Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2077082653\) |
Analytic rank: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.64446 | −1.16281 | −0.581406 | − | 0.813614i | \(-0.697497\pi\) | ||||
−0.581406 | + | 0.813614i | \(0.697497\pi\) | |||||||
\(3\) | −1.94286 | −1.12171 | −0.560855 | − | 0.827914i | \(-0.689527\pi\) | ||||
−0.560855 | + | 0.827914i | \(0.689527\pi\) | |||||||
\(4\) | 0.704260 | 0.352130 | ||||||||
\(5\) | −2.95674 | −1.32229 | −0.661147 | − | 0.750257i | \(-0.729930\pi\) | ||||
−0.661147 | + | 0.750257i | \(0.729930\pi\) | |||||||
\(6\) | 3.19496 | 1.30434 | ||||||||
\(7\) | 4.77511 | 1.80482 | 0.902411 | − | 0.430876i | \(-0.141795\pi\) | ||||
0.902411 | + | 0.430876i | \(0.141795\pi\) | |||||||
\(8\) | 2.13080 | 0.753351 | ||||||||
\(9\) | 0.774694 | 0.258231 | ||||||||
\(10\) | 4.86225 | 1.53758 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.36828 | −0.394987 | ||||||||
\(13\) | −2.28957 | −0.635013 | −0.317507 | − | 0.948256i | \(-0.602846\pi\) | ||||
−0.317507 | + | 0.948256i | \(0.602846\pi\) | |||||||
\(14\) | −7.85249 | −2.09867 | ||||||||
\(15\) | 5.74452 | 1.48323 | ||||||||
\(16\) | −4.91254 | −1.22813 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −1.27396 | −0.300274 | ||||||||
\(19\) | −5.82001 | −1.33520 | −0.667601 | − | 0.744519i | \(-0.732679\pi\) | ||||
−0.667601 | + | 0.744519i | \(0.732679\pi\) | |||||||
\(20\) | −2.08231 | −0.465619 | ||||||||
\(21\) | −9.27736 | −2.02449 | ||||||||
\(22\) | −1.64446 | −0.350601 | ||||||||
\(23\) | −3.60225 | −0.751121 | −0.375560 | − | 0.926798i | \(-0.622550\pi\) | ||||
−0.375560 | + | 0.926798i | \(0.622550\pi\) | |||||||
\(24\) | −4.13983 | −0.845040 | ||||||||
\(25\) | 3.74230 | 0.748460 | ||||||||
\(26\) | 3.76512 | 0.738400 | ||||||||
\(27\) | 4.32345 | 0.832049 | ||||||||
\(28\) | 3.36292 | 0.635532 | ||||||||
\(29\) | −5.58285 | −1.03671 | −0.518354 | − | 0.855166i | \(-0.673455\pi\) | ||||
−0.518354 | + | 0.855166i | \(0.673455\pi\) | |||||||
\(30\) | −9.44665 | −1.72472 | ||||||||
\(31\) | −8.37229 | −1.50371 | −0.751854 | − | 0.659329i | \(-0.770840\pi\) | ||||
−0.751854 | + | 0.659329i | \(0.770840\pi\) | |||||||
\(32\) | 3.81689 | 0.674738 | ||||||||
\(33\) | −1.94286 | −0.338208 | ||||||||
\(34\) | −1.64446 | −0.282023 | ||||||||
\(35\) | −14.1188 | −2.38650 | ||||||||
\(36\) | 0.545586 | 0.0909310 | ||||||||
\(37\) | −7.78932 | −1.28056 | −0.640278 | − | 0.768143i | \(-0.721181\pi\) | ||||
−0.640278 | + | 0.768143i | \(0.721181\pi\) | |||||||
\(38\) | 9.57079 | 1.55259 | ||||||||
\(39\) | 4.44831 | 0.712300 | ||||||||
\(40\) | −6.30021 | −0.996151 | ||||||||
\(41\) | −9.62588 | −1.50331 | −0.751655 | − | 0.659557i | \(-0.770744\pi\) | ||||
−0.751655 | + | 0.659557i | \(0.770744\pi\) | |||||||
\(42\) | 15.2563 | 2.35409 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 0.704260 | 0.106171 | ||||||||
\(45\) | −2.29057 | −0.341458 | ||||||||
\(46\) | 5.92376 | 0.873411 | ||||||||
\(47\) | 6.14277 | 0.896015 | 0.448007 | − | 0.894030i | \(-0.352134\pi\) | ||||
0.448007 | + | 0.894030i | \(0.352134\pi\) | |||||||
\(48\) | 9.54436 | 1.37761 | ||||||||
\(49\) | 15.8017 | 2.25738 | ||||||||
\(50\) | −6.15408 | −0.870318 | ||||||||
\(51\) | −1.94286 | −0.272054 | ||||||||
\(52\) | −1.61245 | −0.223607 | ||||||||
\(53\) | 9.24846 | 1.27037 | 0.635187 | − | 0.772358i | \(-0.280923\pi\) | ||||
0.635187 | + | 0.772358i | \(0.280923\pi\) | |||||||
\(54\) | −7.10976 | −0.967516 | ||||||||
\(55\) | −2.95674 | −0.398687 | ||||||||
\(56\) | 10.1748 | 1.35966 | ||||||||
\(57\) | 11.3074 | 1.49771 | ||||||||
\(58\) | 9.18079 | 1.20550 | ||||||||
\(59\) | 9.16404 | 1.19306 | 0.596528 | − | 0.802592i | \(-0.296546\pi\) | ||||
0.596528 | + | 0.802592i | \(0.296546\pi\) | |||||||
\(60\) | 4.04564 | 0.522289 | ||||||||
\(61\) | −2.77872 | −0.355779 | −0.177889 | − | 0.984050i | \(-0.556927\pi\) | ||||
−0.177889 | + | 0.984050i | \(0.556927\pi\) | |||||||
\(62\) | 13.7679 | 1.74853 | ||||||||
\(63\) | 3.69925 | 0.466062 | ||||||||
\(64\) | 3.54833 | 0.443541 | ||||||||
\(65\) | 6.76967 | 0.839674 | ||||||||
\(66\) | 3.19496 | 0.393272 | ||||||||
\(67\) | 6.69264 | 0.817637 | 0.408818 | − | 0.912616i | \(-0.365941\pi\) | ||||
0.408818 | + | 0.912616i | \(0.365941\pi\) | |||||||
\(68\) | 0.704260 | 0.0854041 | ||||||||
\(69\) | 6.99865 | 0.842539 | ||||||||
\(70\) | 23.2178 | 2.77505 | ||||||||
\(71\) | −5.95574 | −0.706816 | −0.353408 | − | 0.935469i | \(-0.614977\pi\) | ||||
−0.353408 | + | 0.935469i | \(0.614977\pi\) | |||||||
\(72\) | 1.65072 | 0.194539 | ||||||||
\(73\) | 2.32040 | 0.271582 | 0.135791 | − | 0.990738i | \(-0.456642\pi\) | ||||
0.135791 | + | 0.990738i | \(0.456642\pi\) | |||||||
\(74\) | 12.8093 | 1.48905 | ||||||||
\(75\) | −7.27076 | −0.839555 | ||||||||
\(76\) | −4.09880 | −0.470165 | ||||||||
\(77\) | 4.77511 | 0.544174 | ||||||||
\(78\) | −7.31509 | −0.828270 | ||||||||
\(79\) | −4.03573 | −0.454055 | −0.227028 | − | 0.973888i | \(-0.572901\pi\) | ||||
−0.227028 | + | 0.973888i | \(0.572901\pi\) | |||||||
\(80\) | 14.5251 | 1.62395 | ||||||||
\(81\) | −10.7239 | −1.19155 | ||||||||
\(82\) | 15.8294 | 1.74807 | ||||||||
\(83\) | −3.03874 | −0.333545 | −0.166772 | − | 0.985995i | \(-0.553335\pi\) | ||||
−0.166772 | + | 0.985995i | \(0.553335\pi\) | |||||||
\(84\) | −6.53367 | −0.712882 | ||||||||
\(85\) | −2.95674 | −0.320703 | ||||||||
\(86\) | −1.64446 | −0.177327 | ||||||||
\(87\) | 10.8467 | 1.16289 | ||||||||
\(88\) | 2.13080 | 0.227144 | ||||||||
\(89\) | −3.24843 | −0.344333 | −0.172166 | − | 0.985068i | \(-0.555077\pi\) | ||||
−0.172166 | + | 0.985068i | \(0.555077\pi\) | |||||||
\(90\) | 3.76675 | 0.397051 | ||||||||
\(91\) | −10.9330 | −1.14609 | ||||||||
\(92\) | −2.53692 | −0.264492 | ||||||||
\(93\) | 16.2662 | 1.68672 | ||||||||
\(94\) | −10.1016 | −1.04190 | ||||||||
\(95\) | 17.2082 | 1.76553 | ||||||||
\(96\) | −7.41568 | −0.756860 | ||||||||
\(97\) | −12.4311 | −1.26219 | −0.631096 | − | 0.775705i | \(-0.717394\pi\) | ||||
−0.631096 | + | 0.775705i | \(0.717394\pi\) | |||||||
\(98\) | −25.9853 | −2.62491 | ||||||||
\(99\) | 0.774694 | 0.0778597 | ||||||||
\(100\) | 2.63555 | 0.263555 | ||||||||
\(101\) | −7.23369 | −0.719779 | −0.359889 | − | 0.932995i | \(-0.617186\pi\) | ||||
−0.359889 | + | 0.932995i | \(0.617186\pi\) | |||||||
\(102\) | 3.19496 | 0.316348 | ||||||||
\(103\) | −7.89260 | −0.777681 | −0.388840 | − | 0.921305i | \(-0.627124\pi\) | ||||
−0.388840 | + | 0.921305i | \(0.627124\pi\) | |||||||
\(104\) | −4.87861 | −0.478387 | ||||||||
\(105\) | 27.4307 | 2.67696 | ||||||||
\(106\) | −15.2088 | −1.47720 | ||||||||
\(107\) | −18.1335 | −1.75303 | −0.876517 | − | 0.481370i | \(-0.840139\pi\) | ||||
−0.876517 | + | 0.481370i | \(0.840139\pi\) | |||||||
\(108\) | 3.04483 | 0.292989 | ||||||||
\(109\) | −17.5717 | −1.68306 | −0.841530 | − | 0.540210i | \(-0.818345\pi\) | ||||
−0.841530 | + | 0.540210i | \(0.818345\pi\) | |||||||
\(110\) | 4.86225 | 0.463597 | ||||||||
\(111\) | 15.1335 | 1.43641 | ||||||||
\(112\) | −23.4579 | −2.21656 | ||||||||
\(113\) | 17.4238 | 1.63909 | 0.819545 | − | 0.573015i | \(-0.194226\pi\) | ||||
0.819545 | + | 0.573015i | \(0.194226\pi\) | |||||||
\(114\) | −18.5947 | −1.74155 | ||||||||
\(115\) | 10.6509 | 0.993202 | ||||||||
\(116\) | −3.93178 | −0.365056 | ||||||||
\(117\) | −1.77372 | −0.163980 | ||||||||
\(118\) | −15.0699 | −1.38730 | ||||||||
\(119\) | 4.77511 | 0.437734 | ||||||||
\(120\) | 12.2404 | 1.11739 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 4.56951 | 0.413704 | ||||||||
\(123\) | 18.7017 | 1.68628 | ||||||||
\(124\) | −5.89627 | −0.529501 | ||||||||
\(125\) | 3.71869 | 0.332609 | ||||||||
\(126\) | −6.08328 | −0.541942 | ||||||||
\(127\) | 11.3492 | 1.00708 | 0.503540 | − | 0.863972i | \(-0.332031\pi\) | ||||
0.503540 | + | 0.863972i | \(0.332031\pi\) | |||||||
\(128\) | −13.4689 | −1.19049 | ||||||||
\(129\) | −1.94286 | −0.171059 | ||||||||
\(130\) | −11.1325 | −0.976382 | ||||||||
\(131\) | −8.95903 | −0.782754 | −0.391377 | − | 0.920230i | \(-0.628001\pi\) | ||||
−0.391377 | + | 0.920230i | \(0.628001\pi\) | |||||||
\(132\) | −1.36828 | −0.119093 | ||||||||
\(133\) | −27.7912 | −2.40980 | ||||||||
\(134\) | −11.0058 | −0.950757 | ||||||||
\(135\) | −12.7833 | −1.10021 | ||||||||
\(136\) | 2.13080 | 0.182714 | ||||||||
\(137\) | 10.6613 | 0.910854 | 0.455427 | − | 0.890273i | \(-0.349487\pi\) | ||||
0.455427 | + | 0.890273i | \(0.349487\pi\) | |||||||
\(138\) | −11.5090 | −0.979714 | ||||||||
\(139\) | −0.136853 | −0.0116077 | −0.00580387 | − | 0.999983i | \(-0.501847\pi\) | ||||
−0.00580387 | + | 0.999983i | \(0.501847\pi\) | |||||||
\(140\) | −9.94327 | −0.840360 | ||||||||
\(141\) | −11.9345 | −1.00507 | ||||||||
\(142\) | 9.79400 | 0.821894 | ||||||||
\(143\) | −2.28957 | −0.191464 | ||||||||
\(144\) | −3.80571 | −0.317143 | ||||||||
\(145\) | 16.5070 | 1.37083 | ||||||||
\(146\) | −3.81581 | −0.315798 | ||||||||
\(147\) | −30.7004 | −2.53213 | ||||||||
\(148\) | −5.48571 | −0.450923 | ||||||||
\(149\) | −8.76063 | −0.717699 | −0.358849 | − | 0.933395i | \(-0.616831\pi\) | ||||
−0.358849 | + | 0.933395i | \(0.616831\pi\) | |||||||
\(150\) | 11.9565 | 0.976244 | ||||||||
\(151\) | −12.3579 | −1.00567 | −0.502834 | − | 0.864383i | \(-0.667709\pi\) | ||||
−0.502834 | + | 0.864383i | \(0.667709\pi\) | |||||||
\(152\) | −12.4013 | −1.00588 | ||||||||
\(153\) | 0.774694 | 0.0626303 | ||||||||
\(154\) | −7.85249 | −0.632772 | ||||||||
\(155\) | 24.7547 | 1.98834 | ||||||||
\(156\) | 3.13277 | 0.250822 | ||||||||
\(157\) | 4.56302 | 0.364168 | 0.182084 | − | 0.983283i | \(-0.441716\pi\) | ||||
0.182084 | + | 0.983283i | \(0.441716\pi\) | |||||||
\(158\) | 6.63661 | 0.527981 | ||||||||
\(159\) | −17.9684 | −1.42499 | ||||||||
\(160\) | −11.2856 | −0.892202 | ||||||||
\(161\) | −17.2011 | −1.35564 | ||||||||
\(162\) | 17.6351 | 1.38555 | ||||||||
\(163\) | −16.9655 | −1.32884 | −0.664421 | − | 0.747358i | \(-0.731322\pi\) | ||||
−0.664421 | + | 0.747358i | \(0.731322\pi\) | |||||||
\(164\) | −6.77912 | −0.529360 | ||||||||
\(165\) | 5.74452 | 0.447210 | ||||||||
\(166\) | 4.99709 | 0.387850 | ||||||||
\(167\) | 22.7932 | 1.76379 | 0.881894 | − | 0.471447i | \(-0.156268\pi\) | ||||
0.881894 | + | 0.471447i | \(0.156268\pi\) | |||||||
\(168\) | −19.7682 | −1.52515 | ||||||||
\(169\) | −7.75786 | −0.596758 | ||||||||
\(170\) | 4.86225 | 0.372917 | ||||||||
\(171\) | −4.50873 | −0.344791 | ||||||||
\(172\) | 0.704260 | 0.0536993 | ||||||||
\(173\) | −8.59668 | −0.653593 | −0.326797 | − | 0.945095i | \(-0.605969\pi\) | ||||
−0.326797 | + | 0.945095i | \(0.605969\pi\) | |||||||
\(174\) | −17.8370 | −1.35222 | ||||||||
\(175\) | 17.8699 | 1.35084 | ||||||||
\(176\) | −4.91254 | −0.370296 | ||||||||
\(177\) | −17.8044 | −1.33826 | ||||||||
\(178\) | 5.34192 | 0.400394 | ||||||||
\(179\) | −16.0783 | −1.20175 | −0.600873 | − | 0.799345i | \(-0.705180\pi\) | ||||
−0.600873 | + | 0.799345i | \(0.705180\pi\) | |||||||
\(180\) | −1.61315 | −0.120237 | ||||||||
\(181\) | 4.42219 | 0.328699 | 0.164349 | − | 0.986402i | \(-0.447448\pi\) | ||||
0.164349 | + | 0.986402i | \(0.447448\pi\) | |||||||
\(182\) | 17.9789 | 1.33268 | ||||||||
\(183\) | 5.39866 | 0.399080 | ||||||||
\(184\) | −7.67566 | −0.565857 | ||||||||
\(185\) | 23.0310 | 1.69327 | ||||||||
\(186\) | −26.7491 | −1.96134 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | 4.32611 | 0.315514 | ||||||||
\(189\) | 20.6450 | 1.50170 | ||||||||
\(190\) | −28.2983 | −2.05298 | ||||||||
\(191\) | 1.86036 | 0.134611 | 0.0673054 | − | 0.997732i | \(-0.478560\pi\) | ||||
0.0673054 | + | 0.997732i | \(0.478560\pi\) | |||||||
\(192\) | −6.89390 | −0.497524 | ||||||||
\(193\) | 8.14579 | 0.586347 | 0.293173 | − | 0.956059i | \(-0.405289\pi\) | ||||
0.293173 | + | 0.956059i | \(0.405289\pi\) | |||||||
\(194\) | 20.4426 | 1.46769 | ||||||||
\(195\) | −13.1525 | −0.941870 | ||||||||
\(196\) | 11.1285 | 0.794892 | ||||||||
\(197\) | −4.01311 | −0.285922 | −0.142961 | − | 0.989728i | \(-0.545662\pi\) | ||||
−0.142961 | + | 0.989728i | \(0.545662\pi\) | |||||||
\(198\) | −1.27396 | −0.0905361 | ||||||||
\(199\) | 24.6152 | 1.74493 | 0.872463 | − | 0.488680i | \(-0.162521\pi\) | ||||
0.872463 | + | 0.488680i | \(0.162521\pi\) | |||||||
\(200\) | 7.97408 | 0.563853 | ||||||||
\(201\) | −13.0029 | −0.917150 | ||||||||
\(202\) | 11.8955 | 0.836967 | ||||||||
\(203\) | −26.6587 | −1.87107 | ||||||||
\(204\) | −1.36828 | −0.0957985 | ||||||||
\(205\) | 28.4612 | 1.98782 | ||||||||
\(206\) | 12.9791 | 0.904296 | ||||||||
\(207\) | −2.79064 | −0.193963 | ||||||||
\(208\) | 11.2476 | 0.779881 | ||||||||
\(209\) | −5.82001 | −0.402579 | ||||||||
\(210\) | −45.1088 | −3.11280 | ||||||||
\(211\) | −8.14028 | −0.560400 | −0.280200 | − | 0.959942i | \(-0.590401\pi\) | ||||
−0.280200 | + | 0.959942i | \(0.590401\pi\) | |||||||
\(212\) | 6.51332 | 0.447337 | ||||||||
\(213\) | 11.5712 | 0.792842 | ||||||||
\(214\) | 29.8199 | 2.03845 | ||||||||
\(215\) | −2.95674 | −0.201648 | ||||||||
\(216\) | 9.21240 | 0.626824 | ||||||||
\(217\) | −39.9786 | −2.71393 | ||||||||
\(218\) | 28.8960 | 1.95708 | ||||||||
\(219\) | −4.50820 | −0.304636 | ||||||||
\(220\) | −2.08231 | −0.140389 | ||||||||
\(221\) | −2.28957 | −0.154013 | ||||||||
\(222\) | −24.8866 | −1.67028 | ||||||||
\(223\) | 2.66724 | 0.178611 | 0.0893056 | − | 0.996004i | \(-0.471535\pi\) | ||||
0.0893056 | + | 0.996004i | \(0.471535\pi\) | |||||||
\(224\) | 18.2261 | 1.21778 | ||||||||
\(225\) | 2.89914 | 0.193276 | ||||||||
\(226\) | −28.6527 | −1.90595 | ||||||||
\(227\) | 29.3656 | 1.94906 | 0.974532 | − | 0.224250i | \(-0.0719932\pi\) | ||||
0.974532 | + | 0.224250i | \(0.0719932\pi\) | |||||||
\(228\) | 7.96338 | 0.527388 | ||||||||
\(229\) | 4.07694 | 0.269412 | 0.134706 | − | 0.990886i | \(-0.456991\pi\) | ||||
0.134706 | + | 0.990886i | \(0.456991\pi\) | |||||||
\(230\) | −17.5150 | −1.15491 | ||||||||
\(231\) | −9.27736 | −0.610405 | ||||||||
\(232\) | −11.8959 | −0.781005 | ||||||||
\(233\) | 27.1664 | 1.77973 | 0.889866 | − | 0.456223i | \(-0.150798\pi\) | ||||
0.889866 | + | 0.456223i | \(0.150798\pi\) | |||||||
\(234\) | 2.91681 | 0.190678 | ||||||||
\(235\) | −18.1626 | −1.18479 | ||||||||
\(236\) | 6.45387 | 0.420111 | ||||||||
\(237\) | 7.84085 | 0.509318 | ||||||||
\(238\) | −7.85249 | −0.509002 | ||||||||
\(239\) | −16.3415 | −1.05704 | −0.528520 | − | 0.848921i | \(-0.677253\pi\) | ||||
−0.528520 | + | 0.848921i | \(0.677253\pi\) | |||||||
\(240\) | −28.2202 | −1.82160 | ||||||||
\(241\) | −15.1841 | −0.978093 | −0.489047 | − | 0.872258i | \(-0.662655\pi\) | ||||
−0.489047 | + | 0.872258i | \(0.662655\pi\) | |||||||
\(242\) | −1.64446 | −0.105710 | ||||||||
\(243\) | 7.86471 | 0.504521 | ||||||||
\(244\) | −1.95694 | −0.125280 | ||||||||
\(245\) | −46.7214 | −2.98492 | ||||||||
\(246\) | −30.7543 | −1.96082 | ||||||||
\(247\) | 13.3253 | 0.847871 | ||||||||
\(248\) | −17.8397 | −1.13282 | ||||||||
\(249\) | 5.90383 | 0.374140 | ||||||||
\(250\) | −6.11524 | −0.386762 | ||||||||
\(251\) | −6.33278 | −0.399721 | −0.199861 | − | 0.979824i | \(-0.564049\pi\) | ||||
−0.199861 | + | 0.979824i | \(0.564049\pi\) | |||||||
\(252\) | 2.60523 | 0.164114 | ||||||||
\(253\) | −3.60225 | −0.226471 | ||||||||
\(254\) | −18.6634 | −1.17104 | ||||||||
\(255\) | 5.74452 | 0.359736 | ||||||||
\(256\) | 15.0524 | 0.940777 | ||||||||
\(257\) | 25.2212 | 1.57326 | 0.786629 | − | 0.617426i | \(-0.211825\pi\) | ||||
0.786629 | + | 0.617426i | \(0.211825\pi\) | |||||||
\(258\) | 3.19496 | 0.198909 | ||||||||
\(259\) | −37.1949 | −2.31118 | ||||||||
\(260\) | 4.76761 | 0.295674 | ||||||||
\(261\) | −4.32500 | −0.267711 | ||||||||
\(262\) | 14.7328 | 0.910195 | ||||||||
\(263\) | −3.92188 | −0.241833 | −0.120917 | − | 0.992663i | \(-0.538583\pi\) | ||||
−0.120917 | + | 0.992663i | \(0.538583\pi\) | |||||||
\(264\) | −4.13983 | −0.254789 | ||||||||
\(265\) | −27.3453 | −1.67981 | ||||||||
\(266\) | 45.7016 | 2.80214 | ||||||||
\(267\) | 6.31123 | 0.386241 | ||||||||
\(268\) | 4.71336 | 0.287914 | ||||||||
\(269\) | 21.8430 | 1.33179 | 0.665895 | − | 0.746046i | \(-0.268050\pi\) | ||||
0.665895 | + | 0.746046i | \(0.268050\pi\) | |||||||
\(270\) | 21.0217 | 1.27934 | ||||||||
\(271\) | −10.5045 | −0.638105 | −0.319052 | − | 0.947737i | \(-0.603365\pi\) | ||||
−0.319052 | + | 0.947737i | \(0.603365\pi\) | |||||||
\(272\) | −4.91254 | −0.297866 | ||||||||
\(273\) | 21.2412 | 1.28557 | ||||||||
\(274\) | −17.5321 | −1.05915 | ||||||||
\(275\) | 3.74230 | 0.225669 | ||||||||
\(276\) | 4.92887 | 0.296683 | ||||||||
\(277\) | −27.5546 | −1.65560 | −0.827799 | − | 0.561025i | \(-0.810407\pi\) | ||||
−0.827799 | + | 0.561025i | \(0.810407\pi\) | |||||||
\(278\) | 0.225050 | 0.0134976 | ||||||||
\(279\) | −6.48597 | −0.388305 | ||||||||
\(280\) | −30.0842 | −1.79787 | ||||||||
\(281\) | 3.63868 | 0.217066 | 0.108533 | − | 0.994093i | \(-0.465385\pi\) | ||||
0.108533 | + | 0.994093i | \(0.465385\pi\) | |||||||
\(282\) | 19.6259 | 1.16870 | ||||||||
\(283\) | 2.45733 | 0.146073 | 0.0730364 | − | 0.997329i | \(-0.476731\pi\) | ||||
0.0730364 | + | 0.997329i | \(0.476731\pi\) | |||||||
\(284\) | −4.19439 | −0.248891 | ||||||||
\(285\) | −33.4332 | −1.98041 | ||||||||
\(286\) | 3.76512 | 0.222636 | ||||||||
\(287\) | −45.9646 | −2.71321 | ||||||||
\(288\) | 2.95693 | 0.174238 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −27.1452 | −1.59402 | ||||||||
\(291\) | 24.1519 | 1.41581 | ||||||||
\(292\) | 1.63416 | 0.0956321 | ||||||||
\(293\) | −5.87484 | −0.343212 | −0.171606 | − | 0.985166i | \(-0.554896\pi\) | ||||
−0.171606 | + | 0.985166i | \(0.554896\pi\) | |||||||
\(294\) | 50.4857 | 2.94439 | ||||||||
\(295\) | −27.0957 | −1.57757 | ||||||||
\(296\) | −16.5975 | −0.964708 | ||||||||
\(297\) | 4.32345 | 0.250872 | ||||||||
\(298\) | 14.4065 | 0.834548 | ||||||||
\(299\) | 8.24761 | 0.476971 | ||||||||
\(300\) | −5.12050 | −0.295632 | ||||||||
\(301\) | 4.77511 | 0.275233 | ||||||||
\(302\) | 20.3220 | 1.16940 | ||||||||
\(303\) | 14.0540 | 0.807382 | ||||||||
\(304\) | 28.5910 | 1.63981 | ||||||||
\(305\) | 8.21595 | 0.470444 | ||||||||
\(306\) | −1.27396 | −0.0728272 | ||||||||
\(307\) | −15.4638 | −0.882567 | −0.441284 | − | 0.897368i | \(-0.645477\pi\) | ||||
−0.441284 | + | 0.897368i | \(0.645477\pi\) | |||||||
\(308\) | 3.36292 | 0.191620 | ||||||||
\(309\) | 15.3342 | 0.872331 | ||||||||
\(310\) | −40.7082 | −2.31207 | ||||||||
\(311\) | −29.4004 | −1.66714 | −0.833571 | − | 0.552412i | \(-0.813707\pi\) | ||||
−0.833571 | + | 0.552412i | \(0.813707\pi\) | |||||||
\(312\) | 9.47845 | 0.536612 | ||||||||
\(313\) | −21.9524 | −1.24082 | −0.620411 | − | 0.784277i | \(-0.713034\pi\) | ||||
−0.620411 | + | 0.784277i | \(0.713034\pi\) | |||||||
\(314\) | −7.50371 | −0.423459 | ||||||||
\(315\) | −10.9377 | −0.616270 | ||||||||
\(316\) | −2.84220 | −0.159887 | ||||||||
\(317\) | −3.21794 | −0.180737 | −0.0903687 | − | 0.995908i | \(-0.528805\pi\) | ||||
−0.0903687 | + | 0.995908i | \(0.528805\pi\) | |||||||
\(318\) | 29.5484 | 1.65699 | ||||||||
\(319\) | −5.58285 | −0.312579 | ||||||||
\(320\) | −10.4915 | −0.586492 | ||||||||
\(321\) | 35.2309 | 1.96640 | ||||||||
\(322\) | 28.2866 | 1.57635 | ||||||||
\(323\) | −5.82001 | −0.323834 | ||||||||
\(324\) | −7.55244 | −0.419580 | ||||||||
\(325\) | −8.56827 | −0.475282 | ||||||||
\(326\) | 27.8992 | 1.54519 | ||||||||
\(327\) | 34.1392 | 1.88790 | ||||||||
\(328\) | −20.5108 | −1.13252 | ||||||||
\(329\) | 29.3324 | 1.61715 | ||||||||
\(330\) | −9.44665 | −0.520021 | ||||||||
\(331\) | −16.6539 | −0.915380 | −0.457690 | − | 0.889112i | \(-0.651323\pi\) | ||||
−0.457690 | + | 0.889112i | \(0.651323\pi\) | |||||||
\(332\) | −2.14006 | −0.117451 | ||||||||
\(333\) | −6.03434 | −0.330680 | ||||||||
\(334\) | −37.4825 | −2.05095 | ||||||||
\(335\) | −19.7884 | −1.08116 | ||||||||
\(336\) | 45.5754 | 2.48634 | ||||||||
\(337\) | 32.3995 | 1.76492 | 0.882458 | − | 0.470391i | \(-0.155887\pi\) | ||||
0.882458 | + | 0.470391i | \(0.155887\pi\) | |||||||
\(338\) | 12.7575 | 0.693917 | ||||||||
\(339\) | −33.8519 | −1.83858 | ||||||||
\(340\) | −2.08231 | −0.112929 | ||||||||
\(341\) | −8.37229 | −0.453385 | ||||||||
\(342\) | 7.41444 | 0.400927 | ||||||||
\(343\) | 42.0290 | 2.26935 | ||||||||
\(344\) | 2.13080 | 0.114885 | ||||||||
\(345\) | −20.6932 | −1.11408 | ||||||||
\(346\) | 14.1369 | 0.760006 | ||||||||
\(347\) | −1.74904 | −0.0938931 | −0.0469466 | − | 0.998897i | \(-0.514949\pi\) | ||||
−0.0469466 | + | 0.998897i | \(0.514949\pi\) | |||||||
\(348\) | 7.63888 | 0.409487 | ||||||||
\(349\) | −16.8556 | −0.902261 | −0.451131 | − | 0.892458i | \(-0.648979\pi\) | ||||
−0.451131 | + | 0.892458i | \(0.648979\pi\) | |||||||
\(350\) | −29.3864 | −1.57077 | ||||||||
\(351\) | −9.89886 | −0.528362 | ||||||||
\(352\) | 3.81689 | 0.203441 | ||||||||
\(353\) | −9.68542 | −0.515503 | −0.257751 | − | 0.966211i | \(-0.582982\pi\) | ||||
−0.257751 | + | 0.966211i | \(0.582982\pi\) | |||||||
\(354\) | 29.2787 | 1.55615 | ||||||||
\(355\) | 17.6096 | 0.934619 | ||||||||
\(356\) | −2.28774 | −0.121250 | ||||||||
\(357\) | −9.27736 | −0.491010 | ||||||||
\(358\) | 26.4401 | 1.39740 | ||||||||
\(359\) | 25.5976 | 1.35099 | 0.675494 | − | 0.737365i | \(-0.263930\pi\) | ||||
0.675494 | + | 0.737365i | \(0.263930\pi\) | |||||||
\(360\) | −4.88073 | −0.257237 | ||||||||
\(361\) | 14.8725 | 0.782764 | ||||||||
\(362\) | −7.27213 | −0.382215 | ||||||||
\(363\) | −1.94286 | −0.101974 | ||||||||
\(364\) | −7.69965 | −0.403571 | ||||||||
\(365\) | −6.86080 | −0.359111 | ||||||||
\(366\) | −8.87790 | −0.464055 | ||||||||
\(367\) | −9.80014 | −0.511563 | −0.255782 | − | 0.966735i | \(-0.582333\pi\) | ||||
−0.255782 | + | 0.966735i | \(0.582333\pi\) | |||||||
\(368\) | 17.6962 | 0.922477 | ||||||||
\(369\) | −7.45711 | −0.388202 | ||||||||
\(370\) | −37.8736 | −1.96896 | ||||||||
\(371\) | 44.1624 | 2.29280 | ||||||||
\(372\) | 11.4556 | 0.593946 | ||||||||
\(373\) | 21.5707 | 1.11689 | 0.558443 | − | 0.829543i | \(-0.311399\pi\) | ||||
0.558443 | + | 0.829543i | \(0.311399\pi\) | |||||||
\(374\) | −1.64446 | −0.0850332 | ||||||||
\(375\) | −7.22488 | −0.373091 | ||||||||
\(376\) | 13.0890 | 0.675013 | ||||||||
\(377\) | 12.7823 | 0.658324 | ||||||||
\(378\) | −33.9499 | −1.74619 | ||||||||
\(379\) | −23.1734 | −1.19034 | −0.595168 | − | 0.803601i | \(-0.702915\pi\) | ||||
−0.595168 | + | 0.803601i | \(0.702915\pi\) | |||||||
\(380\) | 12.1191 | 0.621696 | ||||||||
\(381\) | −22.0499 | −1.12965 | ||||||||
\(382\) | −3.05929 | −0.156527 | ||||||||
\(383\) | 34.5842 | 1.76717 | 0.883586 | − | 0.468269i | \(-0.155122\pi\) | ||||
0.883586 | + | 0.468269i | \(0.155122\pi\) | |||||||
\(384\) | 26.1681 | 1.33539 | ||||||||
\(385\) | −14.1188 | −0.719558 | ||||||||
\(386\) | −13.3955 | −0.681811 | ||||||||
\(387\) | 0.774694 | 0.0393799 | ||||||||
\(388\) | −8.75476 | −0.444455 | ||||||||
\(389\) | −33.6067 | −1.70393 | −0.851963 | − | 0.523601i | \(-0.824588\pi\) | ||||
−0.851963 | + | 0.523601i | \(0.824588\pi\) | |||||||
\(390\) | 21.6288 | 1.09522 | ||||||||
\(391\) | −3.60225 | −0.182173 | ||||||||
\(392\) | 33.6702 | 1.70060 | ||||||||
\(393\) | 17.4061 | 0.878022 | ||||||||
\(394\) | 6.59941 | 0.332473 | ||||||||
\(395\) | 11.9326 | 0.600394 | ||||||||
\(396\) | 0.545586 | 0.0274167 | ||||||||
\(397\) | −9.00556 | −0.451976 | −0.225988 | − | 0.974130i | \(-0.572561\pi\) | ||||
−0.225988 | + | 0.974130i | \(0.572561\pi\) | |||||||
\(398\) | −40.4788 | −2.02902 | ||||||||
\(399\) | 53.9943 | 2.70310 | ||||||||
\(400\) | −18.3842 | −0.919210 | ||||||||
\(401\) | 8.56851 | 0.427891 | 0.213945 | − | 0.976846i | \(-0.431369\pi\) | ||||
0.213945 | + | 0.976846i | \(0.431369\pi\) | |||||||
\(402\) | 21.3827 | 1.06647 | ||||||||
\(403\) | 19.1690 | 0.954875 | ||||||||
\(404\) | −5.09440 | −0.253456 | ||||||||
\(405\) | 31.7079 | 1.57558 | ||||||||
\(406\) | 43.8393 | 2.17571 | ||||||||
\(407\) | −7.78932 | −0.386102 | ||||||||
\(408\) | −4.13983 | −0.204952 | ||||||||
\(409\) | 10.1428 | 0.501530 | 0.250765 | − | 0.968048i | \(-0.419318\pi\) | ||||
0.250765 | + | 0.968048i | \(0.419318\pi\) | |||||||
\(410\) | −46.8034 | −2.31146 | ||||||||
\(411\) | −20.7133 | −1.02171 | ||||||||
\(412\) | −5.55844 | −0.273845 | ||||||||
\(413\) | 43.7593 | 2.15325 | ||||||||
\(414\) | 4.58910 | 0.225542 | ||||||||
\(415\) | 8.98475 | 0.441044 | ||||||||
\(416\) | −8.73906 | −0.428468 | ||||||||
\(417\) | 0.265886 | 0.0130205 | ||||||||
\(418\) | 9.57079 | 0.468123 | ||||||||
\(419\) | −20.5572 | −1.00428 | −0.502142 | − | 0.864785i | \(-0.667455\pi\) | ||||
−0.502142 | + | 0.864785i | \(0.667455\pi\) | |||||||
\(420\) | 19.3184 | 0.942639 | ||||||||
\(421\) | 35.6523 | 1.73759 | 0.868793 | − | 0.495175i | \(-0.164896\pi\) | ||||
0.868793 | + | 0.495175i | \(0.164896\pi\) | |||||||
\(422\) | 13.3864 | 0.651639 | ||||||||
\(423\) | 4.75876 | 0.231379 | ||||||||
\(424\) | 19.7066 | 0.957037 | ||||||||
\(425\) | 3.74230 | 0.181528 | ||||||||
\(426\) | −19.0283 | −0.921926 | ||||||||
\(427\) | −13.2687 | −0.642117 | ||||||||
\(428\) | −12.7707 | −0.617296 | ||||||||
\(429\) | 4.44831 | 0.214767 | ||||||||
\(430\) | 4.86225 | 0.234478 | ||||||||
\(431\) | 7.85944 | 0.378576 | 0.189288 | − | 0.981922i | \(-0.439382\pi\) | ||||
0.189288 | + | 0.981922i | \(0.439382\pi\) | |||||||
\(432\) | −21.2391 | −1.02187 | ||||||||
\(433\) | 22.3319 | 1.07320 | 0.536600 | − | 0.843837i | \(-0.319708\pi\) | ||||
0.536600 | + | 0.843837i | \(0.319708\pi\) | |||||||
\(434\) | 65.7434 | 3.15578 | ||||||||
\(435\) | −32.0708 | −1.53768 | ||||||||
\(436\) | −12.3750 | −0.592656 | ||||||||
\(437\) | 20.9651 | 1.00290 | ||||||||
\(438\) | 7.41357 | 0.354234 | ||||||||
\(439\) | −28.7777 | −1.37348 | −0.686742 | − | 0.726901i | \(-0.740960\pi\) | ||||
−0.686742 | + | 0.726901i | \(0.740960\pi\) | |||||||
\(440\) | −6.30021 | −0.300351 | ||||||||
\(441\) | 12.2415 | 0.582927 | ||||||||
\(442\) | 3.76512 | 0.179088 | ||||||||
\(443\) | 5.48444 | 0.260574 | 0.130287 | − | 0.991476i | \(-0.458410\pi\) | ||||
0.130287 | + | 0.991476i | \(0.458410\pi\) | |||||||
\(444\) | 10.6580 | 0.505804 | ||||||||
\(445\) | 9.60475 | 0.455309 | ||||||||
\(446\) | −4.38617 | −0.207691 | ||||||||
\(447\) | 17.0207 | 0.805049 | ||||||||
\(448\) | 16.9437 | 0.800513 | ||||||||
\(449\) | 9.92615 | 0.468444 | 0.234222 | − | 0.972183i | \(-0.424746\pi\) | ||||
0.234222 | + | 0.972183i | \(0.424746\pi\) | |||||||
\(450\) | −4.76753 | −0.224743 | ||||||||
\(451\) | −9.62588 | −0.453265 | ||||||||
\(452\) | 12.2709 | 0.577173 | ||||||||
\(453\) | 24.0096 | 1.12807 | ||||||||
\(454\) | −48.2907 | −2.26639 | ||||||||
\(455\) | 32.3259 | 1.51546 | ||||||||
\(456\) | 24.0939 | 1.12830 | ||||||||
\(457\) | −22.4088 | −1.04824 | −0.524121 | − | 0.851644i | \(-0.675606\pi\) | ||||
−0.524121 | + | 0.851644i | \(0.675606\pi\) | |||||||
\(458\) | −6.70438 | −0.313275 | ||||||||
\(459\) | 4.32345 | 0.201801 | ||||||||
\(460\) | 7.50101 | 0.349736 | ||||||||
\(461\) | −10.5041 | −0.489224 | −0.244612 | − | 0.969621i | \(-0.578661\pi\) | ||||
−0.244612 | + | 0.969621i | \(0.578661\pi\) | |||||||
\(462\) | 15.2563 | 0.709786 | ||||||||
\(463\) | 12.0208 | 0.558652 | 0.279326 | − | 0.960196i | \(-0.409889\pi\) | ||||
0.279326 | + | 0.960196i | \(0.409889\pi\) | |||||||
\(464\) | 27.4259 | 1.27322 | ||||||||
\(465\) | −48.0948 | −2.23034 | ||||||||
\(466\) | −44.6742 | −2.06949 | ||||||||
\(467\) | −35.0169 | −1.62039 | −0.810194 | − | 0.586162i | \(-0.800638\pi\) | ||||
−0.810194 | + | 0.586162i | \(0.800638\pi\) | |||||||
\(468\) | −1.24916 | −0.0577424 | ||||||||
\(469\) | 31.9581 | 1.47569 | ||||||||
\(470\) | 29.8677 | 1.37769 | ||||||||
\(471\) | −8.86529 | −0.408491 | ||||||||
\(472\) | 19.5267 | 0.898790 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | −12.8940 | −0.592241 | ||||||||
\(475\) | −21.7802 | −0.999346 | ||||||||
\(476\) | 3.36292 | 0.154139 | ||||||||
\(477\) | 7.16473 | 0.328050 | ||||||||
\(478\) | 26.8729 | 1.22914 | ||||||||
\(479\) | 1.88956 | 0.0863361 | 0.0431680 | − | 0.999068i | \(-0.486255\pi\) | ||||
0.0431680 | + | 0.999068i | \(0.486255\pi\) | |||||||
\(480\) | 21.9262 | 1.00079 | ||||||||
\(481\) | 17.8342 | 0.813170 | ||||||||
\(482\) | 24.9697 | 1.13734 | ||||||||
\(483\) | 33.4193 | 1.52063 | ||||||||
\(484\) | 0.704260 | 0.0320118 | ||||||||
\(485\) | 36.7556 | 1.66899 | ||||||||
\(486\) | −12.9332 | −0.586663 | ||||||||
\(487\) | −5.29052 | −0.239737 | −0.119868 | − | 0.992790i | \(-0.538247\pi\) | ||||
−0.119868 | + | 0.992790i | \(0.538247\pi\) | |||||||
\(488\) | −5.92089 | −0.268026 | ||||||||
\(489\) | 32.9616 | 1.49057 | ||||||||
\(490\) | 76.8317 | 3.47090 | ||||||||
\(491\) | 9.06938 | 0.409295 | 0.204648 | − | 0.978836i | \(-0.434395\pi\) | ||||
0.204648 | + | 0.978836i | \(0.434395\pi\) | |||||||
\(492\) | 13.1709 | 0.593788 | ||||||||
\(493\) | −5.58285 | −0.251439 | ||||||||
\(494\) | −21.9130 | −0.985914 | ||||||||
\(495\) | −2.29057 | −0.102953 | ||||||||
\(496\) | 41.1292 | 1.84676 | ||||||||
\(497\) | −28.4393 | −1.27568 | ||||||||
\(498\) | −9.70864 | −0.435055 | ||||||||
\(499\) | −20.3970 | −0.913094 | −0.456547 | − | 0.889699i | \(-0.650914\pi\) | ||||
−0.456547 | + | 0.889699i | \(0.650914\pi\) | |||||||
\(500\) | 2.61892 | 0.117122 | ||||||||
\(501\) | −44.2839 | −1.97846 | ||||||||
\(502\) | 10.4140 | 0.464801 | ||||||||
\(503\) | −43.6014 | −1.94409 | −0.972046 | − | 0.234791i | \(-0.924559\pi\) | ||||
−0.972046 | + | 0.234791i | \(0.924559\pi\) | |||||||
\(504\) | 7.88235 | 0.351108 | ||||||||
\(505\) | 21.3881 | 0.951759 | ||||||||
\(506\) | 5.92376 | 0.263343 | ||||||||
\(507\) | 15.0724 | 0.669389 | ||||||||
\(508\) | 7.99279 | 0.354623 | ||||||||
\(509\) | 38.8502 | 1.72201 | 0.861003 | − | 0.508599i | \(-0.169836\pi\) | ||||
0.861003 | + | 0.508599i | \(0.169836\pi\) | |||||||
\(510\) | −9.44665 | −0.418305 | ||||||||
\(511\) | 11.0801 | 0.490157 | ||||||||
\(512\) | 2.18460 | 0.0965466 | ||||||||
\(513\) | −25.1625 | −1.11095 | ||||||||
\(514\) | −41.4754 | −1.82940 | ||||||||
\(515\) | 23.3363 | 1.02832 | ||||||||
\(516\) | −1.36828 | −0.0602350 | ||||||||
\(517\) | 6.14277 | 0.270159 | ||||||||
\(518\) | 61.1656 | 2.68746 | ||||||||
\(519\) | 16.7021 | 0.733141 | ||||||||
\(520\) | 14.4248 | 0.632569 | ||||||||
\(521\) | 31.2427 | 1.36877 | 0.684384 | − | 0.729122i | \(-0.260071\pi\) | ||||
0.684384 | + | 0.729122i | \(0.260071\pi\) | |||||||
\(522\) | 7.11230 | 0.311297 | ||||||||
\(523\) | −14.7705 | −0.645867 | −0.322934 | − | 0.946422i | \(-0.604669\pi\) | ||||
−0.322934 | + | 0.946422i | \(0.604669\pi\) | |||||||
\(524\) | −6.30949 | −0.275631 | ||||||||
\(525\) | −34.7187 | −1.51525 | ||||||||
\(526\) | 6.44938 | 0.281206 | ||||||||
\(527\) | −8.37229 | −0.364703 | ||||||||
\(528\) | 9.54436 | 0.415365 | ||||||||
\(529\) | −10.0238 | −0.435818 | ||||||||
\(530\) | 44.9683 | 1.95330 | ||||||||
\(531\) | 7.09933 | 0.308085 | ||||||||
\(532\) | −19.5722 | −0.848564 | ||||||||
\(533\) | 22.0391 | 0.954621 | ||||||||
\(534\) | −10.3786 | −0.449125 | ||||||||
\(535\) | 53.6161 | 2.31803 | ||||||||
\(536\) | 14.2607 | 0.615967 | ||||||||
\(537\) | 31.2378 | 1.34801 | ||||||||
\(538\) | −35.9200 | −1.54862 | ||||||||
\(539\) | 15.8017 | 0.680626 | ||||||||
\(540\) | −9.00278 | −0.387418 | ||||||||
\(541\) | 37.1509 | 1.59724 | 0.798621 | − | 0.601835i | \(-0.205563\pi\) | ||||
0.798621 | + | 0.601835i | \(0.205563\pi\) | |||||||
\(542\) | 17.2743 | 0.741995 | ||||||||
\(543\) | −8.59169 | −0.368705 | ||||||||
\(544\) | 3.81689 | 0.163648 | ||||||||
\(545\) | 51.9548 | 2.22550 | ||||||||
\(546\) | −34.9303 | −1.49488 | ||||||||
\(547\) | 7.30496 | 0.312337 | 0.156169 | − | 0.987730i | \(-0.450086\pi\) | ||||
0.156169 | + | 0.987730i | \(0.450086\pi\) | |||||||
\(548\) | 7.50831 | 0.320739 | ||||||||
\(549\) | −2.15266 | −0.0918732 | ||||||||
\(550\) | −6.15408 | −0.262411 | ||||||||
\(551\) | 32.4922 | 1.38422 | ||||||||
\(552\) | 14.9127 | 0.634727 | ||||||||
\(553\) | −19.2711 | −0.819489 | ||||||||
\(554\) | 45.3126 | 1.92515 | ||||||||
\(555\) | −44.7459 | −1.89936 | ||||||||
\(556\) | −0.0963802 | −0.00408743 | ||||||||
\(557\) | 22.3229 | 0.945852 | 0.472926 | − | 0.881102i | \(-0.343198\pi\) | ||||
0.472926 | + | 0.881102i | \(0.343198\pi\) | |||||||
\(558\) | 10.6659 | 0.451525 | ||||||||
\(559\) | −2.28957 | −0.0968386 | ||||||||
\(560\) | 69.3589 | 2.93095 | ||||||||
\(561\) | −1.94286 | −0.0820275 | ||||||||
\(562\) | −5.98368 | −0.252406 | ||||||||
\(563\) | −17.0300 | −0.717728 | −0.358864 | − | 0.933390i | \(-0.616836\pi\) | ||||
−0.358864 | + | 0.933390i | \(0.616836\pi\) | |||||||
\(564\) | −8.40501 | −0.353915 | ||||||||
\(565\) | −51.5175 | −2.16736 | ||||||||
\(566\) | −4.04098 | −0.169855 | ||||||||
\(567\) | −51.2080 | −2.15053 | ||||||||
\(568\) | −12.6905 | −0.532481 | ||||||||
\(569\) | 15.7258 | 0.659262 | 0.329631 | − | 0.944110i | \(-0.393076\pi\) | ||||
0.329631 | + | 0.944110i | \(0.393076\pi\) | |||||||
\(570\) | 54.9796 | 2.30284 | ||||||||
\(571\) | −26.0892 | −1.09180 | −0.545900 | − | 0.837850i | \(-0.683812\pi\) | ||||
−0.545900 | + | 0.837850i | \(0.683812\pi\) | |||||||
\(572\) | −1.61245 | −0.0674201 | ||||||||
\(573\) | −3.61441 | −0.150994 | ||||||||
\(574\) | 75.5871 | 3.15495 | ||||||||
\(575\) | −13.4807 | −0.562184 | ||||||||
\(576\) | 2.74887 | 0.114536 | ||||||||
\(577\) | −25.7780 | −1.07315 | −0.536577 | − | 0.843851i | \(-0.680283\pi\) | ||||
−0.536577 | + | 0.843851i | \(0.680283\pi\) | |||||||
\(578\) | −1.64446 | −0.0684007 | ||||||||
\(579\) | −15.8261 | −0.657710 | ||||||||
\(580\) | 11.6252 | 0.482712 | ||||||||
\(581\) | −14.5103 | −0.601989 | ||||||||
\(582\) | −39.7170 | −1.64632 | ||||||||
\(583\) | 9.24846 | 0.383032 | ||||||||
\(584\) | 4.94429 | 0.204596 | ||||||||
\(585\) | 5.24442 | 0.216830 | ||||||||
\(586\) | 9.66096 | 0.399090 | ||||||||
\(587\) | −20.6768 | −0.853421 | −0.426711 | − | 0.904388i | \(-0.640328\pi\) | ||||
−0.426711 | + | 0.904388i | \(0.640328\pi\) | |||||||
\(588\) | −21.6211 | −0.891638 | ||||||||
\(589\) | 48.7268 | 2.00775 | ||||||||
\(590\) | 44.5578 | 1.83442 | ||||||||
\(591\) | 7.79689 | 0.320721 | ||||||||
\(592\) | 38.2653 | 1.57270 | ||||||||
\(593\) | −27.5109 | −1.12974 | −0.564869 | − | 0.825181i | \(-0.691073\pi\) | ||||
−0.564869 | + | 0.825181i | \(0.691073\pi\) | |||||||
\(594\) | −7.10976 | −0.291717 | ||||||||
\(595\) | −14.1188 | −0.578812 | ||||||||
\(596\) | −6.16976 | −0.252723 | ||||||||
\(597\) | −47.8238 | −1.95730 | ||||||||
\(598\) | −13.5629 | −0.554628 | ||||||||
\(599\) | 34.9211 | 1.42684 | 0.713418 | − | 0.700739i | \(-0.247146\pi\) | ||||
0.713418 | + | 0.700739i | \(0.247146\pi\) | |||||||
\(600\) | −15.4925 | −0.632479 | ||||||||
\(601\) | −43.6928 | −1.78227 | −0.891133 | − | 0.453742i | \(-0.850089\pi\) | ||||
−0.891133 | + | 0.453742i | \(0.850089\pi\) | |||||||
\(602\) | −7.85249 | −0.320044 | ||||||||
\(603\) | 5.18475 | 0.211139 | ||||||||
\(604\) | −8.70315 | −0.354126 | ||||||||
\(605\) | −2.95674 | −0.120209 | ||||||||
\(606\) | −23.1113 | −0.938833 | ||||||||
\(607\) | −21.9130 | −0.889423 | −0.444711 | − | 0.895674i | \(-0.646694\pi\) | ||||
−0.444711 | + | 0.895674i | \(0.646694\pi\) | |||||||
\(608\) | −22.2144 | −0.900912 | ||||||||
\(609\) | 51.7941 | 2.09880 | ||||||||
\(610\) | −13.5108 | −0.547038 | ||||||||
\(611\) | −14.0643 | −0.568981 | ||||||||
\(612\) | 0.545586 | 0.0220540 | ||||||||
\(613\) | 44.1446 | 1.78298 | 0.891491 | − | 0.453038i | \(-0.149660\pi\) | ||||
0.891491 | + | 0.453038i | \(0.149660\pi\) | |||||||
\(614\) | 25.4297 | 1.02626 | ||||||||
\(615\) | −55.2960 | −2.22975 | ||||||||
\(616\) | 10.1748 | 0.409954 | ||||||||
\(617\) | 19.4359 | 0.782461 | 0.391230 | − | 0.920293i | \(-0.372050\pi\) | ||||
0.391230 | + | 0.920293i | \(0.372050\pi\) | |||||||
\(618\) | −25.2165 | −1.01436 | ||||||||
\(619\) | −12.9647 | −0.521096 | −0.260548 | − | 0.965461i | \(-0.583903\pi\) | ||||
−0.260548 | + | 0.965461i | \(0.583903\pi\) | |||||||
\(620\) | 17.4337 | 0.700156 | ||||||||
\(621\) | −15.5741 | −0.624969 | ||||||||
\(622\) | 48.3478 | 1.93857 | ||||||||
\(623\) | −15.5116 | −0.621459 | ||||||||
\(624\) | −21.8525 | −0.874800 | ||||||||
\(625\) | −29.7067 | −1.18827 | ||||||||
\(626\) | 36.0999 | 1.44284 | ||||||||
\(627\) | 11.3074 | 0.451576 | ||||||||
\(628\) | 3.21355 | 0.128235 | ||||||||
\(629\) | −7.78932 | −0.310581 | ||||||||
\(630\) | 17.9867 | 0.716606 | ||||||||
\(631\) | 33.6831 | 1.34090 | 0.670452 | − | 0.741953i | \(-0.266100\pi\) | ||||
0.670452 | + | 0.741953i | \(0.266100\pi\) | |||||||
\(632\) | −8.59933 | −0.342063 | ||||||||
\(633\) | 15.8154 | 0.628606 | ||||||||
\(634\) | 5.29178 | 0.210163 | ||||||||
\(635\) | −33.5566 | −1.33165 | ||||||||
\(636\) | −12.6545 | −0.501782 | ||||||||
\(637\) | −36.1791 | −1.43347 | ||||||||
\(638\) | 9.18079 | 0.363471 | ||||||||
\(639\) | −4.61388 | −0.182522 | ||||||||
\(640\) | 39.8240 | 1.57418 | ||||||||
\(641\) | −13.1907 | −0.521002 | −0.260501 | − | 0.965474i | \(-0.583888\pi\) | ||||
−0.260501 | + | 0.965474i | \(0.583888\pi\) | |||||||
\(642\) | −57.9359 | −2.28655 | ||||||||
\(643\) | −29.5366 | −1.16481 | −0.582404 | − | 0.812899i | \(-0.697888\pi\) | ||||
−0.582404 | + | 0.812899i | \(0.697888\pi\) | |||||||
\(644\) | −12.1141 | −0.477361 | ||||||||
\(645\) | 5.74452 | 0.226190 | ||||||||
\(646\) | 9.57079 | 0.376558 | ||||||||
\(647\) | 0.481803 | 0.0189416 | 0.00947081 | − | 0.999955i | \(-0.496985\pi\) | ||||
0.00947081 | + | 0.999955i | \(0.496985\pi\) | |||||||
\(648\) | −22.8505 | −0.897653 | ||||||||
\(649\) | 9.16404 | 0.359720 | ||||||||
\(650\) | 14.0902 | 0.552663 | ||||||||
\(651\) | 77.6728 | 3.04424 | ||||||||
\(652\) | −11.9481 | −0.467925 | ||||||||
\(653\) | 47.2058 | 1.84731 | 0.923653 | − | 0.383229i | \(-0.125188\pi\) | ||||
0.923653 | + | 0.383229i | \(0.125188\pi\) | |||||||
\(654\) | −56.1407 | −2.19528 | ||||||||
\(655\) | 26.4895 | 1.03503 | ||||||||
\(656\) | 47.2875 | 1.84627 | ||||||||
\(657\) | 1.79760 | 0.0701309 | ||||||||
\(658\) | −48.2360 | −1.88044 | ||||||||
\(659\) | 40.1909 | 1.56562 | 0.782808 | − | 0.622263i | \(-0.213787\pi\) | ||||
0.782808 | + | 0.622263i | \(0.213787\pi\) | |||||||
\(660\) | 4.04564 | 0.157476 | ||||||||
\(661\) | −19.0399 | −0.740568 | −0.370284 | − | 0.928919i | \(-0.620740\pi\) | ||||
−0.370284 | + | 0.928919i | \(0.620740\pi\) | |||||||
\(662\) | 27.3867 | 1.06441 | ||||||||
\(663\) | 4.44831 | 0.172758 | ||||||||
\(664\) | −6.47493 | −0.251276 | ||||||||
\(665\) | 82.1713 | 3.18647 | ||||||||
\(666\) | 9.92325 | 0.384518 | ||||||||
\(667\) | 20.1108 | 0.778693 | ||||||||
\(668\) | 16.0523 | 0.621083 | ||||||||
\(669\) | −5.18206 | −0.200350 | ||||||||
\(670\) | 32.5413 | 1.25718 | ||||||||
\(671\) | −2.77872 | −0.107271 | ||||||||
\(672\) | −35.4107 | −1.36600 | ||||||||
\(673\) | 5.94965 | 0.229342 | 0.114671 | − | 0.993404i | \(-0.463419\pi\) | ||||
0.114671 | + | 0.993404i | \(0.463419\pi\) | |||||||
\(674\) | −53.2799 | −2.05226 | ||||||||
\(675\) | 16.1797 | 0.622755 | ||||||||
\(676\) | −5.46355 | −0.210137 | ||||||||
\(677\) | 29.4847 | 1.13319 | 0.566594 | − | 0.823997i | \(-0.308261\pi\) | ||||
0.566594 | + | 0.823997i | \(0.308261\pi\) | |||||||
\(678\) | 55.6682 | 2.13792 | ||||||||
\(679\) | −59.3601 | −2.27803 | ||||||||
\(680\) | −6.30021 | −0.241602 | ||||||||
\(681\) | −57.0532 | −2.18628 | ||||||||
\(682\) | 13.7679 | 0.527201 | ||||||||
\(683\) | 40.9665 | 1.56754 | 0.783771 | − | 0.621050i | \(-0.213294\pi\) | ||||
0.783771 | + | 0.621050i | \(0.213294\pi\) | |||||||
\(684\) | −3.17532 | −0.121411 | ||||||||
\(685\) | −31.5226 | −1.20442 | ||||||||
\(686\) | −69.1151 | −2.63883 | ||||||||
\(687\) | −7.92091 | −0.302202 | ||||||||
\(688\) | −4.91254 | −0.187289 | ||||||||
\(689\) | −21.1750 | −0.806704 | ||||||||
\(690\) | 34.0292 | 1.29547 | ||||||||
\(691\) | −20.5544 | −0.781927 | −0.390963 | − | 0.920406i | \(-0.627858\pi\) | ||||
−0.390963 | + | 0.920406i | \(0.627858\pi\) | |||||||
\(692\) | −6.05430 | −0.230150 | ||||||||
\(693\) | 3.69925 | 0.140523 | ||||||||
\(694\) | 2.87622 | 0.109180 | ||||||||
\(695\) | 0.404639 | 0.0153488 | ||||||||
\(696\) | 23.1121 | 0.876060 | ||||||||
\(697\) | −9.62588 | −0.364606 | ||||||||
\(698\) | 27.7185 | 1.04916 | ||||||||
\(699\) | −52.7805 | −1.99634 | ||||||||
\(700\) | 12.5851 | 0.475670 | ||||||||
\(701\) | −44.2235 | −1.67030 | −0.835148 | − | 0.550025i | \(-0.814618\pi\) | ||||
−0.835148 | + | 0.550025i | \(0.814618\pi\) | |||||||
\(702\) | 16.2783 | 0.614385 | ||||||||
\(703\) | 45.3339 | 1.70980 | ||||||||
\(704\) | 3.54833 | 0.133733 | ||||||||
\(705\) | 35.2873 | 1.32899 | ||||||||
\(706\) | 15.9273 | 0.599432 | ||||||||
\(707\) | −34.5417 | −1.29907 | ||||||||
\(708\) | −12.5389 | −0.471242 | ||||||||
\(709\) | 28.1386 | 1.05677 | 0.528383 | − | 0.849006i | \(-0.322798\pi\) | ||||
0.528383 | + | 0.849006i | \(0.322798\pi\) | |||||||
\(710\) | −28.9583 | −1.08679 | ||||||||
\(711\) | −3.12646 | −0.117251 | ||||||||
\(712\) | −6.92174 | −0.259403 | ||||||||
\(713\) | 30.1591 | 1.12947 | ||||||||
\(714\) | 15.2563 | 0.570952 | ||||||||
\(715\) | 6.76967 | 0.253171 | ||||||||
\(716\) | −11.3233 | −0.423171 | ||||||||
\(717\) | 31.7491 | 1.18569 | ||||||||
\(718\) | −42.0943 | −1.57094 | ||||||||
\(719\) | −13.1666 | −0.491032 | −0.245516 | − | 0.969392i | \(-0.578957\pi\) | ||||
−0.245516 | + | 0.969392i | \(0.578957\pi\) | |||||||
\(720\) | 11.2525 | 0.419356 | ||||||||
\(721\) | −37.6880 | −1.40357 | ||||||||
\(722\) | −24.4573 | −0.910207 | ||||||||
\(723\) | 29.5005 | 1.09714 | ||||||||
\(724\) | 3.11437 | 0.115745 | ||||||||
\(725\) | −20.8927 | −0.775935 | ||||||||
\(726\) | 3.19496 | 0.118576 | ||||||||
\(727\) | −25.3974 | −0.941939 | −0.470969 | − | 0.882150i | \(-0.656096\pi\) | ||||
−0.470969 | + | 0.882150i | \(0.656096\pi\) | |||||||
\(728\) | −23.2959 | −0.863404 | ||||||||
\(729\) | 16.8918 | 0.625622 | ||||||||
\(730\) | 11.2823 | 0.417578 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | 3.80206 | 0.140528 | ||||||||
\(733\) | −15.7470 | −0.581628 | −0.290814 | − | 0.956780i | \(-0.593926\pi\) | ||||
−0.290814 | + | 0.956780i | \(0.593926\pi\) | |||||||
\(734\) | 16.1160 | 0.594852 | ||||||||
\(735\) | 90.7731 | 3.34821 | ||||||||
\(736\) | −13.7494 | −0.506810 | ||||||||
\(737\) | 6.69264 | 0.246527 | ||||||||
\(738\) | 12.2629 | 0.451405 | ||||||||
\(739\) | 33.1785 | 1.22049 | 0.610245 | − | 0.792213i | \(-0.291071\pi\) | ||||
0.610245 | + | 0.792213i | \(0.291071\pi\) | |||||||
\(740\) | 16.2198 | 0.596252 | ||||||||
\(741\) | −25.8892 | −0.951064 | ||||||||
\(742\) | −72.6235 | −2.66609 | ||||||||
\(743\) | −7.68842 | −0.282061 | −0.141030 | − | 0.990005i | \(-0.545042\pi\) | ||||
−0.141030 | + | 0.990005i | \(0.545042\pi\) | |||||||
\(744\) | 34.6599 | 1.27069 | ||||||||
\(745\) | 25.9029 | 0.949009 | ||||||||
\(746\) | −35.4722 | −1.29873 | ||||||||
\(747\) | −2.35409 | −0.0861317 | ||||||||
\(748\) | 0.704260 | 0.0257503 | ||||||||
\(749\) | −86.5896 | −3.16392 | ||||||||
\(750\) | 11.8810 | 0.433834 | ||||||||
\(751\) | 1.82447 | 0.0665760 | 0.0332880 | − | 0.999446i | \(-0.489402\pi\) | ||||
0.0332880 | + | 0.999446i | \(0.489402\pi\) | |||||||
\(752\) | −30.1766 | −1.10043 | ||||||||
\(753\) | 12.3037 | 0.448371 | ||||||||
\(754\) | −21.0201 | −0.765506 | ||||||||
\(755\) | 36.5390 | 1.32979 | ||||||||
\(756\) | 14.5394 | 0.528794 | ||||||||
\(757\) | −22.6835 | −0.824445 | −0.412222 | − | 0.911083i | \(-0.635247\pi\) | ||||
−0.412222 | + | 0.911083i | \(0.635247\pi\) | |||||||
\(758\) | 38.1078 | 1.38414 | ||||||||
\(759\) | 6.99865 | 0.254035 | ||||||||
\(760\) | 36.6673 | 1.33006 | ||||||||
\(761\) | −20.8028 | −0.754100 | −0.377050 | − | 0.926193i | \(-0.623062\pi\) | ||||
−0.377050 | + | 0.926193i | \(0.623062\pi\) | |||||||
\(762\) | 36.2602 | 1.31357 | ||||||||
\(763\) | −83.9067 | −3.03763 | ||||||||
\(764\) | 1.31018 | 0.0474005 | ||||||||
\(765\) | −2.29057 | −0.0828156 | ||||||||
\(766\) | −56.8725 | −2.05489 | ||||||||
\(767\) | −20.9817 | −0.757606 | ||||||||
\(768\) | −29.2447 | −1.05528 | ||||||||
\(769\) | 7.17586 | 0.258768 | 0.129384 | − | 0.991595i | \(-0.458700\pi\) | ||||
0.129384 | + | 0.991595i | \(0.458700\pi\) | |||||||
\(770\) | 23.2178 | 0.836710 | ||||||||
\(771\) | −49.0013 | −1.76474 | ||||||||
\(772\) | 5.73675 | 0.206470 | ||||||||
\(773\) | 19.0414 | 0.684872 | 0.342436 | − | 0.939541i | \(-0.388748\pi\) | ||||
0.342436 | + | 0.939541i | \(0.388748\pi\) | |||||||
\(774\) | −1.27396 | −0.0457914 | ||||||||
\(775\) | −31.3316 | −1.12547 | ||||||||
\(776\) | −26.4882 | −0.950872 | ||||||||
\(777\) | 72.2643 | 2.59247 | ||||||||
\(778\) | 55.2650 | 1.98135 | ||||||||
\(779\) | 56.0227 | 2.00722 | ||||||||
\(780\) | −9.26278 | −0.331661 | ||||||||
\(781\) | −5.95574 | −0.213113 | ||||||||
\(782\) | 5.92376 | 0.211833 | ||||||||
\(783\) | −24.1372 | −0.862592 | ||||||||
\(784\) | −77.6263 | −2.77237 | ||||||||
\(785\) | −13.4916 | −0.481537 | ||||||||
\(786\) | −28.6237 | −1.02097 | ||||||||
\(787\) | −38.7395 | −1.38091 | −0.690456 | − | 0.723374i | \(-0.742590\pi\) | ||||
−0.690456 | + | 0.723374i | \(0.742590\pi\) | |||||||
\(788\) | −2.82627 | −0.100682 | ||||||||
\(789\) | 7.61965 | 0.271267 | ||||||||
\(790\) | −19.6227 | −0.698145 | ||||||||
\(791\) | 83.2004 | 2.95827 | ||||||||
\(792\) | 1.65072 | 0.0586556 | ||||||||
\(793\) | 6.36208 | 0.225924 | ||||||||
\(794\) | 14.8093 | 0.525563 | ||||||||
\(795\) | 53.1280 | 1.88425 | ||||||||
\(796\) | 17.3355 | 0.614441 | ||||||||
\(797\) | −14.5289 | −0.514639 | −0.257320 | − | 0.966326i | \(-0.582839\pi\) | ||||
−0.257320 | + | 0.966326i | \(0.582839\pi\) | |||||||
\(798\) | −88.7917 | −3.14319 | ||||||||
\(799\) | 6.14277 | 0.217315 | ||||||||
\(800\) | 14.2840 | 0.505015 | ||||||||
\(801\) | −2.51654 | −0.0889175 | ||||||||
\(802\) | −14.0906 | −0.497556 | ||||||||
\(803\) | 2.32040 | 0.0818850 | ||||||||
\(804\) | −9.15739 | −0.322956 | ||||||||
\(805\) | 50.8592 | 1.79255 | ||||||||
\(806\) | −31.5227 | −1.11034 | ||||||||
\(807\) | −42.4378 | −1.49388 | ||||||||
\(808\) | −15.4135 | −0.542246 | ||||||||
\(809\) | 22.4885 | 0.790654 | 0.395327 | − | 0.918540i | \(-0.370631\pi\) | ||||
0.395327 | + | 0.918540i | \(0.370631\pi\) | |||||||
\(810\) | −52.1424 | −1.83210 | ||||||||
\(811\) | 30.5584 | 1.07305 | 0.536525 | − | 0.843884i | \(-0.319737\pi\) | ||||
0.536525 | + | 0.843884i | \(0.319737\pi\) | |||||||
\(812\) | −18.7747 | −0.658862 | ||||||||
\(813\) | 20.4088 | 0.715768 | ||||||||
\(814\) | 12.8093 | 0.448964 | ||||||||
\(815\) | 50.1626 | 1.75712 | ||||||||
\(816\) | 9.54436 | 0.334119 | ||||||||
\(817\) | −5.82001 | −0.203616 | ||||||||
\(818\) | −16.6795 | −0.583185 | ||||||||
\(819\) | −8.46970 | −0.295955 | ||||||||
\(820\) | 20.0441 | 0.699970 | ||||||||
\(821\) | −27.7881 | −0.969810 | −0.484905 | − | 0.874567i | \(-0.661146\pi\) | ||||
−0.484905 | + | 0.874567i | \(0.661146\pi\) | |||||||
\(822\) | 34.0623 | 1.18806 | ||||||||
\(823\) | 4.67070 | 0.162810 | 0.0814051 | − | 0.996681i | \(-0.474059\pi\) | ||||
0.0814051 | + | 0.996681i | \(0.474059\pi\) | |||||||
\(824\) | −16.8175 | −0.585866 | ||||||||
\(825\) | −7.27076 | −0.253135 | ||||||||
\(826\) | −71.9606 | −2.50383 | ||||||||
\(827\) | 28.3357 | 0.985330 | 0.492665 | − | 0.870219i | \(-0.336023\pi\) | ||||
0.492665 | + | 0.870219i | \(0.336023\pi\) | |||||||
\(828\) | −1.96534 | −0.0683001 | ||||||||
\(829\) | 21.9316 | 0.761716 | 0.380858 | − | 0.924634i | \(-0.375629\pi\) | ||||
0.380858 | + | 0.924634i | \(0.375629\pi\) | |||||||
\(830\) | −14.7751 | −0.512851 | ||||||||
\(831\) | 53.5347 | 1.85710 | ||||||||
\(832\) | −8.12416 | −0.281655 | ||||||||
\(833\) | 15.8017 | 0.547496 | ||||||||
\(834\) | −0.437240 | −0.0151404 | ||||||||
\(835\) | −67.3934 | −2.33225 | ||||||||
\(836\) | −4.09880 | −0.141760 | ||||||||
\(837\) | −36.1972 | −1.25116 | ||||||||
\(838\) | 33.8055 | 1.16779 | ||||||||
\(839\) | 26.6214 | 0.919072 | 0.459536 | − | 0.888159i | \(-0.348016\pi\) | ||||
0.459536 | + | 0.888159i | \(0.348016\pi\) | |||||||
\(840\) | 58.4493 | 2.01669 | ||||||||
\(841\) | 2.16818 | 0.0747648 | ||||||||
\(842\) | −58.6289 | −2.02048 | ||||||||
\(843\) | −7.06944 | −0.243484 | ||||||||
\(844\) | −5.73287 | −0.197334 | ||||||||
\(845\) | 22.9380 | 0.789090 | ||||||||
\(846\) | −7.82561 | −0.269050 | ||||||||
\(847\) | 4.77511 | 0.164075 | ||||||||
\(848\) | −45.4334 | −1.56019 | ||||||||
\(849\) | −4.77423 | −0.163851 | ||||||||
\(850\) | −6.15408 | −0.211083 | ||||||||
\(851\) | 28.0591 | 0.961853 | ||||||||
\(852\) | 8.14910 | 0.279184 | ||||||||
\(853\) | 33.2826 | 1.13957 | 0.569787 | − | 0.821792i | \(-0.307026\pi\) | ||||
0.569787 | + | 0.821792i | \(0.307026\pi\) | |||||||
\(854\) | 21.8199 | 0.746661 | ||||||||
\(855\) | 13.3311 | 0.455915 | ||||||||
\(856\) | −38.6389 | −1.32065 | ||||||||
\(857\) | −39.8814 | −1.36232 | −0.681162 | − | 0.732133i | \(-0.738525\pi\) | ||||
−0.681162 | + | 0.732133i | \(0.738525\pi\) | |||||||
\(858\) | −7.31509 | −0.249733 | ||||||||
\(859\) | 29.0384 | 0.990777 | 0.495388 | − | 0.868672i | \(-0.335026\pi\) | ||||
0.495388 | + | 0.868672i | \(0.335026\pi\) | |||||||
\(860\) | −2.08231 | −0.0710063 | ||||||||
\(861\) | 89.3027 | 3.04343 | ||||||||
\(862\) | −12.9246 | −0.440212 | ||||||||
\(863\) | 25.1673 | 0.856704 | 0.428352 | − | 0.903612i | \(-0.359094\pi\) | ||||
0.428352 | + | 0.903612i | \(0.359094\pi\) | |||||||
\(864\) | 16.5022 | 0.561415 | ||||||||
\(865\) | 25.4181 | 0.864242 | ||||||||
\(866\) | −36.7239 | −1.24793 | ||||||||
\(867\) | −1.94286 | −0.0659829 | ||||||||
\(868\) | −28.1554 | −0.955655 | ||||||||
\(869\) | −4.03573 | −0.136903 | ||||||||
\(870\) | 52.7392 | 1.78803 | ||||||||
\(871\) | −15.3233 | −0.519210 | ||||||||
\(872\) | −37.4417 | −1.26793 | ||||||||
\(873\) | −9.63033 | −0.325937 | ||||||||
\(874\) | −34.4764 | −1.16618 | ||||||||
\(875\) | 17.7571 | 0.600301 | ||||||||
\(876\) | −3.17494 | −0.107271 | ||||||||
\(877\) | 25.6479 | 0.866067 | 0.433033 | − | 0.901378i | \(-0.357443\pi\) | ||||
0.433033 | + | 0.901378i | \(0.357443\pi\) | |||||||
\(878\) | 47.3238 | 1.59710 | ||||||||
\(879\) | 11.4140 | 0.384984 | ||||||||
\(880\) | 14.5251 | 0.489641 | ||||||||
\(881\) | 39.6620 | 1.33625 | 0.668124 | − | 0.744050i | \(-0.267098\pi\) | ||||
0.668124 | + | 0.744050i | \(0.267098\pi\) | |||||||
\(882\) | −20.1306 | −0.677834 | ||||||||
\(883\) | 11.4480 | 0.385257 | 0.192629 | − | 0.981272i | \(-0.438299\pi\) | ||||
0.192629 | + | 0.981272i | \(0.438299\pi\) | |||||||
\(884\) | −1.61245 | −0.0542327 | ||||||||
\(885\) | 52.6430 | 1.76958 | ||||||||
\(886\) | −9.01896 | −0.302998 | ||||||||
\(887\) | −25.5448 | −0.857709 | −0.428855 | − | 0.903374i | \(-0.641083\pi\) | ||||
−0.428855 | + | 0.903374i | \(0.641083\pi\) | |||||||
\(888\) | 32.2465 | 1.08212 | ||||||||
\(889\) | 54.1937 | 1.81760 | ||||||||
\(890\) | −15.7947 | −0.529438 | ||||||||
\(891\) | −10.7239 | −0.359265 | ||||||||
\(892\) | 1.87843 | 0.0628944 | ||||||||
\(893\) | −35.7510 | −1.19636 | ||||||||
\(894\) | −27.9898 | −0.936120 | ||||||||
\(895\) | 47.5392 | 1.58906 | ||||||||
\(896\) | −64.3154 | −2.14863 | ||||||||
\(897\) | −16.0239 | −0.535023 | ||||||||
\(898\) | −16.3232 | −0.544712 | ||||||||
\(899\) | 46.7412 | 1.55891 | ||||||||
\(900\) | 2.04175 | 0.0680582 | ||||||||
\(901\) | 9.24846 | 0.308111 | ||||||||
\(902\) | 15.8294 | 0.527061 | ||||||||
\(903\) | −9.27736 | −0.308731 | ||||||||
\(904\) | 37.1265 | 1.23481 | ||||||||
\(905\) | −13.0753 | −0.434636 | ||||||||
\(906\) | −39.4828 | −1.31173 | ||||||||
\(907\) | 23.7587 | 0.788895 | 0.394448 | − | 0.918918i | \(-0.370936\pi\) | ||||
0.394448 | + | 0.918918i | \(0.370936\pi\) | |||||||
\(908\) | 20.6810 | 0.686324 | ||||||||
\(909\) | −5.60389 | −0.185869 | ||||||||
\(910\) | −53.1588 | −1.76220 | ||||||||
\(911\) | 27.0870 | 0.897431 | 0.448716 | − | 0.893675i | \(-0.351882\pi\) | ||||
0.448716 | + | 0.893675i | \(0.351882\pi\) | |||||||
\(912\) | −55.5483 | −1.83939 | ||||||||
\(913\) | −3.03874 | −0.100568 | ||||||||
\(914\) | 36.8505 | 1.21891 | ||||||||
\(915\) | −15.9624 | −0.527701 | ||||||||
\(916\) | 2.87123 | 0.0948679 | ||||||||
\(917\) | −42.7803 | −1.41273 | ||||||||
\(918\) | −7.10976 | −0.234657 | ||||||||
\(919\) | −6.51543 | −0.214924 | −0.107462 | − | 0.994209i | \(-0.534272\pi\) | ||||
−0.107462 | + | 0.994209i | \(0.534272\pi\) | |||||||
\(920\) | 22.6949 | 0.748229 | ||||||||
\(921\) | 30.0440 | 0.989984 | ||||||||
\(922\) | 17.2736 | 0.568875 | ||||||||
\(923\) | 13.6361 | 0.448838 | ||||||||
\(924\) | −6.53367 | −0.214942 | ||||||||
\(925\) | −29.1500 | −0.958446 | ||||||||
\(926\) | −19.7677 | −0.649607 | ||||||||
\(927\) | −6.11435 | −0.200821 | ||||||||
\(928\) | −21.3091 | −0.699507 | ||||||||
\(929\) | 19.0451 | 0.624849 | 0.312425 | − | 0.949943i | \(-0.398859\pi\) | ||||
0.312425 | + | 0.949943i | \(0.398859\pi\) | |||||||
\(930\) | 79.0902 | 2.59347 | ||||||||
\(931\) | −91.9659 | −3.01406 | ||||||||
\(932\) | 19.1322 | 0.626697 | ||||||||
\(933\) | 57.1207 | 1.87005 | ||||||||
\(934\) | 57.5840 | 1.88421 | ||||||||
\(935\) | −2.95674 | −0.0966957 | ||||||||
\(936\) | −3.77943 | −0.123535 | ||||||||
\(937\) | −2.95270 | −0.0964606 | −0.0482303 | − | 0.998836i | \(-0.515358\pi\) | ||||
−0.0482303 | + | 0.998836i | \(0.515358\pi\) | |||||||
\(938\) | −52.5539 | −1.71595 | ||||||||
\(939\) | 42.6503 | 1.39184 | ||||||||
\(940\) | −12.7912 | −0.417202 | ||||||||
\(941\) | 54.7847 | 1.78593 | 0.892966 | − | 0.450125i | \(-0.148621\pi\) | ||||
0.892966 | + | 0.450125i | \(0.148621\pi\) | |||||||
\(942\) | 14.5786 | 0.474998 | ||||||||
\(943\) | 34.6748 | 1.12917 | ||||||||
\(944\) | −45.0187 | −1.46523 | ||||||||
\(945\) | −61.0417 | −1.98569 | ||||||||
\(946\) | −1.64446 | −0.0534661 | ||||||||
\(947\) | 9.55200 | 0.310398 | 0.155199 | − | 0.987883i | \(-0.450398\pi\) | ||||
0.155199 | + | 0.987883i | \(0.450398\pi\) | |||||||
\(948\) | 5.52200 | 0.179346 | ||||||||
\(949\) | −5.31271 | −0.172458 | ||||||||
\(950\) | 35.8168 | 1.16205 | ||||||||
\(951\) | 6.25199 | 0.202735 | ||||||||
\(952\) | 10.1748 | 0.329767 | ||||||||
\(953\) | 55.6199 | 1.80170 | 0.900852 | − | 0.434125i | \(-0.142943\pi\) | ||||
0.900852 | + | 0.434125i | \(0.142943\pi\) | |||||||
\(954\) | −11.7821 | −0.381461 | ||||||||
\(955\) | −5.50059 | −0.177995 | ||||||||
\(956\) | −11.5086 | −0.372216 | ||||||||
\(957\) | 10.8467 | 0.350623 | ||||||||
\(958\) | −3.10731 | −0.100393 | ||||||||
\(959\) | 50.9087 | 1.64393 | ||||||||
\(960\) | 20.3835 | 0.657873 | ||||||||
\(961\) | 39.0953 | 1.26114 | ||||||||
\(962\) | −29.3277 | −0.945564 | ||||||||
\(963\) | −14.0479 | −0.452688 | ||||||||
\(964\) | −10.6935 | −0.344416 | ||||||||
\(965\) | −24.0850 | −0.775323 | ||||||||
\(966\) | −54.9569 | −1.76821 | ||||||||
\(967\) | 52.7756 | 1.69715 | 0.848575 | − | 0.529075i | \(-0.177461\pi\) | ||||
0.848575 | + | 0.529075i | \(0.177461\pi\) | |||||||
\(968\) | 2.13080 | 0.0684864 | ||||||||
\(969\) | 11.3074 | 0.363248 | ||||||||
\(970\) | −60.4433 | −1.94072 | ||||||||
\(971\) | 35.3771 | 1.13531 | 0.567653 | − | 0.823268i | \(-0.307851\pi\) | ||||
0.567653 | + | 0.823268i | \(0.307851\pi\) | |||||||
\(972\) | 5.53880 | 0.177657 | ||||||||
\(973\) | −0.653489 | −0.0209499 | ||||||||
\(974\) | 8.70007 | 0.278768 | ||||||||
\(975\) | 16.6469 | 0.533128 | ||||||||
\(976\) | 13.6506 | 0.436944 | ||||||||
\(977\) | 5.57192 | 0.178262 | 0.0891308 | − | 0.996020i | \(-0.471591\pi\) | ||||
0.0891308 | + | 0.996020i | \(0.471591\pi\) | |||||||
\(978\) | −54.2041 | −1.73326 | ||||||||
\(979\) | −3.24843 | −0.103820 | ||||||||
\(980\) | −32.9040 | −1.05108 | ||||||||
\(981\) | −13.6127 | −0.434619 | ||||||||
\(982\) | −14.9143 | −0.475933 | ||||||||
\(983\) | 17.5270 | 0.559023 | 0.279511 | − | 0.960142i | \(-0.409827\pi\) | ||||
0.279511 | + | 0.960142i | \(0.409827\pi\) | |||||||
\(984\) | 39.8495 | 1.27036 | ||||||||
\(985\) | 11.8657 | 0.378073 | ||||||||
\(986\) | 9.18079 | 0.292376 | ||||||||
\(987\) | −56.9886 | −1.81397 | ||||||||
\(988\) | 9.38450 | 0.298561 | ||||||||
\(989\) | −3.60225 | −0.114545 | ||||||||
\(990\) | 3.76675 | 0.119715 | ||||||||
\(991\) | −16.4255 | −0.521774 | −0.260887 | − | 0.965369i | \(-0.584015\pi\) | ||||
−0.260887 | + | 0.965369i | \(0.584015\pi\) | |||||||
\(992\) | −31.9562 | −1.01461 | ||||||||
\(993\) | 32.3561 | 1.02679 | ||||||||
\(994\) | 46.7674 | 1.48337 | ||||||||
\(995\) | −72.7807 | −2.30730 | ||||||||
\(996\) | 4.15783 | 0.131746 | ||||||||
\(997\) | 9.17777 | 0.290663 | 0.145331 | − | 0.989383i | \(-0.453575\pi\) | ||||
0.145331 | + | 0.989383i | \(0.453575\pi\) | |||||||
\(998\) | 33.5421 | 1.06176 | ||||||||
\(999\) | −33.6768 | −1.06549 |
(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 | 8041.2.a.j.1.19 | ✓ | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.j.1.19 | ✓ | 82 | 1.1 | even | 1 | trivial |