Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(1,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, 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("1792.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.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: | \(14.3091920422\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{16})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 896) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.84776\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.61313 | −1.50869 | −0.754344 | − | 0.656479i | \(-0.772045\pi\) | ||||
−0.754344 | + | 0.656479i | \(0.772045\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.61313 | 1.16863 | 0.584313 | − | 0.811529i | \(-0.301364\pi\) | ||||
0.584313 | + | 0.811529i | \(0.301364\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.82843 | 1.27614 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.16478 | 0.652707 | 0.326354 | − | 0.945248i | \(-0.394180\pi\) | ||||
0.326354 | + | 0.945248i | \(0.394180\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.448342 | 0.124348 | 0.0621738 | − | 0.998065i | \(-0.480197\pi\) | ||||
0.0621738 | + | 0.998065i | \(0.480197\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.82843 | −1.76309 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.65685 | −1.85706 | −0.928530 | − | 0.371257i | \(-0.878927\pi\) | ||||
−0.928530 | + | 0.371257i | \(0.878927\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.77791 | −1.09613 | −0.548064 | − | 0.836436i | \(-0.684635\pi\) | ||||
−0.548064 | + | 0.836436i | \(0.684635\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.61313 | 0.570231 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.82843 | −1.42383 | −0.711913 | − | 0.702268i | \(-0.752171\pi\) | ||||
−0.711913 | + | 0.702268i | \(0.752171\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.82843 | 0.365685 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.16478 | −0.416613 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.55582 | 1.77447 | 0.887236 | − | 0.461316i | \(-0.152623\pi\) | ||||
0.887236 | + | 0.461316i | \(0.152623\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.65685 | 1.01600 | 0.508001 | − | 0.861357i | \(-0.330385\pi\) | ||||
0.508001 | + | 0.861357i | \(0.330385\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.65685 | −0.984732 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.61313 | −0.441699 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.22625 | 0.859191 | 0.429595 | − | 0.903022i | \(-0.358656\pi\) | ||||
0.429595 | + | 0.903022i | \(0.358656\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.17157 | −0.187602 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.65685 | 0.571105 | 0.285552 | − | 0.958363i | \(-0.407823\pi\) | ||||
0.285552 | + | 0.958363i | \(0.407823\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.16478 | −0.330127 | −0.165063 | − | 0.986283i | \(-0.552783\pi\) | ||||
−0.165063 | + | 0.986283i | \(0.552783\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.0042 | 1.49133 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.00000 | −1.16692 | −0.583460 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583460 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 20.0083 | 2.80173 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.4525 | −1.43576 | −0.717881 | − | 0.696166i | \(-0.754888\pi\) | ||||
−0.717881 | + | 0.696166i | \(0.754888\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.65685 | 0.762770 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.4853 | 1.65372 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.448342 | −0.0583691 | −0.0291845 | − | 0.999574i | \(-0.509291\pi\) | ||||
−0.0291845 | + | 0.999574i | \(0.509291\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.1689 | −1.55807 | −0.779037 | − | 0.626978i | \(-0.784292\pi\) | ||||
−0.779037 | + | 0.626978i | \(0.784292\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.82843 | −0.482336 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.17157 | 0.145316 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.06147 | −0.374018 | −0.187009 | − | 0.982358i | \(-0.559879\pi\) | ||||
−0.187009 | + | 0.982358i | \(0.559879\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 17.8435 | 2.14811 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.34315 | −0.278080 | −0.139040 | − | 0.990287i | \(-0.544402\pi\) | ||||
−0.139040 | + | 0.990287i | \(0.544402\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.6569 | −1.36433 | −0.682166 | − | 0.731198i | \(-0.738962\pi\) | ||||
−0.682166 | + | 0.731198i | \(0.738962\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.77791 | −0.551706 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.16478 | −0.246700 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.34315 | −0.263624 | −0.131812 | − | 0.991275i | \(-0.542080\pi\) | ||||
−0.131812 | + | 0.991275i | \(0.542080\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.82843 | −0.647603 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.0656 | 1.43414 | 0.717070 | − | 0.697002i | \(-0.245483\pi\) | ||||
0.717070 | + | 0.697002i | \(0.245483\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20.0083 | −2.17021 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −24.9706 | −2.67713 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.448342 | −0.0469990 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.7821 | −1.53283 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12.4853 | −1.28096 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0000 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.28772 | 0.832947 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.77791 | −0.475420 | −0.237710 | − | 0.971336i | \(-0.576397\pi\) | ||||
−0.237710 | + | 0.971336i | \(0.576397\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.6569 | −1.34565 | −0.672825 | − | 0.739802i | \(-0.734919\pi\) | ||||
−0.672825 | + | 0.739802i | \(0.734919\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.82843 | 0.666386 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.5140 | 1.30644 | 0.653222 | − | 0.757166i | \(-0.273417\pi\) | ||||
0.653222 | + | 0.757166i | \(0.273417\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.3492 | −1.08705 | −0.543527 | − | 0.839391i | \(-0.682912\pi\) | ||||
−0.543527 | + | 0.839391i | \(0.682912\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.6569 | −1.29625 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.82843 | 0.830509 | 0.415254 | − | 0.909705i | \(-0.363693\pi\) | ||||
0.415254 | + | 0.909705i | \(0.363693\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.8435 | −1.66392 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.71644 | 0.158685 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.65685 | 0.701903 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.31371 | −0.573973 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.55582 | −0.861619 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.28772 | −0.741276 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.48528 | −0.398004 | −0.199002 | − | 0.979999i | \(-0.563770\pi\) | ||||
−0.199002 | + | 0.979999i | \(0.563770\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.65685 | 0.498058 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.2919 | −1.59817 | −0.799085 | − | 0.601219i | \(-0.794682\pi\) | ||||
−0.799085 | + | 0.601219i | \(0.794682\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.77791 | 0.414297 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.65685 | −0.486864 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.00000 | −0.170872 | −0.0854358 | − | 0.996344i | \(-0.527228\pi\) | ||||
−0.0854358 | + | 0.996344i | \(0.527228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.5600 | 1.65906 | 0.829528 | − | 0.558465i | \(-0.188610\pi\) | ||||
0.829528 | + | 0.558465i | \(0.188610\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 20.9050 | 1.76052 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.970563 | 0.0811625 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 24.9706 | 2.07369 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.61313 | −0.215527 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.5754 | −1.35791 | −0.678956 | − | 0.734179i | \(-0.737567\pi\) | ||||
−0.678956 | + | 0.734179i | \(0.737567\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.1421 | 1.47639 | 0.738193 | − | 0.674590i | \(-0.235679\pi\) | ||||
0.738193 | + | 0.674590i | \(0.235679\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −29.3137 | −2.36987 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.7821 | 1.18732 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.77791 | 0.381319 | 0.190659 | − | 0.981656i | \(-0.438937\pi\) | ||||
0.190659 | + | 0.981656i | \(0.438937\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 27.3137 | 2.16612 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.82843 | 0.538155 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.95815 | 0.310026 | 0.155013 | − | 0.987912i | \(-0.450458\pi\) | ||||
0.155013 | + | 0.987912i | \(0.450458\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −14.7821 | −1.15078 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.0000 | −1.23812 | −0.619059 | − | 0.785345i | \(-0.712486\pi\) | ||||
−0.619059 | + | 0.785345i | \(0.712486\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7990 | −0.984538 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −18.2919 | −1.39882 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.1271 | −1.22612 | −0.613060 | − | 0.790036i | \(-0.710062\pi\) | ||||
−0.613060 | + | 0.790036i | \(0.710062\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.82843 | −0.138216 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.17157 | 0.0880608 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.1731 | −1.65730 | −0.828648 | − | 0.559770i | \(-0.810889\pi\) | ||||
−0.828648 | + | 0.559770i | \(0.810889\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.61313 | −0.194232 | −0.0971161 | − | 0.995273i | \(-0.530962\pi\) | ||||
−0.0971161 | + | 0.995273i | \(0.530962\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 31.7990 | 2.35065 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 13.6569 | 1.00407 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.5754 | −1.21212 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.16478 | 0.157465 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.3137 | 1.39749 | 0.698745 | − | 0.715370i | \(-0.253742\pi\) | ||||
0.698745 | + | 0.715370i | \(0.253742\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.7990 | 0.993273 | 0.496637 | − | 0.867959i | \(-0.334568\pi\) | ||||
0.496637 | + | 0.867959i | \(0.334568\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.06147 | −0.219236 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.12293 | 0.436241 | 0.218121 | − | 0.975922i | \(-0.430007\pi\) | ||||
0.218121 | + | 0.975922i | \(0.430007\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.97056 | −0.635906 | −0.317953 | − | 0.948106i | \(-0.602995\pi\) | ||||
−0.317953 | + | 0.948106i | \(0.602995\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.00000 | 0.564276 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.55582 | −0.670687 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.55582 | 0.667407 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −26.1421 | −1.81700 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.3431 | −0.715450 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.18440 | −0.632280 | −0.316140 | − | 0.948712i | \(-0.602387\pi\) | ||||
−0.316140 | + | 0.948712i | \(0.602387\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.12293 | 0.419537 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.65685 | −0.385794 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.65685 | −0.384012 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 30.4608 | 2.05835 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.43289 | −0.230921 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.97056 | −0.600713 | −0.300357 | − | 0.953827i | \(-0.597106\pi\) | ||||
−0.300357 | + | 0.953827i | \(0.597106\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.00000 | 0.466667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.3337 | 0.951363 | 0.475682 | − | 0.879618i | \(-0.342201\pi\) | ||||
0.475682 | + | 0.879618i | \(0.342201\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.67459 | −0.374988 | −0.187494 | − | 0.982266i | \(-0.560036\pi\) | ||||
−0.187494 | + | 0.982266i | \(0.560036\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.65685 | 0.372194 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.0000 | 0.655122 | 0.327561 | − | 0.944830i | \(-0.393773\pi\) | ||||
0.327561 | + | 0.944830i | \(0.393773\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.9050 | −1.36369 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.12293 | 0.397727 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.1421 | −1.17352 | −0.586759 | − | 0.809762i | \(-0.699596\pi\) | ||||
−0.586759 | + | 0.809762i | \(0.699596\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.31371 | 0.0846234 | 0.0423117 | − | 0.999104i | \(-0.486528\pi\) | ||||
0.0423117 | + | 0.999104i | \(0.486528\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.7248 | 1.39364 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.61313 | 0.166946 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.14214 | −0.136301 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −34.1421 | −2.16367 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.819760 | −0.0517428 | −0.0258714 | − | 0.999665i | \(-0.508236\pi\) | ||||
−0.0258714 | + | 0.999665i | \(0.508236\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.7821 | −0.929341 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 52.2843 | 3.27417 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.31371 | −0.580973 | −0.290487 | − | 0.956879i | \(-0.593817\pi\) | ||||
−0.290487 | + | 0.956879i | \(0.593817\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.22625 | −0.324743 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 36.5838 | 2.26448 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.34315 | −0.144485 | −0.0722423 | − | 0.997387i | \(-0.523015\pi\) | ||||
−0.0722423 | + | 0.997387i | \(0.523015\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −27.3137 | −1.67787 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.22625 | −0.319841 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.21080 | −0.500621 | −0.250311 | − | 0.968166i | \(-0.580533\pi\) | ||||
−0.250311 | + | 0.968166i | \(0.580533\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.34315 | −0.142336 | −0.0711680 | − | 0.997464i | \(-0.522673\pi\) | ||||
−0.0711680 | + | 0.997464i | \(0.522673\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.17157 | 0.0709068 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.95815 | 0.238685 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.7821 | 0.888169 | 0.444084 | − | 0.895985i | \(-0.353529\pi\) | ||||
0.444084 | + | 0.895985i | \(0.353529\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 21.6569 | 1.29656 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.00000 | 0.119310 | 0.0596550 | − | 0.998219i | \(-0.481000\pi\) | ||||
0.0596550 | + | 0.998219i | \(0.481000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.8281 | −1.23810 | −0.619051 | − | 0.785351i | \(-0.712482\pi\) | ||||
−0.619051 | + | 0.785351i | \(0.712482\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 32.6256 | 1.93257 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.65685 | −0.215857 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 41.6274 | 2.44867 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 26.1313 | 1.53184 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.9008 | −0.636834 | −0.318417 | − | 0.947951i | \(-0.603151\pi\) | ||||
−0.318417 | + | 0.947951i | \(0.603151\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.17157 | −0.0682116 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.68629 | −0.271926 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.06147 | −0.177049 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.16478 | 0.124776 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.4853 | 0.717261 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −31.7990 | −1.82080 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.73606 | 0.498593 | 0.249297 | − | 0.968427i | \(-0.419801\pi\) | ||||
0.249297 | + | 0.968427i | \(0.419801\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 35.6871 | 2.03017 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.6274 | −0.829445 | −0.414722 | − | 0.909948i | \(-0.636121\pi\) | ||||
−0.414722 | + | 0.909948i | \(0.636121\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.34315 | 0.471582 | 0.235791 | − | 0.971804i | \(-0.424232\pi\) | ||||
0.235791 | + | 0.971804i | \(0.424232\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10.0042 | −0.563671 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.65914 | 0.486346 | 0.243173 | − | 0.969983i | \(-0.421812\pi\) | ||||
0.243173 | + | 0.969983i | \(0.421812\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.6863 | 1.15821 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −35.3137 | −1.97102 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 36.5838 | 2.03558 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.819760 | 0.0454721 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 29.6569 | 1.64003 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.00000 | 0.441054 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.7402 | 1.03006 | 0.515028 | − | 0.857173i | \(-0.327782\pi\) | ||||
0.515028 | + | 0.857173i | \(0.327782\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 20.0083 | 1.09645 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.00000 | −0.437087 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.1716 | 0.608554 | 0.304277 | − | 0.952584i | \(-0.401585\pi\) | ||||
0.304277 | + | 0.952584i | \(0.401585\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −23.0698 | −1.25298 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.2459 | 0.663151 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 46.6274 | 2.51034 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.6173 | 0.677332 | 0.338666 | − | 0.940907i | \(-0.390024\pi\) | ||||
0.338666 | + | 0.940907i | \(0.390024\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.6215 | 1.21090 | 0.605449 | − | 0.795884i | \(-0.292993\pi\) | ||||
0.605449 | + | 0.795884i | \(0.292993\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.970563 | −0.0518048 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.6569 | 0.833330 | 0.416665 | − | 0.909060i | \(-0.363199\pi\) | ||||
0.416665 | + | 0.909060i | \(0.363199\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.12293 | −0.324972 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −20.0083 | −1.05895 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.82843 | −0.360391 | −0.180195 | − | 0.983631i | \(-0.557673\pi\) | ||||
−0.180195 | + | 0.983631i | \(0.557673\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.82843 | 0.201496 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.4985 | 0.865947 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −30.4608 | −1.59439 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.9706 | 1.30345 | 0.651726 | − | 0.758454i | \(-0.274045\pi\) | ||||
0.651726 | + | 0.758454i | \(0.274045\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.0000 | 0.728811 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.4525 | 0.542667 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.8937 | −1.75495 | −0.877475 | − | 0.479622i | \(-0.840774\pi\) | ||||
−0.877475 | + | 0.479622i | \(0.840774\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 21.6569 | 1.11836 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.28427 | 0.220651 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.0698 | 1.18502 | 0.592508 | − | 0.805565i | \(-0.298138\pi\) | ||||
0.592508 | + | 0.805565i | \(0.298138\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.7206 | 0.600465 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.3137 | −0.986884 | −0.493442 | − | 0.869779i | \(-0.664262\pi\) | ||||
−0.493442 | + | 0.869779i | \(0.664262\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.65685 | −0.288300 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.28772 | −0.421288 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.0083 | 1.01446 | 0.507231 | − | 0.861810i | \(-0.330669\pi\) | ||||
0.507231 | + | 0.861810i | \(0.330669\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 52.2843 | 2.64413 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 47.7990 | 2.41114 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.12293 | −0.308078 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.2919 | 0.918043 | 0.459022 | − | 0.888425i | \(-0.348200\pi\) | ||||
0.459022 | + | 0.888425i | \(0.348200\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.4853 | −0.625046 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.51472 | 0.475142 | 0.237571 | − | 0.971370i | \(-0.423649\pi\) | ||||
0.237571 | + | 0.971370i | \(0.423649\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.53620 | 0.126337 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −15.2304 | −0.756805 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.3137 | 0.560800 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.31371 | −0.262746 | −0.131373 | − | 0.991333i | \(-0.541939\pi\) | ||||
−0.131373 | + | 0.991333i | \(0.541939\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.22625 | 0.257792 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.448342 | 0.0220614 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 34.1421 | 1.67597 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −51.1127 | −2.50300 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.0656 | −0.638298 | −0.319149 | − | 0.947705i | \(-0.603397\pi\) | ||||
−0.319149 | + | 0.947705i | \(0.603397\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.53620 | 0.123607 | 0.0618035 | − | 0.998088i | \(-0.480315\pi\) | ||||
0.0618035 | + | 0.998088i | \(0.480315\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −30.6274 | −1.48916 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.0000 | −0.679100 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.1689 | 0.588897 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.53620 | −0.122449 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.82843 | 0.328914 | 0.164457 | − | 0.986384i | \(-0.447413\pi\) | ||||
0.164457 | + | 0.986384i | \(0.447413\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.3431 | −0.593174 | −0.296587 | − | 0.955006i | \(-0.595848\pi\) | ||||
−0.296587 | + | 0.955006i | \(0.595848\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −65.2512 | −3.12856 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 32.6256 | 1.56069 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.970563 | −0.0463224 | −0.0231612 | − | 0.999732i | \(-0.507373\pi\) | ||||
−0.0231612 | + | 0.999732i | \(0.507373\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.82843 | 0.182306 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.18440 | −0.436364 | −0.218182 | − | 0.975908i | \(-0.570013\pi\) | ||||
−0.218182 | + | 0.975908i | \(0.570013\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.22625 | 0.247748 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 43.3137 | 2.04867 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.6274 | −1.16224 | −0.581120 | − | 0.813818i | \(-0.697385\pi\) | ||||
−0.581120 | + | 0.813818i | \(0.697385\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.91630 | 0.372764 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −47.4077 | −2.22741 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.17157 | −0.0549242 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.4853 | 0.490481 | 0.245240 | − | 0.969462i | \(-0.421133\pi\) | ||||
0.245240 | + | 0.969462i | \(0.421133\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 16.5754 | 0.773675 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.3756 | 0.483239 | 0.241619 | − | 0.970371i | \(-0.422321\pi\) | ||||
0.241619 | + | 0.970371i | \(0.422321\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.00000 | −0.371792 | −0.185896 | − | 0.982569i | \(-0.559519\pi\) | ||||
−0.185896 | + | 0.982569i | \(0.559519\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −38.6274 | −1.79130 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.34502 | 0.0622403 | 0.0311202 | − | 0.999516i | \(-0.490093\pi\) | ||||
0.0311202 | + | 0.999516i | \(0.490093\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.06147 | 0.141365 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.4853 | −0.575291 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.68629 | −0.215476 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.73606 | −0.400838 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −40.0166 | −1.83224 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.65685 | 0.258468 | 0.129234 | − | 0.991614i | \(-0.458748\pi\) | ||||
0.129234 | + | 0.991614i | \(0.458748\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.34315 | 0.106838 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −17.8435 | −0.811909 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −26.1313 | −1.18656 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.7990 | 1.44095 | 0.720475 | − | 0.693481i | \(-0.243924\pi\) | ||||
0.720475 | + | 0.693481i | \(0.243924\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.3431 | −0.467733 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.6256 | −1.47237 | −0.736187 | − | 0.676779i | \(-0.763375\pi\) | ||||
−0.736187 | + | 0.676779i | \(0.763375\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −73.1675 | −3.29530 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 21.6569 | 0.973403 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.34315 | 0.105104 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.7206 | 0.524686 | 0.262343 | − | 0.964975i | \(-0.415505\pi\) | ||||
0.262343 | + | 0.964975i | \(0.415505\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 41.8100 | 1.86793 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.65685 | −0.252227 | −0.126113 | − | 0.992016i | \(-0.540250\pi\) | ||||
−0.126113 | + | 0.992016i | \(0.540250\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.4853 | −0.555588 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 33.4454 | 1.48536 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.50981 | 0.155570 | 0.0777848 | − | 0.996970i | \(-0.475215\pi\) | ||||
0.0777848 | + | 0.996970i | \(0.475215\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.6569 | 0.515669 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.3431 | 0.456661 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −35.6871 | −1.57256 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.3183 | −0.761657 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 42.1421 | 1.84983 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.6863 | −0.643418 | −0.321709 | − | 0.946839i | \(-0.604257\pi\) | ||||
−0.321709 | + | 0.946839i | \(0.604257\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.46796 | 0.326551 | 0.163276 | − | 0.986581i | \(-0.447794\pi\) | ||||
0.163276 | + | 0.986581i | \(0.447794\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.77791 | 0.208525 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −43.3137 | −1.88677 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.6274 | 1.02728 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.71644 | −0.0744873 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.63952 | 0.0710155 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 35.3137 | 1.52674 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 57.9411 | 2.50034 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.16478 | 0.0932439 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.3575 | 1.34816 | 0.674082 | − | 0.738656i | \(-0.264539\pi\) | ||||
0.674082 | + | 0.738656i | \(0.264539\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.82843 | 0.293036 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −29.6569 | −1.27036 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 43.9748 | 1.88023 | 0.940113 | − | 0.340862i | \(-0.110719\pi\) | ||||
0.940113 | + | 0.340862i | \(0.110719\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −46.5879 | −1.98832 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −45.6569 | −1.94505 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.34315 | 0.0996407 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −35.6871 | −1.51483 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.7821 | −0.626337 | −0.313168 | − | 0.949698i | \(-0.601390\pi\) | ||||
−0.313168 | + | 0.949698i | \(0.601390\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.970563 | −0.0410504 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 43.3137 | 1.82871 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.7666 | 0.748774 | 0.374387 | − | 0.927273i | \(-0.377853\pi\) | ||||
0.374387 | + | 0.927273i | \(0.377853\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23.0698 | 0.970553 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.82843 | 0.244771 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.5147 | 0.734255 | 0.367128 | − | 0.930171i | \(-0.380341\pi\) | ||||
0.367128 | + | 0.930171i | \(0.380341\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.7402 | −0.784254 | −0.392127 | − | 0.919911i | \(-0.628261\pi\) | ||||
−0.392127 | + | 0.919911i | \(0.628261\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −50.4692 | −2.10838 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.4853 | −0.520672 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.9706 | −0.956277 | −0.478139 | − | 0.878284i | \(-0.658688\pi\) | ||||
−0.478139 | + | 0.878284i | \(0.658688\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −36.0585 | −1.49854 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.0656 | −0.542054 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.6274 | −0.937132 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.48528 | 0.185444 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −33.4454 | −1.38044 | −0.690219 | − | 0.723600i | \(-0.742486\pi\) | ||||
−0.690219 | + | 0.723600i | \(0.742486\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.0279 | −1.11367 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.0000 | −0.658152 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25.3137 | −1.03951 | −0.519755 | − | 0.854316i | \(-0.673977\pi\) | ||||
−0.519755 | + | 0.854316i | \(0.673977\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.0083 | 0.820261 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 23.4412 | 0.959385 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.00000 | −0.326871 | −0.163436 | − | 0.986554i | \(-0.552258\pi\) | ||||
−0.163436 | + | 0.986554i | \(0.552258\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.3137 | −1.68522 | −0.842611 | − | 0.538523i | \(-0.818982\pi\) | ||||
−0.842611 | + | 0.538523i | \(0.818982\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.7206 | −0.477300 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16.4985 | −0.670760 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.3137 | 1.10863 | 0.554315 | − | 0.832307i | \(-0.312980\pi\) | ||||
0.554315 | + | 0.832307i | \(0.312980\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 24.9706 | 1.01186 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.58673 | −0.145104 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.1313 | −1.05543 | −0.527716 | − | 0.849421i | \(-0.676951\pi\) | ||||
−0.527716 | + | 0.849421i | \(0.676951\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −24.9706 | −1.00691 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.7990 | 1.68276 | 0.841382 | − | 0.540441i | \(-0.181743\pi\) | ||||
0.841382 | + | 0.540441i | \(0.181743\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.9706 | 1.36540 | 0.682698 | − | 0.730701i | \(-0.260807\pi\) | ||||
0.682698 | + | 0.730701i | \(0.260807\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.7821 | 0.593184 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.00000 | −0.0801283 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.7990 | −1.23196 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 27.0279 | 1.07939 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −40.0166 | −1.59557 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.6274 | −1.21926 | −0.609629 | − | 0.792687i | \(-0.708682\pi\) | ||||
−0.609629 | + | 0.792687i | \(0.708682\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.0000 | 0.953914 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.7206 | −0.465118 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.448342 | 0.0177639 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.97056 | −0.354870 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.4558 | 1.08444 | 0.542220 | − | 0.840236i | \(-0.317584\pi\) | ||||
0.542220 | + | 0.840236i | \(0.317584\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.98454 | 0.117699 | 0.0588495 | − | 0.998267i | \(-0.481257\pi\) | ||||
0.0588495 | + | 0.998267i | \(0.481257\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.7821 | 0.582044 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.6569 | −1.16593 | −0.582966 | − | 0.812497i | \(-0.698108\pi\) | ||||
−0.582966 | + | 0.812497i | \(0.698108\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.970563 | −0.0380979 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.7821 | 0.579355 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.5445 | 0.882236 | 0.441118 | − | 0.897449i | \(-0.354582\pi\) | ||||
0.441118 | + | 0.897449i | \(0.354582\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −47.7990 | −1.86766 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −44.6274 | −1.74108 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.0811 | −0.392703 | −0.196352 | − | 0.980534i | \(-0.562909\pi\) | ||||
−0.196352 | + | 0.980534i | \(0.562909\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.448342 | −0.0174385 | −0.00871923 | − | 0.999962i | \(-0.502775\pi\) | ||||
−0.00871923 | + | 0.999962i | \(0.502775\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.97056 | 0.348388 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.4853 | 0.484158 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −65.2512 | −2.52654 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.4412 | 0.906290 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26.3431 | −1.01697 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.6274 | 1.10351 | 0.551753 | − | 0.834008i | \(-0.313959\pi\) | ||||
0.551753 | + | 0.834008i | \(0.313959\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.95815 | −0.152349 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.73606 | −0.335754 | −0.167877 | − | 0.985808i | \(-0.553691\pi\) | ||||
−0.167877 | + | 0.985808i | \(0.553691\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.0000 | 0.383765 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −37.4558 | −1.43531 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.59767 | 0.214189 | 0.107094 | − | 0.994249i | \(-0.465845\pi\) | ||||
0.107094 | + | 0.994249i | \(0.465845\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.22625 | −0.199685 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.8284 | 0.565740 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.68629 | −0.178533 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.7640 | 1.36053 | 0.680263 | − | 0.732968i | \(-0.261865\pi\) | ||||
0.680263 | + | 0.732968i | \(0.261865\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.28772 | −0.314824 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 51.1127 | 1.93882 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.0000 | −1.06058 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −26.1313 | −0.988375 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.9133 | 1.54528 | 0.772638 | − | 0.634847i | \(-0.218937\pi\) | ||||
0.772638 | + | 0.634847i | \(0.218937\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.9706 | −0.941783 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 54.6274 | 2.05739 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.77791 | 0.179692 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.4721 | 0.656179 | 0.328090 | − | 0.944647i | \(-0.393595\pi\) | ||||
0.328090 | + | 0.944647i | \(0.393595\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.97056 | −0.336422 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −38.6274 | −1.44661 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.53620 | 0.0948486 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 47.4077 | 1.77047 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.31371 | 0.123580 | 0.0617902 | − | 0.998089i | \(-0.480319\pi\) | ||||
0.0617902 | + | 0.998089i | \(0.480319\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.6569 | 0.508608 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.43289 | −0.127670 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.4721 | 0.648898 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.6863 | −0.767212 | −0.383606 | − | 0.923497i | \(-0.625318\pi\) | ||||
−0.383606 | + | 0.923497i | \(0.625318\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −39.2843 | −1.45497 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.5754 | 0.613065 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.7248 | 0.802423 | 0.401211 | − | 0.915986i | \(-0.368589\pi\) | ||||
0.401211 | + | 0.915986i | \(0.368589\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.82843 | −0.251870 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.62742 | −0.244124 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.8632 | 0.914606 | 0.457303 | − | 0.889311i | \(-0.348815\pi\) | ||||
0.457303 | + | 0.889311i | \(0.348815\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.59767 | 0.205636 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.5147 | −1.00942 | −0.504709 | − | 0.863290i | \(-0.668400\pi\) | ||||
−0.504709 | + | 0.863290i | \(0.668400\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −43.3137 | −1.58689 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 50.0208 | 1.83017 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.5140 | −0.493790 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.4558 | 1.65871 | 0.829354 | − | 0.558724i | \(-0.188709\pi\) | ||||
0.829354 | + | 0.558724i | \(0.188709\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.14214 | 0.0780638 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 47.4077 | 1.72534 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.5445 | −0.819395 | −0.409697 | − | 0.912221i | \(-0.634366\pi\) | ||||
−0.409697 | + | 0.912221i | \(0.634366\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 38.6274 | 1.40209 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.9706 | −0.687682 | −0.343841 | − | 0.939028i | \(-0.611728\pi\) | ||||
−0.343841 | + | 0.939028i | \(0.611728\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.3492 | 0.410868 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −76.6004 | −2.76949 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.201010 | −0.00725806 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.2548 | 1.27132 | 0.635661 | − | 0.771968i | \(-0.280728\pi\) | ||||
0.635661 | + | 0.771968i | \(0.280728\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.3379 | 0.876508 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.73606 | 0.314214 | 0.157107 | − | 0.987582i | \(-0.449783\pi\) | ||||
0.157107 | + | 0.987582i | \(0.449783\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.3431 | 0.371537 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13.6569 | 0.489937 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.4721 | −0.626004 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.07241 | −0.181505 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −20.6863 | −0.739268 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.4853 | 0.445619 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.46796 | 0.266204 | 0.133102 | − | 0.991102i | \(-0.457506\pi\) | ||||
0.133102 | + | 0.991102i | \(0.457506\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.12293 | 0.217982 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.82843 | −0.313903 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.45584 | −0.193743 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 71.3742 | 2.53138 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27.4763 | 0.973260 | 0.486630 | − | 0.873608i | \(-0.338226\pi\) | ||||
0.486630 | + | 0.873608i | \(0.338226\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 61.2548 | 2.16704 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.65685 | 0.270542 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −25.2346 | −0.890509 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.8435 | 0.628902 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21.4558 | 0.755281 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.1716 | 1.09593 | 0.547967 | − | 0.836500i | \(-0.315402\pi\) | ||||
0.547967 | + | 0.836500i | \(0.315402\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.9819 | 0.736775 | 0.368388 | − | 0.929672i | \(-0.379910\pi\) | ||||
0.368388 | + | 0.929672i | \(0.379910\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.12293 | 0.214741 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.3431 | 0.362305 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.3431 | 0.361861 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.71644 | −0.0599774 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.65914 | −0.302206 | −0.151103 | − | 0.988518i | \(-0.548283\pi\) | ||||
−0.151103 | + | 0.988518i | \(0.548283\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.9706 | −1.42814 | −0.714072 | − | 0.700072i | \(-0.753151\pi\) | ||||
−0.714072 | + | 0.700072i | \(0.753151\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10.3431 | −0.360102 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.9778 | 0.381734 | 0.190867 | − | 0.981616i | \(-0.438870\pi\) | ||||
0.190867 | + | 0.981616i | \(0.438870\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.19986 | 0.215330 | 0.107665 | − | 0.994187i | \(-0.465663\pi\) | ||||
0.107665 | + | 0.994187i | \(0.465663\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −38.6274 | −1.33997 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.65685 | −0.265294 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −41.8100 | −1.44690 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −12.2459 | −0.423279 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.2843 | −1.25267 | −0.626336 | − | 0.779553i | \(-0.715446\pi\) | ||||
−0.626336 | + | 0.779553i | \(0.715446\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 62.3137 | 2.14875 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.22625 | −0.180002 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −33.4454 | −1.15056 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.31371 | 0.216942 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 54.4264 | 1.86791 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −35.6871 | −1.22334 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47.3308 | 1.62057 | 0.810287 | − | 0.586033i | \(-0.199311\pi\) | ||||
0.810287 | + | 0.586033i | \(0.199311\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −47.7990 | −1.63469 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.627417 | −0.0214322 | −0.0107161 | − | 0.999943i | \(-0.503411\pi\) | ||||
−0.0107161 | + | 0.999943i | \(0.503411\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.50981 | 0.119753 | 0.0598766 | − | 0.998206i | \(-0.480929\pi\) | ||||
0.0598766 | + | 0.998206i | \(0.480929\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.55582 | 0.325661 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −51.3137 | −1.74674 | −0.873369 | − | 0.487058i | \(-0.838070\pi\) | ||||
−0.873369 | + | 0.487058i | \(0.838070\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −42.1421 | −1.43288 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −108.778 | −3.69428 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.07241 | −0.172070 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.37258 | −0.0465082 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −38.2843 | −1.29573 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.28772 | 0.280176 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.2542 | 1.08915 | 0.544573 | − | 0.838713i | \(-0.316692\pi\) | ||||
0.544573 | + | 0.838713i | \(0.316692\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 28.4853 | 0.960785 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.9706 | 0.369608 | 0.184804 | − | 0.982775i | \(-0.440835\pi\) | ||||
0.184804 | + | 0.982775i | \(0.440835\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51.7373 | −1.74110 | −0.870549 | − | 0.492082i | \(-0.836236\pi\) | ||||
−0.870549 | + | 0.492082i | \(0.836236\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.06147 | 0.102910 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.6274 | 0.759754 | 0.379877 | − | 0.925037i | \(-0.375966\pi\) | ||||
0.379877 | + | 0.925037i | \(0.375966\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.48528 | 0.150432 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12.6173 | −0.422695 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 38.2233 | 1.27909 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −57.9411 | −1.93676 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.00000 | 0.267112 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 54.0559 | 1.80286 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 80.0333 | 2.66630 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.65685 | −0.188248 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.82843 | −0.226985 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.26810 | −0.0421066 | −0.0210533 | − | 0.999778i | \(-0.506702\pi\) | ||||
−0.0210533 | + | 0.999778i | \(0.506702\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.2919 | −0.606703 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.8284 | −1.28644 | −0.643222 | − | 0.765680i | \(-0.722403\pi\) | ||||
−0.643222 | + | 0.765680i | \(0.722403\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.2843 | 0.936073 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 83.0948 | 2.74703 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.2919 | 0.604051 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.34315 | −0.0772932 | −0.0386466 | − | 0.999253i | \(-0.512305\pi\) | ||||
−0.0386466 | + | 0.999253i | \(0.512305\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.8284 | −0.752222 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.05053 | −0.0345786 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.55582 | 0.314193 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −52.2843 | −1.71724 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.2843 | 0.337416 | 0.168708 | − | 0.985666i | \(-0.446041\pi\) | ||||
0.168708 | + | 0.985666i | \(0.446041\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.77791 | −0.156590 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 38.2233 | 1.25137 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −43.3137 | −1.41651 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.2843 | 1.25069 | 0.625346 | − | 0.780347i | \(-0.284958\pi\) | ||||
0.625346 | + | 0.780347i | \(0.284958\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.8017 | −0.711471 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.7749 | 1.23143 | 0.615714 | − | 0.787970i | \(-0.288868\pi\) | ||||
0.615714 | + | 0.787970i | \(0.288868\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.9706 | −0.813153 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.65685 | 0.184017 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −48.3044 | −1.56968 | −0.784841 | − | 0.619698i | \(-0.787255\pi\) | ||||
−0.784841 | + | 0.619698i | \(0.787255\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.22625 | −0.169651 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.6274 | −0.733744 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37.3137 | −1.20871 | −0.604355 | − | 0.796715i | \(-0.706569\pi\) | ||||
−0.604355 | + | 0.796715i | \(0.706569\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 50.4692 | 1.63314 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −54.0559 | −1.74738 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.00000 | 0.0645834 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 51.7373 | 1.66721 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 36.0585 | 1.16076 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.8579 | 0.960164 | 0.480082 | − | 0.877224i | \(-0.340607\pi\) | ||||
0.480082 | + | 0.877224i | \(0.340607\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −95.5980 | −3.07105 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52.5570 | 1.68663 | 0.843317 | − | 0.537416i | \(-0.180599\pi\) | ||||
0.843317 | + | 0.537416i | \(0.180599\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.5600 | −0.627064 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.14214 | −0.0686032 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.0000 | 0.959785 | 0.479893 | − | 0.877327i | \(-0.340676\pi\) | ||||
0.479893 | + | 0.877327i | \(0.340676\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.32957 | 0.138374 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −43.4495 | −1.38724 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23.0294 | −0.734525 | −0.367262 | − | 0.930117i | \(-0.619705\pi\) | ||||
−0.367262 | + | 0.930117i | \(0.619705\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.0000 | 0.509802 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −20.9050 | −0.665414 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.7821 | 0.470043 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.6569 | −0.942081 | −0.471041 | − | 0.882112i | \(-0.656121\pi\) | ||||
−0.471041 | + | 0.882112i | \(0.656121\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −48.9706 | −1.55403 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.4412 | −0.743136 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.0769232 | 0.00243618 | 0.00121809 | − | 0.999999i | \(-0.499612\pi\) | ||||
0.00121809 | + | 0.999999i | \(0.499612\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.3137 | −0.357950 |
(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 | 1792.2.a.u.1.1 | 4 | ||
4.3 | odd | 2 | 1792.2.a.w.1.4 | 4 | |||
8.3 | odd | 2 | 1792.2.a.w.1.1 | 4 | |||
8.5 | even | 2 | inner | 1792.2.a.u.1.4 | 4 | ||
16.3 | odd | 4 | 896.2.b.f.449.4 | yes | 4 | ||
16.5 | even | 4 | 896.2.b.h.449.4 | yes | 4 | ||
16.11 | odd | 4 | 896.2.b.f.449.1 | ✓ | 4 | ||
16.13 | even | 4 | 896.2.b.h.449.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.2.b.f.449.1 | ✓ | 4 | 16.11 | odd | 4 | ||
896.2.b.f.449.4 | yes | 4 | 16.3 | odd | 4 | ||
896.2.b.h.449.1 | yes | 4 | 16.13 | even | 4 | ||
896.2.b.h.449.4 | yes | 4 | 16.5 | even | 4 | ||
1792.2.a.u.1.1 | 4 | 1.1 | even | 1 | trivial | ||
1792.2.a.u.1.4 | 4 | 8.5 | even | 2 | inner | ||
1792.2.a.w.1.1 | 4 | 8.3 | odd | 2 | |||
1792.2.a.w.1.4 | 4 | 4.3 | odd | 2 |