Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9702,2,Mod(1,9702)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9702, 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("9702.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9702.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: | \(77.4708600410\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 3234) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9702.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.23607 | −1.44721 | −0.723607 | − | 0.690212i | \(-0.757517\pi\) | ||||
−0.723607 | + | 0.690212i | \(0.757517\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.23607 | 1.02333 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.763932 | −0.185281 | −0.0926404 | − | 0.995700i | \(-0.529531\pi\) | ||||
−0.0926404 | + | 0.995700i | \(0.529531\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.70820 | −1.30955 | −0.654776 | − | 0.755823i | \(-0.727237\pi\) | ||||
−0.654776 | + | 0.755823i | \(0.727237\pi\) | |||||||
\(20\) | −3.23607 | −0.723607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −6.47214 | −1.34953 | −0.674767 | − | 0.738031i | \(-0.735756\pi\) | ||||
−0.674767 | + | 0.738031i | \(0.735756\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.47214 | 1.09443 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.47214 | 0.830455 | 0.415227 | − | 0.909718i | \(-0.363702\pi\) | ||||
0.415227 | + | 0.909718i | \(0.363702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.23607 | 1.29964 | 0.649818 | − | 0.760090i | \(-0.274845\pi\) | ||||
0.649818 | + | 0.760090i | \(0.274845\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.763932 | 0.131013 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.94427 | 1.14163 | 0.570816 | − | 0.821078i | \(-0.306627\pi\) | ||||
0.570816 | + | 0.821078i | \(0.306627\pi\) | |||||||
\(38\) | 5.70820 | 0.925993 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.23607 | 0.511667 | ||||||||
\(41\) | −0.763932 | −0.119306 | −0.0596531 | − | 0.998219i | \(-0.518999\pi\) | ||||
−0.0596531 | + | 0.998219i | \(0.518999\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.47214 | −0.376997 | −0.188499 | − | 0.982073i | \(-0.560362\pi\) | ||||
−0.188499 | + | 0.982073i | \(0.560362\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.47214 | 0.954264 | ||||||||
\(47\) | −9.70820 | −1.41609 | −0.708044 | − | 0.706169i | \(-0.750422\pi\) | ||||
−0.708044 | + | 0.706169i | \(0.750422\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.47214 | −0.773877 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.23607 | −0.436351 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.47214 | −0.587220 | ||||||||
\(59\) | −10.4721 | −1.36336 | −0.681678 | − | 0.731652i | \(-0.738749\pi\) | ||||
−0.681678 | + | 0.731652i | \(0.738749\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(62\) | −7.23607 | −0.918982 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.4164 | −1.39474 | −0.697368 | − | 0.716713i | \(-0.745646\pi\) | ||||
−0.697368 | + | 0.716713i | \(0.745646\pi\) | |||||||
\(68\) | −0.763932 | −0.0926404 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.47214 | −0.768101 | −0.384051 | − | 0.923312i | \(-0.625471\pi\) | ||||
−0.384051 | + | 0.923312i | \(0.625471\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.29180 | 0.268234 | 0.134117 | − | 0.990965i | \(-0.457180\pi\) | ||||
0.134117 | + | 0.990965i | \(0.457180\pi\) | |||||||
\(74\) | −6.94427 | −0.807255 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.70820 | −0.654776 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.4164 | −1.73448 | −0.867241 | − | 0.497889i | \(-0.834109\pi\) | ||||
−0.867241 | + | 0.497889i | \(0.834109\pi\) | |||||||
\(80\) | −3.23607 | −0.361803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.763932 | 0.0843622 | ||||||||
\(83\) | −3.23607 | −0.355205 | −0.177602 | − | 0.984102i | \(-0.556834\pi\) | ||||
−0.177602 | + | 0.984102i | \(0.556834\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.47214 | 0.268141 | ||||||||
\(86\) | 2.47214 | 0.266577 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 2.47214 | 0.262046 | 0.131023 | − | 0.991379i | \(-0.458174\pi\) | ||||
0.131023 | + | 0.991379i | \(0.458174\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.47214 | −0.674767 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.70820 | 1.00132 | ||||||||
\(95\) | 18.4721 | 1.89520 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.47214 | 0.547214 | ||||||||
\(101\) | −12.0000 | −1.19404 | −0.597022 | − | 0.802225i | \(-0.703650\pi\) | ||||
−0.597022 | + | 0.802225i | \(0.703650\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.2361 | −1.50125 | −0.750627 | − | 0.660726i | \(-0.770249\pi\) | ||||
−0.750627 | + | 0.660726i | \(0.770249\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | 16.9443 | 1.63806 | 0.819032 | − | 0.573747i | \(-0.194511\pi\) | ||||
0.819032 | + | 0.573747i | \(0.194511\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.00000 | 0.574696 | 0.287348 | − | 0.957826i | \(-0.407226\pi\) | ||||
0.287348 | + | 0.957826i | \(0.407226\pi\) | |||||||
\(110\) | 3.23607 | 0.308547 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.4164 | 1.26211 | 0.631055 | − | 0.775738i | \(-0.282622\pi\) | ||||
0.631055 | + | 0.775738i | \(0.282622\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.9443 | 1.95306 | ||||||||
\(116\) | 4.47214 | 0.415227 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.4721 | 0.964038 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.23607 | 0.649818 | ||||||||
\(125\) | −1.52786 | −0.136656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.47214 | 0.219367 | 0.109683 | − | 0.993967i | \(-0.465016\pi\) | ||||
0.109683 | + | 0.993967i | \(0.465016\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.2361 | 0.981700 | 0.490850 | − | 0.871244i | \(-0.336686\pi\) | ||||
0.490850 | + | 0.871244i | \(0.336686\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 11.4164 | 0.986227 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.763932 | 0.0655066 | ||||||||
\(137\) | 7.52786 | 0.643149 | 0.321574 | − | 0.946884i | \(-0.395788\pi\) | ||||
0.321574 | + | 0.946884i | \(0.395788\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.1803 | −1.03312 | −0.516561 | − | 0.856250i | \(-0.672788\pi\) | ||||
−0.516561 | + | 0.856250i | \(0.672788\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.47214 | 0.543130 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.4721 | −1.20185 | ||||||||
\(146\) | −2.29180 | −0.189670 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.94427 | 0.570816 | ||||||||
\(149\) | 6.00000 | 0.491539 | 0.245770 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 5.70820 | 0.462996 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −23.4164 | −1.88085 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.2361 | 1.53521 | 0.767603 | − | 0.640926i | \(-0.221449\pi\) | ||||
0.767603 | + | 0.640926i | \(0.221449\pi\) | |||||||
\(158\) | 15.4164 | 1.22646 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.23607 | 0.255834 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.0000 | −0.939913 | −0.469956 | − | 0.882690i | \(-0.655730\pi\) | ||||
−0.469956 | + | 0.882690i | \(0.655730\pi\) | |||||||
\(164\) | −0.763932 | −0.0596531 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.23607 | 0.251168 | ||||||||
\(167\) | 9.52786 | 0.737288 | 0.368644 | − | 0.929571i | \(-0.379822\pi\) | ||||
0.368644 | + | 0.929571i | \(0.379822\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | −2.47214 | −0.189604 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.47214 | −0.188499 | ||||||||
\(173\) | −7.41641 | −0.563859 | −0.281930 | − | 0.959435i | \(-0.590974\pi\) | ||||
−0.281930 | + | 0.959435i | \(0.590974\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.47214 | −0.185294 | ||||||||
\(179\) | 14.4721 | 1.08170 | 0.540849 | − | 0.841120i | \(-0.318103\pi\) | ||||
0.540849 | + | 0.841120i | \(0.318103\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.70820 | 0.126970 | 0.0634849 | − | 0.997983i | \(-0.479779\pi\) | ||||
0.0634849 | + | 0.997983i | \(0.479779\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.47214 | 0.477132 | ||||||||
\(185\) | −22.4721 | −1.65218 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.763932 | −0.0558642 | ||||||||
\(188\) | −9.70820 | −0.708044 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −18.4721 | −1.34011 | ||||||||
\(191\) | 1.52786 | 0.110552 | 0.0552762 | − | 0.998471i | \(-0.482396\pi\) | ||||
0.0552762 | + | 0.998471i | \(0.482396\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.9443 | 1.65156 | 0.825782 | − | 0.563989i | \(-0.190734\pi\) | ||||
0.825782 | + | 0.563989i | \(0.190734\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.3607 | −1.59313 | −0.796566 | − | 0.604551i | \(-0.793352\pi\) | ||||
−0.796566 | + | 0.604551i | \(0.793352\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.1246 | −1.21393 | −0.606966 | − | 0.794728i | \(-0.707614\pi\) | ||||
−0.606966 | + | 0.794728i | \(0.707614\pi\) | |||||||
\(200\) | −5.47214 | −0.386938 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.0000 | 0.844317 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.47214 | 0.172661 | ||||||||
\(206\) | 15.2361 | 1.06155 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.70820 | −0.394845 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.4164 | −1.61205 | −0.806026 | − | 0.591880i | \(-0.798386\pi\) | ||||
−0.806026 | + | 0.591880i | \(0.798386\pi\) | |||||||
\(212\) | 6.00000 | 0.412082 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −16.9443 | −1.15829 | ||||||||
\(215\) | 8.00000 | 0.545595 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −6.00000 | −0.406371 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.23607 | −0.218176 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.29180 | 0.153470 | 0.0767350 | − | 0.997052i | \(-0.475550\pi\) | ||||
0.0767350 | + | 0.997052i | \(0.475550\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.4164 | −0.892446 | ||||||||
\(227\) | −22.6525 | −1.50350 | −0.751749 | − | 0.659450i | \(-0.770789\pi\) | ||||
−0.751749 | + | 0.659450i | \(0.770789\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.29180 | −0.415774 | −0.207887 | − | 0.978153i | \(-0.566659\pi\) | ||||
−0.207887 | + | 0.978153i | \(0.566659\pi\) | |||||||
\(230\) | −20.9443 | −1.38102 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.47214 | −0.293610 | ||||||||
\(233\) | 26.9443 | 1.76518 | 0.882589 | − | 0.470145i | \(-0.155799\pi\) | ||||
0.882589 | + | 0.470145i | \(0.155799\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 31.4164 | 2.04938 | ||||||||
\(236\) | −10.4721 | −0.681678 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.18034 | 0.269279 | 0.134640 | − | 0.990895i | \(-0.457012\pi\) | ||||
0.134640 | + | 0.990895i | \(0.457012\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −7.23607 | −0.459491 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.52786 | 0.0966306 | ||||||||
\(251\) | 2.47214 | 0.156040 | 0.0780199 | − | 0.996952i | \(-0.475140\pi\) | ||||
0.0780199 | + | 0.996952i | \(0.475140\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.47214 | −0.406900 | ||||||||
\(254\) | −2.47214 | −0.155116 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.5279 | 0.843845 | 0.421922 | − | 0.906632i | \(-0.361355\pi\) | ||||
0.421922 | + | 0.906632i | \(0.361355\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11.2361 | −0.694167 | ||||||||
\(263\) | 18.4721 | 1.13904 | 0.569520 | − | 0.821977i | \(-0.307129\pi\) | ||||
0.569520 | + | 0.821977i | \(0.307129\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −19.4164 | −1.19274 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −11.4164 | −0.697368 | ||||||||
\(269\) | −14.2918 | −0.871386 | −0.435693 | − | 0.900095i | \(-0.643497\pi\) | ||||
−0.435693 | + | 0.900095i | \(0.643497\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.47214 | −0.393154 | −0.196577 | − | 0.980488i | \(-0.562983\pi\) | ||||
−0.196577 | + | 0.980488i | \(0.562983\pi\) | |||||||
\(272\) | −0.763932 | −0.0463202 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.52786 | −0.454775 | ||||||||
\(275\) | 5.47214 | 0.329982 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.0000 | 1.56219 | 0.781094 | − | 0.624413i | \(-0.214662\pi\) | ||||
0.781094 | + | 0.624413i | \(0.214662\pi\) | |||||||
\(278\) | 12.1803 | 0.730528 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.8885 | 0.947831 | 0.473916 | − | 0.880570i | \(-0.342840\pi\) | ||||
0.473916 | + | 0.880570i | \(0.342840\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.2918 | −0.611784 | −0.305892 | − | 0.952066i | \(-0.598955\pi\) | ||||
−0.305892 | + | 0.952066i | \(0.598955\pi\) | |||||||
\(284\) | −6.47214 | −0.384051 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4164 | −0.965671 | ||||||||
\(290\) | 14.4721 | 0.849833 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.29180 | 0.134117 | ||||||||
\(293\) | −31.4164 | −1.83537 | −0.917683 | − | 0.397313i | \(-0.869943\pi\) | ||||
−0.917683 | + | 0.397313i | \(0.869943\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 33.8885 | 1.97307 | ||||||||
\(296\) | −6.94427 | −0.403628 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.00000 | −0.347571 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.70820 | −0.327388 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.5967 | 1.34674 | 0.673369 | − | 0.739307i | \(-0.264847\pi\) | ||||
0.673369 | + | 0.739307i | \(0.264847\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 23.4164 | 1.32996 | ||||||||
\(311\) | 22.6525 | 1.28450 | 0.642252 | − | 0.766494i | \(-0.278000\pi\) | ||||
0.642252 | + | 0.766494i | \(0.278000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.4721 | −0.818013 | −0.409007 | − | 0.912531i | \(-0.634125\pi\) | ||||
−0.409007 | + | 0.912531i | \(0.634125\pi\) | |||||||
\(314\) | −19.2361 | −1.08555 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.4164 | −0.867241 | ||||||||
\(317\) | −3.88854 | −0.218402 | −0.109201 | − | 0.994020i | \(-0.534829\pi\) | ||||
−0.109201 | + | 0.994020i | \(0.534829\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.47214 | 0.250392 | ||||||||
\(320\) | −3.23607 | −0.180902 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.36068 | 0.242635 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 12.0000 | 0.664619 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.763932 | 0.0421811 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.4164 | 1.06722 | 0.533611 | − | 0.845730i | \(-0.320835\pi\) | ||||
0.533611 | + | 0.845730i | \(0.320835\pi\) | |||||||
\(332\) | −3.23607 | −0.177602 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9.52786 | −0.521342 | ||||||||
\(335\) | 36.9443 | 2.01848 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.0000 | −0.980522 | −0.490261 | − | 0.871576i | \(-0.663099\pi\) | ||||
−0.490261 | + | 0.871576i | \(0.663099\pi\) | |||||||
\(338\) | 13.0000 | 0.707107 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.47214 | 0.134070 | ||||||||
\(341\) | 7.23607 | 0.391855 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.47214 | 0.133289 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.41641 | 0.398709 | ||||||||
\(347\) | −26.8328 | −1.44046 | −0.720231 | − | 0.693735i | \(-0.755964\pi\) | ||||
−0.720231 | + | 0.693735i | \(0.755964\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.4164 | 1.46757 | 0.733783 | − | 0.679384i | \(-0.237753\pi\) | ||||
0.733783 | + | 0.679384i | \(0.237753\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −20.3607 | −1.08369 | −0.541845 | − | 0.840479i | \(-0.682274\pi\) | ||||
−0.541845 | + | 0.840479i | \(0.682274\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.9443 | 1.11161 | ||||||||
\(356\) | 2.47214 | 0.131023 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.4721 | −0.764876 | ||||||||
\(359\) | −10.4721 | −0.552698 | −0.276349 | − | 0.961057i | \(-0.589125\pi\) | ||||
−0.276349 | + | 0.961057i | \(0.589125\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.5836 | 0.714926 | ||||||||
\(362\) | −1.70820 | −0.0897812 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.41641 | −0.388193 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.7082 | −1.13316 | −0.566580 | − | 0.824007i | \(-0.691734\pi\) | ||||
−0.566580 | + | 0.824007i | \(0.691734\pi\) | |||||||
\(368\) | −6.47214 | −0.337383 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 22.4721 | 1.16827 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.4164 | 1.31601 | 0.658006 | − | 0.753013i | \(-0.271400\pi\) | ||||
0.658006 | + | 0.753013i | \(0.271400\pi\) | |||||||
\(374\) | 0.763932 | 0.0395020 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.70820 | 0.500662 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.00000 | −0.205466 | −0.102733 | − | 0.994709i | \(-0.532759\pi\) | ||||
−0.102733 | + | 0.994709i | \(0.532759\pi\) | |||||||
\(380\) | 18.4721 | 0.947601 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.52786 | −0.0781723 | ||||||||
\(383\) | 30.6525 | 1.56627 | 0.783134 | − | 0.621853i | \(-0.213620\pi\) | ||||
0.783134 | + | 0.621853i | \(0.213620\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −22.9443 | −1.16783 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.9443 | −0.554897 | −0.277448 | − | 0.960741i | \(-0.589489\pi\) | ||||
−0.277448 | + | 0.960741i | \(0.589489\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.94427 | 0.250043 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 22.3607 | 1.12651 | ||||||||
\(395\) | 49.8885 | 2.51017 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.1803 | 1.21358 | 0.606788 | − | 0.794864i | \(-0.292458\pi\) | ||||
0.606788 | + | 0.794864i | \(0.292458\pi\) | |||||||
\(398\) | 17.1246 | 0.858379 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.47214 | 0.273607 | ||||||||
\(401\) | −0.472136 | −0.0235773 | −0.0117887 | − | 0.999931i | \(-0.503753\pi\) | ||||
−0.0117887 | + | 0.999931i | \(0.503753\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −12.0000 | −0.597022 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.94427 | 0.344215 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.23607 | −0.357801 | −0.178900 | − | 0.983867i | \(-0.557254\pi\) | ||||
−0.178900 | + | 0.983867i | \(0.557254\pi\) | |||||||
\(410\) | −2.47214 | −0.122090 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −15.2361 | −0.750627 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.4721 | 0.514057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.70820 | 0.279197 | ||||||||
\(419\) | 32.9443 | 1.60943 | 0.804717 | − | 0.593659i | \(-0.202317\pi\) | ||||
0.804717 | + | 0.593659i | \(0.202317\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.9443 | −1.11824 | −0.559118 | − | 0.829088i | \(-0.688860\pi\) | ||||
−0.559118 | + | 0.829088i | \(0.688860\pi\) | |||||||
\(422\) | 23.4164 | 1.13989 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | −4.18034 | −0.202776 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 16.9443 | 0.819032 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.00000 | −0.385794 | ||||||||
\(431\) | 13.5279 | 0.651614 | 0.325807 | − | 0.945436i | \(-0.394364\pi\) | ||||
0.325807 | + | 0.945436i | \(0.394364\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.8885 | 1.24412 | 0.622062 | − | 0.782968i | \(-0.286295\pi\) | ||||
0.622062 | + | 0.782968i | \(0.286295\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.00000 | 0.287348 | ||||||||
\(437\) | 36.9443 | 1.76728 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.58359 | −0.218763 | −0.109381 | − | 0.994000i | \(-0.534887\pi\) | ||||
−0.109381 | + | 0.994000i | \(0.534887\pi\) | |||||||
\(440\) | 3.23607 | 0.154273 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.4164 | 0.922501 | 0.461251 | − | 0.887270i | \(-0.347401\pi\) | ||||
0.461251 | + | 0.887270i | \(0.347401\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.00000 | −0.379236 | ||||||||
\(446\) | −2.29180 | −0.108520 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.4721 | −1.34368 | −0.671842 | − | 0.740695i | \(-0.734496\pi\) | ||||
−0.671842 | + | 0.740695i | \(0.734496\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.763932 | −0.0359722 | ||||||||
\(452\) | 13.4164 | 0.631055 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 22.6525 | 1.06313 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.0000 | 0.842004 | 0.421002 | − | 0.907060i | \(-0.361678\pi\) | ||||
0.421002 | + | 0.907060i | \(0.361678\pi\) | |||||||
\(458\) | 6.29180 | 0.293996 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 20.9443 | 0.976532 | ||||||||
\(461\) | 26.8328 | 1.24973 | 0.624864 | − | 0.780733i | \(-0.285154\pi\) | ||||
0.624864 | + | 0.780733i | \(0.285154\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.8885 | 1.57493 | 0.787467 | − | 0.616357i | \(-0.211392\pi\) | ||||
0.787467 | + | 0.616357i | \(0.211392\pi\) | |||||||
\(464\) | 4.47214 | 0.207614 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −26.9443 | −1.24817 | ||||||||
\(467\) | 5.88854 | 0.272489 | 0.136245 | − | 0.990675i | \(-0.456497\pi\) | ||||
0.136245 | + | 0.990675i | \(0.456497\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −31.4164 | −1.44913 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.4721 | 0.482019 | ||||||||
\(473\) | −2.47214 | −0.113669 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −31.2361 | −1.43321 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −35.7771 | −1.63470 | −0.817348 | − | 0.576144i | \(-0.804557\pi\) | ||||
−0.817348 | + | 0.576144i | \(0.804557\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −4.18034 | −0.190409 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.0557 | 0.863497 | 0.431749 | − | 0.901994i | \(-0.357897\pi\) | ||||
0.431749 | + | 0.901994i | \(0.357897\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.88854 | −0.265746 | −0.132873 | − | 0.991133i | \(-0.542420\pi\) | ||||
−0.132873 | + | 0.991133i | \(0.542420\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.41641 | −0.153867 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.23607 | 0.324909 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.4164 | −0.869198 | −0.434599 | − | 0.900624i | \(-0.643110\pi\) | ||||
−0.434599 | + | 0.900624i | \(0.643110\pi\) | |||||||
\(500\) | −1.52786 | −0.0683282 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.47214 | −0.110337 | ||||||||
\(503\) | 21.3050 | 0.949941 | 0.474970 | − | 0.880002i | \(-0.342459\pi\) | ||||
0.474970 | + | 0.880002i | \(0.342459\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 38.8328 | 1.72804 | ||||||||
\(506\) | 6.47214 | 0.287722 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.47214 | 0.109683 | ||||||||
\(509\) | −11.2361 | −0.498030 | −0.249015 | − | 0.968500i | \(-0.580107\pi\) | ||||
−0.249015 | + | 0.968500i | \(0.580107\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13.5279 | −0.596689 | ||||||||
\(515\) | 49.3050 | 2.17264 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.70820 | −0.426966 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 41.3050 | 1.80960 | 0.904801 | − | 0.425834i | \(-0.140019\pi\) | ||||
0.904801 | + | 0.425834i | \(0.140019\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.7082 | 1.64886 | 0.824432 | − | 0.565961i | \(-0.191495\pi\) | ||||
0.824432 | + | 0.565961i | \(0.191495\pi\) | |||||||
\(524\) | 11.2361 | 0.490850 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.4721 | −0.805423 | ||||||||
\(527\) | −5.52786 | −0.240798 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.8885 | 0.821241 | ||||||||
\(530\) | 19.4164 | 0.843395 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −54.8328 | −2.37063 | ||||||||
\(536\) | 11.4164 | 0.493114 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 14.2918 | 0.616163 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.41641 | −0.232870 | −0.116435 | − | 0.993198i | \(-0.537147\pi\) | ||||
−0.116435 | + | 0.993198i | \(0.537147\pi\) | |||||||
\(542\) | 6.47214 | 0.278002 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.763932 | 0.0327533 | ||||||||
\(545\) | −19.4164 | −0.831708 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.5279 | 1.26252 | 0.631260 | − | 0.775571i | \(-0.282538\pi\) | ||||
0.631260 | + | 0.775571i | \(0.282538\pi\) | |||||||
\(548\) | 7.52786 | 0.321574 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.47214 | −0.233333 | ||||||||
\(551\) | −25.5279 | −1.08752 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −26.0000 | −1.10463 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.1803 | −0.516561 | ||||||||
\(557\) | 37.4164 | 1.58538 | 0.792692 | − | 0.609622i | \(-0.208679\pi\) | ||||
0.792692 | + | 0.609622i | \(0.208679\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.8885 | −0.670218 | ||||||||
\(563\) | 11.2361 | 0.473544 | 0.236772 | − | 0.971565i | \(-0.423911\pi\) | ||||
0.236772 | + | 0.971565i | \(0.423911\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −43.4164 | −1.82654 | ||||||||
\(566\) | 10.2918 | 0.432596 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.47214 | 0.271565 | ||||||||
\(569\) | 17.0557 | 0.715013 | 0.357507 | − | 0.933911i | \(-0.383627\pi\) | ||||
0.357507 | + | 0.933911i | \(0.383627\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.4721 | −1.10782 | −0.553912 | − | 0.832575i | \(-0.686866\pi\) | ||||
−0.553912 | + | 0.832575i | \(0.686866\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −35.4164 | −1.47697 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.5836 | 0.523862 | 0.261931 | − | 0.965087i | \(-0.415641\pi\) | ||||
0.261931 | + | 0.965087i | \(0.415641\pi\) | |||||||
\(578\) | 16.4164 | 0.682833 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −14.4721 | −0.600923 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.00000 | 0.248495 | ||||||||
\(584\) | −2.29180 | −0.0948352 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 31.4164 | 1.29780 | ||||||||
\(587\) | 26.4721 | 1.09262 | 0.546311 | − | 0.837582i | \(-0.316032\pi\) | ||||
0.546311 | + | 0.837582i | \(0.316032\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −41.3050 | −1.70194 | ||||||||
\(590\) | −33.8885 | −1.39517 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.94427 | 0.285408 | ||||||||
\(593\) | 23.2361 | 0.954191 | 0.477095 | − | 0.878851i | \(-0.341690\pi\) | ||||
0.477095 | + | 0.878851i | \(0.341690\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.00000 | 0.245770 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.3050 | 1.52424 | 0.762120 | − | 0.647436i | \(-0.224159\pi\) | ||||
0.762120 | + | 0.647436i | \(0.224159\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.7082 | 0.559169 | 0.279585 | − | 0.960121i | \(-0.409803\pi\) | ||||
0.279585 | + | 0.960121i | \(0.409803\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.23607 | −0.131565 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.00000 | 0.324710 | 0.162355 | − | 0.986732i | \(-0.448091\pi\) | ||||
0.162355 | + | 0.986732i | \(0.448091\pi\) | |||||||
\(608\) | 5.70820 | 0.231498 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.52786 | 0.142489 | 0.0712445 | − | 0.997459i | \(-0.477303\pi\) | ||||
0.0712445 | + | 0.997459i | \(0.477303\pi\) | |||||||
\(614\) | −23.5967 | −0.952287 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.8885 | 0.478615 | 0.239307 | − | 0.970944i | \(-0.423080\pi\) | ||||
0.239307 | + | 0.970944i | \(0.423080\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.8328 | 1.40005 | 0.700025 | − | 0.714119i | \(-0.253172\pi\) | ||||
0.700025 | + | 0.714119i | \(0.253172\pi\) | |||||||
\(620\) | −23.4164 | −0.940426 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −22.6525 | −0.908282 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.4164 | −0.896656 | ||||||||
\(626\) | 14.4721 | 0.578423 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 19.2361 | 0.767603 | ||||||||
\(629\) | −5.30495 | −0.211522 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.8885 | −1.03061 | −0.515303 | − | 0.857008i | \(-0.672321\pi\) | ||||
−0.515303 | + | 0.857008i | \(0.672321\pi\) | |||||||
\(632\) | 15.4164 | 0.613232 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.88854 | 0.154434 | ||||||||
\(635\) | −8.00000 | −0.317470 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.47214 | −0.177054 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.23607 | 0.127917 | ||||||||
\(641\) | 0.111456 | 0.00440225 | 0.00220113 | − | 0.999998i | \(-0.499299\pi\) | ||||
0.00220113 | + | 0.999998i | \(0.499299\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.5836 | −0.653993 | −0.326997 | − | 0.945026i | \(-0.606037\pi\) | ||||
−0.326997 | + | 0.945026i | \(0.606037\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.36068 | −0.171569 | ||||||||
\(647\) | −31.0132 | −1.21925 | −0.609626 | − | 0.792689i | \(-0.708681\pi\) | ||||
−0.609626 | + | 0.792689i | \(0.708681\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.4721 | −0.411067 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.0000 | −0.469956 | ||||||||
\(653\) | −2.94427 | −0.115218 | −0.0576091 | − | 0.998339i | \(-0.518348\pi\) | ||||
−0.0576091 | + | 0.998339i | \(0.518348\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −36.3607 | −1.42073 | ||||||||
\(656\) | −0.763932 | −0.0298265 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.8885 | 0.852657 | 0.426328 | − | 0.904569i | \(-0.359807\pi\) | ||||
0.426328 | + | 0.904569i | \(0.359807\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.5967 | 1.69572 | 0.847858 | − | 0.530223i | \(-0.177892\pi\) | ||||
0.847858 | + | 0.530223i | \(0.177892\pi\) | |||||||
\(662\) | −19.4164 | −0.754640 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.23607 | 0.125584 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28.9443 | −1.12073 | ||||||||
\(668\) | 9.52786 | 0.368644 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −36.9443 | −1.42728 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.0557 | 0.657450 | 0.328725 | − | 0.944426i | \(-0.393381\pi\) | ||||
0.328725 | + | 0.944426i | \(0.393381\pi\) | |||||||
\(674\) | 18.0000 | 0.693334 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13.0000 | −0.500000 | ||||||||
\(677\) | −37.5279 | −1.44231 | −0.721156 | − | 0.692772i | \(-0.756389\pi\) | ||||
−0.721156 | + | 0.692772i | \(0.756389\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.47214 | −0.0948021 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.23607 | −0.277083 | ||||||||
\(683\) | −40.3607 | −1.54436 | −0.772179 | − | 0.635405i | \(-0.780833\pi\) | ||||
−0.772179 | + | 0.635405i | \(0.780833\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.3607 | −0.930774 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.47214 | −0.0942493 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.4721 | 1.00705 | 0.503524 | − | 0.863981i | \(-0.332037\pi\) | ||||
0.503524 | + | 0.863981i | \(0.332037\pi\) | |||||||
\(692\) | −7.41641 | −0.281930 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 26.8328 | 1.01856 | ||||||||
\(695\) | 39.4164 | 1.49515 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.583592 | 0.0221051 | ||||||||
\(698\) | −27.4164 | −1.03773 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.8885 | 1.65765 | 0.828824 | − | 0.559510i | \(-0.189011\pi\) | ||||
0.828824 | + | 0.559510i | \(0.189011\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −39.6393 | −1.49503 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20.3607 | 0.766284 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.9443 | 0.861690 | 0.430845 | − | 0.902426i | \(-0.358216\pi\) | ||||
0.430845 | + | 0.902426i | \(0.358216\pi\) | |||||||
\(710\) | −20.9443 | −0.786025 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.47214 | −0.0926472 | ||||||||
\(713\) | −46.8328 | −1.75390 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14.4721 | 0.540849 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.4721 | 0.390817 | ||||||||
\(719\) | 33.7082 | 1.25710 | 0.628552 | − | 0.777768i | \(-0.283648\pi\) | ||||
0.628552 | + | 0.777768i | \(0.283648\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −13.5836 | −0.505529 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.70820 | 0.0634849 | ||||||||
\(725\) | 24.4721 | 0.908872 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.7639 | −1.51185 | −0.755925 | − | 0.654658i | \(-0.772813\pi\) | ||||
−0.755925 | + | 0.654658i | \(0.772813\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.41641 | 0.274494 | ||||||||
\(731\) | 1.88854 | 0.0698503 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.8328 | −1.13884 | −0.569418 | − | 0.822048i | \(-0.692831\pi\) | ||||
−0.569418 | + | 0.822048i | \(0.692831\pi\) | |||||||
\(734\) | 21.7082 | 0.801264 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.47214 | 0.238566 | ||||||||
\(737\) | −11.4164 | −0.420529 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.5836 | 0.610037 | 0.305019 | − | 0.952346i | \(-0.401337\pi\) | ||||
0.305019 | + | 0.952346i | \(0.401337\pi\) | |||||||
\(740\) | −22.4721 | −0.826092 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.88854 | −0.362775 | −0.181388 | − | 0.983412i | \(-0.558059\pi\) | ||||
−0.181388 | + | 0.983412i | \(0.558059\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.4164 | −0.711362 | ||||||||
\(746\) | −25.4164 | −0.930561 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.763932 | −0.0279321 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.8328 | 1.41703 | 0.708515 | − | 0.705696i | \(-0.249366\pi\) | ||||
0.708515 | + | 0.705696i | \(0.249366\pi\) | |||||||
\(752\) | −9.70820 | −0.354022 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.05573 | 0.183754 | 0.0918768 | − | 0.995770i | \(-0.470713\pi\) | ||||
0.0918768 | + | 0.995770i | \(0.470713\pi\) | |||||||
\(758\) | 4.00000 | 0.145287 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −18.4721 | −0.670055 | ||||||||
\(761\) | −17.1246 | −0.620767 | −0.310383 | − | 0.950611i | \(-0.600457\pi\) | ||||
−0.310383 | + | 0.950611i | \(0.600457\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.52786 | 0.0552762 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −30.6525 | −1.10752 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −46.0689 | −1.66129 | −0.830643 | − | 0.556805i | \(-0.812027\pi\) | ||||
−0.830643 | + | 0.556805i | \(0.812027\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 22.9443 | 0.825782 | ||||||||
\(773\) | 43.9574 | 1.58104 | 0.790519 | − | 0.612437i | \(-0.209811\pi\) | ||||
0.790519 | + | 0.612437i | \(0.209811\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 39.5967 | 1.42236 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.9443 | 0.392371 | ||||||||
\(779\) | 4.36068 | 0.156238 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.47214 | −0.231591 | ||||||||
\(782\) | −4.94427 | −0.176807 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −62.2492 | −2.22177 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.5410 | −1.58772 | −0.793858 | − | 0.608103i | \(-0.791931\pi\) | ||||
−0.793858 | + | 0.608103i | \(0.791931\pi\) | |||||||
\(788\) | −22.3607 | −0.796566 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −49.8885 | −1.77495 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −24.1803 | −0.858128 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −17.1246 | −0.606966 | ||||||||
\(797\) | 53.1246 | 1.88177 | 0.940885 | − | 0.338726i | \(-0.109996\pi\) | ||||
0.940885 | + | 0.338726i | \(0.109996\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.41641 | 0.262374 | ||||||||
\(800\) | −5.47214 | −0.193469 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.472136 | 0.0166717 | ||||||||
\(803\) | 2.29180 | 0.0808757 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.0000 | 0.422159 | ||||||||
\(809\) | 8.83282 | 0.310545 | 0.155273 | − | 0.987872i | \(-0.450374\pi\) | ||||
0.155273 | + | 0.987872i | \(0.450374\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.5967 | 1.10951 | 0.554756 | − | 0.832013i | \(-0.312812\pi\) | ||||
0.554756 | + | 0.832013i | \(0.312812\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.94427 | −0.243397 | ||||||||
\(815\) | 38.8328 | 1.36025 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.1115 | 0.493697 | ||||||||
\(818\) | 7.23607 | 0.253003 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.47214 | 0.0863307 | ||||||||
\(821\) | 41.7771 | 1.45803 | 0.729015 | − | 0.684498i | \(-0.239978\pi\) | ||||
0.729015 | + | 0.684498i | \(0.239978\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.8328 | 0.795902 | 0.397951 | − | 0.917407i | \(-0.369721\pi\) | ||||
0.397951 | + | 0.917407i | \(0.369721\pi\) | |||||||
\(824\) | 15.2361 | 0.530774 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 52.7214 | 1.83330 | 0.916651 | − | 0.399689i | \(-0.130882\pi\) | ||||
0.916651 | + | 0.399689i | \(0.130882\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.4853 | 1.30192 | 0.650959 | − | 0.759113i | \(-0.274367\pi\) | ||||
0.650959 | + | 0.759113i | \(0.274367\pi\) | |||||||
\(830\) | −10.4721 | −0.363493 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30.8328 | −1.06701 | ||||||||
\(836\) | −5.70820 | −0.197422 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −32.9443 | −1.13804 | ||||||||
\(839\) | 20.7639 | 0.716851 | 0.358425 | − | 0.933558i | \(-0.383314\pi\) | ||||
0.358425 | + | 0.933558i | \(0.383314\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 22.9443 | 0.790712 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −23.4164 | −0.806026 | ||||||||
\(845\) | 42.0689 | 1.44721 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.18034 | 0.143384 | ||||||||
\(851\) | −44.9443 | −1.54067 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.88854 | −0.0646625 | −0.0323313 | − | 0.999477i | \(-0.510293\pi\) | ||||
−0.0323313 | + | 0.999477i | \(0.510293\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.9443 | −0.579143 | ||||||||
\(857\) | 6.87539 | 0.234859 | 0.117429 | − | 0.993081i | \(-0.462535\pi\) | ||||
0.117429 | + | 0.993081i | \(0.462535\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.5836 | 0.565825 | 0.282912 | − | 0.959146i | \(-0.408699\pi\) | ||||
0.282912 | + | 0.959146i | \(0.408699\pi\) | |||||||
\(860\) | 8.00000 | 0.272798 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13.5279 | −0.460761 | ||||||||
\(863\) | −0.360680 | −0.0122777 | −0.00613884 | − | 0.999981i | \(-0.501954\pi\) | ||||
−0.00613884 | + | 0.999981i | \(0.501954\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.0000 | 0.816024 | ||||||||
\(866\) | −25.8885 | −0.879729 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.4164 | −0.522966 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −6.00000 | −0.203186 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −36.9443 | −1.24966 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.0000 | 1.01303 | 0.506514 | − | 0.862232i | \(-0.330934\pi\) | ||||
0.506514 | + | 0.862232i | \(0.330934\pi\) | |||||||
\(878\) | 4.58359 | 0.154689 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.23607 | −0.109088 | ||||||||
\(881\) | −26.8328 | −0.904021 | −0.452010 | − | 0.892013i | \(-0.649293\pi\) | ||||
−0.452010 | + | 0.892013i | \(0.649293\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.0000 | 0.403832 | 0.201916 | − | 0.979403i | \(-0.435283\pi\) | ||||
0.201916 | + | 0.979403i | \(0.435283\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −19.4164 | −0.652307 | ||||||||
\(887\) | −19.0557 | −0.639829 | −0.319914 | − | 0.947446i | \(-0.603654\pi\) | ||||
−0.319914 | + | 0.947446i | \(0.603654\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 8.00000 | 0.268161 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.29180 | 0.0767350 | ||||||||
\(893\) | 55.4164 | 1.85444 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −46.8328 | −1.56545 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 28.4721 | 0.950127 | ||||||||
\(899\) | 32.3607 | 1.07929 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.58359 | −0.152702 | ||||||||
\(902\) | 0.763932 | 0.0254362 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.4164 | −0.446223 | ||||||||
\(905\) | −5.52786 | −0.183752 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.3050 | 0.973055 | 0.486527 | − | 0.873665i | \(-0.338263\pi\) | ||||
0.486527 | + | 0.873665i | \(0.338263\pi\) | |||||||
\(908\) | −22.6525 | −0.751749 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.58359 | 0.151861 | 0.0759306 | − | 0.997113i | \(-0.475807\pi\) | ||||
0.0759306 | + | 0.997113i | \(0.475807\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.23607 | −0.107098 | ||||||||
\(914\) | −18.0000 | −0.595387 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.29180 | −0.207887 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53.6656 | 1.77027 | 0.885133 | − | 0.465338i | \(-0.154067\pi\) | ||||
0.885133 | + | 0.465338i | \(0.154067\pi\) | |||||||
\(920\) | −20.9443 | −0.690512 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −26.8328 | −0.883692 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.0000 | 1.24943 | ||||||||
\(926\) | −33.8885 | −1.11365 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.47214 | −0.146805 | ||||||||
\(929\) | −36.3607 | −1.19296 | −0.596478 | − | 0.802630i | \(-0.703434\pi\) | ||||
−0.596478 | + | 0.802630i | \(0.703434\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 26.9443 | 0.882589 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.88854 | −0.192679 | ||||||||
\(935\) | 2.47214 | 0.0808475 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −47.5967 | −1.55492 | −0.777459 | − | 0.628934i | \(-0.783492\pi\) | ||||
−0.777459 | + | 0.628934i | \(0.783492\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 31.4164 | 1.02469 | ||||||||
\(941\) | −52.3607 | −1.70691 | −0.853455 | − | 0.521167i | \(-0.825497\pi\) | ||||
−0.853455 | + | 0.521167i | \(0.825497\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.94427 | 0.161008 | ||||||||
\(944\) | −10.4721 | −0.340839 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.47214 | 0.0803761 | ||||||||
\(947\) | 2.11146 | 0.0686131 | 0.0343066 | − | 0.999411i | \(-0.489078\pi\) | ||||
0.0343066 | + | 0.999411i | \(0.489078\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 31.2361 | 1.01343 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.0557 | 0.422917 | 0.211458 | − | 0.977387i | \(-0.432179\pi\) | ||||
0.211458 | + | 0.977387i | \(0.432179\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.94427 | −0.159993 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 35.7771 | 1.15591 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.3607 | 0.689054 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.18034 | 0.134640 | ||||||||
\(965\) | −74.2492 | −2.39017 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.16718 | 0.0375341 | 0.0187671 | − | 0.999824i | \(-0.494026\pi\) | ||||
0.0187671 | + | 0.999824i | \(0.494026\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −56.9443 | −1.82743 | −0.913714 | − | 0.406357i | \(-0.866799\pi\) | ||||
−0.913714 | + | 0.406357i | \(0.866799\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −19.0557 | −0.610585 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23.8885 | −0.764262 | −0.382131 | − | 0.924108i | \(-0.624810\pi\) | ||||
−0.382131 | + | 0.924108i | \(0.624810\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.47214 | 0.0790098 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.88854 | 0.187911 | ||||||||
\(983\) | 38.2918 | 1.22132 | 0.610659 | − | 0.791893i | \(-0.290904\pi\) | ||||
0.610659 | + | 0.791893i | \(0.290904\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 72.3607 | 2.30560 | ||||||||
\(986\) | 3.41641 | 0.108801 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.0000 | 0.508770 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.8328 | 0.725308 | 0.362654 | − | 0.931924i | \(-0.381871\pi\) | ||||
0.362654 | + | 0.931924i | \(0.381871\pi\) | |||||||
\(992\) | −7.23607 | −0.229745 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 55.4164 | 1.75682 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.2492 | 0.831321 | 0.415661 | − | 0.909520i | \(-0.363550\pi\) | ||||
0.415661 | + | 0.909520i | \(0.363550\pi\) | |||||||
\(998\) | 19.4164 | 0.614616 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 9702.2.a.ck.1.1 | 2 | ||
3.2 | odd | 2 | 3234.2.a.be.1.2 | yes | 2 | ||
7.6 | odd | 2 | 9702.2.a.cw.1.2 | 2 | |||
21.20 | even | 2 | 3234.2.a.bb.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3234.2.a.bb.1.1 | ✓ | 2 | 21.20 | even | 2 | ||
3234.2.a.be.1.2 | yes | 2 | 3.2 | odd | 2 | ||
9702.2.a.ck.1.1 | 2 | 1.1 | even | 1 | trivial | ||
9702.2.a.cw.1.2 | 2 | 7.6 | odd | 2 |