Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9800,2,Mod(1,9800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(78.2533939809\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.28825\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9800.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.28825 | −1.32112 | −0.660560 | − | 0.750774i | \(-0.729681\pi\) | ||||
−0.660560 | + | 0.750774i | \(0.729681\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.23607 | 0.745356 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | −0.150756 | − | 0.988571i | \(-0.548171\pi\) | ||||
−0.150756 | + | 0.988571i | \(0.548171\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.874032 | −0.242413 | −0.121206 | − | 0.992627i | \(-0.538676\pi\) | ||||
−0.121206 | + | 0.992627i | \(0.538676\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.57649 | 1.10996 | 0.554981 | − | 0.831863i | \(-0.312725\pi\) | ||||
0.554981 | + | 0.831863i | \(0.312725\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.16228 | 0.725476 | 0.362738 | − | 0.931891i | \(-0.381842\pi\) | ||||
0.362738 | + | 0.931891i | \(0.381842\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | 0.104257 | − | 0.994550i | \(-0.466753\pi\) | ||||
0.104257 | + | 0.994550i | \(0.466753\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.74806 | 0.336415 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.70820 | −1.61707 | −0.808536 | − | 0.588446i | \(-0.799740\pi\) | ||||
−0.808536 | + | 0.588446i | \(0.799740\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.62210 | −0.470942 | −0.235471 | − | 0.971881i | \(-0.575663\pi\) | ||||
−0.235471 | + | 0.971881i | \(0.575663\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.28825 | 0.398332 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.236068 | 0.0388093 | 0.0194047 | − | 0.999812i | \(-0.493823\pi\) | ||||
0.0194047 | + | 0.999812i | \(0.493823\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.69316 | −1.51382 | −0.756909 | − | 0.653520i | \(-0.773291\pi\) | ||||
−0.756909 | + | 0.653520i | \(0.773291\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.23607 | −0.340997 | −0.170499 | − | 0.985358i | \(-0.554538\pi\) | ||||
−0.170499 | + | 0.985358i | \(0.554538\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.41421 | −0.206284 | −0.103142 | − | 0.994667i | \(-0.532890\pi\) | ||||
−0.103142 | + | 0.994667i | \(0.532890\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.4721 | −1.46639 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.23607 | −0.169787 | −0.0848935 | − | 0.996390i | \(-0.527055\pi\) | ||||
−0.0848935 | + | 0.996390i | \(0.527055\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.23607 | −0.958441 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.1074 | 1.44606 | 0.723029 | − | 0.690818i | \(-0.242749\pi\) | ||||
0.723029 | + | 0.690818i | \(0.242749\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.11667 | −0.655123 | −0.327561 | − | 0.944830i | \(-0.606227\pi\) | ||||
−0.327561 | + | 0.944830i | \(0.606227\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.47214 | 0.912867 | 0.456433 | − | 0.889758i | \(-0.349127\pi\) | ||||
0.456433 | + | 0.889758i | \(0.349127\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.28825 | −0.275472 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.70820 | 0.796117 | 0.398059 | − | 0.917360i | \(-0.369684\pi\) | ||||
0.398059 | + | 0.917360i | \(0.369684\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.95595 | 0.345967 | 0.172984 | − | 0.984925i | \(-0.444659\pi\) | ||||
0.172984 | + | 0.984925i | \(0.444659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.9443 | −1.34384 | −0.671918 | − | 0.740626i | \(-0.734529\pi\) | ||||
−0.671918 | + | 0.740626i | \(0.734529\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.7082 | −1.18980 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.27895 | 0.908733 | 0.454366 | − | 0.890815i | \(-0.349866\pi\) | ||||
0.454366 | + | 0.890815i | \(0.349866\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 19.9265 | 2.13635 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.95440 | −0.207165 | −0.103583 | − | 0.994621i | \(-0.533031\pi\) | ||||
−0.103583 | + | 0.994621i | \(0.533031\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.00000 | 0.622171 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.8554 | 1.30527 | 0.652636 | − | 0.757671i | \(-0.273663\pi\) | ||||
0.652636 | + | 0.757671i | \(0.273663\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.23607 | −0.224733 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.02546 | 0.898067 | 0.449034 | − | 0.893515i | \(-0.351768\pi\) | ||||
0.449034 | + | 0.893515i | \(0.351768\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.5672 | 1.04122 | 0.520608 | − | 0.853796i | \(-0.325705\pi\) | ||||
0.520608 | + | 0.853796i | \(0.325705\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.4164 | 1.29701 | 0.648507 | − | 0.761209i | \(-0.275394\pi\) | ||||
0.648507 | + | 0.761209i | \(0.275394\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.52786 | −0.242125 | −0.121063 | − | 0.992645i | \(-0.538630\pi\) | ||||
−0.121063 | + | 0.992645i | \(0.538630\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.540182 | −0.0512718 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.1803 | −1.42805 | −0.714023 | − | 0.700122i | \(-0.753129\pi\) | ||||
−0.714023 | + | 0.700122i | \(0.753129\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.95440 | −0.180684 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 22.1803 | 1.99993 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −22.1246 | −1.96324 | −0.981621 | − | 0.190841i | \(-0.938878\pi\) | ||||
−0.981621 | + | 0.190841i | \(0.938878\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.11667 | 0.450498 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.16073 | −0.188784 | −0.0943918 | − | 0.995535i | \(-0.530091\pi\) | ||||
−0.0943918 | + | 0.995535i | \(0.530091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.05573 | −0.0901969 | −0.0450985 | − | 0.998983i | \(-0.514360\pi\) | ||||
−0.0450985 | + | 0.998983i | \(0.514360\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.9374 | 1.26697 | 0.633485 | − | 0.773755i | \(-0.281624\pi\) | ||||
0.633485 | + | 0.773755i | \(0.281624\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.23607 | 0.272526 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.874032 | 0.0730902 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.6525 | 1.28230 | 0.641150 | − | 0.767415i | \(-0.278457\pi\) | ||||
0.641150 | + | 0.767415i | \(0.278457\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.7639 | −1.12009 | −0.560046 | − | 0.828461i | \(-0.689217\pi\) | ||||
−0.560046 | + | 0.828461i | \(0.689217\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.2333 | 0.827317 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.6746 | 1.72982 | 0.864910 | − | 0.501928i | \(-0.167376\pi\) | ||||
0.864910 | + | 0.501928i | \(0.167376\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.82843 | 0.224309 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.2361 | 1.03673 | 0.518364 | − | 0.855160i | \(-0.326541\pi\) | ||||
0.518364 | + | 0.855160i | \(0.326541\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.7642 | −1.29726 | −0.648628 | − | 0.761106i | \(-0.724657\pi\) | ||||
−0.648628 | + | 0.761106i | \(0.724657\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.2361 | −0.941236 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.07107 | 0.540738 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.40647 | −0.639132 | −0.319566 | − | 0.947564i | \(-0.603537\pi\) | ||||
−0.319566 | + | 0.947564i | \(0.603537\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −25.4164 | −1.91041 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.1803 | 1.20938 | 0.604688 | − | 0.796463i | \(-0.293298\pi\) | ||||
0.604688 | + | 0.796463i | \(0.293298\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.6020 | −1.01103 | −0.505513 | − | 0.862819i | \(-0.668697\pi\) | ||||
−0.505513 | + | 0.862819i | \(0.668697\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.7082 | 0.865495 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.57649 | −0.334666 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.7639 | −1.21300 | −0.606498 | − | 0.795085i | \(-0.707426\pi\) | ||||
−0.606498 | + | 0.795085i | \(0.707426\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.23607 | 0.160956 | 0.0804778 | − | 0.996756i | \(-0.474355\pi\) | ||||
0.0804778 | + | 0.996756i | \(0.474355\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −26.4164 | −1.88209 | −0.941046 | − | 0.338280i | \(-0.890155\pi\) | ||||
−0.941046 | + | 0.338280i | \(0.890155\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.5216 | 0.887632 | 0.443816 | − | 0.896118i | \(-0.353624\pi\) | ||||
0.443816 | + | 0.896118i | \(0.353624\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −17.0981 | −1.20601 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.23607 | 0.155417 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.16228 | −0.218739 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.52786 | −0.105182 | −0.0525912 | − | 0.998616i | \(-0.516748\pi\) | ||||
−0.0525912 | + | 0.998616i | \(0.516748\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15.3500 | −1.05177 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.76393 | −0.457064 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.00000 | −0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.61280 | 0.576756 | 0.288378 | − | 0.957517i | \(-0.406884\pi\) | ||||
0.288378 | + | 0.957517i | \(0.406884\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.5563 | 1.03251 | 0.516256 | − | 0.856435i | \(-0.327325\pi\) | ||||
0.516256 | + | 0.856435i | \(0.327325\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.5486 | −1.49005 | −0.745027 | − | 0.667034i | \(-0.767563\pi\) | ||||
−0.745027 | + | 0.667034i | \(0.767563\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 28.4164 | 1.86162 | 0.930810 | − | 0.365502i | \(-0.119103\pi\) | ||||
0.930810 | + | 0.365502i | \(0.119103\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 27.3314 | 1.77537 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.23607 | 0.597432 | 0.298716 | − | 0.954342i | \(-0.403442\pi\) | ||||
0.298716 | + | 0.954342i | \(0.403442\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.90724 | 0.187272 | 0.0936358 | − | 0.995607i | \(-0.470151\pi\) | ||||
0.0936358 | + | 0.995607i | \(0.470151\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 19.2588 | 1.23545 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.76393 | −0.175865 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.9443 | −1.20054 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.74806 | −0.110337 | −0.0551684 | − | 0.998477i | \(-0.517570\pi\) | ||||
−0.0551684 | + | 0.998477i | \(0.517570\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.00000 | −0.0628695 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.461370 | 0.0287795 | 0.0143897 | − | 0.999896i | \(-0.495419\pi\) | ||||
0.0143897 | + | 0.999896i | \(0.495419\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.4721 | −1.20529 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.29180 | 0.202981 | 0.101490 | − | 0.994837i | \(-0.467639\pi\) | ||||
0.101490 | + | 0.994837i | \(0.467639\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.47214 | 0.273690 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.6839 | 0.956262 | 0.478131 | − | 0.878288i | \(-0.341314\pi\) | ||||
0.478131 | + | 0.878288i | \(0.341314\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.7456 | −1.74617 | −0.873087 | − | 0.487565i | \(-0.837885\pi\) | ||||
−0.873087 | + | 0.487565i | \(0.837885\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.05573 | −0.183601 | −0.0918005 | − | 0.995777i | \(-0.529262\pi\) | ||||
−0.0918005 | + | 0.995777i | \(0.529262\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.86319 | −0.351020 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.6525 | 1.17237 | 0.586184 | − | 0.810178i | \(-0.300629\pi\) | ||||
0.586184 | + | 0.810178i | \(0.300629\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.73567 | −0.340950 | −0.170475 | − | 0.985362i | \(-0.554530\pi\) | ||||
−0.170475 | + | 0.985362i | \(0.554530\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.94427 | 0.232016 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −29.4164 | −1.72442 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.8477 | −1.15951 | −0.579757 | − | 0.814789i | \(-0.696853\pi\) | ||||
−0.579757 | + | 0.814789i | \(0.696853\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.74806 | −0.101433 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.874032 | −0.0505466 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −20.6525 | −1.18645 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.0323 | −1.71404 | −0.857018 | − | 0.515287i | \(-0.827686\pi\) | ||||
−0.857018 | + | 0.515287i | \(0.827686\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −24.1803 | −1.37557 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.0509 | 1.02357 | 0.511787 | − | 0.859112i | \(-0.328984\pi\) | ||||
0.511787 | + | 0.859112i | \(0.328984\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.5672 | −0.597293 | −0.298647 | − | 0.954364i | \(-0.596535\pi\) | ||||
−0.298647 | + | 0.954364i | \(0.596535\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.5279 | −0.591304 | −0.295652 | − | 0.955296i | \(-0.595537\pi\) | ||||
−0.295652 | + | 0.955296i | \(0.595537\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.70820 | 0.487566 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.7000 | −1.71351 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.4721 | 0.805251 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.78437 | 0.319877 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.0000 | −0.824475 | −0.412237 | − | 0.911077i | \(-0.635253\pi\) | ||||
−0.412237 | + | 0.911077i | \(0.635253\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.527864 | 0.0289268 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.6525 | 1.01607 | 0.508033 | − | 0.861338i | \(-0.330373\pi\) | ||||
0.508033 | + | 0.861338i | \(0.330373\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 34.7363 | 1.88662 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.62210 | 0.141994 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.8885 | −0.584528 | −0.292264 | − | 0.956338i | \(-0.594409\pi\) | ||||
−0.292264 | + | 0.956338i | \(0.594409\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.65530 | 0.249193 | 0.124596 | − | 0.992208i | \(-0.460236\pi\) | ||||
0.124596 | + | 0.992208i | \(0.460236\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.52786 | −0.0815513 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.5927 | −1.04281 | −0.521406 | − | 0.853309i | \(-0.674592\pi\) | ||||
−0.521406 | + | 0.853309i | \(0.674592\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.1803 | −0.906744 | −0.453372 | − | 0.891321i | \(-0.649779\pi\) | ||||
−0.453372 | + | 0.891321i | \(0.649779\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.00000 | −0.473684 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 22.8825 | 1.20102 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.2666 | 0.640309 | 0.320154 | − | 0.947365i | \(-0.396265\pi\) | ||||
0.320154 | + | 0.947365i | \(0.396265\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −21.6746 | −1.12833 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.1803 | 1.09668 | 0.548338 | − | 0.836257i | \(-0.315261\pi\) | ||||
0.548338 | + | 0.836257i | \(0.315261\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.61125 | 0.391999 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.1803 | 0.574295 | 0.287148 | − | 0.957886i | \(-0.407293\pi\) | ||||
0.287148 | + | 0.957886i | \(0.407293\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 50.6265 | 2.59368 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.95440 | −0.0998649 | −0.0499325 | − | 0.998753i | \(-0.515901\pi\) | ||||
−0.0499325 | + | 0.998753i | \(0.515901\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.00000 | −0.254164 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.1803 | −1.17529 | −0.587645 | − | 0.809119i | \(-0.699945\pi\) | ||||
−0.587645 | + | 0.809119i | \(0.699945\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.57649 | 0.231443 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.94427 | 0.249406 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.23179 | −0.463330 | −0.231665 | − | 0.972796i | \(-0.574417\pi\) | ||||
−0.231665 | + | 0.972796i | \(0.574417\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.29180 | −0.364135 | −0.182067 | − | 0.983286i | \(-0.558279\pi\) | ||||
−0.182067 | + | 0.983286i | \(0.558279\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.29180 | 0.114162 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.236068 | −0.0117015 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.7202 | −0.975100 | −0.487550 | − | 0.873095i | \(-0.662109\pi\) | ||||
−0.487550 | + | 0.873095i | \(0.662109\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.41577 | 0.119161 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −34.1803 | −1.67382 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.27585 | −0.306595 | −0.153298 | − | 0.988180i | \(-0.548989\pi\) | ||||
−0.153298 | + | 0.988180i | \(0.548989\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.0689 | −1.70915 | −0.854576 | − | 0.519326i | \(-0.826183\pi\) | ||||
−0.854576 | + | 0.519326i | \(0.826183\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.16228 | −0.153755 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.00000 | −0.0965609 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.81966 | −0.376660 | −0.188330 | − | 0.982106i | \(-0.560307\pi\) | ||||
−0.188330 | + | 0.982106i | \(0.560307\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.0509 | 0.867472 | 0.433736 | − | 0.901040i | \(-0.357195\pi\) | ||||
0.433736 | + | 0.901040i | \(0.357195\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.16228 | 0.151272 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 36.4056 | 1.73754 | 0.868772 | − | 0.495212i | \(-0.164910\pi\) | ||||
0.868772 | + | 0.495212i | \(0.164910\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.8197 | 0.656592 | 0.328296 | − | 0.944575i | \(-0.393526\pi\) | ||||
0.328296 | + | 0.944575i | \(0.393526\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −35.8167 | −1.69407 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.7082 | 0.694123 | 0.347062 | − | 0.937842i | \(-0.387179\pi\) | ||||
0.347062 | + | 0.937842i | \(0.387179\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.69316 | 0.456433 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 31.4953 | 1.47978 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.7639 | −0.737406 | −0.368703 | − | 0.929547i | \(-0.620198\pi\) | ||||
−0.368703 | + | 0.929547i | \(0.620198\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.00000 | 0.373408 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.35621 | −0.342613 | −0.171306 | − | 0.985218i | \(-0.554799\pi\) | ||||
−0.171306 | + | 0.985218i | \(0.554799\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.4164 | −0.623513 | −0.311757 | − | 0.950162i | \(-0.600917\pi\) | ||||
−0.311757 | + | 0.950162i | \(0.600917\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.8840 | −1.10522 | −0.552610 | − | 0.833440i | \(-0.686368\pi\) | ||||
−0.552610 | + | 0.833440i | \(0.686368\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −49.5967 | −2.28530 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.23607 | 0.102815 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.76393 | −0.126552 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −26.1723 | −1.19584 | −0.597920 | − | 0.801555i | \(-0.704006\pi\) | ||||
−0.597920 | + | 0.801555i | \(0.704006\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.206331 | −0.00940788 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.0000 | 0.589086 | 0.294543 | − | 0.955638i | \(-0.404833\pi\) | ||||
0.294543 | + | 0.955638i | \(0.404833\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −30.2874 | −1.36964 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.1246 | −1.17899 | −0.589494 | − | 0.807773i | \(-0.700673\pi\) | ||||
−0.589494 | + | 0.807773i | \(0.700673\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −39.8530 | −1.79489 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.9443 | −1.38526 | −0.692628 | − | 0.721295i | \(-0.743547\pi\) | ||||
−0.692628 | + | 0.721295i | \(0.743547\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 38.3607 | 1.71383 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.1251 | −1.20945 | −0.604724 | − | 0.796435i | \(-0.706717\pi\) | ||||
−0.604724 | + | 0.796435i | \(0.706717\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 27.9991 | 1.24348 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.618993 | −0.0274364 | −0.0137182 | − | 0.999906i | \(-0.504367\pi\) | ||||
−0.0137182 | + | 0.999906i | \(0.504367\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.52786 | 0.244061 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.41421 | 0.0621970 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.2361 | 0.844370 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.23954 | 0.0981159 | 0.0490580 | − | 0.998796i | \(-0.484378\pi\) | ||||
0.0490580 | + | 0.998796i | \(0.484378\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.7264 | 0.512758 | 0.256379 | − | 0.966576i | \(-0.417470\pi\) | ||||
0.256379 | + | 0.966576i | \(0.417470\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.0000 | −0.522728 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.0000 | −0.956522 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 24.8369 | 1.07783 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.47214 | 0.366969 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −37.0246 | −1.59773 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.0132 | 1.46234 | 0.731170 | − | 0.682195i | \(-0.238975\pi\) | ||||
0.731170 | + | 0.682195i | \(0.238975\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 31.1246 | 1.33568 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.6525 | 1.52439 | 0.762195 | − | 0.647348i | \(-0.224122\pi\) | ||||
0.762195 | + | 0.647348i | \(0.224122\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.4412 | −0.488300 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.5378 | −1.17315 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.7639 | −1.17640 | −0.588198 | − | 0.808717i | \(-0.700162\pi\) | ||||
−0.588198 | + | 0.808717i | \(0.700162\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.95440 | 0.0826621 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.4721 | 0.442134 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.7279 | −0.536418 | −0.268209 | − | 0.963361i | \(-0.586432\pi\) | ||||
−0.268209 | + | 0.963361i | \(0.586432\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.8885 | −0.959538 | −0.479769 | − | 0.877395i | \(-0.659279\pi\) | ||||
−0.479769 | + | 0.877395i | \(0.659279\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.1246 | 0.423702 | 0.211851 | − | 0.977302i | \(-0.432051\pi\) | ||||
0.211851 | + | 0.977302i | \(0.432051\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 38.3600 | 1.60251 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.7124 | −1.11205 | −0.556027 | − | 0.831164i | \(-0.687675\pi\) | ||||
−0.556027 | + | 0.831164i | \(0.687675\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.11667 | −0.212642 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.23607 | 0.0511927 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.5834 | −1.05594 | −0.527969 | − | 0.849264i | \(-0.677046\pi\) | ||||
−0.527969 | + | 0.849264i | \(0.677046\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.29180 | −0.341658 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 60.4472 | 2.48647 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.0618 | 0.536383 | 0.268191 | − | 0.963366i | \(-0.413574\pi\) | ||||
0.268191 | + | 0.963366i | \(0.413574\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −28.6525 | −1.17267 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.05573 | 0.329148 | 0.164574 | − | 0.986365i | \(-0.447375\pi\) | ||||
0.164574 | + | 0.986365i | \(0.447375\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.7912 | −1.09284 | −0.546419 | − | 0.837512i | \(-0.684009\pi\) | ||||
−0.546419 | + | 0.837512i | \(0.684009\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.7082 | 0.680411 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.61125 | 0.308931 | 0.154466 | − | 0.987998i | \(-0.450634\pi\) | ||||
0.154466 | + | 0.987998i | \(0.450634\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.23607 | 0.0500060 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.9443 | −0.967100 | −0.483550 | − | 0.875317i | \(-0.660653\pi\) | ||||
−0.483550 | + | 0.875317i | \(0.660653\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.3050 | 0.575896 | 0.287948 | − | 0.957646i | \(-0.407027\pi\) | ||||
0.287948 | + | 0.957646i | \(0.407027\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.95750 | −0.159065 | −0.0795326 | − | 0.996832i | \(-0.525343\pi\) | ||||
−0.0795326 | + | 0.996832i | \(0.525343\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.74806 | 0.0701474 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.23607 | 0.288981 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.08036 | 0.0430769 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.4721 | −1.01403 | −0.507015 | − | 0.861937i | \(-0.669251\pi\) | ||||
−0.507015 | + | 0.861937i | \(0.669251\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.49613 | 0.138959 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.0000 | 0.593391 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.3050 | −1.43396 | −0.716980 | − | 0.697094i | \(-0.754476\pi\) | ||||
−0.716980 | + | 0.697094i | \(0.754476\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.2179 | −0.955059 | −0.477530 | − | 0.878616i | \(-0.658468\pi\) | ||||
−0.477530 | + | 0.878616i | \(0.658468\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.6429 | −0.811557 | −0.405778 | − | 0.913971i | \(-0.633000\pi\) | ||||
−0.405778 | + | 0.913971i | \(0.633000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.1074 | −0.436003 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.47214 | −0.175008 | −0.0875041 | − | 0.996164i | \(-0.527889\pi\) | ||||
−0.0875041 | + | 0.996164i | \(0.527889\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.60970 | 0.257869 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.4164 | 0.990083 | 0.495041 | − | 0.868869i | \(-0.335153\pi\) | ||||
0.495041 | + | 0.868869i | \(0.335153\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 50.4202 | 1.96112 | 0.980560 | − | 0.196222i | \(-0.0628673\pi\) | ||||
0.980560 | + | 0.196222i | \(0.0628673\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.15298 | 0.355472 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.70820 | −0.337183 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.7082 | −0.761963 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.11667 | 0.197527 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.0689 | −1.69873 | −0.849365 | − | 0.527805i | \(-0.823015\pi\) | ||||
−0.849365 | + | 0.527805i | \(0.823015\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.81913 | −0.338947 | −0.169473 | − | 0.985535i | \(-0.554207\pi\) | ||||
−0.169473 | + | 0.985535i | \(0.554207\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −35.5967 | −1.36407 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.0557 | 0.614355 | 0.307178 | − | 0.951652i | \(-0.400615\pi\) | ||||
0.307178 | + | 0.951652i | \(0.400615\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 51.5967 | 1.96854 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.08036 | 0.0411586 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.8570 | 0.527145 | 0.263572 | − | 0.964640i | \(-0.415099\pi\) | ||||
0.263572 | + | 0.964640i | \(0.415099\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −44.3607 | −1.68028 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −65.0237 | −2.45942 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −45.3050 | −1.71114 | −0.855572 | − | 0.517683i | \(-0.826794\pi\) | ||||
−0.855572 | + | 0.517683i | \(0.826794\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.746512 | 0.0281553 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.9443 | −1.01191 | −0.505957 | − | 0.862559i | \(-0.668860\pi\) | ||||
−0.505957 | + | 0.862559i | \(0.668860\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −26.7082 | −1.00164 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.62210 | −0.0981983 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.1344 | −0.789278 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.78127 | 0.141018 | 0.0705088 | − | 0.997511i | \(-0.477538\pi\) | ||||
0.0705088 | + | 0.997511i | \(0.477538\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.65248 | −0.247408 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.5980 | −1.46861 | −0.734304 | − | 0.678821i | \(-0.762491\pi\) | ||||
−0.734304 | + | 0.678821i | \(0.762491\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.9443 | −0.442380 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.2333 | −0.378494 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −44.4295 | −1.64104 | −0.820521 | − | 0.571617i | \(-0.806316\pi\) | ||||
−0.820521 | + | 0.571617i | \(0.806316\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.47214 | −0.275240 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −49.3607 | −1.81576 | −0.907881 | − | 0.419228i | \(-0.862301\pi\) | ||||
−0.907881 | + | 0.419228i | \(0.862301\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.32456 | 0.232338 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.1803 | 0.813718 | 0.406859 | − | 0.913491i | \(-0.366624\pi\) | ||||
0.406859 | + | 0.913491i | \(0.366624\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 18.5123 | 0.677329 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.11146 | −0.223010 | −0.111505 | − | 0.993764i | \(-0.535567\pi\) | ||||
−0.111505 | + | 0.993764i | \(0.535567\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.00000 | 0.145768 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.05573 | −0.220099 | −0.110050 | − | 0.993926i | \(-0.535101\pi\) | ||||
−0.110050 | + | 0.993926i | \(0.535101\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.28825 | 0.0830581 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.9814 | −0.434326 | −0.217163 | − | 0.976135i | \(-0.569680\pi\) | ||||
−0.217163 | + | 0.976135i | \(0.569680\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.70820 | −0.350543 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.7518 | 0.748330 | 0.374165 | − | 0.927362i | \(-0.377929\pi\) | ||||
0.374165 | + | 0.927362i | \(0.377929\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.05573 | −0.0380211 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.2495 | −0.908162 | −0.454081 | − | 0.890960i | \(-0.650032\pi\) | ||||
−0.454081 | + | 0.890960i | \(0.650032\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −30.6525 | −1.09824 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.70820 | −0.240038 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15.2225 | −0.544008 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.87558 | −0.0668573 | −0.0334287 | − | 0.999441i | \(-0.510643\pi\) | ||||
−0.0334287 | + | 0.999441i | \(0.510643\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.53244 | −0.268162 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.47214 | 0.158810 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.0323 | 1.06380 | 0.531900 | − | 0.846807i | \(-0.321478\pi\) | ||||
0.531900 | + | 0.846807i | \(0.321478\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.47214 | −0.228968 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.37016 | −0.154412 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.95595 | −0.104313 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −35.8885 | −1.26334 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.29180 | −0.186050 | −0.0930248 | − | 0.995664i | \(-0.529654\pi\) | ||||
−0.0930248 | + | 0.995664i | \(0.529654\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.3122 | 0.362109 | 0.181054 | − | 0.983473i | \(-0.442049\pi\) | ||||
0.181054 | + | 0.983473i | \(0.442049\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 65.7771 | 2.30690 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.07107 | −0.247385 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.4164 | 0.607837 | 0.303918 | − | 0.952698i | \(-0.401705\pi\) | ||||
0.303918 | + | 0.952698i | \(0.401705\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −52.3050 | −1.82324 | −0.911618 | − | 0.411038i | \(-0.865166\pi\) | ||||
−0.911618 | + | 0.411038i | \(0.865166\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.2361 | 0.703677 | 0.351839 | − | 0.936061i | \(-0.385557\pi\) | ||||
0.351839 | + | 0.936061i | \(0.385557\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.89794 | −0.309038 | −0.154519 | − | 0.987990i | \(-0.549383\pi\) | ||||
−0.154519 | + | 0.987990i | \(0.549383\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.99226 | 0.242559 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.58359 | −0.158432 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.1058 | −0.348892 | −0.174446 | − | 0.984667i | \(-0.555813\pi\) | ||||
−0.174446 | + | 0.984667i | \(0.555813\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 46.8328 | 1.61492 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −44.9697 | −1.54884 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.1246 | 0.450436 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.236068 | 0.00809231 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.7140 | −0.948909 | −0.474454 | − | 0.880280i | \(-0.657355\pi\) | ||||
−0.474454 | + | 0.880280i | \(0.657355\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −52.3746 | −1.78908 | −0.894541 | − | 0.446985i | \(-0.852498\pi\) | ||||
−0.894541 | + | 0.446985i | \(0.852498\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −46.5114 | −1.58695 | −0.793475 | − | 0.608603i | \(-0.791730\pi\) | ||||
−0.793475 | + | 0.608603i | \(0.791730\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.1246 | 0.821211 | 0.410606 | − | 0.911813i | \(-0.365317\pi\) | ||||
0.410606 | + | 0.911813i | \(0.365317\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.02546 | −0.306521 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.9443 | 0.405182 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.53089 | −0.221291 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 28.7456 | 0.972893 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.7082 | 0.395358 | 0.197679 | − | 0.980267i | \(-0.436660\pi\) | ||||
0.197679 | + | 0.980267i | \(0.436660\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 45.4164 | 1.53186 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.0053 | −0.673996 | −0.336998 | − | 0.941505i | \(-0.609412\pi\) | ||||
−0.336998 | + | 0.941505i | \(0.609412\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.3607 | 0.920760 | 0.460380 | − | 0.887722i | \(-0.347713\pi\) | ||||
0.460380 | + | 0.887722i | \(0.347713\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.0146 | −0.470565 | −0.235282 | − | 0.971927i | \(-0.575601\pi\) | ||||
−0.235282 | + | 0.971927i | \(0.575601\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.7082 | 0.358738 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.47214 | −0.149654 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.00000 | 0.0667781 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.8337 | 0.761548 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.65685 | −0.188457 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.0000 | 1.06254 | 0.531271 | − | 0.847202i | \(-0.321714\pi\) | ||||
0.531271 | + | 0.847202i | \(0.321714\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 20.1815 | 0.669380 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.3607 | −1.17155 | −0.585776 | − | 0.810473i | \(-0.699210\pi\) | ||||
−0.585776 | + | 0.810473i | \(0.699210\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.27895 | −0.273993 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.5967 | 1.53708 | 0.768542 | − | 0.639799i | \(-0.220982\pi\) | ||||
0.768542 | + | 0.639799i | \(0.220982\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 68.7214 | 2.26445 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.86319 | −0.192989 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 23.6290 | 0.776077 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.19704 | −0.203318 | −0.101659 | − | 0.994819i | \(-0.532415\pi\) | ||||
−0.101659 | + | 0.994819i | \(0.532415\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −41.3050 | −1.35226 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −57.4612 | −1.87717 | −0.938587 | − | 0.345041i | \(-0.887865\pi\) | ||||
−0.938587 | + | 0.345041i | \(0.887865\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.1803 | 0.789096 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43.8105 | 1.42818 | 0.714091 | − | 0.700053i | \(-0.246840\pi\) | ||||
0.714091 | + | 0.700053i | \(0.246840\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.69316 | −0.315653 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.88854 | −0.191352 | −0.0956760 | − | 0.995413i | \(-0.530501\pi\) | ||||
−0.0956760 | + | 0.995413i | \(0.530501\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.58359 | −0.0838669 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.0903 | 0.781183 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.7639 | −0.445857 | −0.222929 | − | 0.974835i | \(-0.571562\pi\) | ||||
−0.222929 | + | 0.974835i | \(0.571562\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −19.9265 | −0.644133 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.1246 | −0.778213 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 30.0000 | 0.966736 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.4721 | 0.465393 | 0.232696 | − | 0.972549i | \(-0.425245\pi\) | ||||
0.232696 | + | 0.972549i | \(0.425245\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −33.1158 | −1.06383 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49.5949 | −1.59158 | −0.795788 | − | 0.605575i | \(-0.792943\pi\) | ||||
−0.795788 | + | 0.605575i | \(0.792943\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −54.5967 | −1.74670 | −0.873352 | − | 0.487089i | \(-0.838059\pi\) | ||||
−0.873352 | + | 0.487089i | \(0.838059\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.95440 | 0.0624627 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.65248 | −0.180470 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 45.4612 | 1.44999 | 0.724993 | − | 0.688756i | \(-0.241843\pi\) | ||||
0.724993 | + | 0.688756i | \(0.241843\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.23607 | −0.0711028 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45.6525 | −1.45020 | −0.725099 | − | 0.688644i | \(-0.758206\pi\) | ||||
−0.725099 | + | 0.688644i | \(0.758206\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 34.3237 | 1.08923 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.5595 | 0.556113 | 0.278057 | − | 0.960565i | \(-0.410310\pi\) | ||||
0.278057 | + | 0.960565i | \(0.410310\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.412662 | 0.0130560 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 9800.2.a.cn.1.1 | yes | 4 | |
5.4 | even | 2 | 9800.2.a.cm.1.4 | yes | 4 | ||
7.6 | odd | 2 | inner | 9800.2.a.cn.1.4 | yes | 4 | |
35.34 | odd | 2 | 9800.2.a.cm.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9800.2.a.cm.1.1 | ✓ | 4 | 35.34 | odd | 2 | ||
9800.2.a.cm.1.4 | yes | 4 | 5.4 | even | 2 | ||
9800.2.a.cn.1.1 | yes | 4 | 1.1 | even | 1 | trivial | |
9800.2.a.cn.1.4 | yes | 4 | 7.6 | odd | 2 | inner |