Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9800,2,Mod(1,9800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, 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("9800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.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: | \(78.2533939809\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 18x^{6} + 85x^{4} - 38x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.402377\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9800.1 |
$q$-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 | ||||||||
\(3\) | 0.402377 | 0.232313 | 0.116156 | − | 0.993231i | \(-0.462943\pi\) | ||||
0.116156 | + | 0.993231i | \(0.462943\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.83809 | −0.946031 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.46025 | −1.64633 | −0.823163 | − | 0.567805i | \(-0.807793\pi\) | ||||
−0.823163 | + | 0.567805i | \(0.807793\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.97046 | 1.37856 | 0.689279 | − | 0.724496i | \(-0.257927\pi\) | ||||
0.689279 | + | 0.724496i | \(0.257927\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.78705 | 1.64610 | 0.823051 | − | 0.567968i | \(-0.192270\pi\) | ||||
0.823051 | + | 0.567968i | \(0.192270\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.859799 | 0.197251 | 0.0986257 | − | 0.995125i | \(-0.468555\pi\) | ||||
0.0986257 | + | 0.995125i | \(0.468555\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.40714 | 1.12747 | 0.563733 | − | 0.825957i | \(-0.309365\pi\) | ||||
0.563733 | + | 0.825957i | \(0.309365\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.34912 | −0.452087 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.29834 | −1.72666 | −0.863329 | − | 0.504641i | \(-0.831625\pi\) | ||||
−0.863329 | + | 0.504641i | \(0.831625\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.99413 | −1.25618 | −0.628092 | − | 0.778139i | \(-0.716164\pi\) | ||||
−0.628092 | + | 0.778139i | \(0.716164\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.19708 | −0.382462 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.76025 | 0.453782 | 0.226891 | − | 0.973920i | \(-0.427144\pi\) | ||||
0.226891 | + | 0.973920i | \(0.427144\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.53854 | 1.48967 | 0.744835 | − | 0.667249i | \(-0.232528\pi\) | ||||
0.744835 | + | 0.667249i | \(0.232528\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.76025 | −0.725931 | −0.362965 | − | 0.931803i | \(-0.618236\pi\) | ||||
−0.362965 | + | 0.931803i | \(0.618236\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.1262 | 1.62292 | 0.811459 | − | 0.584410i | \(-0.198674\pi\) | ||||
0.811459 | + | 0.584410i | \(0.198674\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.73095 | 0.382410 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.89120 | −0.259776 | −0.129888 | − | 0.991529i | \(-0.541462\pi\) | ||||
−0.129888 | + | 0.991529i | \(0.541462\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.345964 | 0.0458240 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.2031 | −1.45852 | −0.729260 | − | 0.684237i | \(-0.760135\pi\) | ||||
−0.729260 | + | 0.684237i | \(0.760135\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.50482 | 0.704820 | 0.352410 | − | 0.935846i | \(-0.385362\pi\) | ||||
0.352410 | + | 0.935846i | \(0.385362\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.86191 | −0.471807 | −0.235903 | − | 0.971777i | \(-0.575805\pi\) | ||||
−0.235903 | + | 0.971777i | \(0.575805\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.17571 | 0.261925 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.4364 | −1.23858 | −0.619288 | − | 0.785164i | \(-0.712579\pi\) | ||||
−0.619288 | + | 0.785164i | \(0.712579\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.173406 | 0.0202956 | 0.0101478 | − | 0.999949i | \(-0.496770\pi\) | ||||
0.0101478 | + | 0.999949i | \(0.496770\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.13095 | 0.577277 | 0.288639 | − | 0.957438i | \(-0.406797\pi\) | ||||
0.288639 | + | 0.957438i | \(0.406797\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.56905 | 0.841005 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.43972 | 0.706851 | 0.353425 | − | 0.935463i | \(-0.385017\pi\) | ||||
0.353425 | + | 0.935463i | \(0.385017\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.74144 | −0.401124 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.51482 | 0.690570 | 0.345285 | − | 0.938498i | \(-0.387782\pi\) | ||||
0.345285 | + | 0.938498i | \(0.387782\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.81428 | −0.291827 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.94270 | −0.907994 | −0.453997 | − | 0.891003i | \(-0.650002\pi\) | ||||
−0.453997 | + | 0.891003i | \(0.650002\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.4967 | 1.55748 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.91898 | −0.588961 | −0.294480 | − | 0.955658i | \(-0.595147\pi\) | ||||
−0.294480 | + | 0.955658i | \(0.595147\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.03734 | 0.594877 | 0.297438 | − | 0.954741i | \(-0.403868\pi\) | ||||
0.297438 | + | 0.954741i | \(0.403868\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.6514 | −1.70643 | −0.853215 | − | 0.521560i | \(-0.825350\pi\) | ||||
−0.853215 | + | 0.521560i | \(0.825350\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.54523 | −0.435355 | −0.217677 | − | 0.976021i | \(-0.569848\pi\) | ||||
−0.217677 | + | 0.976021i | \(0.569848\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.11066 | 0.105419 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.4895 | 1.55121 | 0.775603 | − | 0.631221i | \(-0.217446\pi\) | ||||
0.775603 | + | 0.631221i | \(0.217446\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −14.1066 | −1.30416 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.8143 | 1.71039 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.83809 | 0.346069 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.5745 | −1.38202 | −0.691008 | − | 0.722847i | \(-0.742833\pi\) | ||||
−0.691008 | + | 0.722847i | \(0.742833\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.91542 | −0.168643 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.1699 | 0.888548 | 0.444274 | − | 0.895891i | \(-0.353462\pi\) | ||||
0.444274 | + | 0.895891i | \(0.353462\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.32929 | 0.540748 | 0.270374 | − | 0.962755i | \(-0.412853\pi\) | ||||
0.270374 | + | 0.962755i | \(0.412853\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.25448 | −0.445679 | −0.222839 | − | 0.974855i | \(-0.571533\pi\) | ||||
−0.222839 | + | 0.974855i | \(0.571533\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.47691 | 0.377024 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −27.1399 | −2.26956 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.65404 | 0.381274 | 0.190637 | − | 0.981661i | \(-0.438945\pi\) | ||||
0.190637 | + | 0.981661i | \(0.438945\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.8188 | 1.69421 | 0.847106 | − | 0.531423i | \(-0.178343\pi\) | ||||
0.847106 | + | 0.531423i | \(0.178343\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −19.2623 | −1.55726 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.7949 | 1.18076 | 0.590379 | − | 0.807126i | \(-0.298978\pi\) | ||||
0.590379 | + | 0.807126i | \(0.298978\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.760975 | −0.0603492 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.1143 | 0.792212 | 0.396106 | − | 0.918205i | \(-0.370361\pi\) | ||||
0.396106 | + | 0.918205i | \(0.370361\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.0416 | 1.00919 | 0.504594 | − | 0.863357i | \(-0.331642\pi\) | ||||
0.504594 | + | 0.863357i | \(0.331642\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.7055 | 0.900421 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.44019 | −0.186606 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.16754 | 0.316852 | 0.158426 | − | 0.987371i | \(-0.449358\pi\) | ||||
0.158426 | + | 0.987371i | \(0.449358\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.50787 | −0.338832 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.239753 | 0.0179200 | 0.00895998 | − | 0.999960i | \(-0.497148\pi\) | ||||
0.00895998 | + | 0.999960i | \(0.497148\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.5959 | −1.15924 | −0.579619 | − | 0.814888i | \(-0.696798\pi\) | ||||
−0.579619 | + | 0.814888i | \(0.696798\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.21501 | 0.163738 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −37.0590 | −2.71002 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.83261 | 0.132603 | 0.0663016 | − | 0.997800i | \(-0.478880\pi\) | ||||
0.0663016 | + | 0.997800i | \(0.478880\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.7338 | 1.70840 | 0.854200 | − | 0.519945i | \(-0.174048\pi\) | ||||
0.854200 | + | 0.519945i | \(0.174048\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.88665 | 0.134418 | 0.0672089 | − | 0.997739i | \(-0.478591\pi\) | ||||
0.0672089 | + | 0.997739i | \(0.478591\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.2919 | 1.08401 | 0.542006 | − | 0.840375i | \(-0.317665\pi\) | ||||
0.542006 | + | 0.840375i | \(0.317665\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.55394 | −0.109607 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.3460 | −1.06662 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.69471 | −0.324740 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.0038 | 1.58365 | 0.791824 | − | 0.610749i | \(-0.209132\pi\) | ||||
0.791824 | + | 0.610749i | \(0.209132\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.19938 | −0.287737 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.0697744 | 0.00471492 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 33.7348 | 2.26925 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.35325 | 0.291515 | 0.145758 | − | 0.989320i | \(-0.453438\pi\) | ||||
0.145758 | + | 0.989320i | \(0.453438\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.57175 | 0.502555 | 0.251277 | − | 0.967915i | \(-0.419149\pi\) | ||||
0.251277 | + | 0.967915i | \(0.419149\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.29774 | −0.548330 | −0.274165 | − | 0.961683i | \(-0.588401\pi\) | ||||
−0.274165 | + | 0.961683i | \(0.588401\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.2690 | 1.06582 | 0.532910 | − | 0.846172i | \(-0.321098\pi\) | ||||
0.532910 | + | 0.846172i | \(0.321098\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.06458 | 0.134109 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.45932 | −0.223765 | −0.111882 | − | 0.993721i | \(-0.535688\pi\) | ||||
−0.111882 | + | 0.993721i | \(0.535688\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.3197 | −1.30891 | −0.654454 | − | 0.756102i | \(-0.727102\pi\) | ||||
−0.654454 | + | 0.756102i | \(0.727102\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.0930 | 0.647464 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.27360 | 0.271923 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.59120 | 0.164210 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.0867 | 1.70970 | 0.854849 | − | 0.518876i | \(-0.173649\pi\) | ||||
0.854849 | + | 0.518876i | \(0.173649\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −29.5243 | −1.85618 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.87399 | 0.491166 | 0.245583 | − | 0.969376i | \(-0.421021\pi\) | ||||
0.245583 | + | 0.969376i | \(0.421021\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 26.3895 | 1.63347 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.2983 | 1.06666 | 0.533331 | − | 0.845907i | \(-0.320940\pi\) | ||||
0.533331 | + | 0.845907i | \(0.320940\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.62142 | 0.160428 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.2251 | −1.59897 | −0.799486 | − | 0.600685i | \(-0.794895\pi\) | ||||
−0.799486 | + | 0.600685i | \(0.794895\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.21075 | 0.195039 | 0.0975195 | − | 0.995234i | \(-0.468909\pi\) | ||||
0.0975195 | + | 0.995234i | \(0.468909\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.61760 | 0.0971922 | 0.0485961 | − | 0.998819i | \(-0.484525\pi\) | ||||
0.0485961 | + | 0.998819i | \(0.484525\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 19.8500 | 1.18839 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.65404 | 0.516257 | 0.258128 | − | 0.966111i | \(-0.416894\pi\) | ||||
0.258128 | + | 0.966111i | \(0.416894\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.9646 | 0.949000 | 0.474500 | − | 0.880256i | \(-0.342629\pi\) | ||||
0.474500 | + | 0.880256i | \(0.342629\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 29.0641 | 1.70965 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.59834 | −0.210938 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.0239 | 1.28665 | 0.643324 | − | 0.765594i | \(-0.277555\pi\) | ||||
0.643324 | + | 0.765594i | \(0.277555\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.8267 | 0.744283 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 26.8760 | 1.55428 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.38166 | −0.136823 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.8144 | 0.845502 | 0.422751 | − | 0.906246i | \(-0.361065\pi\) | ||||
0.422751 | + | 0.906246i | \(0.361065\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.42929 | 0.138197 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.0216 | −1.53225 | −0.766126 | − | 0.642690i | \(-0.777818\pi\) | ||||
−0.766126 | + | 0.642690i | \(0.777818\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.5423 | 1.72635 | 0.863177 | − | 0.504902i | \(-0.168471\pi\) | ||||
0.863177 | + | 0.504902i | \(0.168471\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.1895 | −1.41479 | −0.707393 | − | 0.706821i | \(-0.750129\pi\) | ||||
−0.707393 | + | 0.706821i | \(0.750129\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 50.7712 | 2.84264 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.10254 | −0.396425 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.83550 | 0.324696 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.82890 | −0.101138 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 34.5364 | 1.89829 | 0.949147 | − | 0.314834i | \(-0.101949\pi\) | ||||
0.949147 | + | 0.314834i | \(0.101949\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.83384 | −0.429292 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.34596 | 0.454634 | 0.227317 | − | 0.973821i | \(-0.427005\pi\) | ||||
0.227317 | + | 0.973821i | \(0.427005\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.63501 | 0.360365 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 38.1897 | 2.06809 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.5398 | −0.995266 | −0.497633 | − | 0.867388i | \(-0.665797\pi\) | ||||
−0.497633 | + | 0.867388i | \(0.665797\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.6411 | 1.74724 | 0.873619 | − | 0.486611i | \(-0.161767\pi\) | ||||
0.873619 | + | 0.486611i | \(0.161767\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.6762 | −0.623229 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.307217 | −0.0163515 | −0.00817576 | − | 0.999967i | \(-0.502602\pi\) | ||||
−0.00817576 | + | 0.999967i | \(0.502602\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.3778 | 0.653278 | 0.326639 | − | 0.945149i | \(-0.394084\pi\) | ||||
0.326639 | + | 0.945149i | \(0.394084\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.2607 | −0.961092 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.57044 | 0.397345 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.6730 | 1.80992 | 0.904959 | − | 0.425499i | \(-0.139902\pi\) | ||||
0.904959 | + | 0.425499i | \(0.139902\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −27.0713 | −1.40927 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.1126 | 1.35206 | 0.676030 | − | 0.736874i | \(-0.263699\pi\) | ||||
0.676030 | + | 0.736874i | \(0.263699\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −46.2170 | −2.38030 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.16572 | −0.316712 | −0.158356 | − | 0.987382i | \(-0.550619\pi\) | ||||
−0.158356 | + | 0.987382i | \(0.550619\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.26683 | −0.321060 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.7102 | −0.547264 | −0.273632 | − | 0.961834i | \(-0.588225\pi\) | ||||
−0.273632 | + | 0.961834i | \(0.588225\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 13.5100 | 0.686753 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.5426 | −1.14296 | −0.571479 | − | 0.820617i | \(-0.693630\pi\) | ||||
−0.571479 | + | 0.820617i | \(0.693630\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.6985 | 1.85592 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.09213 | 0.206421 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.4458 | 1.67860 | 0.839299 | − | 0.543670i | \(-0.182966\pi\) | ||||
0.839299 | + | 0.543670i | \(0.182966\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.22597 | −0.260973 | −0.130486 | − | 0.991450i | \(-0.541654\pi\) | ||||
−0.130486 | + | 0.991450i | \(0.541654\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −34.7641 | −1.73172 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.0716 | −0.747073 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.9445 | −0.590619 | −0.295310 | − | 0.955402i | \(-0.595423\pi\) | ||||
−0.295310 | + | 0.955402i | \(0.595423\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.54676 | 0.125623 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.11428 | −0.103537 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.4553 | −1.39013 | −0.695067 | − | 0.718945i | \(-0.744625\pi\) | ||||
−0.695067 | + | 0.718945i | \(0.744625\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.56357 | 0.173678 | 0.0868388 | − | 0.996222i | \(-0.472323\pi\) | ||||
0.0868388 | + | 0.996222i | \(0.472323\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −31.5771 | −1.53533 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.9205 | −0.527246 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.9974 | −0.577895 | −0.288947 | − | 0.957345i | \(-0.593305\pi\) | ||||
−0.288947 | + | 0.957345i | \(0.593305\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.5203 | 0.553629 | 0.276814 | − | 0.960923i | \(-0.410721\pi\) | ||||
0.276814 | + | 0.960923i | \(0.410721\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.64905 | 0.222394 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.86394 | 0.136688 | 0.0683441 | − | 0.997662i | \(-0.478228\pi\) | ||||
0.0683441 | + | 0.997662i | \(0.478228\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.8188 | 0.561530 | 0.280765 | − | 0.959777i | \(-0.409412\pi\) | ||||
0.280765 | + | 0.959777i | \(0.409412\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.87268 | 0.0885746 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.4612 | −0.493693 | −0.246847 | − | 0.969055i | \(-0.579394\pi\) | ||||
−0.246847 | + | 0.969055i | \(0.579394\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −52.0828 | −2.45248 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.37702 | 0.393587 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.29286 | −0.154033 | −0.0770167 | − | 0.997030i | \(-0.524539\pi\) | ||||
−0.0770167 | + | 0.997030i | \(0.524539\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −15.9436 | −0.744182 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.66513 | 0.263851 | 0.131926 | − | 0.991260i | \(-0.457884\pi\) | ||||
0.131926 | + | 0.991260i | \(0.457884\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.24431 | −0.150776 | −0.0753878 | − | 0.997154i | \(-0.524019\pi\) | ||||
−0.0753878 | + | 0.997154i | \(0.524019\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.0096 | −0.463188 | −0.231594 | − | 0.972812i | \(-0.574394\pi\) | ||||
−0.231594 | + | 0.972812i | \(0.574394\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.95311 | 0.274305 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 25.9921 | 1.19512 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.36740 | 0.245756 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −32.9470 | −1.50539 | −0.752693 | − | 0.658371i | \(-0.771246\pi\) | ||||
−0.752693 | + | 0.658371i | \(0.771246\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.7197 | 0.625565 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.1152 | −0.911507 | −0.455754 | − | 0.890106i | \(-0.650630\pi\) | ||||
−0.455754 | + | 0.890106i | \(0.650630\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.06976 | 0.184041 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.1602 | −0.458525 | −0.229263 | − | 0.973365i | \(-0.573631\pi\) | ||||
−0.229263 | + | 0.973365i | \(0.573631\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −63.1083 | −2.84225 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.3791 | −1.00182 | −0.500912 | − | 0.865498i | \(-0.667002\pi\) | ||||
−0.500912 | + | 0.865498i | \(0.667002\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.24763 | 0.234447 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.67042 | 0.342007 | 0.171004 | − | 0.985270i | \(-0.445299\pi\) | ||||
0.171004 | + | 0.985270i | \(0.445299\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.71002 | 0.209179 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.0745813 | 0.00330576 | 0.00165288 | − | 0.999999i | \(-0.499474\pi\) | ||||
0.00165288 | + | 0.999999i | \(0.499474\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.01977 | −0.0891749 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −60.7516 | −2.67185 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.67692 | 0.0736087 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.4085 | −1.11317 | −0.556584 | − | 0.830791i | \(-0.687888\pi\) | ||||
−0.556584 | + | 0.830791i | \(0.687888\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.7790 | −1.17096 | −0.585482 | − | 0.810686i | \(-0.699095\pi\) | ||||
−0.585482 | + | 0.810686i | \(0.699095\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −47.4695 | −2.06781 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.23716 | 0.271181 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 31.7954 | 1.37980 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 47.4110 | 2.05360 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.0964710 | 0.00416303 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.31926 | 0.0997129 | 0.0498564 | − | 0.998756i | \(-0.484124\pi\) | ||||
0.0498564 | + | 0.998756i | \(0.484124\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.27545 | −0.269305 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.5800 | 0.666153 | 0.333076 | − | 0.942900i | \(-0.391913\pi\) | ||||
0.333076 | + | 0.942900i | \(0.391913\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.6232 | −0.666781 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.99470 | −0.340586 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.71262 | −0.284423 | −0.142211 | − | 0.989836i | \(-0.545421\pi\) | ||||
−0.142211 | + | 0.989836i | \(0.545421\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.6606 | −1.00074 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.9117 | −0.629572 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.3302 | −0.435366 | −0.217683 | − | 0.976020i | \(-0.569850\pi\) | ||||
−0.217683 | + | 0.976020i | \(0.569850\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.8410 | −0.957544 | −0.478772 | − | 0.877939i | \(-0.658918\pi\) | ||||
−0.478772 | + | 0.877939i | \(0.658918\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.0540 | 0.588143 | 0.294071 | − | 0.955783i | \(-0.404990\pi\) | ||||
0.294071 | + | 0.955783i | \(0.404990\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.737402 | 0.0308054 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.8186 | 1.32463 | 0.662313 | − | 0.749227i | \(-0.269575\pi\) | ||||
0.662313 | + | 0.749227i | \(0.269575\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.54996 | 0.396883 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.3264 | 0.427676 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 31.2423 | 1.28951 | 0.644754 | − | 0.764390i | \(-0.276960\pi\) | ||||
0.644754 | + | 0.764390i | \(0.276960\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.01355 | −0.247784 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.759143 | 0.0312270 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.80706 | 0.115272 | 0.0576360 | − | 0.998338i | \(-0.481644\pi\) | ||||
0.0576360 | + | 0.998338i | \(0.481644\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.15310 | 0.251830 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.6038 | −0.514978 | −0.257489 | − | 0.966281i | \(-0.582895\pi\) | ||||
−0.257489 | + | 0.966281i | \(0.582895\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.2563 | 0.459154 | 0.229577 | − | 0.973290i | \(-0.426266\pi\) | ||||
0.229577 | + | 0.973290i | \(0.426266\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.9604 | 0.446344 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.4581 | −0.830371 | −0.415185 | − | 0.909737i | \(-0.636283\pi\) | ||||
−0.415185 | + | 0.909737i | \(0.636283\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 55.3022 | 2.23729 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.2976 | 0.940981 | 0.470491 | − | 0.882405i | \(-0.344077\pi\) | ||||
0.470491 | + | 0.882405i | \(0.344077\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.75766 | −0.191536 | −0.0957680 | − | 0.995404i | \(-0.530531\pi\) | ||||
−0.0957680 | + | 0.995404i | \(0.530531\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.5368 | 0.745057 | 0.372529 | − | 0.928021i | \(-0.378491\pi\) | ||||
0.372529 | + | 0.928021i | \(0.378491\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.7020 | −0.509714 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.88905 | −0.0754412 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.7339 | 0.746971 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.99286 | −0.238572 | −0.119286 | − | 0.992860i | \(-0.538061\pi\) | ||||
−0.119286 | + | 0.992860i | \(0.538061\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.25621 | 0.367901 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 29.6196 | 1.17173 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 44.1100 | 1.74224 | 0.871121 | − | 0.491069i | \(-0.163394\pi\) | ||||
0.871121 | + | 0.491069i | \(0.163394\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.5499 | 0.849846 | 0.424923 | − | 0.905230i | \(-0.360301\pi\) | ||||
0.424923 | + | 0.905230i | \(0.360301\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −50.5430 | −1.98705 | −0.993526 | − | 0.113606i | \(-0.963760\pi\) | ||||
−0.993526 | + | 0.113606i | \(0.963760\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 61.1717 | 2.40120 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.88861 | −0.230439 | −0.115220 | − | 0.993340i | \(-0.536757\pi\) | ||||
−0.115220 | + | 0.993340i | \(0.536757\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.492141 | −0.0192002 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.8198 | −0.733114 | −0.366557 | − | 0.930396i | \(-0.619463\pi\) | ||||
−0.366557 | + | 0.930396i | \(0.619463\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.9156 | 0.852419 | 0.426209 | − | 0.904625i | \(-0.359849\pi\) | ||||
0.426209 | + | 0.904625i | \(0.359849\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.5741 | 0.527174 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −50.2774 | −1.94675 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.75165 | 0.0677227 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.0577 | −1.16036 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.22597 | 0.239994 | 0.119997 | − | 0.992774i | \(-0.461712\pi\) | ||||
0.119997 | + | 0.992774i | \(0.461712\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.8802 | −1.30212 | −0.651061 | − | 0.759025i | \(-0.725676\pi\) | ||||
−0.651061 | + | 0.759025i | \(0.725676\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.04670 | 0.116750 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.89379 | −0.187256 | −0.0936278 | − | 0.995607i | \(-0.529846\pi\) | ||||
−0.0936278 | + | 0.995607i | \(0.529846\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.33882 | −0.127384 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.40013 | −0.358116 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.5131 | 0.704271 | 0.352136 | − | 0.935949i | \(-0.385456\pi\) | ||||
0.352136 | + | 0.935949i | \(0.385456\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 64.7386 | 2.45215 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.54629 | 0.247604 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.1348 | 0.873788 | 0.436894 | − | 0.899513i | \(-0.356078\pi\) | ||||
0.436894 | + | 0.899513i | \(0.356078\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.37326 | 0.0895091 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 47.6963 | 1.79127 | 0.895635 | − | 0.444789i | \(-0.146722\pi\) | ||||
0.895635 | + | 0.444789i | \(0.146722\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.5621 | −0.546122 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −37.8183 | −1.41630 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.39195 | −0.0519834 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.4102 | 0.947642 | 0.473821 | − | 0.880621i | \(-0.342874\pi\) | ||||
0.473821 | + | 0.880621i | \(0.342874\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.17620 | −0.304076 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.78695 | 0.0662744 | 0.0331372 | − | 0.999451i | \(-0.489450\pi\) | ||||
0.0331372 | + | 0.999451i | \(0.489450\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.6460 | −0.690591 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −32.3080 | −1.19496 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.0748 | −0.519864 | −0.259932 | − | 0.965627i | \(-0.583700\pi\) | ||||
−0.259932 | + | 0.965627i | \(0.583700\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.0870 | 0.776748 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.1628 | 0.888844 | 0.444422 | − | 0.895817i | \(-0.353409\pi\) | ||||
0.444422 | + | 0.895817i | \(0.353409\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.71960 | 0.0631710 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.6579 | −1.19810 | −0.599050 | − | 0.800711i | \(-0.704455\pi\) | ||||
−0.599050 | + | 0.800711i | \(0.704455\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18.2765 | −0.668703 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.2871 | −1.25116 | −0.625578 | − | 0.780162i | \(-0.715137\pi\) | ||||
−0.625578 | + | 0.780162i | \(0.715137\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.8991 | 0.397185 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.1452 | 0.477772 | 0.238886 | − | 0.971048i | \(-0.423218\pi\) | ||||
0.238886 | + | 0.971048i | \(0.423218\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.8799 | −0.431213 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39.2129 | 1.42147 | 0.710734 | − | 0.703461i | \(-0.248363\pi\) | ||||
0.710734 | + | 0.703461i | \(0.248363\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −55.6846 | −2.01065 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.8339 | 0.426742 | 0.213371 | − | 0.976971i | \(-0.431556\pi\) | ||||
0.213371 | + | 0.976971i | \(0.431556\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.16831 | 0.114104 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 51.8065 | 1.86335 | 0.931676 | − | 0.363291i | \(-0.118347\pi\) | ||||
0.931676 | + | 0.363291i | \(0.118347\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.20123 | 0.293840 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 56.9855 | 2.03910 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21.8429 | 0.780600 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.7399 | −0.881881 | −0.440940 | − | 0.897536i | \(-0.645355\pi\) | ||||
−0.440940 | + | 0.897536i | \(0.645355\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.96046 | 0.247799 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.3615 | 0.971635 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.33277 | −0.118053 | −0.0590264 | − | 0.998256i | \(-0.518800\pi\) | ||||
−0.0590264 | + | 0.998256i | \(0.518800\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 75.5138 | 2.67149 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.4897 | −0.653300 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.946837 | −0.0334131 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.5524 | −0.371461 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.21883 | 0.148326 | 0.0741631 | − | 0.997246i | \(-0.476371\pi\) | ||||
0.0741631 | + | 0.997246i | \(0.476371\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.7657 | −0.483380 | −0.241690 | − | 0.970353i | \(-0.577702\pi\) | ||||
−0.241690 | + | 0.970353i | \(0.577702\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.29193 | 0.0453100 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.09286 | −0.143191 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.2252 | 1.26427 | 0.632135 | − | 0.774859i | \(-0.282179\pi\) | ||||
0.632135 | + | 0.774859i | \(0.282179\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.7119 | 0.931118 | 0.465559 | − | 0.885017i | \(-0.345853\pi\) | ||||
0.465559 | + | 0.885017i | \(0.345853\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −55.8703 | −1.94280 | −0.971400 | − | 0.237449i | \(-0.923689\pi\) | ||||
−0.971400 | + | 0.237449i | \(0.923689\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.5979 | 0.611199 | 0.305600 | − | 0.952160i | \(-0.401143\pi\) | ||||
0.305600 | + | 0.952160i | \(0.401143\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.650885 | 0.0225790 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.4300 | 0.567905 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.56870 | −0.330348 | −0.165174 | − | 0.986264i | \(-0.552819\pi\) | ||||
−0.165174 | + | 0.986264i | \(0.552819\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57.4591 | 1.98135 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.48219 | 0.119933 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.42381 | 0.220465 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.9250 | 0.511624 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.2026 | −0.383569 | −0.191784 | − | 0.981437i | \(-0.561427\pi\) | ||||
−0.191784 | + | 0.981437i | \(0.561427\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30.4891 | 1.04149 | 0.520744 | − | 0.853713i | \(-0.325655\pi\) | ||||
0.520744 | + | 0.853713i | \(0.325655\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.4774 | −1.17635 | −0.588176 | − | 0.808733i | \(-0.700154\pi\) | ||||
−0.588176 | + | 0.808733i | \(0.700154\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 55.4155 | 1.88637 | 0.943183 | − | 0.332274i | \(-0.107816\pi\) | ||||
0.943183 | + | 0.332274i | \(0.107816\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.6947 | 0.397173 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28.0162 | −0.950386 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.1954 | −0.650413 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 25.3802 | 0.858990 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.908794 | 0.0306878 | 0.0153439 | − | 0.999882i | \(-0.495116\pi\) | ||||
0.0153439 | + | 0.999882i | \(0.495116\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.86191 | 0.298905 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −51.5348 | −1.73625 | −0.868126 | − | 0.496344i | \(-0.834676\pi\) | ||||
−0.868126 | + | 0.496344i | \(0.834676\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.3047 | −0.952530 | −0.476265 | − | 0.879302i | \(-0.658010\pi\) | ||||
−0.476265 | + | 0.879302i | \(0.658010\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.36739 | 0.113066 | 0.0565330 | − | 0.998401i | \(-0.481995\pi\) | ||||
0.0565330 | + | 0.998401i | \(0.481995\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −41.3289 | −1.38457 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.56627 | 0.320123 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.8143 | 0.361078 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 65.0338 | 2.16900 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.8357 | −0.427618 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43.4695 | −1.44338 | −0.721691 | − | 0.692215i | \(-0.756635\pi\) | ||||
−0.721691 | + | 0.692215i | \(0.756635\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.7986 | 0.557175 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.9276 | 0.362049 | 0.181024 | − | 0.983479i | \(-0.442059\pi\) | ||||
0.181024 | + | 0.983479i | \(0.442059\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35.1624 | −1.16371 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.165425 | 0.00545687 | 0.00272844 | − | 0.999996i | \(-0.499132\pi\) | ||||
0.00272844 | + | 0.999996i | \(0.499132\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.96097 | 0.196421 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −51.8739 | −1.70745 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.1345 | −0.562772 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −50.6798 | −1.66275 | −0.831376 | − | 0.555711i | \(-0.812446\pi\) | ||||
−0.831376 | + | 0.555711i | \(0.812446\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.8729 | −0.355962 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.5069 | 1.15996 | 0.579980 | − | 0.814631i | \(-0.303060\pi\) | ||||
0.579980 | + | 0.814631i | \(0.303060\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.2895 | 0.401054 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.813025 | 0.0265039 | 0.0132519 | − | 0.999912i | \(-0.495782\pi\) | ||||
0.0132519 | + | 0.999912i | \(0.495782\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 51.5762 | 1.67955 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40.1281 | 1.30399 | 0.651995 | − | 0.758224i | \(-0.273933\pi\) | ||||
0.651995 | + | 0.758224i | \(0.273933\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.861905 | 0.0279786 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.1357 | −0.328672 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.949783 | −0.0307665 | −0.0153833 | − | 0.999882i | \(-0.504897\pi\) | ||||
−0.0153833 | + | 0.999882i | \(0.504897\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.4292 | 0.660381 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.9179 | 0.577997 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 50.0964 | 1.61434 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.1648 | −0.712772 | −0.356386 | − | 0.934339i | \(-0.615991\pi\) | ||||
−0.356386 | + | 0.934339i | \(0.615991\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.34807 | 0.0754310 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.6789 | −0.791983 | −0.395992 | − | 0.918254i | \(-0.629599\pi\) | ||||
−0.395992 | + | 0.918254i | \(0.629599\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.5162 | −0.624380 | −0.312190 | − | 0.950020i | \(-0.601063\pi\) | ||||
−0.312190 | + | 0.950020i | \(0.601063\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −35.5725 | −1.13690 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.8998 | 0.411859 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.6405 | −0.817805 | −0.408903 | − | 0.912578i | \(-0.634088\pi\) | ||||
−0.408903 | + | 0.912578i | \(0.634088\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25.7393 | −0.818463 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.2045 | −1.15008 | −0.575038 | − | 0.818127i | \(-0.695013\pi\) | ||||
−0.575038 | + | 0.818127i | \(0.695013\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.8967 | 0.440998 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.5358 | 0.935409 | 0.467704 | − | 0.883885i | \(-0.345081\pi\) | ||||
0.467704 | + | 0.883885i | \(0.345081\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.48414 | −0.205149 |
(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 | 9800.2.a.da.1.5 | yes | 8 | |
5.4 | even | 2 | 9800.2.a.cz.1.4 | ✓ | 8 | ||
7.6 | odd | 2 | inner | 9800.2.a.da.1.4 | yes | 8 | |
35.34 | odd | 2 | 9800.2.a.cz.1.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9800.2.a.cz.1.4 | ✓ | 8 | 5.4 | even | 2 | ||
9800.2.a.cz.1.5 | yes | 8 | 35.34 | odd | 2 | ||
9800.2.a.da.1.4 | yes | 8 | 7.6 | odd | 2 | inner | |
9800.2.a.da.1.5 | yes | 8 | 1.1 | even | 1 | trivial |