Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0679214517\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.242773.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 7x^{3} + 4x^{2} + 6x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 502) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.37208\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.37208 | 0.792172 | 0.396086 | − | 0.918213i | \(-0.370368\pi\) | ||||
0.396086 | + | 0.918213i | \(0.370368\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.64633 | 0.736262 | 0.368131 | − | 0.929774i | \(-0.379998\pi\) | ||||
0.368131 | + | 0.929774i | \(0.379998\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.43111 | 0.918872 | 0.459436 | − | 0.888211i | \(-0.348052\pi\) | ||||
0.459436 | + | 0.888211i | \(0.348052\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.11739 | −0.372463 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.53201 | −1.36645 | −0.683226 | − | 0.730207i | \(-0.739424\pi\) | ||||
−0.683226 | + | 0.730207i | \(0.739424\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.20294 | −1.44304 | −0.721519 | − | 0.692395i | \(-0.756556\pi\) | ||||
−0.721519 | + | 0.692395i | \(0.756556\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.25890 | 0.583246 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.87449 | −0.697167 | −0.348584 | − | 0.937278i | \(-0.613337\pi\) | ||||
−0.348584 | + | 0.937278i | \(0.613337\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.37515 | −1.23314 | −0.616572 | − | 0.787299i | \(-0.711479\pi\) | ||||
−0.616572 | + | 0.787299i | \(0.711479\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.33568 | 0.727905 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.08556 | 1.26893 | 0.634463 | − | 0.772953i | \(-0.281221\pi\) | ||||
0.634463 | + | 0.772953i | \(0.281221\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.28959 | −0.457919 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.64940 | −1.08723 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.08249 | −0.386708 | −0.193354 | − | 0.981129i | \(-0.561937\pi\) | ||||
−0.193354 | + | 0.981129i | \(0.561937\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.99013 | 1.07586 | 0.537929 | − | 0.842990i | \(-0.319207\pi\) | ||||
0.537929 | + | 0.842990i | \(0.319207\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.21829 | −1.08247 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.00241 | 0.676530 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.717021 | 0.117878 | 0.0589388 | − | 0.998262i | \(-0.481228\pi\) | ||||
0.0589388 | + | 0.998262i | \(0.481228\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.13887 | −1.14313 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.17882 | −1.12114 | −0.560572 | − | 0.828106i | \(-0.689419\pi\) | ||||
−0.560572 | + | 0.828106i | \(0.689419\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.58731 | 0.242062 | 0.121031 | − | 0.992649i | \(-0.461380\pi\) | ||||
0.121031 | + | 0.992649i | \(0.461380\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.83959 | −0.274230 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.70536 | 1.12394 | 0.561971 | − | 0.827157i | \(-0.310043\pi\) | ||||
0.561971 | + | 0.827157i | \(0.310043\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.08972 | −0.155674 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.94404 | −0.552276 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.8881 | −1.63295 | −0.816477 | − | 0.577378i | \(-0.804076\pi\) | ||||
−0.816477 | + | 0.577378i | \(0.804076\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.46119 | −1.00607 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.37515 | −0.976862 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.43658 | −0.837972 | −0.418986 | − | 0.907993i | \(-0.637614\pi\) | ||||
−0.418986 | + | 0.907993i | \(0.637614\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.6549 | −1.62029 | −0.810145 | − | 0.586229i | \(-0.800612\pi\) | ||||
−0.810145 | + | 0.586229i | \(0.800612\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.71649 | −0.342246 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.56577 | −1.06245 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.54736 | −0.433378 | −0.216689 | − | 0.976241i | \(-0.569526\pi\) | ||||
−0.216689 | + | 0.976241i | \(0.569526\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.34989 | 1.00521 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.7859 | 1.51740 | 0.758701 | − | 0.651439i | \(-0.225834\pi\) | ||||
0.758701 | + | 0.651439i | \(0.225834\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.8523 | 1.27017 | 0.635085 | − | 0.772442i | \(-0.280965\pi\) | ||||
0.635085 | + | 0.772442i | \(0.280965\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.14151 | −0.362751 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11.0178 | −1.25559 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.05902 | −0.906711 | −0.453356 | − | 0.891330i | \(-0.649773\pi\) | ||||
−0.453356 | + | 0.891330i | \(0.649773\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.39927 | −0.488808 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.44495 | −1.03672 | −0.518359 | − | 0.855163i | \(-0.673457\pi\) | ||||
−0.518359 | + | 0.855163i | \(0.673457\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.73237 | −0.513297 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.85735 | −0.306340 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.22334 | 0.129674 | 0.0648369 | − | 0.997896i | \(-0.479347\pi\) | ||||
0.0648369 | + | 0.997896i | \(0.479347\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.6489 | −1.32597 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.21895 | 0.852266 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.84928 | −0.907917 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.9462 | 1.11142 | 0.555710 | − | 0.831376i | \(-0.312446\pi\) | ||||
0.555710 | + | 0.831376i | \(0.312446\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.06402 | 0.508953 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.48526 | −0.147789 | −0.0738946 | − | 0.997266i | \(-0.523543\pi\) | ||||
−0.0738946 | + | 0.997266i | \(0.523543\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.4680 | −1.72117 | −0.860586 | − | 0.509306i | \(-0.829902\pi\) | ||||
−0.860586 | + | 0.509306i | \(0.829902\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.49163 | 0.535929 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.58735 | −0.636823 | −0.318412 | − | 0.947953i | \(-0.603149\pi\) | ||||
−0.318412 | + | 0.947953i | \(0.603149\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.8826 | 1.61706 | 0.808528 | − | 0.588458i | \(-0.200265\pi\) | ||||
0.808528 | + | 0.588458i | \(0.200265\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.983813 | 0.0933794 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.25952 | −0.118485 | −0.0592426 | − | 0.998244i | \(-0.518869\pi\) | ||||
−0.0592426 | + | 0.998244i | \(0.518869\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.0188 | 0.934261 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.81371 | 0.537478 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.98820 | −0.640607 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.53911 | 0.867191 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.84994 | −0.888139 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0011 | −1.07341 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.3534 | 1.80607 | 0.903037 | − | 0.429562i | \(-0.141332\pi\) | ||||
0.903037 | + | 0.429562i | \(0.141332\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.17792 | 0.191755 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.8271 | 1.38282 | 0.691411 | − | 0.722461i | \(-0.256989\pi\) | ||||
0.691411 | + | 0.722461i | \(0.256989\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.0676 | −1.13310 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.30078 | −0.800484 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.28657 | −0.195355 | −0.0976776 | − | 0.995218i | \(-0.531141\pi\) | ||||
−0.0976776 | + | 0.995218i | \(0.531141\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.37165 | 0.201161 | 0.100580 | − | 0.994929i | \(-0.467930\pi\) | ||||
0.100580 | + | 0.994929i | \(0.467930\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.5724 | 0.890355 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 23.5798 | 1.97184 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.42846 | −0.284718 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.49518 | −0.123321 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.75053 | −0.716871 | −0.358436 | − | 0.933554i | \(-0.616690\pi\) | ||||
−0.358436 | + | 0.933554i | \(0.616690\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.6668 | −1.11219 | −0.556094 | − | 0.831119i | \(-0.687701\pi\) | ||||
−0.556094 | + | 0.831119i | \(0.687701\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.21193 | 0.259669 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.86173 | 0.792113 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.95277 | −0.554892 | −0.277446 | − | 0.960741i | \(-0.589488\pi\) | ||||
−0.277446 | + | 0.960741i | \(0.589488\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16.3114 | −1.29358 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14.7946 | 1.16598 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.12160 | −0.166176 | −0.0830882 | − | 0.996542i | \(-0.526478\pi\) | ||||
−0.0830882 | + | 0.996542i | \(0.526478\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −10.2374 | −0.796978 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.3600 | −1.11121 | −0.555604 | − | 0.831447i | \(-0.687513\pi\) | ||||
−0.555604 | + | 0.831447i | \(0.687513\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.0706 | 1.08236 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.00613 | 0.459301 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.9004 | 1.74109 | 0.870543 | − | 0.492093i | \(-0.163768\pi\) | ||||
0.870543 | + | 0.492093i | \(0.163768\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.56625 | −0.420769 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.83152 | −0.663818 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.0662 | 1.42507 | 0.712537 | − | 0.701634i | \(-0.247546\pi\) | ||||
0.712537 | + | 0.701634i | \(0.247546\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.12479 | 0.603911 | 0.301955 | − | 0.953322i | \(-0.402361\pi\) | ||||
0.301955 | + | 0.953322i | \(0.402361\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −17.3635 | −1.28355 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.18045 | 0.0867887 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.0272 | 0.952645 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.7343 | −0.999023 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.4153 | 0.825980 | 0.412990 | − | 0.910736i | \(-0.364484\pi\) | ||||
0.412990 | + | 0.910736i | \(0.364484\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.0805 | −1.08552 | −0.542759 | − | 0.839888i | \(-0.682620\pi\) | ||||
−0.542759 | + | 0.839888i | \(0.682620\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −11.7529 | −0.841646 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.1673 | 1.79309 | 0.896547 | − | 0.442949i | \(-0.146068\pi\) | ||||
0.896547 | + | 0.442949i | \(0.146068\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.55336 | 0.677220 | 0.338610 | − | 0.940927i | \(-0.390043\pi\) | ||||
0.338610 | + | 0.940927i | \(0.390043\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.86726 | −0.343310 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.06275 | −0.355336 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.8187 | −0.825455 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.79993 | −0.472628 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.3602 | 1.68503 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.66739 | 0.183631 | 0.0918153 | − | 0.995776i | \(-0.470733\pi\) | ||||
0.0918153 | + | 0.995776i | \(0.470733\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 17.5433 | 1.20204 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.61323 | 0.178221 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.5626 | 0.988577 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.8903 | 1.00619 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.9558 | 1.00604 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.0310 | −1.00655 | −0.503277 | − | 0.864125i | \(-0.667872\pi\) | ||||
−0.503277 | + | 0.864125i | \(0.667872\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.55837 | 0.170558 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.54337 | −0.500671 | −0.250336 | − | 0.968159i | \(-0.580541\pi\) | ||||
−0.250336 | + | 0.968159i | \(0.580541\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.52262 | 0.166699 | 0.0833497 | − | 0.996520i | \(-0.473438\pi\) | ||||
0.0833497 | + | 0.996520i | \(0.473438\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.1173 | −0.994647 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.5406 | −1.01810 | −0.509048 | − | 0.860738i | \(-0.670002\pi\) | ||||
−0.509048 | + | 0.860738i | \(0.670002\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.6856 | 0.827515 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.0576 | −0.718271 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.8331 | −0.894788 | −0.447394 | − | 0.894337i | \(-0.647648\pi\) | ||||
−0.447394 | + | 0.894337i | \(0.647648\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.70824 | −0.625363 | −0.312681 | − | 0.949858i | \(-0.601227\pi\) | ||||
−0.312681 | + | 0.949858i | \(0.601227\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.9120 | 0.700007 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.79403 | −0.114617 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 27.9666 | 1.77947 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.9593 | −0.821259 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −27.5798 | −1.73393 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.49320 | −0.406620 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.23580 | −0.326600 | −0.163300 | − | 0.986576i | \(-0.552214\pi\) | ||||
−0.163300 | + | 0.986576i | \(0.552214\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.74316 | 0.108314 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.32695 | 0.144035 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.0859 | −0.621925 | −0.310963 | − | 0.950422i | \(-0.600651\pi\) | ||||
−0.310963 | + | 0.950422i | \(0.600651\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −19.5717 | −1.20228 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.67852 | 0.102724 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.3697 | −0.815163 | −0.407581 | − | 0.913169i | \(-0.633628\pi\) | ||||
−0.407581 | + | 0.913169i | \(0.633628\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.256741 | 0.0155959 | 0.00779794 | − | 0.999970i | \(-0.497518\pi\) | ||||
0.00779794 | + | 0.999970i | \(0.497518\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −17.3554 | −1.05039 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.3765 | 0.625724 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.88220 | −0.593764 | −0.296882 | − | 0.954914i | \(-0.595947\pi\) | ||||
−0.296882 | + | 0.954914i | \(0.595947\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.69330 | −0.400718 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.7694 | −0.881067 | −0.440533 | − | 0.897736i | \(-0.645211\pi\) | ||||
−0.440533 | + | 0.897736i | \(0.645211\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.36222 | 0.497082 | 0.248541 | − | 0.968621i | \(-0.420049\pi\) | ||||
0.248541 | + | 0.968621i | \(0.420049\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −12.1419 | −0.719226 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −17.4525 | −1.03019 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.73729 | −0.513958 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.0191 | 0.880436 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.7351 | 0.919254 | 0.459627 | − | 0.888112i | \(-0.347983\pi\) | ||||
0.459627 | + | 0.888112i | \(0.347983\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.5967 | −0.616966 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 25.6031 | 1.48564 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −31.6628 | −1.83111 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.85891 | 0.222424 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.03790 | −0.117075 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −20.8341 | −1.19296 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.9168 | −1.47915 | −0.739576 | − | 0.673073i | \(-0.764974\pi\) | ||||
−0.739576 | + | 0.673073i | \(0.764974\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −23.9675 | −1.36346 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.7485 | 0.836311 | 0.418155 | − | 0.908376i | \(-0.362677\pi\) | ||||
0.418155 | + | 0.908376i | \(0.362677\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.1258 | 1.75933 | 0.879667 | − | 0.475590i | \(-0.157765\pi\) | ||||
0.879667 | + | 0.475590i | \(0.157765\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.47225 | −0.251983 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.7048 | −0.657406 | −0.328703 | − | 0.944433i | \(-0.606612\pi\) | ||||
−0.328703 | + | 0.944433i | \(0.606612\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.43786 | 0.528418 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.03839 | −0.504474 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.4508 | 0.859707 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.9126 | 0.660794 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 23.1643 | 1.28099 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.7325 | 1.03276 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.1367 | −1.32667 | −0.663336 | − | 0.748322i | \(-0.730860\pi\) | ||||
−0.663336 | + | 0.748322i | \(0.730860\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.801192 | −0.0439050 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.84012 | −0.319080 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.64108 | −0.361762 | −0.180881 | − | 0.983505i | \(-0.557895\pi\) | ||||
−0.180881 | + | 0.983505i | \(0.557895\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.72816 | −0.0938607 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −27.1473 | −1.47011 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.6670 | −1.06192 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13.7467 | 0.740096 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 33.4782 | 1.79721 | 0.898603 | − | 0.438763i | \(-0.144583\pi\) | ||||
0.898603 | + | 0.438763i | \(0.144583\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.8861 | 0.850361 | 0.425181 | − | 0.905109i | \(-0.360211\pi\) | ||||
0.425181 | + | 0.905109i | \(0.360211\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 29.3935 | 1.56891 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.6140 | −0.937500 | −0.468750 | − | 0.883331i | \(-0.655296\pi\) | ||||
−0.468750 | + | 0.883331i | \(0.655296\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.0498 | 1.11721 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.58839 | −0.507471 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.7644 | −0.937569 | −0.468785 | − | 0.883313i | \(-0.655308\pi\) | ||||
−0.468785 | + | 0.883313i | \(0.655308\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.89224 | 0.520644 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.0884 | 0.686965 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 17.8665 | 0.935178 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.6552 | 1.54799 | 0.773994 | − | 0.633193i | \(-0.218256\pi\) | ||||
0.773994 | + | 0.633193i | \(0.218256\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.02154 | 0.417585 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −28.9012 | −1.50048 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −36.2760 | −1.87830 | −0.939151 | − | 0.343505i | \(-0.888386\pi\) | ||||
−0.939151 | + | 0.343505i | \(0.888386\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −16.4665 | −0.850325 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.8351 | 0.558035 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.2590 | −1.45157 | −0.725784 | − | 0.687922i | \(-0.758523\pi\) | ||||
−0.725784 | + | 0.687922i | \(0.758523\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 27.9266 | 1.43072 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 34.8981 | 1.78321 | 0.891605 | − | 0.452813i | \(-0.149580\pi\) | ||||
0.891605 | + | 0.452813i | \(0.149580\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.1389 | −0.924446 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.77364 | −0.0901591 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 32.3747 | 1.64146 | 0.820732 | − | 0.571313i | \(-0.193566\pi\) | ||||
0.820732 | + | 0.571313i | \(0.193566\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.4929 | −0.884653 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.7161 | 1.09543 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.2678 | −0.667577 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −37.0827 | −1.86113 | −0.930563 | − | 0.366132i | \(-0.880682\pi\) | ||||
−0.930563 | + | 0.366132i | \(0.880682\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −17.9298 | −0.897612 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.828629 | 0.0413797 | 0.0206899 | − | 0.999786i | \(-0.493414\pi\) | ||||
0.0206899 | + | 0.999786i | \(0.493414\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −31.1663 | −1.55250 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.24266 | −0.359891 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.24955 | −0.161074 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.50740 | 0.173430 | 0.0867150 | − | 0.996233i | \(-0.472363\pi\) | ||||
0.0867150 | + | 0.996233i | \(0.472363\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.13737 | −0.154755 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15.6480 | −0.769989 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.5495 | −0.763296 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.25410 | 0.159354 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.69308 | −0.229272 | −0.114636 | − | 0.993408i | \(-0.536570\pi\) | ||||
−0.114636 | + | 0.993408i | \(0.536570\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.781966 | 0.0381107 | 0.0190553 | − | 0.999818i | \(-0.493934\pi\) | ||||
0.0190553 | + | 0.999818i | \(0.493934\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.60988 | −0.418627 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.58142 | 0.319246 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −30.7654 | −1.48884 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 32.3534 | 1.56204 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.5010 | 0.698490 | 0.349245 | − | 0.937031i | \(-0.386438\pi\) | ||||
0.349245 | + | 0.937031i | \(0.386438\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.7415 | −0.612316 | −0.306158 | − | 0.951981i | \(-0.599044\pi\) | ||||
−0.306158 | + | 0.951981i | \(0.599044\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.70414 | −0.225546 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −32.7108 | −1.56477 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.0542769 | −0.00259050 | −0.00129525 | − | 0.999999i | \(-0.500412\pi\) | ||||
−0.00129525 | + | 0.999999i | \(0.500412\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.21764 | 0.0579828 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.1733 | 1.24353 | 0.621765 | − | 0.783204i | \(-0.286416\pi\) | ||||
0.621765 | + | 0.783204i | \(0.286416\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.01402 | 0.0954739 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.0064 | −0.567885 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.41106 | −0.208171 | −0.104085 | − | 0.994568i | \(-0.533192\pi\) | ||||
−0.104085 | + | 0.994568i | \(0.533192\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.5345 | 1.53199 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.7520 | −0.881044 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −20.8243 | −0.976258 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.4874 | 1.37936 | 0.689681 | − | 0.724113i | \(-0.257751\pi\) | ||||
0.689681 | + | 0.724113i | \(0.257751\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 16.2392 | 0.757979 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.2732 | 1.31682 | 0.658408 | − | 0.752662i | \(-0.271230\pi\) | ||||
0.658408 | + | 0.752662i | \(0.271230\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.5575 | −0.583597 | −0.291798 | − | 0.956480i | \(-0.594254\pi\) | ||||
−0.291798 | + | 0.956480i | \(0.594254\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.5311 | 0.627490 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.6913 | 1.69787 | 0.848935 | − | 0.528497i | \(-0.177244\pi\) | ||||
0.848935 | + | 0.528497i | \(0.177244\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.62400 | −0.398219 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.53978 | −0.439570 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.19369 | −0.330766 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.3069 | 0.564680 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.2836 | 0.608215 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.77059 | 0.0809004 | 0.0404502 | − | 0.999182i | \(-0.487121\pi\) | ||||
0.0404502 | + | 0.999182i | \(0.487121\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.73062 | −0.170102 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 20.2995 | 0.923658 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.0211 | 0.818296 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.81798 | 0.0823805 | 0.0411903 | − | 0.999151i | \(-0.486885\pi\) | ||||
0.0411903 | + | 0.999151i | \(0.486885\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.91101 | −0.131640 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.3423 | −0.557000 | −0.278500 | − | 0.960436i | \(-0.589837\pi\) | ||||
−0.278500 | + | 0.960436i | \(0.589837\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.98610 | 0.269600 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.33705 | 0.374723 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 31.0838 | 1.39430 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.7996 | 0.931120 | 0.465560 | − | 0.885016i | \(-0.345853\pi\) | ||||
0.465560 | + | 0.885016i | \(0.345853\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.7031 | −0.880268 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.5971 | −1.09673 | −0.548366 | − | 0.836239i | \(-0.684750\pi\) | ||||
−0.548366 | + | 0.836239i | \(0.684750\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.44523 | −0.108812 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.3061 | 0.857413 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.41535 | −0.417328 | −0.208664 | − | 0.977987i | \(-0.566912\pi\) | ||||
−0.208664 | + | 0.977987i | \(0.566912\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.3832 | 1.16712 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 30.3664 | 1.34071 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −28.7581 | −1.26723 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −34.9207 | −1.53581 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 31.4212 | 1.37924 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.5179 | 1.46845 | 0.734223 | − | 0.678909i | \(-0.237547\pi\) | ||||
0.734223 | + | 0.678909i | \(0.237547\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.4214 | −0.761786 | −0.380893 | − | 0.924619i | \(-0.624383\pi\) | ||||
−0.380893 | + | 0.924619i | \(0.624383\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.63735 | −0.333321 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.2186 | −0.750053 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.0340 | 0.610173 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.19217 | 0.312113 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 37.3510 | 1.61785 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.8450 | −0.468869 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 26.1604 | 1.12890 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.93861 | 0.212721 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.5644 | −1.40005 | −0.700027 | − | 0.714116i | \(-0.746829\pi\) | ||||
−0.700027 | + | 0.714116i | \(0.746829\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.1479 | 0.478401 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 27.7943 | 1.19058 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.4173 | −0.958495 | −0.479248 | − | 0.877680i | \(-0.659090\pi\) | ||||
−0.479248 | + | 0.877680i | \(0.659090\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.1404 | 0.603498 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.1937 | 0.476867 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.5924 | −0.833152 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.61968 | 0.0687516 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.4988 | −0.529590 | −0.264795 | − | 0.964305i | \(-0.585304\pi\) | ||||
−0.264795 | + | 0.964305i | \(0.585304\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.25867 | −0.349304 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.8744 | 0.754659 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.1096 | 1.22682 | 0.613411 | − | 0.789764i | \(-0.289797\pi\) | ||||
0.613411 | + | 0.789764i | \(0.289797\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.07358 | −0.0872361 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10.6951 | −0.449152 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.20206 | −0.260004 | −0.130002 | − | 0.991514i | \(-0.541498\pi\) | ||||
−0.130002 | + | 0.991514i | \(0.541498\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.76421 | 0.241225 | 0.120612 | − | 0.992700i | \(-0.461514\pi\) | ||||
0.120612 | + | 0.992700i | \(0.461514\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.6627 | 0.654319 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.9335 | −0.581065 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.1975 | −0.424527 | −0.212264 | − | 0.977212i | \(-0.568084\pi\) | ||||
−0.212264 | + | 0.977212i | \(0.568084\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20.6917 | −0.859918 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.9617 | −0.952612 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 53.8769 | 2.23135 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.57130 | 0.395724 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.7660 | −0.526909 | −0.263455 | − | 0.964672i | \(-0.584862\pi\) | ||||
−0.263455 | + | 0.964672i | \(0.584862\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32.1978 | −1.32669 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 34.5316 | 1.42044 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.5891 | −0.640168 | −0.320084 | − | 0.947389i | \(-0.603711\pi\) | ||||
−0.320084 | + | 0.947389i | \(0.603711\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.5049 | −0.471655 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.1080 | 0.536475 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.25188 | −0.337163 | −0.168581 | − | 0.985688i | \(-0.553919\pi\) | ||||
−0.168581 | + | 0.985688i | \(0.553919\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.1843 | −0.782546 | −0.391273 | − | 0.920275i | \(-0.627965\pi\) | ||||
−0.391273 | + | 0.920275i | \(0.627965\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.96378 | 0.161417 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.7045 | 0.638480 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.4124 | −1.27499 | −0.637494 | − | 0.770455i | \(-0.720029\pi\) | ||||
−0.637494 | + | 0.770455i | \(0.720029\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.94651 | −0.281487 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −40.0905 | −1.62189 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −47.3925 | −1.91417 | −0.957083 | − | 0.289813i | \(-0.906407\pi\) | ||||
−0.957083 | + | 0.289813i | \(0.906407\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −16.2163 | −0.653902 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.6954 | −0.511099 | −0.255550 | − | 0.966796i | \(-0.582256\pi\) | ||||
−0.255550 | + | 0.966796i | \(0.582256\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.7371 | 1.51678 | 0.758390 | − | 0.651801i | \(-0.225986\pi\) | ||||
0.758390 | + | 0.651801i | \(0.225986\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −34.3797 | −1.37961 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.97407 | 0.119154 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.30978 | −0.332391 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 33.4242 | 1.33484 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.06107 | −0.0821804 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.8240 | 0.868798 | 0.434399 | − | 0.900721i | \(-0.356961\pi\) | ||||
0.434399 | + | 0.900721i | \(0.356961\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.65988 | 0.145467 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 33.5085 | 1.32974 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.66974 | 0.224643 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.2868 | −0.565176 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.1755 | −1.23136 | −0.615678 | − | 0.787998i | \(-0.711118\pi\) | ||||
−0.615678 | + | 0.787998i | \(0.711118\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.83624 | 0.269595 | 0.134798 | − | 0.990873i | \(-0.456962\pi\) | ||||
0.134798 | + | 0.990873i | \(0.456962\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.58557 | 0.141182 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.1377 | −1.26346 | −0.631731 | − | 0.775187i | \(-0.717655\pi\) | ||||
−0.631731 | + | 0.775187i | \(0.717655\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 29.1706 | 1.14505 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.9812 | 0.783123 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −45.1652 | −1.76745 | −0.883725 | − | 0.468006i | \(-0.844973\pi\) | ||||
−0.883725 | + | 0.468006i | \(0.844973\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.0567 | 1.01812 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.1263 | −0.473092 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.642445 | −0.0250261 | −0.0125130 | − | 0.999922i | \(-0.503983\pi\) | ||||
−0.0125130 | + | 0.999922i | \(0.503983\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.7027 | 1.54425 | 0.772127 | − | 0.635468i | \(-0.219193\pi\) | ||||
0.772127 | + | 0.635468i | \(0.219193\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 20.5206 | 0.796955 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −21.5135 | −0.834259 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.6731 | −0.490704 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.6238 | −0.797363 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 57.3520 | 2.21405 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.9142 | 1.69277 | 0.846384 | − | 0.532573i | \(-0.178775\pi\) | ||||
0.846384 | + | 0.532573i | \(0.178775\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.9348 | 0.497862 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.4535 | 0.401759 | 0.200879 | − | 0.979616i | \(-0.435620\pi\) | ||||
0.200879 | + | 0.979616i | \(0.435620\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.6114 | 1.02125 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.3501 | −0.396618 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.5758 | 0.825575 | 0.412788 | − | 0.910827i | \(-0.364555\pi\) | ||||
0.412788 | + | 0.910827i | \(0.364555\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.76446 | −0.143833 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.46124 | 0.132055 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 61.8531 | 2.35641 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.4628 | 1.19690 | 0.598451 | − | 0.801159i | \(-0.295783\pi\) | ||||
0.598451 | + | 0.801159i | \(0.295783\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12.3112 | 0.467663 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.90452 | 0.148107 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.6355 | 0.781624 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −21.3229 | −0.806507 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.4297 | −0.620541 | −0.310270 | − | 0.950648i | \(-0.600420\pi\) | ||||
−0.310270 | + | 0.950648i | \(0.600420\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.85410 | −0.145360 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17.4056 | 0.655534 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.61083 | −0.135799 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.88453 | 0.296110 | 0.148055 | − | 0.988979i | \(-0.452699\pi\) | ||||
0.148055 | + | 0.988979i | \(0.452699\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.00507 | 0.337716 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 36.4533 | 1.36519 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 38.8201 | 1.45179 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.9801 | −0.708826 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.6960 | −1.10747 | −0.553736 | − | 0.832692i | \(-0.686798\pi\) | ||||
−0.553736 | + | 0.832692i | \(0.686798\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −42.4665 | −1.58154 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.3205 | −0.495395 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.76805 | 0.177081 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.8430 | −0.476320 | −0.238160 | − | 0.971226i | \(-0.576544\pi\) | ||||
−0.238160 | + | 0.971226i | \(0.576544\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.1700 | 1.04333 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.56270 | −0.168758 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.2694 | 0.416246 | 0.208123 | − | 0.978103i | \(-0.433265\pi\) | ||||
0.208123 | + | 0.978103i | \(0.433265\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.46156 | −0.0907962 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.0766 | 0.592191 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −41.0944 | −1.51168 | −0.755842 | − | 0.654754i | \(-0.772772\pi\) | ||||
−0.755842 | + | 0.654754i | \(0.772772\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 38.3725 | 1.40965 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.0330 | −0.404763 | −0.202382 | − | 0.979307i | \(-0.564868\pi\) | ||||
−0.202382 | + | 0.979307i | \(0.564868\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.4063 | −0.527805 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.5537 | 0.386139 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.0146 | −0.585159 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.57041 | 0.276248 | 0.138124 | − | 0.990415i | \(-0.455893\pi\) | ||||
0.138124 | + | 0.990415i | \(0.455893\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.37208 | 0.0500015 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.5001 | −0.818861 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.28508 | −0.301126 | −0.150563 | − | 0.988600i | \(-0.548109\pi\) | ||||
−0.150563 | + | 0.988600i | \(0.548109\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −37.8418 | −1.37357 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.7079 | −1.40316 | −0.701581 | − | 0.712590i | \(-0.747522\pi\) | ||||
−0.701581 | + | 0.712590i | \(0.747522\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 41.0433 | 1.48587 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.28790 | 0.191184 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 33.4892 | 1.20922 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.4046 | 1.02430 | 0.512148 | − | 0.858897i | \(-0.328850\pi\) | ||||
0.512148 | + | 0.858897i | \(0.328850\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.18395 | −0.258724 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.51143 | −0.0543625 | −0.0271813 | − | 0.999631i | \(-0.508653\pi\) | ||||
−0.0271813 | + | 0.999631i | \(0.508653\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.7150 | −0.492656 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.39175 | 0.0858037 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 38.5872 | 1.38253 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −57.9456 | −2.07346 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.7648 | 0.420440 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.4466 | −0.408545 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.5362 | −1.01720 | −0.508602 | − | 0.861002i | \(-0.669838\pi\) | ||||
−0.508602 | + | 0.861002i | \(0.669838\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.8387 | −0.492672 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.06202 | −0.108873 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 65.8426 | 2.33814 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −26.8540 | −0.952414 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.0271 | 0.390600 | 0.195300 | − | 0.980744i | \(-0.437432\pi\) | ||||
0.195300 | + | 0.980744i | \(0.437432\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.1490 | −0.783575 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.36695 | −0.0482987 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −49.1829 | −1.73563 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.3569 | 0.858467 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.3443 | −0.645749 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.9339 | −0.384417 | −0.192208 | − | 0.981354i | \(-0.561565\pi\) | ||||
−0.192208 | + | 0.981354i | \(0.561565\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.99122 | −0.245495 | −0.122748 | − | 0.992438i | \(-0.539171\pi\) | ||||
−0.122748 | + | 0.992438i | \(0.539171\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.352269 | 0.0123546 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.49285 | −0.122349 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.53201 | −0.298497 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 14.1338 | 0.493874 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.73460 | 0.235039 | 0.117520 | − | 0.993071i | \(-0.462506\pi\) | ||||
0.117520 | + | 0.993071i | \(0.462506\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.33766 | −0.0814857 | −0.0407429 | − | 0.999170i | \(-0.512972\pi\) | ||||
−0.0407429 | + | 0.999170i | \(0.512972\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 14.2374 | 0.495681 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.2008 | 0.945864 | 0.472932 | − | 0.881099i | \(-0.343196\pi\) | ||||
0.472932 | + | 0.881099i | \(0.343196\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.0110 | −0.625547 | −0.312773 | − | 0.949828i | \(-0.601258\pi\) | ||||
−0.312773 | + | 0.949828i | \(0.601258\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.5592 | −0.470363 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.13238 | 0.108531 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23.6413 | −0.818140 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −33.8406 | −1.16970 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.8396 | 1.09922 | 0.549612 | − | 0.835420i | \(-0.314775\pi\) | ||||
0.549612 | + | 0.835420i | \(0.314775\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.6632 | −0.850457 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −20.2648 | −0.697957 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 23.1649 | 0.796897 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.1906 | 0.796838 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.4737 | 0.393775 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.36347 | 0.149578 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.8391 | −1.46678 | −0.733391 | − | 0.679807i | \(-0.762064\pi\) | ||||
−0.733391 | + | 0.679807i | \(0.762064\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.88809 | 0.338165 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −45.4153 | −1.55136 | −0.775678 | − | 0.631129i | \(-0.782592\pi\) | ||||
−0.775678 | + | 0.631129i | \(0.782592\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.5393 | −1.24671 | −0.623353 | − | 0.781940i | \(-0.714230\pi\) | ||||
−0.623353 | + | 0.781940i | \(0.714230\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −23.9463 | −0.816086 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.46830 | 0.152103 | 0.0760514 | − | 0.997104i | \(-0.475769\pi\) | ||||
0.0760514 | + | 0.997104i | \(0.475769\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 37.7016 | 1.28189 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.9883 | −0.407143 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 36.5236 | 1.23898 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.4567 | 0.625381 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.2312 | −0.413963 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −29.1759 | −0.986326 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.8397 | −0.737474 | −0.368737 | − | 0.929534i | \(-0.620210\pi\) | ||||
−0.368737 | + | 0.929534i | \(0.620210\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21.5898 | 0.728207 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.5631 | 1.60244 | 0.801220 | − | 0.598370i | \(-0.204185\pi\) | ||||
0.801220 | + | 0.598370i | \(0.204185\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.6165 | −0.727454 | −0.363727 | − | 0.931506i | \(-0.618496\pi\) | ||||
−0.363727 | + | 0.931506i | \(0.618496\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.5396 | −0.488744 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.9754 | −0.603555 | −0.301777 | − | 0.953378i | \(-0.597580\pi\) | ||||
−0.301777 | + | 0.953378i | \(0.597580\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 49.4814 | 1.65955 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19.9375 | 0.667933 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −41.4174 | −1.38598 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31.3893 | 1.04923 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −43.4440 | −1.45055 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.4744 | −0.416044 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.1722 | 1.13844 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.29475 | 0.176198 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.3761 | 0.444636 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.0112 | −0.398825 | −0.199413 | − | 0.979916i | \(-0.563903\pi\) | ||||
−0.199413 | + | 0.979916i | \(0.563903\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.65962 | 0.0550460 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.2924 | 0.473527 | 0.236764 | − | 0.971567i | \(-0.423913\pi\) | ||||
0.236764 | + | 0.971567i | \(0.423913\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42.8046 | 1.41663 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −28.5861 | −0.945028 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 38.4774 | 1.27064 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.0682 | 1.45368 | 0.726838 | − | 0.686809i | \(-0.240989\pi\) | ||||
0.726838 | + | 0.686809i | \(0.240989\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −35.5600 | −1.17174 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −66.5241 | −2.18967 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.64169 | −0.0539784 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 19.5185 | 0.641073 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.45633 | 0.0805894 | 0.0402947 | − | 0.999188i | \(-0.487170\pi\) | ||||
0.0402947 | + | 0.999188i | \(0.487170\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.85739 | 0.191968 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20.2362 | 0.662502 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.4471 | 0.701396 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.89265 | 0.290510 | 0.145255 | − | 0.989394i | \(-0.453600\pi\) | ||||
0.145255 | + | 0.989394i | \(0.453600\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 42.7072 | 1.39370 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.7881 | −0.612476 | −0.306238 | − | 0.951955i | \(-0.599070\pi\) | ||||
−0.306238 | + | 0.951955i | \(0.599070\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −43.6871 | −1.42265 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −22.6112 | −0.735542 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.2408 | −1.11268 | −0.556338 | − | 0.830956i | \(-0.687794\pi\) | ||||
−0.556338 | + | 0.830956i | \(0.687794\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −56.4641 | −1.83290 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.0599 | −0.520779 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.9789 | −0.388034 | −0.194017 | − | 0.980998i | \(-0.562152\pi\) | ||||
−0.194017 | + | 0.980998i | \(0.562152\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.7933 | 0.608137 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.9495 | 0.418598 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.55891 | −0.179506 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.88164 | 0.157472 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.36064 | 0.237193 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −24.8275 | −0.799226 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.01631 | 0.0326822 | 0.0163411 | − | 0.999866i | \(-0.494798\pi\) | ||||
0.0163411 | + | 0.999866i | \(0.494798\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21.1998 | 0.681036 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.97721 | 0.320184 | 0.160092 | − | 0.987102i | \(-0.448821\pi\) | ||||
0.160092 | + | 0.987102i | \(0.448821\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.76573 | 0.184841 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16.3451 | 0.523463 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.1303 | −0.420075 | −0.210037 | − | 0.977693i | \(-0.567359\pi\) | ||||
−0.210037 | + | 0.977693i | \(0.567359\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.54419 | −0.177193 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.8644 | −0.602293 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.6521 | −0.658699 | −0.329350 | − | 0.944208i | \(-0.606829\pi\) | ||||
−0.329350 | + | 0.944208i | \(0.606829\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41.4337 | 1.32019 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 25.7026 | 0.818123 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.65964 | 0.307159 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.39362 | −0.139568 | −0.0697840 | − | 0.997562i | \(-0.522231\pi\) | ||||
−0.0697840 | + | 0.997562i | \(0.522231\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −33.1175 | −1.05095 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.7280 | 0.498611 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48.8690 | 1.54770 | 0.773848 | − | 0.633371i | \(-0.218329\pi\) | ||||
0.773848 | + | 0.633371i | \(0.218329\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.05074 | −0.128160 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4016.2.a.e.1.4 | 5 | ||
4.3 | odd | 2 | 502.2.a.c.1.2 | ✓ | 5 | ||
12.11 | even | 2 | 4518.2.a.v.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
502.2.a.c.1.2 | ✓ | 5 | 4.3 | odd | 2 | ||
4016.2.a.e.1.4 | 5 | 1.1 | even | 1 | trivial | ||
4518.2.a.v.1.1 | 5 | 12.11 | even | 2 |