(927\) | 17.4819 | 0.574179 | ||||||||
\(928\) | 74.5321 | 2.44664 | ||||||||
\(929\) | −14.3792 | −0.471767 | −0.235884 | − | 0.971781i | \(-0.575798\pi\) | ||||
−0.235884 | + | 0.971781i | \(0.575798\pi\) | |||||||
\(930\) | 65.0161 | 2.13196 | ||||||||
\(931\) | −1.83380 | −0.0601003 | ||||||||
\(932\) | 73.3656 | 2.40317 | ||||||||
\(933\) | −48.4277 | −1.58545 | ||||||||
\(934\) | −68.9554 | −2.25629 | ||||||||
\(935\) | 1.95309 | 0.0638729 | ||||||||
\(936\) | −59.8565 | −1.95647 | ||||||||
\(937\) | −24.8632 | −0.812244 | −0.406122 | − | 0.913819i | \(-0.633119\pi\) | ||||
−0.406122 | + | 0.913819i | \(0.633119\pi\) | |||||||
\(938\) | 6.59393 | 0.215299 | ||||||||
\(939\) | −55.5544 | −1.81295 | ||||||||
\(940\) | 24.7842 | 0.808371 | ||||||||
\(941\) | −53.0030 | −1.72785 | −0.863923 | − | 0.503623i | \(-0.832000\pi\) | ||||
−0.863923 | + | 0.503623i | \(0.832000\pi\) | |||||||
\(942\) | −71.0581 | −2.31520 | ||||||||
\(943\) | −18.4478 | −0.600742 | ||||||||
\(944\) | 58.4569 | 1.90261 | ||||||||
\(945\) | −7.68212 | −0.249899 | ||||||||
\(946\) | 1.20322 | 0.0391202 | ||||||||
\(947\) | −21.2878 | −0.691761 | −0.345880 | − | 0.938279i | \(-0.612420\pi\) | ||||
−0.345880 | + | 0.938279i | \(0.612420\pi\) | |||||||
\(948\) | −8.39664 | −0.272710 | ||||||||
\(949\) | 27.3528 | 0.887908 | ||||||||
\(950\) | 8.35185 | 0.270970 | ||||||||
\(951\) | 9.96523 | 0.323145 | ||||||||
\(952\) | 151.869 | 4.92209 | ||||||||
\(953\) | 59.4457 | 1.92563 | 0.962817 | − | 0.270154i | \(-0.0870745\pi\) | ||||
0.962817 | + | 0.270154i | \(0.0870745\pi\) | |||||||
\(954\) | 87.6923 | 2.83914 | ||||||||
\(955\) | −9.65146 | −0.312314 | ||||||||
\(956\) | −39.9911 | −1.29341 | ||||||||
\(957\) | −5.27115 | −0.170392 | ||||||||
\(958\) | −59.5627 | −1.92438 | ||||||||
\(959\) | −2.60713 | −0.0841886 | ||||||||
\(960\) | −17.2240 | −0.555902 | ||||||||
\(961\) | 57.5249 | 1.85564 | ||||||||
\(962\) | 58.5598 | 1.88805 | ||||||||
\(963\) | −66.3804 | −2.13908 | ||||||||
\(964\) | 60.2730 | 1.94126 | ||||||||
\(965\) | 16.5722 | 0.533476 | ||||||||
\(966\) | −28.7995 | −0.926609 | ||||||||
\(967\) | −4.61942 | −0.148551 | −0.0742753 | − | 0.997238i | \(-0.523664\pi\) | ||||
−0.0742753 | + | 0.997238i | \(0.523664\pi\) | |||||||
\(968\) | 78.8721 | 2.53505 | ||||||||
\(969\) | −65.2136 | −2.09496 | ||||||||
\(970\) | 8.25632 | 0.265095 | ||||||||
\(971\) | −1.58904 | −0.0509947 | −0.0254974 | − | 0.999675i | \(-0.508117\pi\) | ||||
−0.0254974 | + | 0.999675i | \(0.508117\pi\) | |||||||
\(972\) | 100.034 | 3.20860 | ||||||||
\(973\) | 4.23569 | 0.135790 | ||||||||
\(974\) | 98.2074 | 3.14677 | ||||||||
\(975\) | −5.43920 | −0.174194 | ||||||||
\(976\) | 96.0823 | 3.07552 | ||||||||
\(977\) | −9.58052 | −0.306508 | −0.153254 | − | 0.988187i | \(-0.548975\pi\) | ||||
−0.153254 | + | 0.988187i | \(0.548975\pi\) | |||||||
\(978\) | 57.7527 | 1.84673 | ||||||||
\(979\) | −2.05319 | −0.0656203 | ||||||||
\(980\) | 2.72647 | 0.0870940 | ||||||||
\(981\) | −15.9842 | −0.510337 | ||||||||
\(982\) | −82.6235 | −2.63662 | ||||||||
\(983\) | 6.52689 | 0.208176 | 0.104088 | − | 0.994568i | \(-0.466808\pi\) | ||||
0.104088 | + | 0.994568i | \(0.466808\pi\) | |||||||
\(984\) | 233.283 | 7.43678 | ||||||||
\(985\) | −3.54848 | −0.113064 | ||||||||
\(986\) | −154.859 | −4.93173 | ||||||||
\(987\) | −37.9505 | −1.20798 | ||||||||
\(988\) | −31.3697 | −0.998002 | ||||||||
\(989\) | −2.74380 | −0.0872477 | ||||||||
\(990\) | 2.69095 | 0.0855241 | ||||||||
\(991\) | −0.309693 | −0.00983771 | −0.00491885 | − | 0.999988i | \(-0.501566\pi\) | ||||
−0.00491885 | + | 0.999988i | \(0.501566\pi\) | |||||||
\(992\) | −90.1696 | −2.86289 | ||||||||
\(993\) | 57.9042 | 1.83753 | ||||||||
\(994\) | 41.8374 | 1.32700 | ||||||||
\(995\) | 9.54313 | 0.302538 | ||||||||
\(996\) | 63.5460 | 2.01353 | ||||||||
\(997\) | 36.7274 | 1.16317 | 0.581584 | − | 0.813487i | \(-0.302433\pi\) | ||||
0.581584 | + | 0.813487i | \(0.302433\pi\) | |||||||
\(998\) | −56.8825 | −1.80058 | ||||||||
\(999\) | 30.6721 | 0.970424 |
(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 | 8005.2.a.e.1.8 | ✓ | 126 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8005.2.a.e.1.8 | ✓ | 126 | 1.1 | even | 1 | trivial |