Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2200,2,Mod(1,2200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2200.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2200 = 2^{3} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2200.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: | \(17.5670884447\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 7x + 6 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.59261\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2200.1 |
$q$-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 | ||||||||
\(3\) | −2.59261 | −1.49685 | −0.748423 | − | 0.663221i | \(-0.769189\pi\) | ||||
−0.748423 | + | 0.663221i | \(0.769189\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.72165 | 1.02869 | 0.514344 | − | 0.857584i | \(-0.328036\pi\) | ||||
0.514344 | + | 0.857584i | \(0.328036\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.72165 | 1.24055 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.59261 | −1.11387 | −0.556936 | − | 0.830555i | \(-0.688023\pi\) | ||||
−0.556936 | + | 0.830555i | \(0.688023\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.18523 | 1.87782 | 0.938910 | − | 0.344162i | \(-0.111837\pi\) | ||||
0.938910 | + | 0.344162i | \(0.111837\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.05619 | −1.53979 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.407385 | 0.0849457 | 0.0424728 | − | 0.999098i | \(-0.486476\pi\) | ||||
0.0424728 | + | 0.999098i | \(0.486476\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.87096 | −0.360067 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.46358 | 1.38595 | 0.692976 | − | 0.720961i | \(-0.256299\pi\) | ||||
0.692976 | + | 0.720961i | \(0.256299\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.44330 | −0.798041 | −0.399020 | − | 0.916942i | \(-0.630650\pi\) | ||||
−0.399020 | + | 0.916942i | \(0.630650\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.59261 | −0.451316 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.31427 | −1.20246 | −0.601229 | − | 0.799077i | \(-0.705322\pi\) | ||||
−0.601229 | + | 0.799077i | \(0.705322\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.59261 | −0.415151 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.31427 | −0.517601 | −0.258801 | − | 0.965931i | \(-0.583327\pi\) | ||||
−0.258801 | + | 0.965931i | \(0.583327\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.49950 | −1.14366 | −0.571831 | − | 0.820371i | \(-0.693767\pi\) | ||||
−0.571831 | + | 0.820371i | \(0.693767\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.05619 | 1.02925 | 0.514626 | − | 0.857415i | \(-0.327931\pi\) | ||||
0.514626 | + | 0.857415i | \(0.327931\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.407385 | 0.0581979 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.9069 | 1.66730 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.979724 | 0.134575 | 0.0672877 | − | 0.997734i | \(-0.478565\pi\) | ||||
0.0672877 | + | 0.997734i | \(0.478565\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −21.2211 | −2.81081 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.05619 | 0.918638 | 0.459319 | − | 0.888271i | \(-0.348093\pi\) | ||||
0.459319 | + | 0.888271i | \(0.348093\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.46358 | −0.571503 | −0.285751 | − | 0.958304i | \(-0.592243\pi\) | ||||
−0.285751 | + | 0.958304i | \(0.592243\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10.1290 | 1.27614 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.25807 | −0.275868 | −0.137934 | − | 0.990441i | \(-0.544046\pi\) | ||||
−0.137934 | + | 0.990441i | \(0.544046\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.05619 | −0.127151 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.3143 | 1.22408 | 0.612039 | − | 0.790828i | \(-0.290350\pi\) | ||||
0.612039 | + | 0.790828i | \(0.290350\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.1650 | −1.42380 | −0.711900 | − | 0.702281i | \(-0.752165\pi\) | ||||
−0.711900 | + | 0.702281i | \(0.752165\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.72165 | 0.310161 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.14931 | 0.354325 | 0.177163 | − | 0.984182i | \(-0.443308\pi\) | ||||
0.177163 | + | 0.984182i | \(0.443308\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.31427 | −0.701585 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.6488 | 1.82744 | 0.913722 | − | 0.406340i | \(-0.133195\pi\) | ||||
0.913722 | + | 0.406340i | \(0.133195\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −19.3502 | −2.07456 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.27835 | 0.877503 | 0.438752 | − | 0.898608i | \(-0.355421\pi\) | ||||
0.438752 | + | 0.898608i | \(0.355421\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.72165 | 0.285307 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.5198 | 1.19454 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.03592 | 0.308251 | 0.154125 | − | 0.988051i | \(-0.450744\pi\) | ||||
0.154125 | + | 0.988051i | \(0.450744\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.72165 | 0.374040 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.59261 | 0.556486 | 0.278243 | − | 0.960511i | \(-0.410248\pi\) | ||||
0.278243 | + | 0.960511i | \(0.410248\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.64881 | −0.458061 | −0.229030 | − | 0.973419i | \(-0.573555\pi\) | ||||
−0.229030 | + | 0.973419i | \(0.573555\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.701375 | 0.0678045 | 0.0339023 | − | 0.999425i | \(-0.489207\pi\) | ||||
0.0339023 | + | 0.999425i | \(0.489207\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.27835 | 0.409791 | 0.204896 | − | 0.978784i | \(-0.434314\pi\) | ||||
0.204896 | + | 0.978784i | \(0.434314\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18.9631 | 1.79990 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.6847 | 1.09921 | 0.549603 | − | 0.835426i | \(-0.314779\pi\) | ||||
0.549603 | + | 0.835426i | \(0.314779\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.72165 | 0.344067 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.4995 | −1.14583 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.59261 | 0.774770 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.51977 | 0.844743 | 0.422372 | − | 0.906423i | \(-0.361198\pi\) | ||||
0.422372 | + | 0.906423i | \(0.361198\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 19.4433 | 1.71189 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 22.4792 | 1.96402 | 0.982009 | − | 0.188833i | \(-0.0604704\pi\) | ||||
0.982009 | + | 0.188833i | \(0.0604704\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 22.2773 | 1.93169 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.5354 | 1.32728 | 0.663640 | − | 0.748052i | \(-0.269011\pi\) | ||||
0.663640 | + | 0.748052i | \(0.269011\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.3299 | 1.13063 | 0.565314 | − | 0.824876i | \(-0.308755\pi\) | ||||
0.565314 | + | 0.824876i | \(0.308755\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.2940 | −1.54063 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.05619 | −0.0871133 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.628532 | −0.0514913 | −0.0257457 | − | 0.999669i | \(-0.508196\pi\) | ||||
−0.0257457 | + | 0.999669i | \(0.508196\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.1280 | −1.55662 | −0.778308 | − | 0.627882i | \(-0.783922\pi\) | ||||
−0.778308 | + | 0.627882i | \(0.783922\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −17.0921 | −1.38182 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.88660 | 0.709228 | 0.354614 | − | 0.935013i | \(-0.384612\pi\) | ||||
0.354614 | + | 0.935013i | \(0.384612\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.54005 | −0.201439 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.10876 | 0.0873826 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.8340 | 1.63185 | 0.815924 | − | 0.578159i | \(-0.196229\pi\) | ||||
0.815924 | + | 0.578159i | \(0.196229\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.4267 | 1.34851 | 0.674257 | − | 0.738496i | \(-0.264464\pi\) | ||||
0.674257 | + | 0.738496i | \(0.264464\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 30.4626 | 2.32953 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.18523 | −0.622311 | −0.311156 | − | 0.950359i | \(-0.600716\pi\) | ||||
−0.311156 | + | 0.950359i | \(0.600716\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −18.2940 | −1.37506 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.7217 | −0.801374 | −0.400687 | − | 0.916215i | \(-0.631228\pi\) | ||||
−0.400687 | + | 0.916215i | \(0.631228\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.4626 | 1.74396 | 0.871980 | − | 0.489542i | \(-0.162836\pi\) | ||||
0.871980 | + | 0.489542i | \(0.162836\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.5723 | 0.855452 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.59261 | −0.335845 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.09211 | −0.370397 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.5354 | −1.12410 | −0.562052 | − | 0.827102i | \(-0.689988\pi\) | ||||
−0.562052 | + | 0.827102i | \(0.689988\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.62954 | −0.117297 | −0.0586485 | − | 0.998279i | \(-0.518679\pi\) | ||||
−0.0586485 | + | 0.998279i | \(0.518679\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.77784 | −0.197913 | −0.0989566 | − | 0.995092i | \(-0.531551\pi\) | ||||
−0.0989566 | + | 0.995092i | \(0.531551\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −26.1639 | −1.85471 | −0.927356 | − | 0.374179i | \(-0.877924\pi\) | ||||
−0.927356 | + | 0.374179i | \(0.877924\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.85431 | 0.412931 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.3133 | 1.42571 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.51615 | 0.105379 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.18523 | 0.566184 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.38711 | −0.164335 | −0.0821677 | − | 0.996619i | \(-0.526184\pi\) | ||||
−0.0821677 | + | 0.996619i | \(0.526184\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −26.7409 | −1.83226 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.0931 | −0.820934 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 31.5390 | 2.13121 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.59261 | −0.308933 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.4267 | 1.70269 | 0.851347 | − | 0.524603i | \(-0.175786\pi\) | ||||
0.851347 | + | 0.524603i | \(0.175786\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.2783 | 0.682198 | 0.341099 | − | 0.940027i | \(-0.389201\pi\) | ||||
0.341099 | + | 0.940027i | \(0.389201\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 29.0349 | 1.91868 | 0.959340 | − | 0.282252i | \(-0.0910814\pi\) | ||||
0.959340 | + | 0.282252i | \(0.0910814\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.05619 | −0.464263 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.90688 | 0.386973 | 0.193486 | − | 0.981103i | \(-0.438020\pi\) | ||||
0.193486 | + | 0.981103i | \(0.438020\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.16495 | −0.530371 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.79449 | 0.245445 | 0.122723 | − | 0.992441i | \(-0.460837\pi\) | ||||
0.122723 | + | 0.992441i | \(0.460837\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.5916 | −1.51967 | −0.759834 | − | 0.650117i | \(-0.774720\pi\) | ||||
−0.759834 | + | 0.650117i | \(0.774720\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.9833 | 1.41023 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.18523 | 0.520814 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −43.1639 | −2.73540 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.5916 | −1.36285 | −0.681425 | − | 0.731888i | \(-0.738639\pi\) | ||||
−0.681425 | + | 0.731888i | \(0.738639\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.407385 | 0.0256121 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.01564 | −0.250489 | −0.125244 | − | 0.992126i | \(-0.539972\pi\) | ||||
−0.125244 | + | 0.992126i | \(0.539972\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.9069 | −1.23695 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 27.7768 | 1.71934 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −29.2404 | −1.80304 | −0.901521 | − | 0.432736i | \(-0.857548\pi\) | ||||
−0.901521 | + | 0.432736i | \(0.857548\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −21.4626 | −1.31349 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.03592 | −0.489959 | −0.244979 | − | 0.969528i | \(-0.578781\pi\) | ||||
−0.244979 | + | 0.969528i | \(0.578781\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.4267 | −1.18009 | −0.590043 | − | 0.807372i | \(-0.700889\pi\) | ||||
−0.590043 | + | 0.807372i | \(0.700889\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.05619 | −0.427060 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.83041 | −0.109979 | −0.0549894 | − | 0.998487i | \(-0.517513\pi\) | ||||
−0.0549894 | + | 0.998487i | \(0.517513\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −16.5364 | −0.990010 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.6847 | 1.05498 | 0.527491 | − | 0.849561i | \(-0.323133\pi\) | ||||
0.527491 | + | 0.849561i | \(0.323133\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.8507 | 1.00167 | 0.500835 | − | 0.865543i | \(-0.333026\pi\) | ||||
0.500835 | + | 0.865543i | \(0.333026\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.02028 | −0.532450 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.09211 | 0.240712 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.87096 | −0.461404 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −28.3705 | −1.65742 | −0.828710 | − | 0.559678i | \(-0.810925\pi\) | ||||
−0.828710 | + | 0.559678i | \(0.810925\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.87096 | −0.108564 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.407385 | 0.0235597 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.4110 | −1.17647 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.4995 | −0.832974 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.29399 | −0.130925 | −0.0654625 | − | 0.997855i | \(-0.520852\pi\) | ||||
−0.0654625 | + | 0.997855i | \(0.520852\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.0526 | 0.685647 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.2581 | 0.638387 | 0.319193 | − | 0.947690i | \(-0.396588\pi\) | ||||
0.319193 | + | 0.947690i | \(0.396588\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.18523 | 0.406133 | 0.203067 | − | 0.979165i | \(-0.434909\pi\) | ||||
0.203067 | + | 0.979165i | \(0.434909\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29.5198 | 1.65800 | 0.828998 | − | 0.559252i | \(-0.188912\pi\) | ||||
0.828998 | + | 0.559252i | \(0.188912\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.46358 | 0.417880 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.81840 | −0.101493 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −37.5916 | −2.09165 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.0921 | −0.613395 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.2045 | 1.05878 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.12904 | −0.336882 | −0.168441 | − | 0.985712i | \(-0.553873\pi\) | ||||
−0.168441 | + | 0.985712i | \(0.553873\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −27.2211 | −1.49171 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.0000 | −0.544735 | −0.272367 | − | 0.962193i | \(-0.587807\pi\) | ||||
−0.272367 | + | 0.962193i | \(0.587807\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −30.2940 | −1.64534 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.44330 | −0.240618 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.9428 | −0.968820 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.7217 | 0.790300 | 0.395150 | − | 0.918617i | \(-0.370693\pi\) | ||||
0.395150 | + | 0.918617i | \(0.370693\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.2976 | 1.72885 | 0.864426 | − | 0.502760i | \(-0.167682\pi\) | ||||
0.864426 | + | 0.502760i | \(0.167682\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.87096 | −0.0998646 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.37046 | 0.179391 | 0.0896957 | − | 0.995969i | \(-0.471411\pi\) | ||||
0.0896957 | + | 0.995969i | \(0.471411\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 32.4064 | 1.71513 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.7419 | −1.04194 | −0.520970 | − | 0.853575i | \(-0.674429\pi\) | ||||
−0.520970 | + | 0.853575i | \(0.674429\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 47.9980 | 2.52621 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.59261 | −0.136077 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.4792 | 1.59100 | 0.795501 | − | 0.605952i | \(-0.207208\pi\) | ||||
0.795501 | + | 0.605952i | \(0.207208\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.3345 | −0.642111 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.66647 | 0.138436 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.4985 | −1.42382 | −0.711909 | − | 0.702272i | \(-0.752169\pi\) | ||||
−0.711909 | + | 0.702272i | \(0.752169\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.46358 | 0.384394 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.87096 | 0.198838 | 0.0994190 | − | 0.995046i | \(-0.468302\pi\) | ||||
0.0994190 | + | 0.995046i | \(0.468302\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −24.6811 | −1.26445 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −33.2414 | −1.69856 | −0.849279 | − | 0.527945i | \(-0.822963\pi\) | ||||
−0.849279 | + | 0.527945i | \(0.822963\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −27.9105 | −1.41877 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.9980 | 1.72377 | 0.861883 | − | 0.507107i | \(-0.169285\pi\) | ||||
0.861883 | + | 0.507107i | \(0.169285\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.87096 | −0.0946187 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −58.2800 | −2.93983 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.85069 | 0.143072 | 0.0715360 | − | 0.997438i | \(-0.477210\pi\) | ||||
0.0715360 | + | 0.997438i | \(0.477210\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −57.7566 | −2.89144 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.0967 | 0.803833 | 0.401917 | − | 0.915676i | \(-0.368344\pi\) | ||||
0.401917 | + | 0.915676i | \(0.368344\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.44330 | −0.221337 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.31427 | −0.362555 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.757568 | 0.0374593 | 0.0187297 | − | 0.999825i | \(-0.494038\pi\) | ||||
0.0187297 | + | 0.999825i | \(0.494038\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −40.2773 | −1.98673 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.2045 | 0.944991 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −34.5593 | −1.69238 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.8700 | 1.80122 | 0.900608 | − | 0.434633i | \(-0.143122\pi\) | ||||
0.900608 | + | 0.434633i | \(0.143122\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.2055 | −1.56960 | −0.784800 | − | 0.619749i | \(-0.787234\pi\) | ||||
−0.784800 | + | 0.619749i | \(0.787234\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 26.2607 | 1.27684 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.1483 | −0.587898 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.59261 | −0.125173 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.9428 | 0.864274 | 0.432137 | − | 0.901808i | \(-0.357760\pi\) | ||||
0.432137 | + | 0.901808i | \(0.357760\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.2258 | −0.683647 | −0.341824 | − | 0.939764i | \(-0.611045\pi\) | ||||
−0.341824 | + | 0.939764i | \(0.611045\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.33454 | 0.159513 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.70601 | −0.463243 | −0.231621 | − | 0.972806i | \(-0.574403\pi\) | ||||
−0.231621 | + | 0.972806i | \(0.574403\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.51615 | 0.0721974 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.44431 | −0.211156 | −0.105578 | − | 0.994411i | \(-0.533669\pi\) | ||||
−0.105578 | + | 0.994411i | \(0.533669\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.62954 | 0.0770746 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.4479 | −0.587454 | −0.293727 | − | 0.955889i | \(-0.594896\pi\) | ||||
−0.293727 | + | 0.955889i | \(0.594896\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.31427 | −0.156063 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 49.5916 | 2.33002 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.2368 | 0.759525 | 0.379762 | − | 0.925084i | \(-0.376006\pi\) | ||||
0.379762 | + | 0.925084i | \(0.376006\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.59261 | 0.401069 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −41.8689 | −1.95003 | −0.975016 | − | 0.222136i | \(-0.928697\pi\) | ||||
−0.975016 | + | 0.222136i | \(0.928697\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.7014 | 0.869127 | 0.434563 | − | 0.900641i | \(-0.356903\pi\) | ||||
0.434563 | + | 0.900641i | \(0.356903\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.2820 | 0.568342 | 0.284171 | − | 0.958774i | \(-0.408282\pi\) | ||||
0.284171 | + | 0.958774i | \(0.408282\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.14569 | −0.283781 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.0395 | −1.06161 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.49950 | −0.344827 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.64619 | 0.166948 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.75757 | 0.308761 | 0.154381 | − | 0.988011i | \(-0.450662\pi\) | ||||
0.154381 | + | 0.988011i | \(0.450662\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.31427 | −0.333502 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.87459 | −0.130798 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.0395 | 1.54248 | 0.771239 | − | 0.636545i | \(-0.219637\pi\) | ||||
0.771239 | + | 0.636545i | \(0.219637\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −54.0146 | −2.44263 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.3299 | −0.782088 | −0.391044 | − | 0.920372i | \(-0.627886\pi\) | ||||
−0.391044 | + | 0.920372i | \(0.627886\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −34.2773 | −1.54377 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 28.0718 | 1.25919 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.0931 | −0.630895 | −0.315447 | − | 0.948943i | \(-0.602155\pi\) | ||||
−0.315447 | + | 0.948943i | \(0.602155\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −45.1806 | −2.01852 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.7825 | 0.703706 | 0.351853 | − | 0.936055i | \(-0.385552\pi\) | ||||
0.351853 | + | 0.936055i | \(0.385552\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 31.1114 | 1.38170 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.3907 | −0.593534 | −0.296767 | − | 0.954950i | \(-0.595908\pi\) | ||||
−0.296767 | + | 0.954950i | \(0.595908\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −33.1088 | −1.46465 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −15.3143 | −0.676141 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.05619 | 0.310331 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.2211 | 0.931505 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.6857 | 0.511961 | 0.255981 | − | 0.966682i | \(-0.417602\pi\) | ||||
0.255981 | + | 0.966682i | \(0.417602\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.9022 | 0.826538 | 0.413269 | − | 0.910609i | \(-0.364387\pi\) | ||||
0.413269 | + | 0.910609i | \(0.364387\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.4064 | 0.888916 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8340 | −0.992784 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 26.2607 | 1.13962 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.31427 | −0.143557 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 27.7971 | 1.19953 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.407385 | 0.0175473 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.8497 | −0.466464 | −0.233232 | − | 0.972421i | \(-0.574930\pi\) | ||||
−0.233232 | + | 0.972421i | \(0.574930\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −60.8294 | −2.61044 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −44.9621 | −1.92244 | −0.961220 | − | 0.275784i | \(-0.911062\pi\) | ||||
−0.961220 | + | 0.275784i | \(0.911062\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.6119 | −0.708978 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 61.0911 | 2.60257 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.57133 | 0.364490 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.99899 | −0.0847000 | −0.0423500 | − | 0.999103i | \(-0.513484\pi\) | ||||
−0.0423500 | + | 0.999103i | \(0.513484\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.49950 | −0.317195 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.9069 | 0.502709 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −28.8340 | −1.21521 | −0.607605 | − | 0.794239i | \(-0.707870\pi\) | ||||
−0.607605 | + | 0.794239i | \(0.707870\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −17.1852 | −0.721712 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.6894 | 1.07695 | 0.538477 | − | 0.842640i | \(-0.319000\pi\) | ||||
0.538477 | + | 0.842640i | \(0.319000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.4792 | −1.52661 | −0.763304 | − | 0.646040i | \(-0.776424\pi\) | ||||
−0.763304 | + | 0.646040i | \(0.776424\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 40.2773 | 1.68261 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.1078 | −1.50319 | −0.751593 | − | 0.659628i | \(-0.770714\pi\) | ||||
−0.751593 | + | 0.659628i | \(0.770714\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.22477 | 0.175576 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 45.3122 | 1.87987 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.979724 | 0.0405760 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.77784 | −0.238477 | −0.119239 | − | 0.992866i | \(-0.538045\pi\) | ||||
−0.119239 | + | 0.992866i | \(0.538045\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.3694 | −1.49858 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.20188 | 0.296246 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.9418 | 1.35276 | 0.676379 | − | 0.736554i | \(-0.263548\pi\) | ||||
0.676379 | + | 0.736554i | \(0.263548\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 67.8330 | 2.77622 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.14830 | −0.332931 | −0.166465 | − | 0.986047i | \(-0.553235\pi\) | ||||
−0.166465 | + | 0.986047i | \(0.553235\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.39073 | 0.301474 | 0.150737 | − | 0.988574i | \(-0.451835\pi\) | ||||
0.150737 | + | 0.988574i | \(0.451835\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.40376 | −0.342228 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.9980 | 1.13640 | 0.568202 | − | 0.822889i | \(-0.307639\pi\) | ||||
0.568202 | + | 0.822889i | \(0.307639\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −52.6644 | −2.13407 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.05619 | 0.285463 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.0036 | 1.57534 | 0.787671 | − | 0.616096i | \(-0.211287\pi\) | ||||
0.787671 | + | 0.616096i | \(0.211287\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.1686 | −1.05351 | −0.526754 | − | 0.850018i | \(-0.676591\pi\) | ||||
−0.526754 | + | 0.850018i | \(0.676591\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.2820 | −0.895588 | −0.447794 | − | 0.894137i | \(-0.647790\pi\) | ||||
−0.447794 | + | 0.894137i | \(0.647790\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.762203 | −0.0305862 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.5308 | 0.902677 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −21.2211 | −0.847491 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33.5916 | 1.33939 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.1629 | 1.36000 | 0.680002 | − | 0.733210i | \(-0.261979\pi\) | ||||
0.680002 | + | 0.733210i | \(0.261979\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.18885 | 0.245985 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.407385 | 0.0161412 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 38.3861 | 1.51853 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.37046 | −0.212120 | −0.106060 | − | 0.994360i | \(-0.533824\pi\) | ||||
−0.106060 | + | 0.994360i | \(0.533824\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.8856 | 0.626467 | 0.313233 | − | 0.949676i | \(-0.398588\pi\) | ||||
0.313233 | + | 0.949676i | \(0.398588\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.87197 | 0.191537 | 0.0957685 | − | 0.995404i | \(-0.469469\pi\) | ||||
0.0957685 | + | 0.995404i | \(0.469469\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.05619 | 0.276980 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 31.3528 | 1.22881 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.8101 | −0.657831 | −0.328916 | − | 0.944359i | \(-0.606683\pi\) | ||||
−0.328916 | + | 0.944359i | \(0.606683\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −45.2737 | −1.76630 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.79449 | 0.108858 | 0.0544290 | − | 0.998518i | \(-0.482666\pi\) | ||||
0.0544290 | + | 0.998518i | \(0.482666\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.4267 | 1.30015 | 0.650073 | − | 0.759872i | \(-0.274738\pi\) | ||||
0.650073 | + | 0.759872i | \(0.274738\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.9069 | 0.462425 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.04055 | 0.117731 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −65.9215 | −2.54867 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.46358 | −0.172315 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.9115 | 0.459155 | 0.229578 | − | 0.973290i | \(-0.426266\pi\) | ||||
0.229578 | + | 0.973290i | \(0.426266\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.4277 | 0.516067 | 0.258033 | − | 0.966136i | \(-0.416926\pi\) | ||||
0.258033 | + | 0.966136i | \(0.416926\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.26271 | 0.317094 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.6478 | −1.02115 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −47.7160 | −1.82580 | −0.912901 | − | 0.408181i | \(-0.866163\pi\) | ||||
−0.912901 | + | 0.408181i | \(0.866163\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −75.2763 | −2.87197 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.979724 | 0.0373245 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.2450 | −1.11253 | −0.556267 | − | 0.831004i | \(-0.687767\pi\) | ||||
−0.556267 | + | 0.831004i | \(0.687767\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.1290 | 0.384770 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.2211 | 0.576542 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15.3143 | −0.579239 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.6442 | 0.704181 | 0.352090 | − | 0.935966i | \(-0.385471\pi\) | ||||
0.352090 | + | 0.935966i | \(0.385471\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −59.8689 | −2.25800 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.2211 | 0.572450 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.3705 | −1.14059 | −0.570293 | − | 0.821441i | \(-0.693170\pi\) | ||||
−0.570293 | + | 0.821441i | \(0.693170\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.7206 | 0.439558 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.81014 | −0.0677901 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.83766 | −0.367394 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.49950 | 0.167803 | 0.0839014 | − | 0.996474i | \(-0.473262\pi\) | ||||
0.0839014 | + | 0.996474i | \(0.473262\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.6524 | −0.471201 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 61.1639 | 2.27471 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.7925 | 1.43873 | 0.719367 | − | 0.694631i | \(-0.244432\pi\) | ||||
0.719367 | + | 0.694631i | \(0.244432\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −38.0516 | −1.40932 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 34.4423 | 1.27389 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.5547 | 1.09163 | 0.545813 | − | 0.837907i | \(-0.316221\pi\) | ||||
0.545813 | + | 0.837907i | \(0.316221\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.25807 | −0.0831772 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.9079 | 0.401253 | 0.200627 | − | 0.979668i | \(-0.435702\pi\) | ||||
0.200627 | + | 0.979668i | \(0.435702\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.2211 | −0.779578 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.94743 | 0.291563 | 0.145782 | − | 0.989317i | \(-0.453430\pi\) | ||||
0.145782 | + | 0.989317i | \(0.453430\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 61.9611 | 2.26704 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.90890 | 0.0697497 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.2783 | −0.666986 | −0.333493 | − | 0.942753i | \(-0.608227\pi\) | ||||
−0.333493 | + | 0.942753i | \(0.608227\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 55.9787 | 2.03998 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.2727 | −1.10028 | −0.550140 | − | 0.835072i | \(-0.685426\pi\) | ||||
−0.550140 | + | 0.835072i | \(0.685426\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.05619 | −0.0383374 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.7429 | 0.534431 | 0.267216 | − | 0.963637i | \(-0.413896\pi\) | ||||
0.267216 | + | 0.963637i | \(0.413896\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.6442 | 0.421547 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.05619 | 0.254784 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.94280 | 0.142181 | 0.0710905 | − | 0.997470i | \(-0.477352\pi\) | ||||
0.0710905 | + | 0.997470i | \(0.477352\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.4110 | 0.374943 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −52.6478 | −1.89361 | −0.946805 | − | 0.321808i | \(-0.895709\pi\) | ||||
−0.946805 | + | 0.321808i | \(0.895709\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 51.6109 | 1.85153 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −27.1280 | −0.971962 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.3143 | 0.369073 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −13.9641 | −0.499036 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.5713 | 1.58880 | 0.794398 | − | 0.607397i | \(-0.207786\pi\) | ||||
0.794398 | + | 0.607397i | \(0.207786\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 75.8091 | 2.69888 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 31.8017 | 1.13074 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.46358 | −0.158506 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.03693 | 0.320104 | 0.160052 | − | 0.987109i | \(-0.448834\pi\) | ||||
0.160052 | + | 0.987109i | \(0.448834\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.4064 | −1.14646 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 30.8091 | 1.08859 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.1650 | −0.429292 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.8340 | 0.733393 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.14468 | 0.321510 | 0.160755 | − | 0.986994i | \(-0.448607\pi\) | ||||
0.160755 | + | 0.986994i | \(0.448607\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.35482 | −0.0475741 | −0.0237870 | − | 0.999717i | \(-0.507572\pi\) | ||||
−0.0237870 | + | 0.999717i | \(0.507572\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 50.3658 | 1.76641 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −61.3851 | −2.14759 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.1290 | 0.353937 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.2414 | −0.950732 | −0.475366 | − | 0.879788i | \(-0.657684\pi\) | ||||
−0.475366 | + | 0.879788i | \(0.657684\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.96771 | 0.242879 | 0.121440 | − | 0.992599i | \(-0.461249\pi\) | ||||
0.121440 | + | 0.992599i | \(0.461249\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.68472 | 0.0933570 | 0.0466785 | − | 0.998910i | \(-0.485136\pi\) | ||||
0.0466785 | + | 0.998910i | \(0.485136\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.2222 | −0.702345 | −0.351172 | − | 0.936311i | \(-0.614217\pi\) | ||||
−0.351172 | + | 0.936311i | \(0.614217\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.74555 | 0.164621 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.87096 | −0.0648250 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.31326 | 0.287348 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 35.5344 | 1.22678 | 0.613392 | − | 0.789779i | \(-0.289805\pi\) | ||||
0.613392 | + | 0.789779i | \(0.289805\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.7050 | 0.920862 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −45.8497 | −1.57915 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.72165 | 0.0935170 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −43.6873 | −1.49935 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.97972 | −0.102144 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.3253 | 0.901360 | 0.450680 | − | 0.892686i | \(-0.351182\pi\) | ||||
0.450680 | + | 0.892686i | \(0.351182\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −48.1270 | −1.64399 | −0.821994 | − | 0.569496i | \(-0.807138\pi\) | ||||
−0.821994 | + | 0.569496i | \(0.807138\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.8148 | 1.39258 | 0.696291 | − | 0.717760i | \(-0.254832\pi\) | ||||
0.696291 | + | 0.717760i | \(0.254832\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23.3861 | 0.796996 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39.8866 | −1.35776 | −0.678878 | − | 0.734251i | \(-0.737533\pi\) | ||||
−0.678878 | + | 0.734251i | \(0.737533\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.6093 | −0.360310 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.14931 | 0.106833 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.25807 | −0.0765119 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.2986 | 0.382401 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.7263 | −0.395969 | −0.197984 | − | 0.980205i | \(-0.563439\pi\) | ||||
−0.197984 | + | 0.980205i | \(0.563439\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 73.5537 | 2.48090 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.7363 | −0.395405 | −0.197703 | − | 0.980262i | \(-0.563348\pi\) | ||||
−0.197703 | + | 0.980262i | \(0.563348\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.0146 | −0.471630 | −0.235815 | − | 0.971798i | \(-0.575776\pi\) | ||||
−0.235815 | + | 0.971798i | \(0.575776\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.12904 | −0.138639 | −0.0693197 | − | 0.997594i | \(-0.522083\pi\) | ||||
−0.0693197 | + | 0.997594i | \(0.522083\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 25.9095 | 0.868977 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.31427 | −0.211536 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 57.7566 | 1.93275 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.05619 | −0.0352653 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −33.1629 | −1.10605 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.49950 | −0.149900 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 52.9179 | 1.76100 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.2258 | −0.837608 | −0.418804 | − | 0.908077i | \(-0.637551\pi\) | ||||
−0.418804 | + | 0.908077i | \(0.637551\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 20.8138 | 0.690349 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.7419 | −0.654079 | −0.327040 | − | 0.945011i | \(-0.606051\pi\) | ||||
−0.327040 | + | 0.945011i | \(0.606051\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.6488 | 0.550995 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 61.1806 | 2.02036 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39.1114 | 1.29017 | 0.645083 | − | 0.764113i | \(-0.276823\pi\) | ||||
0.645083 | + | 0.764113i | \(0.276823\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.94743 | 0.195975 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.3143 | 0.339498 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.3012 | −0.568247 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.670093 | −0.0219850 | −0.0109925 | − | 0.999940i | \(-0.503499\pi\) | ||||
−0.0109925 | + | 0.999940i | \(0.503499\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.33454 | 0.109285 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −29.1878 | −0.955567 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.3715 | −1.02486 | −0.512431 | − | 0.858729i | \(-0.671255\pi\) | ||||
−0.512431 | + | 0.858729i | \(0.671255\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −18.6285 | −0.607919 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.5703 | −1.28996 | −0.644978 | − | 0.764201i | \(-0.723133\pi\) | ||||
−0.644978 | + | 0.764201i | \(0.723133\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.35018 | −0.0439680 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.31427 | −0.302673 | −0.151336 | − | 0.988482i | \(-0.548358\pi\) | ||||
−0.151336 | + | 0.988482i | \(0.548358\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.1650 | −0.394891 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −76.5334 | −2.48177 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.7409 | −0.866223 | −0.433112 | − | 0.901340i | \(-0.642584\pi\) | ||||
−0.433112 | + | 0.901340i | \(0.642584\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −19.3502 | −0.625503 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 42.2820 | 1.36536 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.2571 | −0.363131 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.61027 | 0.0841149 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.0442 | −0.933998 | −0.466999 | − | 0.884258i | \(-0.654665\pi\) | ||||
−0.466999 | + | 0.884258i | \(0.654665\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 97.4606 | 3.13088 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.3482 | −1.32693 | −0.663463 | − | 0.748209i | \(-0.730914\pi\) | ||||
−0.663463 | + | 0.748209i | \(0.730914\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36.2794 | 1.16306 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.9105 | −0.477029 | −0.238515 | − | 0.971139i | \(-0.576661\pi\) | ||||
−0.238515 | + | 0.971139i | \(0.576661\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.27835 | 0.264577 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.9225 | 0.508367 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.4682 | −0.684730 | −0.342365 | − | 0.939567i | \(-0.611228\pi\) | ||||
−0.342365 | + | 0.939567i | \(0.611228\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −49.7899 | −1.58483 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.05518 | −0.0971492 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.47922 | 0.110521 | 0.0552605 | − | 0.998472i | \(-0.482401\pi\) | ||||
0.0552605 | + | 0.998472i | \(0.482401\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.8902 | 0.504261 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.4054 | −0.741255 | −0.370628 | − | 0.928782i | \(-0.620857\pi\) | ||||
−0.370628 | + | 0.928782i | \(0.620857\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 13.6847 | 0.432966 |
(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 | 2200.2.a.v.1.1 | yes | 3 | |
4.3 | odd | 2 | 4400.2.a.by.1.3 | 3 | |||
5.2 | odd | 4 | 2200.2.b.m.1849.5 | 6 | |||
5.3 | odd | 4 | 2200.2.b.m.1849.2 | 6 | |||
5.4 | even | 2 | 2200.2.a.u.1.3 | ✓ | 3 | ||
20.3 | even | 4 | 4400.2.b.bb.4049.5 | 6 | |||
20.7 | even | 4 | 4400.2.b.bb.4049.2 | 6 | |||
20.19 | odd | 2 | 4400.2.a.bz.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2200.2.a.u.1.3 | ✓ | 3 | 5.4 | even | 2 | ||
2200.2.a.v.1.1 | yes | 3 | 1.1 | even | 1 | trivial | |
2200.2.b.m.1849.2 | 6 | 5.3 | odd | 4 | |||
2200.2.b.m.1849.5 | 6 | 5.2 | odd | 4 | |||
4400.2.a.by.1.3 | 3 | 4.3 | odd | 2 | |||
4400.2.a.bz.1.1 | 3 | 20.19 | odd | 2 | |||
4400.2.b.bb.4049.2 | 6 | 20.7 | even | 4 | |||
4400.2.b.bb.4049.5 | 6 | 20.3 | even | 4 |