Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.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: | \(48.2216577807\) |
Analytic rank: | \(1\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.53522 | −1.79267 | −0.896337 | − | 0.443373i | \(-0.853782\pi\) | ||||
−0.896337 | + | 0.443373i | \(0.853782\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.42736 | 2.21368 | ||||||||
\(5\) | 3.72510 | 1.66591 | 0.832957 | − | 0.553338i | \(-0.186646\pi\) | ||||
0.832957 | + | 0.553338i | \(0.186646\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.951731 | −0.359720 | −0.179860 | − | 0.983692i | \(-0.557565\pi\) | ||||
−0.179860 | + | 0.983692i | \(0.557565\pi\) | |||||||
\(8\) | −6.15390 | −2.17573 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −9.44395 | −2.98644 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.53766 | −0.426470 | −0.213235 | − | 0.977001i | \(-0.568400\pi\) | ||||
−0.213235 | + | 0.977001i | \(0.568400\pi\) | |||||||
\(14\) | 2.41285 | 0.644861 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6.74680 | 1.68670 | ||||||||
\(17\) | −1.23784 | −0.300220 | −0.150110 | − | 0.988669i | \(-0.547963\pi\) | ||||
−0.150110 | + | 0.988669i | \(0.547963\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.40090 | −1.00964 | −0.504818 | − | 0.863226i | \(-0.668440\pi\) | ||||
−0.504818 | + | 0.863226i | \(0.668440\pi\) | |||||||
\(20\) | 16.4923 | 3.68780 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.53522 | −0.540512 | ||||||||
\(23\) | −7.09979 | −1.48041 | −0.740204 | − | 0.672382i | \(-0.765271\pi\) | ||||
−0.740204 | + | 0.672382i | \(0.765271\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.87634 | 1.77527 | ||||||||
\(26\) | 3.89831 | 0.764522 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.21365 | −0.796306 | ||||||||
\(29\) | −5.35857 | −0.995061 | −0.497530 | − | 0.867447i | \(-0.665760\pi\) | ||||
−0.497530 | + | 0.867447i | \(0.665760\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.23453 | 0.221727 | 0.110864 | − | 0.993836i | \(-0.464638\pi\) | ||||
0.110864 | + | 0.993836i | \(0.464638\pi\) | |||||||
\(32\) | −4.79684 | −0.847970 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.13820 | 0.538197 | ||||||||
\(35\) | −3.54529 | −0.599263 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.2150 | 1.67933 | 0.839666 | − | 0.543103i | \(-0.182751\pi\) | ||||
0.839666 | + | 0.543103i | \(0.182751\pi\) | |||||||
\(38\) | 11.1573 | 1.80995 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −22.9239 | −3.62458 | ||||||||
\(41\) | −11.9783 | −1.87069 | −0.935345 | − | 0.353737i | \(-0.884911\pi\) | ||||
−0.935345 | + | 0.353737i | \(0.884911\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.81440 | 1.34418 | 0.672092 | − | 0.740468i | \(-0.265396\pi\) | ||||
0.672092 | + | 0.740468i | \(0.265396\pi\) | |||||||
\(44\) | 4.42736 | 0.667450 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 17.9995 | 2.65389 | ||||||||
\(47\) | −2.41608 | −0.352421 | −0.176211 | − | 0.984352i | \(-0.556384\pi\) | ||||
−0.176211 | + | 0.984352i | \(0.556384\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.09421 | −0.870601 | ||||||||
\(50\) | −22.5035 | −3.18248 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.80777 | −0.944068 | ||||||||
\(53\) | −7.04502 | −0.967708 | −0.483854 | − | 0.875149i | \(-0.660763\pi\) | ||||
−0.483854 | + | 0.875149i | \(0.660763\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.72510 | 0.502292 | ||||||||
\(56\) | 5.85686 | 0.782655 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 13.5852 | 1.78382 | ||||||||
\(59\) | 14.6121 | 1.90233 | 0.951165 | − | 0.308682i | \(-0.0998878\pi\) | ||||
0.951165 | + | 0.308682i | \(0.0998878\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | −3.12980 | −0.397485 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.33253 | −0.166566 | ||||||||
\(65\) | −5.72793 | −0.710462 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.3286 | 1.26184 | 0.630921 | − | 0.775847i | \(-0.282677\pi\) | ||||
0.630921 | + | 0.775847i | \(0.282677\pi\) | |||||||
\(68\) | −5.48036 | −0.664591 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 8.98810 | 1.07428 | ||||||||
\(71\) | 8.17395 | 0.970069 | 0.485035 | − | 0.874495i | \(-0.338807\pi\) | ||||
0.485035 | + | 0.874495i | \(0.338807\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.6682 | 1.83382 | 0.916909 | − | 0.399096i | \(-0.130676\pi\) | ||||
0.916909 | + | 0.399096i | \(0.130676\pi\) | |||||||
\(74\) | −25.8973 | −3.01050 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −19.4844 | −2.23501 | ||||||||
\(77\) | −0.951731 | −0.108460 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.88000 | −0.886570 | −0.443285 | − | 0.896381i | \(-0.646187\pi\) | ||||
−0.443285 | + | 0.896381i | \(0.646187\pi\) | |||||||
\(80\) | 25.1325 | 2.80990 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 30.3676 | 3.35354 | ||||||||
\(83\) | 1.94530 | 0.213524 | 0.106762 | − | 0.994285i | \(-0.465952\pi\) | ||||
0.106762 | + | 0.994285i | \(0.465952\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.61107 | −0.500141 | ||||||||
\(86\) | −22.3465 | −2.40968 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.15390 | −0.656008 | ||||||||
\(89\) | 0.524054 | 0.0555496 | 0.0277748 | − | 0.999614i | \(-0.491158\pi\) | ||||
0.0277748 | + | 0.999614i | \(0.491158\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.46344 | 0.153410 | ||||||||
\(92\) | −31.4333 | −3.27715 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.12530 | 0.631776 | ||||||||
\(95\) | −16.3938 | −1.68197 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.3403 | −1.55757 | −0.778783 | − | 0.627293i | \(-0.784163\pi\) | ||||
−0.778783 | + | 0.627293i | \(0.784163\pi\) | |||||||
\(98\) | 15.4502 | 1.56070 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 39.2987 | 3.92987 | ||||||||
\(101\) | −10.6548 | −1.06019 | −0.530097 | − | 0.847937i | \(-0.677845\pi\) | ||||
−0.530097 | + | 0.847937i | \(0.677845\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.38207 | −0.234712 | −0.117356 | − | 0.993090i | \(-0.537442\pi\) | ||||
−0.117356 | + | 0.993090i | \(0.537442\pi\) | |||||||
\(104\) | 9.46261 | 0.927885 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 17.8607 | 1.73479 | ||||||||
\(107\) | −3.15962 | −0.305452 | −0.152726 | − | 0.988269i | \(-0.548805\pi\) | ||||
−0.152726 | + | 0.988269i | \(0.548805\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.86104 | 0.848733 | 0.424367 | − | 0.905490i | \(-0.360497\pi\) | ||||
0.424367 | + | 0.905490i | \(0.360497\pi\) | |||||||
\(110\) | −9.44395 | −0.900445 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.42114 | −0.606740 | ||||||||
\(113\) | −19.2881 | −1.81447 | −0.907237 | − | 0.420619i | \(-0.861813\pi\) | ||||
−0.907237 | + | 0.420619i | \(0.861813\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −26.4474 | −2.46623 | ||||||||
\(116\) | −23.7243 | −2.20275 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −37.0449 | −3.41026 | ||||||||
\(119\) | 1.17809 | 0.107995 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.53522 | −0.229528 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.46569 | 0.490834 | ||||||||
\(125\) | 14.4397 | 1.29153 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.0608953 | −0.00540358 | −0.00270179 | − | 0.999996i | \(-0.500860\pi\) | ||||
−0.00270179 | + | 0.999996i | \(0.500860\pi\) | |||||||
\(128\) | 12.9719 | 1.14657 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 14.5216 | 1.27363 | ||||||||
\(131\) | −0.616348 | −0.0538506 | −0.0269253 | − | 0.999637i | \(-0.508572\pi\) | ||||
−0.0269253 | + | 0.999637i | \(0.508572\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.18847 | 0.363186 | ||||||||
\(134\) | −26.1854 | −2.26207 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.61754 | 0.653199 | ||||||||
\(137\) | 3.01013 | 0.257173 | 0.128586 | − | 0.991698i | \(-0.458956\pi\) | ||||
0.128586 | + | 0.991698i | \(0.458956\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.7278 | −1.67329 | −0.836645 | − | 0.547745i | \(-0.815486\pi\) | ||||
−0.836645 | + | 0.547745i | \(0.815486\pi\) | |||||||
\(140\) | −15.6963 | −1.32658 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −20.7228 | −1.73902 | ||||||||
\(143\) | −1.53766 | −0.128586 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −19.9612 | −1.65768 | ||||||||
\(146\) | −39.7223 | −3.28744 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 45.2254 | 3.71750 | ||||||||
\(149\) | −8.52305 | −0.698236 | −0.349118 | − | 0.937079i | \(-0.613519\pi\) | ||||
−0.349118 | + | 0.937079i | \(0.613519\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.34321 | 0.434824 | 0.217412 | − | 0.976080i | \(-0.430238\pi\) | ||||
0.217412 | + | 0.976080i | \(0.430238\pi\) | |||||||
\(152\) | 27.0827 | 2.19670 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.41285 | 0.194433 | ||||||||
\(155\) | 4.59873 | 0.369379 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.25602 | −0.180050 | −0.0900249 | − | 0.995940i | \(-0.528695\pi\) | ||||
−0.0900249 | + | 0.995940i | \(0.528695\pi\) | |||||||
\(158\) | 19.9776 | 1.58933 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −17.8687 | −1.41264 | ||||||||
\(161\) | 6.75709 | 0.532533 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.1474 | −1.49974 | −0.749868 | − | 0.661587i | \(-0.769883\pi\) | ||||
−0.749868 | + | 0.661587i | \(0.769883\pi\) | |||||||
\(164\) | −53.0321 | −4.14111 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.93176 | −0.382779 | ||||||||
\(167\) | −11.8088 | −0.913794 | −0.456897 | − | 0.889520i | \(-0.651039\pi\) | ||||
−0.456897 | + | 0.889520i | \(0.651039\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.6356 | −0.818123 | ||||||||
\(170\) | 11.6901 | 0.896589 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 39.0245 | 2.97559 | ||||||||
\(173\) | −10.6238 | −0.807711 | −0.403855 | − | 0.914823i | \(-0.632330\pi\) | ||||
−0.403855 | + | 0.914823i | \(0.632330\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.44788 | −0.638600 | ||||||||
\(176\) | 6.74680 | 0.508559 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.32859 | −0.0995823 | ||||||||
\(179\) | −4.27447 | −0.319489 | −0.159744 | − | 0.987158i | \(-0.551067\pi\) | ||||
−0.159744 | + | 0.987158i | \(0.551067\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.9745 | −1.48469 | −0.742347 | − | 0.670016i | \(-0.766287\pi\) | ||||
−0.742347 | + | 0.670016i | \(0.766287\pi\) | |||||||
\(182\) | −3.71014 | −0.275014 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 43.6914 | 3.22097 | ||||||||
\(185\) | 38.0518 | 2.79762 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.23784 | −0.0905197 | ||||||||
\(188\) | −10.6968 | −0.780148 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 41.5619 | 3.01522 | ||||||||
\(191\) | −23.3200 | −1.68738 | −0.843689 | − | 0.536833i | \(-0.819621\pi\) | ||||
−0.843689 | + | 0.536833i | \(0.819621\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.75281 | 0.702023 | 0.351011 | − | 0.936371i | \(-0.385838\pi\) | ||||
0.351011 | + | 0.936371i | \(0.385838\pi\) | |||||||
\(194\) | 38.8910 | 2.79221 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −26.9813 | −1.92723 | ||||||||
\(197\) | 1.24715 | 0.0888560 | 0.0444280 | − | 0.999013i | \(-0.485853\pi\) | ||||
0.0444280 | + | 0.999013i | \(0.485853\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.3799 | −1.65736 | −0.828680 | − | 0.559722i | \(-0.810908\pi\) | ||||
−0.828680 | + | 0.559722i | \(0.810908\pi\) | |||||||
\(200\) | −54.6241 | −3.86251 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 27.0124 | 1.90058 | ||||||||
\(203\) | 5.09991 | 0.357944 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −44.6202 | −3.11641 | ||||||||
\(206\) | 6.03907 | 0.420762 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −10.3743 | −0.719327 | ||||||||
\(209\) | −4.40090 | −0.304417 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.1316 | −1.59244 | −0.796222 | − | 0.605004i | \(-0.793171\pi\) | ||||
−0.796222 | + | 0.605004i | \(0.793171\pi\) | |||||||
\(212\) | −31.1908 | −2.14220 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.01033 | 0.547575 | ||||||||
\(215\) | 32.8345 | 2.23929 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.17494 | −0.0797599 | ||||||||
\(218\) | −22.4647 | −1.52150 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 16.4923 | 1.11191 | ||||||||
\(221\) | 1.90337 | 0.128035 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.7382 | 1.79052 | 0.895260 | − | 0.445544i | \(-0.146990\pi\) | ||||
0.895260 | + | 0.445544i | \(0.146990\pi\) | |||||||
\(224\) | 4.56530 | 0.305032 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 48.8997 | 3.25276 | ||||||||
\(227\) | −18.9121 | −1.25524 | −0.627621 | − | 0.778519i | \(-0.715971\pi\) | ||||
−0.627621 | + | 0.778519i | \(0.715971\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.5554 | 1.29226 | 0.646128 | − | 0.763229i | \(-0.276387\pi\) | ||||
0.646128 | + | 0.763229i | \(0.276387\pi\) | |||||||
\(230\) | 67.0500 | 4.42115 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 32.9761 | 2.16499 | ||||||||
\(233\) | 16.5038 | 1.08120 | 0.540600 | − | 0.841280i | \(-0.318197\pi\) | ||||
0.540600 | + | 0.841280i | \(0.318197\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.00012 | −0.587103 | ||||||||
\(236\) | 64.6929 | 4.21115 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.98672 | −0.193600 | ||||||||
\(239\) | 10.7789 | 0.697232 | 0.348616 | − | 0.937266i | \(-0.386652\pi\) | ||||
0.348616 | + | 0.937266i | \(0.386652\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.3180 | −0.857890 | −0.428945 | − | 0.903331i | \(-0.641115\pi\) | ||||
−0.428945 | + | 0.903331i | \(0.641115\pi\) | |||||||
\(242\) | −2.53522 | −0.162970 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.42736 | 0.283433 | ||||||||
\(245\) | −22.7015 | −1.45035 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.76708 | 0.430579 | ||||||||
\(248\) | −7.59715 | −0.482420 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −36.6079 | −2.31529 | ||||||||
\(251\) | 6.64024 | 0.419128 | 0.209564 | − | 0.977795i | \(-0.432796\pi\) | ||||
0.209564 | + | 0.977795i | \(0.432796\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.09979 | −0.446360 | ||||||||
\(254\) | 0.154383 | 0.00968686 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −30.2217 | −1.88886 | ||||||||
\(257\) | −18.2840 | −1.14052 | −0.570261 | − | 0.821464i | \(-0.693158\pi\) | ||||
−0.570261 | + | 0.821464i | \(0.693158\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.72191 | −0.604090 | ||||||||
\(260\) | −25.3596 | −1.57274 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.56258 | 0.0965366 | ||||||||
\(263\) | 16.5782 | 1.02225 | 0.511126 | − | 0.859506i | \(-0.329228\pi\) | ||||
0.511126 | + | 0.859506i | \(0.329228\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −26.2434 | −1.61212 | ||||||||
\(266\) | −10.6187 | −0.651075 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 45.7285 | 2.79332 | ||||||||
\(269\) | −10.9254 | −0.666132 | −0.333066 | − | 0.942903i | \(-0.608083\pi\) | ||||
−0.333066 | + | 0.942903i | \(0.608083\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.4907 | 0.940994 | 0.470497 | − | 0.882402i | \(-0.344075\pi\) | ||||
0.470497 | + | 0.882402i | \(0.344075\pi\) | |||||||
\(272\) | −8.35145 | −0.506381 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.63135 | −0.461027 | ||||||||
\(275\) | 8.87634 | 0.535263 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.6114 | −1.05816 | −0.529082 | − | 0.848571i | \(-0.677464\pi\) | ||||
−0.529082 | + | 0.848571i | \(0.677464\pi\) | |||||||
\(278\) | 50.0144 | 2.99966 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 21.8174 | 1.30384 | ||||||||
\(281\) | −23.9635 | −1.42954 | −0.714771 | − | 0.699358i | \(-0.753469\pi\) | ||||
−0.714771 | + | 0.699358i | \(0.753469\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.7493 | 1.59008 | 0.795040 | − | 0.606558i | \(-0.207450\pi\) | ||||
0.795040 | + | 0.606558i | \(0.207450\pi\) | |||||||
\(284\) | 36.1890 | 2.14742 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.89831 | 0.230512 | ||||||||
\(287\) | 11.4001 | 0.672925 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.4678 | −0.909868 | ||||||||
\(290\) | 50.6060 | 2.97169 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 69.3686 | 4.05949 | ||||||||
\(293\) | −13.0240 | −0.760870 | −0.380435 | − | 0.924808i | \(-0.624226\pi\) | ||||
−0.380435 | + | 0.924808i | \(0.624226\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 54.4314 | 3.16912 | ||||||||
\(296\) | −62.8620 | −3.65378 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 21.6079 | 1.25171 | ||||||||
\(299\) | 10.9171 | 0.631350 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.38894 | −0.483530 | ||||||||
\(302\) | −13.5462 | −0.779499 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −29.6920 | −1.70295 | ||||||||
\(305\) | 3.72510 | 0.213298 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.78896 | 0.102101 | 0.0510506 | − | 0.998696i | \(-0.483743\pi\) | ||||
0.0510506 | + | 0.998696i | \(0.483743\pi\) | |||||||
\(308\) | −4.21365 | −0.240095 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −11.6588 | −0.662175 | ||||||||
\(311\) | 4.69404 | 0.266175 | 0.133087 | − | 0.991104i | \(-0.457511\pi\) | ||||
0.133087 | + | 0.991104i | \(0.457511\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.2738 | 1.48508 | 0.742541 | − | 0.669800i | \(-0.233620\pi\) | ||||
0.742541 | + | 0.669800i | \(0.233620\pi\) | |||||||
\(314\) | 5.71951 | 0.322771 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −34.8876 | −1.96258 | ||||||||
\(317\) | −12.4347 | −0.698404 | −0.349202 | − | 0.937047i | \(-0.613547\pi\) | ||||
−0.349202 | + | 0.937047i | \(0.613547\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.35857 | −0.300022 | ||||||||
\(320\) | −4.96381 | −0.277485 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −17.1307 | −0.954658 | ||||||||
\(323\) | 5.44760 | 0.303113 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.6488 | −0.757098 | ||||||||
\(326\) | 48.5428 | 2.68854 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 73.7130 | 4.07012 | ||||||||
\(329\) | 2.29946 | 0.126773 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.49136 | 0.356798 | 0.178399 | − | 0.983958i | \(-0.442908\pi\) | ||||
0.178399 | + | 0.983958i | \(0.442908\pi\) | |||||||
\(332\) | 8.61253 | 0.472674 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 29.9380 | 1.63813 | ||||||||
\(335\) | 38.4751 | 2.10212 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.1826 | 0.663627 | 0.331814 | − | 0.943345i | \(-0.392339\pi\) | ||||
0.331814 | + | 0.943345i | \(0.392339\pi\) | |||||||
\(338\) | 26.9636 | 1.46663 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −20.4149 | −1.10715 | ||||||||
\(341\) | 1.23453 | 0.0668533 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.4622 | 0.672893 | ||||||||
\(344\) | −54.2430 | −2.92458 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 26.9336 | 1.44796 | ||||||||
\(347\) | 3.47254 | 0.186416 | 0.0932080 | − | 0.995647i | \(-0.470288\pi\) | ||||
0.0932080 | + | 0.995647i | \(0.470288\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.9457 | −1.01414 | −0.507069 | − | 0.861906i | \(-0.669271\pi\) | ||||
−0.507069 | + | 0.861906i | \(0.669271\pi\) | |||||||
\(350\) | 21.4173 | 1.14480 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.79684 | −0.255672 | ||||||||
\(353\) | −23.8117 | −1.26737 | −0.633685 | − | 0.773591i | \(-0.718459\pi\) | ||||
−0.633685 | + | 0.773591i | \(0.718459\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 30.4487 | 1.61605 | ||||||||
\(356\) | 2.32018 | 0.122969 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.8367 | 0.572740 | ||||||||
\(359\) | 22.4083 | 1.18267 | 0.591334 | − | 0.806427i | \(-0.298602\pi\) | ||||
0.591334 | + | 0.806427i | \(0.298602\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.367910 | 0.0193637 | ||||||||
\(362\) | 50.6399 | 2.66157 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.47917 | 0.339601 | ||||||||
\(365\) | 58.3654 | 3.05498 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.9397 | 0.779845 | 0.389923 | − | 0.920848i | \(-0.372502\pi\) | ||||
0.389923 | + | 0.920848i | \(0.372502\pi\) | |||||||
\(368\) | −47.9008 | −2.49700 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −96.4698 | −5.01522 | ||||||||
\(371\) | 6.70496 | 0.348104 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −30.2393 | −1.56573 | −0.782866 | − | 0.622190i | \(-0.786243\pi\) | ||||
−0.782866 | + | 0.622190i | \(0.786243\pi\) | |||||||
\(374\) | 3.13820 | 0.162272 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 14.8683 | 0.766774 | ||||||||
\(377\) | 8.23965 | 0.424364 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.74598 | 0.500618 | 0.250309 | − | 0.968166i | \(-0.419468\pi\) | ||||
0.250309 | + | 0.968166i | \(0.419468\pi\) | |||||||
\(380\) | −72.5811 | −3.72333 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 59.1215 | 3.02492 | ||||||||
\(383\) | −2.20960 | −0.112905 | −0.0564526 | − | 0.998405i | \(-0.517979\pi\) | ||||
−0.0564526 | + | 0.998405i | \(0.517979\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.54529 | −0.180685 | ||||||||
\(386\) | −24.7256 | −1.25850 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −67.9168 | −3.44795 | ||||||||
\(389\) | 11.8827 | 0.602478 | 0.301239 | − | 0.953549i | \(-0.402600\pi\) | ||||
0.301239 | + | 0.953549i | \(0.402600\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.78839 | 0.444448 | ||||||||
\(392\) | 37.5032 | 1.89420 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.16181 | −0.159290 | ||||||||
\(395\) | −29.3538 | −1.47695 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.12121 | −0.106461 | −0.0532303 | − | 0.998582i | \(-0.516952\pi\) | ||||
−0.0532303 | + | 0.998582i | \(0.516952\pi\) | |||||||
\(398\) | 59.2734 | 2.97111 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 59.8868 | 2.99434 | ||||||||
\(401\) | 2.29783 | 0.114748 | 0.0573741 | − | 0.998353i | \(-0.481727\pi\) | ||||
0.0573741 | + | 0.998353i | \(0.481727\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.89828 | −0.0945601 | ||||||||
\(404\) | −47.1727 | −2.34693 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.9294 | −0.641676 | ||||||||
\(407\) | 10.2150 | 0.506338 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.53852 | 0.125522 | 0.0627608 | − | 0.998029i | \(-0.480009\pi\) | ||||
0.0627608 | + | 0.998029i | \(0.480009\pi\) | |||||||
\(410\) | 113.122 | 5.58670 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.5463 | −0.519577 | ||||||||
\(413\) | −13.9068 | −0.684307 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.24641 | 0.355712 | ||||||||
\(416\) | 7.37591 | 0.361634 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 11.1573 | 0.545720 | ||||||||
\(419\) | −3.19459 | −0.156066 | −0.0780329 | − | 0.996951i | \(-0.524864\pi\) | ||||
−0.0780329 | + | 0.996951i | \(0.524864\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.11087 | −0.346562 | −0.173281 | − | 0.984872i | \(-0.555437\pi\) | ||||
−0.173281 | + | 0.984872i | \(0.555437\pi\) | |||||||
\(422\) | 58.6438 | 2.85473 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 43.3544 | 2.10547 | ||||||||
\(425\) | −10.9875 | −0.532971 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.951731 | −0.0460575 | ||||||||
\(428\) | −13.9888 | −0.676172 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −83.2428 | −4.01432 | ||||||||
\(431\) | 7.24051 | 0.348763 | 0.174382 | − | 0.984678i | \(-0.444207\pi\) | ||||
0.174382 | + | 0.984678i | \(0.444207\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.83179 | −0.184144 | −0.0920719 | − | 0.995752i | \(-0.529349\pi\) | ||||
−0.0920719 | + | 0.995752i | \(0.529349\pi\) | |||||||
\(434\) | 2.97873 | 0.142983 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 39.2310 | 1.87882 | ||||||||
\(437\) | 31.2454 | 1.49467 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.5778 | −1.17303 | −0.586517 | − | 0.809937i | \(-0.699501\pi\) | ||||
−0.586517 | + | 0.809937i | \(0.699501\pi\) | |||||||
\(440\) | −22.9239 | −1.09285 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.82548 | −0.229525 | ||||||||
\(443\) | 6.10789 | 0.290194 | 0.145097 | − | 0.989417i | \(-0.453651\pi\) | ||||
0.145097 | + | 0.989417i | \(0.453651\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.95215 | 0.0925408 | ||||||||
\(446\) | −67.7873 | −3.20982 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.26821 | 0.0599174 | ||||||||
\(449\) | −19.8224 | −0.935476 | −0.467738 | − | 0.883867i | \(-0.654931\pi\) | ||||
−0.467738 | + | 0.883867i | \(0.654931\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.9783 | −0.564034 | ||||||||
\(452\) | −85.3955 | −4.01667 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 47.9464 | 2.25024 | ||||||||
\(455\) | 5.45145 | 0.255568 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.8471 | 1.48975 | 0.744873 | − | 0.667207i | \(-0.232510\pi\) | ||||
0.744873 | + | 0.667207i | \(0.232510\pi\) | |||||||
\(458\) | −49.5773 | −2.31659 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −117.092 | −5.45945 | ||||||||
\(461\) | −12.1889 | −0.567694 | −0.283847 | − | 0.958870i | \(-0.591611\pi\) | ||||
−0.283847 | + | 0.958870i | \(0.591611\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.20136 | 0.427623 | 0.213812 | − | 0.976875i | \(-0.431412\pi\) | ||||
0.213812 | + | 0.976875i | \(0.431412\pi\) | |||||||
\(464\) | −36.1532 | −1.67837 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −41.8408 | −1.93824 | ||||||||
\(467\) | −14.9650 | −0.692498 | −0.346249 | − | 0.938143i | \(-0.612545\pi\) | ||||
−0.346249 | + | 0.938143i | \(0.612545\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.83007 | −0.453910 | ||||||||
\(470\) | 22.8173 | 1.05248 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −89.9213 | −4.13896 | ||||||||
\(473\) | 8.81440 | 0.405287 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −39.0639 | −1.79237 | ||||||||
\(476\) | 5.21583 | 0.239067 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −27.3270 | −1.24991 | ||||||||
\(479\) | −32.0402 | −1.46395 | −0.731977 | − | 0.681330i | \(-0.761402\pi\) | ||||
−0.731977 | + | 0.681330i | \(0.761402\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.7072 | −0.716185 | ||||||||
\(482\) | 33.7642 | 1.53792 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.42736 | 0.201244 | ||||||||
\(485\) | −57.1439 | −2.59477 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.0911 | −0.955728 | −0.477864 | − | 0.878434i | \(-0.658589\pi\) | ||||
−0.477864 | + | 0.878434i | \(0.658589\pi\) | |||||||
\(488\) | −6.15390 | −0.278574 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 57.5534 | 2.60000 | ||||||||
\(491\) | −15.5542 | −0.701952 | −0.350976 | − | 0.936384i | \(-0.614150\pi\) | ||||
−0.350976 | + | 0.936384i | \(0.614150\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.63304 | 0.298737 | ||||||||
\(494\) | −17.1561 | −0.771888 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.32910 | 0.373987 | ||||||||
\(497\) | −7.77940 | −0.348954 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.9129 | −1.24956 | −0.624778 | − | 0.780803i | \(-0.714810\pi\) | ||||
−0.624778 | + | 0.780803i | \(0.714810\pi\) | |||||||
\(500\) | 63.9298 | 2.85903 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −16.8345 | −0.751360 | ||||||||
\(503\) | 20.2569 | 0.903211 | 0.451606 | − | 0.892218i | \(-0.350851\pi\) | ||||
0.451606 | + | 0.892218i | \(0.350851\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −39.6902 | −1.76619 | ||||||||
\(506\) | 17.9995 | 0.800178 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.269605 | −0.0119618 | ||||||||
\(509\) | 3.75634 | 0.166497 | 0.0832485 | − | 0.996529i | \(-0.473470\pi\) | ||||
0.0832485 | + | 0.996529i | \(0.473470\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.9119 | −0.659662 | ||||||||
\(512\) | 50.6749 | 2.23954 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 46.3539 | 2.04458 | ||||||||
\(515\) | −8.87343 | −0.391010 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.41608 | −0.106259 | ||||||||
\(518\) | 24.6472 | 1.08294 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 35.2491 | 1.54578 | ||||||||
\(521\) | −13.7087 | −0.600588 | −0.300294 | − | 0.953847i | \(-0.597085\pi\) | ||||
−0.300294 | + | 0.953847i | \(0.597085\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.1809 | 1.40717 | 0.703586 | − | 0.710611i | \(-0.251581\pi\) | ||||
0.703586 | + | 0.710611i | \(0.251581\pi\) | |||||||
\(524\) | −2.72880 | −0.119208 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −42.0293 | −1.83257 | ||||||||
\(527\) | −1.52814 | −0.0665670 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.4070 | 1.19161 | ||||||||
\(530\) | 66.5328 | 2.89000 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 18.5439 | 0.803979 | ||||||||
\(533\) | 18.4185 | 0.797793 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.7699 | −0.508856 | ||||||||
\(536\) | −63.5613 | −2.74543 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 27.6983 | 1.19416 | ||||||||
\(539\) | −6.09421 | −0.262496 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.1341 | −1.03761 | −0.518804 | − | 0.854894i | \(-0.673622\pi\) | ||||
−0.518804 | + | 0.854894i | \(0.673622\pi\) | |||||||
\(542\) | −39.2724 | −1.68690 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.93772 | 0.254577 | ||||||||
\(545\) | 33.0082 | 1.41392 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.8925 | −1.19260 | −0.596299 | − | 0.802762i | \(-0.703363\pi\) | ||||
−0.596299 | + | 0.802762i | \(0.703363\pi\) | |||||||
\(548\) | 13.3269 | 0.569298 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −22.5035 | −0.959552 | ||||||||
\(551\) | 23.5825 | 1.00465 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.49964 | 0.318917 | ||||||||
\(554\) | 44.6487 | 1.89694 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −87.3421 | −3.70413 | ||||||||
\(557\) | 22.9190 | 0.971108 | 0.485554 | − | 0.874207i | \(-0.338618\pi\) | ||||
0.485554 | + | 0.874207i | \(0.338618\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.5535 | −0.573254 | ||||||||
\(560\) | −23.9193 | −1.01078 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 60.7528 | 2.56270 | ||||||||
\(563\) | −2.08076 | −0.0876937 | −0.0438469 | − | 0.999038i | \(-0.513961\pi\) | ||||
−0.0438469 | + | 0.999038i | \(0.513961\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −71.8501 | −3.02276 | ||||||||
\(566\) | −67.8154 | −2.85049 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −50.3017 | −2.11061 | ||||||||
\(569\) | −46.1126 | −1.93314 | −0.966570 | − | 0.256402i | \(-0.917463\pi\) | ||||
−0.966570 | + | 0.256402i | \(0.917463\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.4548 | 0.772308 | 0.386154 | − | 0.922434i | \(-0.373803\pi\) | ||||
0.386154 | + | 0.922434i | \(0.373803\pi\) | |||||||
\(572\) | −6.80777 | −0.284647 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −28.9018 | −1.20634 | ||||||||
\(575\) | −63.0201 | −2.62812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.03683 | 0.0431638 | 0.0215819 | − | 0.999767i | \(-0.493130\pi\) | ||||
0.0215819 | + | 0.999767i | \(0.493130\pi\) | |||||||
\(578\) | 39.2142 | 1.63110 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −88.3753 | −3.66958 | ||||||||
\(581\) | −1.85140 | −0.0768089 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.04502 | −0.291775 | ||||||||
\(584\) | −96.4203 | −3.98990 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 33.0187 | 1.36399 | ||||||||
\(587\) | −24.5792 | −1.01449 | −0.507245 | − | 0.861802i | \(-0.669336\pi\) | ||||
−0.507245 | + | 0.861802i | \(0.669336\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.43302 | −0.223864 | ||||||||
\(590\) | −137.996 | −5.68120 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 68.9184 | 2.83253 | ||||||||
\(593\) | −45.7292 | −1.87787 | −0.938937 | − | 0.344089i | \(-0.888188\pi\) | ||||
−0.938937 | + | 0.344089i | \(0.888188\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.38849 | 0.179911 | ||||||||
\(596\) | −37.7346 | −1.54567 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −27.6772 | −1.13180 | ||||||||
\(599\) | 4.29437 | 0.175463 | 0.0877316 | − | 0.996144i | \(-0.472038\pi\) | ||||
0.0877316 | + | 0.996144i | \(0.472038\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.6658 | 0.557439 | 0.278719 | − | 0.960373i | \(-0.410090\pi\) | ||||
0.278719 | + | 0.960373i | \(0.410090\pi\) | |||||||
\(602\) | 21.2678 | 0.866812 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 23.6563 | 0.962562 | ||||||||
\(605\) | 3.72510 | 0.151447 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.8576 | −1.45542 | −0.727708 | − | 0.685887i | \(-0.759414\pi\) | ||||
−0.727708 | + | 0.685887i | \(0.759414\pi\) | |||||||
\(608\) | 21.1104 | 0.856140 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.44395 | −0.382374 | ||||||||
\(611\) | 3.71510 | 0.150297 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.12777 | 0.368667 | 0.184333 | − | 0.982864i | \(-0.440987\pi\) | ||||
0.184333 | + | 0.982864i | \(0.440987\pi\) | |||||||
\(614\) | −4.53541 | −0.183034 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.85686 | 0.235980 | ||||||||
\(617\) | −31.3560 | −1.26234 | −0.631172 | − | 0.775643i | \(-0.717426\pi\) | ||||
−0.631172 | + | 0.775643i | \(0.717426\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.0164 | 1.00549 | 0.502746 | − | 0.864434i | \(-0.332323\pi\) | ||||
0.502746 | + | 0.864434i | \(0.332323\pi\) | |||||||
\(620\) | 20.3602 | 0.817686 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11.9004 | −0.477164 | ||||||||
\(623\) | −0.498758 | −0.0199823 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.40766 | 0.376306 | ||||||||
\(626\) | −66.6100 | −2.66227 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.98820 | −0.398573 | ||||||||
\(629\) | −12.6445 | −0.504169 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.1969 | 1.08269 | 0.541345 | − | 0.840801i | \(-0.317915\pi\) | ||||
0.541345 | + | 0.840801i | \(0.317915\pi\) | |||||||
\(632\) | 48.4928 | 1.92894 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 31.5248 | 1.25201 | ||||||||
\(635\) | −0.226841 | −0.00900190 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.37082 | 0.371285 | ||||||||
\(638\) | 13.5852 | 0.537842 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 48.3217 | 1.91008 | ||||||||
\(641\) | 24.0469 | 0.949794 | 0.474897 | − | 0.880041i | \(-0.342485\pi\) | ||||
0.474897 | + | 0.880041i | \(0.342485\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.8173 | 0.505465 | 0.252732 | − | 0.967536i | \(-0.418671\pi\) | ||||
0.252732 | + | 0.967536i | \(0.418671\pi\) | |||||||
\(644\) | 29.9161 | 1.17886 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.8109 | −0.543382 | ||||||||
\(647\) | 44.1154 | 1.73436 | 0.867179 | − | 0.497997i | \(-0.165931\pi\) | ||||
0.867179 | + | 0.497997i | \(0.165931\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.6121 | 0.573574 | ||||||||
\(650\) | 34.6027 | 1.35723 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −84.7722 | −3.31994 | ||||||||
\(653\) | 1.44701 | 0.0566259 | 0.0283129 | − | 0.999599i | \(-0.490987\pi\) | ||||
0.0283129 | + | 0.999599i | \(0.490987\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.29596 | −0.0897105 | ||||||||
\(656\) | −80.8149 | −3.15529 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.82963 | −0.227263 | ||||||||
\(659\) | −5.36239 | −0.208889 | −0.104444 | − | 0.994531i | \(-0.533306\pi\) | ||||
−0.104444 | + | 0.994531i | \(0.533306\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.8255 | 1.08229 | 0.541143 | − | 0.840931i | \(-0.317992\pi\) | ||||
0.541143 | + | 0.840931i | \(0.317992\pi\) | |||||||
\(662\) | −16.4571 | −0.639622 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.9712 | −0.464571 | ||||||||
\(665\) | 15.6025 | 0.605037 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 38.0447 | 1.47310 | ||||||||
\(668\) | −52.2819 | −2.02285 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −97.5430 | −3.76842 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.2181 | −1.70448 | −0.852241 | − | 0.523149i | \(-0.824757\pi\) | ||||
−0.852241 | + | 0.523149i | \(0.824757\pi\) | |||||||
\(674\) | −30.8856 | −1.18967 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −47.0876 | −1.81106 | ||||||||
\(677\) | 33.1718 | 1.27490 | 0.637448 | − | 0.770494i | \(-0.279990\pi\) | ||||
0.637448 | + | 0.770494i | \(0.279990\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.5998 | 0.560289 | ||||||||
\(680\) | 28.3761 | 1.08817 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.12980 | −0.119846 | ||||||||
\(683\) | 34.4018 | 1.31635 | 0.658175 | − | 0.752865i | \(-0.271329\pi\) | ||||
0.658175 | + | 0.752865i | \(0.271329\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.2130 | 0.428427 | ||||||||
\(686\) | −31.5944 | −1.20628 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 59.4690 | 2.26723 | ||||||||
\(689\) | 10.8328 | 0.412699 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −48.1463 | −1.83157 | −0.915787 | − | 0.401665i | \(-0.868432\pi\) | ||||
−0.915787 | + | 0.401665i | \(0.868432\pi\) | |||||||
\(692\) | −47.0353 | −1.78801 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.80368 | −0.334183 | ||||||||
\(695\) | −73.4880 | −2.78756 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.8272 | 0.561619 | ||||||||
\(698\) | 48.0315 | 1.81802 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −37.4018 | −1.41366 | ||||||||
\(701\) | 9.58358 | 0.361967 | 0.180983 | − | 0.983486i | \(-0.442072\pi\) | ||||
0.180983 | + | 0.983486i | \(0.442072\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −44.9551 | −1.69551 | ||||||||
\(704\) | −1.33253 | −0.0502217 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 60.3681 | 2.27198 | ||||||||
\(707\) | 10.1405 | 0.381373 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.95650 | −0.298813 | −0.149406 | − | 0.988776i | \(-0.547736\pi\) | ||||
−0.149406 | + | 0.988776i | \(0.547736\pi\) | |||||||
\(710\) | −77.1944 | −2.89705 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.22498 | −0.120861 | ||||||||
\(713\) | −8.76487 | −0.328247 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.72793 | −0.214212 | ||||||||
\(716\) | −18.9246 | −0.707246 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −56.8102 | −2.12014 | ||||||||
\(719\) | 23.0223 | 0.858587 | 0.429294 | − | 0.903165i | \(-0.358763\pi\) | ||||
0.429294 | + | 0.903165i | \(0.358763\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.26709 | 0.0844307 | ||||||||
\(722\) | −0.932733 | −0.0347127 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −88.4344 | −3.28664 | ||||||||
\(725\) | −47.5644 | −1.76650 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.2774 | 1.08584 | 0.542920 | − | 0.839784i | \(-0.317319\pi\) | ||||
0.542920 | + | 0.839784i | \(0.317319\pi\) | |||||||
\(728\) | −9.00585 | −0.333779 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −147.969 | −5.47659 | ||||||||
\(731\) | −10.9108 | −0.403551 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.6122 | −1.50005 | −0.750023 | − | 0.661412i | \(-0.769957\pi\) | ||||
−0.750023 | + | 0.661412i | \(0.769957\pi\) | |||||||
\(734\) | −37.8755 | −1.39801 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 34.0565 | 1.25534 | ||||||||
\(737\) | 10.3286 | 0.380460 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.9408 | 0.770321 | 0.385160 | − | 0.922850i | \(-0.374146\pi\) | ||||
0.385160 | + | 0.922850i | \(0.374146\pi\) | |||||||
\(740\) | 168.469 | 6.19304 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −16.9986 | −0.624038 | ||||||||
\(743\) | −22.1711 | −0.813377 | −0.406689 | − | 0.913567i | \(-0.633317\pi\) | ||||
−0.406689 | + | 0.913567i | \(0.633317\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −31.7492 | −1.16320 | ||||||||
\(746\) | 76.6634 | 2.80685 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.48036 | −0.200382 | ||||||||
\(749\) | 3.00710 | 0.109877 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.45803 | 0.272147 | 0.136074 | − | 0.990699i | \(-0.456552\pi\) | ||||
0.136074 | + | 0.990699i | \(0.456552\pi\) | |||||||
\(752\) | −16.3008 | −0.594429 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −20.8894 | −0.760746 | ||||||||
\(755\) | 19.9040 | 0.724380 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.0595 | −1.34695 | −0.673475 | − | 0.739210i | \(-0.735199\pi\) | ||||
−0.673475 | + | 0.739210i | \(0.735199\pi\) | |||||||
\(758\) | −24.7083 | −0.897444 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 100.886 | 3.65951 | ||||||||
\(761\) | 31.6016 | 1.14556 | 0.572778 | − | 0.819711i | \(-0.305866\pi\) | ||||
0.572778 | + | 0.819711i | \(0.305866\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.43332 | −0.305307 | ||||||||
\(764\) | −103.246 | −3.73531 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.60183 | 0.202402 | ||||||||
\(767\) | −22.4684 | −0.811287 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.3899 | −0.843460 | −0.421730 | − | 0.906722i | \(-0.638577\pi\) | ||||
−0.421730 | + | 0.906722i | \(0.638577\pi\) | |||||||
\(770\) | 8.98810 | 0.323909 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 43.1792 | 1.55405 | ||||||||
\(773\) | 31.0588 | 1.11711 | 0.558555 | − | 0.829468i | \(-0.311356\pi\) | ||||
0.558555 | + | 0.829468i | \(0.311356\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.9581 | 0.393625 | ||||||||
\(776\) | 94.4024 | 3.38885 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −30.1254 | −1.08005 | ||||||||
\(779\) | 52.7151 | 1.88872 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.17395 | 0.292487 | ||||||||
\(782\) | −22.2805 | −0.796751 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −41.1164 | −1.46844 | ||||||||
\(785\) | −8.40388 | −0.299947 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.5467 | 0.661117 | 0.330558 | − | 0.943786i | \(-0.392763\pi\) | ||||
0.330558 | + | 0.943786i | \(0.392763\pi\) | |||||||
\(788\) | 5.52160 | 0.196699 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 74.4184 | 2.64769 | ||||||||
\(791\) | 18.3571 | 0.652704 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.53766 | −0.0546039 | ||||||||
\(794\) | 5.37775 | 0.190849 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −103.511 | −3.66887 | ||||||||
\(797\) | 25.4905 | 0.902921 | 0.451461 | − | 0.892291i | \(-0.350903\pi\) | ||||
0.451461 | + | 0.892291i | \(0.350903\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.99071 | 0.105804 | ||||||||
\(800\) | −42.5784 | −1.50537 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5.82552 | −0.205706 | ||||||||
\(803\) | 15.6682 | 0.552917 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.1708 | 0.887154 | ||||||||
\(806\) | 4.81257 | 0.169515 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 65.5687 | 2.30670 | ||||||||
\(809\) | −11.5648 | −0.406597 | −0.203299 | − | 0.979117i | \(-0.565166\pi\) | ||||
−0.203299 | + | 0.979117i | \(0.565166\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.1672 | −0.848625 | −0.424313 | − | 0.905516i | \(-0.639484\pi\) | ||||
−0.424313 | + | 0.905516i | \(0.639484\pi\) | |||||||
\(812\) | 22.5791 | 0.792373 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −25.8973 | −0.907698 | ||||||||
\(815\) | −71.3257 | −2.49843 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −38.7913 | −1.35714 | ||||||||
\(818\) | −6.43571 | −0.225019 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −197.550 | −6.89873 | ||||||||
\(821\) | 39.1543 | 1.36649 | 0.683247 | − | 0.730187i | \(-0.260567\pi\) | ||||
0.683247 | + | 0.730187i | \(0.260567\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.9250 | 1.28712 | 0.643562 | − | 0.765394i | \(-0.277456\pi\) | ||||
0.643562 | + | 0.765394i | \(0.277456\pi\) | |||||||
\(824\) | 14.6590 | 0.510671 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 35.2568 | 1.22674 | ||||||||
\(827\) | 27.4711 | 0.955263 | 0.477631 | − | 0.878560i | \(-0.341495\pi\) | ||||
0.477631 | + | 0.878560i | \(0.341495\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −42.1370 | −1.46348 | −0.731738 | − | 0.681586i | \(-0.761291\pi\) | ||||
−0.731738 | + | 0.681586i | \(0.761291\pi\) | |||||||
\(830\) | −18.3713 | −0.637677 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.04898 | 0.0710356 | ||||||||
\(833\) | 7.54365 | 0.261372 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −43.9890 | −1.52230 | ||||||||
\(836\) | −19.4844 | −0.673881 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.09899 | 0.279775 | ||||||||
\(839\) | 40.3633 | 1.39350 | 0.696748 | − | 0.717316i | \(-0.254630\pi\) | ||||
0.696748 | + | 0.717316i | \(0.254630\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.285774 | −0.00985429 | ||||||||
\(842\) | 18.0276 | 0.621273 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −102.412 | −3.52516 | ||||||||
\(845\) | −39.6186 | −1.36292 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.951731 | −0.0327019 | ||||||||
\(848\) | −47.5313 | −1.63223 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 27.8557 | 0.955443 | ||||||||
\(851\) | −72.5242 | −2.48610 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.7694 | 0.368738 | 0.184369 | − | 0.982857i | \(-0.440976\pi\) | ||||
0.184369 | + | 0.982857i | \(0.440976\pi\) | |||||||
\(854\) | 2.41285 | 0.0825660 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.4440 | 0.664581 | ||||||||
\(857\) | 27.9239 | 0.953862 | 0.476931 | − | 0.878941i | \(-0.341749\pi\) | ||||
0.476931 | + | 0.878941i | \(0.341749\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.54206 | −0.154973 | −0.0774866 | − | 0.996993i | \(-0.524689\pi\) | ||||
−0.0774866 | + | 0.996993i | \(0.524689\pi\) | |||||||
\(860\) | 145.370 | 4.95708 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −18.3563 | −0.625219 | ||||||||
\(863\) | −24.6926 | −0.840546 | −0.420273 | − | 0.907398i | \(-0.638066\pi\) | ||||
−0.420273 | + | 0.907398i | \(0.638066\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −39.5746 | −1.34558 | ||||||||
\(866\) | 9.71443 | 0.330110 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.20187 | −0.176563 | ||||||||
\(869\) | −7.88000 | −0.267311 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.8819 | −0.538138 | ||||||||
\(872\) | −54.5299 | −1.84662 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −79.2142 | −2.67946 | ||||||||
\(875\) | −13.7427 | −0.464589 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.3084 | 1.39488 | 0.697442 | − | 0.716641i | \(-0.254321\pi\) | ||||
0.697442 | + | 0.716641i | \(0.254321\pi\) | |||||||
\(878\) | 62.3102 | 2.10287 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 25.1325 | 0.847215 | ||||||||
\(881\) | 50.4986 | 1.70134 | 0.850670 | − | 0.525700i | \(-0.176197\pi\) | ||||
0.850670 | + | 0.525700i | \(0.176197\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.2599 | 0.580842 | 0.290421 | − | 0.956899i | \(-0.406205\pi\) | ||||
0.290421 | + | 0.956899i | \(0.406205\pi\) | |||||||
\(884\) | 8.42693 | 0.283428 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.4849 | −0.520224 | ||||||||
\(887\) | 19.8671 | 0.667074 | 0.333537 | − | 0.942737i | \(-0.391758\pi\) | ||||
0.333537 | + | 0.942737i | \(0.391758\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.0579559 | 0.00194378 | ||||||||
\(890\) | −4.94914 | −0.165896 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 118.380 | 3.96364 | ||||||||
\(893\) | 10.6329 | 0.355817 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.9228 | −0.532241 | ||||||||
\(896\) | −12.3458 | −0.412444 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 50.2542 | 1.67700 | ||||||||
\(899\) | −6.61529 | −0.220632 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.72060 | 0.290525 | ||||||||
\(902\) | 30.3676 | 1.01113 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 118.697 | 3.94781 | ||||||||
\(905\) | −74.4070 | −2.47337 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.4581 | −0.513277 | −0.256638 | − | 0.966508i | \(-0.582615\pi\) | ||||
−0.256638 | + | 0.966508i | \(0.582615\pi\) | |||||||
\(908\) | −83.7307 | −2.77870 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −13.8206 | −0.458150 | ||||||||
\(911\) | 5.86489 | 0.194312 | 0.0971562 | − | 0.995269i | \(-0.469025\pi\) | ||||
0.0971562 | + | 0.995269i | \(0.469025\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.94530 | 0.0643799 | ||||||||
\(914\) | −80.7396 | −2.67063 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 86.5787 | 2.86064 | ||||||||
\(917\) | 0.586598 | 0.0193712 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.9978 | −1.25343 | −0.626716 | − | 0.779248i | \(-0.715601\pi\) | ||||
−0.626716 | + | 0.779248i | \(0.715601\pi\) | |||||||
\(920\) | 162.755 | 5.36586 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 30.9016 | 1.01769 | ||||||||
\(923\) | −12.5688 | −0.413705 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 90.6716 | 2.98126 | ||||||||
\(926\) | −23.3275 | −0.766589 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 25.7042 | 0.843781 | ||||||||
\(929\) | −8.20155 | −0.269084 | −0.134542 | − | 0.990908i | \(-0.542956\pi\) | ||||
−0.134542 | + | 0.990908i | \(0.542956\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.8200 | 0.878990 | ||||||||
\(932\) | 73.0683 | 2.39343 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 37.9397 | 1.24142 | ||||||||
\(935\) | −4.61107 | −0.150798 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 56.2620 | 1.83800 | 0.918999 | − | 0.394259i | \(-0.128999\pi\) | ||||
0.918999 | + | 0.394259i | \(0.128999\pi\) | |||||||
\(938\) | 24.9214 | 0.813713 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −39.8468 | −1.29966 | ||||||||
\(941\) | 46.9435 | 1.53031 | 0.765157 | − | 0.643844i | \(-0.222661\pi\) | ||||
0.765157 | + | 0.643844i | \(0.222661\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 85.0431 | 2.76938 | ||||||||
\(944\) | 98.5848 | 3.20866 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22.3465 | −0.726547 | ||||||||
\(947\) | −52.9734 | −1.72140 | −0.860702 | − | 0.509110i | \(-0.829975\pi\) | ||||
−0.860702 | + | 0.509110i | \(0.829975\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.0923 | −0.782069 | ||||||||
\(950\) | 99.0356 | 3.21314 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.24985 | −0.234969 | ||||||||
\(953\) | 0.446509 | 0.0144638 | 0.00723191 | − | 0.999974i | \(-0.497698\pi\) | ||||
0.00723191 | + | 0.999974i | \(0.497698\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −86.8693 | −2.81102 | ||||||||
\(956\) | 47.7223 | 1.54345 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 81.2291 | 2.62439 | ||||||||
\(959\) | −2.86483 | −0.0925102 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.4759 | −0.950837 | ||||||||
\(962\) | 39.8212 | 1.28389 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −58.9637 | −1.89909 | ||||||||
\(965\) | 36.3301 | 1.16951 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.4533 | −0.914997 | −0.457499 | − | 0.889210i | \(-0.651255\pi\) | ||||
−0.457499 | + | 0.889210i | \(0.651255\pi\) | |||||||
\(968\) | −6.15390 | −0.197794 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 144.873 | 4.65158 | ||||||||
\(971\) | 15.7288 | 0.504760 | 0.252380 | − | 0.967628i | \(-0.418787\pi\) | ||||
0.252380 | + | 0.967628i | \(0.418787\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.7756 | 0.601917 | ||||||||
\(974\) | 53.4706 | 1.71331 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.74680 | 0.215960 | ||||||||
\(977\) | −31.3215 | −1.00206 | −0.501032 | − | 0.865429i | \(-0.667046\pi\) | ||||
−0.501032 | + | 0.865429i | \(0.667046\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.524054 | 0.0167488 | ||||||||
\(980\) | −100.508 | −3.21060 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 39.4334 | 1.25837 | ||||||||
\(983\) | −13.2756 | −0.423427 | −0.211714 | − | 0.977332i | \(-0.567904\pi\) | ||||
−0.211714 | + | 0.977332i | \(0.567904\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.64576 | 0.148026 | ||||||||
\(986\) | −16.8162 | −0.535538 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 29.9603 | 0.953165 | ||||||||
\(989\) | −62.5804 | −1.98994 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.57868 | −0.304277 | −0.152138 | − | 0.988359i | \(-0.548616\pi\) | ||||
−0.152138 | + | 0.988359i | \(0.548616\pi\) | |||||||
\(992\) | −5.92182 | −0.188018 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 19.7225 | 0.625560 | ||||||||
\(995\) | −87.0925 | −2.76102 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.9918 | −1.26655 | −0.633277 | − | 0.773925i | \(-0.718291\pi\) | ||||
−0.633277 | + | 0.773925i | \(0.718291\pi\) | |||||||
\(998\) | 70.7656 | 2.24004 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6039.2.a.m.1.2 | ✓ | 25 | |
3.2 | odd | 2 | 6039.2.a.p.1.24 | yes | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6039.2.a.m.1.2 | ✓ | 25 | 1.1 | even | 1 | trivial | |
6039.2.a.p.1.24 | yes | 25 | 3.2 | odd | 2 |