Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [232,4,Mod(1,232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(232, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("232.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 232 = 2^{3} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 232.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: | \(13.6884431213\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 34x^{3} + 74x^{2} + 94x - 198 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(4.30242\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 232.1 |
$q$-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 | ||||||||
\(3\) | 7.82921 | 1.50673 | 0.753366 | − | 0.657602i | \(-0.228429\pi\) | ||||
0.753366 | + | 0.657602i | \(0.228429\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.04208 | −0.629863 | −0.314931 | − | 0.949114i | \(-0.601982\pi\) | ||||
−0.314931 | + | 0.949114i | \(0.601982\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 14.1473 | 0.763880 | 0.381940 | − | 0.924187i | \(-0.375256\pi\) | ||||
0.381940 | + | 0.924187i | \(0.375256\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 34.2965 | 1.27024 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −16.9982 | −0.465922 | −0.232961 | − | 0.972486i | \(-0.574842\pi\) | ||||
−0.232961 | + | 0.972486i | \(0.574842\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 62.0351 | 1.32349 | 0.661747 | − | 0.749727i | \(-0.269815\pi\) | ||||
0.661747 | + | 0.749727i | \(0.269815\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −55.1339 | −0.949034 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 104.842 | 1.49576 | 0.747881 | − | 0.663833i | \(-0.231071\pi\) | ||||
0.747881 | + | 0.663833i | \(0.231071\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −9.38323 | −0.113298 | −0.0566490 | − | 0.998394i | \(-0.518042\pi\) | ||||
−0.0566490 | + | 0.998394i | \(0.518042\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 110.762 | 1.15096 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 173.620 | 1.57401 | 0.787005 | − | 0.616947i | \(-0.211631\pi\) | ||||
0.787005 | + | 0.616947i | \(0.211631\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −75.4091 | −0.603273 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 57.1255 | 0.407178 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −28.2215 | −0.163507 | −0.0817536 | − | 0.996653i | \(-0.526052\pi\) | ||||
−0.0817536 | + | 0.996653i | \(0.526052\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −133.082 | −0.702020 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −99.6261 | −0.481140 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −171.527 | −0.762130 | −0.381065 | − | 0.924548i | \(-0.624443\pi\) | ||||
−0.381065 | + | 0.924548i | \(0.624443\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 485.685 | 1.99415 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 92.0027 | 0.350449 | 0.175225 | − | 0.984529i | \(-0.443935\pi\) | ||||
0.175225 | + | 0.984529i | \(0.443935\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −519.014 | −1.84067 | −0.920335 | − | 0.391131i | \(-0.872084\pi\) | ||||
−0.920335 | + | 0.391131i | \(0.872084\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −241.518 | −0.800077 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 109.612 | 0.340182 | 0.170091 | − | 0.985428i | \(-0.445594\pi\) | ||||
0.170091 | + | 0.985428i | \(0.445594\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −142.855 | −0.416487 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 820.830 | 2.25371 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 140.553 | 0.364273 | 0.182136 | − | 0.983273i | \(-0.441699\pi\) | ||||
0.182136 | + | 0.983273i | \(0.441699\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 119.703 | 0.293467 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −73.4632 | −0.170710 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 353.254 | 0.779487 | 0.389744 | − | 0.920923i | \(-0.372564\pi\) | ||||
0.389744 | + | 0.920923i | \(0.372564\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −185.355 | −0.389053 | −0.194526 | − | 0.980897i | \(-0.562317\pi\) | ||||
−0.194526 | + | 0.980897i | \(0.562317\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 485.201 | 0.970311 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −436.856 | −0.833620 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 574.840 | 1.04818 | 0.524088 | − | 0.851664i | \(-0.324406\pi\) | ||||
0.524088 | + | 0.851664i | \(0.324406\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1359.30 | 2.37161 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 535.054 | 0.894355 | 0.447177 | − | 0.894445i | \(-0.352429\pi\) | ||||
0.447177 | + | 0.894445i | \(0.352429\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −508.723 | −0.815637 | −0.407818 | − | 0.913063i | \(-0.633710\pi\) | ||||
−0.407818 | + | 0.913063i | \(0.633710\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −590.393 | −0.908970 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −240.478 | −0.355909 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −61.0156 | −0.0868961 | −0.0434481 | − | 0.999056i | \(-0.513834\pi\) | ||||
−0.0434481 | + | 0.999056i | \(0.513834\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −478.757 | −0.656731 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −826.753 | −1.09335 | −0.546674 | − | 0.837345i | \(-0.684106\pi\) | ||||
−0.546674 | + | 0.837345i | \(0.684106\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −738.306 | −0.942124 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 227.047 | 0.279793 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −938.445 | −1.11770 | −0.558848 | − | 0.829270i | \(-0.688757\pi\) | ||||
−0.558848 | + | 0.829270i | \(0.688757\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 877.626 | 1.01099 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −220.952 | −0.246361 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 66.0775 | 0.0713621 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −888.766 | −0.930315 | −0.465158 | − | 0.885228i | \(-0.654002\pi\) | ||||
−0.465158 | + | 0.885228i | \(0.654002\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −582.978 | −0.591833 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1551.83 | −1.52884 | −0.764420 | − | 0.644719i | \(-0.776974\pi\) | ||||
−0.764420 | + | 0.644719i | \(0.776974\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −402.438 | −0.384984 | −0.192492 | − | 0.981299i | \(-0.561657\pi\) | ||||
−0.192492 | + | 0.981299i | \(0.561657\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −779.994 | −0.724948 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −821.553 | −0.742267 | −0.371133 | − | 0.928580i | \(-0.621031\pi\) | ||||
−0.371133 | + | 0.928580i | \(0.621031\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 803.052 | 0.705674 | 0.352837 | − | 0.935685i | \(-0.385217\pi\) | ||||
0.352837 | + | 0.935685i | \(0.385217\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1342.92 | −1.14832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −735.506 | −0.612306 | −0.306153 | − | 0.951982i | \(-0.599042\pi\) | ||||
−0.306153 | + | 0.951982i | \(0.599042\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1222.64 | −0.991410 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2127.58 | 1.68116 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1483.23 | 1.14258 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1042.06 | −0.782916 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 720.308 | 0.528033 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1411.30 | 1.00984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1895.16 | −1.32416 | −0.662078 | − | 0.749435i | \(-0.730325\pi\) | ||||
−0.662078 | + | 0.749435i | \(0.730325\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4063.46 | −2.77340 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1145.54 | −0.764020 | −0.382010 | − | 0.924158i | \(-0.624768\pi\) | ||||
−0.382010 | + | 0.924158i | \(0.624768\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −132.747 | −0.0865461 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −402.283 | −0.256466 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2871.41 | 1.79067 | 0.895334 | − | 0.445396i | \(-0.146937\pi\) | ||||
0.895334 | + | 0.445396i | \(0.146937\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 777.734 | 0.474579 | 0.237290 | − | 0.971439i | \(-0.423741\pi\) | ||||
0.237290 | + | 0.971439i | \(0.423741\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 858.174 | 0.512562 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1054.48 | −0.616646 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −204.220 | −0.116963 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1118.44 | −0.627534 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2373.29 | 1.30488 | 0.652440 | − | 0.757840i | \(-0.273745\pi\) | ||||
0.652440 | + | 0.757840i | \(0.273745\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 102.190 | 0.0550733 | 0.0275366 | − | 0.999621i | \(-0.491234\pi\) | ||||
0.0275366 | + | 0.999621i | \(0.491234\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3595.71 | 1.89998 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 198.738 | 0.102987 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 585.462 | 0.297611 | 0.148805 | − | 0.988866i | \(-0.452457\pi\) | ||||
0.148805 | + | 0.988866i | \(0.452457\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1100.42 | 0.548861 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2456.24 | 1.20235 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1440.36 | 0.692131 | 0.346066 | − | 0.938210i | \(-0.387517\pi\) | ||||
0.346066 | + | 0.938210i | \(0.387517\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 937.176 | 0.442176 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3338.00 | 1.54672 | 0.773359 | − | 0.633968i | \(-0.218575\pi\) | ||||
0.773359 | + | 0.633968i | \(0.218575\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1651.35 | 0.751638 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −321.812 | −0.143916 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3612.07 | −1.58740 | −0.793701 | − | 0.608308i | \(-0.791849\pi\) | ||||
−0.793701 | + | 0.608308i | \(0.791849\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1066.83 | −0.460828 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2765.70 | 1.17448 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2415.54 | −1.00864 | −0.504319 | − | 0.863517i | \(-0.668256\pi\) | ||||
−0.504319 | + | 0.863517i | \(0.668256\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1755.89 | −0.721073 | −0.360537 | − | 0.932745i | \(-0.617406\pi\) | ||||
−0.360537 | + | 0.932745i | \(0.617406\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1451.18 | −0.586198 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1207.90 | 0.480037 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1782.13 | −0.696909 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 808.170 | 0.311035 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1156.10 | 0.437972 | 0.218986 | − | 0.975728i | \(-0.429725\pi\) | ||||
0.218986 | + | 0.975728i | \(0.429725\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3214.73 | −1.19897 | −0.599485 | − | 0.800386i | \(-0.704628\pi\) | ||||
−0.599485 | + | 0.800386i | \(0.704628\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3420.23 | −1.25604 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3924.03 | −1.41916 | −0.709582 | − | 0.704623i | \(-0.751116\pi\) | ||||
−0.709582 | + | 0.704623i | \(0.751116\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4463.80 | 1.59010 | 0.795051 | − | 0.606543i | \(-0.207444\pi\) | ||||
0.795051 | + | 0.606543i | \(0.207444\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4500.54 | 1.57932 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 410.271 | 0.141849 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −647.890 | −0.220735 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5954.54 | 1.99937 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 159.498 | 0.0527881 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4881.35 | 1.59263 | 0.796317 | − | 0.604880i | \(-0.206779\pi\) | ||||
0.796317 | + | 0.604880i | \(0.206779\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4189.05 | 1.34755 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3654.93 | 1.15937 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −399.256 | −0.124900 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3982.90 | −1.22895 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6503.89 | 1.97963 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1533.22 | −0.460414 | −0.230207 | − | 0.973142i | \(-0.573940\pi\) | ||||
−0.230207 | + | 0.973142i | \(0.573940\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2586.27 | −0.766301 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3110.06 | −0.909348 | −0.454674 | − | 0.890658i | \(-0.650244\pi\) | ||||
−0.454674 | + | 0.890658i | \(0.650244\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4686.03 | −1.35223 | −0.676117 | − | 0.736794i | \(-0.736339\pi\) | ||||
−0.676117 | + | 0.736794i | \(0.736339\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1882.75 | −0.536259 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −908.748 | −0.255511 | −0.127756 | − | 0.991806i | \(-0.540777\pi\) | ||||
−0.127756 | + | 0.991806i | \(0.540777\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −771.896 | −0.214268 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −477.704 | −0.130929 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.3950 | −0.00497854 | −0.00248927 | − | 0.999997i | \(-0.500792\pi\) | ||||
−0.00248927 | + | 0.999997i | \(0.500792\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6199.96 | 1.65716 | 0.828578 | − | 0.559874i | \(-0.189151\pi\) | ||||
0.828578 | + | 0.559874i | \(0.189151\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5290.68 | −1.39670 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1006.00 | 0.262330 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −582.089 | −0.149949 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6472.82 | −1.64738 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3325.41 | 0.836248 | 0.418124 | − | 0.908390i | \(-0.362688\pi\) | ||||
0.418124 | + | 0.908390i | \(0.362688\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2951.22 | −0.733366 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5780.35 | −1.41953 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2713.20 | 0.658541 | 0.329271 | − | 0.944236i | \(-0.393197\pi\) | ||||
0.329271 | + | 0.944236i | \(0.393197\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2426.63 | −0.582176 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 994.597 | 0.235878 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6234.94 | 1.46184 | 0.730918 | − | 0.682465i | \(-0.239092\pi\) | ||||
0.730918 | + | 0.682465i | \(0.239092\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −989.787 | −0.229442 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7347.28 | −1.68407 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5745.23 | −1.30220 | −0.651102 | − | 0.758990i | \(-0.725693\pi\) | ||||
−0.651102 | + | 0.758990i | \(0.725693\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8855.53 | 1.98500 | 0.992501 | − | 0.122238i | \(-0.0390072\pi\) | ||||
0.992501 | + | 0.122238i | \(0.0390072\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6871.12 | 1.52329 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1281.82 | 0.281078 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2805.71 | −0.608588 | −0.304294 | − | 0.952578i | \(-0.598420\pi\) | ||||
−0.304294 | + | 0.952578i | \(0.598420\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −967.896 | −0.207693 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5133.23 | 1.08976 | 0.544881 | − | 0.838514i | \(-0.316575\pi\) | ||||
0.544881 | + | 0.838514i | \(0.316575\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2928.86 | 0.615204 | 0.307602 | − | 0.951515i | \(-0.400473\pi\) | ||||
0.307602 | + | 0.951515i | \(0.400473\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 517.334 | 0.107524 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1301.59 | 0.267701 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6078.87 | 1.23730 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6958.34 | −1.40173 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5685.37 | 1.13359 | 0.566796 | − | 0.823858i | \(-0.308183\pi\) | ||||
0.566796 | + | 0.823858i | \(0.308183\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2487.64 | −0.490970 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −971.031 | −0.189713 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10770.5 | 2.08319 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7342.62 | −1.40605 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12149.6 | −2.30355 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1305.28 | 0.245050 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2879.21 | 0.535262 | 0.267631 | − | 0.963522i | \(-0.413759\pi\) | ||||
0.267631 | + | 0.963522i | \(0.413759\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3150.77 | −0.580068 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 513.825 | 0.0936860 | 0.0468430 | − | 0.998902i | \(-0.485084\pi\) | ||||
0.0468430 | + | 0.998902i | \(0.485084\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1508.76 | −0.272460 | −0.136230 | − | 0.990677i | \(-0.543499\pi\) | ||||
−0.136230 | + | 0.990677i | \(0.543499\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3416.82 | −0.611163 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5411.89 | 0.958872 | 0.479436 | − | 0.877577i | \(-0.340841\pi\) | ||||
0.479436 | + | 0.877577i | \(0.340841\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −492.947 | −0.0865196 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6432.11 | −1.11840 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −983.758 | −0.169467 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4678.01 | −0.798429 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6287.26 | 1.06326 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1550.71 | 0.259858 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10354.1 | 1.71938 | 0.859688 | − | 0.510820i | \(-0.170658\pi\) | ||||
0.859688 | + | 0.510820i | \(0.170658\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5882.75 | −0.968087 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4048.07 | −0.660208 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4707.20 | 0.760882 | 0.380441 | − | 0.924805i | \(-0.375772\pi\) | ||||
0.380441 | + | 0.924805i | \(0.375772\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5758.43 | −0.922581 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 479.714 | 0.0761817 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6873.52 | −1.08203 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9572.33 | −1.49379 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6733.27 | −1.04167 | −0.520837 | − | 0.853656i | \(-0.674380\pi\) | ||||
−0.520837 | + | 0.853656i | \(0.674380\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9272.50 | −1.42219 | −0.711097 | − | 0.703094i | \(-0.751801\pi\) | ||||
−0.711097 | + | 0.703094i | \(0.751801\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3543.79 | 0.538898 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5776.97 | 0.871041 | 0.435520 | − | 0.900179i | \(-0.356564\pi\) | ||||
0.435520 | + | 0.900179i | \(0.356564\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3767.89 | −0.563321 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11612.5 | 1.72157 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3821.93 | 0.561877 | 0.280938 | − | 0.959726i | \(-0.409354\pi\) | ||||
0.280938 | + | 0.959726i | \(0.409354\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6770.95 | −0.987164 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8158.51 | −1.17964 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3582.47 | 0.513739 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9481.16 | −1.34854 | −0.674268 | − | 0.738487i | \(-0.735541\pi\) | ||||
−0.674268 | + | 0.738487i | \(0.735541\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3155.37 | 0.445154 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1988.44 | 0.278261 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11849.6 | −1.64490 | −0.822450 | − | 0.568837i | \(-0.807394\pi\) | ||||
−0.822450 | + | 0.568837i | \(0.807394\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11049.3 | 1.52156 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1799.02 | 0.245767 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14650.4 | −1.98560 | −0.992799 | − | 0.119794i | \(-0.961776\pi\) | ||||
−0.992799 | + | 0.119794i | \(0.961776\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14837.6 | −1.99515 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2202.45 | −0.293837 | −0.146919 | − | 0.989149i | \(-0.546936\pi\) | ||||
−0.146919 | + | 0.989149i | \(0.546936\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1693.46 | 0.224174 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −17800.3 | −2.33809 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5614.61 | 0.731804 | 0.365902 | − | 0.930653i | \(-0.380760\pi\) | ||||
0.365902 | + | 0.930653i | \(0.380760\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18202.7 | 2.35434 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8968.70 | −1.15117 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 429.677 | 0.0547326 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1672.32 | 0.211414 | 0.105707 | − | 0.994397i | \(-0.466289\pi\) | ||||
0.105707 | + | 0.994397i | \(0.466289\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1039.30 | −0.130402 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1183.01 | −0.147324 | −0.0736619 | − | 0.997283i | \(-0.523469\pi\) | ||||
−0.0736619 | + | 0.997283i | \(0.523469\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1750.72 | −0.216401 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3371.45 | 0.413651 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2915.64 | 0.355093 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6264.74 | −0.757388 | −0.378694 | − | 0.925522i | \(-0.623627\pi\) | ||||
−0.378694 | + | 0.925522i | \(0.623627\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22480.9 | 2.69805 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4997.58 | 0.595435 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5822.06 | 0.688659 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6089.04 | 0.715063 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4224.75 | −0.492584 | −0.246292 | − | 0.969196i | \(-0.579212\pi\) | ||||
−0.246292 | + | 0.969196i | \(0.579212\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10801.7 | 1.25046 | 0.625231 | − | 0.780440i | \(-0.285005\pi\) | ||||
0.625231 | + | 0.780440i | \(0.285005\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3759.30 | 0.432112 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7906.05 | −0.902352 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2622.26 | −0.297190 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8255.77 | −0.929120 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13127.7 | 1.46715 | 0.733574 | − | 0.679610i | \(-0.237851\pi\) | ||||
0.733574 | + | 0.679610i | \(0.237851\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11403.2 | −1.26559 | −0.632797 | − | 0.774318i | \(-0.718093\pi\) | ||||
−0.632797 | + | 0.774318i | \(0.718093\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1598.88 | −0.176231 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1629.11 | −0.178332 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14656.2 | 1.59339 | 0.796697 | − | 0.604378i | \(-0.206578\pi\) | ||||
0.796697 | + | 0.604378i | \(0.206578\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4899.42 | −0.529038 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6136.95 | 0.658184 | 0.329092 | − | 0.944298i | \(-0.393257\pi\) | ||||
0.329092 | + | 0.944298i | \(0.393257\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6608.61 | 0.703995 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18580.9 | 1.96610 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18012.1 | −1.89319 | −0.946594 | − | 0.322428i | \(-0.895501\pi\) | ||||
−0.946594 | + | 0.322428i | \(0.895501\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1563.88 | −0.163282 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 800.063 | 0.0829807 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6180.31 | −0.636786 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 715.440 | 0.0732316 | 0.0366158 | − | 0.999329i | \(-0.488342\pi\) | ||||
0.0366158 | + | 0.999329i | \(0.488342\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5989.16 | 0.609042 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16471.2 | −1.66408 | −0.832038 | − | 0.554719i | \(-0.812826\pi\) | ||||
−0.832038 | + | 0.554719i | \(0.812826\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3844.07 | 0.385851 | 0.192925 | − | 0.981213i | \(-0.438202\pi\) | ||||
0.192925 | + | 0.981213i | \(0.438202\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1555.96 | 0.155174 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15072.5 | 1.49352 | 0.746759 | − | 0.665094i | \(-0.231609\pi\) | ||||
0.746759 | + | 0.665094i | \(0.231609\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8132.41 | 0.800682 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4583.70 | 0.448420 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8822.29 | 0.857610 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 707.581 | 0.0683496 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4820.48 | 0.462714 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8856.14 | 0.844776 | 0.422388 | − | 0.906415i | \(-0.361192\pi\) | ||||
0.422388 | + | 0.906415i | \(0.361192\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10640.7 | −1.00867 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 19230.4 | 1.81163 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6258.76 | 0.585971 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6998.94 | 0.651237 | 0.325618 | − | 0.945501i | \(-0.394428\pi\) | ||||
0.325618 | + | 0.945501i | \(0.394428\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11276.8 | 1.04286 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2169.60 | −0.199415 | −0.0997076 | − | 0.995017i | \(-0.531791\pi\) | ||||
−0.0997076 | + | 0.995017i | \(0.531791\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3040.42 | 0.277756 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4105.38 | 0.372774 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7569.55 | 0.683180 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17541.6 | −1.57368 | −0.786842 | − | 0.617155i | \(-0.788285\pi\) | ||||
−0.786842 | + | 0.617155i | \(0.788285\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 26133.9 | 2.33049 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16190.4 | −1.43517 | −0.717587 | − | 0.696469i | \(-0.754753\pi\) | ||||
−0.717587 | + | 0.696469i | \(0.754753\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10928.1 | 0.962959 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12928.8 | 1.13252 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1493.11 | 0.130021 | 0.0650106 | − | 0.997885i | \(-0.479292\pi\) | ||||
0.0650106 | + | 0.997885i | \(0.479292\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7197.03 | −0.623049 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −536.022 | −0.0461325 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2834.00 | 0.242487 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1863.20 | −0.158498 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −28279.6 | −2.39179 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7026.84 | −0.590886 | −0.295443 | − | 0.955360i | \(-0.595467\pi\) | ||||
−0.295443 | + | 0.955360i | \(0.595467\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21924.1 | 1.83303 | 0.916514 | − | 0.400003i | \(-0.130991\pi\) | ||||
0.916514 | + | 0.400003i | \(0.130991\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8352.45 | −0.694345 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2958.80 | −0.244568 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17976.8 | 1.47750 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12115.4 | 0.990135 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5707.39 | 0.463817 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5785.44 | 0.467526 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −18911.8 | −1.51975 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2428.28 | 0.194051 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −983.325 | −0.0781450 | −0.0390725 | − | 0.999236i | \(-0.512440\pi\) | ||||
−0.0390725 | + | 0.999236i | \(0.512440\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13747.2 | −1.08646 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5655.16 | −0.444478 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6100.54 | 0.476856 | 0.238428 | − | 0.971160i | \(-0.423368\pi\) | ||||
0.238428 | + | 0.971160i | \(0.423368\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6357.01 | −0.494190 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −272.114 | −0.0210389 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −863.204 | −0.0663782 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9456.93 | 0.723287 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7531.50 | 0.572926 | 0.286463 | − | 0.958091i | \(-0.407520\pi\) | ||||
0.286463 | + | 0.958091i | \(0.407520\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32197.0 | −2.43612 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13952.6 | −1.05005 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19553.5 | −1.46373 | −0.731866 | − | 0.681449i | \(-0.761350\pi\) | ||||
−0.731866 | + | 0.681449i | \(0.761350\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5179.49 | 0.385669 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6773.10 | −0.501664 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23656.9 | 1.74297 | 0.871483 | − | 0.490426i | \(-0.163159\pi\) | ||||
0.871483 | + | 0.490426i | \(0.163159\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5466.08 | −0.400610 | −0.200305 | − | 0.979734i | \(-0.564193\pi\) | ||||
−0.200305 | + | 0.979734i | \(0.564193\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9051.37 | 0.659907 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13092.5 | −0.949557 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −653.065 | −0.0471187 | −0.0235593 | − | 0.999722i | \(-0.507500\pi\) | ||||
−0.0235593 | + | 0.999722i | \(0.507500\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −25168.8 | −1.80653 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11696.3 | −0.835187 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2389.15 | −0.169723 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −14982.6 | −1.05890 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19414.4 | −1.36511 | −0.682554 | − | 0.730835i | \(-0.739131\pi\) | ||||
−0.682554 | + | 0.730835i | \(0.739131\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 264.809 | 0.0185250 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −30722.0 | −2.13830 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18910.6 | 1.30955 | 0.654777 | − | 0.755822i | \(-0.272763\pi\) | ||||
0.654777 | + | 0.755822i | \(0.272763\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10445.0 | −0.719670 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 34948.0 | 2.39586 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12128.7 | −0.827322 | −0.413661 | − | 0.910431i | \(-0.635750\pi\) | ||||
−0.413661 | + | 0.910431i | \(0.635750\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25803.3 | −1.75131 | −0.875656 | − | 0.482936i | \(-0.839570\pi\) | ||||
−0.875656 | + | 0.482936i | \(0.839570\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19715.0 | 1.33144 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7338.28 | 0.493130 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12183.6 | 0.814690 | 0.407345 | − | 0.913274i | \(-0.366455\pi\) | ||||
0.407345 | + | 0.913274i | \(0.366455\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3212.09 | 0.213728 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6799.78 | 0.450229 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16519.2 | −1.08843 | −0.544213 | − | 0.838947i | \(-0.683171\pi\) | ||||
−0.544213 | + | 0.838947i | \(0.683171\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5072.47 | −0.332588 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6518.09 | −0.425297 | −0.212649 | − | 0.977129i | \(-0.568209\pi\) | ||||
−0.212649 | + | 0.977129i | \(0.568209\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4344.67 | −0.282111 | −0.141056 | − | 0.990002i | \(-0.545050\pi\) | ||||
−0.141056 | + | 0.990002i | \(0.545050\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9918.12 | 0.640902 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13276.4 | −0.853787 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −512.326 | −0.0327889 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1248.74 | 0.0795374 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −17983.2 | −1.13996 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2989.38 | 0.188598 | 0.0942989 | − | 0.995544i | \(-0.469939\pi\) | ||||
0.0942989 | + | 0.995544i | \(0.469939\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 38217.1 | 2.39967 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13345.8 | 0.834037 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8862.02 | −0.551218 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18350.5 | 1.13604 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15375.4 | 0.947411 | 0.473706 | − | 0.880683i | \(-0.342916\pi\) | ||||
0.473706 | + | 0.880683i | \(0.342916\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16966.5 | −1.04058 | −0.520291 | − | 0.853989i | \(-0.674177\pi\) | ||||
−0.520291 | + | 0.853989i | \(0.674177\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 28615.2 | 1.74686 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12379.7 | −0.752234 | −0.376117 | − | 0.926572i | \(-0.622741\pi\) | ||||
−0.376117 | + | 0.926572i | \(0.622741\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6004.68 | −0.363181 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3125.86 | −0.188191 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30418.3 | 1.82291 | 0.911453 | − | 0.411403i | \(-0.134961\pi\) | ||||
0.911453 | + | 0.411403i | \(0.134961\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8067.01 | 0.481228 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −17447.4 | −1.03605 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6069.11 | −0.358754 | −0.179377 | − | 0.983780i | \(-0.557408\pi\) | ||||
−0.179377 | + | 0.983780i | \(0.557408\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24894.6 | −1.46489 | −0.732443 | − | 0.680829i | \(-0.761620\pi\) | ||||
−0.732443 | + | 0.680829i | \(0.761620\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 50920.3 | 2.98277 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 934.815 | 0.0545121 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5034.97 | 0.292286 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12003.9 | −0.693720 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3150.69 | 0.181268 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21677.5 | 1.24162 | 0.620808 | − | 0.783963i | \(-0.286805\pi\) | ||||
0.620808 | + | 0.783963i | \(0.286805\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4307.79 | −0.245640 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21322.2 | −1.21046 | −0.605228 | − | 0.796052i | \(-0.706918\pi\) | ||||
−0.605228 | + | 0.796052i | \(0.706918\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12573.6 | −0.710649 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24349.3 | −1.37014 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.7459 | 0.00217068 | 0.00108534 | − | 0.999999i | \(-0.499655\pi\) | ||||
0.00108534 | + | 0.999999i | \(0.499655\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20220.7 | −1.12787 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −36687.9 | −2.03745 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8719.23 | 0.482113 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27812.0 | 1.53114 | 0.765571 | − | 0.643351i | \(-0.222456\pi\) | ||||
0.765571 | + | 0.643351i | \(0.222456\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8247.54 | −0.452090 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5476.86 | −0.298920 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9645.76 | 0.524188 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7114.78 | −0.384987 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23404.8 | 1.26104 | 0.630519 | − | 0.776174i | \(-0.282842\pi\) | ||||
0.630519 | + | 0.776174i | \(0.282842\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1609.47 | 0.0863477 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6043.33 | −0.322844 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21954.1 | −1.16785 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8525.03 | 0.451572 | 0.225786 | − | 0.974177i | \(-0.427505\pi\) | ||||
0.225786 | + | 0.974177i | \(0.427505\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2092.62 | −0.110379 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4899.80 | −0.257362 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7425.76 | 0.388402 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −144.018 | −0.00750132 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13242.3 | −0.686862 | −0.343431 | − | 0.939178i | \(-0.611589\pi\) | ||||
−0.343431 | + | 0.939178i | \(0.611589\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5693.39 | −0.294082 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 48540.8 | 2.49689 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2186.86 | −0.112025 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5299.22 | 0.270340 | 0.135170 | − | 0.990822i | \(-0.456842\pi\) | ||||
0.135170 | + | 0.990822i | \(0.456842\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28495.4 | −1.44771 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −54414.5 | −2.75320 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28433.7 | 1.43278 | 0.716388 | − | 0.697702i | \(-0.245794\pi\) | ||||
0.716388 | + | 0.697702i | \(0.245794\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7876.15 | 0.395260 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9771.23 | −0.488369 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19450.7 | −0.968209 | −0.484105 | − | 0.875010i | \(-0.660855\pi\) | ||||
−0.484105 | + | 0.875010i | \(0.660855\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4557.30 | −0.225933 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15260.1 | −0.753484 | −0.376742 | − | 0.926318i | \(-0.622956\pi\) | ||||
−0.376742 | + | 0.926318i | \(0.622956\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16712.9 | −0.821896 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −28354.7 | −1.38881 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11622.7 | −0.567003 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23290.8 | 1.13168 | 0.565841 | − | 0.824514i | \(-0.308551\pi\) | ||||
0.565841 | + | 0.824514i | \(0.308551\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26035.3 | 1.26000 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −719.627 | −0.0346886 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22951.5 | −1.10196 | −0.550981 | − | 0.834517i | \(-0.685747\pi\) | ||||
−0.550981 | + | 0.834517i | \(0.685747\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −23105.7 | −1.10499 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14975.4 | 0.713349 | 0.356675 | − | 0.934229i | \(-0.383910\pi\) | ||||
0.356675 | + | 0.934229i | \(0.383910\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11361.0 | 0.539050 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −25321.3 | −1.19672 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 21914.1 | 1.03165 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30907.7 | 1.44936 | 0.724682 | − | 0.689084i | \(-0.241987\pi\) | ||||
0.724682 | + | 0.689084i | \(0.241987\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21242.2 | 0.992244 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3728.71 | −0.173496 | −0.0867479 | − | 0.996230i | \(-0.527647\pi\) | ||||
−0.0867479 | + | 0.996230i | \(0.527647\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2128.16 | 0.0986395 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −18998.6 | −0.877182 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −863.283 | −0.0397051 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9094.94 | −0.416700 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1656.64 | 0.0756111 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4122.87 | −0.187454 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33291.9 | 1.50791 | 0.753957 | − | 0.656923i | \(-0.228142\pi\) | ||||
0.753957 | + | 0.656923i | \(0.228142\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 48814.7 | 2.20260 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10405.4 | −0.467729 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11498.5 | −0.514909 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7749.24 | −0.345707 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −36436.3 | −1.61937 | −0.809687 | − | 0.586862i | \(-0.800363\pi\) | ||||
−0.809687 | + | 0.586862i | \(0.800363\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11491.9 | 0.508831 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −32185.4 | −1.41974 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8647.37 | 0.380024 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17297.1 | −0.757318 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −44980.6 | −1.96207 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9776.41 | 0.424871 | 0.212435 | − | 0.977175i | \(-0.431861\pi\) | ||||
0.212435 | + | 0.977175i | \(0.431861\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30799.9 | 1.33358 | 0.666788 | − | 0.745248i | \(-0.267669\pi\) | ||||
0.666788 | + | 0.745248i | \(0.267669\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 69331.8 | 2.99086 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10143.1 | −0.435948 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4870.02 | 0.208544 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 30099.5 | 1.28420 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3080.42 | −0.130947 | −0.0654735 | − | 0.997854i | \(-0.520856\pi\) | ||||
−0.0654735 | + | 0.997854i | \(0.520856\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23048.4 | 0.976204 | 0.488102 | − | 0.872787i | \(-0.337689\pi\) | ||||
0.488102 | + | 0.872787i | \(0.337689\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10035.6 | 0.423510 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13260.3 | −0.557565 | −0.278783 | − | 0.960354i | \(-0.589931\pi\) | ||||
−0.278783 | + | 0.960354i | \(0.589931\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34413.4 | −1.44177 | −0.720885 | − | 0.693055i | \(-0.756264\pi\) | ||||
−0.720885 | + | 0.693055i | \(0.756264\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21966.5 | −0.916978 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14977.2 | −0.622965 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23506.5 | −0.974221 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1612.17 | −0.0665766 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5440.08 | 0.223853 | 0.111926 | − | 0.993717i | \(-0.464298\pi\) | ||||
0.111926 | + | 0.993717i | \(0.464298\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 40189.1 | 1.64198 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11628.9 | −0.473429 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14742.3 | −0.598054 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22930.7 | 0.926947 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −29780.4 | −1.19960 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22303.5 | 0.895261 | 0.447631 | − | 0.894219i | \(-0.352268\pi\) | ||||
0.447631 | + | 0.894219i | \(0.352268\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2266.22 | 0.0906470 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13859.0 | 0.552411 | 0.276205 | − | 0.961099i | \(-0.410923\pi\) | ||||
0.276205 | + | 0.961099i | \(0.410923\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24629.1 | −0.978270 | −0.489135 | − | 0.872208i | \(-0.662687\pi\) | ||||
−0.489135 | + | 0.872208i | \(0.662687\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10190.4 | 0.403354 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33140.6 | −1.30721 | −0.653604 | − | 0.756837i | \(-0.726744\pi\) | ||||
−0.653604 | + | 0.756837i | \(0.726744\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25436.5 | 0.999846 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 47592.7 | 1.86428 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1037.16 | 0.0404869 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35660.2 | 1.38726 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −30481.5 | −1.18172 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 19966.0 | 0.771398 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2224.74 | 0.0856604 | 0.0428302 | − | 0.999082i | \(-0.486363\pi\) | ||||
0.0428302 | + | 0.999082i | \(0.486363\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 44511.9 | 1.70802 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24242.9 | 0.927087 | 0.463544 | − | 0.886074i | \(-0.346578\pi\) | ||||
0.463544 | + | 0.886074i | \(0.346578\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24060.4 | 0.916984 | 0.458492 | − | 0.888698i | \(-0.348390\pi\) | ||||
0.458492 | + | 0.888698i | \(0.348390\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −19476.3 | −0.739760 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9727.38 | 0.368223 | 0.184111 | − | 0.982905i | \(-0.441059\pi\) | ||||
0.184111 | + | 0.982905i | \(0.441059\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26811.3 | −1.01150 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8138.00 | 0.305986 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1028.51 | −0.0385419 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17010.5 | 0.635304 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 84324.5 | 3.13881 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −818.422 | −0.0303625 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14735.9 | 0.544865 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −57486.9 | −2.11854 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12365.1 | 0.454177 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4523.40 | 0.165598 | 0.0827988 | − | 0.996566i | \(-0.473614\pi\) | ||||
0.0827988 | + | 0.996566i | \(0.473614\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −53222.2 | −1.94199 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24396.1 | 0.887245 | 0.443623 | − | 0.896214i | \(-0.353693\pi\) | ||||
0.443623 | + | 0.896214i | \(0.353693\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14053.3 | 0.509415 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10219.3 | 0.369224 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16206.3 | −0.583620 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −51701.0 | −1.85578 | −0.927888 | − | 0.372858i | \(-0.878378\pi\) | ||||
−0.927888 | + | 0.372858i | \(0.878378\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22541.9 | 0.806496 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 33192.1 | 1.18367 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12934.7 | 0.459772 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13802.2 | −0.489022 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8172.60 | −0.288627 | −0.144313 | − | 0.989532i | \(-0.546097\pi\) | ||||
−0.144313 | + | 0.989532i | \(0.546097\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1340.44 | 0.0471871 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4022.84 | 0.141160 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12549.9 | 0.438957 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40385.8 | 1.40806 | 0.704028 | − | 0.710173i | \(-0.251383\pi\) | ||||
0.704028 | + | 0.710173i | \(0.251383\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11812.4 | −0.410525 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3540.29 | 0.122646 | 0.0613232 | − | 0.998118i | \(-0.480468\pi\) | ||||
0.0613232 | + | 0.998118i | \(0.480468\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15973.5 | 0.551610 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5691.20 | −0.195910 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 53975.8 | 1.85214 | 0.926071 | − | 0.377349i | \(-0.123164\pi\) | ||||
0.926071 | + | 0.377349i | \(0.123164\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −31558.7 | −1.07949 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 42370.8 | 1.44476 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19500.7 | −0.662843 | −0.331421 | − | 0.943483i | \(-0.607528\pi\) | ||||
−0.331421 | + | 0.943483i | \(0.607528\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8141.37 | −0.275862 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3859.39 | −0.130362 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 40622.6 | 1.36786 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28994.5 | −0.973265 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −28176.4 | −0.942857 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22638.4 | 0.755186 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18203.2 | −0.605354 | −0.302677 | − | 0.953093i | \(-0.597880\pi\) | ||||
−0.302677 | + | 0.953093i | \(0.597880\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7702.04 | −0.255341 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10588.8 | 0.349961 | 0.174981 | − | 0.984572i | \(-0.444014\pi\) | ||||
0.174981 | + | 0.984572i | \(0.444014\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11002.8 | 0.362522 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −36625.1 | −1.20302 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24805.8 | 0.812290 | 0.406145 | − | 0.913809i | \(-0.366873\pi\) | ||||
0.406145 | + | 0.913809i | \(0.366873\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15951.9 | 0.520760 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 27541.8 | 0.896375 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2760.27 | −0.0895613 | −0.0447807 | − | 0.998997i | \(-0.514259\pi\) | ||||
−0.0447807 | + | 0.998997i | \(0.514259\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27633.3 | 0.893878 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12140.8 | 0.391536 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −90111.0 | −2.89723 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5609.17 | −0.179799 | −0.0898997 | − | 0.995951i | \(-0.528655\pi\) | ||||
−0.0898997 | + | 0.995951i | \(0.528655\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 81064.5 | 2.59064 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −31434.4 | −1.00155 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3629.31 | −0.115287 | −0.0576436 | − | 0.998337i | \(-0.518359\pi\) | ||||
−0.0576436 | + | 0.998337i | \(0.518359\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9798.55 | −0.310323 |
(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 | 232.4.a.d.1.5 | ✓ | 5 | |
3.2 | odd | 2 | 2088.4.a.f.1.4 | 5 | |||
4.3 | odd | 2 | 464.4.a.m.1.1 | 5 | |||
8.3 | odd | 2 | 1856.4.a.ba.1.5 | 5 | |||
8.5 | even | 2 | 1856.4.a.z.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
232.4.a.d.1.5 | ✓ | 5 | 1.1 | even | 1 | trivial | |
464.4.a.m.1.1 | 5 | 4.3 | odd | 2 | |||
1856.4.a.z.1.1 | 5 | 8.5 | even | 2 | |||
1856.4.a.ba.1.5 | 5 | 8.3 | odd | 2 | |||
2088.4.a.f.1.4 | 5 | 3.2 | odd | 2 |