Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.8962916974\) |
Analytic rank: | \(0\) |
Dimension: | \(77\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.62668 | −1.51651 | −0.758257 | − | 0.651955i | \(-0.773949\pi\) | ||||
−0.758257 | + | 0.651955i | \(0.773949\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.854809 | 0.382282 | 0.191141 | − | 0.981563i | \(-0.438781\pi\) | ||||
0.191141 | + | 0.981563i | \(0.438781\pi\) | |||||||
\(6\) | 2.62668 | 1.07234 | ||||||||
\(7\) | 1.79286 | 0.677638 | 0.338819 | − | 0.940852i | \(-0.389973\pi\) | ||||
0.338819 | + | 0.940852i | \(0.389973\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 3.89945 | 1.29982 | ||||||||
\(10\) | −0.854809 | −0.270314 | ||||||||
\(11\) | 1.39811 | 0.421547 | 0.210773 | − | 0.977535i | \(-0.432402\pi\) | ||||
0.210773 | + | 0.977535i | \(0.432402\pi\) | |||||||
\(12\) | −2.62668 | −0.758257 | ||||||||
\(13\) | 4.58926 | 1.27283 | 0.636416 | − | 0.771346i | \(-0.280416\pi\) | ||||
0.636416 | + | 0.771346i | \(0.280416\pi\) | |||||||
\(14\) | −1.79286 | −0.479162 | ||||||||
\(15\) | −2.24531 | −0.579737 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.16383 | 1.00988 | 0.504938 | − | 0.863155i | \(-0.331515\pi\) | ||||
0.504938 | + | 0.863155i | \(0.331515\pi\) | |||||||
\(18\) | −3.89945 | −0.919110 | ||||||||
\(19\) | 7.03095 | 1.61301 | 0.806505 | − | 0.591228i | \(-0.201356\pi\) | ||||
0.806505 | + | 0.591228i | \(0.201356\pi\) | |||||||
\(20\) | 0.854809 | 0.191141 | ||||||||
\(21\) | −4.70927 | −1.02765 | ||||||||
\(22\) | −1.39811 | −0.298078 | ||||||||
\(23\) | −6.43702 | −1.34221 | −0.671105 | − | 0.741362i | \(-0.734180\pi\) | ||||
−0.671105 | + | 0.741362i | \(0.734180\pi\) | |||||||
\(24\) | 2.62668 | 0.536169 | ||||||||
\(25\) | −4.26930 | −0.853860 | ||||||||
\(26\) | −4.58926 | −0.900028 | ||||||||
\(27\) | −2.36257 | −0.454677 | ||||||||
\(28\) | 1.79286 | 0.338819 | ||||||||
\(29\) | 4.33951 | 0.805827 | 0.402913 | − | 0.915238i | \(-0.367998\pi\) | ||||
0.402913 | + | 0.915238i | \(0.367998\pi\) | |||||||
\(30\) | 2.24531 | 0.409936 | ||||||||
\(31\) | 3.24386 | 0.582615 | 0.291307 | − | 0.956630i | \(-0.405910\pi\) | ||||
0.291307 | + | 0.956630i | \(0.405910\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −3.67239 | −0.639282 | ||||||||
\(34\) | −4.16383 | −0.714090 | ||||||||
\(35\) | 1.53255 | 0.259049 | ||||||||
\(36\) | 3.89945 | 0.649909 | ||||||||
\(37\) | 3.51846 | 0.578431 | 0.289215 | − | 0.957264i | \(-0.406606\pi\) | ||||
0.289215 | + | 0.957264i | \(0.406606\pi\) | |||||||
\(38\) | −7.03095 | −1.14057 | ||||||||
\(39\) | −12.0545 | −1.93027 | ||||||||
\(40\) | −0.854809 | −0.135157 | ||||||||
\(41\) | 7.42613 | 1.15977 | 0.579883 | − | 0.814700i | \(-0.303098\pi\) | ||||
0.579883 | + | 0.814700i | \(0.303098\pi\) | |||||||
\(42\) | 4.70927 | 0.726657 | ||||||||
\(43\) | 5.43299 | 0.828523 | 0.414261 | − | 0.910158i | \(-0.364040\pi\) | ||||
0.414261 | + | 0.910158i | \(0.364040\pi\) | |||||||
\(44\) | 1.39811 | 0.210773 | ||||||||
\(45\) | 3.33329 | 0.496897 | ||||||||
\(46\) | 6.43702 | 0.949086 | ||||||||
\(47\) | 9.18945 | 1.34042 | 0.670210 | − | 0.742172i | \(-0.266204\pi\) | ||||
0.670210 | + | 0.742172i | \(0.266204\pi\) | |||||||
\(48\) | −2.62668 | −0.379129 | ||||||||
\(49\) | −3.78565 | −0.540807 | ||||||||
\(50\) | 4.26930 | 0.603770 | ||||||||
\(51\) | −10.9370 | −1.53149 | ||||||||
\(52\) | 4.58926 | 0.636416 | ||||||||
\(53\) | 13.3398 | 1.83236 | 0.916179 | − | 0.400769i | \(-0.131257\pi\) | ||||
0.916179 | + | 0.400769i | \(0.131257\pi\) | |||||||
\(54\) | 2.36257 | 0.321505 | ||||||||
\(55\) | 1.19512 | 0.161150 | ||||||||
\(56\) | −1.79286 | −0.239581 | ||||||||
\(57\) | −18.4681 | −2.44615 | ||||||||
\(58\) | −4.33951 | −0.569805 | ||||||||
\(59\) | 15.0144 | 1.95471 | 0.977353 | − | 0.211614i | \(-0.0678721\pi\) | ||||
0.977353 | + | 0.211614i | \(0.0678721\pi\) | |||||||
\(60\) | −2.24531 | −0.289868 | ||||||||
\(61\) | −10.2707 | −1.31503 | −0.657514 | − | 0.753442i | \(-0.728392\pi\) | ||||
−0.657514 | + | 0.753442i | \(0.728392\pi\) | |||||||
\(62\) | −3.24386 | −0.411971 | ||||||||
\(63\) | 6.99118 | 0.880805 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.92294 | 0.486581 | ||||||||
\(66\) | 3.67239 | 0.452040 | ||||||||
\(67\) | 3.19534 | 0.390373 | 0.195187 | − | 0.980766i | \(-0.437469\pi\) | ||||
0.195187 | + | 0.980766i | \(0.437469\pi\) | |||||||
\(68\) | 4.16383 | 0.504938 | ||||||||
\(69\) | 16.9080 | 2.03548 | ||||||||
\(70\) | −1.53255 | −0.183175 | ||||||||
\(71\) | −5.20239 | −0.617411 | −0.308705 | − | 0.951158i | \(-0.599896\pi\) | ||||
−0.308705 | + | 0.951158i | \(0.599896\pi\) | |||||||
\(72\) | −3.89945 | −0.459555 | ||||||||
\(73\) | 4.59082 | 0.537315 | 0.268657 | − | 0.963236i | \(-0.413420\pi\) | ||||
0.268657 | + | 0.963236i | \(0.413420\pi\) | |||||||
\(74\) | −3.51846 | −0.409012 | ||||||||
\(75\) | 11.2141 | 1.29489 | ||||||||
\(76\) | 7.03095 | 0.806505 | ||||||||
\(77\) | 2.50662 | 0.285656 | ||||||||
\(78\) | 12.0545 | 1.36491 | ||||||||
\(79\) | 12.9027 | 1.45166 | 0.725832 | − | 0.687872i | \(-0.241455\pi\) | ||||
0.725832 | + | 0.687872i | \(0.241455\pi\) | |||||||
\(80\) | 0.854809 | 0.0955706 | ||||||||
\(81\) | −5.49263 | −0.610292 | ||||||||
\(82\) | −7.42613 | −0.820079 | ||||||||
\(83\) | 8.96203 | 0.983710 | 0.491855 | − | 0.870677i | \(-0.336319\pi\) | ||||
0.491855 | + | 0.870677i | \(0.336319\pi\) | |||||||
\(84\) | −4.70927 | −0.513824 | ||||||||
\(85\) | 3.55928 | 0.386058 | ||||||||
\(86\) | −5.43299 | −0.585854 | ||||||||
\(87\) | −11.3985 | −1.22205 | ||||||||
\(88\) | −1.39811 | −0.149039 | ||||||||
\(89\) | −2.56615 | −0.272011 | −0.136006 | − | 0.990708i | \(-0.543426\pi\) | ||||
−0.136006 | + | 0.990708i | \(0.543426\pi\) | |||||||
\(90\) | −3.33329 | −0.351359 | ||||||||
\(91\) | 8.22790 | 0.862519 | ||||||||
\(92\) | −6.43702 | −0.671105 | ||||||||
\(93\) | −8.52059 | −0.883544 | ||||||||
\(94\) | −9.18945 | −0.947819 | ||||||||
\(95\) | 6.01012 | 0.616625 | ||||||||
\(96\) | 2.62668 | 0.268084 | ||||||||
\(97\) | −13.9084 | −1.41219 | −0.706095 | − | 0.708118i | \(-0.749545\pi\) | ||||
−0.706095 | + | 0.708118i | \(0.749545\pi\) | |||||||
\(98\) | 3.78565 | 0.382408 | ||||||||
\(99\) | 5.45187 | 0.547933 | ||||||||
\(100\) | −4.26930 | −0.426930 | ||||||||
\(101\) | −18.6206 | −1.85282 | −0.926411 | − | 0.376514i | \(-0.877123\pi\) | ||||
−0.926411 | + | 0.376514i | \(0.877123\pi\) | |||||||
\(102\) | 10.9370 | 1.08293 | ||||||||
\(103\) | −7.47862 | −0.736890 | −0.368445 | − | 0.929649i | \(-0.620110\pi\) | ||||
−0.368445 | + | 0.929649i | \(0.620110\pi\) | |||||||
\(104\) | −4.58926 | −0.450014 | ||||||||
\(105\) | −4.02553 | −0.392851 | ||||||||
\(106\) | −13.3398 | −1.29567 | ||||||||
\(107\) | 16.1348 | 1.55981 | 0.779906 | − | 0.625897i | \(-0.215267\pi\) | ||||
0.779906 | + | 0.625897i | \(0.215267\pi\) | |||||||
\(108\) | −2.36257 | −0.227339 | ||||||||
\(109\) | 14.6084 | 1.39923 | 0.699616 | − | 0.714519i | \(-0.253354\pi\) | ||||
0.699616 | + | 0.714519i | \(0.253354\pi\) | |||||||
\(110\) | −1.19512 | −0.113950 | ||||||||
\(111\) | −9.24186 | −0.877198 | ||||||||
\(112\) | 1.79286 | 0.169409 | ||||||||
\(113\) | −11.4365 | −1.07586 | −0.537928 | − | 0.842991i | \(-0.680793\pi\) | ||||
−0.537928 | + | 0.842991i | \(0.680793\pi\) | |||||||
\(114\) | 18.4681 | 1.72969 | ||||||||
\(115\) | −5.50242 | −0.513103 | ||||||||
\(116\) | 4.33951 | 0.402913 | ||||||||
\(117\) | 17.8956 | 1.65445 | ||||||||
\(118\) | −15.0144 | −1.38219 | ||||||||
\(119\) | 7.46516 | 0.684330 | ||||||||
\(120\) | 2.24531 | 0.204968 | ||||||||
\(121\) | −9.04528 | −0.822298 | ||||||||
\(122\) | 10.2707 | 0.929866 | ||||||||
\(123\) | −19.5061 | −1.75880 | ||||||||
\(124\) | 3.24386 | 0.291307 | ||||||||
\(125\) | −7.92348 | −0.708698 | ||||||||
\(126\) | −6.99118 | −0.622823 | ||||||||
\(127\) | 9.05839 | 0.803802 | 0.401901 | − | 0.915683i | \(-0.368350\pi\) | ||||
0.401901 | + | 0.915683i | \(0.368350\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −14.2707 | −1.25647 | ||||||||
\(130\) | −3.92294 | −0.344065 | ||||||||
\(131\) | −3.80330 | −0.332296 | −0.166148 | − | 0.986101i | \(-0.553133\pi\) | ||||
−0.166148 | + | 0.986101i | \(0.553133\pi\) | |||||||
\(132\) | −3.67239 | −0.319641 | ||||||||
\(133\) | 12.6055 | 1.09304 | ||||||||
\(134\) | −3.19534 | −0.276036 | ||||||||
\(135\) | −2.01955 | −0.173815 | ||||||||
\(136\) | −4.16383 | −0.357045 | ||||||||
\(137\) | 20.6547 | 1.76465 | 0.882326 | − | 0.470638i | \(-0.155976\pi\) | ||||
0.882326 | + | 0.470638i | \(0.155976\pi\) | |||||||
\(138\) | −16.9080 | −1.43930 | ||||||||
\(139\) | 6.77841 | 0.574937 | 0.287469 | − | 0.957790i | \(-0.407186\pi\) | ||||
0.287469 | + | 0.957790i | \(0.407186\pi\) | |||||||
\(140\) | 1.53255 | 0.129524 | ||||||||
\(141\) | −24.1378 | −2.03277 | ||||||||
\(142\) | 5.20239 | 0.436575 | ||||||||
\(143\) | 6.41630 | 0.536558 | ||||||||
\(144\) | 3.89945 | 0.324954 | ||||||||
\(145\) | 3.70945 | 0.308053 | ||||||||
\(146\) | −4.59082 | −0.379939 | ||||||||
\(147\) | 9.94369 | 0.820142 | ||||||||
\(148\) | 3.51846 | 0.289215 | ||||||||
\(149\) | 5.51127 | 0.451500 | 0.225750 | − | 0.974185i | \(-0.427517\pi\) | ||||
0.225750 | + | 0.974185i | \(0.427517\pi\) | |||||||
\(150\) | −11.2141 | −0.915627 | ||||||||
\(151\) | −9.42711 | −0.767167 | −0.383584 | − | 0.923506i | \(-0.625310\pi\) | ||||
−0.383584 | + | 0.923506i | \(0.625310\pi\) | |||||||
\(152\) | −7.03095 | −0.570285 | ||||||||
\(153\) | 16.2366 | 1.31265 | ||||||||
\(154\) | −2.50662 | −0.201989 | ||||||||
\(155\) | 2.77288 | 0.222723 | ||||||||
\(156\) | −12.0545 | −0.965134 | ||||||||
\(157\) | −14.6278 | −1.16743 | −0.583715 | − | 0.811959i | \(-0.698401\pi\) | ||||
−0.583715 | + | 0.811959i | \(0.698401\pi\) | |||||||
\(158\) | −12.9027 | −1.02648 | ||||||||
\(159\) | −35.0393 | −2.77880 | ||||||||
\(160\) | −0.854809 | −0.0675786 | ||||||||
\(161\) | −11.5407 | −0.909533 | ||||||||
\(162\) | 5.49263 | 0.431542 | ||||||||
\(163\) | −1.17571 | −0.0920884 | −0.0460442 | − | 0.998939i | \(-0.514662\pi\) | ||||
−0.0460442 | + | 0.998939i | \(0.514662\pi\) | |||||||
\(164\) | 7.42613 | 0.579883 | ||||||||
\(165\) | −3.13919 | −0.244386 | ||||||||
\(166\) | −8.96203 | −0.695588 | ||||||||
\(167\) | 6.13476 | 0.474722 | 0.237361 | − | 0.971422i | \(-0.423718\pi\) | ||||
0.237361 | + | 0.971422i | \(0.423718\pi\) | |||||||
\(168\) | 4.70927 | 0.363328 | ||||||||
\(169\) | 8.06129 | 0.620099 | ||||||||
\(170\) | −3.55928 | −0.272984 | ||||||||
\(171\) | 27.4168 | 2.09662 | ||||||||
\(172\) | 5.43299 | 0.414261 | ||||||||
\(173\) | 6.25113 | 0.475264 | 0.237632 | − | 0.971355i | \(-0.423629\pi\) | ||||
0.237632 | + | 0.971355i | \(0.423629\pi\) | |||||||
\(174\) | 11.3985 | 0.864118 | ||||||||
\(175\) | −7.65426 | −0.578608 | ||||||||
\(176\) | 1.39811 | 0.105387 | ||||||||
\(177\) | −39.4380 | −2.96434 | ||||||||
\(178\) | 2.56615 | 0.192341 | ||||||||
\(179\) | −3.65995 | −0.273557 | −0.136779 | − | 0.990602i | \(-0.543675\pi\) | ||||
−0.136779 | + | 0.990602i | \(0.543675\pi\) | |||||||
\(180\) | 3.33329 | 0.248449 | ||||||||
\(181\) | −17.3263 | −1.28786 | −0.643928 | − | 0.765086i | \(-0.722696\pi\) | ||||
−0.643928 | + | 0.765086i | \(0.722696\pi\) | |||||||
\(182\) | −8.22790 | −0.609893 | ||||||||
\(183\) | 26.9779 | 1.99426 | ||||||||
\(184\) | 6.43702 | 0.474543 | ||||||||
\(185\) | 3.00761 | 0.221124 | ||||||||
\(186\) | 8.52059 | 0.624760 | ||||||||
\(187\) | 5.82150 | 0.425710 | ||||||||
\(188\) | 9.18945 | 0.670210 | ||||||||
\(189\) | −4.23576 | −0.308106 | ||||||||
\(190\) | −6.01012 | −0.436020 | ||||||||
\(191\) | 17.2881 | 1.25092 | 0.625460 | − | 0.780256i | \(-0.284911\pi\) | ||||
0.625460 | + | 0.780256i | \(0.284911\pi\) | |||||||
\(192\) | −2.62668 | −0.189564 | ||||||||
\(193\) | −15.8238 | −1.13902 | −0.569512 | − | 0.821983i | \(-0.692868\pi\) | ||||
−0.569512 | + | 0.821983i | \(0.692868\pi\) | |||||||
\(194\) | 13.9084 | 0.998569 | ||||||||
\(195\) | −10.3043 | −0.737907 | ||||||||
\(196\) | −3.78565 | −0.270404 | ||||||||
\(197\) | −12.0973 | −0.861899 | −0.430950 | − | 0.902376i | \(-0.641821\pi\) | ||||
−0.430950 | + | 0.902376i | \(0.641821\pi\) | |||||||
\(198\) | −5.45187 | −0.387447 | ||||||||
\(199\) | −18.1581 | −1.28720 | −0.643598 | − | 0.765364i | \(-0.722559\pi\) | ||||
−0.643598 | + | 0.765364i | \(0.722559\pi\) | |||||||
\(200\) | 4.26930 | 0.301885 | ||||||||
\(201\) | −8.39314 | −0.592007 | ||||||||
\(202\) | 18.6206 | 1.31014 | ||||||||
\(203\) | 7.78014 | 0.546059 | ||||||||
\(204\) | −10.9370 | −0.765746 | ||||||||
\(205\) | 6.34792 | 0.443358 | ||||||||
\(206\) | 7.47862 | 0.521060 | ||||||||
\(207\) | −25.1008 | −1.74463 | ||||||||
\(208\) | 4.58926 | 0.318208 | ||||||||
\(209\) | 9.83005 | 0.679959 | ||||||||
\(210\) | 4.02553 | 0.277788 | ||||||||
\(211\) | −9.69641 | −0.667529 | −0.333764 | − | 0.942657i | \(-0.608319\pi\) | ||||
−0.333764 | + | 0.942657i | \(0.608319\pi\) | |||||||
\(212\) | 13.3398 | 0.916179 | ||||||||
\(213\) | 13.6650 | 0.936312 | ||||||||
\(214\) | −16.1348 | −1.10295 | ||||||||
\(215\) | 4.64417 | 0.316730 | ||||||||
\(216\) | 2.36257 | 0.160753 | ||||||||
\(217\) | 5.81579 | 0.394802 | ||||||||
\(218\) | −14.6084 | −0.989406 | ||||||||
\(219\) | −12.0586 | −0.814846 | ||||||||
\(220\) | 1.19512 | 0.0805749 | ||||||||
\(221\) | 19.1089 | 1.28540 | ||||||||
\(222\) | 9.24186 | 0.620273 | ||||||||
\(223\) | −13.9655 | −0.935200 | −0.467600 | − | 0.883940i | \(-0.654881\pi\) | ||||
−0.467600 | + | 0.883940i | \(0.654881\pi\) | |||||||
\(224\) | −1.79286 | −0.119791 | ||||||||
\(225\) | −16.6479 | −1.10986 | ||||||||
\(226\) | 11.4365 | 0.760745 | ||||||||
\(227\) | 8.81918 | 0.585350 | 0.292675 | − | 0.956212i | \(-0.405455\pi\) | ||||
0.292675 | + | 0.956212i | \(0.405455\pi\) | |||||||
\(228\) | −18.4681 | −1.22308 | ||||||||
\(229\) | −17.8260 | −1.17797 | −0.588986 | − | 0.808143i | \(-0.700473\pi\) | ||||
−0.588986 | + | 0.808143i | \(0.700473\pi\) | |||||||
\(230\) | 5.50242 | 0.362819 | ||||||||
\(231\) | −6.58409 | −0.433201 | ||||||||
\(232\) | −4.33951 | −0.284903 | ||||||||
\(233\) | −13.1809 | −0.863511 | −0.431755 | − | 0.901991i | \(-0.642106\pi\) | ||||
−0.431755 | + | 0.901991i | \(0.642106\pi\) | |||||||
\(234\) | −17.8956 | −1.16987 | ||||||||
\(235\) | 7.85522 | 0.512418 | ||||||||
\(236\) | 15.0144 | 0.977353 | ||||||||
\(237\) | −33.8912 | −2.20147 | ||||||||
\(238\) | −7.46516 | −0.483895 | ||||||||
\(239\) | 13.2733 | 0.858579 | 0.429289 | − | 0.903167i | \(-0.358764\pi\) | ||||
0.429289 | + | 0.903167i | \(0.358764\pi\) | |||||||
\(240\) | −2.24531 | −0.144934 | ||||||||
\(241\) | −9.51088 | −0.612649 | −0.306325 | − | 0.951927i | \(-0.599099\pi\) | ||||
−0.306325 | + | 0.951927i | \(0.599099\pi\) | |||||||
\(242\) | 9.04528 | 0.581453 | ||||||||
\(243\) | 21.5151 | 1.38019 | ||||||||
\(244\) | −10.2707 | −0.657514 | ||||||||
\(245\) | −3.23601 | −0.206741 | ||||||||
\(246\) | 19.5061 | 1.24366 | ||||||||
\(247\) | 32.2668 | 2.05309 | ||||||||
\(248\) | −3.24386 | −0.205985 | ||||||||
\(249\) | −23.5404 | −1.49181 | ||||||||
\(250\) | 7.92348 | 0.501125 | ||||||||
\(251\) | −25.2709 | −1.59508 | −0.797542 | − | 0.603263i | \(-0.793867\pi\) | ||||
−0.797542 | + | 0.603263i | \(0.793867\pi\) | |||||||
\(252\) | 6.99118 | 0.440403 | ||||||||
\(253\) | −8.99967 | −0.565804 | ||||||||
\(254\) | −9.05839 | −0.568374 | ||||||||
\(255\) | −9.34908 | −0.585462 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.815232 | 0.0508528 | 0.0254264 | − | 0.999677i | \(-0.491906\pi\) | ||||
0.0254264 | + | 0.999677i | \(0.491906\pi\) | |||||||
\(258\) | 14.2707 | 0.888457 | ||||||||
\(259\) | 6.30810 | 0.391966 | ||||||||
\(260\) | 3.92294 | 0.243290 | ||||||||
\(261\) | 16.9217 | 1.04743 | ||||||||
\(262\) | 3.80330 | 0.234969 | ||||||||
\(263\) | −25.4272 | −1.56791 | −0.783954 | − | 0.620819i | \(-0.786800\pi\) | ||||
−0.783954 | + | 0.620819i | \(0.786800\pi\) | |||||||
\(264\) | 3.67239 | 0.226020 | ||||||||
\(265\) | 11.4030 | 0.700478 | ||||||||
\(266\) | −12.6055 | −0.772893 | ||||||||
\(267\) | 6.74045 | 0.412509 | ||||||||
\(268\) | 3.19534 | 0.195187 | ||||||||
\(269\) | −18.1899 | −1.10906 | −0.554530 | − | 0.832164i | \(-0.687102\pi\) | ||||
−0.554530 | + | 0.832164i | \(0.687102\pi\) | |||||||
\(270\) | 2.01955 | 0.122906 | ||||||||
\(271\) | −9.42443 | −0.572493 | −0.286247 | − | 0.958156i | \(-0.592408\pi\) | ||||
−0.286247 | + | 0.958156i | \(0.592408\pi\) | |||||||
\(272\) | 4.16383 | 0.252469 | ||||||||
\(273\) | −21.6121 | −1.30802 | ||||||||
\(274\) | −20.6547 | −1.24780 | ||||||||
\(275\) | −5.96896 | −0.359942 | ||||||||
\(276\) | 16.9080 | 1.01774 | ||||||||
\(277\) | 22.4304 | 1.34771 | 0.673855 | − | 0.738864i | \(-0.264637\pi\) | ||||
0.673855 | + | 0.738864i | \(0.264637\pi\) | |||||||
\(278\) | −6.77841 | −0.406542 | ||||||||
\(279\) | 12.6493 | 0.757293 | ||||||||
\(280\) | −1.53255 | −0.0915876 | ||||||||
\(281\) | 9.63200 | 0.574597 | 0.287299 | − | 0.957841i | \(-0.407243\pi\) | ||||
0.287299 | + | 0.957841i | \(0.407243\pi\) | |||||||
\(282\) | 24.1378 | 1.43738 | ||||||||
\(283\) | −18.2230 | −1.08324 | −0.541622 | − | 0.840622i | \(-0.682189\pi\) | ||||
−0.541622 | + | 0.840622i | \(0.682189\pi\) | |||||||
\(284\) | −5.20239 | −0.308705 | ||||||||
\(285\) | −15.7867 | −0.935121 | ||||||||
\(286\) | −6.41630 | −0.379404 | ||||||||
\(287\) | 13.3140 | 0.785901 | ||||||||
\(288\) | −3.89945 | −0.229777 | ||||||||
\(289\) | 0.337458 | 0.0198505 | ||||||||
\(290\) | −3.70945 | −0.217826 | ||||||||
\(291\) | 36.5331 | 2.14161 | ||||||||
\(292\) | 4.59082 | 0.268657 | ||||||||
\(293\) | 11.5816 | 0.676604 | 0.338302 | − | 0.941038i | \(-0.390147\pi\) | ||||
0.338302 | + | 0.941038i | \(0.390147\pi\) | |||||||
\(294\) | −9.94369 | −0.579928 | ||||||||
\(295\) | 12.8344 | 0.747250 | ||||||||
\(296\) | −3.51846 | −0.204506 | ||||||||
\(297\) | −3.30314 | −0.191668 | ||||||||
\(298\) | −5.51127 | −0.319259 | ||||||||
\(299\) | −29.5411 | −1.70841 | ||||||||
\(300\) | 11.2141 | 0.647446 | ||||||||
\(301\) | 9.74059 | 0.561438 | ||||||||
\(302\) | 9.42711 | 0.542469 | ||||||||
\(303\) | 48.9104 | 2.80983 | ||||||||
\(304\) | 7.03095 | 0.403252 | ||||||||
\(305\) | −8.77949 | −0.502712 | ||||||||
\(306\) | −16.2366 | −0.928187 | ||||||||
\(307\) | −24.7384 | −1.41189 | −0.705947 | − | 0.708264i | \(-0.749479\pi\) | ||||
−0.705947 | + | 0.708264i | \(0.749479\pi\) | |||||||
\(308\) | 2.50662 | 0.142828 | ||||||||
\(309\) | 19.6440 | 1.11751 | ||||||||
\(310\) | −2.77288 | −0.157489 | ||||||||
\(311\) | 19.6832 | 1.11613 | 0.558066 | − | 0.829796i | \(-0.311544\pi\) | ||||
0.558066 | + | 0.829796i | \(0.311544\pi\) | |||||||
\(312\) | 12.0545 | 0.682453 | ||||||||
\(313\) | 26.9784 | 1.52491 | 0.762456 | − | 0.647040i | \(-0.223993\pi\) | ||||
0.762456 | + | 0.647040i | \(0.223993\pi\) | |||||||
\(314\) | 14.6278 | 0.825497 | ||||||||
\(315\) | 5.97612 | 0.336716 | ||||||||
\(316\) | 12.9027 | 0.725832 | ||||||||
\(317\) | 5.08898 | 0.285826 | 0.142913 | − | 0.989735i | \(-0.454353\pi\) | ||||
0.142913 | + | 0.989735i | \(0.454353\pi\) | |||||||
\(318\) | 35.0393 | 1.96491 | ||||||||
\(319\) | 6.06712 | 0.339693 | ||||||||
\(320\) | 0.854809 | 0.0477853 | ||||||||
\(321\) | −42.3810 | −2.36548 | ||||||||
\(322\) | 11.5407 | 0.643137 | ||||||||
\(323\) | 29.2756 | 1.62894 | ||||||||
\(324\) | −5.49263 | −0.305146 | ||||||||
\(325\) | −19.5929 | −1.08682 | ||||||||
\(326\) | 1.17571 | 0.0651163 | ||||||||
\(327\) | −38.3716 | −2.12196 | ||||||||
\(328\) | −7.42613 | −0.410039 | ||||||||
\(329\) | 16.4754 | 0.908319 | ||||||||
\(330\) | 3.13919 | 0.172807 | ||||||||
\(331\) | −17.9887 | −0.988749 | −0.494374 | − | 0.869249i | \(-0.664603\pi\) | ||||
−0.494374 | + | 0.869249i | \(0.664603\pi\) | |||||||
\(332\) | 8.96203 | 0.491855 | ||||||||
\(333\) | 13.7200 | 0.751854 | ||||||||
\(334\) | −6.13476 | −0.335679 | ||||||||
\(335\) | 2.73141 | 0.149233 | ||||||||
\(336\) | −4.70927 | −0.256912 | ||||||||
\(337\) | −12.0506 | −0.656437 | −0.328219 | − | 0.944602i | \(-0.606448\pi\) | ||||
−0.328219 | + | 0.944602i | \(0.606448\pi\) | |||||||
\(338\) | −8.06129 | −0.438477 | ||||||||
\(339\) | 30.0400 | 1.63155 | ||||||||
\(340\) | 3.55928 | 0.193029 | ||||||||
\(341\) | 4.53528 | 0.245599 | ||||||||
\(342\) | −27.4168 | −1.48253 | ||||||||
\(343\) | −19.3372 | −1.04411 | ||||||||
\(344\) | −5.43299 | −0.292927 | ||||||||
\(345\) | 14.4531 | 0.778129 | ||||||||
\(346\) | −6.25113 | −0.336063 | ||||||||
\(347\) | 4.32749 | 0.232312 | 0.116156 | − | 0.993231i | \(-0.462943\pi\) | ||||
0.116156 | + | 0.993231i | \(0.462943\pi\) | |||||||
\(348\) | −11.3985 | −0.611024 | ||||||||
\(349\) | 7.97325 | 0.426798 | 0.213399 | − | 0.976965i | \(-0.431547\pi\) | ||||
0.213399 | + | 0.976965i | \(0.431547\pi\) | |||||||
\(350\) | 7.65426 | 0.409138 | ||||||||
\(351\) | −10.8425 | −0.578727 | ||||||||
\(352\) | −1.39811 | −0.0745196 | ||||||||
\(353\) | 8.60601 | 0.458052 | 0.229026 | − | 0.973420i | \(-0.426446\pi\) | ||||
0.229026 | + | 0.973420i | \(0.426446\pi\) | |||||||
\(354\) | 39.4380 | 2.09611 | ||||||||
\(355\) | −4.44705 | −0.236025 | ||||||||
\(356\) | −2.56615 | −0.136006 | ||||||||
\(357\) | −19.6086 | −1.03780 | ||||||||
\(358\) | 3.65995 | 0.193434 | ||||||||
\(359\) | −11.4828 | −0.606040 | −0.303020 | − | 0.952984i | \(-0.597995\pi\) | ||||
−0.303020 | + | 0.952984i | \(0.597995\pi\) | |||||||
\(360\) | −3.33329 | −0.175680 | ||||||||
\(361\) | 30.4342 | 1.60180 | ||||||||
\(362\) | 17.3263 | 0.910652 | ||||||||
\(363\) | 23.7591 | 1.24703 | ||||||||
\(364\) | 8.22790 | 0.431259 | ||||||||
\(365\) | 3.92427 | 0.205406 | ||||||||
\(366\) | −26.9779 | −1.41016 | ||||||||
\(367\) | −26.0578 | −1.36021 | −0.680104 | − | 0.733115i | \(-0.738065\pi\) | ||||
−0.680104 | + | 0.733115i | \(0.738065\pi\) | |||||||
\(368\) | −6.43702 | −0.335553 | ||||||||
\(369\) | 28.9578 | 1.50748 | ||||||||
\(370\) | −3.00761 | −0.156358 | ||||||||
\(371\) | 23.9163 | 1.24168 | ||||||||
\(372\) | −8.52059 | −0.441772 | ||||||||
\(373\) | −28.1289 | −1.45646 | −0.728230 | − | 0.685333i | \(-0.759657\pi\) | ||||
−0.728230 | + | 0.685333i | \(0.759657\pi\) | |||||||
\(374\) | −5.82150 | −0.301022 | ||||||||
\(375\) | 20.8125 | 1.07475 | ||||||||
\(376\) | −9.18945 | −0.473910 | ||||||||
\(377\) | 19.9151 | 1.02568 | ||||||||
\(378\) | 4.23576 | 0.217864 | ||||||||
\(379\) | −21.9273 | −1.12633 | −0.563164 | − | 0.826345i | \(-0.690416\pi\) | ||||
−0.563164 | + | 0.826345i | \(0.690416\pi\) | |||||||
\(380\) | 6.01012 | 0.308312 | ||||||||
\(381\) | −23.7935 | −1.21898 | ||||||||
\(382\) | −17.2881 | −0.884534 | ||||||||
\(383\) | −18.4116 | −0.940790 | −0.470395 | − | 0.882456i | \(-0.655889\pi\) | ||||
−0.470395 | + | 0.882456i | \(0.655889\pi\) | |||||||
\(384\) | 2.62668 | 0.134042 | ||||||||
\(385\) | 2.14268 | 0.109201 | ||||||||
\(386\) | 15.8238 | 0.805412 | ||||||||
\(387\) | 21.1857 | 1.07693 | ||||||||
\(388\) | −13.9084 | −0.706095 | ||||||||
\(389\) | −14.2023 | −0.720086 | −0.360043 | − | 0.932936i | \(-0.617238\pi\) | ||||
−0.360043 | + | 0.932936i | \(0.617238\pi\) | |||||||
\(390\) | 10.3043 | 0.521779 | ||||||||
\(391\) | −26.8026 | −1.35547 | ||||||||
\(392\) | 3.78565 | 0.191204 | ||||||||
\(393\) | 9.99006 | 0.503932 | ||||||||
\(394\) | 12.0973 | 0.609455 | ||||||||
\(395\) | 11.0293 | 0.554945 | ||||||||
\(396\) | 5.45187 | 0.273967 | ||||||||
\(397\) | 12.4757 | 0.626140 | 0.313070 | − | 0.949730i | \(-0.398643\pi\) | ||||
0.313070 | + | 0.949730i | \(0.398643\pi\) | |||||||
\(398\) | 18.1581 | 0.910185 | ||||||||
\(399\) | −33.1106 | −1.65761 | ||||||||
\(400\) | −4.26930 | −0.213465 | ||||||||
\(401\) | −14.5417 | −0.726176 | −0.363088 | − | 0.931755i | \(-0.618278\pi\) | ||||
−0.363088 | + | 0.931755i | \(0.618278\pi\) | |||||||
\(402\) | 8.39314 | 0.418612 | ||||||||
\(403\) | 14.8869 | 0.741570 | ||||||||
\(404\) | −18.6206 | −0.926411 | ||||||||
\(405\) | −4.69515 | −0.233304 | ||||||||
\(406\) | −7.78014 | −0.386122 | ||||||||
\(407\) | 4.91919 | 0.243835 | ||||||||
\(408\) | 10.9370 | 0.541464 | ||||||||
\(409\) | −33.6657 | −1.66466 | −0.832332 | − | 0.554278i | \(-0.812994\pi\) | ||||
−0.832332 | + | 0.554278i | \(0.812994\pi\) | |||||||
\(410\) | −6.34792 | −0.313501 | ||||||||
\(411\) | −54.2534 | −2.67612 | ||||||||
\(412\) | −7.47862 | −0.368445 | ||||||||
\(413\) | 26.9187 | 1.32458 | ||||||||
\(414\) | 25.1008 | 1.23364 | ||||||||
\(415\) | 7.66082 | 0.376055 | ||||||||
\(416\) | −4.58926 | −0.225007 | ||||||||
\(417\) | −17.8047 | −0.871901 | ||||||||
\(418\) | −9.83005 | −0.480803 | ||||||||
\(419\) | 14.6756 | 0.716952 | 0.358476 | − | 0.933539i | \(-0.383296\pi\) | ||||
0.358476 | + | 0.933539i | \(0.383296\pi\) | |||||||
\(420\) | −4.02553 | −0.196426 | ||||||||
\(421\) | 8.02186 | 0.390962 | 0.195481 | − | 0.980708i | \(-0.437373\pi\) | ||||
0.195481 | + | 0.980708i | \(0.437373\pi\) | |||||||
\(422\) | 9.69641 | 0.472014 | ||||||||
\(423\) | 35.8338 | 1.74230 | ||||||||
\(424\) | −13.3398 | −0.647836 | ||||||||
\(425\) | −17.7766 | −0.862293 | ||||||||
\(426\) | −13.6650 | −0.662073 | ||||||||
\(427\) | −18.4139 | −0.891113 | ||||||||
\(428\) | 16.1348 | 0.779906 | ||||||||
\(429\) | −16.8536 | −0.813698 | ||||||||
\(430\) | −4.64417 | −0.223962 | ||||||||
\(431\) | −7.96699 | −0.383757 | −0.191878 | − | 0.981419i | \(-0.561458\pi\) | ||||
−0.191878 | + | 0.981419i | \(0.561458\pi\) | |||||||
\(432\) | −2.36257 | −0.113669 | ||||||||
\(433\) | 11.7495 | 0.564647 | 0.282324 | − | 0.959319i | \(-0.408895\pi\) | ||||
0.282324 | + | 0.959319i | \(0.408895\pi\) | |||||||
\(434\) | −5.81579 | −0.279167 | ||||||||
\(435\) | −9.74354 | −0.467167 | ||||||||
\(436\) | 14.6084 | 0.699616 | ||||||||
\(437\) | −45.2583 | −2.16500 | ||||||||
\(438\) | 12.0586 | 0.576183 | ||||||||
\(439\) | 23.9236 | 1.14181 | 0.570906 | − | 0.821016i | \(-0.306592\pi\) | ||||
0.570906 | + | 0.821016i | \(0.306592\pi\) | |||||||
\(440\) | −1.19512 | −0.0569750 | ||||||||
\(441\) | −14.7620 | −0.702950 | ||||||||
\(442\) | −19.1089 | −0.908917 | ||||||||
\(443\) | −14.5183 | −0.689785 | −0.344893 | − | 0.938642i | \(-0.612085\pi\) | ||||
−0.344893 | + | 0.938642i | \(0.612085\pi\) | |||||||
\(444\) | −9.24186 | −0.438599 | ||||||||
\(445\) | −2.19357 | −0.103985 | ||||||||
\(446\) | 13.9655 | 0.661286 | ||||||||
\(447\) | −14.4763 | −0.684707 | ||||||||
\(448\) | 1.79286 | 0.0847047 | ||||||||
\(449\) | −13.9199 | −0.656923 | −0.328461 | − | 0.944517i | \(-0.606530\pi\) | ||||
−0.328461 | + | 0.944517i | \(0.606530\pi\) | |||||||
\(450\) | 16.6479 | 0.784791 | ||||||||
\(451\) | 10.3826 | 0.488895 | ||||||||
\(452\) | −11.4365 | −0.537928 | ||||||||
\(453\) | 24.7620 | 1.16342 | ||||||||
\(454\) | −8.81918 | −0.413905 | ||||||||
\(455\) | 7.03329 | 0.329726 | ||||||||
\(456\) | 18.4681 | 0.864846 | ||||||||
\(457\) | 34.2333 | 1.60137 | 0.800683 | − | 0.599088i | \(-0.204470\pi\) | ||||
0.800683 | + | 0.599088i | \(0.204470\pi\) | |||||||
\(458\) | 17.8260 | 0.832952 | ||||||||
\(459\) | −9.83734 | −0.459168 | ||||||||
\(460\) | −5.50242 | −0.256552 | ||||||||
\(461\) | 30.6217 | 1.42619 | 0.713097 | − | 0.701065i | \(-0.247292\pi\) | ||||
0.713097 | + | 0.701065i | \(0.247292\pi\) | |||||||
\(462\) | 6.58409 | 0.306320 | ||||||||
\(463\) | 2.79958 | 0.130107 | 0.0650537 | − | 0.997882i | \(-0.479278\pi\) | ||||
0.0650537 | + | 0.997882i | \(0.479278\pi\) | |||||||
\(464\) | 4.33951 | 0.201457 | ||||||||
\(465\) | −7.28348 | −0.337763 | ||||||||
\(466\) | 13.1809 | 0.610594 | ||||||||
\(467\) | 18.1898 | 0.841726 | 0.420863 | − | 0.907124i | \(-0.361727\pi\) | ||||
0.420863 | + | 0.907124i | \(0.361727\pi\) | |||||||
\(468\) | 17.8956 | 0.827224 | ||||||||
\(469\) | 5.72880 | 0.264532 | ||||||||
\(470\) | −7.85522 | −0.362334 | ||||||||
\(471\) | 38.4227 | 1.77042 | ||||||||
\(472\) | −15.0144 | −0.691093 | ||||||||
\(473\) | 7.59592 | 0.349261 | ||||||||
\(474\) | 33.8912 | 1.55667 | ||||||||
\(475\) | −30.0172 | −1.37728 | ||||||||
\(476\) | 7.46516 | 0.342165 | ||||||||
\(477\) | 52.0178 | 2.38173 | ||||||||
\(478\) | −13.2733 | −0.607107 | ||||||||
\(479\) | 11.2498 | 0.514014 | 0.257007 | − | 0.966409i | \(-0.417264\pi\) | ||||
0.257007 | + | 0.966409i | \(0.417264\pi\) | |||||||
\(480\) | 2.24531 | 0.102484 | ||||||||
\(481\) | 16.1471 | 0.736244 | ||||||||
\(482\) | 9.51088 | 0.433209 | ||||||||
\(483\) | 30.3137 | 1.37932 | ||||||||
\(484\) | −9.04528 | −0.411149 | ||||||||
\(485\) | −11.8891 | −0.539855 | ||||||||
\(486\) | −21.5151 | −0.975945 | ||||||||
\(487\) | 0.183892 | 0.00833294 | 0.00416647 | − | 0.999991i | \(-0.498674\pi\) | ||||
0.00416647 | + | 0.999991i | \(0.498674\pi\) | |||||||
\(488\) | 10.2707 | 0.464933 | ||||||||
\(489\) | 3.08820 | 0.139653 | ||||||||
\(490\) | 3.23601 | 0.146188 | ||||||||
\(491\) | −13.3053 | −0.600461 | −0.300230 | − | 0.953867i | \(-0.597064\pi\) | ||||
−0.300230 | + | 0.953867i | \(0.597064\pi\) | |||||||
\(492\) | −19.5061 | −0.879401 | ||||||||
\(493\) | 18.0690 | 0.813785 | ||||||||
\(494\) | −32.2668 | −1.45175 | ||||||||
\(495\) | 4.66031 | 0.209465 | ||||||||
\(496\) | 3.24386 | 0.145654 | ||||||||
\(497\) | −9.32717 | −0.418381 | ||||||||
\(498\) | 23.5404 | 1.05487 | ||||||||
\(499\) | −12.7933 | −0.572707 | −0.286353 | − | 0.958124i | \(-0.592443\pi\) | ||||
−0.286353 | + | 0.958124i | \(0.592443\pi\) | |||||||
\(500\) | −7.92348 | −0.354349 | ||||||||
\(501\) | −16.1141 | −0.719923 | ||||||||
\(502\) | 25.2709 | 1.12789 | ||||||||
\(503\) | 30.8891 | 1.37728 | 0.688638 | − | 0.725105i | \(-0.258209\pi\) | ||||
0.688638 | + | 0.725105i | \(0.258209\pi\) | |||||||
\(504\) | −6.99118 | −0.311412 | ||||||||
\(505\) | −15.9171 | −0.708301 | ||||||||
\(506\) | 8.99967 | 0.400084 | ||||||||
\(507\) | −21.1744 | −0.940390 | ||||||||
\(508\) | 9.05839 | 0.401901 | ||||||||
\(509\) | −1.90594 | −0.0844795 | −0.0422397 | − | 0.999108i | \(-0.513449\pi\) | ||||
−0.0422397 | + | 0.999108i | \(0.513449\pi\) | |||||||
\(510\) | 9.34908 | 0.413984 | ||||||||
\(511\) | 8.23070 | 0.364105 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −16.6111 | −0.733399 | ||||||||
\(514\) | −0.815232 | −0.0359583 | ||||||||
\(515\) | −6.39279 | −0.281700 | ||||||||
\(516\) | −14.2707 | −0.628234 | ||||||||
\(517\) | 12.8479 | 0.565049 | ||||||||
\(518\) | −6.30810 | −0.277162 | ||||||||
\(519\) | −16.4197 | −0.720745 | ||||||||
\(520\) | −3.92294 | −0.172032 | ||||||||
\(521\) | −13.2261 | −0.579445 | −0.289722 | − | 0.957111i | \(-0.593563\pi\) | ||||
−0.289722 | + | 0.957111i | \(0.593563\pi\) | |||||||
\(522\) | −16.9217 | −0.740643 | ||||||||
\(523\) | −15.3727 | −0.672200 | −0.336100 | − | 0.941826i | \(-0.609108\pi\) | ||||
−0.336100 | + | 0.941826i | \(0.609108\pi\) | |||||||
\(524\) | −3.80330 | −0.166148 | ||||||||
\(525\) | 20.1053 | 0.877468 | ||||||||
\(526\) | 25.4272 | 1.10868 | ||||||||
\(527\) | 13.5069 | 0.588369 | ||||||||
\(528\) | −3.67239 | −0.159820 | ||||||||
\(529\) | 18.4352 | 0.801530 | ||||||||
\(530\) | −11.4030 | −0.495313 | ||||||||
\(531\) | 58.5479 | 2.54076 | ||||||||
\(532\) | 12.6055 | 0.546518 | ||||||||
\(533\) | 34.0804 | 1.47619 | ||||||||
\(534\) | −6.74045 | −0.291688 | ||||||||
\(535\) | 13.7922 | 0.596288 | ||||||||
\(536\) | −3.19534 | −0.138018 | ||||||||
\(537\) | 9.61351 | 0.414853 | ||||||||
\(538\) | 18.1899 | 0.784223 | ||||||||
\(539\) | −5.29276 | −0.227975 | ||||||||
\(540\) | −2.01955 | −0.0869075 | ||||||||
\(541\) | 28.4009 | 1.22105 | 0.610525 | − | 0.791997i | \(-0.290958\pi\) | ||||
0.610525 | + | 0.791997i | \(0.290958\pi\) | |||||||
\(542\) | 9.42443 | 0.404814 | ||||||||
\(543\) | 45.5107 | 1.95305 | ||||||||
\(544\) | −4.16383 | −0.178523 | ||||||||
\(545\) | 12.4874 | 0.534901 | ||||||||
\(546\) | 21.6121 | 0.924911 | ||||||||
\(547\) | 34.5878 | 1.47887 | 0.739434 | − | 0.673229i | \(-0.235093\pi\) | ||||
0.739434 | + | 0.673229i | \(0.235093\pi\) | |||||||
\(548\) | 20.6547 | 0.882326 | ||||||||
\(549\) | −40.0501 | −1.70930 | ||||||||
\(550\) | 5.96896 | 0.254517 | ||||||||
\(551\) | 30.5109 | 1.29981 | ||||||||
\(552\) | −16.9080 | −0.719652 | ||||||||
\(553\) | 23.1327 | 0.983702 | ||||||||
\(554\) | −22.4304 | −0.952975 | ||||||||
\(555\) | −7.90002 | −0.335337 | ||||||||
\(556\) | 6.77841 | 0.287469 | ||||||||
\(557\) | −24.9401 | −1.05675 | −0.528373 | − | 0.849012i | \(-0.677198\pi\) | ||||
−0.528373 | + | 0.849012i | \(0.677198\pi\) | |||||||
\(558\) | −12.6493 | −0.535487 | ||||||||
\(559\) | 24.9334 | 1.05457 | ||||||||
\(560\) | 1.53255 | 0.0647622 | ||||||||
\(561\) | −15.2912 | −0.645595 | ||||||||
\(562\) | −9.63200 | −0.406302 | ||||||||
\(563\) | −26.1339 | −1.10141 | −0.550706 | − | 0.834699i | \(-0.685642\pi\) | ||||
−0.550706 | + | 0.834699i | \(0.685642\pi\) | |||||||
\(564\) | −24.1378 | −1.01638 | ||||||||
\(565\) | −9.77603 | −0.411280 | ||||||||
\(566\) | 18.2230 | 0.765969 | ||||||||
\(567\) | −9.84753 | −0.413557 | ||||||||
\(568\) | 5.20239 | 0.218288 | ||||||||
\(569\) | −9.66767 | −0.405290 | −0.202645 | − | 0.979252i | \(-0.564954\pi\) | ||||
−0.202645 | + | 0.979252i | \(0.564954\pi\) | |||||||
\(570\) | 15.7867 | 0.661230 | ||||||||
\(571\) | 15.4616 | 0.647046 | 0.323523 | − | 0.946220i | \(-0.395133\pi\) | ||||
0.323523 | + | 0.946220i | \(0.395133\pi\) | |||||||
\(572\) | 6.41630 | 0.268279 | ||||||||
\(573\) | −45.4102 | −1.89704 | ||||||||
\(574\) | −13.3140 | −0.555716 | ||||||||
\(575\) | 27.4816 | 1.14606 | ||||||||
\(576\) | 3.89945 | 0.162477 | ||||||||
\(577\) | 26.6487 | 1.10940 | 0.554700 | − | 0.832050i | \(-0.312833\pi\) | ||||
0.554700 | + | 0.832050i | \(0.312833\pi\) | |||||||
\(578\) | −0.337458 | −0.0140364 | ||||||||
\(579\) | 41.5641 | 1.72735 | ||||||||
\(580\) | 3.70945 | 0.154027 | ||||||||
\(581\) | 16.0677 | 0.666599 | ||||||||
\(582\) | −36.5331 | −1.51434 | ||||||||
\(583\) | 18.6505 | 0.772424 | ||||||||
\(584\) | −4.59082 | −0.189970 | ||||||||
\(585\) | 15.2973 | 0.632466 | ||||||||
\(586\) | −11.5816 | −0.478432 | ||||||||
\(587\) | 5.65942 | 0.233589 | 0.116795 | − | 0.993156i | \(-0.462738\pi\) | ||||
0.116795 | + | 0.993156i | \(0.462738\pi\) | |||||||
\(588\) | 9.94369 | 0.410071 | ||||||||
\(589\) | 22.8074 | 0.939763 | ||||||||
\(590\) | −12.8344 | −0.528385 | ||||||||
\(591\) | 31.7758 | 1.30708 | ||||||||
\(592\) | 3.51846 | 0.144608 | ||||||||
\(593\) | 18.9259 | 0.777195 | 0.388598 | − | 0.921408i | \(-0.372960\pi\) | ||||
0.388598 | + | 0.921408i | \(0.372960\pi\) | |||||||
\(594\) | 3.30314 | 0.135529 | ||||||||
\(595\) | 6.38129 | 0.261607 | ||||||||
\(596\) | 5.51127 | 0.225750 | ||||||||
\(597\) | 47.6956 | 1.95205 | ||||||||
\(598\) | 29.5411 | 1.20803 | ||||||||
\(599\) | −6.03648 | −0.246644 | −0.123322 | − | 0.992367i | \(-0.539355\pi\) | ||||
−0.123322 | + | 0.992367i | \(0.539355\pi\) | |||||||
\(600\) | −11.2141 | −0.457813 | ||||||||
\(601\) | 13.7806 | 0.562122 | 0.281061 | − | 0.959690i | \(-0.409314\pi\) | ||||
0.281061 | + | 0.959690i | \(0.409314\pi\) | |||||||
\(602\) | −9.74059 | −0.396997 | ||||||||
\(603\) | 12.4601 | 0.507414 | ||||||||
\(604\) | −9.42711 | −0.383584 | ||||||||
\(605\) | −7.73199 | −0.314350 | ||||||||
\(606\) | −48.9104 | −1.98685 | ||||||||
\(607\) | 16.5217 | 0.670597 | 0.335298 | − | 0.942112i | \(-0.391163\pi\) | ||||
0.335298 | + | 0.942112i | \(0.391163\pi\) | |||||||
\(608\) | −7.03095 | −0.285143 | ||||||||
\(609\) | −20.4359 | −0.828106 | ||||||||
\(610\) | 8.77949 | 0.355471 | ||||||||
\(611\) | 42.1728 | 1.70613 | ||||||||
\(612\) | 16.2366 | 0.656327 | ||||||||
\(613\) | −26.2590 | −1.06059 | −0.530295 | − | 0.847813i | \(-0.677919\pi\) | ||||
−0.530295 | + | 0.847813i | \(0.677919\pi\) | |||||||
\(614\) | 24.7384 | 0.998360 | ||||||||
\(615\) | −16.6740 | −0.672359 | ||||||||
\(616\) | −2.50662 | −0.100995 | ||||||||
\(617\) | −32.8817 | −1.32377 | −0.661884 | − | 0.749607i | \(-0.730243\pi\) | ||||
−0.661884 | + | 0.749607i | \(0.730243\pi\) | |||||||
\(618\) | −19.6440 | −0.790196 | ||||||||
\(619\) | −6.10571 | −0.245409 | −0.122705 | − | 0.992443i | \(-0.539157\pi\) | ||||
−0.122705 | + | 0.992443i | \(0.539157\pi\) | |||||||
\(620\) | 2.77288 | 0.111362 | ||||||||
\(621\) | 15.2079 | 0.610273 | ||||||||
\(622\) | −19.6832 | −0.789225 | ||||||||
\(623\) | −4.60075 | −0.184325 | ||||||||
\(624\) | −12.0545 | −0.482567 | ||||||||
\(625\) | 14.5734 | 0.582938 | ||||||||
\(626\) | −26.9784 | −1.07828 | ||||||||
\(627\) | −25.8204 | −1.03117 | ||||||||
\(628\) | −14.6278 | −0.583715 | ||||||||
\(629\) | 14.6502 | 0.584143 | ||||||||
\(630\) | −5.97612 | −0.238094 | ||||||||
\(631\) | 41.1629 | 1.63867 | 0.819335 | − | 0.573315i | \(-0.194343\pi\) | ||||
0.819335 | + | 0.573315i | \(0.194343\pi\) | |||||||
\(632\) | −12.9027 | −0.513241 | ||||||||
\(633\) | 25.4694 | 1.01232 | ||||||||
\(634\) | −5.08898 | −0.202109 | ||||||||
\(635\) | 7.74319 | 0.307279 | ||||||||
\(636\) | −35.0393 | −1.38940 | ||||||||
\(637\) | −17.3733 | −0.688356 | ||||||||
\(638\) | −6.06712 | −0.240200 | ||||||||
\(639\) | −20.2865 | −0.802521 | ||||||||
\(640\) | −0.854809 | −0.0337893 | ||||||||
\(641\) | −32.4758 | −1.28272 | −0.641359 | − | 0.767241i | \(-0.721629\pi\) | ||||
−0.641359 | + | 0.767241i | \(0.721629\pi\) | |||||||
\(642\) | 42.3810 | 1.67265 | ||||||||
\(643\) | 20.5401 | 0.810022 | 0.405011 | − | 0.914312i | \(-0.367268\pi\) | ||||
0.405011 | + | 0.914312i | \(0.367268\pi\) | |||||||
\(644\) | −11.5407 | −0.454766 | ||||||||
\(645\) | −12.1987 | −0.480325 | ||||||||
\(646\) | −29.2756 | −1.15183 | ||||||||
\(647\) | −30.1269 | −1.18441 | −0.592205 | − | 0.805787i | \(-0.701742\pi\) | ||||
−0.592205 | + | 0.805787i | \(0.701742\pi\) | |||||||
\(648\) | 5.49263 | 0.215771 | ||||||||
\(649\) | 20.9918 | 0.824000 | ||||||||
\(650\) | 19.5929 | 0.768498 | ||||||||
\(651\) | −15.2762 | −0.598723 | ||||||||
\(652\) | −1.17571 | −0.0460442 | ||||||||
\(653\) | 42.0664 | 1.64619 | 0.823093 | − | 0.567906i | \(-0.192246\pi\) | ||||
0.823093 | + | 0.567906i | \(0.192246\pi\) | |||||||
\(654\) | 38.3716 | 1.50045 | ||||||||
\(655\) | −3.25110 | −0.127031 | ||||||||
\(656\) | 7.42613 | 0.289942 | ||||||||
\(657\) | 17.9017 | 0.698411 | ||||||||
\(658\) | −16.4754 | −0.642278 | ||||||||
\(659\) | −8.63696 | −0.336448 | −0.168224 | − | 0.985749i | \(-0.553803\pi\) | ||||
−0.168224 | + | 0.985749i | \(0.553803\pi\) | |||||||
\(660\) | −3.13919 | −0.122193 | ||||||||
\(661\) | −46.9973 | −1.82798 | −0.913992 | − | 0.405733i | \(-0.867016\pi\) | ||||
−0.913992 | + | 0.405733i | \(0.867016\pi\) | |||||||
\(662\) | 17.9887 | 0.699151 | ||||||||
\(663\) | −50.1929 | −1.94933 | ||||||||
\(664\) | −8.96203 | −0.347794 | ||||||||
\(665\) | 10.7753 | 0.417848 | ||||||||
\(666\) | −13.7200 | −0.531641 | ||||||||
\(667\) | −27.9335 | −1.08159 | ||||||||
\(668\) | 6.13476 | 0.237361 | ||||||||
\(669\) | 36.6829 | 1.41824 | ||||||||
\(670\) | −2.73141 | −0.105523 | ||||||||
\(671\) | −14.3596 | −0.554346 | ||||||||
\(672\) | 4.70927 | 0.181664 | ||||||||
\(673\) | −5.05267 | −0.194766 | −0.0973830 | − | 0.995247i | \(-0.531047\pi\) | ||||
−0.0973830 | + | 0.995247i | \(0.531047\pi\) | |||||||
\(674\) | 12.0506 | 0.464171 | ||||||||
\(675\) | 10.0865 | 0.388231 | ||||||||
\(676\) | 8.06129 | 0.310050 | ||||||||
\(677\) | −8.93098 | −0.343246 | −0.171623 | − | 0.985163i | \(-0.554901\pi\) | ||||
−0.171623 | + | 0.985163i | \(0.554901\pi\) | |||||||
\(678\) | −30.0400 | −1.15368 | ||||||||
\(679\) | −24.9359 | −0.956953 | ||||||||
\(680\) | −3.55928 | −0.136492 | ||||||||
\(681\) | −23.1652 | −0.887691 | ||||||||
\(682\) | −4.53528 | −0.173665 | ||||||||
\(683\) | 26.7911 | 1.02513 | 0.512566 | − | 0.858648i | \(-0.328695\pi\) | ||||
0.512566 | + | 0.858648i | \(0.328695\pi\) | |||||||
\(684\) | 27.4168 | 1.04831 | ||||||||
\(685\) | 17.6558 | 0.674595 | ||||||||
\(686\) | 19.3372 | 0.738297 | ||||||||
\(687\) | 46.8231 | 1.78641 | ||||||||
\(688\) | 5.43299 | 0.207131 | ||||||||
\(689\) | 61.2196 | 2.33228 | ||||||||
\(690\) | −14.4531 | −0.550220 | ||||||||
\(691\) | 31.2062 | 1.18714 | 0.593571 | − | 0.804782i | \(-0.297718\pi\) | ||||
0.593571 | + | 0.804782i | \(0.297718\pi\) | |||||||
\(692\) | 6.25113 | 0.237632 | ||||||||
\(693\) | 9.77444 | 0.371300 | ||||||||
\(694\) | −4.32749 | −0.164269 | ||||||||
\(695\) | 5.79425 | 0.219788 | ||||||||
\(696\) | 11.3985 | 0.432059 | ||||||||
\(697\) | 30.9211 | 1.17122 | ||||||||
\(698\) | −7.97325 | −0.301792 | ||||||||
\(699\) | 34.6221 | 1.30953 | ||||||||
\(700\) | −7.65426 | −0.289304 | ||||||||
\(701\) | −29.3651 | −1.10910 | −0.554552 | − | 0.832149i | \(-0.687110\pi\) | ||||
−0.554552 | + | 0.832149i | \(0.687110\pi\) | |||||||
\(702\) | 10.8425 | 0.409222 | ||||||||
\(703\) | 24.7381 | 0.933014 | ||||||||
\(704\) | 1.39811 | 0.0526933 | ||||||||
\(705\) | −20.6332 | −0.777090 | ||||||||
\(706\) | −8.60601 | −0.323892 | ||||||||
\(707\) | −33.3842 | −1.25554 | ||||||||
\(708\) | −39.4380 | −1.48217 | ||||||||
\(709\) | 19.6656 | 0.738558 | 0.369279 | − | 0.929319i | \(-0.379605\pi\) | ||||
0.369279 | + | 0.929319i | \(0.379605\pi\) | |||||||
\(710\) | 4.44705 | 0.166895 | ||||||||
\(711\) | 50.3133 | 1.88690 | ||||||||
\(712\) | 2.56615 | 0.0961704 | ||||||||
\(713\) | −20.8808 | −0.781992 | ||||||||
\(714\) | 19.6086 | 0.733833 | ||||||||
\(715\) | 5.48471 | 0.205116 | ||||||||
\(716\) | −3.65995 | −0.136779 | ||||||||
\(717\) | −34.8647 | −1.30205 | ||||||||
\(718\) | 11.4828 | 0.428535 | ||||||||
\(719\) | −4.74756 | −0.177054 | −0.0885271 | − | 0.996074i | \(-0.528216\pi\) | ||||
−0.0885271 | + | 0.996074i | \(0.528216\pi\) | |||||||
\(720\) | 3.33329 | 0.124224 | ||||||||
\(721\) | −13.4081 | −0.499345 | ||||||||
\(722\) | −30.4342 | −1.13264 | ||||||||
\(723\) | 24.9820 | 0.929092 | ||||||||
\(724\) | −17.3263 | −0.643928 | ||||||||
\(725\) | −18.5267 | −0.688063 | ||||||||
\(726\) | −23.7591 | −0.881782 | ||||||||
\(727\) | −3.26857 | −0.121224 | −0.0606122 | − | 0.998161i | \(-0.519305\pi\) | ||||
−0.0606122 | + | 0.998161i | \(0.519305\pi\) | |||||||
\(728\) | −8.22790 | −0.304946 | ||||||||
\(729\) | −40.0354 | −1.48279 | ||||||||
\(730\) | −3.92427 | −0.145244 | ||||||||
\(731\) | 22.6220 | 0.836706 | ||||||||
\(732\) | 26.9779 | 0.997130 | ||||||||
\(733\) | −17.7987 | −0.657411 | −0.328706 | − | 0.944432i | \(-0.606612\pi\) | ||||
−0.328706 | + | 0.944432i | \(0.606612\pi\) | |||||||
\(734\) | 26.0578 | 0.961813 | ||||||||
\(735\) | 8.49996 | 0.313526 | ||||||||
\(736\) | 6.43702 | 0.237272 | ||||||||
\(737\) | 4.46745 | 0.164560 | ||||||||
\(738\) | −28.9578 | −1.06595 | ||||||||
\(739\) | 22.1082 | 0.813262 | 0.406631 | − | 0.913593i | \(-0.366704\pi\) | ||||
0.406631 | + | 0.913593i | \(0.366704\pi\) | |||||||
\(740\) | 3.00761 | 0.110562 | ||||||||
\(741\) | −84.7547 | −3.11354 | ||||||||
\(742\) | −23.9163 | −0.877997 | ||||||||
\(743\) | 36.2103 | 1.32843 | 0.664214 | − | 0.747543i | \(-0.268766\pi\) | ||||
0.664214 | + | 0.747543i | \(0.268766\pi\) | |||||||
\(744\) | 8.52059 | 0.312380 | ||||||||
\(745\) | 4.71108 | 0.172601 | ||||||||
\(746\) | 28.1289 | 1.02987 | ||||||||
\(747\) | 34.9470 | 1.27864 | ||||||||
\(748\) | 5.82150 | 0.212855 | ||||||||
\(749\) | 28.9275 | 1.05699 | ||||||||
\(750\) | −20.8125 | −0.759964 | ||||||||
\(751\) | 31.6501 | 1.15493 | 0.577465 | − | 0.816416i | \(-0.304042\pi\) | ||||
0.577465 | + | 0.816416i | \(0.304042\pi\) | |||||||
\(752\) | 9.18945 | 0.335105 | ||||||||
\(753\) | 66.3785 | 2.41897 | ||||||||
\(754\) | −19.9151 | −0.725266 | ||||||||
\(755\) | −8.05838 | −0.293274 | ||||||||
\(756\) | −4.23576 | −0.154053 | ||||||||
\(757\) | 32.2734 | 1.17300 | 0.586499 | − | 0.809950i | \(-0.300506\pi\) | ||||
0.586499 | + | 0.809950i | \(0.300506\pi\) | |||||||
\(758\) | 21.9273 | 0.796434 | ||||||||
\(759\) | 23.6393 | 0.858051 | ||||||||
\(760\) | −6.01012 | −0.218010 | ||||||||
\(761\) | 0.674180 | 0.0244390 | 0.0122195 | − | 0.999925i | \(-0.496110\pi\) | ||||
0.0122195 | + | 0.999925i | \(0.496110\pi\) | |||||||
\(762\) | 23.7935 | 0.861948 | ||||||||
\(763\) | 26.1909 | 0.948172 | ||||||||
\(764\) | 17.2881 | 0.625460 | ||||||||
\(765\) | 13.8792 | 0.501805 | ||||||||
\(766\) | 18.4116 | 0.665239 | ||||||||
\(767\) | 68.9049 | 2.48801 | ||||||||
\(768\) | −2.62668 | −0.0947822 | ||||||||
\(769\) | 20.2062 | 0.728653 | 0.364326 | − | 0.931271i | \(-0.381299\pi\) | ||||
0.364326 | + | 0.931271i | \(0.381299\pi\) | |||||||
\(770\) | −2.14268 | −0.0772169 | ||||||||
\(771\) | −2.14135 | −0.0771190 | ||||||||
\(772\) | −15.8238 | −0.569512 | ||||||||
\(773\) | −40.8794 | −1.47033 | −0.735165 | − | 0.677888i | \(-0.762895\pi\) | ||||
−0.735165 | + | 0.677888i | \(0.762895\pi\) | |||||||
\(774\) | −21.1857 | −0.761503 | ||||||||
\(775\) | −13.8490 | −0.497472 | ||||||||
\(776\) | 13.9084 | 0.499284 | ||||||||
\(777\) | −16.5694 | −0.594423 | ||||||||
\(778\) | 14.2023 | 0.509178 | ||||||||
\(779\) | 52.2127 | 1.87071 | ||||||||
\(780\) | −10.3043 | −0.368953 | ||||||||
\(781\) | −7.27353 | −0.260267 | ||||||||
\(782\) | 26.8026 | 0.958460 | ||||||||
\(783\) | −10.2524 | −0.366391 | ||||||||
\(784\) | −3.78565 | −0.135202 | ||||||||
\(785\) | −12.5040 | −0.446287 | ||||||||
\(786\) | −9.99006 | −0.356334 | ||||||||
\(787\) | −0.586423 | −0.0209037 | −0.0104519 | − | 0.999945i | \(-0.503327\pi\) | ||||
−0.0104519 | + | 0.999945i | \(0.503327\pi\) | |||||||
\(788\) | −12.0973 | −0.430950 | ||||||||
\(789\) | 66.7891 | 2.37776 | ||||||||
\(790\) | −11.0293 | −0.392406 | ||||||||
\(791\) | −20.5041 | −0.729040 | ||||||||
\(792\) | −5.45187 | −0.193724 | ||||||||
\(793\) | −47.1349 | −1.67381 | ||||||||
\(794\) | −12.4757 | −0.442748 | ||||||||
\(795\) | −29.9519 | −1.06229 | ||||||||
\(796\) | −18.1581 | −0.643598 | ||||||||
\(797\) | 40.4574 | 1.43307 | 0.716537 | − | 0.697549i | \(-0.245726\pi\) | ||||
0.716537 | + | 0.697549i | \(0.245726\pi\) | |||||||
\(798\) | 33.1106 | 1.17210 | ||||||||
\(799\) | 38.2633 | 1.35366 | ||||||||
\(800\) | 4.26930 | 0.150943 | ||||||||
\(801\) | −10.0066 | −0.353565 | ||||||||
\(802\) | 14.5417 | 0.513484 | ||||||||
\(803\) | 6.41848 | 0.226503 | ||||||||
\(804\) | −8.39314 | −0.296003 | ||||||||
\(805\) | −9.86508 | −0.347698 | ||||||||
\(806\) | −14.8869 | −0.524369 | ||||||||
\(807\) | 47.7791 | 1.68190 | ||||||||
\(808\) | 18.6206 | 0.655071 | ||||||||
\(809\) | 26.7279 | 0.939704 | 0.469852 | − | 0.882745i | \(-0.344307\pi\) | ||||
0.469852 | + | 0.882745i | \(0.344307\pi\) | |||||||
\(810\) | 4.69515 | 0.164971 | ||||||||
\(811\) | −16.8999 | −0.593435 | −0.296717 | − | 0.954965i | \(-0.595892\pi\) | ||||
−0.296717 | + | 0.954965i | \(0.595892\pi\) | |||||||
\(812\) | 7.78014 | 0.273029 | ||||||||
\(813\) | 24.7550 | 0.868195 | ||||||||
\(814\) | −4.91919 | −0.172418 | ||||||||
\(815\) | −1.00500 | −0.0352038 | ||||||||
\(816\) | −10.9370 | −0.382873 | ||||||||
\(817\) | 38.1990 | 1.33642 | ||||||||
\(818\) | 33.6657 | 1.17709 | ||||||||
\(819\) | 32.0843 | 1.12112 | ||||||||
\(820\) | 6.34792 | 0.221679 | ||||||||
\(821\) | −52.8740 | −1.84532 | −0.922658 | − | 0.385620i | \(-0.873988\pi\) | ||||
−0.922658 | + | 0.385620i | \(0.873988\pi\) | |||||||
\(822\) | 54.2534 | 1.89230 | ||||||||
\(823\) | 41.6115 | 1.45049 | 0.725243 | − | 0.688493i | \(-0.241727\pi\) | ||||
0.725243 | + | 0.688493i | \(0.241727\pi\) | |||||||
\(824\) | 7.47862 | 0.260530 | ||||||||
\(825\) | 15.6786 | 0.545857 | ||||||||
\(826\) | −26.9187 | −0.936622 | ||||||||
\(827\) | −48.2422 | −1.67754 | −0.838772 | − | 0.544483i | \(-0.816726\pi\) | ||||
−0.838772 | + | 0.544483i | \(0.816726\pi\) | |||||||
\(828\) | −25.1008 | −0.872314 | ||||||||
\(829\) | 27.6293 | 0.959605 | 0.479802 | − | 0.877377i | \(-0.340708\pi\) | ||||
0.479802 | + | 0.877377i | \(0.340708\pi\) | |||||||
\(830\) | −7.66082 | −0.265911 | ||||||||
\(831\) | −58.9174 | −2.04382 | ||||||||
\(832\) | 4.58926 | 0.159104 | ||||||||
\(833\) | −15.7628 | −0.546148 | ||||||||
\(834\) | 17.8047 | 0.616527 | ||||||||
\(835\) | 5.24405 | 0.181478 | ||||||||
\(836\) | 9.83005 | 0.339979 | ||||||||
\(837\) | −7.66386 | −0.264902 | ||||||||
\(838\) | −14.6756 | −0.506962 | ||||||||
\(839\) | 38.7610 | 1.33818 | 0.669090 | − | 0.743182i | \(-0.266684\pi\) | ||||
0.669090 | + | 0.743182i | \(0.266684\pi\) | |||||||
\(840\) | 4.02553 | 0.138894 | ||||||||
\(841\) | −10.1687 | −0.350643 | ||||||||
\(842\) | −8.02186 | −0.276452 | ||||||||
\(843\) | −25.3002 | −0.871385 | ||||||||
\(844\) | −9.69641 | −0.333764 | ||||||||
\(845\) | 6.89087 | 0.237053 | ||||||||
\(846\) | −35.8338 | −1.23199 | ||||||||
\(847\) | −16.2169 | −0.557221 | ||||||||
\(848\) | 13.3398 | 0.458090 | ||||||||
\(849\) | 47.8659 | 1.64275 | ||||||||
\(850\) | 17.7766 | 0.609734 | ||||||||
\(851\) | −22.6484 | −0.776376 | ||||||||
\(852\) | 13.6650 | 0.468156 | ||||||||
\(853\) | 26.2095 | 0.897397 | 0.448698 | − | 0.893683i | \(-0.351888\pi\) | ||||
0.448698 | + | 0.893683i | \(0.351888\pi\) | |||||||
\(854\) | 18.4139 | 0.630112 | ||||||||
\(855\) | 23.4362 | 0.801500 | ||||||||
\(856\) | −16.1348 | −0.551477 | ||||||||
\(857\) | −18.9087 | −0.645908 | −0.322954 | − | 0.946415i | \(-0.604676\pi\) | ||||
−0.322954 | + | 0.946415i | \(0.604676\pi\) | |||||||
\(858\) | 16.8536 | 0.575371 | ||||||||
\(859\) | −44.9505 | −1.53369 | −0.766845 | − | 0.641832i | \(-0.778175\pi\) | ||||
−0.766845 | + | 0.641832i | \(0.778175\pi\) | |||||||
\(860\) | 4.64417 | 0.158365 | ||||||||
\(861\) | −34.9717 | −1.19183 | ||||||||
\(862\) | 7.96699 | 0.271357 | ||||||||
\(863\) | 13.5828 | 0.462362 | 0.231181 | − | 0.972911i | \(-0.425741\pi\) | ||||
0.231181 | + | 0.972911i | \(0.425741\pi\) | |||||||
\(864\) | 2.36257 | 0.0803763 | ||||||||
\(865\) | 5.34352 | 0.181685 | ||||||||
\(866\) | −11.7495 | −0.399266 | ||||||||
\(867\) | −0.886394 | −0.0301035 | ||||||||
\(868\) | 5.81579 | 0.197401 | ||||||||
\(869\) | 18.0394 | 0.611944 | ||||||||
\(870\) | 9.74354 | 0.330337 | ||||||||
\(871\) | 14.6643 | 0.496879 | ||||||||
\(872\) | −14.6084 | −0.494703 | ||||||||
\(873\) | −54.2353 | −1.83559 | ||||||||
\(874\) | 45.2583 | 1.53089 | ||||||||
\(875\) | −14.2057 | −0.480240 | ||||||||
\(876\) | −12.0586 | −0.407423 | ||||||||
\(877\) | −21.6707 | −0.731767 | −0.365883 | − | 0.930661i | \(-0.619233\pi\) | ||||
−0.365883 | + | 0.930661i | \(0.619233\pi\) | |||||||
\(878\) | −23.9236 | −0.807382 | ||||||||
\(879\) | −30.4212 | −1.02608 | ||||||||
\(880\) | 1.19512 | 0.0402874 | ||||||||
\(881\) | −51.9407 | −1.74993 | −0.874963 | − | 0.484190i | \(-0.839114\pi\) | ||||
−0.874963 | + | 0.484190i | \(0.839114\pi\) | |||||||
\(882\) | 14.7620 | 0.497061 | ||||||||
\(883\) | −8.02180 | −0.269955 | −0.134978 | − | 0.990849i | \(-0.543096\pi\) | ||||
−0.134978 | + | 0.990849i | \(0.543096\pi\) | |||||||
\(884\) | 19.1089 | 0.642701 | ||||||||
\(885\) | −33.7120 | −1.13321 | ||||||||
\(886\) | 14.5183 | 0.487752 | ||||||||
\(887\) | 53.2708 | 1.78866 | 0.894330 | − | 0.447408i | \(-0.147653\pi\) | ||||
0.894330 | + | 0.447408i | \(0.147653\pi\) | |||||||
\(888\) | 9.24186 | 0.310136 | ||||||||
\(889\) | 16.2404 | 0.544687 | ||||||||
\(890\) | 2.19357 | 0.0735285 | ||||||||
\(891\) | −7.67931 | −0.257267 | ||||||||
\(892\) | −13.9655 | −0.467600 | ||||||||
\(893\) | 64.6105 | 2.16211 | ||||||||
\(894\) | 14.4763 | 0.484161 | ||||||||
\(895\) | −3.12855 | −0.104576 | ||||||||
\(896\) | −1.79286 | −0.0598953 | ||||||||
\(897\) | 77.5951 | 2.59083 | ||||||||
\(898\) | 13.9199 | 0.464515 | ||||||||
\(899\) | 14.0768 | 0.469486 | ||||||||
\(900\) | −16.6479 | −0.554931 | ||||||||
\(901\) | 55.5445 | 1.85046 | ||||||||
\(902\) | −10.3826 | −0.345701 | ||||||||
\(903\) | −25.5854 | −0.851430 | ||||||||
\(904\) | 11.4365 | 0.380372 | ||||||||
\(905\) | −14.8107 | −0.492324 | ||||||||
\(906\) | −24.7620 | −0.822663 | ||||||||
\(907\) | 35.1878 | 1.16839 | 0.584196 | − | 0.811613i | \(-0.301410\pi\) | ||||
0.584196 | + | 0.811613i | \(0.301410\pi\) | |||||||
\(908\) | 8.81918 | 0.292675 | ||||||||
\(909\) | −72.6102 | −2.40833 | ||||||||
\(910\) | −7.03329 | −0.233151 | ||||||||
\(911\) | 26.9190 | 0.891867 | 0.445934 | − | 0.895066i | \(-0.352872\pi\) | ||||
0.445934 | + | 0.895066i | \(0.352872\pi\) | |||||||
\(912\) | −18.4681 | −0.611538 | ||||||||
\(913\) | 12.5299 | 0.414680 | ||||||||
\(914\) | −34.2333 | −1.13234 | ||||||||
\(915\) | 23.0609 | 0.762370 | ||||||||
\(916\) | −17.8260 | −0.588986 | ||||||||
\(917\) | −6.81879 | −0.225176 | ||||||||
\(918\) | 9.83734 | 0.324681 | ||||||||
\(919\) | −18.4655 | −0.609121 | −0.304560 | − | 0.952493i | \(-0.598510\pi\) | ||||
−0.304560 | + | 0.952493i | \(0.598510\pi\) | |||||||
\(920\) | 5.50242 | 0.181409 | ||||||||
\(921\) | 64.9799 | 2.14116 | ||||||||
\(922\) | −30.6217 | −1.00847 | ||||||||
\(923\) | −23.8751 | −0.785859 | ||||||||
\(924\) | −6.58409 | −0.216601 | ||||||||
\(925\) | −15.0213 | −0.493899 | ||||||||
\(926\) | −2.79958 | −0.0919998 | ||||||||
\(927\) | −29.1625 | −0.957823 | ||||||||
\(928\) | −4.33951 | −0.142451 | ||||||||
\(929\) | −7.28308 | −0.238950 | −0.119475 | − | 0.992837i | \(-0.538121\pi\) | ||||
−0.119475 | + | 0.992837i | \(0.538121\pi\) | |||||||
\(930\) | 7.28348 | 0.238835 | ||||||||
\(931\) | −26.6167 | −0.872327 | ||||||||
\(932\) | −13.1809 | −0.431755 | ||||||||
\(933\) | −51.7015 | −1.69263 | ||||||||
\(934\) | −18.1898 | −0.595190 | ||||||||
\(935\) | 4.97627 | 0.162741 | ||||||||
\(936\) | −17.8956 | −0.584936 | ||||||||
\(937\) | −39.8225 | −1.30095 | −0.650473 | − | 0.759529i | \(-0.725429\pi\) | ||||
−0.650473 | + | 0.759529i | \(0.725429\pi\) | |||||||
\(938\) | −5.72880 | −0.187052 | ||||||||
\(939\) | −70.8638 | −2.31255 | ||||||||
\(940\) | 7.85522 | 0.256209 | ||||||||
\(941\) | −56.7318 | −1.84940 | −0.924702 | − | 0.380692i | \(-0.875686\pi\) | ||||
−0.924702 | + | 0.380692i | \(0.875686\pi\) | |||||||
\(942\) | −38.4227 | −1.25188 | ||||||||
\(943\) | −47.8021 | −1.55665 | ||||||||
\(944\) | 15.0144 | 0.488677 | ||||||||
\(945\) | −3.62077 | −0.117784 | ||||||||
\(946\) | −7.59592 | −0.246965 | ||||||||
\(947\) | 9.83411 | 0.319566 | 0.159783 | − | 0.987152i | \(-0.448921\pi\) | ||||
0.159783 | + | 0.987152i | \(0.448921\pi\) | |||||||
\(948\) | −33.8912 | −1.10073 | ||||||||
\(949\) | 21.0685 | 0.683911 | ||||||||
\(950\) | 30.0172 | 0.973888 | ||||||||
\(951\) | −13.3671 | −0.433459 | ||||||||
\(952\) | −7.46516 | −0.241947 | ||||||||
\(953\) | 46.4862 | 1.50584 | 0.752918 | − | 0.658114i | \(-0.228646\pi\) | ||||
0.752918 | + | 0.658114i | \(0.228646\pi\) | |||||||
\(954\) | −52.0178 | −1.68414 | ||||||||
\(955\) | 14.7780 | 0.478204 | ||||||||
\(956\) | 13.2733 | 0.429289 | ||||||||
\(957\) | −15.9364 | −0.515150 | ||||||||
\(958\) | −11.2498 | −0.363463 | ||||||||
\(959\) | 37.0311 | 1.19580 | ||||||||
\(960\) | −2.24531 | −0.0724671 | ||||||||
\(961\) | −20.4774 | −0.660560 | ||||||||
\(962\) | −16.1471 | −0.520603 | ||||||||
\(963\) | 62.9170 | 2.02747 | ||||||||
\(964\) | −9.51088 | −0.306325 | ||||||||
\(965\) | −13.5263 | −0.435429 | ||||||||
\(966\) | −30.3137 | −0.975327 | ||||||||
\(967\) | −43.1669 | −1.38816 | −0.694078 | − | 0.719900i | \(-0.744188\pi\) | ||||
−0.694078 | + | 0.719900i | \(0.744188\pi\) | |||||||
\(968\) | 9.04528 | 0.290726 | ||||||||
\(969\) | −76.8978 | −2.47031 | ||||||||
\(970\) | 11.8891 | 0.381735 | ||||||||
\(971\) | −21.1048 | −0.677287 | −0.338643 | − | 0.940915i | \(-0.609968\pi\) | ||||
−0.338643 | + | 0.940915i | \(0.609968\pi\) | |||||||
\(972\) | 21.5151 | 0.690097 | ||||||||
\(973\) | 12.1527 | 0.389599 | ||||||||
\(974\) | −0.183892 | −0.00589228 | ||||||||
\(975\) | 51.4644 | 1.64818 | ||||||||
\(976\) | −10.2707 | −0.328757 | ||||||||
\(977\) | −55.5374 | −1.77680 | −0.888400 | − | 0.459070i | \(-0.848183\pi\) | ||||
−0.888400 | + | 0.459070i | \(0.848183\pi\) | |||||||
\(978\) | −3.08820 | −0.0987499 | ||||||||
\(979\) | −3.58776 | −0.114665 | ||||||||
\(980\) | −3.23601 | −0.103370 | ||||||||
\(981\) | 56.9648 | 1.81875 | ||||||||
\(982\) | 13.3053 | 0.424590 | ||||||||
\(983\) | 16.7990 | 0.535803 | 0.267902 | − | 0.963446i | \(-0.413670\pi\) | ||||
0.267902 | + | 0.963446i | \(0.413670\pi\) | |||||||
\(984\) | 19.5061 | 0.621831 | ||||||||
\(985\) | −10.3409 | −0.329489 | ||||||||
\(986\) | −18.0690 | −0.575433 | ||||||||
\(987\) | −43.2756 | −1.37748 | ||||||||
\(988\) | 32.2668 | 1.02654 | ||||||||
\(989\) | −34.9722 | −1.11205 | ||||||||
\(990\) | −4.66031 | −0.148114 | ||||||||
\(991\) | 36.2646 | 1.15198 | 0.575991 | − | 0.817456i | \(-0.304616\pi\) | ||||
0.575991 | + | 0.817456i | \(0.304616\pi\) | |||||||
\(992\) | −3.24386 | −0.102993 | ||||||||
\(993\) | 47.2506 | 1.49945 | ||||||||
\(994\) | 9.32717 | 0.295840 | ||||||||
\(995\) | −15.5217 | −0.492072 | ||||||||
\(996\) | −23.5404 | −0.745906 | ||||||||
\(997\) | 35.8129 | 1.13420 | 0.567102 | − | 0.823647i | \(-0.308064\pi\) | ||||
0.567102 | + | 0.823647i | \(0.308064\pi\) | |||||||
\(998\) | 12.7933 | 0.404965 | ||||||||
\(999\) | −8.31261 | −0.262999 |
(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 | 8002.2.a.e.1.7 | ✓ | 77 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.e.1.7 | ✓ | 77 | 1.1 | even | 1 | trivial |