Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4024,2,Mod(1,4024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4024, 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("4024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4024 = 2^{3} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4024.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: | \(32.1318017734\) |
Analytic rank: | \(0\) |
Dimension: | \(33\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 4024.1 |
$q$-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 | ||||||||
\(3\) | −0.648270 | −0.374279 | −0.187140 | − | 0.982333i | \(-0.559922\pi\) | ||||
−0.187140 | + | 0.982333i | \(0.559922\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.57860 | 1.15318 | 0.576592 | − | 0.817032i | \(-0.304382\pi\) | ||||
0.576592 | + | 0.817032i | \(0.304382\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.91468 | −0.723681 | −0.361841 | − | 0.932240i | \(-0.617852\pi\) | ||||
−0.361841 | + | 0.932240i | \(0.617852\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.57975 | −0.859915 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.67275 | −0.805863 | −0.402932 | − | 0.915230i | \(-0.632009\pi\) | ||||
−0.402932 | + | 0.915230i | \(0.632009\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.76049 | −0.765623 | −0.382811 | − | 0.923827i | \(-0.625044\pi\) | ||||
−0.382811 | + | 0.923827i | \(0.625044\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.67163 | −0.431613 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.56676 | −1.35014 | −0.675068 | − | 0.737755i | \(-0.735886\pi\) | ||||
−0.675068 | + | 0.737755i | \(0.735886\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.65257 | 1.29679 | 0.648394 | − | 0.761305i | \(-0.275441\pi\) | ||||
0.648394 | + | 0.761305i | \(0.275441\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.24123 | 0.270859 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.28435 | −0.267805 | −0.133903 | − | 0.990994i | \(-0.542751\pi\) | ||||
−0.133903 | + | 0.990994i | \(0.542751\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.64916 | 0.329833 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.61718 | 0.696127 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.23268 | −0.600293 | −0.300147 | − | 0.953893i | \(-0.597036\pi\) | ||||
−0.300147 | + | 0.953893i | \(0.597036\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.44930 | 0.439908 | 0.219954 | − | 0.975510i | \(-0.429409\pi\) | ||||
0.219954 | + | 0.975510i | \(0.429409\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.73266 | 0.301618 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.93719 | −0.834537 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.30868 | −0.215145 | −0.107573 | − | 0.994197i | \(-0.534308\pi\) | ||||
−0.107573 | + | 0.994197i | \(0.534308\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.78955 | 0.286557 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.94787 | 1.39742 | 0.698711 | − | 0.715404i | \(-0.253757\pi\) | ||||
0.698711 | + | 0.715404i | \(0.253757\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.24431 | 0.342254 | 0.171127 | − | 0.985249i | \(-0.445259\pi\) | ||||
0.171127 | + | 0.985249i | \(0.445259\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.65212 | −0.991640 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.6304 | 1.55060 | 0.775299 | − | 0.631594i | \(-0.217599\pi\) | ||||
0.775299 | + | 0.631594i | \(0.217599\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.33400 | −0.476286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.60876 | 0.505328 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.69860 | 1.05748 | 0.528742 | − | 0.848783i | \(-0.322664\pi\) | ||||
0.528742 | + | 0.848783i | \(0.322664\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.89193 | −0.929308 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.66439 | −0.485361 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.71042 | 0.613245 | 0.306622 | − | 0.951831i | \(-0.400801\pi\) | ||||
0.306622 | + | 0.951831i | \(0.400801\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.59506 | 1.10048 | 0.550242 | − | 0.835005i | \(-0.314535\pi\) | ||||
0.550242 | + | 0.835005i | \(0.314535\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.93939 | 0.622304 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.11820 | −0.882904 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0357 | 1.47040 | 0.735199 | − | 0.677851i | \(-0.237089\pi\) | ||||
0.735199 | + | 0.677851i | \(0.237089\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.832606 | 0.100234 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.07555 | 1.07707 | 0.538535 | − | 0.842603i | \(-0.318978\pi\) | ||||
0.538535 | + | 0.842603i | \(0.318978\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.09100 | −0.244733 | −0.122366 | − | 0.992485i | \(-0.539048\pi\) | ||||
−0.122366 | + | 0.992485i | \(0.539048\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.06910 | −0.123449 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.11745 | 0.583188 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.24817 | −0.252939 | −0.126470 | − | 0.991970i | \(-0.540365\pi\) | ||||
−0.126470 | + | 0.991970i | \(0.540365\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.39432 | 0.599369 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.3986 | 1.79998 | 0.899990 | − | 0.435911i | \(-0.143574\pi\) | ||||
0.899990 | + | 0.435911i | \(0.143574\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.3544 | −1.55696 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.09565 | 0.224677 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.73787 | 0.396213 | 0.198107 | − | 0.980180i | \(-0.436521\pi\) | ||||
0.198107 | + | 0.980180i | \(0.436521\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.28546 | 0.554067 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.58781 | −0.164648 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.5757 | 1.49544 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.84264 | −0.187092 | −0.0935460 | − | 0.995615i | \(-0.529820\pi\) | ||||
−0.0935460 | + | 0.995615i | \(0.529820\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.89500 | 0.692974 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.36849 | −0.235674 | −0.117837 | − | 0.993033i | \(-0.537596\pi\) | ||||
−0.117837 | + | 0.993033i | \(0.537596\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.80611 | −0.572093 | −0.286046 | − | 0.958216i | \(-0.592341\pi\) | ||||
−0.286046 | + | 0.958216i | \(0.592341\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.20063 | 0.312350 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.00579 | −0.290581 | −0.145291 | − | 0.989389i | \(-0.546412\pi\) | ||||
−0.145291 | + | 0.989389i | \(0.546412\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.2203 | 1.74518 | 0.872592 | − | 0.488450i | \(-0.162437\pi\) | ||||
0.872592 | + | 0.488450i | \(0.162437\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.848377 | 0.0805244 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −20.6599 | −1.94352 | −0.971758 | − | 0.235979i | \(-0.924170\pi\) | ||||
−0.971758 | + | 0.235979i | \(0.924170\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.31182 | −0.308829 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.12137 | 0.658371 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.6586 | 0.977069 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.85643 | −0.350585 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.80064 | −0.523026 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.64046 | −0.772826 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.72813 | 0.419554 | 0.209777 | − | 0.977749i | \(-0.432726\pi\) | ||||
0.209777 | + | 0.977749i | \(0.432726\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.45492 | −0.128098 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.40430 | 0.122694 | 0.0613470 | − | 0.998116i | \(-0.480460\pi\) | ||||
0.0613470 | + | 0.998116i | \(0.480460\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.8229 | −0.938462 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.32726 | 0.802763 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.74666 | 0.320099 | 0.160049 | − | 0.987109i | \(-0.448835\pi\) | ||||
0.160049 | + | 0.987109i | \(0.448835\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.2043 | 1.54407 | 0.772034 | − | 0.635582i | \(-0.219240\pi\) | ||||
0.772034 | + | 0.635582i | \(0.219240\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.89135 | −0.580357 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.37809 | 0.616987 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.33577 | −0.692248 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.16133 | 0.178264 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.82576 | −0.313418 | −0.156709 | − | 0.987645i | \(-0.550089\pi\) | ||||
−0.156709 | + | 0.987645i | \(0.550089\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.5593 | −1.18482 | −0.592410 | − | 0.805637i | \(-0.701823\pi\) | ||||
−0.592410 | + | 0.805637i | \(0.701823\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.3608 | 1.16100 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.31577 | 0.507295 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.19924 | −0.335136 | −0.167568 | − | 0.985861i | \(-0.553591\pi\) | ||||
−0.167568 | + | 0.985861i | \(0.553591\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.99077 | −0.395794 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.45912 | 0.193806 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.7761 | −1.31400 | −0.657002 | − | 0.753889i | \(-0.728176\pi\) | ||||
−0.657002 | + | 0.753889i | \(0.728176\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.46784 | 0.347821 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.23614 | −0.327802 | −0.163901 | − | 0.986477i | \(-0.552408\pi\) | ||||
−0.163901 | + | 0.986477i | \(0.552408\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.37968 | −0.413822 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.5822 | −1.11513 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.92393 | −0.602445 | −0.301223 | − | 0.953554i | \(-0.597395\pi\) | ||||
−0.301223 | + | 0.953554i | \(0.597395\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.15762 | −0.238694 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.05363 | −0.229525 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.95476 | −0.295593 | −0.147796 | − | 0.989018i | \(-0.547218\pi\) | ||||
−0.147796 | + | 0.989018i | \(0.547218\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.1875 | 1.42620 | 0.713099 | − | 0.701063i | \(-0.247291\pi\) | ||||
0.713099 | + | 0.701063i | \(0.247291\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.57192 | −0.411888 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.37455 | −0.248102 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.8785 | 1.08803 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.92575 | −0.503774 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.40078 | −0.246072 | −0.123036 | − | 0.992402i | \(-0.539263\pi\) | ||||
−0.123036 | + | 0.992402i | \(0.539263\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.8697 | −0.782418 | −0.391209 | − | 0.920302i | \(-0.627943\pi\) | ||||
−0.391209 | + | 0.920302i | \(0.627943\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.61452 | 0.330452 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.3891 | 0.882690 | 0.441345 | − | 0.897337i | \(-0.354501\pi\) | ||||
0.441345 | + | 0.897337i | \(0.354501\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.74391 | −0.690727 | −0.345364 | − | 0.938469i | \(-0.612244\pi\) | ||||
−0.345364 | + | 0.938469i | \(0.612244\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.80241 | −0.550339 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.18955 | 0.434421 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 23.0729 | 1.61148 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.31329 | 0.230290 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.1079 | −1.04503 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.14740 | −0.354361 | −0.177181 | − | 0.984178i | \(-0.556698\pi\) | ||||
−0.177181 | + | 0.984178i | \(0.556698\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.88341 | −0.403125 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.78716 | 0.394681 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.68963 | −0.318353 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.35553 | 0.0915984 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.3670 | 1.03370 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.7951 | 0.990751 | 0.495376 | − | 0.868679i | \(-0.335030\pi\) | ||||
0.495376 | + | 0.868679i | \(0.335030\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.25442 | −0.283628 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.64011 | −0.374347 | −0.187174 | − | 0.982327i | \(-0.559933\pi\) | ||||
−0.187174 | + | 0.982327i | \(0.559933\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.11347 | 0.0735800 | 0.0367900 | − | 0.999323i | \(-0.488287\pi\) | ||||
0.0367900 | + | 0.999323i | \(0.488287\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.31749 | −0.218275 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.4053 | −1.33679 | −0.668397 | − | 0.743804i | \(-0.733019\pi\) | ||||
−0.668397 | + | 0.743804i | \(0.733019\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 27.4114 | 1.78812 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.45742 | 0.0946699 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.05079 | 0.520763 | 0.260381 | − | 0.965506i | \(-0.416152\pi\) | ||||
0.260381 | + | 0.965506i | \(0.416152\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.1149 | 0.844807 | 0.422403 | − | 0.906408i | \(-0.361187\pi\) | ||||
0.422403 | + | 0.906408i | \(0.361187\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.3485 | −0.920459 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.59704 | −0.549245 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.6039 | −0.992851 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.6307 | −0.673695 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.70438 | −0.423176 | −0.211588 | − | 0.977359i | \(-0.567864\pi\) | ||||
−0.211588 | + | 0.977359i | \(0.567864\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.43274 | 0.215814 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.30555 | 0.582736 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.7157 | 1.22983 | 0.614916 | − | 0.788593i | \(-0.289190\pi\) | ||||
0.614916 | + | 0.788593i | \(0.289190\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.50570 | 0.155697 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.33949 | 0.516201 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.80491 | −0.172958 | −0.0864791 | − | 0.996254i | \(-0.527562\pi\) | ||||
−0.0864791 | + | 0.996254i | \(0.527562\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.8516 | 1.21947 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.42315 | −0.148294 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.8295 | 0.660285 | 0.330143 | − | 0.943931i | \(-0.392903\pi\) | ||||
0.330143 | + | 0.943931i | \(0.392903\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.98337 | 0.181227 | 0.0906133 | − | 0.995886i | \(-0.471117\pi\) | ||||
0.0906133 | + | 0.995886i | \(0.471117\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.42641 | −0.207376 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.40779 | −0.265800 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.96101 | 0.598499 | 0.299249 | − | 0.954175i | \(-0.403264\pi\) | ||||
0.299249 | + | 0.954175i | \(0.403264\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.31858 | −0.378283 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.84482 | −0.110053 | −0.0550264 | − | 0.998485i | \(-0.517524\pi\) | ||||
−0.0550264 | + | 0.998485i | \(0.517524\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 29.7679 | 1.76952 | 0.884760 | − | 0.466047i | \(-0.154322\pi\) | ||||
0.884760 | + | 0.466047i | \(0.154322\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.44900 | −0.559710 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −17.1323 | −1.01129 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.9888 | 0.822870 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.19453 | 0.0700246 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.7148 | 1.21017 | 0.605087 | − | 0.796159i | \(-0.293138\pi\) | ||||
0.605087 | + | 0.796159i | \(0.293138\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.1463 | 0.707184 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.66781 | −0.560983 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.54544 | 0.205038 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.29713 | −0.247682 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.53542 | 0.0882078 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 22.1632 | 1.26906 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.3197 | −0.646051 | −0.323026 | − | 0.946390i | \(-0.604700\pi\) | ||||
−0.323026 | + | 0.946390i | \(0.604700\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.76393 | 0.214122 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.6967 | 1.17360 | 0.586801 | − | 0.809731i | \(-0.300387\pi\) | ||||
0.586801 | + | 0.809731i | \(0.300387\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.6375 | 1.84478 | 0.922389 | − | 0.386262i | \(-0.126234\pi\) | ||||
0.922389 | + | 0.386262i | \(0.126234\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 12.7367 | 0.717631 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.3782 | −0.807558 | −0.403779 | − | 0.914856i | \(-0.632304\pi\) | ||||
−0.403779 | + | 0.914856i | \(0.632304\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.64013 | 0.483754 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.94857 | 0.108758 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −31.4665 | −1.75084 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.55250 | −0.252527 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.8117 | −0.653186 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −20.3538 | −1.12214 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.1108 | −1.16036 | −0.580178 | − | 0.814489i | \(-0.697017\pi\) | ||||
−0.580178 | + | 0.814489i | \(0.697017\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.37606 | 0.185007 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 31.0353 | 1.69564 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.53486 | −0.192556 | −0.0962781 | − | 0.995354i | \(-0.530694\pi\) | ||||
−0.0962781 | + | 0.995354i | \(0.530694\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.3932 | 0.727418 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.54636 | −0.354506 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.7863 | 1.06836 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.14695 | 0.115588 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.89530 | −0.531207 | −0.265604 | − | 0.964082i | \(-0.585571\pi\) | ||||
−0.265604 | + | 0.964082i | \(0.585571\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.2859 | −0.550594 | −0.275297 | − | 0.961359i | \(-0.588776\pi\) | ||||
−0.275297 | + | 0.961359i | \(0.588776\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.98521 | −0.532971 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.0825 | −1.22856 | −0.614278 | − | 0.789090i | \(-0.710553\pi\) | ||||
−0.614278 | + | 0.789090i | \(0.710553\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 23.4022 | 1.24206 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.90963 | −0.365696 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.7149 | 0.671068 | 0.335534 | − | 0.942028i | \(-0.391083\pi\) | ||||
0.335534 | + | 0.942028i | \(0.391083\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.9516 | 0.681661 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.50001 | 0.131217 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.39184 | −0.282222 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.8194 | 0.877963 | 0.438981 | − | 0.898496i | \(-0.355339\pi\) | ||||
0.438981 | + | 0.898496i | \(0.355339\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −23.0832 | −1.20166 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.7404 | −0.765281 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.25938 | −0.0652080 | −0.0326040 | − | 0.999468i | \(-0.510380\pi\) | ||||
−0.0326040 | + | 0.999468i | \(0.510380\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.60135 | 0.289253 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.92378 | 0.459598 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.5546 | 0.798988 | 0.399494 | − | 0.916736i | \(-0.369186\pi\) | ||||
0.399494 | + | 0.916736i | \(0.369186\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.06511 | −0.157030 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.9081 | −1.27274 | −0.636371 | − | 0.771383i | \(-0.719565\pi\) | ||||
−0.636371 | + | 0.771383i | \(0.719565\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.1958 | 0.672523 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.78974 | −0.294309 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.9475 | 0.605761 | 0.302880 | − | 0.953029i | \(-0.402052\pi\) | ||||
0.302880 | + | 0.953029i | \(0.402052\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.14966 | 0.361574 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.910365 | −0.0459218 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.79713 | −0.291685 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.8350 | −1.54757 | −0.773783 | − | 0.633451i | \(-0.781638\pi\) | ||||
−0.773783 | + | 0.633451i | \(0.781638\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.01614 | 0.351247 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.5310 | 0.875456 | 0.437728 | − | 0.899108i | \(-0.355783\pi\) | ||||
0.437728 | + | 0.899108i | \(0.355783\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.76128 | −0.336804 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.9098 | 0.691183 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.49776 | 0.173378 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.5063 | 0.964526 | 0.482263 | − | 0.876027i | \(-0.339815\pi\) | ||||
0.482263 | + | 0.876027i | \(0.339815\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.42885 | −0.119806 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.01895 | −0.443794 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 42.2854 | 2.07571 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.8013 | −0.577912 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.1343 | 1.08133 | 0.540665 | − | 0.841238i | \(-0.318173\pi\) | ||||
0.540665 | + | 0.841238i | \(0.318173\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.06389 | −0.198062 | −0.0990310 | − | 0.995084i | \(-0.531574\pi\) | ||||
−0.0990310 | + | 0.995084i | \(0.531574\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −27.4236 | −1.33338 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.18049 | −0.445319 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.4568 | −0.796400 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.78300 | −0.230925 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.03357 | −0.0979538 | −0.0489769 | − | 0.998800i | \(-0.515596\pi\) | ||||
−0.0489769 | + | 0.998800i | \(0.515596\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.7584 | 1.18981 | 0.594907 | − | 0.803794i | \(-0.297189\pi\) | ||||
0.594907 | + | 0.803794i | \(0.297189\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.40384 | 0.259094 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.25988 | −0.347287 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.06163 | −0.337033 | −0.168517 | − | 0.985699i | \(-0.553898\pi\) | ||||
−0.168517 | + | 0.985699i | \(0.553898\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.60087 | 0.409565 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.8472 | 0.657900 | 0.328950 | − | 0.944347i | \(-0.393305\pi\) | ||||
0.328950 | + | 0.944347i | \(0.393305\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.63846 | 0.456907 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.48012 | 0.117306 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.1112 | 0.477179 | 0.238589 | − | 0.971121i | \(-0.423315\pi\) | ||||
0.238589 | + | 0.971121i | \(0.423315\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −23.9154 | −1.12613 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.43836 | 0.443453 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.6291 | 0.638941 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.97208 | −0.466474 | −0.233237 | − | 0.972420i | \(-0.574932\pi\) | ||||
−0.233237 | + | 0.972420i | \(0.574932\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −20.1360 | −0.939867 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.8329 | 1.66890 | 0.834452 | − | 0.551081i | \(-0.185785\pi\) | ||||
0.834452 | + | 0.551081i | \(0.185785\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.2210 | 0.614432 | 0.307216 | − | 0.951640i | \(-0.400603\pi\) | ||||
0.307216 | + | 0.951640i | \(0.400603\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.09432 | −0.189870 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.9241 | −0.968252 | −0.484126 | − | 0.874998i | \(-0.660862\pi\) | ||||
−0.484126 | + | 0.874998i | \(0.660862\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.0446 | −1.06410 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.72224 | 0.125434 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.99846 | −0.275810 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.32201 | 0.427723 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −19.8604 | −0.909347 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.6248 | 1.62774 | 0.813870 | − | 0.581048i | \(-0.197357\pi\) | ||||
0.813870 | + | 0.581048i | \(0.197357\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.61260 | 0.164720 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.59417 | −0.0725374 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.75143 | −0.215751 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.1742 | −0.461037 | −0.230518 | − | 0.973068i | \(-0.574042\pi\) | ||||
−0.230518 | + | 0.973068i | \(0.574042\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.8754 | 0.491804 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.24937 | 0.327160 | 0.163580 | − | 0.986530i | \(-0.447696\pi\) | ||||
0.163580 | + | 0.986530i | \(0.447696\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.9955 | 0.810478 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 17.7794 | 0.799126 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17.3768 | −0.779455 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.4136 | −0.734773 | −0.367386 | − | 0.930068i | \(-0.619747\pi\) | ||||
−0.367386 | + | 0.930068i | \(0.619747\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.74616 | 0.122689 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.10739 | −0.271775 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.48749 | 0.154885 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.8893 | 1.14752 | 0.573761 | − | 0.819023i | \(-0.305484\pi\) | ||||
0.573761 | + | 0.819023i | \(0.305484\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.00359 | 0.177109 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 20.4464 | 0.902730 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14.9716 | −0.659728 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −28.4123 | −1.24957 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.13685 | 0.225483 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.9141 | −0.565779 | −0.282889 | − | 0.959153i | \(-0.591293\pi\) | ||||
−0.282889 | + | 0.959153i | \(0.591293\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.6441 | 1.12134 | 0.560670 | − | 0.828040i | \(-0.310544\pi\) | ||||
0.560670 | + | 0.828040i | \(0.310544\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.04699 | 0.0893380 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.6347 | −0.593936 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.3504 | −0.928280 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.1517 | −0.527338 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.7005 | −1.06990 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.75073 | −0.335093 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.56375 | 0.110634 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.91093 | 0.383821 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.0219 | −0.860809 | −0.430404 | − | 0.902636i | \(-0.641629\pi\) | ||||
−0.430404 | + | 0.902636i | \(0.641629\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.4387 | −0.533796 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 46.9827 | 2.01252 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.4075 | 1.30013 | 0.650066 | − | 0.759878i | \(-0.274741\pi\) | ||||
0.650066 | + | 0.759878i | \(0.274741\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −22.1731 | −0.946323 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18.2729 | −0.778454 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.30453 | 0.183047 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.18762 | 0.0928594 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −30.0571 | −1.27356 | −0.636781 | − | 0.771045i | \(-0.719734\pi\) | ||||
−0.636781 | + | 0.771045i | \(0.719734\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.19539 | −0.262037 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.64531 | −0.407225 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.88828 | −0.374596 | −0.187298 | − | 0.982303i | \(-0.559973\pi\) | ||||
−0.187298 | + | 0.982303i | \(0.559973\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −53.2735 | −2.24123 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10.3284 | −0.433752 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.15804 | 0.216236 | 0.108118 | − | 0.994138i | \(-0.465518\pi\) | ||||
0.108118 | + | 0.994138i | \(0.465518\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.5299 | 1.02654 | 0.513271 | − | 0.858227i | \(-0.328434\pi\) | ||||
0.513271 | + | 0.858227i | \(0.328434\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.20462 | 0.0920995 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.11810 | −0.0883309 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 43.6288 | 1.81629 | 0.908146 | − | 0.418653i | \(-0.137498\pi\) | ||||
0.908146 | + | 0.418653i | \(0.137498\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.04651 | 0.292843 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −31.3981 | −1.30261 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.5764 | −0.852187 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 18.3631 | 0.759222 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.96110 | 0.328590 | 0.164295 | − | 0.986411i | \(-0.447465\pi\) | ||||
0.164295 | + | 0.986411i | \(0.447465\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.8449 | 0.570468 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.03152 | −0.330372 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.0999 | −0.866471 | −0.433235 | − | 0.901281i | \(-0.642628\pi\) | ||||
−0.433235 | + | 0.901281i | \(0.642628\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 27.4841 | 1.12674 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.31669 | 0.258525 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.8856 | 1.38453 | 0.692264 | − | 0.721645i | \(-0.256614\pi\) | ||||
0.692264 | + | 0.721645i | \(0.256614\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.7178 | 1.74249 | 0.871247 | − | 0.490845i | \(-0.163312\pi\) | ||||
0.871247 | + | 0.490845i | \(0.163312\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −31.0491 | −1.26442 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.94419 | −0.404289 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.42273 | −0.220102 | −0.110051 | − | 0.993926i | \(-0.535101\pi\) | ||||
−0.110051 | + | 0.993926i | \(0.535101\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.01250 | −0.162595 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29.3450 | −1.18717 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.9547 | −0.967522 | −0.483761 | − | 0.875200i | \(-0.660730\pi\) | ||||
−0.483761 | + | 0.875200i | \(0.660730\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −14.9575 | −0.603145 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 43.1866 | 1.73863 | 0.869313 | − | 0.494261i | \(-0.164561\pi\) | ||||
0.869313 | + | 0.494261i | \(0.164561\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.5985 | −1.22986 | −0.614929 | − | 0.788583i | \(-0.710815\pi\) | ||||
−0.614929 | + | 0.788583i | \(0.710815\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.64573 | −0.186427 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.15682 | −0.286732 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.5261 | −1.22104 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.79399 | 0.391134 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.28509 | 0.290476 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.9223 | −0.992140 | −0.496070 | − | 0.868283i | \(-0.665224\pi\) | ||||
−0.496070 | + | 0.868283i | \(0.665224\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.33691 | 0.132630 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.1919 | 0.483823 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.20348 | 0.364655 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23.4126 | −0.926189 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.88975 | −0.0746405 | −0.0373202 | − | 0.999303i | \(-0.511882\pi\) | ||||
−0.0373202 | + | 0.999303i | \(0.511882\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.4524 | −0.924871 | −0.462435 | − | 0.886653i | \(-0.653024\pi\) | ||||
−0.462435 | + | 0.886653i | \(0.653024\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.75165 | −0.147721 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.0224 | 0.394021 | 0.197011 | − | 0.980401i | \(-0.436877\pi\) | ||||
0.197011 | + | 0.980401i | \(0.436877\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.5898 | −0.494191 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.04015 | 0.119153 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.4614 | −1.11378 | −0.556890 | − | 0.830586i | \(-0.688006\pi\) | ||||
−0.556890 | + | 0.830586i | \(0.688006\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.62112 | 0.141489 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.39424 | 0.210450 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.7038 | 1.39082 | 0.695410 | − | 0.718613i | \(-0.255223\pi\) | ||||
0.695410 | + | 0.718613i | \(0.255223\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.00684 | 0.155848 | 0.0779240 | − | 0.996959i | \(-0.475171\pi\) | ||||
0.0779240 | + | 0.996959i | \(0.475171\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.96196 | −0.386891 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −27.9078 | −1.08222 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.15189 | 0.160762 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.59121 | −0.370817 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.9724 | −0.886840 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.82474 | −0.0703386 | −0.0351693 | − | 0.999381i | \(-0.511197\pi\) | ||||
−0.0351693 | + | 0.999381i | \(0.511197\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.96533 | 0.229605 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.80117 | 0.338257 | 0.169128 | − | 0.985594i | \(-0.445905\pi\) | ||||
0.169128 | + | 0.985594i | \(0.445905\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.52807 | 0.135395 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.65631 | 0.140110 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.9409 | −0.495171 | −0.247585 | − | 0.968866i | \(-0.579637\pi\) | ||||
−0.247585 | + | 0.968866i | \(0.579637\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.66113 | 0.369133 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.721828 | −0.0275395 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −21.2519 | −0.809634 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.3649 | 0.736675 | 0.368337 | − | 0.929692i | \(-0.379927\pi\) | ||||
0.368337 | + | 0.929692i | \(0.379927\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −13.2017 | −0.501492 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 46.9415 | 1.78059 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −49.8106 | −1.88671 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.2281 | 0.500334 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.0601 | 0.719888 | 0.359944 | − | 0.932974i | \(-0.382796\pi\) | ||||
0.359944 | + | 0.932974i | \(0.382796\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.39740 | −0.278998 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −17.7700 | −0.669258 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.53491 | 0.170553 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.6676 | −1.41464 | −0.707319 | − | 0.706895i | \(-0.750095\pi\) | ||||
−0.707319 | + | 0.706895i | \(0.750095\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.79972 | 0.217506 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.14576 | −0.117810 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.0251 | 0.711499 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.21909 | −0.194911 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −38.9875 | −1.45399 | −0.726994 | − | 0.686644i | \(-0.759083\pi\) | ||||
−0.726994 | + | 0.686644i | \(0.759083\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.1168 | 0.414013 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.50202 | −0.316193 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.33121 | −0.197996 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.29239 | 0.0479321 | 0.0239660 | − | 0.999713i | \(-0.492371\pi\) | ||||
0.0239660 | + | 0.999713i | \(0.492371\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6.88124 | −0.254861 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.4935 | −0.462089 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −48.9143 | −1.80669 | −0.903345 | − | 0.428915i | \(-0.858896\pi\) | ||||
−0.903345 | + | 0.428915i | \(0.858896\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.57321 | 0.205571 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −32.1684 | −1.18494 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.6610 | −1.09110 | −0.545548 | − | 0.838079i | \(-0.683678\pi\) | ||||
−0.545548 | + | 0.838079i | \(0.683678\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.1155 | 0.371603 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.9188 | 1.35442 | 0.677210 | − | 0.735790i | \(-0.263189\pi\) | ||||
0.677210 | + | 0.735790i | \(0.263189\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.86508 | −0.361429 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −42.3042 | −1.54783 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.75514 | 0.210288 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.2117 | −0.628063 | −0.314031 | − | 0.949413i | \(-0.601680\pi\) | ||||
−0.314031 | + | 0.949413i | \(0.601680\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.34625 | 0.158386 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −37.5426 | −1.36631 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.80869 | 0.356503 | 0.178251 | − | 0.983985i | \(-0.442956\pi\) | ||||
0.178251 | + | 0.983985i | \(0.442956\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.22534 | −0.0807748 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.0180 | 0.689403 | 0.344702 | − | 0.938712i | \(-0.387980\pi\) | ||||
0.344702 | + | 0.938712i | \(0.387980\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −34.8860 | −1.26296 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 37.0308 | 1.33885 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.0031 | −0.469514 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.2218 | −1.16195 | −0.580974 | − | 0.813922i | \(-0.697328\pi\) | ||||
−0.580974 | + | 0.813922i | \(0.697328\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.7811 | −0.460300 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.1222 | 0.795680 | 0.397840 | − | 0.917455i | \(-0.369760\pi\) | ||||
0.397840 | + | 0.917455i | \(0.369760\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.03930 | 0.145096 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.62437 | −0.0582740 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 50.5784 | 1.81216 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.2566 | −0.867971 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11.6932 | −0.417881 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.8281 | −0.386473 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.8853 | 0.530604 | 0.265302 | − | 0.964165i | \(-0.414528\pi\) | ||||
0.265302 | + | 0.964165i | \(0.414528\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.81834 | 0.0647347 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 39.5570 | 1.40649 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.7266 | −0.842556 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.8692 | −0.456423 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.10523 | 0.287102 | 0.143551 | − | 0.989643i | \(-0.454148\pi\) | ||||
0.143551 | + | 0.989643i | \(0.454148\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −59.1767 | −2.09352 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.64275 | −0.340710 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.58871 | 0.197221 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.34108 | 0.223494 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.02043 | −0.247131 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −45.5535 | −1.60158 | −0.800788 | − | 0.598947i | \(-0.795586\pi\) | ||||
−0.800788 | + | 0.598947i | \(0.795586\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.3463 | 0.890030 | 0.445015 | − | 0.895523i | \(-0.353198\pi\) | ||||
0.445015 | + | 0.895523i | \(0.353198\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.93403 | −0.0678294 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −43.2587 | −1.51529 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.6861 | 0.443831 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13.6351 | −0.476450 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.1849 | −0.599757 | −0.299879 | − | 0.953977i | \(-0.596946\pi\) | ||||
−0.299879 | + | 0.953977i | \(0.596946\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.9285 | −0.590091 | −0.295045 | − | 0.955483i | \(-0.595335\pi\) | ||||
−0.295045 | + | 0.955483i | \(0.595335\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.85744 | 0.0994833 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.2882 | 1.67914 | 0.839572 | − | 0.543248i | \(-0.182806\pi\) | ||||
0.839572 | + | 0.543248i | \(0.182806\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.4609 | −1.19688 | −0.598438 | − | 0.801169i | \(-0.704212\pi\) | ||||
−0.598438 | + | 0.801169i | \(0.704212\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.45743 | −0.224006 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.5596 | 0.643051 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.9233 | −0.378016 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.85958 | 0.306232 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.3049 | −0.735528 | −0.367764 | − | 0.929919i | \(-0.619877\pi\) | ||||
−0.367764 | + | 0.929919i | \(0.619877\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.5498 | −0.639648 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.19594 | 0.0411904 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.8720 | −0.477212 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.38384 | 0.253712 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19.2977 | −0.662294 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.68080 | 0.0576171 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.9581 | 1.47086 | 0.735429 | − | 0.677602i | \(-0.236981\pi\) | ||||
0.735429 | + | 0.677602i | \(0.236981\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −37.6016 | −1.28595 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.6944 | 0.877704 | 0.438852 | − | 0.898559i | \(-0.355385\pi\) | ||||
0.438852 | + | 0.898559i | \(0.355385\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.84616 | 0.199469 | 0.0997343 | − | 0.995014i | \(-0.468201\pi\) | ||||
0.0997343 | + | 0.995014i | \(0.468201\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.1064 | 0.378504 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.1925 | −0.517159 | −0.258580 | − | 0.965990i | \(-0.583254\pi\) | ||||
−0.258580 | + | 0.965990i | \(0.583254\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.4326 | −0.694730 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.06851 | −0.307983 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.00879 | 0.203834 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −33.2245 | −1.12577 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.75355 | 0.160883 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16.5437 | 0.559280 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.27552 | −0.144374 | −0.0721871 | − | 0.997391i | \(-0.522998\pi\) | ||||
−0.0721871 | + | 0.997391i | \(0.522998\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.4288 | −0.452943 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.3696 | −1.05687 | −0.528434 | − | 0.848974i | \(-0.677221\pi\) | ||||
−0.528434 | + | 0.848974i | \(0.677221\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.4660 | −1.19353 | −0.596763 | − | 0.802417i | \(-0.703547\pi\) | ||||
−0.596763 | + | 0.802417i | \(0.703547\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.87407 | −0.264684 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.5445 | 1.22704 | 0.613522 | − | 0.789678i | \(-0.289752\pi\) | ||||
0.613522 | + | 0.789678i | \(0.289752\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.05286 | −0.303623 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −14.4177 | −0.483010 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 60.0889 | 2.01080 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.1977 | −0.340873 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.29840 | −0.0767414 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.91781 | −0.264074 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −42.8562 | −1.42775 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.78570 | 0.0927024 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 49.4769 | 1.64467 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.8754 | 0.460724 | 0.230362 | − | 0.973105i | \(-0.426009\pi\) | ||||
0.230362 | + | 0.973105i | \(0.426009\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.11011 | 0.202659 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.1478 | −0.468737 | −0.234369 | − | 0.972148i | \(-0.575302\pi\) | ||||
−0.234369 | + | 0.972148i | \(0.575302\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −43.8293 | −1.45054 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14.3677 | −0.474983 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.68878 | −0.0887914 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.9761 | 1.35168 | 0.675838 | − | 0.737050i | \(-0.263782\pi\) | ||||
0.675838 | + | 0.737050i | \(0.263782\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.33825 | 0.241803 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −25.0530 | −0.824629 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.15822 | −0.0709619 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.9783 | 0.491951 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.8227 | 0.519125 | 0.259562 | − | 0.965726i | \(-0.416422\pi\) | ||||
0.259562 | + | 0.965726i | \(0.416422\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.8457 | −0.617642 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.4171 | −0.439255 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 38.3657 | 1.25469 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.12795 | −0.134854 | −0.0674271 | − | 0.997724i | \(-0.521479\pi\) | ||||
−0.0674271 | + | 0.997724i | \(0.521479\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.1579 | −0.690462 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 44.5172 | 1.45122 | 0.725609 | − | 0.688107i | \(-0.241558\pi\) | ||||
0.725609 | + | 0.688107i | \(0.241558\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.4922 | −0.374237 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −17.8587 | −0.580944 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.5361 | 1.08978 | 0.544889 | − | 0.838508i | \(-0.316572\pi\) | ||||
0.544889 | + | 0.838508i | \(0.316572\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.77219 | 0.187373 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.32094 | 0.302252 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.1278 | 0.749183 | 0.374591 | − | 0.927190i | \(-0.377783\pi\) | ||||
0.374591 | + | 0.927190i | \(0.377783\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.76924 | −0.283766 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.60114 | −0.181059 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.17366 | −0.231650 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.0009 | −0.806481 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.75419 | 0.249875 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −28.0286 | −0.902272 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −59.9784 | −1.92878 | −0.964388 | − | 0.264491i | \(-0.914796\pi\) | ||||
−0.964388 | + | 0.264491i | \(0.914796\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 20.3988 | 0.655304 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.9981 | 1.44406 | 0.722029 | − | 0.691862i | \(-0.243210\pi\) | ||||
0.722029 | + | 0.691862i | \(0.243210\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −34.8554 | −1.11741 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.95125 | 0.0945157 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.02251 | 0.0966988 | 0.0483494 | − | 0.998830i | \(-0.484604\pi\) | ||||
0.0483494 | + | 0.998830i | \(0.484604\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.99037 | −0.319294 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −47.0036 | −1.50071 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24.1315 | 0.769677 | 0.384838 | − | 0.922984i | \(-0.374257\pi\) | ||||
0.384838 | + | 0.922984i | \(0.374257\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 31.9466 | 1.01790 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.1947 | 0.419993 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.88247 | −0.0916573 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 57.1238 | 1.81460 | 0.907299 | − | 0.420487i | \(-0.138141\pi\) | ||||
0.907299 | + | 0.420487i | \(0.138141\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.6855 | 0.434297 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25.1256 | −0.796535 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.0433 | 0.729790 | 0.364895 | − | 0.931049i | \(-0.381105\pi\) | ||||
0.364895 | + | 0.931049i | \(0.381105\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.73373 | −0.149769 |
(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 | 4024.2.a.g.1.13 | ✓ | 33 | |
4.3 | odd | 2 | 8048.2.a.x.1.21 | 33 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.g.1.13 | ✓ | 33 | 1.1 | even | 1 | trivial | |
8048.2.a.x.1.21 | 33 | 4.3 | odd | 2 |