Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8011,2,Mod(1,8011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8011, 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("8011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8011.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: | \(63.9681570592\) |
Analytic rank: | \(1\) |
Dimension: | \(309\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 8011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.75364 | −1.94712 | −0.973560 | − | 0.228430i | \(-0.926641\pi\) | ||||
−0.973560 | + | 0.228430i | \(0.926641\pi\) | |||||||
\(3\) | −0.00102412 | −0.000591277 0 | −0.000295639 | − | 1.00000i | \(-0.500094\pi\) | ||||
−0.000295639 | 1.00000i | \(0.500094\pi\) | ||||||||
\(4\) | 5.58256 | 2.79128 | ||||||||
\(5\) | −3.57698 | −1.59967 | −0.799837 | − | 0.600217i | \(-0.795081\pi\) | ||||
−0.799837 | + | 0.600217i | \(0.795081\pi\) | |||||||
\(6\) | 0.00282007 | 0.00115129 | ||||||||
\(7\) | 1.05818 | 0.399955 | 0.199978 | − | 0.979800i | \(-0.435913\pi\) | ||||
0.199978 | + | 0.979800i | \(0.435913\pi\) | |||||||
\(8\) | −9.86509 | −3.48784 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 9.84973 | 3.11476 | ||||||||
\(11\) | 1.12064 | 0.337885 | 0.168942 | − | 0.985626i | \(-0.445965\pi\) | ||||
0.168942 | + | 0.985626i | \(0.445965\pi\) | |||||||
\(12\) | −0.00571722 | −0.00165042 | ||||||||
\(13\) | 3.71956 | 1.03162 | 0.515810 | − | 0.856703i | \(-0.327491\pi\) | ||||
0.515810 | + | 0.856703i | \(0.327491\pi\) | |||||||
\(14\) | −2.91386 | −0.778761 | ||||||||
\(15\) | 0.00366327 | 0.000945851 0 | ||||||||
\(16\) | 15.9998 | 3.99996 | ||||||||
\(17\) | −4.93358 | −1.19657 | −0.598285 | − | 0.801284i | \(-0.704151\pi\) | ||||
−0.598285 | + | 0.801284i | \(0.704151\pi\) | |||||||
\(18\) | 8.26093 | 1.94712 | ||||||||
\(19\) | 5.04681 | 1.15782 | 0.578909 | − | 0.815392i | \(-0.303479\pi\) | ||||
0.578909 | + | 0.815392i | \(0.303479\pi\) | |||||||
\(20\) | −19.9687 | −4.46514 | ||||||||
\(21\) | −0.00108371 | −0.000236484 0 | ||||||||
\(22\) | −3.08584 | −0.657902 | ||||||||
\(23\) | 1.51598 | 0.316103 | 0.158052 | − | 0.987431i | \(-0.449479\pi\) | ||||
0.158052 | + | 0.987431i | \(0.449479\pi\) | |||||||
\(24\) | 0.0101031 | 0.00206228 | ||||||||
\(25\) | 7.79478 | 1.55896 | ||||||||
\(26\) | −10.2423 | −2.00869 | ||||||||
\(27\) | 0.00614473 | 0.00118255 | ||||||||
\(28\) | 5.90736 | 1.11639 | ||||||||
\(29\) | 1.91463 | 0.355538 | 0.177769 | − | 0.984072i | \(-0.443112\pi\) | ||||
0.177769 | + | 0.984072i | \(0.443112\pi\) | |||||||
\(30\) | −0.0100873 | −0.00184169 | ||||||||
\(31\) | −1.66684 | −0.299374 | −0.149687 | − | 0.988733i | \(-0.547827\pi\) | ||||
−0.149687 | + | 0.988733i | \(0.547827\pi\) | |||||||
\(32\) | −24.3277 | −4.30057 | ||||||||
\(33\) | −0.00114767 | −0.000199784 0 | ||||||||
\(34\) | 13.5853 | 2.32987 | ||||||||
\(35\) | −3.78509 | −0.639798 | ||||||||
\(36\) | −16.7477 | −2.79128 | ||||||||
\(37\) | 3.29072 | 0.540991 | 0.270495 | − | 0.962721i | \(-0.412813\pi\) | ||||
0.270495 | + | 0.962721i | \(0.412813\pi\) | |||||||
\(38\) | −13.8971 | −2.25441 | ||||||||
\(39\) | −0.00380928 | −0.000609974 0 | ||||||||
\(40\) | 35.2872 | 5.57940 | ||||||||
\(41\) | −5.99915 | −0.936910 | −0.468455 | − | 0.883487i | \(-0.655189\pi\) | ||||
−0.468455 | + | 0.883487i | \(0.655189\pi\) | |||||||
\(42\) | 0.00298415 | 0.000460464 0 | ||||||||
\(43\) | −8.67231 | −1.32252 | −0.661258 | − | 0.750159i | \(-0.729977\pi\) | ||||
−0.661258 | + | 0.750159i | \(0.729977\pi\) | |||||||
\(44\) | 6.25602 | 0.943131 | ||||||||
\(45\) | 10.7309 | 1.59967 | ||||||||
\(46\) | −4.17446 | −0.615491 | ||||||||
\(47\) | 1.21334 | 0.176984 | 0.0884918 | − | 0.996077i | \(-0.471795\pi\) | ||||
0.0884918 | + | 0.996077i | \(0.471795\pi\) | |||||||
\(48\) | −0.0163858 | −0.00236509 | ||||||||
\(49\) | −5.88025 | −0.840036 | ||||||||
\(50\) | −21.4641 | −3.03548 | ||||||||
\(51\) | 0.00505259 | 0.000707504 0 | ||||||||
\(52\) | 20.7647 | 2.87954 | ||||||||
\(53\) | 0.668065 | 0.0917658 | 0.0458829 | − | 0.998947i | \(-0.485390\pi\) | ||||
0.0458829 | + | 0.998947i | \(0.485390\pi\) | |||||||
\(54\) | −0.0169204 | −0.00230258 | ||||||||
\(55\) | −4.00849 | −0.540505 | ||||||||
\(56\) | −10.4391 | −1.39498 | ||||||||
\(57\) | −0.00516855 | −0.000684591 0 | ||||||||
\(58\) | −5.27221 | −0.692275 | ||||||||
\(59\) | −2.48011 | −0.322883 | −0.161442 | − | 0.986882i | \(-0.551614\pi\) | ||||
−0.161442 | + | 0.986882i | \(0.551614\pi\) | |||||||
\(60\) | 0.0204504 | 0.00264013 | ||||||||
\(61\) | −5.18149 | −0.663421 | −0.331711 | − | 0.943381i | \(-0.607626\pi\) | ||||
−0.331711 | + | 0.943381i | \(0.607626\pi\) | |||||||
\(62\) | 4.58989 | 0.582917 | ||||||||
\(63\) | −3.17454 | −0.399955 | ||||||||
\(64\) | 34.9902 | 4.37377 | ||||||||
\(65\) | −13.3048 | −1.65026 | ||||||||
\(66\) | 0.00316027 | 0.000389003 0 | ||||||||
\(67\) | 2.50599 | 0.306156 | 0.153078 | − | 0.988214i | \(-0.451081\pi\) | ||||
0.153078 | + | 0.988214i | \(0.451081\pi\) | |||||||
\(68\) | −27.5420 | −3.33996 | ||||||||
\(69\) | −0.00155255 | −0.000186905 0 | ||||||||
\(70\) | 10.4228 | 1.24576 | ||||||||
\(71\) | −0.521666 | −0.0619104 | −0.0309552 | − | 0.999521i | \(-0.509855\pi\) | ||||
−0.0309552 | + | 0.999521i | \(0.509855\pi\) | |||||||
\(72\) | 29.5953 | 3.48784 | ||||||||
\(73\) | −9.31782 | −1.09057 | −0.545284 | − | 0.838251i | \(-0.683578\pi\) | ||||
−0.545284 | + | 0.838251i | \(0.683578\pi\) | |||||||
\(74\) | −9.06147 | −1.05337 | ||||||||
\(75\) | −0.00798281 | −0.000921776 0 | ||||||||
\(76\) | 28.1741 | 3.23179 | ||||||||
\(77\) | 1.18584 | 0.135139 | ||||||||
\(78\) | 0.0104894 | 0.00118769 | ||||||||
\(79\) | −1.37692 | −0.154916 | −0.0774579 | − | 0.996996i | \(-0.524680\pi\) | ||||
−0.0774579 | + | 0.996996i | \(0.524680\pi\) | |||||||
\(80\) | −57.2311 | −6.39863 | ||||||||
\(81\) | 8.99999 | 0.999999 | ||||||||
\(82\) | 16.5195 | 1.82428 | ||||||||
\(83\) | 9.43789 | 1.03594 | 0.517971 | − | 0.855398i | \(-0.326687\pi\) | ||||
0.517971 | + | 0.855398i | \(0.326687\pi\) | |||||||
\(84\) | −0.00604986 | −0.000660094 0 | ||||||||
\(85\) | 17.6473 | 1.91412 | ||||||||
\(86\) | 23.8805 | 2.57510 | ||||||||
\(87\) | −0.00196082 | −0.000210221 0 | ||||||||
\(88\) | −11.0552 | −1.17849 | ||||||||
\(89\) | −10.8598 | −1.15113 | −0.575566 | − | 0.817755i | \(-0.695218\pi\) | ||||
−0.575566 | + | 0.817755i | \(0.695218\pi\) | |||||||
\(90\) | −29.5492 | −3.11476 | ||||||||
\(91\) | 3.93597 | 0.412602 | ||||||||
\(92\) | 8.46303 | 0.882332 | ||||||||
\(93\) | 0.00170705 | 0.000177013 0 | ||||||||
\(94\) | −3.34110 | −0.344608 | ||||||||
\(95\) | −18.0523 | −1.85213 | ||||||||
\(96\) | 0.0249145 | 0.00254283 | ||||||||
\(97\) | 15.7581 | 1.59999 | 0.799996 | − | 0.600006i | \(-0.204835\pi\) | ||||
0.799996 | + | 0.600006i | \(0.204835\pi\) | |||||||
\(98\) | 16.1921 | 1.63565 | ||||||||
\(99\) | −3.36191 | −0.337885 | ||||||||
\(100\) | 43.5148 | 4.35148 | ||||||||
\(101\) | 8.79755 | 0.875389 | 0.437694 | − | 0.899124i | \(-0.355795\pi\) | ||||
0.437694 | + | 0.899124i | \(0.355795\pi\) | |||||||
\(102\) | −0.0139130 | −0.00137760 | ||||||||
\(103\) | 5.83894 | 0.575328 | 0.287664 | − | 0.957731i | \(-0.407121\pi\) | ||||
0.287664 | + | 0.957731i | \(0.407121\pi\) | |||||||
\(104\) | −36.6938 | −3.59812 | ||||||||
\(105\) | 0.00387640 | 0.000378298 0 | ||||||||
\(106\) | −1.83961 | −0.178679 | ||||||||
\(107\) | 8.19799 | 0.792529 | 0.396265 | − | 0.918136i | \(-0.370306\pi\) | ||||
0.396265 | + | 0.918136i | \(0.370306\pi\) | |||||||
\(108\) | 0.0343033 | 0.00330084 | ||||||||
\(109\) | −18.9645 | −1.81647 | −0.908234 | − | 0.418463i | \(-0.862569\pi\) | ||||
−0.908234 | + | 0.418463i | \(0.862569\pi\) | |||||||
\(110\) | 11.0380 | 1.05243 | ||||||||
\(111\) | −0.00337010 | −0.000319876 0 | ||||||||
\(112\) | 16.9307 | 1.59980 | ||||||||
\(113\) | 11.6215 | 1.09326 | 0.546628 | − | 0.837375i | \(-0.315911\pi\) | ||||
0.546628 | + | 0.837375i | \(0.315911\pi\) | |||||||
\(114\) | 0.0142323 | 0.00133298 | ||||||||
\(115\) | −5.42262 | −0.505662 | ||||||||
\(116\) | 10.6885 | 0.992405 | ||||||||
\(117\) | −11.1587 | −1.03162 | ||||||||
\(118\) | 6.82935 | 0.628692 | ||||||||
\(119\) | −5.22063 | −0.478574 | ||||||||
\(120\) | −0.0361385 | −0.00329897 | ||||||||
\(121\) | −9.74417 | −0.885834 | ||||||||
\(122\) | 14.2680 | 1.29176 | ||||||||
\(123\) | 0.00614387 | 0.000553974 0 | ||||||||
\(124\) | −9.30524 | −0.835635 | ||||||||
\(125\) | −9.99687 | −0.894147 | ||||||||
\(126\) | 8.74157 | 0.778761 | ||||||||
\(127\) | 2.69020 | 0.238717 | 0.119358 | − | 0.992851i | \(-0.461916\pi\) | ||||
0.119358 | + | 0.992851i | \(0.461916\pi\) | |||||||
\(128\) | −47.6951 | −4.21569 | ||||||||
\(129\) | 0.00888151 | 0.000781974 0 | ||||||||
\(130\) | 36.6366 | 3.21325 | ||||||||
\(131\) | 15.8175 | 1.38198 | 0.690992 | − | 0.722863i | \(-0.257174\pi\) | ||||
0.690992 | + | 0.722863i | \(0.257174\pi\) | |||||||
\(132\) | −0.00640693 | −0.000557652 0 | ||||||||
\(133\) | 5.34044 | 0.463075 | ||||||||
\(134\) | −6.90062 | −0.596123 | ||||||||
\(135\) | −0.0219796 | −0.00189170 | ||||||||
\(136\) | 48.6703 | 4.17344 | ||||||||
\(137\) | 3.06338 | 0.261722 | 0.130861 | − | 0.991401i | \(-0.458226\pi\) | ||||
0.130861 | + | 0.991401i | \(0.458226\pi\) | |||||||
\(138\) | 0.00427516 | 0.000363926 0 | ||||||||
\(139\) | −2.14301 | −0.181768 | −0.0908839 | − | 0.995861i | \(-0.528969\pi\) | ||||
−0.0908839 | + | 0.995861i | \(0.528969\pi\) | |||||||
\(140\) | −21.1305 | −1.78585 | ||||||||
\(141\) | −0.00124261 | −0.000104646 0 | ||||||||
\(142\) | 1.43648 | 0.120547 | ||||||||
\(143\) | 4.16827 | 0.348569 | ||||||||
\(144\) | −47.9995 | −3.99996 | ||||||||
\(145\) | −6.84859 | −0.568744 | ||||||||
\(146\) | 25.6580 | 2.12347 | ||||||||
\(147\) | 0.00602210 | 0.000496694 0 | ||||||||
\(148\) | 18.3706 | 1.51006 | ||||||||
\(149\) | 6.62073 | 0.542391 | 0.271196 | − | 0.962524i | \(-0.412581\pi\) | ||||
0.271196 | + | 0.962524i | \(0.412581\pi\) | |||||||
\(150\) | 0.0219818 | 0.00179481 | ||||||||
\(151\) | 6.27182 | 0.510394 | 0.255197 | − | 0.966889i | \(-0.417860\pi\) | ||||
0.255197 | + | 0.966889i | \(0.417860\pi\) | |||||||
\(152\) | −49.7872 | −4.03828 | ||||||||
\(153\) | 14.8007 | 1.19657 | ||||||||
\(154\) | −3.26537 | −0.263131 | ||||||||
\(155\) | 5.96226 | 0.478900 | ||||||||
\(156\) | −0.0212656 | −0.00170261 | ||||||||
\(157\) | 15.7361 | 1.25588 | 0.627940 | − | 0.778262i | \(-0.283898\pi\) | ||||
0.627940 | + | 0.778262i | \(0.283898\pi\) | |||||||
\(158\) | 3.79155 | 0.301640 | ||||||||
\(159\) | −0.000684181 0 | −5.42591e−5 0 | ||||||||
\(160\) | 87.0197 | 6.87951 | ||||||||
\(161\) | 1.60418 | 0.126427 | ||||||||
\(162\) | −24.7828 | −1.94712 | ||||||||
\(163\) | 8.05560 | 0.630964 | 0.315482 | − | 0.948932i | \(-0.397834\pi\) | ||||
0.315482 | + | 0.948932i | \(0.397834\pi\) | |||||||
\(164\) | −33.4906 | −2.61518 | ||||||||
\(165\) | 0.00410519 | 0.000319589 0 | ||||||||
\(166\) | −25.9886 | −2.01711 | ||||||||
\(167\) | 15.0217 | 1.16241 | 0.581207 | − | 0.813756i | \(-0.302581\pi\) | ||||
0.581207 | + | 0.813756i | \(0.302581\pi\) | |||||||
\(168\) | 0.0106909 | 0.000824819 0 | ||||||||
\(169\) | 0.835116 | 0.0642397 | ||||||||
\(170\) | −48.5945 | −3.72702 | ||||||||
\(171\) | −15.1404 | −1.15782 | ||||||||
\(172\) | −48.4137 | −3.69151 | ||||||||
\(173\) | 7.07465 | 0.537875 | 0.268938 | − | 0.963158i | \(-0.413327\pi\) | ||||
0.268938 | + | 0.963158i | \(0.413327\pi\) | |||||||
\(174\) | 0.00539939 | 0.000409327 0 | ||||||||
\(175\) | 8.24829 | 0.623512 | ||||||||
\(176\) | 17.9300 | 1.35153 | ||||||||
\(177\) | 0.00253994 | 0.000190913 0 | ||||||||
\(178\) | 29.9039 | 2.24139 | ||||||||
\(179\) | 15.2020 | 1.13625 | 0.568126 | − | 0.822942i | \(-0.307669\pi\) | ||||
0.568126 | + | 0.822942i | \(0.307669\pi\) | |||||||
\(180\) | 59.9061 | 4.46513 | ||||||||
\(181\) | 1.57660 | 0.117188 | 0.0585938 | − | 0.998282i | \(-0.481338\pi\) | ||||
0.0585938 | + | 0.998282i | \(0.481338\pi\) | |||||||
\(182\) | −10.8383 | −0.803385 | ||||||||
\(183\) | 0.00530648 | 0.000392266 0 | ||||||||
\(184\) | −14.9553 | −1.10252 | ||||||||
\(185\) | −11.7708 | −0.865409 | ||||||||
\(186\) | −0.00470061 | −0.000344665 0 | ||||||||
\(187\) | −5.52875 | −0.404302 | ||||||||
\(188\) | 6.77353 | 0.494011 | ||||||||
\(189\) | 0.00650224 | 0.000472969 0 | ||||||||
\(190\) | 49.7097 | 3.60632 | ||||||||
\(191\) | 4.40718 | 0.318892 | 0.159446 | − | 0.987207i | \(-0.449029\pi\) | ||||
0.159446 | + | 0.987207i | \(0.449029\pi\) | |||||||
\(192\) | −0.0358342 | −0.00258611 | ||||||||
\(193\) | −0.849967 | −0.0611820 | −0.0305910 | − | 0.999532i | \(-0.509739\pi\) | ||||
−0.0305910 | + | 0.999532i | \(0.509739\pi\) | |||||||
\(194\) | −43.3922 | −3.11538 | ||||||||
\(195\) | 0.0136257 | 0.000975759 0 | ||||||||
\(196\) | −32.8269 | −2.34478 | ||||||||
\(197\) | 19.7168 | 1.40476 | 0.702382 | − | 0.711800i | \(-0.252120\pi\) | ||||
0.702382 | + | 0.711800i | \(0.252120\pi\) | |||||||
\(198\) | 9.25750 | 0.657902 | ||||||||
\(199\) | −0.357550 | −0.0253461 | −0.0126730 | − | 0.999920i | \(-0.504034\pi\) | ||||
−0.0126730 | + | 0.999920i | \(0.504034\pi\) | |||||||
\(200\) | −76.8962 | −5.43739 | ||||||||
\(201\) | −0.00256645 | −0.000181023 0 | ||||||||
\(202\) | −24.2253 | −1.70449 | ||||||||
\(203\) | 2.02603 | 0.142199 | ||||||||
\(204\) | 0.0282064 | 0.00197484 | ||||||||
\(205\) | 21.4588 | 1.49875 | ||||||||
\(206\) | −16.0784 | −1.12023 | ||||||||
\(207\) | −4.54793 | −0.316103 | ||||||||
\(208\) | 59.5124 | 4.12644 | ||||||||
\(209\) | 5.65564 | 0.391209 | ||||||||
\(210\) | −0.0106742 | −0.000736592 0 | ||||||||
\(211\) | −8.82070 | −0.607242 | −0.303621 | − | 0.952793i | \(-0.598196\pi\) | ||||
−0.303621 | + | 0.952793i | \(0.598196\pi\) | |||||||
\(212\) | 3.72951 | 0.256144 | ||||||||
\(213\) | 0.000534250 0 | 3.66062e−5 0 | ||||||||
\(214\) | −22.5743 | −1.54315 | ||||||||
\(215\) | 31.0207 | 2.11559 | ||||||||
\(216\) | −0.0606184 | −0.00412456 | ||||||||
\(217\) | −1.76382 | −0.119736 | ||||||||
\(218\) | 52.2214 | 3.53688 | ||||||||
\(219\) | 0.00954259 | 0.000644829 0 | ||||||||
\(220\) | −22.3777 | −1.50870 | ||||||||
\(221\) | −18.3507 | −1.23440 | ||||||||
\(222\) | 0.00928006 | 0.000622837 0 | ||||||||
\(223\) | −16.9325 | −1.13389 | −0.566944 | − | 0.823757i | \(-0.691874\pi\) | ||||
−0.566944 | + | 0.823757i | \(0.691874\pi\) | |||||||
\(224\) | −25.7431 | −1.72004 | ||||||||
\(225\) | −23.3843 | −1.55896 | ||||||||
\(226\) | −32.0014 | −2.12870 | ||||||||
\(227\) | −9.90977 | −0.657735 | −0.328867 | − | 0.944376i | \(-0.606667\pi\) | ||||
−0.328867 | + | 0.944376i | \(0.606667\pi\) | |||||||
\(228\) | −0.0288537 | −0.00191089 | ||||||||
\(229\) | 9.05410 | 0.598312 | 0.299156 | − | 0.954204i | \(-0.403295\pi\) | ||||
0.299156 | + | 0.954204i | \(0.403295\pi\) | |||||||
\(230\) | 14.9320 | 0.984585 | ||||||||
\(231\) | −0.00121444 | −7.99045e−5 0 | ||||||||
\(232\) | −18.8880 | −1.24006 | ||||||||
\(233\) | −5.41132 | −0.354508 | −0.177254 | − | 0.984165i | \(-0.556721\pi\) | ||||
−0.177254 | + | 0.984165i | \(0.556721\pi\) | |||||||
\(234\) | 30.7270 | 2.00869 | ||||||||
\(235\) | −4.34009 | −0.283116 | ||||||||
\(236\) | −13.8454 | −0.901257 | ||||||||
\(237\) | 0.00141014 | 9.15982e−5 0 | ||||||||
\(238\) | 14.3757 | 0.931841 | ||||||||
\(239\) | −3.79226 | −0.245301 | −0.122650 | − | 0.992450i | \(-0.539139\pi\) | ||||
−0.122650 | + | 0.992450i | \(0.539139\pi\) | |||||||
\(240\) | 0.0586117 | 0.00378337 | ||||||||
\(241\) | −21.5186 | −1.38614 | −0.693069 | − | 0.720871i | \(-0.743742\pi\) | ||||
−0.693069 | + | 0.720871i | \(0.743742\pi\) | |||||||
\(242\) | 26.8320 | 1.72483 | ||||||||
\(243\) | −0.0276513 | −0.00177383 | ||||||||
\(244\) | −28.9260 | −1.85179 | ||||||||
\(245\) | 21.0335 | 1.34378 | ||||||||
\(246\) | −0.0169180 | −0.00107865 | ||||||||
\(247\) | 18.7719 | 1.19443 | ||||||||
\(248\) | 16.4435 | 1.04417 | ||||||||
\(249\) | −0.00966555 | −0.000612530 0 | ||||||||
\(250\) | 27.5278 | 1.74101 | ||||||||
\(251\) | −23.9430 | −1.51127 | −0.755636 | − | 0.654992i | \(-0.772672\pi\) | ||||
−0.755636 | + | 0.654992i | \(0.772672\pi\) | |||||||
\(252\) | −17.7221 | −1.11639 | ||||||||
\(253\) | 1.69886 | 0.106806 | ||||||||
\(254\) | −7.40786 | −0.464811 | ||||||||
\(255\) | −0.0180730 | −0.00113178 | ||||||||
\(256\) | 61.3549 | 3.83468 | ||||||||
\(257\) | −26.5751 | −1.65771 | −0.828854 | − | 0.559465i | \(-0.811007\pi\) | ||||
−0.828854 | + | 0.559465i | \(0.811007\pi\) | |||||||
\(258\) | −0.0244565 | −0.00152260 | ||||||||
\(259\) | 3.48218 | 0.216372 | ||||||||
\(260\) | −74.2747 | −4.60632 | ||||||||
\(261\) | −5.74389 | −0.355538 | ||||||||
\(262\) | −43.5558 | −2.69089 | ||||||||
\(263\) | −13.2504 | −0.817058 | −0.408529 | − | 0.912745i | \(-0.633958\pi\) | ||||
−0.408529 | + | 0.912745i | \(0.633958\pi\) | |||||||
\(264\) | 0.0113219 | 0.000696813 0 | ||||||||
\(265\) | −2.38966 | −0.146795 | ||||||||
\(266\) | −14.7057 | −0.901663 | ||||||||
\(267\) | 0.0111217 | 0.000680638 0 | ||||||||
\(268\) | 13.9899 | 0.854567 | ||||||||
\(269\) | 7.05049 | 0.429876 | 0.214938 | − | 0.976628i | \(-0.431045\pi\) | ||||
0.214938 | + | 0.976628i | \(0.431045\pi\) | |||||||
\(270\) | 0.0605240 | 0.00368337 | ||||||||
\(271\) | −22.9213 | −1.39237 | −0.696186 | − | 0.717862i | \(-0.745121\pi\) | ||||
−0.696186 | + | 0.717862i | \(0.745121\pi\) | |||||||
\(272\) | −78.9366 | −4.78623 | ||||||||
\(273\) | −0.00403091 | −0.000243962 0 | ||||||||
\(274\) | −8.43545 | −0.509604 | ||||||||
\(275\) | 8.73512 | 0.526747 | ||||||||
\(276\) | −0.00866718 | −0.000521703 0 | ||||||||
\(277\) | 1.70432 | 0.102403 | 0.0512014 | − | 0.998688i | \(-0.483695\pi\) | ||||
0.0512014 | + | 0.998688i | \(0.483695\pi\) | |||||||
\(278\) | 5.90109 | 0.353924 | ||||||||
\(279\) | 5.00052 | 0.299373 | ||||||||
\(280\) | 37.3403 | 2.23151 | ||||||||
\(281\) | 3.67539 | 0.219256 | 0.109628 | − | 0.993973i | \(-0.465034\pi\) | ||||
0.109628 | + | 0.993973i | \(0.465034\pi\) | |||||||
\(282\) | 0.00342170 | 0.000203759 0 | ||||||||
\(283\) | 2.60223 | 0.154687 | 0.0773433 | − | 0.997005i | \(-0.475356\pi\) | ||||
0.0773433 | + | 0.997005i | \(0.475356\pi\) | |||||||
\(284\) | −2.91223 | −0.172809 | ||||||||
\(285\) | 0.0184878 | 0.00109512 | ||||||||
\(286\) | −11.4779 | −0.678705 | ||||||||
\(287\) | −6.34819 | −0.374722 | ||||||||
\(288\) | 72.9831 | 4.30057 | ||||||||
\(289\) | 7.34023 | 0.431778 | ||||||||
\(290\) | 18.8586 | 1.10741 | ||||||||
\(291\) | −0.0161382 | −0.000946039 0 | ||||||||
\(292\) | −52.0173 | −3.04408 | ||||||||
\(293\) | 10.2148 | 0.596755 | 0.298378 | − | 0.954448i | \(-0.403555\pi\) | ||||
0.298378 | + | 0.954448i | \(0.403555\pi\) | |||||||
\(294\) | −0.0165827 | −0.000967124 0 | ||||||||
\(295\) | 8.87131 | 0.516508 | ||||||||
\(296\) | −32.4633 | −1.88689 | ||||||||
\(297\) | 0.00688601 | 0.000399567 0 | ||||||||
\(298\) | −18.2311 | −1.05610 | ||||||||
\(299\) | 5.63877 | 0.326098 | ||||||||
\(300\) | −0.0445645 | −0.00257293 | ||||||||
\(301\) | −9.17688 | −0.528947 | ||||||||
\(302\) | −17.2704 | −0.993798 | ||||||||
\(303\) | −0.00900977 | −0.000517598 0 | ||||||||
\(304\) | 80.7481 | 4.63122 | ||||||||
\(305\) | 18.5341 | 1.06126 | ||||||||
\(306\) | −40.7560 | −2.32986 | ||||||||
\(307\) | 0.199172 | 0.0113674 | 0.00568368 | − | 0.999984i | \(-0.498191\pi\) | ||||
0.00568368 | + | 0.999984i | \(0.498191\pi\) | |||||||
\(308\) | 6.62001 | 0.377210 | ||||||||
\(309\) | −0.00597979 | −0.000340179 0 | ||||||||
\(310\) | −16.4179 | −0.932476 | ||||||||
\(311\) | 8.16345 | 0.462907 | 0.231453 | − | 0.972846i | \(-0.425652\pi\) | ||||
0.231453 | + | 0.972846i | \(0.425652\pi\) | |||||||
\(312\) | 0.0375789 | 0.00212749 | ||||||||
\(313\) | −22.5820 | −1.27641 | −0.638206 | − | 0.769866i | \(-0.720323\pi\) | ||||
−0.638206 | + | 0.769866i | \(0.720323\pi\) | |||||||
\(314\) | −43.3317 | −2.44535 | ||||||||
\(315\) | 11.3553 | 0.639797 | ||||||||
\(316\) | −7.68674 | −0.432413 | ||||||||
\(317\) | −22.0878 | −1.24058 | −0.620288 | − | 0.784374i | \(-0.712984\pi\) | ||||
−0.620288 | + | 0.784374i | \(0.712984\pi\) | |||||||
\(318\) | 0.00188399 | 0.000105649 0 | ||||||||
\(319\) | 2.14560 | 0.120131 | ||||||||
\(320\) | −125.159 | −6.99660 | ||||||||
\(321\) | −0.00839574 | −0.000468605 0 | ||||||||
\(322\) | −4.41734 | −0.246169 | ||||||||
\(323\) | −24.8988 | −1.38541 | ||||||||
\(324\) | 50.2430 | 2.79128 | ||||||||
\(325\) | 28.9931 | 1.60825 | ||||||||
\(326\) | −22.1823 | −1.22856 | ||||||||
\(327\) | 0.0194220 | 0.00107404 | ||||||||
\(328\) | 59.1822 | 3.26779 | ||||||||
\(329\) | 1.28393 | 0.0707855 | ||||||||
\(330\) | −0.0113042 | −0.000622278 0 | ||||||||
\(331\) | −17.4510 | −0.959195 | −0.479597 | − | 0.877489i | \(-0.659217\pi\) | ||||
−0.479597 | + | 0.877489i | \(0.659217\pi\) | |||||||
\(332\) | 52.6876 | 2.89161 | ||||||||
\(333\) | −9.87215 | −0.540991 | ||||||||
\(334\) | −41.3644 | −2.26336 | ||||||||
\(335\) | −8.96389 | −0.489750 | ||||||||
\(336\) | −0.0173392 | −0.000945928 0 | ||||||||
\(337\) | −3.73514 | −0.203466 | −0.101733 | − | 0.994812i | \(-0.532439\pi\) | ||||
−0.101733 | + | 0.994812i | \(0.532439\pi\) | |||||||
\(338\) | −2.29961 | −0.125083 | ||||||||
\(339\) | −0.0119018 | −0.000646418 0 | ||||||||
\(340\) | 98.5172 | 5.34285 | ||||||||
\(341\) | −1.86792 | −0.101154 | ||||||||
\(342\) | 41.6913 | 2.25441 | ||||||||
\(343\) | −13.6296 | −0.735932 | ||||||||
\(344\) | 85.5532 | 4.61272 | ||||||||
\(345\) | 0.00555343 | 0.000298986 0 | ||||||||
\(346\) | −19.4811 | −1.04731 | ||||||||
\(347\) | −20.3418 | −1.09200 | −0.546002 | − | 0.837784i | \(-0.683851\pi\) | ||||
−0.546002 | + | 0.837784i | \(0.683851\pi\) | |||||||
\(348\) | −0.0109464 | −0.000586787 0 | ||||||||
\(349\) | 15.4986 | 0.829621 | 0.414810 | − | 0.909908i | \(-0.363848\pi\) | ||||
0.414810 | + | 0.909908i | \(0.363848\pi\) | |||||||
\(350\) | −22.7129 | −1.21405 | ||||||||
\(351\) | 0.0228557 | 0.00121995 | ||||||||
\(352\) | −27.2625 | −1.45310 | ||||||||
\(353\) | 15.4448 | 0.822045 | 0.411022 | − | 0.911625i | \(-0.365172\pi\) | ||||
0.411022 | + | 0.911625i | \(0.365172\pi\) | |||||||
\(354\) | −0.00699409 | −0.000371732 0 | ||||||||
\(355\) | 1.86599 | 0.0990364 | ||||||||
\(356\) | −60.6252 | −3.21313 | ||||||||
\(357\) | 0.00534656 | 0.000282970 0 | ||||||||
\(358\) | −41.8609 | −2.21242 | ||||||||
\(359\) | −25.3802 | −1.33951 | −0.669757 | − | 0.742581i | \(-0.733602\pi\) | ||||
−0.669757 | + | 0.742581i | \(0.733602\pi\) | |||||||
\(360\) | −105.862 | −5.57940 | ||||||||
\(361\) | 6.47027 | 0.340540 | ||||||||
\(362\) | −4.34139 | −0.228179 | ||||||||
\(363\) | 0.00997923 | 0.000523774 0 | ||||||||
\(364\) | 21.9728 | 1.15169 | ||||||||
\(365\) | 33.3297 | 1.74455 | ||||||||
\(366\) | −0.0146122 | −0.000763789 0 | ||||||||
\(367\) | 11.5878 | 0.604877 | 0.302438 | − | 0.953169i | \(-0.402199\pi\) | ||||
0.302438 | + | 0.953169i | \(0.402199\pi\) | |||||||
\(368\) | 24.2554 | 1.26440 | ||||||||
\(369\) | 17.9975 | 0.936910 | ||||||||
\(370\) | 32.4127 | 1.68506 | ||||||||
\(371\) | 0.706934 | 0.0367022 | ||||||||
\(372\) | 0.00952971 | 0.000494092 0 | ||||||||
\(373\) | 2.26634 | 0.117347 | 0.0586733 | − | 0.998277i | \(-0.481313\pi\) | ||||
0.0586733 | + | 0.998277i | \(0.481313\pi\) | |||||||
\(374\) | 15.2242 | 0.787226 | ||||||||
\(375\) | 0.0102380 | 0.000528689 0 | ||||||||
\(376\) | −11.9697 | −0.617290 | ||||||||
\(377\) | 7.12158 | 0.366780 | ||||||||
\(378\) | −0.0179049 | −0.000920927 0 | ||||||||
\(379\) | 13.9325 | 0.715663 | 0.357832 | − | 0.933786i | \(-0.383516\pi\) | ||||
0.357832 | + | 0.933786i | \(0.383516\pi\) | |||||||
\(380\) | −100.778 | −5.16981 | ||||||||
\(381\) | −0.00275510 | −0.000141148 0 | ||||||||
\(382\) | −12.1358 | −0.620922 | ||||||||
\(383\) | −9.46492 | −0.483635 | −0.241817 | − | 0.970322i | \(-0.577744\pi\) | ||||
−0.241817 | + | 0.970322i | \(0.577744\pi\) | |||||||
\(384\) | 0.0488456 | 0.00249264 | ||||||||
\(385\) | −4.24171 | −0.216178 | ||||||||
\(386\) | 2.34051 | 0.119129 | ||||||||
\(387\) | 26.0169 | 1.32252 | ||||||||
\(388\) | 87.9704 | 4.46602 | ||||||||
\(389\) | 19.5389 | 0.990660 | 0.495330 | − | 0.868705i | \(-0.335047\pi\) | ||||
0.495330 | + | 0.868705i | \(0.335047\pi\) | |||||||
\(390\) | −0.0375204 | −0.00189992 | ||||||||
\(391\) | −7.47920 | −0.378239 | ||||||||
\(392\) | 58.0092 | 2.92991 | ||||||||
\(393\) | −0.0161991 | −0.000817136 0 | ||||||||
\(394\) | −54.2931 | −2.73525 | ||||||||
\(395\) | 4.92522 | 0.247815 | ||||||||
\(396\) | −18.7681 | −0.943130 | ||||||||
\(397\) | 13.8591 | 0.695569 | 0.347784 | − | 0.937575i | \(-0.386934\pi\) | ||||
0.347784 | + | 0.937575i | \(0.386934\pi\) | |||||||
\(398\) | 0.984566 | 0.0493519 | ||||||||
\(399\) | −0.00546926 | −0.000273806 0 | ||||||||
\(400\) | 124.715 | 6.23576 | ||||||||
\(401\) | 9.74807 | 0.486795 | 0.243398 | − | 0.969927i | \(-0.421738\pi\) | ||||
0.243398 | + | 0.969927i | \(0.421738\pi\) | |||||||
\(402\) | 0.00706708 | 0.000352474 0 | ||||||||
\(403\) | −6.19991 | −0.308840 | ||||||||
\(404\) | 49.1128 | 2.44345 | ||||||||
\(405\) | −32.1928 | −1.59967 | ||||||||
\(406\) | −5.57895 | −0.276879 | ||||||||
\(407\) | 3.68770 | 0.182793 | ||||||||
\(408\) | −0.0498443 | −0.00246766 | ||||||||
\(409\) | 37.3649 | 1.84757 | 0.923787 | − | 0.382906i | \(-0.125077\pi\) | ||||
0.923787 | + | 0.382906i | \(0.125077\pi\) | |||||||
\(410\) | −59.0900 | −2.91825 | ||||||||
\(411\) | −0.00313727 | −0.000154750 0 | ||||||||
\(412\) | 32.5962 | 1.60590 | ||||||||
\(413\) | −2.62441 | −0.129139 | ||||||||
\(414\) | 12.5234 | 0.615491 | ||||||||
\(415\) | −33.7591 | −1.65717 | ||||||||
\(416\) | −90.4883 | −4.43655 | ||||||||
\(417\) | 0.00219470 | 0.000107475 0 | ||||||||
\(418\) | −15.5736 | −0.761730 | ||||||||
\(419\) | 39.4272 | 1.92615 | 0.963073 | − | 0.269242i | \(-0.0867731\pi\) | ||||
0.963073 | + | 0.269242i | \(0.0867731\pi\) | |||||||
\(420\) | 0.0216402 | 0.00105594 | ||||||||
\(421\) | −25.6528 | −1.25024 | −0.625121 | − | 0.780528i | \(-0.714950\pi\) | ||||
−0.625121 | + | 0.780528i | \(0.714950\pi\) | |||||||
\(422\) | 24.2891 | 1.18237 | ||||||||
\(423\) | −3.64001 | −0.176983 | ||||||||
\(424\) | −6.59053 | −0.320064 | ||||||||
\(425\) | −38.4562 | −1.86540 | ||||||||
\(426\) | −0.00147113 | −7.12767e−5 0 | ||||||||
\(427\) | −5.48295 | −0.265339 | ||||||||
\(428\) | 45.7658 | 2.21217 | ||||||||
\(429\) | −0.00426882 | −0.000206101 0 | ||||||||
\(430\) | −85.4199 | −4.11932 | ||||||||
\(431\) | 22.0071 | 1.06005 | 0.530023 | − | 0.847984i | \(-0.322183\pi\) | ||||
0.530023 | + | 0.847984i | \(0.322183\pi\) | |||||||
\(432\) | 0.0983148 | 0.00473017 | ||||||||
\(433\) | 26.5614 | 1.27646 | 0.638230 | − | 0.769845i | \(-0.279667\pi\) | ||||
0.638230 | + | 0.769845i | \(0.279667\pi\) | |||||||
\(434\) | 4.85694 | 0.233140 | ||||||||
\(435\) | 0.00701380 | 0.000336286 0 | ||||||||
\(436\) | −105.870 | −5.07027 | ||||||||
\(437\) | 7.65085 | 0.365990 | ||||||||
\(438\) | −0.0262769 | −0.00125556 | ||||||||
\(439\) | −28.8109 | −1.37507 | −0.687534 | − | 0.726152i | \(-0.741307\pi\) | ||||
−0.687534 | + | 0.726152i | \(0.741307\pi\) | |||||||
\(440\) | 39.5442 | 1.88519 | ||||||||
\(441\) | 17.6407 | 0.840036 | ||||||||
\(442\) | 50.5314 | 2.40354 | ||||||||
\(443\) | 12.3633 | 0.587397 | 0.293699 | − | 0.955898i | \(-0.405114\pi\) | ||||
0.293699 | + | 0.955898i | \(0.405114\pi\) | |||||||
\(444\) | −0.0188138 | −0.000892862 0 | ||||||||
\(445\) | 38.8451 | 1.84144 | ||||||||
\(446\) | 46.6262 | 2.20782 | ||||||||
\(447\) | −0.00678044 | −0.000320704 0 | ||||||||
\(448\) | 37.0259 | 1.74931 | ||||||||
\(449\) | 30.4236 | 1.43578 | 0.717889 | − | 0.696157i | \(-0.245108\pi\) | ||||
0.717889 | + | 0.696157i | \(0.245108\pi\) | |||||||
\(450\) | 64.3921 | 3.03547 | ||||||||
\(451\) | −6.72287 | −0.316568 | ||||||||
\(452\) | 64.8776 | 3.05159 | ||||||||
\(453\) | −0.00642311 | −0.000301784 0 | ||||||||
\(454\) | 27.2880 | 1.28069 | ||||||||
\(455\) | −14.0789 | −0.660028 | ||||||||
\(456\) | 0.0509882 | 0.00238774 | ||||||||
\(457\) | −13.0611 | −0.610973 | −0.305487 | − | 0.952196i | \(-0.598819\pi\) | ||||
−0.305487 | + | 0.952196i | \(0.598819\pi\) | |||||||
\(458\) | −24.9318 | −1.16499 | ||||||||
\(459\) | −0.0303156 | −0.00141501 | ||||||||
\(460\) | −30.2721 | −1.41144 | ||||||||
\(461\) | 20.3143 | 0.946130 | 0.473065 | − | 0.881027i | \(-0.343148\pi\) | ||||
0.473065 | + | 0.881027i | \(0.343148\pi\) | |||||||
\(462\) | 0.00334414 | 0.000155584 0 | ||||||||
\(463\) | 26.1012 | 1.21303 | 0.606513 | − | 0.795074i | \(-0.292568\pi\) | ||||
0.606513 | + | 0.795074i | \(0.292568\pi\) | |||||||
\(464\) | 30.6338 | 1.42214 | ||||||||
\(465\) | −0.00610608 | −0.000283163 0 | ||||||||
\(466\) | 14.9009 | 0.690269 | ||||||||
\(467\) | −25.6555 | −1.18720 | −0.593598 | − | 0.804762i | \(-0.702293\pi\) | ||||
−0.593598 | + | 0.804762i | \(0.702293\pi\) | |||||||
\(468\) | −62.2939 | −2.87954 | ||||||||
\(469\) | 2.65180 | 0.122449 | ||||||||
\(470\) | 11.9511 | 0.551261 | ||||||||
\(471\) | −0.0161157 | −0.000742574 0 | ||||||||
\(472\) | 24.4665 | 1.12616 | ||||||||
\(473\) | −9.71851 | −0.446858 | ||||||||
\(474\) | −0.00388301 | −0.000178353 0 | ||||||||
\(475\) | 39.3388 | 1.80499 | ||||||||
\(476\) | −29.1445 | −1.33583 | ||||||||
\(477\) | −2.00420 | −0.0917658 | ||||||||
\(478\) | 10.4425 | 0.477630 | ||||||||
\(479\) | −11.8431 | −0.541126 | −0.270563 | − | 0.962702i | \(-0.587210\pi\) | ||||
−0.270563 | + | 0.962702i | \(0.587210\pi\) | |||||||
\(480\) | −0.0891188 | −0.00406770 | ||||||||
\(481\) | 12.2400 | 0.558097 | ||||||||
\(482\) | 59.2547 | 2.69898 | ||||||||
\(483\) | −0.00164288 | −7.47534e−5 0 | ||||||||
\(484\) | −54.3974 | −2.47261 | ||||||||
\(485\) | −56.3663 | −2.55946 | ||||||||
\(486\) | 0.0761418 | 0.00345386 | ||||||||
\(487\) | −14.2819 | −0.647175 | −0.323587 | − | 0.946198i | \(-0.604889\pi\) | ||||
−0.323587 | + | 0.946198i | \(0.604889\pi\) | |||||||
\(488\) | 51.1159 | 2.31391 | ||||||||
\(489\) | −0.00824992 | −0.000373074 0 | ||||||||
\(490\) | −57.9189 | −2.61651 | ||||||||
\(491\) | 20.6828 | 0.933402 | 0.466701 | − | 0.884415i | \(-0.345442\pi\) | ||||
0.466701 | + | 0.884415i | \(0.345442\pi\) | |||||||
\(492\) | 0.0342985 | 0.00154630 | ||||||||
\(493\) | −9.44598 | −0.425426 | ||||||||
\(494\) | −51.6911 | −2.32569 | ||||||||
\(495\) | 12.0255 | 0.540505 | ||||||||
\(496\) | −26.6692 | −1.19748 | ||||||||
\(497\) | −0.552017 | −0.0247614 | ||||||||
\(498\) | 0.0266155 | 0.00119267 | ||||||||
\(499\) | −34.6901 | −1.55294 | −0.776471 | − | 0.630153i | \(-0.782992\pi\) | ||||
−0.776471 | + | 0.630153i | \(0.782992\pi\) | |||||||
\(500\) | −55.8081 | −2.49582 | ||||||||
\(501\) | −0.0153840 | −0.000687309 0 | ||||||||
\(502\) | 65.9306 | 2.94263 | ||||||||
\(503\) | −12.7272 | −0.567478 | −0.283739 | − | 0.958902i | \(-0.591575\pi\) | ||||
−0.283739 | + | 0.958902i | \(0.591575\pi\) | |||||||
\(504\) | 31.3172 | 1.39498 | ||||||||
\(505\) | −31.4686 | −1.40034 | ||||||||
\(506\) | −4.67806 | −0.207965 | ||||||||
\(507\) | −0.000855262 0 | −3.79835e−5 0 | ||||||||
\(508\) | 15.0182 | 0.666326 | ||||||||
\(509\) | −5.90528 | −0.261747 | −0.130873 | − | 0.991399i | \(-0.541778\pi\) | ||||
−0.130873 | + | 0.991399i | \(0.541778\pi\) | |||||||
\(510\) | 0.0497667 | 0.00220371 | ||||||||
\(511\) | −9.85995 | −0.436178 | ||||||||
\(512\) | −73.5595 | −3.25090 | ||||||||
\(513\) | 0.0310113 | 0.00136918 | ||||||||
\(514\) | 73.1783 | 3.22776 | ||||||||
\(515\) | −20.8858 | −0.920337 | ||||||||
\(516\) | 0.0495816 | 0.00218271 | ||||||||
\(517\) | 1.35971 | 0.0598000 | ||||||||
\(518\) | −9.58868 | −0.421302 | ||||||||
\(519\) | −0.00724531 | −0.000318034 0 | ||||||||
\(520\) | 131.253 | 5.75582 | ||||||||
\(521\) | −33.1775 | −1.45353 | −0.726767 | − | 0.686884i | \(-0.758978\pi\) | ||||
−0.726767 | + | 0.686884i | \(0.758978\pi\) | |||||||
\(522\) | 15.8166 | 0.692275 | ||||||||
\(523\) | 39.5374 | 1.72885 | 0.864425 | − | 0.502761i | \(-0.167683\pi\) | ||||
0.864425 | + | 0.502761i | \(0.167683\pi\) | |||||||
\(524\) | 88.3023 | 3.85750 | ||||||||
\(525\) | −0.00844726 | −0.000368669 0 | ||||||||
\(526\) | 36.4870 | 1.59091 | ||||||||
\(527\) | 8.22350 | 0.358221 | ||||||||
\(528\) | −0.0183625 | −0.000799127 0 | ||||||||
\(529\) | −20.7018 | −0.900079 | ||||||||
\(530\) | 6.58026 | 0.285828 | ||||||||
\(531\) | 7.44033 | 0.322883 | ||||||||
\(532\) | 29.8133 | 1.29257 | ||||||||
\(533\) | −22.3142 | −0.966536 | ||||||||
\(534\) | −0.0306253 | −0.00132529 | ||||||||
\(535\) | −29.3240 | −1.26779 | ||||||||
\(536\) | −24.7219 | −1.06782 | ||||||||
\(537\) | −0.0155687 | −0.000671840 0 | ||||||||
\(538\) | −19.4145 | −0.837020 | ||||||||
\(539\) | −6.58963 | −0.283835 | ||||||||
\(540\) | −0.122702 | −0.00528027 | ||||||||
\(541\) | 2.25655 | 0.0970166 | 0.0485083 | − | 0.998823i | \(-0.484553\pi\) | ||||
0.0485083 | + | 0.998823i | \(0.484553\pi\) | |||||||
\(542\) | 63.1172 | 2.71112 | ||||||||
\(543\) | −0.00161463 | −6.92904e−5 0 | ||||||||
\(544\) | 120.023 | 5.14593 | ||||||||
\(545\) | 67.8356 | 2.90576 | ||||||||
\(546\) | 0.0110997 | 0.000475024 0 | ||||||||
\(547\) | −40.7039 | −1.74037 | −0.870185 | − | 0.492724i | \(-0.836001\pi\) | ||||
−0.870185 | + | 0.492724i | \(0.836001\pi\) | |||||||
\(548\) | 17.1015 | 0.730539 | ||||||||
\(549\) | 15.5445 | 0.663421 | ||||||||
\(550\) | −24.0534 | −1.02564 | ||||||||
\(551\) | 9.66277 | 0.411648 | ||||||||
\(552\) | 0.0153160 | 0.000651893 0 | ||||||||
\(553\) | −1.45703 | −0.0619593 | ||||||||
\(554\) | −4.69310 | −0.199391 | ||||||||
\(555\) | 0.0120548 | 0.000511697 0 | ||||||||
\(556\) | −11.9635 | −0.507365 | ||||||||
\(557\) | −25.2934 | −1.07171 | −0.535857 | − | 0.844308i | \(-0.680012\pi\) | ||||
−0.535857 | + | 0.844308i | \(0.680012\pi\) | |||||||
\(558\) | −13.7697 | −0.582916 | ||||||||
\(559\) | −32.2572 | −1.36433 | ||||||||
\(560\) | −60.5609 | −2.55917 | ||||||||
\(561\) | 0.00566212 | 0.000239055 0 | ||||||||
\(562\) | −10.1207 | −0.426917 | ||||||||
\(563\) | −35.6912 | −1.50420 | −0.752102 | − | 0.659046i | \(-0.770960\pi\) | ||||
−0.752102 | + | 0.659046i | \(0.770960\pi\) | |||||||
\(564\) | −0.00693693 | −0.000292097 0 | ||||||||
\(565\) | −41.5698 | −1.74885 | ||||||||
\(566\) | −7.16562 | −0.301194 | ||||||||
\(567\) | 9.52362 | 0.399955 | ||||||||
\(568\) | 5.14628 | 0.215933 | ||||||||
\(569\) | −42.4181 | −1.77826 | −0.889130 | − | 0.457654i | \(-0.848690\pi\) | ||||
−0.889130 | + | 0.457654i | \(0.848690\pi\) | |||||||
\(570\) | −0.0509088 | −0.00213234 | ||||||||
\(571\) | −46.7357 | −1.95583 | −0.977915 | − | 0.209003i | \(-0.932978\pi\) | ||||
−0.977915 | + | 0.209003i | \(0.932978\pi\) | |||||||
\(572\) | 23.2696 | 0.972952 | ||||||||
\(573\) | −0.00451349 | −0.000188554 0 | ||||||||
\(574\) | 17.4807 | 0.729629 | ||||||||
\(575\) | 11.8167 | 0.492791 | ||||||||
\(576\) | −104.970 | −4.37377 | ||||||||
\(577\) | −14.7132 | −0.612517 | −0.306258 | − | 0.951948i | \(-0.599077\pi\) | ||||
−0.306258 | + | 0.951948i | \(0.599077\pi\) | |||||||
\(578\) | −20.2124 | −0.840725 | ||||||||
\(579\) | 0.000870471 0 | 3.61755e−5 0 | ||||||||
\(580\) | −38.2327 | −1.58752 | ||||||||
\(581\) | 9.98700 | 0.414331 | ||||||||
\(582\) | 0.0444389 | 0.00184205 | ||||||||
\(583\) | 0.748658 | 0.0310063 | ||||||||
\(584\) | 91.9212 | 3.80373 | ||||||||
\(585\) | 39.9143 | 1.65025 | ||||||||
\(586\) | −28.1279 | −1.16195 | ||||||||
\(587\) | −18.3658 | −0.758038 | −0.379019 | − | 0.925389i | \(-0.623739\pi\) | ||||
−0.379019 | + | 0.925389i | \(0.623739\pi\) | |||||||
\(588\) | 0.0336187 | 0.00138641 | ||||||||
\(589\) | −8.41223 | −0.346620 | ||||||||
\(590\) | −24.4284 | −1.00570 | ||||||||
\(591\) | −0.0201924 | −0.000830605 0 | ||||||||
\(592\) | 52.6510 | 2.16394 | ||||||||
\(593\) | −5.48753 | −0.225346 | −0.112673 | − | 0.993632i | \(-0.535941\pi\) | ||||
−0.112673 | + | 0.993632i | \(0.535941\pi\) | |||||||
\(594\) | −0.0189616 | −0.000778005 0 | ||||||||
\(595\) | 18.6741 | 0.765562 | ||||||||
\(596\) | 36.9606 | 1.51397 | ||||||||
\(597\) | 0.000366175 0 | 1.49866e−5 0 | ||||||||
\(598\) | −15.5272 | −0.634953 | ||||||||
\(599\) | −42.5735 | −1.73950 | −0.869752 | − | 0.493489i | \(-0.835721\pi\) | ||||
−0.869752 | + | 0.493489i | \(0.835721\pi\) | |||||||
\(600\) | 0.0787512 | 0.00321500 | ||||||||
\(601\) | −5.83223 | −0.237902 | −0.118951 | − | 0.992900i | \(-0.537953\pi\) | ||||
−0.118951 | + | 0.992900i | \(0.537953\pi\) | |||||||
\(602\) | 25.2699 | 1.02992 | ||||||||
\(603\) | −7.51798 | −0.306156 | ||||||||
\(604\) | 35.0128 | 1.42465 | ||||||||
\(605\) | 34.8547 | 1.41705 | ||||||||
\(606\) | 0.0248097 | 0.00100783 | ||||||||
\(607\) | 5.98587 | 0.242959 | 0.121480 | − | 0.992594i | \(-0.461236\pi\) | ||||
0.121480 | + | 0.992594i | \(0.461236\pi\) | |||||||
\(608\) | −122.777 | −4.97927 | ||||||||
\(609\) | −0.00207490 | −8.40791e−5 0 | ||||||||
\(610\) | −51.0362 | −2.06640 | ||||||||
\(611\) | 4.51308 | 0.182580 | ||||||||
\(612\) | 82.6260 | 3.33996 | ||||||||
\(613\) | −9.10084 | −0.367579 | −0.183790 | − | 0.982966i | \(-0.558837\pi\) | ||||
−0.183790 | + | 0.982966i | \(0.558837\pi\) | |||||||
\(614\) | −0.548450 | −0.0221336 | ||||||||
\(615\) | −0.0219765 | −0.000886178 0 | ||||||||
\(616\) | −11.6984 | −0.471342 | ||||||||
\(617\) | −14.8184 | −0.596564 | −0.298282 | − | 0.954478i | \(-0.596414\pi\) | ||||
−0.298282 | + | 0.954478i | \(0.596414\pi\) | |||||||
\(618\) | 0.0164662 | 0.000662369 0 | ||||||||
\(619\) | 19.3505 | 0.777761 | 0.388881 | − | 0.921288i | \(-0.372862\pi\) | ||||
0.388881 | + | 0.921288i | \(0.372862\pi\) | |||||||
\(620\) | 33.2847 | 1.33674 | ||||||||
\(621\) | 0.00931528 | 0.000373809 0 | ||||||||
\(622\) | −22.4792 | −0.901336 | ||||||||
\(623\) | −11.4916 | −0.460401 | ||||||||
\(624\) | −0.0609480 | −0.00243987 | ||||||||
\(625\) | −3.21530 | −0.128612 | ||||||||
\(626\) | 62.1829 | 2.48533 | ||||||||
\(627\) | −0.00579207 | −0.000231313 0 | ||||||||
\(628\) | 87.8479 | 3.50551 | ||||||||
\(629\) | −16.2350 | −0.647333 | ||||||||
\(630\) | −31.2684 | −1.24576 | ||||||||
\(631\) | −17.2331 | −0.686038 | −0.343019 | − | 0.939329i | \(-0.611449\pi\) | ||||
−0.343019 | + | 0.939329i | \(0.611449\pi\) | |||||||
\(632\) | 13.5835 | 0.540321 | ||||||||
\(633\) | 0.00903347 | 0.000359048 0 | ||||||||
\(634\) | 60.8220 | 2.41555 | ||||||||
\(635\) | −9.62280 | −0.381869 | ||||||||
\(636\) | −0.00381948 | −0.000151452 0 | ||||||||
\(637\) | −21.8719 | −0.866598 | ||||||||
\(638\) | −5.90823 | −0.233909 | ||||||||
\(639\) | 1.56500 | 0.0619103 | ||||||||
\(640\) | 170.604 | 6.74372 | ||||||||
\(641\) | −8.84162 | −0.349223 | −0.174611 | − | 0.984637i | \(-0.555867\pi\) | ||||
−0.174611 | + | 0.984637i | \(0.555867\pi\) | |||||||
\(642\) | 0.0231189 | 0.000912430 0 | ||||||||
\(643\) | −27.6545 | −1.09059 | −0.545294 | − | 0.838245i | \(-0.683582\pi\) | ||||
−0.545294 | + | 0.838245i | \(0.683582\pi\) | |||||||
\(644\) | 8.95542 | 0.352893 | ||||||||
\(645\) | −0.0317690 | −0.00125090 | ||||||||
\(646\) | 68.5626 | 2.69756 | ||||||||
\(647\) | 15.7630 | 0.619708 | 0.309854 | − | 0.950784i | \(-0.399720\pi\) | ||||
0.309854 | + | 0.950784i | \(0.399720\pi\) | |||||||
\(648\) | −88.7858 | −3.48783 | ||||||||
\(649\) | −2.77930 | −0.109097 | ||||||||
\(650\) | −79.8368 | −3.13146 | ||||||||
\(651\) | 0.00180637 | 7.07972e−5 0 | ||||||||
\(652\) | 44.9709 | 1.76120 | ||||||||
\(653\) | 9.62727 | 0.376744 | 0.188372 | − | 0.982098i | \(-0.439679\pi\) | ||||
0.188372 | + | 0.982098i | \(0.439679\pi\) | |||||||
\(654\) | −0.0534812 | −0.00209128 | ||||||||
\(655\) | −56.5790 | −2.21072 | ||||||||
\(656\) | −95.9855 | −3.74761 | ||||||||
\(657\) | 27.9535 | 1.09057 | ||||||||
\(658\) | −3.53549 | −0.137828 | ||||||||
\(659\) | −2.07885 | −0.0809805 | −0.0404902 | − | 0.999180i | \(-0.512892\pi\) | ||||
−0.0404902 | + | 0.999180i | \(0.512892\pi\) | |||||||
\(660\) | 0.0229175 | 0.000892061 0 | ||||||||
\(661\) | 36.1601 | 1.40646 | 0.703231 | − | 0.710961i | \(-0.251740\pi\) | ||||
0.703231 | + | 0.710961i | \(0.251740\pi\) | |||||||
\(662\) | 48.0539 | 1.86767 | ||||||||
\(663\) | 0.0187934 | 0.000729876 0 | ||||||||
\(664\) | −93.1057 | −3.61320 | ||||||||
\(665\) | −19.1026 | −0.740769 | ||||||||
\(666\) | 27.1844 | 1.05337 | ||||||||
\(667\) | 2.90253 | 0.112387 | ||||||||
\(668\) | 83.8595 | 3.24462 | ||||||||
\(669\) | 0.0173410 | 0.000670442 0 | ||||||||
\(670\) | 24.6834 | 0.953602 | ||||||||
\(671\) | −5.80656 | −0.224160 | ||||||||
\(672\) | 0.0263641 | 0.00101702 | ||||||||
\(673\) | 35.9885 | 1.38725 | 0.693627 | − | 0.720335i | \(-0.256012\pi\) | ||||
0.693627 | + | 0.720335i | \(0.256012\pi\) | |||||||
\(674\) | 10.2852 | 0.396173 | ||||||||
\(675\) | 0.0478969 | 0.00184355 | ||||||||
\(676\) | 4.66209 | 0.179311 | ||||||||
\(677\) | −29.6214 | −1.13844 | −0.569222 | − | 0.822184i | \(-0.692756\pi\) | ||||
−0.569222 | + | 0.822184i | \(0.692756\pi\) | |||||||
\(678\) | 0.0327734 | 0.00125865 | ||||||||
\(679\) | 16.6749 | 0.639925 | ||||||||
\(680\) | −174.092 | −6.67614 | ||||||||
\(681\) | 0.0101488 | 0.000388904 0 | ||||||||
\(682\) | 5.14360 | 0.196959 | ||||||||
\(683\) | 25.2912 | 0.967742 | 0.483871 | − | 0.875139i | \(-0.339230\pi\) | ||||
0.483871 | + | 0.875139i | \(0.339230\pi\) | |||||||
\(684\) | −84.5223 | −3.23179 | ||||||||
\(685\) | −10.9576 | −0.418670 | ||||||||
\(686\) | 37.5312 | 1.43295 | ||||||||
\(687\) | −0.00927251 | −0.000353768 0 | ||||||||
\(688\) | −138.756 | −5.29001 | ||||||||
\(689\) | 2.48491 | 0.0946675 | ||||||||
\(690\) | −0.0152922 | −0.000582163 0 | ||||||||
\(691\) | 24.9051 | 0.947434 | 0.473717 | − | 0.880677i | \(-0.342912\pi\) | ||||
0.473717 | + | 0.880677i | \(0.342912\pi\) | |||||||
\(692\) | 39.4946 | 1.50136 | ||||||||
\(693\) | −3.55751 | −0.135139 | ||||||||
\(694\) | 56.0140 | 2.12626 | ||||||||
\(695\) | 7.66550 | 0.290769 | ||||||||
\(696\) | 0.0193436 | 0.000733218 0 | ||||||||
\(697\) | 29.5973 | 1.12108 | ||||||||
\(698\) | −42.6776 | −1.61537 | ||||||||
\(699\) | 0.00554186 | 0.000209612 0 | ||||||||
\(700\) | 46.0466 | 1.74040 | ||||||||
\(701\) | 35.9673 | 1.35847 | 0.679233 | − | 0.733923i | \(-0.262313\pi\) | ||||
0.679233 | + | 0.733923i | \(0.262313\pi\) | |||||||
\(702\) | −0.0629365 | −0.00237538 | ||||||||
\(703\) | 16.6076 | 0.626368 | ||||||||
\(704\) | 39.2113 | 1.47783 | ||||||||
\(705\) | 0.00444478 | 0.000167400 0 | ||||||||
\(706\) | −42.5295 | −1.60062 | ||||||||
\(707\) | 9.30940 | 0.350116 | ||||||||
\(708\) | 0.0141794 | 0.000532893 0 | ||||||||
\(709\) | 49.9585 | 1.87623 | 0.938115 | − | 0.346325i | \(-0.112570\pi\) | ||||
0.938115 | + | 0.346325i | \(0.112570\pi\) | |||||||
\(710\) | −5.13827 | −0.192836 | ||||||||
\(711\) | 4.13076 | 0.154916 | ||||||||
\(712\) | 107.133 | 4.01496 | ||||||||
\(713\) | −2.52689 | −0.0946329 | ||||||||
\(714\) | −0.0147225 | −0.000550977 0 | ||||||||
\(715\) | −14.9098 | −0.557596 | ||||||||
\(716\) | 84.8661 | 3.17160 | ||||||||
\(717\) | 0.00388374 | 0.000145041 0 | ||||||||
\(718\) | 69.8879 | 2.60819 | ||||||||
\(719\) | −44.4042 | −1.65600 | −0.827999 | − | 0.560729i | \(-0.810521\pi\) | ||||
−0.827999 | + | 0.560729i | \(0.810521\pi\) | |||||||
\(720\) | 171.693 | 6.39863 | ||||||||
\(721\) | 6.17866 | 0.230105 | ||||||||
\(722\) | −17.8168 | −0.663073 | ||||||||
\(723\) | 0.0220377 | 0.000819592 0 | ||||||||
\(724\) | 8.80145 | 0.327103 | ||||||||
\(725\) | 14.9241 | 0.554268 | ||||||||
\(726\) | −0.0274792 | −0.00101985 | ||||||||
\(727\) | −47.8407 | −1.77431 | −0.887156 | − | 0.461470i | \(-0.847322\pi\) | ||||
−0.887156 | + | 0.461470i | \(0.847322\pi\) | |||||||
\(728\) | −38.8287 | −1.43909 | ||||||||
\(729\) | −26.9999 | −0.999998 | ||||||||
\(730\) | −91.7780 | −3.39686 | ||||||||
\(731\) | 42.7856 | 1.58248 | ||||||||
\(732\) | 0.0296237 | 0.00109492 | ||||||||
\(733\) | 31.6661 | 1.16962 | 0.584808 | − | 0.811172i | \(-0.301170\pi\) | ||||
0.584808 | + | 0.811172i | \(0.301170\pi\) | |||||||
\(734\) | −31.9086 | −1.17777 | ||||||||
\(735\) | −0.0215409 | −0.000794549 0 | ||||||||
\(736\) | −36.8802 | −1.35942 | ||||||||
\(737\) | 2.80831 | 0.103445 | ||||||||
\(738\) | −49.5586 | −1.82428 | ||||||||
\(739\) | 11.3232 | 0.416532 | 0.208266 | − | 0.978072i | \(-0.433218\pi\) | ||||
0.208266 | + | 0.978072i | \(0.433218\pi\) | |||||||
\(740\) | −65.7114 | −2.41560 | ||||||||
\(741\) | −0.0192247 | −0.000706238 0 | ||||||||
\(742\) | −1.94665 | −0.0714636 | ||||||||
\(743\) | 27.2577 | 0.999989 | 0.499994 | − | 0.866029i | \(-0.333335\pi\) | ||||
0.499994 | + | 0.866029i | \(0.333335\pi\) | |||||||
\(744\) | −0.0168402 | −0.000617392 0 | ||||||||
\(745\) | −23.6822 | −0.867649 | ||||||||
\(746\) | −6.24070 | −0.228488 | ||||||||
\(747\) | −28.3137 | −1.03594 | ||||||||
\(748\) | −30.8646 | −1.12852 | ||||||||
\(749\) | 8.67496 | 0.316976 | ||||||||
\(750\) | −0.0281919 | −0.00102942 | ||||||||
\(751\) | −22.7829 | −0.831358 | −0.415679 | − | 0.909511i | \(-0.636456\pi\) | ||||
−0.415679 | + | 0.909511i | \(0.636456\pi\) | |||||||
\(752\) | 19.4132 | 0.707927 | ||||||||
\(753\) | 0.0245206 | 0.000893581 0 | ||||||||
\(754\) | −19.6103 | −0.714165 | ||||||||
\(755\) | −22.4342 | −0.816463 | ||||||||
\(756\) | 0.0362992 | 0.00132019 | ||||||||
\(757\) | 29.2048 | 1.06147 | 0.530733 | − | 0.847539i | \(-0.321917\pi\) | ||||
0.530733 | + | 0.847539i | \(0.321917\pi\) | |||||||
\(758\) | −38.3651 | −1.39348 | ||||||||
\(759\) | −0.00173984 | −6.31522e−5 0 | ||||||||
\(760\) | 178.088 | 6.45993 | ||||||||
\(761\) | −22.3133 | −0.808857 | −0.404429 | − | 0.914570i | \(-0.632530\pi\) | ||||
−0.404429 | + | 0.914570i | \(0.632530\pi\) | |||||||
\(762\) | 0.00758656 | 0.000274832 0 | ||||||||
\(763\) | −20.0679 | −0.726506 | ||||||||
\(764\) | 24.6033 | 0.890118 | ||||||||
\(765\) | −52.9419 | −1.91412 | ||||||||
\(766\) | 26.0630 | 0.941695 | ||||||||
\(767\) | −9.22492 | −0.333093 | ||||||||
\(768\) | −0.0628350 | −0.00226736 | ||||||||
\(769\) | 31.3592 | 1.13084 | 0.565421 | − | 0.824803i | \(-0.308714\pi\) | ||||
0.565421 | + | 0.824803i | \(0.308714\pi\) | |||||||
\(770\) | 11.6802 | 0.420924 | ||||||||
\(771\) | 0.0272161 | 0.000980165 0 | ||||||||
\(772\) | −4.74499 | −0.170776 | ||||||||
\(773\) | −13.3046 | −0.478535 | −0.239267 | − | 0.970954i | \(-0.576907\pi\) | ||||
−0.239267 | + | 0.970954i | \(0.576907\pi\) | |||||||
\(774\) | −71.6414 | −2.57510 | ||||||||
\(775\) | −12.9927 | −0.466710 | ||||||||
\(776\) | −155.455 | −5.58051 | ||||||||
\(777\) | −0.00356618 | −0.000127936 0 | ||||||||
\(778\) | −53.8031 | −1.92893 | ||||||||
\(779\) | −30.2766 | −1.08477 | ||||||||
\(780\) | 0.0760664 | 0.00272362 | ||||||||
\(781\) | −0.584598 | −0.0209186 | ||||||||
\(782\) | 20.5951 | 0.736478 | ||||||||
\(783\) | 0.0117649 | 0.000420443 0 | ||||||||
\(784\) | −94.0831 | −3.36011 | ||||||||
\(785\) | −56.2878 | −2.00900 | ||||||||
\(786\) | 0.0446065 | 0.00159106 | ||||||||
\(787\) | −45.0714 | −1.60662 | −0.803311 | − | 0.595560i | \(-0.796930\pi\) | ||||
−0.803311 | + | 0.595560i | \(0.796930\pi\) | |||||||
\(788\) | 110.070 | 3.92109 | ||||||||
\(789\) | 0.0135701 | 0.000483108 0 | ||||||||
\(790\) | −13.5623 | −0.482525 | ||||||||
\(791\) | 12.2976 | 0.437254 | ||||||||
\(792\) | 33.1655 | 1.17849 | ||||||||
\(793\) | −19.2728 | −0.684399 | ||||||||
\(794\) | −38.1631 | −1.35436 | ||||||||
\(795\) | 0.00244730 | 8.67968e−5 0 | ||||||||
\(796\) | −1.99605 | −0.0707480 | ||||||||
\(797\) | 0.214721 | 0.00760580 | 0.00380290 | − | 0.999993i | \(-0.498789\pi\) | ||||
0.00380290 | + | 0.999993i | \(0.498789\pi\) | |||||||
\(798\) | 0.0150604 | 0.000533133 0 | ||||||||
\(799\) | −5.98610 | −0.211773 | ||||||||
\(800\) | −189.629 | −6.70440 | ||||||||
\(801\) | 32.5793 | 1.15113 | ||||||||
\(802\) | −26.8427 | −0.947849 | ||||||||
\(803\) | −10.4419 | −0.368486 | ||||||||
\(804\) | −0.0143273 | −0.000505286 0 | ||||||||
\(805\) | −5.73812 | −0.202242 | ||||||||
\(806\) | 17.0724 | 0.601348 | ||||||||
\(807\) | −0.00722057 | −0.000254176 0 | ||||||||
\(808\) | −86.7886 | −3.05321 | ||||||||
\(809\) | 16.2001 | 0.569564 | 0.284782 | − | 0.958592i | \(-0.408079\pi\) | ||||
0.284782 | + | 0.958592i | \(0.408079\pi\) | |||||||
\(810\) | 88.6475 | 3.11475 | ||||||||
\(811\) | 28.8992 | 1.01479 | 0.507394 | − | 0.861714i | \(-0.330609\pi\) | ||||
0.507394 | + | 0.861714i | \(0.330609\pi\) | |||||||
\(812\) | 11.3104 | 0.396917 | ||||||||
\(813\) | 0.0234743 | 0.000823278 0 | ||||||||
\(814\) | −10.1546 | −0.355919 | ||||||||
\(815\) | −28.8147 | −1.00934 | ||||||||
\(816\) | 0.0808407 | 0.00282999 | ||||||||
\(817\) | −43.7675 | −1.53123 | ||||||||
\(818\) | −102.890 | −3.59745 | ||||||||
\(819\) | −11.8079 | −0.412601 | ||||||||
\(820\) | 119.795 | 4.18343 | ||||||||
\(821\) | 28.2273 | 0.985140 | 0.492570 | − | 0.870273i | \(-0.336058\pi\) | ||||
0.492570 | + | 0.870273i | \(0.336058\pi\) | |||||||
\(822\) | 0.00863893 | 0.000301317 0 | ||||||||
\(823\) | 22.4922 | 0.784029 | 0.392014 | − | 0.919959i | \(-0.371778\pi\) | ||||
0.392014 | + | 0.919959i | \(0.371778\pi\) | |||||||
\(824\) | −57.6017 | −2.00665 | ||||||||
\(825\) | −0.00894583 | −0.000311454 0 | ||||||||
\(826\) | 7.22669 | 0.251449 | ||||||||
\(827\) | −23.7645 | −0.826374 | −0.413187 | − | 0.910646i | \(-0.635584\pi\) | ||||
−0.413187 | + | 0.910646i | \(0.635584\pi\) | |||||||
\(828\) | −25.3891 | −0.882332 | ||||||||
\(829\) | −27.9799 | −0.971781 | −0.485890 | − | 0.874020i | \(-0.661505\pi\) | ||||
−0.485890 | + | 0.874020i | \(0.661505\pi\) | |||||||
\(830\) | 92.9606 | 3.22671 | ||||||||
\(831\) | −0.00174544 | −6.05485e−5 0 | ||||||||
\(832\) | 130.148 | 4.51207 | ||||||||
\(833\) | 29.0107 | 1.00516 | ||||||||
\(834\) | −0.00604344 | −0.000209267 0 | ||||||||
\(835\) | −53.7323 | −1.85948 | ||||||||
\(836\) | 31.5729 | 1.09197 | ||||||||
\(837\) | −0.0102423 | −0.000354026 0 | ||||||||
\(838\) | −108.569 | −3.75044 | ||||||||
\(839\) | −20.1404 | −0.695323 | −0.347662 | − | 0.937620i | \(-0.613024\pi\) | ||||
−0.347662 | + | 0.937620i | \(0.613024\pi\) | |||||||
\(840\) | −0.0382410 | −0.00131944 | ||||||||
\(841\) | −25.3342 | −0.873593 | ||||||||
\(842\) | 70.6388 | 2.43437 | ||||||||
\(843\) | −0.00376405 | −0.000129641 0 | ||||||||
\(844\) | −49.2421 | −1.69498 | ||||||||
\(845\) | −2.98719 | −0.102763 | ||||||||
\(846\) | 10.0233 | 0.344608 | ||||||||
\(847\) | −10.3111 | −0.354294 | ||||||||
\(848\) | 10.6889 | 0.367060 | ||||||||
\(849\) | −0.00266500 | −9.14627e−5 0 | ||||||||
\(850\) | 105.895 | 3.63216 | ||||||||
\(851\) | 4.98865 | 0.171009 | ||||||||
\(852\) | 0.00298248 | 0.000102178 0 | ||||||||
\(853\) | −14.5695 | −0.498849 | −0.249424 | − | 0.968394i | \(-0.580241\pi\) | ||||
−0.249424 | + | 0.968394i | \(0.580241\pi\) | |||||||
\(854\) | 15.0981 | 0.516647 | ||||||||
\(855\) | 54.1570 | 1.85213 | ||||||||
\(856\) | −80.8739 | −2.76421 | ||||||||
\(857\) | 16.6515 | 0.568806 | 0.284403 | − | 0.958705i | \(-0.408205\pi\) | ||||
0.284403 | + | 0.958705i | \(0.408205\pi\) | |||||||
\(858\) | 0.0117548 | 0.000401303 0 | ||||||||
\(859\) | −47.5804 | −1.62342 | −0.811711 | − | 0.584059i | \(-0.801464\pi\) | ||||
−0.811711 | + | 0.584059i | \(0.801464\pi\) | |||||||
\(860\) | 173.175 | 5.90521 | ||||||||
\(861\) | 0.00650133 | 0.000221565 0 | ||||||||
\(862\) | −60.5998 | −2.06404 | ||||||||
\(863\) | 32.0205 | 1.08999 | 0.544995 | − | 0.838439i | \(-0.316531\pi\) | ||||
0.544995 | + | 0.838439i | \(0.316531\pi\) | |||||||
\(864\) | −0.149487 | −0.00508566 | ||||||||
\(865\) | −25.3059 | −0.860425 | ||||||||
\(866\) | −73.1407 | −2.48542 | ||||||||
\(867\) | −0.00751730 | −0.000255301 0 | ||||||||
\(868\) | −9.84663 | −0.334217 | ||||||||
\(869\) | −1.54303 | −0.0523437 | ||||||||
\(870\) | −0.0193135 | −0.000654789 0 | ||||||||
\(871\) | 9.32119 | 0.315837 | ||||||||
\(872\) | 187.086 | 6.33555 | ||||||||
\(873\) | −47.2742 | −1.59999 | ||||||||
\(874\) | −21.0677 | −0.712626 | ||||||||
\(875\) | −10.5785 | −0.357619 | ||||||||
\(876\) | 0.0532721 | 0.00179990 | ||||||||
\(877\) | 31.2185 | 1.05417 | 0.527086 | − | 0.849812i | \(-0.323284\pi\) | ||||
0.527086 | + | 0.849812i | \(0.323284\pi\) | |||||||
\(878\) | 79.3349 | 2.67742 | ||||||||
\(879\) | −0.0104612 | −0.000352848 0 | ||||||||
\(880\) | −64.1353 | −2.16200 | ||||||||
\(881\) | −43.2924 | −1.45856 | −0.729279 | − | 0.684216i | \(-0.760144\pi\) | ||||
−0.729279 | + | 0.684216i | \(0.760144\pi\) | |||||||
\(882\) | −48.5764 | −1.63565 | ||||||||
\(883\) | 5.48623 | 0.184626 | 0.0923132 | − | 0.995730i | \(-0.470574\pi\) | ||||
0.0923132 | + | 0.995730i | \(0.470574\pi\) | |||||||
\(884\) | −102.444 | −3.44557 | ||||||||
\(885\) | −0.00908531 | −0.000305399 0 | ||||||||
\(886\) | −34.0441 | −1.14373 | ||||||||
\(887\) | −55.4269 | −1.86105 | −0.930526 | − | 0.366226i | \(-0.880650\pi\) | ||||
−0.930526 | + | 0.366226i | \(0.880650\pi\) | |||||||
\(888\) | 0.0332463 | 0.00111567 | ||||||||
\(889\) | 2.84672 | 0.0954760 | ||||||||
\(890\) | −106.966 | −3.58550 | ||||||||
\(891\) | 10.0857 | 0.337884 | ||||||||
\(892\) | −94.5269 | −3.16500 | ||||||||
\(893\) | 6.12348 | 0.204915 | ||||||||
\(894\) | 0.0186709 | 0.000624449 0 | ||||||||
\(895\) | −54.3773 | −1.81763 | ||||||||
\(896\) | −50.4700 | −1.68609 | ||||||||
\(897\) | −0.00577479 | −0.000192815 0 | ||||||||
\(898\) | −83.7758 | −2.79563 | ||||||||
\(899\) | −3.19138 | −0.106439 | ||||||||
\(900\) | −130.544 | −4.35148 | ||||||||
\(901\) | −3.29595 | −0.109804 | ||||||||
\(902\) | 18.5124 | 0.616396 | ||||||||
\(903\) | 0.00939825 | 0.000312754 0 | ||||||||
\(904\) | −114.647 | −3.81310 | ||||||||
\(905\) | −5.63946 | −0.187462 | ||||||||
\(906\) | 0.0176870 | 0.000587610 0 | ||||||||
\(907\) | −6.15403 | −0.204341 | −0.102171 | − | 0.994767i | \(-0.532579\pi\) | ||||
−0.102171 | + | 0.994767i | \(0.532579\pi\) | |||||||
\(908\) | −55.3219 | −1.83592 | ||||||||
\(909\) | −26.3926 | −0.875388 | ||||||||
\(910\) | 38.7682 | 1.28515 | ||||||||
\(911\) | 6.90940 | 0.228919 | 0.114459 | − | 0.993428i | \(-0.463486\pi\) | ||||
0.114459 | + | 0.993428i | \(0.463486\pi\) | |||||||
\(912\) | −0.0826960 | −0.00273834 | ||||||||
\(913\) | 10.5764 | 0.350029 | ||||||||
\(914\) | 35.9657 | 1.18964 | ||||||||
\(915\) | −0.0189812 | −0.000627498 0 | ||||||||
\(916\) | 50.5451 | 1.67006 | ||||||||
\(917\) | 16.7378 | 0.552731 | ||||||||
\(918\) | 0.0834783 | 0.00275519 | ||||||||
\(919\) | −47.5377 | −1.56813 | −0.784063 | − | 0.620681i | \(-0.786856\pi\) | ||||
−0.784063 | + | 0.620681i | \(0.786856\pi\) | |||||||
\(920\) | 53.4946 | 1.76367 | ||||||||
\(921\) | −0.000203977 0 | −6.72126e−6 0 | ||||||||
\(922\) | −55.9383 | −1.84223 | ||||||||
\(923\) | −1.94037 | −0.0638680 | ||||||||
\(924\) | −0.00677970 | −0.000223036 0 | ||||||||
\(925\) | 25.6504 | 0.843381 | ||||||||
\(926\) | −71.8734 | −2.36191 | ||||||||
\(927\) | −17.5168 | −0.575328 | ||||||||
\(928\) | −46.5785 | −1.52902 | ||||||||
\(929\) | −40.9710 | −1.34421 | −0.672107 | − | 0.740454i | \(-0.734611\pi\) | ||||
−0.672107 | + | 0.740454i | \(0.734611\pi\) | |||||||
\(930\) | 0.0168140 | 0.000551352 0 | ||||||||
\(931\) | −29.6765 | −0.972608 | ||||||||
\(932\) | −30.2090 | −0.989530 | ||||||||
\(933\) | −0.00836038 | −0.000273706 0 | ||||||||
\(934\) | 70.6462 | 2.31161 | ||||||||
\(935\) | 19.7762 | 0.646752 | ||||||||
\(936\) | 110.081 | 3.59812 | ||||||||
\(937\) | 50.5632 | 1.65183 | 0.825914 | − | 0.563797i | \(-0.190660\pi\) | ||||
0.825914 | + | 0.563797i | \(0.190660\pi\) | |||||||
\(938\) | −7.30211 | −0.238422 | ||||||||
\(939\) | 0.0231268 | 0.000754714 0 | ||||||||
\(940\) | −24.2288 | −0.790256 | ||||||||
\(941\) | 8.79487 | 0.286704 | 0.143352 | − | 0.989672i | \(-0.454212\pi\) | ||||
0.143352 | + | 0.989672i | \(0.454212\pi\) | |||||||
\(942\) | 0.0443770 | 0.00144588 | ||||||||
\(943\) | −9.09458 | −0.296160 | ||||||||
\(944\) | −39.6814 | −1.29152 | ||||||||
\(945\) | −0.0232584 | −0.000756596 0 | ||||||||
\(946\) | 26.7613 | 0.870086 | ||||||||
\(947\) | 10.4108 | 0.338304 | 0.169152 | − | 0.985590i | \(-0.445897\pi\) | ||||
0.169152 | + | 0.985590i | \(0.445897\pi\) | |||||||
\(948\) | 0.00787217 | 0.000255676 0 | ||||||||
\(949\) | −34.6582 | −1.12505 | ||||||||
\(950\) | −108.325 | −3.51453 | ||||||||
\(951\) | 0.0226206 | 0.000733524 0 | ||||||||
\(952\) | 51.5020 | 1.66919 | ||||||||
\(953\) | −43.2718 | −1.40171 | −0.700856 | − | 0.713303i | \(-0.747198\pi\) | ||||
−0.700856 | + | 0.713303i | \(0.747198\pi\) | |||||||
\(954\) | 5.51884 | 0.178679 | ||||||||
\(955\) | −15.7644 | −0.510124 | ||||||||
\(956\) | −21.1705 | −0.684703 | ||||||||
\(957\) | −0.00219736 | −7.10306e−5 0 | ||||||||
\(958\) | 32.6118 | 1.05364 | ||||||||
\(959\) | 3.24161 | 0.104677 | ||||||||
\(960\) | 0.128178 | 0.00413693 | ||||||||
\(961\) | −28.2216 | −0.910375 | ||||||||
\(962\) | −33.7047 | −1.08668 | ||||||||
\(963\) | −24.5940 | −0.792529 | ||||||||
\(964\) | −120.129 | −3.86910 | ||||||||
\(965\) | 3.04031 | 0.0978712 | ||||||||
\(966\) | 0.00452390 | 0.000145554 0 | ||||||||
\(967\) | 5.41354 | 0.174088 | 0.0870438 | − | 0.996204i | \(-0.472258\pi\) | ||||
0.0870438 | + | 0.996204i | \(0.472258\pi\) | |||||||
\(968\) | 96.1272 | 3.08964 | ||||||||
\(969\) | 0.0254995 | 0.000819161 0 | ||||||||
\(970\) | 155.213 | 4.98359 | ||||||||
\(971\) | −36.6382 | −1.17578 | −0.587888 | − | 0.808943i | \(-0.700040\pi\) | ||||
−0.587888 | + | 0.808943i | \(0.700040\pi\) | |||||||
\(972\) | −0.154365 | −0.00495126 | ||||||||
\(973\) | −2.26769 | −0.0726989 | ||||||||
\(974\) | 39.3273 | 1.26013 | ||||||||
\(975\) | −0.0296925 | −0.000950922 0 | ||||||||
\(976\) | −82.9030 | −2.65366 | ||||||||
\(977\) | −39.3517 | −1.25897 | −0.629487 | − | 0.777011i | \(-0.716735\pi\) | ||||
−0.629487 | + | 0.777011i | \(0.716735\pi\) | |||||||
\(978\) | 0.0227174 | 0.000726421 0 | ||||||||
\(979\) | −12.1698 | −0.388950 | ||||||||
\(980\) | 117.421 | 3.75088 | ||||||||
\(981\) | 56.8934 | 1.81647 | ||||||||
\(982\) | −56.9531 | −1.81745 | ||||||||
\(983\) | 29.2889 | 0.934171 | 0.467085 | − | 0.884212i | \(-0.345304\pi\) | ||||
0.467085 | + | 0.884212i | \(0.345304\pi\) | |||||||
\(984\) | −0.0606098 | −0.00193217 | ||||||||
\(985\) | −70.5266 | −2.24716 | ||||||||
\(986\) | 26.0109 | 0.828355 | ||||||||
\(987\) | −0.00131490 | −4.18538e−5 0 | ||||||||
\(988\) | 104.795 | 3.33398 | ||||||||
\(989\) | −13.1470 | −0.418051 | ||||||||
\(990\) | −33.1139 | −1.05243 | ||||||||
\(991\) | −8.15791 | −0.259144 | −0.129572 | − | 0.991570i | \(-0.541360\pi\) | ||||
−0.129572 | + | 0.991570i | \(0.541360\pi\) | |||||||
\(992\) | 40.5504 | 1.28748 | ||||||||
\(993\) | 0.0178720 | 0.000567150 0 | ||||||||
\(994\) | 1.52006 | 0.0482134 | ||||||||
\(995\) | 1.27895 | 0.0405454 | ||||||||
\(996\) | −0.0539585 | −0.00170974 | ||||||||
\(997\) | 11.6400 | 0.368643 | 0.184322 | − | 0.982866i | \(-0.440991\pi\) | ||||
0.184322 | + | 0.982866i | \(0.440991\pi\) | |||||||
\(998\) | 95.5242 | 3.02377 | ||||||||
\(999\) | 0.0202206 | 0.000639751 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8011.2.a.a.1.4 | ✓ | 309 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8011.2.a.a.1.4 | ✓ | 309 | 1.1 | even | 1 | trivial |