Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5077,2,Mod(1,5077)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5077, 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("5077.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5077 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5077.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: | \(40.5400491062\) |
Analytic rank: | \(0\) |
Dimension: | \(216\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 5077.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.71481 | −1.91966 | −0.959829 | − | 0.280586i | \(-0.909471\pi\) | ||||
−0.959829 | + | 0.280586i | \(0.909471\pi\) | |||||||
\(3\) | 1.77107 | 1.02253 | 0.511263 | − | 0.859425i | \(-0.329178\pi\) | ||||
0.511263 | + | 0.859425i | \(0.329178\pi\) | |||||||
\(4\) | 5.37017 | 2.68509 | ||||||||
\(5\) | 1.86347 | 0.833370 | 0.416685 | − | 0.909051i | \(-0.363192\pi\) | ||||
0.416685 | + | 0.909051i | \(0.363192\pi\) | |||||||
\(6\) | −4.80810 | −1.96290 | ||||||||
\(7\) | 4.83883 | 1.82891 | 0.914454 | − | 0.404691i | \(-0.132621\pi\) | ||||
0.914454 | + | 0.404691i | \(0.132621\pi\) | |||||||
\(8\) | −9.14936 | −3.23479 | ||||||||
\(9\) | 0.136673 | 0.0455577 | ||||||||
\(10\) | −5.05896 | −1.59978 | ||||||||
\(11\) | 3.13265 | 0.944529 | 0.472264 | − | 0.881457i | \(-0.343437\pi\) | ||||
0.472264 | + | 0.881457i | \(0.343437\pi\) | |||||||
\(12\) | 9.51093 | 2.74557 | ||||||||
\(13\) | 1.94787 | 0.540243 | 0.270122 | − | 0.962826i | \(-0.412936\pi\) | ||||
0.270122 | + | 0.962826i | \(0.412936\pi\) | |||||||
\(14\) | −13.1365 | −3.51088 | ||||||||
\(15\) | 3.30033 | 0.852142 | ||||||||
\(16\) | 14.0984 | 3.52460 | ||||||||
\(17\) | 5.73713 | 1.39146 | 0.695729 | − | 0.718304i | \(-0.255081\pi\) | ||||
0.695729 | + | 0.718304i | \(0.255081\pi\) | |||||||
\(18\) | −0.371041 | −0.0874552 | ||||||||
\(19\) | −6.55967 | −1.50489 | −0.752445 | − | 0.658655i | \(-0.771126\pi\) | ||||
−0.752445 | + | 0.658655i | \(0.771126\pi\) | |||||||
\(20\) | 10.0072 | 2.23767 | ||||||||
\(21\) | 8.56989 | 1.87010 | ||||||||
\(22\) | −8.50453 | −1.81317 | ||||||||
\(23\) | 0.545186 | 0.113679 | 0.0568395 | − | 0.998383i | \(-0.481898\pi\) | ||||
0.0568395 | + | 0.998383i | \(0.481898\pi\) | |||||||
\(24\) | −16.2041 | −3.30765 | ||||||||
\(25\) | −1.52747 | −0.305495 | ||||||||
\(26\) | −5.28810 | −1.03708 | ||||||||
\(27\) | −5.07114 | −0.975941 | ||||||||
\(28\) | 25.9854 | 4.91077 | ||||||||
\(29\) | 5.56086 | 1.03263 | 0.516313 | − | 0.856400i | \(-0.327304\pi\) | ||||
0.516313 | + | 0.856400i | \(0.327304\pi\) | |||||||
\(30\) | −8.95976 | −1.63582 | ||||||||
\(31\) | 1.85084 | 0.332421 | 0.166211 | − | 0.986090i | \(-0.446847\pi\) | ||||
0.166211 | + | 0.986090i | \(0.446847\pi\) | |||||||
\(32\) | −19.9757 | −3.53124 | ||||||||
\(33\) | 5.54813 | 0.965805 | ||||||||
\(34\) | −15.5752 | −2.67112 | ||||||||
\(35\) | 9.01703 | 1.52416 | ||||||||
\(36\) | 0.733958 | 0.122326 | ||||||||
\(37\) | 1.35875 | 0.223378 | 0.111689 | − | 0.993743i | \(-0.464374\pi\) | ||||
0.111689 | + | 0.993743i | \(0.464374\pi\) | |||||||
\(38\) | 17.8082 | 2.88887 | ||||||||
\(39\) | 3.44981 | 0.552412 | ||||||||
\(40\) | −17.0496 | −2.69578 | ||||||||
\(41\) | 6.54345 | 1.02191 | 0.510957 | − | 0.859606i | \(-0.329291\pi\) | ||||
0.510957 | + | 0.859606i | \(0.329291\pi\) | |||||||
\(42\) | −23.2656 | −3.58996 | ||||||||
\(43\) | −9.17990 | −1.39992 | −0.699961 | − | 0.714181i | \(-0.746799\pi\) | ||||
−0.699961 | + | 0.714181i | \(0.746799\pi\) | |||||||
\(44\) | 16.8229 | 2.53614 | ||||||||
\(45\) | 0.254686 | 0.0379664 | ||||||||
\(46\) | −1.48007 | −0.218225 | ||||||||
\(47\) | 7.16793 | 1.04555 | 0.522775 | − | 0.852471i | \(-0.324897\pi\) | ||||
0.522775 | + | 0.852471i | \(0.324897\pi\) | |||||||
\(48\) | 24.9692 | 3.60399 | ||||||||
\(49\) | 16.4143 | 2.34490 | ||||||||
\(50\) | 4.14679 | 0.586445 | ||||||||
\(51\) | 10.1608 | 1.42280 | ||||||||
\(52\) | 10.4604 | 1.45060 | ||||||||
\(53\) | −7.86968 | −1.08098 | −0.540492 | − | 0.841349i | \(-0.681762\pi\) | ||||
−0.540492 | + | 0.841349i | \(0.681762\pi\) | |||||||
\(54\) | 13.7672 | 1.87347 | ||||||||
\(55\) | 5.83760 | 0.787142 | ||||||||
\(56\) | −44.2722 | −5.91613 | ||||||||
\(57\) | −11.6176 | −1.53879 | ||||||||
\(58\) | −15.0967 | −1.98229 | ||||||||
\(59\) | 1.74437 | 0.227097 | 0.113549 | − | 0.993532i | \(-0.463778\pi\) | ||||
0.113549 | + | 0.993532i | \(0.463778\pi\) | |||||||
\(60\) | 17.7233 | 2.28807 | ||||||||
\(61\) | −7.92126 | −1.01421 | −0.507107 | − | 0.861883i | \(-0.669285\pi\) | ||||
−0.507107 | + | 0.861883i | \(0.669285\pi\) | |||||||
\(62\) | −5.02468 | −0.638135 | ||||||||
\(63\) | 0.661338 | 0.0833208 | ||||||||
\(64\) | 26.0334 | 3.25417 | ||||||||
\(65\) | 3.62981 | 0.450222 | ||||||||
\(66\) | −15.0621 | −1.85401 | ||||||||
\(67\) | 4.79617 | 0.585946 | 0.292973 | − | 0.956121i | \(-0.405355\pi\) | ||||
0.292973 | + | 0.956121i | \(0.405355\pi\) | |||||||
\(68\) | 30.8094 | 3.73619 | ||||||||
\(69\) | 0.965559 | 0.116240 | ||||||||
\(70\) | −24.4795 | −2.92586 | ||||||||
\(71\) | −7.79224 | −0.924769 | −0.462384 | − | 0.886680i | \(-0.653006\pi\) | ||||
−0.462384 | + | 0.886680i | \(0.653006\pi\) | |||||||
\(72\) | −1.25047 | −0.147370 | ||||||||
\(73\) | −12.2852 | −1.43787 | −0.718936 | − | 0.695076i | \(-0.755371\pi\) | ||||
−0.718936 | + | 0.695076i | \(0.755371\pi\) | |||||||
\(74\) | −3.68875 | −0.428809 | ||||||||
\(75\) | −2.70526 | −0.312376 | ||||||||
\(76\) | −35.2265 | −4.04076 | ||||||||
\(77\) | 15.1584 | 1.72746 | ||||||||
\(78\) | −9.36557 | −1.06044 | ||||||||
\(79\) | 4.36881 | 0.491530 | 0.245765 | − | 0.969329i | \(-0.420961\pi\) | ||||
0.245765 | + | 0.969329i | \(0.420961\pi\) | |||||||
\(80\) | 26.2720 | 2.93730 | ||||||||
\(81\) | −9.39134 | −1.04348 | ||||||||
\(82\) | −17.7642 | −1.96173 | ||||||||
\(83\) | 0.938894 | 0.103057 | 0.0515285 | − | 0.998672i | \(-0.483591\pi\) | ||||
0.0515285 | + | 0.998672i | \(0.483591\pi\) | |||||||
\(84\) | 46.0218 | 5.02139 | ||||||||
\(85\) | 10.6910 | 1.15960 | ||||||||
\(86\) | 24.9216 | 2.68737 | ||||||||
\(87\) | 9.84864 | 1.05589 | ||||||||
\(88\) | −28.6617 | −3.05535 | ||||||||
\(89\) | −0.422521 | −0.0447871 | −0.0223936 | − | 0.999749i | \(-0.507129\pi\) | ||||
−0.0223936 | + | 0.999749i | \(0.507129\pi\) | |||||||
\(90\) | −0.691424 | −0.0728825 | ||||||||
\(91\) | 9.42544 | 0.988054 | ||||||||
\(92\) | 2.92774 | 0.305238 | ||||||||
\(93\) | 3.27796 | 0.339909 | ||||||||
\(94\) | −19.4595 | −2.00710 | ||||||||
\(95\) | −12.2238 | −1.25413 | ||||||||
\(96\) | −35.3783 | −3.61078 | ||||||||
\(97\) | −2.43594 | −0.247332 | −0.123666 | − | 0.992324i | \(-0.539465\pi\) | ||||
−0.123666 | + | 0.992324i | \(0.539465\pi\) | |||||||
\(98\) | −44.5617 | −4.50141 | ||||||||
\(99\) | 0.428149 | 0.0430306 | ||||||||
\(100\) | −8.20280 | −0.820280 | ||||||||
\(101\) | 4.50717 | 0.448480 | 0.224240 | − | 0.974534i | \(-0.428010\pi\) | ||||
0.224240 | + | 0.974534i | \(0.428010\pi\) | |||||||
\(102\) | −27.5847 | −2.73129 | ||||||||
\(103\) | 10.8445 | 1.06854 | 0.534268 | − | 0.845315i | \(-0.320587\pi\) | ||||
0.534268 | + | 0.845315i | \(0.320587\pi\) | |||||||
\(104\) | −17.8218 | −1.74757 | ||||||||
\(105\) | 15.9697 | 1.55849 | ||||||||
\(106\) | 21.3646 | 2.07512 | ||||||||
\(107\) | 1.06109 | 0.102580 | 0.0512899 | − | 0.998684i | \(-0.483667\pi\) | ||||
0.0512899 | + | 0.998684i | \(0.483667\pi\) | |||||||
\(108\) | −27.2329 | −2.62049 | ||||||||
\(109\) | 3.14990 | 0.301706 | 0.150853 | − | 0.988556i | \(-0.451798\pi\) | ||||
0.150853 | + | 0.988556i | \(0.451798\pi\) | |||||||
\(110\) | −15.8480 | −1.51104 | ||||||||
\(111\) | 2.40644 | 0.228409 | ||||||||
\(112\) | 68.2198 | 6.44617 | ||||||||
\(113\) | 14.9772 | 1.40894 | 0.704469 | − | 0.709735i | \(-0.251185\pi\) | ||||
0.704469 | + | 0.709735i | \(0.251185\pi\) | |||||||
\(114\) | 31.5395 | 2.95395 | ||||||||
\(115\) | 1.01594 | 0.0947367 | ||||||||
\(116\) | 29.8628 | 2.77269 | ||||||||
\(117\) | 0.266222 | 0.0246122 | ||||||||
\(118\) | −4.73562 | −0.435949 | ||||||||
\(119\) | 27.7610 | 2.54485 | ||||||||
\(120\) | −30.1959 | −2.75650 | ||||||||
\(121\) | −1.18652 | −0.107865 | ||||||||
\(122\) | 21.5047 | 1.94694 | ||||||||
\(123\) | 11.5889 | 1.04493 | ||||||||
\(124\) | 9.93934 | 0.892579 | ||||||||
\(125\) | −12.1638 | −1.08796 | ||||||||
\(126\) | −1.79541 | −0.159947 | ||||||||
\(127\) | 20.5485 | 1.82338 | 0.911692 | − | 0.410874i | \(-0.134776\pi\) | ||||
0.911692 | + | 0.410874i | \(0.134776\pi\) | |||||||
\(128\) | −30.7241 | −2.71565 | ||||||||
\(129\) | −16.2582 | −1.43145 | ||||||||
\(130\) | −9.85423 | −0.864273 | ||||||||
\(131\) | 13.2404 | 1.15682 | 0.578411 | − | 0.815746i | \(-0.303673\pi\) | ||||
0.578411 | + | 0.815746i | \(0.303673\pi\) | |||||||
\(132\) | 29.7944 | 2.59327 | ||||||||
\(133\) | −31.7411 | −2.75231 | ||||||||
\(134\) | −13.0207 | −1.12482 | ||||||||
\(135\) | −9.44992 | −0.813320 | ||||||||
\(136\) | −52.4911 | −4.50107 | ||||||||
\(137\) | −6.65916 | −0.568930 | −0.284465 | − | 0.958686i | \(-0.591816\pi\) | ||||
−0.284465 | + | 0.958686i | \(0.591816\pi\) | |||||||
\(138\) | −2.62131 | −0.223140 | ||||||||
\(139\) | −17.0027 | −1.44215 | −0.721076 | − | 0.692856i | \(-0.756352\pi\) | ||||
−0.721076 | + | 0.692856i | \(0.756352\pi\) | |||||||
\(140\) | 48.4230 | 4.09249 | ||||||||
\(141\) | 12.6949 | 1.06910 | ||||||||
\(142\) | 21.1544 | 1.77524 | ||||||||
\(143\) | 6.10200 | 0.510275 | ||||||||
\(144\) | 1.92687 | 0.160573 | ||||||||
\(145\) | 10.3625 | 0.860559 | ||||||||
\(146\) | 33.3519 | 2.76022 | ||||||||
\(147\) | 29.0708 | 2.39772 | ||||||||
\(148\) | 7.29674 | 0.599788 | ||||||||
\(149\) | 11.8891 | 0.973993 | 0.486996 | − | 0.873404i | \(-0.338093\pi\) | ||||
0.486996 | + | 0.873404i | \(0.338093\pi\) | |||||||
\(150\) | 7.34424 | 0.599655 | ||||||||
\(151\) | 6.92064 | 0.563193 | 0.281597 | − | 0.959533i | \(-0.409136\pi\) | ||||
0.281597 | + | 0.959533i | \(0.409136\pi\) | |||||||
\(152\) | 60.0168 | 4.86800 | ||||||||
\(153\) | 0.784111 | 0.0633916 | ||||||||
\(154\) | −41.1520 | −3.31612 | ||||||||
\(155\) | 3.44899 | 0.277030 | ||||||||
\(156\) | 18.5261 | 1.48327 | ||||||||
\(157\) | −1.24263 | −0.0991730 | −0.0495865 | − | 0.998770i | \(-0.515790\pi\) | ||||
−0.0495865 | + | 0.998770i | \(0.515790\pi\) | |||||||
\(158\) | −11.8605 | −0.943569 | ||||||||
\(159\) | −13.9377 | −1.10533 | ||||||||
\(160\) | −37.2242 | −2.94283 | ||||||||
\(161\) | 2.63806 | 0.207908 | ||||||||
\(162\) | 25.4957 | 2.00313 | ||||||||
\(163\) | −10.0515 | −0.787292 | −0.393646 | − | 0.919262i | \(-0.628786\pi\) | ||||
−0.393646 | + | 0.919262i | \(0.628786\pi\) | |||||||
\(164\) | 35.1394 | 2.74393 | ||||||||
\(165\) | 10.3388 | 0.804872 | ||||||||
\(166\) | −2.54892 | −0.197834 | ||||||||
\(167\) | 3.29704 | 0.255133 | 0.127566 | − | 0.991830i | \(-0.459283\pi\) | ||||
0.127566 | + | 0.991830i | \(0.459283\pi\) | |||||||
\(168\) | −78.4090 | −6.04939 | ||||||||
\(169\) | −9.20579 | −0.708137 | ||||||||
\(170\) | −29.0239 | −2.22603 | ||||||||
\(171\) | −0.896530 | −0.0685594 | ||||||||
\(172\) | −49.2976 | −3.75891 | ||||||||
\(173\) | 17.9537 | 1.36500 | 0.682499 | − | 0.730887i | \(-0.260893\pi\) | ||||
0.682499 | + | 0.730887i | \(0.260893\pi\) | |||||||
\(174\) | −26.7372 | −2.02694 | ||||||||
\(175\) | −7.39119 | −0.558721 | ||||||||
\(176\) | 44.1653 | 3.32909 | ||||||||
\(177\) | 3.08939 | 0.232213 | ||||||||
\(178\) | 1.14706 | 0.0859760 | ||||||||
\(179\) | 19.2278 | 1.43715 | 0.718576 | − | 0.695449i | \(-0.244794\pi\) | ||||
0.718576 | + | 0.695449i | \(0.244794\pi\) | |||||||
\(180\) | 1.36771 | 0.101943 | ||||||||
\(181\) | 9.25669 | 0.688045 | 0.344022 | − | 0.938961i | \(-0.388210\pi\) | ||||
0.344022 | + | 0.938961i | \(0.388210\pi\) | |||||||
\(182\) | −25.5882 | −1.89673 | ||||||||
\(183\) | −14.0291 | −1.03706 | ||||||||
\(184\) | −4.98810 | −0.367728 | ||||||||
\(185\) | 2.53200 | 0.186156 | ||||||||
\(186\) | −8.89904 | −0.652509 | ||||||||
\(187\) | 17.9724 | 1.31427 | ||||||||
\(188\) | 38.4930 | 2.80739 | ||||||||
\(189\) | −24.5384 | −1.78491 | ||||||||
\(190\) | 33.1851 | 2.40750 | ||||||||
\(191\) | −6.85279 | −0.495850 | −0.247925 | − | 0.968779i | \(-0.579749\pi\) | ||||
−0.247925 | + | 0.968779i | \(0.579749\pi\) | |||||||
\(192\) | 46.1068 | 3.32747 | ||||||||
\(193\) | 6.25790 | 0.450453 | 0.225227 | − | 0.974306i | \(-0.427688\pi\) | ||||
0.225227 | + | 0.974306i | \(0.427688\pi\) | |||||||
\(194\) | 6.61310 | 0.474793 | ||||||||
\(195\) | 6.42863 | 0.460364 | ||||||||
\(196\) | 88.1477 | 6.29626 | ||||||||
\(197\) | −1.69869 | −0.121027 | −0.0605133 | − | 0.998167i | \(-0.519274\pi\) | ||||
−0.0605133 | + | 0.998167i | \(0.519274\pi\) | |||||||
\(198\) | −1.16234 | −0.0826040 | ||||||||
\(199\) | 13.4152 | 0.950981 | 0.475491 | − | 0.879721i | \(-0.342271\pi\) | ||||
0.475491 | + | 0.879721i | \(0.342271\pi\) | |||||||
\(200\) | 13.9754 | 0.988211 | ||||||||
\(201\) | 8.49434 | 0.599144 | ||||||||
\(202\) | −12.2361 | −0.860928 | ||||||||
\(203\) | 26.9081 | 1.88858 | ||||||||
\(204\) | 54.5654 | 3.82034 | ||||||||
\(205\) | 12.1935 | 0.851633 | ||||||||
\(206\) | −29.4406 | −2.05122 | ||||||||
\(207\) | 0.0745122 | 0.00517896 | ||||||||
\(208\) | 27.4619 | 1.90414 | ||||||||
\(209\) | −20.5491 | −1.42141 | ||||||||
\(210\) | −43.3548 | −2.99176 | ||||||||
\(211\) | −23.2703 | −1.60200 | −0.800998 | − | 0.598667i | \(-0.795697\pi\) | ||||
−0.800998 | + | 0.598667i | \(0.795697\pi\) | |||||||
\(212\) | −42.2615 | −2.90253 | ||||||||
\(213\) | −13.8006 | −0.945599 | ||||||||
\(214\) | −2.88066 | −0.196918 | ||||||||
\(215\) | −17.1065 | −1.16665 | ||||||||
\(216\) | 46.3977 | 3.15696 | ||||||||
\(217\) | 8.95592 | 0.607967 | ||||||||
\(218\) | −8.55137 | −0.579172 | ||||||||
\(219\) | −21.7579 | −1.47026 | ||||||||
\(220\) | 31.3489 | 2.11354 | ||||||||
\(221\) | 11.1752 | 0.751726 | ||||||||
\(222\) | −6.53302 | −0.438468 | ||||||||
\(223\) | −19.5494 | −1.30912 | −0.654561 | − | 0.756009i | \(-0.727147\pi\) | ||||
−0.654561 | + | 0.756009i | \(0.727147\pi\) | |||||||
\(224\) | −96.6591 | −6.45831 | ||||||||
\(225\) | −0.208765 | −0.0139176 | ||||||||
\(226\) | −40.6602 | −2.70468 | ||||||||
\(227\) | −21.6602 | −1.43764 | −0.718819 | − | 0.695197i | \(-0.755317\pi\) | ||||
−0.718819 | + | 0.695197i | \(0.755317\pi\) | |||||||
\(228\) | −62.3885 | −4.13178 | ||||||||
\(229\) | −11.2409 | −0.742821 | −0.371410 | − | 0.928469i | \(-0.621126\pi\) | ||||
−0.371410 | + | 0.928469i | \(0.621126\pi\) | |||||||
\(230\) | −2.75807 | −0.181862 | ||||||||
\(231\) | 26.8465 | 1.76637 | ||||||||
\(232\) | −50.8783 | −3.34032 | ||||||||
\(233\) | −29.0867 | −1.90553 | −0.952767 | − | 0.303702i | \(-0.901777\pi\) | ||||
−0.952767 | + | 0.303702i | \(0.901777\pi\) | |||||||
\(234\) | −0.722741 | −0.0472471 | ||||||||
\(235\) | 13.3572 | 0.871329 | ||||||||
\(236\) | 9.36756 | 0.609776 | ||||||||
\(237\) | 7.73745 | 0.502602 | ||||||||
\(238\) | −75.3658 | −4.88524 | ||||||||
\(239\) | −25.8779 | −1.67390 | −0.836950 | − | 0.547279i | \(-0.815664\pi\) | ||||
−0.836950 | + | 0.547279i | \(0.815664\pi\) | |||||||
\(240\) | 46.5294 | 3.00346 | ||||||||
\(241\) | −17.4017 | −1.12094 | −0.560470 | − | 0.828175i | \(-0.689380\pi\) | ||||
−0.560470 | + | 0.828175i | \(0.689380\pi\) | |||||||
\(242\) | 3.22116 | 0.207064 | ||||||||
\(243\) | −1.41926 | −0.0910455 | ||||||||
\(244\) | −42.5386 | −2.72325 | ||||||||
\(245\) | 30.5876 | 1.95417 | ||||||||
\(246\) | −31.4615 | −2.00591 | ||||||||
\(247\) | −12.7774 | −0.813007 | ||||||||
\(248\) | −16.9340 | −1.07531 | ||||||||
\(249\) | 1.66284 | 0.105378 | ||||||||
\(250\) | 33.0223 | 2.08851 | ||||||||
\(251\) | 18.8223 | 1.18805 | 0.594027 | − | 0.804445i | \(-0.297537\pi\) | ||||
0.594027 | + | 0.804445i | \(0.297537\pi\) | |||||||
\(252\) | 3.55150 | 0.223724 | ||||||||
\(253\) | 1.70787 | 0.107373 | ||||||||
\(254\) | −55.7852 | −3.50027 | ||||||||
\(255\) | 18.9344 | 1.18572 | ||||||||
\(256\) | 31.3433 | 1.95895 | ||||||||
\(257\) | −8.80268 | −0.549096 | −0.274548 | − | 0.961573i | \(-0.588528\pi\) | ||||
−0.274548 | + | 0.961573i | \(0.588528\pi\) | |||||||
\(258\) | 44.1379 | 2.74790 | ||||||||
\(259\) | 6.57478 | 0.408537 | ||||||||
\(260\) | 19.4927 | 1.20889 | ||||||||
\(261\) | 0.760020 | 0.0470440 | ||||||||
\(262\) | −35.9452 | −2.22070 | ||||||||
\(263\) | −15.0573 | −0.928475 | −0.464237 | − | 0.885711i | \(-0.653672\pi\) | ||||
−0.464237 | + | 0.885711i | \(0.653672\pi\) | |||||||
\(264\) | −50.7618 | −3.12417 | ||||||||
\(265\) | −14.6649 | −0.900859 | ||||||||
\(266\) | 86.1710 | 5.28348 | ||||||||
\(267\) | −0.748312 | −0.0457960 | ||||||||
\(268\) | 25.7563 | 1.57332 | ||||||||
\(269\) | −0.462306 | −0.0281873 | −0.0140937 | − | 0.999901i | \(-0.504486\pi\) | ||||
−0.0140937 | + | 0.999901i | \(0.504486\pi\) | |||||||
\(270\) | 25.6547 | 1.56130 | ||||||||
\(271\) | 23.9990 | 1.45784 | 0.728918 | − | 0.684601i | \(-0.240024\pi\) | ||||
0.728918 | + | 0.684601i | \(0.240024\pi\) | |||||||
\(272\) | 80.8844 | 4.90434 | ||||||||
\(273\) | 16.6931 | 1.01031 | ||||||||
\(274\) | 18.0783 | 1.09215 | ||||||||
\(275\) | −4.78504 | −0.288549 | ||||||||
\(276\) | 5.18522 | 0.312114 | ||||||||
\(277\) | −17.0435 | −1.02405 | −0.512023 | − | 0.858972i | \(-0.671104\pi\) | ||||
−0.512023 | + | 0.858972i | \(0.671104\pi\) | |||||||
\(278\) | 46.1591 | 2.76844 | ||||||||
\(279\) | 0.252960 | 0.0151443 | ||||||||
\(280\) | −82.5001 | −4.93032 | ||||||||
\(281\) | 21.7216 | 1.29580 | 0.647902 | − | 0.761724i | \(-0.275647\pi\) | ||||
0.647902 | + | 0.761724i | \(0.275647\pi\) | |||||||
\(282\) | −34.4641 | −2.05231 | ||||||||
\(283\) | 3.11864 | 0.185384 | 0.0926919 | − | 0.995695i | \(-0.470453\pi\) | ||||
0.0926919 | + | 0.995695i | \(0.470453\pi\) | |||||||
\(284\) | −41.8457 | −2.48308 | ||||||||
\(285\) | −21.6491 | −1.28238 | ||||||||
\(286\) | −16.5658 | −0.979554 | ||||||||
\(287\) | 31.6627 | 1.86899 | ||||||||
\(288\) | −2.73014 | −0.160875 | ||||||||
\(289\) | 15.9147 | 0.936157 | ||||||||
\(290\) | −28.1322 | −1.65198 | ||||||||
\(291\) | −4.31421 | −0.252903 | ||||||||
\(292\) | −65.9735 | −3.86081 | ||||||||
\(293\) | 8.97534 | 0.524345 | 0.262172 | − | 0.965021i | \(-0.415561\pi\) | ||||
0.262172 | + | 0.965021i | \(0.415561\pi\) | |||||||
\(294\) | −78.9216 | −4.60280 | ||||||||
\(295\) | 3.25058 | 0.189256 | ||||||||
\(296\) | −12.4317 | −0.722579 | ||||||||
\(297\) | −15.8861 | −0.921805 | ||||||||
\(298\) | −32.2766 | −1.86973 | ||||||||
\(299\) | 1.06195 | 0.0614143 | ||||||||
\(300\) | −14.5277 | −0.838756 | ||||||||
\(301\) | −44.4200 | −2.56033 | ||||||||
\(302\) | −18.7882 | −1.08114 | ||||||||
\(303\) | 7.98248 | 0.458582 | ||||||||
\(304\) | −92.4808 | −5.30414 | ||||||||
\(305\) | −14.7611 | −0.845215 | ||||||||
\(306\) | −2.12871 | −0.121690 | ||||||||
\(307\) | 11.5206 | 0.657513 | 0.328757 | − | 0.944415i | \(-0.393370\pi\) | ||||
0.328757 | + | 0.944415i | \(0.393370\pi\) | |||||||
\(308\) | 81.4030 | 4.63837 | ||||||||
\(309\) | 19.2063 | 1.09261 | ||||||||
\(310\) | −9.36335 | −0.531802 | ||||||||
\(311\) | 10.4869 | 0.594655 | 0.297328 | − | 0.954776i | \(-0.403905\pi\) | ||||
0.297328 | + | 0.954776i | \(0.403905\pi\) | |||||||
\(312\) | −31.5636 | −1.78694 | ||||||||
\(313\) | −22.6451 | −1.27998 | −0.639988 | − | 0.768385i | \(-0.721061\pi\) | ||||
−0.639988 | + | 0.768385i | \(0.721061\pi\) | |||||||
\(314\) | 3.37351 | 0.190378 | ||||||||
\(315\) | 1.23239 | 0.0694370 | ||||||||
\(316\) | 23.4613 | 1.31980 | ||||||||
\(317\) | 16.8636 | 0.947156 | 0.473578 | − | 0.880752i | \(-0.342962\pi\) | ||||
0.473578 | + | 0.880752i | \(0.342962\pi\) | |||||||
\(318\) | 37.8382 | 2.12186 | ||||||||
\(319\) | 17.4202 | 0.975345 | ||||||||
\(320\) | 48.5124 | 2.71193 | ||||||||
\(321\) | 1.87926 | 0.104890 | ||||||||
\(322\) | −7.16183 | −0.399113 | ||||||||
\(323\) | −37.6337 | −2.09399 | ||||||||
\(324\) | −50.4331 | −2.80184 | ||||||||
\(325\) | −2.97533 | −0.165041 | ||||||||
\(326\) | 27.2878 | 1.51133 | ||||||||
\(327\) | 5.57868 | 0.308502 | ||||||||
\(328\) | −59.8684 | −3.30568 | ||||||||
\(329\) | 34.6844 | 1.91221 | ||||||||
\(330\) | −28.0678 | −1.54508 | ||||||||
\(331\) | 12.9496 | 0.711776 | 0.355888 | − | 0.934529i | \(-0.384178\pi\) | ||||
0.355888 | + | 0.934529i | \(0.384178\pi\) | |||||||
\(332\) | 5.04202 | 0.276717 | ||||||||
\(333\) | 0.185705 | 0.0101766 | ||||||||
\(334\) | −8.95083 | −0.489768 | ||||||||
\(335\) | 8.93753 | 0.488310 | ||||||||
\(336\) | 120.822 | 6.59137 | ||||||||
\(337\) | −19.5380 | −1.06430 | −0.532152 | − | 0.846649i | \(-0.678616\pi\) | ||||
−0.532152 | + | 0.846649i | \(0.678616\pi\) | |||||||
\(338\) | 24.9919 | 1.35938 | ||||||||
\(339\) | 26.5256 | 1.44067 | ||||||||
\(340\) | 57.4124 | 3.11362 | ||||||||
\(341\) | 5.79804 | 0.313981 | ||||||||
\(342\) | 2.43390 | 0.131610 | ||||||||
\(343\) | 45.5543 | 2.45970 | ||||||||
\(344\) | 83.9902 | 4.52845 | ||||||||
\(345\) | 1.79929 | 0.0968707 | ||||||||
\(346\) | −48.7409 | −2.62033 | ||||||||
\(347\) | −27.9164 | −1.49863 | −0.749317 | − | 0.662212i | \(-0.769618\pi\) | ||||
−0.749317 | + | 0.662212i | \(0.769618\pi\) | |||||||
\(348\) | 52.8889 | 2.83514 | ||||||||
\(349\) | 6.40692 | 0.342955 | 0.171477 | − | 0.985188i | \(-0.445146\pi\) | ||||
0.171477 | + | 0.985188i | \(0.445146\pi\) | |||||||
\(350\) | 20.0656 | 1.07255 | ||||||||
\(351\) | −9.87794 | −0.527246 | ||||||||
\(352\) | −62.5768 | −3.33536 | ||||||||
\(353\) | −4.81923 | −0.256502 | −0.128251 | − | 0.991742i | \(-0.540936\pi\) | ||||
−0.128251 | + | 0.991742i | \(0.540936\pi\) | |||||||
\(354\) | −8.38710 | −0.445769 | ||||||||
\(355\) | −14.5206 | −0.770674 | ||||||||
\(356\) | −2.26901 | −0.120257 | ||||||||
\(357\) | 49.1666 | 2.60217 | ||||||||
\(358\) | −52.1997 | −2.75884 | ||||||||
\(359\) | −15.2860 | −0.806764 | −0.403382 | − | 0.915032i | \(-0.632165\pi\) | ||||
−0.403382 | + | 0.915032i | \(0.632165\pi\) | |||||||
\(360\) | −2.33022 | −0.122813 | ||||||||
\(361\) | 24.0292 | 1.26470 | ||||||||
\(362\) | −25.1301 | −1.32081 | ||||||||
\(363\) | −2.10140 | −0.110295 | ||||||||
\(364\) | 50.6162 | 2.65301 | ||||||||
\(365\) | −22.8931 | −1.19828 | ||||||||
\(366\) | 38.0862 | 1.99080 | ||||||||
\(367\) | −19.2143 | −1.00298 | −0.501490 | − | 0.865163i | \(-0.667215\pi\) | ||||
−0.501490 | + | 0.865163i | \(0.667215\pi\) | |||||||
\(368\) | 7.68625 | 0.400673 | ||||||||
\(369\) | 0.894313 | 0.0465561 | ||||||||
\(370\) | −6.87388 | −0.357356 | ||||||||
\(371\) | −38.0800 | −1.97702 | ||||||||
\(372\) | 17.6032 | 0.912685 | ||||||||
\(373\) | −30.5361 | −1.58110 | −0.790550 | − | 0.612397i | \(-0.790205\pi\) | ||||
−0.790550 | + | 0.612397i | \(0.790205\pi\) | |||||||
\(374\) | −48.7916 | −2.52295 | ||||||||
\(375\) | −21.5428 | −1.11247 | ||||||||
\(376\) | −65.5820 | −3.38213 | ||||||||
\(377\) | 10.8319 | 0.557869 | ||||||||
\(378\) | 66.6170 | 3.42641 | ||||||||
\(379\) | −15.6478 | −0.803775 | −0.401888 | − | 0.915689i | \(-0.631646\pi\) | ||||
−0.401888 | + | 0.915689i | \(0.631646\pi\) | |||||||
\(380\) | −65.6436 | −3.36745 | ||||||||
\(381\) | 36.3927 | 1.86446 | ||||||||
\(382\) | 18.6040 | 0.951863 | ||||||||
\(383\) | −12.6981 | −0.648844 | −0.324422 | − | 0.945912i | \(-0.605170\pi\) | ||||
−0.324422 | + | 0.945912i | \(0.605170\pi\) | |||||||
\(384\) | −54.4144 | −2.77682 | ||||||||
\(385\) | 28.2472 | 1.43961 | ||||||||
\(386\) | −16.9890 | −0.864716 | ||||||||
\(387\) | −1.25465 | −0.0637772 | ||||||||
\(388\) | −13.0814 | −0.664108 | ||||||||
\(389\) | 9.81419 | 0.497599 | 0.248800 | − | 0.968555i | \(-0.419964\pi\) | ||||
0.248800 | + | 0.968555i | \(0.419964\pi\) | |||||||
\(390\) | −17.4525 | −0.883741 | ||||||||
\(391\) | 3.12780 | 0.158180 | ||||||||
\(392\) | −150.180 | −7.58526 | ||||||||
\(393\) | 23.4497 | 1.18288 | ||||||||
\(394\) | 4.61161 | 0.232330 | ||||||||
\(395\) | 8.14116 | 0.409626 | ||||||||
\(396\) | 2.29923 | 0.115541 | ||||||||
\(397\) | 20.2262 | 1.01512 | 0.507562 | − | 0.861615i | \(-0.330547\pi\) | ||||
0.507562 | + | 0.861615i | \(0.330547\pi\) | |||||||
\(398\) | −36.4198 | −1.82556 | ||||||||
\(399\) | −56.2156 | −2.81430 | ||||||||
\(400\) | −21.5349 | −1.07675 | ||||||||
\(401\) | −7.02651 | −0.350887 | −0.175444 | − | 0.984490i | \(-0.556136\pi\) | ||||
−0.175444 | + | 0.984490i | \(0.556136\pi\) | |||||||
\(402\) | −23.0605 | −1.15015 | ||||||||
\(403\) | 3.60521 | 0.179588 | ||||||||
\(404\) | 24.2043 | 1.20421 | ||||||||
\(405\) | −17.5005 | −0.869607 | ||||||||
\(406\) | −73.0502 | −3.62542 | ||||||||
\(407\) | 4.25649 | 0.210987 | ||||||||
\(408\) | −92.9652 | −4.60246 | ||||||||
\(409\) | −23.7931 | −1.17649 | −0.588246 | − | 0.808682i | \(-0.700182\pi\) | ||||
−0.588246 | + | 0.808682i | \(0.700182\pi\) | |||||||
\(410\) | −33.1031 | −1.63484 | ||||||||
\(411\) | −11.7938 | −0.581745 | ||||||||
\(412\) | 58.2366 | 2.86911 | ||||||||
\(413\) | 8.44071 | 0.415340 | ||||||||
\(414\) | −0.202286 | −0.00994182 | ||||||||
\(415\) | 1.74960 | 0.0858846 | ||||||||
\(416\) | −38.9102 | −1.90773 | ||||||||
\(417\) | −30.1129 | −1.47464 | ||||||||
\(418\) | 55.7869 | 2.72863 | ||||||||
\(419\) | −28.1605 | −1.37573 | −0.687865 | − | 0.725839i | \(-0.741452\pi\) | ||||
−0.687865 | + | 0.725839i | \(0.741452\pi\) | |||||||
\(420\) | 85.7603 | 4.18467 | ||||||||
\(421\) | 36.9646 | 1.80155 | 0.900773 | − | 0.434290i | \(-0.143001\pi\) | ||||
0.900773 | + | 0.434290i | \(0.143001\pi\) | |||||||
\(422\) | 63.1745 | 3.07529 | ||||||||
\(423\) | 0.979663 | 0.0476328 | ||||||||
\(424\) | 72.0025 | 3.49675 | ||||||||
\(425\) | −8.76331 | −0.425083 | ||||||||
\(426\) | 37.4659 | 1.81523 | ||||||||
\(427\) | −38.3297 | −1.85490 | ||||||||
\(428\) | 5.69825 | 0.275435 | ||||||||
\(429\) | 10.8070 | 0.521769 | ||||||||
\(430\) | 46.4408 | 2.23957 | ||||||||
\(431\) | 18.7231 | 0.901858 | 0.450929 | − | 0.892560i | \(-0.351093\pi\) | ||||
0.450929 | + | 0.892560i | \(0.351093\pi\) | |||||||
\(432\) | −71.4950 | −3.43980 | ||||||||
\(433\) | 7.51540 | 0.361167 | 0.180583 | − | 0.983560i | \(-0.442201\pi\) | ||||
0.180583 | + | 0.983560i | \(0.442201\pi\) | |||||||
\(434\) | −24.3136 | −1.16709 | ||||||||
\(435\) | 18.3527 | 0.879943 | ||||||||
\(436\) | 16.9155 | 0.810106 | ||||||||
\(437\) | −3.57624 | −0.171075 | ||||||||
\(438\) | 59.0684 | 2.82240 | ||||||||
\(439\) | −19.2646 | −0.919451 | −0.459726 | − | 0.888061i | \(-0.652052\pi\) | ||||
−0.459726 | + | 0.888061i | \(0.652052\pi\) | |||||||
\(440\) | −53.4103 | −2.54624 | ||||||||
\(441\) | 2.24339 | 0.106828 | ||||||||
\(442\) | −30.3385 | −1.44306 | ||||||||
\(443\) | 36.7261 | 1.74491 | 0.872454 | − | 0.488696i | \(-0.162527\pi\) | ||||
0.872454 | + | 0.488696i | \(0.162527\pi\) | |||||||
\(444\) | 12.9230 | 0.613298 | ||||||||
\(445\) | −0.787356 | −0.0373242 | ||||||||
\(446\) | 53.0727 | 2.51307 | ||||||||
\(447\) | 21.0564 | 0.995932 | ||||||||
\(448\) | 125.971 | 5.95157 | ||||||||
\(449\) | −22.9828 | −1.08462 | −0.542312 | − | 0.840177i | \(-0.682451\pi\) | ||||
−0.542312 | + | 0.840177i | \(0.682451\pi\) | |||||||
\(450\) | 0.566755 | 0.0267171 | ||||||||
\(451\) | 20.4983 | 0.965228 | ||||||||
\(452\) | 80.4302 | 3.78312 | ||||||||
\(453\) | 12.2569 | 0.575880 | ||||||||
\(454\) | 58.8033 | 2.75977 | ||||||||
\(455\) | 17.5640 | 0.823415 | ||||||||
\(456\) | 106.294 | 4.97766 | ||||||||
\(457\) | −1.64189 | −0.0768043 | −0.0384021 | − | 0.999262i | \(-0.512227\pi\) | ||||
−0.0384021 | + | 0.999262i | \(0.512227\pi\) | |||||||
\(458\) | 30.5169 | 1.42596 | ||||||||
\(459\) | −29.0938 | −1.35798 | ||||||||
\(460\) | 5.45576 | 0.254376 | ||||||||
\(461\) | −35.9968 | −1.67654 | −0.838269 | − | 0.545257i | \(-0.816432\pi\) | ||||
−0.838269 | + | 0.545257i | \(0.816432\pi\) | |||||||
\(462\) | −72.8829 | −3.39082 | ||||||||
\(463\) | 0.0996890 | 0.00463294 | 0.00231647 | − | 0.999997i | \(-0.499263\pi\) | ||||
0.00231647 | + | 0.999997i | \(0.499263\pi\) | |||||||
\(464\) | 78.3992 | 3.63959 | ||||||||
\(465\) | 6.10839 | 0.283270 | ||||||||
\(466\) | 78.9648 | 3.65797 | ||||||||
\(467\) | 11.7359 | 0.543073 | 0.271537 | − | 0.962428i | \(-0.412468\pi\) | ||||
0.271537 | + | 0.962428i | \(0.412468\pi\) | |||||||
\(468\) | 1.42966 | 0.0660860 | ||||||||
\(469\) | 23.2079 | 1.07164 | ||||||||
\(470\) | −36.2623 | −1.67265 | ||||||||
\(471\) | −2.20079 | −0.101407 | ||||||||
\(472\) | −15.9599 | −0.734612 | ||||||||
\(473\) | −28.7574 | −1.32227 | ||||||||
\(474\) | −21.0057 | −0.964823 | ||||||||
\(475\) | 10.0197 | 0.459736 | ||||||||
\(476\) | 149.081 | 6.83314 | ||||||||
\(477\) | −1.07557 | −0.0492471 | ||||||||
\(478\) | 70.2534 | 3.21332 | ||||||||
\(479\) | −38.5412 | −1.76099 | −0.880497 | − | 0.474051i | \(-0.842791\pi\) | ||||
−0.880497 | + | 0.474051i | \(0.842791\pi\) | |||||||
\(480\) | −65.9264 | −3.00912 | ||||||||
\(481\) | 2.64668 | 0.120678 | ||||||||
\(482\) | 47.2422 | 2.15182 | ||||||||
\(483\) | 4.67218 | 0.212592 | ||||||||
\(484\) | −6.37179 | −0.289627 | ||||||||
\(485\) | −4.53930 | −0.206119 | ||||||||
\(486\) | 3.85301 | 0.174776 | ||||||||
\(487\) | −6.23699 | −0.282625 | −0.141313 | − | 0.989965i | \(-0.545132\pi\) | ||||
−0.141313 | + | 0.989965i | \(0.545132\pi\) | |||||||
\(488\) | 72.4745 | 3.28077 | ||||||||
\(489\) | −17.8018 | −0.805026 | ||||||||
\(490\) | −83.0394 | −3.75134 | ||||||||
\(491\) | −37.9215 | −1.71137 | −0.855686 | − | 0.517495i | \(-0.826865\pi\) | ||||
−0.855686 | + | 0.517495i | \(0.826865\pi\) | |||||||
\(492\) | 62.2342 | 2.80574 | ||||||||
\(493\) | 31.9034 | 1.43686 | ||||||||
\(494\) | 34.6882 | 1.56069 | ||||||||
\(495\) | 0.797843 | 0.0358604 | ||||||||
\(496\) | 26.0939 | 1.17165 | ||||||||
\(497\) | −37.7054 | −1.69132 | ||||||||
\(498\) | −4.51430 | −0.202290 | ||||||||
\(499\) | 36.9368 | 1.65352 | 0.826759 | − | 0.562557i | \(-0.190182\pi\) | ||||
0.826759 | + | 0.562557i | \(0.190182\pi\) | |||||||
\(500\) | −65.3215 | −2.92127 | ||||||||
\(501\) | 5.83928 | 0.260880 | ||||||||
\(502\) | −51.0990 | −2.28066 | ||||||||
\(503\) | 19.5867 | 0.873329 | 0.436664 | − | 0.899624i | \(-0.356160\pi\) | ||||
0.436664 | + | 0.899624i | \(0.356160\pi\) | |||||||
\(504\) | −6.05082 | −0.269525 | ||||||||
\(505\) | 8.39897 | 0.373749 | ||||||||
\(506\) | −4.63655 | −0.206120 | ||||||||
\(507\) | −16.3041 | −0.724088 | ||||||||
\(508\) | 110.349 | 4.89594 | ||||||||
\(509\) | 3.19049 | 0.141416 | 0.0707081 | − | 0.997497i | \(-0.477474\pi\) | ||||
0.0707081 | + | 0.997497i | \(0.477474\pi\) | |||||||
\(510\) | −51.4033 | −2.27618 | ||||||||
\(511\) | −59.4459 | −2.62973 | ||||||||
\(512\) | −23.6427 | −1.04487 | ||||||||
\(513\) | 33.2650 | 1.46868 | ||||||||
\(514\) | 23.8976 | 1.05408 | ||||||||
\(515\) | 20.2083 | 0.890486 | ||||||||
\(516\) | −87.3093 | −3.84358 | ||||||||
\(517\) | 22.4546 | 0.987552 | ||||||||
\(518\) | −17.8492 | −0.784251 | ||||||||
\(519\) | 31.7972 | 1.39574 | ||||||||
\(520\) | −33.2104 | −1.45637 | ||||||||
\(521\) | −2.21851 | −0.0971945 | −0.0485973 | − | 0.998818i | \(-0.515475\pi\) | ||||
−0.0485973 | + | 0.998818i | \(0.515475\pi\) | |||||||
\(522\) | −2.06331 | −0.0903084 | ||||||||
\(523\) | −0.480417 | −0.0210072 | −0.0105036 | − | 0.999945i | \(-0.503343\pi\) | ||||
−0.0105036 | + | 0.999945i | \(0.503343\pi\) | |||||||
\(524\) | 71.1033 | 3.10616 | ||||||||
\(525\) | −13.0903 | −0.571307 | ||||||||
\(526\) | 40.8777 | 1.78235 | ||||||||
\(527\) | 10.6185 | 0.462550 | ||||||||
\(528\) | 78.2197 | 3.40408 | ||||||||
\(529\) | −22.7028 | −0.987077 | ||||||||
\(530\) | 39.8124 | 1.72934 | ||||||||
\(531\) | 0.238408 | 0.0103460 | ||||||||
\(532\) | −170.455 | −7.39018 | ||||||||
\(533\) | 12.7458 | 0.552082 | ||||||||
\(534\) | 2.03152 | 0.0879126 | ||||||||
\(535\) | 1.97732 | 0.0854868 | ||||||||
\(536\) | −43.8819 | −1.89541 | ||||||||
\(537\) | 34.0536 | 1.46952 | ||||||||
\(538\) | 1.25507 | 0.0541100 | ||||||||
\(539\) | 51.4203 | 2.21483 | ||||||||
\(540\) | −50.7477 | −2.18383 | ||||||||
\(541\) | 40.3067 | 1.73292 | 0.866461 | − | 0.499245i | \(-0.166389\pi\) | ||||
0.866461 | + | 0.499245i | \(0.166389\pi\) | |||||||
\(542\) | −65.1526 | −2.79854 | ||||||||
\(543\) | 16.3942 | 0.703543 | ||||||||
\(544\) | −114.603 | −4.91357 | ||||||||
\(545\) | 5.86975 | 0.251432 | ||||||||
\(546\) | −45.3184 | −1.93945 | ||||||||
\(547\) | −23.0346 | −0.984888 | −0.492444 | − | 0.870344i | \(-0.663896\pi\) | ||||
−0.492444 | + | 0.870344i | \(0.663896\pi\) | |||||||
\(548\) | −35.7608 | −1.52763 | ||||||||
\(549\) | −1.08262 | −0.0462053 | ||||||||
\(550\) | 12.9904 | 0.553915 | ||||||||
\(551\) | −36.4774 | −1.55399 | ||||||||
\(552\) | −8.83425 | −0.376011 | ||||||||
\(553\) | 21.1400 | 0.898962 | ||||||||
\(554\) | 46.2699 | 1.96582 | ||||||||
\(555\) | 4.48433 | 0.190349 | ||||||||
\(556\) | −91.3075 | −3.87230 | ||||||||
\(557\) | −1.92300 | −0.0814802 | −0.0407401 | − | 0.999170i | \(-0.512972\pi\) | ||||
−0.0407401 | + | 0.999170i | \(0.512972\pi\) | |||||||
\(558\) | −0.686739 | −0.0290720 | ||||||||
\(559\) | −17.8813 | −0.756298 | ||||||||
\(560\) | 127.126 | 5.37204 | ||||||||
\(561\) | 31.8303 | 1.34388 | ||||||||
\(562\) | −58.9700 | −2.48750 | ||||||||
\(563\) | −16.2179 | −0.683505 | −0.341752 | − | 0.939790i | \(-0.611020\pi\) | ||||
−0.341752 | + | 0.939790i | \(0.611020\pi\) | |||||||
\(564\) | 68.1736 | 2.87063 | ||||||||
\(565\) | 27.9096 | 1.17417 | ||||||||
\(566\) | −8.46650 | −0.355873 | ||||||||
\(567\) | −45.4431 | −1.90843 | ||||||||
\(568\) | 71.2940 | 2.99143 | ||||||||
\(569\) | 16.4625 | 0.690142 | 0.345071 | − | 0.938576i | \(-0.387855\pi\) | ||||
0.345071 | + | 0.938576i | \(0.387855\pi\) | |||||||
\(570\) | 58.7730 | 2.46173 | ||||||||
\(571\) | −4.89710 | −0.204937 | −0.102469 | − | 0.994736i | \(-0.532674\pi\) | ||||
−0.102469 | + | 0.994736i | \(0.532674\pi\) | |||||||
\(572\) | 32.7688 | 1.37013 | ||||||||
\(573\) | −12.1367 | −0.507019 | ||||||||
\(574\) | −85.9580 | −3.58782 | ||||||||
\(575\) | −0.832757 | −0.0347284 | ||||||||
\(576\) | 3.55806 | 0.148252 | ||||||||
\(577\) | −33.8889 | −1.41081 | −0.705406 | − | 0.708804i | \(-0.749235\pi\) | ||||
−0.705406 | + | 0.708804i | \(0.749235\pi\) | |||||||
\(578\) | −43.2052 | −1.79710 | ||||||||
\(579\) | 11.0831 | 0.460600 | ||||||||
\(580\) | 55.6484 | 2.31067 | ||||||||
\(581\) | 4.54315 | 0.188482 | ||||||||
\(582\) | 11.7122 | 0.485488 | ||||||||
\(583\) | −24.6529 | −1.02102 | ||||||||
\(584\) | 112.402 | 4.65121 | ||||||||
\(585\) | 0.496097 | 0.0205111 | ||||||||
\(586\) | −24.3663 | −1.00656 | ||||||||
\(587\) | 27.7584 | 1.14571 | 0.572855 | − | 0.819656i | \(-0.305836\pi\) | ||||
0.572855 | + | 0.819656i | \(0.305836\pi\) | |||||||
\(588\) | 156.115 | 6.43809 | ||||||||
\(589\) | −12.1409 | −0.500258 | ||||||||
\(590\) | −8.82470 | −0.363307 | ||||||||
\(591\) | −3.00849 | −0.123753 | ||||||||
\(592\) | 19.1562 | 0.787317 | ||||||||
\(593\) | −20.0951 | −0.825207 | −0.412603 | − | 0.910911i | \(-0.635380\pi\) | ||||
−0.412603 | + | 0.910911i | \(0.635380\pi\) | |||||||
\(594\) | 43.1277 | 1.76955 | ||||||||
\(595\) | 51.7319 | 2.12080 | ||||||||
\(596\) | 63.8465 | 2.61525 | ||||||||
\(597\) | 23.7593 | 0.972402 | ||||||||
\(598\) | −2.88300 | −0.117894 | ||||||||
\(599\) | 13.1037 | 0.535403 | 0.267701 | − | 0.963502i | \(-0.413736\pi\) | ||||
0.267701 | + | 0.963502i | \(0.413736\pi\) | |||||||
\(600\) | 24.7514 | 1.01047 | ||||||||
\(601\) | −37.5086 | −1.53001 | −0.765005 | − | 0.644025i | \(-0.777263\pi\) | ||||
−0.765005 | + | 0.644025i | \(0.777263\pi\) | |||||||
\(602\) | 120.592 | 4.91495 | ||||||||
\(603\) | 0.655508 | 0.0266943 | ||||||||
\(604\) | 37.1650 | 1.51222 | ||||||||
\(605\) | −2.21104 | −0.0898915 | ||||||||
\(606\) | −21.6709 | −0.880320 | ||||||||
\(607\) | 40.6738 | 1.65090 | 0.825449 | − | 0.564476i | \(-0.190922\pi\) | ||||
0.825449 | + | 0.564476i | \(0.190922\pi\) | |||||||
\(608\) | 131.034 | 5.31413 | ||||||||
\(609\) | 47.6559 | 1.93112 | ||||||||
\(610\) | 40.0734 | 1.62252 | ||||||||
\(611\) | 13.9622 | 0.564851 | ||||||||
\(612\) | 4.21081 | 0.170212 | ||||||||
\(613\) | 36.3755 | 1.46919 | 0.734597 | − | 0.678503i | \(-0.237371\pi\) | ||||
0.734597 | + | 0.678503i | \(0.237371\pi\) | |||||||
\(614\) | −31.2761 | −1.26220 | ||||||||
\(615\) | 21.5955 | 0.870816 | ||||||||
\(616\) | −138.689 | −5.58795 | ||||||||
\(617\) | −30.2481 | −1.21774 | −0.608871 | − | 0.793269i | \(-0.708377\pi\) | ||||
−0.608871 | + | 0.793269i | \(0.708377\pi\) | |||||||
\(618\) | −52.1413 | −2.09743 | ||||||||
\(619\) | 29.2455 | 1.17547 | 0.587737 | − | 0.809052i | \(-0.300019\pi\) | ||||
0.587737 | + | 0.809052i | \(0.300019\pi\) | |||||||
\(620\) | 18.5217 | 0.743849 | ||||||||
\(621\) | −2.76471 | −0.110944 | ||||||||
\(622\) | −28.4698 | −1.14153 | ||||||||
\(623\) | −2.04451 | −0.0819115 | ||||||||
\(624\) | 48.6369 | 1.94703 | ||||||||
\(625\) | −15.0295 | −0.601178 | ||||||||
\(626\) | 61.4770 | 2.45712 | ||||||||
\(627\) | −36.3938 | −1.45343 | ||||||||
\(628\) | −6.67316 | −0.266288 | ||||||||
\(629\) | 7.79534 | 0.310821 | ||||||||
\(630\) | −3.34569 | −0.133295 | ||||||||
\(631\) | −5.26560 | −0.209620 | −0.104810 | − | 0.994492i | \(-0.533423\pi\) | ||||
−0.104810 | + | 0.994492i | \(0.533423\pi\) | |||||||
\(632\) | −39.9719 | −1.59000 | ||||||||
\(633\) | −41.2133 | −1.63808 | ||||||||
\(634\) | −45.7815 | −1.81821 | ||||||||
\(635\) | 38.2915 | 1.51955 | ||||||||
\(636\) | −74.8479 | −2.96791 | ||||||||
\(637\) | 31.9730 | 1.26682 | ||||||||
\(638\) | −47.2925 | −1.87233 | ||||||||
\(639\) | −1.06499 | −0.0421303 | ||||||||
\(640\) | −57.2535 | −2.26314 | ||||||||
\(641\) | −15.4626 | −0.610735 | −0.305368 | − | 0.952235i | \(-0.598779\pi\) | ||||
−0.305368 | + | 0.952235i | \(0.598779\pi\) | |||||||
\(642\) | −5.10184 | −0.201354 | ||||||||
\(643\) | 2.49487 | 0.0983882 | 0.0491941 | − | 0.998789i | \(-0.484335\pi\) | ||||
0.0491941 | + | 0.998789i | \(0.484335\pi\) | |||||||
\(644\) | 14.1668 | 0.558252 | ||||||||
\(645\) | −30.2967 | −1.19293 | ||||||||
\(646\) | 102.168 | 4.01975 | ||||||||
\(647\) | 34.0810 | 1.33986 | 0.669932 | − | 0.742423i | \(-0.266323\pi\) | ||||
0.669932 | + | 0.742423i | \(0.266323\pi\) | |||||||
\(648\) | 85.9248 | 3.37544 | ||||||||
\(649\) | 5.46449 | 0.214500 | ||||||||
\(650\) | 8.07743 | 0.316823 | ||||||||
\(651\) | 15.8615 | 0.621662 | ||||||||
\(652\) | −53.9781 | −2.11395 | ||||||||
\(653\) | 36.3173 | 1.42121 | 0.710603 | − | 0.703594i | \(-0.248422\pi\) | ||||
0.710603 | + | 0.703594i | \(0.248422\pi\) | |||||||
\(654\) | −15.1450 | −0.592218 | ||||||||
\(655\) | 24.6732 | 0.964060 | ||||||||
\(656\) | 92.2522 | 3.60184 | ||||||||
\(657\) | −1.67905 | −0.0655061 | ||||||||
\(658\) | −94.1614 | −3.67079 | ||||||||
\(659\) | −22.9519 | −0.894078 | −0.447039 | − | 0.894514i | \(-0.647521\pi\) | ||||
−0.447039 | + | 0.894514i | \(0.647521\pi\) | |||||||
\(660\) | 55.5210 | 2.16115 | ||||||||
\(661\) | 34.3123 | 1.33459 | 0.667297 | − | 0.744792i | \(-0.267451\pi\) | ||||
0.667297 | + | 0.744792i | \(0.267451\pi\) | |||||||
\(662\) | −35.1557 | −1.36637 | ||||||||
\(663\) | 19.7920 | 0.768659 | ||||||||
\(664\) | −8.59028 | −0.333368 | ||||||||
\(665\) | −59.1487 | −2.29369 | ||||||||
\(666\) | −0.504153 | −0.0195355 | ||||||||
\(667\) | 3.03170 | 0.117388 | ||||||||
\(668\) | 17.7057 | 0.685053 | ||||||||
\(669\) | −34.6232 | −1.33861 | ||||||||
\(670\) | −24.2637 | −0.937387 | ||||||||
\(671\) | −24.8145 | −0.957955 | ||||||||
\(672\) | −171.190 | −6.60378 | ||||||||
\(673\) | 41.1979 | 1.58806 | 0.794032 | − | 0.607877i | \(-0.207978\pi\) | ||||
0.794032 | + | 0.607877i | \(0.207978\pi\) | |||||||
\(674\) | 53.0419 | 2.04310 | ||||||||
\(675\) | 7.74603 | 0.298145 | ||||||||
\(676\) | −49.4367 | −1.90141 | ||||||||
\(677\) | 8.77820 | 0.337374 | 0.168687 | − | 0.985670i | \(-0.446047\pi\) | ||||
0.168687 | + | 0.985670i | \(0.446047\pi\) | |||||||
\(678\) | −72.0120 | −2.76560 | ||||||||
\(679\) | −11.7871 | −0.452347 | ||||||||
\(680\) | −97.8157 | −3.75106 | ||||||||
\(681\) | −38.3617 | −1.47002 | ||||||||
\(682\) | −15.7406 | −0.602737 | ||||||||
\(683\) | 12.5580 | 0.480518 | 0.240259 | − | 0.970709i | \(-0.422768\pi\) | ||||
0.240259 | + | 0.970709i | \(0.422768\pi\) | |||||||
\(684\) | −4.81452 | −0.184088 | ||||||||
\(685\) | −12.4091 | −0.474129 | ||||||||
\(686\) | −123.671 | −4.72178 | ||||||||
\(687\) | −19.9084 | −0.759553 | ||||||||
\(688\) | −129.422 | −4.93416 | ||||||||
\(689\) | −15.3291 | −0.583994 | ||||||||
\(690\) | −4.88473 | −0.185959 | ||||||||
\(691\) | −49.5280 | −1.88413 | −0.942066 | − | 0.335426i | \(-0.891120\pi\) | ||||
−0.942066 | + | 0.335426i | \(0.891120\pi\) | |||||||
\(692\) | 96.4146 | 3.66513 | ||||||||
\(693\) | 2.07174 | 0.0786989 | ||||||||
\(694\) | 75.7877 | 2.87686 | ||||||||
\(695\) | −31.6841 | −1.20185 | ||||||||
\(696\) | −90.1088 | −3.41557 | ||||||||
\(697\) | 37.5406 | 1.42195 | ||||||||
\(698\) | −17.3935 | −0.658355 | ||||||||
\(699\) | −51.5145 | −1.94846 | ||||||||
\(700\) | −39.6920 | −1.50022 | ||||||||
\(701\) | 42.3113 | 1.59807 | 0.799037 | − | 0.601281i | \(-0.205343\pi\) | ||||
0.799037 | + | 0.601281i | \(0.205343\pi\) | |||||||
\(702\) | 26.8167 | 1.01213 | ||||||||
\(703\) | −8.91297 | −0.336159 | ||||||||
\(704\) | 81.5533 | 3.07366 | ||||||||
\(705\) | 23.6565 | 0.890956 | ||||||||
\(706\) | 13.0833 | 0.492395 | ||||||||
\(707\) | 21.8094 | 0.820228 | ||||||||
\(708\) | 16.5906 | 0.623511 | ||||||||
\(709\) | 32.8555 | 1.23391 | 0.616957 | − | 0.786997i | \(-0.288365\pi\) | ||||
0.616957 | + | 0.786997i | \(0.288365\pi\) | |||||||
\(710\) | 39.4207 | 1.47943 | ||||||||
\(711\) | 0.597099 | 0.0223930 | ||||||||
\(712\) | 3.86580 | 0.144877 | ||||||||
\(713\) | 1.00905 | 0.0377893 | ||||||||
\(714\) | −133.478 | −4.99528 | ||||||||
\(715\) | 11.3709 | 0.425248 | ||||||||
\(716\) | 103.256 | 3.85887 | ||||||||
\(717\) | −45.8314 | −1.71161 | ||||||||
\(718\) | 41.4985 | 1.54871 | ||||||||
\(719\) | −35.4464 | −1.32193 | −0.660964 | − | 0.750418i | \(-0.729852\pi\) | ||||
−0.660964 | + | 0.750418i | \(0.729852\pi\) | |||||||
\(720\) | 3.59067 | 0.133816 | ||||||||
\(721\) | 52.4745 | 1.95425 | ||||||||
\(722\) | −65.2347 | −2.42778 | ||||||||
\(723\) | −30.8195 | −1.14619 | ||||||||
\(724\) | 49.7100 | 1.84746 | ||||||||
\(725\) | −8.49406 | −0.315462 | ||||||||
\(726\) | 5.70489 | 0.211728 | ||||||||
\(727\) | 46.2553 | 1.71552 | 0.857758 | − | 0.514054i | \(-0.171857\pi\) | ||||
0.857758 | + | 0.514054i | \(0.171857\pi\) | |||||||
\(728\) | −86.2368 | −3.19615 | ||||||||
\(729\) | 25.6604 | 0.950386 | ||||||||
\(730\) | 62.1503 | 2.30029 | ||||||||
\(731\) | −52.6663 | −1.94793 | ||||||||
\(732\) | −75.3386 | −2.78459 | ||||||||
\(733\) | −38.8504 | −1.43497 | −0.717487 | − | 0.696572i | \(-0.754708\pi\) | ||||
−0.717487 | + | 0.696572i | \(0.754708\pi\) | |||||||
\(734\) | 52.1632 | 1.92538 | ||||||||
\(735\) | 54.1726 | 1.99819 | ||||||||
\(736\) | −10.8905 | −0.401428 | ||||||||
\(737\) | 15.0247 | 0.553443 | ||||||||
\(738\) | −2.42789 | −0.0893718 | ||||||||
\(739\) | −24.8497 | −0.914112 | −0.457056 | − | 0.889438i | \(-0.651096\pi\) | ||||
−0.457056 | + | 0.889438i | \(0.651096\pi\) | |||||||
\(740\) | 13.5973 | 0.499845 | ||||||||
\(741\) | −22.6296 | −0.831320 | ||||||||
\(742\) | 103.380 | 3.79520 | ||||||||
\(743\) | 13.3748 | 0.490674 | 0.245337 | − | 0.969438i | \(-0.421101\pi\) | ||||
0.245337 | + | 0.969438i | \(0.421101\pi\) | |||||||
\(744\) | −29.9913 | −1.09953 | ||||||||
\(745\) | 22.1550 | 0.811696 | ||||||||
\(746\) | 82.8996 | 3.03517 | ||||||||
\(747\) | 0.128322 | 0.00469504 | ||||||||
\(748\) | 96.5149 | 3.52894 | ||||||||
\(749\) | 5.13445 | 0.187609 | ||||||||
\(750\) | 58.4846 | 2.13555 | ||||||||
\(751\) | −30.6552 | −1.11862 | −0.559312 | − | 0.828958i | \(-0.688934\pi\) | ||||
−0.559312 | + | 0.828958i | \(0.688934\pi\) | |||||||
\(752\) | 101.056 | 3.68514 | ||||||||
\(753\) | 33.3356 | 1.21482 | ||||||||
\(754\) | −29.4064 | −1.07092 | ||||||||
\(755\) | 12.8964 | 0.469348 | ||||||||
\(756\) | −131.775 | −4.79263 | ||||||||
\(757\) | 45.2241 | 1.64370 | 0.821848 | − | 0.569706i | \(-0.192943\pi\) | ||||
0.821848 | + | 0.569706i | \(0.192943\pi\) | |||||||
\(758\) | 42.4808 | 1.54297 | ||||||||
\(759\) | 3.02476 | 0.109792 | ||||||||
\(760\) | 111.840 | 4.05685 | ||||||||
\(761\) | −14.3095 | −0.518720 | −0.259360 | − | 0.965781i | \(-0.583512\pi\) | ||||
−0.259360 | + | 0.965781i | \(0.583512\pi\) | |||||||
\(762\) | −98.7992 | −3.57912 | ||||||||
\(763\) | 15.2418 | 0.551792 | ||||||||
\(764\) | −36.8006 | −1.33140 | ||||||||
\(765\) | 1.46117 | 0.0528287 | ||||||||
\(766\) | 34.4729 | 1.24556 | ||||||||
\(767\) | 3.39781 | 0.122688 | ||||||||
\(768\) | 55.5110 | 2.00308 | ||||||||
\(769\) | −6.65959 | −0.240151 | −0.120075 | − | 0.992765i | \(-0.538314\pi\) | ||||
−0.120075 | + | 0.992765i | \(0.538314\pi\) | |||||||
\(770\) | −76.6856 | −2.76356 | ||||||||
\(771\) | −15.5901 | −0.561464 | ||||||||
\(772\) | 33.6060 | 1.20951 | ||||||||
\(773\) | 9.74075 | 0.350350 | 0.175175 | − | 0.984537i | \(-0.443951\pi\) | ||||
0.175175 | + | 0.984537i | \(0.443951\pi\) | |||||||
\(774\) | 3.40612 | 0.122430 | ||||||||
\(775\) | −2.82711 | −0.101553 | ||||||||
\(776\) | 22.2873 | 0.800067 | ||||||||
\(777\) | 11.6444 | 0.417739 | ||||||||
\(778\) | −26.6436 | −0.955220 | ||||||||
\(779\) | −42.9228 | −1.53787 | ||||||||
\(780\) | 34.5228 | 1.23612 | ||||||||
\(781\) | −24.4103 | −0.873471 | ||||||||
\(782\) | −8.49137 | −0.303651 | ||||||||
\(783\) | −28.1999 | −1.00778 | ||||||||
\(784\) | 231.416 | 8.26484 | ||||||||
\(785\) | −2.31561 | −0.0826478 | ||||||||
\(786\) | −63.6613 | −2.27072 | ||||||||
\(787\) | −38.0087 | −1.35486 | −0.677431 | − | 0.735586i | \(-0.736907\pi\) | ||||
−0.677431 | + | 0.735586i | \(0.736907\pi\) | |||||||
\(788\) | −9.12225 | −0.324967 | ||||||||
\(789\) | −26.6675 | −0.949389 | ||||||||
\(790\) | −22.1017 | −0.786342 | ||||||||
\(791\) | 72.4723 | 2.57682 | ||||||||
\(792\) | −3.91729 | −0.139195 | ||||||||
\(793\) | −15.4296 | −0.547922 | ||||||||
\(794\) | −54.9102 | −1.94869 | ||||||||
\(795\) | −25.9725 | −0.921151 | ||||||||
\(796\) | 72.0421 | 2.55347 | ||||||||
\(797\) | 47.2815 | 1.67480 | 0.837398 | − | 0.546594i | \(-0.184076\pi\) | ||||
0.837398 | + | 0.546594i | \(0.184076\pi\) | |||||||
\(798\) | 152.615 | 5.40250 | ||||||||
\(799\) | 41.1233 | 1.45484 | ||||||||
\(800\) | 30.5124 | 1.07877 | ||||||||
\(801\) | −0.0577472 | −0.00204040 | ||||||||
\(802\) | 19.0756 | 0.673583 | ||||||||
\(803\) | −38.4852 | −1.35811 | ||||||||
\(804\) | 45.6161 | 1.60875 | ||||||||
\(805\) | 4.91595 | 0.173265 | ||||||||
\(806\) | −9.78744 | −0.344748 | ||||||||
\(807\) | −0.818774 | −0.0288222 | ||||||||
\(808\) | −41.2377 | −1.45074 | ||||||||
\(809\) | −32.9644 | −1.15897 | −0.579484 | − | 0.814984i | \(-0.696746\pi\) | ||||
−0.579484 | + | 0.814984i | \(0.696746\pi\) | |||||||
\(810\) | 47.5104 | 1.66935 | ||||||||
\(811\) | 38.0375 | 1.33568 | 0.667839 | − | 0.744306i | \(-0.267220\pi\) | ||||
0.667839 | + | 0.744306i | \(0.267220\pi\) | |||||||
\(812\) | 144.501 | 5.07099 | ||||||||
\(813\) | 42.5038 | 1.49067 | ||||||||
\(814\) | −11.5556 | −0.405022 | ||||||||
\(815\) | −18.7306 | −0.656105 | ||||||||
\(816\) | 143.252 | 5.01481 | ||||||||
\(817\) | 60.2171 | 2.10673 | ||||||||
\(818\) | 64.5936 | 2.25846 | ||||||||
\(819\) | 1.28820 | 0.0450135 | ||||||||
\(820\) | 65.4813 | 2.28671 | ||||||||
\(821\) | −13.7396 | −0.479514 | −0.239757 | − | 0.970833i | \(-0.577068\pi\) | ||||
−0.239757 | + | 0.970833i | \(0.577068\pi\) | |||||||
\(822\) | 32.0179 | 1.11675 | ||||||||
\(823\) | −43.4574 | −1.51483 | −0.757414 | − | 0.652934i | \(-0.773538\pi\) | ||||
−0.757414 | + | 0.652934i | \(0.773538\pi\) | |||||||
\(824\) | −99.2199 | −3.45649 | ||||||||
\(825\) | −8.47461 | −0.295048 | ||||||||
\(826\) | −22.9149 | −0.797311 | ||||||||
\(827\) | 24.5983 | 0.855366 | 0.427683 | − | 0.903929i | \(-0.359330\pi\) | ||||
0.427683 | + | 0.903929i | \(0.359330\pi\) | |||||||
\(828\) | 0.400143 | 0.0139059 | ||||||||
\(829\) | −25.9415 | −0.900985 | −0.450492 | − | 0.892780i | \(-0.648752\pi\) | ||||
−0.450492 | + | 0.892780i | \(0.648752\pi\) | |||||||
\(830\) | −4.74983 | −0.164869 | ||||||||
\(831\) | −30.1852 | −1.04711 | ||||||||
\(832\) | 50.7097 | 1.75804 | ||||||||
\(833\) | 94.1710 | 3.26283 | ||||||||
\(834\) | 81.7507 | 2.83080 | ||||||||
\(835\) | 6.14394 | 0.212620 | ||||||||
\(836\) | −110.352 | −3.81662 | ||||||||
\(837\) | −9.38588 | −0.324424 | ||||||||
\(838\) | 76.4503 | 2.64093 | ||||||||
\(839\) | 18.4066 | 0.635465 | 0.317732 | − | 0.948180i | \(-0.397079\pi\) | ||||
0.317732 | + | 0.948180i | \(0.397079\pi\) | |||||||
\(840\) | −146.113 | −5.04138 | ||||||||
\(841\) | 1.92314 | 0.0663152 | ||||||||
\(842\) | −100.352 | −3.45835 | ||||||||
\(843\) | 38.4704 | 1.32499 | ||||||||
\(844\) | −124.966 | −4.30150 | ||||||||
\(845\) | −17.1547 | −0.590140 | ||||||||
\(846\) | −2.65959 | −0.0914387 | ||||||||
\(847\) | −5.74135 | −0.197275 | ||||||||
\(848\) | −110.950 | −3.81003 | ||||||||
\(849\) | 5.52331 | 0.189560 | ||||||||
\(850\) | 23.7907 | 0.816014 | ||||||||
\(851\) | 0.740773 | 0.0253934 | ||||||||
\(852\) | −74.1114 | −2.53902 | ||||||||
\(853\) | 46.0794 | 1.57773 | 0.788864 | − | 0.614568i | \(-0.210670\pi\) | ||||
0.788864 | + | 0.614568i | \(0.210670\pi\) | |||||||
\(854\) | 104.058 | 3.56078 | ||||||||
\(855\) | −1.67066 | −0.0571353 | ||||||||
\(856\) | −9.70832 | −0.331824 | ||||||||
\(857\) | −17.8912 | −0.611152 | −0.305576 | − | 0.952168i | \(-0.598849\pi\) | ||||
−0.305576 | + | 0.952168i | \(0.598849\pi\) | |||||||
\(858\) | −29.3390 | −1.00162 | ||||||||
\(859\) | 8.72940 | 0.297843 | 0.148922 | − | 0.988849i | \(-0.452420\pi\) | ||||
0.148922 | + | 0.988849i | \(0.452420\pi\) | |||||||
\(860\) | −91.8647 | −3.13256 | ||||||||
\(861\) | 56.0766 | 1.91109 | ||||||||
\(862\) | −50.8295 | −1.73126 | ||||||||
\(863\) | −56.1905 | −1.91275 | −0.956374 | − | 0.292144i | \(-0.905631\pi\) | ||||
−0.956374 | + | 0.292144i | \(0.905631\pi\) | |||||||
\(864\) | 101.300 | 3.44628 | ||||||||
\(865\) | 33.4563 | 1.13755 | ||||||||
\(866\) | −20.4028 | −0.693317 | ||||||||
\(867\) | 28.1859 | 0.957244 | ||||||||
\(868\) | 48.0948 | 1.63244 | ||||||||
\(869\) | 13.6860 | 0.464264 | ||||||||
\(870\) | −49.8239 | −1.68919 | ||||||||
\(871\) | 9.34234 | 0.316553 | ||||||||
\(872\) | −28.8196 | −0.975954 | ||||||||
\(873\) | −0.332927 | −0.0112679 | ||||||||
\(874\) | 9.70879 | 0.328405 | ||||||||
\(875\) | −58.8584 | −1.98978 | ||||||||
\(876\) | −116.843 | −3.94777 | ||||||||
\(877\) | 39.4851 | 1.33332 | 0.666659 | − | 0.745363i | \(-0.267724\pi\) | ||||
0.666659 | + | 0.745363i | \(0.267724\pi\) | |||||||
\(878\) | 52.2998 | 1.76503 | ||||||||
\(879\) | 15.8959 | 0.536156 | ||||||||
\(880\) | 82.3008 | 2.77436 | ||||||||
\(881\) | 14.4808 | 0.487872 | 0.243936 | − | 0.969791i | \(-0.421561\pi\) | ||||
0.243936 | + | 0.969791i | \(0.421561\pi\) | |||||||
\(882\) | −6.09038 | −0.205074 | ||||||||
\(883\) | −12.5576 | −0.422596 | −0.211298 | − | 0.977422i | \(-0.567769\pi\) | ||||
−0.211298 | + | 0.977422i | \(0.567769\pi\) | |||||||
\(884\) | 60.0128 | 2.01845 | ||||||||
\(885\) | 5.75699 | 0.193519 | ||||||||
\(886\) | −99.7041 | −3.34963 | ||||||||
\(887\) | 3.17216 | 0.106511 | 0.0532553 | − | 0.998581i | \(-0.483040\pi\) | ||||
0.0532553 | + | 0.998581i | \(0.483040\pi\) | |||||||
\(888\) | −22.0174 | −0.738855 | ||||||||
\(889\) | 99.4308 | 3.33480 | ||||||||
\(890\) | 2.13752 | 0.0716498 | ||||||||
\(891\) | −29.4198 | −0.985599 | ||||||||
\(892\) | −104.983 | −3.51511 | ||||||||
\(893\) | −47.0192 | −1.57344 | ||||||||
\(894\) | −57.1639 | −1.91185 | ||||||||
\(895\) | 35.8304 | 1.19768 | ||||||||
\(896\) | −148.669 | −4.96668 | ||||||||
\(897\) | 1.88079 | 0.0627977 | ||||||||
\(898\) | 62.3938 | 2.08211 | ||||||||
\(899\) | 10.2923 | 0.343267 | ||||||||
\(900\) | −1.12110 | −0.0373700 | ||||||||
\(901\) | −45.1494 | −1.50414 | ||||||||
\(902\) | −55.6490 | −1.85291 | ||||||||
\(903\) | −78.6707 | −2.61800 | ||||||||
\(904\) | −137.032 | −4.55762 | ||||||||
\(905\) | 17.2496 | 0.573396 | ||||||||
\(906\) | −33.2751 | −1.10549 | ||||||||
\(907\) | 43.8157 | 1.45488 | 0.727439 | − | 0.686173i | \(-0.240711\pi\) | ||||
0.727439 | + | 0.686173i | \(0.240711\pi\) | |||||||
\(908\) | −116.319 | −3.86018 | ||||||||
\(909\) | 0.616008 | 0.0204317 | ||||||||
\(910\) | −47.6830 | −1.58067 | ||||||||
\(911\) | 0.486012 | 0.0161023 | 0.00805115 | − | 0.999968i | \(-0.497437\pi\) | ||||
0.00805115 | + | 0.999968i | \(0.497437\pi\) | |||||||
\(912\) | −163.790 | −5.42362 | ||||||||
\(913\) | 2.94122 | 0.0973403 | ||||||||
\(914\) | 4.45741 | 0.147438 | ||||||||
\(915\) | −26.1428 | −0.864254 | ||||||||
\(916\) | −60.3657 | −1.99454 | ||||||||
\(917\) | 64.0682 | 2.11572 | ||||||||
\(918\) | 78.9840 | 2.60686 | ||||||||
\(919\) | −13.6658 | −0.450793 | −0.225396 | − | 0.974267i | \(-0.572368\pi\) | ||||
−0.225396 | + | 0.974267i | \(0.572368\pi\) | |||||||
\(920\) | −9.29519 | −0.306453 | ||||||||
\(921\) | 20.4037 | 0.672324 | ||||||||
\(922\) | 97.7243 | 3.21838 | ||||||||
\(923\) | −15.1783 | −0.499600 | ||||||||
\(924\) | 144.170 | 4.74285 | ||||||||
\(925\) | −2.07546 | −0.0682407 | ||||||||
\(926\) | −0.270636 | −0.00889366 | ||||||||
\(927\) | 1.48215 | 0.0486801 | ||||||||
\(928\) | −111.082 | −3.64645 | ||||||||
\(929\) | 4.45820 | 0.146269 | 0.0731344 | − | 0.997322i | \(-0.476700\pi\) | ||||
0.0731344 | + | 0.997322i | \(0.476700\pi\) | |||||||
\(930\) | −16.5831 | −0.543781 | ||||||||
\(931\) | −107.672 | −3.52882 | ||||||||
\(932\) | −156.201 | −5.11652 | ||||||||
\(933\) | 18.5729 | 0.608050 | ||||||||
\(934\) | −31.8607 | −1.04251 | ||||||||
\(935\) | 33.4911 | 1.09528 | ||||||||
\(936\) | −2.43576 | −0.0796154 | ||||||||
\(937\) | 59.4901 | 1.94346 | 0.971728 | − | 0.236103i | \(-0.0758704\pi\) | ||||
0.971728 | + | 0.236103i | \(0.0758704\pi\) | |||||||
\(938\) | −63.0049 | −2.05718 | ||||||||
\(939\) | −40.1059 | −1.30881 | ||||||||
\(940\) | 71.7306 | 2.33959 | ||||||||
\(941\) | −19.4501 | −0.634056 | −0.317028 | − | 0.948416i | \(-0.602685\pi\) | ||||
−0.317028 | + | 0.948416i | \(0.602685\pi\) | |||||||
\(942\) | 5.97471 | 0.194666 | ||||||||
\(943\) | 3.56739 | 0.116170 | ||||||||
\(944\) | 24.5928 | 0.800428 | ||||||||
\(945\) | −45.7266 | −1.48749 | ||||||||
\(946\) | 78.0707 | 2.53830 | ||||||||
\(947\) | 35.3764 | 1.14958 | 0.574789 | − | 0.818302i | \(-0.305084\pi\) | ||||
0.574789 | + | 0.818302i | \(0.305084\pi\) | |||||||
\(948\) | 41.5515 | 1.34953 | ||||||||
\(949\) | −23.9300 | −0.776800 | ||||||||
\(950\) | −27.2016 | −0.882536 | ||||||||
\(951\) | 29.8666 | 0.968490 | ||||||||
\(952\) | −253.996 | −8.23205 | ||||||||
\(953\) | 27.7804 | 0.899894 | 0.449947 | − | 0.893055i | \(-0.351443\pi\) | ||||
0.449947 | + | 0.893055i | \(0.351443\pi\) | |||||||
\(954\) | 2.91997 | 0.0945376 | ||||||||
\(955\) | −12.7700 | −0.413227 | ||||||||
\(956\) | −138.969 | −4.49457 | ||||||||
\(957\) | 30.8523 | 0.997314 | ||||||||
\(958\) | 104.632 | 3.38051 | ||||||||
\(959\) | −32.2225 | −1.04052 | ||||||||
\(960\) | 85.9187 | 2.77301 | ||||||||
\(961\) | −27.5744 | −0.889496 | ||||||||
\(962\) | −7.18522 | −0.231661 | ||||||||
\(963\) | 0.145023 | 0.00467330 | ||||||||
\(964\) | −93.4500 | −3.00982 | ||||||||
\(965\) | 11.6614 | 0.375394 | ||||||||
\(966\) | −12.6841 | −0.408103 | ||||||||
\(967\) | 54.3047 | 1.74632 | 0.873161 | − | 0.487432i | \(-0.162066\pi\) | ||||
0.873161 | + | 0.487432i | \(0.162066\pi\) | |||||||
\(968\) | 10.8559 | 0.348921 | ||||||||
\(969\) | −66.6517 | −2.14116 | ||||||||
\(970\) | 12.3233 | 0.395678 | ||||||||
\(971\) | 4.35799 | 0.139854 | 0.0699272 | − | 0.997552i | \(-0.477723\pi\) | ||||
0.0699272 | + | 0.997552i | \(0.477723\pi\) | |||||||
\(972\) | −7.62167 | −0.244465 | ||||||||
\(973\) | −82.2733 | −2.63756 | ||||||||
\(974\) | 16.9322 | 0.542544 | ||||||||
\(975\) | −5.26950 | −0.168759 | ||||||||
\(976\) | −111.677 | −3.57470 | ||||||||
\(977\) | 39.7648 | 1.27219 | 0.636094 | − | 0.771612i | \(-0.280549\pi\) | ||||
0.636094 | + | 0.771612i | \(0.280549\pi\) | |||||||
\(978\) | 48.3285 | 1.54537 | ||||||||
\(979\) | −1.32361 | −0.0423027 | ||||||||
\(980\) | 164.261 | 5.24711 | ||||||||
\(981\) | 0.430507 | 0.0137450 | ||||||||
\(982\) | 102.949 | 3.28525 | ||||||||
\(983\) | −43.1950 | −1.37771 | −0.688854 | − | 0.724900i | \(-0.741886\pi\) | ||||
−0.688854 | + | 0.724900i | \(0.741886\pi\) | |||||||
\(984\) | −106.031 | −3.38014 | ||||||||
\(985\) | −3.16546 | −0.100860 | ||||||||
\(986\) | −86.6115 | −2.75827 | ||||||||
\(987\) | 61.4283 | 1.95529 | ||||||||
\(988\) | −68.6169 | −2.18299 | ||||||||
\(989\) | −5.00475 | −0.159142 | ||||||||
\(990\) | −2.16599 | −0.0688396 | ||||||||
\(991\) | −34.3512 | −1.09120 | −0.545600 | − | 0.838045i | \(-0.683698\pi\) | ||||
−0.545600 | + | 0.838045i | \(0.683698\pi\) | |||||||
\(992\) | −36.9719 | −1.17386 | ||||||||
\(993\) | 22.9347 | 0.727809 | ||||||||
\(994\) | 102.363 | 3.24675 | ||||||||
\(995\) | 24.9989 | 0.792519 | ||||||||
\(996\) | 8.92975 | 0.282950 | ||||||||
\(997\) | −23.7018 | −0.750645 | −0.375322 | − | 0.926894i | \(-0.622468\pi\) | ||||
−0.375322 | + | 0.926894i | \(0.622468\pi\) | |||||||
\(998\) | −100.276 | −3.17419 | ||||||||
\(999\) | −6.89043 | −0.218003 |
(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 | 5077.2.a.c.1.2 | ✓ | 216 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5077.2.a.c.1.2 | ✓ | 216 | 1.1 | even | 1 | trivial |