Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1890,2,Mod(1,1890)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1890, 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("1890.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1890.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: | \(15.0917259820\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{97}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 24 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(5.42443\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1890.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −6.42443 | −1.93704 | −0.968519 | − | 0.248939i | \(-0.919918\pi\) | ||||
−0.968519 | + | 0.248939i | \(0.919918\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.42443 | 1.31562 | 0.657809 | − | 0.753185i | \(-0.271484\pi\) | ||||
0.657809 | + | 0.753185i | \(0.271484\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.42443 | 1.93270 | 0.966348 | − | 0.257237i | \(-0.0828122\pi\) | ||||
0.966348 | + | 0.257237i | \(0.0828122\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.42443 | 1.36969 | ||||||||
\(23\) | 3.42443 | 0.714043 | 0.357021 | − | 0.934096i | \(-0.383792\pi\) | ||||
0.357021 | + | 0.934096i | \(0.383792\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 3.42443 | 0.635900 | 0.317950 | − | 0.948107i | \(-0.397006\pi\) | ||||
0.317950 | + | 0.948107i | \(0.397006\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.42443 | −0.255835 | −0.127917 | − | 0.991785i | \(-0.540829\pi\) | ||||
−0.127917 | + | 0.991785i | \(0.540829\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.42443 | −0.930282 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.84886 | −1.45474 | −0.727372 | − | 0.686244i | \(-0.759258\pi\) | ||||
−0.727372 | + | 0.686244i | \(0.759258\pi\) | |||||||
\(38\) | −8.42443 | −1.36662 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −10.4244 | −1.62802 | −0.814011 | − | 0.580849i | \(-0.802721\pi\) | ||||
−0.814011 | + | 0.580849i | \(0.802721\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.00000 | −1.06749 | −0.533745 | − | 0.845645i | \(-0.679216\pi\) | ||||
−0.533745 | + | 0.845645i | \(0.679216\pi\) | |||||||
\(44\) | −6.42443 | −0.968519 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.42443 | −0.504904 | ||||||||
\(47\) | −10.4244 | −1.52056 | −0.760280 | − | 0.649596i | \(-0.774938\pi\) | ||||
−0.760280 | + | 0.649596i | \(0.774938\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | −5.00000 | −0.686803 | −0.343401 | − | 0.939189i | \(-0.611579\pi\) | ||||
−0.343401 | + | 0.939189i | \(0.611579\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.42443 | 0.866270 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.42443 | −0.449650 | ||||||||
\(59\) | −7.42443 | −0.966578 | −0.483289 | − | 0.875461i | \(-0.660558\pi\) | ||||
−0.483289 | + | 0.875461i | \(0.660558\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.8489 | 1.38905 | 0.694527 | − | 0.719467i | \(-0.255614\pi\) | ||||
0.694527 | + | 0.719467i | \(0.255614\pi\) | |||||||
\(62\) | 1.42443 | 0.180903 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.00000 | −0.366508 | −0.183254 | − | 0.983066i | \(-0.558663\pi\) | ||||
−0.183254 | + | 0.983066i | \(0.558663\pi\) | |||||||
\(68\) | 5.42443 | 0.657809 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −5.42443 | −0.643761 | −0.321881 | − | 0.946780i | \(-0.604315\pi\) | ||||
−0.321881 | + | 0.946780i | \(0.604315\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.42443 | 0.283758 | 0.141879 | − | 0.989884i | \(-0.454686\pi\) | ||||
0.141879 | + | 0.989884i | \(0.454686\pi\) | |||||||
\(74\) | 8.84886 | 1.02866 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.42443 | 0.966348 | ||||||||
\(77\) | 6.42443 | 0.732132 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.4244 | 1.15119 | ||||||||
\(83\) | −7.57557 | −0.831527 | −0.415763 | − | 0.909473i | \(-0.636486\pi\) | ||||
−0.415763 | + | 0.909473i | \(0.636486\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.42443 | −0.588362 | ||||||||
\(86\) | 7.00000 | 0.754829 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.42443 | 0.684846 | ||||||||
\(89\) | −1.00000 | −0.106000 | −0.0529999 | − | 0.998595i | \(-0.516878\pi\) | ||||
−0.0529999 | + | 0.998595i | \(0.516878\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 3.42443 | 0.357021 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.4244 | 1.07520 | ||||||||
\(95\) | −8.42443 | −0.864328 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0000 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 13.2733 | 1.32074 | 0.660371 | − | 0.750940i | \(-0.270399\pi\) | ||||
0.660371 | + | 0.750940i | \(0.270399\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.42443 | −0.928617 | −0.464308 | − | 0.885674i | \(-0.653697\pi\) | ||||
−0.464308 | + | 0.885674i | \(0.653697\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.00000 | 0.485643 | ||||||||
\(107\) | −2.84886 | −0.275409 | −0.137705 | − | 0.990473i | \(-0.543973\pi\) | ||||
−0.137705 | + | 0.990473i | \(0.543973\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.42443 | −0.232218 | −0.116109 | − | 0.993236i | \(-0.537042\pi\) | ||||
−0.116109 | + | 0.993236i | \(0.537042\pi\) | |||||||
\(110\) | −6.42443 | −0.612545 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −19.2733 | −1.81308 | −0.906539 | − | 0.422122i | \(-0.861285\pi\) | ||||
−0.906539 | + | 0.422122i | \(0.861285\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.42443 | −0.319330 | ||||||||
\(116\) | 3.42443 | 0.317950 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.42443 | 0.683474 | ||||||||
\(119\) | −5.42443 | −0.497257 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 30.2733 | 2.75212 | ||||||||
\(122\) | −10.8489 | −0.982209 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.42443 | −0.127917 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.5756 | −1.02717 | −0.513583 | − | 0.858040i | \(-0.671682\pi\) | ||||
−0.513583 | + | 0.858040i | \(0.671682\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.00000 | 0.0877058 | ||||||||
\(131\) | 20.2733 | 1.77129 | 0.885643 | − | 0.464367i | \(-0.153718\pi\) | ||||
0.885643 | + | 0.464367i | \(0.153718\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.42443 | −0.730491 | ||||||||
\(134\) | 3.00000 | 0.259161 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.42443 | −0.465141 | ||||||||
\(137\) | −2.42443 | −0.207133 | −0.103566 | − | 0.994623i | \(-0.533025\pi\) | ||||
−0.103566 | + | 0.994623i | \(0.533025\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.42443 | 0.455208 | ||||||||
\(143\) | −6.42443 | −0.537238 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.42443 | −0.284383 | ||||||||
\(146\) | −2.42443 | −0.200647 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.84886 | −0.727372 | ||||||||
\(149\) | −0.575571 | −0.0471526 | −0.0235763 | − | 0.999722i | \(-0.507505\pi\) | ||||
−0.0235763 | + | 0.999722i | \(0.507505\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.8489 | −1.37114 | −0.685570 | − | 0.728006i | \(-0.740447\pi\) | ||||
−0.685570 | + | 0.728006i | \(0.740447\pi\) | |||||||
\(152\) | −8.42443 | −0.683311 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.42443 | −0.517695 | ||||||||
\(155\) | 1.42443 | 0.114413 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.42443 | 0.592534 | 0.296267 | − | 0.955105i | \(-0.404258\pi\) | ||||
0.296267 | + | 0.955105i | \(0.404258\pi\) | |||||||
\(158\) | 8.00000 | 0.636446 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −3.42443 | −0.269883 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.57557 | −0.201734 | −0.100867 | − | 0.994900i | \(-0.532162\pi\) | ||||
−0.100867 | + | 0.994900i | \(0.532162\pi\) | |||||||
\(164\) | −10.4244 | −0.814011 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.57557 | 0.587978 | ||||||||
\(167\) | −1.15114 | −0.0890781 | −0.0445390 | − | 0.999008i | \(-0.514182\pi\) | ||||
−0.0445390 | + | 0.999008i | \(0.514182\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 5.42443 | 0.416035 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.00000 | −0.533745 | ||||||||
\(173\) | −18.0000 | −1.36851 | −0.684257 | − | 0.729241i | \(-0.739873\pi\) | ||||
−0.684257 | + | 0.729241i | \(0.739873\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −6.42443 | −0.484260 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.00000 | 0.0749532 | ||||||||
\(179\) | 21.2733 | 1.59004 | 0.795020 | − | 0.606583i | \(-0.207460\pi\) | ||||
0.795020 | + | 0.606583i | \(0.207460\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.2733 | −1.65556 | −0.827780 | − | 0.561053i | \(-0.810397\pi\) | ||||
−0.827780 | + | 0.561053i | \(0.810397\pi\) | |||||||
\(182\) | 1.00000 | 0.0741249 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.42443 | −0.252452 | ||||||||
\(185\) | 8.84886 | 0.650581 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −34.8489 | −2.54840 | ||||||||
\(188\) | −10.4244 | −0.760280 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.42443 | 0.611172 | ||||||||
\(191\) | 20.4244 | 1.47786 | 0.738930 | − | 0.673782i | \(-0.235331\pi\) | ||||
0.738930 | + | 0.673782i | \(0.235331\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.4244 | 1.11027 | 0.555137 | − | 0.831759i | \(-0.312666\pi\) | ||||
0.555137 | + | 0.831759i | \(0.312666\pi\) | |||||||
\(194\) | 10.0000 | 0.717958 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 22.4244 | 1.59767 | 0.798837 | − | 0.601547i | \(-0.205449\pi\) | ||||
0.798837 | + | 0.601547i | \(0.205449\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.00000 | −0.212664 | −0.106332 | − | 0.994331i | \(-0.533911\pi\) | ||||
−0.106332 | + | 0.994331i | \(0.533911\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −13.2733 | −0.933905 | ||||||||
\(203\) | −3.42443 | −0.240348 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.4244 | 0.728074 | ||||||||
\(206\) | 9.42443 | 0.656631 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −54.1221 | −3.74371 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.42443 | 0.511119 | 0.255559 | − | 0.966793i | \(-0.417740\pi\) | ||||
0.255559 | + | 0.966793i | \(0.417740\pi\) | |||||||
\(212\) | −5.00000 | −0.343401 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.84886 | 0.194744 | ||||||||
\(215\) | 7.00000 | 0.477396 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.42443 | 0.0966965 | ||||||||
\(218\) | 2.42443 | 0.164203 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.42443 | 0.433135 | ||||||||
\(221\) | 5.42443 | 0.364887 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.15114 | −0.478876 | −0.239438 | − | 0.970912i | \(-0.576963\pi\) | ||||
−0.239438 | + | 0.970912i | \(0.576963\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 19.2733 | 1.28204 | ||||||||
\(227\) | 11.0000 | 0.730096 | 0.365048 | − | 0.930989i | \(-0.381053\pi\) | ||||
0.365048 | + | 0.930989i | \(0.381053\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.00000 | 0.132164 | 0.0660819 | − | 0.997814i | \(-0.478950\pi\) | ||||
0.0660819 | + | 0.997814i | \(0.478950\pi\) | |||||||
\(230\) | 3.42443 | 0.225800 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.42443 | −0.224825 | ||||||||
\(233\) | 14.4244 | 0.944976 | 0.472488 | − | 0.881337i | \(-0.343356\pi\) | ||||
0.472488 | + | 0.881337i | \(0.343356\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.4244 | 0.680015 | ||||||||
\(236\) | −7.42443 | −0.483289 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.42443 | 0.351614 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.0000 | 1.03065 | 0.515325 | − | 0.856995i | \(-0.327671\pi\) | ||||
0.515325 | + | 0.856995i | \(0.327671\pi\) | |||||||
\(242\) | −30.2733 | −1.94604 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.8489 | 0.694527 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.42443 | 0.536034 | ||||||||
\(248\) | 1.42443 | 0.0904513 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 8.84886 | 0.558535 | 0.279267 | − | 0.960213i | \(-0.409908\pi\) | ||||
0.279267 | + | 0.960213i | \(0.409908\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −22.0000 | −1.38313 | ||||||||
\(254\) | 11.5756 | 0.726316 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.84886 | −0.427220 | −0.213610 | − | 0.976919i | \(-0.568522\pi\) | ||||
−0.213610 | + | 0.976919i | \(0.568522\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.84886 | 0.549841 | ||||||||
\(260\) | −1.00000 | −0.0620174 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −20.2733 | −1.25249 | ||||||||
\(263\) | −18.5756 | −1.14542 | −0.572709 | − | 0.819758i | \(-0.694108\pi\) | ||||
−0.572709 | + | 0.819758i | \(0.694108\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.00000 | 0.307148 | ||||||||
\(266\) | 8.42443 | 0.516535 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.00000 | −0.183254 | ||||||||
\(269\) | −8.84886 | −0.539524 | −0.269762 | − | 0.962927i | \(-0.586945\pi\) | ||||
−0.269762 | + | 0.962927i | \(0.586945\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.6977 | −1.37879 | −0.689394 | − | 0.724387i | \(-0.742123\pi\) | ||||
−0.689394 | + | 0.724387i | \(0.742123\pi\) | |||||||
\(272\) | 5.42443 | 0.328904 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.42443 | 0.146465 | ||||||||
\(275\) | −6.42443 | −0.387408 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.1511 | −0.670007 | −0.335004 | − | 0.942217i | \(-0.608738\pi\) | ||||
−0.335004 | + | 0.942217i | \(0.608738\pi\) | |||||||
\(278\) | 4.00000 | 0.239904 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | 3.15114 | 0.187981 | 0.0939907 | − | 0.995573i | \(-0.470038\pi\) | ||||
0.0939907 | + | 0.995573i | \(0.470038\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.0000 | 1.30776 | 0.653882 | − | 0.756596i | \(-0.273139\pi\) | ||||
0.653882 | + | 0.756596i | \(0.273139\pi\) | |||||||
\(284\) | −5.42443 | −0.321881 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.42443 | 0.379884 | ||||||||
\(287\) | 10.4244 | 0.615335 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.4244 | 0.730849 | ||||||||
\(290\) | 3.42443 | 0.201089 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.42443 | 0.141879 | ||||||||
\(293\) | −18.0000 | −1.05157 | −0.525786 | − | 0.850617i | \(-0.676229\pi\) | ||||
−0.525786 | + | 0.850617i | \(0.676229\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.42443 | 0.432267 | ||||||||
\(296\) | 8.84886 | 0.514329 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.575571 | 0.0333419 | ||||||||
\(299\) | 3.42443 | 0.198040 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.00000 | 0.403473 | ||||||||
\(302\) | 16.8489 | 0.969543 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.42443 | 0.483174 | ||||||||
\(305\) | −10.8489 | −0.621204 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.0000 | −0.913168 | −0.456584 | − | 0.889680i | \(-0.650927\pi\) | ||||
−0.456584 | + | 0.889680i | \(0.650927\pi\) | |||||||
\(308\) | 6.42443 | 0.366066 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.42443 | −0.0809021 | ||||||||
\(311\) | −27.6977 | −1.57059 | −0.785297 | − | 0.619120i | \(-0.787490\pi\) | ||||
−0.785297 | + | 0.619120i | \(0.787490\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.2733 | −0.750251 | −0.375125 | − | 0.926974i | \(-0.622400\pi\) | ||||
−0.375125 | + | 0.926974i | \(0.622400\pi\) | |||||||
\(314\) | −7.42443 | −0.418985 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | 21.5756 | 1.21180 | 0.605902 | − | 0.795539i | \(-0.292812\pi\) | ||||
0.605902 | + | 0.795539i | \(0.292812\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.0000 | −1.23176 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.42443 | 0.190836 | ||||||||
\(323\) | 45.6977 | 2.54269 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 2.57557 | 0.142648 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10.4244 | 0.575593 | ||||||||
\(329\) | 10.4244 | 0.574717 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.1221 | −1.38084 | −0.690419 | − | 0.723410i | \(-0.742574\pi\) | ||||
−0.690419 | + | 0.723410i | \(0.742574\pi\) | |||||||
\(332\) | −7.57557 | −0.415763 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.15114 | 0.0629877 | ||||||||
\(335\) | 3.00000 | 0.163908 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.27329 | −0.232781 | −0.116390 | − | 0.993204i | \(-0.537132\pi\) | ||||
−0.116390 | + | 0.993204i | \(0.537132\pi\) | |||||||
\(338\) | 12.0000 | 0.652714 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.42443 | −0.294181 | ||||||||
\(341\) | 9.15114 | 0.495562 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 7.00000 | 0.377415 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.0000 | 0.967686 | ||||||||
\(347\) | −19.6977 | −1.05743 | −0.528714 | − | 0.848800i | \(-0.677326\pi\) | ||||
−0.528714 | + | 0.848800i | \(0.677326\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.4244 | −1.25388 | −0.626940 | − | 0.779067i | \(-0.715693\pi\) | ||||
−0.626940 | + | 0.779067i | \(0.715693\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.42443 | 0.342423 | ||||||||
\(353\) | −17.4244 | −0.927409 | −0.463704 | − | 0.885990i | \(-0.653480\pi\) | ||||
−0.463704 | + | 0.885990i | \(0.653480\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.42443 | 0.287899 | ||||||||
\(356\) | −1.00000 | −0.0529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −21.2733 | −1.12433 | ||||||||
\(359\) | 23.8489 | 1.25869 | 0.629347 | − | 0.777124i | \(-0.283322\pi\) | ||||
0.629347 | + | 0.777124i | \(0.283322\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 51.9710 | 2.73532 | ||||||||
\(362\) | 22.2733 | 1.17066 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.00000 | −0.0524142 | ||||||||
\(365\) | −2.42443 | −0.126900 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.27329 | 0.118665 | 0.0593323 | − | 0.998238i | \(-0.481103\pi\) | ||||
0.0593323 | + | 0.998238i | \(0.481103\pi\) | |||||||
\(368\) | 3.42443 | 0.178511 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.84886 | −0.460030 | ||||||||
\(371\) | 5.00000 | 0.259587 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.69772 | −0.502129 | −0.251064 | − | 0.967970i | \(-0.580781\pi\) | ||||
−0.251064 | + | 0.967970i | \(0.580781\pi\) | |||||||
\(374\) | 34.8489 | 1.80199 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.4244 | 0.537599 | ||||||||
\(377\) | 3.42443 | 0.176367 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −37.6977 | −1.93640 | −0.968201 | − | 0.250174i | \(-0.919512\pi\) | ||||
−0.968201 | + | 0.250174i | \(0.919512\pi\) | |||||||
\(380\) | −8.42443 | −0.432164 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −20.4244 | −1.04500 | ||||||||
\(383\) | 8.00000 | 0.408781 | 0.204390 | − | 0.978889i | \(-0.434479\pi\) | ||||
0.204390 | + | 0.978889i | \(0.434479\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.42443 | −0.327419 | ||||||||
\(386\) | −15.4244 | −0.785083 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.0000 | −0.507673 | ||||||||
\(389\) | 31.6977 | 1.60714 | 0.803569 | − | 0.595212i | \(-0.202932\pi\) | ||||
0.803569 | + | 0.595212i | \(0.202932\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.5756 | 0.939407 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −22.4244 | −1.12973 | ||||||||
\(395\) | 8.00000 | 0.402524 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.6977 | 0.587092 | 0.293546 | − | 0.955945i | \(-0.405165\pi\) | ||||
0.293546 | + | 0.955945i | \(0.405165\pi\) | |||||||
\(398\) | 3.00000 | 0.150376 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 5.15114 | 0.257236 | 0.128618 | − | 0.991694i | \(-0.458946\pi\) | ||||
0.128618 | + | 0.991694i | \(0.458946\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.42443 | −0.0709559 | ||||||||
\(404\) | 13.2733 | 0.660371 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.42443 | 0.169952 | ||||||||
\(407\) | 56.8489 | 2.81789 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.69772 | −0.380628 | −0.190314 | − | 0.981723i | \(-0.560951\pi\) | ||||
−0.190314 | + | 0.981723i | \(0.560951\pi\) | |||||||
\(410\) | −10.4244 | −0.514826 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.42443 | −0.464308 | ||||||||
\(413\) | 7.42443 | 0.365332 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.57557 | 0.371870 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 54.1221 | 2.64720 | ||||||||
\(419\) | 2.27329 | 0.111057 | 0.0555287 | − | 0.998457i | \(-0.482316\pi\) | ||||
0.0555287 | + | 0.998457i | \(0.482316\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.2733 | 1.71911 | 0.859557 | − | 0.511039i | \(-0.170739\pi\) | ||||
0.859557 | + | 0.511039i | \(0.170739\pi\) | |||||||
\(422\) | −7.42443 | −0.361416 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.00000 | 0.242821 | ||||||||
\(425\) | 5.42443 | 0.263123 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.8489 | −0.525013 | ||||||||
\(428\) | −2.84886 | −0.137705 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.00000 | −0.337570 | ||||||||
\(431\) | −37.2733 | −1.79539 | −0.897696 | − | 0.440616i | \(-0.854760\pi\) | ||||
−0.897696 | + | 0.440616i | \(0.854760\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.2733 | −1.59901 | −0.799506 | − | 0.600658i | \(-0.794905\pi\) | ||||
−0.799506 | + | 0.600658i | \(0.794905\pi\) | |||||||
\(434\) | −1.42443 | −0.0683748 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.42443 | −0.116109 | ||||||||
\(437\) | 28.8489 | 1.38003 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.1511 | −0.675397 | −0.337699 | − | 0.941254i | \(-0.609648\pi\) | ||||
−0.337699 | + | 0.941254i | \(0.609648\pi\) | |||||||
\(440\) | −6.42443 | −0.306273 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.42443 | −0.258014 | ||||||||
\(443\) | −5.69772 | −0.270707 | −0.135353 | − | 0.990797i | \(-0.543217\pi\) | ||||
−0.135353 | + | 0.990797i | \(0.543217\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.00000 | 0.0474045 | ||||||||
\(446\) | 7.15114 | 0.338616 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −13.6977 | −0.646435 | −0.323218 | − | 0.946325i | \(-0.604765\pi\) | ||||
−0.323218 | + | 0.946325i | \(0.604765\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 66.9710 | 3.15354 | ||||||||
\(452\) | −19.2733 | −0.906539 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11.0000 | −0.516256 | ||||||||
\(455\) | 1.00000 | 0.0468807 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.4244 | 0.815080 | 0.407540 | − | 0.913187i | \(-0.366387\pi\) | ||||
0.407540 | + | 0.913187i | \(0.366387\pi\) | |||||||
\(458\) | −2.00000 | −0.0934539 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.42443 | −0.159665 | ||||||||
\(461\) | 26.4244 | 1.23071 | 0.615354 | − | 0.788251i | \(-0.289013\pi\) | ||||
0.615354 | + | 0.788251i | \(0.289013\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 42.9710 | 1.99703 | 0.998516 | − | 0.0544606i | \(-0.0173439\pi\) | ||||
0.998516 | + | 0.0544606i | \(0.0173439\pi\) | |||||||
\(464\) | 3.42443 | 0.158975 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.4244 | −0.668199 | ||||||||
\(467\) | 12.0000 | 0.555294 | 0.277647 | − | 0.960683i | \(-0.410445\pi\) | ||||
0.277647 | + | 0.960683i | \(0.410445\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.00000 | 0.138527 | ||||||||
\(470\) | −10.4244 | −0.480843 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.42443 | 0.341737 | ||||||||
\(473\) | 44.9710 | 2.06777 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.42443 | 0.386539 | ||||||||
\(476\) | −5.42443 | −0.248628 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.00000 | −0.365529 | −0.182765 | − | 0.983157i | \(-0.558505\pi\) | ||||
−0.182765 | + | 0.983157i | \(0.558505\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.84886 | −0.403473 | ||||||||
\(482\) | −16.0000 | −0.728780 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 30.2733 | 1.37606 | ||||||||
\(485\) | 10.0000 | 0.454077 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.42443 | −0.291119 | −0.145559 | − | 0.989350i | \(-0.546498\pi\) | ||||
−0.145559 | + | 0.989350i | \(0.546498\pi\) | |||||||
\(488\) | −10.8489 | −0.491105 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | 17.6977 | 0.798687 | 0.399343 | − | 0.916801i | \(-0.369238\pi\) | ||||
0.399343 | + | 0.916801i | \(0.369238\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.5756 | 0.836602 | ||||||||
\(494\) | −8.42443 | −0.379033 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.42443 | −0.0639587 | ||||||||
\(497\) | 5.42443 | 0.243319 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.15114 | −0.141064 | −0.0705322 | − | 0.997509i | \(-0.522470\pi\) | ||||
−0.0705322 | + | 0.997509i | \(0.522470\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8.84886 | −0.394944 | ||||||||
\(503\) | −28.9710 | −1.29175 | −0.645877 | − | 0.763442i | \(-0.723508\pi\) | ||||
−0.645877 | + | 0.763442i | \(0.723508\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.2733 | −0.590654 | ||||||||
\(506\) | 22.0000 | 0.978019 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.5756 | −0.513583 | ||||||||
\(509\) | 3.15114 | 0.139672 | 0.0698360 | − | 0.997558i | \(-0.477752\pi\) | ||||
0.0698360 | + | 0.997558i | \(0.477752\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.42443 | −0.107250 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.84886 | 0.302090 | ||||||||
\(515\) | 9.42443 | 0.415290 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 66.9710 | 2.94538 | ||||||||
\(518\) | −8.84886 | −0.388796 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.00000 | 0.0438529 | ||||||||
\(521\) | −21.0000 | −0.920027 | −0.460013 | − | 0.887912i | \(-0.652155\pi\) | ||||
−0.460013 | + | 0.887912i | \(0.652155\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.8489 | 0.561841 | 0.280921 | − | 0.959731i | \(-0.409360\pi\) | ||||
0.280921 | + | 0.959731i | \(0.409360\pi\) | |||||||
\(524\) | 20.2733 | 0.885643 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.5756 | 0.809933 | ||||||||
\(527\) | −7.72671 | −0.336581 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.2733 | −0.490143 | ||||||||
\(530\) | −5.00000 | −0.217186 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.42443 | −0.365245 | ||||||||
\(533\) | −10.4244 | −0.451532 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.84886 | 0.123167 | ||||||||
\(536\) | 3.00000 | 0.129580 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.84886 | 0.381501 | ||||||||
\(539\) | −6.42443 | −0.276720 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.7267 | 0.547164 | 0.273582 | − | 0.961849i | \(-0.411791\pi\) | ||||
0.273582 | + | 0.961849i | \(0.411791\pi\) | |||||||
\(542\) | 22.6977 | 0.974950 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.42443 | −0.232570 | ||||||||
\(545\) | 2.42443 | 0.103851 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.6977 | −1.26978 | −0.634891 | − | 0.772601i | \(-0.718955\pi\) | ||||
−0.634891 | + | 0.772601i | \(0.718955\pi\) | |||||||
\(548\) | −2.42443 | −0.103566 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.42443 | 0.273939 | ||||||||
\(551\) | 28.8489 | 1.22900 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.00000 | 0.340195 | ||||||||
\(554\) | 11.1511 | 0.473767 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.00000 | −0.169638 | ||||||||
\(557\) | 10.2733 | 0.435293 | 0.217647 | − | 0.976028i | \(-0.430162\pi\) | ||||
0.217647 | + | 0.976028i | \(0.430162\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.00000 | −0.296068 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.15114 | −0.132923 | ||||||||
\(563\) | −5.00000 | −0.210725 | −0.105362 | − | 0.994434i | \(-0.533600\pi\) | ||||
−0.105362 | + | 0.994434i | \(0.533600\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.2733 | 0.810833 | ||||||||
\(566\) | −22.0000 | −0.924729 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.42443 | 0.227604 | ||||||||
\(569\) | 27.6977 | 1.16115 | 0.580574 | − | 0.814207i | \(-0.302828\pi\) | ||||
0.580574 | + | 0.814207i | \(0.302828\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.2733 | −1.01581 | −0.507903 | − | 0.861414i | \(-0.669579\pi\) | ||||
−0.507903 | + | 0.861414i | \(0.669579\pi\) | |||||||
\(572\) | −6.42443 | −0.268619 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10.4244 | −0.435107 | ||||||||
\(575\) | 3.42443 | 0.142809 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.2733 | −1.38519 | −0.692593 | − | 0.721329i | \(-0.743532\pi\) | ||||
−0.692593 | + | 0.721329i | \(0.743532\pi\) | |||||||
\(578\) | −12.4244 | −0.516788 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.42443 | −0.142192 | ||||||||
\(581\) | 7.57557 | 0.314288 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 32.1221 | 1.33036 | ||||||||
\(584\) | −2.42443 | −0.100324 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.0000 | 0.743573 | ||||||||
\(587\) | 4.27329 | 0.176377 | 0.0881887 | − | 0.996104i | \(-0.471892\pi\) | ||||
0.0881887 | + | 0.996104i | \(0.471892\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.0000 | −0.494451 | ||||||||
\(590\) | −7.42443 | −0.305659 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.84886 | −0.363686 | ||||||||
\(593\) | 38.8489 | 1.59533 | 0.797666 | − | 0.603100i | \(-0.206068\pi\) | ||||
0.797666 | + | 0.603100i | \(0.206068\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.42443 | 0.222380 | ||||||||
\(596\) | −0.575571 | −0.0235763 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.42443 | −0.140035 | ||||||||
\(599\) | −29.8489 | −1.21959 | −0.609796 | − | 0.792559i | \(-0.708748\pi\) | ||||
−0.609796 | + | 0.792559i | \(0.708748\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.0000 | 1.14214 | 0.571072 | − | 0.820900i | \(-0.306528\pi\) | ||||
0.571072 | + | 0.820900i | \(0.306528\pi\) | |||||||
\(602\) | −7.00000 | −0.285299 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −16.8489 | −0.685570 | ||||||||
\(605\) | −30.2733 | −1.23078 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −39.4244 | −1.60019 | −0.800094 | − | 0.599875i | \(-0.795217\pi\) | ||||
−0.800094 | + | 0.599875i | \(0.795217\pi\) | |||||||
\(608\) | −8.42443 | −0.341656 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.8489 | 0.439257 | ||||||||
\(611\) | −10.4244 | −0.421727 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.30228 | 0.254547 | 0.127273 | − | 0.991868i | \(-0.459377\pi\) | ||||
0.127273 | + | 0.991868i | \(0.459377\pi\) | |||||||
\(614\) | 16.0000 | 0.645707 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.42443 | −0.258848 | ||||||||
\(617\) | 10.0000 | 0.402585 | 0.201292 | − | 0.979531i | \(-0.435486\pi\) | ||||
0.201292 | + | 0.979531i | \(0.435486\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.7267 | 0.511530 | 0.255765 | − | 0.966739i | \(-0.417673\pi\) | ||||
0.255765 | + | 0.966739i | \(0.417673\pi\) | |||||||
\(620\) | 1.42443 | 0.0572064 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 27.6977 | 1.11058 | ||||||||
\(623\) | 1.00000 | 0.0400642 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 13.2733 | 0.530507 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.42443 | 0.296267 | ||||||||
\(629\) | −48.0000 | −1.91389 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.8489 | −0.989217 | −0.494609 | − | 0.869116i | \(-0.664689\pi\) | ||||
−0.494609 | + | 0.869116i | \(0.664689\pi\) | |||||||
\(632\) | 8.00000 | 0.318223 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −21.5756 | −0.856875 | ||||||||
\(635\) | 11.5756 | 0.459363 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 22.0000 | 0.870988 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 10.8489 | 0.428504 | 0.214252 | − | 0.976778i | \(-0.431269\pi\) | ||||
0.214252 | + | 0.976778i | \(0.431269\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −36.5466 | −1.44126 | −0.720628 | − | 0.693322i | \(-0.756146\pi\) | ||||
−0.720628 | + | 0.693322i | \(0.756146\pi\) | |||||||
\(644\) | −3.42443 | −0.134941 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −45.6977 | −1.79795 | ||||||||
\(647\) | −10.4244 | −0.409827 | −0.204913 | − | 0.978780i | \(-0.565691\pi\) | ||||
−0.204913 | + | 0.978780i | \(0.565691\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 47.6977 | 1.87230 | ||||||||
\(650\) | −1.00000 | −0.0392232 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.57557 | −0.100867 | ||||||||
\(653\) | −18.2733 | −0.715089 | −0.357544 | − | 0.933896i | \(-0.616386\pi\) | ||||
−0.357544 | + | 0.933896i | \(0.616386\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.2733 | −0.792143 | ||||||||
\(656\) | −10.4244 | −0.407006 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −10.4244 | −0.406387 | ||||||||
\(659\) | −8.54657 | −0.332927 | −0.166464 | − | 0.986048i | \(-0.553235\pi\) | ||||
−0.166464 | + | 0.986048i | \(0.553235\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.30228 | 0.322921 | 0.161461 | − | 0.986879i | \(-0.448379\pi\) | ||||
0.161461 | + | 0.986879i | \(0.448379\pi\) | |||||||
\(662\) | 25.1221 | 0.976400 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.57557 | 0.293989 | ||||||||
\(665\) | 8.42443 | 0.326685 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.7267 | 0.454060 | ||||||||
\(668\) | −1.15114 | −0.0445390 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.00000 | −0.115900 | ||||||||
\(671\) | −69.6977 | −2.69065 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.1221 | 1.66224 | 0.831118 | − | 0.556096i | \(-0.187701\pi\) | ||||
0.831118 | + | 0.556096i | \(0.187701\pi\) | |||||||
\(674\) | 4.27329 | 0.164601 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.0000 | −0.461538 | ||||||||
\(677\) | −30.5466 | −1.17400 | −0.587000 | − | 0.809587i | \(-0.699691\pi\) | ||||
−0.587000 | + | 0.809587i | \(0.699691\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.0000 | 0.383765 | ||||||||
\(680\) | 5.42443 | 0.208017 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9.15114 | −0.350415 | ||||||||
\(683\) | −23.6977 | −0.906768 | −0.453384 | − | 0.891315i | \(-0.649783\pi\) | ||||
−0.453384 | + | 0.891315i | \(0.649783\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.42443 | 0.0926327 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.00000 | −0.266872 | ||||||||
\(689\) | −5.00000 | −0.190485 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 51.8199 | 1.97132 | 0.985660 | − | 0.168742i | \(-0.0539706\pi\) | ||||
0.985660 | + | 0.168742i | \(0.0539706\pi\) | |||||||
\(692\) | −18.0000 | −0.684257 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19.6977 | 0.747715 | ||||||||
\(695\) | 4.00000 | 0.151729 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −56.5466 | −2.14185 | ||||||||
\(698\) | 23.4244 | 0.886628 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | 8.54657 | 0.322800 | 0.161400 | − | 0.986889i | \(-0.448399\pi\) | ||||
0.161400 | + | 0.986889i | \(0.448399\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −74.5466 | −2.81158 | ||||||||
\(704\) | −6.42443 | −0.242130 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17.4244 | 0.655777 | ||||||||
\(707\) | −13.2733 | −0.499193 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.12214 | 0.305034 | 0.152517 | − | 0.988301i | \(-0.451262\pi\) | ||||
0.152517 | + | 0.988301i | \(0.451262\pi\) | |||||||
\(710\) | −5.42443 | −0.203575 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.00000 | 0.0374766 | ||||||||
\(713\) | −4.87786 | −0.182677 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.42443 | 0.240260 | ||||||||
\(716\) | 21.2733 | 0.795020 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −23.8489 | −0.890031 | ||||||||
\(719\) | 6.84886 | 0.255419 | 0.127710 | − | 0.991812i | \(-0.459237\pi\) | ||||
0.127710 | + | 0.991812i | \(0.459237\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.42443 | 0.350984 | ||||||||
\(722\) | −51.9710 | −1.93416 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −22.2733 | −0.827780 | ||||||||
\(725\) | 3.42443 | 0.127180 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.72671 | 0.138216 | 0.0691081 | − | 0.997609i | \(-0.477985\pi\) | ||||
0.0691081 | + | 0.997609i | \(0.477985\pi\) | |||||||
\(728\) | 1.00000 | 0.0370625 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.42443 | 0.0897321 | ||||||||
\(731\) | −37.9710 | −1.40441 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.84886 | 0.142161 | 0.0710804 | − | 0.997471i | \(-0.477355\pi\) | ||||
0.0710804 | + | 0.997471i | \(0.477355\pi\) | |||||||
\(734\) | −2.27329 | −0.0839085 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.42443 | −0.126226 | ||||||||
\(737\) | 19.2733 | 0.709941 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.0000 | 1.17714 | 0.588570 | − | 0.808447i | \(-0.299691\pi\) | ||||
0.588570 | + | 0.808447i | \(0.299691\pi\) | |||||||
\(740\) | 8.84886 | 0.325290 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.00000 | −0.183556 | ||||||||
\(743\) | 25.1221 | 0.921642 | 0.460821 | − | 0.887493i | \(-0.347555\pi\) | ||||
0.460821 | + | 0.887493i | \(0.347555\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.575571 | 0.0210873 | ||||||||
\(746\) | 9.69772 | 0.355059 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −34.8489 | −1.27420 | ||||||||
\(749\) | 2.84886 | 0.104095 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.1511 | −0.406911 | −0.203455 | − | 0.979084i | \(-0.565217\pi\) | ||||
−0.203455 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(752\) | −10.4244 | −0.380140 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.42443 | −0.124710 | ||||||||
\(755\) | 16.8489 | 0.613193 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.3954 | 1.43185 | 0.715926 | − | 0.698177i | \(-0.246005\pi\) | ||||
0.715926 | + | 0.698177i | \(0.246005\pi\) | |||||||
\(758\) | 37.6977 | 1.36924 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.42443 | 0.305586 | ||||||||
\(761\) | 12.5756 | 0.455864 | 0.227932 | − | 0.973677i | \(-0.426804\pi\) | ||||
0.227932 | + | 0.973677i | \(0.426804\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.42443 | 0.0877702 | ||||||||
\(764\) | 20.4244 | 0.738930 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.00000 | −0.289052 | ||||||||
\(767\) | −7.42443 | −0.268081 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.5466 | 0.885172 | 0.442586 | − | 0.896726i | \(-0.354061\pi\) | ||||
0.442586 | + | 0.896726i | \(0.354061\pi\) | |||||||
\(770\) | 6.42443 | 0.231520 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 15.4244 | 0.555137 | ||||||||
\(773\) | 16.8489 | 0.606011 | 0.303006 | − | 0.952989i | \(-0.402010\pi\) | ||||
0.303006 | + | 0.952989i | \(0.402010\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.42443 | −0.0511670 | ||||||||
\(776\) | 10.0000 | 0.358979 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −31.6977 | −1.13642 | ||||||||
\(779\) | −87.8199 | −3.14647 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34.8489 | 1.24699 | ||||||||
\(782\) | −18.5756 | −0.664261 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −7.42443 | −0.264989 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.8489 | −0.671889 | −0.335945 | − | 0.941882i | \(-0.609055\pi\) | ||||
−0.335945 | + | 0.941882i | \(0.609055\pi\) | |||||||
\(788\) | 22.4244 | 0.798837 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.00000 | −0.284627 | ||||||||
\(791\) | 19.2733 | 0.685279 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.8489 | 0.385254 | ||||||||
\(794\) | −11.6977 | −0.415136 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.00000 | −0.106332 | ||||||||
\(797\) | −44.5466 | −1.57792 | −0.788960 | − | 0.614444i | \(-0.789380\pi\) | ||||
−0.788960 | + | 0.614444i | \(0.789380\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −56.5466 | −2.00047 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5.15114 | −0.181893 | ||||||||
\(803\) | −15.5756 | −0.549650 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.42443 | 0.120695 | ||||||||
\(806\) | 1.42443 | 0.0501734 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.2733 | −0.466953 | ||||||||
\(809\) | −28.8489 | −1.01427 | −0.507136 | − | 0.861866i | \(-0.669296\pi\) | ||||
−0.507136 | + | 0.861866i | \(0.669296\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.9710 | 1.43869 | 0.719343 | − | 0.694655i | \(-0.244443\pi\) | ||||
0.719343 | + | 0.694655i | \(0.244443\pi\) | |||||||
\(812\) | −3.42443 | −0.120174 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −56.8489 | −1.99255 | ||||||||
\(815\) | 2.57557 | 0.0902183 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −58.9710 | −2.06313 | ||||||||
\(818\) | 7.69772 | 0.269144 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.4244 | 0.364037 | ||||||||
\(821\) | 12.5756 | 0.438890 | 0.219445 | − | 0.975625i | \(-0.429575\pi\) | ||||
0.219445 | + | 0.975625i | \(0.429575\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.2733 | 0.880971 | 0.440486 | − | 0.897760i | \(-0.354806\pi\) | ||||
0.440486 | + | 0.897760i | \(0.354806\pi\) | |||||||
\(824\) | 9.42443 | 0.328316 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.42443 | −0.258329 | ||||||||
\(827\) | −36.5466 | −1.27085 | −0.635424 | − | 0.772163i | \(-0.719175\pi\) | ||||
−0.635424 | + | 0.772163i | \(0.719175\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.8489 | 1.34928 | 0.674638 | − | 0.738148i | \(-0.264300\pi\) | ||||
0.674638 | + | 0.738148i | \(0.264300\pi\) | |||||||
\(830\) | −7.57557 | −0.262952 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 5.42443 | 0.187945 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.15114 | 0.0398369 | ||||||||
\(836\) | −54.1221 | −1.87185 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.27329 | −0.0785294 | ||||||||
\(839\) | 0.848858 | 0.0293058 | 0.0146529 | − | 0.999893i | \(-0.495336\pi\) | ||||
0.0146529 | + | 0.999893i | \(0.495336\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.2733 | −0.595631 | ||||||||
\(842\) | −35.2733 | −1.21560 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.42443 | 0.255559 | ||||||||
\(845\) | 12.0000 | 0.412813 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −30.2733 | −1.04020 | ||||||||
\(848\) | −5.00000 | −0.171701 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.42443 | −0.186056 | ||||||||
\(851\) | −30.3023 | −1.03875 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.2733 | −0.625665 | −0.312833 | − | 0.949808i | \(-0.601278\pi\) | ||||
−0.312833 | + | 0.949808i | \(0.601278\pi\) | |||||||
\(854\) | 10.8489 | 0.371240 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.84886 | 0.0973720 | ||||||||
\(857\) | −18.2733 | −0.624204 | −0.312102 | − | 0.950049i | \(-0.601033\pi\) | ||||
−0.312102 | + | 0.950049i | \(0.601033\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.5756 | −0.531432 | −0.265716 | − | 0.964051i | \(-0.585608\pi\) | ||||
−0.265716 | + | 0.964051i | \(0.585608\pi\) | |||||||
\(860\) | 7.00000 | 0.238698 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 37.2733 | 1.26953 | ||||||||
\(863\) | 50.2733 | 1.71132 | 0.855661 | − | 0.517536i | \(-0.173151\pi\) | ||||
0.855661 | + | 0.517536i | \(0.173151\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.0000 | 0.612018 | ||||||||
\(866\) | 33.2733 | 1.13067 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.42443 | 0.0483483 | ||||||||
\(869\) | 51.3954 | 1.74347 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.00000 | −0.101651 | ||||||||
\(872\) | 2.42443 | 0.0821015 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −28.8489 | −0.975827 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.0000 | 1.08056 | 0.540282 | − | 0.841484i | \(-0.318318\pi\) | ||||
0.540282 | + | 0.841484i | \(0.318318\pi\) | |||||||
\(878\) | 14.1511 | 0.477578 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.42443 | 0.216567 | ||||||||
\(881\) | 26.2733 | 0.885170 | 0.442585 | − | 0.896727i | \(-0.354062\pi\) | ||||
0.442585 | + | 0.896727i | \(0.354062\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.4244 | −0.586379 | −0.293189 | − | 0.956054i | \(-0.594717\pi\) | ||||
−0.293189 | + | 0.956054i | \(0.594717\pi\) | |||||||
\(884\) | 5.42443 | 0.182443 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.69772 | 0.191418 | ||||||||
\(887\) | 2.12214 | 0.0712546 | 0.0356273 | − | 0.999365i | \(-0.488657\pi\) | ||||
0.0356273 | + | 0.999365i | \(0.488657\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.5756 | 0.388232 | ||||||||
\(890\) | −1.00000 | −0.0335201 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.15114 | −0.239438 | ||||||||
\(893\) | −87.8199 | −2.93878 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.2733 | −0.711088 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 13.6977 | 0.457099 | ||||||||
\(899\) | −4.87786 | −0.162686 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27.1221 | −0.903570 | ||||||||
\(902\) | −66.9710 | −2.22989 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.2733 | 0.641020 | ||||||||
\(905\) | 22.2733 | 0.740389 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52.6687 | 1.74884 | 0.874418 | − | 0.485173i | \(-0.161243\pi\) | ||||
0.874418 | + | 0.485173i | \(0.161243\pi\) | |||||||
\(908\) | 11.0000 | 0.365048 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.00000 | −0.0331497 | ||||||||
\(911\) | 5.27329 | 0.174712 | 0.0873559 | − | 0.996177i | \(-0.472158\pi\) | ||||
0.0873559 | + | 0.996177i | \(0.472158\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 48.6687 | 1.61070 | ||||||||
\(914\) | −17.4244 | −0.576349 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.00000 | 0.0660819 | ||||||||
\(917\) | −20.2733 | −0.669483 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.8489 | −1.14956 | −0.574779 | − | 0.818309i | \(-0.694912\pi\) | ||||
−0.574779 | + | 0.818309i | \(0.694912\pi\) | |||||||
\(920\) | 3.42443 | 0.112900 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −26.4244 | −0.870242 | ||||||||
\(923\) | −5.42443 | −0.178547 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.84886 | −0.290949 | ||||||||
\(926\) | −42.9710 | −1.41211 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.42443 | −0.112412 | ||||||||
\(929\) | 24.1221 | 0.791422 | 0.395711 | − | 0.918375i | \(-0.370498\pi\) | ||||
0.395711 | + | 0.918375i | \(0.370498\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.42443 | 0.276100 | ||||||||
\(932\) | 14.4244 | 0.472488 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12.0000 | −0.392652 | ||||||||
\(935\) | 34.8489 | 1.13968 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.42443 | 0.0792026 | 0.0396013 | − | 0.999216i | \(-0.487391\pi\) | ||||
0.0396013 | + | 0.999216i | \(0.487391\pi\) | |||||||
\(938\) | −3.00000 | −0.0979535 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 10.4244 | 0.340007 | ||||||||
\(941\) | −4.72671 | −0.154086 | −0.0770432 | − | 0.997028i | \(-0.524548\pi\) | ||||
−0.0770432 | + | 0.997028i | \(0.524548\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −35.6977 | −1.16248 | ||||||||
\(944\) | −7.42443 | −0.241645 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −44.9710 | −1.46213 | ||||||||
\(947\) | 49.6977 | 1.61496 | 0.807479 | − | 0.589896i | \(-0.200831\pi\) | ||||
0.807479 | + | 0.589896i | \(0.200831\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.42443 | 0.0787003 | ||||||||
\(950\) | −8.42443 | −0.273325 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.42443 | 0.175807 | ||||||||
\(953\) | −22.5466 | −0.730355 | −0.365178 | − | 0.930938i | \(-0.618992\pi\) | ||||
−0.365178 | + | 0.930938i | \(0.618992\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.4244 | −0.660919 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.00000 | 0.258468 | ||||||||
\(959\) | 2.42443 | 0.0782889 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.9710 | −0.934548 | ||||||||
\(962\) | 8.84886 | 0.285299 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16.0000 | 0.515325 | ||||||||
\(965\) | −15.4244 | −0.496530 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.72671 | −0.216317 | −0.108158 | − | 0.994134i | \(-0.534495\pi\) | ||||
−0.108158 | + | 0.994134i | \(0.534495\pi\) | |||||||
\(968\) | −30.2733 | −0.973020 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −10.0000 | −0.321081 | ||||||||
\(971\) | −17.4244 | −0.559177 | −0.279588 | − | 0.960120i | \(-0.590198\pi\) | ||||
−0.279588 | + | 0.960120i | \(0.590198\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.00000 | 0.128234 | ||||||||
\(974\) | 6.42443 | 0.205852 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.8489 | 0.347263 | ||||||||
\(977\) | 4.72671 | 0.151221 | 0.0756105 | − | 0.997137i | \(-0.475909\pi\) | ||||
0.0756105 | + | 0.997137i | \(0.475909\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.42443 | 0.205326 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −17.6977 | −0.564757 | ||||||||
\(983\) | 35.3954 | 1.12894 | 0.564469 | − | 0.825454i | \(-0.309081\pi\) | ||||
0.564469 | + | 0.825454i | \(0.309081\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.4244 | −0.714502 | ||||||||
\(986\) | −18.5756 | −0.591567 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.42443 | 0.268017 | ||||||||
\(989\) | −23.9710 | −0.762234 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.54657 | −0.144427 | −0.0722133 | − | 0.997389i | \(-0.523006\pi\) | ||||
−0.0722133 | + | 0.997389i | \(0.523006\pi\) | |||||||
\(992\) | 1.42443 | 0.0452257 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.42443 | −0.172052 | ||||||||
\(995\) | 3.00000 | 0.0951064 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.42443 | −0.108453 | −0.0542264 | − | 0.998529i | \(-0.517269\pi\) | ||||
−0.0542264 | + | 0.998529i | \(0.517269\pi\) | |||||||
\(998\) | 3.15114 | 0.0997477 | ||||||||
\(999\) | 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 | 1890.2.a.y.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 1890.2.a.ba.1.2 | yes | 2 | ||
5.4 | even | 2 | 9450.2.a.es.1.1 | 2 | |||
15.14 | odd | 2 | 9450.2.a.el.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1890.2.a.y.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1890.2.a.ba.1.2 | yes | 2 | 3.2 | odd | 2 | ||
9450.2.a.el.1.2 | 2 | 15.14 | odd | 2 | |||
9450.2.a.es.1.1 | 2 | 5.4 | even | 2 |