Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4027,2,Mod(1,4027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4027, 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("4027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4027 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4027.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: | \(32.1557568940\) |
Analytic rank: | \(0\) |
Dimension: | \(174\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 4027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.54479 | −1.79944 | −0.899721 | − | 0.436466i | \(-0.856230\pi\) | ||||
−0.899721 | + | 0.436466i | \(0.856230\pi\) | |||||||
\(3\) | 0.596838 | 0.344584 | 0.172292 | − | 0.985046i | \(-0.444883\pi\) | ||||
0.172292 | + | 0.985046i | \(0.444883\pi\) | |||||||
\(4\) | 4.47598 | 2.23799 | ||||||||
\(5\) | 4.06364 | 1.81731 | 0.908657 | − | 0.417543i | \(-0.137109\pi\) | ||||
0.908657 | + | 0.417543i | \(0.137109\pi\) | |||||||
\(6\) | −1.51883 | −0.620060 | ||||||||
\(7\) | −0.751735 | −0.284129 | −0.142065 | − | 0.989857i | \(-0.545374\pi\) | ||||
−0.142065 | + | 0.989857i | \(0.545374\pi\) | |||||||
\(8\) | −6.30086 | −2.22769 | ||||||||
\(9\) | −2.64378 | −0.881262 | ||||||||
\(10\) | −10.3411 | −3.27015 | ||||||||
\(11\) | 1.59169 | 0.479913 | 0.239956 | − | 0.970784i | \(-0.422867\pi\) | ||||
0.239956 | + | 0.970784i | \(0.422867\pi\) | |||||||
\(12\) | 2.67143 | 0.771177 | ||||||||
\(13\) | 0.889782 | 0.246781 | 0.123391 | − | 0.992358i | \(-0.460623\pi\) | ||||
0.123391 | + | 0.992358i | \(0.460623\pi\) | |||||||
\(14\) | 1.91301 | 0.511274 | ||||||||
\(15\) | 2.42533 | 0.626219 | ||||||||
\(16\) | 7.08244 | 1.77061 | ||||||||
\(17\) | 6.61510 | 1.60440 | 0.802198 | − | 0.597058i | \(-0.203664\pi\) | ||||
0.802198 | + | 0.597058i | \(0.203664\pi\) | |||||||
\(18\) | 6.72789 | 1.58578 | ||||||||
\(19\) | 4.89661 | 1.12336 | 0.561680 | − | 0.827355i | \(-0.310155\pi\) | ||||
0.561680 | + | 0.827355i | \(0.310155\pi\) | |||||||
\(20\) | 18.1888 | 4.06713 | ||||||||
\(21\) | −0.448664 | −0.0979065 | ||||||||
\(22\) | −4.05052 | −0.863575 | ||||||||
\(23\) | 3.07346 | 0.640860 | 0.320430 | − | 0.947272i | \(-0.396173\pi\) | ||||
0.320430 | + | 0.947272i | \(0.396173\pi\) | |||||||
\(24\) | −3.76059 | −0.767628 | ||||||||
\(25\) | 11.5132 | 2.30263 | ||||||||
\(26\) | −2.26431 | −0.444068 | ||||||||
\(27\) | −3.36842 | −0.648254 | ||||||||
\(28\) | −3.36475 | −0.635879 | ||||||||
\(29\) | 4.87557 | 0.905371 | 0.452686 | − | 0.891670i | \(-0.350466\pi\) | ||||
0.452686 | + | 0.891670i | \(0.350466\pi\) | |||||||
\(30\) | −6.17198 | −1.12684 | ||||||||
\(31\) | 8.96241 | 1.60970 | 0.804848 | − | 0.593481i | \(-0.202247\pi\) | ||||
0.804848 | + | 0.593481i | \(0.202247\pi\) | |||||||
\(32\) | −5.42164 | −0.958420 | ||||||||
\(33\) | 0.949981 | 0.165370 | ||||||||
\(34\) | −16.8341 | −2.88702 | ||||||||
\(35\) | −3.05478 | −0.516352 | ||||||||
\(36\) | −11.8335 | −1.97225 | ||||||||
\(37\) | 8.64979 | 1.42202 | 0.711008 | − | 0.703184i | \(-0.248239\pi\) | ||||
0.711008 | + | 0.703184i | \(0.248239\pi\) | |||||||
\(38\) | −12.4609 | −2.02142 | ||||||||
\(39\) | 0.531056 | 0.0850370 | ||||||||
\(40\) | −25.6044 | −4.04842 | ||||||||
\(41\) | −7.20078 | −1.12457 | −0.562287 | − | 0.826942i | \(-0.690078\pi\) | ||||
−0.562287 | + | 0.826942i | \(0.690078\pi\) | |||||||
\(42\) | 1.14176 | 0.176177 | ||||||||
\(43\) | −2.22059 | −0.338637 | −0.169318 | − | 0.985561i | \(-0.554157\pi\) | ||||
−0.169318 | + | 0.985561i | \(0.554157\pi\) | |||||||
\(44\) | 7.12437 | 1.07404 | ||||||||
\(45\) | −10.7434 | −1.60153 | ||||||||
\(46\) | −7.82132 | −1.15319 | ||||||||
\(47\) | −2.58487 | −0.377043 | −0.188521 | − | 0.982069i | \(-0.560369\pi\) | ||||
−0.188521 | + | 0.982069i | \(0.560369\pi\) | |||||||
\(48\) | 4.22707 | 0.610125 | ||||||||
\(49\) | −6.43489 | −0.919271 | ||||||||
\(50\) | −29.2986 | −4.14345 | ||||||||
\(51\) | 3.94814 | 0.552850 | ||||||||
\(52\) | 3.98265 | 0.552294 | ||||||||
\(53\) | −0.647148 | −0.0888926 | −0.0444463 | − | 0.999012i | \(-0.514152\pi\) | ||||
−0.0444463 | + | 0.999012i | \(0.514152\pi\) | |||||||
\(54\) | 8.57195 | 1.16649 | ||||||||
\(55\) | 6.46805 | 0.872152 | ||||||||
\(56\) | 4.73658 | 0.632952 | ||||||||
\(57\) | 2.92248 | 0.387092 | ||||||||
\(58\) | −12.4073 | −1.62916 | ||||||||
\(59\) | −10.6319 | −1.38416 | −0.692078 | − | 0.721823i | \(-0.743305\pi\) | ||||
−0.692078 | + | 0.721823i | \(0.743305\pi\) | |||||||
\(60\) | 10.8557 | 1.40147 | ||||||||
\(61\) | 9.23648 | 1.18261 | 0.591305 | − | 0.806448i | \(-0.298613\pi\) | ||||
0.591305 | + | 0.806448i | \(0.298613\pi\) | |||||||
\(62\) | −22.8075 | −2.89655 | ||||||||
\(63\) | 1.98743 | 0.250392 | ||||||||
\(64\) | −0.367927 | −0.0459908 | ||||||||
\(65\) | 3.61575 | 0.448479 | ||||||||
\(66\) | −2.41751 | −0.297574 | ||||||||
\(67\) | −6.56328 | −0.801832 | −0.400916 | − | 0.916115i | \(-0.631308\pi\) | ||||
−0.400916 | + | 0.916115i | \(0.631308\pi\) | |||||||
\(68\) | 29.6090 | 3.59062 | ||||||||
\(69\) | 1.83436 | 0.220830 | ||||||||
\(70\) | 7.77379 | 0.929146 | ||||||||
\(71\) | −14.7856 | −1.75473 | −0.877364 | − | 0.479825i | \(-0.840700\pi\) | ||||
−0.877364 | + | 0.479825i | \(0.840700\pi\) | |||||||
\(72\) | 16.6581 | 1.96318 | ||||||||
\(73\) | −7.61205 | −0.890923 | −0.445462 | − | 0.895301i | \(-0.646960\pi\) | ||||
−0.445462 | + | 0.895301i | \(0.646960\pi\) | |||||||
\(74\) | −22.0119 | −2.55884 | ||||||||
\(75\) | 6.87149 | 0.793452 | ||||||||
\(76\) | 21.9171 | 2.51407 | ||||||||
\(77\) | −1.19653 | −0.136357 | ||||||||
\(78\) | −1.35143 | −0.153019 | ||||||||
\(79\) | 1.24194 | 0.139730 | 0.0698648 | − | 0.997556i | \(-0.477743\pi\) | ||||
0.0698648 | + | 0.997556i | \(0.477743\pi\) | |||||||
\(80\) | 28.7805 | 3.21776 | ||||||||
\(81\) | 5.92095 | 0.657883 | ||||||||
\(82\) | 18.3245 | 2.02360 | ||||||||
\(83\) | −0.207324 | −0.0227568 | −0.0113784 | − | 0.999935i | \(-0.503622\pi\) | ||||
−0.0113784 | + | 0.999935i | \(0.503622\pi\) | |||||||
\(84\) | −2.00821 | −0.219114 | ||||||||
\(85\) | 26.8814 | 2.91569 | ||||||||
\(86\) | 5.65095 | 0.609357 | ||||||||
\(87\) | 2.90993 | 0.311977 | ||||||||
\(88\) | −10.0290 | −1.06910 | ||||||||
\(89\) | 16.3645 | 1.73463 | 0.867317 | − | 0.497755i | \(-0.165842\pi\) | ||||
0.867317 | + | 0.497755i | \(0.165842\pi\) | |||||||
\(90\) | 27.3397 | 2.88186 | ||||||||
\(91\) | −0.668881 | −0.0701177 | ||||||||
\(92\) | 13.7567 | 1.43424 | ||||||||
\(93\) | 5.34911 | 0.554676 | ||||||||
\(94\) | 6.57797 | 0.678466 | ||||||||
\(95\) | 19.8981 | 2.04150 | ||||||||
\(96\) | −3.23584 | −0.330257 | ||||||||
\(97\) | −8.12779 | −0.825252 | −0.412626 | − | 0.910901i | \(-0.635388\pi\) | ||||
−0.412626 | + | 0.910901i | \(0.635388\pi\) | |||||||
\(98\) | 16.3755 | 1.65417 | ||||||||
\(99\) | −4.20809 | −0.422928 | ||||||||
\(100\) | 51.5327 | 5.15327 | ||||||||
\(101\) | −16.5090 | −1.64271 | −0.821355 | − | 0.570417i | \(-0.806782\pi\) | ||||
−0.821355 | + | 0.570417i | \(0.806782\pi\) | |||||||
\(102\) | −10.0472 | −0.994822 | ||||||||
\(103\) | −12.6195 | −1.24343 | −0.621716 | − | 0.783242i | \(-0.713564\pi\) | ||||
−0.621716 | + | 0.783242i | \(0.713564\pi\) | |||||||
\(104\) | −5.60640 | −0.549752 | ||||||||
\(105\) | −1.82321 | −0.177927 | ||||||||
\(106\) | 1.64686 | 0.159957 | ||||||||
\(107\) | −5.88071 | −0.568509 | −0.284255 | − | 0.958749i | \(-0.591746\pi\) | ||||
−0.284255 | + | 0.958749i | \(0.591746\pi\) | |||||||
\(108\) | −15.0770 | −1.45079 | ||||||||
\(109\) | −10.5666 | −1.01210 | −0.506049 | − | 0.862505i | \(-0.668894\pi\) | ||||
−0.506049 | + | 0.862505i | \(0.668894\pi\) | |||||||
\(110\) | −16.4599 | −1.56939 | ||||||||
\(111\) | 5.16252 | 0.490005 | ||||||||
\(112\) | −5.32412 | −0.503082 | ||||||||
\(113\) | 15.3333 | 1.44243 | 0.721216 | − | 0.692710i | \(-0.243584\pi\) | ||||
0.721216 | + | 0.692710i | \(0.243584\pi\) | |||||||
\(114\) | −7.43712 | −0.696550 | ||||||||
\(115\) | 12.4894 | 1.16464 | ||||||||
\(116\) | 21.8230 | 2.02621 | ||||||||
\(117\) | −2.35239 | −0.217479 | ||||||||
\(118\) | 27.0560 | 2.49071 | ||||||||
\(119\) | −4.97280 | −0.455856 | ||||||||
\(120\) | −15.2817 | −1.39502 | ||||||||
\(121\) | −8.46652 | −0.769684 | ||||||||
\(122\) | −23.5049 | −2.12804 | ||||||||
\(123\) | −4.29770 | −0.387511 | ||||||||
\(124\) | 40.1156 | 3.60249 | ||||||||
\(125\) | 26.4672 | 2.36729 | ||||||||
\(126\) | −5.05759 | −0.450566 | ||||||||
\(127\) | 5.59628 | 0.496590 | 0.248295 | − | 0.968685i | \(-0.420130\pi\) | ||||
0.248295 | + | 0.968685i | \(0.420130\pi\) | |||||||
\(128\) | 11.7796 | 1.04118 | ||||||||
\(129\) | −1.32533 | −0.116689 | ||||||||
\(130\) | −9.20135 | −0.807012 | ||||||||
\(131\) | 19.3051 | 1.68669 | 0.843347 | − | 0.537369i | \(-0.180582\pi\) | ||||
0.843347 | + | 0.537369i | \(0.180582\pi\) | |||||||
\(132\) | 4.25210 | 0.370097 | ||||||||
\(133\) | −3.68096 | −0.319179 | ||||||||
\(134\) | 16.7022 | 1.44285 | ||||||||
\(135\) | −13.6881 | −1.17808 | ||||||||
\(136\) | −41.6808 | −3.57410 | ||||||||
\(137\) | 3.80008 | 0.324662 | 0.162331 | − | 0.986736i | \(-0.448099\pi\) | ||||
0.162331 | + | 0.986736i | \(0.448099\pi\) | |||||||
\(138\) | −4.66806 | −0.397371 | ||||||||
\(139\) | 9.54205 | 0.809346 | 0.404673 | − | 0.914461i | \(-0.367385\pi\) | ||||
0.404673 | + | 0.914461i | \(0.367385\pi\) | |||||||
\(140\) | −13.6731 | −1.15559 | ||||||||
\(141\) | −1.54275 | −0.129923 | ||||||||
\(142\) | 37.6263 | 3.15753 | ||||||||
\(143\) | 1.41626 | 0.118433 | ||||||||
\(144\) | −18.7245 | −1.56037 | ||||||||
\(145\) | 19.8126 | 1.64534 | ||||||||
\(146\) | 19.3711 | 1.60316 | ||||||||
\(147\) | −3.84059 | −0.316766 | ||||||||
\(148\) | 38.7163 | 3.18246 | ||||||||
\(149\) | −0.583891 | −0.0478342 | −0.0239171 | − | 0.999714i | \(-0.507614\pi\) | ||||
−0.0239171 | + | 0.999714i | \(0.507614\pi\) | |||||||
\(150\) | −17.4865 | −1.42777 | ||||||||
\(151\) | 3.52011 | 0.286463 | 0.143231 | − | 0.989689i | \(-0.454251\pi\) | ||||
0.143231 | + | 0.989689i | \(0.454251\pi\) | |||||||
\(152\) | −30.8529 | −2.50250 | ||||||||
\(153\) | −17.4889 | −1.41389 | ||||||||
\(154\) | 3.04492 | 0.245367 | ||||||||
\(155\) | 36.4200 | 2.92533 | ||||||||
\(156\) | 2.37700 | 0.190312 | ||||||||
\(157\) | −7.64180 | −0.609882 | −0.304941 | − | 0.952371i | \(-0.598637\pi\) | ||||
−0.304941 | + | 0.952371i | \(0.598637\pi\) | |||||||
\(158\) | −3.16049 | −0.251435 | ||||||||
\(159\) | −0.386242 | −0.0306310 | ||||||||
\(160\) | −22.0316 | −1.74175 | ||||||||
\(161\) | −2.31043 | −0.182087 | ||||||||
\(162\) | −15.0676 | −1.18382 | ||||||||
\(163\) | −9.88999 | −0.774644 | −0.387322 | − | 0.921945i | \(-0.626600\pi\) | ||||
−0.387322 | + | 0.921945i | \(0.626600\pi\) | |||||||
\(164\) | −32.2306 | −2.51678 | ||||||||
\(165\) | 3.86038 | 0.300530 | ||||||||
\(166\) | 0.527597 | 0.0409494 | ||||||||
\(167\) | 3.14610 | 0.243452 | 0.121726 | − | 0.992564i | \(-0.461157\pi\) | ||||
0.121726 | + | 0.992564i | \(0.461157\pi\) | |||||||
\(168\) | 2.82697 | 0.218106 | ||||||||
\(169\) | −12.2083 | −0.939099 | ||||||||
\(170\) | −68.4076 | −5.24662 | ||||||||
\(171\) | −12.9456 | −0.989974 | ||||||||
\(172\) | −9.93932 | −0.757866 | ||||||||
\(173\) | −1.05704 | −0.0803649 | −0.0401824 | − | 0.999192i | \(-0.512794\pi\) | ||||
−0.0401824 | + | 0.999192i | \(0.512794\pi\) | |||||||
\(174\) | −7.40517 | −0.561384 | ||||||||
\(175\) | −8.65485 | −0.654245 | ||||||||
\(176\) | 11.2731 | 0.849739 | ||||||||
\(177\) | −6.34552 | −0.476959 | ||||||||
\(178\) | −41.6443 | −3.12137 | ||||||||
\(179\) | −5.90938 | −0.441688 | −0.220844 | − | 0.975309i | \(-0.570881\pi\) | ||||
−0.220844 | + | 0.975309i | \(0.570881\pi\) | |||||||
\(180\) | −48.0872 | −3.58421 | ||||||||
\(181\) | −15.6026 | −1.15973 | −0.579865 | − | 0.814712i | \(-0.696895\pi\) | ||||
−0.579865 | + | 0.814712i | \(0.696895\pi\) | |||||||
\(182\) | 1.70216 | 0.126173 | ||||||||
\(183\) | 5.51268 | 0.407509 | ||||||||
\(184\) | −19.3654 | −1.42764 | ||||||||
\(185\) | 35.1496 | 2.58425 | ||||||||
\(186\) | −13.6124 | −0.998108 | ||||||||
\(187\) | 10.5292 | 0.769970 | ||||||||
\(188\) | −11.5698 | −0.843818 | ||||||||
\(189\) | 2.53216 | 0.184188 | ||||||||
\(190\) | −50.6365 | −3.67356 | ||||||||
\(191\) | 2.15350 | 0.155822 | 0.0779109 | − | 0.996960i | \(-0.475175\pi\) | ||||
0.0779109 | + | 0.996960i | \(0.475175\pi\) | |||||||
\(192\) | −0.219592 | −0.0158477 | ||||||||
\(193\) | 25.4873 | 1.83461 | 0.917307 | − | 0.398181i | \(-0.130358\pi\) | ||||
0.917307 | + | 0.398181i | \(0.130358\pi\) | |||||||
\(194\) | 20.6836 | 1.48499 | ||||||||
\(195\) | 2.15802 | 0.154539 | ||||||||
\(196\) | −28.8025 | −2.05732 | ||||||||
\(197\) | 10.0064 | 0.712924 | 0.356462 | − | 0.934310i | \(-0.383983\pi\) | ||||
0.356462 | + | 0.934310i | \(0.383983\pi\) | |||||||
\(198\) | 10.7087 | 0.761035 | ||||||||
\(199\) | −18.0972 | −1.28288 | −0.641438 | − | 0.767175i | \(-0.721662\pi\) | ||||
−0.641438 | + | 0.767175i | \(0.721662\pi\) | |||||||
\(200\) | −72.5429 | −5.12956 | ||||||||
\(201\) | −3.91721 | −0.276299 | ||||||||
\(202\) | 42.0121 | 2.95596 | ||||||||
\(203\) | −3.66514 | −0.257242 | ||||||||
\(204\) | 17.6718 | 1.23727 | ||||||||
\(205\) | −29.2614 | −2.04370 | ||||||||
\(206\) | 32.1140 | 2.23748 | ||||||||
\(207\) | −8.12556 | −0.564765 | ||||||||
\(208\) | 6.30183 | 0.436953 | ||||||||
\(209\) | 7.79389 | 0.539114 | ||||||||
\(210\) | 4.63969 | 0.320169 | ||||||||
\(211\) | −14.6750 | −1.01027 | −0.505135 | − | 0.863040i | \(-0.668557\pi\) | ||||
−0.505135 | + | 0.863040i | \(0.668557\pi\) | |||||||
\(212\) | −2.89662 | −0.198941 | ||||||||
\(213\) | −8.82461 | −0.604652 | ||||||||
\(214\) | 14.9652 | 1.02300 | ||||||||
\(215\) | −9.02368 | −0.615410 | ||||||||
\(216\) | 21.2240 | 1.44411 | ||||||||
\(217\) | −6.73736 | −0.457362 | ||||||||
\(218\) | 26.8898 | 1.82121 | ||||||||
\(219\) | −4.54316 | −0.306998 | ||||||||
\(220\) | 28.9509 | 1.95187 | ||||||||
\(221\) | 5.88599 | 0.395935 | ||||||||
\(222\) | −13.1376 | −0.881735 | ||||||||
\(223\) | −17.2178 | −1.15299 | −0.576493 | − | 0.817102i | \(-0.695579\pi\) | ||||
−0.576493 | + | 0.817102i | \(0.695579\pi\) | |||||||
\(224\) | 4.07564 | 0.272315 | ||||||||
\(225\) | −30.4383 | −2.02922 | ||||||||
\(226\) | −39.0200 | −2.59557 | ||||||||
\(227\) | 14.2320 | 0.944614 | 0.472307 | − | 0.881434i | \(-0.343421\pi\) | ||||
0.472307 | + | 0.881434i | \(0.343421\pi\) | |||||||
\(228\) | 13.0810 | 0.866309 | ||||||||
\(229\) | 26.9662 | 1.78197 | 0.890987 | − | 0.454029i | \(-0.150014\pi\) | ||||
0.890987 | + | 0.454029i | \(0.150014\pi\) | |||||||
\(230\) | −31.7830 | −2.09571 | ||||||||
\(231\) | −0.714134 | −0.0469866 | ||||||||
\(232\) | −30.7203 | −2.01689 | ||||||||
\(233\) | −8.57031 | −0.561460 | −0.280730 | − | 0.959787i | \(-0.590576\pi\) | ||||
−0.280730 | + | 0.959787i | \(0.590576\pi\) | |||||||
\(234\) | 5.98636 | 0.391340 | ||||||||
\(235\) | −10.5040 | −0.685205 | ||||||||
\(236\) | −47.5882 | −3.09773 | ||||||||
\(237\) | 0.741239 | 0.0481486 | ||||||||
\(238\) | 12.6548 | 0.820286 | ||||||||
\(239\) | −11.0017 | −0.711643 | −0.355822 | − | 0.934554i | \(-0.615799\pi\) | ||||
−0.355822 | + | 0.934554i | \(0.615799\pi\) | |||||||
\(240\) | 17.1773 | 1.10879 | ||||||||
\(241\) | −0.868425 | −0.0559402 | −0.0279701 | − | 0.999609i | \(-0.508904\pi\) | ||||
−0.0279701 | + | 0.999609i | \(0.508904\pi\) | |||||||
\(242\) | 21.5456 | 1.38500 | ||||||||
\(243\) | 13.6391 | 0.874950 | ||||||||
\(244\) | 41.3423 | 2.64667 | ||||||||
\(245\) | −26.1491 | −1.67060 | ||||||||
\(246\) | 10.9368 | 0.697303 | ||||||||
\(247\) | 4.35692 | 0.277224 | ||||||||
\(248\) | −56.4709 | −3.58591 | ||||||||
\(249\) | −0.123739 | −0.00784162 | ||||||||
\(250\) | −67.3535 | −4.25981 | ||||||||
\(251\) | 25.5662 | 1.61373 | 0.806863 | − | 0.590738i | \(-0.201163\pi\) | ||||
0.806863 | + | 0.590738i | \(0.201163\pi\) | |||||||
\(252\) | 8.89568 | 0.560375 | ||||||||
\(253\) | 4.89199 | 0.307557 | ||||||||
\(254\) | −14.2414 | −0.893584 | ||||||||
\(255\) | 16.0438 | 1.00470 | ||||||||
\(256\) | −29.2408 | −1.82755 | ||||||||
\(257\) | 15.7501 | 0.982466 | 0.491233 | − | 0.871028i | \(-0.336546\pi\) | ||||
0.491233 | + | 0.871028i | \(0.336546\pi\) | |||||||
\(258\) | 3.37270 | 0.209975 | ||||||||
\(259\) | −6.50235 | −0.404036 | ||||||||
\(260\) | 16.1840 | 1.00369 | ||||||||
\(261\) | −12.8900 | −0.797869 | ||||||||
\(262\) | −49.1275 | −3.03511 | ||||||||
\(263\) | 19.8859 | 1.22622 | 0.613110 | − | 0.789998i | \(-0.289918\pi\) | ||||
0.613110 | + | 0.789998i | \(0.289918\pi\) | |||||||
\(264\) | −5.98570 | −0.368394 | ||||||||
\(265\) | −2.62977 | −0.161546 | ||||||||
\(266\) | 9.36728 | 0.574345 | ||||||||
\(267\) | 9.76696 | 0.597728 | ||||||||
\(268\) | −29.3771 | −1.79449 | ||||||||
\(269\) | −16.8977 | −1.03027 | −0.515134 | − | 0.857109i | \(-0.672258\pi\) | ||||
−0.515134 | + | 0.857109i | \(0.672258\pi\) | |||||||
\(270\) | 34.8333 | 2.11989 | ||||||||
\(271\) | −16.1903 | −0.983490 | −0.491745 | − | 0.870739i | \(-0.663641\pi\) | ||||
−0.491745 | + | 0.870739i | \(0.663641\pi\) | |||||||
\(272\) | 46.8510 | 2.84076 | ||||||||
\(273\) | −0.399213 | −0.0241615 | ||||||||
\(274\) | −9.67041 | −0.584211 | ||||||||
\(275\) | 18.3254 | 1.10506 | ||||||||
\(276\) | 8.21054 | 0.494216 | ||||||||
\(277\) | 21.1958 | 1.27353 | 0.636765 | − | 0.771058i | \(-0.280272\pi\) | ||||
0.636765 | + | 0.771058i | \(0.280272\pi\) | |||||||
\(278\) | −24.2826 | −1.45637 | ||||||||
\(279\) | −23.6947 | −1.41856 | ||||||||
\(280\) | 19.2478 | 1.15027 | ||||||||
\(281\) | 25.8399 | 1.54148 | 0.770741 | − | 0.637149i | \(-0.219886\pi\) | ||||
0.770741 | + | 0.637149i | \(0.219886\pi\) | |||||||
\(282\) | 3.92598 | 0.233789 | ||||||||
\(283\) | 30.3561 | 1.80448 | 0.902241 | − | 0.431233i | \(-0.141921\pi\) | ||||
0.902241 | + | 0.431233i | \(0.141921\pi\) | |||||||
\(284\) | −66.1801 | −3.92707 | ||||||||
\(285\) | 11.8759 | 0.703469 | ||||||||
\(286\) | −3.60408 | −0.213114 | ||||||||
\(287\) | 5.41308 | 0.319524 | ||||||||
\(288\) | 14.3336 | 0.844618 | ||||||||
\(289\) | 26.7595 | 1.57409 | ||||||||
\(290\) | −50.4189 | −2.96070 | ||||||||
\(291\) | −4.85097 | −0.284369 | ||||||||
\(292\) | −34.0714 | −1.99388 | ||||||||
\(293\) | 13.3191 | 0.778109 | 0.389054 | − | 0.921215i | \(-0.372802\pi\) | ||||
0.389054 | + | 0.921215i | \(0.372802\pi\) | |||||||
\(294\) | 9.77351 | 0.570003 | ||||||||
\(295\) | −43.2042 | −2.51545 | ||||||||
\(296\) | −54.5011 | −3.16781 | ||||||||
\(297\) | −5.36149 | −0.311105 | ||||||||
\(298\) | 1.48588 | 0.0860748 | ||||||||
\(299\) | 2.73471 | 0.158152 | ||||||||
\(300\) | 30.7567 | 1.77574 | ||||||||
\(301\) | 1.66930 | 0.0962166 | ||||||||
\(302\) | −8.95796 | −0.515473 | ||||||||
\(303\) | −9.85322 | −0.566052 | ||||||||
\(304\) | 34.6800 | 1.98903 | ||||||||
\(305\) | 37.5337 | 2.14917 | ||||||||
\(306\) | 44.5056 | 2.54422 | ||||||||
\(307\) | 11.3473 | 0.647625 | 0.323812 | − | 0.946121i | \(-0.395035\pi\) | ||||
0.323812 | + | 0.946121i | \(0.395035\pi\) | |||||||
\(308\) | −5.35564 | −0.305166 | ||||||||
\(309\) | −7.53177 | −0.428468 | ||||||||
\(310\) | −92.6814 | −5.26395 | ||||||||
\(311\) | 28.8444 | 1.63562 | 0.817809 | − | 0.575490i | \(-0.195188\pi\) | ||||
0.817809 | + | 0.575490i | \(0.195188\pi\) | |||||||
\(312\) | −3.34611 | −0.189436 | ||||||||
\(313\) | −7.27211 | −0.411044 | −0.205522 | − | 0.978652i | \(-0.565889\pi\) | ||||
−0.205522 | + | 0.978652i | \(0.565889\pi\) | |||||||
\(314\) | 19.4468 | 1.09745 | ||||||||
\(315\) | 8.07618 | 0.455041 | ||||||||
\(316\) | 5.55892 | 0.312713 | ||||||||
\(317\) | 2.30266 | 0.129330 | 0.0646651 | − | 0.997907i | \(-0.479402\pi\) | ||||
0.0646651 | + | 0.997907i | \(0.479402\pi\) | |||||||
\(318\) | 0.982907 | 0.0551187 | ||||||||
\(319\) | 7.76040 | 0.434499 | ||||||||
\(320\) | −1.49512 | −0.0835798 | ||||||||
\(321\) | −3.50983 | −0.195899 | ||||||||
\(322\) | 5.87956 | 0.327655 | ||||||||
\(323\) | 32.3915 | 1.80231 | ||||||||
\(324\) | 26.5021 | 1.47234 | ||||||||
\(325\) | 10.2442 | 0.568246 | ||||||||
\(326\) | 25.1680 | 1.39393 | ||||||||
\(327\) | −6.30655 | −0.348753 | ||||||||
\(328\) | 45.3712 | 2.50520 | ||||||||
\(329\) | 1.94314 | 0.107129 | ||||||||
\(330\) | −9.82387 | −0.540786 | ||||||||
\(331\) | −13.9717 | −0.767952 | −0.383976 | − | 0.923343i | \(-0.625446\pi\) | ||||
−0.383976 | + | 0.923343i | \(0.625446\pi\) | |||||||
\(332\) | −0.927978 | −0.0509294 | ||||||||
\(333\) | −22.8682 | −1.25317 | ||||||||
\(334\) | −8.00617 | −0.438078 | ||||||||
\(335\) | −26.6708 | −1.45718 | ||||||||
\(336\) | −3.17764 | −0.173354 | ||||||||
\(337\) | −7.20428 | −0.392442 | −0.196221 | − | 0.980560i | \(-0.562867\pi\) | ||||
−0.196221 | + | 0.980560i | \(0.562867\pi\) | |||||||
\(338\) | 31.0676 | 1.68985 | ||||||||
\(339\) | 9.15147 | 0.497040 | ||||||||
\(340\) | 120.320 | 6.52529 | ||||||||
\(341\) | 14.2654 | 0.772514 | ||||||||
\(342\) | 32.9439 | 1.78140 | ||||||||
\(343\) | 10.0995 | 0.545321 | ||||||||
\(344\) | 13.9916 | 0.754379 | ||||||||
\(345\) | 7.45416 | 0.401318 | ||||||||
\(346\) | 2.68994 | 0.144612 | ||||||||
\(347\) | −11.8618 | −0.636774 | −0.318387 | − | 0.947961i | \(-0.603141\pi\) | ||||
−0.318387 | + | 0.947961i | \(0.603141\pi\) | |||||||
\(348\) | 13.0248 | 0.698201 | ||||||||
\(349\) | −9.42552 | −0.504536 | −0.252268 | − | 0.967657i | \(-0.581177\pi\) | ||||
−0.252268 | + | 0.967657i | \(0.581177\pi\) | |||||||
\(350\) | 22.0248 | 1.17728 | ||||||||
\(351\) | −2.99716 | −0.159977 | ||||||||
\(352\) | −8.62957 | −0.459958 | ||||||||
\(353\) | −21.1243 | −1.12433 | −0.562167 | − | 0.827024i | \(-0.690032\pi\) | ||||
−0.562167 | + | 0.827024i | \(0.690032\pi\) | |||||||
\(354\) | 16.1481 | 0.858259 | ||||||||
\(355\) | −60.0834 | −3.18889 | ||||||||
\(356\) | 73.2472 | 3.88210 | ||||||||
\(357\) | −2.96796 | −0.157081 | ||||||||
\(358\) | 15.0382 | 0.794791 | ||||||||
\(359\) | 26.8636 | 1.41780 | 0.708902 | − | 0.705307i | \(-0.249191\pi\) | ||||
0.708902 | + | 0.705307i | \(0.249191\pi\) | |||||||
\(360\) | 67.6926 | 3.56771 | ||||||||
\(361\) | 4.97680 | 0.261937 | ||||||||
\(362\) | 39.7054 | 2.08687 | ||||||||
\(363\) | −5.05314 | −0.265221 | ||||||||
\(364\) | −2.99390 | −0.156923 | ||||||||
\(365\) | −30.9326 | −1.61909 | ||||||||
\(366\) | −14.0286 | −0.733289 | ||||||||
\(367\) | −0.0496759 | −0.00259306 | −0.00129653 | − | 0.999999i | \(-0.500413\pi\) | ||||
−0.00129653 | + | 0.999999i | \(0.500413\pi\) | |||||||
\(368\) | 21.7676 | 1.13471 | ||||||||
\(369\) | 19.0373 | 0.991043 | ||||||||
\(370\) | −89.4486 | −4.65021 | ||||||||
\(371\) | 0.486484 | 0.0252570 | ||||||||
\(372\) | 23.9425 | 1.24136 | ||||||||
\(373\) | 29.7032 | 1.53797 | 0.768986 | − | 0.639265i | \(-0.220761\pi\) | ||||
0.768986 | + | 0.639265i | \(0.220761\pi\) | |||||||
\(374\) | −26.7946 | −1.38552 | ||||||||
\(375\) | 15.7966 | 0.815733 | ||||||||
\(376\) | 16.2869 | 0.839935 | ||||||||
\(377\) | 4.33820 | 0.223429 | ||||||||
\(378\) | −6.44384 | −0.331435 | ||||||||
\(379\) | 7.27050 | 0.373461 | 0.186730 | − | 0.982411i | \(-0.440211\pi\) | ||||
0.186730 | + | 0.982411i | \(0.440211\pi\) | |||||||
\(380\) | 89.0633 | 4.56885 | ||||||||
\(381\) | 3.34007 | 0.171117 | ||||||||
\(382\) | −5.48022 | −0.280392 | ||||||||
\(383\) | 14.1152 | 0.721252 | 0.360626 | − | 0.932711i | \(-0.382563\pi\) | ||||
0.360626 | + | 0.932711i | \(0.382563\pi\) | |||||||
\(384\) | 7.03050 | 0.358774 | ||||||||
\(385\) | −4.86226 | −0.247804 | ||||||||
\(386\) | −64.8599 | −3.30128 | ||||||||
\(387\) | 5.87076 | 0.298428 | ||||||||
\(388\) | −36.3798 | −1.84691 | ||||||||
\(389\) | 28.4979 | 1.44490 | 0.722451 | − | 0.691423i | \(-0.243016\pi\) | ||||
0.722451 | + | 0.691423i | \(0.243016\pi\) | |||||||
\(390\) | −5.49172 | −0.278084 | ||||||||
\(391\) | 20.3312 | 1.02819 | ||||||||
\(392\) | 40.5454 | 2.04785 | ||||||||
\(393\) | 11.5220 | 0.581209 | ||||||||
\(394\) | −25.4642 | −1.28287 | ||||||||
\(395\) | 5.04681 | 0.253933 | ||||||||
\(396\) | −18.8353 | −0.946510 | ||||||||
\(397\) | 11.0392 | 0.554041 | 0.277021 | − | 0.960864i | \(-0.410653\pi\) | ||||
0.277021 | + | 0.960864i | \(0.410653\pi\) | |||||||
\(398\) | 46.0536 | 2.30846 | ||||||||
\(399\) | −2.19693 | −0.109984 | ||||||||
\(400\) | 81.5413 | 4.07707 | ||||||||
\(401\) | −31.4484 | −1.57046 | −0.785230 | − | 0.619204i | \(-0.787455\pi\) | ||||
−0.785230 | + | 0.619204i | \(0.787455\pi\) | |||||||
\(402\) | 9.96850 | 0.497184 | ||||||||
\(403\) | 7.97459 | 0.397243 | ||||||||
\(404\) | −73.8941 | −3.67637 | ||||||||
\(405\) | 24.0606 | 1.19558 | ||||||||
\(406\) | 9.32703 | 0.462893 | ||||||||
\(407\) | 13.7678 | 0.682443 | ||||||||
\(408\) | −24.8767 | −1.23158 | ||||||||
\(409\) | −23.4429 | −1.15917 | −0.579587 | − | 0.814910i | \(-0.696786\pi\) | ||||
−0.579587 | + | 0.814910i | \(0.696786\pi\) | |||||||
\(410\) | 74.4642 | 3.67753 | ||||||||
\(411\) | 2.26803 | 0.111874 | ||||||||
\(412\) | −56.4845 | −2.78279 | ||||||||
\(413\) | 7.99238 | 0.393279 | ||||||||
\(414\) | 20.6779 | 1.01626 | ||||||||
\(415\) | −0.842489 | −0.0413562 | ||||||||
\(416\) | −4.82408 | −0.236520 | ||||||||
\(417\) | 5.69506 | 0.278888 | ||||||||
\(418\) | −19.8338 | −0.970105 | ||||||||
\(419\) | 17.4406 | 0.852030 | 0.426015 | − | 0.904716i | \(-0.359917\pi\) | ||||
0.426015 | + | 0.904716i | \(0.359917\pi\) | |||||||
\(420\) | −8.16065 | −0.398199 | ||||||||
\(421\) | −29.7259 | −1.44875 | −0.724375 | − | 0.689406i | \(-0.757872\pi\) | ||||
−0.724375 | + | 0.689406i | \(0.757872\pi\) | |||||||
\(422\) | 37.3449 | 1.81792 | ||||||||
\(423\) | 6.83385 | 0.332273 | ||||||||
\(424\) | 4.07759 | 0.198025 | ||||||||
\(425\) | 76.1607 | 3.69434 | ||||||||
\(426\) | 22.4568 | 1.08804 | ||||||||
\(427\) | −6.94339 | −0.336014 | ||||||||
\(428\) | −26.3219 | −1.27232 | ||||||||
\(429\) | 0.845276 | 0.0408103 | ||||||||
\(430\) | 22.9634 | 1.10739 | ||||||||
\(431\) | −27.5179 | −1.32549 | −0.662745 | − | 0.748845i | \(-0.730609\pi\) | ||||
−0.662745 | + | 0.748845i | \(0.730609\pi\) | |||||||
\(432\) | −23.8567 | −1.14780 | ||||||||
\(433\) | −10.0841 | −0.484613 | −0.242306 | − | 0.970200i | \(-0.577904\pi\) | ||||
−0.242306 | + | 0.970200i | \(0.577904\pi\) | |||||||
\(434\) | 17.1452 | 0.822996 | ||||||||
\(435\) | 11.8249 | 0.566960 | ||||||||
\(436\) | −47.2959 | −2.26506 | ||||||||
\(437\) | 15.0495 | 0.719916 | ||||||||
\(438\) | 11.5614 | 0.552426 | ||||||||
\(439\) | −27.8354 | −1.32851 | −0.664256 | − | 0.747505i | \(-0.731252\pi\) | ||||
−0.664256 | + | 0.747505i | \(0.731252\pi\) | |||||||
\(440\) | −40.7543 | −1.94289 | ||||||||
\(441\) | 17.0125 | 0.810118 | ||||||||
\(442\) | −14.9786 | −0.712462 | ||||||||
\(443\) | −37.2220 | −1.76847 | −0.884235 | − | 0.467043i | \(-0.845319\pi\) | ||||
−0.884235 | + | 0.467043i | \(0.845319\pi\) | |||||||
\(444\) | 23.1073 | 1.09663 | ||||||||
\(445\) | 66.4995 | 3.15238 | ||||||||
\(446\) | 43.8157 | 2.07473 | ||||||||
\(447\) | −0.348488 | −0.0164829 | ||||||||
\(448\) | 0.276583 | 0.0130673 | ||||||||
\(449\) | 11.0794 | 0.522867 | 0.261434 | − | 0.965221i | \(-0.415805\pi\) | ||||
0.261434 | + | 0.965221i | \(0.415805\pi\) | |||||||
\(450\) | 77.4593 | 3.65147 | ||||||||
\(451\) | −11.4614 | −0.539697 | ||||||||
\(452\) | 68.6314 | 3.22815 | ||||||||
\(453\) | 2.10094 | 0.0987106 | ||||||||
\(454\) | −36.2176 | −1.69978 | ||||||||
\(455\) | −2.71809 | −0.127426 | ||||||||
\(456\) | −18.4142 | −0.862322 | ||||||||
\(457\) | 15.9552 | 0.746352 | 0.373176 | − | 0.927761i | \(-0.378269\pi\) | ||||
0.373176 | + | 0.927761i | \(0.378269\pi\) | |||||||
\(458\) | −68.6233 | −3.20656 | ||||||||
\(459\) | −22.2824 | −1.04006 | ||||||||
\(460\) | 55.9024 | 2.60646 | ||||||||
\(461\) | −3.50016 | −0.163019 | −0.0815093 | − | 0.996673i | \(-0.525974\pi\) | ||||
−0.0815093 | + | 0.996673i | \(0.525974\pi\) | |||||||
\(462\) | 1.81733 | 0.0845496 | ||||||||
\(463\) | 33.6980 | 1.56608 | 0.783040 | − | 0.621971i | \(-0.213668\pi\) | ||||
0.783040 | + | 0.621971i | \(0.213668\pi\) | |||||||
\(464\) | 34.5310 | 1.60306 | ||||||||
\(465\) | 21.7368 | 1.00802 | ||||||||
\(466\) | 21.8097 | 1.01031 | ||||||||
\(467\) | 4.40699 | 0.203931 | 0.101966 | − | 0.994788i | \(-0.467487\pi\) | ||||
0.101966 | + | 0.994788i | \(0.467487\pi\) | |||||||
\(468\) | −10.5293 | −0.486715 | ||||||||
\(469\) | 4.93385 | 0.227824 | ||||||||
\(470\) | 26.7305 | 1.23299 | ||||||||
\(471\) | −4.56092 | −0.210156 | ||||||||
\(472\) | 66.9902 | 3.08347 | ||||||||
\(473\) | −3.53449 | −0.162516 | ||||||||
\(474\) | −1.88630 | −0.0866407 | ||||||||
\(475\) | 56.3755 | 2.58668 | ||||||||
\(476\) | −22.2582 | −1.02020 | ||||||||
\(477\) | 1.71092 | 0.0783376 | ||||||||
\(478\) | 27.9972 | 1.28056 | ||||||||
\(479\) | −17.4431 | −0.796997 | −0.398499 | − | 0.917169i | \(-0.630469\pi\) | ||||
−0.398499 | + | 0.917169i | \(0.630469\pi\) | |||||||
\(480\) | −13.1493 | −0.600180 | ||||||||
\(481\) | 7.69643 | 0.350927 | ||||||||
\(482\) | 2.20996 | 0.100661 | ||||||||
\(483\) | −1.37895 | −0.0627444 | ||||||||
\(484\) | −37.8960 | −1.72255 | ||||||||
\(485\) | −33.0284 | −1.49974 | ||||||||
\(486\) | −34.7088 | −1.57442 | ||||||||
\(487\) | −16.6629 | −0.755068 | −0.377534 | − | 0.925996i | \(-0.623228\pi\) | ||||
−0.377534 | + | 0.925996i | \(0.623228\pi\) | |||||||
\(488\) | −58.1978 | −2.63449 | ||||||||
\(489\) | −5.90272 | −0.266930 | ||||||||
\(490\) | 66.5441 | 3.00615 | ||||||||
\(491\) | −6.65911 | −0.300522 | −0.150261 | − | 0.988646i | \(-0.548011\pi\) | ||||
−0.150261 | + | 0.988646i | \(0.548011\pi\) | |||||||
\(492\) | −19.2364 | −0.867245 | ||||||||
\(493\) | 32.2524 | 1.45257 | ||||||||
\(494\) | −11.0875 | −0.498848 | ||||||||
\(495\) | −17.1001 | −0.768594 | ||||||||
\(496\) | 63.4758 | 2.85015 | ||||||||
\(497\) | 11.1149 | 0.498570 | ||||||||
\(498\) | 0.314890 | 0.0141105 | ||||||||
\(499\) | 0.409460 | 0.0183300 | 0.00916498 | − | 0.999958i | \(-0.497083\pi\) | ||||
0.00916498 | + | 0.999958i | \(0.497083\pi\) | |||||||
\(500\) | 118.466 | 5.29798 | ||||||||
\(501\) | 1.87771 | 0.0838899 | ||||||||
\(502\) | −65.0608 | −2.90381 | ||||||||
\(503\) | −32.9937 | −1.47112 | −0.735558 | − | 0.677462i | \(-0.763080\pi\) | ||||
−0.735558 | + | 0.677462i | \(0.763080\pi\) | |||||||
\(504\) | −12.5225 | −0.557797 | ||||||||
\(505\) | −67.0868 | −2.98532 | ||||||||
\(506\) | −12.4491 | −0.553430 | ||||||||
\(507\) | −7.28637 | −0.323599 | ||||||||
\(508\) | 25.0488 | 1.11136 | ||||||||
\(509\) | 3.71307 | 0.164579 | 0.0822895 | − | 0.996608i | \(-0.473777\pi\) | ||||
0.0822895 | + | 0.996608i | \(0.473777\pi\) | |||||||
\(510\) | −40.8282 | −1.80790 | ||||||||
\(511\) | 5.72225 | 0.253137 | ||||||||
\(512\) | 50.8526 | 2.24739 | ||||||||
\(513\) | −16.4939 | −0.728222 | ||||||||
\(514\) | −40.0808 | −1.76789 | ||||||||
\(515\) | −51.2810 | −2.25971 | ||||||||
\(516\) | −5.93216 | −0.261149 | ||||||||
\(517\) | −4.11432 | −0.180947 | ||||||||
\(518\) | 16.5471 | 0.727040 | ||||||||
\(519\) | −0.630879 | −0.0276925 | ||||||||
\(520\) | −22.7824 | −0.999073 | ||||||||
\(521\) | 15.1139 | 0.662154 | 0.331077 | − | 0.943604i | \(-0.392588\pi\) | ||||
0.331077 | + | 0.943604i | \(0.392588\pi\) | |||||||
\(522\) | 32.8023 | 1.43572 | ||||||||
\(523\) | −24.4498 | −1.06912 | −0.534558 | − | 0.845132i | \(-0.679522\pi\) | ||||
−0.534558 | + | 0.845132i | \(0.679522\pi\) | |||||||
\(524\) | 86.4093 | 3.77481 | ||||||||
\(525\) | −5.16554 | −0.225443 | ||||||||
\(526\) | −50.6056 | −2.20651 | ||||||||
\(527\) | 59.2872 | 2.58259 | ||||||||
\(528\) | 6.72819 | 0.292807 | ||||||||
\(529\) | −13.5539 | −0.589299 | ||||||||
\(530\) | 6.69224 | 0.290692 | ||||||||
\(531\) | 28.1085 | 1.21980 | ||||||||
\(532\) | −16.4759 | −0.714320 | ||||||||
\(533\) | −6.40713 | −0.277524 | ||||||||
\(534\) | −24.8549 | −1.07558 | ||||||||
\(535\) | −23.8971 | −1.03316 | ||||||||
\(536\) | 41.3543 | 1.78623 | ||||||||
\(537\) | −3.52694 | −0.152199 | ||||||||
\(538\) | 43.0011 | 1.85391 | ||||||||
\(539\) | −10.2424 | −0.441170 | ||||||||
\(540\) | −61.2675 | −2.63653 | ||||||||
\(541\) | −25.5179 | −1.09710 | −0.548550 | − | 0.836118i | \(-0.684820\pi\) | ||||
−0.548550 | + | 0.836118i | \(0.684820\pi\) | |||||||
\(542\) | 41.2010 | 1.76973 | ||||||||
\(543\) | −9.31221 | −0.399625 | ||||||||
\(544\) | −35.8647 | −1.53768 | ||||||||
\(545\) | −42.9389 | −1.83930 | ||||||||
\(546\) | 1.01592 | 0.0434772 | ||||||||
\(547\) | −30.7848 | −1.31626 | −0.658132 | − | 0.752903i | \(-0.728653\pi\) | ||||
−0.658132 | + | 0.752903i | \(0.728653\pi\) | |||||||
\(548\) | 17.0091 | 0.726591 | ||||||||
\(549\) | −24.4193 | −1.04219 | ||||||||
\(550\) | −46.6344 | −1.98850 | ||||||||
\(551\) | 23.8738 | 1.01706 | ||||||||
\(552\) | −11.5580 | −0.491942 | ||||||||
\(553\) | −0.933613 | −0.0397013 | ||||||||
\(554\) | −53.9388 | −2.29164 | ||||||||
\(555\) | 20.9786 | 0.890493 | ||||||||
\(556\) | 42.7100 | 1.81131 | ||||||||
\(557\) | −18.8415 | −0.798341 | −0.399171 | − | 0.916877i | \(-0.630702\pi\) | ||||
−0.399171 | + | 0.916877i | \(0.630702\pi\) | |||||||
\(558\) | 60.2981 | 2.55262 | ||||||||
\(559\) | −1.97584 | −0.0835692 | ||||||||
\(560\) | −21.6353 | −0.914259 | ||||||||
\(561\) | 6.28421 | 0.265320 | ||||||||
\(562\) | −65.7573 | −2.77381 | ||||||||
\(563\) | 30.5558 | 1.28777 | 0.643886 | − | 0.765121i | \(-0.277321\pi\) | ||||
0.643886 | + | 0.765121i | \(0.277321\pi\) | |||||||
\(564\) | −6.90532 | −0.290766 | ||||||||
\(565\) | 62.3088 | 2.62135 | ||||||||
\(566\) | −77.2500 | −3.24706 | ||||||||
\(567\) | −4.45099 | −0.186924 | ||||||||
\(568\) | 93.1621 | 3.90900 | ||||||||
\(569\) | −36.8104 | −1.54317 | −0.771586 | − | 0.636125i | \(-0.780536\pi\) | ||||
−0.771586 | + | 0.636125i | \(0.780536\pi\) | |||||||
\(570\) | −30.2218 | −1.26585 | ||||||||
\(571\) | −10.2175 | −0.427591 | −0.213795 | − | 0.976878i | \(-0.568583\pi\) | ||||
−0.213795 | + | 0.976878i | \(0.568583\pi\) | |||||||
\(572\) | 6.33914 | 0.265053 | ||||||||
\(573\) | 1.28529 | 0.0536938 | ||||||||
\(574\) | −13.7752 | −0.574965 | ||||||||
\(575\) | 35.3852 | 1.47567 | ||||||||
\(576\) | 0.972719 | 0.0405299 | ||||||||
\(577\) | 14.4440 | 0.601314 | 0.300657 | − | 0.953732i | \(-0.402794\pi\) | ||||
0.300657 | + | 0.953732i | \(0.402794\pi\) | |||||||
\(578\) | −68.0974 | −2.83248 | ||||||||
\(579\) | 15.2118 | 0.632180 | ||||||||
\(580\) | 88.6807 | 3.68226 | ||||||||
\(581\) | 0.155853 | 0.00646586 | ||||||||
\(582\) | 12.3447 | 0.511706 | ||||||||
\(583\) | −1.03006 | −0.0426607 | ||||||||
\(584\) | 47.9625 | 1.98470 | ||||||||
\(585\) | −9.55927 | −0.395227 | ||||||||
\(586\) | −33.8943 | −1.40016 | ||||||||
\(587\) | 38.3102 | 1.58123 | 0.790616 | − | 0.612312i | \(-0.209760\pi\) | ||||
0.790616 | + | 0.612312i | \(0.209760\pi\) | |||||||
\(588\) | −17.1904 | −0.708920 | ||||||||
\(589\) | 43.8854 | 1.80827 | ||||||||
\(590\) | 109.946 | 4.52640 | ||||||||
\(591\) | 5.97218 | 0.245663 | ||||||||
\(592\) | 61.2616 | 2.51784 | ||||||||
\(593\) | 37.2269 | 1.52873 | 0.764363 | − | 0.644787i | \(-0.223054\pi\) | ||||
0.764363 | + | 0.644787i | \(0.223054\pi\) | |||||||
\(594\) | 13.6439 | 0.559815 | ||||||||
\(595\) | −20.2077 | −0.828434 | ||||||||
\(596\) | −2.61348 | −0.107052 | ||||||||
\(597\) | −10.8011 | −0.442059 | ||||||||
\(598\) | −6.95927 | −0.284586 | ||||||||
\(599\) | −27.4364 | −1.12102 | −0.560511 | − | 0.828147i | \(-0.689395\pi\) | ||||
−0.560511 | + | 0.828147i | \(0.689395\pi\) | |||||||
\(600\) | −43.2963 | −1.76757 | ||||||||
\(601\) | 17.9505 | 0.732216 | 0.366108 | − | 0.930572i | \(-0.380690\pi\) | ||||
0.366108 | + | 0.930572i | \(0.380690\pi\) | |||||||
\(602\) | −4.24802 | −0.173136 | ||||||||
\(603\) | 17.3519 | 0.706624 | ||||||||
\(604\) | 15.7560 | 0.641101 | ||||||||
\(605\) | −34.4049 | −1.39876 | ||||||||
\(606\) | 25.0744 | 1.01858 | ||||||||
\(607\) | −15.7500 | −0.639272 | −0.319636 | − | 0.947540i | \(-0.603561\pi\) | ||||
−0.319636 | + | 0.947540i | \(0.603561\pi\) | |||||||
\(608\) | −26.5477 | −1.07665 | ||||||||
\(609\) | −2.18749 | −0.0886417 | ||||||||
\(610\) | −95.5156 | −3.86731 | ||||||||
\(611\) | −2.29997 | −0.0930470 | ||||||||
\(612\) | −78.2799 | −3.16428 | ||||||||
\(613\) | −1.84663 | −0.0745845 | −0.0372923 | − | 0.999304i | \(-0.511873\pi\) | ||||
−0.0372923 | + | 0.999304i | \(0.511873\pi\) | |||||||
\(614\) | −28.8766 | −1.16536 | ||||||||
\(615\) | −17.4643 | −0.704229 | ||||||||
\(616\) | 7.53917 | 0.303762 | ||||||||
\(617\) | −14.1576 | −0.569962 | −0.284981 | − | 0.958533i | \(-0.591987\pi\) | ||||
−0.284981 | + | 0.958533i | \(0.591987\pi\) | |||||||
\(618\) | 19.1668 | 0.771003 | ||||||||
\(619\) | 5.43999 | 0.218652 | 0.109326 | − | 0.994006i | \(-0.465131\pi\) | ||||
0.109326 | + | 0.994006i | \(0.465131\pi\) | |||||||
\(620\) | 163.015 | 6.54685 | ||||||||
\(621\) | −10.3527 | −0.415440 | ||||||||
\(622\) | −73.4032 | −2.94320 | ||||||||
\(623\) | −12.3018 | −0.492860 | ||||||||
\(624\) | 3.76117 | 0.150567 | ||||||||
\(625\) | 49.9871 | 1.99949 | ||||||||
\(626\) | 18.5060 | 0.739650 | ||||||||
\(627\) | 4.65169 | 0.185770 | ||||||||
\(628\) | −34.2046 | −1.36491 | ||||||||
\(629\) | 57.2192 | 2.28148 | ||||||||
\(630\) | −20.5522 | −0.818821 | ||||||||
\(631\) | −25.5739 | −1.01808 | −0.509039 | − | 0.860743i | \(-0.669999\pi\) | ||||
−0.509039 | + | 0.860743i | \(0.669999\pi\) | |||||||
\(632\) | −7.82532 | −0.311274 | ||||||||
\(633\) | −8.75860 | −0.348123 | ||||||||
\(634\) | −5.85980 | −0.232722 | ||||||||
\(635\) | 22.7413 | 0.902460 | ||||||||
\(636\) | −1.72881 | −0.0685519 | ||||||||
\(637\) | −5.72565 | −0.226859 | ||||||||
\(638\) | −19.7486 | −0.781856 | ||||||||
\(639\) | 39.0900 | 1.54638 | ||||||||
\(640\) | 47.8680 | 1.89215 | ||||||||
\(641\) | −17.4812 | −0.690467 | −0.345234 | − | 0.938517i | \(-0.612200\pi\) | ||||
−0.345234 | + | 0.938517i | \(0.612200\pi\) | |||||||
\(642\) | 8.93179 | 0.352510 | ||||||||
\(643\) | 5.57208 | 0.219741 | 0.109871 | − | 0.993946i | \(-0.464956\pi\) | ||||
0.109871 | + | 0.993946i | \(0.464956\pi\) | |||||||
\(644\) | −10.3414 | −0.407509 | ||||||||
\(645\) | −5.38567 | −0.212061 | ||||||||
\(646\) | −82.4299 | −3.24316 | ||||||||
\(647\) | −39.3096 | −1.54542 | −0.772709 | − | 0.634760i | \(-0.781099\pi\) | ||||
−0.772709 | + | 0.634760i | \(0.781099\pi\) | |||||||
\(648\) | −37.3071 | −1.46556 | ||||||||
\(649\) | −16.9227 | −0.664274 | ||||||||
\(650\) | −26.0694 | −1.02253 | ||||||||
\(651\) | −4.02111 | −0.157600 | ||||||||
\(652\) | −44.2674 | −1.73365 | ||||||||
\(653\) | −24.1760 | −0.946081 | −0.473040 | − | 0.881041i | \(-0.656843\pi\) | ||||
−0.473040 | + | 0.881041i | \(0.656843\pi\) | |||||||
\(654\) | 16.0489 | 0.627561 | ||||||||
\(655\) | 78.4490 | 3.06525 | ||||||||
\(656\) | −50.9991 | −1.99118 | ||||||||
\(657\) | 20.1246 | 0.785136 | ||||||||
\(658\) | −4.94489 | −0.192772 | ||||||||
\(659\) | −7.82605 | −0.304859 | −0.152430 | − | 0.988314i | \(-0.548710\pi\) | ||||
−0.152430 | + | 0.988314i | \(0.548710\pi\) | |||||||
\(660\) | 17.2790 | 0.672584 | ||||||||
\(661\) | −24.2306 | −0.942462 | −0.471231 | − | 0.882010i | \(-0.656190\pi\) | ||||
−0.471231 | + | 0.882010i | \(0.656190\pi\) | |||||||
\(662\) | 35.5550 | 1.38189 | ||||||||
\(663\) | 3.51298 | 0.136433 | ||||||||
\(664\) | 1.30632 | 0.0506950 | ||||||||
\(665\) | −14.9581 | −0.580049 | ||||||||
\(666\) | 58.1948 | 2.25500 | ||||||||
\(667\) | 14.9849 | 0.580216 | ||||||||
\(668\) | 14.0819 | 0.544844 | ||||||||
\(669\) | −10.2762 | −0.397301 | ||||||||
\(670\) | 67.8717 | 2.62211 | ||||||||
\(671\) | 14.7016 | 0.567549 | ||||||||
\(672\) | 2.43250 | 0.0938355 | ||||||||
\(673\) | 32.4551 | 1.25105 | 0.625526 | − | 0.780204i | \(-0.284885\pi\) | ||||
0.625526 | + | 0.780204i | \(0.284885\pi\) | |||||||
\(674\) | 18.3334 | 0.706177 | ||||||||
\(675\) | −38.7812 | −1.49269 | ||||||||
\(676\) | −54.6441 | −2.10169 | ||||||||
\(677\) | 37.8082 | 1.45309 | 0.726543 | − | 0.687121i | \(-0.241126\pi\) | ||||
0.726543 | + | 0.687121i | \(0.241126\pi\) | |||||||
\(678\) | −23.2886 | −0.894394 | ||||||||
\(679\) | 6.10995 | 0.234478 | ||||||||
\(680\) | −169.376 | −6.49527 | ||||||||
\(681\) | 8.49422 | 0.325499 | ||||||||
\(682\) | −36.3025 | −1.39009 | ||||||||
\(683\) | −36.8369 | −1.40952 | −0.704762 | − | 0.709444i | \(-0.748946\pi\) | ||||
−0.704762 | + | 0.709444i | \(0.748946\pi\) | |||||||
\(684\) | −57.9442 | −2.21555 | ||||||||
\(685\) | 15.4421 | 0.590014 | ||||||||
\(686\) | −25.7011 | −0.981273 | ||||||||
\(687\) | 16.0944 | 0.614041 | ||||||||
\(688\) | −15.7272 | −0.599594 | ||||||||
\(689\) | −0.575820 | −0.0219370 | ||||||||
\(690\) | −18.9693 | −0.722149 | ||||||||
\(691\) | −47.2915 | −1.79905 | −0.899527 | − | 0.436864i | \(-0.856089\pi\) | ||||
−0.899527 | + | 0.436864i | \(0.856089\pi\) | |||||||
\(692\) | −4.73127 | −0.179856 | ||||||||
\(693\) | 3.16337 | 0.120166 | ||||||||
\(694\) | 30.1858 | 1.14584 | ||||||||
\(695\) | 38.7754 | 1.47084 | ||||||||
\(696\) | −18.3350 | −0.694988 | ||||||||
\(697\) | −47.6339 | −1.80426 | ||||||||
\(698\) | 23.9860 | 0.907884 | ||||||||
\(699\) | −5.11509 | −0.193470 | ||||||||
\(700\) | −38.7390 | −1.46420 | ||||||||
\(701\) | 6.17292 | 0.233148 | 0.116574 | − | 0.993182i | \(-0.462809\pi\) | ||||
0.116574 | + | 0.993182i | \(0.462809\pi\) | |||||||
\(702\) | 7.62717 | 0.287869 | ||||||||
\(703\) | 42.3546 | 1.59744 | ||||||||
\(704\) | −0.585625 | −0.0220716 | ||||||||
\(705\) | −6.26918 | −0.236111 | ||||||||
\(706\) | 53.7570 | 2.02317 | ||||||||
\(707\) | 12.4104 | 0.466742 | ||||||||
\(708\) | −28.4024 | −1.06743 | ||||||||
\(709\) | 48.6056 | 1.82542 | 0.912711 | − | 0.408607i | \(-0.133985\pi\) | ||||
0.912711 | + | 0.408607i | \(0.133985\pi\) | |||||||
\(710\) | 152.900 | 5.73823 | ||||||||
\(711\) | −3.28343 | −0.123138 | ||||||||
\(712\) | −103.111 | −3.86423 | ||||||||
\(713\) | 27.5456 | 1.03159 | ||||||||
\(714\) | 7.55284 | 0.282658 | ||||||||
\(715\) | 5.75516 | 0.215231 | ||||||||
\(716\) | −26.4503 | −0.988493 | ||||||||
\(717\) | −6.56626 | −0.245221 | ||||||||
\(718\) | −68.3623 | −2.55126 | ||||||||
\(719\) | −52.0520 | −1.94121 | −0.970605 | − | 0.240676i | \(-0.922631\pi\) | ||||
−0.970605 | + | 0.240676i | \(0.922631\pi\) | |||||||
\(720\) | −76.0894 | −2.83569 | ||||||||
\(721\) | 9.48650 | 0.353296 | ||||||||
\(722\) | −12.6649 | −0.471340 | ||||||||
\(723\) | −0.518309 | −0.0192761 | ||||||||
\(724\) | −69.8369 | −2.59547 | ||||||||
\(725\) | 56.1333 | 2.08474 | ||||||||
\(726\) | 12.8592 | 0.477250 | ||||||||
\(727\) | 47.1599 | 1.74906 | 0.874531 | − | 0.484969i | \(-0.161169\pi\) | ||||
0.874531 | + | 0.484969i | \(0.161169\pi\) | |||||||
\(728\) | 4.21453 | 0.156201 | ||||||||
\(729\) | −9.62251 | −0.356389 | ||||||||
\(730\) | 78.7172 | 2.91345 | ||||||||
\(731\) | −14.6894 | −0.543308 | ||||||||
\(732\) | 24.6747 | 0.912001 | ||||||||
\(733\) | −14.4317 | −0.533047 | −0.266523 | − | 0.963828i | \(-0.585875\pi\) | ||||
−0.266523 | + | 0.963828i | \(0.585875\pi\) | |||||||
\(734\) | 0.126415 | 0.00466606 | ||||||||
\(735\) | −15.6068 | −0.575664 | ||||||||
\(736\) | −16.6632 | −0.614213 | ||||||||
\(737\) | −10.4467 | −0.384809 | ||||||||
\(738\) | −48.4461 | −1.78332 | ||||||||
\(739\) | 15.0399 | 0.553251 | 0.276626 | − | 0.960978i | \(-0.410784\pi\) | ||||
0.276626 | + | 0.960978i | \(0.410784\pi\) | |||||||
\(740\) | 157.329 | 5.78353 | ||||||||
\(741\) | 2.60037 | 0.0955271 | ||||||||
\(742\) | −1.23800 | −0.0454485 | ||||||||
\(743\) | 30.6441 | 1.12422 | 0.562112 | − | 0.827061i | \(-0.309989\pi\) | ||||
0.562112 | + | 0.827061i | \(0.309989\pi\) | |||||||
\(744\) | −33.7040 | −1.23565 | ||||||||
\(745\) | −2.37272 | −0.0869298 | ||||||||
\(746\) | −75.5885 | −2.76749 | ||||||||
\(747\) | 0.548120 | 0.0200546 | ||||||||
\(748\) | 47.1284 | 1.72319 | ||||||||
\(749\) | 4.42073 | 0.161530 | ||||||||
\(750\) | −40.1991 | −1.46786 | ||||||||
\(751\) | −6.00695 | −0.219197 | −0.109598 | − | 0.993976i | \(-0.534956\pi\) | ||||
−0.109598 | + | 0.993976i | \(0.534956\pi\) | |||||||
\(752\) | −18.3072 | −0.667596 | ||||||||
\(753\) | 15.2589 | 0.556065 | ||||||||
\(754\) | −11.0398 | −0.402047 | ||||||||
\(755\) | 14.3045 | 0.520593 | ||||||||
\(756\) | 11.3339 | 0.412211 | ||||||||
\(757\) | −5.08382 | −0.184774 | −0.0923872 | − | 0.995723i | \(-0.529450\pi\) | ||||
−0.0923872 | + | 0.995723i | \(0.529450\pi\) | |||||||
\(758\) | −18.5019 | −0.672021 | ||||||||
\(759\) | 2.91972 | 0.105979 | ||||||||
\(760\) | −125.375 | −4.54783 | ||||||||
\(761\) | 3.62296 | 0.131332 | 0.0656660 | − | 0.997842i | \(-0.479083\pi\) | ||||
0.0656660 | + | 0.997842i | \(0.479083\pi\) | |||||||
\(762\) | −8.49980 | −0.307915 | ||||||||
\(763\) | 7.94329 | 0.287566 | ||||||||
\(764\) | 9.63903 | 0.348728 | ||||||||
\(765\) | −71.0685 | −2.56949 | ||||||||
\(766\) | −35.9202 | −1.29785 | ||||||||
\(767\) | −9.46008 | −0.341584 | ||||||||
\(768\) | −17.4520 | −0.629744 | ||||||||
\(769\) | 13.2246 | 0.476891 | 0.238446 | − | 0.971156i | \(-0.423362\pi\) | ||||
0.238446 | + | 0.971156i | \(0.423362\pi\) | |||||||
\(770\) | 12.3735 | 0.445909 | ||||||||
\(771\) | 9.40027 | 0.338543 | ||||||||
\(772\) | 114.081 | 4.10585 | ||||||||
\(773\) | 19.8487 | 0.713908 | 0.356954 | − | 0.934122i | \(-0.383815\pi\) | ||||
0.356954 | + | 0.934122i | \(0.383815\pi\) | |||||||
\(774\) | −14.9399 | −0.537003 | ||||||||
\(775\) | 103.186 | 3.70654 | ||||||||
\(776\) | 51.2121 | 1.83841 | ||||||||
\(777\) | −3.88085 | −0.139225 | ||||||||
\(778\) | −72.5213 | −2.60002 | ||||||||
\(779\) | −35.2594 | −1.26330 | ||||||||
\(780\) | 9.65925 | 0.345857 | ||||||||
\(781\) | −23.5341 | −0.842116 | ||||||||
\(782\) | −51.7388 | −1.85017 | ||||||||
\(783\) | −16.4230 | −0.586910 | ||||||||
\(784\) | −45.5748 | −1.62767 | ||||||||
\(785\) | −31.0535 | −1.10835 | ||||||||
\(786\) | −29.3212 | −1.04585 | ||||||||
\(787\) | −42.7482 | −1.52381 | −0.761904 | − | 0.647690i | \(-0.775735\pi\) | ||||
−0.761904 | + | 0.647690i | \(0.775735\pi\) | |||||||
\(788\) | 44.7883 | 1.59552 | ||||||||
\(789\) | 11.8687 | 0.422536 | ||||||||
\(790\) | −12.8431 | −0.456937 | ||||||||
\(791\) | −11.5266 | −0.409837 | ||||||||
\(792\) | 26.5146 | 0.942154 | ||||||||
\(793\) | 8.21845 | 0.291846 | ||||||||
\(794\) | −28.0925 | −0.996965 | ||||||||
\(795\) | −1.56955 | −0.0556662 | ||||||||
\(796\) | −81.0027 | −2.87106 | ||||||||
\(797\) | −26.2040 | −0.928192 | −0.464096 | − | 0.885785i | \(-0.653621\pi\) | ||||
−0.464096 | + | 0.885785i | \(0.653621\pi\) | |||||||
\(798\) | 5.59075 | 0.197910 | ||||||||
\(799\) | −17.0992 | −0.604926 | ||||||||
\(800\) | −62.4202 | −2.20689 | ||||||||
\(801\) | −43.2642 | −1.52867 | ||||||||
\(802\) | 80.0298 | 2.82595 | ||||||||
\(803\) | −12.1160 | −0.427565 | ||||||||
\(804\) | −17.5334 | −0.618354 | ||||||||
\(805\) | −9.38874 | −0.330909 | ||||||||
\(806\) | −20.2937 | −0.714815 | ||||||||
\(807\) | −10.0852 | −0.355015 | ||||||||
\(808\) | 104.021 | 3.65945 | ||||||||
\(809\) | 38.1138 | 1.34001 | 0.670005 | − | 0.742357i | \(-0.266292\pi\) | ||||
0.670005 | + | 0.742357i | \(0.266292\pi\) | |||||||
\(810\) | −61.2293 | −2.15138 | ||||||||
\(811\) | −10.3856 | −0.364689 | −0.182345 | − | 0.983235i | \(-0.558369\pi\) | ||||
−0.182345 | + | 0.983235i | \(0.558369\pi\) | |||||||
\(812\) | −16.4051 | −0.575706 | ||||||||
\(813\) | −9.66298 | −0.338895 | ||||||||
\(814\) | −35.0362 | −1.22802 | ||||||||
\(815\) | −40.1894 | −1.40777 | ||||||||
\(816\) | 27.9625 | 0.978883 | ||||||||
\(817\) | −10.8734 | −0.380411 | ||||||||
\(818\) | 59.6573 | 2.08587 | ||||||||
\(819\) | 1.76838 | 0.0617921 | ||||||||
\(820\) | −130.973 | −4.57379 | ||||||||
\(821\) | 0.0281231 | 0.000981503 0 | 0.000490751 | − | 1.00000i | \(-0.499844\pi\) | ||||
0.000490751 | 1.00000i | \(0.499844\pi\) | ||||||||
\(822\) | −5.77167 | −0.201310 | ||||||||
\(823\) | −47.7297 | −1.66375 | −0.831876 | − | 0.554962i | \(-0.812733\pi\) | ||||
−0.831876 | + | 0.554962i | \(0.812733\pi\) | |||||||
\(824\) | 79.5135 | 2.76999 | ||||||||
\(825\) | 10.9373 | 0.380787 | ||||||||
\(826\) | −20.3390 | −0.707683 | ||||||||
\(827\) | −19.1070 | −0.664414 | −0.332207 | − | 0.943206i | \(-0.607793\pi\) | ||||
−0.332207 | + | 0.943206i | \(0.607793\pi\) | |||||||
\(828\) | −36.3698 | −1.26394 | ||||||||
\(829\) | −36.9455 | −1.28317 | −0.641585 | − | 0.767052i | \(-0.721723\pi\) | ||||
−0.641585 | + | 0.767052i | \(0.721723\pi\) | |||||||
\(830\) | 2.14396 | 0.0744180 | ||||||||
\(831\) | 12.6504 | 0.438838 | ||||||||
\(832\) | −0.327374 | −0.0113497 | ||||||||
\(833\) | −42.5674 | −1.47487 | ||||||||
\(834\) | −14.4927 | −0.501843 | ||||||||
\(835\) | 12.7846 | 0.442429 | ||||||||
\(836\) | 34.8853 | 1.20653 | ||||||||
\(837\) | −30.1892 | −1.04349 | ||||||||
\(838\) | −44.3828 | −1.53318 | ||||||||
\(839\) | −10.7769 | −0.372059 | −0.186029 | − | 0.982544i | \(-0.559562\pi\) | ||||
−0.186029 | + | 0.982544i | \(0.559562\pi\) | |||||||
\(840\) | 11.4878 | 0.396367 | ||||||||
\(841\) | −5.22879 | −0.180303 | ||||||||
\(842\) | 75.6462 | 2.60694 | ||||||||
\(843\) | 15.4223 | 0.531171 | ||||||||
\(844\) | −65.6851 | −2.26097 | ||||||||
\(845\) | −49.6101 | −1.70664 | ||||||||
\(846\) | −17.3907 | −0.597906 | ||||||||
\(847\) | 6.36458 | 0.218690 | ||||||||
\(848\) | −4.58339 | −0.157394 | ||||||||
\(849\) | 18.1177 | 0.621796 | ||||||||
\(850\) | −193.813 | −6.64774 | ||||||||
\(851\) | 26.5847 | 0.911313 | ||||||||
\(852\) | −39.4988 | −1.35321 | ||||||||
\(853\) | −13.4397 | −0.460167 | −0.230084 | − | 0.973171i | \(-0.573900\pi\) | ||||
−0.230084 | + | 0.973171i | \(0.573900\pi\) | |||||||
\(854\) | 17.6695 | 0.604638 | ||||||||
\(855\) | −52.6062 | −1.79909 | ||||||||
\(856\) | 37.0535 | 1.26646 | ||||||||
\(857\) | 34.9765 | 1.19478 | 0.597388 | − | 0.801952i | \(-0.296205\pi\) | ||||
0.597388 | + | 0.801952i | \(0.296205\pi\) | |||||||
\(858\) | −2.15105 | −0.0734358 | ||||||||
\(859\) | 49.8304 | 1.70019 | 0.850096 | − | 0.526627i | \(-0.176544\pi\) | ||||
0.850096 | + | 0.526627i | \(0.176544\pi\) | |||||||
\(860\) | −40.3898 | −1.37728 | ||||||||
\(861\) | 3.23073 | 0.110103 | ||||||||
\(862\) | 70.0274 | 2.38514 | ||||||||
\(863\) | 40.0338 | 1.36277 | 0.681383 | − | 0.731927i | \(-0.261379\pi\) | ||||
0.681383 | + | 0.731927i | \(0.261379\pi\) | |||||||
\(864\) | 18.2624 | 0.621299 | ||||||||
\(865\) | −4.29541 | −0.146048 | ||||||||
\(866\) | 25.6621 | 0.872033 | ||||||||
\(867\) | 15.9711 | 0.542406 | ||||||||
\(868\) | −30.1563 | −1.02357 | ||||||||
\(869\) | 1.97679 | 0.0670580 | ||||||||
\(870\) | −30.0919 | −1.02021 | ||||||||
\(871\) | −5.83989 | −0.197877 | ||||||||
\(872\) | 66.5787 | 2.25464 | ||||||||
\(873\) | 21.4881 | 0.727263 | ||||||||
\(874\) | −38.2979 | −1.29545 | ||||||||
\(875\) | −19.8963 | −0.672618 | ||||||||
\(876\) | −20.3351 | −0.687059 | ||||||||
\(877\) | 30.1705 | 1.01879 | 0.509393 | − | 0.860534i | \(-0.329870\pi\) | ||||
0.509393 | + | 0.860534i | \(0.329870\pi\) | |||||||
\(878\) | 70.8355 | 2.39058 | ||||||||
\(879\) | 7.94933 | 0.268124 | ||||||||
\(880\) | 45.8096 | 1.54424 | ||||||||
\(881\) | 46.5443 | 1.56812 | 0.784058 | − | 0.620687i | \(-0.213146\pi\) | ||||
0.784058 | + | 0.620687i | \(0.213146\pi\) | |||||||
\(882\) | −43.2933 | −1.45776 | ||||||||
\(883\) | −7.16157 | −0.241006 | −0.120503 | − | 0.992713i | \(-0.538451\pi\) | ||||
−0.120503 | + | 0.992713i | \(0.538451\pi\) | |||||||
\(884\) | 26.3456 | 0.886098 | ||||||||
\(885\) | −25.7859 | −0.866784 | ||||||||
\(886\) | 94.7223 | 3.18226 | ||||||||
\(887\) | 40.3578 | 1.35508 | 0.677541 | − | 0.735485i | \(-0.263046\pi\) | ||||
0.677541 | + | 0.735485i | \(0.263046\pi\) | |||||||
\(888\) | −32.5283 | −1.09158 | ||||||||
\(889\) | −4.20692 | −0.141096 | ||||||||
\(890\) | −169.228 | −5.67252 | ||||||||
\(891\) | 9.42432 | 0.315727 | ||||||||
\(892\) | −77.0664 | −2.58037 | ||||||||
\(893\) | −12.6571 | −0.423554 | ||||||||
\(894\) | 0.886831 | 0.0296601 | ||||||||
\(895\) | −24.0136 | −0.802686 | ||||||||
\(896\) | −8.85512 | −0.295829 | ||||||||
\(897\) | 1.63218 | 0.0544968 | ||||||||
\(898\) | −28.1947 | −0.940869 | ||||||||
\(899\) | 43.6969 | 1.45737 | ||||||||
\(900\) | −136.241 | −4.54138 | ||||||||
\(901\) | −4.28094 | −0.142619 | ||||||||
\(902\) | 29.1669 | 0.971153 | ||||||||
\(903\) | 0.996299 | 0.0331548 | ||||||||
\(904\) | −96.6128 | −3.21329 | ||||||||
\(905\) | −63.4033 | −2.10760 | ||||||||
\(906\) | −5.34645 | −0.177624 | ||||||||
\(907\) | 6.22170 | 0.206588 | 0.103294 | − | 0.994651i | \(-0.467062\pi\) | ||||
0.103294 | + | 0.994651i | \(0.467062\pi\) | |||||||
\(908\) | 63.7023 | 2.11404 | ||||||||
\(909\) | 43.6463 | 1.44766 | ||||||||
\(910\) | 6.91698 | 0.229296 | ||||||||
\(911\) | −15.9935 | −0.529890 | −0.264945 | − | 0.964264i | \(-0.585354\pi\) | ||||
−0.264945 | + | 0.964264i | \(0.585354\pi\) | |||||||
\(912\) | 20.6983 | 0.685390 | ||||||||
\(913\) | −0.329995 | −0.0109213 | ||||||||
\(914\) | −40.6026 | −1.34302 | ||||||||
\(915\) | 22.4015 | 0.740572 | ||||||||
\(916\) | 120.700 | 3.98804 | ||||||||
\(917\) | −14.5123 | −0.479239 | ||||||||
\(918\) | 56.7043 | 1.87152 | ||||||||
\(919\) | 6.37731 | 0.210368 | 0.105184 | − | 0.994453i | \(-0.466457\pi\) | ||||
0.105184 | + | 0.994453i | \(0.466457\pi\) | |||||||
\(920\) | −78.6941 | −2.59447 | ||||||||
\(921\) | 6.77250 | 0.223161 | ||||||||
\(922\) | 8.90718 | 0.293342 | ||||||||
\(923\) | −13.1560 | −0.433034 | ||||||||
\(924\) | −3.19645 | −0.105156 | ||||||||
\(925\) | 99.5864 | 3.27438 | ||||||||
\(926\) | −85.7546 | −2.81807 | ||||||||
\(927\) | 33.3631 | 1.09579 | ||||||||
\(928\) | −26.4336 | −0.867725 | ||||||||
\(929\) | 36.3215 | 1.19167 | 0.595835 | − | 0.803107i | \(-0.296821\pi\) | ||||
0.595835 | + | 0.803107i | \(0.296821\pi\) | |||||||
\(930\) | −55.3158 | −1.81388 | ||||||||
\(931\) | −31.5092 | −1.03267 | ||||||||
\(932\) | −38.3605 | −1.25654 | ||||||||
\(933\) | 17.2155 | 0.563609 | ||||||||
\(934\) | −11.2149 | −0.366963 | ||||||||
\(935\) | 42.7868 | 1.39928 | ||||||||
\(936\) | 14.8221 | 0.484476 | ||||||||
\(937\) | −12.6650 | −0.413748 | −0.206874 | − | 0.978368i | \(-0.566329\pi\) | ||||
−0.206874 | + | 0.978368i | \(0.566329\pi\) | |||||||
\(938\) | −12.5556 | −0.409956 | ||||||||
\(939\) | −4.34027 | −0.141639 | ||||||||
\(940\) | −47.0157 | −1.53348 | ||||||||
\(941\) | 15.8726 | 0.517431 | 0.258715 | − | 0.965954i | \(-0.416701\pi\) | ||||
0.258715 | + | 0.965954i | \(0.416701\pi\) | |||||||
\(942\) | 11.6066 | 0.378164 | ||||||||
\(943\) | −22.1313 | −0.720694 | ||||||||
\(944\) | −75.2999 | −2.45080 | ||||||||
\(945\) | 10.2898 | 0.334727 | ||||||||
\(946\) | 8.99456 | 0.292438 | ||||||||
\(947\) | 24.0174 | 0.780462 | 0.390231 | − | 0.920717i | \(-0.372395\pi\) | ||||
0.390231 | + | 0.920717i | \(0.372395\pi\) | |||||||
\(948\) | 3.31777 | 0.107756 | ||||||||
\(949\) | −6.77307 | −0.219863 | ||||||||
\(950\) | −143.464 | −4.65459 | ||||||||
\(951\) | 1.37431 | 0.0445652 | ||||||||
\(952\) | 31.3329 | 1.01551 | ||||||||
\(953\) | −47.1370 | −1.52692 | −0.763459 | − | 0.645856i | \(-0.776500\pi\) | ||||
−0.763459 | + | 0.645856i | \(0.776500\pi\) | |||||||
\(954\) | −4.35394 | −0.140964 | ||||||||
\(955\) | 8.75105 | 0.283177 | ||||||||
\(956\) | −49.2436 | −1.59265 | ||||||||
\(957\) | 4.63170 | 0.149722 | ||||||||
\(958\) | 44.3892 | 1.43415 | ||||||||
\(959\) | −2.85665 | −0.0922461 | ||||||||
\(960\) | −0.892345 | −0.0288003 | ||||||||
\(961\) | 49.3248 | 1.59112 | ||||||||
\(962\) | −19.5858 | −0.631472 | ||||||||
\(963\) | 15.5473 | 0.501005 | ||||||||
\(964\) | −3.88705 | −0.125194 | ||||||||
\(965\) | 103.571 | 3.33407 | ||||||||
\(966\) | 3.50914 | 0.112905 | ||||||||
\(967\) | −39.0783 | −1.25667 | −0.628336 | − | 0.777942i | \(-0.716264\pi\) | ||||
−0.628336 | + | 0.777942i | \(0.716264\pi\) | |||||||
\(968\) | 53.3464 | 1.71462 | ||||||||
\(969\) | 19.3325 | 0.621049 | ||||||||
\(970\) | 84.0505 | 2.69870 | ||||||||
\(971\) | −39.9791 | −1.28299 | −0.641496 | − | 0.767127i | \(-0.721686\pi\) | ||||
−0.641496 | + | 0.767127i | \(0.721686\pi\) | |||||||
\(972\) | 61.0484 | 1.95813 | ||||||||
\(973\) | −7.17310 | −0.229959 | ||||||||
\(974\) | 42.4037 | 1.35870 | ||||||||
\(975\) | 6.11413 | 0.195809 | ||||||||
\(976\) | 65.4168 | 2.09394 | ||||||||
\(977\) | 19.1459 | 0.612532 | 0.306266 | − | 0.951946i | \(-0.400920\pi\) | ||||
0.306266 | + | 0.951946i | \(0.400920\pi\) | |||||||
\(978\) | 15.0212 | 0.480325 | ||||||||
\(979\) | 26.0472 | 0.832473 | ||||||||
\(980\) | −117.043 | −3.73880 | ||||||||
\(981\) | 27.9358 | 0.891922 | ||||||||
\(982\) | 16.9461 | 0.540771 | ||||||||
\(983\) | 0.0268941 | 0.000857788 0 | 0.000428894 | − | 1.00000i | \(-0.499863\pi\) | ||||
0.000428894 | 1.00000i | \(0.499863\pi\) | ||||||||
\(984\) | 27.0792 | 0.863254 | ||||||||
\(985\) | 40.6623 | 1.29561 | ||||||||
\(986\) | −82.0757 | −2.61382 | ||||||||
\(987\) | 1.15974 | 0.0369149 | ||||||||
\(988\) | 19.5015 | 0.620425 | ||||||||
\(989\) | −6.82489 | −0.217019 | ||||||||
\(990\) | 43.5164 | 1.38304 | ||||||||
\(991\) | 5.07781 | 0.161302 | 0.0806510 | − | 0.996742i | \(-0.474300\pi\) | ||||
0.0806510 | + | 0.996742i | \(0.474300\pi\) | |||||||
\(992\) | −48.5910 | −1.54276 | ||||||||
\(993\) | −8.33882 | −0.264624 | ||||||||
\(994\) | −28.2851 | −0.897147 | ||||||||
\(995\) | −73.5404 | −2.33139 | ||||||||
\(996\) | −0.553852 | −0.0175495 | ||||||||
\(997\) | 12.7721 | 0.404495 | 0.202247 | − | 0.979334i | \(-0.435175\pi\) | ||||
0.202247 | + | 0.979334i | \(0.435175\pi\) | |||||||
\(998\) | −1.04199 | −0.0329837 | ||||||||
\(999\) | −29.1362 | −0.921827 |
(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 | 4027.2.a.c.1.8 | ✓ | 174 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4027.2.a.c.1.8 | ✓ | 174 | 1.1 | even | 1 | trivial |