Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(73\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.45327 | −1.73473 | −0.867363 | − | 0.497677i | \(-0.834187\pi\) | ||||
−0.867363 | + | 0.497677i | \(0.834187\pi\) | |||||||
\(3\) | 3.30020 | 1.90537 | 0.952686 | − | 0.303958i | \(-0.0983081\pi\) | ||||
0.952686 | + | 0.303958i | \(0.0983081\pi\) | |||||||
\(4\) | 4.01854 | 2.00927 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −8.09629 | −3.30530 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −4.95203 | −1.75081 | ||||||||
\(9\) | 7.89132 | 2.63044 | ||||||||
\(10\) | −2.45327 | −0.775793 | ||||||||
\(11\) | 4.61648 | 1.39192 | 0.695960 | − | 0.718080i | \(-0.254979\pi\) | ||||
0.695960 | + | 0.718080i | \(0.254979\pi\) | |||||||
\(12\) | 13.2620 | 3.82841 | ||||||||
\(13\) | 4.15190 | 1.15153 | 0.575766 | − | 0.817615i | \(-0.304704\pi\) | ||||
0.575766 | + | 0.817615i | \(0.304704\pi\) | |||||||
\(14\) | −2.45327 | −0.655664 | ||||||||
\(15\) | 3.30020 | 0.852108 | ||||||||
\(16\) | 4.11160 | 1.02790 | ||||||||
\(17\) | −4.49719 | −1.09073 | −0.545365 | − | 0.838199i | \(-0.683609\pi\) | ||||
−0.545365 | + | 0.838199i | \(0.683609\pi\) | |||||||
\(18\) | −19.3595 | −4.56309 | ||||||||
\(19\) | 1.21864 | 0.279575 | 0.139788 | − | 0.990181i | \(-0.455358\pi\) | ||||
0.139788 | + | 0.990181i | \(0.455358\pi\) | |||||||
\(20\) | 4.01854 | 0.898573 | ||||||||
\(21\) | 3.30020 | 0.720163 | ||||||||
\(22\) | −11.3255 | −2.41460 | ||||||||
\(23\) | 5.38266 | 1.12236 | 0.561181 | − | 0.827693i | \(-0.310347\pi\) | ||||
0.561181 | + | 0.827693i | \(0.310347\pi\) | |||||||
\(24\) | −16.3427 | −3.33594 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −10.1857 | −1.99759 | ||||||||
\(27\) | 16.1423 | 3.10659 | ||||||||
\(28\) | 4.01854 | 0.759433 | ||||||||
\(29\) | −7.49271 | −1.39136 | −0.695681 | − | 0.718351i | \(-0.744897\pi\) | ||||
−0.695681 | + | 0.718351i | \(0.744897\pi\) | |||||||
\(30\) | −8.09629 | −1.47817 | ||||||||
\(31\) | 1.81401 | 0.325805 | 0.162902 | − | 0.986642i | \(-0.447914\pi\) | ||||
0.162902 | + | 0.986642i | \(0.447914\pi\) | |||||||
\(32\) | −0.182804 | −0.0323154 | ||||||||
\(33\) | 15.2353 | 2.65213 | ||||||||
\(34\) | 11.0328 | 1.89212 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 31.7116 | 5.28527 | ||||||||
\(37\) | 2.04212 | 0.335723 | 0.167861 | − | 0.985811i | \(-0.446314\pi\) | ||||
0.167861 | + | 0.985811i | \(0.446314\pi\) | |||||||
\(38\) | −2.98966 | −0.484987 | ||||||||
\(39\) | 13.7021 | 2.19409 | ||||||||
\(40\) | −4.95203 | −0.782985 | ||||||||
\(41\) | −12.0969 | −1.88922 | −0.944611 | − | 0.328193i | \(-0.893560\pi\) | ||||
−0.944611 | + | 0.328193i | \(0.893560\pi\) | |||||||
\(42\) | −8.09629 | −1.24928 | ||||||||
\(43\) | −3.37469 | −0.514635 | −0.257318 | − | 0.966327i | \(-0.582839\pi\) | ||||
−0.257318 | + | 0.966327i | \(0.582839\pi\) | |||||||
\(44\) | 18.5515 | 2.79675 | ||||||||
\(45\) | 7.89132 | 1.17637 | ||||||||
\(46\) | −13.2051 | −1.94699 | ||||||||
\(47\) | −1.81914 | −0.265349 | −0.132674 | − | 0.991160i | \(-0.542356\pi\) | ||||
−0.132674 | + | 0.991160i | \(0.542356\pi\) | |||||||
\(48\) | 13.5691 | 1.95853 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.45327 | −0.346945 | ||||||||
\(51\) | −14.8416 | −2.07825 | ||||||||
\(52\) | 16.6846 | 2.31374 | ||||||||
\(53\) | 1.43972 | 0.197761 | 0.0988805 | − | 0.995099i | \(-0.468474\pi\) | ||||
0.0988805 | + | 0.995099i | \(0.468474\pi\) | |||||||
\(54\) | −39.6015 | −5.38908 | ||||||||
\(55\) | 4.61648 | 0.622486 | ||||||||
\(56\) | −4.95203 | −0.661743 | ||||||||
\(57\) | 4.02176 | 0.532695 | ||||||||
\(58\) | 18.3817 | 2.41363 | ||||||||
\(59\) | −13.3062 | −1.73233 | −0.866163 | − | 0.499761i | \(-0.833421\pi\) | ||||
−0.866163 | + | 0.499761i | \(0.833421\pi\) | |||||||
\(60\) | 13.2620 | 1.71212 | ||||||||
\(61\) | 11.6444 | 1.49091 | 0.745455 | − | 0.666555i | \(-0.232232\pi\) | ||||
0.745455 | + | 0.666555i | \(0.232232\pi\) | |||||||
\(62\) | −4.45025 | −0.565182 | ||||||||
\(63\) | 7.89132 | 0.994213 | ||||||||
\(64\) | −7.77473 | −0.971841 | ||||||||
\(65\) | 4.15190 | 0.514980 | ||||||||
\(66\) | −37.3763 | −4.60071 | ||||||||
\(67\) | −13.1845 | −1.61075 | −0.805374 | − | 0.592767i | \(-0.798035\pi\) | ||||
−0.805374 | + | 0.592767i | \(0.798035\pi\) | |||||||
\(68\) | −18.0722 | −2.19157 | ||||||||
\(69\) | 17.7638 | 2.13851 | ||||||||
\(70\) | −2.45327 | −0.293222 | ||||||||
\(71\) | 16.7367 | 1.98628 | 0.993142 | − | 0.116912i | \(-0.0372995\pi\) | ||||
0.993142 | + | 0.116912i | \(0.0372995\pi\) | |||||||
\(72\) | −39.0781 | −4.60539 | ||||||||
\(73\) | 7.06439 | 0.826824 | 0.413412 | − | 0.910544i | \(-0.364337\pi\) | ||||
0.413412 | + | 0.910544i | \(0.364337\pi\) | |||||||
\(74\) | −5.00988 | −0.582387 | ||||||||
\(75\) | 3.30020 | 0.381074 | ||||||||
\(76\) | 4.89716 | 0.561743 | ||||||||
\(77\) | 4.61648 | 0.526097 | ||||||||
\(78\) | −33.6150 | −3.80615 | ||||||||
\(79\) | 6.79534 | 0.764536 | 0.382268 | − | 0.924052i | \(-0.375143\pi\) | ||||
0.382268 | + | 0.924052i | \(0.375143\pi\) | |||||||
\(80\) | 4.11160 | 0.459691 | ||||||||
\(81\) | 29.5989 | 3.28877 | ||||||||
\(82\) | 29.6770 | 3.27728 | ||||||||
\(83\) | 10.3347 | 1.13438 | 0.567191 | − | 0.823586i | \(-0.308030\pi\) | ||||
0.567191 | + | 0.823586i | \(0.308030\pi\) | |||||||
\(84\) | 13.2620 | 1.44700 | ||||||||
\(85\) | −4.49719 | −0.487789 | ||||||||
\(86\) | 8.27903 | 0.892750 | ||||||||
\(87\) | −24.7274 | −2.65106 | ||||||||
\(88\) | −22.8610 | −2.43699 | ||||||||
\(89\) | 13.0073 | 1.37877 | 0.689384 | − | 0.724396i | \(-0.257881\pi\) | ||||
0.689384 | + | 0.724396i | \(0.257881\pi\) | |||||||
\(90\) | −19.3595 | −2.04068 | ||||||||
\(91\) | 4.15190 | 0.435238 | ||||||||
\(92\) | 21.6304 | 2.25513 | ||||||||
\(93\) | 5.98658 | 0.620779 | ||||||||
\(94\) | 4.46284 | 0.460307 | ||||||||
\(95\) | 1.21864 | 0.125030 | ||||||||
\(96\) | −0.603289 | −0.0615729 | ||||||||
\(97\) | −9.66911 | −0.981749 | −0.490875 | − | 0.871230i | \(-0.663323\pi\) | ||||
−0.490875 | + | 0.871230i | \(0.663323\pi\) | |||||||
\(98\) | −2.45327 | −0.247818 | ||||||||
\(99\) | 36.4301 | 3.66136 | ||||||||
\(100\) | 4.01854 | 0.401854 | ||||||||
\(101\) | −5.59560 | −0.556783 | −0.278392 | − | 0.960468i | \(-0.589801\pi\) | ||||
−0.278392 | + | 0.960468i | \(0.589801\pi\) | |||||||
\(102\) | 36.4106 | 3.60518 | ||||||||
\(103\) | 1.33116 | 0.131163 | 0.0655815 | − | 0.997847i | \(-0.479110\pi\) | ||||
0.0655815 | + | 0.997847i | \(0.479110\pi\) | |||||||
\(104\) | −20.5604 | −2.01611 | ||||||||
\(105\) | 3.30020 | 0.322067 | ||||||||
\(106\) | −3.53203 | −0.343061 | ||||||||
\(107\) | −0.787195 | −0.0761010 | −0.0380505 | − | 0.999276i | \(-0.512115\pi\) | ||||
−0.0380505 | + | 0.999276i | \(0.512115\pi\) | |||||||
\(108\) | 64.8686 | 6.24199 | ||||||||
\(109\) | 6.36750 | 0.609895 | 0.304948 | − | 0.952369i | \(-0.401361\pi\) | ||||
0.304948 | + | 0.952369i | \(0.401361\pi\) | |||||||
\(110\) | −11.3255 | −1.07984 | ||||||||
\(111\) | 6.73941 | 0.639676 | ||||||||
\(112\) | 4.11160 | 0.388510 | ||||||||
\(113\) | 8.04862 | 0.757151 | 0.378575 | − | 0.925571i | \(-0.376414\pi\) | ||||
0.378575 | + | 0.925571i | \(0.376414\pi\) | |||||||
\(114\) | −9.86647 | −0.924080 | ||||||||
\(115\) | 5.38266 | 0.501935 | ||||||||
\(116\) | −30.1098 | −2.79562 | ||||||||
\(117\) | 32.7640 | 3.02903 | ||||||||
\(118\) | 32.6438 | 3.00511 | ||||||||
\(119\) | −4.49719 | −0.412257 | ||||||||
\(120\) | −16.3427 | −1.49188 | ||||||||
\(121\) | 10.3119 | 0.937443 | ||||||||
\(122\) | −28.5668 | −2.58632 | ||||||||
\(123\) | −39.9223 | −3.59967 | ||||||||
\(124\) | 7.28966 | 0.654630 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −19.3595 | −1.72469 | ||||||||
\(127\) | −10.7748 | −0.956106 | −0.478053 | − | 0.878331i | \(-0.658657\pi\) | ||||
−0.478053 | + | 0.878331i | \(0.658657\pi\) | |||||||
\(128\) | 19.4391 | 1.71819 | ||||||||
\(129\) | −11.1371 | −0.980571 | ||||||||
\(130\) | −10.1857 | −0.893349 | ||||||||
\(131\) | −13.3552 | −1.16685 | −0.583424 | − | 0.812168i | \(-0.698287\pi\) | ||||
−0.583424 | + | 0.812168i | \(0.698287\pi\) | |||||||
\(132\) | 61.2237 | 5.32884 | ||||||||
\(133\) | 1.21864 | 0.105670 | ||||||||
\(134\) | 32.3452 | 2.79420 | ||||||||
\(135\) | 16.1423 | 1.38931 | ||||||||
\(136\) | 22.2703 | 1.90966 | ||||||||
\(137\) | −18.4109 | −1.57295 | −0.786475 | − | 0.617622i | \(-0.788096\pi\) | ||||
−0.786475 | + | 0.617622i | \(0.788096\pi\) | |||||||
\(138\) | −43.5795 | −3.70974 | ||||||||
\(139\) | 2.35275 | 0.199558 | 0.0997790 | − | 0.995010i | \(-0.468186\pi\) | ||||
0.0997790 | + | 0.995010i | \(0.468186\pi\) | |||||||
\(140\) | 4.01854 | 0.339629 | ||||||||
\(141\) | −6.00352 | −0.505588 | ||||||||
\(142\) | −41.0598 | −3.44566 | ||||||||
\(143\) | 19.1672 | 1.60284 | ||||||||
\(144\) | 32.4459 | 2.70383 | ||||||||
\(145\) | −7.49271 | −0.622236 | ||||||||
\(146\) | −17.3309 | −1.43431 | ||||||||
\(147\) | 3.30020 | 0.272196 | ||||||||
\(148\) | 8.20635 | 0.674558 | ||||||||
\(149\) | 13.8937 | 1.13821 | 0.569107 | − | 0.822263i | \(-0.307289\pi\) | ||||
0.569107 | + | 0.822263i | \(0.307289\pi\) | |||||||
\(150\) | −8.09629 | −0.661059 | ||||||||
\(151\) | −7.29837 | −0.593933 | −0.296967 | − | 0.954888i | \(-0.595975\pi\) | ||||
−0.296967 | + | 0.954888i | \(0.595975\pi\) | |||||||
\(152\) | −6.03475 | −0.489483 | ||||||||
\(153\) | −35.4888 | −2.86910 | ||||||||
\(154\) | −11.3255 | −0.912633 | ||||||||
\(155\) | 1.81401 | 0.145704 | ||||||||
\(156\) | 55.0625 | 4.40853 | ||||||||
\(157\) | 14.5514 | 1.16132 | 0.580662 | − | 0.814144i | \(-0.302794\pi\) | ||||
0.580662 | + | 0.814144i | \(0.302794\pi\) | |||||||
\(158\) | −16.6708 | −1.32626 | ||||||||
\(159\) | 4.75137 | 0.376808 | ||||||||
\(160\) | −0.182804 | −0.0144519 | ||||||||
\(161\) | 5.38266 | 0.424213 | ||||||||
\(162\) | −72.6142 | −5.70511 | ||||||||
\(163\) | −12.9803 | −1.01670 | −0.508349 | − | 0.861151i | \(-0.669744\pi\) | ||||
−0.508349 | + | 0.861151i | \(0.669744\pi\) | |||||||
\(164\) | −48.6120 | −3.79596 | ||||||||
\(165\) | 15.2353 | 1.18607 | ||||||||
\(166\) | −25.3539 | −1.96784 | ||||||||
\(167\) | −11.2337 | −0.869290 | −0.434645 | − | 0.900602i | \(-0.643126\pi\) | ||||
−0.434645 | + | 0.900602i | \(0.643126\pi\) | |||||||
\(168\) | −16.3427 | −1.26087 | ||||||||
\(169\) | 4.23831 | 0.326024 | ||||||||
\(170\) | 11.0328 | 0.846180 | ||||||||
\(171\) | 9.61669 | 0.735406 | ||||||||
\(172\) | −13.5613 | −1.03404 | ||||||||
\(173\) | −23.7228 | −1.80361 | −0.901805 | − | 0.432144i | \(-0.857757\pi\) | ||||
−0.901805 | + | 0.432144i | \(0.857757\pi\) | |||||||
\(174\) | 60.6631 | 4.59886 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 18.9811 | 1.43075 | ||||||||
\(177\) | −43.9133 | −3.30072 | ||||||||
\(178\) | −31.9104 | −2.39178 | ||||||||
\(179\) | 10.2014 | 0.762489 | 0.381245 | − | 0.924474i | \(-0.375496\pi\) | ||||
0.381245 | + | 0.924474i | \(0.375496\pi\) | |||||||
\(180\) | 31.7116 | 2.36364 | ||||||||
\(181\) | 5.66186 | 0.420843 | 0.210421 | − | 0.977611i | \(-0.432516\pi\) | ||||
0.210421 | + | 0.977611i | \(0.432516\pi\) | |||||||
\(182\) | −10.1857 | −0.755018 | ||||||||
\(183\) | 38.4288 | 2.84074 | ||||||||
\(184\) | −26.6551 | −1.96504 | ||||||||
\(185\) | 2.04212 | 0.150140 | ||||||||
\(186\) | −14.6867 | −1.07688 | ||||||||
\(187\) | −20.7612 | −1.51821 | ||||||||
\(188\) | −7.31029 | −0.533157 | ||||||||
\(189\) | 16.1423 | 1.17418 | ||||||||
\(190\) | −2.98966 | −0.216893 | ||||||||
\(191\) | −13.5830 | −0.982833 | −0.491417 | − | 0.870925i | \(-0.663521\pi\) | ||||
−0.491417 | + | 0.870925i | \(0.663521\pi\) | |||||||
\(192\) | −25.6582 | −1.85172 | ||||||||
\(193\) | 12.9796 | 0.934293 | 0.467147 | − | 0.884180i | \(-0.345282\pi\) | ||||
0.467147 | + | 0.884180i | \(0.345282\pi\) | |||||||
\(194\) | 23.7210 | 1.70307 | ||||||||
\(195\) | 13.7021 | 0.981229 | ||||||||
\(196\) | 4.01854 | 0.287039 | ||||||||
\(197\) | −14.0268 | −0.999366 | −0.499683 | − | 0.866208i | \(-0.666550\pi\) | ||||
−0.499683 | + | 0.866208i | \(0.666550\pi\) | |||||||
\(198\) | −89.3729 | −6.35146 | ||||||||
\(199\) | 7.37991 | 0.523148 | 0.261574 | − | 0.965183i | \(-0.415758\pi\) | ||||
0.261574 | + | 0.965183i | \(0.415758\pi\) | |||||||
\(200\) | −4.95203 | −0.350162 | ||||||||
\(201\) | −43.5116 | −3.06907 | ||||||||
\(202\) | 13.7275 | 0.965866 | ||||||||
\(203\) | −7.49271 | −0.525885 | ||||||||
\(204\) | −59.6418 | −4.17576 | ||||||||
\(205\) | −12.0969 | −0.844886 | ||||||||
\(206\) | −3.26569 | −0.227532 | ||||||||
\(207\) | 42.4762 | 2.95230 | ||||||||
\(208\) | 17.0710 | 1.18366 | ||||||||
\(209\) | 5.62583 | 0.389147 | ||||||||
\(210\) | −8.09629 | −0.558697 | ||||||||
\(211\) | −5.75375 | −0.396104 | −0.198052 | − | 0.980191i | \(-0.563462\pi\) | ||||
−0.198052 | + | 0.980191i | \(0.563462\pi\) | |||||||
\(212\) | 5.78558 | 0.397355 | ||||||||
\(213\) | 55.2346 | 3.78461 | ||||||||
\(214\) | 1.93120 | 0.132014 | ||||||||
\(215\) | −3.37469 | −0.230152 | ||||||||
\(216\) | −79.9373 | −5.43905 | ||||||||
\(217\) | 1.81401 | 0.123143 | ||||||||
\(218\) | −15.6212 | −1.05800 | ||||||||
\(219\) | 23.3139 | 1.57541 | ||||||||
\(220\) | 18.5515 | 1.25074 | ||||||||
\(221\) | −18.6719 | −1.25601 | ||||||||
\(222\) | −16.5336 | −1.10966 | ||||||||
\(223\) | 19.3037 | 1.29267 | 0.646337 | − | 0.763052i | \(-0.276300\pi\) | ||||
0.646337 | + | 0.763052i | \(0.276300\pi\) | |||||||
\(224\) | −0.182804 | −0.0122141 | ||||||||
\(225\) | 7.89132 | 0.526088 | ||||||||
\(226\) | −19.7455 | −1.31345 | ||||||||
\(227\) | 19.0919 | 1.26717 | 0.633586 | − | 0.773672i | \(-0.281582\pi\) | ||||
0.633586 | + | 0.773672i | \(0.281582\pi\) | |||||||
\(228\) | 16.1616 | 1.07033 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | −13.2051 | −0.870720 | ||||||||
\(231\) | 15.2353 | 1.00241 | ||||||||
\(232\) | 37.1041 | 2.43601 | ||||||||
\(233\) | −6.16648 | −0.403980 | −0.201990 | − | 0.979388i | \(-0.564741\pi\) | ||||
−0.201990 | + | 0.979388i | \(0.564741\pi\) | |||||||
\(234\) | −80.3790 | −5.25454 | ||||||||
\(235\) | −1.81914 | −0.118668 | ||||||||
\(236\) | −53.4717 | −3.48071 | ||||||||
\(237\) | 22.4260 | 1.45672 | ||||||||
\(238\) | 11.0328 | 0.715153 | ||||||||
\(239\) | −22.2256 | −1.43766 | −0.718829 | − | 0.695187i | \(-0.755321\pi\) | ||||
−0.718829 | + | 0.695187i | \(0.755321\pi\) | |||||||
\(240\) | 13.5691 | 0.875882 | ||||||||
\(241\) | 4.00615 | 0.258059 | 0.129030 | − | 0.991641i | \(-0.458814\pi\) | ||||
0.129030 | + | 0.991641i | \(0.458814\pi\) | |||||||
\(242\) | −25.2978 | −1.62621 | ||||||||
\(243\) | 49.2554 | 3.15974 | ||||||||
\(244\) | 46.7935 | 2.99564 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 97.9401 | 6.24443 | ||||||||
\(247\) | 5.05968 | 0.321940 | ||||||||
\(248\) | −8.98301 | −0.570422 | ||||||||
\(249\) | 34.1066 | 2.16142 | ||||||||
\(250\) | −2.45327 | −0.155159 | ||||||||
\(251\) | 26.4902 | 1.67205 | 0.836024 | − | 0.548693i | \(-0.184874\pi\) | ||||
0.836024 | + | 0.548693i | \(0.184874\pi\) | |||||||
\(252\) | 31.7116 | 1.99764 | ||||||||
\(253\) | 24.8489 | 1.56224 | ||||||||
\(254\) | 26.4334 | 1.65858 | ||||||||
\(255\) | −14.8416 | −0.929420 | ||||||||
\(256\) | −32.1400 | −2.00875 | ||||||||
\(257\) | −11.3636 | −0.708844 | −0.354422 | − | 0.935086i | \(-0.615322\pi\) | ||||
−0.354422 | + | 0.935086i | \(0.615322\pi\) | |||||||
\(258\) | 27.3224 | 1.70102 | ||||||||
\(259\) | 2.04212 | 0.126891 | ||||||||
\(260\) | 16.6846 | 1.03474 | ||||||||
\(261\) | −59.1273 | −3.65989 | ||||||||
\(262\) | 32.7639 | 2.02416 | ||||||||
\(263\) | 6.04432 | 0.372709 | 0.186355 | − | 0.982483i | \(-0.440333\pi\) | ||||
0.186355 | + | 0.982483i | \(0.440333\pi\) | |||||||
\(264\) | −75.4457 | −4.64336 | ||||||||
\(265\) | 1.43972 | 0.0884414 | ||||||||
\(266\) | −2.98966 | −0.183308 | ||||||||
\(267\) | 42.9266 | 2.62706 | ||||||||
\(268\) | −52.9826 | −3.23643 | ||||||||
\(269\) | 3.06868 | 0.187101 | 0.0935503 | − | 0.995615i | \(-0.470178\pi\) | ||||
0.0935503 | + | 0.995615i | \(0.470178\pi\) | |||||||
\(270\) | −39.6015 | −2.41007 | ||||||||
\(271\) | −10.2213 | −0.620898 | −0.310449 | − | 0.950590i | \(-0.600479\pi\) | ||||
−0.310449 | + | 0.950590i | \(0.600479\pi\) | |||||||
\(272\) | −18.4907 | −1.12116 | ||||||||
\(273\) | 13.7021 | 0.829290 | ||||||||
\(274\) | 45.1670 | 2.72864 | ||||||||
\(275\) | 4.61648 | 0.278384 | ||||||||
\(276\) | 71.3847 | 4.29686 | ||||||||
\(277\) | −17.7750 | −1.06800 | −0.533998 | − | 0.845486i | \(-0.679311\pi\) | ||||
−0.533998 | + | 0.845486i | \(0.679311\pi\) | |||||||
\(278\) | −5.77194 | −0.346178 | ||||||||
\(279\) | 14.3149 | 0.857010 | ||||||||
\(280\) | −4.95203 | −0.295941 | ||||||||
\(281\) | 3.15666 | 0.188311 | 0.0941553 | − | 0.995558i | \(-0.469985\pi\) | ||||
0.0941553 | + | 0.995558i | \(0.469985\pi\) | |||||||
\(282\) | 14.7283 | 0.877055 | ||||||||
\(283\) | −9.90363 | −0.588710 | −0.294355 | − | 0.955696i | \(-0.595105\pi\) | ||||
−0.294355 | + | 0.955696i | \(0.595105\pi\) | |||||||
\(284\) | 67.2573 | 3.99098 | ||||||||
\(285\) | 4.02176 | 0.238228 | ||||||||
\(286\) | −47.0223 | −2.78049 | ||||||||
\(287\) | −12.0969 | −0.714059 | ||||||||
\(288\) | −1.44256 | −0.0850038 | ||||||||
\(289\) | 3.22476 | 0.189692 | ||||||||
\(290\) | 18.3817 | 1.07941 | ||||||||
\(291\) | −31.9100 | −1.87060 | ||||||||
\(292\) | 28.3886 | 1.66131 | ||||||||
\(293\) | −28.0058 | −1.63612 | −0.818058 | − | 0.575135i | \(-0.804949\pi\) | ||||
−0.818058 | + | 0.575135i | \(0.804949\pi\) | |||||||
\(294\) | −8.09629 | −0.472185 | ||||||||
\(295\) | −13.3062 | −0.774720 | ||||||||
\(296\) | −10.1127 | −0.587786 | ||||||||
\(297\) | 74.5207 | 4.32413 | ||||||||
\(298\) | −34.0850 | −1.97449 | ||||||||
\(299\) | 22.3483 | 1.29243 | ||||||||
\(300\) | 13.2620 | 0.765682 | ||||||||
\(301\) | −3.37469 | −0.194514 | ||||||||
\(302\) | 17.9049 | 1.03031 | ||||||||
\(303\) | −18.4666 | −1.06088 | ||||||||
\(304\) | 5.01057 | 0.287376 | ||||||||
\(305\) | 11.6444 | 0.666756 | ||||||||
\(306\) | 87.0637 | 4.97710 | ||||||||
\(307\) | −3.46077 | −0.197517 | −0.0987583 | − | 0.995111i | \(-0.531487\pi\) | ||||
−0.0987583 | + | 0.995111i | \(0.531487\pi\) | |||||||
\(308\) | 18.5515 | 1.05707 | ||||||||
\(309\) | 4.39309 | 0.249914 | ||||||||
\(310\) | −4.45025 | −0.252757 | ||||||||
\(311\) | −1.47297 | −0.0835245 | −0.0417622 | − | 0.999128i | \(-0.513297\pi\) | ||||
−0.0417622 | + | 0.999128i | \(0.513297\pi\) | |||||||
\(312\) | −67.8533 | −3.84144 | ||||||||
\(313\) | −7.83996 | −0.443141 | −0.221570 | − | 0.975144i | \(-0.571118\pi\) | ||||
−0.221570 | + | 0.975144i | \(0.571118\pi\) | |||||||
\(314\) | −35.6984 | −2.01458 | ||||||||
\(315\) | 7.89132 | 0.444625 | ||||||||
\(316\) | 27.3074 | 1.53616 | ||||||||
\(317\) | −16.8953 | −0.948935 | −0.474468 | − | 0.880273i | \(-0.657359\pi\) | ||||
−0.474468 | + | 0.880273i | \(0.657359\pi\) | |||||||
\(318\) | −11.6564 | −0.653658 | ||||||||
\(319\) | −34.5899 | −1.93666 | ||||||||
\(320\) | −7.77473 | −0.434621 | ||||||||
\(321\) | −2.59790 | −0.145001 | ||||||||
\(322\) | −13.2051 | −0.735892 | ||||||||
\(323\) | −5.48047 | −0.304941 | ||||||||
\(324\) | 118.945 | 6.60803 | ||||||||
\(325\) | 4.15190 | 0.230306 | ||||||||
\(326\) | 31.8443 | 1.76369 | ||||||||
\(327\) | 21.0140 | 1.16208 | ||||||||
\(328\) | 59.9044 | 3.30766 | ||||||||
\(329\) | −1.81914 | −0.100292 | ||||||||
\(330\) | −37.3763 | −2.05750 | ||||||||
\(331\) | 14.4108 | 0.792087 | 0.396043 | − | 0.918232i | \(-0.370383\pi\) | ||||
0.396043 | + | 0.918232i | \(0.370383\pi\) | |||||||
\(332\) | 41.5305 | 2.27928 | ||||||||
\(333\) | 16.1150 | 0.883098 | ||||||||
\(334\) | 27.5593 | 1.50798 | ||||||||
\(335\) | −13.1845 | −0.720348 | ||||||||
\(336\) | 13.5691 | 0.740255 | ||||||||
\(337\) | 28.7195 | 1.56445 | 0.782224 | − | 0.622997i | \(-0.214085\pi\) | ||||
0.782224 | + | 0.622997i | \(0.214085\pi\) | |||||||
\(338\) | −10.3977 | −0.565562 | ||||||||
\(339\) | 26.5621 | 1.44265 | ||||||||
\(340\) | −18.0722 | −0.980101 | ||||||||
\(341\) | 8.37431 | 0.453495 | ||||||||
\(342\) | −23.5923 | −1.27573 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 16.7116 | 0.901027 | ||||||||
\(345\) | 17.7638 | 0.956373 | ||||||||
\(346\) | 58.1984 | 3.12877 | ||||||||
\(347\) | −14.9099 | −0.800407 | −0.400204 | − | 0.916426i | \(-0.631061\pi\) | ||||
−0.400204 | + | 0.916426i | \(0.631061\pi\) | |||||||
\(348\) | −99.3682 | −5.32670 | ||||||||
\(349\) | −33.0642 | −1.76988 | −0.884942 | − | 0.465702i | \(-0.845802\pi\) | ||||
−0.884942 | + | 0.465702i | \(0.845802\pi\) | |||||||
\(350\) | −2.45327 | −0.131133 | ||||||||
\(351\) | 67.0214 | 3.57734 | ||||||||
\(352\) | −0.843909 | −0.0449805 | ||||||||
\(353\) | 33.7031 | 1.79384 | 0.896918 | − | 0.442197i | \(-0.145801\pi\) | ||||
0.896918 | + | 0.442197i | \(0.145801\pi\) | |||||||
\(354\) | 107.731 | 5.72585 | ||||||||
\(355\) | 16.7367 | 0.888293 | ||||||||
\(356\) | 52.2703 | 2.77032 | ||||||||
\(357\) | −14.8416 | −0.785503 | ||||||||
\(358\) | −25.0268 | −1.32271 | ||||||||
\(359\) | 20.5452 | 1.08434 | 0.542168 | − | 0.840270i | \(-0.317604\pi\) | ||||
0.542168 | + | 0.840270i | \(0.317604\pi\) | |||||||
\(360\) | −39.0781 | −2.05960 | ||||||||
\(361\) | −17.5149 | −0.921838 | ||||||||
\(362\) | −13.8901 | −0.730046 | ||||||||
\(363\) | 34.0312 | 1.78618 | ||||||||
\(364\) | 16.6846 | 0.874511 | ||||||||
\(365\) | 7.06439 | 0.369767 | ||||||||
\(366\) | −94.2763 | −4.92790 | ||||||||
\(367\) | 34.1882 | 1.78461 | 0.892304 | − | 0.451435i | \(-0.149088\pi\) | ||||
0.892304 | + | 0.451435i | \(0.149088\pi\) | |||||||
\(368\) | 22.1313 | 1.15367 | ||||||||
\(369\) | −95.4606 | −4.96948 | ||||||||
\(370\) | −5.00988 | −0.260451 | ||||||||
\(371\) | 1.43972 | 0.0747466 | ||||||||
\(372\) | 24.0573 | 1.24731 | ||||||||
\(373\) | −16.4680 | −0.852680 | −0.426340 | − | 0.904563i | \(-0.640197\pi\) | ||||
−0.426340 | + | 0.904563i | \(0.640197\pi\) | |||||||
\(374\) | 50.9329 | 2.63368 | ||||||||
\(375\) | 3.30020 | 0.170422 | ||||||||
\(376\) | 9.00843 | 0.464575 | ||||||||
\(377\) | −31.1090 | −1.60220 | ||||||||
\(378\) | −39.6015 | −2.03688 | ||||||||
\(379\) | 12.8552 | 0.660330 | 0.330165 | − | 0.943923i | \(-0.392896\pi\) | ||||
0.330165 | + | 0.943923i | \(0.392896\pi\) | |||||||
\(380\) | 4.89716 | 0.251219 | ||||||||
\(381\) | −35.5589 | −1.82174 | ||||||||
\(382\) | 33.3228 | 1.70495 | ||||||||
\(383\) | −20.6000 | −1.05261 | −0.526305 | − | 0.850296i | \(-0.676423\pi\) | ||||
−0.526305 | + | 0.850296i | \(0.676423\pi\) | |||||||
\(384\) | 64.1530 | 3.27380 | ||||||||
\(385\) | 4.61648 | 0.235278 | ||||||||
\(386\) | −31.8425 | −1.62074 | ||||||||
\(387\) | −26.6307 | −1.35372 | ||||||||
\(388\) | −38.8557 | −1.97260 | ||||||||
\(389\) | −37.8831 | −1.92075 | −0.960375 | − | 0.278712i | \(-0.910092\pi\) | ||||
−0.960375 | + | 0.278712i | \(0.910092\pi\) | |||||||
\(390\) | −33.6150 | −1.70216 | ||||||||
\(391\) | −24.2069 | −1.22419 | ||||||||
\(392\) | −4.95203 | −0.250115 | ||||||||
\(393\) | −44.0748 | −2.22328 | ||||||||
\(394\) | 34.4115 | 1.73362 | ||||||||
\(395\) | 6.79534 | 0.341911 | ||||||||
\(396\) | 146.396 | 7.35667 | ||||||||
\(397\) | −7.91886 | −0.397436 | −0.198718 | − | 0.980057i | \(-0.563678\pi\) | ||||
−0.198718 | + | 0.980057i | \(0.563678\pi\) | |||||||
\(398\) | −18.1049 | −0.907518 | ||||||||
\(399\) | 4.02176 | 0.201340 | ||||||||
\(400\) | 4.11160 | 0.205580 | ||||||||
\(401\) | 9.03341 | 0.451107 | 0.225554 | − | 0.974231i | \(-0.427581\pi\) | ||||
0.225554 | + | 0.974231i | \(0.427581\pi\) | |||||||
\(402\) | 106.746 | 5.32400 | ||||||||
\(403\) | 7.53158 | 0.375174 | ||||||||
\(404\) | −22.4862 | −1.11873 | ||||||||
\(405\) | 29.5989 | 1.47078 | ||||||||
\(406\) | 18.3817 | 0.912266 | ||||||||
\(407\) | 9.42741 | 0.467299 | ||||||||
\(408\) | 73.4963 | 3.63861 | ||||||||
\(409\) | −7.27221 | −0.359588 | −0.179794 | − | 0.983704i | \(-0.557543\pi\) | ||||
−0.179794 | + | 0.983704i | \(0.557543\pi\) | |||||||
\(410\) | 29.6770 | 1.46564 | ||||||||
\(411\) | −60.7597 | −2.99705 | ||||||||
\(412\) | 5.34932 | 0.263542 | ||||||||
\(413\) | −13.3062 | −0.654758 | ||||||||
\(414\) | −104.206 | −5.12143 | ||||||||
\(415\) | 10.3347 | 0.507311 | ||||||||
\(416\) | −0.758983 | −0.0372122 | ||||||||
\(417\) | 7.76456 | 0.380232 | ||||||||
\(418\) | −13.8017 | −0.675063 | ||||||||
\(419\) | 16.4955 | 0.805857 | 0.402929 | − | 0.915231i | \(-0.367992\pi\) | ||||
0.402929 | + | 0.915231i | \(0.367992\pi\) | |||||||
\(420\) | 13.2620 | 0.647119 | ||||||||
\(421\) | 25.2285 | 1.22956 | 0.614782 | − | 0.788697i | \(-0.289244\pi\) | ||||
0.614782 | + | 0.788697i | \(0.289244\pi\) | |||||||
\(422\) | 14.1155 | 0.687132 | ||||||||
\(423\) | −14.3554 | −0.697983 | ||||||||
\(424\) | −7.12955 | −0.346242 | ||||||||
\(425\) | −4.49719 | −0.218146 | ||||||||
\(426\) | −135.505 | −6.56526 | ||||||||
\(427\) | 11.6444 | 0.563511 | ||||||||
\(428\) | −3.16338 | −0.152908 | ||||||||
\(429\) | 63.2555 | 3.05400 | ||||||||
\(430\) | 8.27903 | 0.399250 | ||||||||
\(431\) | 21.0442 | 1.01366 | 0.506832 | − | 0.862045i | \(-0.330816\pi\) | ||||
0.506832 | + | 0.862045i | \(0.330816\pi\) | |||||||
\(432\) | 66.3708 | 3.19327 | ||||||||
\(433\) | −35.0983 | −1.68672 | −0.843358 | − | 0.537352i | \(-0.819425\pi\) | ||||
−0.843358 | + | 0.537352i | \(0.819425\pi\) | |||||||
\(434\) | −4.45025 | −0.213619 | ||||||||
\(435\) | −24.7274 | −1.18559 | ||||||||
\(436\) | 25.5881 | 1.22545 | ||||||||
\(437\) | 6.55953 | 0.313785 | ||||||||
\(438\) | −57.1953 | −2.73290 | ||||||||
\(439\) | 34.2094 | 1.63273 | 0.816363 | − | 0.577539i | \(-0.195987\pi\) | ||||
0.816363 | + | 0.577539i | \(0.195987\pi\) | |||||||
\(440\) | −22.8610 | −1.08985 | ||||||||
\(441\) | 7.89132 | 0.375777 | ||||||||
\(442\) | 45.8073 | 2.17883 | ||||||||
\(443\) | 0.739407 | 0.0351303 | 0.0175651 | − | 0.999846i | \(-0.494409\pi\) | ||||
0.0175651 | + | 0.999846i | \(0.494409\pi\) | |||||||
\(444\) | 27.0826 | 1.28528 | ||||||||
\(445\) | 13.0073 | 0.616604 | ||||||||
\(446\) | −47.3573 | −2.24243 | ||||||||
\(447\) | 45.8519 | 2.16872 | ||||||||
\(448\) | −7.77473 | −0.367322 | ||||||||
\(449\) | −11.9280 | −0.562917 | −0.281459 | − | 0.959573i | \(-0.590818\pi\) | ||||
−0.281459 | + | 0.959573i | \(0.590818\pi\) | |||||||
\(450\) | −19.3595 | −0.912618 | ||||||||
\(451\) | −55.8452 | −2.62965 | ||||||||
\(452\) | 32.3437 | 1.52132 | ||||||||
\(453\) | −24.0861 | −1.13166 | ||||||||
\(454\) | −46.8375 | −2.19819 | ||||||||
\(455\) | 4.15190 | 0.194644 | ||||||||
\(456\) | −19.9159 | −0.932647 | ||||||||
\(457\) | −17.4706 | −0.817241 | −0.408620 | − | 0.912704i | \(-0.633990\pi\) | ||||
−0.408620 | + | 0.912704i | \(0.633990\pi\) | |||||||
\(458\) | −2.45327 | −0.114634 | ||||||||
\(459\) | −72.5952 | −3.38845 | ||||||||
\(460\) | 21.6304 | 1.00852 | ||||||||
\(461\) | −25.5743 | −1.19111 | −0.595556 | − | 0.803314i | \(-0.703068\pi\) | ||||
−0.595556 | + | 0.803314i | \(0.703068\pi\) | |||||||
\(462\) | −37.3763 | −1.73890 | ||||||||
\(463\) | 23.0794 | 1.07259 | 0.536296 | − | 0.844030i | \(-0.319823\pi\) | ||||
0.536296 | + | 0.844030i | \(0.319823\pi\) | |||||||
\(464\) | −30.8070 | −1.43018 | ||||||||
\(465\) | 5.98658 | 0.277621 | ||||||||
\(466\) | 15.1281 | 0.700794 | ||||||||
\(467\) | −11.9470 | −0.552841 | −0.276421 | − | 0.961037i | \(-0.589148\pi\) | ||||
−0.276421 | + | 0.961037i | \(0.589148\pi\) | |||||||
\(468\) | 131.664 | 6.08615 | ||||||||
\(469\) | −13.1845 | −0.608805 | ||||||||
\(470\) | 4.46284 | 0.205856 | ||||||||
\(471\) | 48.0224 | 2.21275 | ||||||||
\(472\) | 65.8930 | 3.03297 | ||||||||
\(473\) | −15.5792 | −0.716331 | ||||||||
\(474\) | −55.0170 | −2.52702 | ||||||||
\(475\) | 1.21864 | 0.0559151 | ||||||||
\(476\) | −18.0722 | −0.828337 | ||||||||
\(477\) | 11.3613 | 0.520198 | ||||||||
\(478\) | 54.5255 | 2.49394 | ||||||||
\(479\) | 16.4726 | 0.752652 | 0.376326 | − | 0.926487i | \(-0.377187\pi\) | ||||
0.376326 | + | 0.926487i | \(0.377187\pi\) | |||||||
\(480\) | −0.603289 | −0.0275362 | ||||||||
\(481\) | 8.47869 | 0.386595 | ||||||||
\(482\) | −9.82818 | −0.447662 | ||||||||
\(483\) | 17.7638 | 0.808283 | ||||||||
\(484\) | 41.4387 | 1.88358 | ||||||||
\(485\) | −9.66911 | −0.439052 | ||||||||
\(486\) | −120.837 | −5.48128 | ||||||||
\(487\) | 24.8391 | 1.12557 | 0.562783 | − | 0.826605i | \(-0.309731\pi\) | ||||
0.562783 | + | 0.826605i | \(0.309731\pi\) | |||||||
\(488\) | −57.6634 | −2.61030 | ||||||||
\(489\) | −42.8376 | −1.93719 | ||||||||
\(490\) | −2.45327 | −0.110828 | ||||||||
\(491\) | −14.4555 | −0.652366 | −0.326183 | − | 0.945307i | \(-0.605763\pi\) | ||||
−0.326183 | + | 0.945307i | \(0.605763\pi\) | |||||||
\(492\) | −160.429 | −7.23271 | ||||||||
\(493\) | 33.6962 | 1.51760 | ||||||||
\(494\) | −12.4128 | −0.558477 | ||||||||
\(495\) | 36.4301 | 1.63741 | ||||||||
\(496\) | 7.45846 | 0.334895 | ||||||||
\(497\) | 16.7367 | 0.750745 | ||||||||
\(498\) | −83.6728 | −3.74947 | ||||||||
\(499\) | 29.5204 | 1.32151 | 0.660757 | − | 0.750600i | \(-0.270235\pi\) | ||||
0.660757 | + | 0.750600i | \(0.270235\pi\) | |||||||
\(500\) | 4.01854 | 0.179715 | ||||||||
\(501\) | −37.0735 | −1.65632 | ||||||||
\(502\) | −64.9877 | −2.90054 | ||||||||
\(503\) | −25.8441 | −1.15233 | −0.576165 | − | 0.817333i | \(-0.695451\pi\) | ||||
−0.576165 | + | 0.817333i | \(0.695451\pi\) | |||||||
\(504\) | −39.0781 | −1.74068 | ||||||||
\(505\) | −5.59560 | −0.249001 | ||||||||
\(506\) | −60.9611 | −2.71005 | ||||||||
\(507\) | 13.9873 | 0.621196 | ||||||||
\(508\) | −43.2989 | −1.92108 | ||||||||
\(509\) | −27.9714 | −1.23981 | −0.619905 | − | 0.784677i | \(-0.712829\pi\) | ||||
−0.619905 | + | 0.784677i | \(0.712829\pi\) | |||||||
\(510\) | 36.4106 | 1.61229 | ||||||||
\(511\) | 7.06439 | 0.312510 | ||||||||
\(512\) | 39.9699 | 1.76644 | ||||||||
\(513\) | 19.6717 | 0.868527 | ||||||||
\(514\) | 27.8781 | 1.22965 | ||||||||
\(515\) | 1.33116 | 0.0586579 | ||||||||
\(516\) | −44.7551 | −1.97023 | ||||||||
\(517\) | −8.39801 | −0.369344 | ||||||||
\(518\) | −5.00988 | −0.220121 | ||||||||
\(519\) | −78.2899 | −3.43655 | ||||||||
\(520\) | −20.5604 | −0.901632 | ||||||||
\(521\) | −27.9086 | −1.22270 | −0.611350 | − | 0.791360i | \(-0.709373\pi\) | ||||
−0.611350 | + | 0.791360i | \(0.709373\pi\) | |||||||
\(522\) | 145.055 | 6.34890 | ||||||||
\(523\) | −10.7976 | −0.472146 | −0.236073 | − | 0.971735i | \(-0.575860\pi\) | ||||
−0.236073 | + | 0.971735i | \(0.575860\pi\) | |||||||
\(524\) | −53.6684 | −2.34451 | ||||||||
\(525\) | 3.30020 | 0.144033 | ||||||||
\(526\) | −14.8284 | −0.646548 | ||||||||
\(527\) | −8.15793 | −0.355365 | ||||||||
\(528\) | 62.6415 | 2.72612 | ||||||||
\(529\) | 5.97298 | 0.259695 | ||||||||
\(530\) | −3.53203 | −0.153421 | ||||||||
\(531\) | −105.004 | −4.55678 | ||||||||
\(532\) | 4.89716 | 0.212319 | ||||||||
\(533\) | −50.2253 | −2.17550 | ||||||||
\(534\) | −105.311 | −4.55723 | ||||||||
\(535\) | −0.787195 | −0.0340334 | ||||||||
\(536\) | 65.2903 | 2.82011 | ||||||||
\(537\) | 33.6667 | 1.45282 | ||||||||
\(538\) | −7.52830 | −0.324568 | ||||||||
\(539\) | 4.61648 | 0.198846 | ||||||||
\(540\) | 64.8686 | 2.79150 | ||||||||
\(541\) | −19.7792 | −0.850376 | −0.425188 | − | 0.905105i | \(-0.639792\pi\) | ||||
−0.425188 | + | 0.905105i | \(0.639792\pi\) | |||||||
\(542\) | 25.0755 | 1.07709 | ||||||||
\(543\) | 18.6853 | 0.801861 | ||||||||
\(544\) | 0.822104 | 0.0352474 | ||||||||
\(545\) | 6.36750 | 0.272754 | ||||||||
\(546\) | −33.6150 | −1.43859 | ||||||||
\(547\) | −16.2242 | −0.693697 | −0.346848 | − | 0.937921i | \(-0.612748\pi\) | ||||
−0.346848 | + | 0.937921i | \(0.612748\pi\) | |||||||
\(548\) | −73.9850 | −3.16048 | ||||||||
\(549\) | 91.8895 | 3.92175 | ||||||||
\(550\) | −11.3255 | −0.482920 | ||||||||
\(551\) | −9.13092 | −0.388990 | ||||||||
\(552\) | −87.9671 | −3.74413 | ||||||||
\(553\) | 6.79534 | 0.288967 | ||||||||
\(554\) | 43.6069 | 1.85268 | ||||||||
\(555\) | 6.73941 | 0.286072 | ||||||||
\(556\) | 9.45464 | 0.400966 | ||||||||
\(557\) | −23.3585 | −0.989732 | −0.494866 | − | 0.868969i | \(-0.664783\pi\) | ||||
−0.494866 | + | 0.868969i | \(0.664783\pi\) | |||||||
\(558\) | −35.1183 | −1.48668 | ||||||||
\(559\) | −14.0114 | −0.592618 | ||||||||
\(560\) | 4.11160 | 0.173747 | ||||||||
\(561\) | −68.5161 | −2.89275 | ||||||||
\(562\) | −7.74415 | −0.326667 | ||||||||
\(563\) | 0.640294 | 0.0269852 | 0.0134926 | − | 0.999909i | \(-0.495705\pi\) | ||||
0.0134926 | + | 0.999909i | \(0.495705\pi\) | |||||||
\(564\) | −24.1254 | −1.01586 | ||||||||
\(565\) | 8.04862 | 0.338608 | ||||||||
\(566\) | 24.2963 | 1.02125 | ||||||||
\(567\) | 29.5989 | 1.24304 | ||||||||
\(568\) | −82.8809 | −3.47760 | ||||||||
\(569\) | 45.2633 | 1.89754 | 0.948768 | − | 0.315974i | \(-0.102331\pi\) | ||||
0.948768 | + | 0.315974i | \(0.102331\pi\) | |||||||
\(570\) | −9.86647 | −0.413261 | ||||||||
\(571\) | −32.3691 | −1.35460 | −0.677302 | − | 0.735705i | \(-0.736851\pi\) | ||||
−0.677302 | + | 0.735705i | \(0.736851\pi\) | |||||||
\(572\) | 77.0241 | 3.22054 | ||||||||
\(573\) | −44.8267 | −1.87266 | ||||||||
\(574\) | 29.6770 | 1.23870 | ||||||||
\(575\) | 5.38266 | 0.224472 | ||||||||
\(576\) | −61.3529 | −2.55637 | ||||||||
\(577\) | 14.4879 | 0.603139 | 0.301569 | − | 0.953444i | \(-0.402489\pi\) | ||||
0.301569 | + | 0.953444i | \(0.402489\pi\) | |||||||
\(578\) | −7.91122 | −0.329063 | ||||||||
\(579\) | 42.8353 | 1.78018 | ||||||||
\(580\) | −30.1098 | −1.25024 | ||||||||
\(581\) | 10.3347 | 0.428756 | ||||||||
\(582\) | 78.2839 | 3.24497 | ||||||||
\(583\) | 6.64644 | 0.275268 | ||||||||
\(584\) | −34.9831 | −1.44761 | ||||||||
\(585\) | 32.7640 | 1.35462 | ||||||||
\(586\) | 68.7059 | 2.83821 | ||||||||
\(587\) | 6.32770 | 0.261172 | 0.130586 | − | 0.991437i | \(-0.458314\pi\) | ||||
0.130586 | + | 0.991437i | \(0.458314\pi\) | |||||||
\(588\) | 13.2620 | 0.546915 | ||||||||
\(589\) | 2.21062 | 0.0910871 | ||||||||
\(590\) | 32.6438 | 1.34393 | ||||||||
\(591\) | −46.2911 | −1.90416 | ||||||||
\(592\) | 8.39639 | 0.345089 | ||||||||
\(593\) | −27.5633 | −1.13189 | −0.565944 | − | 0.824444i | \(-0.691488\pi\) | ||||
−0.565944 | + | 0.824444i | \(0.691488\pi\) | |||||||
\(594\) | −182.820 | −7.50118 | ||||||||
\(595\) | −4.49719 | −0.184367 | ||||||||
\(596\) | 55.8323 | 2.28698 | ||||||||
\(597\) | 24.3552 | 0.996791 | ||||||||
\(598\) | −54.8264 | −2.24202 | ||||||||
\(599\) | −14.0719 | −0.574962 | −0.287481 | − | 0.957786i | \(-0.592818\pi\) | ||||
−0.287481 | + | 0.957786i | \(0.592818\pi\) | |||||||
\(600\) | −16.3427 | −0.667188 | ||||||||
\(601\) | 27.9541 | 1.14027 | 0.570136 | − | 0.821550i | \(-0.306891\pi\) | ||||
0.570136 | + | 0.821550i | \(0.306891\pi\) | |||||||
\(602\) | 8.27903 | 0.337428 | ||||||||
\(603\) | −104.043 | −4.23697 | ||||||||
\(604\) | −29.3288 | −1.19337 | ||||||||
\(605\) | 10.3119 | 0.419237 | ||||||||
\(606\) | 45.3036 | 1.84033 | ||||||||
\(607\) | 24.5146 | 0.995016 | 0.497508 | − | 0.867459i | \(-0.334249\pi\) | ||||
0.497508 | + | 0.867459i | \(0.334249\pi\) | |||||||
\(608\) | −0.222772 | −0.00903460 | ||||||||
\(609\) | −24.7274 | −1.00201 | ||||||||
\(610\) | −28.5668 | −1.15664 | ||||||||
\(611\) | −7.55289 | −0.305557 | ||||||||
\(612\) | −142.613 | −5.76480 | ||||||||
\(613\) | −0.307384 | −0.0124151 | −0.00620755 | − | 0.999981i | \(-0.501976\pi\) | ||||
−0.00620755 | + | 0.999981i | \(0.501976\pi\) | |||||||
\(614\) | 8.49021 | 0.342637 | ||||||||
\(615\) | −39.9223 | −1.60982 | ||||||||
\(616\) | −22.8610 | −0.921094 | ||||||||
\(617\) | 22.9094 | 0.922298 | 0.461149 | − | 0.887323i | \(-0.347437\pi\) | ||||
0.461149 | + | 0.887323i | \(0.347437\pi\) | |||||||
\(618\) | −10.7774 | −0.433532 | ||||||||
\(619\) | −12.4559 | −0.500645 | −0.250323 | − | 0.968162i | \(-0.580537\pi\) | ||||
−0.250323 | + | 0.968162i | \(0.580537\pi\) | |||||||
\(620\) | 7.28966 | 0.292760 | ||||||||
\(621\) | 86.8886 | 3.48672 | ||||||||
\(622\) | 3.61360 | 0.144892 | ||||||||
\(623\) | 13.0073 | 0.521125 | ||||||||
\(624\) | 56.3376 | 2.25531 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 19.2335 | 0.768727 | ||||||||
\(627\) | 18.5664 | 0.741469 | ||||||||
\(628\) | 58.4752 | 2.33342 | ||||||||
\(629\) | −9.18382 | −0.366183 | ||||||||
\(630\) | −19.3595 | −0.771303 | ||||||||
\(631\) | 11.9901 | 0.477317 | 0.238658 | − | 0.971104i | \(-0.423292\pi\) | ||||
0.238658 | + | 0.971104i | \(0.423292\pi\) | |||||||
\(632\) | −33.6508 | −1.33856 | ||||||||
\(633\) | −18.9885 | −0.754726 | ||||||||
\(634\) | 41.4488 | 1.64614 | ||||||||
\(635\) | −10.7748 | −0.427584 | ||||||||
\(636\) | 19.0936 | 0.757110 | ||||||||
\(637\) | 4.15190 | 0.164504 | ||||||||
\(638\) | 84.8585 | 3.35958 | ||||||||
\(639\) | 132.075 | 5.22480 | ||||||||
\(640\) | 19.4391 | 0.768399 | ||||||||
\(641\) | −6.08927 | −0.240512 | −0.120256 | − | 0.992743i | \(-0.538371\pi\) | ||||
−0.120256 | + | 0.992743i | \(0.538371\pi\) | |||||||
\(642\) | 6.37335 | 0.251536 | ||||||||
\(643\) | −8.48814 | −0.334740 | −0.167370 | − | 0.985894i | \(-0.553527\pi\) | ||||
−0.167370 | + | 0.985894i | \(0.553527\pi\) | |||||||
\(644\) | 21.6304 | 0.852358 | ||||||||
\(645\) | −11.1371 | −0.438525 | ||||||||
\(646\) | 13.4451 | 0.528989 | ||||||||
\(647\) | −43.9773 | −1.72893 | −0.864464 | − | 0.502695i | \(-0.832342\pi\) | ||||
−0.864464 | + | 0.502695i | \(0.832342\pi\) | |||||||
\(648\) | −146.575 | −5.75801 | ||||||||
\(649\) | −61.4280 | −2.41126 | ||||||||
\(650\) | −10.1857 | −0.399518 | ||||||||
\(651\) | 5.98658 | 0.234633 | ||||||||
\(652\) | −52.1620 | −2.04282 | ||||||||
\(653\) | −5.71273 | −0.223556 | −0.111778 | − | 0.993733i | \(-0.535655\pi\) | ||||
−0.111778 | + | 0.993733i | \(0.535655\pi\) | |||||||
\(654\) | −51.5531 | −2.01588 | ||||||||
\(655\) | −13.3552 | −0.521830 | ||||||||
\(656\) | −49.7377 | −1.94193 | ||||||||
\(657\) | 55.7473 | 2.17491 | ||||||||
\(658\) | 4.46284 | 0.173980 | ||||||||
\(659\) | 25.4529 | 0.991503 | 0.495752 | − | 0.868464i | \(-0.334893\pi\) | ||||
0.495752 | + | 0.868464i | \(0.334893\pi\) | |||||||
\(660\) | 61.2237 | 2.38313 | ||||||||
\(661\) | 39.8580 | 1.55030 | 0.775148 | − | 0.631780i | \(-0.217675\pi\) | ||||
0.775148 | + | 0.631780i | \(0.217675\pi\) | |||||||
\(662\) | −35.3535 | −1.37405 | ||||||||
\(663\) | −61.6211 | −2.39316 | ||||||||
\(664\) | −51.1779 | −1.98609 | ||||||||
\(665\) | 1.21864 | 0.0472569 | ||||||||
\(666\) | −39.5346 | −1.53193 | ||||||||
\(667\) | −40.3307 | −1.56161 | ||||||||
\(668\) | −45.1431 | −1.74664 | ||||||||
\(669\) | 63.7062 | 2.46302 | ||||||||
\(670\) | 32.3452 | 1.24961 | ||||||||
\(671\) | 53.7561 | 2.07523 | ||||||||
\(672\) | −0.603289 | −0.0232724 | ||||||||
\(673\) | 14.6574 | 0.565002 | 0.282501 | − | 0.959267i | \(-0.408836\pi\) | ||||
0.282501 | + | 0.959267i | \(0.408836\pi\) | |||||||
\(674\) | −70.4566 | −2.71389 | ||||||||
\(675\) | 16.1423 | 0.621318 | ||||||||
\(676\) | 17.0318 | 0.655070 | ||||||||
\(677\) | −9.06983 | −0.348582 | −0.174291 | − | 0.984694i | \(-0.555763\pi\) | ||||
−0.174291 | + | 0.984694i | \(0.555763\pi\) | |||||||
\(678\) | −65.1639 | −2.50261 | ||||||||
\(679\) | −9.66911 | −0.371066 | ||||||||
\(680\) | 22.2703 | 0.854026 | ||||||||
\(681\) | 63.0070 | 2.41443 | ||||||||
\(682\) | −20.5445 | −0.786688 | ||||||||
\(683\) | 47.3216 | 1.81071 | 0.905355 | − | 0.424655i | \(-0.139605\pi\) | ||||
0.905355 | + | 0.424655i | \(0.139605\pi\) | |||||||
\(684\) | 38.6451 | 1.47763 | ||||||||
\(685\) | −18.4109 | −0.703445 | ||||||||
\(686\) | −2.45327 | −0.0936664 | ||||||||
\(687\) | 3.30020 | 0.125910 | ||||||||
\(688\) | −13.8754 | −0.528993 | ||||||||
\(689\) | 5.97759 | 0.227728 | ||||||||
\(690\) | −43.5795 | −1.65904 | ||||||||
\(691\) | 24.8451 | 0.945152 | 0.472576 | − | 0.881290i | \(-0.343324\pi\) | ||||
0.472576 | + | 0.881290i | \(0.343324\pi\) | |||||||
\(692\) | −95.3310 | −3.62394 | ||||||||
\(693\) | 36.4301 | 1.38386 | ||||||||
\(694\) | 36.5781 | 1.38849 | ||||||||
\(695\) | 2.35275 | 0.0892450 | ||||||||
\(696\) | 122.451 | 4.64150 | ||||||||
\(697\) | 54.4022 | 2.06063 | ||||||||
\(698\) | 81.1153 | 3.07026 | ||||||||
\(699\) | −20.3506 | −0.769731 | ||||||||
\(700\) | 4.01854 | 0.151887 | ||||||||
\(701\) | 12.4372 | 0.469747 | 0.234874 | − | 0.972026i | \(-0.424532\pi\) | ||||
0.234874 | + | 0.972026i | \(0.424532\pi\) | |||||||
\(702\) | −164.422 | −6.20570 | ||||||||
\(703\) | 2.48861 | 0.0938599 | ||||||||
\(704\) | −35.8919 | −1.35273 | ||||||||
\(705\) | −6.00352 | −0.226106 | ||||||||
\(706\) | −82.6829 | −3.11181 | ||||||||
\(707\) | −5.59560 | −0.210444 | ||||||||
\(708\) | −176.467 | −6.63205 | ||||||||
\(709\) | 42.5291 | 1.59721 | 0.798607 | − | 0.601853i | \(-0.205571\pi\) | ||||
0.798607 | + | 0.601853i | \(0.205571\pi\) | |||||||
\(710\) | −41.0598 | −1.54095 | ||||||||
\(711\) | 53.6242 | 2.01106 | ||||||||
\(712\) | −64.4124 | −2.41396 | ||||||||
\(713\) | 9.76416 | 0.365671 | ||||||||
\(714\) | 36.4106 | 1.36263 | ||||||||
\(715\) | 19.1672 | 0.716812 | ||||||||
\(716\) | 40.9948 | 1.53205 | ||||||||
\(717\) | −73.3490 | −2.73927 | ||||||||
\(718\) | −50.4030 | −1.88102 | ||||||||
\(719\) | −37.5115 | −1.39894 | −0.699472 | − | 0.714660i | \(-0.746581\pi\) | ||||
−0.699472 | + | 0.714660i | \(0.746581\pi\) | |||||||
\(720\) | 32.4459 | 1.20919 | ||||||||
\(721\) | 1.33116 | 0.0495749 | ||||||||
\(722\) | 42.9688 | 1.59913 | ||||||||
\(723\) | 13.2211 | 0.491698 | ||||||||
\(724\) | 22.7524 | 0.845587 | ||||||||
\(725\) | −7.49271 | −0.278272 | ||||||||
\(726\) | −83.4879 | −3.09853 | ||||||||
\(727\) | −13.9071 | −0.515785 | −0.257892 | − | 0.966174i | \(-0.583028\pi\) | ||||
−0.257892 | + | 0.966174i | \(0.583028\pi\) | |||||||
\(728\) | −20.5604 | −0.762018 | ||||||||
\(729\) | 73.7560 | 2.73170 | ||||||||
\(730\) | −17.3309 | −0.641444 | ||||||||
\(731\) | 15.1766 | 0.561328 | ||||||||
\(732\) | 154.428 | 5.70781 | ||||||||
\(733\) | −38.9654 | −1.43922 | −0.719610 | − | 0.694378i | \(-0.755680\pi\) | ||||
−0.719610 | + | 0.694378i | \(0.755680\pi\) | |||||||
\(734\) | −83.8729 | −3.09580 | ||||||||
\(735\) | 3.30020 | 0.121730 | ||||||||
\(736\) | −0.983969 | −0.0362696 | ||||||||
\(737\) | −60.8661 | −2.24203 | ||||||||
\(738\) | 234.191 | 8.62069 | ||||||||
\(739\) | 18.8906 | 0.694903 | 0.347451 | − | 0.937698i | \(-0.387047\pi\) | ||||
0.347451 | + | 0.937698i | \(0.387047\pi\) | |||||||
\(740\) | 8.20635 | 0.301672 | ||||||||
\(741\) | 16.6980 | 0.613415 | ||||||||
\(742\) | −3.53203 | −0.129665 | ||||||||
\(743\) | −22.8346 | −0.837722 | −0.418861 | − | 0.908050i | \(-0.637571\pi\) | ||||
−0.418861 | + | 0.908050i | \(0.637571\pi\) | |||||||
\(744\) | −29.6457 | −1.08687 | ||||||||
\(745\) | 13.8937 | 0.509025 | ||||||||
\(746\) | 40.4004 | 1.47917 | ||||||||
\(747\) | 81.5545 | 2.98392 | ||||||||
\(748\) | −83.4298 | −3.05049 | ||||||||
\(749\) | −0.787195 | −0.0287635 | ||||||||
\(750\) | −8.09629 | −0.295635 | ||||||||
\(751\) | 10.6325 | 0.387986 | 0.193993 | − | 0.981003i | \(-0.437856\pi\) | ||||
0.193993 | + | 0.981003i | \(0.437856\pi\) | |||||||
\(752\) | −7.47957 | −0.272752 | ||||||||
\(753\) | 87.4230 | 3.18587 | ||||||||
\(754\) | 76.3189 | 2.77937 | ||||||||
\(755\) | −7.29837 | −0.265615 | ||||||||
\(756\) | 64.8686 | 2.35925 | ||||||||
\(757\) | 5.70148 | 0.207224 | 0.103612 | − | 0.994618i | \(-0.466960\pi\) | ||||
0.103612 | + | 0.994618i | \(0.466960\pi\) | |||||||
\(758\) | −31.5374 | −1.14549 | ||||||||
\(759\) | 82.0064 | 2.97664 | ||||||||
\(760\) | −6.03475 | −0.218903 | ||||||||
\(761\) | −13.7575 | −0.498707 | −0.249354 | − | 0.968412i | \(-0.580218\pi\) | ||||
−0.249354 | + | 0.968412i | \(0.580218\pi\) | |||||||
\(762\) | 87.2356 | 3.16021 | ||||||||
\(763\) | 6.36750 | 0.230519 | ||||||||
\(764\) | −54.5840 | −1.97478 | ||||||||
\(765\) | −35.4888 | −1.28310 | ||||||||
\(766\) | 50.5373 | 1.82599 | ||||||||
\(767\) | −55.2463 | −1.99483 | ||||||||
\(768\) | −106.068 | −3.82742 | ||||||||
\(769\) | 44.9301 | 1.62022 | 0.810110 | − | 0.586278i | \(-0.199407\pi\) | ||||
0.810110 | + | 0.586278i | \(0.199407\pi\) | |||||||
\(770\) | −11.3255 | −0.408142 | ||||||||
\(771\) | −37.5023 | −1.35061 | ||||||||
\(772\) | 52.1591 | 1.87725 | ||||||||
\(773\) | −24.3953 | −0.877436 | −0.438718 | − | 0.898625i | \(-0.644567\pi\) | ||||
−0.438718 | + | 0.898625i | \(0.644567\pi\) | |||||||
\(774\) | 65.3324 | 2.34833 | ||||||||
\(775\) | 1.81401 | 0.0651610 | ||||||||
\(776\) | 47.8818 | 1.71885 | ||||||||
\(777\) | 6.73941 | 0.241775 | ||||||||
\(778\) | 92.9375 | 3.33197 | ||||||||
\(779\) | −14.7418 | −0.528180 | ||||||||
\(780\) | 55.0625 | 1.97155 | ||||||||
\(781\) | 77.2648 | 2.76475 | ||||||||
\(782\) | 59.3860 | 2.12364 | ||||||||
\(783\) | −120.950 | −4.32239 | ||||||||
\(784\) | 4.11160 | 0.146843 | ||||||||
\(785\) | 14.5514 | 0.519360 | ||||||||
\(786\) | 108.127 | 3.85678 | ||||||||
\(787\) | −21.6906 | −0.773188 | −0.386594 | − | 0.922250i | \(-0.626349\pi\) | ||||
−0.386594 | + | 0.922250i | \(0.626349\pi\) | |||||||
\(788\) | −56.3672 | −2.00800 | ||||||||
\(789\) | 19.9475 | 0.710149 | ||||||||
\(790\) | −16.6708 | −0.593121 | ||||||||
\(791\) | 8.04862 | 0.286176 | ||||||||
\(792\) | −180.403 | −6.41034 | ||||||||
\(793\) | 48.3464 | 1.71683 | ||||||||
\(794\) | 19.4271 | 0.689442 | ||||||||
\(795\) | 4.75137 | 0.168514 | ||||||||
\(796\) | 29.6565 | 1.05115 | ||||||||
\(797\) | −44.6267 | −1.58076 | −0.790379 | − | 0.612618i | \(-0.790116\pi\) | ||||
−0.790379 | + | 0.612618i | \(0.790116\pi\) | |||||||
\(798\) | −9.86647 | −0.349269 | ||||||||
\(799\) | 8.18102 | 0.289424 | ||||||||
\(800\) | −0.182804 | −0.00646309 | ||||||||
\(801\) | 102.644 | 3.62676 | ||||||||
\(802\) | −22.1614 | −0.782547 | ||||||||
\(803\) | 32.6126 | 1.15087 | ||||||||
\(804\) | −174.853 | −6.16660 | ||||||||
\(805\) | 5.38266 | 0.189714 | ||||||||
\(806\) | −18.4770 | −0.650825 | ||||||||
\(807\) | 10.1272 | 0.356496 | ||||||||
\(808\) | 27.7096 | 0.974821 | ||||||||
\(809\) | 2.13506 | 0.0750648 | 0.0375324 | − | 0.999295i | \(-0.488050\pi\) | ||||
0.0375324 | + | 0.999295i | \(0.488050\pi\) | |||||||
\(810\) | −72.6142 | −2.55140 | ||||||||
\(811\) | 8.28173 | 0.290811 | 0.145405 | − | 0.989372i | \(-0.453551\pi\) | ||||
0.145405 | + | 0.989372i | \(0.453551\pi\) | |||||||
\(812\) | −30.1098 | −1.05665 | ||||||||
\(813\) | −33.7322 | −1.18304 | ||||||||
\(814\) | −23.1280 | −0.810636 | ||||||||
\(815\) | −12.9803 | −0.454681 | ||||||||
\(816\) | −61.0229 | −2.13623 | ||||||||
\(817\) | −4.11253 | −0.143879 | ||||||||
\(818\) | 17.8407 | 0.623786 | ||||||||
\(819\) | 32.7640 | 1.14487 | ||||||||
\(820\) | −48.6120 | −1.69760 | ||||||||
\(821\) | −39.3454 | −1.37316 | −0.686582 | − | 0.727052i | \(-0.740890\pi\) | ||||
−0.686582 | + | 0.727052i | \(0.740890\pi\) | |||||||
\(822\) | 149.060 | 5.19906 | ||||||||
\(823\) | 18.5539 | 0.646747 | 0.323373 | − | 0.946271i | \(-0.395183\pi\) | ||||
0.323373 | + | 0.946271i | \(0.395183\pi\) | |||||||
\(824\) | −6.59194 | −0.229641 | ||||||||
\(825\) | 15.2353 | 0.530425 | ||||||||
\(826\) | 32.6438 | 1.13582 | ||||||||
\(827\) | −41.8382 | −1.45486 | −0.727429 | − | 0.686183i | \(-0.759285\pi\) | ||||
−0.727429 | + | 0.686183i | \(0.759285\pi\) | |||||||
\(828\) | 170.693 | 5.93198 | ||||||||
\(829\) | −3.20690 | −0.111380 | −0.0556902 | − | 0.998448i | \(-0.517736\pi\) | ||||
−0.0556902 | + | 0.998448i | \(0.517736\pi\) | |||||||
\(830\) | −25.3539 | −0.880046 | ||||||||
\(831\) | −58.6610 | −2.03493 | ||||||||
\(832\) | −32.2799 | −1.11911 | ||||||||
\(833\) | −4.49719 | −0.155819 | ||||||||
\(834\) | −19.0486 | −0.659598 | ||||||||
\(835\) | −11.2337 | −0.388758 | ||||||||
\(836\) | 22.6076 | 0.781902 | ||||||||
\(837\) | 29.2823 | 1.01214 | ||||||||
\(838\) | −40.4679 | −1.39794 | ||||||||
\(839\) | −5.38819 | −0.186021 | −0.0930104 | − | 0.995665i | \(-0.529649\pi\) | ||||
−0.0930104 | + | 0.995665i | \(0.529649\pi\) | |||||||
\(840\) | −16.3427 | −0.563877 | ||||||||
\(841\) | 27.1407 | 0.935886 | ||||||||
\(842\) | −61.8924 | −2.13295 | ||||||||
\(843\) | 10.4176 | 0.358802 | ||||||||
\(844\) | −23.1217 | −0.795881 | ||||||||
\(845\) | 4.23831 | 0.145802 | ||||||||
\(846\) | 35.2177 | 1.21081 | ||||||||
\(847\) | 10.3119 | 0.354320 | ||||||||
\(848\) | 5.91956 | 0.203278 | ||||||||
\(849\) | −32.6840 | −1.12171 | ||||||||
\(850\) | 11.0328 | 0.378423 | ||||||||
\(851\) | 10.9920 | 0.376802 | ||||||||
\(852\) | 221.962 | 7.60431 | ||||||||
\(853\) | −50.1428 | −1.71686 | −0.858429 | − | 0.512932i | \(-0.828559\pi\) | ||||
−0.858429 | + | 0.512932i | \(0.828559\pi\) | |||||||
\(854\) | −28.5668 | −0.977537 | ||||||||
\(855\) | 9.61669 | 0.328884 | ||||||||
\(856\) | 3.89821 | 0.133238 | ||||||||
\(857\) | 36.0037 | 1.22986 | 0.614931 | − | 0.788581i | \(-0.289184\pi\) | ||||
0.614931 | + | 0.788581i | \(0.289184\pi\) | |||||||
\(858\) | −155.183 | −5.29786 | ||||||||
\(859\) | −26.3962 | −0.900628 | −0.450314 | − | 0.892870i | \(-0.648688\pi\) | ||||
−0.450314 | + | 0.892870i | \(0.648688\pi\) | |||||||
\(860\) | −13.5613 | −0.462437 | ||||||||
\(861\) | −39.9223 | −1.36055 | ||||||||
\(862\) | −51.6272 | −1.75843 | ||||||||
\(863\) | −36.8111 | −1.25306 | −0.626532 | − | 0.779396i | \(-0.715526\pi\) | ||||
−0.626532 | + | 0.779396i | \(0.715526\pi\) | |||||||
\(864\) | −2.95088 | −0.100391 | ||||||||
\(865\) | −23.7228 | −0.806599 | ||||||||
\(866\) | 86.1056 | 2.92599 | ||||||||
\(867\) | 10.6424 | 0.361433 | ||||||||
\(868\) | 7.28966 | 0.247427 | ||||||||
\(869\) | 31.3705 | 1.06417 | ||||||||
\(870\) | 60.6631 | 2.05667 | ||||||||
\(871\) | −54.7409 | −1.85483 | ||||||||
\(872\) | −31.5321 | −1.06781 | ||||||||
\(873\) | −76.3020 | −2.58243 | ||||||||
\(874\) | −16.0923 | −0.544330 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 93.6879 | 3.16542 | ||||||||
\(877\) | −20.9514 | −0.707477 | −0.353739 | − | 0.935344i | \(-0.615090\pi\) | ||||
−0.353739 | + | 0.935344i | \(0.615090\pi\) | |||||||
\(878\) | −83.9250 | −2.83233 | ||||||||
\(879\) | −92.4248 | −3.11741 | ||||||||
\(880\) | 18.9811 | 0.639853 | ||||||||
\(881\) | 13.5699 | 0.457182 | 0.228591 | − | 0.973523i | \(-0.426588\pi\) | ||||
0.228591 | + | 0.973523i | \(0.426588\pi\) | |||||||
\(882\) | −19.3595 | −0.651870 | ||||||||
\(883\) | 22.3686 | 0.752763 | 0.376382 | − | 0.926465i | \(-0.377168\pi\) | ||||
0.376382 | + | 0.926465i | \(0.377168\pi\) | |||||||
\(884\) | −75.0339 | −2.52366 | ||||||||
\(885\) | −43.9133 | −1.47613 | ||||||||
\(886\) | −1.81397 | −0.0609414 | ||||||||
\(887\) | −28.7208 | −0.964349 | −0.482174 | − | 0.876075i | \(-0.660153\pi\) | ||||
−0.482174 | + | 0.876075i | \(0.660153\pi\) | |||||||
\(888\) | −33.3738 | −1.11995 | ||||||||
\(889\) | −10.7748 | −0.361374 | ||||||||
\(890\) | −31.9104 | −1.06964 | ||||||||
\(891\) | 136.643 | 4.57771 | ||||||||
\(892\) | 77.5729 | 2.59733 | ||||||||
\(893\) | −2.21688 | −0.0741850 | ||||||||
\(894\) | −112.487 | −3.76214 | ||||||||
\(895\) | 10.2014 | 0.340995 | ||||||||
\(896\) | 19.4391 | 0.649416 | ||||||||
\(897\) | 73.7538 | 2.46257 | ||||||||
\(898\) | 29.2626 | 0.976507 | ||||||||
\(899\) | −13.5918 | −0.453312 | ||||||||
\(900\) | 31.7116 | 1.05705 | ||||||||
\(901\) | −6.47471 | −0.215704 | ||||||||
\(902\) | 137.003 | 4.56171 | ||||||||
\(903\) | −11.1371 | −0.370621 | ||||||||
\(904\) | −39.8570 | −1.32563 | ||||||||
\(905\) | 5.66186 | 0.188207 | ||||||||
\(906\) | 59.0897 | 1.96312 | ||||||||
\(907\) | −25.7259 | −0.854215 | −0.427107 | − | 0.904201i | \(-0.640467\pi\) | ||||
−0.427107 | + | 0.904201i | \(0.640467\pi\) | |||||||
\(908\) | 76.7215 | 2.54609 | ||||||||
\(909\) | −44.1567 | −1.46458 | ||||||||
\(910\) | −10.1857 | −0.337654 | ||||||||
\(911\) | 7.15184 | 0.236951 | 0.118476 | − | 0.992957i | \(-0.462199\pi\) | ||||
0.118476 | + | 0.992957i | \(0.462199\pi\) | |||||||
\(912\) | 16.5359 | 0.547557 | ||||||||
\(913\) | 47.7100 | 1.57897 | ||||||||
\(914\) | 42.8602 | 1.41769 | ||||||||
\(915\) | 38.4288 | 1.27042 | ||||||||
\(916\) | 4.01854 | 0.132776 | ||||||||
\(917\) | −13.3552 | −0.441027 | ||||||||
\(918\) | 178.096 | 5.87803 | ||||||||
\(919\) | −22.9002 | −0.755408 | −0.377704 | − | 0.925926i | \(-0.623286\pi\) | ||||
−0.377704 | + | 0.925926i | \(0.623286\pi\) | |||||||
\(920\) | −26.6551 | −0.878792 | ||||||||
\(921\) | −11.4212 | −0.376342 | ||||||||
\(922\) | 62.7406 | 2.06625 | ||||||||
\(923\) | 69.4893 | 2.28727 | ||||||||
\(924\) | 61.2237 | 2.01411 | ||||||||
\(925\) | 2.04212 | 0.0671446 | ||||||||
\(926\) | −56.6201 | −1.86065 | ||||||||
\(927\) | 10.5046 | 0.345016 | ||||||||
\(928\) | 1.36969 | 0.0449624 | ||||||||
\(929\) | −15.8766 | −0.520896 | −0.260448 | − | 0.965488i | \(-0.583870\pi\) | ||||
−0.260448 | + | 0.965488i | \(0.583870\pi\) | |||||||
\(930\) | −14.6867 | −0.481596 | ||||||||
\(931\) | 1.21864 | 0.0399394 | ||||||||
\(932\) | −24.7803 | −0.811705 | ||||||||
\(933\) | −4.86109 | −0.159145 | ||||||||
\(934\) | 29.3092 | 0.959028 | ||||||||
\(935\) | −20.7612 | −0.678964 | ||||||||
\(936\) | −162.248 | −5.30325 | ||||||||
\(937\) | 35.8403 | 1.17085 | 0.585425 | − | 0.810727i | \(-0.300928\pi\) | ||||
0.585425 | + | 0.810727i | \(0.300928\pi\) | |||||||
\(938\) | 32.3452 | 1.05611 | ||||||||
\(939\) | −25.8734 | −0.844347 | ||||||||
\(940\) | −7.31029 | −0.238435 | ||||||||
\(941\) | −9.15363 | −0.298400 | −0.149200 | − | 0.988807i | \(-0.547670\pi\) | ||||
−0.149200 | + | 0.988807i | \(0.547670\pi\) | |||||||
\(942\) | −117.812 | −3.83852 | ||||||||
\(943\) | −65.1136 | −2.12039 | ||||||||
\(944\) | −54.7100 | −1.78066 | ||||||||
\(945\) | 16.1423 | 0.525110 | ||||||||
\(946\) | 38.2200 | 1.24264 | ||||||||
\(947\) | −10.0309 | −0.325960 | −0.162980 | − | 0.986629i | \(-0.552111\pi\) | ||||
−0.162980 | + | 0.986629i | \(0.552111\pi\) | |||||||
\(948\) | 90.1198 | 2.92695 | ||||||||
\(949\) | 29.3307 | 0.952114 | ||||||||
\(950\) | −2.98966 | −0.0969973 | ||||||||
\(951\) | −55.7579 | −1.80807 | ||||||||
\(952\) | 22.2703 | 0.721783 | ||||||||
\(953\) | 31.2434 | 1.01207 | 0.506037 | − | 0.862512i | \(-0.331110\pi\) | ||||
0.506037 | + | 0.862512i | \(0.331110\pi\) | |||||||
\(954\) | −27.8724 | −0.902401 | ||||||||
\(955\) | −13.5830 | −0.439536 | ||||||||
\(956\) | −89.3147 | −2.88864 | ||||||||
\(957\) | −114.154 | −3.69006 | ||||||||
\(958\) | −40.4117 | −1.30564 | ||||||||
\(959\) | −18.4109 | −0.594519 | ||||||||
\(960\) | −25.6582 | −0.828114 | ||||||||
\(961\) | −27.7094 | −0.893851 | ||||||||
\(962\) | −20.8005 | −0.670636 | ||||||||
\(963\) | −6.21200 | −0.200179 | ||||||||
\(964\) | 16.0989 | 0.518511 | ||||||||
\(965\) | 12.9796 | 0.417829 | ||||||||
\(966\) | −43.5795 | −1.40215 | ||||||||
\(967\) | 58.3287 | 1.87573 | 0.937863 | − | 0.347006i | \(-0.112802\pi\) | ||||
0.937863 | + | 0.347006i | \(0.112802\pi\) | |||||||
\(968\) | −51.0647 | −1.64128 | ||||||||
\(969\) | −18.0866 | −0.581026 | ||||||||
\(970\) | 23.7210 | 0.761634 | ||||||||
\(971\) | 5.06433 | 0.162522 | 0.0812611 | − | 0.996693i | \(-0.474105\pi\) | ||||
0.0812611 | + | 0.996693i | \(0.474105\pi\) | |||||||
\(972\) | 197.935 | 6.34877 | ||||||||
\(973\) | 2.35275 | 0.0754258 | ||||||||
\(974\) | −60.9370 | −1.95255 | ||||||||
\(975\) | 13.7021 | 0.438819 | ||||||||
\(976\) | 47.8771 | 1.53251 | ||||||||
\(977\) | −3.00938 | −0.0962787 | −0.0481393 | − | 0.998841i | \(-0.515329\pi\) | ||||
−0.0481393 | + | 0.998841i | \(0.515329\pi\) | |||||||
\(978\) | 105.092 | 3.36048 | ||||||||
\(979\) | 60.0478 | 1.91914 | ||||||||
\(980\) | 4.01854 | 0.128368 | ||||||||
\(981\) | 50.2479 | 1.60429 | ||||||||
\(982\) | 35.4632 | 1.13168 | ||||||||
\(983\) | 16.0530 | 0.512010 | 0.256005 | − | 0.966675i | \(-0.417594\pi\) | ||||
0.256005 | + | 0.966675i | \(0.417594\pi\) | |||||||
\(984\) | 197.696 | 6.30233 | ||||||||
\(985\) | −14.0268 | −0.446930 | ||||||||
\(986\) | −82.6659 | −2.63262 | ||||||||
\(987\) | −6.00352 | −0.191094 | ||||||||
\(988\) | 20.3325 | 0.646865 | ||||||||
\(989\) | −18.1648 | −0.577607 | ||||||||
\(990\) | −89.3729 | −2.84046 | ||||||||
\(991\) | 55.8993 | 1.77570 | 0.887849 | − | 0.460135i | \(-0.152199\pi\) | ||||
0.887849 | + | 0.460135i | \(0.152199\pi\) | |||||||
\(992\) | −0.331607 | −0.0105285 | ||||||||
\(993\) | 47.5584 | 1.50922 | ||||||||
\(994\) | −41.0598 | −1.30234 | ||||||||
\(995\) | 7.37991 | 0.233959 | ||||||||
\(996\) | 137.059 | 4.34288 | ||||||||
\(997\) | 21.5954 | 0.683932 | 0.341966 | − | 0.939712i | \(-0.388907\pi\) | ||||
0.341966 | + | 0.939712i | \(0.388907\pi\) | |||||||
\(998\) | −72.4215 | −2.29246 | ||||||||
\(999\) | 32.9646 | 1.04295 |
(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 | 8015.2.a.o.1.7 | ✓ | 73 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.o.1.7 | ✓ | 73 | 1.1 | even | 1 | trivial |