Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6019,2,Mod(1,6019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6019, 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("6019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6019 = 13 \cdot 463 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6019.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: | \(48.0619569766\) |
Analytic rank: | \(0\) |
Dimension: | \(123\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 6019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.19076 | −1.54910 | −0.774551 | − | 0.632512i | \(-0.782024\pi\) | ||||
−0.774551 | + | 0.632512i | \(0.782024\pi\) | |||||||
\(3\) | 0.906147 | 0.523164 | 0.261582 | − | 0.965181i | \(-0.415756\pi\) | ||||
0.261582 | + | 0.965181i | \(0.415756\pi\) | |||||||
\(4\) | 2.79943 | 1.39972 | ||||||||
\(5\) | −2.56920 | −1.14898 | −0.574490 | − | 0.818512i | \(-0.694800\pi\) | ||||
−0.574490 | + | 0.818512i | \(0.694800\pi\) | |||||||
\(6\) | −1.98515 | −0.810435 | ||||||||
\(7\) | −1.27799 | −0.483036 | −0.241518 | − | 0.970396i | \(-0.577645\pi\) | ||||
−0.241518 | + | 0.970396i | \(0.577645\pi\) | |||||||
\(8\) | −1.75137 | −0.619201 | ||||||||
\(9\) | −2.17890 | −0.726299 | ||||||||
\(10\) | 5.62849 | 1.77989 | ||||||||
\(11\) | 1.29078 | 0.389185 | 0.194593 | − | 0.980884i | \(-0.437662\pi\) | ||||
0.194593 | + | 0.980884i | \(0.437662\pi\) | |||||||
\(12\) | 2.53670 | 0.732282 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 2.79978 | 0.748272 | ||||||||
\(15\) | −2.32807 | −0.601105 | ||||||||
\(16\) | −1.76204 | −0.440510 | ||||||||
\(17\) | −4.22562 | −1.02486 | −0.512432 | − | 0.858728i | \(-0.671255\pi\) | ||||
−0.512432 | + | 0.858728i | \(0.671255\pi\) | |||||||
\(18\) | 4.77344 | 1.12511 | ||||||||
\(19\) | −6.17739 | −1.41719 | −0.708596 | − | 0.705615i | \(-0.750671\pi\) | ||||
−0.708596 | + | 0.705615i | \(0.750671\pi\) | |||||||
\(20\) | −7.19229 | −1.60825 | ||||||||
\(21\) | −1.15805 | −0.252707 | ||||||||
\(22\) | −2.82779 | −0.602887 | ||||||||
\(23\) | −3.55255 | −0.740757 | −0.370379 | − | 0.928881i | \(-0.620772\pi\) | ||||
−0.370379 | + | 0.928881i | \(0.620772\pi\) | |||||||
\(24\) | −1.58700 | −0.323944 | ||||||||
\(25\) | 1.60077 | 0.320154 | ||||||||
\(26\) | 2.19076 | 0.429644 | ||||||||
\(27\) | −4.69284 | −0.903138 | ||||||||
\(28\) | −3.57766 | −0.676114 | ||||||||
\(29\) | −7.68488 | −1.42705 | −0.713523 | − | 0.700632i | \(-0.752902\pi\) | ||||
−0.713523 | + | 0.700632i | \(0.752902\pi\) | |||||||
\(30\) | 5.10025 | 0.931173 | ||||||||
\(31\) | −3.41864 | −0.614006 | −0.307003 | − | 0.951709i | \(-0.599326\pi\) | ||||
−0.307003 | + | 0.951709i | \(0.599326\pi\) | |||||||
\(32\) | 7.36294 | 1.30160 | ||||||||
\(33\) | 1.16964 | 0.203608 | ||||||||
\(34\) | 9.25732 | 1.58762 | ||||||||
\(35\) | 3.28342 | 0.554999 | ||||||||
\(36\) | −6.09968 | −1.01661 | ||||||||
\(37\) | −9.07308 | −1.49161 | −0.745803 | − | 0.666167i | \(-0.767934\pi\) | ||||
−0.745803 | + | 0.666167i | \(0.767934\pi\) | |||||||
\(38\) | 13.5332 | 2.19537 | ||||||||
\(39\) | −0.906147 | −0.145100 | ||||||||
\(40\) | 4.49960 | 0.711450 | ||||||||
\(41\) | −0.101680 | −0.0158797 | −0.00793985 | − | 0.999968i | \(-0.502527\pi\) | ||||
−0.00793985 | + | 0.999968i | \(0.502527\pi\) | |||||||
\(42\) | 2.53701 | 0.391469 | ||||||||
\(43\) | 2.85585 | 0.435512 | 0.217756 | − | 0.976003i | \(-0.430126\pi\) | ||||
0.217756 | + | 0.976003i | \(0.430126\pi\) | |||||||
\(44\) | 3.61345 | 0.544749 | ||||||||
\(45\) | 5.59801 | 0.834503 | ||||||||
\(46\) | 7.78278 | 1.14751 | ||||||||
\(47\) | −12.1142 | −1.76704 | −0.883521 | − | 0.468392i | \(-0.844833\pi\) | ||||
−0.883521 | + | 0.468392i | \(0.844833\pi\) | |||||||
\(48\) | −1.59667 | −0.230459 | ||||||||
\(49\) | −5.36673 | −0.766676 | ||||||||
\(50\) | −3.50691 | −0.495951 | ||||||||
\(51\) | −3.82903 | −0.536172 | ||||||||
\(52\) | −2.79943 | −0.388211 | ||||||||
\(53\) | 3.48865 | 0.479203 | 0.239601 | − | 0.970871i | \(-0.422983\pi\) | ||||
0.239601 | + | 0.970871i | \(0.422983\pi\) | |||||||
\(54\) | 10.2809 | 1.39905 | ||||||||
\(55\) | −3.31627 | −0.447166 | ||||||||
\(56\) | 2.23823 | 0.299097 | ||||||||
\(57\) | −5.59763 | −0.741424 | ||||||||
\(58\) | 16.8357 | 2.21064 | ||||||||
\(59\) | 10.3398 | 1.34612 | 0.673061 | − | 0.739587i | \(-0.264979\pi\) | ||||
0.673061 | + | 0.739587i | \(0.264979\pi\) | |||||||
\(60\) | −6.51728 | −0.841377 | ||||||||
\(61\) | −2.98520 | −0.382216 | −0.191108 | − | 0.981569i | \(-0.561208\pi\) | ||||
−0.191108 | + | 0.981569i | \(0.561208\pi\) | |||||||
\(62\) | 7.48942 | 0.951157 | ||||||||
\(63\) | 2.78462 | 0.350829 | ||||||||
\(64\) | −12.6064 | −1.57580 | ||||||||
\(65\) | 2.56920 | 0.318670 | ||||||||
\(66\) | −2.56240 | −0.315409 | ||||||||
\(67\) | 2.60125 | 0.317793 | 0.158897 | − | 0.987295i | \(-0.449206\pi\) | ||||
0.158897 | + | 0.987295i | \(0.449206\pi\) | |||||||
\(68\) | −11.8293 | −1.43452 | ||||||||
\(69\) | −3.21913 | −0.387538 | ||||||||
\(70\) | −7.19318 | −0.859749 | ||||||||
\(71\) | 12.2545 | 1.45434 | 0.727168 | − | 0.686460i | \(-0.240836\pi\) | ||||
0.727168 | + | 0.686460i | \(0.240836\pi\) | |||||||
\(72\) | 3.81605 | 0.449725 | ||||||||
\(73\) | 4.30531 | 0.503898 | 0.251949 | − | 0.967741i | \(-0.418928\pi\) | ||||
0.251949 | + | 0.967741i | \(0.418928\pi\) | |||||||
\(74\) | 19.8770 | 2.31065 | ||||||||
\(75\) | 1.45053 | 0.167493 | ||||||||
\(76\) | −17.2932 | −1.98367 | ||||||||
\(77\) | −1.64961 | −0.187990 | ||||||||
\(78\) | 1.98515 | 0.224774 | ||||||||
\(79\) | 9.30067 | 1.04641 | 0.523203 | − | 0.852208i | \(-0.324737\pi\) | ||||
0.523203 | + | 0.852208i | \(0.324737\pi\) | |||||||
\(80\) | 4.52703 | 0.506137 | ||||||||
\(81\) | 2.28428 | 0.253809 | ||||||||
\(82\) | 0.222756 | 0.0245993 | ||||||||
\(83\) | 1.50417 | 0.165104 | 0.0825521 | − | 0.996587i | \(-0.473693\pi\) | ||||
0.0825521 | + | 0.996587i | \(0.473693\pi\) | |||||||
\(84\) | −3.24188 | −0.353719 | ||||||||
\(85\) | 10.8564 | 1.17755 | ||||||||
\(86\) | −6.25647 | −0.674653 | ||||||||
\(87\) | −6.96363 | −0.746580 | ||||||||
\(88\) | −2.26063 | −0.240984 | ||||||||
\(89\) | −10.0890 | −1.06944 | −0.534719 | − | 0.845030i | \(-0.679582\pi\) | ||||
−0.534719 | + | 0.845030i | \(0.679582\pi\) | |||||||
\(90\) | −12.2639 | −1.29273 | ||||||||
\(91\) | 1.27799 | 0.133970 | ||||||||
\(92\) | −9.94511 | −1.03685 | ||||||||
\(93\) | −3.09779 | −0.321226 | ||||||||
\(94\) | 26.5394 | 2.73733 | ||||||||
\(95\) | 15.8709 | 1.62832 | ||||||||
\(96\) | 6.67191 | 0.680949 | ||||||||
\(97\) | −6.42623 | −0.652485 | −0.326243 | − | 0.945286i | \(-0.605783\pi\) | ||||
−0.326243 | + | 0.945286i | \(0.605783\pi\) | |||||||
\(98\) | 11.7572 | 1.18766 | ||||||||
\(99\) | −2.81248 | −0.282665 | ||||||||
\(100\) | 4.48125 | 0.448125 | ||||||||
\(101\) | −11.1212 | −1.10660 | −0.553302 | − | 0.832981i | \(-0.686632\pi\) | ||||
−0.553302 | + | 0.832981i | \(0.686632\pi\) | |||||||
\(102\) | 8.38850 | 0.830585 | ||||||||
\(103\) | −7.15985 | −0.705481 | −0.352740 | − | 0.935721i | \(-0.614750\pi\) | ||||
−0.352740 | + | 0.935721i | \(0.614750\pi\) | |||||||
\(104\) | 1.75137 | 0.171736 | ||||||||
\(105\) | 2.97526 | 0.290356 | ||||||||
\(106\) | −7.64279 | −0.742334 | ||||||||
\(107\) | −15.4697 | −1.49551 | −0.747756 | − | 0.663974i | \(-0.768869\pi\) | ||||
−0.747756 | + | 0.663974i | \(0.768869\pi\) | |||||||
\(108\) | −13.1373 | −1.26414 | ||||||||
\(109\) | 1.04938 | 0.100512 | 0.0502560 | − | 0.998736i | \(-0.483996\pi\) | ||||
0.0502560 | + | 0.998736i | \(0.483996\pi\) | |||||||
\(110\) | 7.26515 | 0.692705 | ||||||||
\(111\) | −8.22155 | −0.780355 | ||||||||
\(112\) | 2.25188 | 0.212782 | ||||||||
\(113\) | −7.13940 | −0.671618 | −0.335809 | − | 0.941930i | \(-0.609010\pi\) | ||||
−0.335809 | + | 0.941930i | \(0.609010\pi\) | |||||||
\(114\) | 12.2631 | 1.14854 | ||||||||
\(115\) | 9.12719 | 0.851115 | ||||||||
\(116\) | −21.5133 | −1.99746 | ||||||||
\(117\) | 2.17890 | 0.201439 | ||||||||
\(118\) | −22.6519 | −2.08528 | ||||||||
\(119\) | 5.40031 | 0.495046 | ||||||||
\(120\) | 4.07730 | 0.372205 | ||||||||
\(121\) | −9.33388 | −0.848535 | ||||||||
\(122\) | 6.53986 | 0.592091 | ||||||||
\(123\) | −0.0921368 | −0.00830770 | ||||||||
\(124\) | −9.57025 | −0.859434 | ||||||||
\(125\) | 8.73329 | 0.781129 | ||||||||
\(126\) | −6.10043 | −0.543469 | ||||||||
\(127\) | 9.51610 | 0.844418 | 0.422209 | − | 0.906499i | \(-0.361255\pi\) | ||||
0.422209 | + | 0.906499i | \(0.361255\pi\) | |||||||
\(128\) | 12.8916 | 1.13947 | ||||||||
\(129\) | 2.58782 | 0.227845 | ||||||||
\(130\) | −5.62849 | −0.493652 | ||||||||
\(131\) | −17.2766 | −1.50947 | −0.754733 | − | 0.656032i | \(-0.772234\pi\) | ||||
−0.754733 | + | 0.656032i | \(0.772234\pi\) | |||||||
\(132\) | 3.27432 | 0.284993 | ||||||||
\(133\) | 7.89467 | 0.684555 | ||||||||
\(134\) | −5.69872 | −0.492294 | ||||||||
\(135\) | 12.0568 | 1.03769 | ||||||||
\(136\) | 7.40061 | 0.634597 | ||||||||
\(137\) | −1.25356 | −0.107099 | −0.0535496 | − | 0.998565i | \(-0.517054\pi\) | ||||
−0.0535496 | + | 0.998565i | \(0.517054\pi\) | |||||||
\(138\) | 7.05234 | 0.600335 | ||||||||
\(139\) | −16.7149 | −1.41774 | −0.708869 | − | 0.705340i | \(-0.750794\pi\) | ||||
−0.708869 | + | 0.705340i | \(0.750794\pi\) | |||||||
\(140\) | 9.19170 | 0.776841 | ||||||||
\(141\) | −10.9773 | −0.924453 | ||||||||
\(142\) | −26.8466 | −2.25291 | ||||||||
\(143\) | −1.29078 | −0.107941 | ||||||||
\(144\) | 3.83931 | 0.319942 | ||||||||
\(145\) | 19.7440 | 1.63965 | ||||||||
\(146\) | −9.43190 | −0.780589 | ||||||||
\(147\) | −4.86305 | −0.401098 | ||||||||
\(148\) | −25.3995 | −2.08783 | ||||||||
\(149\) | 11.5828 | 0.948899 | 0.474450 | − | 0.880283i | \(-0.342647\pi\) | ||||
0.474450 | + | 0.880283i | \(0.342647\pi\) | |||||||
\(150\) | −3.17777 | −0.259464 | ||||||||
\(151\) | −11.7529 | −0.956439 | −0.478220 | − | 0.878240i | \(-0.658718\pi\) | ||||
−0.478220 | + | 0.878240i | \(0.658718\pi\) | |||||||
\(152\) | 10.8189 | 0.877527 | ||||||||
\(153\) | 9.20719 | 0.744357 | ||||||||
\(154\) | 3.61390 | 0.291216 | ||||||||
\(155\) | 8.78316 | 0.705480 | ||||||||
\(156\) | −2.53670 | −0.203098 | ||||||||
\(157\) | −11.7519 | −0.937907 | −0.468954 | − | 0.883223i | \(-0.655369\pi\) | ||||
−0.468954 | + | 0.883223i | \(0.655369\pi\) | |||||||
\(158\) | −20.3755 | −1.62099 | ||||||||
\(159\) | 3.16123 | 0.250702 | ||||||||
\(160\) | −18.9168 | −1.49551 | ||||||||
\(161\) | 4.54013 | 0.357812 | ||||||||
\(162\) | −5.00432 | −0.393176 | ||||||||
\(163\) | −12.3337 | −0.966051 | −0.483025 | − | 0.875606i | \(-0.660462\pi\) | ||||
−0.483025 | + | 0.875606i | \(0.660462\pi\) | |||||||
\(164\) | −0.284646 | −0.0222271 | ||||||||
\(165\) | −3.00503 | −0.233941 | ||||||||
\(166\) | −3.29528 | −0.255763 | ||||||||
\(167\) | 16.2031 | 1.25384 | 0.626919 | − | 0.779085i | \(-0.284316\pi\) | ||||
0.626919 | + | 0.779085i | \(0.284316\pi\) | |||||||
\(168\) | 2.02817 | 0.156477 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −23.7839 | −1.82414 | ||||||||
\(171\) | 13.4599 | 1.02930 | ||||||||
\(172\) | 7.99475 | 0.609594 | ||||||||
\(173\) | −3.17007 | −0.241016 | −0.120508 | − | 0.992712i | \(-0.538452\pi\) | ||||
−0.120508 | + | 0.992712i | \(0.538452\pi\) | |||||||
\(174\) | 15.2557 | 1.15653 | ||||||||
\(175\) | −2.04577 | −0.154646 | ||||||||
\(176\) | −2.27441 | −0.171440 | ||||||||
\(177\) | 9.36934 | 0.704243 | ||||||||
\(178\) | 22.1027 | 1.65667 | ||||||||
\(179\) | 13.0697 | 0.976873 | 0.488436 | − | 0.872599i | \(-0.337567\pi\) | ||||
0.488436 | + | 0.872599i | \(0.337567\pi\) | |||||||
\(180\) | 15.6713 | 1.16807 | ||||||||
\(181\) | −15.6007 | −1.15959 | −0.579794 | − | 0.814763i | \(-0.696867\pi\) | ||||
−0.579794 | + | 0.814763i | \(0.696867\pi\) | |||||||
\(182\) | −2.79978 | −0.207533 | ||||||||
\(183\) | −2.70503 | −0.199962 | ||||||||
\(184\) | 6.22181 | 0.458678 | ||||||||
\(185\) | 23.3105 | 1.71382 | ||||||||
\(186\) | 6.78652 | 0.497612 | ||||||||
\(187\) | −5.45435 | −0.398862 | ||||||||
\(188\) | −33.9130 | −2.47336 | ||||||||
\(189\) | 5.99742 | 0.436248 | ||||||||
\(190\) | −34.7694 | −2.52244 | ||||||||
\(191\) | 14.6219 | 1.05801 | 0.529003 | − | 0.848620i | \(-0.322566\pi\) | ||||
0.529003 | + | 0.848620i | \(0.322566\pi\) | |||||||
\(192\) | −11.4232 | −0.824400 | ||||||||
\(193\) | −18.7458 | −1.34935 | −0.674677 | − | 0.738113i | \(-0.735717\pi\) | ||||
−0.674677 | + | 0.738113i | \(0.735717\pi\) | |||||||
\(194\) | 14.0783 | 1.01077 | ||||||||
\(195\) | 2.32807 | 0.166717 | ||||||||
\(196\) | −15.0238 | −1.07313 | ||||||||
\(197\) | 17.8803 | 1.27392 | 0.636961 | − | 0.770896i | \(-0.280191\pi\) | ||||
0.636961 | + | 0.770896i | \(0.280191\pi\) | |||||||
\(198\) | 6.16147 | 0.437876 | ||||||||
\(199\) | −17.9110 | −1.26968 | −0.634838 | − | 0.772645i | \(-0.718933\pi\) | ||||
−0.634838 | + | 0.772645i | \(0.718933\pi\) | |||||||
\(200\) | −2.80354 | −0.198240 | ||||||||
\(201\) | 2.35712 | 0.166258 | ||||||||
\(202\) | 24.3639 | 1.71424 | ||||||||
\(203\) | 9.82123 | 0.689315 | ||||||||
\(204\) | −10.7191 | −0.750489 | ||||||||
\(205\) | 0.261235 | 0.0182455 | ||||||||
\(206\) | 15.6855 | 1.09286 | ||||||||
\(207\) | 7.74063 | 0.538011 | ||||||||
\(208\) | 1.76204 | 0.122176 | ||||||||
\(209\) | −7.97366 | −0.551550 | ||||||||
\(210\) | −6.51808 | −0.449790 | ||||||||
\(211\) | 8.91647 | 0.613835 | 0.306918 | − | 0.951736i | \(-0.400702\pi\) | ||||
0.306918 | + | 0.951736i | \(0.400702\pi\) | |||||||
\(212\) | 9.76624 | 0.670748 | ||||||||
\(213\) | 11.1043 | 0.760857 | ||||||||
\(214\) | 33.8904 | 2.31670 | ||||||||
\(215\) | −7.33723 | −0.500395 | ||||||||
\(216\) | 8.21889 | 0.559224 | ||||||||
\(217\) | 4.36900 | 0.296587 | ||||||||
\(218\) | −2.29893 | −0.155703 | ||||||||
\(219\) | 3.90124 | 0.263622 | ||||||||
\(220\) | −9.28367 | −0.625905 | ||||||||
\(221\) | 4.22562 | 0.284246 | ||||||||
\(222\) | 18.0115 | 1.20885 | ||||||||
\(223\) | 5.72445 | 0.383337 | 0.191669 | − | 0.981460i | \(-0.438610\pi\) | ||||
0.191669 | + | 0.981460i | \(0.438610\pi\) | |||||||
\(224\) | −9.40979 | −0.628718 | ||||||||
\(225\) | −3.48791 | −0.232528 | ||||||||
\(226\) | 15.6407 | 1.04040 | ||||||||
\(227\) | 10.1636 | 0.674581 | 0.337290 | − | 0.941401i | \(-0.390490\pi\) | ||||
0.337290 | + | 0.941401i | \(0.390490\pi\) | |||||||
\(228\) | −15.6702 | −1.03778 | ||||||||
\(229\) | 11.2669 | 0.744539 | 0.372270 | − | 0.928125i | \(-0.378580\pi\) | ||||
0.372270 | + | 0.928125i | \(0.378580\pi\) | |||||||
\(230\) | −19.9955 | −1.31846 | ||||||||
\(231\) | −1.49479 | −0.0983499 | ||||||||
\(232\) | 13.4590 | 0.883629 | ||||||||
\(233\) | 2.95803 | 0.193787 | 0.0968934 | − | 0.995295i | \(-0.469109\pi\) | ||||
0.0968934 | + | 0.995295i | \(0.469109\pi\) | |||||||
\(234\) | −4.77344 | −0.312050 | ||||||||
\(235\) | 31.1238 | 2.03029 | ||||||||
\(236\) | 28.9455 | 1.88419 | ||||||||
\(237\) | 8.42777 | 0.547443 | ||||||||
\(238\) | −11.8308 | −0.766877 | ||||||||
\(239\) | −14.0665 | −0.909888 | −0.454944 | − | 0.890520i | \(-0.650341\pi\) | ||||
−0.454944 | + | 0.890520i | \(0.650341\pi\) | |||||||
\(240\) | 4.10216 | 0.264793 | ||||||||
\(241\) | −10.4597 | −0.673768 | −0.336884 | − | 0.941546i | \(-0.609373\pi\) | ||||
−0.336884 | + | 0.941546i | \(0.609373\pi\) | |||||||
\(242\) | 20.4483 | 1.31447 | ||||||||
\(243\) | 16.1484 | 1.03592 | ||||||||
\(244\) | −8.35687 | −0.534994 | ||||||||
\(245\) | 13.7882 | 0.880895 | ||||||||
\(246\) | 0.201850 | 0.0128695 | ||||||||
\(247\) | 6.17739 | 0.393058 | ||||||||
\(248\) | 5.98729 | 0.380193 | ||||||||
\(249\) | 1.36300 | 0.0863766 | ||||||||
\(250\) | −19.1325 | −1.21005 | ||||||||
\(251\) | −16.9887 | −1.07232 | −0.536159 | − | 0.844117i | \(-0.680125\pi\) | ||||
−0.536159 | + | 0.844117i | \(0.680125\pi\) | |||||||
\(252\) | 7.79534 | 0.491061 | ||||||||
\(253\) | −4.58556 | −0.288292 | ||||||||
\(254\) | −20.8475 | −1.30809 | ||||||||
\(255\) | 9.83754 | 0.616051 | ||||||||
\(256\) | −3.02978 | −0.189361 | ||||||||
\(257\) | −12.2624 | −0.764907 | −0.382453 | − | 0.923975i | \(-0.624921\pi\) | ||||
−0.382453 | + | 0.923975i | \(0.624921\pi\) | |||||||
\(258\) | −5.66929 | −0.352954 | ||||||||
\(259\) | 11.5953 | 0.720499 | ||||||||
\(260\) | 7.19229 | 0.446047 | ||||||||
\(261\) | 16.7446 | 1.03646 | ||||||||
\(262\) | 37.8490 | 2.33832 | ||||||||
\(263\) | 21.7088 | 1.33862 | 0.669310 | − | 0.742983i | \(-0.266590\pi\) | ||||
0.669310 | + | 0.742983i | \(0.266590\pi\) | |||||||
\(264\) | −2.04846 | −0.126074 | ||||||||
\(265\) | −8.96302 | −0.550594 | ||||||||
\(266\) | −17.2953 | −1.06044 | ||||||||
\(267\) | −9.14217 | −0.559491 | ||||||||
\(268\) | 7.28203 | 0.444821 | ||||||||
\(269\) | 24.8563 | 1.51551 | 0.757757 | − | 0.652536i | \(-0.226295\pi\) | ||||
0.757757 | + | 0.652536i | \(0.226295\pi\) | |||||||
\(270\) | −26.4136 | −1.60748 | ||||||||
\(271\) | 16.9142 | 1.02747 | 0.513733 | − | 0.857950i | \(-0.328262\pi\) | ||||
0.513733 | + | 0.857950i | \(0.328262\pi\) | |||||||
\(272\) | 7.44572 | 0.451463 | ||||||||
\(273\) | 1.15805 | 0.0700884 | ||||||||
\(274\) | 2.74626 | 0.165907 | ||||||||
\(275\) | 2.06624 | 0.124599 | ||||||||
\(276\) | −9.01174 | −0.542443 | ||||||||
\(277\) | −23.9205 | −1.43724 | −0.718622 | − | 0.695401i | \(-0.755227\pi\) | ||||
−0.718622 | + | 0.695401i | \(0.755227\pi\) | |||||||
\(278\) | 36.6183 | 2.19622 | ||||||||
\(279\) | 7.44886 | 0.445952 | ||||||||
\(280\) | −5.75046 | −0.343656 | ||||||||
\(281\) | 11.6377 | 0.694245 | 0.347122 | − | 0.937820i | \(-0.387159\pi\) | ||||
0.347122 | + | 0.937820i | \(0.387159\pi\) | |||||||
\(282\) | 24.0486 | 1.43207 | ||||||||
\(283\) | −11.0376 | −0.656116 | −0.328058 | − | 0.944658i | \(-0.606394\pi\) | ||||
−0.328058 | + | 0.944658i | \(0.606394\pi\) | |||||||
\(284\) | 34.3055 | 2.03566 | ||||||||
\(285\) | 14.3814 | 0.851881 | ||||||||
\(286\) | 2.82779 | 0.167211 | ||||||||
\(287\) | 0.129946 | 0.00767047 | ||||||||
\(288\) | −16.0431 | −0.945348 | ||||||||
\(289\) | 0.855864 | 0.0503450 | ||||||||
\(290\) | −43.2543 | −2.53998 | ||||||||
\(291\) | −5.82311 | −0.341357 | ||||||||
\(292\) | 12.0524 | 0.705314 | ||||||||
\(293\) | 17.7828 | 1.03888 | 0.519440 | − | 0.854507i | \(-0.326141\pi\) | ||||
0.519440 | + | 0.854507i | \(0.326141\pi\) | |||||||
\(294\) | 10.6538 | 0.621341 | ||||||||
\(295\) | −26.5649 | −1.54667 | ||||||||
\(296\) | 15.8903 | 0.923604 | ||||||||
\(297\) | −6.05743 | −0.351488 | ||||||||
\(298\) | −25.3751 | −1.46994 | ||||||||
\(299\) | 3.55255 | 0.205449 | ||||||||
\(300\) | 4.06067 | 0.234443 | ||||||||
\(301\) | −3.64975 | −0.210368 | ||||||||
\(302\) | 25.7478 | 1.48162 | ||||||||
\(303\) | −10.0775 | −0.578936 | ||||||||
\(304\) | 10.8848 | 0.624288 | ||||||||
\(305\) | 7.66957 | 0.439158 | ||||||||
\(306\) | −20.1708 | −1.15309 | ||||||||
\(307\) | −23.8798 | −1.36289 | −0.681445 | − | 0.731870i | \(-0.738648\pi\) | ||||
−0.681445 | + | 0.731870i | \(0.738648\pi\) | |||||||
\(308\) | −4.61797 | −0.263133 | ||||||||
\(309\) | −6.48788 | −0.369083 | ||||||||
\(310\) | −19.2418 | −1.09286 | ||||||||
\(311\) | −12.9749 | −0.735742 | −0.367871 | − | 0.929877i | \(-0.619913\pi\) | ||||
−0.367871 | + | 0.929877i | \(0.619913\pi\) | |||||||
\(312\) | 1.58700 | 0.0898459 | ||||||||
\(313\) | −5.53389 | −0.312794 | −0.156397 | − | 0.987694i | \(-0.549988\pi\) | ||||
−0.156397 | + | 0.987694i | \(0.549988\pi\) | |||||||
\(314\) | 25.7457 | 1.45291 | ||||||||
\(315\) | −7.15423 | −0.403095 | ||||||||
\(316\) | 26.0366 | 1.46467 | ||||||||
\(317\) | −16.2846 | −0.914635 | −0.457318 | − | 0.889303i | \(-0.651190\pi\) | ||||
−0.457318 | + | 0.889303i | \(0.651190\pi\) | |||||||
\(318\) | −6.92550 | −0.388363 | ||||||||
\(319\) | −9.91950 | −0.555385 | ||||||||
\(320\) | 32.3882 | 1.81056 | ||||||||
\(321\) | −14.0178 | −0.782398 | ||||||||
\(322\) | −9.94634 | −0.554288 | ||||||||
\(323\) | 26.1033 | 1.45243 | ||||||||
\(324\) | 6.39470 | 0.355261 | ||||||||
\(325\) | −1.60077 | −0.0887948 | ||||||||
\(326\) | 27.0202 | 1.49651 | ||||||||
\(327\) | 0.950890 | 0.0525843 | ||||||||
\(328\) | 0.178078 | 0.00983274 | ||||||||
\(329\) | 15.4819 | 0.853545 | ||||||||
\(330\) | 6.58330 | 0.362399 | ||||||||
\(331\) | −0.273430 | −0.0150290 | −0.00751452 | − | 0.999972i | \(-0.502392\pi\) | ||||
−0.00751452 | + | 0.999972i | \(0.502392\pi\) | |||||||
\(332\) | 4.21082 | 0.231099 | ||||||||
\(333\) | 19.7693 | 1.08335 | ||||||||
\(334\) | −35.4972 | −1.94232 | ||||||||
\(335\) | −6.68313 | −0.365138 | ||||||||
\(336\) | 2.04053 | 0.111320 | ||||||||
\(337\) | 12.2203 | 0.665685 | 0.332842 | − | 0.942982i | \(-0.391992\pi\) | ||||
0.332842 | + | 0.942982i | \(0.391992\pi\) | |||||||
\(338\) | −2.19076 | −0.119162 | ||||||||
\(339\) | −6.46935 | −0.351367 | ||||||||
\(340\) | 30.3919 | 1.64823 | ||||||||
\(341\) | −4.41271 | −0.238962 | ||||||||
\(342\) | −29.4874 | −1.59450 | ||||||||
\(343\) | 15.8046 | 0.853368 | ||||||||
\(344\) | −5.00163 | −0.269670 | ||||||||
\(345\) | 8.27058 | 0.445273 | ||||||||
\(346\) | 6.94485 | 0.373358 | ||||||||
\(347\) | 29.4501 | 1.58097 | 0.790483 | − | 0.612484i | \(-0.209830\pi\) | ||||
0.790483 | + | 0.612484i | \(0.209830\pi\) | |||||||
\(348\) | −19.4942 | −1.04500 | ||||||||
\(349\) | −23.3461 | −1.24969 | −0.624843 | − | 0.780750i | \(-0.714837\pi\) | ||||
−0.624843 | + | 0.780750i | \(0.714837\pi\) | |||||||
\(350\) | 4.48180 | 0.239562 | ||||||||
\(351\) | 4.69284 | 0.250485 | ||||||||
\(352\) | 9.50395 | 0.506562 | ||||||||
\(353\) | −9.39312 | −0.499945 | −0.249973 | − | 0.968253i | \(-0.580422\pi\) | ||||
−0.249973 | + | 0.968253i | \(0.580422\pi\) | |||||||
\(354\) | −20.5260 | −1.09094 | ||||||||
\(355\) | −31.4841 | −1.67100 | ||||||||
\(356\) | −28.2436 | −1.49691 | ||||||||
\(357\) | 4.89348 | 0.258990 | ||||||||
\(358\) | −28.6325 | −1.51328 | ||||||||
\(359\) | −33.4686 | −1.76640 | −0.883202 | − | 0.468992i | \(-0.844617\pi\) | ||||
−0.883202 | + | 0.468992i | \(0.844617\pi\) | |||||||
\(360\) | −9.80417 | −0.516725 | ||||||||
\(361\) | 19.1602 | 1.00843 | ||||||||
\(362\) | 34.1773 | 1.79632 | ||||||||
\(363\) | −8.45788 | −0.443923 | ||||||||
\(364\) | 3.57766 | 0.187520 | ||||||||
\(365\) | −11.0612 | −0.578969 | ||||||||
\(366\) | 5.92608 | 0.309761 | ||||||||
\(367\) | −18.0139 | −0.940318 | −0.470159 | − | 0.882582i | \(-0.655803\pi\) | ||||
−0.470159 | + | 0.882582i | \(0.655803\pi\) | |||||||
\(368\) | 6.25973 | 0.326311 | ||||||||
\(369\) | 0.221550 | 0.0115334 | ||||||||
\(370\) | −51.0678 | −2.65489 | ||||||||
\(371\) | −4.45847 | −0.231472 | ||||||||
\(372\) | −8.67206 | −0.449625 | ||||||||
\(373\) | 0.0147641 | 0.000764455 0 | 0.000382227 | − | 1.00000i | \(-0.499878\pi\) | ||||
0.000382227 | 1.00000i | \(0.499878\pi\) | ||||||||
\(374\) | 11.9492 | 0.617877 | ||||||||
\(375\) | 7.91365 | 0.408659 | ||||||||
\(376\) | 21.2164 | 1.09415 | ||||||||
\(377\) | 7.68488 | 0.395791 | ||||||||
\(378\) | −13.1389 | −0.675793 | ||||||||
\(379\) | 36.0955 | 1.85410 | 0.927050 | − | 0.374937i | \(-0.122336\pi\) | ||||
0.927050 | + | 0.374937i | \(0.122336\pi\) | |||||||
\(380\) | 44.4296 | 2.27919 | ||||||||
\(381\) | 8.62299 | 0.441769 | ||||||||
\(382\) | −32.0332 | −1.63896 | ||||||||
\(383\) | −12.3209 | −0.629571 | −0.314786 | − | 0.949163i | \(-0.601933\pi\) | ||||
−0.314786 | + | 0.949163i | \(0.601933\pi\) | |||||||
\(384\) | 11.6817 | 0.596131 | ||||||||
\(385\) | 4.23817 | 0.215997 | ||||||||
\(386\) | 41.0676 | 2.09029 | ||||||||
\(387\) | −6.22259 | −0.316312 | ||||||||
\(388\) | −17.9898 | −0.913294 | ||||||||
\(389\) | 13.6644 | 0.692813 | 0.346406 | − | 0.938085i | \(-0.387402\pi\) | ||||
0.346406 | + | 0.938085i | \(0.387402\pi\) | |||||||
\(390\) | −5.10025 | −0.258261 | ||||||||
\(391\) | 15.0117 | 0.759175 | ||||||||
\(392\) | 9.39911 | 0.474727 | ||||||||
\(393\) | −15.6552 | −0.789699 | ||||||||
\(394\) | −39.1716 | −1.97343 | ||||||||
\(395\) | −23.8952 | −1.20230 | ||||||||
\(396\) | −7.87334 | −0.395650 | ||||||||
\(397\) | −17.3825 | −0.872403 | −0.436201 | − | 0.899849i | \(-0.643676\pi\) | ||||
−0.436201 | + | 0.899849i | \(0.643676\pi\) | |||||||
\(398\) | 39.2387 | 1.96686 | ||||||||
\(399\) | 7.15373 | 0.358135 | ||||||||
\(400\) | −2.82062 | −0.141031 | ||||||||
\(401\) | 0.328038 | 0.0163814 | 0.00819071 | − | 0.999966i | \(-0.497393\pi\) | ||||
0.00819071 | + | 0.999966i | \(0.497393\pi\) | |||||||
\(402\) | −5.16388 | −0.257551 | ||||||||
\(403\) | 3.41864 | 0.170295 | ||||||||
\(404\) | −31.1331 | −1.54893 | ||||||||
\(405\) | −5.86877 | −0.291622 | ||||||||
\(406\) | −21.5160 | −1.06782 | ||||||||
\(407\) | −11.7114 | −0.580511 | ||||||||
\(408\) | 6.70604 | 0.331999 | ||||||||
\(409\) | −22.6065 | −1.11782 | −0.558910 | − | 0.829228i | \(-0.688780\pi\) | ||||
−0.558910 | + | 0.829228i | \(0.688780\pi\) | |||||||
\(410\) | −0.572304 | −0.0282641 | ||||||||
\(411\) | −1.13591 | −0.0560305 | ||||||||
\(412\) | −20.0435 | −0.987473 | ||||||||
\(413\) | −13.2141 | −0.650225 | ||||||||
\(414\) | −16.9579 | −0.833434 | ||||||||
\(415\) | −3.86451 | −0.189701 | ||||||||
\(416\) | −7.36294 | −0.360998 | ||||||||
\(417\) | −15.1462 | −0.741710 | ||||||||
\(418\) | 17.4684 | 0.854407 | ||||||||
\(419\) | −9.91008 | −0.484139 | −0.242070 | − | 0.970259i | \(-0.577826\pi\) | ||||
−0.242070 | + | 0.970259i | \(0.577826\pi\) | |||||||
\(420\) | 8.32904 | 0.406415 | ||||||||
\(421\) | −30.1026 | −1.46711 | −0.733556 | − | 0.679629i | \(-0.762141\pi\) | ||||
−0.733556 | + | 0.679629i | \(0.762141\pi\) | |||||||
\(422\) | −19.5339 | −0.950893 | ||||||||
\(423\) | 26.3956 | 1.28340 | ||||||||
\(424\) | −6.10990 | −0.296723 | ||||||||
\(425\) | −6.76425 | −0.328114 | ||||||||
\(426\) | −24.3270 | −1.17864 | ||||||||
\(427\) | 3.81507 | 0.184624 | ||||||||
\(428\) | −43.3064 | −2.09329 | ||||||||
\(429\) | −1.16964 | −0.0564706 | ||||||||
\(430\) | 16.0741 | 0.775162 | ||||||||
\(431\) | 7.35190 | 0.354129 | 0.177064 | − | 0.984199i | \(-0.443340\pi\) | ||||
0.177064 | + | 0.984199i | \(0.443340\pi\) | |||||||
\(432\) | 8.26899 | 0.397842 | ||||||||
\(433\) | −4.18323 | −0.201033 | −0.100517 | − | 0.994935i | \(-0.532050\pi\) | ||||
−0.100517 | + | 0.994935i | \(0.532050\pi\) | |||||||
\(434\) | −9.57143 | −0.459443 | ||||||||
\(435\) | 17.8909 | 0.857805 | ||||||||
\(436\) | 2.93766 | 0.140688 | ||||||||
\(437\) | 21.9455 | 1.04979 | ||||||||
\(438\) | −8.54669 | −0.408377 | ||||||||
\(439\) | 34.9869 | 1.66984 | 0.834918 | − | 0.550375i | \(-0.185515\pi\) | ||||
0.834918 | + | 0.550375i | \(0.185515\pi\) | |||||||
\(440\) | 5.80800 | 0.276886 | ||||||||
\(441\) | 11.6936 | 0.556836 | ||||||||
\(442\) | −9.25732 | −0.440326 | ||||||||
\(443\) | −4.59019 | −0.218087 | −0.109043 | − | 0.994037i | \(-0.534779\pi\) | ||||
−0.109043 | + | 0.994037i | \(0.534779\pi\) | |||||||
\(444\) | −23.0157 | −1.09228 | ||||||||
\(445\) | 25.9208 | 1.22876 | ||||||||
\(446\) | −12.5409 | −0.593828 | ||||||||
\(447\) | 10.4957 | 0.496430 | ||||||||
\(448\) | 16.1109 | 0.761166 | ||||||||
\(449\) | 15.8971 | 0.750230 | 0.375115 | − | 0.926978i | \(-0.377603\pi\) | ||||
0.375115 | + | 0.926978i | \(0.377603\pi\) | |||||||
\(450\) | 7.64119 | 0.360209 | ||||||||
\(451\) | −0.131246 | −0.00618014 | ||||||||
\(452\) | −19.9863 | −0.940075 | ||||||||
\(453\) | −10.6499 | −0.500375 | ||||||||
\(454\) | −22.2660 | −1.04499 | ||||||||
\(455\) | −3.28342 | −0.153929 | ||||||||
\(456\) | 9.80350 | 0.459091 | ||||||||
\(457\) | 21.1491 | 0.989311 | 0.494656 | − | 0.869089i | \(-0.335294\pi\) | ||||
0.494656 | + | 0.869089i | \(0.335294\pi\) | |||||||
\(458\) | −24.6831 | −1.15337 | ||||||||
\(459\) | 19.8302 | 0.925593 | ||||||||
\(460\) | 25.5510 | 1.19132 | ||||||||
\(461\) | 24.7211 | 1.15138 | 0.575689 | − | 0.817669i | \(-0.304734\pi\) | ||||
0.575689 | + | 0.817669i | \(0.304734\pi\) | |||||||
\(462\) | 3.27473 | 0.152354 | ||||||||
\(463\) | 1.00000 | 0.0464739 | ||||||||
\(464\) | 13.5411 | 0.628629 | ||||||||
\(465\) | 7.95883 | 0.369082 | ||||||||
\(466\) | −6.48033 | −0.300195 | ||||||||
\(467\) | −35.9169 | −1.66204 | −0.831018 | − | 0.556245i | \(-0.812241\pi\) | ||||
−0.831018 | + | 0.556245i | \(0.812241\pi\) | |||||||
\(468\) | 6.09968 | 0.281958 | ||||||||
\(469\) | −3.32438 | −0.153506 | ||||||||
\(470\) | −68.1849 | −3.14513 | ||||||||
\(471\) | −10.6490 | −0.490680 | ||||||||
\(472\) | −18.1087 | −0.833520 | ||||||||
\(473\) | 3.68627 | 0.169495 | ||||||||
\(474\) | −18.4632 | −0.848045 | ||||||||
\(475\) | −9.88859 | −0.453720 | ||||||||
\(476\) | 15.1178 | 0.692924 | ||||||||
\(477\) | −7.60140 | −0.348044 | ||||||||
\(478\) | 30.8164 | 1.40951 | ||||||||
\(479\) | 9.82554 | 0.448941 | 0.224470 | − | 0.974481i | \(-0.427935\pi\) | ||||
0.224470 | + | 0.974481i | \(0.427935\pi\) | |||||||
\(480\) | −17.1415 | −0.782397 | ||||||||
\(481\) | 9.07308 | 0.413697 | ||||||||
\(482\) | 22.9147 | 1.04374 | ||||||||
\(483\) | 4.11403 | 0.187195 | ||||||||
\(484\) | −26.1296 | −1.18771 | ||||||||
\(485\) | 16.5103 | 0.749692 | ||||||||
\(486\) | −35.3773 | −1.60475 | ||||||||
\(487\) | 39.2819 | 1.78003 | 0.890016 | − | 0.455929i | \(-0.150693\pi\) | ||||
0.890016 | + | 0.455929i | \(0.150693\pi\) | |||||||
\(488\) | 5.22818 | 0.236669 | ||||||||
\(489\) | −11.1762 | −0.505403 | ||||||||
\(490\) | −30.2066 | −1.36460 | ||||||||
\(491\) | 10.7208 | 0.483824 | 0.241912 | − | 0.970298i | \(-0.422225\pi\) | ||||
0.241912 | + | 0.970298i | \(0.422225\pi\) | |||||||
\(492\) | −0.257931 | −0.0116284 | ||||||||
\(493\) | 32.4734 | 1.46253 | ||||||||
\(494\) | −13.5332 | −0.608887 | ||||||||
\(495\) | 7.22581 | 0.324776 | ||||||||
\(496\) | 6.02378 | 0.270476 | ||||||||
\(497\) | −15.6611 | −0.702497 | ||||||||
\(498\) | −2.98601 | −0.133806 | ||||||||
\(499\) | 14.3408 | 0.641983 | 0.320991 | − | 0.947082i | \(-0.395984\pi\) | ||||
0.320991 | + | 0.947082i | \(0.395984\pi\) | |||||||
\(500\) | 24.4483 | 1.09336 | ||||||||
\(501\) | 14.6824 | 0.655963 | ||||||||
\(502\) | 37.2182 | 1.66113 | ||||||||
\(503\) | 7.68994 | 0.342878 | 0.171439 | − | 0.985195i | \(-0.445158\pi\) | ||||
0.171439 | + | 0.985195i | \(0.445158\pi\) | |||||||
\(504\) | −4.87688 | −0.217234 | ||||||||
\(505\) | 28.5726 | 1.27146 | ||||||||
\(506\) | 10.0459 | 0.446593 | ||||||||
\(507\) | 0.906147 | 0.0402434 | ||||||||
\(508\) | 26.6397 | 1.18195 | ||||||||
\(509\) | 25.1726 | 1.11575 | 0.557877 | − | 0.829923i | \(-0.311616\pi\) | ||||
0.557877 | + | 0.829923i | \(0.311616\pi\) | |||||||
\(510\) | −21.5517 | −0.954325 | ||||||||
\(511\) | −5.50215 | −0.243401 | ||||||||
\(512\) | −19.1458 | −0.846132 | ||||||||
\(513\) | 28.9895 | 1.27992 | ||||||||
\(514\) | 26.8640 | 1.18492 | ||||||||
\(515\) | 18.3951 | 0.810583 | ||||||||
\(516\) | 7.24442 | 0.318918 | ||||||||
\(517\) | −15.6368 | −0.687706 | ||||||||
\(518\) | −25.4026 | −1.11613 | ||||||||
\(519\) | −2.87255 | −0.126091 | ||||||||
\(520\) | −4.49960 | −0.197321 | ||||||||
\(521\) | −22.6293 | −0.991408 | −0.495704 | − | 0.868492i | \(-0.665090\pi\) | ||||
−0.495704 | + | 0.868492i | \(0.665090\pi\) | |||||||
\(522\) | −36.6833 | −1.60559 | ||||||||
\(523\) | 13.4710 | 0.589044 | 0.294522 | − | 0.955645i | \(-0.404840\pi\) | ||||
0.294522 | + | 0.955645i | \(0.404840\pi\) | |||||||
\(524\) | −48.3648 | −2.11282 | ||||||||
\(525\) | −1.85377 | −0.0809053 | ||||||||
\(526\) | −47.5587 | −2.07366 | ||||||||
\(527\) | 14.4459 | 0.629272 | ||||||||
\(528\) | −2.06095 | −0.0896913 | ||||||||
\(529\) | −10.3794 | −0.451279 | ||||||||
\(530\) | 19.6358 | 0.852926 | ||||||||
\(531\) | −22.5293 | −0.977687 | ||||||||
\(532\) | 22.1006 | 0.958182 | ||||||||
\(533\) | 0.101680 | 0.00440424 | ||||||||
\(534\) | 20.0283 | 0.866709 | ||||||||
\(535\) | 39.7447 | 1.71831 | ||||||||
\(536\) | −4.55574 | −0.196778 | ||||||||
\(537\) | 11.8430 | 0.511065 | ||||||||
\(538\) | −54.4542 | −2.34769 | ||||||||
\(539\) | −6.92728 | −0.298379 | ||||||||
\(540\) | 33.7523 | 1.45247 | ||||||||
\(541\) | −41.4824 | −1.78347 | −0.891734 | − | 0.452559i | \(-0.850511\pi\) | ||||
−0.891734 | + | 0.452559i | \(0.850511\pi\) | |||||||
\(542\) | −37.0550 | −1.59165 | ||||||||
\(543\) | −14.1365 | −0.606656 | ||||||||
\(544\) | −31.1130 | −1.33396 | ||||||||
\(545\) | −2.69606 | −0.115486 | ||||||||
\(546\) | −2.53701 | −0.108574 | ||||||||
\(547\) | −28.7590 | −1.22965 | −0.614823 | − | 0.788665i | \(-0.710773\pi\) | ||||
−0.614823 | + | 0.788665i | \(0.710773\pi\) | |||||||
\(548\) | −3.50927 | −0.149908 | ||||||||
\(549\) | 6.50444 | 0.277603 | ||||||||
\(550\) | −4.52665 | −0.193017 | ||||||||
\(551\) | 47.4725 | 2.02240 | ||||||||
\(552\) | 5.63788 | 0.239964 | ||||||||
\(553\) | −11.8862 | −0.505452 | ||||||||
\(554\) | 52.4041 | 2.22644 | ||||||||
\(555\) | 21.1228 | 0.896612 | ||||||||
\(556\) | −46.7922 | −1.98443 | ||||||||
\(557\) | −12.9901 | −0.550408 | −0.275204 | − | 0.961386i | \(-0.588745\pi\) | ||||
−0.275204 | + | 0.961386i | \(0.588745\pi\) | |||||||
\(558\) | −16.3187 | −0.690825 | ||||||||
\(559\) | −2.85585 | −0.120789 | ||||||||
\(560\) | −5.78552 | −0.244483 | ||||||||
\(561\) | −4.94244 | −0.208670 | ||||||||
\(562\) | −25.4953 | −1.07546 | ||||||||
\(563\) | −24.2566 | −1.02229 | −0.511146 | − | 0.859494i | \(-0.670779\pi\) | ||||
−0.511146 | + | 0.859494i | \(0.670779\pi\) | |||||||
\(564\) | −30.7301 | −1.29397 | ||||||||
\(565\) | 18.3425 | 0.771675 | ||||||||
\(566\) | 24.1807 | 1.01639 | ||||||||
\(567\) | −2.91930 | −0.122599 | ||||||||
\(568\) | −21.4620 | −0.900527 | ||||||||
\(569\) | −36.7037 | −1.53870 | −0.769350 | − | 0.638828i | \(-0.779420\pi\) | ||||
−0.769350 | + | 0.638828i | \(0.779420\pi\) | |||||||
\(570\) | −31.5062 | −1.31965 | ||||||||
\(571\) | 5.26350 | 0.220271 | 0.110135 | − | 0.993917i | \(-0.464872\pi\) | ||||
0.110135 | + | 0.993917i | \(0.464872\pi\) | |||||||
\(572\) | −3.61345 | −0.151086 | ||||||||
\(573\) | 13.2496 | 0.553511 | ||||||||
\(574\) | −0.284681 | −0.0118823 | ||||||||
\(575\) | −5.68681 | −0.237156 | ||||||||
\(576\) | 27.4680 | 1.14450 | ||||||||
\(577\) | −1.67597 | −0.0697714 | −0.0348857 | − | 0.999391i | \(-0.511107\pi\) | ||||
−0.0348857 | + | 0.999391i | \(0.511107\pi\) | |||||||
\(578\) | −1.87499 | −0.0779895 | ||||||||
\(579\) | −16.9865 | −0.705934 | ||||||||
\(580\) | 55.2719 | 2.29504 | ||||||||
\(581\) | −1.92232 | −0.0797513 | ||||||||
\(582\) | 12.7571 | 0.528797 | ||||||||
\(583\) | 4.50308 | 0.186499 | ||||||||
\(584\) | −7.54017 | −0.312014 | ||||||||
\(585\) | −5.59801 | −0.231449 | ||||||||
\(586\) | −38.9578 | −1.60933 | ||||||||
\(587\) | 40.4229 | 1.66843 | 0.834215 | − | 0.551439i | \(-0.185921\pi\) | ||||
0.834215 | + | 0.551439i | \(0.185921\pi\) | |||||||
\(588\) | −13.6138 | −0.561423 | ||||||||
\(589\) | 21.1183 | 0.870164 | ||||||||
\(590\) | 58.1973 | 2.39594 | ||||||||
\(591\) | 16.2022 | 0.666471 | ||||||||
\(592\) | 15.9871 | 0.657068 | ||||||||
\(593\) | 2.28931 | 0.0940107 | 0.0470053 | − | 0.998895i | \(-0.485032\pi\) | ||||
0.0470053 | + | 0.998895i | \(0.485032\pi\) | |||||||
\(594\) | 13.2704 | 0.544491 | ||||||||
\(595\) | −13.8745 | −0.568798 | ||||||||
\(596\) | 32.4252 | 1.32819 | ||||||||
\(597\) | −16.2300 | −0.664249 | ||||||||
\(598\) | −7.78278 | −0.318261 | ||||||||
\(599\) | 41.8378 | 1.70945 | 0.854724 | − | 0.519083i | \(-0.173727\pi\) | ||||
0.854724 | + | 0.519083i | \(0.173727\pi\) | |||||||
\(600\) | −2.54042 | −0.103712 | ||||||||
\(601\) | 10.3090 | 0.420512 | 0.210256 | − | 0.977646i | \(-0.432570\pi\) | ||||
0.210256 | + | 0.977646i | \(0.432570\pi\) | |||||||
\(602\) | 7.99573 | 0.325882 | ||||||||
\(603\) | −5.66786 | −0.230813 | ||||||||
\(604\) | −32.9015 | −1.33874 | ||||||||
\(605\) | 23.9806 | 0.974949 | ||||||||
\(606\) | 22.0773 | 0.896830 | ||||||||
\(607\) | −12.4473 | −0.505219 | −0.252610 | − | 0.967568i | \(-0.581289\pi\) | ||||
−0.252610 | + | 0.967568i | \(0.581289\pi\) | |||||||
\(608\) | −45.4838 | −1.84461 | ||||||||
\(609\) | 8.89948 | 0.360625 | ||||||||
\(610\) | −16.8022 | −0.680301 | ||||||||
\(611\) | 12.1142 | 0.490089 | ||||||||
\(612\) | 25.7749 | 1.04189 | ||||||||
\(613\) | −0.823248 | −0.0332507 | −0.0166253 | − | 0.999862i | \(-0.505292\pi\) | ||||
−0.0166253 | + | 0.999862i | \(0.505292\pi\) | |||||||
\(614\) | 52.3148 | 2.11125 | ||||||||
\(615\) | 0.236718 | 0.00954537 | ||||||||
\(616\) | 2.88907 | 0.116404 | ||||||||
\(617\) | −28.4544 | −1.14553 | −0.572765 | − | 0.819719i | \(-0.694129\pi\) | ||||
−0.572765 | + | 0.819719i | \(0.694129\pi\) | |||||||
\(618\) | 14.2134 | 0.571746 | ||||||||
\(619\) | 30.0250 | 1.20681 | 0.603404 | − | 0.797436i | \(-0.293811\pi\) | ||||
0.603404 | + | 0.797436i | \(0.293811\pi\) | |||||||
\(620\) | 24.5879 | 0.987472 | ||||||||
\(621\) | 16.6715 | 0.669006 | ||||||||
\(622\) | 28.4250 | 1.13974 | ||||||||
\(623\) | 12.8937 | 0.516577 | ||||||||
\(624\) | 1.59667 | 0.0639179 | ||||||||
\(625\) | −30.4414 | −1.21766 | ||||||||
\(626\) | 12.1234 | 0.484549 | ||||||||
\(627\) | −7.22531 | −0.288551 | ||||||||
\(628\) | −32.8988 | −1.31280 | ||||||||
\(629\) | 38.3394 | 1.52869 | ||||||||
\(630\) | 15.6732 | 0.624435 | ||||||||
\(631\) | 32.0976 | 1.27778 | 0.638892 | − | 0.769296i | \(-0.279393\pi\) | ||||
0.638892 | + | 0.769296i | \(0.279393\pi\) | |||||||
\(632\) | −16.2889 | −0.647937 | ||||||||
\(633\) | 8.07964 | 0.321137 | ||||||||
\(634\) | 35.6757 | 1.41686 | ||||||||
\(635\) | −24.4487 | −0.970219 | ||||||||
\(636\) | 8.84965 | 0.350911 | ||||||||
\(637\) | 5.36673 | 0.212638 | ||||||||
\(638\) | 21.7312 | 0.860348 | ||||||||
\(639\) | −26.7012 | −1.05628 | ||||||||
\(640\) | −33.1212 | −1.30923 | ||||||||
\(641\) | 16.6339 | 0.656999 | 0.328500 | − | 0.944504i | \(-0.393457\pi\) | ||||
0.328500 | + | 0.944504i | \(0.393457\pi\) | |||||||
\(642\) | 30.7097 | 1.21201 | ||||||||
\(643\) | 5.39065 | 0.212586 | 0.106293 | − | 0.994335i | \(-0.466102\pi\) | ||||
0.106293 | + | 0.994335i | \(0.466102\pi\) | |||||||
\(644\) | 12.7098 | 0.500836 | ||||||||
\(645\) | −6.64861 | −0.261789 | ||||||||
\(646\) | −57.1861 | −2.24996 | ||||||||
\(647\) | −21.4867 | −0.844728 | −0.422364 | − | 0.906426i | \(-0.638800\pi\) | ||||
−0.422364 | + | 0.906426i | \(0.638800\pi\) | |||||||
\(648\) | −4.00061 | −0.157159 | ||||||||
\(649\) | 13.3464 | 0.523890 | ||||||||
\(650\) | 3.50691 | 0.137552 | ||||||||
\(651\) | 3.95896 | 0.155164 | ||||||||
\(652\) | −34.5274 | −1.35220 | ||||||||
\(653\) | −15.2095 | −0.595194 | −0.297597 | − | 0.954692i | \(-0.596185\pi\) | ||||
−0.297597 | + | 0.954692i | \(0.596185\pi\) | |||||||
\(654\) | −2.08317 | −0.0814585 | ||||||||
\(655\) | 44.3871 | 1.73435 | ||||||||
\(656\) | 0.179164 | 0.00699517 | ||||||||
\(657\) | −9.38082 | −0.365981 | ||||||||
\(658\) | −33.9171 | −1.32223 | ||||||||
\(659\) | 21.3062 | 0.829971 | 0.414986 | − | 0.909828i | \(-0.363787\pi\) | ||||
0.414986 | + | 0.909828i | \(0.363787\pi\) | |||||||
\(660\) | −8.41238 | −0.327451 | ||||||||
\(661\) | −48.3356 | −1.88004 | −0.940018 | − | 0.341126i | \(-0.889192\pi\) | ||||
−0.940018 | + | 0.341126i | \(0.889192\pi\) | |||||||
\(662\) | 0.599019 | 0.0232815 | ||||||||
\(663\) | 3.82903 | 0.148707 | ||||||||
\(664\) | −2.63435 | −0.102233 | ||||||||
\(665\) | −20.2830 | −0.786539 | ||||||||
\(666\) | −43.3098 | −1.67822 | ||||||||
\(667\) | 27.3009 | 1.05709 | ||||||||
\(668\) | 45.3596 | 1.75502 | ||||||||
\(669\) | 5.18719 | 0.200548 | ||||||||
\(670\) | 14.6411 | 0.565636 | ||||||||
\(671\) | −3.85324 | −0.148753 | ||||||||
\(672\) | −8.52666 | −0.328923 | ||||||||
\(673\) | −25.5190 | −0.983687 | −0.491843 | − | 0.870684i | \(-0.663677\pi\) | ||||
−0.491843 | + | 0.870684i | \(0.663677\pi\) | |||||||
\(674\) | −26.7719 | −1.03121 | ||||||||
\(675\) | −7.51217 | −0.289143 | ||||||||
\(676\) | 2.79943 | 0.107670 | ||||||||
\(677\) | −45.6901 | −1.75601 | −0.878007 | − | 0.478647i | \(-0.841127\pi\) | ||||
−0.878007 | + | 0.478647i | \(0.841127\pi\) | |||||||
\(678\) | 14.1728 | 0.544303 | ||||||||
\(679\) | 8.21268 | 0.315174 | ||||||||
\(680\) | −19.0136 | −0.729139 | ||||||||
\(681\) | 9.20971 | 0.352917 | ||||||||
\(682\) | 9.66720 | 0.370176 | ||||||||
\(683\) | 3.77763 | 0.144547 | 0.0722735 | − | 0.997385i | \(-0.476975\pi\) | ||||
0.0722735 | + | 0.997385i | \(0.476975\pi\) | |||||||
\(684\) | 37.6801 | 1.44073 | ||||||||
\(685\) | 3.22065 | 0.123055 | ||||||||
\(686\) | −34.6241 | −1.32195 | ||||||||
\(687\) | 10.2095 | 0.389517 | ||||||||
\(688\) | −5.03212 | −0.191848 | ||||||||
\(689\) | −3.48865 | −0.132907 | ||||||||
\(690\) | −18.1189 | −0.689773 | ||||||||
\(691\) | 26.2778 | 0.999654 | 0.499827 | − | 0.866125i | \(-0.333397\pi\) | ||||
0.499827 | + | 0.866125i | \(0.333397\pi\) | |||||||
\(692\) | −8.87439 | −0.337353 | ||||||||
\(693\) | 3.59433 | 0.136537 | ||||||||
\(694\) | −64.5182 | −2.44908 | ||||||||
\(695\) | 42.9438 | 1.62895 | ||||||||
\(696\) | 12.1959 | 0.462283 | ||||||||
\(697\) | 0.429660 | 0.0162745 | ||||||||
\(698\) | 51.1457 | 1.93589 | ||||||||
\(699\) | 2.68041 | 0.101382 | ||||||||
\(700\) | −5.72701 | −0.216461 | ||||||||
\(701\) | −5.41725 | −0.204607 | −0.102303 | − | 0.994753i | \(-0.532621\pi\) | ||||
−0.102303 | + | 0.994753i | \(0.532621\pi\) | |||||||
\(702\) | −10.2809 | −0.388028 | ||||||||
\(703\) | 56.0480 | 2.11389 | ||||||||
\(704\) | −16.2721 | −0.613276 | ||||||||
\(705\) | 28.2028 | 1.06218 | ||||||||
\(706\) | 20.5781 | 0.774466 | ||||||||
\(707\) | 14.2129 | 0.534529 | ||||||||
\(708\) | 26.2288 | 0.985740 | ||||||||
\(709\) | 30.0072 | 1.12694 | 0.563472 | − | 0.826135i | \(-0.309465\pi\) | ||||
0.563472 | + | 0.826135i | \(0.309465\pi\) | |||||||
\(710\) | 68.9741 | 2.58855 | ||||||||
\(711\) | −20.2652 | −0.760004 | ||||||||
\(712\) | 17.6696 | 0.662197 | ||||||||
\(713\) | 12.1449 | 0.454829 | ||||||||
\(714\) | −10.7204 | −0.401203 | ||||||||
\(715\) | 3.31627 | 0.124021 | ||||||||
\(716\) | 36.5877 | 1.36734 | ||||||||
\(717\) | −12.7463 | −0.476021 | ||||||||
\(718\) | 73.3217 | 2.73634 | ||||||||
\(719\) | 2.74024 | 0.102194 | 0.0510969 | − | 0.998694i | \(-0.483728\pi\) | ||||
0.0510969 | + | 0.998694i | \(0.483728\pi\) | |||||||
\(720\) | −9.86393 | −0.367607 | ||||||||
\(721\) | 9.15024 | 0.340773 | ||||||||
\(722\) | −41.9754 | −1.56216 | ||||||||
\(723\) | −9.47802 | −0.352491 | ||||||||
\(724\) | −43.6730 | −1.62310 | ||||||||
\(725\) | −12.3017 | −0.456875 | ||||||||
\(726\) | 18.5292 | 0.687682 | ||||||||
\(727\) | −39.1451 | −1.45181 | −0.725906 | − | 0.687794i | \(-0.758579\pi\) | ||||
−0.725906 | + | 0.687794i | \(0.758579\pi\) | |||||||
\(728\) | −2.23823 | −0.0829545 | ||||||||
\(729\) | 7.78001 | 0.288148 | ||||||||
\(730\) | 24.2324 | 0.896881 | ||||||||
\(731\) | −12.0677 | −0.446341 | ||||||||
\(732\) | −7.57256 | −0.279890 | ||||||||
\(733\) | 18.6920 | 0.690403 | 0.345202 | − | 0.938529i | \(-0.387811\pi\) | ||||
0.345202 | + | 0.938529i | \(0.387811\pi\) | |||||||
\(734\) | 39.4642 | 1.45665 | ||||||||
\(735\) | 12.4941 | 0.460853 | ||||||||
\(736\) | −26.1572 | −0.964167 | ||||||||
\(737\) | 3.35765 | 0.123680 | ||||||||
\(738\) | −0.485362 | −0.0178664 | ||||||||
\(739\) | −22.3003 | −0.820329 | −0.410165 | − | 0.912012i | \(-0.634529\pi\) | ||||
−0.410165 | + | 0.912012i | \(0.634529\pi\) | |||||||
\(740\) | 65.2563 | 2.39887 | ||||||||
\(741\) | 5.59763 | 0.205634 | ||||||||
\(742\) | 9.76744 | 0.358574 | ||||||||
\(743\) | 18.3135 | 0.671857 | 0.335928 | − | 0.941888i | \(-0.390950\pi\) | ||||
0.335928 | + | 0.941888i | \(0.390950\pi\) | |||||||
\(744\) | 5.42537 | 0.198904 | ||||||||
\(745\) | −29.7585 | −1.09027 | ||||||||
\(746\) | −0.0323445 | −0.00118422 | ||||||||
\(747\) | −3.27743 | −0.119915 | ||||||||
\(748\) | −15.2691 | −0.558293 | ||||||||
\(749\) | 19.7702 | 0.722386 | ||||||||
\(750\) | −17.3369 | −0.633054 | ||||||||
\(751\) | 25.2719 | 0.922186 | 0.461093 | − | 0.887352i | \(-0.347457\pi\) | ||||
0.461093 | + | 0.887352i | \(0.347457\pi\) | |||||||
\(752\) | 21.3458 | 0.778400 | ||||||||
\(753\) | −15.3943 | −0.560998 | ||||||||
\(754\) | −16.8357 | −0.613121 | ||||||||
\(755\) | 30.1956 | 1.09893 | ||||||||
\(756\) | 16.7894 | 0.610624 | ||||||||
\(757\) | −21.9705 | −0.798531 | −0.399265 | − | 0.916835i | \(-0.630735\pi\) | ||||
−0.399265 | + | 0.916835i | \(0.630735\pi\) | |||||||
\(758\) | −79.0766 | −2.87219 | ||||||||
\(759\) | −4.15519 | −0.150824 | ||||||||
\(760\) | −27.7958 | −1.00826 | ||||||||
\(761\) | 21.0135 | 0.761737 | 0.380869 | − | 0.924629i | \(-0.375625\pi\) | ||||
0.380869 | + | 0.924629i | \(0.375625\pi\) | |||||||
\(762\) | −18.8909 | −0.684346 | ||||||||
\(763\) | −1.34110 | −0.0485510 | ||||||||
\(764\) | 40.9331 | 1.48091 | ||||||||
\(765\) | −23.6551 | −0.855251 | ||||||||
\(766\) | 26.9923 | 0.975270 | ||||||||
\(767\) | −10.3398 | −0.373347 | ||||||||
\(768\) | −2.74542 | −0.0990670 | ||||||||
\(769\) | −32.0159 | −1.15452 | −0.577262 | − | 0.816559i | \(-0.695879\pi\) | ||||
−0.577262 | + | 0.816559i | \(0.695879\pi\) | |||||||
\(770\) | −9.28482 | −0.334602 | ||||||||
\(771\) | −11.1115 | −0.400172 | ||||||||
\(772\) | −52.4777 | −1.88871 | ||||||||
\(773\) | 23.0834 | 0.830251 | 0.415126 | − | 0.909764i | \(-0.363738\pi\) | ||||
0.415126 | + | 0.909764i | \(0.363738\pi\) | |||||||
\(774\) | 13.6322 | 0.490000 | ||||||||
\(775\) | −5.47246 | −0.196576 | ||||||||
\(776\) | 11.2547 | 0.404020 | ||||||||
\(777\) | 10.5071 | 0.376940 | ||||||||
\(778\) | −29.9354 | −1.07324 | ||||||||
\(779\) | 0.628116 | 0.0225046 | ||||||||
\(780\) | 6.51728 | 0.233356 | ||||||||
\(781\) | 15.8178 | 0.566006 | ||||||||
\(782\) | −32.8871 | −1.17604 | ||||||||
\(783\) | 36.0639 | 1.28882 | ||||||||
\(784\) | 9.45641 | 0.337729 | ||||||||
\(785\) | 30.1931 | 1.07764 | ||||||||
\(786\) | 34.2967 | 1.22332 | ||||||||
\(787\) | 26.8607 | 0.957480 | 0.478740 | − | 0.877957i | \(-0.341094\pi\) | ||||
0.478740 | + | 0.877957i | \(0.341094\pi\) | |||||||
\(788\) | 50.0548 | 1.78313 | ||||||||
\(789\) | 19.6714 | 0.700319 | ||||||||
\(790\) | 52.3487 | 1.86248 | ||||||||
\(791\) | 9.12410 | 0.324416 | ||||||||
\(792\) | 4.92568 | 0.175026 | ||||||||
\(793\) | 2.98520 | 0.106008 | ||||||||
\(794\) | 38.0809 | 1.35144 | ||||||||
\(795\) | −8.12182 | −0.288051 | ||||||||
\(796\) | −50.1406 | −1.77719 | ||||||||
\(797\) | 40.8530 | 1.44709 | 0.723544 | − | 0.690279i | \(-0.242512\pi\) | ||||
0.723544 | + | 0.690279i | \(0.242512\pi\) | |||||||
\(798\) | −15.6721 | −0.554787 | ||||||||
\(799\) | 51.1901 | 1.81098 | ||||||||
\(800\) | 11.7864 | 0.416712 | ||||||||
\(801\) | 21.9830 | 0.776731 | ||||||||
\(802\) | −0.718652 | −0.0253765 | ||||||||
\(803\) | 5.55721 | 0.196110 | ||||||||
\(804\) | 6.59859 | 0.232714 | ||||||||
\(805\) | −11.6645 | −0.411119 | ||||||||
\(806\) | −7.48942 | −0.263804 | ||||||||
\(807\) | 22.5235 | 0.792863 | ||||||||
\(808\) | 19.4773 | 0.685210 | ||||||||
\(809\) | −15.4003 | −0.541444 | −0.270722 | − | 0.962658i | \(-0.587262\pi\) | ||||
−0.270722 | + | 0.962658i | \(0.587262\pi\) | |||||||
\(810\) | 12.8571 | 0.451751 | ||||||||
\(811\) | −1.10084 | −0.0386557 | −0.0193279 | − | 0.999813i | \(-0.506153\pi\) | ||||
−0.0193279 | + | 0.999813i | \(0.506153\pi\) | |||||||
\(812\) | 27.4939 | 0.964845 | ||||||||
\(813\) | 15.3268 | 0.537533 | ||||||||
\(814\) | 25.6568 | 0.899270 | ||||||||
\(815\) | 31.6877 | 1.10997 | ||||||||
\(816\) | 6.74692 | 0.236189 | ||||||||
\(817\) | −17.6417 | −0.617204 | ||||||||
\(818\) | 49.5255 | 1.73162 | ||||||||
\(819\) | −2.78462 | −0.0973024 | ||||||||
\(820\) | 0.731310 | 0.0255385 | ||||||||
\(821\) | −24.6508 | −0.860319 | −0.430159 | − | 0.902753i | \(-0.641543\pi\) | ||||
−0.430159 | + | 0.902753i | \(0.641543\pi\) | |||||||
\(822\) | 2.48851 | 0.0867969 | ||||||||
\(823\) | −9.04869 | −0.315418 | −0.157709 | − | 0.987486i | \(-0.550411\pi\) | ||||
−0.157709 | + | 0.987486i | \(0.550411\pi\) | |||||||
\(824\) | 12.5395 | 0.436835 | ||||||||
\(825\) | 1.87232 | 0.0651859 | ||||||||
\(826\) | 28.9490 | 1.00727 | ||||||||
\(827\) | −37.4075 | −1.30079 | −0.650393 | − | 0.759598i | \(-0.725396\pi\) | ||||
−0.650393 | + | 0.759598i | \(0.725396\pi\) | |||||||
\(828\) | 21.6694 | 0.753063 | ||||||||
\(829\) | −1.33060 | −0.0462136 | −0.0231068 | − | 0.999733i | \(-0.507356\pi\) | ||||
−0.0231068 | + | 0.999733i | \(0.507356\pi\) | |||||||
\(830\) | 8.46622 | 0.293867 | ||||||||
\(831\) | −21.6755 | −0.751915 | ||||||||
\(832\) | 12.6064 | 0.437047 | ||||||||
\(833\) | 22.6778 | 0.785738 | ||||||||
\(834\) | 33.1816 | 1.14898 | ||||||||
\(835\) | −41.6291 | −1.44063 | ||||||||
\(836\) | −22.3217 | −0.772013 | ||||||||
\(837\) | 16.0431 | 0.554532 | ||||||||
\(838\) | 21.7106 | 0.749981 | ||||||||
\(839\) | −0.361756 | −0.0124892 | −0.00624461 | − | 0.999981i | \(-0.501988\pi\) | ||||
−0.00624461 | + | 0.999981i | \(0.501988\pi\) | |||||||
\(840\) | −5.21077 | −0.179789 | ||||||||
\(841\) | 30.0574 | 1.03646 | ||||||||
\(842\) | 65.9477 | 2.27271 | ||||||||
\(843\) | 10.5454 | 0.363204 | ||||||||
\(844\) | 24.9611 | 0.859195 | ||||||||
\(845\) | −2.56920 | −0.0883830 | ||||||||
\(846\) | −57.8265 | −1.98812 | ||||||||
\(847\) | 11.9286 | 0.409873 | ||||||||
\(848\) | −6.14714 | −0.211094 | ||||||||
\(849\) | −10.0017 | −0.343257 | ||||||||
\(850\) | 14.8188 | 0.508282 | ||||||||
\(851\) | 32.2325 | 1.10492 | ||||||||
\(852\) | 31.0859 | 1.06498 | ||||||||
\(853\) | −48.7107 | −1.66782 | −0.833912 | − | 0.551898i | \(-0.813904\pi\) | ||||
−0.833912 | + | 0.551898i | \(0.813904\pi\) | |||||||
\(854\) | −8.35790 | −0.286001 | ||||||||
\(855\) | −34.5811 | −1.18265 | ||||||||
\(856\) | 27.0931 | 0.926023 | ||||||||
\(857\) | −1.72863 | −0.0590487 | −0.0295244 | − | 0.999564i | \(-0.509399\pi\) | ||||
−0.0295244 | + | 0.999564i | \(0.509399\pi\) | |||||||
\(858\) | 2.56240 | 0.0874788 | ||||||||
\(859\) | −32.0878 | −1.09482 | −0.547411 | − | 0.836864i | \(-0.684387\pi\) | ||||
−0.547411 | + | 0.836864i | \(0.684387\pi\) | |||||||
\(860\) | −20.5401 | −0.700411 | ||||||||
\(861\) | 0.117750 | 0.00401292 | ||||||||
\(862\) | −16.1063 | −0.548581 | ||||||||
\(863\) | −31.6489 | −1.07734 | −0.538670 | − | 0.842517i | \(-0.681073\pi\) | ||||
−0.538670 | + | 0.842517i | \(0.681073\pi\) | |||||||
\(864\) | −34.5531 | −1.17552 | ||||||||
\(865\) | 8.14452 | 0.276922 | ||||||||
\(866\) | 9.16445 | 0.311421 | ||||||||
\(867\) | 0.775539 | 0.0263387 | ||||||||
\(868\) | 12.2307 | 0.415138 | ||||||||
\(869\) | 12.0051 | 0.407246 | ||||||||
\(870\) | −39.1948 | −1.32883 | ||||||||
\(871\) | −2.60125 | −0.0881400 | ||||||||
\(872\) | −1.83784 | −0.0622372 | ||||||||
\(873\) | 14.0021 | 0.473899 | ||||||||
\(874\) | −48.0773 | −1.62624 | ||||||||
\(875\) | −11.1611 | −0.377314 | ||||||||
\(876\) | 10.9213 | 0.368995 | ||||||||
\(877\) | −38.1768 | −1.28914 | −0.644569 | − | 0.764546i | \(-0.722963\pi\) | ||||
−0.644569 | + | 0.764546i | \(0.722963\pi\) | |||||||
\(878\) | −76.6480 | −2.58674 | ||||||||
\(879\) | 16.1138 | 0.543505 | ||||||||
\(880\) | 5.84340 | 0.196981 | ||||||||
\(881\) | 49.1164 | 1.65477 | 0.827386 | − | 0.561633i | \(-0.189827\pi\) | ||||
0.827386 | + | 0.561633i | \(0.189827\pi\) | |||||||
\(882\) | −25.6178 | −0.862596 | ||||||||
\(883\) | 35.5485 | 1.19630 | 0.598151 | − | 0.801384i | \(-0.295902\pi\) | ||||
0.598151 | + | 0.801384i | \(0.295902\pi\) | |||||||
\(884\) | 11.8293 | 0.397864 | ||||||||
\(885\) | −24.0717 | −0.809161 | ||||||||
\(886\) | 10.0560 | 0.337838 | ||||||||
\(887\) | 30.7066 | 1.03103 | 0.515514 | − | 0.856881i | \(-0.327601\pi\) | ||||
0.515514 | + | 0.856881i | \(0.327601\pi\) | |||||||
\(888\) | 14.3989 | 0.483197 | ||||||||
\(889\) | −12.1615 | −0.407884 | ||||||||
\(890\) | −56.7862 | −1.90348 | ||||||||
\(891\) | 2.94851 | 0.0987787 | ||||||||
\(892\) | 16.0252 | 0.536563 | ||||||||
\(893\) | 74.8343 | 2.50424 | ||||||||
\(894\) | −22.9936 | −0.769021 | ||||||||
\(895\) | −33.5785 | −1.12241 | ||||||||
\(896\) | −16.4754 | −0.550406 | ||||||||
\(897\) | 3.21913 | 0.107484 | ||||||||
\(898\) | −34.8267 | −1.16218 | ||||||||
\(899\) | 26.2718 | 0.876215 | ||||||||
\(900\) | −9.76418 | −0.325473 | ||||||||
\(901\) | −14.7417 | −0.491117 | ||||||||
\(902\) | 0.287529 | 0.00957367 | ||||||||
\(903\) | −3.30721 | −0.110057 | ||||||||
\(904\) | 12.5037 | 0.415867 | ||||||||
\(905\) | 40.0812 | 1.33234 | ||||||||
\(906\) | 23.3313 | 0.775132 | ||||||||
\(907\) | −24.5580 | −0.815436 | −0.407718 | − | 0.913108i | \(-0.633675\pi\) | ||||
−0.407718 | + | 0.913108i | \(0.633675\pi\) | |||||||
\(908\) | 28.4523 | 0.944222 | ||||||||
\(909\) | 24.2320 | 0.803725 | ||||||||
\(910\) | 7.19318 | 0.238452 | ||||||||
\(911\) | 15.2207 | 0.504285 | 0.252143 | − | 0.967690i | \(-0.418865\pi\) | ||||
0.252143 | + | 0.967690i | \(0.418865\pi\) | |||||||
\(912\) | 9.86326 | 0.326605 | ||||||||
\(913\) | 1.94155 | 0.0642561 | ||||||||
\(914\) | −46.3325 | −1.53254 | ||||||||
\(915\) | 6.94976 | 0.229752 | ||||||||
\(916\) | 31.5410 | 1.04214 | ||||||||
\(917\) | 22.0794 | 0.729127 | ||||||||
\(918\) | −43.4432 | −1.43384 | ||||||||
\(919\) | 43.8269 | 1.44572 | 0.722858 | − | 0.690997i | \(-0.242828\pi\) | ||||
0.722858 | + | 0.690997i | \(0.242828\pi\) | |||||||
\(920\) | −15.9851 | −0.527011 | ||||||||
\(921\) | −21.6386 | −0.713015 | ||||||||
\(922\) | −54.1581 | −1.78360 | ||||||||
\(923\) | −12.2545 | −0.403360 | ||||||||
\(924\) | −4.18456 | −0.137662 | ||||||||
\(925\) | −14.5239 | −0.477544 | ||||||||
\(926\) | −2.19076 | −0.0719929 | ||||||||
\(927\) | 15.6006 | 0.512390 | ||||||||
\(928\) | −56.5833 | −1.85744 | ||||||||
\(929\) | −36.1646 | −1.18652 | −0.593261 | − | 0.805010i | \(-0.702160\pi\) | ||||
−0.593261 | + | 0.805010i | \(0.702160\pi\) | |||||||
\(930\) | −17.4359 | −0.571746 | ||||||||
\(931\) | 33.1524 | 1.08653 | ||||||||
\(932\) | 8.28080 | 0.271247 | ||||||||
\(933\) | −11.7572 | −0.384914 | ||||||||
\(934\) | 78.6854 | 2.57466 | ||||||||
\(935\) | 14.0133 | 0.458284 | ||||||||
\(936\) | −3.81605 | −0.124731 | ||||||||
\(937\) | 32.5647 | 1.06384 | 0.531921 | − | 0.846794i | \(-0.321470\pi\) | ||||
0.531921 | + | 0.846794i | \(0.321470\pi\) | |||||||
\(938\) | 7.28293 | 0.237796 | ||||||||
\(939\) | −5.01452 | −0.163643 | ||||||||
\(940\) | 87.1291 | 2.84184 | ||||||||
\(941\) | 8.31442 | 0.271042 | 0.135521 | − | 0.990774i | \(-0.456729\pi\) | ||||
0.135521 | + | 0.990774i | \(0.456729\pi\) | |||||||
\(942\) | 23.3294 | 0.760113 | ||||||||
\(943\) | 0.361222 | 0.0117630 | ||||||||
\(944\) | −18.2191 | −0.592981 | ||||||||
\(945\) | −15.4086 | −0.501240 | ||||||||
\(946\) | −8.07574 | −0.262565 | ||||||||
\(947\) | −56.5394 | −1.83728 | −0.918642 | − | 0.395091i | \(-0.870713\pi\) | ||||
−0.918642 | + | 0.395091i | \(0.870713\pi\) | |||||||
\(948\) | 23.5930 | 0.766265 | ||||||||
\(949\) | −4.30531 | −0.139756 | ||||||||
\(950\) | 21.6635 | 0.702858 | ||||||||
\(951\) | −14.7563 | −0.478505 | ||||||||
\(952\) | −9.45793 | −0.306533 | ||||||||
\(953\) | −15.0950 | −0.488975 | −0.244487 | − | 0.969652i | \(-0.578620\pi\) | ||||
−0.244487 | + | 0.969652i | \(0.578620\pi\) | |||||||
\(954\) | 16.6529 | 0.539156 | ||||||||
\(955\) | −37.5666 | −1.21563 | ||||||||
\(956\) | −39.3783 | −1.27358 | ||||||||
\(957\) | −8.98853 | −0.290558 | ||||||||
\(958\) | −21.5254 | −0.695455 | ||||||||
\(959\) | 1.60205 | 0.0517327 | ||||||||
\(960\) | 29.3485 | 0.947219 | ||||||||
\(961\) | −19.3129 | −0.622997 | ||||||||
\(962\) | −19.8770 | −0.640859 | ||||||||
\(963\) | 33.7069 | 1.08619 | ||||||||
\(964\) | −29.2812 | −0.943084 | ||||||||
\(965\) | 48.1617 | 1.55038 | ||||||||
\(966\) | −9.01285 | −0.289984 | ||||||||
\(967\) | −26.2728 | −0.844876 | −0.422438 | − | 0.906392i | \(-0.638826\pi\) | ||||
−0.422438 | + | 0.906392i | \(0.638826\pi\) | |||||||
\(968\) | 16.3471 | 0.525414 | ||||||||
\(969\) | 23.6535 | 0.759859 | ||||||||
\(970\) | −36.1700 | −1.16135 | ||||||||
\(971\) | −45.9733 | −1.47535 | −0.737676 | − | 0.675155i | \(-0.764077\pi\) | ||||
−0.737676 | + | 0.675155i | \(0.764077\pi\) | |||||||
\(972\) | 45.2064 | 1.45000 | ||||||||
\(973\) | 21.3615 | 0.684819 | ||||||||
\(974\) | −86.0572 | −2.75745 | ||||||||
\(975\) | −1.45053 | −0.0464543 | ||||||||
\(976\) | 5.26005 | 0.168370 | ||||||||
\(977\) | 1.69184 | 0.0541268 | 0.0270634 | − | 0.999634i | \(-0.491384\pi\) | ||||
0.0270634 | + | 0.999634i | \(0.491384\pi\) | |||||||
\(978\) | 24.4843 | 0.782921 | ||||||||
\(979\) | −13.0228 | −0.416209 | ||||||||
\(980\) | 38.5991 | 1.23300 | ||||||||
\(981\) | −2.28648 | −0.0730018 | ||||||||
\(982\) | −23.4868 | −0.749493 | ||||||||
\(983\) | −0.176270 | −0.00562214 | −0.00281107 | − | 0.999996i | \(-0.500895\pi\) | ||||
−0.00281107 | + | 0.999996i | \(0.500895\pi\) | |||||||
\(984\) | 0.161365 | 0.00514414 | ||||||||
\(985\) | −45.9381 | −1.46371 | ||||||||
\(986\) | −71.1414 | −2.26560 | ||||||||
\(987\) | 14.0289 | 0.446544 | ||||||||
\(988\) | 17.2932 | 0.550170 | ||||||||
\(989\) | −10.1455 | −0.322609 | ||||||||
\(990\) | −15.8300 | −0.503111 | ||||||||
\(991\) | 24.4492 | 0.776655 | 0.388327 | − | 0.921522i | \(-0.373053\pi\) | ||||
0.388327 | + | 0.921522i | \(0.373053\pi\) | |||||||
\(992\) | −25.1712 | −0.799188 | ||||||||
\(993\) | −0.247768 | −0.00786266 | ||||||||
\(994\) | 34.3097 | 1.08824 | ||||||||
\(995\) | 46.0168 | 1.45883 | ||||||||
\(996\) | 3.81563 | 0.120903 | ||||||||
\(997\) | 44.2260 | 1.40065 | 0.700325 | − | 0.713824i | \(-0.253038\pi\) | ||||
0.700325 | + | 0.713824i | \(0.253038\pi\) | |||||||
\(998\) | −31.4173 | −0.994497 | ||||||||
\(999\) | 42.5786 | 1.34713 |
(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 | 6019.2.a.d.1.16 | ✓ | 123 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6019.2.a.d.1.16 | ✓ | 123 | 1.1 | even | 1 | trivial |