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 | 1.17 | ||
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 | ||||||||
\(3\) | 0.410265 | 0.236867 | 0.118433 | − | 0.992962i | \(-0.462213\pi\) | ||||
0.118433 | + | 0.992962i | \(0.462213\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.21207 | −1.88370 | −0.941848 | − | 0.336038i | \(-0.890913\pi\) | ||||
−0.941848 | + | 0.336038i | \(0.890913\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.36092 | 1.27031 | 0.635154 | − | 0.772385i | \(-0.280937\pi\) | ||||
0.635154 | + | 0.772385i | \(0.280937\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.83168 | −0.943894 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.13893 | 1.24793 | 0.623967 | − | 0.781451i | \(-0.285520\pi\) | ||||
0.623967 | + | 0.781451i | \(0.285520\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.22425 | −0.894245 | −0.447122 | − | 0.894473i | \(-0.647551\pi\) | ||||
−0.447122 | + | 0.894473i | \(0.647551\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.72807 | −0.446185 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.83674 | 1.17308 | 0.586541 | − | 0.809919i | \(-0.300489\pi\) | ||||
0.586541 | + | 0.809919i | \(0.300489\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.13255 | −1.63632 | −0.818159 | − | 0.574991i | \(-0.805005\pi\) | ||||
−0.818159 | + | 0.574991i | \(0.805005\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.37887 | 0.300894 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.264477 | −0.0551472 | −0.0275736 | − | 0.999620i | \(-0.508778\pi\) | ||||
−0.0275736 | + | 0.999620i | \(0.508778\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.7416 | 2.54831 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.39254 | −0.460444 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.92998 | −1.28686 | −0.643432 | − | 0.765503i | \(-0.722490\pi\) | ||||
−0.643432 | + | 0.765503i | \(0.722490\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.07140 | 0.192429 | 0.0962147 | − | 0.995361i | \(-0.469326\pi\) | ||||
0.0962147 | + | 0.995361i | \(0.469326\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.69806 | 0.295594 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −14.1564 | −2.39288 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.79815 | 0.953210 | 0.476605 | − | 0.879117i | \(-0.341867\pi\) | ||||
0.476605 | + | 0.879117i | \(0.341867\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.32280 | −0.211817 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.24932 | 0.195111 | 0.0975553 | − | 0.995230i | \(-0.468898\pi\) | ||||
0.0975553 | + | 0.995230i | \(0.468898\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.97547 | 0.606253 | 0.303126 | − | 0.952950i | \(-0.401970\pi\) | ||||
0.303126 | + | 0.952950i | \(0.401970\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11.9273 | 1.77801 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.96976 | −1.16251 | −0.581255 | − | 0.813722i | \(-0.697438\pi\) | ||||
−0.581255 | + | 0.813722i | \(0.697438\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.29578 | 0.613684 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.98435 | 0.277864 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.9969 | 1.92263 | 0.961313 | − | 0.275460i | \(-0.0888301\pi\) | ||||
0.961313 | + | 0.275460i | \(0.0888301\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −17.4335 | −2.35073 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.92624 | −0.387590 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.88127 | 0.244921 | 0.122460 | − | 0.992473i | \(-0.460922\pi\) | ||||
0.122460 | + | 0.992473i | \(0.460922\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.0212 | −1.66719 | −0.833596 | − | 0.552374i | \(-0.813722\pi\) | ||||
−0.833596 | + | 0.552374i | \(0.813722\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.51706 | −1.19904 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 13.5808 | 1.68449 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.34403 | 0.897215 | 0.448608 | − | 0.893729i | \(-0.351920\pi\) | ||||
0.448608 | + | 0.893729i | \(0.351920\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.108506 | −0.0130625 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.5632 | 1.60965 | 0.804826 | − | 0.593510i | \(-0.202258\pi\) | ||||
0.804826 | + | 0.593510i | \(0.202258\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.49323 | −0.291810 | −0.145905 | − | 0.989299i | \(-0.546609\pi\) | ||||
−0.145905 | + | 0.989299i | \(0.546609\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.22742 | 0.603611 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.9106 | 1.58526 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.07702 | −0.908736 | −0.454368 | − | 0.890814i | \(-0.650135\pi\) | ||||
−0.454368 | + | 0.890814i | \(0.650135\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.51347 | 0.834830 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.1672 | −1.11599 | −0.557997 | − | 0.829843i | \(-0.688430\pi\) | ||||
−0.557997 | + | 0.829843i | \(0.688430\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20.3727 | −2.20973 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.84313 | −0.304816 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.18164 | 0.337253 | 0.168627 | − | 0.985680i | \(-0.446067\pi\) | ||||
0.168627 | + | 0.985680i | \(0.446067\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.8364 | −1.13597 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.439559 | 0.0455801 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 30.0428 | 3.08233 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.00896 | 0.711652 | 0.355826 | − | 0.934552i | \(-0.384200\pi\) | ||||
0.355826 | + | 0.934552i | \(0.384200\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.7201 | −1.17792 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.13363 | 0.709823 | 0.354911 | − | 0.934900i | \(-0.384511\pi\) | ||||
0.354911 | + | 0.934900i | \(0.384511\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.64606 | 0.851922 | 0.425961 | − | 0.904742i | \(-0.359936\pi\) | ||||
0.425961 | + | 0.904742i | \(0.359936\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.80790 | −0.566793 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.00657 | 0.193982 | 0.0969912 | − | 0.995285i | \(-0.469078\pi\) | ||||
0.0969912 | + | 0.995285i | \(0.469078\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.48178 | −0.333494 | −0.166747 | − | 0.986000i | \(-0.553326\pi\) | ||||
−0.166747 | + | 0.986000i | \(0.553326\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.37878 | 0.225784 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.5080 | 1.64701 | 0.823505 | − | 0.567308i | \(-0.192015\pi\) | ||||
0.823505 | + | 0.567308i | \(0.192015\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.11400 | 0.103881 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.13004 | 0.844072 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.2559 | 1.49018 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.13072 | 0.557338 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.512552 | 0.0462152 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −32.6081 | −2.91655 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.74768 | 0.243817 | 0.121909 | − | 0.992541i | \(-0.461099\pi\) | ||||
0.121909 | + | 0.992541i | \(0.461099\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.63100 | 0.143601 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.58654 | 0.837580 | 0.418790 | − | 0.908083i | \(-0.362454\pi\) | ||||
0.418790 | + | 0.908083i | \(0.362454\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −23.9719 | −2.07863 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.0775 | 0.867337 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.1551 | 1.20935 | 0.604677 | − | 0.796471i | \(-0.293302\pi\) | ||||
0.604677 | + | 0.796471i | \(0.293302\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.03212 | 0.257181 | 0.128591 | − | 0.991698i | \(-0.458955\pi\) | ||||
0.128591 | + | 0.991698i | \(0.458955\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.26972 | −0.275360 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.3449 | −1.11596 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 29.1896 | 2.42406 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.76241 | 0.145361 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.35096 | 0.766061 | 0.383030 | − | 0.923736i | \(-0.374880\pi\) | ||||
0.383030 | + | 0.923736i | \(0.374880\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0486 | −0.980504 | −0.490252 | − | 0.871581i | \(-0.663095\pi\) | ||||
−0.490252 | + | 0.871581i | \(0.663095\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.6961 | −1.10727 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.51282 | −0.362479 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.85173 | −0.227593 | −0.113796 | − | 0.993504i | \(-0.536301\pi\) | ||||
−0.113796 | + | 0.993504i | \(0.536301\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.74245 | 0.455406 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.888885 | −0.0700539 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.7867 | 1.00153 | 0.500764 | − | 0.865584i | \(-0.333052\pi\) | ||||
0.500764 | + | 0.865584i | \(0.333052\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.15235 | −0.556810 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.3443 | 1.26476 | 0.632381 | − | 0.774658i | \(-0.282078\pi\) | ||||
0.632381 | + | 0.774658i | \(0.282078\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.60424 | −0.200326 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 20.1971 | 1.54451 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.23063 | 0.245620 | 0.122810 | − | 0.992430i | \(-0.460809\pi\) | ||||
0.122810 | + | 0.992430i | \(0.460809\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 42.8234 | 3.23714 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.771821 | 0.0580136 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.9167 | −1.56339 | −0.781694 | − | 0.623662i | \(-0.785644\pi\) | ||||
−0.781694 | + | 0.623662i | \(0.785644\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.1263 | −1.19866 | −0.599328 | − | 0.800504i | \(-0.704565\pi\) | ||||
−0.599328 | + | 0.800504i | \(0.704565\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.34214 | −0.394903 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −24.4222 | −1.79556 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.0189 | 1.46393 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.04113 | −0.584906 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.1057 | 1.09301 | 0.546506 | − | 0.837455i | \(-0.315958\pi\) | ||||
0.546506 | + | 0.837455i | \(0.315958\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.5469 | 1.19107 | 0.595535 | − | 0.803329i | \(-0.296940\pi\) | ||||
0.595535 | + | 0.803329i | \(0.296940\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.57172 | 0.398999 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.0779 | 1.07426 | 0.537129 | − | 0.843500i | \(-0.319509\pi\) | ||||
0.537129 | + | 0.843500i | \(0.319509\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.05087 | 0.216271 | 0.108135 | − | 0.994136i | \(-0.465512\pi\) | ||||
0.108135 | + | 0.994136i | \(0.465512\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.01300 | 0.212521 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −23.2911 | −1.63472 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.26222 | −0.367529 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.748914 | 0.0520531 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −29.5211 | −2.04202 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.4233 | 1.54368 | 0.771840 | − | 0.635816i | \(-0.219336\pi\) | ||||
0.771840 | + | 0.635816i | \(0.219336\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.56450 | 0.381273 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.7450 | −1.14200 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.60089 | 0.244445 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.02289 | −0.0691202 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.5949 | −1.04902 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.37993 | −0.226337 | −0.113169 | − | 0.993576i | \(-0.536100\pi\) | ||||
−0.113169 | + | 0.993576i | \(0.536100\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −36.0801 | −2.40534 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.3974 | 1.61931 | 0.809655 | − | 0.586907i | \(-0.199654\pi\) | ||||
0.809655 | + | 0.586907i | \(0.199654\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.6787 | 1.49865 | 0.749326 | − | 0.662202i | \(-0.230378\pi\) | ||||
0.749326 | + | 0.662202i | \(0.230378\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.70704 | 0.375496 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.2114 | 1.58614 | 0.793070 | − | 0.609130i | \(-0.208481\pi\) | ||||
0.793070 | + | 0.609130i | \(0.208481\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 33.5692 | 2.18982 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.31372 | −0.215249 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.85452 | −0.119959 | −0.0599795 | − | 0.998200i | \(-0.519104\pi\) | ||||
−0.0599795 | + | 0.998200i | \(0.519104\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.1215 | 0.651985 | 0.325993 | − | 0.945372i | \(-0.394302\pi\) | ||||
0.325993 | + | 0.945372i | \(0.394302\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.2601 | 0.658188 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −18.0942 | −1.15599 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22.9971 | 1.46327 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.17125 | −0.264342 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.41727 | 0.278816 | 0.139408 | − | 0.990235i | \(-0.455480\pi\) | ||||
0.139408 | + | 0.990235i | \(0.455480\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.09465 | −0.0688200 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.35822 | −0.523412 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.8163 | 1.23611 | 0.618055 | − | 0.786135i | \(-0.287921\pi\) | ||||
0.618055 | + | 0.786135i | \(0.287921\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.4871 | 1.21087 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 19.6235 | 1.21466 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.1818 | 1.73776 | 0.868882 | − | 0.495019i | \(-0.164839\pi\) | ||||
0.868882 | + | 0.495019i | \(0.164839\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −58.9561 | −3.62164 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.30532 | 0.0798842 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.37959 | 0.388971 | 0.194485 | − | 0.980905i | \(-0.437696\pi\) | ||||
0.194485 | + | 0.980905i | \(0.437696\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.1955 | 0.680076 | 0.340038 | − | 0.940412i | \(-0.389560\pi\) | ||||
0.340038 | + | 0.940412i | \(0.389560\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.44581 | −0.269073 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 52.7364 | 3.18013 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.1314 | −1.57008 | −0.785042 | − | 0.619443i | \(-0.787359\pi\) | ||||
−0.785042 | + | 0.619443i | \(0.787359\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.03387 | −0.181633 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.54850 | −0.271341 | −0.135670 | − | 0.990754i | \(-0.543319\pi\) | ||||
−0.135670 | + | 0.990754i | \(0.543319\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.4187 | 1.15432 | 0.577162 | − | 0.816630i | \(-0.304160\pi\) | ||||
0.577162 | + | 0.816630i | \(0.304160\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12.3255 | 0.730101 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.19886 | 0.247851 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.39410 | 0.376123 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.87553 | 0.168567 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.94508 | 0.522577 | 0.261289 | − | 0.965261i | \(-0.415853\pi\) | ||||
0.261289 | + | 0.965261i | \(0.415853\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.92406 | −0.461357 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.90254 | −0.574604 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.852738 | 0.0493151 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.3612 | 0.770128 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.92668 | 0.168133 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 54.8462 | 3.14049 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.9511 | −1.30989 | −0.654943 | − | 0.755678i | \(-0.727307\pi\) | ||||
−0.654943 | + | 0.755678i | \(0.727307\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.54718 | 0.201792 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −33.3402 | −1.89055 | −0.945276 | − | 0.326272i | \(-0.894207\pi\) | ||||
−0.945276 | + | 0.326272i | \(0.894207\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.3601 | −0.811680 | −0.405840 | − | 0.913944i | \(-0.633021\pi\) | ||||
−0.405840 | + | 0.913944i | \(0.633021\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 40.0866 | 2.25862 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.42229 | −0.0798840 | −0.0399420 | − | 0.999202i | \(-0.512717\pi\) | ||||
−0.0399420 | + | 0.999202i | \(0.512717\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −28.6827 | −1.60592 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.823226 | 0.0459480 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −34.4983 | −1.91954 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −41.0820 | −2.27882 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.42845 | −0.0789936 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −26.7857 | −1.47675 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.937586 | −0.0515344 | −0.0257672 | − | 0.999668i | \(-0.508203\pi\) | ||||
−0.0257672 | + | 0.999668i | \(0.508203\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.4185 | −0.899730 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −30.9336 | −1.69008 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.3871 | 0.892662 | 0.446331 | − | 0.894868i | \(-0.352730\pi\) | ||||
0.446331 | + | 0.894868i | \(0.352730\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.18291 | 0.390122 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.43445 | 0.240139 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.08865 | −0.490741 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.457034 | 0.0246059 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.5142 | −1.15494 | −0.577470 | − | 0.816412i | \(-0.695960\pi\) | ||||
−0.577470 | + | 0.816412i | \(0.695960\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −35.9721 | −1.92554 | −0.962770 | − | 0.270320i | \(-0.912870\pi\) | ||||
−0.962770 | + | 0.270320i | \(0.912870\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.71413 | 0.411750 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −31.5436 | −1.67890 | −0.839449 | − | 0.543438i | \(-0.817122\pi\) | ||||
−0.839449 | + | 0.543438i | \(0.817122\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −57.1291 | −3.03210 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.66924 | 0.352973 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −36.2750 | −1.91452 | −0.957261 | − | 0.289227i | \(-0.906602\pi\) | ||||
−0.957261 | + | 0.289227i | \(0.906602\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.8732 | 1.67754 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.51522 | 0.132015 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.5017 | 0.549682 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.3867 | 0.959776 | 0.479888 | − | 0.877330i | \(-0.340677\pi\) | ||||
0.479888 | + | 0.877330i | \(0.340677\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.53767 | −0.184164 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 47.0425 | 2.44233 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.2082 | 1.25345 | 0.626726 | − | 0.779240i | \(-0.284395\pi\) | ||||
0.626726 | + | 0.779240i | \(0.284395\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.3780 | −0.690835 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 22.3440 | 1.15077 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.23158 | −0.0632622 | −0.0316311 | − | 0.999500i | \(-0.510070\pi\) | ||||
−0.0316311 | + | 0.999500i | \(0.510070\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.12728 | 0.0577522 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.7396 | −1.16194 | −0.580969 | − | 0.813926i | \(-0.697326\pi\) | ||||
−0.580969 | + | 0.813926i | \(0.697326\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −58.5925 | −2.98615 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.2573 | −0.572239 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.0769 | −0.764429 | −0.382214 | − | 0.924074i | \(-0.624838\pi\) | ||||
−0.382214 | + | 0.924074i | \(0.624838\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.27921 | −0.0646922 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.93302 | 0.198395 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 34.0210 | 1.71178 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.8639 | 0.545246 | 0.272623 | − | 0.962121i | \(-0.412109\pi\) | ||||
0.272623 | + | 0.962121i | \(0.412109\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.83485 | −0.492358 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.8865 | −0.593581 | −0.296791 | − | 0.954943i | \(-0.595916\pi\) | ||||
−0.296791 | + | 0.954943i | \(0.595916\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.45446 | −0.172079 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −31.6473 | −1.57257 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.9981 | 1.18954 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.2652 | −1.00205 | −0.501026 | − | 0.865432i | \(-0.667044\pi\) | ||||
−0.501026 | + | 0.865432i | \(0.667044\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.80736 | 0.286456 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.32281 | 0.311125 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 42.8250 | 2.10219 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.24398 | 0.0609177 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.46963 | −0.267209 | −0.133604 | − | 0.991035i | \(-0.542655\pi\) | ||||
−0.133604 | + | 0.991035i | \(0.542655\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.3527 | 1.67425 | 0.837123 | − | 0.547015i | \(-0.184236\pi\) | ||||
0.837123 | + | 0.547015i | \(0.184236\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22.5678 | 1.09729 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 61.6277 | 2.98938 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −43.7632 | −2.11785 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.47496 | −0.264333 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.85713 | −0.282128 | −0.141064 | − | 0.990000i | \(-0.545052\pi\) | ||||
−0.141064 | + | 0.990000i | \(0.545052\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.13150 | 0.102434 | 0.0512168 | − | 0.998688i | \(-0.483690\pi\) | ||||
0.0512168 | + | 0.998688i | \(0.483690\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.9755 | 0.574180 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.88639 | 0.0902384 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.8927 | −1.23579 | −0.617896 | − | 0.786259i | \(-0.712015\pi\) | ||||
−0.617896 | + | 0.786259i | \(0.712015\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.1643 | −0.579252 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.3441 | −0.538974 | −0.269487 | − | 0.963004i | \(-0.586854\pi\) | ||||
−0.269487 | + | 0.963004i | \(0.586854\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.4013 | −0.635283 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.83638 | 0.181454 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.4795 | 1.39123 | 0.695613 | − | 0.718417i | \(-0.255133\pi\) | ||||
0.695613 | + | 0.718417i | \(0.255133\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.17084 | 0.243485 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.94314 | −0.232249 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 45.6439 | 2.13982 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −36.6285 | −1.71341 | −0.856705 | − | 0.515806i | \(-0.827492\pi\) | ||||
−0.856705 | + | 0.515806i | \(0.827492\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.5721 | −0.540139 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.4126 | 1.18358 | 0.591791 | − | 0.806091i | \(-0.298421\pi\) | ||||
0.591791 | + | 0.806091i | \(0.298421\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.3241 | −1.13044 | −0.565218 | − | 0.824942i | \(-0.691208\pi\) | ||||
−0.565218 | + | 0.824942i | \(0.691208\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.85145 | −0.0858592 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.9330 | 1.29258 | 0.646292 | − | 0.763090i | \(-0.276319\pi\) | ||||
0.646292 | + | 0.763090i | \(0.276319\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.6827 | 1.13974 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.16997 | −0.0539092 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.4542 | 0.756563 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −90.8799 | −4.16985 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −39.6348 | −1.81475 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.8937 | 1.45726 | 0.728631 | − | 0.684907i | \(-0.240157\pi\) | ||||
0.728631 | + | 0.684907i | \(0.240157\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.6947 | −0.852403 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.364679 | −0.0165935 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −29.5223 | −1.34054 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.97200 | 0.451875 | 0.225937 | − | 0.974142i | \(-0.427456\pi\) | ||||
0.225937 | + | 0.974142i | \(0.427456\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.24592 | 0.237229 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.5310 | −0.565515 | −0.282758 | − | 0.959191i | \(-0.591249\pi\) | ||||
−0.282758 | + | 0.959191i | \(0.591249\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −33.5185 | −1.50960 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 49.3660 | 2.21884 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 45.5847 | 2.04476 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.7196 | −1.10660 | −0.553301 | − | 0.832981i | \(-0.686632\pi\) | ||||
−0.553301 | + | 0.832981i | \(0.686632\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.70551 | 0.299580 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −30.0474 | −1.33709 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.06843 | −0.0474506 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.3757 | −0.592866 | −0.296433 | − | 0.955054i | \(-0.595797\pi\) | ||||
−0.296433 | + | 0.955054i | \(0.595797\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.37954 | −0.370689 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.0649 | 0.753433 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −36.4178 | −1.60476 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −32.9863 | −1.45073 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.32541 | 0.0581792 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.01024 | −0.131881 | −0.0659406 | − | 0.997824i | \(-0.521005\pi\) | ||||
−0.0659406 | + | 0.997824i | \(0.521005\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.371149 | 0.0162292 | 0.00811462 | − | 0.999967i | \(-0.497417\pi\) | ||||
0.00811462 | + | 0.999967i | \(0.497417\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 17.5690 | 0.766772 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.18209 | 0.225736 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9301 | −0.996959 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.32717 | −0.231179 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.02811 | −0.174477 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.45182 | −0.365404 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.58140 | −0.370315 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.7799 | 0.765836 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.2639 | −0.527266 | −0.263633 | − | 0.964623i | \(-0.584921\pi\) | ||||
−0.263633 | + | 0.964623i | \(0.584921\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.61605 | −0.283922 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.6655 | 0.628201 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.4868 | −1.56006 | −0.780031 | − | 0.625741i | \(-0.784797\pi\) | ||||
−0.780031 | + | 0.625741i | \(0.784797\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 36.8719 | 1.57365 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 49.4284 | 2.10572 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27.1462 | −1.15437 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.0196 | −0.425308 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.0934 | 1.10561 | 0.552807 | − | 0.833310i | \(-0.313557\pi\) | ||||
0.552807 | + | 0.833310i | \(0.313557\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.8179 | −0.542139 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.21308 | 0.346756 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.5584 | 0.529274 | 0.264637 | − | 0.964348i | \(-0.414748\pi\) | ||||
0.264637 | + | 0.964348i | \(0.414748\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −73.7448 | −3.10247 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 25.2522 | 1.06049 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.7961 | −0.578364 | −0.289182 | − | 0.957274i | \(-0.593383\pi\) | ||||
−0.289182 | + | 0.957274i | \(0.593383\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.9291 | 0.541067 | 0.270534 | − | 0.962711i | \(-0.412800\pi\) | ||||
0.270534 | + | 0.962711i | \(0.412800\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.19736 | 0.258898 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.36985 | −0.140532 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.2876 | 1.59393 | 0.796967 | − | 0.604023i | \(-0.206436\pi\) | ||||
0.796967 | + | 0.604023i | \(0.206436\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.78861 | 0.282125 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −34.1711 | −1.41766 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 57.9322 | 2.39931 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −38.4564 | −1.58998 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 41.9521 | 1.73155 | 0.865775 | − | 0.500434i | \(-0.166826\pi\) | ||||
0.865775 | + | 0.500434i | \(0.166826\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.64182 | −0.314876 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.18595 | 0.254456 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.09406 | 0.0859928 | 0.0429964 | − | 0.999075i | \(-0.486310\pi\) | ||||
0.0429964 | + | 0.999075i | \(0.486310\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −68.4711 | −2.80704 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.25167 | 0.0512274 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.46204 | 0.386608 | 0.193304 | − | 0.981139i | \(-0.438080\pi\) | ||||
0.193304 | + | 0.981139i | \(0.438080\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.1000 | 1.39097 | 0.695484 | − | 0.718542i | \(-0.255190\pi\) | ||||
0.695484 | + | 0.718542i | \(0.255190\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −20.7959 | −0.846876 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −25.8230 | −1.04986 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.3332 | −1.39354 | −0.696770 | − | 0.717294i | \(-0.745380\pi\) | ||||
−0.696770 | + | 0.717294i | \(0.745380\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.55554 | −0.387210 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25.6965 | 1.03957 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.9176 | −0.440957 | −0.220479 | − | 0.975392i | \(-0.570762\pi\) | ||||
−0.220479 | + | 0.975392i | \(0.570762\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.15891 | −0.0870555 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −37.3923 | −1.50536 | −0.752678 | − | 0.658389i | \(-0.771238\pi\) | ||||
−0.752678 | + | 0.658389i | \(0.771238\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.0717 | −0.404817 | −0.202409 | − | 0.979301i | \(-0.564877\pi\) | ||||
−0.202409 | + | 0.979301i | \(0.564877\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.632770 | 0.0253922 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.6932 | 0.428416 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 73.6397 | 2.94559 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.1115 | −0.483686 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 28.0442 | 1.11819 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.11890 | −0.0843520 | −0.0421760 | − | 0.999110i | \(-0.513429\pi\) | ||||
−0.0421760 | + | 0.999110i | \(0.513429\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.19949 | 0.365647 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.5734 | −0.459277 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.8507 | −0.548783 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −38.4066 | −1.51934 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.78686 | −0.189070 | −0.0945348 | − | 0.995522i | \(-0.530136\pi\) | ||||
−0.0945348 | + | 0.995522i | \(0.530136\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.6313 | 1.24742 | 0.623709 | − | 0.781656i | \(-0.285625\pi\) | ||||
0.623709 | + | 0.781656i | \(0.285625\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.86988 | −0.270501 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.7434 | −0.540310 | −0.270155 | − | 0.962817i | \(-0.587075\pi\) | ||||
−0.270155 | + | 0.962817i | \(0.587075\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.78645 | 0.305645 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.47732 | 0.0579008 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.0587916 | −0.00230069 | −0.00115035 | − | 0.999999i | \(-0.500366\pi\) | ||||
−0.00115035 | + | 0.999999i | \(0.500366\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −40.3792 | −1.57775 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.06003 | 0.275438 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.1013 | 0.549308 | 0.274654 | − | 0.961543i | \(-0.411437\pi\) | ||||
0.274654 | + | 0.961543i | \(0.411437\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.47912 | 0.0964265 | 0.0482133 | − | 0.998837i | \(-0.484647\pi\) | ||||
0.0482133 | + | 0.998837i | \(0.484647\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.39803 | −0.248479 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 100.972 | 3.91551 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.83282 | 0.0709670 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.38667 | −0.0536117 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −53.8938 | −2.08055 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.88041 | 0.0724845 | 0.0362423 | − | 0.999343i | \(-0.488461\pi\) | ||||
0.0362423 | + | 0.999343i | \(0.488461\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −30.4847 | −1.17336 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.6258 | 0.446815 | 0.223407 | − | 0.974725i | \(-0.428282\pi\) | ||||
0.223407 | + | 0.974725i | \(0.428282\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 23.5565 | 0.904017 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.0094 | 0.383561 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.350145 | 0.0133979 | 0.00669897 | − | 0.999978i | \(-0.497868\pi\) | ||||
0.00669897 | + | 0.999978i | \(0.497868\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −59.6225 | −2.27806 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.30429 | 0.354981 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −45.1295 | −1.71930 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.9419 | −0.492335 | −0.246167 | − | 0.969227i | \(-0.579171\pi\) | ||||
−0.246167 | + | 0.969227i | \(0.579171\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −39.3904 | −1.49632 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.7715 | −0.484452 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.04263 | 0.228881 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.93309 | 0.375704 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.8216 | −1.61735 | −0.808674 | − | 0.588256i | \(-0.799815\pi\) | ||||
−0.808674 | + | 0.588256i | \(0.799815\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −41.3556 | −1.55976 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.7723 | 0.518695 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 23.9756 | 0.901694 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −47.8206 | −1.79594 | −0.897971 | − | 0.440055i | \(-0.854959\pi\) | ||||
−0.897971 | + | 0.440055i | \(0.854959\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 22.8716 | 0.857751 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.283361 | −0.0106119 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 56.2098 | 2.10213 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.760845 | −0.0284143 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.69842 | −0.0633402 | −0.0316701 | − | 0.999498i | \(-0.510083\pi\) | ||||
−0.0316701 | + | 0.999498i | \(0.510083\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29.0587 | 1.08220 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.15252 | 0.154434 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −88.2988 | −3.27934 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 50.3164 | 1.86613 | 0.933066 | − | 0.359706i | \(-0.117123\pi\) | ||||
0.933066 | + | 0.359706i | \(0.117123\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.3310 | −0.678927 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.2283 | 0.711185 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.24192 | 0.156679 | 0.0783395 | − | 0.996927i | \(-0.475038\pi\) | ||||
0.0783395 | + | 0.996927i | \(0.475038\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.42341 | −0.273817 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 30.3964 | 1.11967 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.1496 | 0.704428 | 0.352214 | − | 0.935920i | \(-0.385429\pi\) | ||||
0.352214 | + | 0.935920i | \(0.385429\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.43491 | 0.346600 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 42.3558 | 1.55388 | 0.776942 | − | 0.629572i | \(-0.216770\pi\) | ||||
0.776942 | + | 0.629572i | \(0.216770\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −39.3870 | −1.44303 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 28.7903 | 1.05338 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.74392 | 0.246417 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.0770 | −0.988053 | −0.494027 | − | 0.869447i | \(-0.664475\pi\) | ||||
−0.494027 | + | 0.869447i | \(0.664475\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.81225 | 0.0660422 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 50.7497 | 1.84697 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.8455 | −1.37552 | −0.687759 | − | 0.725939i | \(-0.741405\pi\) | ||||
−0.687759 | + | 0.725939i | \(0.741405\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.449097 | −0.0163012 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.5873 | 1.29004 | 0.645019 | − | 0.764166i | \(-0.276849\pi\) | ||||
0.645019 | + | 0.764166i | \(0.276849\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.7020 | −0.423640 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 57.6891 | 2.08575 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.06569 | −0.219019 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.9803 | 1.36960 | 0.684802 | − | 0.728729i | \(-0.259889\pi\) | ||||
0.684802 | + | 0.728729i | \(0.259889\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.12996 | 0.292793 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.7036 | 0.600786 | 0.300393 | − | 0.953816i | \(-0.402882\pi\) | ||||
0.300393 | + | 0.953816i | \(0.402882\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.6513 | 0.490370 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.99489 | 0.286815 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.91082 | −0.319263 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 56.1370 | 2.00874 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 16.5802 | 0.592529 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.0117 | 0.428716 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.94706 | 0.283282 | 0.141641 | − | 0.989918i | \(-0.454762\pi\) | ||||
0.141641 | + | 0.989918i | \(0.454762\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.5620 | 0.411619 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 58.8429 | 2.09221 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 41.9835 | 1.49088 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −24.1876 | −0.857847 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.76611 | −0.310511 | −0.155256 | − | 0.987874i | \(-0.549620\pi\) | ||||
−0.155256 | + | 0.987874i | \(0.549620\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38.5477 | −1.36372 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.00940 | −0.318332 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.3193 | −0.364160 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.74405 | 0.131960 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.61733 | 0.0921343 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.02651 | 0.247039 | 0.123519 | − | 0.992342i | \(-0.460582\pi\) | ||||
0.123519 | + | 0.992342i | \(0.460582\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.74637 | 0.342241 | 0.171121 | − | 0.985250i | \(-0.445261\pi\) | ||||
0.171121 | + | 0.985250i | \(0.445261\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.59311 | 0.161087 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −53.8584 | −1.88658 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28.3552 | −0.992023 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 30.6853 | 1.07223 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.40971 | −0.119000 | −0.0594998 | − | 0.998228i | \(-0.518951\pi\) | ||||
−0.0594998 | + | 0.998228i | \(0.518951\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.84363 | −0.238554 | −0.119277 | − | 0.992861i | \(-0.538058\pi\) | ||||
−0.119277 | + | 0.992861i | \(0.538058\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 21.6359 | 0.753266 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.8563 | 1.21207 | 0.606036 | − | 0.795437i | \(-0.292759\pi\) | ||||
0.606036 | + | 0.795437i | \(0.292759\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.9587 | 0.971047 | 0.485523 | − | 0.874224i | \(-0.338629\pi\) | ||||
0.485523 | + | 0.874224i | \(0.338629\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.7208 | −0.371901 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.7776 | 0.719902 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −68.8435 | −2.38243 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.56337 | −0.0886030 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −51.8984 | −1.79173 | −0.895865 | − | 0.444326i | \(-0.853443\pi\) | ||||
−0.895865 | + | 0.444326i | \(0.853443\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.0246 | 0.656021 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.86609 | −0.0642716 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.9693 | 0.377354 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.6049 | 0.707991 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.96683 | 0.273421 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.53348 | −0.0525669 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.5182 | −0.497094 | −0.248547 | − | 0.968620i | \(-0.579953\pi\) | ||||
−0.248547 | + | 0.968620i | \(0.579953\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −85.0717 | −2.90939 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.51805 | −0.222652 | −0.111326 | − | 0.993784i | \(-0.535510\pi\) | ||||
−0.111326 | + | 0.993784i | \(0.535510\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.9016 | −0.644913 | −0.322456 | − | 0.946584i | \(-0.604509\pi\) | ||||
−0.322456 | + | 0.946584i | \(0.604509\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.72265 | 0.0587076 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −40.4662 | −1.37749 | −0.688743 | − | 0.725005i | \(-0.741837\pi\) | ||||
−0.688743 | + | 0.725005i | \(0.741837\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.6076 | −0.462674 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.62328 | 0.0890911 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −33.4302 | −1.13404 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.6789 | −0.802330 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −19.8471 | −0.671724 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −109.593 | −3.70492 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.3146 | −1.29379 | −0.646896 | − | 0.762578i | \(-0.723933\pi\) | ||||
−0.646896 | + | 0.762578i | \(0.723933\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.66986 | 0.123781 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −48.1919 | −1.62363 | −0.811813 | − | 0.583917i | \(-0.801519\pi\) | ||||
−0.811813 | + | 0.583917i | \(0.801519\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.0449 | 0.809176 | 0.404588 | − | 0.914499i | \(-0.367415\pi\) | ||||
0.404588 | + | 0.914499i | \(0.367415\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.25097 | −0.109280 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.95712 | 0.132867 | 0.0664336 | − | 0.997791i | \(-0.478838\pi\) | ||||
0.0664336 | + | 0.997791i | \(0.478838\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.23473 | 0.309723 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 31.0977 | 1.04181 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 56.8447 | 1.90224 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 88.1027 | 2.94495 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.349849 | 0.0116811 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.42479 | −0.247631 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 67.6995 | 2.25540 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.48165 | 0.182418 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 67.9250 | 2.25790 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 46.3721 | 1.53976 | 0.769880 | − | 0.638189i | \(-0.220316\pi\) | ||||
0.769880 | + | 0.638189i | \(0.220316\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −20.2002 | −0.669998 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.0731 | −0.433133 | −0.216566 | − | 0.976268i | \(-0.569486\pi\) | ||||
−0.216566 | + | 0.976268i | \(0.569486\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −42.0813 | −1.39269 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 22.5015 | 0.743877 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 32.2196 | 1.06398 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 55.9346 | 1.84511 | 0.922556 | − | 0.385864i | \(-0.126097\pi\) | ||||
0.922556 | + | 0.385864i | \(0.126097\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.41603 | −0.310269 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −43.7310 | −1.43942 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 73.8776 | 2.42908 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −24.4829 | −0.804124 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.7469 | 0.680684 | 0.340342 | − | 0.940302i | \(-0.389457\pi\) | ||||
0.340342 | + | 0.940302i | \(0.389457\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30.6399 | −1.00418 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.6783 | −0.447809 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −84.3212 | −2.75760 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.5805 | −0.705006 | −0.352503 | − | 0.935811i | \(-0.614669\pi\) | ||||
−0.352503 | + | 0.935811i | \(0.614669\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.89145 | −0.192260 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 53.5707 | 1.74636 | 0.873178 | − | 0.487401i | \(-0.162055\pi\) | ||||
0.873178 | + | 0.487401i | \(0.162055\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.330415 | −0.0107598 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 33.8698 | 1.10179 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.27841 | 0.236516 | 0.118258 | − | 0.992983i | \(-0.462269\pi\) | ||||
0.118258 | + | 0.992983i | \(0.462269\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.03878 | 0.260950 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.583518 | −0.0189219 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.6483 | 1.08998 | 0.544988 | − | 0.838444i | \(-0.316534\pi\) | ||||
0.544988 | + | 0.838444i | \(0.316534\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −63.6265 | −2.05890 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.7675 | −0.380390 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 47.5743 | 1.53625 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.8521 | −0.962971 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.68196 | −0.183099 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −69.6966 | −2.24361 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.9918 | 0.417788 | 0.208894 | − | 0.977938i | \(-0.433014\pi\) | ||||
0.208894 | + | 0.977938i | \(0.433014\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.1535 | −0.454675 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.30177 | 0.202233 | 0.101117 | − | 0.994875i | \(-0.467758\pi\) | ||||
0.101117 | + | 0.994875i | \(0.467758\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.1907 | 0.326700 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −16.8545 | −0.539776 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −42.7142 | −1.36655 | −0.683275 | − | 0.730161i | \(-0.739445\pi\) | ||||
−0.683275 | + | 0.730161i | \(0.739445\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.1686 | 0.420870 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.85929 | 0.314783 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.161818 | −0.00516121 | −0.00258060 | − | 0.999997i | \(-0.500821\pi\) | ||||
−0.00258060 | + | 0.999997i | \(0.500821\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −63.5093 | −2.02358 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.9893 | −0.349792 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.05142 | −0.0334331 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.47381 | 0.269179 | 0.134590 | − | 0.990901i | \(-0.457028\pi\) | ||||
0.134590 | + | 0.990901i | \(0.457028\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.384659 | −0.0122068 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.8505 | −0.407389 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.6467 | −1.06560 | −0.532800 | − | 0.846241i | \(-0.678860\pi\) | ||||
−0.532800 | + | 0.846241i | \(0.678860\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −13.8723 | −0.438900 |
(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.1.17 | ✓ | 33 | |
4.3 | odd | 2 | 8048.2.a.x.1.17 | 33 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.g.1.17 | ✓ | 33 | 1.1 | even | 1 | trivial | |
8048.2.a.x.1.17 | 33 | 4.3 | odd | 2 |