Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, 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("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0679214517\) |
Analytic rank: | \(0\) |
Dimension: | \(23\) |
Twist minimal: | no (minimal twist has level 2008) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.15579 | 0.667297 | 0.333649 | − | 0.942697i | \(-0.391720\pi\) | ||||
0.333649 | + | 0.942697i | \(0.391720\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.09592 | −1.83175 | −0.915876 | − | 0.401460i | \(-0.868503\pi\) | ||||
−0.915876 | + | 0.401460i | \(0.868503\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.621313 | 0.234834 | 0.117417 | − | 0.993083i | \(-0.462539\pi\) | ||||
0.117417 | + | 0.993083i | \(0.462539\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.66414 | −0.554714 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.176674 | −0.0532693 | −0.0266346 | − | 0.999645i | \(-0.508479\pi\) | ||||
−0.0266346 | + | 0.999645i | \(0.508479\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.62113 | −1.83637 | −0.918185 | − | 0.396152i | \(-0.870345\pi\) | ||||
−0.918185 | + | 0.396152i | \(0.870345\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.73404 | −1.22232 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.87879 | −1.18328 | −0.591640 | − | 0.806202i | \(-0.701519\pi\) | ||||
−0.591640 | + | 0.806202i | \(0.701519\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.67634 | 1.53166 | 0.765828 | − | 0.643045i | \(-0.222329\pi\) | ||||
0.765828 | + | 0.643045i | \(0.222329\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.718109 | 0.156704 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.95079 | −0.406769 | −0.203384 | − | 0.979099i | \(-0.565194\pi\) | ||||
−0.203384 | + | 0.979099i | \(0.565194\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.7766 | 2.35532 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.39078 | −1.03746 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.79872 | −0.891100 | −0.445550 | − | 0.895257i | \(-0.646992\pi\) | ||||
−0.445550 | + | 0.895257i | \(0.646992\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.71027 | 0.666385 | 0.333192 | − | 0.942859i | \(-0.391874\pi\) | ||||
0.333192 | + | 0.942859i | \(0.391874\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.204199 | −0.0355464 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.54485 | −0.430158 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.22498 | 1.02338 | 0.511690 | − | 0.859170i | \(-0.329020\pi\) | ||||
0.511690 | + | 0.859170i | \(0.329020\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.65265 | −1.22541 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.84850 | 0.288688 | 0.144344 | − | 0.989528i | \(-0.453893\pi\) | ||||
0.144344 | + | 0.989528i | \(0.453893\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.89738 | 1.05184 | 0.525920 | − | 0.850534i | \(-0.323721\pi\) | ||||
0.525920 | + | 0.850534i | \(0.323721\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.81620 | 1.01610 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.545127 | 0.0795150 | 0.0397575 | − | 0.999209i | \(-0.487341\pi\) | ||||
0.0397575 | + | 0.999209i | \(0.487341\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.61397 | −0.944853 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.63887 | −0.789600 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.30758 | −0.591692 | −0.295846 | − | 0.955236i | \(-0.595602\pi\) | ||||
−0.295846 | + | 0.955236i | \(0.595602\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.723644 | 0.0975761 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.71646 | 1.02207 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.0491 | −1.43847 | −0.719237 | − | 0.694765i | \(-0.755508\pi\) | ||||
−0.719237 | + | 0.694765i | \(0.755508\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.06372 | −0.392269 | −0.196135 | − | 0.980577i | \(-0.562839\pi\) | ||||
−0.196135 | + | 0.980577i | \(0.562839\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.03395 | −0.130266 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 27.1196 | 3.36378 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.29195 | 1.13519 | 0.567596 | − | 0.823307i | \(-0.307873\pi\) | ||||
0.567596 | + | 0.823307i | \(0.307873\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.25471 | −0.271436 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.86513 | 0.814741 | 0.407370 | − | 0.913263i | \(-0.366446\pi\) | ||||
0.407370 | + | 0.913263i | \(0.366446\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.09365 | 0.596167 | 0.298083 | − | 0.954540i | \(-0.403653\pi\) | ||||
0.298083 | + | 0.954540i | \(0.403653\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13.6113 | 1.57170 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.109770 | −0.0125095 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.28093 | 0.819169 | 0.409584 | − | 0.912272i | \(-0.365674\pi\) | ||||
0.409584 | + | 0.912272i | \(0.365674\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.23820 | −0.137578 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 18.1951 | 1.99717 | 0.998586 | − | 0.0531544i | \(-0.0169276\pi\) | ||||
0.998586 | + | 0.0531544i | \(0.0169276\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 19.9832 | 2.16748 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.54633 | −0.594629 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.4585 | 1.63860 | 0.819298 | − | 0.573368i | \(-0.194363\pi\) | ||||
0.819298 | + | 0.573368i | \(0.194363\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.11379 | −0.431243 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.28831 | 0.444677 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −27.3458 | −2.80562 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.30697 | 0.843445 | 0.421722 | − | 0.906725i | \(-0.361426\pi\) | ||||
0.421722 | + | 0.906725i | \(0.361426\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.294011 | 0.0295492 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.59493 | −0.954731 | −0.477365 | − | 0.878705i | \(-0.658408\pi\) | ||||
−0.477365 | + | 0.878705i | \(0.658408\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.65954 | −0.557651 | −0.278825 | − | 0.960342i | \(-0.589945\pi\) | ||||
−0.278825 | + | 0.960342i | \(0.589945\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.94132 | −0.287044 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.7163 | −1.51935 | −0.759674 | − | 0.650304i | \(-0.774641\pi\) | ||||
−0.759674 | + | 0.650304i | \(0.774641\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.9298 | 1.33424 | 0.667118 | − | 0.744952i | \(-0.267528\pi\) | ||||
0.667118 | + | 0.744952i | \(0.267528\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.19479 | 0.682899 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.6659 | 1.09743 | 0.548717 | − | 0.836008i | \(-0.315117\pi\) | ||||
0.548717 | + | 0.836008i | \(0.315117\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.99030 | 0.745099 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.0185 | 1.01866 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.03126 | −0.277875 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9688 | −0.997162 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.13649 | 0.192641 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −27.7564 | −2.48261 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.4141 | −1.54525 | −0.772624 | − | 0.634864i | \(-0.781056\pi\) | ||||
−0.772624 | + | 0.634864i | \(0.781056\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.97194 | 0.701890 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.4754 | −1.17735 | −0.588675 | − | 0.808370i | \(-0.700350\pi\) | ||||
−0.588675 | + | 0.808370i | \(0.700350\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.14810 | 0.359686 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 22.0802 | 1.90036 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.07181 | 0.604186 | 0.302093 | − | 0.953279i | \(-0.402315\pi\) | ||||
0.302093 | + | 0.953279i | \(0.402315\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.12679 | 0.774124 | 0.387062 | − | 0.922054i | \(-0.373490\pi\) | ||||
0.387062 | + | 0.922054i | \(0.373490\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.630054 | 0.0530601 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.16978 | 0.0978221 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.6552 | 1.63227 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.64438 | −0.630498 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.03604 | 0.330645 | 0.165322 | − | 0.986240i | \(-0.447134\pi\) | ||||
0.165322 | + | 0.986240i | \(0.447134\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.1672 | 1.39705 | 0.698525 | − | 0.715585i | \(-0.253840\pi\) | ||||
0.698525 | + | 0.715585i | \(0.253840\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.11901 | 0.656383 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.1970 | −1.22065 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.9500 | −1.03352 | −0.516760 | − | 0.856130i | \(-0.672862\pi\) | ||||
−0.516760 | + | 0.856130i | \(0.672862\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.97867 | −0.394834 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.21205 | −0.0955232 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.48780 | −0.116533 | −0.0582666 | − | 0.998301i | \(-0.518557\pi\) | ||||
−0.0582666 | + | 0.998301i | \(0.518557\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.836382 | 0.0651123 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.1588 | 1.40517 | 0.702584 | − | 0.711600i | \(-0.252029\pi\) | ||||
0.702584 | + | 0.711600i | \(0.252029\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 30.8393 | 2.37226 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.1104 | −0.849632 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.60318 | 0.121888 | 0.0609439 | − | 0.998141i | \(-0.480589\pi\) | ||||
0.0609439 | + | 0.998141i | \(0.480589\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.31695 | 0.553110 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.7705 | −0.959890 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.35905 | 0.475298 | 0.237649 | − | 0.971351i | \(-0.423623\pi\) | ||||
0.237649 | + | 0.971351i | \(0.423623\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.2799 | −1.06142 | −0.530709 | − | 0.847554i | \(-0.678074\pi\) | ||||
−0.530709 | + | 0.847554i | \(0.678074\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.54103 | −0.261760 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −25.4970 | −1.87458 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.861956 | 0.0630325 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.34936 | −0.243630 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.85686 | 0.713217 | 0.356609 | − | 0.934254i | \(-0.383933\pi\) | ||||
0.356609 | + | 0.934254i | \(0.383933\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.8826 | −1.79109 | −0.895545 | − | 0.444971i | \(-0.853214\pi\) | ||||
−0.895545 | + | 0.444971i | \(0.853214\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 31.3447 | 2.24464 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.59600 | −0.184957 | −0.0924787 | − | 0.995715i | \(-0.529479\pi\) | ||||
−0.0924787 | + | 0.995715i | \(0.529479\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.1845 | 1.00551 | 0.502755 | − | 0.864429i | \(-0.332320\pi\) | ||||
0.502755 | + | 0.864429i | \(0.332320\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.7396 | 0.757511 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.98151 | −0.209261 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.57133 | −0.528805 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.24640 | 0.225640 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.17954 | −0.0815902 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.99464 | −0.550374 | −0.275187 | − | 0.961391i | \(-0.588740\pi\) | ||||
−0.275187 | + | 0.961391i | \(0.588740\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.93467 | 0.543674 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −28.2511 | −1.92671 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.30524 | 0.156490 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.88721 | 0.397821 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 32.3031 | 2.17294 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.532491 | 0.0356583 | 0.0178291 | − | 0.999841i | \(-0.494325\pi\) | ||||
0.0178291 | + | 0.999841i | \(0.494325\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −19.5979 | −1.30653 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.38209 | −0.158105 | −0.0790525 | − | 0.996870i | \(-0.525189\pi\) | ||||
−0.0790525 | + | 0.996870i | \(0.525189\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.8726 | −1.51146 | −0.755732 | − | 0.654882i | \(-0.772719\pi\) | ||||
−0.755732 | + | 0.654882i | \(0.772719\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.126871 | −0.00834752 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.8670 | 1.17051 | 0.585253 | − | 0.810850i | \(-0.300995\pi\) | ||||
0.585253 | + | 0.810850i | \(0.300995\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.23280 | −0.145652 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.41525 | 0.546629 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.6266 | 1.01080 | 0.505401 | − | 0.862884i | \(-0.331344\pi\) | ||||
0.505401 | + | 0.862884i | \(0.331344\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.48709 | −0.353455 | −0.176727 | − | 0.984260i | \(-0.556551\pi\) | ||||
−0.176727 | + | 0.984260i | \(0.556551\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.7412 | 0.945651 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 27.0903 | 1.73074 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −44.2049 | −2.81269 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 21.0298 | 1.33271 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.344655 | 0.0216683 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 23.0964 | 1.44635 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.10440 | 0.505538 | 0.252769 | − | 0.967527i | \(-0.418659\pi\) | ||||
0.252769 | + | 0.967527i | \(0.418659\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.86766 | 0.240325 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.98575 | 0.494306 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.89980 | 0.610448 | 0.305224 | − | 0.952281i | \(-0.401269\pi\) | ||||
0.305224 | + | 0.952281i | \(0.401269\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.6435 | 1.08383 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.8668 | 1.09343 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.7770 | 0.718054 | 0.359027 | − | 0.933327i | \(-0.383109\pi\) | ||||
0.359027 | + | 0.933327i | \(0.383109\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.1836 | 1.83353 | 0.916763 | − | 0.399432i | \(-0.130793\pi\) | ||||
0.916763 | + | 0.399432i | \(0.130793\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.75469 | −0.287767 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.08062 | −0.125466 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −30.7074 | −1.84503 | −0.922516 | − | 0.385960i | \(-0.873870\pi\) | ||||
−0.922516 | + | 0.385960i | \(0.873870\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.17442 | −0.369653 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.98785 | 0.237895 | 0.118948 | − | 0.992901i | \(-0.462048\pi\) | ||||
0.118948 | + | 0.992901i | \(0.462048\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.9321 | 1.60095 | 0.800474 | − | 0.599368i | \(-0.204581\pi\) | ||||
0.800474 | + | 0.599368i | \(0.204581\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −31.6060 | −1.87218 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.14850 | 0.0677938 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.80261 | 0.400153 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.60113 | 0.562828 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.717962 | 0.0419438 | 0.0209719 | − | 0.999780i | \(-0.493324\pi\) | ||||
0.0209719 | + | 0.999780i | \(0.493324\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 45.2564 | 2.63493 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.952412 | 0.0552646 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.9165 | 0.746978 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.28543 | 0.247008 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.0897 | −0.637089 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.5488 | 0.718540 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.8617 | −1.47600 | −0.738001 | − | 0.674799i | \(-0.764230\pi\) | ||||
−0.738001 | + | 0.674799i | \(0.764230\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.54125 | −0.372119 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.54054 | −0.484290 | −0.242145 | − | 0.970240i | \(-0.577851\pi\) | ||||
−0.242145 | + | 0.970240i | \(0.577851\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.77877 | −0.326635 | −0.163318 | − | 0.986574i | \(-0.552220\pi\) | ||||
−0.163318 | + | 0.986574i | \(0.552220\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.23500 | 0.238615 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.7025 | 0.881941 | 0.440970 | − | 0.897522i | \(-0.354634\pi\) | ||||
0.440970 | + | 0.897522i | \(0.354634\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.847810 | 0.0474682 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.1647 | −1.01386 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −32.5724 | −1.81238 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −77.9743 | −4.32524 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.1000 | 0.890332 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.338695 | 0.0186728 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.5004 | 1.73142 | 0.865709 | − | 0.500548i | \(-0.166868\pi\) | ||||
0.865709 | + | 0.500548i | \(0.166868\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.3593 | −0.567684 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −38.0591 | −2.07939 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.5754 | 1.55660 | 0.778300 | − | 0.627893i | \(-0.216082\pi\) | ||||
0.778300 | + | 0.627893i | \(0.216082\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.4833 | 0.732315 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.655509 | −0.0354978 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.45854 | −0.456718 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.23513 | 0.497203 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.66818 | 0.519015 | 0.259507 | − | 0.965741i | \(-0.416440\pi\) | ||||
0.259507 | + | 0.965741i | \(0.416440\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.4603 | −1.09522 | −0.547608 | − | 0.836735i | \(-0.684462\pi\) | ||||
−0.547608 | + | 0.836735i | \(0.684462\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 35.6931 | 1.90515 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.3991 | −1.51153 | −0.755767 | − | 0.654841i | \(-0.772736\pi\) | ||||
−0.755767 | + | 0.654841i | \(0.772736\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −28.1190 | −1.49240 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.50351 | −0.185425 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.2598 | −0.699827 | −0.349914 | − | 0.936782i | \(-0.613789\pi\) | ||||
−0.349914 | + | 0.936782i | \(0.613789\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 25.5735 | 1.34597 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.6776 | −0.665404 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −20.8632 | −1.09203 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.13315 | 0.424547 | 0.212273 | − | 0.977210i | \(-0.431913\pi\) | ||||
0.212273 | + | 0.977210i | \(0.431913\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.07617 | −0.160139 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.67636 | −0.138950 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.63673 | 0.240081 | 0.120040 | − | 0.992769i | \(-0.461698\pi\) | ||||
0.120040 | + | 0.992769i | \(0.461698\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −32.0806 | −1.65664 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 31.7729 | 1.63639 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.92306 | 0.252881 | 0.126440 | − | 0.991974i | \(-0.459645\pi\) | ||||
0.126440 | + | 0.991974i | \(0.459645\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −20.1271 | −1.03114 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.8916 | −1.57849 | −0.789244 | − | 0.614080i | \(-0.789527\pi\) | ||||
−0.789244 | + | 0.614080i | \(0.789527\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.449610 | 0.0229142 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.4782 | −0.583471 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.8261 | 1.46154 | 0.730770 | − | 0.682624i | \(-0.239161\pi\) | ||||
0.730770 | + | 0.682624i | \(0.239161\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.51751 | 0.481321 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.5748 | −0.785642 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −29.8221 | −1.50051 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.2631 | −0.665654 | −0.332827 | − | 0.942988i | \(-0.608003\pi\) | ||||
−0.332827 | + | 0.942988i | \(0.608003\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.79434 | 0.240017 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.2827 | −0.513495 | −0.256748 | − | 0.966478i | \(-0.582651\pi\) | ||||
−0.256748 | + | 0.966478i | \(0.582651\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.5662 | −1.22373 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.07158 | 0.252009 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.09979 | −0.0545147 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.97111 | −0.146912 | −0.0734559 | − | 0.997298i | \(-0.523403\pi\) | ||||
−0.0734559 | + | 0.997298i | \(0.523403\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.17355 | 0.403172 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.86497 | −0.337803 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −74.5258 | −3.65833 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.5487 | 0.516571 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.443124 | 0.0216480 | 0.0108240 | − | 0.999941i | \(-0.496555\pi\) | ||||
0.0108240 | + | 0.999941i | \(0.496555\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.7536 | 0.719045 | 0.359522 | − | 0.933136i | \(-0.382940\pi\) | ||||
0.359522 | + | 0.933136i | \(0.382940\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.907170 | −0.0441081 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −57.4555 | −2.78700 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.90353 | −0.0921183 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.35203 | 0.0652764 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.6553 | 0.754091 | 0.377045 | − | 0.926195i | \(-0.376940\pi\) | ||||
0.377045 | + | 0.926195i | \(0.376940\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.6406 | 1.71278 | 0.856388 | − | 0.516332i | \(-0.172703\pi\) | ||||
0.856388 | + | 0.516332i | \(0.172703\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 22.7173 | 1.08921 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.0242 | −0.623030 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.10726 | −0.386938 | −0.193469 | − | 0.981106i | \(-0.561974\pi\) | ||||
−0.193469 | + | 0.981106i | \(0.561974\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.0066 | 0.524123 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.3263 | −1.06076 | −0.530378 | − | 0.847761i | \(-0.677950\pi\) | ||||
−0.530378 | + | 0.847761i | \(0.677950\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −63.3168 | −3.00150 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.66482 | 0.220639 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.9038 | −0.514582 | −0.257291 | − | 0.966334i | \(-0.582830\pi\) | ||||
−0.257291 | + | 0.966334i | \(0.582830\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.326583 | −0.0153782 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19.8418 | 0.932248 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.8498 | 0.789930 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.4789 | −0.817629 | −0.408814 | − | 0.912618i | \(-0.634058\pi\) | ||||
−0.408814 | + | 0.912618i | \(0.634058\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 26.3005 | 1.22760 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.16799 | −0.287272 | −0.143636 | − | 0.989631i | \(-0.545879\pi\) | ||||
−0.143636 | + | 0.989631i | \(0.545879\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.6042 | 0.585768 | 0.292884 | − | 0.956148i | \(-0.405385\pi\) | ||||
0.292884 | + | 0.956148i | \(0.405385\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −17.5646 | −0.814538 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −33.8888 | −1.56819 | −0.784093 | − | 0.620643i | \(-0.786871\pi\) | ||||
−0.784093 | + | 0.620643i | \(0.786871\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.77321 | 0.266582 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.9675 | −0.689665 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.21859 | −0.0560307 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 78.6245 | 3.60754 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.16843 | 0.328220 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 41.2752 | 1.88591 | 0.942956 | − | 0.332917i | \(-0.108033\pi\) | ||||
0.942956 | + | 0.332917i | \(0.108033\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −41.2164 | −1.87931 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.40088 | −0.0637424 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −34.0247 | −1.54498 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.0800 | −1.18180 | −0.590898 | − | 0.806746i | \(-0.701227\pi\) | ||||
−0.590898 | + | 0.806746i | \(0.701227\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.71958 | −0.0777623 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.95179 | −0.403989 | −0.201994 | − | 0.979387i | \(-0.564742\pi\) | ||||
−0.201994 | + | 0.979387i | \(0.564742\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.4120 | 1.05442 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.20425 | −0.0541269 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.26539 | 0.191329 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.94870 | 0.132002 | 0.0660010 | − | 0.997820i | \(-0.478976\pi\) | ||||
0.0660010 | + | 0.997820i | \(0.478976\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.9878 | 0.937666 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.04092 | −0.180176 | −0.0900878 | − | 0.995934i | \(-0.528715\pi\) | ||||
−0.0900878 | + | 0.995934i | \(0.528715\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 39.3001 | 1.74883 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 35.6439 | 1.58300 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.0547 | −0.445667 | −0.222834 | − | 0.974856i | \(-0.571531\pi\) | ||||
−0.222834 | + | 0.974856i | \(0.571531\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.16475 | 0.140000 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −35.9907 | −1.58903 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 23.1810 | 1.02148 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.0963099 | −0.00423570 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.85295 | 0.0813354 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.1483 | −0.619850 | −0.309925 | − | 0.950761i | \(-0.600304\pi\) | ||||
−0.309925 | + | 0.950761i | \(0.600304\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 44.6455 | 1.95221 | 0.976106 | − | 0.217295i | \(-0.0697234\pi\) | ||||
0.976106 | + | 0.217295i | \(0.0697234\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.45688 | 0.369089 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.1016 | −0.788520 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.1944 | −0.834539 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.3873 | 0.797942 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.2392 | −0.530138 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 64.3726 | 2.78307 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.34975 | 0.317165 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.16852 | 0.0503316 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 42.6957 | 1.83563 | 0.917816 | − | 0.397005i | \(-0.129951\pi\) | ||||
0.917816 | + | 0.397005i | \(0.129951\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16.5046 | −0.708281 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −57.0555 | −2.44399 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.3069 | −1.59513 | −0.797563 | − | 0.603235i | \(-0.793878\pi\) | ||||
−0.797563 | + | 0.603235i | \(0.793878\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.09847 | 0.217597 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −32.0379 | −1.36486 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.52374 | 0.192369 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −29.4693 | −1.25090 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.47875 | −0.274514 | −0.137257 | − | 0.990536i | \(-0.543829\pi\) | ||||
−0.137257 | + | 0.990536i | \(0.543829\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −45.6684 | −1.93157 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.996243 | 0.0420614 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.47270 | −0.0620671 | −0.0310335 | − | 0.999518i | \(-0.509880\pi\) | ||||
−0.0310335 | + | 0.999518i | \(0.509880\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −47.7826 | −2.01023 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.769311 | −0.0323080 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −30.0094 | −1.25806 | −0.629030 | − | 0.777381i | \(-0.716548\pi\) | ||||
−0.629030 | + | 0.777381i | \(0.716548\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.9014 | 1.41873 | 0.709366 | − | 0.704841i | \(-0.248981\pi\) | ||||
0.709366 | + | 0.704841i | \(0.248981\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.3925 | 0.475928 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22.9737 | −0.958069 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.4242 | 1.10005 | 0.550027 | − | 0.835147i | \(-0.314618\pi\) | ||||
0.550027 | + | 0.835147i | \(0.314618\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −28.7592 | −1.19519 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.3049 | 0.469005 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.761038 | 0.0315190 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −45.1309 | −1.86593 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 31.1846 | 1.28713 | 0.643563 | − | 0.765393i | \(-0.277455\pi\) | ||||
0.643563 | + | 0.765393i | \(0.277455\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.7710 | 1.02067 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.00044 | −0.123422 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.9552 | 0.449875 | 0.224938 | − | 0.974373i | \(-0.427782\pi\) | ||||
0.224938 | + | 0.974373i | \(0.427782\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.4158 | 0.508998 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.3943 | 0.670974 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −34.2254 | −1.39841 | −0.699206 | − | 0.714920i | \(-0.746463\pi\) | ||||
−0.699206 | + | 0.714920i | \(0.746463\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.0090 | 0.530647 | 0.265323 | − | 0.964159i | \(-0.414521\pi\) | ||||
0.265323 | + | 0.964159i | \(0.414521\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.4631 | −0.629708 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 44.9273 | 1.82655 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.895769 | 0.0363581 | 0.0181791 | − | 0.999835i | \(-0.494213\pi\) | ||||
0.0181791 | + | 0.999835i | \(0.494213\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.44601 | −0.139639 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.60936 | −0.146019 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.1728 | 0.653212 | 0.326606 | − | 0.945161i | \(-0.394095\pi\) | ||||
0.326606 | + | 0.945161i | \(0.394095\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.75089 | −0.352870 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.5442 | 0.545267 | 0.272633 | − | 0.962118i | \(-0.412105\pi\) | ||||
0.272633 | + | 0.962118i | \(0.412105\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.95361 | 0.319683 | 0.159841 | − | 0.987143i | \(-0.448902\pi\) | ||||
0.159841 | + | 0.987143i | \(0.448902\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.5163 | 0.422005 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.60456 | 0.384799 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 54.8051 | 2.19220 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.36330 | −0.0544449 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −30.3704 | −1.21095 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.8274 | 1.14760 | 0.573800 | − | 0.818995i | \(-0.305469\pi\) | ||||
0.573800 | + | 0.818995i | \(0.305469\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.24015 | −0.367263 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 71.3267 | 2.83051 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 43.7919 | 1.73510 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.4246 | −0.451948 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.1175 | 1.54505 | 0.772524 | − | 0.634985i | \(-0.218994\pi\) | ||||
0.772524 | + | 0.634985i | \(0.218994\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.17610 | 0.243562 | 0.121781 | − | 0.992557i | \(-0.461139\pi\) | ||||
0.121781 | + | 0.992557i | \(0.461139\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −32.6525 | −1.28569 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.77971 | 0.187910 | 0.0939548 | − | 0.995576i | \(-0.470049\pi\) | ||||
0.0939548 | + | 0.995576i | \(0.470049\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.95210 | 0.0766265 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.66438 | 0.104425 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.9339 | −0.506144 | −0.253072 | − | 0.967447i | \(-0.581441\pi\) | ||||
−0.253072 | + | 0.967447i | \(0.581441\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 55.1941 | 2.15661 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.47657 | −0.330702 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.6390 | 1.15457 | 0.577285 | − | 0.816543i | \(-0.304112\pi\) | ||||
0.577285 | + | 0.816543i | \(0.304112\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.1729 | 1.40696 | 0.703481 | − | 0.710714i | \(-0.251628\pi\) | ||||
0.703481 | + | 0.710714i | \(0.251628\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 37.3357 | 1.45000 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.9903 | −0.658855 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.36131 | 0.362471 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.615450 | 0.0237947 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.541280 | 0.0208959 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.81880 | −0.301393 | −0.150696 | − | 0.988580i | \(-0.548152\pi\) | ||||
−0.150696 | + | 0.988580i | \(0.548152\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −63.4850 | −2.44354 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.61795 | −0.139049 | −0.0695245 | − | 0.997580i | \(-0.522148\pi\) | ||||
−0.0695245 | + | 0.997580i | \(0.522148\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.16123 | 0.198070 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.75321 | −0.105503 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.68227 | 0.0643704 | 0.0321852 | − | 0.999482i | \(-0.489753\pi\) | ||||
0.0321852 | + | 0.999482i | \(0.489753\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −28.9656 | −1.10672 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.4360 | −1.00860 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28.5210 | 1.08657 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.8337 | −1.51534 | −0.757672 | − | 0.652635i | \(-0.773663\pi\) | ||||
−0.757672 | + | 0.652635i | \(0.773663\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.182673 | 0.00693917 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −37.3826 | −1.41800 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.01846 | −0.341599 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 20.6506 | 0.781076 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.65966 | −0.0626845 | −0.0313423 | − | 0.999509i | \(-0.509978\pi\) | ||||
−0.0313423 | + | 0.999509i | \(0.509978\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41.5601 | 1.56747 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.58065 | −0.0971931 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.96145 | −0.224204 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.3607 | 0.727105 | 0.363552 | − | 0.931574i | \(-0.381564\pi\) | ||||
0.363552 | + | 0.931574i | \(0.381564\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.1165 | −0.454405 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.23798 | −0.271064 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.79134 | −0.179186 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18.0612 | 0.674506 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.7607 | −0.662363 | −0.331181 | − | 0.943567i | \(-0.607447\pi\) | ||||
−0.331181 | + | 0.943567i | \(0.607447\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.51635 | −0.130956 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.34194 | −0.235859 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −56.5126 | −2.09882 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.3612 | −1.08895 | −0.544473 | − | 0.838779i | \(-0.683270\pi\) | ||||
−0.544473 | + | 0.838779i | \(0.683270\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.7524 | 0.768609 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −33.6509 | −1.24462 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.9740 | −1.03324 | −0.516622 | − | 0.856214i | \(-0.672811\pi\) | ||||
−0.516622 | + | 0.856214i | \(0.672811\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 31.3108 | 1.15492 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.64165 | −0.0604709 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.94807 | −0.145232 | −0.0726160 | − | 0.997360i | \(-0.523135\pi\) | ||||
−0.0726160 | + | 0.997360i | \(0.523135\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −51.0917 | −1.87690 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.8304 | −0.470701 | −0.235351 | − | 0.971911i | \(-0.575624\pi\) | ||||
−0.235351 | + | 0.971911i | \(0.575624\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.5313 | −0.605660 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −30.2793 | −1.10786 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.76472 | −0.356795 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.6222 | 0.387611 | 0.193805 | − | 0.981040i | \(-0.437917\pi\) | ||||
0.193805 | + | 0.981040i | \(0.437917\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.15579 | 0.0421194 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −70.3157 | −2.55905 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.07752 | 0.0755086 | 0.0377543 | − | 0.999287i | \(-0.487980\pi\) | ||||
0.0377543 | + | 0.999287i | \(0.487980\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.398350 | 0.0144592 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.610314 | 0.0221239 | 0.0110619 | − | 0.999939i | \(-0.496479\pi\) | ||||
0.0110619 | + | 0.999939i | \(0.496479\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.65479 | 0.313324 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −33.2548 | −1.20233 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 73.1577 | 2.64157 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.9945 | 1.55042 | 0.775210 | − | 0.631704i | \(-0.217644\pi\) | ||||
0.775210 | + | 0.631704i | \(0.217644\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.36701 | 0.337344 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.3483 | 1.01962 | 0.509809 | − | 0.860288i | \(-0.329716\pi\) | ||||
0.509809 | + | 0.860288i | \(0.329716\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 43.6944 | 1.56955 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.47022 | 0.160368 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.3412 | 0.442170 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.21289 | −0.0434006 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 25.8689 | 0.924478 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 53.0421 | 1.89315 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.3435 | −1.36680 | −0.683399 | − | 0.730045i | \(-0.739499\pi\) | ||||
−0.683399 | + | 0.730045i | \(0.739499\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.4421 | 0.407350 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.24817 | 0.257715 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.2853 | 0.720351 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 20.3923 | 0.723239 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.48153 | 0.265010 | 0.132505 | − | 0.991182i | \(-0.457698\pi\) | ||||
0.132505 | + | 0.991182i | \(0.457698\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.65956 | −0.0940886 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −25.7251 | −0.908953 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.899917 | −0.0317574 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.96448 | 0.174975 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.6117 | 0.479156 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 34.6803 | 1.21929 | 0.609646 | − | 0.792674i | \(-0.291311\pi\) | ||||
0.609646 | + | 0.792674i | \(0.291311\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.0793 | −1.37226 | −0.686130 | − | 0.727479i | \(-0.740692\pi\) | ||||
−0.686130 | + | 0.727479i | \(0.740692\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 34.8860 | 1.22351 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.09390 | 0.213460 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 46.0492 | 1.61106 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.84594 | 0.239217 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.7662 | −0.794545 | −0.397273 | − | 0.917701i | \(-0.630043\pi\) | ||||
−0.397273 | + | 0.917701i | \(0.630043\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.9505 | −0.730289 | −0.365145 | − | 0.930951i | \(-0.618980\pi\) | ||||
−0.365145 | + | 0.930951i | \(0.618980\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.40476 | −0.0837232 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.80711 | −0.271480 | −0.135740 | − | 0.990744i | \(-0.543341\pi\) | ||||
−0.135740 | + | 0.990744i | \(0.543341\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.4966 | −1.23285 | −0.616423 | − | 0.787415i | \(-0.711419\pi\) | ||||
−0.616423 | + | 0.787415i | \(0.711419\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −35.4914 | −1.23118 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 32.2682 | 1.11803 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −74.3770 | −2.57392 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −20.0013 | −0.691345 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 28.3734 | 0.979559 | 0.489780 | − | 0.871846i | \(-0.337077\pi\) | ||||
0.489780 | + | 0.871846i | \(0.337077\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.97228 | −0.205941 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.60913 | 0.158747 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −126.316 | −4.34539 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.81505 | −0.234168 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 31.1279 | 1.06831 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.1437 | −0.416279 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.0270 | 1.67865 | 0.839326 | − | 0.543628i | \(-0.182950\pi\) | ||||
0.839326 | + | 0.543628i | \(0.182950\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 45.5072 | 1.55632 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −32.1040 | −1.09665 | −0.548325 | − | 0.836265i | \(-0.684734\pi\) | ||||
−0.548325 | + | 0.836265i | \(0.684734\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.31632 | −0.283749 | −0.141875 | − | 0.989885i | \(-0.545313\pi\) | ||||
−0.141875 | + | 0.989885i | \(0.545313\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.32743 | 0.0452386 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46.7903 | −1.59276 | −0.796380 | − | 0.604796i | \(-0.793255\pi\) | ||||
−0.796380 | + | 0.604796i | \(0.793255\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.56652 | −0.223268 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.86240 | 0.267021 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.28635 | −0.0436365 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −61.5232 | −2.08463 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13.8240 | −0.467871 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −17.2454 | −0.583001 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.5910 | 0.594007 | 0.297004 | − | 0.954876i | \(-0.404013\pi\) | ||||
0.297004 | + | 0.954876i | \(0.404013\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.829815 | 0.0279890 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.9312 | −1.44639 | −0.723195 | − | 0.690644i | \(-0.757327\pi\) | ||||
−0.723195 | + | 0.690644i | \(0.757327\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.2432 | 0.546628 | 0.273314 | − | 0.961925i | \(-0.411880\pi\) | ||||
0.273314 | + | 0.961925i | \(0.411880\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 52.3070 | 1.75828 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.1735 | 0.912398 | 0.456199 | − | 0.889878i | \(-0.349210\pi\) | ||||
0.456199 | + | 0.889878i | \(0.349210\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.8196 | −0.362877 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.218758 | 0.00732867 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.63945 | 0.121790 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26.0462 | −0.870628 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.9287 | 0.498456 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.8046 | −0.593815 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.0158 | 0.700138 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.95307 | 0.164828 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 58.4894 | 1.94425 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.4060 | 1.07602 | 0.538011 | − | 0.842938i | \(-0.319176\pi\) | ||||
0.538011 | + | 0.842938i | \(0.319176\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.9673 | 0.529603 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.2655 | −0.737688 | −0.368844 | − | 0.929491i | \(-0.620246\pi\) | ||||
−0.368844 | + | 0.929491i | \(0.620246\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.21461 | −0.106388 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14.5038 | 0.479480 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.37244 | −0.276482 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53.9357 | 1.77918 | 0.889588 | − | 0.456764i | \(-0.150992\pi\) | ||||
0.889588 | + | 0.456764i | \(0.150992\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29.8907 | −0.984933 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −45.4549 | −1.49617 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 73.3090 | 2.41039 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.41828 | 0.309337 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.0362 | 0.985456 | 0.492728 | − | 0.870183i | \(-0.336000\pi\) | ||||
0.492728 | + | 0.870183i | \(0.336000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −44.1571 | −1.44719 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.87110 | −0.323165 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.53051 | −0.115460 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.90313 | 0.160178 | 0.0800892 | − | 0.996788i | \(-0.474479\pi\) | ||||
0.0800892 | + | 0.996788i | \(0.474479\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.67906 | −0.217963 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.8436 | −1.13587 | −0.567934 | − | 0.823074i | \(-0.692257\pi\) | ||||
−0.567934 | + | 0.823074i | \(0.692257\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.60605 | −0.117429 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.7187 | 0.446271 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −53.9666 | −1.75368 | −0.876840 | − | 0.480782i | \(-0.840353\pi\) | ||||
−0.876840 | + | 0.480782i | \(0.840353\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −33.7257 | −1.09478 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.1489 | 0.588517 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.8743 | 0.579005 | 0.289502 | − | 0.957177i | \(-0.406510\pi\) | ||||
0.289502 | + | 0.957177i | \(0.406510\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −40.3729 | −1.30644 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.979893 | 0.0316754 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.39381 | 0.141884 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.2339 | −0.555931 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 26.1541 | 0.842804 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 101.917 | 3.28083 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.2898 | 0.909739 | 0.454869 | − | 0.890558i | \(-0.349686\pi\) | ||||
0.454869 | + | 0.890558i | \(0.349686\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −37.6470 | −1.20940 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.5535 | 0.370770 | 0.185385 | − | 0.982666i | \(-0.440647\pi\) | ||||
0.185385 | + | 0.982666i | \(0.440647\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.67060 | 0.181791 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −90.1221 | −2.88622 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.3097 | −0.873714 | −0.436857 | − | 0.899531i | \(-0.643908\pi\) | ||||
−0.436857 | + | 0.899531i | \(0.643908\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.73112 | −0.0872868 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.1812 | −0.740119 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.50331 | −0.175528 | −0.0877641 | − | 0.996141i | \(-0.527972\pi\) | ||||
−0.0877641 | + | 0.996141i | \(0.527972\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.6330 | 0.338796 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.391461 | 0.0124603 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.4554 | −0.427855 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.3080 | 0.708636 | 0.354318 | − | 0.935125i | \(-0.384713\pi\) | ||||
0.354318 | + | 0.935125i | \(0.384713\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 36.4079 | 1.15537 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −58.0985 | −1.84184 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.01117 | −0.0320240 | −0.0160120 | − | 0.999872i | \(-0.505097\pi\) | ||||
−0.0160120 | + | 0.999872i | \(0.505097\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −33.5575 | −1.06171 |
(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 | 4016.2.a.m.1.15 | 23 | ||
4.3 | odd | 2 | 2008.2.a.d.1.9 | ✓ | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.2.a.d.1.9 | ✓ | 23 | 4.3 | odd | 2 | ||
4016.2.a.m.1.15 | 23 | 1.1 | even | 1 | trivial |