Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2088,4,Mod(1,2088)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2088, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2088.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2088 = 2^{3} \cdot 3^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2088.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: | \(123.195988092\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 232) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(4.30242\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2088.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7.04208 | 0.629863 | 0.314931 | − | 0.949114i | \(-0.398018\pi\) | ||||
0.314931 | + | 0.949114i | \(0.398018\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 14.1473 | 0.763880 | 0.381940 | − | 0.924187i | \(-0.375256\pi\) | ||||
0.381940 | + | 0.924187i | \(0.375256\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 16.9982 | 0.465922 | 0.232961 | − | 0.972486i | \(-0.425158\pi\) | ||||
0.232961 | + | 0.972486i | \(0.425158\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 62.0351 | 1.32349 | 0.661747 | − | 0.749727i | \(-0.269815\pi\) | ||||
0.661747 | + | 0.749727i | \(0.269815\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −104.842 | −1.49576 | −0.747881 | − | 0.663833i | \(-0.768929\pi\) | ||||
−0.747881 | + | 0.663833i | \(0.768929\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −9.38323 | −0.113298 | −0.0566490 | − | 0.998394i | \(-0.518042\pi\) | ||||
−0.0566490 | + | 0.998394i | \(0.518042\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −173.620 | −1.57401 | −0.787005 | − | 0.616947i | \(-0.788369\pi\) | ||||
−0.787005 | + | 0.616947i | \(0.788369\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −75.4091 | −0.603273 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 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 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 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 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −92.0027 | −0.350449 | −0.175225 | − | 0.984529i | \(-0.556065\pi\) | ||||
−0.175225 | + | 0.984529i | \(0.556065\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −519.014 | −1.84067 | −0.920335 | − | 0.391131i | \(-0.872084\pi\) | ||||
−0.920335 | + | 0.391131i | \(0.872084\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −109.612 | −0.340182 | −0.170091 | − | 0.985428i | \(-0.554406\pi\) | ||||
−0.170091 | + | 0.985428i | \(0.554406\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −142.855 | −0.416487 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −140.553 | −0.364273 | −0.182136 | − | 0.983273i | \(-0.558301\pi\) | ||||
−0.182136 | + | 0.983273i | \(0.558301\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 119.703 | 0.293467 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −353.254 | −0.779487 | −0.389744 | − | 0.920923i | \(-0.627436\pi\) | ||||
−0.389744 | + | 0.920923i | \(0.627436\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −185.355 | −0.389053 | −0.194526 | − | 0.980897i | \(-0.562317\pi\) | ||||
−0.194526 | + | 0.980897i | \(0.562317\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 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 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −535.054 | −0.894355 | −0.447177 | − | 0.894445i | \(-0.647571\pi\) | ||||
−0.447177 | + | 0.894445i | \(0.647571\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −508.723 | −0.815637 | −0.407818 | − | 0.913063i | \(-0.633710\pi\) | ||||
−0.407818 | + | 0.913063i | \(0.633710\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 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 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 826.753 | 1.09335 | 0.546674 | − | 0.837345i | \(-0.315894\pi\) | ||||
0.546674 | + | 0.837345i | \(0.315894\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −738.306 | −0.942124 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 938.445 | 1.11770 | 0.558848 | − | 0.829270i | \(-0.311243\pi\) | ||||
0.558848 | + | 0.829270i | \(0.311243\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 877.626 | 1.01099 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 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 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1551.83 | 1.52884 | 0.764420 | − | 0.644719i | \(-0.223026\pi\) | ||||
0.764420 | + | 0.644719i | \(0.223026\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −402.438 | −0.384984 | −0.192492 | − | 0.981299i | \(-0.561657\pi\) | ||||
−0.192492 | + | 0.981299i | \(0.561657\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 821.553 | 0.742267 | 0.371133 | − | 0.928580i | \(-0.378969\pi\) | ||||
0.371133 | + | 0.928580i | \(0.378969\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 803.052 | 0.705674 | 0.352837 | − | 0.935685i | \(-0.385217\pi\) | ||||
0.352837 | + | 0.935685i | \(0.385217\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 735.506 | 0.612306 | 0.306153 | − | 0.951982i | \(-0.400958\pi\) | ||||
0.306153 | + | 0.951982i | \(0.400958\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1222.64 | −0.991410 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1483.23 | −1.14258 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1042.06 | −0.782916 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 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 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1145.54 | 0.764020 | 0.382010 | − | 0.924158i | \(-0.375232\pi\) | ||||
0.382010 | + | 0.924158i | \(0.375232\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −132.747 | −0.0865461 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2871.41 | −1.79067 | −0.895334 | − | 0.445396i | \(-0.853063\pi\) | ||||
−0.895334 | + | 0.445396i | \(0.853063\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 777.734 | 0.474579 | 0.237290 | − | 0.971439i | \(-0.423741\pi\) | ||||
0.237290 | + | 0.971439i | \(0.423741\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1054.48 | 0.616646 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −204.220 | −0.116963 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2373.29 | −1.30488 | −0.652440 | − | 0.757840i | \(-0.726255\pi\) | ||||
−0.652440 | + | 0.757840i | \(0.726255\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 102.190 | 0.0550733 | 0.0275366 | − | 0.999621i | \(-0.491234\pi\) | ||||
0.0275366 | + | 0.999621i | \(0.491234\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 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 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 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 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3338.00 | −1.54672 | −0.773359 | − | 0.633968i | \(-0.781425\pi\) | ||||
−0.773359 | + | 0.633968i | \(0.781425\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1651.35 | 0.751638 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3612.07 | 1.58740 | 0.793701 | − | 0.608308i | \(-0.208151\pi\) | ||||
0.793701 | + | 0.608308i | \(0.208151\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1066.83 | −0.460828 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2415.54 | 1.00864 | 0.504319 | − | 0.863517i | \(-0.331744\pi\) | ||||
0.504319 | + | 0.863517i | \(0.331744\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1755.89 | −0.721073 | −0.360537 | − | 0.932745i | \(-0.617406\pi\) | ||||
−0.360537 | + | 0.932745i | \(0.617406\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1207.90 | −0.480037 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1782.13 | −0.696909 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1156.10 | −0.437972 | −0.218986 | − | 0.975728i | \(-0.570275\pi\) | ||||
−0.218986 | + | 0.975728i | \(0.570275\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3214.73 | −1.19897 | −0.599485 | − | 0.800386i | \(-0.704628\pi\) | ||||
−0.599485 | + | 0.800386i | \(0.704628\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3924.03 | 1.41916 | 0.709582 | − | 0.704623i | \(-0.248884\pi\) | ||||
0.709582 | + | 0.704623i | \(0.248884\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4463.80 | 1.59010 | 0.795051 | − | 0.606543i | \(-0.207444\pi\) | ||||
0.795051 | + | 0.606543i | \(0.207444\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −410.271 | −0.141849 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −647.890 | −0.220735 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3654.93 | −1.15937 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −399.256 | −0.124900 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 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 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3110.06 | 0.909348 | 0.454674 | − | 0.890658i | \(-0.349756\pi\) | ||||
0.454674 | + | 0.890658i | \(0.349756\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4686.03 | −1.35223 | −0.676117 | − | 0.736794i | \(-0.736339\pi\) | ||||
−0.676117 | + | 0.736794i | \(0.736339\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 908.748 | 0.255511 | 0.127756 | − | 0.991806i | \(-0.459223\pi\) | ||||
0.127756 | + | 0.991806i | \(0.459223\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −771.896 | −0.214268 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.3950 | 0.00497854 | 0.00248927 | − | 0.999997i | \(-0.499208\pi\) | ||||
0.00248927 | + | 0.999997i | \(0.499208\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6199.96 | 1.65716 | 0.828578 | − | 0.559874i | \(-0.189151\pi\) | ||||
0.828578 | + | 0.559874i | \(0.189151\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1006.00 | −0.262330 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −582.089 | −0.149949 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3325.41 | −0.836248 | −0.418124 | − | 0.908390i | \(-0.637312\pi\) | ||||
−0.418124 | + | 0.908390i | \(0.637312\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2951.22 | −0.733366 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2713.20 | −0.658541 | −0.329271 | − | 0.944236i | \(-0.606803\pi\) | ||||
−0.329271 | + | 0.944236i | \(0.606803\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2426.63 | −0.582176 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6234.94 | −1.46184 | −0.730918 | − | 0.682465i | \(-0.760908\pi\) | ||||
−0.730918 | + | 0.682465i | \(0.760908\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −989.787 | −0.229442 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5745.23 | 1.30220 | 0.651102 | − | 0.758990i | \(-0.274307\pi\) | ||||
0.651102 | + | 0.758990i | \(0.274307\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8855.53 | 1.98500 | 0.992501 | − | 0.122238i | \(-0.0390072\pi\) | ||||
0.992501 | + | 0.122238i | \(0.0390072\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 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 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5133.23 | −1.08976 | −0.544881 | − | 0.838514i | \(-0.683425\pi\) | ||||
−0.544881 | + | 0.838514i | \(0.683425\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2928.86 | 0.615204 | 0.307602 | − | 0.951515i | \(-0.400473\pi\) | ||||
0.307602 | + | 0.951515i | \(0.400473\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1301.59 | −0.267701 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6078.87 | 1.23730 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5685.37 | −1.13359 | −0.566796 | − | 0.823858i | \(-0.691817\pi\) | ||||
−0.566796 | + | 0.823858i | \(0.691817\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2487.64 | −0.490970 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10770.5 | −2.08319 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7342.62 | −1.40605 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 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 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −513.825 | −0.0936860 | −0.0468430 | − | 0.998902i | \(-0.514916\pi\) | ||||
−0.0468430 | + | 0.998902i | \(0.514916\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1508.76 | −0.272460 | −0.136230 | − | 0.990677i | \(-0.543499\pi\) | ||||
−0.136230 | + | 0.990677i | \(0.543499\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5411.89 | −0.958872 | −0.479436 | − | 0.877577i | \(-0.659159\pi\) | ||||
−0.479436 | + | 0.877577i | \(0.659159\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −492.947 | −0.0865196 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 983.758 | 0.169467 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4678.01 | −0.798429 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −479.714 | −0.0761817 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6873.52 | −1.08203 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6733.27 | 1.04167 | 0.520837 | − | 0.853656i | \(-0.325620\pi\) | ||||
0.520837 | + | 0.853656i | \(0.325620\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9272.50 | −1.42219 | −0.711097 | − | 0.703094i | \(-0.751801\pi\) | ||||
−0.711097 | + | 0.703094i | \(0.751801\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5776.97 | −0.871041 | −0.435520 | − | 0.900179i | \(-0.643436\pi\) | ||||
−0.435520 | + | 0.900179i | \(0.643436\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3767.89 | −0.563321 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3821.93 | −0.561877 | −0.280938 | − | 0.959726i | \(-0.590646\pi\) | ||||
−0.280938 | + | 0.959726i | \(0.590646\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6770.95 | −0.987164 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 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 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 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 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 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 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2202.45 | 0.293837 | 0.146919 | − | 0.989149i | \(-0.453064\pi\) | ||||
0.146919 | + | 0.989149i | \(0.453064\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1693.46 | 0.224174 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5614.61 | −0.731804 | −0.365902 | − | 0.930653i | \(-0.619240\pi\) | ||||
−0.365902 | + | 0.930653i | \(0.619240\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18202.7 | 2.35434 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 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 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1183.01 | 0.147324 | 0.0736619 | − | 0.997283i | \(-0.476531\pi\) | ||||
0.0736619 | + | 0.997283i | \(0.476531\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1750.72 | −0.216401 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 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 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4997.58 | −0.595435 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5822.06 | 0.688659 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4224.75 | 0.492584 | 0.246292 | − | 0.969196i | \(-0.420788\pi\) | ||||
0.246292 | + | 0.969196i | \(0.420788\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10801.7 | 1.25046 | 0.625231 | − | 0.780440i | \(-0.285005\pi\) | ||||
0.625231 | + | 0.780440i | \(0.285005\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7906.05 | 0.902352 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2622.26 | −0.297190 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13127.7 | −1.46715 | −0.733574 | − | 0.679610i | \(-0.762149\pi\) | ||||
−0.733574 | + | 0.679610i | \(0.762149\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11403.2 | −1.26559 | −0.632797 | − | 0.774318i | \(-0.718093\pi\) | ||||
−0.632797 | + | 0.774318i | \(0.718093\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 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 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6136.95 | −0.658184 | −0.329092 | − | 0.944298i | \(-0.606743\pi\) | ||||
−0.329092 | + | 0.944298i | \(0.606743\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6608.61 | 0.703995 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18012.1 | 1.89319 | 0.946594 | − | 0.322428i | \(-0.104499\pi\) | ||||
0.946594 | + | 0.322428i | \(0.104499\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1563.88 | −0.163282 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 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 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16471.2 | 1.66408 | 0.832038 | − | 0.554719i | \(-0.187174\pi\) | ||||
0.832038 | + | 0.554719i | \(0.187174\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3844.07 | 0.385851 | 0.192925 | − | 0.981213i | \(-0.438202\pi\) | ||||
0.192925 | + | 0.981213i | \(0.438202\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15072.5 | −1.49352 | −0.746759 | − | 0.665094i | \(-0.768391\pi\) | ||||
−0.746759 | + | 0.665094i | \(0.768391\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8132.41 | 0.800682 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8822.29 | −0.857610 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 707.581 | 0.0683496 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8856.14 | −0.844776 | −0.422388 | − | 0.906415i | \(-0.638808\pi\) | ||||
−0.422388 | + | 0.906415i | \(0.638808\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10640.7 | −1.00867 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 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 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2169.60 | 0.199415 | 0.0997076 | − | 0.995017i | \(-0.468209\pi\) | ||||
0.0997076 | + | 0.995017i | \(0.468209\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3040.42 | 0.277756 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 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 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16190.4 | 1.43517 | 0.717587 | − | 0.696469i | \(-0.245247\pi\) | ||||
0.717587 | + | 0.696469i | \(0.245247\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10928.1 | 0.962959 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1493.11 | −0.130021 | −0.0650106 | − | 0.997885i | \(-0.520708\pi\) | ||||
−0.0650106 | + | 0.997885i | \(0.520708\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7197.03 | −0.623049 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2834.00 | −0.242487 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1863.20 | −0.158498 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7026.84 | 0.590886 | 0.295443 | − | 0.955360i | \(-0.404533\pi\) | ||||
0.295443 | + | 0.955360i | \(0.404533\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21924.1 | 1.83303 | 0.916514 | − | 0.400003i | \(-0.130991\pi\) | ||||
0.916514 | + | 0.400003i | \(0.130991\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2958.80 | 0.244568 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17976.8 | 1.47750 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5707.39 | −0.463817 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5785.44 | 0.467526 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 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 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 272.114 | 0.0210389 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −863.204 | −0.0663782 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7531.50 | −0.572926 | −0.286463 | − | 0.958091i | \(-0.592480\pi\) | ||||
−0.286463 | + | 0.958091i | \(0.592480\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32197.0 | −2.43612 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19553.5 | 1.46373 | 0.731866 | − | 0.681449i | \(-0.238650\pi\) | ||||
0.731866 | + | 0.681449i | \(0.238650\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5179.49 | 0.385669 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23656.9 | −1.74297 | −0.871483 | − | 0.490426i | \(-0.836841\pi\) | ||||
−0.871483 | + | 0.490426i | \(0.836841\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5466.08 | −0.400610 | −0.200305 | − | 0.979734i | \(-0.564193\pi\) | ||||
−0.200305 | + | 0.979734i | \(0.564193\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11696.3 | 0.835187 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2389.15 | −0.169723 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19414.4 | 1.36511 | 0.682554 | − | 0.730835i | \(-0.260869\pi\) | ||||
0.682554 | + | 0.730835i | \(0.260869\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 264.809 | 0.0185250 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18910.6 | −1.30955 | −0.654777 | − | 0.755822i | \(-0.727237\pi\) | ||||
−0.654777 | + | 0.755822i | \(0.727237\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10445.0 | −0.719670 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12128.7 | 0.827322 | 0.413661 | − | 0.910431i | \(-0.364250\pi\) | ||||
0.413661 | + | 0.910431i | \(0.364250\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25803.3 | −1.75131 | −0.875656 | − | 0.482936i | \(-0.839570\pi\) | ||||
−0.875656 | + | 0.482936i | \(0.839570\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 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 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 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 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6518.09 | 0.425297 | 0.212649 | − | 0.977129i | \(-0.431791\pi\) | ||||
0.212649 | + | 0.977129i | \(0.431791\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4344.67 | −0.282111 | −0.141056 | − | 0.990002i | \(-0.545050\pi\) | ||||
−0.141056 | + | 0.990002i | \(0.545050\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13276.4 | 0.853787 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −512.326 | −0.0327889 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 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 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13345.8 | −0.834037 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8862.02 | −0.551218 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15375.4 | −0.947411 | −0.473706 | − | 0.880683i | \(-0.657084\pi\) | ||||
−0.473706 | + | 0.880683i | \(0.657084\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16966.5 | −1.04058 | −0.520291 | − | 0.853989i | \(-0.674177\pi\) | ||||
−0.520291 | + | 0.853989i | \(0.674177\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12379.7 | 0.752234 | 0.376117 | − | 0.926572i | \(-0.377259\pi\) | ||||
0.376117 | + | 0.926572i | \(0.377259\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6004.68 | −0.363181 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −30418.3 | −1.82291 | −0.911453 | − | 0.411403i | \(-0.865039\pi\) | ||||
−0.911453 | + | 0.411403i | \(0.865039\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8067.01 | 0.481228 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6069.11 | 0.358754 | 0.179377 | − | 0.983780i | \(-0.442592\pi\) | ||||
0.179377 | + | 0.983780i | \(0.442592\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24894.6 | −1.46489 | −0.732443 | − | 0.680829i | \(-0.761620\pi\) | ||||
−0.732443 | + | 0.680829i | \(0.761620\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −934.815 | −0.0545121 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5034.97 | 0.292286 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21322.2 | 1.21046 | 0.605228 | − | 0.796052i | \(-0.293082\pi\) | ||||
0.605228 | + | 0.796052i | \(0.293082\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12573.6 | −0.710649 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −38.7459 | −0.00217068 | −0.00108534 | − | 0.999999i | \(-0.500345\pi\) | ||||
−0.00108534 | + | 0.999999i | \(0.500345\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20220.7 | −1.12787 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 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 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5476.86 | 0.298920 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9645.76 | 0.524188 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23404.8 | −1.26104 | −0.630519 | − | 0.776174i | \(-0.717158\pi\) | ||||
−0.630519 | + | 0.776174i | \(0.717158\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1609.47 | 0.0863477 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 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 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4899.80 | 0.257362 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7425.76 | 0.388402 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13242.3 | 0.686862 | 0.343431 | − | 0.939178i | \(-0.388411\pi\) | ||||
0.343431 | + | 0.939178i | \(0.388411\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5693.39 | −0.294082 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 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 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 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 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 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 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15260.1 | 0.753484 | 0.376742 | − | 0.926318i | \(-0.377044\pi\) | ||||
0.376742 | + | 0.926318i | \(0.377044\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16712.9 | −0.821896 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 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 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 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 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14975.4 | −0.713349 | −0.356675 | − | 0.934229i | \(-0.616090\pi\) | ||||
−0.356675 | + | 0.934229i | \(0.616090\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11361.0 | 0.539050 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3728.71 | 0.173496 | 0.0867479 | − | 0.996230i | \(-0.472353\pi\) | ||||
0.0867479 | + | 0.996230i | \(0.472353\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2128.16 | 0.0986395 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 863.283 | 0.0397051 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9094.94 | −0.416700 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 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 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10405.4 | 0.467729 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11498.5 | −0.514909 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36436.3 | 1.61937 | 0.809687 | − | 0.586862i | \(-0.199637\pi\) | ||||
0.809687 | + | 0.586862i | \(0.199637\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11491.9 | 0.508831 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8647.37 | −0.380024 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17297.1 | −0.757318 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9776.41 | −0.424871 | −0.212435 | − | 0.977175i | \(-0.568139\pi\) | ||||
−0.212435 | + | 0.977175i | \(0.568139\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30799.9 | 1.33358 | 0.666788 | − | 0.745248i | \(-0.267669\pi\) | ||||
0.666788 | + | 0.745248i | \(0.267669\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10143.1 | 0.435948 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4870.02 | 0.208544 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3080.42 | 0.130947 | 0.0654735 | − | 0.997854i | \(-0.479144\pi\) | ||||
0.0654735 | + | 0.997854i | \(0.479144\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23048.4 | 0.976204 | 0.488102 | − | 0.872787i | \(-0.337689\pi\) | ||||
0.488102 | + | 0.872787i | \(0.337689\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13260.3 | 0.557565 | 0.278783 | − | 0.960354i | \(-0.410069\pi\) | ||||
0.278783 | + | 0.960354i | \(0.410069\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34413.4 | −1.44177 | −0.720885 | − | 0.693055i | \(-0.756264\pi\) | ||||
−0.720885 | + | 0.693055i | \(0.756264\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14977.2 | 0.622965 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23506.5 | −0.974221 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5440.08 | −0.223853 | −0.111926 | − | 0.993717i | \(-0.535702\pi\) | ||||
−0.111926 | + | 0.993717i | \(0.535702\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11628.9 | 0.473429 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14742.3 | −0.598054 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 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 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13859.0 | −0.552411 | −0.276205 | − | 0.961099i | \(-0.589077\pi\) | ||||
−0.276205 | + | 0.961099i | \(0.589077\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24629.1 | −0.978270 | −0.489135 | − | 0.872208i | \(-0.662687\pi\) | ||||
−0.489135 | + | 0.872208i | \(0.662687\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33140.6 | 1.30721 | 0.653604 | − | 0.756837i | \(-0.273256\pi\) | ||||
0.653604 | + | 0.756837i | \(0.273256\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25436.5 | 0.999846 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1037.16 | −0.0404869 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35660.2 | 1.38726 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 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 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24242.9 | −0.927087 | −0.463544 | − | 0.886074i | \(-0.653422\pi\) | ||||
−0.463544 | + | 0.886074i | \(0.653422\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24060.4 | 0.916984 | 0.458492 | − | 0.888698i | \(-0.348390\pi\) | ||||
0.458492 | + | 0.888698i | \(0.348390\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9727.38 | −0.368223 | −0.184111 | − | 0.982905i | \(-0.558941\pi\) | ||||
−0.184111 | + | 0.982905i | \(0.558941\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26811.3 | −1.01150 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1028.51 | 0.0385419 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17010.5 | 0.635304 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 818.422 | 0.0303625 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14735.9 | 0.544865 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 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 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24396.1 | −0.887245 | −0.443623 | − | 0.896214i | \(-0.646307\pi\) | ||||
−0.443623 | + | 0.896214i | \(0.646307\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14053.3 | 0.509415 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 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 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −33192.1 | −1.18367 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12934.7 | 0.459772 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8172.60 | 0.288627 | 0.144313 | − | 0.989532i | \(-0.453903\pi\) | ||||
0.144313 | + | 0.989532i | \(0.453903\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1340.44 | 0.0471871 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 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 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3540.29 | −0.122646 | −0.0613232 | − | 0.998118i | \(-0.519532\pi\) | ||||
−0.0613232 | + | 0.998118i | \(0.519532\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15973.5 | 0.551610 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −53975.8 | −1.85214 | −0.926071 | − | 0.377349i | \(-0.876836\pi\) | ||||
−0.926071 | + | 0.377349i | \(0.876836\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −31558.7 | −1.07949 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19500.7 | 0.662843 | 0.331421 | − | 0.943483i | \(-0.392472\pi\) | ||||
0.331421 | + | 0.943483i | \(0.392472\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8141.37 | −0.275862 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −40622.6 | −1.36786 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28994.5 | −0.973265 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 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 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10588.8 | −0.349961 | −0.174981 | − | 0.984572i | \(-0.555986\pi\) | ||||
−0.174981 | + | 0.984572i | \(0.555986\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11002.8 | 0.362522 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24805.8 | −0.812290 | −0.406145 | − | 0.913809i | \(-0.633127\pi\) | ||||
−0.406145 | + | 0.913809i | \(0.633127\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15951.9 | 0.520760 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2760.27 | 0.0895613 | 0.0447807 | − | 0.998997i | \(-0.485741\pi\) | ||||
0.0447807 | + | 0.998997i | \(0.485741\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27633.3 | 0.893878 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 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 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 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 | ||||||||
\(999\) | 0 | 0 |
(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 | 2088.4.a.f.1.4 | 5 | ||
3.2 | odd | 2 | 232.4.a.d.1.5 | ✓ | 5 | ||
12.11 | even | 2 | 464.4.a.m.1.1 | 5 | |||
24.5 | odd | 2 | 1856.4.a.z.1.1 | 5 | |||
24.11 | even | 2 | 1856.4.a.ba.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
232.4.a.d.1.5 | ✓ | 5 | 3.2 | odd | 2 | ||
464.4.a.m.1.1 | 5 | 12.11 | even | 2 | |||
1856.4.a.z.1.1 | 5 | 24.5 | odd | 2 | |||
1856.4.a.ba.1.5 | 5 | 24.11 | even | 2 | |||
2088.4.a.f.1.4 | 5 | 1.1 | even | 1 | trivial |