Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [619,2,Mod(1,619)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(619, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("619.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 619.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: | \(4.94273988512\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 619.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.39793 | 0.988487 | 0.494243 | − | 0.869324i | \(-0.335445\pi\) | ||||
0.494243 | + | 0.869324i | \(0.335445\pi\) | |||||||
\(3\) | 2.10519 | 1.21543 | 0.607715 | − | 0.794155i | \(-0.292086\pi\) | ||||
0.607715 | + | 0.794155i | \(0.292086\pi\) | |||||||
\(4\) | −0.0457880 | −0.0228940 | ||||||||
\(5\) | 3.90881 | 1.74807 | 0.874037 | − | 0.485859i | \(-0.161493\pi\) | ||||
0.874037 | + | 0.485859i | \(0.161493\pi\) | |||||||
\(6\) | 2.94291 | 1.20144 | ||||||||
\(7\) | −1.82243 | −0.688814 | −0.344407 | − | 0.938820i | \(-0.611920\pi\) | ||||
−0.344407 | + | 0.938820i | \(0.611920\pi\) | |||||||
\(8\) | −2.85987 | −1.01112 | ||||||||
\(9\) | 1.43181 | 0.477272 | ||||||||
\(10\) | 5.46425 | 1.72795 | ||||||||
\(11\) | 4.06764 | 1.22644 | 0.613220 | − | 0.789913i | \(-0.289874\pi\) | ||||
0.613220 | + | 0.789913i | \(0.289874\pi\) | |||||||
\(12\) | −0.0963923 | −0.0278260 | ||||||||
\(13\) | −2.56773 | −0.712161 | −0.356081 | − | 0.934455i | \(-0.615887\pi\) | ||||
−0.356081 | + | 0.934455i | \(0.615887\pi\) | |||||||
\(14\) | −2.54763 | −0.680884 | ||||||||
\(15\) | 8.22879 | 2.12466 | ||||||||
\(16\) | −3.90633 | −0.976582 | ||||||||
\(17\) | 2.96017 | 0.717947 | 0.358973 | − | 0.933348i | \(-0.383127\pi\) | ||||
0.358973 | + | 0.933348i | \(0.383127\pi\) | |||||||
\(18\) | 2.00158 | 0.471777 | ||||||||
\(19\) | −3.33421 | −0.764919 | −0.382460 | − | 0.923972i | \(-0.624923\pi\) | ||||
−0.382460 | + | 0.923972i | \(0.624923\pi\) | |||||||
\(20\) | −0.178977 | −0.0400204 | ||||||||
\(21\) | −3.83656 | −0.837206 | ||||||||
\(22\) | 5.68628 | 1.21232 | ||||||||
\(23\) | −9.09190 | −1.89579 | −0.947896 | − | 0.318580i | \(-0.896794\pi\) | ||||
−0.947896 | + | 0.318580i | \(0.896794\pi\) | |||||||
\(24\) | −6.02057 | −1.22894 | ||||||||
\(25\) | 10.2788 | 2.05576 | ||||||||
\(26\) | −3.58952 | −0.703962 | ||||||||
\(27\) | −3.30132 | −0.635340 | ||||||||
\(28\) | 0.0834454 | 0.0157697 | ||||||||
\(29\) | 7.13218 | 1.32441 | 0.662206 | − | 0.749322i | \(-0.269620\pi\) | ||||
0.662206 | + | 0.749322i | \(0.269620\pi\) | |||||||
\(30\) | 11.5033 | 2.10020 | ||||||||
\(31\) | 3.95596 | 0.710512 | 0.355256 | − | 0.934769i | \(-0.384394\pi\) | ||||
0.355256 | + | 0.934769i | \(0.384394\pi\) | |||||||
\(32\) | 0.258965 | 0.0457789 | ||||||||
\(33\) | 8.56314 | 1.49065 | ||||||||
\(34\) | 4.13812 | 0.709681 | ||||||||
\(35\) | −7.12354 | −1.20410 | ||||||||
\(36\) | −0.0655599 | −0.0109266 | ||||||||
\(37\) | −2.67606 | −0.439942 | −0.219971 | − | 0.975506i | \(-0.570596\pi\) | ||||
−0.219971 | + | 0.975506i | \(0.570596\pi\) | |||||||
\(38\) | −4.66099 | −0.756113 | ||||||||
\(39\) | −5.40556 | −0.865582 | ||||||||
\(40\) | −11.1787 | −1.76751 | ||||||||
\(41\) | −9.73483 | −1.52032 | −0.760162 | − | 0.649733i | \(-0.774881\pi\) | ||||
−0.760162 | + | 0.649733i | \(0.774881\pi\) | |||||||
\(42\) | −5.36325 | −0.827567 | ||||||||
\(43\) | 3.74301 | 0.570804 | 0.285402 | − | 0.958408i | \(-0.407873\pi\) | ||||
0.285402 | + | 0.958408i | \(0.407873\pi\) | |||||||
\(44\) | −0.186249 | −0.0280781 | ||||||||
\(45\) | 5.59670 | 0.834306 | ||||||||
\(46\) | −12.7098 | −1.87397 | ||||||||
\(47\) | −6.42485 | −0.937161 | −0.468580 | − | 0.883421i | \(-0.655234\pi\) | ||||
−0.468580 | + | 0.883421i | \(0.655234\pi\) | |||||||
\(48\) | −8.22355 | −1.18697 | ||||||||
\(49\) | −3.67874 | −0.525535 | ||||||||
\(50\) | 14.3691 | 2.03210 | ||||||||
\(51\) | 6.23171 | 0.872615 | ||||||||
\(52\) | 0.117571 | 0.0163042 | ||||||||
\(53\) | 1.59008 | 0.218414 | 0.109207 | − | 0.994019i | \(-0.465169\pi\) | ||||
0.109207 | + | 0.994019i | \(0.465169\pi\) | |||||||
\(54\) | −4.61502 | −0.628025 | ||||||||
\(55\) | 15.8996 | 2.14391 | ||||||||
\(56\) | 5.21192 | 0.696472 | ||||||||
\(57\) | −7.01913 | −0.929707 | ||||||||
\(58\) | 9.97029 | 1.30916 | ||||||||
\(59\) | −11.4488 | −1.49051 | −0.745256 | − | 0.666779i | \(-0.767673\pi\) | ||||
−0.745256 | + | 0.666779i | \(0.767673\pi\) | |||||||
\(60\) | −0.376779 | −0.0486420 | ||||||||
\(61\) | 11.9419 | 1.52901 | 0.764504 | − | 0.644619i | \(-0.222984\pi\) | ||||
0.764504 | + | 0.644619i | \(0.222984\pi\) | |||||||
\(62\) | 5.53016 | 0.702331 | ||||||||
\(63\) | −2.60938 | −0.328752 | ||||||||
\(64\) | 8.17467 | 1.02183 | ||||||||
\(65\) | −10.0368 | −1.24491 | ||||||||
\(66\) | 11.9707 | 1.47349 | ||||||||
\(67\) | −1.47790 | −0.180554 | −0.0902772 | − | 0.995917i | \(-0.528775\pi\) | ||||
−0.0902772 | + | 0.995917i | \(0.528775\pi\) | |||||||
\(68\) | −0.135540 | −0.0164367 | ||||||||
\(69\) | −19.1402 | −2.30420 | ||||||||
\(70\) | −9.95823 | −1.19024 | ||||||||
\(71\) | 15.1260 | 1.79512 | 0.897561 | − | 0.440890i | \(-0.145337\pi\) | ||||
0.897561 | + | 0.440890i | \(0.145337\pi\) | |||||||
\(72\) | −4.09481 | −0.482578 | ||||||||
\(73\) | −7.51431 | −0.879483 | −0.439741 | − | 0.898124i | \(-0.644930\pi\) | ||||
−0.439741 | + | 0.898124i | \(0.644930\pi\) | |||||||
\(74\) | −3.74095 | −0.434877 | ||||||||
\(75\) | 21.6388 | 2.49864 | ||||||||
\(76\) | 0.152667 | 0.0175121 | ||||||||
\(77\) | −7.41299 | −0.844789 | ||||||||
\(78\) | −7.55660 | −0.855617 | ||||||||
\(79\) | 1.32751 | 0.149356 | 0.0746782 | − | 0.997208i | \(-0.476207\pi\) | ||||
0.0746782 | + | 0.997208i | \(0.476207\pi\) | |||||||
\(80\) | −15.2691 | −1.70714 | ||||||||
\(81\) | −11.2454 | −1.24948 | ||||||||
\(82\) | −13.6086 | −1.50282 | ||||||||
\(83\) | 9.23897 | 1.01411 | 0.507055 | − | 0.861914i | \(-0.330734\pi\) | ||||
0.507055 | + | 0.861914i | \(0.330734\pi\) | |||||||
\(84\) | 0.175668 | 0.0191670 | ||||||||
\(85\) | 11.5708 | 1.25502 | ||||||||
\(86\) | 5.23248 | 0.564232 | ||||||||
\(87\) | 15.0146 | 1.60973 | ||||||||
\(88\) | −11.6329 | −1.24007 | ||||||||
\(89\) | 6.11475 | 0.648162 | 0.324081 | − | 0.946029i | \(-0.394945\pi\) | ||||
0.324081 | + | 0.946029i | \(0.394945\pi\) | |||||||
\(90\) | 7.82380 | 0.824701 | ||||||||
\(91\) | 4.67952 | 0.490547 | ||||||||
\(92\) | 0.416300 | 0.0434022 | ||||||||
\(93\) | 8.32804 | 0.863578 | ||||||||
\(94\) | −8.98150 | −0.926371 | ||||||||
\(95\) | −13.0328 | −1.33714 | ||||||||
\(96\) | 0.545169 | 0.0556411 | ||||||||
\(97\) | 14.0971 | 1.43134 | 0.715671 | − | 0.698438i | \(-0.246121\pi\) | ||||
0.715671 | + | 0.698438i | \(0.246121\pi\) | |||||||
\(98\) | −5.14263 | −0.519484 | ||||||||
\(99\) | 5.82411 | 0.585345 | ||||||||
\(100\) | −0.470646 | −0.0470646 | ||||||||
\(101\) | 1.48940 | 0.148201 | 0.0741004 | − | 0.997251i | \(-0.476391\pi\) | ||||
0.0741004 | + | 0.997251i | \(0.476391\pi\) | |||||||
\(102\) | 8.71151 | 0.862568 | ||||||||
\(103\) | −16.7916 | −1.65452 | −0.827260 | − | 0.561819i | \(-0.810102\pi\) | ||||
−0.827260 | + | 0.561819i | \(0.810102\pi\) | |||||||
\(104\) | 7.34339 | 0.720078 | ||||||||
\(105\) | −14.9964 | −1.46350 | ||||||||
\(106\) | 2.22282 | 0.215899 | ||||||||
\(107\) | −2.61690 | −0.252985 | −0.126492 | − | 0.991968i | \(-0.540372\pi\) | ||||
−0.126492 | + | 0.991968i | \(0.540372\pi\) | |||||||
\(108\) | 0.151161 | 0.0145455 | ||||||||
\(109\) | 17.2308 | 1.65041 | 0.825206 | − | 0.564832i | \(-0.191059\pi\) | ||||
0.825206 | + | 0.564832i | \(0.191059\pi\) | |||||||
\(110\) | 22.2266 | 2.11922 | ||||||||
\(111\) | −5.63361 | −0.534719 | ||||||||
\(112\) | 7.11902 | 0.672684 | ||||||||
\(113\) | −18.5328 | −1.74342 | −0.871710 | − | 0.490023i | \(-0.836989\pi\) | ||||
−0.871710 | + | 0.490023i | \(0.836989\pi\) | |||||||
\(114\) | −9.81226 | −0.919003 | ||||||||
\(115\) | −35.5385 | −3.31399 | ||||||||
\(116\) | −0.326568 | −0.0303211 | ||||||||
\(117\) | −3.67652 | −0.339894 | ||||||||
\(118\) | −16.0047 | −1.47335 | ||||||||
\(119\) | −5.39471 | −0.494532 | ||||||||
\(120\) | −23.5333 | −2.14828 | ||||||||
\(121\) | 5.54568 | 0.504153 | ||||||||
\(122\) | 16.6940 | 1.51140 | ||||||||
\(123\) | −20.4936 | −1.84785 | ||||||||
\(124\) | −0.181135 | −0.0162664 | ||||||||
\(125\) | 20.6339 | 1.84555 | ||||||||
\(126\) | −3.64774 | −0.324967 | ||||||||
\(127\) | −0.429692 | −0.0381290 | −0.0190645 | − | 0.999818i | \(-0.506069\pi\) | ||||
−0.0190645 | + | 0.999818i | \(0.506069\pi\) | |||||||
\(128\) | 10.9097 | 0.964290 | ||||||||
\(129\) | 7.87974 | 0.693773 | ||||||||
\(130\) | −14.0307 | −1.23058 | ||||||||
\(131\) | −5.27070 | −0.460504 | −0.230252 | − | 0.973131i | \(-0.573955\pi\) | ||||
−0.230252 | + | 0.973131i | \(0.573955\pi\) | |||||||
\(132\) | −0.392089 | −0.0341270 | ||||||||
\(133\) | 6.07636 | 0.526888 | ||||||||
\(134\) | −2.06600 | −0.178476 | ||||||||
\(135\) | −12.9043 | −1.11062 | ||||||||
\(136\) | −8.46571 | −0.725928 | ||||||||
\(137\) | −3.67358 | −0.313855 | −0.156928 | − | 0.987610i | \(-0.550159\pi\) | ||||
−0.156928 | + | 0.987610i | \(0.550159\pi\) | |||||||
\(138\) | −26.7566 | −2.27767 | ||||||||
\(139\) | 14.1968 | 1.20415 | 0.602077 | − | 0.798438i | \(-0.294340\pi\) | ||||
0.602077 | + | 0.798438i | \(0.294340\pi\) | |||||||
\(140\) | 0.326173 | 0.0275666 | ||||||||
\(141\) | −13.5255 | −1.13905 | ||||||||
\(142\) | 21.1451 | 1.77445 | ||||||||
\(143\) | −10.4446 | −0.873422 | ||||||||
\(144\) | −5.59314 | −0.466095 | ||||||||
\(145\) | 27.8784 | 2.31517 | ||||||||
\(146\) | −10.5045 | −0.869357 | ||||||||
\(147\) | −7.74444 | −0.638751 | ||||||||
\(148\) | 0.122531 | 0.0100720 | ||||||||
\(149\) | −6.70971 | −0.549681 | −0.274840 | − | 0.961490i | \(-0.588625\pi\) | ||||
−0.274840 | + | 0.961490i | \(0.588625\pi\) | |||||||
\(150\) | 30.2496 | 2.46987 | ||||||||
\(151\) | 3.13432 | 0.255068 | 0.127534 | − | 0.991834i | \(-0.459294\pi\) | ||||
0.127534 | + | 0.991834i | \(0.459294\pi\) | |||||||
\(152\) | 9.53540 | 0.773423 | ||||||||
\(153\) | 4.23842 | 0.342656 | ||||||||
\(154\) | −10.3629 | −0.835063 | ||||||||
\(155\) | 15.4631 | 1.24203 | ||||||||
\(156\) | 0.247510 | 0.0198166 | ||||||||
\(157\) | 1.34412 | 0.107273 | 0.0536364 | − | 0.998561i | \(-0.482919\pi\) | ||||
0.0536364 | + | 0.998561i | \(0.482919\pi\) | |||||||
\(158\) | 1.85577 | 0.147637 | ||||||||
\(159\) | 3.34741 | 0.265467 | ||||||||
\(160\) | 1.01224 | 0.0800249 | ||||||||
\(161\) | 16.5694 | 1.30585 | ||||||||
\(162\) | −15.7202 | −1.23510 | ||||||||
\(163\) | −23.3324 | −1.82753 | −0.913767 | − | 0.406238i | \(-0.866840\pi\) | ||||
−0.913767 | + | 0.406238i | \(0.866840\pi\) | |||||||
\(164\) | 0.445738 | 0.0348063 | ||||||||
\(165\) | 33.4717 | 2.60577 | ||||||||
\(166\) | 12.9154 | 1.00243 | ||||||||
\(167\) | 1.80311 | 0.139529 | 0.0697643 | − | 0.997564i | \(-0.477775\pi\) | ||||
0.0697643 | + | 0.997564i | \(0.477775\pi\) | |||||||
\(168\) | 10.9721 | 0.846514 | ||||||||
\(169\) | −6.40674 | −0.492827 | ||||||||
\(170\) | 16.1751 | 1.24057 | ||||||||
\(171\) | −4.77397 | −0.365074 | ||||||||
\(172\) | −0.171385 | −0.0130680 | ||||||||
\(173\) | −13.8430 | −1.05247 | −0.526233 | − | 0.850340i | \(-0.676396\pi\) | ||||
−0.526233 | + | 0.850340i | \(0.676396\pi\) | |||||||
\(174\) | 20.9893 | 1.59120 | ||||||||
\(175\) | −18.7324 | −1.41604 | ||||||||
\(176\) | −15.8895 | −1.19772 | ||||||||
\(177\) | −24.1019 | −1.81161 | ||||||||
\(178\) | 8.54800 | 0.640700 | ||||||||
\(179\) | −16.9237 | −1.26494 | −0.632469 | − | 0.774585i | \(-0.717959\pi\) | ||||
−0.632469 | + | 0.774585i | \(0.717959\pi\) | |||||||
\(180\) | −0.256261 | −0.0191006 | ||||||||
\(181\) | 6.28833 | 0.467408 | 0.233704 | − | 0.972308i | \(-0.424915\pi\) | ||||
0.233704 | + | 0.972308i | \(0.424915\pi\) | |||||||
\(182\) | 6.54165 | 0.484899 | ||||||||
\(183\) | 25.1400 | 1.85840 | ||||||||
\(184\) | 26.0017 | 1.91687 | ||||||||
\(185\) | −10.4602 | −0.769051 | ||||||||
\(186\) | 11.6420 | 0.853635 | ||||||||
\(187\) | 12.0409 | 0.880518 | ||||||||
\(188\) | 0.294181 | 0.0214553 | ||||||||
\(189\) | 6.01644 | 0.437631 | ||||||||
\(190\) | −18.2189 | −1.32174 | ||||||||
\(191\) | 23.0612 | 1.66865 | 0.834323 | − | 0.551275i | \(-0.185859\pi\) | ||||
0.834323 | + | 0.551275i | \(0.185859\pi\) | |||||||
\(192\) | 17.2092 | 1.24197 | ||||||||
\(193\) | 22.3229 | 1.60684 | 0.803418 | − | 0.595415i | \(-0.203012\pi\) | ||||
0.803418 | + | 0.595415i | \(0.203012\pi\) | |||||||
\(194\) | 19.7067 | 1.41486 | ||||||||
\(195\) | −21.1293 | −1.51310 | ||||||||
\(196\) | 0.168442 | 0.0120316 | ||||||||
\(197\) | 7.74217 | 0.551607 | 0.275804 | − | 0.961214i | \(-0.411056\pi\) | ||||
0.275804 | + | 0.961214i | \(0.411056\pi\) | |||||||
\(198\) | 8.14170 | 0.578605 | ||||||||
\(199\) | 19.1916 | 1.36045 | 0.680227 | − | 0.733002i | \(-0.261881\pi\) | ||||
0.680227 | + | 0.733002i | \(0.261881\pi\) | |||||||
\(200\) | −29.3961 | −2.07862 | ||||||||
\(201\) | −3.11126 | −0.219451 | ||||||||
\(202\) | 2.08208 | 0.146495 | ||||||||
\(203\) | −12.9979 | −0.912274 | ||||||||
\(204\) | −0.285338 | −0.0199776 | ||||||||
\(205\) | −38.0516 | −2.65764 | ||||||||
\(206\) | −23.4734 | −1.63547 | ||||||||
\(207\) | −13.0179 | −0.904808 | ||||||||
\(208\) | 10.0304 | 0.695484 | ||||||||
\(209\) | −13.5623 | −0.938127 | ||||||||
\(210\) | −20.9639 | −1.44665 | ||||||||
\(211\) | 6.89545 | 0.474702 | 0.237351 | − | 0.971424i | \(-0.423721\pi\) | ||||
0.237351 | + | 0.971424i | \(0.423721\pi\) | |||||||
\(212\) | −0.0728064 | −0.00500037 | ||||||||
\(213\) | 31.8430 | 2.18185 | ||||||||
\(214\) | −3.65824 | −0.250072 | ||||||||
\(215\) | 14.6307 | 0.997808 | ||||||||
\(216\) | 9.44136 | 0.642403 | ||||||||
\(217\) | −7.20947 | −0.489411 | ||||||||
\(218\) | 24.0875 | 1.63141 | ||||||||
\(219\) | −15.8190 | −1.06895 | ||||||||
\(220\) | −0.728012 | −0.0490826 | ||||||||
\(221\) | −7.60093 | −0.511294 | ||||||||
\(222\) | −7.87540 | −0.528562 | ||||||||
\(223\) | −6.29320 | −0.421424 | −0.210712 | − | 0.977548i | \(-0.567578\pi\) | ||||
−0.210712 | + | 0.977548i | \(0.567578\pi\) | |||||||
\(224\) | −0.471945 | −0.0315332 | ||||||||
\(225\) | 14.7174 | 0.981158 | ||||||||
\(226\) | −25.9076 | −1.72335 | ||||||||
\(227\) | 9.01887 | 0.598603 | 0.299302 | − | 0.954159i | \(-0.403246\pi\) | ||||
0.299302 | + | 0.954159i | \(0.403246\pi\) | |||||||
\(228\) | 0.321392 | 0.0212847 | ||||||||
\(229\) | 16.0739 | 1.06219 | 0.531097 | − | 0.847311i | \(-0.321780\pi\) | ||||
0.531097 | + | 0.847311i | \(0.321780\pi\) | |||||||
\(230\) | −49.6804 | −3.27583 | ||||||||
\(231\) | −15.6057 | −1.02678 | ||||||||
\(232\) | −20.3971 | −1.33914 | ||||||||
\(233\) | 9.93384 | 0.650788 | 0.325394 | − | 0.945579i | \(-0.394503\pi\) | ||||
0.325394 | + | 0.945579i | \(0.394503\pi\) | |||||||
\(234\) | −5.13952 | −0.335981 | ||||||||
\(235\) | −25.1135 | −1.63823 | ||||||||
\(236\) | 0.524219 | 0.0341237 | ||||||||
\(237\) | 2.79465 | 0.181532 | ||||||||
\(238\) | −7.54143 | −0.488838 | ||||||||
\(239\) | −5.63614 | −0.364571 | −0.182286 | − | 0.983246i | \(-0.558350\pi\) | ||||
−0.182286 | + | 0.983246i | \(0.558350\pi\) | |||||||
\(240\) | −32.1443 | −2.07491 | ||||||||
\(241\) | −6.89445 | −0.444110 | −0.222055 | − | 0.975034i | \(-0.571277\pi\) | ||||
−0.222055 | + | 0.975034i | \(0.571277\pi\) | |||||||
\(242\) | 7.75248 | 0.498348 | ||||||||
\(243\) | −13.7696 | −0.883320 | ||||||||
\(244\) | −0.546797 | −0.0350051 | ||||||||
\(245\) | −14.3795 | −0.918674 | ||||||||
\(246\) | −28.6487 | −1.82657 | ||||||||
\(247\) | 8.56135 | 0.544746 | ||||||||
\(248\) | −11.3135 | −0.718411 | ||||||||
\(249\) | 19.4498 | 1.23258 | ||||||||
\(250\) | 28.8448 | 1.82431 | ||||||||
\(251\) | 6.50916 | 0.410854 | 0.205427 | − | 0.978672i | \(-0.434142\pi\) | ||||
0.205427 | + | 0.978672i | \(0.434142\pi\) | |||||||
\(252\) | 0.119478 | 0.00752643 | ||||||||
\(253\) | −36.9826 | −2.32507 | ||||||||
\(254\) | −0.600680 | −0.0376900 | ||||||||
\(255\) | 24.3586 | 1.52540 | ||||||||
\(256\) | −1.09833 | −0.0686457 | ||||||||
\(257\) | 6.61342 | 0.412534 | 0.206267 | − | 0.978496i | \(-0.433869\pi\) | ||||
0.206267 | + | 0.978496i | \(0.433869\pi\) | |||||||
\(258\) | 11.0153 | 0.685785 | ||||||||
\(259\) | 4.87694 | 0.303038 | ||||||||
\(260\) | 0.459564 | 0.0285010 | ||||||||
\(261\) | 10.2120 | 0.632104 | ||||||||
\(262\) | −7.36808 | −0.455202 | ||||||||
\(263\) | −1.67328 | −0.103179 | −0.0515894 | − | 0.998668i | \(-0.516429\pi\) | ||||
−0.0515894 | + | 0.998668i | \(0.516429\pi\) | |||||||
\(264\) | −24.4895 | −1.50722 | ||||||||
\(265\) | 6.21532 | 0.381804 | ||||||||
\(266\) | 8.49434 | 0.520821 | ||||||||
\(267\) | 12.8727 | 0.787796 | ||||||||
\(268\) | 0.0676701 | 0.00413361 | ||||||||
\(269\) | 14.8051 | 0.902684 | 0.451342 | − | 0.892351i | \(-0.350945\pi\) | ||||
0.451342 | + | 0.892351i | \(0.350945\pi\) | |||||||
\(270\) | −18.0393 | −1.09783 | ||||||||
\(271\) | 3.80387 | 0.231068 | 0.115534 | − | 0.993304i | \(-0.463142\pi\) | ||||
0.115534 | + | 0.993304i | \(0.463142\pi\) | |||||||
\(272\) | −11.5634 | −0.701134 | ||||||||
\(273\) | 9.85127 | 0.596226 | ||||||||
\(274\) | −5.13542 | −0.310242 | ||||||||
\(275\) | 41.8105 | 2.52127 | ||||||||
\(276\) | 0.876389 | 0.0527524 | ||||||||
\(277\) | 4.51184 | 0.271090 | 0.135545 | − | 0.990771i | \(-0.456721\pi\) | ||||
0.135545 | + | 0.990771i | \(0.456721\pi\) | |||||||
\(278\) | 19.8461 | 1.19029 | ||||||||
\(279\) | 5.66421 | 0.339107 | ||||||||
\(280\) | 20.3724 | 1.21748 | ||||||||
\(281\) | 23.8229 | 1.42115 | 0.710577 | − | 0.703620i | \(-0.248434\pi\) | ||||
0.710577 | + | 0.703620i | \(0.248434\pi\) | |||||||
\(282\) | −18.9077 | −1.12594 | ||||||||
\(283\) | −25.2254 | −1.49949 | −0.749747 | − | 0.661725i | \(-0.769825\pi\) | ||||
−0.749747 | + | 0.661725i | \(0.769825\pi\) | |||||||
\(284\) | −0.692587 | −0.0410975 | ||||||||
\(285\) | −27.4365 | −1.62520 | ||||||||
\(286\) | −14.6008 | −0.863366 | ||||||||
\(287\) | 17.7411 | 1.04722 | ||||||||
\(288\) | 0.370789 | 0.0218490 | ||||||||
\(289\) | −8.23739 | −0.484552 | ||||||||
\(290\) | 38.9720 | 2.28852 | ||||||||
\(291\) | 29.6770 | 1.73970 | ||||||||
\(292\) | 0.344065 | 0.0201349 | ||||||||
\(293\) | 27.0327 | 1.57926 | 0.789632 | − | 0.613580i | \(-0.210271\pi\) | ||||
0.789632 | + | 0.613580i | \(0.210271\pi\) | |||||||
\(294\) | −10.8262 | −0.631397 | ||||||||
\(295\) | −44.7514 | −2.60552 | ||||||||
\(296\) | 7.65319 | 0.444833 | ||||||||
\(297\) | −13.4286 | −0.779206 | ||||||||
\(298\) | −9.37971 | −0.543352 | ||||||||
\(299\) | 23.3456 | 1.35011 | ||||||||
\(300\) | −0.990799 | −0.0572038 | ||||||||
\(301\) | −6.82139 | −0.393178 | ||||||||
\(302\) | 4.38157 | 0.252131 | ||||||||
\(303\) | 3.13547 | 0.180128 | ||||||||
\(304\) | 13.0245 | 0.747006 | ||||||||
\(305\) | 46.6788 | 2.67282 | ||||||||
\(306\) | 5.92502 | 0.338711 | ||||||||
\(307\) | 0.337749 | 0.0192764 | 0.00963819 | − | 0.999954i | \(-0.496932\pi\) | ||||
0.00963819 | + | 0.999954i | \(0.496932\pi\) | |||||||
\(308\) | 0.339426 | 0.0193406 | ||||||||
\(309\) | −35.3494 | −2.01096 | ||||||||
\(310\) | 21.6164 | 1.22773 | ||||||||
\(311\) | 4.79950 | 0.272154 | 0.136077 | − | 0.990698i | \(-0.456550\pi\) | ||||
0.136077 | + | 0.990698i | \(0.456550\pi\) | |||||||
\(312\) | 15.4592 | 0.875205 | ||||||||
\(313\) | 6.45585 | 0.364906 | 0.182453 | − | 0.983215i | \(-0.441596\pi\) | ||||
0.182453 | + | 0.983215i | \(0.441596\pi\) | |||||||
\(314\) | 1.87899 | 0.106038 | ||||||||
\(315\) | −10.1996 | −0.574682 | ||||||||
\(316\) | −0.0607839 | −0.00341936 | ||||||||
\(317\) | 14.8403 | 0.833513 | 0.416756 | − | 0.909018i | \(-0.363167\pi\) | ||||
0.416756 | + | 0.909018i | \(0.363167\pi\) | |||||||
\(318\) | 4.67945 | 0.262411 | ||||||||
\(319\) | 29.0111 | 1.62431 | ||||||||
\(320\) | 31.9533 | 1.78624 | ||||||||
\(321\) | −5.50906 | −0.307486 | ||||||||
\(322\) | 23.1628 | 1.29081 | ||||||||
\(323\) | −9.86982 | −0.549171 | ||||||||
\(324\) | 0.514902 | 0.0286057 | ||||||||
\(325\) | −26.3933 | −1.46404 | ||||||||
\(326\) | −32.6171 | −1.80649 | ||||||||
\(327\) | 36.2741 | 2.00596 | ||||||||
\(328\) | 27.8403 | 1.53723 | ||||||||
\(329\) | 11.7088 | 0.645530 | ||||||||
\(330\) | 46.7912 | 2.57577 | ||||||||
\(331\) | −7.46778 | −0.410466 | −0.205233 | − | 0.978713i | \(-0.565795\pi\) | ||||
−0.205233 | + | 0.978713i | \(0.565795\pi\) | |||||||
\(332\) | −0.423034 | −0.0232170 | ||||||||
\(333\) | −3.83162 | −0.209972 | ||||||||
\(334\) | 2.52062 | 0.137922 | ||||||||
\(335\) | −5.77684 | −0.315622 | ||||||||
\(336\) | 14.9869 | 0.817600 | ||||||||
\(337\) | 31.2200 | 1.70066 | 0.850330 | − | 0.526250i | \(-0.176402\pi\) | ||||
0.850330 | + | 0.526250i | \(0.176402\pi\) | |||||||
\(338\) | −8.95619 | −0.487152 | ||||||||
\(339\) | −39.0150 | −2.11901 | ||||||||
\(340\) | −0.529801 | −0.0287325 | ||||||||
\(341\) | 16.0914 | 0.871399 | ||||||||
\(342\) | −6.67368 | −0.360871 | ||||||||
\(343\) | 19.4613 | 1.05081 | ||||||||
\(344\) | −10.7045 | −0.577150 | ||||||||
\(345\) | −74.8153 | −4.02792 | ||||||||
\(346\) | −19.3516 | −1.04035 | ||||||||
\(347\) | 12.6664 | 0.679967 | 0.339983 | − | 0.940431i | \(-0.389579\pi\) | ||||
0.339983 | + | 0.940431i | \(0.389579\pi\) | |||||||
\(348\) | −0.687487 | −0.0368532 | ||||||||
\(349\) | −16.6138 | −0.889315 | −0.444657 | − | 0.895701i | \(-0.646675\pi\) | ||||
−0.444657 | + | 0.895701i | \(0.646675\pi\) | |||||||
\(350\) | −26.1867 | −1.39974 | ||||||||
\(351\) | 8.47692 | 0.452464 | ||||||||
\(352\) | 1.05337 | 0.0561450 | ||||||||
\(353\) | 9.37962 | 0.499227 | 0.249613 | − | 0.968346i | \(-0.419696\pi\) | ||||
0.249613 | + | 0.968346i | \(0.419696\pi\) | |||||||
\(354\) | −33.6929 | −1.79076 | ||||||||
\(355\) | 59.1246 | 3.13801 | ||||||||
\(356\) | −0.279982 | −0.0148390 | ||||||||
\(357\) | −11.3569 | −0.601069 | ||||||||
\(358\) | −23.6582 | −1.25038 | ||||||||
\(359\) | −21.0027 | −1.10848 | −0.554241 | − | 0.832356i | \(-0.686991\pi\) | ||||
−0.554241 | + | 0.832356i | \(0.686991\pi\) | |||||||
\(360\) | −16.0058 | −0.843581 | ||||||||
\(361\) | −7.88307 | −0.414898 | ||||||||
\(362\) | 8.79065 | 0.462027 | ||||||||
\(363\) | 11.6747 | 0.612763 | ||||||||
\(364\) | −0.214266 | −0.0112306 | ||||||||
\(365\) | −29.3720 | −1.53740 | ||||||||
\(366\) | 35.1440 | 1.83701 | ||||||||
\(367\) | 12.0236 | 0.627627 | 0.313813 | − | 0.949485i | \(-0.398393\pi\) | ||||
0.313813 | + | 0.949485i | \(0.398393\pi\) | |||||||
\(368\) | 35.5159 | 1.85140 | ||||||||
\(369\) | −13.9385 | −0.725608 | ||||||||
\(370\) | −14.6227 | −0.760197 | ||||||||
\(371\) | −2.89781 | −0.150447 | ||||||||
\(372\) | −0.381324 | −0.0197707 | ||||||||
\(373\) | −8.30339 | −0.429933 | −0.214967 | − | 0.976621i | \(-0.568964\pi\) | ||||
−0.214967 | + | 0.976621i | \(0.568964\pi\) | |||||||
\(374\) | 16.8324 | 0.870380 | ||||||||
\(375\) | 43.4383 | 2.24314 | ||||||||
\(376\) | 18.3742 | 0.947579 | ||||||||
\(377\) | −18.3135 | −0.943195 | ||||||||
\(378\) | 8.41057 | 0.432593 | ||||||||
\(379\) | −11.8196 | −0.607133 | −0.303566 | − | 0.952810i | \(-0.598177\pi\) | ||||
−0.303566 | + | 0.952810i | \(0.598177\pi\) | |||||||
\(380\) | 0.596745 | 0.0306124 | ||||||||
\(381\) | −0.904582 | −0.0463432 | ||||||||
\(382\) | 32.2379 | 1.64943 | ||||||||
\(383\) | 5.44234 | 0.278091 | 0.139045 | − | 0.990286i | \(-0.455597\pi\) | ||||
0.139045 | + | 0.990286i | \(0.455597\pi\) | |||||||
\(384\) | 22.9670 | 1.17203 | ||||||||
\(385\) | −28.9760 | −1.47675 | ||||||||
\(386\) | 31.2059 | 1.58834 | ||||||||
\(387\) | 5.35930 | 0.272429 | ||||||||
\(388\) | −0.645477 | −0.0327691 | ||||||||
\(389\) | 1.80435 | 0.0914841 | 0.0457421 | − | 0.998953i | \(-0.485435\pi\) | ||||
0.0457421 | + | 0.998953i | \(0.485435\pi\) | |||||||
\(390\) | −29.5373 | −1.49568 | ||||||||
\(391\) | −26.9136 | −1.36108 | ||||||||
\(392\) | 10.5207 | 0.531377 | ||||||||
\(393\) | −11.0958 | −0.559710 | ||||||||
\(394\) | 10.8230 | 0.545256 | ||||||||
\(395\) | 5.18898 | 0.261086 | ||||||||
\(396\) | −0.266674 | −0.0134009 | ||||||||
\(397\) | −24.4295 | −1.22608 | −0.613040 | − | 0.790052i | \(-0.710054\pi\) | ||||
−0.613040 | + | 0.790052i | \(0.710054\pi\) | |||||||
\(398\) | 26.8285 | 1.34479 | ||||||||
\(399\) | 12.7919 | 0.640395 | ||||||||
\(400\) | −40.1524 | −2.00762 | ||||||||
\(401\) | 11.1686 | 0.557735 | 0.278868 | − | 0.960330i | \(-0.410041\pi\) | ||||
0.278868 | + | 0.960330i | \(0.410041\pi\) | |||||||
\(402\) | −4.34933 | −0.216925 | ||||||||
\(403\) | −10.1579 | −0.505999 | ||||||||
\(404\) | −0.0681966 | −0.00339291 | ||||||||
\(405\) | −43.9560 | −2.18419 | ||||||||
\(406\) | −18.1702 | −0.901771 | ||||||||
\(407\) | −10.8852 | −0.539562 | ||||||||
\(408\) | −17.8219 | −0.882316 | ||||||||
\(409\) | 3.26343 | 0.161366 | 0.0806832 | − | 0.996740i | \(-0.474290\pi\) | ||||
0.0806832 | + | 0.996740i | \(0.474290\pi\) | |||||||
\(410\) | −53.1935 | −2.62704 | ||||||||
\(411\) | −7.73358 | −0.381470 | ||||||||
\(412\) | 0.768851 | 0.0378786 | ||||||||
\(413\) | 20.8647 | 1.02669 | ||||||||
\(414\) | −18.1982 | −0.894390 | ||||||||
\(415\) | 36.1134 | 1.77274 | ||||||||
\(416\) | −0.664952 | −0.0326020 | ||||||||
\(417\) | 29.8869 | 1.46357 | ||||||||
\(418\) | −18.9592 | −0.927326 | ||||||||
\(419\) | 11.2453 | 0.549368 | 0.274684 | − | 0.961535i | \(-0.411427\pi\) | ||||
0.274684 | + | 0.961535i | \(0.411427\pi\) | |||||||
\(420\) | 0.686655 | 0.0335053 | ||||||||
\(421\) | −8.53714 | −0.416075 | −0.208037 | − | 0.978121i | \(-0.566708\pi\) | ||||
−0.208037 | + | 0.978121i | \(0.566708\pi\) | |||||||
\(422\) | 9.63936 | 0.469237 | ||||||||
\(423\) | −9.19920 | −0.447280 | ||||||||
\(424\) | −4.54742 | −0.220842 | ||||||||
\(425\) | 30.4271 | 1.47593 | ||||||||
\(426\) | 44.5143 | 2.15673 | ||||||||
\(427\) | −21.7634 | −1.05320 | ||||||||
\(428\) | 0.119822 | 0.00579183 | ||||||||
\(429\) | −21.9879 | −1.06158 | ||||||||
\(430\) | 20.4528 | 0.986320 | ||||||||
\(431\) | 23.9686 | 1.15453 | 0.577263 | − | 0.816558i | \(-0.304121\pi\) | ||||
0.577263 | + | 0.816558i | \(0.304121\pi\) | |||||||
\(432\) | 12.8961 | 0.620462 | ||||||||
\(433\) | 27.2069 | 1.30748 | 0.653740 | − | 0.756719i | \(-0.273199\pi\) | ||||
0.653740 | + | 0.756719i | \(0.273199\pi\) | |||||||
\(434\) | −10.0783 | −0.483776 | ||||||||
\(435\) | 58.6892 | 2.81393 | ||||||||
\(436\) | −0.788963 | −0.0377845 | ||||||||
\(437\) | 30.3143 | 1.45013 | ||||||||
\(438\) | −22.1139 | −1.05664 | ||||||||
\(439\) | −29.8150 | −1.42299 | −0.711496 | − | 0.702690i | \(-0.751982\pi\) | ||||
−0.711496 | + | 0.702690i | \(0.751982\pi\) | |||||||
\(440\) | −45.4709 | −2.16774 | ||||||||
\(441\) | −5.26728 | −0.250823 | ||||||||
\(442\) | −10.6256 | −0.505407 | ||||||||
\(443\) | −39.7850 | −1.89024 | −0.945122 | − | 0.326718i | \(-0.894057\pi\) | ||||
−0.945122 | + | 0.326718i | \(0.894057\pi\) | |||||||
\(444\) | 0.257952 | 0.0122418 | ||||||||
\(445\) | 23.9014 | 1.13304 | ||||||||
\(446\) | −8.79746 | −0.416572 | ||||||||
\(447\) | −14.1252 | −0.668099 | ||||||||
\(448\) | −14.8978 | −0.703854 | ||||||||
\(449\) | −23.0458 | −1.08760 | −0.543799 | − | 0.839216i | \(-0.683015\pi\) | ||||
−0.543799 | + | 0.839216i | \(0.683015\pi\) | |||||||
\(450\) | 20.5739 | 0.969862 | ||||||||
\(451\) | −39.5977 | −1.86459 | ||||||||
\(452\) | 0.848579 | 0.0399138 | ||||||||
\(453\) | 6.59834 | 0.310017 | ||||||||
\(454\) | 12.6078 | 0.591711 | ||||||||
\(455\) | 18.2914 | 0.857512 | ||||||||
\(456\) | 20.0738 | 0.940042 | ||||||||
\(457\) | 11.6277 | 0.543920 | 0.271960 | − | 0.962309i | \(-0.412328\pi\) | ||||
0.271960 | + | 0.962309i | \(0.412328\pi\) | |||||||
\(458\) | 22.4702 | 1.04997 | ||||||||
\(459\) | −9.77248 | −0.456140 | ||||||||
\(460\) | 1.62724 | 0.0758703 | ||||||||
\(461\) | −29.5994 | −1.37858 | −0.689292 | − | 0.724484i | \(-0.742078\pi\) | ||||
−0.689292 | + | 0.724484i | \(0.742078\pi\) | |||||||
\(462\) | −21.8158 | −1.01496 | ||||||||
\(463\) | 37.2162 | 1.72959 | 0.864793 | − | 0.502129i | \(-0.167450\pi\) | ||||
0.864793 | + | 0.502129i | \(0.167450\pi\) | |||||||
\(464\) | −27.8606 | −1.29340 | ||||||||
\(465\) | 32.5528 | 1.50960 | ||||||||
\(466\) | 13.8868 | 0.643295 | ||||||||
\(467\) | 11.6426 | 0.538757 | 0.269379 | − | 0.963034i | \(-0.413182\pi\) | ||||
0.269379 | + | 0.963034i | \(0.413182\pi\) | |||||||
\(468\) | 0.168340 | 0.00778153 | ||||||||
\(469\) | 2.69337 | 0.124368 | ||||||||
\(470\) | −35.1070 | −1.61937 | ||||||||
\(471\) | 2.82963 | 0.130383 | ||||||||
\(472\) | 32.7422 | 1.50708 | ||||||||
\(473\) | 15.2252 | 0.700056 | ||||||||
\(474\) | 3.90673 | 0.179442 | ||||||||
\(475\) | −34.2717 | −1.57249 | ||||||||
\(476\) | 0.247013 | 0.0113218 | ||||||||
\(477\) | 2.27670 | 0.104243 | ||||||||
\(478\) | −7.87893 | −0.360374 | ||||||||
\(479\) | −21.0171 | −0.960294 | −0.480147 | − | 0.877188i | \(-0.659417\pi\) | ||||
−0.480147 | + | 0.877188i | \(0.659417\pi\) | |||||||
\(480\) | 2.13096 | 0.0972647 | ||||||||
\(481\) | 6.87141 | 0.313309 | ||||||||
\(482\) | −9.63796 | −0.438997 | ||||||||
\(483\) | 34.8816 | 1.58717 | ||||||||
\(484\) | −0.253925 | −0.0115421 | ||||||||
\(485\) | 55.1028 | 2.50209 | ||||||||
\(486\) | −19.2490 | −0.873150 | ||||||||
\(487\) | −23.6622 | −1.07224 | −0.536118 | − | 0.844143i | \(-0.680110\pi\) | ||||
−0.536118 | + | 0.844143i | \(0.680110\pi\) | |||||||
\(488\) | −34.1524 | −1.54601 | ||||||||
\(489\) | −49.1191 | −2.22124 | ||||||||
\(490\) | −20.1016 | −0.908097 | ||||||||
\(491\) | −3.74577 | −0.169044 | −0.0845222 | − | 0.996422i | \(-0.526936\pi\) | ||||
−0.0845222 | + | 0.996422i | \(0.526936\pi\) | |||||||
\(492\) | 0.938362 | 0.0423046 | ||||||||
\(493\) | 21.1125 | 0.950857 | ||||||||
\(494\) | 11.9682 | 0.538474 | ||||||||
\(495\) | 22.7653 | 1.02323 | ||||||||
\(496\) | −15.4533 | −0.693873 | ||||||||
\(497\) | −27.5660 | −1.23651 | ||||||||
\(498\) | 27.1894 | 1.21839 | ||||||||
\(499\) | −37.1028 | −1.66095 | −0.830474 | − | 0.557058i | \(-0.811930\pi\) | ||||
−0.830474 | + | 0.557058i | \(0.811930\pi\) | |||||||
\(500\) | −0.944785 | −0.0422521 | ||||||||
\(501\) | 3.79588 | 0.169587 | ||||||||
\(502\) | 9.09935 | 0.406124 | ||||||||
\(503\) | −0.661745 | −0.0295058 | −0.0147529 | − | 0.999891i | \(-0.504696\pi\) | ||||
−0.0147529 | + | 0.999891i | \(0.504696\pi\) | |||||||
\(504\) | 7.46250 | 0.332406 | ||||||||
\(505\) | 5.82179 | 0.259066 | ||||||||
\(506\) | −51.6991 | −2.29830 | ||||||||
\(507\) | −13.4874 | −0.598996 | ||||||||
\(508\) | 0.0196747 | 0.000872925 0 | ||||||||
\(509\) | −18.2795 | −0.810227 | −0.405113 | − | 0.914266i | \(-0.632768\pi\) | ||||
−0.405113 | + | 0.914266i | \(0.632768\pi\) | |||||||
\(510\) | 34.0517 | 1.50783 | ||||||||
\(511\) | 13.6943 | 0.605801 | ||||||||
\(512\) | −23.3548 | −1.03215 | ||||||||
\(513\) | 11.0073 | 0.485984 | ||||||||
\(514\) | 9.24510 | 0.407784 | ||||||||
\(515\) | −65.6350 | −2.89223 | ||||||||
\(516\) | −0.360797 | −0.0158832 | ||||||||
\(517\) | −26.1340 | −1.14937 | ||||||||
\(518\) | 6.81763 | 0.299549 | ||||||||
\(519\) | −29.1422 | −1.27920 | ||||||||
\(520\) | 28.7039 | 1.25875 | ||||||||
\(521\) | −12.4144 | −0.543883 | −0.271941 | − | 0.962314i | \(-0.587666\pi\) | ||||
−0.271941 | + | 0.962314i | \(0.587666\pi\) | |||||||
\(522\) | 14.2756 | 0.624827 | ||||||||
\(523\) | 3.75347 | 0.164128 | 0.0820640 | − | 0.996627i | \(-0.473849\pi\) | ||||
0.0820640 | + | 0.996627i | \(0.473849\pi\) | |||||||
\(524\) | 0.241335 | 0.0105428 | ||||||||
\(525\) | −39.4353 | −1.72110 | ||||||||
\(526\) | −2.33913 | −0.101991 | ||||||||
\(527\) | 11.7103 | 0.510110 | ||||||||
\(528\) | −33.4504 | −1.45574 | ||||||||
\(529\) | 59.6626 | 2.59403 | ||||||||
\(530\) | 8.68859 | 0.377408 | ||||||||
\(531\) | −16.3926 | −0.711379 | ||||||||
\(532\) | −0.278224 | −0.0120626 | ||||||||
\(533\) | 24.9964 | 1.08272 | ||||||||
\(534\) | 17.9952 | 0.778726 | ||||||||
\(535\) | −10.2290 | −0.442236 | ||||||||
\(536\) | 4.22661 | 0.182562 | ||||||||
\(537\) | −35.6276 | −1.53745 | ||||||||
\(538\) | 20.6966 | 0.892292 | ||||||||
\(539\) | −14.9638 | −0.644536 | ||||||||
\(540\) | 0.590860 | 0.0254266 | ||||||||
\(541\) | −36.1009 | −1.55210 | −0.776050 | − | 0.630671i | \(-0.782780\pi\) | ||||
−0.776050 | + | 0.630671i | \(0.782780\pi\) | |||||||
\(542\) | 5.31754 | 0.228408 | ||||||||
\(543\) | 13.2381 | 0.568102 | ||||||||
\(544\) | 0.766579 | 0.0328668 | ||||||||
\(545\) | 67.3520 | 2.88504 | ||||||||
\(546\) | 13.7714 | 0.589361 | ||||||||
\(547\) | 16.2537 | 0.694958 | 0.347479 | − | 0.937688i | \(-0.387038\pi\) | ||||
0.347479 | + | 0.937688i | \(0.387038\pi\) | |||||||
\(548\) | 0.168206 | 0.00718540 | ||||||||
\(549\) | 17.0986 | 0.729752 | ||||||||
\(550\) | 58.4482 | 2.49224 | ||||||||
\(551\) | −23.7802 | −1.01307 | ||||||||
\(552\) | 54.7384 | 2.32982 | ||||||||
\(553\) | −2.41929 | −0.102879 | ||||||||
\(554\) | 6.30724 | 0.267969 | ||||||||
\(555\) | −22.0207 | −0.934728 | ||||||||
\(556\) | −0.650041 | −0.0275679 | ||||||||
\(557\) | −11.9802 | −0.507619 | −0.253809 | − | 0.967254i | \(-0.581684\pi\) | ||||
−0.253809 | + | 0.967254i | \(0.581684\pi\) | |||||||
\(558\) | 7.91817 | 0.335203 | ||||||||
\(559\) | −9.61106 | −0.406505 | ||||||||
\(560\) | 27.8269 | 1.17590 | ||||||||
\(561\) | 25.3484 | 1.07021 | ||||||||
\(562\) | 33.3027 | 1.40479 | ||||||||
\(563\) | −38.3464 | −1.61611 | −0.808055 | − | 0.589107i | \(-0.799480\pi\) | ||||
−0.808055 | + | 0.589107i | \(0.799480\pi\) | |||||||
\(564\) | 0.619306 | 0.0260775 | ||||||||
\(565\) | −72.4413 | −3.04763 | ||||||||
\(566\) | −35.2634 | −1.48223 | ||||||||
\(567\) | 20.4939 | 0.860662 | ||||||||
\(568\) | −43.2583 | −1.81508 | ||||||||
\(569\) | 31.4489 | 1.31841 | 0.659203 | − | 0.751965i | \(-0.270894\pi\) | ||||
0.659203 | + | 0.751965i | \(0.270894\pi\) | |||||||
\(570\) | −38.3543 | −1.60648 | ||||||||
\(571\) | 9.85904 | 0.412588 | 0.206294 | − | 0.978490i | \(-0.433860\pi\) | ||||
0.206294 | + | 0.978490i | \(0.433860\pi\) | |||||||
\(572\) | 0.478237 | 0.0199961 | ||||||||
\(573\) | 48.5481 | 2.02812 | ||||||||
\(574\) | 24.8008 | 1.03516 | ||||||||
\(575\) | −93.4540 | −3.89730 | ||||||||
\(576\) | 11.7046 | 0.487692 | ||||||||
\(577\) | −15.2362 | −0.634292 | −0.317146 | − | 0.948377i | \(-0.602725\pi\) | ||||
−0.317146 | + | 0.948377i | \(0.602725\pi\) | |||||||
\(578\) | −11.5153 | −0.478974 | ||||||||
\(579\) | 46.9939 | 1.95300 | ||||||||
\(580\) | −1.27649 | −0.0530035 | ||||||||
\(581\) | −16.8374 | −0.698533 | ||||||||
\(582\) | 41.4864 | 1.71967 | ||||||||
\(583\) | 6.46786 | 0.267871 | ||||||||
\(584\) | 21.4899 | 0.889260 | ||||||||
\(585\) | −14.3708 | −0.594161 | ||||||||
\(586\) | 37.7898 | 1.56108 | ||||||||
\(587\) | −9.30734 | −0.384155 | −0.192077 | − | 0.981380i | \(-0.561522\pi\) | ||||
−0.192077 | + | 0.981380i | \(0.561522\pi\) | |||||||
\(588\) | 0.354602 | 0.0146236 | ||||||||
\(589\) | −13.1900 | −0.543484 | ||||||||
\(590\) | −62.5593 | −2.57553 | ||||||||
\(591\) | 16.2987 | 0.670440 | ||||||||
\(592\) | 10.4536 | 0.429639 | ||||||||
\(593\) | 24.8888 | 1.02206 | 0.511031 | − | 0.859562i | \(-0.329264\pi\) | ||||
0.511031 | + | 0.859562i | \(0.329264\pi\) | |||||||
\(594\) | −18.7722 | −0.770235 | ||||||||
\(595\) | −21.0869 | −0.864479 | ||||||||
\(596\) | 0.307224 | 0.0125844 | ||||||||
\(597\) | 40.4018 | 1.65354 | ||||||||
\(598\) | 32.6355 | 1.33457 | ||||||||
\(599\) | −28.8020 | −1.17682 | −0.588409 | − | 0.808564i | \(-0.700245\pi\) | ||||
−0.588409 | + | 0.808564i | \(0.700245\pi\) | |||||||
\(600\) | −61.8843 | −2.52642 | ||||||||
\(601\) | −4.36509 | −0.178056 | −0.0890279 | − | 0.996029i | \(-0.528376\pi\) | ||||
−0.0890279 | + | 0.996029i | \(0.528376\pi\) | |||||||
\(602\) | −9.53583 | −0.388651 | ||||||||
\(603\) | −2.11608 | −0.0861735 | ||||||||
\(604\) | −0.143514 | −0.00583951 | ||||||||
\(605\) | 21.6770 | 0.881296 | ||||||||
\(606\) | 4.38317 | 0.178054 | ||||||||
\(607\) | −41.6146 | −1.68909 | −0.844543 | − | 0.535488i | \(-0.820128\pi\) | ||||
−0.844543 | + | 0.535488i | \(0.820128\pi\) | |||||||
\(608\) | −0.863441 | −0.0350172 | ||||||||
\(609\) | −27.3630 | −1.10881 | ||||||||
\(610\) | 65.2538 | 2.64205 | ||||||||
\(611\) | 16.4973 | 0.667409 | ||||||||
\(612\) | −0.194068 | −0.00784475 | ||||||||
\(613\) | −33.4091 | −1.34938 | −0.674691 | − | 0.738101i | \(-0.735723\pi\) | ||||
−0.674691 | + | 0.738101i | \(0.735723\pi\) | |||||||
\(614\) | 0.472150 | 0.0190544 | ||||||||
\(615\) | −80.1058 | −3.23018 | ||||||||
\(616\) | 21.2002 | 0.854181 | ||||||||
\(617\) | −39.6814 | −1.59751 | −0.798756 | − | 0.601655i | \(-0.794508\pi\) | ||||
−0.798756 | + | 0.601655i | \(0.794508\pi\) | |||||||
\(618\) | −49.4160 | −1.98780 | ||||||||
\(619\) | 1.00000 | 0.0401934 | ||||||||
\(620\) | −0.708025 | −0.0284350 | ||||||||
\(621\) | 30.0153 | 1.20447 | ||||||||
\(622\) | 6.70937 | 0.269021 | ||||||||
\(623\) | −11.1437 | −0.446464 | ||||||||
\(624\) | 21.1159 | 0.845312 | ||||||||
\(625\) | 29.2600 | 1.17040 | ||||||||
\(626\) | 9.02483 | 0.360705 | ||||||||
\(627\) | −28.5513 | −1.14023 | ||||||||
\(628\) | −0.0615447 | −0.00245590 | ||||||||
\(629\) | −7.92160 | −0.315855 | ||||||||
\(630\) | −14.2583 | −0.568066 | ||||||||
\(631\) | 36.3762 | 1.44811 | 0.724056 | − | 0.689741i | \(-0.242276\pi\) | ||||
0.724056 | + | 0.689741i | \(0.242276\pi\) | |||||||
\(632\) | −3.79650 | −0.151017 | ||||||||
\(633\) | 14.5162 | 0.576968 | ||||||||
\(634\) | 20.7457 | 0.823916 | ||||||||
\(635\) | −1.67959 | −0.0666523 | ||||||||
\(636\) | −0.153271 | −0.00607760 | ||||||||
\(637\) | 9.44603 | 0.374265 | ||||||||
\(638\) | 40.5556 | 1.60561 | ||||||||
\(639\) | 21.6576 | 0.856761 | ||||||||
\(640\) | 42.6440 | 1.68565 | ||||||||
\(641\) | −2.56023 | −0.101123 | −0.0505615 | − | 0.998721i | \(-0.516101\pi\) | ||||
−0.0505615 | + | 0.998721i | \(0.516101\pi\) | |||||||
\(642\) | −7.70128 | −0.303945 | ||||||||
\(643\) | −15.3718 | −0.606205 | −0.303102 | − | 0.952958i | \(-0.598022\pi\) | ||||
−0.303102 | + | 0.952958i | \(0.598022\pi\) | |||||||
\(644\) | −0.758677 | −0.0298961 | ||||||||
\(645\) | 30.8004 | 1.21277 | ||||||||
\(646\) | −13.7973 | −0.542849 | ||||||||
\(647\) | 34.7874 | 1.36763 | 0.683817 | − | 0.729653i | \(-0.260319\pi\) | ||||
0.683817 | + | 0.729653i | \(0.260319\pi\) | |||||||
\(648\) | 32.1603 | 1.26337 | ||||||||
\(649\) | −46.5697 | −1.82802 | ||||||||
\(650\) | −36.8960 | −1.44718 | ||||||||
\(651\) | −15.1773 | −0.594845 | ||||||||
\(652\) | 1.06834 | 0.0418396 | ||||||||
\(653\) | −33.8299 | −1.32386 | −0.661932 | − | 0.749564i | \(-0.730263\pi\) | ||||
−0.661932 | + | 0.749564i | \(0.730263\pi\) | |||||||
\(654\) | 50.7087 | 1.98287 | ||||||||
\(655\) | −20.6022 | −0.804994 | ||||||||
\(656\) | 38.0274 | 1.48472 | ||||||||
\(657\) | −10.7591 | −0.419752 | ||||||||
\(658\) | 16.3682 | 0.638098 | ||||||||
\(659\) | 0.903033 | 0.0351772 | 0.0175886 | − | 0.999845i | \(-0.494401\pi\) | ||||
0.0175886 | + | 0.999845i | \(0.494401\pi\) | |||||||
\(660\) | −1.53260 | −0.0596565 | ||||||||
\(661\) | −18.8171 | −0.731901 | −0.365950 | − | 0.930634i | \(-0.619256\pi\) | ||||
−0.365950 | + | 0.930634i | \(0.619256\pi\) | |||||||
\(662\) | −10.4394 | −0.405740 | ||||||||
\(663\) | −16.0014 | −0.621442 | ||||||||
\(664\) | −26.4223 | −1.02538 | ||||||||
\(665\) | 23.7514 | 0.921039 | ||||||||
\(666\) | −5.35635 | −0.207554 | ||||||||
\(667\) | −64.8450 | −2.51081 | ||||||||
\(668\) | −0.0825605 | −0.00319436 | ||||||||
\(669\) | −13.2484 | −0.512212 | ||||||||
\(670\) | −8.07562 | −0.311989 | ||||||||
\(671\) | 48.5755 | 1.87524 | ||||||||
\(672\) | −0.993533 | −0.0383264 | ||||||||
\(673\) | −3.47042 | −0.133775 | −0.0668874 | − | 0.997761i | \(-0.521307\pi\) | ||||
−0.0668874 | + | 0.997761i | \(0.521307\pi\) | |||||||
\(674\) | 43.6434 | 1.68108 | ||||||||
\(675\) | −33.9337 | −1.30611 | ||||||||
\(676\) | 0.293352 | 0.0112828 | ||||||||
\(677\) | 19.4420 | 0.747215 | 0.373608 | − | 0.927587i | \(-0.378121\pi\) | ||||
0.373608 | + | 0.927587i | \(0.378121\pi\) | |||||||
\(678\) | −54.5403 | −2.09461 | ||||||||
\(679\) | −25.6910 | −0.985929 | ||||||||
\(680\) | −33.0909 | −1.26898 | ||||||||
\(681\) | 18.9864 | 0.727561 | ||||||||
\(682\) | 22.4947 | 0.861367 | ||||||||
\(683\) | −17.1368 | −0.655723 | −0.327861 | − | 0.944726i | \(-0.606328\pi\) | ||||
−0.327861 | + | 0.944726i | \(0.606328\pi\) | |||||||
\(684\) | 0.218590 | 0.00835801 | ||||||||
\(685\) | −14.3594 | −0.548643 | ||||||||
\(686\) | 27.2055 | 1.03871 | ||||||||
\(687\) | 33.8386 | 1.29102 | ||||||||
\(688\) | −14.6214 | −0.557437 | ||||||||
\(689\) | −4.08290 | −0.155546 | ||||||||
\(690\) | −104.587 | −3.98154 | ||||||||
\(691\) | −34.0837 | −1.29661 | −0.648303 | − | 0.761383i | \(-0.724521\pi\) | ||||
−0.648303 | + | 0.761383i | \(0.724521\pi\) | |||||||
\(692\) | 0.633844 | 0.0240951 | ||||||||
\(693\) | −10.6140 | −0.403194 | ||||||||
\(694\) | 17.7067 | 0.672138 | ||||||||
\(695\) | 55.4925 | 2.10495 | ||||||||
\(696\) | −42.9397 | −1.62763 | ||||||||
\(697\) | −28.8167 | −1.09151 | ||||||||
\(698\) | −23.2249 | −0.879076 | ||||||||
\(699\) | 20.9126 | 0.790987 | ||||||||
\(700\) | 0.857721 | 0.0324188 | ||||||||
\(701\) | 29.8339 | 1.12681 | 0.563405 | − | 0.826181i | \(-0.309491\pi\) | ||||
0.563405 | + | 0.826181i | \(0.309491\pi\) | |||||||
\(702\) | 11.8502 | 0.447255 | ||||||||
\(703\) | 8.92254 | 0.336520 | ||||||||
\(704\) | 33.2516 | 1.25322 | ||||||||
\(705\) | −52.8687 | −1.99115 | ||||||||
\(706\) | 13.1121 | 0.493479 | ||||||||
\(707\) | −2.71433 | −0.102083 | ||||||||
\(708\) | 1.10358 | 0.0414750 | ||||||||
\(709\) | 24.2367 | 0.910227 | 0.455114 | − | 0.890433i | \(-0.349599\pi\) | ||||
0.455114 | + | 0.890433i | \(0.349599\pi\) | |||||||
\(710\) | 82.6521 | 3.10188 | ||||||||
\(711\) | 1.90075 | 0.0712835 | ||||||||
\(712\) | −17.4874 | −0.655368 | ||||||||
\(713\) | −35.9672 | −1.34698 | ||||||||
\(714\) | −15.8761 | −0.594149 | ||||||||
\(715\) | −40.8260 | −1.52681 | ||||||||
\(716\) | 0.774903 | 0.0289595 | ||||||||
\(717\) | −11.8651 | −0.443111 | ||||||||
\(718\) | −29.3604 | −1.09572 | ||||||||
\(719\) | 2.19158 | 0.0817320 | 0.0408660 | − | 0.999165i | \(-0.486988\pi\) | ||||
0.0408660 | + | 0.999165i | \(0.486988\pi\) | |||||||
\(720\) | −21.8625 | −0.814768 | ||||||||
\(721\) | 30.6015 | 1.13966 | ||||||||
\(722\) | −11.0200 | −0.410121 | ||||||||
\(723\) | −14.5141 | −0.539785 | ||||||||
\(724\) | −0.287930 | −0.0107008 | ||||||||
\(725\) | 73.3104 | 2.72268 | ||||||||
\(726\) | 16.3204 | 0.605708 | ||||||||
\(727\) | 0.694630 | 0.0257624 | 0.0128812 | − | 0.999917i | \(-0.495900\pi\) | ||||
0.0128812 | + | 0.999917i | \(0.495900\pi\) | |||||||
\(728\) | −13.3828 | −0.496000 | ||||||||
\(729\) | 4.74846 | 0.175869 | ||||||||
\(730\) | −41.0601 | −1.51970 | ||||||||
\(731\) | 11.0800 | 0.409807 | ||||||||
\(732\) | −1.15111 | −0.0425463 | ||||||||
\(733\) | 4.53396 | 0.167465 | 0.0837327 | − | 0.996488i | \(-0.473316\pi\) | ||||
0.0837327 | + | 0.996488i | \(0.473316\pi\) | |||||||
\(734\) | 16.8082 | 0.620401 | ||||||||
\(735\) | −30.2716 | −1.11658 | ||||||||
\(736\) | −2.35448 | −0.0867873 | ||||||||
\(737\) | −6.01157 | −0.221439 | ||||||||
\(738\) | −19.4850 | −0.717254 | ||||||||
\(739\) | −6.53051 | −0.240229 | −0.120114 | − | 0.992760i | \(-0.538326\pi\) | ||||
−0.120114 | + | 0.992760i | \(0.538326\pi\) | |||||||
\(740\) | 0.478952 | 0.0176066 | ||||||||
\(741\) | 18.0233 | 0.662101 | ||||||||
\(742\) | −4.05094 | −0.148715 | ||||||||
\(743\) | −18.1924 | −0.667413 | −0.333706 | − | 0.942677i | \(-0.608299\pi\) | ||||
−0.333706 | + | 0.942677i | \(0.608299\pi\) | |||||||
\(744\) | −23.8171 | −0.873178 | ||||||||
\(745\) | −26.2270 | −0.960883 | ||||||||
\(746\) | −11.6076 | −0.424983 | ||||||||
\(747\) | 13.2285 | 0.484005 | ||||||||
\(748\) | −0.551328 | −0.0201586 | ||||||||
\(749\) | 4.76911 | 0.174260 | ||||||||
\(750\) | 60.7237 | 2.21732 | ||||||||
\(751\) | 2.77215 | 0.101157 | 0.0505787 | − | 0.998720i | \(-0.483893\pi\) | ||||
0.0505787 | + | 0.998720i | \(0.483893\pi\) | |||||||
\(752\) | 25.0976 | 0.915214 | ||||||||
\(753\) | 13.7030 | 0.499365 | ||||||||
\(754\) | −25.6011 | −0.932336 | ||||||||
\(755\) | 12.2515 | 0.445877 | ||||||||
\(756\) | −0.275480 | −0.0100191 | ||||||||
\(757\) | 39.5313 | 1.43679 | 0.718395 | − | 0.695635i | \(-0.244877\pi\) | ||||
0.718395 | + | 0.695635i | \(0.244877\pi\) | |||||||
\(758\) | −16.5230 | −0.600143 | ||||||||
\(759\) | −77.8552 | −2.82597 | ||||||||
\(760\) | 37.2721 | 1.35200 | ||||||||
\(761\) | −19.3164 | −0.700220 | −0.350110 | − | 0.936709i | \(-0.613856\pi\) | ||||
−0.350110 | + | 0.936709i | \(0.613856\pi\) | |||||||
\(762\) | −1.26454 | −0.0458096 | ||||||||
\(763\) | −31.4020 | −1.13683 | ||||||||
\(764\) | −1.05592 | −0.0382020 | ||||||||
\(765\) | 16.5672 | 0.598988 | ||||||||
\(766\) | 7.60802 | 0.274889 | ||||||||
\(767\) | 29.3976 | 1.06148 | ||||||||
\(768\) | −2.31219 | −0.0834341 | ||||||||
\(769\) | 36.0089 | 1.29851 | 0.649257 | − | 0.760569i | \(-0.275080\pi\) | ||||
0.649257 | + | 0.760569i | \(0.275080\pi\) | |||||||
\(770\) | −40.5065 | −1.45975 | ||||||||
\(771\) | 13.9225 | 0.501406 | ||||||||
\(772\) | −1.02212 | −0.0367869 | ||||||||
\(773\) | 6.72033 | 0.241713 | 0.120857 | − | 0.992670i | \(-0.461436\pi\) | ||||
0.120857 | + | 0.992670i | \(0.461436\pi\) | |||||||
\(774\) | 7.49194 | 0.269292 | ||||||||
\(775\) | 40.6626 | 1.46064 | ||||||||
\(776\) | −40.3158 | −1.44725 | ||||||||
\(777\) | 10.2669 | 0.368322 | ||||||||
\(778\) | 2.52236 | 0.0904308 | ||||||||
\(779\) | 32.4579 | 1.16293 | ||||||||
\(780\) | 0.967469 | 0.0346409 | ||||||||
\(781\) | 61.5270 | 2.20161 | ||||||||
\(782\) | −37.6233 | −1.34541 | ||||||||
\(783\) | −23.5456 | −0.841452 | ||||||||
\(784\) | 14.3704 | 0.513228 | ||||||||
\(785\) | 5.25393 | 0.187521 | ||||||||
\(786\) | −15.5112 | −0.553266 | ||||||||
\(787\) | −48.7796 | −1.73880 | −0.869402 | − | 0.494105i | \(-0.835496\pi\) | ||||
−0.869402 | + | 0.494105i | \(0.835496\pi\) | |||||||
\(788\) | −0.354498 | −0.0126285 | ||||||||
\(789\) | −3.52257 | −0.125407 | ||||||||
\(790\) | 7.25384 | 0.258080 | ||||||||
\(791\) | 33.7748 | 1.20089 | ||||||||
\(792\) | −16.6562 | −0.591852 | ||||||||
\(793\) | −30.6637 | −1.08890 | ||||||||
\(794\) | −34.1507 | −1.21196 | ||||||||
\(795\) | 13.0844 | 0.464056 | ||||||||
\(796\) | −0.878742 | −0.0311462 | ||||||||
\(797\) | 13.1872 | 0.467116 | 0.233558 | − | 0.972343i | \(-0.424963\pi\) | ||||
0.233558 | + | 0.972343i | \(0.424963\pi\) | |||||||
\(798\) | 17.8822 | 0.633022 | ||||||||
\(799\) | −19.0186 | −0.672831 | ||||||||
\(800\) | 2.66185 | 0.0941106 | ||||||||
\(801\) | 8.75519 | 0.309350 | ||||||||
\(802\) | 15.6130 | 0.551314 | ||||||||
\(803\) | −30.5655 | −1.07863 | ||||||||
\(804\) | 0.142458 | 0.00502411 | ||||||||
\(805\) | 64.7665 | 2.28272 | ||||||||
\(806\) | −14.2000 | −0.500173 | ||||||||
\(807\) | 31.1676 | 1.09715 | ||||||||
\(808\) | −4.25949 | −0.149848 | ||||||||
\(809\) | −1.81667 | −0.0638709 | −0.0319354 | − | 0.999490i | \(-0.510167\pi\) | ||||
−0.0319354 | + | 0.999490i | \(0.510167\pi\) | |||||||
\(810\) | −61.4474 | −2.15904 | ||||||||
\(811\) | −28.0102 | −0.983573 | −0.491786 | − | 0.870716i | \(-0.663656\pi\) | ||||
−0.491786 | + | 0.870716i | \(0.663656\pi\) | |||||||
\(812\) | 0.595148 | 0.0208856 | ||||||||
\(813\) | 8.00785 | 0.280848 | ||||||||
\(814\) | −15.2168 | −0.533350 | ||||||||
\(815\) | −91.2020 | −3.19467 | ||||||||
\(816\) | −24.3431 | −0.852180 | ||||||||
\(817\) | −12.4800 | −0.436619 | ||||||||
\(818\) | 4.56205 | 0.159508 | ||||||||
\(819\) | 6.70021 | 0.234124 | ||||||||
\(820\) | 1.74231 | 0.0608440 | ||||||||
\(821\) | 42.3402 | 1.47768 | 0.738841 | − | 0.673880i | \(-0.235373\pi\) | ||||
0.738841 | + | 0.673880i | \(0.235373\pi\) | |||||||
\(822\) | −10.8110 | −0.377078 | ||||||||
\(823\) | −25.5973 | −0.892267 | −0.446133 | − | 0.894967i | \(-0.647199\pi\) | ||||
−0.446133 | + | 0.894967i | \(0.647199\pi\) | |||||||
\(824\) | 48.0217 | 1.67291 | ||||||||
\(825\) | 88.0190 | 3.06443 | ||||||||
\(826\) | 29.1674 | 1.01487 | ||||||||
\(827\) | 4.68739 | 0.162996 | 0.0814982 | − | 0.996673i | \(-0.474030\pi\) | ||||
0.0814982 | + | 0.996673i | \(0.474030\pi\) | |||||||
\(828\) | 0.596064 | 0.0207147 | ||||||||
\(829\) | 13.9510 | 0.484538 | 0.242269 | − | 0.970209i | \(-0.422108\pi\) | ||||
0.242269 | + | 0.970209i | \(0.422108\pi\) | |||||||
\(830\) | 50.4841 | 1.75233 | ||||||||
\(831\) | 9.49826 | 0.329491 | ||||||||
\(832\) | −20.9904 | −0.727710 | ||||||||
\(833\) | −10.8897 | −0.377306 | ||||||||
\(834\) | 41.7798 | 1.44672 | ||||||||
\(835\) | 7.04800 | 0.243906 | ||||||||
\(836\) | 0.620992 | 0.0214775 | ||||||||
\(837\) | −13.0599 | −0.451417 | ||||||||
\(838\) | 15.7201 | 0.543043 | ||||||||
\(839\) | −24.3899 | −0.842033 | −0.421017 | − | 0.907053i | \(-0.638327\pi\) | ||||
−0.421017 | + | 0.907053i | \(0.638327\pi\) | |||||||
\(840\) | 42.8878 | 1.47977 | ||||||||
\(841\) | 21.8680 | 0.754068 | ||||||||
\(842\) | −11.9343 | −0.411284 | ||||||||
\(843\) | 50.1516 | 1.72731 | ||||||||
\(844\) | −0.315729 | −0.0108678 | ||||||||
\(845\) | −25.0428 | −0.861497 | ||||||||
\(846\) | −12.8598 | −0.442131 | ||||||||
\(847\) | −10.1066 | −0.347268 | ||||||||
\(848\) | −6.21137 | −0.213299 | ||||||||
\(849\) | −53.1042 | −1.82253 | ||||||||
\(850\) | 42.5349 | 1.45894 | ||||||||
\(851\) | 24.3305 | 0.834038 | ||||||||
\(852\) | −1.45803 | −0.0499512 | ||||||||
\(853\) | 37.9997 | 1.30109 | 0.650543 | − | 0.759469i | \(-0.274541\pi\) | ||||
0.650543 | + | 0.759469i | \(0.274541\pi\) | |||||||
\(854\) | −30.4237 | −1.04108 | ||||||||
\(855\) | −18.6605 | −0.638177 | ||||||||
\(856\) | 7.48399 | 0.255797 | ||||||||
\(857\) | −27.0615 | −0.924404 | −0.462202 | − | 0.886775i | \(-0.652940\pi\) | ||||
−0.462202 | + | 0.886775i | \(0.652940\pi\) | |||||||
\(858\) | −30.7375 | −1.04936 | ||||||||
\(859\) | −27.4404 | −0.936254 | −0.468127 | − | 0.883661i | \(-0.655071\pi\) | ||||
−0.468127 | + | 0.883661i | \(0.655071\pi\) | |||||||
\(860\) | −0.669912 | −0.0228438 | ||||||||
\(861\) | 37.3482 | 1.27282 | ||||||||
\(862\) | 33.5064 | 1.14123 | ||||||||
\(863\) | 9.19224 | 0.312907 | 0.156454 | − | 0.987685i | \(-0.449994\pi\) | ||||
0.156454 | + | 0.987685i | \(0.449994\pi\) | |||||||
\(864\) | −0.854926 | −0.0290852 | ||||||||
\(865\) | −54.1098 | −1.83979 | ||||||||
\(866\) | 38.0334 | 1.29243 | ||||||||
\(867\) | −17.3413 | −0.588940 | ||||||||
\(868\) | 0.330107 | 0.0112046 | ||||||||
\(869\) | 5.39982 | 0.183176 | ||||||||
\(870\) | 82.0434 | 2.78153 | ||||||||
\(871\) | 3.79486 | 0.128584 | ||||||||
\(872\) | −49.2779 | −1.66876 | ||||||||
\(873\) | 20.1844 | 0.683139 | ||||||||
\(874\) | 42.3773 | 1.43343 | ||||||||
\(875\) | −37.6039 | −1.27124 | ||||||||
\(876\) | 0.724321 | 0.0244725 | ||||||||
\(877\) | −34.4625 | −1.16372 | −0.581858 | − | 0.813290i | \(-0.697674\pi\) | ||||
−0.581858 | + | 0.813290i | \(0.697674\pi\) | |||||||
\(878\) | −41.6793 | −1.40661 | ||||||||
\(879\) | 56.9088 | 1.91949 | ||||||||
\(880\) | −62.1092 | −2.09370 | ||||||||
\(881\) | −4.94477 | −0.166594 | −0.0832968 | − | 0.996525i | \(-0.526545\pi\) | ||||
−0.0832968 | + | 0.996525i | \(0.526545\pi\) | |||||||
\(882\) | −7.36329 | −0.247935 | ||||||||
\(883\) | 48.8962 | 1.64549 | 0.822745 | − | 0.568411i | \(-0.192442\pi\) | ||||
0.822745 | + | 0.568411i | \(0.192442\pi\) | |||||||
\(884\) | 0.348031 | 0.0117056 | ||||||||
\(885\) | −94.2100 | −3.16683 | ||||||||
\(886\) | −55.6167 | −1.86848 | ||||||||
\(887\) | −53.2472 | −1.78787 | −0.893933 | − | 0.448200i | \(-0.852065\pi\) | ||||
−0.893933 | + | 0.448200i | \(0.852065\pi\) | |||||||
\(888\) | 16.1114 | 0.540663 | ||||||||
\(889\) | 0.783084 | 0.0262638 | ||||||||
\(890\) | 33.4125 | 1.11999 | ||||||||
\(891\) | −45.7420 | −1.53242 | ||||||||
\(892\) | 0.288153 | 0.00964807 | ||||||||
\(893\) | 21.4218 | 0.716852 | ||||||||
\(894\) | −19.7461 | −0.660407 | ||||||||
\(895\) | −66.1517 | −2.21121 | ||||||||
\(896\) | −19.8822 | −0.664217 | ||||||||
\(897\) | 49.1468 | 1.64096 | ||||||||
\(898\) | −32.2164 | −1.07508 | ||||||||
\(899\) | 28.2146 | 0.941010 | ||||||||
\(900\) | −0.673878 | −0.0224626 | ||||||||
\(901\) | 4.70690 | 0.156810 | ||||||||
\(902\) | −55.3549 | −1.84312 | ||||||||
\(903\) | −14.3603 | −0.477881 | ||||||||
\(904\) | 53.0014 | 1.76280 | ||||||||
\(905\) | 24.5799 | 0.817064 | ||||||||
\(906\) | 9.22402 | 0.306448 | ||||||||
\(907\) | 47.7279 | 1.58478 | 0.792389 | − | 0.610016i | \(-0.208837\pi\) | ||||
0.792389 | + | 0.610016i | \(0.208837\pi\) | |||||||
\(908\) | −0.412956 | −0.0137044 | ||||||||
\(909\) | 2.13255 | 0.0707321 | ||||||||
\(910\) | 25.5701 | 0.847640 | ||||||||
\(911\) | 51.9321 | 1.72059 | 0.860294 | − | 0.509798i | \(-0.170280\pi\) | ||||
0.860294 | + | 0.509798i | \(0.170280\pi\) | |||||||
\(912\) | 27.4190 | 0.907935 | ||||||||
\(913\) | 37.5808 | 1.24374 | ||||||||
\(914\) | 16.2547 | 0.537658 | ||||||||
\(915\) | 98.2676 | 3.24863 | ||||||||
\(916\) | −0.735992 | −0.0243179 | ||||||||
\(917\) | 9.60550 | 0.317201 | ||||||||
\(918\) | −13.6613 | −0.450889 | ||||||||
\(919\) | −15.7211 | −0.518590 | −0.259295 | − | 0.965798i | \(-0.583490\pi\) | ||||
−0.259295 | + | 0.965798i | \(0.583490\pi\) | |||||||
\(920\) | 101.636 | 3.35083 | ||||||||
\(921\) | 0.711026 | 0.0234291 | ||||||||
\(922\) | −41.3780 | −1.36271 | ||||||||
\(923\) | −38.8395 | −1.27842 | ||||||||
\(924\) | 0.714555 | 0.0235071 | ||||||||
\(925\) | −27.5068 | −0.904416 | ||||||||
\(926\) | 52.0258 | 1.70967 | ||||||||
\(927\) | −24.0424 | −0.789656 | ||||||||
\(928\) | 1.84698 | 0.0606301 | ||||||||
\(929\) | −42.3764 | −1.39033 | −0.695163 | − | 0.718852i | \(-0.744668\pi\) | ||||
−0.695163 | + | 0.718852i | \(0.744668\pi\) | |||||||
\(930\) | 45.5065 | 1.49222 | ||||||||
\(931\) | 12.2657 | 0.401992 | ||||||||
\(932\) | −0.454850 | −0.0148991 | ||||||||
\(933\) | 10.1038 | 0.330785 | ||||||||
\(934\) | 16.2756 | 0.532555 | ||||||||
\(935\) | 47.0656 | 1.53921 | ||||||||
\(936\) | 10.5144 | 0.343673 | ||||||||
\(937\) | 15.5160 | 0.506885 | 0.253442 | − | 0.967350i | \(-0.418437\pi\) | ||||
0.253442 | + | 0.967350i | \(0.418437\pi\) | |||||||
\(938\) | 3.76515 | 0.122937 | ||||||||
\(939\) | 13.5908 | 0.443518 | ||||||||
\(940\) | 1.14990 | 0.0375055 | ||||||||
\(941\) | 24.7888 | 0.808090 | 0.404045 | − | 0.914739i | \(-0.367604\pi\) | ||||
0.404045 | + | 0.914739i | \(0.367604\pi\) | |||||||
\(942\) | 3.95563 | 0.128881 | ||||||||
\(943\) | 88.5080 | 2.88222 | ||||||||
\(944\) | 44.7229 | 1.45561 | ||||||||
\(945\) | 23.5171 | 0.765012 | ||||||||
\(946\) | 21.2838 | 0.691997 | ||||||||
\(947\) | −15.0199 | −0.488081 | −0.244041 | − | 0.969765i | \(-0.578473\pi\) | ||||
−0.244041 | + | 0.969765i | \(0.578473\pi\) | |||||||
\(948\) | −0.127961 | −0.00415600 | ||||||||
\(949\) | 19.2947 | 0.626334 | ||||||||
\(950\) | −47.9095 | −1.55439 | ||||||||
\(951\) | 31.2416 | 1.01308 | ||||||||
\(952\) | 15.4282 | 0.500030 | ||||||||
\(953\) | −44.0306 | −1.42629 | −0.713145 | − | 0.701016i | \(-0.752730\pi\) | ||||
−0.713145 | + | 0.701016i | \(0.752730\pi\) | |||||||
\(954\) | 3.18267 | 0.103043 | ||||||||
\(955\) | 90.1417 | 2.91692 | ||||||||
\(956\) | 0.258067 | 0.00834649 | ||||||||
\(957\) | 61.0738 | 1.97424 | ||||||||
\(958\) | −29.3804 | −0.949237 | ||||||||
\(959\) | 6.69486 | 0.216188 | ||||||||
\(960\) | 67.2676 | 2.17105 | ||||||||
\(961\) | −15.3504 | −0.495173 | ||||||||
\(962\) | 9.60576 | 0.309702 | ||||||||
\(963\) | −3.74691 | −0.120743 | ||||||||
\(964\) | 0.315683 | 0.0101675 | ||||||||
\(965\) | 87.2560 | 2.80887 | ||||||||
\(966\) | 48.7621 | 1.56890 | ||||||||
\(967\) | 39.5267 | 1.27109 | 0.635546 | − | 0.772063i | \(-0.280775\pi\) | ||||
0.635546 | + | 0.772063i | \(0.280775\pi\) | |||||||
\(968\) | −15.8599 | −0.509757 | ||||||||
\(969\) | −20.7778 | −0.667480 | ||||||||
\(970\) | 77.0300 | 2.47328 | ||||||||
\(971\) | −56.0487 | −1.79869 | −0.899344 | − | 0.437243i | \(-0.855955\pi\) | ||||
−0.899344 | + | 0.437243i | \(0.855955\pi\) | |||||||
\(972\) | 0.630482 | 0.0202227 | ||||||||
\(973\) | −25.8726 | −0.829439 | ||||||||
\(974\) | −33.0781 | −1.05989 | ||||||||
\(975\) | −55.5628 | −1.77943 | ||||||||
\(976\) | −46.6491 | −1.49320 | ||||||||
\(977\) | −41.0962 | −1.31478 | −0.657392 | − | 0.753549i | \(-0.728340\pi\) | ||||
−0.657392 | + | 0.753549i | \(0.728340\pi\) | |||||||
\(978\) | −68.6651 | −2.19567 | ||||||||
\(979\) | 24.8726 | 0.794932 | ||||||||
\(980\) | 0.658409 | 0.0210321 | ||||||||
\(981\) | 24.6713 | 0.787695 | ||||||||
\(982\) | −5.23634 | −0.167098 | ||||||||
\(983\) | −31.9949 | −1.02048 | −0.510239 | − | 0.860032i | \(-0.670443\pi\) | ||||
−0.510239 | + | 0.860032i | \(0.670443\pi\) | |||||||
\(984\) | 58.6092 | 1.86839 | ||||||||
\(985\) | 30.2627 | 0.964250 | ||||||||
\(986\) | 29.5138 | 0.939910 | ||||||||
\(987\) | 24.6493 | 0.784597 | ||||||||
\(988\) | −0.392007 | −0.0124714 | ||||||||
\(989\) | −34.0311 | −1.08213 | ||||||||
\(990\) | 31.8244 | 1.01145 | ||||||||
\(991\) | −6.63765 | −0.210852 | −0.105426 | − | 0.994427i | \(-0.533621\pi\) | ||||
−0.105426 | + | 0.994427i | \(0.533621\pi\) | |||||||
\(992\) | 1.02445 | 0.0325264 | ||||||||
\(993\) | −15.7211 | −0.498893 | ||||||||
\(994\) | −38.5354 | −1.22227 | ||||||||
\(995\) | 75.0162 | 2.37817 | ||||||||
\(996\) | −0.890565 | −0.0282186 | ||||||||
\(997\) | −35.3560 | −1.11973 | −0.559867 | − | 0.828582i | \(-0.689148\pi\) | ||||
−0.559867 | + | 0.828582i | \(0.689148\pi\) | |||||||
\(998\) | −51.8671 | −1.64182 | ||||||||
\(999\) | 8.83454 | 0.279513 |
(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 | 619.2.a.b.1.19 | ✓ | 30 | |
3.2 | odd | 2 | 5571.2.a.g.1.12 | 30 | |||
4.3 | odd | 2 | 9904.2.a.n.1.8 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
619.2.a.b.1.19 | ✓ | 30 | 1.1 | even | 1 | trivial | |
5571.2.a.g.1.12 | 30 | 3.2 | odd | 2 | |||
9904.2.a.n.1.8 | 30 | 4.3 | odd | 2 |