Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.557584 | −0.394271 | −0.197136 | − | 0.980376i | \(-0.563164\pi\) | ||||
−0.197136 | + | 0.980376i | \(0.563164\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.68910 | −0.844550 | ||||||||
\(5\) | 2.57031 | 1.14948 | 0.574739 | − | 0.818337i | \(-0.305104\pi\) | ||||
0.574739 | + | 0.818337i | \(0.305104\pi\) | |||||||
\(6\) | 0.557584 | 0.227633 | ||||||||
\(7\) | 2.28117 | 0.862201 | 0.431101 | − | 0.902304i | \(-0.358125\pi\) | ||||
0.431101 | + | 0.902304i | \(0.358125\pi\) | |||||||
\(8\) | 2.05698 | 0.727253 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.43316 | −0.453206 | ||||||||
\(11\) | −2.42518 | −0.731220 | −0.365610 | − | 0.930768i | \(-0.619140\pi\) | ||||
−0.365610 | + | 0.930768i | \(0.619140\pi\) | |||||||
\(12\) | 1.68910 | 0.487601 | ||||||||
\(13\) | 5.98863 | 1.66095 | 0.830474 | − | 0.557058i | \(-0.188070\pi\) | ||||
0.830474 | + | 0.557058i | \(0.188070\pi\) | |||||||
\(14\) | −1.27194 | −0.339941 | ||||||||
\(15\) | −2.57031 | −0.663651 | ||||||||
\(16\) | 2.23126 | 0.557815 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −0.557584 | −0.131424 | ||||||||
\(19\) | 4.65582 | 1.06812 | 0.534059 | − | 0.845447i | \(-0.320666\pi\) | ||||
0.534059 | + | 0.845447i | \(0.320666\pi\) | |||||||
\(20\) | −4.34151 | −0.970791 | ||||||||
\(21\) | −2.28117 | −0.497792 | ||||||||
\(22\) | 1.35224 | 0.288299 | ||||||||
\(23\) | 0.860875 | 0.179505 | 0.0897524 | − | 0.995964i | \(-0.471392\pi\) | ||||
0.0897524 | + | 0.995964i | \(0.471392\pi\) | |||||||
\(24\) | −2.05698 | −0.419880 | ||||||||
\(25\) | 1.60649 | 0.321298 | ||||||||
\(26\) | −3.33917 | −0.654864 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −3.85312 | −0.728172 | ||||||||
\(29\) | −5.60357 | −1.04056 | −0.520279 | − | 0.853997i | \(-0.674172\pi\) | ||||
−0.520279 | + | 0.853997i | \(0.674172\pi\) | |||||||
\(30\) | 1.43316 | 0.261659 | ||||||||
\(31\) | −7.14237 | −1.28281 | −0.641404 | − | 0.767203i | \(-0.721648\pi\) | ||||
−0.641404 | + | 0.767203i | \(0.721648\pi\) | |||||||
\(32\) | −5.35808 | −0.947184 | ||||||||
\(33\) | 2.42518 | 0.422170 | ||||||||
\(34\) | 0.557584 | 0.0956249 | ||||||||
\(35\) | 5.86331 | 0.991081 | ||||||||
\(36\) | −1.68910 | −0.281517 | ||||||||
\(37\) | −7.55997 | −1.24285 | −0.621426 | − | 0.783473i | \(-0.713446\pi\) | ||||
−0.621426 | + | 0.783473i | \(0.713446\pi\) | |||||||
\(38\) | −2.59601 | −0.421128 | ||||||||
\(39\) | −5.98863 | −0.958948 | ||||||||
\(40\) | 5.28708 | 0.835961 | ||||||||
\(41\) | 7.64575 | 1.19406 | 0.597032 | − | 0.802217i | \(-0.296346\pi\) | ||||
0.597032 | + | 0.802217i | \(0.296346\pi\) | |||||||
\(42\) | 1.27194 | 0.196265 | ||||||||
\(43\) | −10.6920 | −1.63052 | −0.815260 | − | 0.579095i | \(-0.803406\pi\) | ||||
−0.815260 | + | 0.579095i | \(0.803406\pi\) | |||||||
\(44\) | 4.09638 | 0.617552 | ||||||||
\(45\) | 2.57031 | 0.383159 | ||||||||
\(46\) | −0.480010 | −0.0707736 | ||||||||
\(47\) | −11.4803 | −1.67457 | −0.837284 | − | 0.546768i | \(-0.815858\pi\) | ||||
−0.837284 | + | 0.546768i | \(0.815858\pi\) | |||||||
\(48\) | −2.23126 | −0.322054 | ||||||||
\(49\) | −1.79626 | −0.256609 | ||||||||
\(50\) | −0.895754 | −0.126679 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −10.1154 | −1.40275 | ||||||||
\(53\) | −1.24871 | −0.171524 | −0.0857618 | − | 0.996316i | \(-0.527332\pi\) | ||||
−0.0857618 | + | 0.996316i | \(0.527332\pi\) | |||||||
\(54\) | 0.557584 | 0.0758776 | ||||||||
\(55\) | −6.23347 | −0.840521 | ||||||||
\(56\) | 4.69233 | 0.627039 | ||||||||
\(57\) | −4.65582 | −0.616678 | ||||||||
\(58\) | 3.12446 | 0.410262 | ||||||||
\(59\) | 10.3301 | 1.34487 | 0.672435 | − | 0.740156i | \(-0.265249\pi\) | ||||
0.672435 | + | 0.740156i | \(0.265249\pi\) | |||||||
\(60\) | 4.34151 | 0.560487 | ||||||||
\(61\) | −12.6616 | −1.62115 | −0.810576 | − | 0.585634i | \(-0.800846\pi\) | ||||
−0.810576 | + | 0.585634i | \(0.800846\pi\) | |||||||
\(62\) | 3.98247 | 0.505775 | ||||||||
\(63\) | 2.28117 | 0.287400 | ||||||||
\(64\) | −1.47494 | −0.184367 | ||||||||
\(65\) | 15.3926 | 1.90922 | ||||||||
\(66\) | −1.35224 | −0.166450 | ||||||||
\(67\) | 0.360054 | 0.0439875 | 0.0219938 | − | 0.999758i | \(-0.492999\pi\) | ||||
0.0219938 | + | 0.999758i | \(0.492999\pi\) | |||||||
\(68\) | 1.68910 | 0.204833 | ||||||||
\(69\) | −0.860875 | −0.103637 | ||||||||
\(70\) | −3.26929 | −0.390755 | ||||||||
\(71\) | −6.84154 | −0.811941 | −0.405970 | − | 0.913886i | \(-0.633066\pi\) | ||||
−0.405970 | + | 0.913886i | \(0.633066\pi\) | |||||||
\(72\) | 2.05698 | 0.242418 | ||||||||
\(73\) | −6.78327 | −0.793922 | −0.396961 | − | 0.917836i | \(-0.629935\pi\) | ||||
−0.396961 | + | 0.917836i | \(0.629935\pi\) | |||||||
\(74\) | 4.21532 | 0.490021 | ||||||||
\(75\) | −1.60649 | −0.185502 | ||||||||
\(76\) | −7.86414 | −0.902079 | ||||||||
\(77\) | −5.53226 | −0.630459 | ||||||||
\(78\) | 3.33917 | 0.378086 | ||||||||
\(79\) | −13.1176 | −1.47584 | −0.737921 | − | 0.674887i | \(-0.764192\pi\) | ||||
−0.737921 | + | 0.674887i | \(0.764192\pi\) | |||||||
\(80\) | 5.73503 | 0.641195 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.26315 | −0.470786 | ||||||||
\(83\) | −7.63054 | −0.837560 | −0.418780 | − | 0.908088i | \(-0.637542\pi\) | ||||
−0.418780 | + | 0.908088i | \(0.637542\pi\) | |||||||
\(84\) | 3.85312 | 0.420410 | ||||||||
\(85\) | −2.57031 | −0.278789 | ||||||||
\(86\) | 5.96171 | 0.642868 | ||||||||
\(87\) | 5.60357 | 0.600766 | ||||||||
\(88\) | −4.98856 | −0.531783 | ||||||||
\(89\) | −5.84324 | −0.619382 | −0.309691 | − | 0.950837i | \(-0.600226\pi\) | ||||
−0.309691 | + | 0.950837i | \(0.600226\pi\) | |||||||
\(90\) | −1.43316 | −0.151069 | ||||||||
\(91\) | 13.6611 | 1.43207 | ||||||||
\(92\) | −1.45410 | −0.151601 | ||||||||
\(93\) | 7.14237 | 0.740630 | ||||||||
\(94\) | 6.40121 | 0.660235 | ||||||||
\(95\) | 11.9669 | 1.22778 | ||||||||
\(96\) | 5.35808 | 0.546857 | ||||||||
\(97\) | −2.78593 | −0.282868 | −0.141434 | − | 0.989948i | \(-0.545171\pi\) | ||||
−0.141434 | + | 0.989948i | \(0.545171\pi\) | |||||||
\(98\) | 1.00157 | 0.101174 | ||||||||
\(99\) | −2.42518 | −0.243740 | ||||||||
\(100\) | −2.71353 | −0.271353 | ||||||||
\(101\) | −9.86245 | −0.981350 | −0.490675 | − | 0.871343i | \(-0.663250\pi\) | ||||
−0.490675 | + | 0.871343i | \(0.663250\pi\) | |||||||
\(102\) | −0.557584 | −0.0552091 | ||||||||
\(103\) | 10.6391 | 1.04830 | 0.524150 | − | 0.851626i | \(-0.324383\pi\) | ||||
0.524150 | + | 0.851626i | \(0.324383\pi\) | |||||||
\(104\) | 12.3185 | 1.20793 | ||||||||
\(105\) | −5.86331 | −0.572201 | ||||||||
\(106\) | 0.696261 | 0.0676268 | ||||||||
\(107\) | 4.70455 | 0.454806 | 0.227403 | − | 0.973801i | \(-0.426977\pi\) | ||||
0.227403 | + | 0.973801i | \(0.426977\pi\) | |||||||
\(108\) | 1.68910 | 0.162534 | ||||||||
\(109\) | −14.6987 | −1.40788 | −0.703939 | − | 0.710261i | \(-0.748577\pi\) | ||||
−0.703939 | + | 0.710261i | \(0.748577\pi\) | |||||||
\(110\) | 3.47569 | 0.331394 | ||||||||
\(111\) | 7.55997 | 0.717561 | ||||||||
\(112\) | 5.08988 | 0.480949 | ||||||||
\(113\) | −10.7705 | −1.01320 | −0.506599 | − | 0.862182i | \(-0.669098\pi\) | ||||
−0.506599 | + | 0.862182i | \(0.669098\pi\) | |||||||
\(114\) | 2.59601 | 0.243139 | ||||||||
\(115\) | 2.21271 | 0.206337 | ||||||||
\(116\) | 9.46499 | 0.878803 | ||||||||
\(117\) | 5.98863 | 0.553649 | ||||||||
\(118\) | −5.75992 | −0.530244 | ||||||||
\(119\) | −2.28117 | −0.209115 | ||||||||
\(120\) | −5.28708 | −0.482643 | ||||||||
\(121\) | −5.11848 | −0.465317 | ||||||||
\(122\) | 7.05990 | 0.639174 | ||||||||
\(123\) | −7.64575 | −0.689394 | ||||||||
\(124\) | 12.0642 | 1.08340 | ||||||||
\(125\) | −8.72237 | −0.780152 | ||||||||
\(126\) | −1.27194 | −0.113314 | ||||||||
\(127\) | −18.7363 | −1.66258 | −0.831290 | − | 0.555839i | \(-0.812397\pi\) | ||||
−0.831290 | + | 0.555839i | \(0.812397\pi\) | |||||||
\(128\) | 11.5386 | 1.01987 | ||||||||
\(129\) | 10.6920 | 0.941381 | ||||||||
\(130\) | −8.58269 | −0.752752 | ||||||||
\(131\) | 15.2673 | 1.33391 | 0.666954 | − | 0.745099i | \(-0.267598\pi\) | ||||
0.666954 | + | 0.745099i | \(0.267598\pi\) | |||||||
\(132\) | −4.09638 | −0.356544 | ||||||||
\(133\) | 10.6207 | 0.920932 | ||||||||
\(134\) | −0.200760 | −0.0173430 | ||||||||
\(135\) | −2.57031 | −0.221217 | ||||||||
\(136\) | −2.05698 | −0.176385 | ||||||||
\(137\) | −14.4760 | −1.23677 | −0.618383 | − | 0.785877i | \(-0.712212\pi\) | ||||
−0.618383 | + | 0.785877i | \(0.712212\pi\) | |||||||
\(138\) | 0.480010 | 0.0408612 | ||||||||
\(139\) | 20.2579 | 1.71825 | 0.859126 | − | 0.511764i | \(-0.171008\pi\) | ||||
0.859126 | + | 0.511764i | \(0.171008\pi\) | |||||||
\(140\) | −9.90372 | −0.837017 | ||||||||
\(141\) | 11.4803 | 0.966813 | ||||||||
\(142\) | 3.81473 | 0.320125 | ||||||||
\(143\) | −14.5235 | −1.21452 | ||||||||
\(144\) | 2.23126 | 0.185938 | ||||||||
\(145\) | −14.4029 | −1.19610 | ||||||||
\(146\) | 3.78224 | 0.313021 | ||||||||
\(147\) | 1.79626 | 0.148153 | ||||||||
\(148\) | 12.7696 | 1.04965 | ||||||||
\(149\) | −0.913554 | −0.0748413 | −0.0374206 | − | 0.999300i | \(-0.511914\pi\) | ||||
−0.0374206 | + | 0.999300i | \(0.511914\pi\) | |||||||
\(150\) | 0.895754 | 0.0731380 | ||||||||
\(151\) | 11.5558 | 0.940398 | 0.470199 | − | 0.882561i | \(-0.344182\pi\) | ||||
0.470199 | + | 0.882561i | \(0.344182\pi\) | |||||||
\(152\) | 9.57694 | 0.776792 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 3.08470 | 0.248572 | ||||||||
\(155\) | −18.3581 | −1.47456 | ||||||||
\(156\) | 10.1154 | 0.809880 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | 7.31415 | 0.581882 | ||||||||
\(159\) | 1.24871 | 0.0990292 | ||||||||
\(160\) | −13.7719 | −1.08877 | ||||||||
\(161\) | 1.96380 | 0.154769 | ||||||||
\(162\) | −0.557584 | −0.0438079 | ||||||||
\(163\) | 7.21230 | 0.564911 | 0.282455 | − | 0.959280i | \(-0.408851\pi\) | ||||
0.282455 | + | 0.959280i | \(0.408851\pi\) | |||||||
\(164\) | −12.9144 | −1.00845 | ||||||||
\(165\) | 6.23347 | 0.485275 | ||||||||
\(166\) | 4.25467 | 0.330226 | ||||||||
\(167\) | 22.2178 | 1.71926 | 0.859631 | − | 0.510916i | \(-0.170694\pi\) | ||||
0.859631 | + | 0.510916i | \(0.170694\pi\) | |||||||
\(168\) | −4.69233 | −0.362021 | ||||||||
\(169\) | 22.8637 | 1.75875 | ||||||||
\(170\) | 1.43316 | 0.109919 | ||||||||
\(171\) | 4.65582 | 0.356039 | ||||||||
\(172\) | 18.0599 | 1.37706 | ||||||||
\(173\) | −5.66663 | −0.430826 | −0.215413 | − | 0.976523i | \(-0.569110\pi\) | ||||
−0.215413 | + | 0.976523i | \(0.569110\pi\) | |||||||
\(174\) | −3.12446 | −0.236865 | ||||||||
\(175\) | 3.66468 | 0.277024 | ||||||||
\(176\) | −5.41121 | −0.407885 | ||||||||
\(177\) | −10.3301 | −0.776461 | ||||||||
\(178\) | 3.25810 | 0.244205 | ||||||||
\(179\) | −3.06701 | −0.229239 | −0.114619 | − | 0.993409i | \(-0.536565\pi\) | ||||
−0.114619 | + | 0.993409i | \(0.536565\pi\) | |||||||
\(180\) | −4.34151 | −0.323597 | ||||||||
\(181\) | −23.2615 | −1.72901 | −0.864506 | − | 0.502623i | \(-0.832368\pi\) | ||||
−0.864506 | + | 0.502623i | \(0.832368\pi\) | |||||||
\(182\) | −7.61721 | −0.564625 | ||||||||
\(183\) | 12.6616 | 0.935972 | ||||||||
\(184\) | 1.77080 | 0.130545 | ||||||||
\(185\) | −19.4315 | −1.42863 | ||||||||
\(186\) | −3.98247 | −0.292009 | ||||||||
\(187\) | 2.42518 | 0.177347 | ||||||||
\(188\) | 19.3913 | 1.41426 | ||||||||
\(189\) | −2.28117 | −0.165931 | ||||||||
\(190\) | −6.67255 | −0.484078 | ||||||||
\(191\) | 16.4607 | 1.19106 | 0.595528 | − | 0.803334i | \(-0.296943\pi\) | ||||
0.595528 | + | 0.803334i | \(0.296943\pi\) | |||||||
\(192\) | 1.47494 | 0.106444 | ||||||||
\(193\) | −10.7056 | −0.770609 | −0.385305 | − | 0.922789i | \(-0.625904\pi\) | ||||
−0.385305 | + | 0.922789i | \(0.625904\pi\) | |||||||
\(194\) | 1.55339 | 0.111527 | ||||||||
\(195\) | −15.3926 | −1.10229 | ||||||||
\(196\) | 3.03407 | 0.216719 | ||||||||
\(197\) | 2.97115 | 0.211686 | 0.105843 | − | 0.994383i | \(-0.466246\pi\) | ||||
0.105843 | + | 0.994383i | \(0.466246\pi\) | |||||||
\(198\) | 1.35224 | 0.0960998 | ||||||||
\(199\) | 0.00311595 | 0.000220884 0 | 0.000110442 | − | 1.00000i | \(-0.499965\pi\) | ||||
0.000110442 | 1.00000i | \(0.499965\pi\) | ||||||||
\(200\) | 3.30453 | 0.233665 | ||||||||
\(201\) | −0.360054 | −0.0253962 | ||||||||
\(202\) | 5.49914 | 0.386918 | ||||||||
\(203\) | −12.7827 | −0.897170 | ||||||||
\(204\) | −1.68910 | −0.118261 | ||||||||
\(205\) | 19.6519 | 1.37255 | ||||||||
\(206\) | −5.93218 | −0.413315 | ||||||||
\(207\) | 0.860875 | 0.0598349 | ||||||||
\(208\) | 13.3622 | 0.926501 | ||||||||
\(209\) | −11.2912 | −0.781029 | ||||||||
\(210\) | 3.26929 | 0.225602 | ||||||||
\(211\) | 7.48494 | 0.515285 | 0.257642 | − | 0.966240i | \(-0.417054\pi\) | ||||
0.257642 | + | 0.966240i | \(0.417054\pi\) | |||||||
\(212\) | 2.10920 | 0.144860 | ||||||||
\(213\) | 6.84154 | 0.468774 | ||||||||
\(214\) | −2.62318 | −0.179317 | ||||||||
\(215\) | −27.4818 | −1.87425 | ||||||||
\(216\) | −2.05698 | −0.139960 | ||||||||
\(217\) | −16.2930 | −1.10604 | ||||||||
\(218\) | 8.19575 | 0.555086 | ||||||||
\(219\) | 6.78327 | 0.458371 | ||||||||
\(220\) | 10.5290 | 0.709862 | ||||||||
\(221\) | −5.98863 | −0.402839 | ||||||||
\(222\) | −4.21532 | −0.282914 | ||||||||
\(223\) | 21.5652 | 1.44411 | 0.722056 | − | 0.691835i | \(-0.243197\pi\) | ||||
0.722056 | + | 0.691835i | \(0.243197\pi\) | |||||||
\(224\) | −12.2227 | −0.816663 | ||||||||
\(225\) | 1.60649 | 0.107099 | ||||||||
\(226\) | 6.00543 | 0.399475 | ||||||||
\(227\) | −2.09643 | −0.139145 | −0.0695726 | − | 0.997577i | \(-0.522164\pi\) | ||||
−0.0695726 | + | 0.997577i | \(0.522164\pi\) | |||||||
\(228\) | 7.86414 | 0.520815 | ||||||||
\(229\) | 7.93938 | 0.524649 | 0.262324 | − | 0.964980i | \(-0.415511\pi\) | ||||
0.262324 | + | 0.964980i | \(0.415511\pi\) | |||||||
\(230\) | −1.23377 | −0.0813527 | ||||||||
\(231\) | 5.53226 | 0.363996 | ||||||||
\(232\) | −11.5265 | −0.756749 | ||||||||
\(233\) | 10.4908 | 0.687276 | 0.343638 | − | 0.939102i | \(-0.388341\pi\) | ||||
0.343638 | + | 0.939102i | \(0.388341\pi\) | |||||||
\(234\) | −3.33917 | −0.218288 | ||||||||
\(235\) | −29.5078 | −1.92488 | ||||||||
\(236\) | −17.4486 | −1.13581 | ||||||||
\(237\) | 13.1176 | 0.852078 | ||||||||
\(238\) | 1.27194 | 0.0824479 | ||||||||
\(239\) | −2.06358 | −0.133482 | −0.0667409 | − | 0.997770i | \(-0.521260\pi\) | ||||
−0.0667409 | + | 0.997770i | \(0.521260\pi\) | |||||||
\(240\) | −5.73503 | −0.370194 | ||||||||
\(241\) | −17.6112 | −1.13444 | −0.567219 | − | 0.823567i | \(-0.691981\pi\) | ||||
−0.567219 | + | 0.823567i | \(0.691981\pi\) | |||||||
\(242\) | 2.85399 | 0.183461 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 21.3867 | 1.36914 | ||||||||
\(245\) | −4.61695 | −0.294966 | ||||||||
\(246\) | 4.26315 | 0.271808 | ||||||||
\(247\) | 27.8820 | 1.77409 | ||||||||
\(248\) | −14.6917 | −0.932927 | ||||||||
\(249\) | 7.63054 | 0.483566 | ||||||||
\(250\) | 4.86345 | 0.307592 | ||||||||
\(251\) | −24.4298 | −1.54200 | −0.770999 | − | 0.636837i | \(-0.780242\pi\) | ||||
−0.770999 | + | 0.636837i | \(0.780242\pi\) | |||||||
\(252\) | −3.85312 | −0.242724 | ||||||||
\(253\) | −2.08778 | −0.131258 | ||||||||
\(254\) | 10.4471 | 0.655508 | ||||||||
\(255\) | 2.57031 | 0.160959 | ||||||||
\(256\) | −3.48385 | −0.217740 | ||||||||
\(257\) | 0.168260 | 0.0104957 | 0.00524787 | − | 0.999986i | \(-0.498330\pi\) | ||||
0.00524787 | + | 0.999986i | \(0.498330\pi\) | |||||||
\(258\) | −5.96171 | −0.371160 | ||||||||
\(259\) | −17.2456 | −1.07159 | ||||||||
\(260\) | −25.9997 | −1.61243 | ||||||||
\(261\) | −5.60357 | −0.346852 | ||||||||
\(262\) | −8.51279 | −0.525922 | ||||||||
\(263\) | 13.4461 | 0.829124 | 0.414562 | − | 0.910021i | \(-0.363935\pi\) | ||||
0.414562 | + | 0.910021i | \(0.363935\pi\) | |||||||
\(264\) | 4.98856 | 0.307025 | ||||||||
\(265\) | −3.20957 | −0.197162 | ||||||||
\(266\) | −5.92194 | −0.363097 | ||||||||
\(267\) | 5.84324 | 0.357600 | ||||||||
\(268\) | −0.608166 | −0.0371497 | ||||||||
\(269\) | −11.1882 | −0.682156 | −0.341078 | − | 0.940035i | \(-0.610792\pi\) | ||||
−0.341078 | + | 0.940035i | \(0.610792\pi\) | |||||||
\(270\) | 1.43316 | 0.0872196 | ||||||||
\(271\) | 12.8358 | 0.779720 | 0.389860 | − | 0.920874i | \(-0.372523\pi\) | ||||
0.389860 | + | 0.920874i | \(0.372523\pi\) | |||||||
\(272\) | −2.23126 | −0.135290 | ||||||||
\(273\) | −13.6611 | −0.826807 | ||||||||
\(274\) | 8.07157 | 0.487621 | ||||||||
\(275\) | −3.89604 | −0.234940 | ||||||||
\(276\) | 1.45410 | 0.0875267 | ||||||||
\(277\) | −12.8645 | −0.772952 | −0.386476 | − | 0.922299i | \(-0.626308\pi\) | ||||
−0.386476 | + | 0.922299i | \(0.626308\pi\) | |||||||
\(278\) | −11.2955 | −0.677458 | ||||||||
\(279\) | −7.14237 | −0.427603 | ||||||||
\(280\) | 12.0607 | 0.720767 | ||||||||
\(281\) | 26.9236 | 1.60613 | 0.803064 | − | 0.595893i | \(-0.203202\pi\) | ||||
0.803064 | + | 0.595893i | \(0.203202\pi\) | |||||||
\(282\) | −6.40121 | −0.381187 | ||||||||
\(283\) | −16.5871 | −0.986001 | −0.493000 | − | 0.870029i | \(-0.664100\pi\) | ||||
−0.493000 | + | 0.870029i | \(0.664100\pi\) | |||||||
\(284\) | 11.5560 | 0.685725 | ||||||||
\(285\) | −11.9669 | −0.708857 | ||||||||
\(286\) | 8.09809 | 0.478850 | ||||||||
\(287\) | 17.4412 | 1.02952 | ||||||||
\(288\) | −5.35808 | −0.315728 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 8.03084 | 0.471587 | ||||||||
\(291\) | 2.78593 | 0.163314 | ||||||||
\(292\) | 11.4576 | 0.670507 | ||||||||
\(293\) | 32.8754 | 1.92060 | 0.960299 | − | 0.278972i | \(-0.0899935\pi\) | ||||
0.960299 | + | 0.278972i | \(0.0899935\pi\) | |||||||
\(294\) | −1.00157 | −0.0584126 | ||||||||
\(295\) | 26.5517 | 1.54590 | ||||||||
\(296\) | −15.5507 | −0.903868 | ||||||||
\(297\) | 2.42518 | 0.140723 | ||||||||
\(298\) | 0.509383 | 0.0295078 | ||||||||
\(299\) | 5.15546 | 0.298148 | ||||||||
\(300\) | 2.71353 | 0.156665 | ||||||||
\(301\) | −24.3904 | −1.40584 | ||||||||
\(302\) | −6.44333 | −0.370772 | ||||||||
\(303\) | 9.86245 | 0.566583 | ||||||||
\(304\) | 10.3883 | 0.595812 | ||||||||
\(305\) | −32.5442 | −1.86348 | ||||||||
\(306\) | 0.557584 | 0.0318750 | ||||||||
\(307\) | −9.51912 | −0.543285 | −0.271643 | − | 0.962398i | \(-0.587567\pi\) | ||||
−0.271643 | + | 0.962398i | \(0.587567\pi\) | |||||||
\(308\) | 9.34454 | 0.532454 | ||||||||
\(309\) | −10.6391 | −0.605236 | ||||||||
\(310\) | 10.2362 | 0.581377 | ||||||||
\(311\) | 5.96578 | 0.338288 | 0.169144 | − | 0.985591i | \(-0.445900\pi\) | ||||
0.169144 | + | 0.985591i | \(0.445900\pi\) | |||||||
\(312\) | −12.3185 | −0.697399 | ||||||||
\(313\) | 5.60364 | 0.316736 | 0.158368 | − | 0.987380i | \(-0.449377\pi\) | ||||
0.158368 | + | 0.987380i | \(0.449377\pi\) | |||||||
\(314\) | 0.557584 | 0.0314663 | ||||||||
\(315\) | 5.86331 | 0.330360 | ||||||||
\(316\) | 22.1569 | 1.24642 | ||||||||
\(317\) | −17.3820 | −0.976268 | −0.488134 | − | 0.872769i | \(-0.662322\pi\) | ||||
−0.488134 | + | 0.872769i | \(0.662322\pi\) | |||||||
\(318\) | −0.696261 | −0.0390444 | ||||||||
\(319\) | 13.5897 | 0.760877 | ||||||||
\(320\) | −3.79104 | −0.211926 | ||||||||
\(321\) | −4.70455 | −0.262582 | ||||||||
\(322\) | −1.09498 | −0.0610211 | ||||||||
\(323\) | −4.65582 | −0.259057 | ||||||||
\(324\) | −1.68910 | −0.0938389 | ||||||||
\(325\) | 9.62069 | 0.533660 | ||||||||
\(326\) | −4.02146 | −0.222728 | ||||||||
\(327\) | 14.6987 | 0.812839 | ||||||||
\(328\) | 15.7272 | 0.868388 | ||||||||
\(329\) | −26.1884 | −1.44382 | ||||||||
\(330\) | −3.47569 | −0.191330 | ||||||||
\(331\) | 7.45842 | 0.409952 | 0.204976 | − | 0.978767i | \(-0.434288\pi\) | ||||
0.204976 | + | 0.978767i | \(0.434288\pi\) | |||||||
\(332\) | 12.8887 | 0.707362 | ||||||||
\(333\) | −7.55997 | −0.414284 | ||||||||
\(334\) | −12.3883 | −0.677856 | ||||||||
\(335\) | 0.925449 | 0.0505627 | ||||||||
\(336\) | −5.08988 | −0.277676 | ||||||||
\(337\) | −15.2165 | −0.828893 | −0.414447 | − | 0.910074i | \(-0.636025\pi\) | ||||
−0.414447 | + | 0.910074i | \(0.636025\pi\) | |||||||
\(338\) | −12.7484 | −0.693424 | ||||||||
\(339\) | 10.7705 | 0.584971 | ||||||||
\(340\) | 4.34151 | 0.235451 | ||||||||
\(341\) | 17.3216 | 0.938015 | ||||||||
\(342\) | −2.59601 | −0.140376 | ||||||||
\(343\) | −20.0658 | −1.08345 | ||||||||
\(344\) | −21.9933 | −1.18580 | ||||||||
\(345\) | −2.21271 | −0.119129 | ||||||||
\(346\) | 3.15962 | 0.169862 | ||||||||
\(347\) | 16.3866 | 0.879680 | 0.439840 | − | 0.898076i | \(-0.355035\pi\) | ||||
0.439840 | + | 0.898076i | \(0.355035\pi\) | |||||||
\(348\) | −9.46499 | −0.507377 | ||||||||
\(349\) | −24.0635 | −1.28809 | −0.644045 | − | 0.764988i | \(-0.722745\pi\) | ||||
−0.644045 | + | 0.764988i | \(0.722745\pi\) | |||||||
\(350\) | −2.04337 | −0.109223 | ||||||||
\(351\) | −5.98863 | −0.319649 | ||||||||
\(352\) | 12.9943 | 0.692600 | ||||||||
\(353\) | 19.1711 | 1.02038 | 0.510189 | − | 0.860063i | \(-0.329576\pi\) | ||||
0.510189 | + | 0.860063i | \(0.329576\pi\) | |||||||
\(354\) | 5.75992 | 0.306136 | ||||||||
\(355\) | −17.5849 | −0.933308 | ||||||||
\(356\) | 9.86981 | 0.523099 | ||||||||
\(357\) | 2.28117 | 0.120732 | ||||||||
\(358\) | 1.71011 | 0.0903823 | ||||||||
\(359\) | 13.0198 | 0.687157 | 0.343578 | − | 0.939124i | \(-0.388361\pi\) | ||||
0.343578 | + | 0.939124i | \(0.388361\pi\) | |||||||
\(360\) | 5.28708 | 0.278654 | ||||||||
\(361\) | 2.67663 | 0.140875 | ||||||||
\(362\) | 12.9702 | 0.681700 | ||||||||
\(363\) | 5.11848 | 0.268651 | ||||||||
\(364\) | −23.0749 | −1.20946 | ||||||||
\(365\) | −17.4351 | −0.912595 | ||||||||
\(366\) | −7.05990 | −0.369027 | ||||||||
\(367\) | −0.448480 | −0.0234105 | −0.0117052 | − | 0.999931i | \(-0.503726\pi\) | ||||
−0.0117052 | + | 0.999931i | \(0.503726\pi\) | |||||||
\(368\) | 1.92083 | 0.100130 | ||||||||
\(369\) | 7.64575 | 0.398022 | ||||||||
\(370\) | 10.8347 | 0.563268 | ||||||||
\(371\) | −2.84852 | −0.147888 | ||||||||
\(372\) | −12.0642 | −0.625499 | ||||||||
\(373\) | 25.1547 | 1.30246 | 0.651229 | − | 0.758881i | \(-0.274254\pi\) | ||||
0.651229 | + | 0.758881i | \(0.274254\pi\) | |||||||
\(374\) | −1.35224 | −0.0699229 | ||||||||
\(375\) | 8.72237 | 0.450421 | ||||||||
\(376\) | −23.6147 | −1.21784 | ||||||||
\(377\) | −33.5577 | −1.72831 | ||||||||
\(378\) | 1.27194 | 0.0654218 | ||||||||
\(379\) | −8.21734 | −0.422096 | −0.211048 | − | 0.977476i | \(-0.567688\pi\) | ||||
−0.211048 | + | 0.977476i | \(0.567688\pi\) | |||||||
\(380\) | −20.2133 | −1.03692 | ||||||||
\(381\) | 18.7363 | 0.959891 | ||||||||
\(382\) | −9.17824 | −0.469600 | ||||||||
\(383\) | −18.4339 | −0.941927 | −0.470963 | − | 0.882153i | \(-0.656094\pi\) | ||||
−0.470963 | + | 0.882153i | \(0.656094\pi\) | |||||||
\(384\) | −11.5386 | −0.588825 | ||||||||
\(385\) | −14.2196 | −0.724699 | ||||||||
\(386\) | 5.96930 | 0.303829 | ||||||||
\(387\) | −10.6920 | −0.543507 | ||||||||
\(388\) | 4.70571 | 0.238896 | ||||||||
\(389\) | 11.7237 | 0.594415 | 0.297207 | − | 0.954813i | \(-0.403945\pi\) | ||||
0.297207 | + | 0.954813i | \(0.403945\pi\) | |||||||
\(390\) | 8.58269 | 0.434601 | ||||||||
\(391\) | −0.860875 | −0.0435363 | ||||||||
\(392\) | −3.69488 | −0.186620 | ||||||||
\(393\) | −15.2673 | −0.770132 | ||||||||
\(394\) | −1.65667 | −0.0834616 | ||||||||
\(395\) | −33.7162 | −1.69645 | ||||||||
\(396\) | 4.09638 | 0.205851 | ||||||||
\(397\) | −1.62892 | −0.0817529 | −0.0408765 | − | 0.999164i | \(-0.513015\pi\) | ||||
−0.0408765 | + | 0.999164i | \(0.513015\pi\) | |||||||
\(398\) | −0.00173740 | −8.70882e−5 0 | ||||||||
\(399\) | −10.6207 | −0.531701 | ||||||||
\(400\) | 3.58450 | 0.179225 | ||||||||
\(401\) | −7.92567 | −0.395789 | −0.197894 | − | 0.980223i | \(-0.563410\pi\) | ||||
−0.197894 | + | 0.980223i | \(0.563410\pi\) | |||||||
\(402\) | 0.200760 | 0.0100130 | ||||||||
\(403\) | −42.7730 | −2.13068 | ||||||||
\(404\) | 16.6587 | 0.828799 | ||||||||
\(405\) | 2.57031 | 0.127720 | ||||||||
\(406\) | 7.12743 | 0.353728 | ||||||||
\(407\) | 18.3343 | 0.908799 | ||||||||
\(408\) | 2.05698 | 0.101836 | ||||||||
\(409\) | −7.49370 | −0.370540 | −0.185270 | − | 0.982688i | \(-0.559316\pi\) | ||||
−0.185270 | + | 0.982688i | \(0.559316\pi\) | |||||||
\(410\) | −10.9576 | −0.541158 | ||||||||
\(411\) | 14.4760 | 0.714047 | ||||||||
\(412\) | −17.9705 | −0.885342 | ||||||||
\(413\) | 23.5648 | 1.15955 | ||||||||
\(414\) | −0.480010 | −0.0235912 | ||||||||
\(415\) | −19.6128 | −0.962757 | ||||||||
\(416\) | −32.0876 | −1.57322 | ||||||||
\(417\) | −20.2579 | −0.992033 | ||||||||
\(418\) | 6.29580 | 0.307938 | ||||||||
\(419\) | 21.4723 | 1.04899 | 0.524496 | − | 0.851413i | \(-0.324254\pi\) | ||||
0.524496 | + | 0.851413i | \(0.324254\pi\) | |||||||
\(420\) | 9.90372 | 0.483252 | ||||||||
\(421\) | 15.7215 | 0.766221 | 0.383110 | − | 0.923703i | \(-0.374853\pi\) | ||||
0.383110 | + | 0.923703i | \(0.374853\pi\) | |||||||
\(422\) | −4.17348 | −0.203162 | ||||||||
\(423\) | −11.4803 | −0.558190 | ||||||||
\(424\) | −2.56858 | −0.124741 | ||||||||
\(425\) | −1.60649 | −0.0779263 | ||||||||
\(426\) | −3.81473 | −0.184824 | ||||||||
\(427\) | −28.8833 | −1.39776 | ||||||||
\(428\) | −7.94645 | −0.384106 | ||||||||
\(429\) | 14.5235 | 0.701203 | ||||||||
\(430\) | 15.3234 | 0.738962 | ||||||||
\(431\) | 22.3477 | 1.07645 | 0.538226 | − | 0.842801i | \(-0.319095\pi\) | ||||
0.538226 | + | 0.842801i | \(0.319095\pi\) | |||||||
\(432\) | −2.23126 | −0.107351 | ||||||||
\(433\) | 21.3451 | 1.02578 | 0.512890 | − | 0.858455i | \(-0.328575\pi\) | ||||
0.512890 | + | 0.858455i | \(0.328575\pi\) | |||||||
\(434\) | 9.08470 | 0.436080 | ||||||||
\(435\) | 14.4029 | 0.690567 | ||||||||
\(436\) | 24.8275 | 1.18902 | ||||||||
\(437\) | 4.00807 | 0.191732 | ||||||||
\(438\) | −3.78224 | −0.180723 | ||||||||
\(439\) | 25.4189 | 1.21318 | 0.606589 | − | 0.795015i | \(-0.292537\pi\) | ||||
0.606589 | + | 0.795015i | \(0.292537\pi\) | |||||||
\(440\) | −12.8222 | −0.611272 | ||||||||
\(441\) | −1.79626 | −0.0855363 | ||||||||
\(442\) | 3.33917 | 0.158828 | ||||||||
\(443\) | 7.98059 | 0.379169 | 0.189585 | − | 0.981864i | \(-0.439286\pi\) | ||||
0.189585 | + | 0.981864i | \(0.439286\pi\) | |||||||
\(444\) | −12.7696 | −0.606016 | ||||||||
\(445\) | −15.0189 | −0.711965 | ||||||||
\(446\) | −12.0244 | −0.569372 | ||||||||
\(447\) | 0.913554 | 0.0432096 | ||||||||
\(448\) | −3.36458 | −0.158962 | ||||||||
\(449\) | −4.58022 | −0.216154 | −0.108077 | − | 0.994143i | \(-0.534469\pi\) | ||||
−0.108077 | + | 0.994143i | \(0.534469\pi\) | |||||||
\(450\) | −0.895754 | −0.0422263 | ||||||||
\(451\) | −18.5423 | −0.873125 | ||||||||
\(452\) | 18.1924 | 0.855697 | ||||||||
\(453\) | −11.5558 | −0.542939 | ||||||||
\(454\) | 1.16894 | 0.0548610 | ||||||||
\(455\) | 35.1132 | 1.64613 | ||||||||
\(456\) | −9.57694 | −0.448481 | ||||||||
\(457\) | 29.9508 | 1.40104 | 0.700520 | − | 0.713633i | \(-0.252952\pi\) | ||||
0.700520 | + | 0.713633i | \(0.252952\pi\) | |||||||
\(458\) | −4.42687 | −0.206854 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −3.73750 | −0.174262 | ||||||||
\(461\) | −23.1577 | −1.07856 | −0.539281 | − | 0.842126i | \(-0.681304\pi\) | ||||
−0.539281 | + | 0.842126i | \(0.681304\pi\) | |||||||
\(462\) | −3.08470 | −0.143513 | ||||||||
\(463\) | 1.97968 | 0.0920035 | 0.0460017 | − | 0.998941i | \(-0.485352\pi\) | ||||
0.0460017 | + | 0.998941i | \(0.485352\pi\) | |||||||
\(464\) | −12.5030 | −0.580438 | ||||||||
\(465\) | 18.3581 | 0.851337 | ||||||||
\(466\) | −5.84951 | −0.270973 | ||||||||
\(467\) | 31.0397 | 1.43635 | 0.718173 | − | 0.695864i | \(-0.244978\pi\) | ||||
0.718173 | + | 0.695864i | \(0.244978\pi\) | |||||||
\(468\) | −10.1154 | −0.467584 | ||||||||
\(469\) | 0.821344 | 0.0379261 | ||||||||
\(470\) | 16.4531 | 0.758925 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 21.2489 | 0.978061 | ||||||||
\(473\) | 25.9302 | 1.19227 | ||||||||
\(474\) | −7.31415 | −0.335950 | ||||||||
\(475\) | 7.47953 | 0.343184 | ||||||||
\(476\) | 3.85312 | 0.176608 | ||||||||
\(477\) | −1.24871 | −0.0571745 | ||||||||
\(478\) | 1.15062 | 0.0526280 | ||||||||
\(479\) | −11.0544 | −0.505090 | −0.252545 | − | 0.967585i | \(-0.581268\pi\) | ||||
−0.252545 | + | 0.967585i | \(0.581268\pi\) | |||||||
\(480\) | 13.7719 | 0.628600 | ||||||||
\(481\) | −45.2739 | −2.06431 | ||||||||
\(482\) | 9.81973 | 0.447276 | ||||||||
\(483\) | −1.96380 | −0.0893561 | ||||||||
\(484\) | 8.64563 | 0.392983 | ||||||||
\(485\) | −7.16069 | −0.325150 | ||||||||
\(486\) | 0.557584 | 0.0252925 | ||||||||
\(487\) | −31.8709 | −1.44421 | −0.722105 | − | 0.691784i | \(-0.756825\pi\) | ||||
−0.722105 | + | 0.691784i | \(0.756825\pi\) | |||||||
\(488\) | −26.0447 | −1.17899 | ||||||||
\(489\) | −7.21230 | −0.326151 | ||||||||
\(490\) | 2.57434 | 0.116297 | ||||||||
\(491\) | −37.3317 | −1.68476 | −0.842379 | − | 0.538885i | \(-0.818846\pi\) | ||||
−0.842379 | + | 0.538885i | \(0.818846\pi\) | |||||||
\(492\) | 12.9144 | 0.582227 | ||||||||
\(493\) | 5.60357 | 0.252372 | ||||||||
\(494\) | −15.5465 | −0.699472 | ||||||||
\(495\) | −6.23347 | −0.280174 | ||||||||
\(496\) | −15.9365 | −0.715569 | ||||||||
\(497\) | −15.6067 | −0.700057 | ||||||||
\(498\) | −4.25467 | −0.190656 | ||||||||
\(499\) | −27.8344 | −1.24604 | −0.623020 | − | 0.782206i | \(-0.714095\pi\) | ||||
−0.623020 | + | 0.782206i | \(0.714095\pi\) | |||||||
\(500\) | 14.7330 | 0.658878 | ||||||||
\(501\) | −22.2178 | −0.992616 | ||||||||
\(502\) | 13.6217 | 0.607966 | ||||||||
\(503\) | 43.3557 | 1.93314 | 0.966569 | − | 0.256408i | \(-0.0825392\pi\) | ||||
0.966569 | + | 0.256408i | \(0.0825392\pi\) | |||||||
\(504\) | 4.69233 | 0.209013 | ||||||||
\(505\) | −25.3495 | −1.12804 | ||||||||
\(506\) | 1.16411 | 0.0517511 | ||||||||
\(507\) | −22.8637 | −1.01541 | ||||||||
\(508\) | 31.6475 | 1.40413 | ||||||||
\(509\) | 4.03475 | 0.178837 | 0.0894187 | − | 0.995994i | \(-0.471499\pi\) | ||||
0.0894187 | + | 0.995994i | \(0.471499\pi\) | |||||||
\(510\) | −1.43316 | −0.0634616 | ||||||||
\(511\) | −15.4738 | −0.684520 | ||||||||
\(512\) | −21.1346 | −0.934026 | ||||||||
\(513\) | −4.65582 | −0.205559 | ||||||||
\(514\) | −0.0938189 | −0.00413817 | ||||||||
\(515\) | 27.3457 | 1.20500 | ||||||||
\(516\) | −18.0599 | −0.795044 | ||||||||
\(517\) | 27.8417 | 1.22448 | ||||||||
\(518\) | 9.61587 | 0.422497 | ||||||||
\(519\) | 5.66663 | 0.248738 | ||||||||
\(520\) | 31.6624 | 1.38849 | ||||||||
\(521\) | 1.75526 | 0.0768994 | 0.0384497 | − | 0.999261i | \(-0.487758\pi\) | ||||
0.0384497 | + | 0.999261i | \(0.487758\pi\) | |||||||
\(522\) | 3.12446 | 0.136754 | ||||||||
\(523\) | −3.12261 | −0.136542 | −0.0682711 | − | 0.997667i | \(-0.521748\pi\) | ||||
−0.0682711 | + | 0.997667i | \(0.521748\pi\) | |||||||
\(524\) | −25.7880 | −1.12655 | ||||||||
\(525\) | −3.66468 | −0.159940 | ||||||||
\(526\) | −7.49735 | −0.326900 | ||||||||
\(527\) | 7.14237 | 0.311127 | ||||||||
\(528\) | 5.41121 | 0.235493 | ||||||||
\(529\) | −22.2589 | −0.967778 | ||||||||
\(530\) | 1.78961 | 0.0777355 | ||||||||
\(531\) | 10.3301 | 0.448290 | ||||||||
\(532\) | −17.9394 | −0.777774 | ||||||||
\(533\) | 45.7876 | 1.98328 | ||||||||
\(534\) | −3.25810 | −0.140992 | ||||||||
\(535\) | 12.0921 | 0.522789 | ||||||||
\(536\) | 0.740624 | 0.0319901 | ||||||||
\(537\) | 3.06701 | 0.132351 | ||||||||
\(538\) | 6.23836 | 0.268955 | ||||||||
\(539\) | 4.35626 | 0.187638 | ||||||||
\(540\) | 4.34151 | 0.186829 | ||||||||
\(541\) | 22.3133 | 0.959325 | 0.479663 | − | 0.877453i | \(-0.340759\pi\) | ||||
0.479663 | + | 0.877453i | \(0.340759\pi\) | |||||||
\(542\) | −7.15704 | −0.307421 | ||||||||
\(543\) | 23.2615 | 0.998245 | ||||||||
\(544\) | 5.35808 | 0.229726 | ||||||||
\(545\) | −37.7801 | −1.61832 | ||||||||
\(546\) | 7.61721 | 0.325986 | ||||||||
\(547\) | −6.96561 | −0.297828 | −0.148914 | − | 0.988850i | \(-0.547578\pi\) | ||||
−0.148914 | + | 0.988850i | \(0.547578\pi\) | |||||||
\(548\) | 24.4514 | 1.04451 | ||||||||
\(549\) | −12.6616 | −0.540384 | ||||||||
\(550\) | 2.17237 | 0.0926301 | ||||||||
\(551\) | −26.0892 | −1.11144 | ||||||||
\(552\) | −1.77080 | −0.0753704 | ||||||||
\(553\) | −29.9234 | −1.27247 | ||||||||
\(554\) | 7.17304 | 0.304753 | ||||||||
\(555\) | 19.4315 | 0.824820 | ||||||||
\(556\) | −34.2176 | −1.45115 | ||||||||
\(557\) | 21.4567 | 0.909150 | 0.454575 | − | 0.890708i | \(-0.349791\pi\) | ||||
0.454575 | + | 0.890708i | \(0.349791\pi\) | |||||||
\(558\) | 3.98247 | 0.168592 | ||||||||
\(559\) | −64.0307 | −2.70821 | ||||||||
\(560\) | 13.0826 | 0.552840 | ||||||||
\(561\) | −2.42518 | −0.102391 | ||||||||
\(562\) | −15.0122 | −0.633251 | ||||||||
\(563\) | −44.8900 | −1.89189 | −0.945944 | − | 0.324329i | \(-0.894861\pi\) | ||||
−0.945944 | + | 0.324329i | \(0.894861\pi\) | |||||||
\(564\) | −19.3913 | −0.816522 | ||||||||
\(565\) | −27.6834 | −1.16465 | ||||||||
\(566\) | 9.24870 | 0.388752 | ||||||||
\(567\) | 2.28117 | 0.0958002 | ||||||||
\(568\) | −14.0729 | −0.590487 | ||||||||
\(569\) | 14.8993 | 0.624611 | 0.312305 | − | 0.949982i | \(-0.398899\pi\) | ||||
0.312305 | + | 0.949982i | \(0.398899\pi\) | |||||||
\(570\) | 6.67255 | 0.279482 | ||||||||
\(571\) | 20.4277 | 0.854872 | 0.427436 | − | 0.904046i | \(-0.359417\pi\) | ||||
0.427436 | + | 0.904046i | \(0.359417\pi\) | |||||||
\(572\) | 24.5317 | 1.02572 | ||||||||
\(573\) | −16.4607 | −0.687657 | ||||||||
\(574\) | −9.72496 | −0.405912 | ||||||||
\(575\) | 1.38299 | 0.0576746 | ||||||||
\(576\) | −1.47494 | −0.0614557 | ||||||||
\(577\) | 28.7380 | 1.19638 | 0.598188 | − | 0.801356i | \(-0.295887\pi\) | ||||
0.598188 | + | 0.801356i | \(0.295887\pi\) | |||||||
\(578\) | −0.557584 | −0.0231924 | ||||||||
\(579\) | 10.7056 | 0.444911 | ||||||||
\(580\) | 24.3280 | 1.01016 | ||||||||
\(581\) | −17.4066 | −0.722146 | ||||||||
\(582\) | −1.55339 | −0.0643900 | ||||||||
\(583\) | 3.02835 | 0.125422 | ||||||||
\(584\) | −13.9531 | −0.577382 | ||||||||
\(585\) | 15.3926 | 0.636407 | ||||||||
\(586\) | −18.3308 | −0.757237 | ||||||||
\(587\) | −21.1509 | −0.872989 | −0.436495 | − | 0.899707i | \(-0.643780\pi\) | ||||
−0.436495 | + | 0.899707i | \(0.643780\pi\) | |||||||
\(588\) | −3.03407 | −0.125123 | ||||||||
\(589\) | −33.2536 | −1.37019 | ||||||||
\(590\) | −14.8048 | −0.609503 | ||||||||
\(591\) | −2.97115 | −0.122217 | ||||||||
\(592\) | −16.8683 | −0.693281 | ||||||||
\(593\) | 4.18862 | 0.172006 | 0.0860030 | − | 0.996295i | \(-0.472591\pi\) | ||||
0.0860030 | + | 0.996295i | \(0.472591\pi\) | |||||||
\(594\) | −1.35224 | −0.0554832 | ||||||||
\(595\) | −5.86331 | −0.240372 | ||||||||
\(596\) | 1.54308 | 0.0632072 | ||||||||
\(597\) | −0.00311595 | −0.000127527 0 | ||||||||
\(598\) | −2.87460 | −0.117551 | ||||||||
\(599\) | −31.5329 | −1.28840 | −0.644200 | − | 0.764857i | \(-0.722810\pi\) | ||||
−0.644200 | + | 0.764857i | \(0.722810\pi\) | |||||||
\(600\) | −3.30453 | −0.134907 | ||||||||
\(601\) | −0.898549 | −0.0366526 | −0.0183263 | − | 0.999832i | \(-0.505834\pi\) | ||||
−0.0183263 | + | 0.999832i | \(0.505834\pi\) | |||||||
\(602\) | 13.5997 | 0.554281 | ||||||||
\(603\) | 0.360054 | 0.0146625 | ||||||||
\(604\) | −19.5189 | −0.794213 | ||||||||
\(605\) | −13.1561 | −0.534871 | ||||||||
\(606\) | −5.49914 | −0.223387 | ||||||||
\(607\) | −2.27389 | −0.0922943 | −0.0461472 | − | 0.998935i | \(-0.514694\pi\) | ||||
−0.0461472 | + | 0.998935i | \(0.514694\pi\) | |||||||
\(608\) | −24.9462 | −1.01170 | ||||||||
\(609\) | 12.7827 | 0.517981 | ||||||||
\(610\) | 18.1461 | 0.734716 | ||||||||
\(611\) | −68.7511 | −2.78137 | ||||||||
\(612\) | 1.68910 | 0.0682778 | ||||||||
\(613\) | −17.4478 | −0.704711 | −0.352356 | − | 0.935866i | \(-0.614619\pi\) | ||||
−0.352356 | + | 0.935866i | \(0.614619\pi\) | |||||||
\(614\) | 5.30771 | 0.214202 | ||||||||
\(615\) | −19.6519 | −0.792442 | ||||||||
\(616\) | −11.3798 | −0.458504 | ||||||||
\(617\) | 11.7395 | 0.472616 | 0.236308 | − | 0.971678i | \(-0.424063\pi\) | ||||
0.236308 | + | 0.971678i | \(0.424063\pi\) | |||||||
\(618\) | 5.93218 | 0.238627 | ||||||||
\(619\) | 0.193779 | 0.00778865 | 0.00389433 | − | 0.999992i | \(-0.498760\pi\) | ||||
0.00389433 | + | 0.999992i | \(0.498760\pi\) | |||||||
\(620\) | 31.0087 | 1.24534 | ||||||||
\(621\) | −0.860875 | −0.0345457 | ||||||||
\(622\) | −3.32642 | −0.133377 | ||||||||
\(623\) | −13.3294 | −0.534032 | ||||||||
\(624\) | −13.3622 | −0.534916 | ||||||||
\(625\) | −30.4516 | −1.21807 | ||||||||
\(626\) | −3.12450 | −0.124880 | ||||||||
\(627\) | 11.2912 | 0.450928 | ||||||||
\(628\) | 1.68910 | 0.0674024 | ||||||||
\(629\) | 7.55997 | 0.301436 | ||||||||
\(630\) | −3.26929 | −0.130252 | ||||||||
\(631\) | −7.13757 | −0.284142 | −0.142071 | − | 0.989856i | \(-0.545376\pi\) | ||||
−0.142071 | + | 0.989856i | \(0.545376\pi\) | |||||||
\(632\) | −26.9826 | −1.07331 | ||||||||
\(633\) | −7.48494 | −0.297500 | ||||||||
\(634\) | 9.69190 | 0.384915 | ||||||||
\(635\) | −48.1581 | −1.91110 | ||||||||
\(636\) | −2.10920 | −0.0836351 | ||||||||
\(637\) | −10.7571 | −0.426214 | ||||||||
\(638\) | −7.57740 | −0.299992 | ||||||||
\(639\) | −6.84154 | −0.270647 | ||||||||
\(640\) | 29.6577 | 1.17232 | ||||||||
\(641\) | −37.3037 | −1.47341 | −0.736703 | − | 0.676216i | \(-0.763619\pi\) | ||||
−0.736703 | + | 0.676216i | \(0.763619\pi\) | |||||||
\(642\) | 2.62318 | 0.103529 | ||||||||
\(643\) | −15.5799 | −0.614411 | −0.307206 | − | 0.951643i | \(-0.599394\pi\) | ||||
−0.307206 | + | 0.951643i | \(0.599394\pi\) | |||||||
\(644\) | −3.31706 | −0.130710 | ||||||||
\(645\) | 27.4818 | 1.08210 | ||||||||
\(646\) | 2.59601 | 0.102139 | ||||||||
\(647\) | 8.41034 | 0.330645 | 0.165322 | − | 0.986240i | \(-0.447134\pi\) | ||||
0.165322 | + | 0.986240i | \(0.447134\pi\) | |||||||
\(648\) | 2.05698 | 0.0808059 | ||||||||
\(649\) | −25.0525 | −0.983396 | ||||||||
\(650\) | −5.36434 | −0.210407 | ||||||||
\(651\) | 16.2930 | 0.638572 | ||||||||
\(652\) | −12.1823 | −0.477095 | ||||||||
\(653\) | 1.19781 | 0.0468738 | 0.0234369 | − | 0.999725i | \(-0.492539\pi\) | ||||
0.0234369 | + | 0.999725i | \(0.492539\pi\) | |||||||
\(654\) | −8.19575 | −0.320479 | ||||||||
\(655\) | 39.2416 | 1.53330 | ||||||||
\(656\) | 17.0596 | 0.666067 | ||||||||
\(657\) | −6.78327 | −0.264641 | ||||||||
\(658\) | 14.6023 | 0.569255 | ||||||||
\(659\) | −12.0572 | −0.469681 | −0.234840 | − | 0.972034i | \(-0.575457\pi\) | ||||
−0.234840 | + | 0.972034i | \(0.575457\pi\) | |||||||
\(660\) | −10.5290 | −0.409839 | ||||||||
\(661\) | 19.4807 | 0.757711 | 0.378856 | − | 0.925456i | \(-0.376318\pi\) | ||||
0.378856 | + | 0.925456i | \(0.376318\pi\) | |||||||
\(662\) | −4.15870 | −0.161632 | ||||||||
\(663\) | 5.98863 | 0.232579 | ||||||||
\(664\) | −15.6959 | −0.609119 | ||||||||
\(665\) | 27.2985 | 1.05859 | ||||||||
\(666\) | 4.21532 | 0.163340 | ||||||||
\(667\) | −4.82397 | −0.186785 | ||||||||
\(668\) | −37.5280 | −1.45200 | ||||||||
\(669\) | −21.5652 | −0.833758 | ||||||||
\(670\) | −0.516016 | −0.0199354 | ||||||||
\(671\) | 30.7067 | 1.18542 | ||||||||
\(672\) | 12.2227 | 0.471501 | ||||||||
\(673\) | −21.8095 | −0.840693 | −0.420346 | − | 0.907364i | \(-0.638091\pi\) | ||||
−0.420346 | + | 0.907364i | \(0.638091\pi\) | |||||||
\(674\) | 8.48446 | 0.326809 | ||||||||
\(675\) | −1.60649 | −0.0618339 | ||||||||
\(676\) | −38.6191 | −1.48535 | ||||||||
\(677\) | −25.6392 | −0.985395 | −0.492698 | − | 0.870201i | \(-0.663989\pi\) | ||||
−0.492698 | + | 0.870201i | \(0.663989\pi\) | |||||||
\(678\) | −6.00543 | −0.230637 | ||||||||
\(679\) | −6.35517 | −0.243889 | ||||||||
\(680\) | −5.28708 | −0.202750 | ||||||||
\(681\) | 2.09643 | 0.0803355 | ||||||||
\(682\) | −9.65823 | −0.369833 | ||||||||
\(683\) | 25.6713 | 0.982284 | 0.491142 | − | 0.871079i | \(-0.336580\pi\) | ||||
0.491142 | + | 0.871079i | \(0.336580\pi\) | |||||||
\(684\) | −7.86414 | −0.300693 | ||||||||
\(685\) | −37.2077 | −1.42163 | ||||||||
\(686\) | 11.1884 | 0.427173 | ||||||||
\(687\) | −7.93938 | −0.302906 | ||||||||
\(688\) | −23.8567 | −0.909528 | ||||||||
\(689\) | −7.47807 | −0.284892 | ||||||||
\(690\) | 1.23377 | 0.0469690 | ||||||||
\(691\) | −34.8985 | −1.32760 | −0.663800 | − | 0.747910i | \(-0.731057\pi\) | ||||
−0.663800 | + | 0.747910i | \(0.731057\pi\) | |||||||
\(692\) | 9.57151 | 0.363854 | ||||||||
\(693\) | −5.53226 | −0.210153 | ||||||||
\(694\) | −9.13692 | −0.346833 | ||||||||
\(695\) | 52.0691 | 1.97509 | ||||||||
\(696\) | 11.5265 | 0.436909 | ||||||||
\(697\) | −7.64575 | −0.289603 | ||||||||
\(698\) | 13.4174 | 0.507857 | ||||||||
\(699\) | −10.4908 | −0.396799 | ||||||||
\(700\) | −6.19001 | −0.233960 | ||||||||
\(701\) | 32.7128 | 1.23554 | 0.617772 | − | 0.786357i | \(-0.288035\pi\) | ||||
0.617772 | + | 0.786357i | \(0.288035\pi\) | |||||||
\(702\) | 3.33917 | 0.126029 | ||||||||
\(703\) | −35.1979 | −1.32751 | ||||||||
\(704\) | 3.57699 | 0.134813 | ||||||||
\(705\) | 29.5078 | 1.11133 | ||||||||
\(706\) | −10.6895 | −0.402306 | ||||||||
\(707\) | −22.4979 | −0.846121 | ||||||||
\(708\) | 17.4486 | 0.655760 | ||||||||
\(709\) | 25.2635 | 0.948789 | 0.474394 | − | 0.880312i | \(-0.342667\pi\) | ||||
0.474394 | + | 0.880312i | \(0.342667\pi\) | |||||||
\(710\) | 9.80504 | 0.367977 | ||||||||
\(711\) | −13.1176 | −0.491947 | ||||||||
\(712\) | −12.0194 | −0.450448 | ||||||||
\(713\) | −6.14869 | −0.230270 | ||||||||
\(714\) | −1.27194 | −0.0476013 | ||||||||
\(715\) | −37.3300 | −1.39606 | ||||||||
\(716\) | 5.18048 | 0.193604 | ||||||||
\(717\) | 2.06358 | 0.0770657 | ||||||||
\(718\) | −7.25961 | −0.270926 | ||||||||
\(719\) | 25.0704 | 0.934967 | 0.467483 | − | 0.884002i | \(-0.345161\pi\) | ||||
0.467483 | + | 0.884002i | \(0.345161\pi\) | |||||||
\(720\) | 5.73503 | 0.213732 | ||||||||
\(721\) | 24.2696 | 0.903846 | ||||||||
\(722\) | −1.49245 | −0.0555431 | ||||||||
\(723\) | 17.6112 | 0.654968 | ||||||||
\(724\) | 39.2910 | 1.46024 | ||||||||
\(725\) | −9.00209 | −0.334329 | ||||||||
\(726\) | −2.85399 | −0.105921 | ||||||||
\(727\) | −28.0600 | −1.04069 | −0.520344 | − | 0.853957i | \(-0.674196\pi\) | ||||
−0.520344 | + | 0.853957i | \(0.674196\pi\) | |||||||
\(728\) | 28.1006 | 1.04148 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 9.72154 | 0.359810 | ||||||||
\(731\) | 10.6920 | 0.395459 | ||||||||
\(732\) | −21.3867 | −0.790475 | ||||||||
\(733\) | 12.8857 | 0.475944 | 0.237972 | − | 0.971272i | \(-0.423517\pi\) | ||||
0.237972 | + | 0.971272i | \(0.423517\pi\) | |||||||
\(734\) | 0.250065 | 0.00923007 | ||||||||
\(735\) | 4.61695 | 0.170299 | ||||||||
\(736\) | −4.61264 | −0.170024 | ||||||||
\(737\) | −0.873196 | −0.0321646 | ||||||||
\(738\) | −4.26315 | −0.156929 | ||||||||
\(739\) | −6.60328 | −0.242906 | −0.121453 | − | 0.992597i | \(-0.538755\pi\) | ||||
−0.121453 | + | 0.992597i | \(0.538755\pi\) | |||||||
\(740\) | 32.8217 | 1.20655 | ||||||||
\(741\) | −27.8820 | −1.02427 | ||||||||
\(742\) | 1.58829 | 0.0583080 | ||||||||
\(743\) | −28.5658 | −1.04798 | −0.523990 | − | 0.851725i | \(-0.675557\pi\) | ||||
−0.523990 | + | 0.851725i | \(0.675557\pi\) | |||||||
\(744\) | 14.6917 | 0.538625 | ||||||||
\(745\) | −2.34812 | −0.0860284 | ||||||||
\(746\) | −14.0258 | −0.513522 | ||||||||
\(747\) | −7.63054 | −0.279187 | ||||||||
\(748\) | −4.09638 | −0.149778 | ||||||||
\(749\) | 10.7319 | 0.392134 | ||||||||
\(750\) | −4.86345 | −0.177588 | ||||||||
\(751\) | 8.20013 | 0.299227 | 0.149613 | − | 0.988745i | \(-0.452197\pi\) | ||||
0.149613 | + | 0.988745i | \(0.452197\pi\) | |||||||
\(752\) | −25.6154 | −0.934099 | ||||||||
\(753\) | 24.4298 | 0.890272 | ||||||||
\(754\) | 18.7113 | 0.681424 | ||||||||
\(755\) | 29.7020 | 1.08097 | ||||||||
\(756\) | 3.85312 | 0.140137 | ||||||||
\(757\) | −38.8721 | −1.41283 | −0.706416 | − | 0.707797i | \(-0.749689\pi\) | ||||
−0.706416 | + | 0.707797i | \(0.749689\pi\) | |||||||
\(758\) | 4.58186 | 0.166420 | ||||||||
\(759\) | 2.08778 | 0.0757816 | ||||||||
\(760\) | 24.6157 | 0.892905 | ||||||||
\(761\) | 11.0561 | 0.400782 | 0.200391 | − | 0.979716i | \(-0.435779\pi\) | ||||
0.200391 | + | 0.979716i | \(0.435779\pi\) | |||||||
\(762\) | −10.4471 | −0.378458 | ||||||||
\(763\) | −33.5302 | −1.21387 | ||||||||
\(764\) | −27.8038 | −1.00591 | ||||||||
\(765\) | −2.57031 | −0.0929297 | ||||||||
\(766\) | 10.2784 | 0.371375 | ||||||||
\(767\) | 61.8634 | 2.23376 | ||||||||
\(768\) | 3.48385 | 0.125712 | ||||||||
\(769\) | −1.74873 | −0.0630609 | −0.0315305 | − | 0.999503i | \(-0.510038\pi\) | ||||
−0.0315305 | + | 0.999503i | \(0.510038\pi\) | |||||||
\(770\) | 7.92863 | 0.285728 | ||||||||
\(771\) | −0.168260 | −0.00605972 | ||||||||
\(772\) | 18.0829 | 0.650818 | ||||||||
\(773\) | 37.4020 | 1.34526 | 0.672628 | − | 0.739981i | \(-0.265165\pi\) | ||||
0.672628 | + | 0.739981i | \(0.265165\pi\) | |||||||
\(774\) | 5.96171 | 0.214289 | ||||||||
\(775\) | −11.4742 | −0.412164 | ||||||||
\(776\) | −5.73060 | −0.205717 | ||||||||
\(777\) | 17.2456 | 0.618682 | ||||||||
\(778\) | −6.53694 | −0.234361 | ||||||||
\(779\) | 35.5972 | 1.27540 | ||||||||
\(780\) | 25.9997 | 0.930939 | ||||||||
\(781\) | 16.5920 | 0.593708 | ||||||||
\(782\) | 0.480010 | 0.0171651 | ||||||||
\(783\) | 5.60357 | 0.200255 | ||||||||
\(784\) | −4.00792 | −0.143140 | ||||||||
\(785\) | −2.57031 | −0.0917383 | ||||||||
\(786\) | 8.51279 | 0.303641 | ||||||||
\(787\) | 44.4020 | 1.58276 | 0.791380 | − | 0.611324i | \(-0.209363\pi\) | ||||
0.791380 | + | 0.611324i | \(0.209363\pi\) | |||||||
\(788\) | −5.01857 | −0.178779 | ||||||||
\(789\) | −13.4461 | −0.478695 | ||||||||
\(790\) | 18.7996 | 0.668861 | ||||||||
\(791\) | −24.5692 | −0.873582 | ||||||||
\(792\) | −4.98856 | −0.177261 | ||||||||
\(793\) | −75.8256 | −2.69265 | ||||||||
\(794\) | 0.908257 | 0.0322328 | ||||||||
\(795\) | 3.20957 | 0.113832 | ||||||||
\(796\) | −0.00526315 | −0.000186547 0 | ||||||||
\(797\) | 23.3214 | 0.826085 | 0.413042 | − | 0.910712i | \(-0.364466\pi\) | ||||
0.413042 | + | 0.910712i | \(0.364466\pi\) | |||||||
\(798\) | 5.92194 | 0.209634 | ||||||||
\(799\) | 11.4803 | 0.406143 | ||||||||
\(800\) | −8.60771 | −0.304329 | ||||||||
\(801\) | −5.84324 | −0.206461 | ||||||||
\(802\) | 4.41923 | 0.156048 | ||||||||
\(803\) | 16.4507 | 0.580532 | ||||||||
\(804\) | 0.608166 | 0.0214484 | ||||||||
\(805\) | 5.04758 | 0.177904 | ||||||||
\(806\) | 23.8496 | 0.840065 | ||||||||
\(807\) | 11.1882 | 0.393843 | ||||||||
\(808\) | −20.2869 | −0.713690 | ||||||||
\(809\) | 36.3204 | 1.27696 | 0.638478 | − | 0.769640i | \(-0.279564\pi\) | ||||
0.638478 | + | 0.769640i | \(0.279564\pi\) | |||||||
\(810\) | −1.43316 | −0.0503562 | ||||||||
\(811\) | −23.9469 | −0.840891 | −0.420445 | − | 0.907318i | \(-0.638126\pi\) | ||||
−0.420445 | + | 0.907318i | \(0.638126\pi\) | |||||||
\(812\) | 21.5913 | 0.757705 | ||||||||
\(813\) | −12.8358 | −0.450172 | ||||||||
\(814\) | −10.2229 | −0.358313 | ||||||||
\(815\) | 18.5378 | 0.649352 | ||||||||
\(816\) | 2.23126 | 0.0781097 | ||||||||
\(817\) | −49.7802 | −1.74159 | ||||||||
\(818\) | 4.17837 | 0.146093 | ||||||||
\(819\) | 13.6611 | 0.477357 | ||||||||
\(820\) | −33.1941 | −1.15919 | ||||||||
\(821\) | −15.4203 | −0.538171 | −0.269086 | − | 0.963116i | \(-0.586721\pi\) | ||||
−0.269086 | + | 0.963116i | \(0.586721\pi\) | |||||||
\(822\) | −8.07157 | −0.281528 | ||||||||
\(823\) | −41.3441 | −1.44116 | −0.720582 | − | 0.693370i | \(-0.756125\pi\) | ||||
−0.720582 | + | 0.693370i | \(0.756125\pi\) | |||||||
\(824\) | 21.8844 | 0.762380 | ||||||||
\(825\) | 3.89604 | 0.135643 | ||||||||
\(826\) | −13.1394 | −0.457177 | ||||||||
\(827\) | −4.02627 | −0.140007 | −0.0700035 | − | 0.997547i | \(-0.522301\pi\) | ||||
−0.0700035 | + | 0.997547i | \(0.522301\pi\) | |||||||
\(828\) | −1.45410 | −0.0505336 | ||||||||
\(829\) | 13.2272 | 0.459401 | 0.229700 | − | 0.973261i | \(-0.426225\pi\) | ||||
0.229700 | + | 0.973261i | \(0.426225\pi\) | |||||||
\(830\) | 10.9358 | 0.379587 | ||||||||
\(831\) | 12.8645 | 0.446264 | ||||||||
\(832\) | −8.83285 | −0.306224 | ||||||||
\(833\) | 1.79626 | 0.0622368 | ||||||||
\(834\) | 11.2955 | 0.391130 | ||||||||
\(835\) | 57.1065 | 1.97625 | ||||||||
\(836\) | 19.0720 | 0.659618 | ||||||||
\(837\) | 7.14237 | 0.246877 | ||||||||
\(838\) | −11.9726 | −0.413587 | ||||||||
\(839\) | −22.7731 | −0.786216 | −0.393108 | − | 0.919492i | \(-0.628600\pi\) | ||||
−0.393108 | + | 0.919492i | \(0.628600\pi\) | |||||||
\(840\) | −12.0607 | −0.416135 | ||||||||
\(841\) | 2.40002 | 0.0827592 | ||||||||
\(842\) | −8.76608 | −0.302099 | ||||||||
\(843\) | −26.9236 | −0.927299 | ||||||||
\(844\) | −12.6428 | −0.435184 | ||||||||
\(845\) | 58.7668 | 2.02164 | ||||||||
\(846\) | 6.40121 | 0.220078 | ||||||||
\(847\) | −11.6761 | −0.401197 | ||||||||
\(848\) | −2.78620 | −0.0956784 | ||||||||
\(849\) | 16.5871 | 0.569268 | ||||||||
\(850\) | 0.895754 | 0.0307241 | ||||||||
\(851\) | −6.50819 | −0.223098 | ||||||||
\(852\) | −11.5560 | −0.395903 | ||||||||
\(853\) | −21.5422 | −0.737592 | −0.368796 | − | 0.929510i | \(-0.620230\pi\) | ||||
−0.368796 | + | 0.929510i | \(0.620230\pi\) | |||||||
\(854\) | 16.1048 | 0.551096 | ||||||||
\(855\) | 11.9669 | 0.409259 | ||||||||
\(856\) | 9.67717 | 0.330759 | ||||||||
\(857\) | 15.3627 | 0.524779 | 0.262389 | − | 0.964962i | \(-0.415490\pi\) | ||||
0.262389 | + | 0.964962i | \(0.415490\pi\) | |||||||
\(858\) | −8.09809 | −0.276464 | ||||||||
\(859\) | 27.6812 | 0.944471 | 0.472235 | − | 0.881473i | \(-0.343447\pi\) | ||||
0.472235 | + | 0.881473i | \(0.343447\pi\) | |||||||
\(860\) | 46.4196 | 1.58289 | ||||||||
\(861\) | −17.4412 | −0.594396 | ||||||||
\(862\) | −12.4607 | −0.424414 | ||||||||
\(863\) | −1.19662 | −0.0407335 | −0.0203667 | − | 0.999793i | \(-0.506483\pi\) | ||||
−0.0203667 | + | 0.999793i | \(0.506483\pi\) | |||||||
\(864\) | 5.35808 | 0.182286 | ||||||||
\(865\) | −14.5650 | −0.495225 | ||||||||
\(866\) | −11.9017 | −0.404435 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 27.5205 | 0.934105 | ||||||||
\(869\) | 31.8125 | 1.07917 | ||||||||
\(870\) | −8.03084 | −0.272271 | ||||||||
\(871\) | 2.15623 | 0.0730610 | ||||||||
\(872\) | −30.2349 | −1.02388 | ||||||||
\(873\) | −2.78593 | −0.0942893 | ||||||||
\(874\) | −2.23484 | −0.0755945 | ||||||||
\(875\) | −19.8972 | −0.672648 | ||||||||
\(876\) | −11.4576 | −0.387117 | ||||||||
\(877\) | 3.50001 | 0.118187 | 0.0590935 | − | 0.998252i | \(-0.481179\pi\) | ||||
0.0590935 | + | 0.998252i | \(0.481179\pi\) | |||||||
\(878\) | −14.1732 | −0.478322 | ||||||||
\(879\) | −32.8754 | −1.10886 | ||||||||
\(880\) | −13.9085 | −0.468855 | ||||||||
\(881\) | −56.9316 | −1.91807 | −0.959037 | − | 0.283282i | \(-0.908577\pi\) | ||||
−0.959037 | + | 0.283282i | \(0.908577\pi\) | |||||||
\(882\) | 1.00157 | 0.0337245 | ||||||||
\(883\) | 10.2254 | 0.344112 | 0.172056 | − | 0.985087i | \(-0.444959\pi\) | ||||
0.172056 | + | 0.985087i | \(0.444959\pi\) | |||||||
\(884\) | 10.1154 | 0.340218 | ||||||||
\(885\) | −26.5517 | −0.892524 | ||||||||
\(886\) | −4.44985 | −0.149496 | ||||||||
\(887\) | −5.02440 | −0.168703 | −0.0843514 | − | 0.996436i | \(-0.526882\pi\) | ||||
−0.0843514 | + | 0.996436i | \(0.526882\pi\) | |||||||
\(888\) | 15.5507 | 0.521849 | ||||||||
\(889\) | −42.7407 | −1.43348 | ||||||||
\(890\) | 8.37431 | 0.280708 | ||||||||
\(891\) | −2.42518 | −0.0812467 | ||||||||
\(892\) | −36.4258 | −1.21962 | ||||||||
\(893\) | −53.4500 | −1.78864 | ||||||||
\(894\) | −0.509383 | −0.0170363 | ||||||||
\(895\) | −7.88316 | −0.263505 | ||||||||
\(896\) | 26.3214 | 0.879337 | ||||||||
\(897\) | −5.15546 | −0.172136 | ||||||||
\(898\) | 2.55386 | 0.0852233 | ||||||||
\(899\) | 40.0228 | 1.33484 | ||||||||
\(900\) | −2.71353 | −0.0904508 | ||||||||
\(901\) | 1.24871 | 0.0416006 | ||||||||
\(902\) | 10.3389 | 0.344248 | ||||||||
\(903\) | 24.3904 | 0.811660 | ||||||||
\(904\) | −22.1546 | −0.736852 | ||||||||
\(905\) | −59.7892 | −1.98746 | ||||||||
\(906\) | 6.44333 | 0.214065 | ||||||||
\(907\) | 58.1444 | 1.93065 | 0.965326 | − | 0.261048i | \(-0.0840681\pi\) | ||||
0.965326 | + | 0.261048i | \(0.0840681\pi\) | |||||||
\(908\) | 3.54109 | 0.117515 | ||||||||
\(909\) | −9.86245 | −0.327117 | ||||||||
\(910\) | −19.5786 | −0.649023 | ||||||||
\(911\) | −13.1575 | −0.435927 | −0.217963 | − | 0.975957i | \(-0.569941\pi\) | ||||
−0.217963 | + | 0.975957i | \(0.569941\pi\) | |||||||
\(912\) | −10.3883 | −0.343992 | ||||||||
\(913\) | 18.5055 | 0.612441 | ||||||||
\(914\) | −16.7001 | −0.552390 | ||||||||
\(915\) | 32.5442 | 1.07588 | ||||||||
\(916\) | −13.4104 | −0.443092 | ||||||||
\(917\) | 34.8273 | 1.15010 | ||||||||
\(918\) | −0.557584 | −0.0184030 | ||||||||
\(919\) | −15.0798 | −0.497436 | −0.248718 | − | 0.968576i | \(-0.580009\pi\) | ||||
−0.248718 | + | 0.968576i | \(0.580009\pi\) | |||||||
\(920\) | 4.55152 | 0.150059 | ||||||||
\(921\) | 9.51912 | 0.313666 | ||||||||
\(922\) | 12.9124 | 0.425246 | ||||||||
\(923\) | −40.9714 | −1.34859 | ||||||||
\(924\) | −9.34454 | −0.307413 | ||||||||
\(925\) | −12.1450 | −0.399326 | ||||||||
\(926\) | −1.10384 | −0.0362744 | ||||||||
\(927\) | 10.6391 | 0.349433 | ||||||||
\(928\) | 30.0244 | 0.985599 | ||||||||
\(929\) | 8.61431 | 0.282626 | 0.141313 | − | 0.989965i | \(-0.454868\pi\) | ||||
0.141313 | + | 0.989965i | \(0.454868\pi\) | |||||||
\(930\) | −10.2362 | −0.335658 | ||||||||
\(931\) | −8.36307 | −0.274088 | ||||||||
\(932\) | −17.7200 | −0.580439 | ||||||||
\(933\) | −5.96578 | −0.195311 | ||||||||
\(934\) | −17.3073 | −0.566311 | ||||||||
\(935\) | 6.23347 | 0.203856 | ||||||||
\(936\) | 12.3185 | 0.402643 | ||||||||
\(937\) | −2.26912 | −0.0741288 | −0.0370644 | − | 0.999313i | \(-0.511801\pi\) | ||||
−0.0370644 | + | 0.999313i | \(0.511801\pi\) | |||||||
\(938\) | −0.457968 | −0.0149532 | ||||||||
\(939\) | −5.60364 | −0.182868 | ||||||||
\(940\) | 49.8417 | 1.62566 | ||||||||
\(941\) | −45.7976 | −1.49296 | −0.746479 | − | 0.665409i | \(-0.768257\pi\) | ||||
−0.746479 | + | 0.665409i | \(0.768257\pi\) | |||||||
\(942\) | −0.557584 | −0.0181671 | ||||||||
\(943\) | 6.58203 | 0.214340 | ||||||||
\(944\) | 23.0492 | 0.750188 | ||||||||
\(945\) | −5.86331 | −0.190734 | ||||||||
\(946\) | −14.4582 | −0.470078 | ||||||||
\(947\) | 44.2873 | 1.43914 | 0.719572 | − | 0.694418i | \(-0.244338\pi\) | ||||
0.719572 | + | 0.694418i | \(0.244338\pi\) | |||||||
\(948\) | −22.1569 | −0.719622 | ||||||||
\(949\) | −40.6225 | −1.31866 | ||||||||
\(950\) | −4.17047 | −0.135308 | ||||||||
\(951\) | 17.3820 | 0.563648 | ||||||||
\(952\) | −4.69233 | −0.152079 | ||||||||
\(953\) | 6.83616 | 0.221445 | 0.110722 | − | 0.993851i | \(-0.464684\pi\) | ||||
0.110722 | + | 0.993851i | \(0.464684\pi\) | |||||||
\(954\) | 0.696261 | 0.0225423 | ||||||||
\(955\) | 42.3092 | 1.36909 | ||||||||
\(956\) | 3.48559 | 0.112732 | ||||||||
\(957\) | −13.5897 | −0.439292 | ||||||||
\(958\) | 6.16377 | 0.199142 | ||||||||
\(959\) | −33.0221 | −1.06634 | ||||||||
\(960\) | 3.79104 | 0.122355 | ||||||||
\(961\) | 20.0135 | 0.645597 | ||||||||
\(962\) | 25.2440 | 0.813899 | ||||||||
\(963\) | 4.70455 | 0.151602 | ||||||||
\(964\) | 29.7471 | 0.958089 | ||||||||
\(965\) | −27.5168 | −0.885798 | ||||||||
\(966\) | 1.09498 | 0.0352305 | ||||||||
\(967\) | 1.54153 | 0.0495722 | 0.0247861 | − | 0.999693i | \(-0.492110\pi\) | ||||
0.0247861 | + | 0.999693i | \(0.492110\pi\) | |||||||
\(968\) | −10.5286 | −0.338403 | ||||||||
\(969\) | 4.65582 | 0.149566 | ||||||||
\(970\) | 3.99269 | 0.128197 | ||||||||
\(971\) | −56.6339 | −1.81747 | −0.908734 | − | 0.417375i | \(-0.862950\pi\) | ||||
−0.908734 | + | 0.417375i | \(0.862950\pi\) | |||||||
\(972\) | 1.68910 | 0.0541779 | ||||||||
\(973\) | 46.2117 | 1.48148 | ||||||||
\(974\) | 17.7707 | 0.569411 | ||||||||
\(975\) | −9.62069 | −0.308109 | ||||||||
\(976\) | −28.2513 | −0.904302 | ||||||||
\(977\) | −8.93841 | −0.285965 | −0.142982 | − | 0.989725i | \(-0.545669\pi\) | ||||
−0.142982 | + | 0.989725i | \(0.545669\pi\) | |||||||
\(978\) | 4.02146 | 0.128592 | ||||||||
\(979\) | 14.1709 | 0.452905 | ||||||||
\(980\) | 7.79849 | 0.249114 | ||||||||
\(981\) | −14.6987 | −0.469293 | ||||||||
\(982\) | 20.8156 | 0.664252 | ||||||||
\(983\) | −12.5330 | −0.399741 | −0.199870 | − | 0.979822i | \(-0.564052\pi\) | ||||
−0.199870 | + | 0.979822i | \(0.564052\pi\) | |||||||
\(984\) | −15.7272 | −0.501364 | ||||||||
\(985\) | 7.63678 | 0.243328 | ||||||||
\(986\) | −3.12446 | −0.0995032 | ||||||||
\(987\) | 26.1884 | 0.833587 | ||||||||
\(988\) | −47.0954 | −1.49831 | ||||||||
\(989\) | −9.20450 | −0.292686 | ||||||||
\(990\) | 3.47569 | 0.110465 | ||||||||
\(991\) | 58.0655 | 1.84451 | 0.922256 | − | 0.386581i | \(-0.126344\pi\) | ||||
0.922256 | + | 0.386581i | \(0.126344\pi\) | |||||||
\(992\) | 38.2694 | 1.21506 | ||||||||
\(993\) | −7.45842 | −0.236686 | ||||||||
\(994\) | 8.70205 | 0.276012 | ||||||||
\(995\) | 0.00800895 | 0.000253901 0 | ||||||||
\(996\) | −12.8887 | −0.408395 | ||||||||
\(997\) | 39.9132 | 1.26406 | 0.632032 | − | 0.774942i | \(-0.282221\pi\) | ||||
0.632032 | + | 0.774942i | \(0.282221\pi\) | |||||||
\(998\) | 15.5200 | 0.491278 | ||||||||
\(999\) | 7.55997 | 0.239187 |
(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 | 8007.2.a.f.1.20 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.f.1.20 | ✓ | 48 | 1.1 | even | 1 | trivial |