Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(1\) |
Dimension: | \(44\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.27 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 | ||||||||
\(3\) | 0.278140 | 0.160584 | 0.0802921 | − | 0.996771i | \(-0.474415\pi\) | ||||
0.0802921 | + | 0.996771i | \(0.474415\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.58670 | 0.709593 | 0.354796 | − | 0.934944i | \(-0.384550\pi\) | ||||
0.354796 | + | 0.934944i | \(0.384550\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.49171 | −0.941777 | −0.470889 | − | 0.882193i | \(-0.656067\pi\) | ||||
−0.470889 | + | 0.882193i | \(0.656067\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.92264 | −0.974213 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.31839 | 1.60356 | 0.801778 | − | 0.597622i | \(-0.203888\pi\) | ||||
0.801778 | + | 0.597622i | \(0.203888\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.17786 | −1.15873 | −0.579365 | − | 0.815069i | \(-0.696699\pi\) | ||||
−0.579365 | + | 0.815069i | \(0.696699\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.441324 | 0.113949 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.16226 | −0.766960 | −0.383480 | − | 0.923549i | \(-0.625275\pi\) | ||||
−0.383480 | + | 0.923549i | \(0.625275\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.18165 | 1.18875 | 0.594376 | − | 0.804187i | \(-0.297399\pi\) | ||||
0.594376 | + | 0.804187i | \(0.297399\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.693044 | −0.151235 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.27106 | −0.473550 | −0.236775 | − | 0.971565i | \(-0.576090\pi\) | ||||
−0.236775 | + | 0.971565i | \(0.576090\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.48239 | −0.496478 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.64732 | −0.317027 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.70849 | 0.874345 | 0.437173 | − | 0.899378i | \(-0.355980\pi\) | ||||
0.437173 | + | 0.899378i | \(0.355980\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.466223 | −0.0837361 | −0.0418680 | − | 0.999123i | \(-0.513331\pi\) | ||||
−0.0418680 | + | 0.999123i | \(0.513331\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.47926 | 0.257506 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.95359 | −0.668278 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.71895 | 0.775791 | 0.387896 | − | 0.921703i | \(-0.373202\pi\) | ||||
0.387896 | + | 0.921703i | \(0.373202\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.16203 | −0.186074 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.53789 | 0.708699 | 0.354349 | − | 0.935113i | \(-0.384702\pi\) | ||||
0.354349 | + | 0.935113i | \(0.384702\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.13155 | 0.477557 | 0.238778 | − | 0.971074i | \(-0.423253\pi\) | ||||
0.238778 | + | 0.971074i | \(0.423253\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.63734 | −0.691294 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.59850 | −0.233165 | −0.116583 | − | 0.993181i | \(-0.537194\pi\) | ||||
−0.116583 | + | 0.993181i | \(0.537194\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.791388 | −0.113055 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.879550 | −0.123162 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.67829 | −0.505252 | −0.252626 | − | 0.967564i | \(-0.581294\pi\) | ||||
−0.252626 | + | 0.967564i | \(0.581294\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.43868 | 1.13787 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.44122 | 0.190895 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.30428 | −0.430181 | −0.215090 | − | 0.976594i | \(-0.569005\pi\) | ||||
−0.215090 | + | 0.976594i | \(0.569005\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.92274 | −0.886365 | −0.443183 | − | 0.896431i | \(-0.646151\pi\) | ||||
−0.443183 | + | 0.896431i | \(0.646151\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.28236 | 0.917491 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.62900 | −0.822226 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.2927 | −1.50179 | −0.750897 | − | 0.660420i | \(-0.770378\pi\) | ||||
−0.750897 | + | 0.660420i | \(0.770378\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.631673 | −0.0760445 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0893 | 1.43474 | 0.717370 | − | 0.696693i | \(-0.245346\pi\) | ||||
0.717370 | + | 0.696693i | \(0.245346\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.02316 | −0.587917 | −0.293958 | − | 0.955818i | \(-0.594973\pi\) | ||||
−0.293958 | + | 0.955818i | \(0.594973\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.690452 | −0.0797265 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13.2519 | −1.51019 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.9398 | −1.45584 | −0.727922 | − | 0.685660i | \(-0.759514\pi\) | ||||
−0.727922 | + | 0.685660i | \(0.759514\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.30973 | 0.923303 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.3149 | −1.35173 | −0.675866 | − | 0.737024i | \(-0.736230\pi\) | ||||
−0.675866 | + | 0.737024i | \(0.736230\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.01755 | −0.544229 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.30962 | 0.140406 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.2492 | −1.61641 | −0.808205 | − | 0.588902i | \(-0.799561\pi\) | ||||
−0.808205 | + | 0.588902i | \(0.799561\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.4100 | 1.09126 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.129675 | −0.0134467 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.22171 | 0.843530 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.89871 | 0.395854 | 0.197927 | − | 0.980217i | \(-0.436579\pi\) | ||||
0.197927 | + | 0.980217i | \(0.436579\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −15.5437 | −1.56220 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.95625 | 0.294158 | 0.147079 | − | 0.989125i | \(-0.453013\pi\) | ||||
0.147079 | + | 0.989125i | \(0.453013\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00210 | 0.197273 | 0.0986366 | − | 0.995124i | \(-0.468552\pi\) | ||||
0.0986366 | + | 0.995124i | \(0.468552\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.09965 | −0.107315 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.8999 | −1.63378 | −0.816889 | − | 0.576796i | \(-0.804303\pi\) | ||||
−0.816889 | + | 0.576796i | \(0.804303\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.73753 | 0.262208 | 0.131104 | − | 0.991369i | \(-0.458148\pi\) | ||||
0.131104 | + | 0.991369i | \(0.458148\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.31253 | 0.124580 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.8926 | 1.40098 | 0.700491 | − | 0.713661i | \(-0.252964\pi\) | ||||
0.700491 | + | 0.713661i | \(0.252964\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.60349 | −0.336027 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.2104 | 1.12885 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.87943 | 0.722306 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.2853 | 1.57139 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.26217 | 0.113806 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.8723 | −1.06189 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.64634 | 0.855974 | 0.427987 | − | 0.903785i | \(-0.359223\pi\) | ||||
0.427987 | + | 0.903785i | \(0.359223\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.871009 | 0.0766880 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.3574 | −0.904931 | −0.452465 | − | 0.891782i | \(-0.649455\pi\) | ||||
−0.452465 | + | 0.891782i | \(0.649455\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.9112 | −1.11954 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.61380 | −0.224960 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.7335 | −1.77138 | −0.885692 | − | 0.464274i | \(-0.846315\pi\) | ||||
−0.885692 | + | 0.464274i | \(0.846315\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.3132 | −1.04439 | −0.522195 | − | 0.852826i | \(-0.674887\pi\) | ||||
−0.522195 | + | 0.852826i | \(0.674887\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.444607 | −0.0374426 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −22.2195 | −1.85809 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.47095 | 0.620429 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.220117 | −0.0181549 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.314134 | 0.0257349 | 0.0128674 | − | 0.999917i | \(-0.495904\pi\) | ||||
0.0128674 | + | 0.999917i | \(0.495904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.56907 | −0.209068 | −0.104534 | − | 0.994521i | \(-0.533335\pi\) | ||||
−0.104534 | + | 0.994521i | \(0.533335\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.24214 | 0.747183 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.739755 | −0.0594185 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.6045 | 1.96366 | 0.981828 | − | 0.189772i | \(-0.0607749\pi\) | ||||
0.981828 | + | 0.189772i | \(0.0607749\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.02308 | −0.0811355 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.65883 | 0.445978 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.0969 | −1.65243 | −0.826217 | − | 0.563352i | \(-0.809511\pi\) | ||||
−0.826217 | + | 0.563352i | \(0.809511\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.34713 | 0.182724 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.3314 | −1.41853 | −0.709265 | − | 0.704942i | \(-0.750973\pi\) | ||||
−0.709265 | + | 0.704942i | \(0.750973\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.45449 | 0.342653 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −15.1441 | −1.15810 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.78749 | −0.211929 | −0.105964 | − | 0.994370i | \(-0.533793\pi\) | ||||
−0.105964 | + | 0.994370i | \(0.533793\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.18540 | 0.467572 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.919052 | −0.0690802 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.93477 | −0.443585 | −0.221793 | − | 0.975094i | \(-0.571191\pi\) | ||||
−0.221793 | + | 0.975094i | \(0.571191\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.676298 | 0.0502689 | 0.0251344 | − | 0.999684i | \(-0.491999\pi\) | ||||
0.0251344 | + | 0.999684i | \(0.491999\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.92549 | −0.142336 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.48755 | 0.550496 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.8181 | −1.22986 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.10465 | 0.298569 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.93976 | 0.357429 | 0.178714 | − | 0.983901i | \(-0.442806\pi\) | ||||
0.178714 | + | 0.983901i | \(0.442806\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.427481 | 0.0307707 | 0.0153854 | − | 0.999882i | \(-0.495102\pi\) | ||||
0.0153854 | + | 0.999882i | \(0.495102\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.84379 | −0.132036 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.6733 | −0.831691 | −0.415845 | − | 0.909435i | \(-0.636514\pi\) | ||||
−0.415845 | + | 0.909435i | \(0.636514\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.6843 | −1.53716 | −0.768579 | − | 0.639755i | \(-0.779036\pi\) | ||||
−0.768579 | + | 0.639755i | \(0.779036\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.41909 | −0.241164 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.7322 | −0.823439 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.20025 | 0.502887 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.63750 | 0.461338 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 27.5580 | 1.90623 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.7958 | −1.22511 | −0.612557 | − | 0.790427i | \(-0.709859\pi\) | ||||
−0.612557 | + | 0.790427i | \(0.709859\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.36253 | 0.230396 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.96882 | 0.338871 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.16169 | 0.0788608 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.39714 | −0.0944101 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.2115 | 0.888699 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.56036 | 0.439314 | 0.219657 | − | 0.975577i | \(-0.429506\pi\) | ||||
0.219657 | + | 0.975577i | \(0.429506\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.25513 | 0.483675 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.50792 | −0.431946 | −0.215973 | − | 0.976399i | \(-0.569292\pi\) | ||||
−0.215973 | + | 0.976399i | \(0.569292\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.9817 | 0.857853 | 0.428927 | − | 0.903339i | \(-0.358892\pi\) | ||||
0.428927 | + | 0.903339i | \(0.358892\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.68588 | −0.242513 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.51412 | −0.623291 | −0.311646 | − | 0.950198i | \(-0.600880\pi\) | ||||
−0.311646 | + | 0.950198i | \(0.600880\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.53634 | −0.165452 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.59908 | −0.233785 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.4019 | 1.38437 | 0.692187 | − | 0.721718i | \(-0.256647\pi\) | ||||
0.692187 | + | 0.721718i | \(0.256647\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.72856 | −0.626671 | −0.313336 | − | 0.949642i | \(-0.601447\pi\) | ||||
−0.313336 | + | 0.949642i | \(0.601447\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.25323 | 0.465295 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.25569 | −0.0802233 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.6482 | −1.37744 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.42526 | −0.217067 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.75019 | 0.299830 | 0.149915 | − | 0.988699i | \(-0.452100\pi\) | ||||
0.149915 | + | 0.988699i | \(0.452100\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.0784 | −0.759363 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.39558 | −0.0873946 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.8109 | −0.736743 | −0.368371 | − | 0.929679i | \(-0.620085\pi\) | ||||
−0.368371 | + | 0.929679i | \(0.620085\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.7583 | −0.730623 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.7612 | −0.851798 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.75823 | −0.293405 | −0.146703 | − | 0.989181i | \(-0.546866\pi\) | ||||
−0.146703 | + | 0.989181i | \(0.546866\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.83634 | −0.358523 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.24140 | −0.259570 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.3181 | −0.629103 | −0.314551 | − | 0.949240i | \(-0.601854\pi\) | ||||
−0.314551 | + | 0.949240i | \(0.601854\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.9663 | 0.666153 | 0.333076 | − | 0.942900i | \(-0.391913\pi\) | ||||
0.333076 | + | 0.942900i | \(0.391913\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.89544 | 0.175240 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.2023 | −0.796130 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.3300 | 0.861007 | 0.430504 | − | 0.902589i | \(-0.358336\pi\) | ||||
0.430504 | + | 0.902589i | \(0.358336\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.36260 | 0.0815768 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.91149 | 0.591270 | 0.295635 | − | 0.955301i | \(-0.404469\pi\) | ||||
0.295635 | + | 0.955301i | \(0.404469\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.90578 | 0.113287 | 0.0566434 | − | 0.998394i | \(-0.481960\pi\) | ||||
0.0566434 | + | 0.998394i | \(0.481960\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.28679 | 0.135457 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.3071 | −0.667436 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00012 | −0.411772 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.08439 | 0.0635679 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.0845 | −0.589142 | −0.294571 | − | 0.955630i | \(-0.595177\pi\) | ||||
−0.294571 | + | 0.955630i | \(0.595177\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.24289 | −0.305253 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.76110 | −0.508371 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.48818 | 0.548716 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.80291 | −0.449752 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.822252 | 0.0472372 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.9843 | −0.628958 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.8752 | 1.41970 | 0.709850 | − | 0.704353i | \(-0.248763\pi\) | ||||
0.709850 | + | 0.704353i | \(0.248763\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.556865 | 0.0316789 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.0379 | −1.36306 | −0.681531 | − | 0.731789i | \(-0.738686\pi\) | ||||
−0.681531 | + | 0.731789i | \(0.738686\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.12359 | 0.346126 | 0.173063 | − | 0.984911i | \(-0.444634\pi\) | ||||
0.173063 | + | 0.984911i | \(0.444634\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 11.5549 | 0.651045 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.9177 | 1.51185 | 0.755924 | − | 0.654659i | \(-0.227188\pi\) | ||||
0.755924 | + | 0.654659i | \(0.227188\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.0416 | 1.40206 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.70054 | −0.262359 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.3857 | −0.911726 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.3711 | 0.575284 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.761417 | 0.0421064 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.98300 | 0.219590 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.2369 | 1.22225 | 0.611125 | − | 0.791534i | \(-0.290717\pi\) | ||||
0.611125 | + | 0.791534i | \(0.290717\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −13.7918 | −0.755786 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.5048 | −1.06566 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.9032 | 1.90130 | 0.950650 | − | 0.310265i | \(-0.100418\pi\) | ||||
0.950650 | + | 0.310265i | \(0.100418\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.14224 | 0.224976 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.47956 | −0.134275 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.4139 | 1.04825 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.00227 | −0.0539606 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.6429 | −1.05449 | −0.527243 | − | 0.849714i | \(-0.676774\pi\) | ||||
−0.527243 | + | 0.849714i | \(0.676774\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.5312 | −0.777839 | −0.388920 | − | 0.921272i | \(-0.627152\pi\) | ||||
−0.388920 | + | 0.921272i | \(0.627152\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.88228 | 0.367349 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.8987 | −0.686528 | −0.343264 | − | 0.939239i | \(-0.611533\pi\) | ||||
−0.343264 | + | 0.939239i | \(0.611533\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.1821 | 1.01808 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.19158 | 0.115991 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.9031 | 0.839333 | 0.419667 | − | 0.907678i | \(-0.362147\pi\) | ||||
0.419667 | + | 0.907678i | \(0.362147\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.84949 | 0.413131 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.80773 | 0.252340 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.97024 | −0.417181 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.55160 | −0.446390 | −0.223195 | − | 0.974774i | \(-0.571649\pi\) | ||||
−0.223195 | + | 0.974774i | \(0.571649\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −13.2626 | −0.690423 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.16523 | 0.475835 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.9876 | −0.620693 | −0.310346 | − | 0.950624i | \(-0.600445\pi\) | ||||
−0.310346 | + | 0.950624i | \(0.600445\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.30216 | −0.170523 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19.6714 | −1.01313 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.65175 | 0.187578 | 0.0937888 | − | 0.995592i | \(-0.470102\pi\) | ||||
0.0937888 | + | 0.995592i | \(0.470102\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.68303 | 0.137456 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.6726 | −1.26071 | −0.630355 | − | 0.776307i | \(-0.717090\pi\) | ||||
−0.630355 | + | 0.776307i | \(0.717090\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21.0267 | −1.07162 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.15239 | −0.465242 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.8541 | 1.56437 | 0.782183 | − | 0.623049i | \(-0.214106\pi\) | ||||
0.782183 | + | 0.623049i | \(0.214106\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.18169 | 0.363194 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.88081 | −0.145318 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −20.5316 | −1.03306 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.21276 | −0.311809 | −0.155905 | − | 0.987772i | \(-0.549829\pi\) | ||||
−0.155905 | + | 0.987772i | \(0.549829\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.59111 | −0.179780 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.7692 | −1.53654 | −0.768270 | − | 0.640126i | \(-0.778882\pi\) | ||||
−0.768270 | + | 0.640126i | \(0.778882\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.94781 | 0.0970275 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.1850 | 0.655169 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.0972 | 1.24402 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.8667 | 1.72405 | 0.862025 | − | 0.506866i | \(-0.169196\pi\) | ||||
0.862025 | + | 0.506866i | \(0.169196\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.76682 | −0.284456 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.23330 | 0.405134 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19.5400 | −0.959180 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.42479 | −0.167713 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.51925 | −0.171926 | −0.0859632 | − | 0.996298i | \(-0.527397\pi\) | ||||
−0.0859632 | + | 0.996298i | \(0.527397\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.94511 | 0.338484 | 0.169242 | − | 0.985575i | \(-0.445868\pi\) | ||||
0.169242 | + | 0.985575i | \(0.445868\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.67184 | 0.227153 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.84996 | 0.380779 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.2494 | 0.834759 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.18012 | −0.298379 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.4362 | 0.984376 | 0.492188 | − | 0.870489i | \(-0.336197\pi\) | ||||
0.492188 | + | 0.870489i | \(0.336197\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.57364 | 0.460080 | 0.230040 | − | 0.973181i | \(-0.426114\pi\) | ||||
0.230040 | + | 0.973181i | \(0.426114\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.07797 | 0.0996310 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.7679 | −0.562933 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.0237 | 0.573862 | 0.286931 | − | 0.957951i | \(-0.407365\pi\) | ||||
0.286931 | + | 0.957951i | \(0.407365\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.31294 | 0.110140 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.7043 | 0.746135 | 0.373068 | − | 0.927804i | \(-0.378306\pi\) | ||||
0.373068 | + | 0.927804i | \(0.378306\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.1958 | −1.14699 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.0873733 | 0.00413262 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.1199 | −1.04390 | −0.521952 | − | 0.852975i | \(-0.674796\pi\) | ||||
−0.521952 | + | 0.852975i | \(0.674796\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.1343 | 1.13644 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.714562 | −0.0335731 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.5175 | 0.774353 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.96675 | −0.0920009 | −0.0460004 | − | 0.998941i | \(-0.514648\pi\) | ||||
−0.0460004 | + | 0.998941i | \(0.514648\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.20926 | 0.243147 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.8317 | −0.783933 | −0.391966 | − | 0.919980i | \(-0.628205\pi\) | ||||
−0.391966 | + | 0.919980i | \(0.628205\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.3927 | −0.575936 | −0.287968 | − | 0.957640i | \(-0.592980\pi\) | ||||
−0.287968 | + | 0.957640i | \(0.592980\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.205755 | −0.00954167 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.4711 | −1.36376 | −0.681880 | − | 0.731464i | \(-0.738837\pi\) | ||||
−0.681880 | + | 0.731464i | \(0.738837\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 30.6298 | 1.41435 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.84351 | 0.315332 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.6548 | 0.765789 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.8629 | −0.590190 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.7503 | 0.492223 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.5295 | 1.21216 | 0.606082 | − | 0.795402i | \(-0.292740\pi\) | ||||
0.606082 | + | 0.795402i | \(0.292740\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.7151 | −0.898932 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.57395 | 0.0716170 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.18608 | 0.280895 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.1334 | −0.595133 | −0.297567 | − | 0.954701i | \(-0.596175\pi\) | ||||
−0.297567 | + | 0.954701i | \(0.596175\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.86788 | −0.265355 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.43276 | 0.245177 | 0.122588 | − | 0.992458i | \(-0.460880\pi\) | ||||
0.122588 | + | 0.992458i | \(0.460880\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.8895 | −0.670588 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −24.6632 | −1.10853 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −30.1231 | −1.35121 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.9981 | −0.805707 | −0.402854 | − | 0.915264i | \(-0.631982\pi\) | ||||
−0.402854 | + | 0.915264i | \(0.631982\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.09871 | −0.227793 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.6584 | −0.921112 | −0.460556 | − | 0.887631i | \(-0.652350\pi\) | ||||
−0.460556 | + | 0.887631i | \(0.652350\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.69068 | 0.208733 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.23897 | 0.0550247 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.3084 | 1.03313 | 0.516564 | − | 0.856249i | \(-0.327211\pi\) | ||||
0.516564 | + | 0.856249i | \(0.327211\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.5163 | 0.553687 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.53585 | −0.376867 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.17673 | 0.139984 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.50145 | −0.373893 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.775311 | −0.0340324 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.7892 | 0.998414 | 0.499207 | − | 0.866483i | \(-0.333625\pi\) | ||||
0.499207 | + | 0.866483i | \(0.333625\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.5606 | −0.680416 | −0.340208 | − | 0.940350i | \(-0.610497\pi\) | ||||
−0.340208 | + | 0.940350i | \(0.610497\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.72041 | 0.0750846 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.47432 | 0.0642223 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.8423 | −0.775751 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.65722 | 0.419088 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.9586 | −0.821190 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −26.8151 | −1.15932 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.65070 | −0.0712328 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.20891 | −0.181291 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.00911 | −0.215359 | −0.107679 | − | 0.994186i | \(-0.534342\pi\) | ||||
−0.107679 | + | 0.994186i | \(0.534342\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.188106 | 0.00807238 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.34363 | 0.186061 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.38513 | 0.273008 | 0.136504 | − | 0.990639i | \(-0.456413\pi\) | ||||
0.136504 | + | 0.990639i | \(0.456413\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 20.2327 | 0.863509 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.3978 | 1.03938 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 32.2423 | 1.37108 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.08259 | 0.0884009 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.33105 | −0.268255 | −0.134128 | − | 0.990964i | \(-0.542823\pi\) | ||||
−0.134128 | + | 0.990964i | \(0.542823\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.0832 | −0.553359 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.67779 | −0.197497 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.9729 | −0.841759 | −0.420880 | − | 0.907117i | \(-0.638278\pi\) | ||||
−0.420880 | + | 0.907117i | \(0.638278\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23.6301 | 0.994127 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −20.7054 | −0.869546 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.9790 | 0.502186 | 0.251093 | − | 0.967963i | \(-0.419210\pi\) | ||||
0.251093 | + | 0.967963i | \(0.419210\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.5625 | −0.818666 | −0.409333 | − | 0.912385i | \(-0.634239\pi\) | ||||
−0.409333 | + | 0.912385i | \(0.634239\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.37394 | 0.0573974 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.63767 | 0.235107 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.9014 | −0.745247 | −0.372623 | − | 0.927983i | \(-0.621542\pi\) | ||||
−0.372623 | + | 0.927983i | \(0.621542\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.118899 | 0.00494129 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.6851 | 1.27303 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.5626 | −0.810200 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 19.3742 | 0.801023 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.3919 | −1.17186 | −0.585930 | − | 0.810362i | \(-0.699271\pi\) | ||||
−0.585930 | + | 0.810362i | \(0.699271\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.41580 | −0.0995415 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.24682 | −0.133556 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.44153 | 0.305587 | 0.152794 | − | 0.988258i | \(-0.451173\pi\) | ||||
0.152794 | + | 0.988258i | \(0.451173\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.5023 | 0.512543 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.03127 | −0.246843 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.9049 | −0.772433 | −0.386216 | − | 0.922408i | \(-0.626218\pi\) | ||||
−0.386216 | + | 0.922408i | \(0.626218\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.6229 | −1.00439 | −0.502194 | − | 0.864755i | \(-0.667474\pi\) | ||||
−0.502194 | + | 0.864755i | \(0.667474\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 35.9271 | 1.46307 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 27.4265 | 1.11505 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.4784 | 0.668836 | 0.334418 | − | 0.942425i | \(-0.391460\pi\) | ||||
0.334418 | + | 0.942425i | \(0.391460\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.26319 | −0.132231 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.67831 | 0.270175 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.5886 | −0.548839 | −0.274419 | − | 0.961610i | \(-0.588486\pi\) | ||||
−0.274419 | + | 0.961610i | \(0.588486\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.00268 | 0.0807557 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.83640 | 0.275223 | 0.137612 | − | 0.990486i | \(-0.456057\pi\) | ||||
0.137612 | + | 0.990486i | \(0.456057\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.8366 | 1.36001 | 0.680003 | − | 0.733209i | \(-0.261978\pi\) | ||||
0.680003 | + | 0.733209i | \(0.261978\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.74117 | 0.150128 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 37.9965 | 1.52230 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.42578 | −0.257031 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.66499 | 0.306110 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.9226 | −0.595001 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 49.3139 | 1.96316 | 0.981578 | − | 0.191060i | \(-0.0611924\pi\) | ||||
0.981578 | + | 0.191060i | \(0.0611924\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.94972 | −0.196734 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.3058 | 0.607393 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.30631 | 0.131001 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −35.3327 | −1.39774 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.2970 | 0.683191 | 0.341596 | − | 0.939847i | \(-0.389033\pi\) | ||||
0.341596 | + | 0.939847i | \(0.389033\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.3460 | 0.802366 | 0.401183 | − | 0.915998i | \(-0.368599\pi\) | ||||
0.401183 | + | 0.915998i | \(0.368599\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.38203 | 0.0544173 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.0241 | −0.826541 | −0.413270 | − | 0.910608i | \(-0.635614\pi\) | ||||
−0.413270 | + | 0.910608i | \(0.635614\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.5735 | −0.689819 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.323113 | 0.0126638 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.4175 | −0.955530 | −0.477765 | − | 0.878488i | \(-0.658553\pi\) | ||||
−0.477765 | + | 0.878488i | \(0.658553\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.4341 | −0.642132 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.6809 | 0.572756 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.5985 | −1.03613 | −0.518064 | − | 0.855342i | \(-0.673347\pi\) | ||||
−0.518064 | + | 0.855342i | \(0.673347\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.9783 | −1.55497 | −0.777487 | − | 0.628899i | \(-0.783506\pi\) | ||||
−0.777487 | + | 0.628899i | \(0.783506\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.67464 | 0.142711 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −20.4861 | −0.794417 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.6933 | −0.414046 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.82470 | 0.0705469 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −36.8178 | −1.42134 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.23630 | 0.0476561 | 0.0238280 | − | 0.999716i | \(-0.492415\pi\) | ||||
0.0238280 | + | 0.999716i | \(0.492415\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.08930 | 0.157397 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.8016 | 1.06850 | 0.534251 | − | 0.845326i | \(-0.320594\pi\) | ||||
0.534251 | + | 0.845326i | \(0.320594\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.71446 | −0.372807 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.81011 | −0.0693637 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.659163 | −0.0252222 | −0.0126111 | − | 0.999920i | \(-0.504014\pi\) | ||||
−0.0126111 | + | 0.999920i | \(0.504014\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −32.8978 | −1.25696 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.61072 | 0.137758 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.3674 | 0.585451 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.0771 | 1.10615 | 0.553073 | − | 0.833133i | \(-0.313455\pi\) | ||||
0.553073 | + | 0.833133i | \(0.313455\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 38.7305 | 1.47125 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.5373 | −0.741092 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.3500 | −0.543544 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.64626 | −0.100091 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.4430 | 0.394427 | 0.197213 | − | 0.980361i | \(-0.436811\pi\) | ||||
0.197213 | + | 0.980361i | \(0.436811\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.4520 | 0.922224 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.705456 | −0.0265690 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.36613 | −0.277032 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −46.7017 | −1.75392 | −0.876960 | − | 0.480564i | \(-0.840432\pi\) | ||||
−0.876960 | + | 0.480564i | \(0.840432\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 37.8184 | 1.41830 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.05882 | 0.0396532 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −35.2556 | −1.31848 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.95272 | 0.222308 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −46.3746 | −1.72948 | −0.864741 | − | 0.502218i | \(-0.832517\pi\) | ||||
−0.864741 | + | 0.502218i | \(0.832517\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.98866 | −0.185787 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.70590 | −0.100634 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.6883 | −0.434093 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.373294 | −0.0138447 | −0.00692235 | − | 0.999976i | \(-0.502203\pi\) | ||||
−0.00692235 | + | 0.999976i | \(0.502203\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.9118 | −0.848584 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.90277 | −0.366267 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.0591 | −0.888642 | −0.444321 | − | 0.895868i | \(-0.646555\pi\) | ||||
−0.444321 | + | 0.895868i | \(0.646555\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.349258 | −0.0128826 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −65.3774 | −2.40821 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.57096 | −0.131360 | −0.0656800 | − | 0.997841i | \(-0.520922\pi\) | ||||
−0.0656800 | + | 0.997841i | \(0.520922\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.02123 | −0.221195 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.89842 | 0.216392 | 0.108196 | − | 0.994130i | \(-0.465493\pi\) | ||||
0.108196 | + | 0.994130i | \(0.465493\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.498436 | 0.0182613 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 35.9919 | 1.31688 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 42.1097 | 1.53865 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.32122 | 0.0481479 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.07634 | −0.148353 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.88934 | −0.323089 | −0.161544 | − | 0.986865i | \(-0.551647\pi\) | ||||
−0.161544 | + | 0.986865i | \(0.551647\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.35949 | −0.121942 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 41.0345 | 1.48750 | 0.743750 | − | 0.668458i | \(-0.233045\pi\) | ||||
0.743750 | + | 0.668458i | \(0.233045\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.82113 | −0.246941 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 14.6645 | 0.530195 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.8048 | 0.498463 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.0124 | 0.721667 | 0.360834 | − | 0.932630i | \(-0.382492\pi\) | ||||
0.360834 | + | 0.932630i | \(0.382492\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.28508 | −0.118309 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 48.4597 | 1.74297 | 0.871487 | − | 0.490419i | \(-0.163156\pi\) | ||||
0.871487 | + | 0.490419i | \(0.163156\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.15735 | 0.0415732 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.27044 | −0.117326 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 23.5137 | 0.842467 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 64.2958 | 2.30068 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.75640 | −0.277191 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 39.0400 | 1.39340 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −50.8456 | −1.81245 | −0.906226 | − | 0.422794i | \(-0.861049\pi\) | ||||
−0.906226 | + | 0.422794i | \(0.861049\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.32345 | −0.0471162 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −37.1081 | −1.31941 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.9222 | 1.02706 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.62332 | −0.0575732 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.19747 | −0.290369 | −0.145185 | − | 0.989405i | \(-0.546378\pi\) | ||||
−0.145185 | + | 0.989405i | \(0.546378\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.05487 | 0.178829 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 44.5678 | 1.57473 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −26.7151 | −0.942757 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.97885 | 0.316463 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.86986 | −0.101024 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.90765 | −0.0670693 | −0.0335347 | − | 0.999438i | \(-0.510676\pi\) | ||||
−0.0335347 | + | 0.999438i | \(0.510676\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.8725 | 0.592472 | 0.296236 | − | 0.955115i | \(-0.404269\pi\) | ||||
0.296236 | + | 0.955115i | \(0.404269\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.05015 | 0.106974 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −33.4743 | −1.17255 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.2266 | 0.567697 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −30.4247 | −1.06312 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.7184 | 1.21168 | 0.605841 | − | 0.795586i | \(-0.292837\pi\) | ||||
0.605841 | + | 0.795586i | \(0.292837\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.4354 | −0.712332 | −0.356166 | − | 0.934423i | \(-0.615916\pi\) | ||||
−0.356166 | + | 0.934423i | \(0.615916\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.67209 | −0.127846 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.3289 | 0.811225 | 0.405612 | − | 0.914045i | \(-0.367058\pi\) | ||||
0.405612 | + | 0.914045i | \(0.367058\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.6949 | −0.788227 | −0.394114 | − | 0.919062i | \(-0.628948\pi\) | ||||
−0.394114 | + | 0.919062i | \(0.628948\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.98575 | 0.138264 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.50257 | 0.0867091 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −29.0865 | −1.00658 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.768019 | 0.0265466 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.4196 | 0.601393 | 0.300696 | − | 0.953720i | \(-0.402781\pi\) | ||||
0.300696 | + | 0.953720i | \(0.402781\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.83009 | −0.235520 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.75678 | 0.0949485 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.06793 | 0.243144 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −43.0699 | −1.47990 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.530073 | 0.0181921 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.7170 | −0.367376 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.0103 | −1.06177 | −0.530887 | − | 0.847443i | \(-0.678141\pi\) | ||||
−0.530887 | + | 0.847443i | \(0.678141\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −24.0291 | −0.821777 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.3182 | −0.864855 | −0.432427 | − | 0.901669i | \(-0.642343\pi\) | ||||
−0.432427 | + | 0.901669i | \(0.642343\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.4794 | −0.732869 | −0.366434 | − | 0.930444i | \(-0.619422\pi\) | ||||
−0.366434 | + | 0.930444i | \(0.619422\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.14495 | −0.107180 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.5454 | 0.631291 | 0.315646 | − | 0.948877i | \(-0.397779\pi\) | ||||
0.315646 | + | 0.948877i | \(0.397779\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.42290 | −0.150383 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.94701 | −0.0661240 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −68.8190 | −2.33452 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 51.3572 | 1.74017 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.3945 | −0.385646 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 29.5823 | 1.00006 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35.2153 | −1.18914 | −0.594569 | − | 0.804045i | \(-0.702677\pi\) | ||||
−0.594569 | + | 0.804045i | \(0.702677\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.80490 | −0.0946069 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.75356 | 0.261224 | 0.130612 | − | 0.991434i | \(-0.458306\pi\) | ||||
0.130612 | + | 0.991434i | \(0.458306\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.7798 | −0.968518 | −0.484259 | − | 0.874925i | \(-0.660911\pi\) | ||||
−0.484259 | + | 0.874925i | \(0.660911\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.45826 | −0.0490188 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.5055 | −0.386318 | −0.193159 | − | 0.981167i | \(-0.561873\pi\) | ||||
−0.193159 | + | 0.981167i | \(0.561873\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.0359 | −0.806137 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 44.1944 | 1.48057 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.28287 | −0.277176 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.41668 | −0.314765 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.63904 | 0.0881150 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.19521 | −0.0732143 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.6317 | 0.387509 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.17030 | −0.0722231 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.07308 | 0.0356704 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.38439 | −0.211990 | −0.105995 | − | 0.994367i | \(-0.533803\pi\) | ||||
−0.105995 | + | 0.994367i | \(0.533803\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.64006 | −0.286573 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.6633 | −0.784001 | −0.392001 | − | 0.919965i | \(-0.628217\pi\) | ||||
−0.392001 | + | 0.919965i | \(0.628217\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −65.4953 | −2.16758 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.05517 | −0.101001 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 25.8076 | 0.852243 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.2900 | 1.19710 | 0.598548 | − | 0.801087i | \(-0.295745\pi\) | ||||
0.598548 | + | 0.801087i | \(0.295745\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.91878 | 0.227981 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −50.5075 | −1.66247 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.7143 | −0.385164 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.85143 | −0.192186 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 36.8539 | 1.20914 | 0.604569 | − | 0.796553i | \(-0.293345\pi\) | ||||
0.604569 | + | 0.796553i | \(0.293345\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.10070 | −0.134395 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.68589 | −0.218886 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −26.6853 | −0.872702 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52.5859 | 1.71791 | 0.858954 | − | 0.512053i | \(-0.171115\pi\) | ||||
0.858954 | + | 0.512053i | \(0.171115\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.70321 | 0.0555823 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.0363 | 0.490170 | 0.245085 | − | 0.969502i | \(-0.421184\pi\) | ||||
0.245085 | + | 0.969502i | \(0.421184\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.3058 | −0.335604 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.51283 | 0.211862 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 48.1553 | 1.56484 | 0.782418 | − | 0.622753i | \(-0.213986\pi\) | ||||
0.782418 | + | 0.622753i | \(0.213986\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.9861 | 0.681236 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.48689 | 0.242779 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.1339 | 1.20288 | 0.601442 | − | 0.798916i | \(-0.294593\pi\) | ||||
0.601442 | + | 0.798916i | \(0.294593\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.83790 | 0.253629 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.96507 | 0.225149 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 51.6619 | 1.66825 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7826 | −0.992988 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 49.3924 | 1.59165 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.678282 | 0.0218347 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.7318 | −0.409428 | −0.204714 | − | 0.978822i | \(-0.565626\pi\) | ||||
−0.204714 | + | 0.978822i | \(0.565626\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.55752 | −0.146409 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 53.5608 | 1.71885 | 0.859423 | − | 0.511264i | \(-0.170823\pi\) | ||||
0.859423 | + | 0.511264i | \(0.170823\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.6809 | 0.983583 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.88461 | 0.0923815 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32.6257 | 1.04379 | 0.521895 | − | 0.853010i | \(-0.325225\pi\) | ||||
0.521895 | + | 0.853010i | \(0.325225\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −81.1011 | −2.59200 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.00081 | −0.255446 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29.6145 | −0.944556 | −0.472278 | − | 0.881450i | \(-0.656568\pi\) | ||||
−0.472278 | + | 0.881450i | \(0.656568\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.5221 | −0.590162 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.10783 | 0.0352626 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.11195 | −0.226147 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.7361 | 1.03990 | 0.519949 | − | 0.854197i | \(-0.325951\pi\) | ||||
0.519949 | + | 0.854197i | \(0.325951\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.18496 | 0.196274 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −34.4064 | −1.09076 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.1839 | 1.05094 | 0.525472 | − | 0.850811i | \(-0.323889\pi\) | ||||
0.525472 | + | 0.850811i | \(0.323889\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.77364 | −0.245947 |
(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 | 6008.2.a.b.1.27 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.b.1.27 | ✓ | 44 | 1.1 | even | 1 | trivial |