Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8029,2,Mod(1,8029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8029, 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("8029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8029 = 7 \cdot 31 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8029.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: | \(64.1118877829\) |
Analytic rank: | \(0\) |
Dimension: | \(71\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 8029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.30726 | −1.63148 | −0.815741 | − | 0.578417i | \(-0.803670\pi\) | ||||
−0.815741 | + | 0.578417i | \(0.803670\pi\) | |||||||
\(3\) | 1.92904 | 1.11373 | 0.556865 | − | 0.830603i | \(-0.312004\pi\) | ||||
0.556865 | + | 0.830603i | \(0.312004\pi\) | |||||||
\(4\) | 3.32347 | 1.66173 | ||||||||
\(5\) | 4.29364 | 1.92017 | 0.960086 | − | 0.279704i | \(-0.0902365\pi\) | ||||
0.960086 | + | 0.279704i | \(0.0902365\pi\) | |||||||
\(6\) | −4.45079 | −1.81703 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −3.05358 | −1.07961 | ||||||||
\(9\) | 0.721177 | 0.240392 | ||||||||
\(10\) | −9.90655 | −3.13273 | ||||||||
\(11\) | 1.39887 | 0.421775 | 0.210887 | − | 0.977510i | \(-0.432365\pi\) | ||||
0.210887 | + | 0.977510i | \(0.432365\pi\) | |||||||
\(12\) | 6.41108 | 1.85072 | ||||||||
\(13\) | 2.11313 | 0.586078 | 0.293039 | − | 0.956101i | \(-0.405333\pi\) | ||||
0.293039 | + | 0.956101i | \(0.405333\pi\) | |||||||
\(14\) | 2.30726 | 0.616642 | ||||||||
\(15\) | 8.28257 | 2.13855 | ||||||||
\(16\) | 0.398494 | 0.0996235 | ||||||||
\(17\) | −3.41873 | −0.829163 | −0.414582 | − | 0.910012i | \(-0.636072\pi\) | ||||
−0.414582 | + | 0.910012i | \(0.636072\pi\) | |||||||
\(18\) | −1.66395 | −0.392196 | ||||||||
\(19\) | 4.04767 | 0.928599 | 0.464300 | − | 0.885678i | \(-0.346306\pi\) | ||||
0.464300 | + | 0.885678i | \(0.346306\pi\) | |||||||
\(20\) | 14.2698 | 3.19081 | ||||||||
\(21\) | −1.92904 | −0.420950 | ||||||||
\(22\) | −3.22756 | −0.688118 | ||||||||
\(23\) | −1.11969 | −0.233472 | −0.116736 | − | 0.993163i | \(-0.537243\pi\) | ||||
−0.116736 | + | 0.993163i | \(0.537243\pi\) | |||||||
\(24\) | −5.89047 | −1.20239 | ||||||||
\(25\) | 13.4353 | 2.68706 | ||||||||
\(26\) | −4.87556 | −0.956175 | ||||||||
\(27\) | −4.39593 | −0.845997 | ||||||||
\(28\) | −3.32347 | −0.628076 | ||||||||
\(29\) | 5.91808 | 1.09896 | 0.549480 | − | 0.835507i | \(-0.314826\pi\) | ||||
0.549480 | + | 0.835507i | \(0.314826\pi\) | |||||||
\(30\) | −19.1101 | −3.48901 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 5.18774 | 0.917071 | ||||||||
\(33\) | 2.69847 | 0.469743 | ||||||||
\(34\) | 7.88791 | 1.35276 | ||||||||
\(35\) | −4.29364 | −0.725757 | ||||||||
\(36\) | 2.39681 | 0.399468 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | −9.33904 | −1.51499 | ||||||||
\(39\) | 4.07631 | 0.652732 | ||||||||
\(40\) | −13.1110 | −2.07303 | ||||||||
\(41\) | 8.70509 | 1.35951 | 0.679753 | − | 0.733441i | \(-0.262087\pi\) | ||||
0.679753 | + | 0.733441i | \(0.262087\pi\) | |||||||
\(42\) | 4.45079 | 0.686772 | ||||||||
\(43\) | 0.320874 | 0.0489328 | 0.0244664 | − | 0.999701i | \(-0.492211\pi\) | ||||
0.0244664 | + | 0.999701i | \(0.492211\pi\) | |||||||
\(44\) | 4.64909 | 0.700877 | ||||||||
\(45\) | 3.09647 | 0.461595 | ||||||||
\(46\) | 2.58343 | 0.380906 | ||||||||
\(47\) | 13.0091 | 1.89757 | 0.948785 | − | 0.315921i | \(-0.102313\pi\) | ||||
0.948785 | + | 0.315921i | \(0.102313\pi\) | |||||||
\(48\) | 0.768709 | 0.110954 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −30.9988 | −4.38389 | ||||||||
\(51\) | −6.59485 | −0.923463 | ||||||||
\(52\) | 7.02293 | 0.973905 | ||||||||
\(53\) | −9.51840 | −1.30745 | −0.653726 | − | 0.756731i | \(-0.726795\pi\) | ||||
−0.653726 | + | 0.756731i | \(0.726795\pi\) | |||||||
\(54\) | 10.1426 | 1.38023 | ||||||||
\(55\) | 6.00623 | 0.809880 | ||||||||
\(56\) | 3.05358 | 0.408052 | ||||||||
\(57\) | 7.80810 | 1.03421 | ||||||||
\(58\) | −13.6546 | −1.79293 | ||||||||
\(59\) | −5.46939 | −0.712055 | −0.356027 | − | 0.934476i | \(-0.615869\pi\) | ||||
−0.356027 | + | 0.934476i | \(0.615869\pi\) | |||||||
\(60\) | 27.5269 | 3.55370 | ||||||||
\(61\) | 10.5744 | 1.35391 | 0.676957 | − | 0.736022i | \(-0.263298\pi\) | ||||
0.676957 | + | 0.736022i | \(0.263298\pi\) | |||||||
\(62\) | 2.30726 | 0.293023 | ||||||||
\(63\) | −0.721177 | −0.0908598 | ||||||||
\(64\) | −12.7665 | −1.59581 | ||||||||
\(65\) | 9.07303 | 1.12537 | ||||||||
\(66\) | −6.22607 | −0.766377 | ||||||||
\(67\) | −3.91995 | −0.478898 | −0.239449 | − | 0.970909i | \(-0.576967\pi\) | ||||
−0.239449 | + | 0.970909i | \(0.576967\pi\) | |||||||
\(68\) | −11.3620 | −1.37785 | ||||||||
\(69\) | −2.15993 | −0.260025 | ||||||||
\(70\) | 9.90655 | 1.18406 | ||||||||
\(71\) | 12.1447 | 1.44131 | 0.720655 | − | 0.693294i | \(-0.243841\pi\) | ||||
0.720655 | + | 0.693294i | \(0.243841\pi\) | |||||||
\(72\) | −2.20218 | −0.259529 | ||||||||
\(73\) | −4.81354 | −0.563382 | −0.281691 | − | 0.959505i | \(-0.590895\pi\) | ||||
−0.281691 | + | 0.959505i | \(0.590895\pi\) | |||||||
\(74\) | −2.30726 | −0.268214 | ||||||||
\(75\) | 25.9172 | 2.99266 | ||||||||
\(76\) | 13.4523 | 1.54308 | ||||||||
\(77\) | −1.39887 | −0.159416 | ||||||||
\(78\) | −9.40512 | −1.06492 | ||||||||
\(79\) | 5.34478 | 0.601335 | 0.300667 | − | 0.953729i | \(-0.402791\pi\) | ||||
0.300667 | + | 0.953729i | \(0.402791\pi\) | |||||||
\(80\) | 1.71099 | 0.191294 | ||||||||
\(81\) | −10.6434 | −1.18260 | ||||||||
\(82\) | −20.0849 | −2.21801 | ||||||||
\(83\) | −14.7032 | −1.61388 | −0.806941 | − | 0.590632i | \(-0.798879\pi\) | ||||
−0.806941 | + | 0.590632i | \(0.798879\pi\) | |||||||
\(84\) | −6.41108 | −0.699506 | ||||||||
\(85\) | −14.6788 | −1.59214 | ||||||||
\(86\) | −0.740341 | −0.0798330 | ||||||||
\(87\) | 11.4162 | 1.22394 | ||||||||
\(88\) | −4.27156 | −0.455350 | ||||||||
\(89\) | 10.2420 | 1.08565 | 0.542824 | − | 0.839846i | \(-0.317355\pi\) | ||||
0.542824 | + | 0.839846i | \(0.317355\pi\) | |||||||
\(90\) | −7.14438 | −0.753083 | ||||||||
\(91\) | −2.11313 | −0.221517 | ||||||||
\(92\) | −3.72127 | −0.387969 | ||||||||
\(93\) | −1.92904 | −0.200032 | ||||||||
\(94\) | −30.0154 | −3.09585 | ||||||||
\(95\) | 17.3792 | 1.78307 | ||||||||
\(96\) | 10.0073 | 1.02137 | ||||||||
\(97\) | −4.84009 | −0.491437 | −0.245718 | − | 0.969341i | \(-0.579024\pi\) | ||||
−0.245718 | + | 0.969341i | \(0.579024\pi\) | |||||||
\(98\) | −2.30726 | −0.233069 | ||||||||
\(99\) | 1.00883 | 0.101391 | ||||||||
\(100\) | 44.6518 | 4.46518 | ||||||||
\(101\) | 4.56890 | 0.454623 | 0.227311 | − | 0.973822i | \(-0.427007\pi\) | ||||
0.227311 | + | 0.973822i | \(0.427007\pi\) | |||||||
\(102\) | 15.2160 | 1.50661 | ||||||||
\(103\) | 9.43035 | 0.929200 | 0.464600 | − | 0.885521i | \(-0.346198\pi\) | ||||
0.464600 | + | 0.885521i | \(0.346198\pi\) | |||||||
\(104\) | −6.45263 | −0.632733 | ||||||||
\(105\) | −8.28257 | −0.808297 | ||||||||
\(106\) | 21.9614 | 2.13308 | ||||||||
\(107\) | −10.5773 | −1.02255 | −0.511273 | − | 0.859418i | \(-0.670826\pi\) | ||||
−0.511273 | + | 0.859418i | \(0.670826\pi\) | |||||||
\(108\) | −14.6097 | −1.40582 | ||||||||
\(109\) | −13.6464 | −1.30709 | −0.653545 | − | 0.756888i | \(-0.726719\pi\) | ||||
−0.653545 | + | 0.756888i | \(0.726719\pi\) | |||||||
\(110\) | −13.8580 | −1.32130 | ||||||||
\(111\) | 1.92904 | 0.183096 | ||||||||
\(112\) | −0.398494 | −0.0376541 | ||||||||
\(113\) | −13.9576 | −1.31302 | −0.656510 | − | 0.754317i | \(-0.727968\pi\) | ||||
−0.656510 | + | 0.754317i | \(0.727968\pi\) | |||||||
\(114\) | −18.0153 | −1.68729 | ||||||||
\(115\) | −4.80756 | −0.448307 | ||||||||
\(116\) | 19.6685 | 1.82618 | ||||||||
\(117\) | 1.52394 | 0.140889 | ||||||||
\(118\) | 12.6193 | 1.16170 | ||||||||
\(119\) | 3.41873 | 0.313394 | ||||||||
\(120\) | −25.2915 | −2.30879 | ||||||||
\(121\) | −9.04317 | −0.822106 | ||||||||
\(122\) | −24.3980 | −2.20889 | ||||||||
\(123\) | 16.7924 | 1.51412 | ||||||||
\(124\) | −3.32347 | −0.298456 | ||||||||
\(125\) | 36.2181 | 3.23945 | ||||||||
\(126\) | 1.66395 | 0.148236 | ||||||||
\(127\) | 6.70895 | 0.595323 | 0.297661 | − | 0.954671i | \(-0.403793\pi\) | ||||
0.297661 | + | 0.954671i | \(0.403793\pi\) | |||||||
\(128\) | 19.0801 | 1.68646 | ||||||||
\(129\) | 0.618977 | 0.0544979 | ||||||||
\(130\) | −20.9339 | −1.83602 | ||||||||
\(131\) | −10.8841 | −0.950945 | −0.475473 | − | 0.879730i | \(-0.657723\pi\) | ||||
−0.475473 | + | 0.879730i | \(0.657723\pi\) | |||||||
\(132\) | 8.96826 | 0.780587 | ||||||||
\(133\) | −4.04767 | −0.350978 | ||||||||
\(134\) | 9.04435 | 0.781313 | ||||||||
\(135\) | −18.8745 | −1.62446 | ||||||||
\(136\) | 10.4394 | 0.895169 | ||||||||
\(137\) | −3.13779 | −0.268079 | −0.134040 | − | 0.990976i | \(-0.542795\pi\) | ||||
−0.134040 | + | 0.990976i | \(0.542795\pi\) | |||||||
\(138\) | 4.98353 | 0.424226 | ||||||||
\(139\) | −18.8869 | −1.60197 | −0.800984 | − | 0.598685i | \(-0.795690\pi\) | ||||
−0.800984 | + | 0.598685i | \(0.795690\pi\) | |||||||
\(140\) | −14.2698 | −1.20601 | ||||||||
\(141\) | 25.0950 | 2.11338 | ||||||||
\(142\) | −28.0210 | −2.35147 | ||||||||
\(143\) | 2.95600 | 0.247193 | ||||||||
\(144\) | 0.287385 | 0.0239487 | ||||||||
\(145\) | 25.4101 | 2.11019 | ||||||||
\(146\) | 11.1061 | 0.919148 | ||||||||
\(147\) | 1.92904 | 0.159104 | ||||||||
\(148\) | 3.32347 | 0.273187 | ||||||||
\(149\) | −8.28242 | −0.678522 | −0.339261 | − | 0.940692i | \(-0.610177\pi\) | ||||
−0.339261 | + | 0.940692i | \(0.610177\pi\) | |||||||
\(150\) | −59.7978 | −4.88247 | ||||||||
\(151\) | 11.3167 | 0.920944 | 0.460472 | − | 0.887674i | \(-0.347680\pi\) | ||||
0.460472 | + | 0.887674i | \(0.347680\pi\) | |||||||
\(152\) | −12.3599 | −1.00252 | ||||||||
\(153\) | −2.46551 | −0.199324 | ||||||||
\(154\) | 3.22756 | 0.260084 | ||||||||
\(155\) | −4.29364 | −0.344873 | ||||||||
\(156\) | 13.5475 | 1.08467 | ||||||||
\(157\) | 10.7850 | 0.860737 | 0.430369 | − | 0.902653i | \(-0.358384\pi\) | ||||
0.430369 | + | 0.902653i | \(0.358384\pi\) | |||||||
\(158\) | −12.3318 | −0.981066 | ||||||||
\(159\) | −18.3613 | −1.45615 | ||||||||
\(160\) | 22.2743 | 1.76094 | ||||||||
\(161\) | 1.11969 | 0.0882443 | ||||||||
\(162\) | 24.5572 | 1.92940 | ||||||||
\(163\) | 13.0588 | 1.02285 | 0.511423 | − | 0.859329i | \(-0.329118\pi\) | ||||
0.511423 | + | 0.859329i | \(0.329118\pi\) | |||||||
\(164\) | 28.9311 | 2.25914 | ||||||||
\(165\) | 11.5862 | 0.901987 | ||||||||
\(166\) | 33.9241 | 2.63302 | ||||||||
\(167\) | −18.1744 | −1.40638 | −0.703188 | − | 0.711004i | \(-0.748241\pi\) | ||||
−0.703188 | + | 0.711004i | \(0.748241\pi\) | |||||||
\(168\) | 5.89047 | 0.454460 | ||||||||
\(169\) | −8.53467 | −0.656513 | ||||||||
\(170\) | 33.8678 | 2.59754 | ||||||||
\(171\) | 2.91909 | 0.223228 | ||||||||
\(172\) | 1.06641 | 0.0813133 | ||||||||
\(173\) | −14.1896 | −1.07881 | −0.539407 | − | 0.842045i | \(-0.681352\pi\) | ||||
−0.539407 | + | 0.842045i | \(0.681352\pi\) | |||||||
\(174\) | −26.3401 | −1.99684 | ||||||||
\(175\) | −13.4353 | −1.01561 | ||||||||
\(176\) | 0.557440 | 0.0420187 | ||||||||
\(177\) | −10.5507 | −0.793036 | ||||||||
\(178\) | −23.6310 | −1.77122 | ||||||||
\(179\) | 3.69433 | 0.276127 | 0.138063 | − | 0.990423i | \(-0.455912\pi\) | ||||
0.138063 | + | 0.990423i | \(0.455912\pi\) | |||||||
\(180\) | 10.2910 | 0.767047 | ||||||||
\(181\) | 18.8353 | 1.40002 | 0.700008 | − | 0.714135i | \(-0.253180\pi\) | ||||
0.700008 | + | 0.714135i | \(0.253180\pi\) | |||||||
\(182\) | 4.87556 | 0.361400 | ||||||||
\(183\) | 20.3984 | 1.50789 | ||||||||
\(184\) | 3.41908 | 0.252058 | ||||||||
\(185\) | 4.29364 | 0.315674 | ||||||||
\(186\) | 4.45079 | 0.326348 | ||||||||
\(187\) | −4.78235 | −0.349720 | ||||||||
\(188\) | 43.2353 | 3.15326 | ||||||||
\(189\) | 4.39593 | 0.319757 | ||||||||
\(190\) | −40.0985 | −2.90905 | ||||||||
\(191\) | 15.0160 | 1.08652 | 0.543259 | − | 0.839565i | \(-0.317190\pi\) | ||||
0.543259 | + | 0.839565i | \(0.317190\pi\) | |||||||
\(192\) | −24.6270 | −1.77730 | ||||||||
\(193\) | −6.34766 | −0.456915 | −0.228457 | − | 0.973554i | \(-0.573368\pi\) | ||||
−0.228457 | + | 0.973554i | \(0.573368\pi\) | |||||||
\(194\) | 11.1674 | 0.801770 | ||||||||
\(195\) | 17.5022 | 1.25336 | ||||||||
\(196\) | 3.32347 | 0.237390 | ||||||||
\(197\) | −13.6553 | −0.972903 | −0.486451 | − | 0.873708i | \(-0.661709\pi\) | ||||
−0.486451 | + | 0.873708i | \(0.661709\pi\) | |||||||
\(198\) | −2.32764 | −0.165418 | ||||||||
\(199\) | 21.3616 | 1.51429 | 0.757144 | − | 0.653249i | \(-0.226594\pi\) | ||||
0.757144 | + | 0.653249i | \(0.226594\pi\) | |||||||
\(200\) | −41.0259 | −2.90097 | ||||||||
\(201\) | −7.56172 | −0.533362 | ||||||||
\(202\) | −10.5417 | −0.741708 | ||||||||
\(203\) | −5.91808 | −0.415368 | ||||||||
\(204\) | −21.9177 | −1.53455 | ||||||||
\(205\) | 37.3765 | 2.61049 | ||||||||
\(206\) | −21.7583 | −1.51597 | ||||||||
\(207\) | −0.807498 | −0.0561250 | ||||||||
\(208\) | 0.842071 | 0.0583871 | ||||||||
\(209\) | 5.66216 | 0.391660 | ||||||||
\(210\) | 19.1101 | 1.31872 | ||||||||
\(211\) | 22.9427 | 1.57944 | 0.789719 | − | 0.613468i | \(-0.210226\pi\) | ||||
0.789719 | + | 0.613468i | \(0.210226\pi\) | |||||||
\(212\) | −31.6341 | −2.17264 | ||||||||
\(213\) | 23.4275 | 1.60523 | ||||||||
\(214\) | 24.4046 | 1.66827 | ||||||||
\(215\) | 1.37772 | 0.0939594 | ||||||||
\(216\) | 13.4233 | 0.913343 | ||||||||
\(217\) | 1.00000 | 0.0678844 | ||||||||
\(218\) | 31.4859 | 2.13249 | ||||||||
\(219\) | −9.28549 | −0.627455 | ||||||||
\(220\) | 19.9615 | 1.34580 | ||||||||
\(221\) | −7.22423 | −0.485954 | ||||||||
\(222\) | −4.45079 | −0.298718 | ||||||||
\(223\) | 20.4344 | 1.36839 | 0.684195 | − | 0.729299i | \(-0.260154\pi\) | ||||
0.684195 | + | 0.729299i | \(0.260154\pi\) | |||||||
\(224\) | −5.18774 | −0.346620 | ||||||||
\(225\) | 9.68924 | 0.645949 | ||||||||
\(226\) | 32.2039 | 2.14217 | ||||||||
\(227\) | 2.31200 | 0.153453 | 0.0767264 | − | 0.997052i | \(-0.475553\pi\) | ||||
0.0767264 | + | 0.997052i | \(0.475553\pi\) | |||||||
\(228\) | 25.9500 | 1.71858 | ||||||||
\(229\) | −9.09111 | −0.600757 | −0.300379 | − | 0.953820i | \(-0.597113\pi\) | ||||
−0.300379 | + | 0.953820i | \(0.597113\pi\) | |||||||
\(230\) | 11.0923 | 0.731405 | ||||||||
\(231\) | −2.69847 | −0.177546 | ||||||||
\(232\) | −18.0714 | −1.18644 | ||||||||
\(233\) | 13.5067 | 0.884853 | 0.442427 | − | 0.896805i | \(-0.354118\pi\) | ||||
0.442427 | + | 0.896805i | \(0.354118\pi\) | |||||||
\(234\) | −3.51614 | −0.229857 | ||||||||
\(235\) | 55.8563 | 3.64366 | ||||||||
\(236\) | −18.1773 | −1.18324 | ||||||||
\(237\) | 10.3103 | 0.669724 | ||||||||
\(238\) | −7.88791 | −0.511297 | ||||||||
\(239\) | 29.1065 | 1.88274 | 0.941371 | − | 0.337374i | \(-0.109539\pi\) | ||||
0.941371 | + | 0.337374i | \(0.109539\pi\) | |||||||
\(240\) | 3.30056 | 0.213050 | ||||||||
\(241\) | −15.6686 | −1.00930 | −0.504651 | − | 0.863323i | \(-0.668379\pi\) | ||||
−0.504651 | + | 0.863323i | \(0.668379\pi\) | |||||||
\(242\) | 20.8650 | 1.34125 | ||||||||
\(243\) | −7.34377 | −0.471103 | ||||||||
\(244\) | 35.1437 | 2.24985 | ||||||||
\(245\) | 4.29364 | 0.274310 | ||||||||
\(246\) | −38.7446 | −2.47026 | ||||||||
\(247\) | 8.55327 | 0.544231 | ||||||||
\(248\) | 3.05358 | 0.193903 | ||||||||
\(249\) | −28.3629 | −1.79743 | ||||||||
\(250\) | −83.5648 | −5.28510 | ||||||||
\(251\) | 12.4767 | 0.787525 | 0.393762 | − | 0.919212i | \(-0.371173\pi\) | ||||
0.393762 | + | 0.919212i | \(0.371173\pi\) | |||||||
\(252\) | −2.39681 | −0.150985 | ||||||||
\(253\) | −1.56630 | −0.0984727 | ||||||||
\(254\) | −15.4793 | −0.971259 | ||||||||
\(255\) | −28.3159 | −1.77321 | ||||||||
\(256\) | −18.4900 | −1.15562 | ||||||||
\(257\) | 16.1317 | 1.00627 | 0.503133 | − | 0.864209i | \(-0.332181\pi\) | ||||
0.503133 | + | 0.864209i | \(0.332181\pi\) | |||||||
\(258\) | −1.42814 | −0.0889123 | ||||||||
\(259\) | −1.00000 | −0.0621370 | ||||||||
\(260\) | 30.1539 | 1.87007 | ||||||||
\(261\) | 4.26798 | 0.264181 | ||||||||
\(262\) | 25.1124 | 1.55145 | ||||||||
\(263\) | 25.7837 | 1.58989 | 0.794947 | − | 0.606679i | \(-0.207499\pi\) | ||||
0.794947 | + | 0.606679i | \(0.207499\pi\) | |||||||
\(264\) | −8.24000 | −0.507137 | ||||||||
\(265\) | −40.8685 | −2.51053 | ||||||||
\(266\) | 9.33904 | 0.572613 | ||||||||
\(267\) | 19.7572 | 1.20912 | ||||||||
\(268\) | −13.0278 | −0.795800 | ||||||||
\(269\) | 4.57534 | 0.278963 | 0.139482 | − | 0.990225i | \(-0.455456\pi\) | ||||
0.139482 | + | 0.990225i | \(0.455456\pi\) | |||||||
\(270\) | 43.5485 | 2.65028 | ||||||||
\(271\) | −16.2713 | −0.988410 | −0.494205 | − | 0.869345i | \(-0.664541\pi\) | ||||
−0.494205 | + | 0.869345i | \(0.664541\pi\) | |||||||
\(272\) | −1.36234 | −0.0826041 | ||||||||
\(273\) | −4.07631 | −0.246709 | ||||||||
\(274\) | 7.23971 | 0.437367 | ||||||||
\(275\) | 18.7942 | 1.13333 | ||||||||
\(276\) | −7.17845 | −0.432092 | ||||||||
\(277\) | 11.7911 | 0.708457 | 0.354228 | − | 0.935159i | \(-0.384744\pi\) | ||||
0.354228 | + | 0.935159i | \(0.384744\pi\) | |||||||
\(278\) | 43.5771 | 2.61358 | ||||||||
\(279\) | −0.721177 | −0.0431757 | ||||||||
\(280\) | 13.1110 | 0.783531 | ||||||||
\(281\) | −25.6654 | −1.53107 | −0.765536 | − | 0.643393i | \(-0.777526\pi\) | ||||
−0.765536 | + | 0.643393i | \(0.777526\pi\) | |||||||
\(282\) | −57.9008 | −3.44794 | ||||||||
\(283\) | 29.1175 | 1.73086 | 0.865429 | − | 0.501032i | \(-0.167046\pi\) | ||||
0.865429 | + | 0.501032i | \(0.167046\pi\) | |||||||
\(284\) | 40.3625 | 2.39507 | ||||||||
\(285\) | 33.5251 | 1.98586 | ||||||||
\(286\) | −6.82026 | −0.403291 | ||||||||
\(287\) | −8.70509 | −0.513845 | ||||||||
\(288\) | 3.74128 | 0.220457 | ||||||||
\(289\) | −5.31230 | −0.312488 | ||||||||
\(290\) | −58.6277 | −3.44274 | ||||||||
\(291\) | −9.33670 | −0.547327 | ||||||||
\(292\) | −15.9976 | −0.936191 | ||||||||
\(293\) | −20.2013 | −1.18017 | −0.590087 | − | 0.807340i | \(-0.700907\pi\) | ||||
−0.590087 | + | 0.807340i | \(0.700907\pi\) | |||||||
\(294\) | −4.45079 | −0.259576 | ||||||||
\(295\) | −23.4836 | −1.36727 | ||||||||
\(296\) | −3.05358 | −0.177486 | ||||||||
\(297\) | −6.14933 | −0.356820 | ||||||||
\(298\) | 19.1097 | 1.10700 | ||||||||
\(299\) | −2.36606 | −0.136833 | ||||||||
\(300\) | 86.1349 | 4.97300 | ||||||||
\(301\) | −0.320874 | −0.0184949 | ||||||||
\(302\) | −26.1107 | −1.50250 | ||||||||
\(303\) | 8.81357 | 0.506326 | ||||||||
\(304\) | 1.61297 | 0.0925103 | ||||||||
\(305\) | 45.4027 | 2.59975 | ||||||||
\(306\) | 5.68858 | 0.325194 | ||||||||
\(307\) | −16.9571 | −0.967793 | −0.483897 | − | 0.875125i | \(-0.660779\pi\) | ||||
−0.483897 | + | 0.875125i | \(0.660779\pi\) | |||||||
\(308\) | −4.64909 | −0.264907 | ||||||||
\(309\) | 18.1915 | 1.03488 | ||||||||
\(310\) | 9.90655 | 0.562654 | ||||||||
\(311\) | 3.07891 | 0.174589 | 0.0872944 | − | 0.996183i | \(-0.472178\pi\) | ||||
0.0872944 | + | 0.996183i | \(0.472178\pi\) | |||||||
\(312\) | −12.4474 | −0.704693 | ||||||||
\(313\) | −28.8113 | −1.62851 | −0.814256 | − | 0.580506i | \(-0.802855\pi\) | ||||
−0.814256 | + | 0.580506i | \(0.802855\pi\) | |||||||
\(314\) | −24.8839 | −1.40428 | ||||||||
\(315\) | −3.09647 | −0.174466 | ||||||||
\(316\) | 17.7632 | 0.999257 | ||||||||
\(317\) | 21.3359 | 1.19834 | 0.599172 | − | 0.800620i | \(-0.295497\pi\) | ||||
0.599172 | + | 0.800620i | \(0.295497\pi\) | |||||||
\(318\) | 42.3644 | 2.37568 | ||||||||
\(319\) | 8.27861 | 0.463513 | ||||||||
\(320\) | −54.8146 | −3.06423 | ||||||||
\(321\) | −20.4040 | −1.13884 | ||||||||
\(322\) | −2.58343 | −0.143969 | ||||||||
\(323\) | −13.8379 | −0.769960 | ||||||||
\(324\) | −35.3731 | −1.96517 | ||||||||
\(325\) | 28.3906 | 1.57483 | ||||||||
\(326\) | −30.1302 | −1.66876 | ||||||||
\(327\) | −26.3244 | −1.45574 | ||||||||
\(328\) | −26.5817 | −1.46773 | ||||||||
\(329\) | −13.0091 | −0.717214 | ||||||||
\(330\) | −26.7325 | −1.47158 | ||||||||
\(331\) | 25.8065 | 1.41845 | 0.709227 | − | 0.704980i | \(-0.249044\pi\) | ||||
0.709227 | + | 0.704980i | \(0.249044\pi\) | |||||||
\(332\) | −48.8655 | −2.68184 | ||||||||
\(333\) | 0.721177 | 0.0395203 | ||||||||
\(334\) | 41.9331 | 2.29448 | ||||||||
\(335\) | −16.8308 | −0.919566 | ||||||||
\(336\) | −0.768709 | −0.0419365 | ||||||||
\(337\) | −22.7729 | −1.24052 | −0.620258 | − | 0.784398i | \(-0.712972\pi\) | ||||
−0.620258 | + | 0.784398i | \(0.712972\pi\) | |||||||
\(338\) | 19.6917 | 1.07109 | ||||||||
\(339\) | −26.9247 | −1.46235 | ||||||||
\(340\) | −48.7844 | −2.64571 | ||||||||
\(341\) | −1.39887 | −0.0757530 | ||||||||
\(342\) | −6.73510 | −0.364193 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −0.979816 | −0.0528281 | ||||||||
\(345\) | −9.27395 | −0.499293 | ||||||||
\(346\) | 32.7391 | 1.76007 | ||||||||
\(347\) | 5.08848 | 0.273164 | 0.136582 | − | 0.990629i | \(-0.456388\pi\) | ||||
0.136582 | + | 0.990629i | \(0.456388\pi\) | |||||||
\(348\) | 37.9413 | 2.03387 | ||||||||
\(349\) | 28.1154 | 1.50498 | 0.752491 | − | 0.658603i | \(-0.228852\pi\) | ||||
0.752491 | + | 0.658603i | \(0.228852\pi\) | |||||||
\(350\) | 30.9988 | 1.65696 | ||||||||
\(351\) | −9.28919 | −0.495820 | ||||||||
\(352\) | 7.25696 | 0.386798 | ||||||||
\(353\) | 27.6746 | 1.47297 | 0.736484 | − | 0.676455i | \(-0.236485\pi\) | ||||
0.736484 | + | 0.676455i | \(0.236485\pi\) | |||||||
\(354\) | 24.3431 | 1.29382 | ||||||||
\(355\) | 52.1449 | 2.76756 | ||||||||
\(356\) | 34.0389 | 1.80406 | ||||||||
\(357\) | 6.59485 | 0.349036 | ||||||||
\(358\) | −8.52379 | −0.450496 | ||||||||
\(359\) | −28.8774 | −1.52409 | −0.762045 | − | 0.647524i | \(-0.775804\pi\) | ||||
−0.762045 | + | 0.647524i | \(0.775804\pi\) | |||||||
\(360\) | −9.45534 | −0.498340 | ||||||||
\(361\) | −2.61636 | −0.137703 | ||||||||
\(362\) | −43.4580 | −2.28410 | ||||||||
\(363\) | −17.4446 | −0.915603 | ||||||||
\(364\) | −7.02293 | −0.368101 | ||||||||
\(365\) | −20.6676 | −1.08179 | ||||||||
\(366\) | −47.0645 | −2.46010 | ||||||||
\(367\) | 3.08789 | 0.161187 | 0.0805933 | − | 0.996747i | \(-0.474319\pi\) | ||||
0.0805933 | + | 0.996747i | \(0.474319\pi\) | |||||||
\(368\) | −0.446191 | −0.0232593 | ||||||||
\(369\) | 6.27791 | 0.326815 | ||||||||
\(370\) | −9.90655 | −0.515017 | ||||||||
\(371\) | 9.51840 | 0.494170 | ||||||||
\(372\) | −6.41108 | −0.332399 | ||||||||
\(373\) | 10.6862 | 0.553310 | 0.276655 | − | 0.960969i | \(-0.410774\pi\) | ||||
0.276655 | + | 0.960969i | \(0.410774\pi\) | |||||||
\(374\) | 11.0341 | 0.570562 | ||||||||
\(375\) | 69.8661 | 3.60787 | ||||||||
\(376\) | −39.7244 | −2.04863 | ||||||||
\(377\) | 12.5057 | 0.644076 | ||||||||
\(378\) | −10.1426 | −0.521677 | ||||||||
\(379\) | 14.3387 | 0.736528 | 0.368264 | − | 0.929721i | \(-0.379952\pi\) | ||||
0.368264 | + | 0.929721i | \(0.379952\pi\) | |||||||
\(380\) | 57.7593 | 2.96299 | ||||||||
\(381\) | 12.9418 | 0.663028 | ||||||||
\(382\) | −34.6458 | −1.77263 | ||||||||
\(383\) | 7.00517 | 0.357947 | 0.178974 | − | 0.983854i | \(-0.442722\pi\) | ||||
0.178974 | + | 0.983854i | \(0.442722\pi\) | |||||||
\(384\) | 36.8063 | 1.87826 | ||||||||
\(385\) | −6.00623 | −0.306106 | ||||||||
\(386\) | 14.6457 | 0.745448 | ||||||||
\(387\) | 0.231407 | 0.0117631 | ||||||||
\(388\) | −16.0859 | −0.816636 | ||||||||
\(389\) | 24.4251 | 1.23840 | 0.619202 | − | 0.785232i | \(-0.287456\pi\) | ||||
0.619202 | + | 0.785232i | \(0.287456\pi\) | |||||||
\(390\) | −40.3822 | −2.04483 | ||||||||
\(391\) | 3.82793 | 0.193587 | ||||||||
\(392\) | −3.05358 | −0.154229 | ||||||||
\(393\) | −20.9957 | −1.05910 | ||||||||
\(394\) | 31.5065 | 1.58727 | ||||||||
\(395\) | 22.9485 | 1.15467 | ||||||||
\(396\) | 3.35282 | 0.168485 | ||||||||
\(397\) | −17.4894 | −0.877770 | −0.438885 | − | 0.898543i | \(-0.644627\pi\) | ||||
−0.438885 | + | 0.898543i | \(0.644627\pi\) | |||||||
\(398\) | −49.2870 | −2.47053 | ||||||||
\(399\) | −7.80810 | −0.390894 | ||||||||
\(400\) | 5.35389 | 0.267694 | ||||||||
\(401\) | −10.3323 | −0.515972 | −0.257986 | − | 0.966149i | \(-0.583059\pi\) | ||||
−0.257986 | + | 0.966149i | \(0.583059\pi\) | |||||||
\(402\) | 17.4469 | 0.870171 | ||||||||
\(403\) | −2.11313 | −0.105263 | ||||||||
\(404\) | 15.1846 | 0.755461 | ||||||||
\(405\) | −45.6990 | −2.27080 | ||||||||
\(406\) | 13.6546 | 0.677665 | ||||||||
\(407\) | 1.39887 | 0.0693393 | ||||||||
\(408\) | 20.1379 | 0.996976 | ||||||||
\(409\) | −2.51580 | −0.124399 | −0.0621993 | − | 0.998064i | \(-0.519811\pi\) | ||||
−0.0621993 | + | 0.998064i | \(0.519811\pi\) | |||||||
\(410\) | −86.2374 | −4.25896 | ||||||||
\(411\) | −6.05291 | −0.298568 | ||||||||
\(412\) | 31.3414 | 1.54408 | ||||||||
\(413\) | 5.46939 | 0.269131 | ||||||||
\(414\) | 1.86311 | 0.0915669 | ||||||||
\(415\) | −63.1301 | −3.09893 | ||||||||
\(416\) | 10.9624 | 0.537475 | ||||||||
\(417\) | −36.4336 | −1.78416 | ||||||||
\(418\) | −13.0641 | −0.638986 | ||||||||
\(419\) | 8.72331 | 0.426162 | 0.213081 | − | 0.977035i | \(-0.431650\pi\) | ||||
0.213081 | + | 0.977035i | \(0.431650\pi\) | |||||||
\(420\) | −27.5269 | −1.34317 | ||||||||
\(421\) | −10.5817 | −0.515721 | −0.257861 | − | 0.966182i | \(-0.583018\pi\) | ||||
−0.257861 | + | 0.966182i | \(0.583018\pi\) | |||||||
\(422\) | −52.9348 | −2.57683 | ||||||||
\(423\) | 9.38186 | 0.456161 | ||||||||
\(424\) | 29.0652 | 1.41153 | ||||||||
\(425\) | −45.9317 | −2.22801 | ||||||||
\(426\) | −54.0535 | −2.61890 | ||||||||
\(427\) | −10.5744 | −0.511732 | ||||||||
\(428\) | −35.1533 | −1.69920 | ||||||||
\(429\) | 5.70222 | 0.275306 | ||||||||
\(430\) | −3.17875 | −0.153293 | ||||||||
\(431\) | −18.8627 | −0.908583 | −0.454291 | − | 0.890853i | \(-0.650107\pi\) | ||||
−0.454291 | + | 0.890853i | \(0.650107\pi\) | |||||||
\(432\) | −1.75175 | −0.0842812 | ||||||||
\(433\) | 0.797791 | 0.0383394 | 0.0191697 | − | 0.999816i | \(-0.493898\pi\) | ||||
0.0191697 | + | 0.999816i | \(0.493898\pi\) | |||||||
\(434\) | −2.30726 | −0.110752 | ||||||||
\(435\) | 49.0169 | 2.35018 | ||||||||
\(436\) | −45.3534 | −2.17203 | ||||||||
\(437\) | −4.53215 | −0.216802 | ||||||||
\(438\) | 21.4241 | 1.02368 | ||||||||
\(439\) | −34.8042 | −1.66111 | −0.830556 | − | 0.556935i | \(-0.811977\pi\) | ||||
−0.830556 | + | 0.556935i | \(0.811977\pi\) | |||||||
\(440\) | −18.3405 | −0.874351 | ||||||||
\(441\) | 0.721177 | 0.0343418 | ||||||||
\(442\) | 16.6682 | 0.792825 | ||||||||
\(443\) | 17.7165 | 0.841737 | 0.420869 | − | 0.907122i | \(-0.361725\pi\) | ||||
0.420869 | + | 0.907122i | \(0.361725\pi\) | |||||||
\(444\) | 6.41108 | 0.304257 | ||||||||
\(445\) | 43.9754 | 2.08463 | ||||||||
\(446\) | −47.1476 | −2.23250 | ||||||||
\(447\) | −15.9771 | −0.755690 | ||||||||
\(448\) | 12.7665 | 0.603159 | ||||||||
\(449\) | 4.61766 | 0.217921 | 0.108960 | − | 0.994046i | \(-0.465248\pi\) | ||||
0.108960 | + | 0.994046i | \(0.465248\pi\) | |||||||
\(450\) | −22.3556 | −1.05385 | ||||||||
\(451\) | 12.1773 | 0.573406 | ||||||||
\(452\) | −46.3876 | −2.18189 | ||||||||
\(453\) | 21.8304 | 1.02568 | ||||||||
\(454\) | −5.33440 | −0.250356 | ||||||||
\(455\) | −9.07303 | −0.425350 | ||||||||
\(456\) | −23.8427 | −1.11654 | ||||||||
\(457\) | −13.4884 | −0.630959 | −0.315479 | − | 0.948932i | \(-0.602165\pi\) | ||||
−0.315479 | + | 0.948932i | \(0.602165\pi\) | |||||||
\(458\) | 20.9756 | 0.980124 | ||||||||
\(459\) | 15.0285 | 0.701470 | ||||||||
\(460\) | −15.9778 | −0.744967 | ||||||||
\(461\) | −11.5875 | −0.539683 | −0.269841 | − | 0.962905i | \(-0.586971\pi\) | ||||
−0.269841 | + | 0.962905i | \(0.586971\pi\) | |||||||
\(462\) | 6.22607 | 0.289663 | ||||||||
\(463\) | −11.7981 | −0.548305 | −0.274152 | − | 0.961686i | \(-0.588397\pi\) | ||||
−0.274152 | + | 0.961686i | \(0.588397\pi\) | |||||||
\(464\) | 2.35832 | 0.109482 | ||||||||
\(465\) | −8.28257 | −0.384095 | ||||||||
\(466\) | −31.1635 | −1.44362 | ||||||||
\(467\) | −27.9457 | −1.29317 | −0.646586 | − | 0.762841i | \(-0.723804\pi\) | ||||
−0.646586 | + | 0.762841i | \(0.723804\pi\) | |||||||
\(468\) | 5.06477 | 0.234119 | ||||||||
\(469\) | 3.91995 | 0.181006 | ||||||||
\(470\) | −128.875 | −5.94457 | ||||||||
\(471\) | 20.8047 | 0.958628 | ||||||||
\(472\) | 16.7013 | 0.768738 | ||||||||
\(473\) | 0.448860 | 0.0206386 | ||||||||
\(474\) | −23.7885 | −1.09264 | ||||||||
\(475\) | 54.3817 | 2.49520 | ||||||||
\(476\) | 11.3620 | 0.520778 | ||||||||
\(477\) | −6.86445 | −0.314301 | ||||||||
\(478\) | −67.1563 | −3.07166 | ||||||||
\(479\) | 22.5853 | 1.03195 | 0.515975 | − | 0.856604i | \(-0.327430\pi\) | ||||
0.515975 | + | 0.856604i | \(0.327430\pi\) | |||||||
\(480\) | 42.9678 | 1.96120 | ||||||||
\(481\) | 2.11313 | 0.0963506 | ||||||||
\(482\) | 36.1516 | 1.64666 | ||||||||
\(483\) | 2.15993 | 0.0982802 | ||||||||
\(484\) | −30.0547 | −1.36612 | ||||||||
\(485\) | −20.7816 | −0.943643 | ||||||||
\(486\) | 16.9440 | 0.768596 | ||||||||
\(487\) | −11.6778 | −0.529172 | −0.264586 | − | 0.964362i | \(-0.585235\pi\) | ||||
−0.264586 | + | 0.964362i | \(0.585235\pi\) | |||||||
\(488\) | −32.2899 | −1.46169 | ||||||||
\(489\) | 25.1910 | 1.13917 | ||||||||
\(490\) | −9.90655 | −0.447532 | ||||||||
\(491\) | −27.8628 | −1.25743 | −0.628716 | − | 0.777635i | \(-0.716419\pi\) | ||||
−0.628716 | + | 0.777635i | \(0.716419\pi\) | |||||||
\(492\) | 55.8091 | 2.51607 | ||||||||
\(493\) | −20.2323 | −0.911217 | ||||||||
\(494\) | −19.7346 | −0.887904 | ||||||||
\(495\) | 4.33156 | 0.194689 | ||||||||
\(496\) | −0.398494 | −0.0178929 | ||||||||
\(497\) | −12.1447 | −0.544764 | ||||||||
\(498\) | 65.4408 | 2.93247 | ||||||||
\(499\) | −26.8948 | −1.20397 | −0.601987 | − | 0.798506i | \(-0.705624\pi\) | ||||
−0.601987 | + | 0.798506i | \(0.705624\pi\) | |||||||
\(500\) | 120.370 | 5.38310 | ||||||||
\(501\) | −35.0590 | −1.56632 | ||||||||
\(502\) | −28.7871 | −1.28483 | ||||||||
\(503\) | −31.0710 | −1.38539 | −0.692693 | − | 0.721232i | \(-0.743576\pi\) | ||||
−0.692693 | + | 0.721232i | \(0.743576\pi\) | |||||||
\(504\) | 2.20218 | 0.0980927 | ||||||||
\(505\) | 19.6172 | 0.872954 | ||||||||
\(506\) | 3.61388 | 0.160656 | ||||||||
\(507\) | −16.4637 | −0.731177 | ||||||||
\(508\) | 22.2970 | 0.989268 | ||||||||
\(509\) | −0.832404 | −0.0368957 | −0.0184478 | − | 0.999830i | \(-0.505872\pi\) | ||||
−0.0184478 | + | 0.999830i | \(0.505872\pi\) | |||||||
\(510\) | 65.3322 | 2.89296 | ||||||||
\(511\) | 4.81354 | 0.212938 | ||||||||
\(512\) | 4.50095 | 0.198916 | ||||||||
\(513\) | −17.7933 | −0.785592 | ||||||||
\(514\) | −37.2200 | −1.64170 | ||||||||
\(515\) | 40.4905 | 1.78422 | ||||||||
\(516\) | 2.05715 | 0.0905609 | ||||||||
\(517\) | 18.1980 | 0.800347 | ||||||||
\(518\) | 2.30726 | 0.101375 | ||||||||
\(519\) | −27.3722 | −1.20151 | ||||||||
\(520\) | −27.7053 | −1.21496 | ||||||||
\(521\) | 8.99534 | 0.394093 | 0.197047 | − | 0.980394i | \(-0.436865\pi\) | ||||
0.197047 | + | 0.980394i | \(0.436865\pi\) | |||||||
\(522\) | −9.84736 | −0.431007 | ||||||||
\(523\) | 40.2812 | 1.76137 | 0.880686 | − | 0.473701i | \(-0.157082\pi\) | ||||
0.880686 | + | 0.473701i | \(0.157082\pi\) | |||||||
\(524\) | −36.1728 | −1.58022 | ||||||||
\(525\) | −25.9172 | −1.13112 | ||||||||
\(526\) | −59.4899 | −2.59388 | ||||||||
\(527\) | 3.41873 | 0.148922 | ||||||||
\(528\) | 1.07532 | 0.0467974 | ||||||||
\(529\) | −21.7463 | −0.945491 | ||||||||
\(530\) | 94.2945 | 4.09589 | ||||||||
\(531\) | −3.94440 | −0.171172 | ||||||||
\(532\) | −13.4523 | −0.583231 | ||||||||
\(533\) | 18.3950 | 0.796777 | ||||||||
\(534\) | −45.5850 | −1.97265 | ||||||||
\(535\) | −45.4151 | −1.96347 | ||||||||
\(536\) | 11.9699 | 0.517021 | ||||||||
\(537\) | 7.12649 | 0.307531 | ||||||||
\(538\) | −10.5565 | −0.455123 | ||||||||
\(539\) | 1.39887 | 0.0602535 | ||||||||
\(540\) | −62.7288 | −2.69942 | ||||||||
\(541\) | −16.0304 | −0.689200 | −0.344600 | − | 0.938750i | \(-0.611986\pi\) | ||||
−0.344600 | + | 0.938750i | \(0.611986\pi\) | |||||||
\(542\) | 37.5421 | 1.61257 | ||||||||
\(543\) | 36.3339 | 1.55924 | ||||||||
\(544\) | −17.7355 | −0.760402 | ||||||||
\(545\) | −58.5927 | −2.50984 | ||||||||
\(546\) | 9.40512 | 0.402502 | ||||||||
\(547\) | −22.0665 | −0.943496 | −0.471748 | − | 0.881733i | \(-0.656377\pi\) | ||||
−0.471748 | + | 0.881733i | \(0.656377\pi\) | |||||||
\(548\) | −10.4283 | −0.445476 | ||||||||
\(549\) | 7.62602 | 0.325471 | ||||||||
\(550\) | −43.3632 | −1.84901 | ||||||||
\(551\) | 23.9544 | 1.02049 | ||||||||
\(552\) | 6.59553 | 0.280724 | ||||||||
\(553\) | −5.34478 | −0.227283 | ||||||||
\(554\) | −27.2051 | −1.15583 | ||||||||
\(555\) | 8.28257 | 0.351576 | ||||||||
\(556\) | −62.7701 | −2.66204 | ||||||||
\(557\) | 20.0965 | 0.851516 | 0.425758 | − | 0.904837i | \(-0.360007\pi\) | ||||
0.425758 | + | 0.904837i | \(0.360007\pi\) | |||||||
\(558\) | 1.66395 | 0.0704404 | ||||||||
\(559\) | 0.678049 | 0.0286784 | ||||||||
\(560\) | −1.71099 | −0.0723024 | ||||||||
\(561\) | −9.22532 | −0.389493 | ||||||||
\(562\) | 59.2169 | 2.49792 | ||||||||
\(563\) | 10.6001 | 0.446743 | 0.223371 | − | 0.974733i | \(-0.428294\pi\) | ||||
0.223371 | + | 0.974733i | \(0.428294\pi\) | |||||||
\(564\) | 83.4024 | 3.51187 | ||||||||
\(565\) | −59.9288 | −2.52123 | ||||||||
\(566\) | −67.1818 | −2.82386 | ||||||||
\(567\) | 10.6434 | 0.446982 | ||||||||
\(568\) | −37.0848 | −1.55605 | ||||||||
\(569\) | 19.5307 | 0.818770 | 0.409385 | − | 0.912362i | \(-0.365743\pi\) | ||||
0.409385 | + | 0.912362i | \(0.365743\pi\) | |||||||
\(570\) | −77.3513 | −3.23989 | ||||||||
\(571\) | −6.55585 | −0.274354 | −0.137177 | − | 0.990547i | \(-0.543803\pi\) | ||||
−0.137177 | + | 0.990547i | \(0.543803\pi\) | |||||||
\(572\) | 9.82415 | 0.410768 | ||||||||
\(573\) | 28.9663 | 1.21009 | ||||||||
\(574\) | 20.0849 | 0.838329 | ||||||||
\(575\) | −15.0434 | −0.627355 | ||||||||
\(576\) | −9.20688 | −0.383620 | ||||||||
\(577\) | 13.1476 | 0.547341 | 0.273670 | − | 0.961824i | \(-0.411762\pi\) | ||||
0.273670 | + | 0.961824i | \(0.411762\pi\) | |||||||
\(578\) | 12.2569 | 0.509819 | ||||||||
\(579\) | −12.2449 | −0.508879 | ||||||||
\(580\) | 84.4495 | 3.50658 | ||||||||
\(581\) | 14.7032 | 0.609990 | ||||||||
\(582\) | 21.5422 | 0.892954 | ||||||||
\(583\) | −13.3150 | −0.551450 | ||||||||
\(584\) | 14.6985 | 0.608230 | ||||||||
\(585\) | 6.54326 | 0.270530 | ||||||||
\(586\) | 46.6098 | 1.92543 | ||||||||
\(587\) | −11.3558 | −0.468706 | −0.234353 | − | 0.972152i | \(-0.575297\pi\) | ||||
−0.234353 | + | 0.972152i | \(0.575297\pi\) | |||||||
\(588\) | 6.41108 | 0.264389 | ||||||||
\(589\) | −4.04767 | −0.166781 | ||||||||
\(590\) | 54.1828 | 2.23067 | ||||||||
\(591\) | −26.3416 | −1.08355 | ||||||||
\(592\) | 0.398494 | 0.0163780 | ||||||||
\(593\) | 26.6770 | 1.09549 | 0.547746 | − | 0.836645i | \(-0.315486\pi\) | ||||
0.547746 | + | 0.836645i | \(0.315486\pi\) | |||||||
\(594\) | 14.1881 | 0.582146 | ||||||||
\(595\) | 14.6788 | 0.601771 | ||||||||
\(596\) | −27.5263 | −1.12752 | ||||||||
\(597\) | 41.2074 | 1.68651 | ||||||||
\(598\) | 5.45913 | 0.223241 | ||||||||
\(599\) | 22.4145 | 0.915832 | 0.457916 | − | 0.888995i | \(-0.348596\pi\) | ||||
0.457916 | + | 0.888995i | \(0.348596\pi\) | |||||||
\(600\) | −79.1403 | −3.23089 | ||||||||
\(601\) | −11.2532 | −0.459028 | −0.229514 | − | 0.973305i | \(-0.573714\pi\) | ||||
−0.229514 | + | 0.973305i | \(0.573714\pi\) | |||||||
\(602\) | 0.740341 | 0.0301740 | ||||||||
\(603\) | −2.82698 | −0.115123 | ||||||||
\(604\) | 37.6108 | 1.53036 | ||||||||
\(605\) | −38.8281 | −1.57859 | ||||||||
\(606\) | −20.3352 | −0.826062 | ||||||||
\(607\) | 20.9119 | 0.848787 | 0.424393 | − | 0.905478i | \(-0.360487\pi\) | ||||
0.424393 | + | 0.905478i | \(0.360487\pi\) | |||||||
\(608\) | 20.9983 | 0.851592 | ||||||||
\(609\) | −11.4162 | −0.462607 | ||||||||
\(610\) | −104.756 | −4.24144 | ||||||||
\(611\) | 27.4899 | 1.11212 | ||||||||
\(612\) | −8.19403 | −0.331224 | ||||||||
\(613\) | −43.6287 | −1.76215 | −0.881073 | − | 0.472980i | \(-0.843178\pi\) | ||||
−0.881073 | + | 0.472980i | \(0.843178\pi\) | |||||||
\(614\) | 39.1245 | 1.57894 | ||||||||
\(615\) | 72.1006 | 2.90738 | ||||||||
\(616\) | 4.27156 | 0.172106 | ||||||||
\(617\) | 43.6757 | 1.75832 | 0.879159 | − | 0.476529i | \(-0.158105\pi\) | ||||
0.879159 | + | 0.476529i | \(0.158105\pi\) | |||||||
\(618\) | −41.9725 | −1.68838 | ||||||||
\(619\) | −19.3468 | −0.777612 | −0.388806 | − | 0.921320i | \(-0.627112\pi\) | ||||
−0.388806 | + | 0.921320i | \(0.627112\pi\) | |||||||
\(620\) | −14.2698 | −0.573087 | ||||||||
\(621\) | 4.92210 | 0.197517 | ||||||||
\(622\) | −7.10385 | −0.284839 | ||||||||
\(623\) | −10.2420 | −0.410337 | ||||||||
\(624\) | 1.62438 | 0.0650274 | ||||||||
\(625\) | 88.3310 | 3.53324 | ||||||||
\(626\) | 66.4753 | 2.65689 | ||||||||
\(627\) | 10.9225 | 0.436203 | ||||||||
\(628\) | 35.8436 | 1.43032 | ||||||||
\(629\) | −3.41873 | −0.136314 | ||||||||
\(630\) | 7.14438 | 0.284639 | ||||||||
\(631\) | 32.3599 | 1.28823 | 0.644113 | − | 0.764930i | \(-0.277227\pi\) | ||||
0.644113 | + | 0.764930i | \(0.277227\pi\) | |||||||
\(632\) | −16.3207 | −0.649204 | ||||||||
\(633\) | 44.2572 | 1.75907 | ||||||||
\(634\) | −49.2276 | −1.95508 | ||||||||
\(635\) | 28.8058 | 1.14312 | ||||||||
\(636\) | −61.0232 | −2.41973 | ||||||||
\(637\) | 2.11313 | 0.0837254 | ||||||||
\(638\) | −19.1009 | −0.756214 | ||||||||
\(639\) | 8.75847 | 0.346480 | ||||||||
\(640\) | 81.9232 | 3.23830 | ||||||||
\(641\) | 19.6092 | 0.774516 | 0.387258 | − | 0.921971i | \(-0.373422\pi\) | ||||
0.387258 | + | 0.921971i | \(0.373422\pi\) | |||||||
\(642\) | 47.0774 | 1.85800 | ||||||||
\(643\) | −41.0425 | −1.61856 | −0.809280 | − | 0.587423i | \(-0.800142\pi\) | ||||
−0.809280 | + | 0.587423i | \(0.800142\pi\) | |||||||
\(644\) | 3.72127 | 0.146638 | ||||||||
\(645\) | 2.65766 | 0.104645 | ||||||||
\(646\) | 31.9276 | 1.25618 | ||||||||
\(647\) | −18.9003 | −0.743048 | −0.371524 | − | 0.928423i | \(-0.621165\pi\) | ||||
−0.371524 | + | 0.928423i | \(0.621165\pi\) | |||||||
\(648\) | 32.5006 | 1.27675 | ||||||||
\(649\) | −7.65096 | −0.300327 | ||||||||
\(650\) | −65.5046 | −2.56930 | ||||||||
\(651\) | 1.92904 | 0.0756049 | ||||||||
\(652\) | 43.4006 | 1.69970 | ||||||||
\(653\) | 30.5677 | 1.19621 | 0.598104 | − | 0.801419i | \(-0.295921\pi\) | ||||
0.598104 | + | 0.801419i | \(0.295921\pi\) | |||||||
\(654\) | 60.7374 | 2.37502 | ||||||||
\(655\) | −46.7322 | −1.82598 | ||||||||
\(656\) | 3.46893 | 0.135439 | ||||||||
\(657\) | −3.47141 | −0.135433 | ||||||||
\(658\) | 30.0154 | 1.17012 | ||||||||
\(659\) | 4.80866 | 0.187319 | 0.0936594 | − | 0.995604i | \(-0.470144\pi\) | ||||
0.0936594 | + | 0.995604i | \(0.470144\pi\) | |||||||
\(660\) | 38.5064 | 1.49886 | ||||||||
\(661\) | 8.83833 | 0.343771 | 0.171886 | − | 0.985117i | \(-0.445014\pi\) | ||||
0.171886 | + | 0.985117i | \(0.445014\pi\) | |||||||
\(662\) | −59.5424 | −2.31418 | ||||||||
\(663\) | −13.9358 | −0.541221 | ||||||||
\(664\) | 44.8974 | 1.74236 | ||||||||
\(665\) | −17.3792 | −0.673937 | ||||||||
\(666\) | −1.66395 | −0.0644766 | ||||||||
\(667\) | −6.62644 | −0.256577 | ||||||||
\(668\) | −60.4019 | −2.33702 | ||||||||
\(669\) | 39.4187 | 1.52402 | ||||||||
\(670\) | 38.8332 | 1.50026 | ||||||||
\(671\) | 14.7922 | 0.571047 | ||||||||
\(672\) | −10.0073 | −0.386041 | ||||||||
\(673\) | −37.0177 | −1.42693 | −0.713464 | − | 0.700691i | \(-0.752875\pi\) | ||||
−0.713464 | + | 0.700691i | \(0.752875\pi\) | |||||||
\(674\) | 52.5430 | 2.02388 | ||||||||
\(675\) | −59.0607 | −2.27325 | ||||||||
\(676\) | −28.3647 | −1.09095 | ||||||||
\(677\) | −23.6474 | −0.908844 | −0.454422 | − | 0.890786i | \(-0.650154\pi\) | ||||
−0.454422 | + | 0.890786i | \(0.650154\pi\) | |||||||
\(678\) | 62.1224 | 2.38580 | ||||||||
\(679\) | 4.84009 | 0.185746 | ||||||||
\(680\) | 44.8229 | 1.71888 | ||||||||
\(681\) | 4.45993 | 0.170905 | ||||||||
\(682\) | 3.22756 | 0.123590 | ||||||||
\(683\) | 20.2113 | 0.773363 | 0.386682 | − | 0.922213i | \(-0.373621\pi\) | ||||
0.386682 | + | 0.922213i | \(0.373621\pi\) | |||||||
\(684\) | 9.70149 | 0.370946 | ||||||||
\(685\) | −13.4725 | −0.514759 | ||||||||
\(686\) | 2.30726 | 0.0880917 | ||||||||
\(687\) | −17.5371 | −0.669081 | ||||||||
\(688\) | 0.127866 | 0.00487486 | ||||||||
\(689\) | −20.1136 | −0.766269 | ||||||||
\(690\) | 21.3975 | 0.814587 | ||||||||
\(691\) | 7.57622 | 0.288213 | 0.144106 | − | 0.989562i | \(-0.453969\pi\) | ||||
0.144106 | + | 0.989562i | \(0.453969\pi\) | |||||||
\(692\) | −47.1586 | −1.79270 | ||||||||
\(693\) | −1.00883 | −0.0383223 | ||||||||
\(694\) | −11.7405 | −0.445662 | ||||||||
\(695\) | −81.0936 | −3.07606 | ||||||||
\(696\) | −34.8603 | −1.32138 | ||||||||
\(697\) | −29.7603 | −1.12725 | ||||||||
\(698\) | −64.8696 | −2.45535 | ||||||||
\(699\) | 26.0549 | 0.985487 | ||||||||
\(700\) | −44.6518 | −1.68768 | ||||||||
\(701\) | 8.33491 | 0.314805 | 0.157403 | − | 0.987535i | \(-0.449688\pi\) | ||||
0.157403 | + | 0.987535i | \(0.449688\pi\) | |||||||
\(702\) | 21.4326 | 0.808922 | ||||||||
\(703\) | 4.04767 | 0.152661 | ||||||||
\(704\) | −17.8586 | −0.673072 | ||||||||
\(705\) | 107.749 | 4.05805 | ||||||||
\(706\) | −63.8525 | −2.40312 | ||||||||
\(707\) | −4.56890 | −0.171831 | ||||||||
\(708\) | −35.0647 | −1.31781 | ||||||||
\(709\) | −17.8952 | −0.672068 | −0.336034 | − | 0.941850i | \(-0.609086\pi\) | ||||
−0.336034 | + | 0.941850i | \(0.609086\pi\) | |||||||
\(710\) | −120.312 | −4.51523 | ||||||||
\(711\) | 3.85453 | 0.144556 | ||||||||
\(712\) | −31.2748 | −1.17207 | ||||||||
\(713\) | 1.11969 | 0.0419329 | ||||||||
\(714\) | −15.2160 | −0.569446 | ||||||||
\(715\) | 12.6920 | 0.474653 | ||||||||
\(716\) | 12.2780 | 0.458849 | ||||||||
\(717\) | 56.1474 | 2.09686 | ||||||||
\(718\) | 66.6277 | 2.48652 | ||||||||
\(719\) | 17.4259 | 0.649876 | 0.324938 | − | 0.945735i | \(-0.394657\pi\) | ||||
0.324938 | + | 0.945735i | \(0.394657\pi\) | |||||||
\(720\) | 1.23392 | 0.0459857 | ||||||||
\(721\) | −9.43035 | −0.351204 | ||||||||
\(722\) | 6.03664 | 0.224660 | ||||||||
\(723\) | −30.2253 | −1.12409 | ||||||||
\(724\) | 62.5984 | 2.32645 | ||||||||
\(725\) | 79.5112 | 2.95297 | ||||||||
\(726\) | 40.2493 | 1.49379 | ||||||||
\(727\) | −38.7381 | −1.43672 | −0.718359 | − | 0.695673i | \(-0.755106\pi\) | ||||
−0.718359 | + | 0.695673i | \(0.755106\pi\) | |||||||
\(728\) | 6.45263 | 0.239151 | ||||||||
\(729\) | 17.7639 | 0.657923 | ||||||||
\(730\) | 47.6856 | 1.76492 | ||||||||
\(731\) | −1.09698 | −0.0405733 | ||||||||
\(732\) | 67.7934 | 2.50572 | ||||||||
\(733\) | 17.4379 | 0.644085 | 0.322042 | − | 0.946725i | \(-0.395631\pi\) | ||||
0.322042 | + | 0.946725i | \(0.395631\pi\) | |||||||
\(734\) | −7.12458 | −0.262973 | ||||||||
\(735\) | 8.28257 | 0.305507 | ||||||||
\(736\) | −5.80868 | −0.214111 | ||||||||
\(737\) | −5.48349 | −0.201987 | ||||||||
\(738\) | −14.4848 | −0.533193 | ||||||||
\(739\) | −18.6831 | −0.687269 | −0.343635 | − | 0.939103i | \(-0.611658\pi\) | ||||
−0.343635 | + | 0.939103i | \(0.611658\pi\) | |||||||
\(740\) | 14.2698 | 0.524567 | ||||||||
\(741\) | 16.4996 | 0.606126 | ||||||||
\(742\) | −21.9614 | −0.806230 | ||||||||
\(743\) | 33.5624 | 1.23128 | 0.615642 | − | 0.788026i | \(-0.288897\pi\) | ||||
0.615642 | + | 0.788026i | \(0.288897\pi\) | |||||||
\(744\) | 5.89047 | 0.215955 | ||||||||
\(745\) | −35.5617 | −1.30288 | ||||||||
\(746\) | −24.6558 | −0.902715 | ||||||||
\(747\) | −10.6036 | −0.387965 | ||||||||
\(748\) | −15.8940 | −0.581141 | ||||||||
\(749\) | 10.5773 | 0.386486 | ||||||||
\(750\) | −161.199 | −5.88617 | ||||||||
\(751\) | 19.5412 | 0.713068 | 0.356534 | − | 0.934282i | \(-0.383958\pi\) | ||||
0.356534 | + | 0.934282i | \(0.383958\pi\) | |||||||
\(752\) | 5.18404 | 0.189043 | ||||||||
\(753\) | 24.0681 | 0.877089 | ||||||||
\(754\) | −28.8539 | −1.05080 | ||||||||
\(755\) | 48.5900 | 1.76837 | ||||||||
\(756\) | 14.6097 | 0.531350 | ||||||||
\(757\) | −38.0217 | −1.38192 | −0.690961 | − | 0.722892i | \(-0.742812\pi\) | ||||
−0.690961 | + | 0.722892i | \(0.742812\pi\) | |||||||
\(758\) | −33.0831 | −1.20163 | ||||||||
\(759\) | −3.02146 | −0.109672 | ||||||||
\(760\) | −53.0689 | −1.92501 | ||||||||
\(761\) | −11.9877 | −0.434554 | −0.217277 | − | 0.976110i | \(-0.569717\pi\) | ||||
−0.217277 | + | 0.976110i | \(0.569717\pi\) | |||||||
\(762\) | −29.8601 | −1.08172 | ||||||||
\(763\) | 13.6464 | 0.494033 | ||||||||
\(764\) | 49.9051 | 1.80550 | ||||||||
\(765\) | −10.5860 | −0.382737 | ||||||||
\(766\) | −16.1628 | −0.583985 | ||||||||
\(767\) | −11.5576 | −0.417319 | ||||||||
\(768\) | −35.6678 | −1.28705 | ||||||||
\(769\) | 43.5976 | 1.57217 | 0.786084 | − | 0.618119i | \(-0.212105\pi\) | ||||
0.786084 | + | 0.618119i | \(0.212105\pi\) | |||||||
\(770\) | 13.8580 | 0.499406 | ||||||||
\(771\) | 31.1186 | 1.12071 | ||||||||
\(772\) | −21.0962 | −0.759270 | ||||||||
\(773\) | −0.776548 | −0.0279305 | −0.0139652 | − | 0.999902i | \(-0.504445\pi\) | ||||
−0.0139652 | + | 0.999902i | \(0.504445\pi\) | |||||||
\(774\) | −0.533917 | −0.0191912 | ||||||||
\(775\) | −13.4353 | −0.482611 | ||||||||
\(776\) | 14.7796 | 0.530558 | ||||||||
\(777\) | −1.92904 | −0.0692038 | ||||||||
\(778\) | −56.3552 | −2.02043 | ||||||||
\(779\) | 35.2353 | 1.26244 | ||||||||
\(780\) | 58.1679 | 2.08275 | ||||||||
\(781\) | 16.9888 | 0.607908 | ||||||||
\(782\) | −8.83204 | −0.315833 | ||||||||
\(783\) | −26.0155 | −0.929717 | ||||||||
\(784\) | 0.398494 | 0.0142319 | ||||||||
\(785\) | 46.3069 | 1.65276 | ||||||||
\(786\) | 48.4427 | 1.72789 | ||||||||
\(787\) | 3.58891 | 0.127931 | 0.0639653 | − | 0.997952i | \(-0.479625\pi\) | ||||
0.0639653 | + | 0.997952i | \(0.479625\pi\) | |||||||
\(788\) | −45.3831 | −1.61670 | ||||||||
\(789\) | 49.7377 | 1.77071 | ||||||||
\(790\) | −52.9483 | −1.88382 | ||||||||
\(791\) | 13.9576 | 0.496275 | ||||||||
\(792\) | −3.08055 | −0.109463 | ||||||||
\(793\) | 22.3451 | 0.793500 | ||||||||
\(794\) | 40.3528 | 1.43207 | ||||||||
\(795\) | −78.8368 | −2.79605 | ||||||||
\(796\) | 70.9947 | 2.51634 | ||||||||
\(797\) | 35.3104 | 1.25076 | 0.625380 | − | 0.780321i | \(-0.284944\pi\) | ||||
0.625380 | + | 0.780321i | \(0.284944\pi\) | |||||||
\(798\) | 18.0153 | 0.637736 | ||||||||
\(799\) | −44.4745 | −1.57340 | ||||||||
\(800\) | 69.6989 | 2.46423 | ||||||||
\(801\) | 7.38629 | 0.260982 | ||||||||
\(802\) | 23.8394 | 0.841799 | ||||||||
\(803\) | −6.73351 | −0.237620 | ||||||||
\(804\) | −25.1311 | −0.886306 | ||||||||
\(805\) | 4.80756 | 0.169444 | ||||||||
\(806\) | 4.87556 | 0.171734 | ||||||||
\(807\) | 8.82599 | 0.310689 | ||||||||
\(808\) | −13.9515 | −0.490813 | ||||||||
\(809\) | −10.5463 | −0.370787 | −0.185394 | − | 0.982664i | \(-0.559356\pi\) | ||||
−0.185394 | + | 0.982664i | \(0.559356\pi\) | |||||||
\(810\) | 105.440 | 3.70477 | ||||||||
\(811\) | −10.1111 | −0.355047 | −0.177524 | − | 0.984117i | \(-0.556809\pi\) | ||||
−0.177524 | + | 0.984117i | \(0.556809\pi\) | |||||||
\(812\) | −19.6685 | −0.690230 | ||||||||
\(813\) | −31.3879 | −1.10082 | ||||||||
\(814\) | −3.22756 | −0.113126 | ||||||||
\(815\) | 56.0699 | 1.96404 | ||||||||
\(816\) | −2.62801 | −0.0919986 | ||||||||
\(817\) | 1.29879 | 0.0454390 | ||||||||
\(818\) | 5.80462 | 0.202954 | ||||||||
\(819\) | −1.52394 | −0.0532509 | ||||||||
\(820\) | 124.220 | 4.33793 | ||||||||
\(821\) | 12.1586 | 0.424336 | 0.212168 | − | 0.977233i | \(-0.431948\pi\) | ||||
0.212168 | + | 0.977233i | \(0.431948\pi\) | |||||||
\(822\) | 13.9656 | 0.487108 | ||||||||
\(823\) | 2.18408 | 0.0761321 | 0.0380661 | − | 0.999275i | \(-0.487880\pi\) | ||||
0.0380661 | + | 0.999275i | \(0.487880\pi\) | |||||||
\(824\) | −28.7964 | −1.00317 | ||||||||
\(825\) | 36.2547 | 1.26223 | ||||||||
\(826\) | −12.6193 | −0.439083 | ||||||||
\(827\) | −3.49929 | −0.121682 | −0.0608411 | − | 0.998147i | \(-0.519378\pi\) | ||||
−0.0608411 | + | 0.998147i | \(0.519378\pi\) | |||||||
\(828\) | −2.68369 | −0.0932647 | ||||||||
\(829\) | −18.6725 | −0.648522 | −0.324261 | − | 0.945968i | \(-0.605116\pi\) | ||||
−0.324261 | + | 0.945968i | \(0.605116\pi\) | |||||||
\(830\) | 145.658 | 5.05585 | ||||||||
\(831\) | 22.7454 | 0.789029 | ||||||||
\(832\) | −26.9773 | −0.935268 | ||||||||
\(833\) | −3.41873 | −0.118452 | ||||||||
\(834\) | 84.0618 | 2.91082 | ||||||||
\(835\) | −78.0342 | −2.70048 | ||||||||
\(836\) | 18.8180 | 0.650834 | ||||||||
\(837\) | 4.39593 | 0.151946 | ||||||||
\(838\) | −20.1270 | −0.695275 | ||||||||
\(839\) | 39.2784 | 1.35604 | 0.678020 | − | 0.735043i | \(-0.262838\pi\) | ||||
0.678020 | + | 0.735043i | \(0.262838\pi\) | |||||||
\(840\) | 25.2915 | 0.872641 | ||||||||
\(841\) | 6.02365 | 0.207712 | ||||||||
\(842\) | 24.4148 | 0.841390 | ||||||||
\(843\) | −49.5095 | −1.70520 | ||||||||
\(844\) | 76.2492 | 2.62461 | ||||||||
\(845\) | −36.6447 | −1.26062 | ||||||||
\(846\) | −21.6464 | −0.744219 | ||||||||
\(847\) | 9.04317 | 0.310727 | ||||||||
\(848\) | −3.79302 | −0.130253 | ||||||||
\(849\) | 56.1687 | 1.92771 | ||||||||
\(850\) | 105.976 | 3.63496 | ||||||||
\(851\) | −1.11969 | −0.0383826 | ||||||||
\(852\) | 77.8606 | 2.66746 | ||||||||
\(853\) | −18.5575 | −0.635398 | −0.317699 | − | 0.948192i | \(-0.602910\pi\) | ||||
−0.317699 | + | 0.948192i | \(0.602910\pi\) | |||||||
\(854\) | 24.3980 | 0.834881 | ||||||||
\(855\) | 12.5335 | 0.428637 | ||||||||
\(856\) | 32.2987 | 1.10395 | ||||||||
\(857\) | 43.7033 | 1.49288 | 0.746438 | − | 0.665454i | \(-0.231762\pi\) | ||||
0.746438 | + | 0.665454i | \(0.231762\pi\) | |||||||
\(858\) | −13.1565 | −0.449156 | ||||||||
\(859\) | −17.7615 | −0.606014 | −0.303007 | − | 0.952988i | \(-0.597991\pi\) | ||||
−0.303007 | + | 0.952988i | \(0.597991\pi\) | |||||||
\(860\) | 4.57879 | 0.156135 | ||||||||
\(861\) | −16.7924 | −0.572284 | ||||||||
\(862\) | 43.5211 | 1.48234 | ||||||||
\(863\) | 6.20644 | 0.211270 | 0.105635 | − | 0.994405i | \(-0.466313\pi\) | ||||
0.105635 | + | 0.994405i | \(0.466313\pi\) | |||||||
\(864\) | −22.8049 | −0.775840 | ||||||||
\(865\) | −60.9249 | −2.07151 | ||||||||
\(866\) | −1.84071 | −0.0625500 | ||||||||
\(867\) | −10.2476 | −0.348027 | ||||||||
\(868\) | 3.32347 | 0.112806 | ||||||||
\(869\) | 7.47664 | 0.253628 | ||||||||
\(870\) | −113.095 | −3.83428 | ||||||||
\(871\) | −8.28337 | −0.280671 | ||||||||
\(872\) | 41.6705 | 1.41114 | ||||||||
\(873\) | −3.49056 | −0.118138 | ||||||||
\(874\) | 10.4569 | 0.353709 | ||||||||
\(875\) | −36.2181 | −1.22440 | ||||||||
\(876\) | −30.8600 | −1.04266 | ||||||||
\(877\) | 35.6868 | 1.20506 | 0.602528 | − | 0.798098i | \(-0.294160\pi\) | ||||
0.602528 | + | 0.798098i | \(0.294160\pi\) | |||||||
\(878\) | 80.3024 | 2.71008 | ||||||||
\(879\) | −38.9691 | −1.31439 | ||||||||
\(880\) | 2.39345 | 0.0806831 | ||||||||
\(881\) | 39.6969 | 1.33742 | 0.668711 | − | 0.743522i | \(-0.266846\pi\) | ||||
0.668711 | + | 0.743522i | \(0.266846\pi\) | |||||||
\(882\) | −1.66395 | −0.0560280 | ||||||||
\(883\) | −50.1279 | −1.68694 | −0.843470 | − | 0.537176i | \(-0.819491\pi\) | ||||
−0.843470 | + | 0.537176i | \(0.819491\pi\) | |||||||
\(884\) | −24.0095 | −0.807526 | ||||||||
\(885\) | −45.3007 | −1.52277 | ||||||||
\(886\) | −40.8767 | −1.37328 | ||||||||
\(887\) | −25.2144 | −0.846617 | −0.423309 | − | 0.905986i | \(-0.639131\pi\) | ||||
−0.423309 | + | 0.905986i | \(0.639131\pi\) | |||||||
\(888\) | −5.89047 | −0.197671 | ||||||||
\(889\) | −6.70895 | −0.225011 | ||||||||
\(890\) | −101.463 | −3.40104 | ||||||||
\(891\) | −14.8888 | −0.498792 | ||||||||
\(892\) | 67.9131 | 2.27390 | ||||||||
\(893\) | 52.6565 | 1.76208 | ||||||||
\(894\) | 36.8633 | 1.23289 | ||||||||
\(895\) | 15.8621 | 0.530211 | ||||||||
\(896\) | −19.0801 | −0.637423 | ||||||||
\(897\) | −4.56422 | −0.152395 | ||||||||
\(898\) | −10.6542 | −0.355534 | ||||||||
\(899\) | −5.91808 | −0.197379 | ||||||||
\(900\) | 32.2018 | 1.07339 | ||||||||
\(901\) | 32.5408 | 1.08409 | ||||||||
\(902\) | −28.0962 | −0.935501 | ||||||||
\(903\) | −0.618977 | −0.0205983 | ||||||||
\(904\) | 42.6207 | 1.41754 | ||||||||
\(905\) | 80.8719 | 2.68827 | ||||||||
\(906\) | −50.3685 | −1.67338 | ||||||||
\(907\) | −37.6951 | −1.25165 | −0.625823 | − | 0.779965i | \(-0.715237\pi\) | ||||
−0.625823 | + | 0.779965i | \(0.715237\pi\) | |||||||
\(908\) | 7.68386 | 0.254998 | ||||||||
\(909\) | 3.29499 | 0.109288 | ||||||||
\(910\) | 20.9339 | 0.693951 | ||||||||
\(911\) | −32.0233 | −1.06098 | −0.530490 | − | 0.847691i | \(-0.677992\pi\) | ||||
−0.530490 | + | 0.847691i | \(0.677992\pi\) | |||||||
\(912\) | 3.11148 | 0.103031 | ||||||||
\(913\) | −20.5678 | −0.680695 | ||||||||
\(914\) | 31.1212 | 1.02940 | ||||||||
\(915\) | 87.5834 | 2.89542 | ||||||||
\(916\) | −30.2140 | −0.998298 | ||||||||
\(917\) | 10.8841 | 0.359424 | ||||||||
\(918\) | −34.6747 | −1.14444 | ||||||||
\(919\) | 30.2631 | 0.998288 | 0.499144 | − | 0.866519i | \(-0.333648\pi\) | ||||
0.499144 | + | 0.866519i | \(0.333648\pi\) | |||||||
\(920\) | 14.6803 | 0.483995 | ||||||||
\(921\) | −32.7109 | −1.07786 | ||||||||
\(922\) | 26.7354 | 0.880482 | ||||||||
\(923\) | 25.6634 | 0.844720 | ||||||||
\(924\) | −8.96826 | −0.295034 | ||||||||
\(925\) | 13.4353 | 0.441750 | ||||||||
\(926\) | 27.2214 | 0.894549 | ||||||||
\(927\) | 6.80095 | 0.223372 | ||||||||
\(928\) | 30.7014 | 1.00782 | ||||||||
\(929\) | −20.5867 | −0.675428 | −0.337714 | − | 0.941249i | \(-0.609654\pi\) | ||||
−0.337714 | + | 0.941249i | \(0.609654\pi\) | |||||||
\(930\) | 19.1101 | 0.626644 | ||||||||
\(931\) | 4.04767 | 0.132657 | ||||||||
\(932\) | 44.8891 | 1.47039 | ||||||||
\(933\) | 5.93932 | 0.194445 | ||||||||
\(934\) | 64.4780 | 2.10979 | ||||||||
\(935\) | −20.5337 | −0.671523 | ||||||||
\(936\) | −4.65349 | −0.152104 | ||||||||
\(937\) | 28.6268 | 0.935196 | 0.467598 | − | 0.883941i | \(-0.345120\pi\) | ||||
0.467598 | + | 0.883941i | \(0.345120\pi\) | |||||||
\(938\) | −9.04435 | −0.295309 | ||||||||
\(939\) | −55.5780 | −1.81372 | ||||||||
\(940\) | 185.637 | 6.05480 | ||||||||
\(941\) | −52.4613 | −1.71019 | −0.855094 | − | 0.518472i | \(-0.826501\pi\) | ||||
−0.855094 | + | 0.518472i | \(0.826501\pi\) | |||||||
\(942\) | −48.0018 | −1.56398 | ||||||||
\(943\) | −9.74704 | −0.317407 | ||||||||
\(944\) | −2.17952 | −0.0709373 | ||||||||
\(945\) | 18.8745 | 0.613988 | ||||||||
\(946\) | −1.03564 | −0.0336715 | ||||||||
\(947\) | 23.3437 | 0.758568 | 0.379284 | − | 0.925280i | \(-0.376170\pi\) | ||||
0.379284 | + | 0.925280i | \(0.376170\pi\) | |||||||
\(948\) | 34.2658 | 1.11290 | ||||||||
\(949\) | −10.1717 | −0.330186 | ||||||||
\(950\) | −125.473 | −4.07088 | ||||||||
\(951\) | 41.1577 | 1.33463 | ||||||||
\(952\) | −10.4394 | −0.338342 | ||||||||
\(953\) | −7.61229 | −0.246586 | −0.123293 | − | 0.992370i | \(-0.539346\pi\) | ||||
−0.123293 | + | 0.992370i | \(0.539346\pi\) | |||||||
\(954\) | 15.8381 | 0.512777 | ||||||||
\(955\) | 64.4731 | 2.08630 | ||||||||
\(956\) | 96.7344 | 3.12861 | ||||||||
\(957\) | 15.9697 | 0.516228 | ||||||||
\(958\) | −52.1103 | −1.68361 | ||||||||
\(959\) | 3.13779 | 0.101324 | ||||||||
\(960\) | −105.739 | −3.41272 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −4.87556 | −0.157194 | ||||||||
\(963\) | −7.62811 | −0.245812 | ||||||||
\(964\) | −52.0740 | −1.67719 | ||||||||
\(965\) | −27.2545 | −0.877355 | ||||||||
\(966\) | −4.98353 | −0.160342 | ||||||||
\(967\) | −0.0585208 | −0.00188190 | −0.000940952 | − | 1.00000i | \(-0.500300\pi\) | ||||
−0.000940952 | 1.00000i | \(0.500300\pi\) | ||||||||
\(968\) | 27.6141 | 0.887550 | ||||||||
\(969\) | −26.6938 | −0.857527 | ||||||||
\(970\) | 47.9486 | 1.53954 | ||||||||
\(971\) | −27.4773 | −0.881788 | −0.440894 | − | 0.897559i | \(-0.645338\pi\) | ||||
−0.440894 | + | 0.897559i | \(0.645338\pi\) | |||||||
\(972\) | −24.4068 | −0.782848 | ||||||||
\(973\) | 18.8869 | 0.605487 | ||||||||
\(974\) | 26.9438 | 0.863335 | ||||||||
\(975\) | 54.7665 | 1.75393 | ||||||||
\(976\) | 4.21384 | 0.134882 | ||||||||
\(977\) | −21.7156 | −0.694745 | −0.347372 | − | 0.937727i | \(-0.612926\pi\) | ||||
−0.347372 | + | 0.937727i | \(0.612926\pi\) | |||||||
\(978\) | −58.1222 | −1.85854 | ||||||||
\(979\) | 14.3272 | 0.457899 | ||||||||
\(980\) | 14.2698 | 0.455831 | ||||||||
\(981\) | −9.84148 | −0.314214 | ||||||||
\(982\) | 64.2869 | 2.05148 | ||||||||
\(983\) | −19.0261 | −0.606840 | −0.303420 | − | 0.952857i | \(-0.598128\pi\) | ||||
−0.303420 | + | 0.952857i | \(0.598128\pi\) | |||||||
\(984\) | −51.2771 | −1.63465 | ||||||||
\(985\) | −58.6311 | −1.86814 | ||||||||
\(986\) | 46.6812 | 1.48663 | ||||||||
\(987\) | −25.0950 | −0.798783 | ||||||||
\(988\) | 28.4265 | 0.904367 | ||||||||
\(989\) | −0.359281 | −0.0114245 | ||||||||
\(990\) | −9.99404 | −0.317631 | ||||||||
\(991\) | −41.1695 | −1.30779 | −0.653896 | − | 0.756585i | \(-0.726867\pi\) | ||||
−0.653896 | + | 0.756585i | \(0.726867\pi\) | |||||||
\(992\) | −5.18774 | −0.164711 | ||||||||
\(993\) | 49.7816 | 1.57977 | ||||||||
\(994\) | 28.0210 | 0.888772 | ||||||||
\(995\) | 91.7191 | 2.90769 | ||||||||
\(996\) | −94.2633 | −2.98685 | ||||||||
\(997\) | −37.6059 | −1.19099 | −0.595496 | − | 0.803359i | \(-0.703044\pi\) | ||||
−0.595496 | + | 0.803359i | \(0.703044\pi\) | |||||||
\(998\) | 62.0533 | 1.96426 | ||||||||
\(999\) | −4.39593 | −0.139081 |
(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 | 8029.2.a.h.1.8 | ✓ | 71 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8029.2.a.h.1.8 | ✓ | 71 | 1.1 | even | 1 | trivial |