Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8043,2,Mod(1,8043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8043, 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("8043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8043 = 3 \cdot 7 \cdot 383 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8043.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: | \(64.2236783457\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 8043.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.58348 | −1.11969 | −0.559843 | − | 0.828599i | \(-0.689139\pi\) | ||||
−0.559843 | + | 0.828599i | \(0.689139\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.507395 | 0.253697 | ||||||||
\(5\) | −2.03406 | −0.909660 | −0.454830 | − | 0.890578i | \(-0.650300\pi\) | ||||
−0.454830 | + | 0.890578i | \(0.650300\pi\) | |||||||
\(6\) | 1.58348 | 0.646451 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.36350 | 0.835625 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.22089 | 1.01853 | ||||||||
\(11\) | 1.17498 | 0.354271 | 0.177135 | − | 0.984187i | \(-0.443317\pi\) | ||||
0.177135 | + | 0.984187i | \(0.443317\pi\) | |||||||
\(12\) | −0.507395 | −0.146472 | ||||||||
\(13\) | 3.73140 | 1.03490 | 0.517452 | − | 0.855712i | \(-0.326881\pi\) | ||||
0.517452 | + | 0.855712i | \(0.326881\pi\) | |||||||
\(14\) | −1.58348 | −0.423202 | ||||||||
\(15\) | 2.03406 | 0.525193 | ||||||||
\(16\) | −4.75734 | −1.18933 | ||||||||
\(17\) | −8.09560 | −1.96347 | −0.981736 | − | 0.190248i | \(-0.939071\pi\) | ||||
−0.981736 | + | 0.190248i | \(0.939071\pi\) | |||||||
\(18\) | −1.58348 | −0.373229 | ||||||||
\(19\) | −8.31210 | −1.90693 | −0.953463 | − | 0.301510i | \(-0.902509\pi\) | ||||
−0.953463 | + | 0.301510i | \(0.902509\pi\) | |||||||
\(20\) | −1.03207 | −0.230778 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −1.86056 | −0.396672 | ||||||||
\(23\) | 2.49738 | 0.520739 | 0.260370 | − | 0.965509i | \(-0.416156\pi\) | ||||
0.260370 | + | 0.965509i | \(0.416156\pi\) | |||||||
\(24\) | −2.36350 | −0.482448 | ||||||||
\(25\) | −0.862589 | −0.172518 | ||||||||
\(26\) | −5.90858 | −1.15877 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.507395 | 0.0958886 | ||||||||
\(29\) | −3.50435 | −0.650742 | −0.325371 | − | 0.945586i | \(-0.605489\pi\) | ||||
−0.325371 | + | 0.945586i | \(0.605489\pi\) | |||||||
\(30\) | −3.22089 | −0.588051 | ||||||||
\(31\) | 10.4075 | 1.86924 | 0.934618 | − | 0.355654i | \(-0.115742\pi\) | ||||
0.934618 | + | 0.355654i | \(0.115742\pi\) | |||||||
\(32\) | 2.80612 | 0.496057 | ||||||||
\(33\) | −1.17498 | −0.204538 | ||||||||
\(34\) | 12.8192 | 2.19847 | ||||||||
\(35\) | −2.03406 | −0.343819 | ||||||||
\(36\) | 0.507395 | 0.0845658 | ||||||||
\(37\) | −2.40440 | −0.395282 | −0.197641 | − | 0.980275i | \(-0.563328\pi\) | ||||
−0.197641 | + | 0.980275i | \(0.563328\pi\) | |||||||
\(38\) | 13.1620 | 2.13516 | ||||||||
\(39\) | −3.73140 | −0.597502 | ||||||||
\(40\) | −4.80752 | −0.760135 | ||||||||
\(41\) | −6.51764 | −1.01788 | −0.508942 | − | 0.860801i | \(-0.669963\pi\) | ||||
−0.508942 | + | 0.860801i | \(0.669963\pi\) | |||||||
\(42\) | 1.58348 | 0.244336 | ||||||||
\(43\) | 6.17846 | 0.942206 | 0.471103 | − | 0.882078i | \(-0.343856\pi\) | ||||
0.471103 | + | 0.882078i | \(0.343856\pi\) | |||||||
\(44\) | 0.596180 | 0.0898775 | ||||||||
\(45\) | −2.03406 | −0.303220 | ||||||||
\(46\) | −3.95454 | −0.583065 | ||||||||
\(47\) | −8.33923 | −1.21640 | −0.608201 | − | 0.793783i | \(-0.708109\pi\) | ||||
−0.608201 | + | 0.793783i | \(0.708109\pi\) | |||||||
\(48\) | 4.75734 | 0.686663 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.36589 | 0.193166 | ||||||||
\(51\) | 8.09560 | 1.13361 | ||||||||
\(52\) | 1.89329 | 0.262552 | ||||||||
\(53\) | 4.21927 | 0.579562 | 0.289781 | − | 0.957093i | \(-0.406418\pi\) | ||||
0.289781 | + | 0.957093i | \(0.406418\pi\) | |||||||
\(54\) | 1.58348 | 0.215484 | ||||||||
\(55\) | −2.38999 | −0.322266 | ||||||||
\(56\) | 2.36350 | 0.315837 | ||||||||
\(57\) | 8.31210 | 1.10096 | ||||||||
\(58\) | 5.54906 | 0.728627 | ||||||||
\(59\) | 9.57535 | 1.24660 | 0.623302 | − | 0.781981i | \(-0.285791\pi\) | ||||
0.623302 | + | 0.781981i | \(0.285791\pi\) | |||||||
\(60\) | 1.03207 | 0.133240 | ||||||||
\(61\) | −13.7336 | −1.75841 | −0.879204 | − | 0.476446i | \(-0.841925\pi\) | ||||
−0.879204 | + | 0.476446i | \(0.841925\pi\) | |||||||
\(62\) | −16.4800 | −2.09296 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 5.07125 | 0.633907 | ||||||||
\(65\) | −7.58990 | −0.941411 | ||||||||
\(66\) | 1.86056 | 0.229019 | ||||||||
\(67\) | 2.82956 | 0.345686 | 0.172843 | − | 0.984949i | \(-0.444705\pi\) | ||||
0.172843 | + | 0.984949i | \(0.444705\pi\) | |||||||
\(68\) | −4.10767 | −0.498128 | ||||||||
\(69\) | −2.49738 | −0.300649 | ||||||||
\(70\) | 3.22089 | 0.384970 | ||||||||
\(71\) | 3.19338 | 0.378985 | 0.189492 | − | 0.981882i | \(-0.439316\pi\) | ||||
0.189492 | + | 0.981882i | \(0.439316\pi\) | |||||||
\(72\) | 2.36350 | 0.278542 | ||||||||
\(73\) | −4.96110 | −0.580653 | −0.290326 | − | 0.956928i | \(-0.593764\pi\) | ||||
−0.290326 | + | 0.956928i | \(0.593764\pi\) | |||||||
\(74\) | 3.80731 | 0.442591 | ||||||||
\(75\) | 0.862589 | 0.0996032 | ||||||||
\(76\) | −4.21751 | −0.483782 | ||||||||
\(77\) | 1.17498 | 0.133902 | ||||||||
\(78\) | 5.90858 | 0.669015 | ||||||||
\(79\) | 10.7268 | 1.20686 | 0.603432 | − | 0.797414i | \(-0.293799\pi\) | ||||
0.603432 | + | 0.797414i | \(0.293799\pi\) | |||||||
\(80\) | 9.67673 | 1.08189 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.3205 | 1.13971 | ||||||||
\(83\) | −12.9827 | −1.42503 | −0.712516 | − | 0.701655i | \(-0.752445\pi\) | ||||
−0.712516 | + | 0.701655i | \(0.752445\pi\) | |||||||
\(84\) | −0.507395 | −0.0553613 | ||||||||
\(85\) | 16.4670 | 1.78609 | ||||||||
\(86\) | −9.78343 | −1.05497 | ||||||||
\(87\) | 3.50435 | 0.375706 | ||||||||
\(88\) | 2.77708 | 0.296037 | ||||||||
\(89\) | −12.6293 | −1.33871 | −0.669353 | − | 0.742945i | \(-0.733429\pi\) | ||||
−0.669353 | + | 0.742945i | \(0.733429\pi\) | |||||||
\(90\) | 3.22089 | 0.339511 | ||||||||
\(91\) | 3.73140 | 0.391157 | ||||||||
\(92\) | 1.26716 | 0.132110 | ||||||||
\(93\) | −10.4075 | −1.07920 | ||||||||
\(94\) | 13.2050 | 1.36199 | ||||||||
\(95\) | 16.9073 | 1.73466 | ||||||||
\(96\) | −2.80612 | −0.286399 | ||||||||
\(97\) | −12.2662 | −1.24544 | −0.622720 | − | 0.782445i | \(-0.713972\pi\) | ||||
−0.622720 | + | 0.782445i | \(0.713972\pi\) | |||||||
\(98\) | −1.58348 | −0.159955 | ||||||||
\(99\) | 1.17498 | 0.118090 | ||||||||
\(100\) | −0.437673 | −0.0437673 | ||||||||
\(101\) | 10.4030 | 1.03514 | 0.517568 | − | 0.855642i | \(-0.326837\pi\) | ||||
0.517568 | + | 0.855642i | \(0.326837\pi\) | |||||||
\(102\) | −12.8192 | −1.26929 | ||||||||
\(103\) | 15.2288 | 1.50054 | 0.750269 | − | 0.661132i | \(-0.229924\pi\) | ||||
0.750269 | + | 0.661132i | \(0.229924\pi\) | |||||||
\(104\) | 8.81918 | 0.864791 | ||||||||
\(105\) | 2.03406 | 0.198504 | ||||||||
\(106\) | −6.68111 | −0.648927 | ||||||||
\(107\) | 1.38838 | 0.134219 | 0.0671097 | − | 0.997746i | \(-0.478622\pi\) | ||||
0.0671097 | + | 0.997746i | \(0.478622\pi\) | |||||||
\(108\) | −0.507395 | −0.0488241 | ||||||||
\(109\) | 2.93650 | 0.281266 | 0.140633 | − | 0.990062i | \(-0.455086\pi\) | ||||
0.140633 | + | 0.990062i | \(0.455086\pi\) | |||||||
\(110\) | 3.78449 | 0.360837 | ||||||||
\(111\) | 2.40440 | 0.228216 | ||||||||
\(112\) | −4.75734 | −0.449526 | ||||||||
\(113\) | −4.96451 | −0.467021 | −0.233511 | − | 0.972354i | \(-0.575021\pi\) | ||||
−0.233511 | + | 0.972354i | \(0.575021\pi\) | |||||||
\(114\) | −13.1620 | −1.23273 | ||||||||
\(115\) | −5.07982 | −0.473696 | ||||||||
\(116\) | −1.77809 | −0.165091 | ||||||||
\(117\) | 3.73140 | 0.344968 | ||||||||
\(118\) | −15.1623 | −1.39581 | ||||||||
\(119\) | −8.09560 | −0.742123 | ||||||||
\(120\) | 4.80752 | 0.438864 | ||||||||
\(121\) | −9.61941 | −0.874492 | ||||||||
\(122\) | 21.7468 | 1.96887 | ||||||||
\(123\) | 6.51764 | 0.587676 | ||||||||
\(124\) | 5.28069 | 0.474220 | ||||||||
\(125\) | 11.9249 | 1.06659 | ||||||||
\(126\) | −1.58348 | −0.141067 | ||||||||
\(127\) | 4.90100 | 0.434893 | 0.217447 | − | 0.976072i | \(-0.430227\pi\) | ||||
0.217447 | + | 0.976072i | \(0.430227\pi\) | |||||||
\(128\) | −13.6425 | −1.20583 | ||||||||
\(129\) | −6.17846 | −0.543983 | ||||||||
\(130\) | 12.0184 | 1.05409 | ||||||||
\(131\) | 13.3143 | 1.16328 | 0.581639 | − | 0.813447i | \(-0.302412\pi\) | ||||
0.581639 | + | 0.813447i | \(0.302412\pi\) | |||||||
\(132\) | −0.596180 | −0.0518908 | ||||||||
\(133\) | −8.31210 | −0.720750 | ||||||||
\(134\) | −4.48055 | −0.387060 | ||||||||
\(135\) | 2.03406 | 0.175064 | ||||||||
\(136\) | −19.1340 | −1.64073 | ||||||||
\(137\) | 20.6490 | 1.76416 | 0.882082 | − | 0.471095i | \(-0.156141\pi\) | ||||
0.882082 | + | 0.471095i | \(0.156141\pi\) | |||||||
\(138\) | 3.95454 | 0.336632 | ||||||||
\(139\) | −7.72470 | −0.655201 | −0.327600 | − | 0.944816i | \(-0.606240\pi\) | ||||
−0.327600 | + | 0.944816i | \(0.606240\pi\) | |||||||
\(140\) | −1.03207 | −0.0872260 | ||||||||
\(141\) | 8.33923 | 0.702290 | ||||||||
\(142\) | −5.05664 | −0.424344 | ||||||||
\(143\) | 4.38433 | 0.366636 | ||||||||
\(144\) | −4.75734 | −0.396445 | ||||||||
\(145\) | 7.12807 | 0.591954 | ||||||||
\(146\) | 7.85578 | 0.650149 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −1.21998 | −0.100282 | ||||||||
\(149\) | −13.2763 | −1.08763 | −0.543817 | − | 0.839204i | \(-0.683021\pi\) | ||||
−0.543817 | + | 0.839204i | \(0.683021\pi\) | |||||||
\(150\) | −1.36589 | −0.111524 | ||||||||
\(151\) | 1.33666 | 0.108776 | 0.0543879 | − | 0.998520i | \(-0.482679\pi\) | ||||
0.0543879 | + | 0.998520i | \(0.482679\pi\) | |||||||
\(152\) | −19.6457 | −1.59347 | ||||||||
\(153\) | −8.09560 | −0.654491 | ||||||||
\(154\) | −1.86056 | −0.149928 | ||||||||
\(155\) | −21.1694 | −1.70037 | ||||||||
\(156\) | −1.89329 | −0.151585 | ||||||||
\(157\) | −5.99064 | −0.478105 | −0.239053 | − | 0.971007i | \(-0.576837\pi\) | ||||
−0.239053 | + | 0.971007i | \(0.576837\pi\) | |||||||
\(158\) | −16.9857 | −1.35131 | ||||||||
\(159\) | −4.21927 | −0.334610 | ||||||||
\(160\) | −5.70783 | −0.451244 | ||||||||
\(161\) | 2.49738 | 0.196821 | ||||||||
\(162\) | −1.58348 | −0.124410 | ||||||||
\(163\) | 10.6974 | 0.837886 | 0.418943 | − | 0.908012i | \(-0.362401\pi\) | ||||
0.418943 | + | 0.908012i | \(0.362401\pi\) | |||||||
\(164\) | −3.30701 | −0.258234 | ||||||||
\(165\) | 2.38999 | 0.186060 | ||||||||
\(166\) | 20.5577 | 1.59559 | ||||||||
\(167\) | −12.7413 | −0.985949 | −0.492975 | − | 0.870044i | \(-0.664090\pi\) | ||||
−0.492975 | + | 0.870044i | \(0.664090\pi\) | |||||||
\(168\) | −2.36350 | −0.182348 | ||||||||
\(169\) | 0.923340 | 0.0710261 | ||||||||
\(170\) | −26.0750 | −1.99986 | ||||||||
\(171\) | −8.31210 | −0.635642 | ||||||||
\(172\) | 3.13492 | 0.239035 | ||||||||
\(173\) | −17.7462 | −1.34922 | −0.674610 | − | 0.738174i | \(-0.735688\pi\) | ||||
−0.674610 | + | 0.738174i | \(0.735688\pi\) | |||||||
\(174\) | −5.54906 | −0.420673 | ||||||||
\(175\) | −0.862589 | −0.0652056 | ||||||||
\(176\) | −5.58979 | −0.421347 | ||||||||
\(177\) | −9.57535 | −0.719727 | ||||||||
\(178\) | 19.9982 | 1.49893 | ||||||||
\(179\) | −6.76582 | −0.505701 | −0.252850 | − | 0.967505i | \(-0.581368\pi\) | ||||
−0.252850 | + | 0.967505i | \(0.581368\pi\) | |||||||
\(180\) | −1.03207 | −0.0769261 | ||||||||
\(181\) | 11.0685 | 0.822716 | 0.411358 | − | 0.911474i | \(-0.365055\pi\) | ||||
0.411358 | + | 0.911474i | \(0.365055\pi\) | |||||||
\(182\) | −5.90858 | −0.437973 | ||||||||
\(183\) | 13.7336 | 1.01522 | ||||||||
\(184\) | 5.90256 | 0.435143 | ||||||||
\(185\) | 4.89071 | 0.359572 | ||||||||
\(186\) | 16.4800 | 1.20837 | ||||||||
\(187\) | −9.51220 | −0.695601 | ||||||||
\(188\) | −4.23128 | −0.308598 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −26.7723 | −1.94227 | ||||||||
\(191\) | −19.4885 | −1.41014 | −0.705068 | − | 0.709140i | \(-0.749084\pi\) | ||||
−0.705068 | + | 0.709140i | \(0.749084\pi\) | |||||||
\(192\) | −5.07125 | −0.365986 | ||||||||
\(193\) | 3.02241 | 0.217558 | 0.108779 | − | 0.994066i | \(-0.465306\pi\) | ||||
0.108779 | + | 0.994066i | \(0.465306\pi\) | |||||||
\(194\) | 19.4232 | 1.39450 | ||||||||
\(195\) | 7.58990 | 0.543524 | ||||||||
\(196\) | 0.507395 | 0.0362425 | ||||||||
\(197\) | −25.2988 | −1.80247 | −0.901233 | − | 0.433335i | \(-0.857337\pi\) | ||||
−0.901233 | + | 0.433335i | \(0.857337\pi\) | |||||||
\(198\) | −1.86056 | −0.132224 | ||||||||
\(199\) | 3.49513 | 0.247764 | 0.123882 | − | 0.992297i | \(-0.460466\pi\) | ||||
0.123882 | + | 0.992297i | \(0.460466\pi\) | |||||||
\(200\) | −2.03873 | −0.144160 | ||||||||
\(201\) | −2.82956 | −0.199582 | ||||||||
\(202\) | −16.4729 | −1.15903 | ||||||||
\(203\) | −3.50435 | −0.245957 | ||||||||
\(204\) | 4.10767 | 0.287594 | ||||||||
\(205\) | 13.2573 | 0.925929 | ||||||||
\(206\) | −24.1144 | −1.68013 | ||||||||
\(207\) | 2.49738 | 0.173580 | ||||||||
\(208\) | −17.7515 | −1.23085 | ||||||||
\(209\) | −9.76657 | −0.675568 | ||||||||
\(210\) | −3.22089 | −0.222262 | ||||||||
\(211\) | 6.26977 | 0.431629 | 0.215814 | − | 0.976434i | \(-0.430759\pi\) | ||||
0.215814 | + | 0.976434i | \(0.430759\pi\) | |||||||
\(212\) | 2.14084 | 0.147033 | ||||||||
\(213\) | −3.19338 | −0.218807 | ||||||||
\(214\) | −2.19846 | −0.150284 | ||||||||
\(215\) | −12.5674 | −0.857087 | ||||||||
\(216\) | −2.36350 | −0.160816 | ||||||||
\(217\) | 10.4075 | 0.706505 | ||||||||
\(218\) | −4.64988 | −0.314930 | ||||||||
\(219\) | 4.96110 | 0.335240 | ||||||||
\(220\) | −1.21267 | −0.0817580 | ||||||||
\(221\) | −30.2079 | −2.03200 | ||||||||
\(222\) | −3.80731 | −0.255530 | ||||||||
\(223\) | −3.40829 | −0.228236 | −0.114118 | − | 0.993467i | \(-0.536404\pi\) | ||||
−0.114118 | + | 0.993467i | \(0.536404\pi\) | |||||||
\(224\) | 2.80612 | 0.187492 | ||||||||
\(225\) | −0.862589 | −0.0575060 | ||||||||
\(226\) | 7.86117 | 0.522917 | ||||||||
\(227\) | −25.8890 | −1.71831 | −0.859156 | − | 0.511714i | \(-0.829011\pi\) | ||||
−0.859156 | + | 0.511714i | \(0.829011\pi\) | |||||||
\(228\) | 4.21751 | 0.279312 | ||||||||
\(229\) | −6.00764 | −0.396996 | −0.198498 | − | 0.980101i | \(-0.563606\pi\) | ||||
−0.198498 | + | 0.980101i | \(0.563606\pi\) | |||||||
\(230\) | 8.04377 | 0.530391 | ||||||||
\(231\) | −1.17498 | −0.0773082 | ||||||||
\(232\) | −8.28255 | −0.543776 | ||||||||
\(233\) | −10.3213 | −0.676168 | −0.338084 | − | 0.941116i | \(-0.609779\pi\) | ||||
−0.338084 | + | 0.941116i | \(0.609779\pi\) | |||||||
\(234\) | −5.90858 | −0.386256 | ||||||||
\(235\) | 16.9625 | 1.10651 | ||||||||
\(236\) | 4.85848 | 0.316260 | ||||||||
\(237\) | −10.7268 | −0.696783 | ||||||||
\(238\) | 12.8192 | 0.830945 | ||||||||
\(239\) | −16.2362 | −1.05023 | −0.525117 | − | 0.851030i | \(-0.675978\pi\) | ||||
−0.525117 | + | 0.851030i | \(0.675978\pi\) | |||||||
\(240\) | −9.67673 | −0.624630 | ||||||||
\(241\) | 12.5949 | 0.811310 | 0.405655 | − | 0.914026i | \(-0.367043\pi\) | ||||
0.405655 | + | 0.914026i | \(0.367043\pi\) | |||||||
\(242\) | 15.2321 | 0.979157 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −6.96836 | −0.446103 | ||||||||
\(245\) | −2.03406 | −0.129951 | ||||||||
\(246\) | −10.3205 | −0.658012 | ||||||||
\(247\) | −31.0158 | −1.97349 | ||||||||
\(248\) | 24.5981 | 1.56198 | ||||||||
\(249\) | 12.9827 | 0.822743 | ||||||||
\(250\) | −18.8827 | −1.19425 | ||||||||
\(251\) | 22.8035 | 1.43935 | 0.719673 | − | 0.694314i | \(-0.244292\pi\) | ||||
0.719673 | + | 0.694314i | \(0.244292\pi\) | |||||||
\(252\) | 0.507395 | 0.0319629 | ||||||||
\(253\) | 2.93438 | 0.184483 | ||||||||
\(254\) | −7.76061 | −0.486944 | ||||||||
\(255\) | −16.4670 | −1.03120 | ||||||||
\(256\) | 11.4600 | 0.716249 | ||||||||
\(257\) | 18.2621 | 1.13916 | 0.569580 | − | 0.821936i | \(-0.307106\pi\) | ||||
0.569580 | + | 0.821936i | \(0.307106\pi\) | |||||||
\(258\) | 9.78343 | 0.609090 | ||||||||
\(259\) | −2.40440 | −0.149402 | ||||||||
\(260\) | −3.85107 | −0.238833 | ||||||||
\(261\) | −3.50435 | −0.216914 | ||||||||
\(262\) | −21.0829 | −1.30251 | ||||||||
\(263\) | 26.3782 | 1.62655 | 0.813274 | − | 0.581881i | \(-0.197683\pi\) | ||||
0.813274 | + | 0.581881i | \(0.197683\pi\) | |||||||
\(264\) | −2.77708 | −0.170917 | ||||||||
\(265\) | −8.58226 | −0.527204 | ||||||||
\(266\) | 13.1620 | 0.807014 | ||||||||
\(267\) | 12.6293 | 0.772902 | ||||||||
\(268\) | 1.43571 | 0.0876997 | ||||||||
\(269\) | −7.27730 | −0.443705 | −0.221852 | − | 0.975080i | \(-0.571210\pi\) | ||||
−0.221852 | + | 0.975080i | \(0.571210\pi\) | |||||||
\(270\) | −3.22089 | −0.196017 | ||||||||
\(271\) | −10.6407 | −0.646378 | −0.323189 | − | 0.946334i | \(-0.604755\pi\) | ||||
−0.323189 | + | 0.946334i | \(0.604755\pi\) | |||||||
\(272\) | 38.5135 | 2.33523 | ||||||||
\(273\) | −3.73140 | −0.225835 | ||||||||
\(274\) | −32.6972 | −1.97531 | ||||||||
\(275\) | −1.01353 | −0.0611180 | ||||||||
\(276\) | −1.26716 | −0.0762738 | ||||||||
\(277\) | −30.1397 | −1.81092 | −0.905459 | − | 0.424434i | \(-0.860473\pi\) | ||||
−0.905459 | + | 0.424434i | \(0.860473\pi\) | |||||||
\(278\) | 12.2319 | 0.733619 | ||||||||
\(279\) | 10.4075 | 0.623079 | ||||||||
\(280\) | −4.80752 | −0.287304 | ||||||||
\(281\) | −21.8838 | −1.30548 | −0.652739 | − | 0.757583i | \(-0.726380\pi\) | ||||
−0.652739 | + | 0.757583i | \(0.726380\pi\) | |||||||
\(282\) | −13.2050 | −0.786345 | ||||||||
\(283\) | 15.4851 | 0.920495 | 0.460248 | − | 0.887791i | \(-0.347761\pi\) | ||||
0.460248 | + | 0.887791i | \(0.347761\pi\) | |||||||
\(284\) | 1.62031 | 0.0961474 | ||||||||
\(285\) | −16.9073 | −1.00150 | ||||||||
\(286\) | −6.94248 | −0.410517 | ||||||||
\(287\) | −6.51764 | −0.384724 | ||||||||
\(288\) | 2.80612 | 0.165352 | ||||||||
\(289\) | 48.5388 | 2.85522 | ||||||||
\(290\) | −11.2871 | −0.662803 | ||||||||
\(291\) | 12.2662 | 0.719055 | ||||||||
\(292\) | −2.51724 | −0.147310 | ||||||||
\(293\) | 9.98207 | 0.583158 | 0.291579 | − | 0.956547i | \(-0.405819\pi\) | ||||
0.291579 | + | 0.956547i | \(0.405819\pi\) | |||||||
\(294\) | 1.58348 | 0.0923502 | ||||||||
\(295\) | −19.4769 | −1.13399 | ||||||||
\(296\) | −5.68282 | −0.330307 | ||||||||
\(297\) | −1.17498 | −0.0681794 | ||||||||
\(298\) | 21.0226 | 1.21781 | ||||||||
\(299\) | 9.31871 | 0.538915 | ||||||||
\(300\) | 0.437673 | 0.0252691 | ||||||||
\(301\) | 6.17846 | 0.356120 | ||||||||
\(302\) | −2.11657 | −0.121795 | ||||||||
\(303\) | −10.4030 | −0.597636 | ||||||||
\(304\) | 39.5435 | 2.26797 | ||||||||
\(305\) | 27.9350 | 1.59955 | ||||||||
\(306\) | 12.8192 | 0.732824 | ||||||||
\(307\) | 4.79874 | 0.273879 | 0.136939 | − | 0.990579i | \(-0.456273\pi\) | ||||
0.136939 | + | 0.990579i | \(0.456273\pi\) | |||||||
\(308\) | 0.596180 | 0.0339705 | ||||||||
\(309\) | −15.2288 | −0.866336 | ||||||||
\(310\) | 33.5213 | 1.90388 | ||||||||
\(311\) | −5.91843 | −0.335603 | −0.167802 | − | 0.985821i | \(-0.553667\pi\) | ||||
−0.167802 | + | 0.985821i | \(0.553667\pi\) | |||||||
\(312\) | −8.81918 | −0.499288 | ||||||||
\(313\) | 8.13144 | 0.459616 | 0.229808 | − | 0.973236i | \(-0.426190\pi\) | ||||
0.229808 | + | 0.973236i | \(0.426190\pi\) | |||||||
\(314\) | 9.48603 | 0.535328 | ||||||||
\(315\) | −2.03406 | −0.114606 | ||||||||
\(316\) | 5.44274 | 0.306178 | ||||||||
\(317\) | 4.12351 | 0.231600 | 0.115800 | − | 0.993273i | \(-0.463057\pi\) | ||||
0.115800 | + | 0.993273i | \(0.463057\pi\) | |||||||
\(318\) | 6.68111 | 0.374658 | ||||||||
\(319\) | −4.11755 | −0.230539 | ||||||||
\(320\) | −10.3152 | −0.576640 | ||||||||
\(321\) | −1.38838 | −0.0774916 | ||||||||
\(322\) | −3.95454 | −0.220378 | ||||||||
\(323\) | 67.2914 | 3.74420 | ||||||||
\(324\) | 0.507395 | 0.0281886 | ||||||||
\(325\) | −3.21867 | −0.178539 | ||||||||
\(326\) | −16.9391 | −0.938170 | ||||||||
\(327\) | −2.93650 | −0.162389 | ||||||||
\(328\) | −15.4045 | −0.850569 | ||||||||
\(329\) | −8.33923 | −0.459757 | ||||||||
\(330\) | −3.78449 | −0.208329 | ||||||||
\(331\) | −7.88009 | −0.433129 | −0.216565 | − | 0.976268i | \(-0.569485\pi\) | ||||
−0.216565 | + | 0.976268i | \(0.569485\pi\) | |||||||
\(332\) | −6.58734 | −0.361527 | ||||||||
\(333\) | −2.40440 | −0.131761 | ||||||||
\(334\) | 20.1755 | 1.10395 | ||||||||
\(335\) | −5.75551 | −0.314457 | ||||||||
\(336\) | 4.75734 | 0.259534 | ||||||||
\(337\) | 5.71700 | 0.311425 | 0.155712 | − | 0.987802i | \(-0.450233\pi\) | ||||
0.155712 | + | 0.987802i | \(0.450233\pi\) | |||||||
\(338\) | −1.46209 | −0.0795270 | ||||||||
\(339\) | 4.96451 | 0.269635 | ||||||||
\(340\) | 8.35525 | 0.453127 | ||||||||
\(341\) | 12.2286 | 0.662215 | ||||||||
\(342\) | 13.1620 | 0.711720 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 14.6028 | 0.787330 | ||||||||
\(345\) | 5.07982 | 0.273488 | ||||||||
\(346\) | 28.1007 | 1.51070 | ||||||||
\(347\) | −17.0545 | −0.915536 | −0.457768 | − | 0.889072i | \(-0.651351\pi\) | ||||
−0.457768 | + | 0.889072i | \(0.651351\pi\) | |||||||
\(348\) | 1.77809 | 0.0953156 | ||||||||
\(349\) | 7.88885 | 0.422280 | 0.211140 | − | 0.977456i | \(-0.432282\pi\) | ||||
0.211140 | + | 0.977456i | \(0.432282\pi\) | |||||||
\(350\) | 1.36589 | 0.0730099 | ||||||||
\(351\) | −3.73140 | −0.199167 | ||||||||
\(352\) | 3.29715 | 0.175739 | ||||||||
\(353\) | −12.6774 | −0.674752 | −0.337376 | − | 0.941370i | \(-0.609539\pi\) | ||||
−0.337376 | + | 0.941370i | \(0.609539\pi\) | |||||||
\(354\) | 15.1623 | 0.805869 | ||||||||
\(355\) | −6.49554 | −0.344747 | ||||||||
\(356\) | −6.40805 | −0.339626 | ||||||||
\(357\) | 8.09560 | 0.428465 | ||||||||
\(358\) | 10.7135 | 0.566226 | ||||||||
\(359\) | −34.5229 | −1.82205 | −0.911023 | − | 0.412355i | \(-0.864706\pi\) | ||||
−0.911023 | + | 0.412355i | \(0.864706\pi\) | |||||||
\(360\) | −4.80752 | −0.253378 | ||||||||
\(361\) | 50.0910 | 2.63637 | ||||||||
\(362\) | −17.5267 | −0.921183 | ||||||||
\(363\) | 9.61941 | 0.504888 | ||||||||
\(364\) | 1.89329 | 0.0992355 | ||||||||
\(365\) | 10.0912 | 0.528197 | ||||||||
\(366\) | −21.7468 | −1.13672 | ||||||||
\(367\) | 4.22048 | 0.220307 | 0.110154 | − | 0.993915i | \(-0.464866\pi\) | ||||
0.110154 | + | 0.993915i | \(0.464866\pi\) | |||||||
\(368\) | −11.8809 | −0.619333 | ||||||||
\(369\) | −6.51764 | −0.339295 | ||||||||
\(370\) | −7.74432 | −0.402608 | ||||||||
\(371\) | 4.21927 | 0.219054 | ||||||||
\(372\) | −5.28069 | −0.273791 | ||||||||
\(373\) | 33.9458 | 1.75765 | 0.878823 | − | 0.477148i | \(-0.158329\pi\) | ||||
0.878823 | + | 0.477148i | \(0.158329\pi\) | |||||||
\(374\) | 15.0623 | 0.778854 | ||||||||
\(375\) | −11.9249 | −0.615798 | ||||||||
\(376\) | −19.7098 | −1.01646 | ||||||||
\(377\) | −13.0761 | −0.673455 | ||||||||
\(378\) | 1.58348 | 0.0814452 | ||||||||
\(379\) | 32.6135 | 1.67524 | 0.837620 | − | 0.546253i | \(-0.183946\pi\) | ||||
0.837620 | + | 0.546253i | \(0.183946\pi\) | |||||||
\(380\) | 8.57869 | 0.440077 | ||||||||
\(381\) | −4.90100 | −0.251086 | ||||||||
\(382\) | 30.8595 | 1.57891 | ||||||||
\(383\) | −1.00000 | −0.0510976 | ||||||||
\(384\) | 13.6425 | 0.696188 | ||||||||
\(385\) | −2.38999 | −0.121805 | ||||||||
\(386\) | −4.78591 | −0.243597 | ||||||||
\(387\) | 6.17846 | 0.314069 | ||||||||
\(388\) | −6.22378 | −0.315965 | ||||||||
\(389\) | 19.2296 | 0.974978 | 0.487489 | − | 0.873129i | \(-0.337913\pi\) | ||||
0.487489 | + | 0.873129i | \(0.337913\pi\) | |||||||
\(390\) | −12.0184 | −0.608576 | ||||||||
\(391\) | −20.2178 | −1.02246 | ||||||||
\(392\) | 2.36350 | 0.119375 | ||||||||
\(393\) | −13.3143 | −0.671619 | ||||||||
\(394\) | 40.0600 | 2.01820 | ||||||||
\(395\) | −21.8191 | −1.09784 | ||||||||
\(396\) | 0.596180 | 0.0299592 | ||||||||
\(397\) | −7.72827 | −0.387871 | −0.193935 | − | 0.981014i | \(-0.562125\pi\) | ||||
−0.193935 | + | 0.981014i | \(0.562125\pi\) | |||||||
\(398\) | −5.53446 | −0.277417 | ||||||||
\(399\) | 8.31210 | 0.416125 | ||||||||
\(400\) | 4.10363 | 0.205182 | ||||||||
\(401\) | 33.9001 | 1.69289 | 0.846444 | − | 0.532477i | \(-0.178739\pi\) | ||||
0.846444 | + | 0.532477i | \(0.178739\pi\) | |||||||
\(402\) | 4.48055 | 0.223469 | ||||||||
\(403\) | 38.8344 | 1.93448 | ||||||||
\(404\) | 5.27842 | 0.262611 | ||||||||
\(405\) | −2.03406 | −0.101073 | ||||||||
\(406\) | 5.54906 | 0.275395 | ||||||||
\(407\) | −2.82513 | −0.140037 | ||||||||
\(408\) | 19.1340 | 0.947274 | ||||||||
\(409\) | 1.66653 | 0.0824048 | 0.0412024 | − | 0.999151i | \(-0.486881\pi\) | ||||
0.0412024 | + | 0.999151i | \(0.486881\pi\) | |||||||
\(410\) | −20.9926 | −1.03675 | ||||||||
\(411\) | −20.6490 | −1.01854 | ||||||||
\(412\) | 7.72701 | 0.380683 | ||||||||
\(413\) | 9.57535 | 0.471172 | ||||||||
\(414\) | −3.95454 | −0.194355 | ||||||||
\(415\) | 26.4076 | 1.29630 | ||||||||
\(416\) | 10.4708 | 0.513372 | ||||||||
\(417\) | 7.72470 | 0.378280 | ||||||||
\(418\) | 15.4651 | 0.756424 | ||||||||
\(419\) | 27.9606 | 1.36597 | 0.682983 | − | 0.730434i | \(-0.260682\pi\) | ||||
0.682983 | + | 0.730434i | \(0.260682\pi\) | |||||||
\(420\) | 1.03207 | 0.0503600 | ||||||||
\(421\) | −0.833488 | −0.0406217 | −0.0203109 | − | 0.999794i | \(-0.506466\pi\) | ||||
−0.0203109 | + | 0.999794i | \(0.506466\pi\) | |||||||
\(422\) | −9.92803 | −0.483289 | ||||||||
\(423\) | −8.33923 | −0.405467 | ||||||||
\(424\) | 9.97227 | 0.484296 | ||||||||
\(425\) | 6.98318 | 0.338734 | ||||||||
\(426\) | 5.05664 | 0.244995 | ||||||||
\(427\) | −13.7336 | −0.664616 | ||||||||
\(428\) | 0.704455 | 0.0340511 | ||||||||
\(429\) | −4.38433 | −0.211677 | ||||||||
\(430\) | 19.9001 | 0.959669 | ||||||||
\(431\) | −13.2665 | −0.639025 | −0.319513 | − | 0.947582i | \(-0.603519\pi\) | ||||
−0.319513 | + | 0.947582i | \(0.603519\pi\) | |||||||
\(432\) | 4.75734 | 0.228888 | ||||||||
\(433\) | −26.6116 | −1.27887 | −0.639436 | − | 0.768845i | \(-0.720832\pi\) | ||||
−0.639436 | + | 0.768845i | \(0.720832\pi\) | |||||||
\(434\) | −16.4800 | −0.791064 | ||||||||
\(435\) | −7.12807 | −0.341765 | ||||||||
\(436\) | 1.48997 | 0.0713565 | ||||||||
\(437\) | −20.7584 | −0.993011 | ||||||||
\(438\) | −7.85578 | −0.375364 | ||||||||
\(439\) | −3.42227 | −0.163336 | −0.0816680 | − | 0.996660i | \(-0.526025\pi\) | ||||
−0.0816680 | + | 0.996660i | \(0.526025\pi\) | |||||||
\(440\) | −5.64875 | −0.269294 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 47.8335 | 2.27521 | ||||||||
\(443\) | 30.7219 | 1.45964 | 0.729821 | − | 0.683638i | \(-0.239603\pi\) | ||||
0.729821 | + | 0.683638i | \(0.239603\pi\) | |||||||
\(444\) | 1.21998 | 0.0578978 | ||||||||
\(445\) | 25.6888 | 1.21777 | ||||||||
\(446\) | 5.39694 | 0.255553 | ||||||||
\(447\) | 13.2763 | 0.627946 | ||||||||
\(448\) | 5.07125 | 0.239594 | ||||||||
\(449\) | 21.0431 | 0.993087 | 0.496544 | − | 0.868012i | \(-0.334602\pi\) | ||||
0.496544 | + | 0.868012i | \(0.334602\pi\) | |||||||
\(450\) | 1.36589 | 0.0643886 | ||||||||
\(451\) | −7.65811 | −0.360606 | ||||||||
\(452\) | −2.51896 | −0.118482 | ||||||||
\(453\) | −1.33666 | −0.0628017 | ||||||||
\(454\) | 40.9946 | 1.92397 | ||||||||
\(455\) | −7.58990 | −0.355820 | ||||||||
\(456\) | 19.6457 | 0.919993 | ||||||||
\(457\) | 25.9974 | 1.21611 | 0.608054 | − | 0.793896i | \(-0.291950\pi\) | ||||
0.608054 | + | 0.793896i | \(0.291950\pi\) | |||||||
\(458\) | 9.51296 | 0.444511 | ||||||||
\(459\) | 8.09560 | 0.377870 | ||||||||
\(460\) | −2.57747 | −0.120175 | ||||||||
\(461\) | 20.8371 | 0.970479 | 0.485239 | − | 0.874381i | \(-0.338732\pi\) | ||||
0.485239 | + | 0.874381i | \(0.338732\pi\) | |||||||
\(462\) | 1.86056 | 0.0865609 | ||||||||
\(463\) | 33.4805 | 1.55597 | 0.777986 | − | 0.628281i | \(-0.216241\pi\) | ||||
0.777986 | + | 0.628281i | \(0.216241\pi\) | |||||||
\(464\) | 16.6714 | 0.773950 | ||||||||
\(465\) | 21.1694 | 0.981709 | ||||||||
\(466\) | 16.3435 | 0.757096 | ||||||||
\(467\) | −15.8486 | −0.733386 | −0.366693 | − | 0.930342i | \(-0.619510\pi\) | ||||
−0.366693 | + | 0.930342i | \(0.619510\pi\) | |||||||
\(468\) | 1.89329 | 0.0875175 | ||||||||
\(469\) | 2.82956 | 0.130657 | ||||||||
\(470\) | −26.8597 | −1.23895 | ||||||||
\(471\) | 5.99064 | 0.276034 | ||||||||
\(472\) | 22.6314 | 1.04169 | ||||||||
\(473\) | 7.25958 | 0.333796 | ||||||||
\(474\) | 16.9857 | 0.780179 | ||||||||
\(475\) | 7.16993 | 0.328979 | ||||||||
\(476\) | −4.10767 | −0.188275 | ||||||||
\(477\) | 4.21927 | 0.193187 | ||||||||
\(478\) | 25.7097 | 1.17593 | ||||||||
\(479\) | 34.1683 | 1.56119 | 0.780595 | − | 0.625037i | \(-0.214916\pi\) | ||||
0.780595 | + | 0.625037i | \(0.214916\pi\) | |||||||
\(480\) | 5.70783 | 0.260526 | ||||||||
\(481\) | −8.97179 | −0.409078 | ||||||||
\(482\) | −19.9437 | −0.908413 | ||||||||
\(483\) | −2.49738 | −0.113635 | ||||||||
\(484\) | −4.88084 | −0.221856 | ||||||||
\(485\) | 24.9501 | 1.13293 | ||||||||
\(486\) | 1.58348 | 0.0718279 | ||||||||
\(487\) | −37.5504 | −1.70157 | −0.850785 | − | 0.525513i | \(-0.823873\pi\) | ||||
−0.850785 | + | 0.525513i | \(0.823873\pi\) | |||||||
\(488\) | −32.4594 | −1.46937 | ||||||||
\(489\) | −10.6974 | −0.483754 | ||||||||
\(490\) | 3.22089 | 0.145505 | ||||||||
\(491\) | −14.0685 | −0.634904 | −0.317452 | − | 0.948274i | \(-0.602827\pi\) | ||||
−0.317452 | + | 0.948274i | \(0.602827\pi\) | |||||||
\(492\) | 3.30701 | 0.149092 | ||||||||
\(493\) | 28.3698 | 1.27771 | ||||||||
\(494\) | 49.1127 | 2.20968 | ||||||||
\(495\) | −2.38999 | −0.107422 | ||||||||
\(496\) | −49.5118 | −2.22315 | ||||||||
\(497\) | 3.19338 | 0.143243 | ||||||||
\(498\) | −20.5577 | −0.921214 | ||||||||
\(499\) | 7.63867 | 0.341954 | 0.170977 | − | 0.985275i | \(-0.445308\pi\) | ||||
0.170977 | + | 0.985275i | \(0.445308\pi\) | |||||||
\(500\) | 6.05062 | 0.270592 | ||||||||
\(501\) | 12.7413 | 0.569238 | ||||||||
\(502\) | −36.1088 | −1.61161 | ||||||||
\(503\) | −13.4944 | −0.601686 | −0.300843 | − | 0.953674i | \(-0.597268\pi\) | ||||
−0.300843 | + | 0.953674i | \(0.597268\pi\) | |||||||
\(504\) | 2.36350 | 0.105279 | ||||||||
\(505\) | −21.1603 | −0.941623 | ||||||||
\(506\) | −4.64651 | −0.206563 | ||||||||
\(507\) | −0.923340 | −0.0410070 | ||||||||
\(508\) | 2.48674 | 0.110331 | ||||||||
\(509\) | −2.95066 | −0.130786 | −0.0653928 | − | 0.997860i | \(-0.520830\pi\) | ||||
−0.0653928 | + | 0.997860i | \(0.520830\pi\) | |||||||
\(510\) | 26.0750 | 1.15462 | ||||||||
\(511\) | −4.96110 | −0.219466 | ||||||||
\(512\) | 9.13830 | 0.403860 | ||||||||
\(513\) | 8.31210 | 0.366988 | ||||||||
\(514\) | −28.9176 | −1.27550 | ||||||||
\(515\) | −30.9763 | −1.36498 | ||||||||
\(516\) | −3.13492 | −0.138007 | ||||||||
\(517\) | −9.79846 | −0.430936 | ||||||||
\(518\) | 3.80731 | 0.167284 | ||||||||
\(519\) | 17.7462 | 0.778973 | ||||||||
\(520\) | −17.9388 | −0.786667 | ||||||||
\(521\) | −16.1698 | −0.708413 | −0.354206 | − | 0.935167i | \(-0.615249\pi\) | ||||
−0.354206 | + | 0.935167i | \(0.615249\pi\) | |||||||
\(522\) | 5.54906 | 0.242876 | ||||||||
\(523\) | 23.4396 | 1.02494 | 0.512471 | − | 0.858704i | \(-0.328730\pi\) | ||||
0.512471 | + | 0.858704i | \(0.328730\pi\) | |||||||
\(524\) | 6.75562 | 0.295121 | ||||||||
\(525\) | 0.862589 | 0.0376465 | ||||||||
\(526\) | −41.7692 | −1.82122 | ||||||||
\(527\) | −84.2547 | −3.67019 | ||||||||
\(528\) | 5.58979 | 0.243265 | ||||||||
\(529\) | −16.7631 | −0.728831 | ||||||||
\(530\) | 13.5898 | 0.590303 | ||||||||
\(531\) | 9.57535 | 0.415535 | ||||||||
\(532\) | −4.21751 | −0.182852 | ||||||||
\(533\) | −24.3199 | −1.05341 | ||||||||
\(534\) | −19.9982 | −0.865408 | ||||||||
\(535\) | −2.82404 | −0.122094 | ||||||||
\(536\) | 6.68769 | 0.288864 | ||||||||
\(537\) | 6.76582 | 0.291967 | ||||||||
\(538\) | 11.5234 | 0.496810 | ||||||||
\(539\) | 1.17498 | 0.0506101 | ||||||||
\(540\) | 1.03207 | 0.0444133 | ||||||||
\(541\) | −36.5762 | −1.57253 | −0.786267 | − | 0.617887i | \(-0.787989\pi\) | ||||
−0.786267 | + | 0.617887i | \(0.787989\pi\) | |||||||
\(542\) | 16.8493 | 0.723741 | ||||||||
\(543\) | −11.0685 | −0.474995 | ||||||||
\(544\) | −22.7173 | −0.973994 | ||||||||
\(545\) | −5.97303 | −0.255857 | ||||||||
\(546\) | 5.90858 | 0.252864 | ||||||||
\(547\) | 27.1642 | 1.16146 | 0.580728 | − | 0.814098i | \(-0.302768\pi\) | ||||
0.580728 | + | 0.814098i | \(0.302768\pi\) | |||||||
\(548\) | 10.4772 | 0.447564 | ||||||||
\(549\) | −13.7336 | −0.586136 | ||||||||
\(550\) | 1.60490 | 0.0684330 | ||||||||
\(551\) | 29.1285 | 1.24092 | ||||||||
\(552\) | −5.90256 | −0.251230 | ||||||||
\(553\) | 10.7268 | 0.456152 | ||||||||
\(554\) | 47.7255 | 2.02766 | ||||||||
\(555\) | −4.89071 | −0.207599 | ||||||||
\(556\) | −3.91947 | −0.166223 | ||||||||
\(557\) | 17.2971 | 0.732901 | 0.366451 | − | 0.930438i | \(-0.380573\pi\) | ||||
0.366451 | + | 0.930438i | \(0.380573\pi\) | |||||||
\(558\) | −16.4800 | −0.697652 | ||||||||
\(559\) | 23.0543 | 0.975092 | ||||||||
\(560\) | 9.67673 | 0.408916 | ||||||||
\(561\) | 9.51220 | 0.401605 | ||||||||
\(562\) | 34.6525 | 1.46173 | ||||||||
\(563\) | −34.5133 | −1.45456 | −0.727280 | − | 0.686341i | \(-0.759216\pi\) | ||||
−0.727280 | + | 0.686341i | \(0.759216\pi\) | |||||||
\(564\) | 4.23128 | 0.178169 | ||||||||
\(565\) | 10.0981 | 0.424831 | ||||||||
\(566\) | −24.5203 | −1.03067 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 7.54757 | 0.316689 | ||||||||
\(569\) | 8.65891 | 0.363000 | 0.181500 | − | 0.983391i | \(-0.441905\pi\) | ||||
0.181500 | + | 0.983391i | \(0.441905\pi\) | |||||||
\(570\) | 26.7723 | 1.12137 | ||||||||
\(571\) | −4.29822 | −0.179875 | −0.0899375 | − | 0.995947i | \(-0.528667\pi\) | ||||
−0.0899375 | + | 0.995947i | \(0.528667\pi\) | |||||||
\(572\) | 2.22459 | 0.0930146 | ||||||||
\(573\) | 19.4885 | 0.814142 | ||||||||
\(574\) | 10.3205 | 0.430770 | ||||||||
\(575\) | −2.15421 | −0.0898368 | ||||||||
\(576\) | 5.07125 | 0.211302 | ||||||||
\(577\) | 36.4562 | 1.51769 | 0.758845 | − | 0.651271i | \(-0.225764\pi\) | ||||
0.758845 | + | 0.651271i | \(0.225764\pi\) | |||||||
\(578\) | −76.8600 | −3.19695 | ||||||||
\(579\) | −3.02241 | −0.125607 | ||||||||
\(580\) | 3.61675 | 0.150177 | ||||||||
\(581\) | −12.9827 | −0.538612 | ||||||||
\(582\) | −19.4232 | −0.805116 | ||||||||
\(583\) | 4.95757 | 0.205322 | ||||||||
\(584\) | −11.7256 | −0.485208 | ||||||||
\(585\) | −7.58990 | −0.313804 | ||||||||
\(586\) | −15.8064 | −0.652955 | ||||||||
\(587\) | 24.6640 | 1.01799 | 0.508996 | − | 0.860769i | \(-0.330017\pi\) | ||||
0.508996 | + | 0.860769i | \(0.330017\pi\) | |||||||
\(588\) | −0.507395 | −0.0209246 | ||||||||
\(589\) | −86.5079 | −3.56449 | ||||||||
\(590\) | 30.8411 | 1.26971 | ||||||||
\(591\) | 25.2988 | 1.04065 | ||||||||
\(592\) | 11.4386 | 0.470122 | ||||||||
\(593\) | −3.78538 | −0.155447 | −0.0777234 | − | 0.996975i | \(-0.524765\pi\) | ||||
−0.0777234 | + | 0.996975i | \(0.524765\pi\) | |||||||
\(594\) | 1.86056 | 0.0763396 | ||||||||
\(595\) | 16.4670 | 0.675080 | ||||||||
\(596\) | −6.73631 | −0.275930 | ||||||||
\(597\) | −3.49513 | −0.143046 | ||||||||
\(598\) | −14.7560 | −0.603416 | ||||||||
\(599\) | 21.6900 | 0.886228 | 0.443114 | − | 0.896465i | \(-0.353874\pi\) | ||||
0.443114 | + | 0.896465i | \(0.353874\pi\) | |||||||
\(600\) | 2.03873 | 0.0832310 | ||||||||
\(601\) | 0.767439 | 0.0313045 | 0.0156522 | − | 0.999877i | \(-0.495018\pi\) | ||||
0.0156522 | + | 0.999877i | \(0.495018\pi\) | |||||||
\(602\) | −9.78343 | −0.398743 | ||||||||
\(603\) | 2.82956 | 0.115229 | ||||||||
\(604\) | 0.678214 | 0.0275961 | ||||||||
\(605\) | 19.5665 | 0.795491 | ||||||||
\(606\) | 16.4729 | 0.669165 | ||||||||
\(607\) | −10.5297 | −0.427386 | −0.213693 | − | 0.976901i | \(-0.568549\pi\) | ||||
−0.213693 | + | 0.976901i | \(0.568549\pi\) | |||||||
\(608\) | −23.3248 | −0.945944 | ||||||||
\(609\) | 3.50435 | 0.142004 | ||||||||
\(610\) | −44.2344 | −1.79100 | ||||||||
\(611\) | −31.1170 | −1.25886 | ||||||||
\(612\) | −4.10767 | −0.166043 | ||||||||
\(613\) | 14.3641 | 0.580161 | 0.290080 | − | 0.957002i | \(-0.406318\pi\) | ||||
0.290080 | + | 0.957002i | \(0.406318\pi\) | |||||||
\(614\) | −7.59869 | −0.306658 | ||||||||
\(615\) | −13.2573 | −0.534585 | ||||||||
\(616\) | 2.77708 | 0.111892 | ||||||||
\(617\) | 12.2239 | 0.492114 | 0.246057 | − | 0.969255i | \(-0.420865\pi\) | ||||
0.246057 | + | 0.969255i | \(0.420865\pi\) | |||||||
\(618\) | 24.1144 | 0.970025 | ||||||||
\(619\) | −49.0827 | −1.97280 | −0.986400 | − | 0.164363i | \(-0.947443\pi\) | ||||
−0.986400 | + | 0.164363i | \(0.947443\pi\) | |||||||
\(620\) | −10.7413 | −0.431379 | ||||||||
\(621\) | −2.49738 | −0.100216 | ||||||||
\(622\) | 9.37168 | 0.375770 | ||||||||
\(623\) | −12.6293 | −0.505983 | ||||||||
\(624\) | 17.7515 | 0.710630 | ||||||||
\(625\) | −19.9430 | −0.797720 | ||||||||
\(626\) | −12.8759 | −0.514626 | ||||||||
\(627\) | 9.76657 | 0.390039 | ||||||||
\(628\) | −3.03962 | −0.121294 | ||||||||
\(629\) | 19.4651 | 0.776124 | ||||||||
\(630\) | 3.22089 | 0.128323 | ||||||||
\(631\) | 27.3662 | 1.08943 | 0.544716 | − | 0.838620i | \(-0.316637\pi\) | ||||
0.544716 | + | 0.838620i | \(0.316637\pi\) | |||||||
\(632\) | 25.3529 | 1.00849 | ||||||||
\(633\) | −6.26977 | −0.249201 | ||||||||
\(634\) | −6.52948 | −0.259319 | ||||||||
\(635\) | −9.96894 | −0.395605 | ||||||||
\(636\) | −2.14084 | −0.0848897 | ||||||||
\(637\) | 3.73140 | 0.147843 | ||||||||
\(638\) | 6.52005 | 0.258131 | ||||||||
\(639\) | 3.19338 | 0.126328 | ||||||||
\(640\) | 27.7496 | 1.09690 | ||||||||
\(641\) | 30.0221 | 1.18580 | 0.592900 | − | 0.805276i | \(-0.297983\pi\) | ||||
0.592900 | + | 0.805276i | \(0.297983\pi\) | |||||||
\(642\) | 2.19846 | 0.0867663 | ||||||||
\(643\) | 36.6432 | 1.44507 | 0.722534 | − | 0.691335i | \(-0.242977\pi\) | ||||
0.722534 | + | 0.691335i | \(0.242977\pi\) | |||||||
\(644\) | 1.26716 | 0.0499329 | ||||||||
\(645\) | 12.5674 | 0.494840 | ||||||||
\(646\) | −106.554 | −4.19233 | ||||||||
\(647\) | 17.2026 | 0.676306 | 0.338153 | − | 0.941091i | \(-0.390198\pi\) | ||||
0.338153 | + | 0.941091i | \(0.390198\pi\) | |||||||
\(648\) | 2.36350 | 0.0928472 | ||||||||
\(649\) | 11.2509 | 0.441635 | ||||||||
\(650\) | 5.09668 | 0.199908 | ||||||||
\(651\) | −10.4075 | −0.407901 | ||||||||
\(652\) | 5.42781 | 0.212570 | ||||||||
\(653\) | 14.1311 | 0.552993 | 0.276496 | − | 0.961015i | \(-0.410827\pi\) | ||||
0.276496 | + | 0.961015i | \(0.410827\pi\) | |||||||
\(654\) | 4.64988 | 0.181825 | ||||||||
\(655\) | −27.0822 | −1.05819 | ||||||||
\(656\) | 31.0066 | 1.21060 | ||||||||
\(657\) | −4.96110 | −0.193551 | ||||||||
\(658\) | 13.2050 | 0.514783 | ||||||||
\(659\) | 19.4818 | 0.758901 | 0.379451 | − | 0.925212i | \(-0.376113\pi\) | ||||
0.379451 | + | 0.925212i | \(0.376113\pi\) | |||||||
\(660\) | 1.21267 | 0.0472030 | ||||||||
\(661\) | −22.5821 | −0.878344 | −0.439172 | − | 0.898403i | \(-0.644728\pi\) | ||||
−0.439172 | + | 0.898403i | \(0.644728\pi\) | |||||||
\(662\) | 12.4779 | 0.484969 | ||||||||
\(663\) | 30.2079 | 1.17318 | ||||||||
\(664\) | −30.6846 | −1.19079 | ||||||||
\(665\) | 16.9073 | 0.655638 | ||||||||
\(666\) | 3.80731 | 0.147530 | ||||||||
\(667\) | −8.75169 | −0.338867 | ||||||||
\(668\) | −6.46485 | −0.250133 | ||||||||
\(669\) | 3.40829 | 0.131772 | ||||||||
\(670\) | 9.11371 | 0.352093 | ||||||||
\(671\) | −16.1368 | −0.622952 | ||||||||
\(672\) | −2.80612 | −0.108249 | ||||||||
\(673\) | −19.5706 | −0.754390 | −0.377195 | − | 0.926134i | \(-0.623111\pi\) | ||||
−0.377195 | + | 0.926134i | \(0.623111\pi\) | |||||||
\(674\) | −9.05273 | −0.348698 | ||||||||
\(675\) | 0.862589 | 0.0332011 | ||||||||
\(676\) | 0.468498 | 0.0180191 | ||||||||
\(677\) | −29.1476 | −1.12023 | −0.560117 | − | 0.828413i | \(-0.689244\pi\) | ||||
−0.560117 | + | 0.828413i | \(0.689244\pi\) | |||||||
\(678\) | −7.86117 | −0.301907 | ||||||||
\(679\) | −12.2662 | −0.470732 | ||||||||
\(680\) | 38.9197 | 1.49250 | ||||||||
\(681\) | 25.8890 | 0.992068 | ||||||||
\(682\) | −19.3637 | −0.741474 | ||||||||
\(683\) | −40.4250 | −1.54682 | −0.773410 | − | 0.633906i | \(-0.781450\pi\) | ||||
−0.773410 | + | 0.633906i | \(0.781450\pi\) | |||||||
\(684\) | −4.21751 | −0.161261 | ||||||||
\(685\) | −42.0014 | −1.60479 | ||||||||
\(686\) | −1.58348 | −0.0604574 | ||||||||
\(687\) | 6.00764 | 0.229206 | ||||||||
\(688\) | −29.3930 | −1.12060 | ||||||||
\(689\) | 15.7438 | 0.599791 | ||||||||
\(690\) | −8.04377 | −0.306221 | ||||||||
\(691\) | 47.9232 | 1.82308 | 0.911541 | − | 0.411208i | \(-0.134893\pi\) | ||||
0.911541 | + | 0.411208i | \(0.134893\pi\) | |||||||
\(692\) | −9.00434 | −0.342294 | ||||||||
\(693\) | 1.17498 | 0.0446339 | ||||||||
\(694\) | 27.0054 | 1.02511 | ||||||||
\(695\) | 15.7125 | 0.596010 | ||||||||
\(696\) | 8.28255 | 0.313949 | ||||||||
\(697\) | 52.7642 | 1.99859 | ||||||||
\(698\) | −12.4918 | −0.472822 | ||||||||
\(699\) | 10.3213 | 0.390386 | ||||||||
\(700\) | −0.437673 | −0.0165425 | ||||||||
\(701\) | −44.1271 | −1.66666 | −0.833329 | − | 0.552778i | \(-0.813568\pi\) | ||||
−0.833329 | + | 0.552778i | \(0.813568\pi\) | |||||||
\(702\) | 5.90858 | 0.223005 | ||||||||
\(703\) | 19.9856 | 0.753773 | ||||||||
\(704\) | 5.95864 | 0.224575 | ||||||||
\(705\) | −16.9625 | −0.638846 | ||||||||
\(706\) | 20.0744 | 0.755510 | ||||||||
\(707\) | 10.4030 | 0.391245 | ||||||||
\(708\) | −4.85848 | −0.182593 | ||||||||
\(709\) | −33.6912 | −1.26530 | −0.632650 | − | 0.774438i | \(-0.718033\pi\) | ||||
−0.632650 | + | 0.774438i | \(0.718033\pi\) | |||||||
\(710\) | 10.2855 | 0.386009 | ||||||||
\(711\) | 10.7268 | 0.402288 | ||||||||
\(712\) | −29.8495 | −1.11866 | ||||||||
\(713\) | 25.9914 | 0.973384 | ||||||||
\(714\) | −12.8192 | −0.479746 | ||||||||
\(715\) | −8.91800 | −0.333514 | ||||||||
\(716\) | −3.43294 | −0.128295 | ||||||||
\(717\) | 16.2362 | 0.606353 | ||||||||
\(718\) | 54.6661 | 2.04012 | ||||||||
\(719\) | 18.9323 | 0.706057 | 0.353029 | − | 0.935613i | \(-0.385152\pi\) | ||||
0.353029 | + | 0.935613i | \(0.385152\pi\) | |||||||
\(720\) | 9.67673 | 0.360630 | ||||||||
\(721\) | 15.2288 | 0.567150 | ||||||||
\(722\) | −79.3178 | −2.95190 | ||||||||
\(723\) | −12.5949 | −0.468410 | ||||||||
\(724\) | 5.61610 | 0.208721 | ||||||||
\(725\) | 3.02282 | 0.112265 | ||||||||
\(726\) | −15.2321 | −0.565317 | ||||||||
\(727\) | 6.78906 | 0.251792 | 0.125896 | − | 0.992043i | \(-0.459819\pi\) | ||||
0.125896 | + | 0.992043i | \(0.459819\pi\) | |||||||
\(728\) | 8.81918 | 0.326860 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −15.9792 | −0.591415 | ||||||||
\(731\) | −50.0183 | −1.84999 | ||||||||
\(732\) | 6.96836 | 0.257558 | ||||||||
\(733\) | 21.4982 | 0.794054 | 0.397027 | − | 0.917807i | \(-0.370042\pi\) | ||||
0.397027 | + | 0.917807i | \(0.370042\pi\) | |||||||
\(734\) | −6.68303 | −0.246675 | ||||||||
\(735\) | 2.03406 | 0.0750275 | ||||||||
\(736\) | 7.00795 | 0.258316 | ||||||||
\(737\) | 3.32469 | 0.122467 | ||||||||
\(738\) | 10.3205 | 0.379904 | ||||||||
\(739\) | 4.08334 | 0.150208 | 0.0751041 | − | 0.997176i | \(-0.476071\pi\) | ||||
0.0751041 | + | 0.997176i | \(0.476071\pi\) | |||||||
\(740\) | 2.48152 | 0.0912225 | ||||||||
\(741\) | 31.0158 | 1.13939 | ||||||||
\(742\) | −6.68111 | −0.245271 | ||||||||
\(743\) | −2.66701 | −0.0978431 | −0.0489216 | − | 0.998803i | \(-0.515578\pi\) | ||||
−0.0489216 | + | 0.998803i | \(0.515578\pi\) | |||||||
\(744\) | −24.5981 | −0.901809 | ||||||||
\(745\) | 27.0048 | 0.989378 | ||||||||
\(746\) | −53.7523 | −1.96801 | ||||||||
\(747\) | −12.9827 | −0.475011 | ||||||||
\(748\) | −4.82644 | −0.176472 | ||||||||
\(749\) | 1.38838 | 0.0507302 | ||||||||
\(750\) | 18.8827 | 0.689500 | ||||||||
\(751\) | 51.9749 | 1.89659 | 0.948295 | − | 0.317391i | \(-0.102807\pi\) | ||||
0.948295 | + | 0.317391i | \(0.102807\pi\) | |||||||
\(752\) | 39.6726 | 1.44671 | ||||||||
\(753\) | −22.8035 | −0.831006 | ||||||||
\(754\) | 20.7057 | 0.754059 | ||||||||
\(755\) | −2.71885 | −0.0989491 | ||||||||
\(756\) | −0.507395 | −0.0184538 | ||||||||
\(757\) | 14.3161 | 0.520326 | 0.260163 | − | 0.965565i | \(-0.416224\pi\) | ||||
0.260163 | + | 0.965565i | \(0.416224\pi\) | |||||||
\(758\) | −51.6426 | −1.87574 | ||||||||
\(759\) | −2.93438 | −0.106511 | ||||||||
\(760\) | 39.9605 | 1.44952 | ||||||||
\(761\) | −1.05740 | −0.0383307 | −0.0191653 | − | 0.999816i | \(-0.506101\pi\) | ||||
−0.0191653 | + | 0.999816i | \(0.506101\pi\) | |||||||
\(762\) | 7.76061 | 0.281137 | ||||||||
\(763\) | 2.93650 | 0.106309 | ||||||||
\(764\) | −9.88834 | −0.357748 | ||||||||
\(765\) | 16.4670 | 0.595364 | ||||||||
\(766\) | 1.58348 | 0.0572133 | ||||||||
\(767\) | 35.7294 | 1.29012 | ||||||||
\(768\) | −11.4600 | −0.413526 | ||||||||
\(769\) | 37.7716 | 1.36208 | 0.681040 | − | 0.732246i | \(-0.261528\pi\) | ||||
0.681040 | + | 0.732246i | \(0.261528\pi\) | |||||||
\(770\) | 3.78449 | 0.136384 | ||||||||
\(771\) | −18.2621 | −0.657695 | ||||||||
\(772\) | 1.53356 | 0.0551939 | ||||||||
\(773\) | 36.3383 | 1.30700 | 0.653498 | − | 0.756928i | \(-0.273301\pi\) | ||||
0.653498 | + | 0.756928i | \(0.273301\pi\) | |||||||
\(774\) | −9.78343 | −0.351658 | ||||||||
\(775\) | −8.97737 | −0.322477 | ||||||||
\(776\) | −28.9911 | −1.04072 | ||||||||
\(777\) | 2.40440 | 0.0862575 | ||||||||
\(778\) | −30.4495 | −1.09167 | ||||||||
\(779\) | 54.1752 | 1.94103 | ||||||||
\(780\) | 3.85107 | 0.137891 | ||||||||
\(781\) | 3.75217 | 0.134263 | ||||||||
\(782\) | 32.0144 | 1.14483 | ||||||||
\(783\) | 3.50435 | 0.125235 | ||||||||
\(784\) | −4.75734 | −0.169905 | ||||||||
\(785\) | 12.1853 | 0.434913 | ||||||||
\(786\) | 21.0829 | 0.752003 | ||||||||
\(787\) | −3.97456 | −0.141678 | −0.0708388 | − | 0.997488i | \(-0.522568\pi\) | ||||
−0.0708388 | + | 0.997488i | \(0.522568\pi\) | |||||||
\(788\) | −12.8365 | −0.457281 | ||||||||
\(789\) | −26.3782 | −0.939088 | ||||||||
\(790\) | 34.5500 | 1.22923 | ||||||||
\(791\) | −4.96451 | −0.176518 | ||||||||
\(792\) | 2.77708 | 0.0986791 | ||||||||
\(793\) | −51.2456 | −1.81978 | ||||||||
\(794\) | 12.2375 | 0.434293 | ||||||||
\(795\) | 8.58226 | 0.304382 | ||||||||
\(796\) | 1.77341 | 0.0628569 | ||||||||
\(797\) | 41.3980 | 1.46639 | 0.733196 | − | 0.680018i | \(-0.238028\pi\) | ||||
0.733196 | + | 0.680018i | \(0.238028\pi\) | |||||||
\(798\) | −13.1620 | −0.465930 | ||||||||
\(799\) | 67.5111 | 2.38837 | ||||||||
\(800\) | −2.42053 | −0.0855787 | ||||||||
\(801\) | −12.6293 | −0.446235 | ||||||||
\(802\) | −53.6799 | −1.89550 | ||||||||
\(803\) | −5.82921 | −0.205708 | ||||||||
\(804\) | −1.43571 | −0.0506334 | ||||||||
\(805\) | −5.07982 | −0.179040 | ||||||||
\(806\) | −61.4933 | −2.16601 | ||||||||
\(807\) | 7.27730 | 0.256173 | ||||||||
\(808\) | 24.5875 | 0.864986 | ||||||||
\(809\) | −47.1729 | −1.65851 | −0.829256 | − | 0.558869i | \(-0.811236\pi\) | ||||
−0.829256 | + | 0.558869i | \(0.811236\pi\) | |||||||
\(810\) | 3.22089 | 0.113170 | ||||||||
\(811\) | 45.1440 | 1.58522 | 0.792610 | − | 0.609728i | \(-0.208721\pi\) | ||||
0.792610 | + | 0.609728i | \(0.208721\pi\) | |||||||
\(812\) | −1.77809 | −0.0623987 | ||||||||
\(813\) | 10.6407 | 0.373187 | ||||||||
\(814\) | 4.47353 | 0.156797 | ||||||||
\(815\) | −21.7592 | −0.762192 | ||||||||
\(816\) | −38.5135 | −1.34824 | ||||||||
\(817\) | −51.3559 | −1.79672 | ||||||||
\(818\) | −2.63891 | −0.0922675 | ||||||||
\(819\) | 3.73140 | 0.130386 | ||||||||
\(820\) | 6.72667 | 0.234906 | ||||||||
\(821\) | 15.9729 | 0.557459 | 0.278730 | − | 0.960370i | \(-0.410087\pi\) | ||||
0.278730 | + | 0.960370i | \(0.410087\pi\) | |||||||
\(822\) | 32.6972 | 1.14045 | ||||||||
\(823\) | 23.6259 | 0.823547 | 0.411773 | − | 0.911286i | \(-0.364910\pi\) | ||||
0.411773 | + | 0.911286i | \(0.364910\pi\) | |||||||
\(824\) | 35.9933 | 1.25389 | ||||||||
\(825\) | 1.01353 | 0.0352865 | ||||||||
\(826\) | −15.1623 | −0.527565 | ||||||||
\(827\) | 26.3407 | 0.915955 | 0.457978 | − | 0.888964i | \(-0.348574\pi\) | ||||
0.457978 | + | 0.888964i | \(0.348574\pi\) | |||||||
\(828\) | 1.26716 | 0.0440367 | ||||||||
\(829\) | −18.4133 | −0.639519 | −0.319760 | − | 0.947499i | \(-0.603602\pi\) | ||||
−0.319760 | + | 0.947499i | \(0.603602\pi\) | |||||||
\(830\) | −41.8157 | −1.45144 | ||||||||
\(831\) | 30.1397 | 1.04553 | ||||||||
\(832\) | 18.9229 | 0.656032 | ||||||||
\(833\) | −8.09560 | −0.280496 | ||||||||
\(834\) | −12.2319 | −0.423555 | ||||||||
\(835\) | 25.9165 | 0.896879 | ||||||||
\(836\) | −4.95551 | −0.171390 | ||||||||
\(837\) | −10.4075 | −0.359735 | ||||||||
\(838\) | −44.2750 | −1.52945 | ||||||||
\(839\) | −35.0262 | −1.20924 | −0.604620 | − | 0.796514i | \(-0.706675\pi\) | ||||
−0.604620 | + | 0.796514i | \(0.706675\pi\) | |||||||
\(840\) | 4.80752 | 0.165875 | ||||||||
\(841\) | −16.7195 | −0.576535 | ||||||||
\(842\) | 1.31981 | 0.0454836 | ||||||||
\(843\) | 21.8838 | 0.753718 | ||||||||
\(844\) | 3.18125 | 0.109503 | ||||||||
\(845\) | −1.87813 | −0.0646097 | ||||||||
\(846\) | 13.2050 | 0.453996 | ||||||||
\(847\) | −9.61941 | −0.330527 | ||||||||
\(848\) | −20.0725 | −0.689293 | ||||||||
\(849\) | −15.4851 | −0.531448 | ||||||||
\(850\) | −11.0577 | −0.379276 | ||||||||
\(851\) | −6.00470 | −0.205839 | ||||||||
\(852\) | −1.62031 | −0.0555107 | ||||||||
\(853\) | 7.20790 | 0.246794 | 0.123397 | − | 0.992357i | \(-0.460621\pi\) | ||||
0.123397 | + | 0.992357i | \(0.460621\pi\) | |||||||
\(854\) | 21.7468 | 0.744161 | ||||||||
\(855\) | 16.9073 | 0.578218 | ||||||||
\(856\) | 3.28143 | 0.112157 | ||||||||
\(857\) | 7.31936 | 0.250025 | 0.125012 | − | 0.992155i | \(-0.460103\pi\) | ||||
0.125012 | + | 0.992155i | \(0.460103\pi\) | |||||||
\(858\) | 6.94248 | 0.237012 | ||||||||
\(859\) | −49.4834 | −1.68835 | −0.844176 | − | 0.536065i | \(-0.819910\pi\) | ||||
−0.844176 | + | 0.536065i | \(0.819910\pi\) | |||||||
\(860\) | −6.37661 | −0.217441 | ||||||||
\(861\) | 6.51764 | 0.222120 | ||||||||
\(862\) | 21.0072 | 0.715508 | ||||||||
\(863\) | −46.5393 | −1.58422 | −0.792108 | − | 0.610381i | \(-0.791016\pi\) | ||||
−0.792108 | + | 0.610381i | \(0.791016\pi\) | |||||||
\(864\) | −2.80612 | −0.0954663 | ||||||||
\(865\) | 36.0969 | 1.22733 | ||||||||
\(866\) | 42.1388 | 1.43193 | ||||||||
\(867\) | −48.5388 | −1.64846 | ||||||||
\(868\) | 5.28069 | 0.179238 | ||||||||
\(869\) | 12.6039 | 0.427557 | ||||||||
\(870\) | 11.2871 | 0.382669 | ||||||||
\(871\) | 10.5582 | 0.357752 | ||||||||
\(872\) | 6.94044 | 0.235033 | ||||||||
\(873\) | −12.2662 | −0.415146 | ||||||||
\(874\) | 32.8705 | 1.11186 | ||||||||
\(875\) | 11.9249 | 0.403134 | ||||||||
\(876\) | 2.51724 | 0.0850495 | ||||||||
\(877\) | 12.5085 | 0.422382 | 0.211191 | − | 0.977445i | \(-0.432266\pi\) | ||||
0.211191 | + | 0.977445i | \(0.432266\pi\) | |||||||
\(878\) | 5.41908 | 0.182885 | ||||||||
\(879\) | −9.98207 | −0.336687 | ||||||||
\(880\) | 11.3700 | 0.383282 | ||||||||
\(881\) | 40.5582 | 1.36644 | 0.683221 | − | 0.730212i | \(-0.260579\pi\) | ||||
0.683221 | + | 0.730212i | \(0.260579\pi\) | |||||||
\(882\) | −1.58348 | −0.0533184 | ||||||||
\(883\) | 16.9527 | 0.570503 | 0.285251 | − | 0.958453i | \(-0.407923\pi\) | ||||
0.285251 | + | 0.958453i | \(0.407923\pi\) | |||||||
\(884\) | −15.3273 | −0.515514 | ||||||||
\(885\) | 19.4769 | 0.654707 | ||||||||
\(886\) | −48.6474 | −1.63434 | ||||||||
\(887\) | 3.93843 | 0.132240 | 0.0661198 | − | 0.997812i | \(-0.478938\pi\) | ||||
0.0661198 | + | 0.997812i | \(0.478938\pi\) | |||||||
\(888\) | 5.68282 | 0.190703 | ||||||||
\(889\) | 4.90100 | 0.164374 | ||||||||
\(890\) | −40.6776 | −1.36352 | ||||||||
\(891\) | 1.17498 | 0.0393634 | ||||||||
\(892\) | −1.72935 | −0.0579029 | ||||||||
\(893\) | 69.3165 | 2.31959 | ||||||||
\(894\) | −21.0226 | −0.703102 | ||||||||
\(895\) | 13.7621 | 0.460016 | ||||||||
\(896\) | −13.6425 | −0.455762 | ||||||||
\(897\) | −9.31871 | −0.311143 | ||||||||
\(898\) | −33.3213 | −1.11195 | ||||||||
\(899\) | −36.4714 | −1.21639 | ||||||||
\(900\) | −0.437673 | −0.0145891 | ||||||||
\(901\) | −34.1576 | −1.13795 | ||||||||
\(902\) | 12.1264 | 0.403766 | ||||||||
\(903\) | −6.17846 | −0.205606 | ||||||||
\(904\) | −11.7336 | −0.390255 | ||||||||
\(905\) | −22.5140 | −0.748392 | ||||||||
\(906\) | 2.11657 | 0.0703183 | ||||||||
\(907\) | 22.2551 | 0.738968 | 0.369484 | − | 0.929237i | \(-0.379534\pi\) | ||||
0.369484 | + | 0.929237i | \(0.379534\pi\) | |||||||
\(908\) | −13.1359 | −0.435931 | ||||||||
\(909\) | 10.4030 | 0.345046 | ||||||||
\(910\) | 12.0184 | 0.398407 | ||||||||
\(911\) | −27.1176 | −0.898447 | −0.449224 | − | 0.893419i | \(-0.648299\pi\) | ||||
−0.449224 | + | 0.893419i | \(0.648299\pi\) | |||||||
\(912\) | −39.5435 | −1.30942 | ||||||||
\(913\) | −15.2544 | −0.504847 | ||||||||
\(914\) | −41.1663 | −1.36166 | ||||||||
\(915\) | −27.9350 | −0.923503 | ||||||||
\(916\) | −3.04825 | −0.100717 | ||||||||
\(917\) | 13.3143 | 0.439678 | ||||||||
\(918\) | −12.8192 | −0.423096 | ||||||||
\(919\) | −0.0136658 | −0.000450794 0 | −0.000225397 | − | 1.00000i | \(-0.500072\pi\) | ||||
−0.000225397 | 1.00000i | \(0.500072\pi\) | ||||||||
\(920\) | −12.0062 | −0.395832 | ||||||||
\(921\) | −4.79874 | −0.158124 | ||||||||
\(922\) | −32.9950 | −1.08663 | ||||||||
\(923\) | 11.9158 | 0.392213 | ||||||||
\(924\) | −0.596180 | −0.0196129 | ||||||||
\(925\) | 2.07401 | 0.0681931 | ||||||||
\(926\) | −53.0156 | −1.74220 | ||||||||
\(927\) | 15.2288 | 0.500180 | ||||||||
\(928\) | −9.83364 | −0.322805 | ||||||||
\(929\) | 35.1265 | 1.15246 | 0.576232 | − | 0.817286i | \(-0.304522\pi\) | ||||
0.576232 | + | 0.817286i | \(0.304522\pi\) | |||||||
\(930\) | −33.5213 | −1.09921 | ||||||||
\(931\) | −8.31210 | −0.272418 | ||||||||
\(932\) | −5.23695 | −0.171542 | ||||||||
\(933\) | 5.91843 | 0.193761 | ||||||||
\(934\) | 25.0959 | 0.821162 | ||||||||
\(935\) | 19.3484 | 0.632760 | ||||||||
\(936\) | 8.81918 | 0.288264 | ||||||||
\(937\) | 9.27557 | 0.303020 | 0.151510 | − | 0.988456i | \(-0.451586\pi\) | ||||
0.151510 | + | 0.988456i | \(0.451586\pi\) | |||||||
\(938\) | −4.48055 | −0.146295 | ||||||||
\(939\) | −8.13144 | −0.265359 | ||||||||
\(940\) | 8.60669 | 0.280719 | ||||||||
\(941\) | −47.5286 | −1.54939 | −0.774693 | − | 0.632337i | \(-0.782096\pi\) | ||||
−0.774693 | + | 0.632337i | \(0.782096\pi\) | |||||||
\(942\) | −9.48603 | −0.309072 | ||||||||
\(943\) | −16.2770 | −0.530052 | ||||||||
\(944\) | −45.5532 | −1.48263 | ||||||||
\(945\) | 2.03406 | 0.0661681 | ||||||||
\(946\) | −11.4954 | −0.373747 | ||||||||
\(947\) | 40.3978 | 1.31275 | 0.656376 | − | 0.754434i | \(-0.272089\pi\) | ||||
0.656376 | + | 0.754434i | \(0.272089\pi\) | |||||||
\(948\) | −5.44274 | −0.176772 | ||||||||
\(949\) | −18.5118 | −0.600920 | ||||||||
\(950\) | −11.3534 | −0.368353 | ||||||||
\(951\) | −4.12351 | −0.133714 | ||||||||
\(952\) | −19.1340 | −0.620136 | ||||||||
\(953\) | −2.58733 | −0.0838117 | −0.0419059 | − | 0.999122i | \(-0.513343\pi\) | ||||
−0.0419059 | + | 0.999122i | \(0.513343\pi\) | |||||||
\(954\) | −6.68111 | −0.216309 | ||||||||
\(955\) | 39.6408 | 1.28275 | ||||||||
\(956\) | −8.23817 | −0.266442 | ||||||||
\(957\) | 4.11755 | 0.133102 | ||||||||
\(958\) | −54.1047 | −1.74804 | ||||||||
\(959\) | 20.6490 | 0.666792 | ||||||||
\(960\) | 10.3152 | 0.332923 | ||||||||
\(961\) | 77.3153 | 2.49404 | ||||||||
\(962\) | 14.2066 | 0.458039 | ||||||||
\(963\) | 1.38838 | 0.0447398 | ||||||||
\(964\) | 6.39060 | 0.205827 | ||||||||
\(965\) | −6.14777 | −0.197904 | ||||||||
\(966\) | 3.95454 | 0.127235 | ||||||||
\(967\) | −28.0460 | −0.901899 | −0.450949 | − | 0.892550i | \(-0.648914\pi\) | ||||
−0.450949 | + | 0.892550i | \(0.648914\pi\) | |||||||
\(968\) | −22.7355 | −0.730747 | ||||||||
\(969\) | −67.2914 | −2.16171 | ||||||||
\(970\) | −39.5079 | −1.26852 | ||||||||
\(971\) | −25.9142 | −0.831625 | −0.415813 | − | 0.909450i | \(-0.636503\pi\) | ||||
−0.415813 | + | 0.909450i | \(0.636503\pi\) | |||||||
\(972\) | −0.507395 | −0.0162747 | ||||||||
\(973\) | −7.72470 | −0.247643 | ||||||||
\(974\) | 59.4601 | 1.90523 | ||||||||
\(975\) | 3.21867 | 0.103080 | ||||||||
\(976\) | 65.3354 | 2.09134 | ||||||||
\(977\) | −6.52762 | −0.208837 | −0.104419 | − | 0.994533i | \(-0.533298\pi\) | ||||
−0.104419 | + | 0.994533i | \(0.533298\pi\) | |||||||
\(978\) | 16.9391 | 0.541653 | ||||||||
\(979\) | −14.8392 | −0.474264 | ||||||||
\(980\) | −1.03207 | −0.0329683 | ||||||||
\(981\) | 2.93650 | 0.0937554 | ||||||||
\(982\) | 22.2772 | 0.710894 | ||||||||
\(983\) | 60.1942 | 1.91990 | 0.959949 | − | 0.280175i | \(-0.0903926\pi\) | ||||
0.959949 | + | 0.280175i | \(0.0903926\pi\) | |||||||
\(984\) | 15.4045 | 0.491076 | ||||||||
\(985\) | 51.4594 | 1.63963 | ||||||||
\(986\) | −44.9229 | −1.43064 | ||||||||
\(987\) | 8.33923 | 0.265441 | ||||||||
\(988\) | −15.7372 | −0.500668 | ||||||||
\(989\) | 15.4299 | 0.490643 | ||||||||
\(990\) | 3.78449 | 0.120279 | ||||||||
\(991\) | −53.8861 | −1.71175 | −0.855874 | − | 0.517184i | \(-0.826980\pi\) | ||||
−0.855874 | + | 0.517184i | \(0.826980\pi\) | |||||||
\(992\) | 29.2046 | 0.927248 | ||||||||
\(993\) | 7.88009 | 0.250067 | ||||||||
\(994\) | −5.05664 | −0.160387 | ||||||||
\(995\) | −7.10932 | −0.225381 | ||||||||
\(996\) | 6.58734 | 0.208728 | ||||||||
\(997\) | −26.1583 | −0.828442 | −0.414221 | − | 0.910176i | \(-0.635946\pi\) | ||||
−0.414221 | + | 0.910176i | \(0.635946\pi\) | |||||||
\(998\) | −12.0956 | −0.382881 | ||||||||
\(999\) | 2.40440 | 0.0760720 |
(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 | 8043.2.a.t.1.15 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8043.2.a.t.1.15 | ✓ | 52 | 1.1 | even | 1 | trivial |