Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6007,2,Mod(1,6007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6007 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6007.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: | \(47.9661364942\) |
Analytic rank: | \(0\) |
Dimension: | \(261\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 6007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.53967 | −1.79582 | −0.897909 | − | 0.440182i | \(-0.854914\pi\) | ||||
−0.897909 | + | 0.440182i | \(0.854914\pi\) | |||||||
\(3\) | 2.55882 | 1.47734 | 0.738668 | − | 0.674070i | \(-0.235455\pi\) | ||||
0.738668 | + | 0.674070i | \(0.235455\pi\) | |||||||
\(4\) | 4.44992 | 2.22496 | ||||||||
\(5\) | 2.30710 | 1.03177 | 0.515884 | − | 0.856658i | \(-0.327464\pi\) | ||||
0.515884 | + | 0.856658i | \(0.327464\pi\) | |||||||
\(6\) | −6.49855 | −2.65302 | ||||||||
\(7\) | −1.02038 | −0.385669 | −0.192834 | − | 0.981231i | \(-0.561768\pi\) | ||||
−0.192834 | + | 0.981231i | \(0.561768\pi\) | |||||||
\(8\) | −6.22199 | −2.19980 | ||||||||
\(9\) | 3.54756 | 1.18252 | ||||||||
\(10\) | −5.85928 | −1.85287 | ||||||||
\(11\) | −5.18117 | −1.56218 | −0.781090 | − | 0.624418i | \(-0.785336\pi\) | ||||
−0.781090 | + | 0.624418i | \(0.785336\pi\) | |||||||
\(12\) | 11.3865 | 3.28701 | ||||||||
\(13\) | 3.30137 | 0.915636 | 0.457818 | − | 0.889046i | \(-0.348631\pi\) | ||||
0.457818 | + | 0.889046i | \(0.348631\pi\) | |||||||
\(14\) | 2.59144 | 0.692591 | ||||||||
\(15\) | 5.90346 | 1.52427 | ||||||||
\(16\) | 6.90195 | 1.72549 | ||||||||
\(17\) | 2.75231 | 0.667534 | 0.333767 | − | 0.942656i | \(-0.391680\pi\) | ||||
0.333767 | + | 0.942656i | \(0.391680\pi\) | |||||||
\(18\) | −9.00962 | −2.12359 | ||||||||
\(19\) | 1.75773 | 0.403252 | 0.201626 | − | 0.979463i | \(-0.435377\pi\) | ||||
0.201626 | + | 0.979463i | \(0.435377\pi\) | |||||||
\(20\) | 10.2664 | 2.29564 | ||||||||
\(21\) | −2.61098 | −0.569762 | ||||||||
\(22\) | 13.1585 | 2.80539 | ||||||||
\(23\) | −1.22522 | −0.255476 | −0.127738 | − | 0.991808i | \(-0.540772\pi\) | ||||
−0.127738 | + | 0.991808i | \(0.540772\pi\) | |||||||
\(24\) | −15.9209 | −3.24985 | ||||||||
\(25\) | 0.322725 | 0.0645451 | ||||||||
\(26\) | −8.38440 | −1.64432 | ||||||||
\(27\) | 1.40110 | 0.269642 | ||||||||
\(28\) | −4.54063 | −0.858098 | ||||||||
\(29\) | 1.71453 | 0.318380 | 0.159190 | − | 0.987248i | \(-0.449112\pi\) | ||||
0.159190 | + | 0.987248i | \(0.449112\pi\) | |||||||
\(30\) | −14.9928 | −2.73731 | ||||||||
\(31\) | 1.16098 | 0.208519 | 0.104259 | − | 0.994550i | \(-0.466753\pi\) | ||||
0.104259 | + | 0.994550i | \(0.466753\pi\) | |||||||
\(32\) | −5.08469 | −0.898855 | ||||||||
\(33\) | −13.2577 | −2.30786 | ||||||||
\(34\) | −6.98997 | −1.19877 | ||||||||
\(35\) | −2.35413 | −0.397921 | ||||||||
\(36\) | 15.7863 | 2.63106 | ||||||||
\(37\) | 4.45544 | 0.732470 | 0.366235 | − | 0.930522i | \(-0.380647\pi\) | ||||
0.366235 | + | 0.930522i | \(0.380647\pi\) | |||||||
\(38\) | −4.46406 | −0.724167 | ||||||||
\(39\) | 8.44762 | 1.35270 | ||||||||
\(40\) | −14.3548 | −2.26969 | ||||||||
\(41\) | 11.7238 | 1.83096 | 0.915478 | − | 0.402369i | \(-0.131813\pi\) | ||||
0.915478 | + | 0.402369i | \(0.131813\pi\) | |||||||
\(42\) | 6.63102 | 1.02319 | ||||||||
\(43\) | 7.10289 | 1.08318 | 0.541590 | − | 0.840643i | \(-0.317822\pi\) | ||||
0.541590 | + | 0.840643i | \(0.317822\pi\) | |||||||
\(44\) | −23.0558 | −3.47579 | ||||||||
\(45\) | 8.18458 | 1.22009 | ||||||||
\(46\) | 3.11165 | 0.458788 | ||||||||
\(47\) | 10.7693 | 1.57087 | 0.785435 | − | 0.618944i | \(-0.212439\pi\) | ||||
0.785435 | + | 0.618944i | \(0.212439\pi\) | |||||||
\(48\) | 17.6608 | 2.54912 | ||||||||
\(49\) | −5.95882 | −0.851259 | ||||||||
\(50\) | −0.819616 | −0.115911 | ||||||||
\(51\) | 7.04268 | 0.986172 | ||||||||
\(52\) | 14.6909 | 2.03725 | ||||||||
\(53\) | 11.0554 | 1.51858 | 0.759288 | − | 0.650755i | \(-0.225547\pi\) | ||||
0.759288 | + | 0.650755i | \(0.225547\pi\) | |||||||
\(54\) | −3.55833 | −0.484227 | ||||||||
\(55\) | −11.9535 | −1.61181 | ||||||||
\(56\) | 6.34882 | 0.848396 | ||||||||
\(57\) | 4.49772 | 0.595738 | ||||||||
\(58\) | −4.35434 | −0.571752 | ||||||||
\(59\) | 7.40508 | 0.964060 | 0.482030 | − | 0.876155i | \(-0.339900\pi\) | ||||
0.482030 | + | 0.876155i | \(0.339900\pi\) | |||||||
\(60\) | 26.2699 | 3.39143 | ||||||||
\(61\) | −1.02359 | −0.131057 | −0.0655284 | − | 0.997851i | \(-0.520873\pi\) | ||||
−0.0655284 | + | 0.997851i | \(0.520873\pi\) | |||||||
\(62\) | −2.94851 | −0.374461 | ||||||||
\(63\) | −3.61987 | −0.456061 | ||||||||
\(64\) | −0.890461 | −0.111308 | ||||||||
\(65\) | 7.61661 | 0.944724 | ||||||||
\(66\) | 33.6701 | 4.14450 | ||||||||
\(67\) | −15.2186 | −1.85925 | −0.929625 | − | 0.368507i | \(-0.879869\pi\) | ||||
−0.929625 | + | 0.368507i | \(0.879869\pi\) | |||||||
\(68\) | 12.2476 | 1.48524 | ||||||||
\(69\) | −3.13511 | −0.377423 | ||||||||
\(70\) | 5.97872 | 0.714593 | ||||||||
\(71\) | 2.13498 | 0.253376 | 0.126688 | − | 0.991943i | \(-0.459565\pi\) | ||||
0.126688 | + | 0.991943i | \(0.459565\pi\) | |||||||
\(72\) | −22.0728 | −2.60131 | ||||||||
\(73\) | −10.9239 | −1.27855 | −0.639274 | − | 0.768979i | \(-0.720765\pi\) | ||||
−0.639274 | + | 0.768979i | \(0.720765\pi\) | |||||||
\(74\) | −11.3153 | −1.31538 | ||||||||
\(75\) | 0.825796 | 0.0953547 | ||||||||
\(76\) | 7.82178 | 0.897219 | ||||||||
\(77\) | 5.28678 | 0.602485 | ||||||||
\(78\) | −21.4542 | −2.42921 | ||||||||
\(79\) | −5.83197 | −0.656148 | −0.328074 | − | 0.944652i | \(-0.606399\pi\) | ||||
−0.328074 | + | 0.944652i | \(0.606399\pi\) | |||||||
\(80\) | 15.9235 | 1.78030 | ||||||||
\(81\) | −7.05751 | −0.784168 | ||||||||
\(82\) | −29.7747 | −3.28806 | ||||||||
\(83\) | −16.7163 | −1.83485 | −0.917426 | − | 0.397907i | \(-0.869737\pi\) | ||||
−0.917426 | + | 0.397907i | \(0.869737\pi\) | |||||||
\(84\) | −11.6186 | −1.26770 | ||||||||
\(85\) | 6.34987 | 0.688740 | ||||||||
\(86\) | −18.0390 | −1.94519 | ||||||||
\(87\) | 4.38717 | 0.470354 | ||||||||
\(88\) | 32.2372 | 3.43649 | ||||||||
\(89\) | −6.28305 | −0.666002 | −0.333001 | − | 0.942927i | \(-0.608061\pi\) | ||||
−0.333001 | + | 0.942927i | \(0.608061\pi\) | |||||||
\(90\) | −20.7861 | −2.19105 | ||||||||
\(91\) | −3.36867 | −0.353133 | ||||||||
\(92\) | −5.45212 | −0.568423 | ||||||||
\(93\) | 2.97074 | 0.308052 | ||||||||
\(94\) | −27.3506 | −2.82100 | ||||||||
\(95\) | 4.05527 | 0.416062 | ||||||||
\(96\) | −13.0108 | −1.32791 | ||||||||
\(97\) | −10.4758 | −1.06365 | −0.531827 | − | 0.846853i | \(-0.678494\pi\) | ||||
−0.531827 | + | 0.846853i | \(0.678494\pi\) | |||||||
\(98\) | 15.1334 | 1.52871 | ||||||||
\(99\) | −18.3805 | −1.84731 | ||||||||
\(100\) | 1.43610 | 0.143610 | ||||||||
\(101\) | 13.5733 | 1.35059 | 0.675296 | − | 0.737547i | \(-0.264016\pi\) | ||||
0.675296 | + | 0.737547i | \(0.264016\pi\) | |||||||
\(102\) | −17.8861 | −1.77098 | ||||||||
\(103\) | 5.59633 | 0.551423 | 0.275711 | − | 0.961240i | \(-0.411087\pi\) | ||||
0.275711 | + | 0.961240i | \(0.411087\pi\) | |||||||
\(104\) | −20.5411 | −2.01422 | ||||||||
\(105\) | −6.02380 | −0.587862 | ||||||||
\(106\) | −28.0771 | −2.72709 | ||||||||
\(107\) | 5.01637 | 0.484951 | 0.242475 | − | 0.970158i | \(-0.422041\pi\) | ||||
0.242475 | + | 0.970158i | \(0.422041\pi\) | |||||||
\(108\) | 6.23478 | 0.599942 | ||||||||
\(109\) | 12.5933 | 1.20622 | 0.603110 | − | 0.797658i | \(-0.293928\pi\) | ||||
0.603110 | + | 0.797658i | \(0.293928\pi\) | |||||||
\(110\) | 30.3579 | 2.89451 | ||||||||
\(111\) | 11.4007 | 1.08210 | ||||||||
\(112\) | −7.04264 | −0.665467 | ||||||||
\(113\) | 7.45181 | 0.701008 | 0.350504 | − | 0.936561i | \(-0.386010\pi\) | ||||
0.350504 | + | 0.936561i | \(0.386010\pi\) | |||||||
\(114\) | −11.4227 | −1.06984 | ||||||||
\(115\) | −2.82671 | −0.263592 | ||||||||
\(116\) | 7.62952 | 0.708383 | ||||||||
\(117\) | 11.7118 | 1.08276 | ||||||||
\(118\) | −18.8065 | −1.73128 | ||||||||
\(119\) | −2.80842 | −0.257447 | ||||||||
\(120\) | −36.7312 | −3.35309 | ||||||||
\(121\) | 15.8445 | 1.44041 | ||||||||
\(122\) | 2.59957 | 0.235354 | ||||||||
\(123\) | 29.9992 | 2.70493 | ||||||||
\(124\) | 5.16628 | 0.463945 | ||||||||
\(125\) | −10.7910 | −0.965172 | ||||||||
\(126\) | 9.19327 | 0.819002 | ||||||||
\(127\) | −12.7484 | −1.13124 | −0.565618 | − | 0.824668i | \(-0.691362\pi\) | ||||
−0.565618 | + | 0.824668i | \(0.691362\pi\) | |||||||
\(128\) | 12.4309 | 1.09874 | ||||||||
\(129\) | 18.1750 | 1.60022 | ||||||||
\(130\) | −19.3437 | −1.69655 | ||||||||
\(131\) | 12.8701 | 1.12447 | 0.562233 | − | 0.826979i | \(-0.309942\pi\) | ||||
0.562233 | + | 0.826979i | \(0.309942\pi\) | |||||||
\(132\) | −58.9956 | −5.13491 | ||||||||
\(133\) | −1.79356 | −0.155522 | ||||||||
\(134\) | 38.6503 | 3.33887 | ||||||||
\(135\) | 3.23248 | 0.278207 | ||||||||
\(136\) | −17.1249 | −1.46844 | ||||||||
\(137\) | −13.1482 | −1.12332 | −0.561661 | − | 0.827367i | \(-0.689838\pi\) | ||||
−0.561661 | + | 0.827367i | \(0.689838\pi\) | |||||||
\(138\) | 7.96215 | 0.677783 | ||||||||
\(139\) | 10.1850 | 0.863877 | 0.431939 | − | 0.901903i | \(-0.357830\pi\) | ||||
0.431939 | + | 0.901903i | \(0.357830\pi\) | |||||||
\(140\) | −10.4757 | −0.885358 | ||||||||
\(141\) | 27.5568 | 2.32070 | ||||||||
\(142\) | −5.42214 | −0.455016 | ||||||||
\(143\) | −17.1050 | −1.43039 | ||||||||
\(144\) | 24.4850 | 2.04042 | ||||||||
\(145\) | 3.95560 | 0.328494 | ||||||||
\(146\) | 27.7431 | 2.29604 | ||||||||
\(147\) | −15.2475 | −1.25760 | ||||||||
\(148\) | 19.8264 | 1.62972 | ||||||||
\(149\) | 2.42024 | 0.198274 | 0.0991370 | − | 0.995074i | \(-0.468392\pi\) | ||||
0.0991370 | + | 0.995074i | \(0.468392\pi\) | |||||||
\(150\) | −2.09725 | −0.171240 | ||||||||
\(151\) | 18.0697 | 1.47049 | 0.735245 | − | 0.677802i | \(-0.237067\pi\) | ||||
0.735245 | + | 0.677802i | \(0.237067\pi\) | |||||||
\(152\) | −10.9366 | −0.887075 | ||||||||
\(153\) | 9.76399 | 0.789372 | ||||||||
\(154\) | −13.4267 | −1.08195 | ||||||||
\(155\) | 2.67851 | 0.215143 | ||||||||
\(156\) | 37.5912 | 3.00971 | ||||||||
\(157\) | 9.96183 | 0.795040 | 0.397520 | − | 0.917593i | \(-0.369871\pi\) | ||||
0.397520 | + | 0.917593i | \(0.369871\pi\) | |||||||
\(158\) | 14.8113 | 1.17832 | ||||||||
\(159\) | 28.2888 | 2.24345 | ||||||||
\(160\) | −11.7309 | −0.927410 | ||||||||
\(161\) | 1.25019 | 0.0985290 | ||||||||
\(162\) | 17.9237 | 1.40822 | ||||||||
\(163\) | 13.4563 | 1.05398 | 0.526988 | − | 0.849873i | \(-0.323321\pi\) | ||||
0.526988 | + | 0.849873i | \(0.323321\pi\) | |||||||
\(164\) | 52.1701 | 4.07380 | ||||||||
\(165\) | −30.5868 | −2.38118 | ||||||||
\(166\) | 42.4539 | 3.29506 | ||||||||
\(167\) | −2.92638 | −0.226450 | −0.113225 | − | 0.993569i | \(-0.536118\pi\) | ||||
−0.113225 | + | 0.993569i | \(0.536118\pi\) | |||||||
\(168\) | 16.2455 | 1.25337 | ||||||||
\(169\) | −2.10093 | −0.161610 | ||||||||
\(170\) | −16.1266 | −1.23685 | ||||||||
\(171\) | 6.23566 | 0.476853 | ||||||||
\(172\) | 31.6073 | 2.41003 | ||||||||
\(173\) | 5.81056 | 0.441769 | 0.220884 | − | 0.975300i | \(-0.429106\pi\) | ||||
0.220884 | + | 0.975300i | \(0.429106\pi\) | |||||||
\(174\) | −11.1420 | −0.844670 | ||||||||
\(175\) | −0.329304 | −0.0248930 | ||||||||
\(176\) | −35.7601 | −2.69552 | ||||||||
\(177\) | 18.9483 | 1.42424 | ||||||||
\(178\) | 15.9569 | 1.19602 | ||||||||
\(179\) | −2.72686 | −0.203815 | −0.101908 | − | 0.994794i | \(-0.532495\pi\) | ||||
−0.101908 | + | 0.994794i | \(0.532495\pi\) | |||||||
\(180\) | 36.4207 | 2.71464 | ||||||||
\(181\) | 5.80475 | 0.431464 | 0.215732 | − | 0.976453i | \(-0.430786\pi\) | ||||
0.215732 | + | 0.976453i | \(0.430786\pi\) | |||||||
\(182\) | 8.55531 | 0.634162 | ||||||||
\(183\) | −2.61917 | −0.193615 | ||||||||
\(184\) | 7.62329 | 0.561997 | ||||||||
\(185\) | 10.2792 | 0.755739 | ||||||||
\(186\) | −7.54471 | −0.553205 | ||||||||
\(187\) | −14.2602 | −1.04281 | ||||||||
\(188\) | 47.9227 | 3.49512 | ||||||||
\(189\) | −1.42966 | −0.103992 | ||||||||
\(190\) | −10.2991 | −0.747172 | ||||||||
\(191\) | −7.44099 | −0.538411 | −0.269206 | − | 0.963083i | \(-0.586761\pi\) | ||||
−0.269206 | + | 0.963083i | \(0.586761\pi\) | |||||||
\(192\) | −2.27853 | −0.164439 | ||||||||
\(193\) | −15.5409 | −1.11866 | −0.559328 | − | 0.828946i | \(-0.688941\pi\) | ||||
−0.559328 | + | 0.828946i | \(0.688941\pi\) | |||||||
\(194\) | 26.6050 | 1.91013 | ||||||||
\(195\) | 19.4895 | 1.39567 | ||||||||
\(196\) | −26.5163 | −1.89402 | ||||||||
\(197\) | −14.3071 | −1.01934 | −0.509668 | − | 0.860371i | \(-0.670232\pi\) | ||||
−0.509668 | + | 0.860371i | \(0.670232\pi\) | |||||||
\(198\) | 46.6804 | 3.31743 | ||||||||
\(199\) | −4.98745 | −0.353551 | −0.176776 | − | 0.984251i | \(-0.556567\pi\) | ||||
−0.176776 | + | 0.984251i | \(0.556567\pi\) | |||||||
\(200\) | −2.00799 | −0.141987 | ||||||||
\(201\) | −38.9417 | −2.74674 | ||||||||
\(202\) | −34.4716 | −2.42542 | ||||||||
\(203\) | −1.74948 | −0.122789 | ||||||||
\(204\) | 31.3393 | 2.19419 | ||||||||
\(205\) | 27.0481 | 1.88912 | ||||||||
\(206\) | −14.2128 | −0.990255 | ||||||||
\(207\) | −4.34653 | −0.302105 | ||||||||
\(208\) | 22.7859 | 1.57992 | ||||||||
\(209\) | −9.10712 | −0.629952 | ||||||||
\(210\) | 15.2985 | 1.05569 | ||||||||
\(211\) | 8.96046 | 0.616864 | 0.308432 | − | 0.951246i | \(-0.400196\pi\) | ||||
0.308432 | + | 0.951246i | \(0.400196\pi\) | |||||||
\(212\) | 49.1957 | 3.37877 | ||||||||
\(213\) | 5.46303 | 0.374321 | ||||||||
\(214\) | −12.7399 | −0.870883 | ||||||||
\(215\) | 16.3871 | 1.11759 | ||||||||
\(216\) | −8.71761 | −0.593159 | ||||||||
\(217\) | −1.18465 | −0.0804191 | ||||||||
\(218\) | −31.9828 | −2.16615 | ||||||||
\(219\) | −27.9523 | −1.88884 | ||||||||
\(220\) | −53.1921 | −3.58621 | ||||||||
\(221\) | 9.08642 | 0.611219 | ||||||||
\(222\) | −28.9539 | −1.94326 | ||||||||
\(223\) | −3.40434 | −0.227971 | −0.113986 | − | 0.993482i | \(-0.536362\pi\) | ||||
−0.113986 | + | 0.993482i | \(0.536362\pi\) | |||||||
\(224\) | 5.18834 | 0.346660 | ||||||||
\(225\) | 1.14489 | 0.0763258 | ||||||||
\(226\) | −18.9251 | −1.25888 | ||||||||
\(227\) | 25.6341 | 1.70139 | 0.850696 | − | 0.525657i | \(-0.176181\pi\) | ||||
0.850696 | + | 0.525657i | \(0.176181\pi\) | |||||||
\(228\) | 20.0145 | 1.32549 | ||||||||
\(229\) | 17.3574 | 1.14701 | 0.573504 | − | 0.819203i | \(-0.305584\pi\) | ||||
0.573504 | + | 0.819203i | \(0.305584\pi\) | |||||||
\(230\) | 7.17890 | 0.473362 | ||||||||
\(231\) | 13.5279 | 0.890072 | ||||||||
\(232\) | −10.6678 | −0.700374 | ||||||||
\(233\) | 8.05580 | 0.527753 | 0.263876 | − | 0.964556i | \(-0.414999\pi\) | ||||
0.263876 | + | 0.964556i | \(0.414999\pi\) | |||||||
\(234\) | −29.7441 | −1.94443 | ||||||||
\(235\) | 24.8460 | 1.62077 | ||||||||
\(236\) | 32.9520 | 2.14499 | ||||||||
\(237\) | −14.9230 | −0.969350 | ||||||||
\(238\) | 7.13245 | 0.462328 | ||||||||
\(239\) | 20.8865 | 1.35103 | 0.675516 | − | 0.737345i | \(-0.263921\pi\) | ||||
0.675516 | + | 0.737345i | \(0.263921\pi\) | |||||||
\(240\) | 40.7454 | 2.63010 | ||||||||
\(241\) | 6.79573 | 0.437752 | 0.218876 | − | 0.975753i | \(-0.429761\pi\) | ||||
0.218876 | + | 0.975753i | \(0.429761\pi\) | |||||||
\(242\) | −40.2398 | −2.58671 | ||||||||
\(243\) | −22.2622 | −1.42812 | ||||||||
\(244\) | −4.55488 | −0.291596 | ||||||||
\(245\) | −13.7476 | −0.878302 | ||||||||
\(246\) | −76.1880 | −4.85757 | ||||||||
\(247\) | 5.80294 | 0.369232 | ||||||||
\(248\) | −7.22361 | −0.458700 | ||||||||
\(249\) | −42.7740 | −2.71069 | ||||||||
\(250\) | 27.4055 | 1.73327 | ||||||||
\(251\) | 0.344721 | 0.0217586 | 0.0108793 | − | 0.999941i | \(-0.496537\pi\) | ||||
0.0108793 | + | 0.999941i | \(0.496537\pi\) | |||||||
\(252\) | −16.1081 | −1.01472 | ||||||||
\(253\) | 6.34806 | 0.399099 | ||||||||
\(254\) | 32.3767 | 2.03149 | ||||||||
\(255\) | 16.2482 | 1.01750 | ||||||||
\(256\) | −29.7893 | −1.86183 | ||||||||
\(257\) | 5.64934 | 0.352396 | 0.176198 | − | 0.984355i | \(-0.443620\pi\) | ||||
0.176198 | + | 0.984355i | \(0.443620\pi\) | |||||||
\(258\) | −46.1585 | −2.87370 | ||||||||
\(259\) | −4.54626 | −0.282491 | ||||||||
\(260\) | 33.8933 | 2.10197 | ||||||||
\(261\) | 6.08239 | 0.376490 | ||||||||
\(262\) | −32.6858 | −2.01934 | ||||||||
\(263\) | 23.0457 | 1.42106 | 0.710529 | − | 0.703668i | \(-0.248456\pi\) | ||||
0.710529 | + | 0.703668i | \(0.248456\pi\) | |||||||
\(264\) | 82.4891 | 5.07685 | ||||||||
\(265\) | 25.5060 | 1.56682 | ||||||||
\(266\) | 4.55506 | 0.279289 | ||||||||
\(267\) | −16.0772 | −0.983907 | ||||||||
\(268\) | −67.7216 | −4.13676 | ||||||||
\(269\) | 25.9750 | 1.58373 | 0.791863 | − | 0.610699i | \(-0.209111\pi\) | ||||
0.791863 | + | 0.610699i | \(0.209111\pi\) | |||||||
\(270\) | −8.20943 | −0.499610 | ||||||||
\(271\) | −2.54862 | −0.154818 | −0.0774089 | − | 0.996999i | \(-0.524665\pi\) | ||||
−0.0774089 | + | 0.996999i | \(0.524665\pi\) | |||||||
\(272\) | 18.9963 | 1.15182 | ||||||||
\(273\) | −8.61982 | −0.521695 | ||||||||
\(274\) | 33.3920 | 2.01728 | ||||||||
\(275\) | −1.67209 | −0.100831 | ||||||||
\(276\) | −13.9510 | −0.839752 | ||||||||
\(277\) | 8.58487 | 0.515815 | 0.257907 | − | 0.966170i | \(-0.416967\pi\) | ||||
0.257907 | + | 0.966170i | \(0.416967\pi\) | |||||||
\(278\) | −25.8664 | −1.55137 | ||||||||
\(279\) | 4.11865 | 0.246577 | ||||||||
\(280\) | 14.6474 | 0.875348 | ||||||||
\(281\) | −3.84255 | −0.229228 | −0.114614 | − | 0.993410i | \(-0.536563\pi\) | ||||
−0.114614 | + | 0.993410i | \(0.536563\pi\) | |||||||
\(282\) | −69.9852 | −4.16756 | ||||||||
\(283\) | 10.5341 | 0.626188 | 0.313094 | − | 0.949722i | \(-0.398635\pi\) | ||||
0.313094 | + | 0.949722i | \(0.398635\pi\) | |||||||
\(284\) | 9.50049 | 0.563751 | ||||||||
\(285\) | 10.3767 | 0.614664 | ||||||||
\(286\) | 43.4410 | 2.56872 | ||||||||
\(287\) | −11.9628 | −0.706143 | ||||||||
\(288\) | −18.0382 | −1.06291 | ||||||||
\(289\) | −9.42477 | −0.554398 | ||||||||
\(290\) | −10.0459 | −0.589916 | ||||||||
\(291\) | −26.8056 | −1.57137 | ||||||||
\(292\) | −48.6105 | −2.84472 | ||||||||
\(293\) | 23.5698 | 1.37696 | 0.688482 | − | 0.725253i | \(-0.258277\pi\) | ||||
0.688482 | + | 0.725253i | \(0.258277\pi\) | |||||||
\(294\) | 38.7237 | 2.25841 | ||||||||
\(295\) | 17.0843 | 0.994686 | ||||||||
\(296\) | −27.7217 | −1.61129 | ||||||||
\(297\) | −7.25933 | −0.421229 | ||||||||
\(298\) | −6.14662 | −0.356064 | ||||||||
\(299\) | −4.04490 | −0.233923 | ||||||||
\(300\) | 3.67473 | 0.212160 | ||||||||
\(301\) | −7.24768 | −0.417749 | ||||||||
\(302\) | −45.8910 | −2.64073 | ||||||||
\(303\) | 34.7316 | 1.99528 | ||||||||
\(304\) | 12.1318 | 0.695806 | ||||||||
\(305\) | −2.36152 | −0.135220 | ||||||||
\(306\) | −24.7973 | −1.41757 | ||||||||
\(307\) | 0.981817 | 0.0560353 | 0.0280176 | − | 0.999607i | \(-0.491081\pi\) | ||||
0.0280176 | + | 0.999607i | \(0.491081\pi\) | |||||||
\(308\) | 23.5258 | 1.34050 | ||||||||
\(309\) | 14.3200 | 0.814636 | ||||||||
\(310\) | −6.80252 | −0.386357 | ||||||||
\(311\) | −18.3664 | −1.04146 | −0.520732 | − | 0.853720i | \(-0.674341\pi\) | ||||
−0.520732 | + | 0.853720i | \(0.674341\pi\) | |||||||
\(312\) | −52.5610 | −2.97568 | ||||||||
\(313\) | 15.9350 | 0.900698 | 0.450349 | − | 0.892853i | \(-0.351300\pi\) | ||||
0.450349 | + | 0.892853i | \(0.351300\pi\) | |||||||
\(314\) | −25.2997 | −1.42775 | ||||||||
\(315\) | −8.35141 | −0.470549 | ||||||||
\(316\) | −25.9518 | −1.45990 | ||||||||
\(317\) | 25.4270 | 1.42812 | 0.714061 | − | 0.700084i | \(-0.246854\pi\) | ||||
0.714061 | + | 0.700084i | \(0.246854\pi\) | |||||||
\(318\) | −71.8441 | −4.02882 | ||||||||
\(319\) | −8.88326 | −0.497367 | ||||||||
\(320\) | −2.05439 | −0.114844 | ||||||||
\(321\) | 12.8360 | 0.716435 | ||||||||
\(322\) | −3.17508 | −0.176940 | ||||||||
\(323\) | 4.83784 | 0.269184 | ||||||||
\(324\) | −31.4054 | −1.74474 | ||||||||
\(325\) | 1.06544 | 0.0590998 | ||||||||
\(326\) | −34.1744 | −1.89275 | ||||||||
\(327\) | 32.2240 | 1.78199 | ||||||||
\(328\) | −72.9455 | −4.02774 | ||||||||
\(329\) | −10.9889 | −0.605836 | ||||||||
\(330\) | 77.6804 | 4.27617 | ||||||||
\(331\) | −6.81250 | −0.374449 | −0.187224 | − | 0.982317i | \(-0.559949\pi\) | ||||
−0.187224 | + | 0.982317i | \(0.559949\pi\) | |||||||
\(332\) | −74.3862 | −4.08247 | ||||||||
\(333\) | 15.8059 | 0.866160 | ||||||||
\(334\) | 7.43205 | 0.406664 | ||||||||
\(335\) | −35.1109 | −1.91831 | ||||||||
\(336\) | −18.0208 | −0.983117 | ||||||||
\(337\) | 21.2560 | 1.15789 | 0.578945 | − | 0.815367i | \(-0.303465\pi\) | ||||
0.578945 | + | 0.815367i | \(0.303465\pi\) | |||||||
\(338\) | 5.33566 | 0.290222 | ||||||||
\(339\) | 19.0678 | 1.03562 | ||||||||
\(340\) | 28.2564 | 1.53242 | ||||||||
\(341\) | −6.01524 | −0.325744 | ||||||||
\(342\) | −15.8365 | −0.856341 | ||||||||
\(343\) | 13.2230 | 0.713973 | ||||||||
\(344\) | −44.1941 | −2.38279 | ||||||||
\(345\) | −7.23303 | −0.389413 | ||||||||
\(346\) | −14.7569 | −0.793336 | ||||||||
\(347\) | −0.120187 | −0.00645199 | −0.00322599 | − | 0.999995i | \(-0.501027\pi\) | ||||
−0.00322599 | + | 0.999995i | \(0.501027\pi\) | |||||||
\(348\) | 19.5226 | 1.04652 | ||||||||
\(349\) | −9.34700 | −0.500333 | −0.250167 | − | 0.968203i | \(-0.580485\pi\) | ||||
−0.250167 | + | 0.968203i | \(0.580485\pi\) | |||||||
\(350\) | 0.836323 | 0.0447033 | ||||||||
\(351\) | 4.62555 | 0.246894 | ||||||||
\(352\) | 26.3446 | 1.40417 | ||||||||
\(353\) | −30.3926 | −1.61763 | −0.808817 | − | 0.588061i | \(-0.799892\pi\) | ||||
−0.808817 | + | 0.588061i | \(0.799892\pi\) | |||||||
\(354\) | −48.1223 | −2.55767 | ||||||||
\(355\) | 4.92562 | 0.261425 | ||||||||
\(356\) | −27.9591 | −1.48183 | ||||||||
\(357\) | −7.18623 | −0.380336 | ||||||||
\(358\) | 6.92533 | 0.366015 | ||||||||
\(359\) | −21.1123 | −1.11426 | −0.557131 | − | 0.830425i | \(-0.688098\pi\) | ||||
−0.557131 | + | 0.830425i | \(0.688098\pi\) | |||||||
\(360\) | −50.9243 | −2.68395 | ||||||||
\(361\) | −15.9104 | −0.837388 | ||||||||
\(362\) | −14.7421 | −0.774830 | ||||||||
\(363\) | 40.5432 | 2.12797 | ||||||||
\(364\) | −14.9903 | −0.785706 | ||||||||
\(365\) | −25.2026 | −1.31916 | ||||||||
\(366\) | 6.65183 | 0.347697 | ||||||||
\(367\) | −6.16946 | −0.322043 | −0.161022 | − | 0.986951i | \(-0.551479\pi\) | ||||
−0.161022 | + | 0.986951i | \(0.551479\pi\) | |||||||
\(368\) | −8.45639 | −0.440820 | ||||||||
\(369\) | 41.5910 | 2.16514 | ||||||||
\(370\) | −26.1057 | −1.35717 | ||||||||
\(371\) | −11.2808 | −0.585668 | ||||||||
\(372\) | 13.2196 | 0.685403 | ||||||||
\(373\) | 22.3248 | 1.15594 | 0.577968 | − | 0.816059i | \(-0.303846\pi\) | ||||
0.577968 | + | 0.816059i | \(0.303846\pi\) | |||||||
\(374\) | 36.2162 | 1.87269 | ||||||||
\(375\) | −27.6121 | −1.42588 | ||||||||
\(376\) | −67.0067 | −3.45561 | ||||||||
\(377\) | 5.66030 | 0.291520 | ||||||||
\(378\) | 3.63086 | 0.186751 | ||||||||
\(379\) | −20.8606 | −1.07154 | −0.535768 | − | 0.844365i | \(-0.679978\pi\) | ||||
−0.535768 | + | 0.844365i | \(0.679978\pi\) | |||||||
\(380\) | 18.0456 | 0.925722 | ||||||||
\(381\) | −32.6208 | −1.67121 | ||||||||
\(382\) | 18.8977 | 0.966888 | ||||||||
\(383\) | 6.76595 | 0.345724 | 0.172862 | − | 0.984946i | \(-0.444699\pi\) | ||||
0.172862 | + | 0.984946i | \(0.444699\pi\) | |||||||
\(384\) | 31.8083 | 1.62321 | ||||||||
\(385\) | 12.1972 | 0.621624 | ||||||||
\(386\) | 39.4687 | 2.00890 | ||||||||
\(387\) | 25.1979 | 1.28088 | ||||||||
\(388\) | −46.6163 | −2.36659 | ||||||||
\(389\) | 14.2493 | 0.722468 | 0.361234 | − | 0.932475i | \(-0.382356\pi\) | ||||
0.361234 | + | 0.932475i | \(0.382356\pi\) | |||||||
\(390\) | −49.4970 | −2.50638 | ||||||||
\(391\) | −3.37219 | −0.170539 | ||||||||
\(392\) | 37.0757 | 1.87260 | ||||||||
\(393\) | 32.9323 | 1.66121 | ||||||||
\(394\) | 36.3352 | 1.83054 | ||||||||
\(395\) | −13.4550 | −0.676992 | ||||||||
\(396\) | −81.7917 | −4.11019 | ||||||||
\(397\) | −15.7114 | −0.788534 | −0.394267 | − | 0.918996i | \(-0.629002\pi\) | ||||
−0.394267 | + | 0.918996i | \(0.629002\pi\) | |||||||
\(398\) | 12.6665 | 0.634913 | ||||||||
\(399\) | −4.58941 | −0.229758 | ||||||||
\(400\) | 2.22743 | 0.111372 | ||||||||
\(401\) | 20.7408 | 1.03575 | 0.517873 | − | 0.855458i | \(-0.326724\pi\) | ||||
0.517873 | + | 0.855458i | \(0.326724\pi\) | |||||||
\(402\) | 98.8990 | 4.93264 | ||||||||
\(403\) | 3.83284 | 0.190927 | ||||||||
\(404\) | 60.4000 | 3.00501 | ||||||||
\(405\) | −16.2824 | −0.809079 | ||||||||
\(406\) | 4.44310 | 0.220507 | ||||||||
\(407\) | −23.0844 | −1.14425 | ||||||||
\(408\) | −43.8194 | −2.16938 | ||||||||
\(409\) | 4.75593 | 0.235166 | 0.117583 | − | 0.993063i | \(-0.462485\pi\) | ||||
0.117583 | + | 0.993063i | \(0.462485\pi\) | |||||||
\(410\) | −68.6932 | −3.39252 | ||||||||
\(411\) | −33.6438 | −1.65952 | ||||||||
\(412\) | 24.9032 | 1.22689 | ||||||||
\(413\) | −7.55603 | −0.371808 | ||||||||
\(414\) | 11.0388 | 0.542525 | ||||||||
\(415\) | −38.5662 | −1.89314 | ||||||||
\(416\) | −16.7865 | −0.823024 | ||||||||
\(417\) | 26.0615 | 1.27624 | ||||||||
\(418\) | 23.1291 | 1.13128 | ||||||||
\(419\) | 19.8817 | 0.971286 | 0.485643 | − | 0.874157i | \(-0.338585\pi\) | ||||
0.485643 | + | 0.874157i | \(0.338585\pi\) | |||||||
\(420\) | −26.8054 | −1.30797 | ||||||||
\(421\) | 9.94035 | 0.484463 | 0.242232 | − | 0.970218i | \(-0.422121\pi\) | ||||
0.242232 | + | 0.970218i | \(0.422121\pi\) | |||||||
\(422\) | −22.7566 | −1.10777 | ||||||||
\(423\) | 38.2049 | 1.85758 | ||||||||
\(424\) | −68.7866 | −3.34057 | ||||||||
\(425\) | 0.888242 | 0.0430861 | ||||||||
\(426\) | −13.8743 | −0.672211 | ||||||||
\(427\) | 1.04445 | 0.0505445 | ||||||||
\(428\) | 22.3224 | 1.07900 | ||||||||
\(429\) | −43.7685 | −2.11316 | ||||||||
\(430\) | −41.6178 | −2.00699 | ||||||||
\(431\) | −27.1220 | −1.30642 | −0.653211 | − | 0.757176i | \(-0.726578\pi\) | ||||
−0.653211 | + | 0.757176i | \(0.726578\pi\) | |||||||
\(432\) | 9.67031 | 0.465263 | ||||||||
\(433\) | 26.0933 | 1.25396 | 0.626982 | − | 0.779034i | \(-0.284290\pi\) | ||||
0.626982 | + | 0.779034i | \(0.284290\pi\) | |||||||
\(434\) | 3.00861 | 0.144418 | ||||||||
\(435\) | 10.1217 | 0.485296 | ||||||||
\(436\) | 56.0392 | 2.68379 | ||||||||
\(437\) | −2.15361 | −0.103021 | ||||||||
\(438\) | 70.9896 | 3.39202 | ||||||||
\(439\) | −22.8457 | −1.09037 | −0.545183 | − | 0.838317i | \(-0.683540\pi\) | ||||
−0.545183 | + | 0.838317i | \(0.683540\pi\) | |||||||
\(440\) | 74.3744 | 3.54566 | ||||||||
\(441\) | −21.1392 | −1.00663 | ||||||||
\(442\) | −23.0765 | −1.09764 | ||||||||
\(443\) | −27.1714 | −1.29095 | −0.645477 | − | 0.763780i | \(-0.723341\pi\) | ||||
−0.645477 | + | 0.763780i | \(0.723341\pi\) | |||||||
\(444\) | 50.7321 | 2.40764 | ||||||||
\(445\) | −14.4956 | −0.687159 | ||||||||
\(446\) | 8.64589 | 0.409395 | ||||||||
\(447\) | 6.19297 | 0.292917 | ||||||||
\(448\) | 0.908613 | 0.0429279 | ||||||||
\(449\) | 21.2661 | 1.00361 | 0.501804 | − | 0.864981i | \(-0.332670\pi\) | ||||
0.501804 | + | 0.864981i | \(0.332670\pi\) | |||||||
\(450\) | −2.90763 | −0.137067 | ||||||||
\(451\) | −60.7432 | −2.86028 | ||||||||
\(452\) | 33.1600 | 1.55971 | ||||||||
\(453\) | 46.2370 | 2.17241 | ||||||||
\(454\) | −65.1021 | −3.05539 | ||||||||
\(455\) | −7.77187 | −0.364351 | ||||||||
\(456\) | −27.9848 | −1.31051 | ||||||||
\(457\) | −24.9142 | −1.16544 | −0.582720 | − | 0.812673i | \(-0.698011\pi\) | ||||
−0.582720 | + | 0.812673i | \(0.698011\pi\) | |||||||
\(458\) | −44.0820 | −2.05982 | ||||||||
\(459\) | 3.85626 | 0.179995 | ||||||||
\(460\) | −12.5786 | −0.586481 | ||||||||
\(461\) | 28.8723 | 1.34472 | 0.672359 | − | 0.740225i | \(-0.265281\pi\) | ||||
0.672359 | + | 0.740225i | \(0.265281\pi\) | |||||||
\(462\) | −34.3564 | −1.59841 | ||||||||
\(463\) | 10.9407 | 0.508457 | 0.254228 | − | 0.967144i | \(-0.418178\pi\) | ||||
0.254228 | + | 0.967144i | \(0.418178\pi\) | |||||||
\(464\) | 11.8336 | 0.549361 | ||||||||
\(465\) | 6.85381 | 0.317838 | ||||||||
\(466\) | −20.4591 | −0.947748 | ||||||||
\(467\) | 22.0729 | 1.02141 | 0.510705 | − | 0.859756i | \(-0.329384\pi\) | ||||
0.510705 | + | 0.859756i | \(0.329384\pi\) | |||||||
\(468\) | 52.1166 | 2.40909 | ||||||||
\(469\) | 15.5288 | 0.717055 | ||||||||
\(470\) | −63.1006 | −2.91061 | ||||||||
\(471\) | 25.4905 | 1.17454 | ||||||||
\(472\) | −46.0743 | −2.12074 | ||||||||
\(473\) | −36.8013 | −1.69212 | ||||||||
\(474\) | 37.8994 | 1.74078 | ||||||||
\(475\) | 0.567266 | 0.0260279 | ||||||||
\(476\) | −12.4972 | −0.572810 | ||||||||
\(477\) | 39.2197 | 1.79575 | ||||||||
\(478\) | −53.0447 | −2.42621 | ||||||||
\(479\) | −22.7668 | −1.04024 | −0.520121 | − | 0.854093i | \(-0.674113\pi\) | ||||
−0.520121 | + | 0.854093i | \(0.674113\pi\) | |||||||
\(480\) | −30.0173 | −1.37009 | ||||||||
\(481\) | 14.7091 | 0.670676 | ||||||||
\(482\) | −17.2589 | −0.786122 | ||||||||
\(483\) | 3.19902 | 0.145560 | ||||||||
\(484\) | 70.5068 | 3.20485 | ||||||||
\(485\) | −24.1687 | −1.09744 | ||||||||
\(486\) | 56.5386 | 2.56464 | ||||||||
\(487\) | −37.4386 | −1.69650 | −0.848252 | − | 0.529594i | \(-0.822344\pi\) | ||||
−0.848252 | + | 0.529594i | \(0.822344\pi\) | |||||||
\(488\) | 6.36874 | 0.288299 | ||||||||
\(489\) | 34.4321 | 1.55707 | ||||||||
\(490\) | 34.9144 | 1.57727 | ||||||||
\(491\) | −28.8888 | −1.30373 | −0.651867 | − | 0.758333i | \(-0.726014\pi\) | ||||
−0.651867 | + | 0.758333i | \(0.726014\pi\) | |||||||
\(492\) | 133.494 | 6.01837 | ||||||||
\(493\) | 4.71892 | 0.212530 | ||||||||
\(494\) | −14.7375 | −0.663073 | ||||||||
\(495\) | −42.4057 | −1.90599 | ||||||||
\(496\) | 8.01304 | 0.359796 | ||||||||
\(497\) | −2.17850 | −0.0977191 | ||||||||
\(498\) | 108.632 | 4.86791 | ||||||||
\(499\) | 36.1214 | 1.61702 | 0.808509 | − | 0.588484i | \(-0.200275\pi\) | ||||
0.808509 | + | 0.588484i | \(0.200275\pi\) | |||||||
\(500\) | −48.0189 | −2.14747 | ||||||||
\(501\) | −7.48809 | −0.334543 | ||||||||
\(502\) | −0.875477 | −0.0390744 | ||||||||
\(503\) | −16.4678 | −0.734265 | −0.367133 | − | 0.930169i | \(-0.619660\pi\) | ||||
−0.367133 | + | 0.930169i | \(0.619660\pi\) | |||||||
\(504\) | 22.5228 | 1.00324 | ||||||||
\(505\) | 31.3150 | 1.39350 | ||||||||
\(506\) | −16.1220 | −0.716709 | ||||||||
\(507\) | −5.37590 | −0.238752 | ||||||||
\(508\) | −56.7293 | −2.51695 | ||||||||
\(509\) | −9.46445 | −0.419504 | −0.209752 | − | 0.977755i | \(-0.567266\pi\) | ||||
−0.209752 | + | 0.977755i | \(0.567266\pi\) | |||||||
\(510\) | −41.2650 | −1.82724 | ||||||||
\(511\) | 11.1466 | 0.493096 | ||||||||
\(512\) | 50.7934 | 2.24477 | ||||||||
\(513\) | 2.46276 | 0.108733 | ||||||||
\(514\) | −14.3475 | −0.632839 | ||||||||
\(515\) | 12.9113 | 0.568940 | ||||||||
\(516\) | 80.8774 | 3.56043 | ||||||||
\(517\) | −55.7978 | −2.45398 | ||||||||
\(518\) | 11.5460 | 0.507302 | ||||||||
\(519\) | 14.8682 | 0.652641 | ||||||||
\(520\) | −47.3904 | −2.07821 | ||||||||
\(521\) | 14.5936 | 0.639355 | 0.319678 | − | 0.947526i | \(-0.396425\pi\) | ||||
0.319678 | + | 0.947526i | \(0.396425\pi\) | |||||||
\(522\) | −15.4473 | −0.676108 | ||||||||
\(523\) | −7.93496 | −0.346972 | −0.173486 | − | 0.984836i | \(-0.555503\pi\) | ||||
−0.173486 | + | 0.984836i | \(0.555503\pi\) | |||||||
\(524\) | 57.2709 | 2.50189 | ||||||||
\(525\) | −0.842629 | −0.0367754 | ||||||||
\(526\) | −58.5284 | −2.55196 | ||||||||
\(527\) | 3.19539 | 0.139193 | ||||||||
\(528\) | −91.5038 | −3.98219 | ||||||||
\(529\) | −21.4988 | −0.934732 | ||||||||
\(530\) | −64.7767 | −2.81372 | ||||||||
\(531\) | 26.2700 | 1.14002 | ||||||||
\(532\) | −7.98122 | −0.346030 | ||||||||
\(533\) | 38.7048 | 1.67649 | ||||||||
\(534\) | 40.8307 | 1.76692 | ||||||||
\(535\) | 11.5733 | 0.500357 | ||||||||
\(536\) | 94.6900 | 4.08999 | ||||||||
\(537\) | −6.97755 | −0.301104 | ||||||||
\(538\) | −65.9680 | −2.84408 | ||||||||
\(539\) | 30.8736 | 1.32982 | ||||||||
\(540\) | 14.3843 | 0.619000 | ||||||||
\(541\) | −37.1944 | −1.59911 | −0.799557 | − | 0.600590i | \(-0.794932\pi\) | ||||
−0.799557 | + | 0.600590i | \(0.794932\pi\) | |||||||
\(542\) | 6.47266 | 0.278025 | ||||||||
\(543\) | 14.8533 | 0.637416 | ||||||||
\(544\) | −13.9947 | −0.600016 | ||||||||
\(545\) | 29.0541 | 1.24454 | ||||||||
\(546\) | 21.8915 | 0.936869 | ||||||||
\(547\) | 36.3923 | 1.55602 | 0.778010 | − | 0.628251i | \(-0.216229\pi\) | ||||
0.778010 | + | 0.628251i | \(0.216229\pi\) | |||||||
\(548\) | −58.5082 | −2.49935 | ||||||||
\(549\) | −3.63123 | −0.154977 | ||||||||
\(550\) | 4.24657 | 0.181074 | ||||||||
\(551\) | 3.01369 | 0.128387 | ||||||||
\(552\) | 19.5066 | 0.830257 | ||||||||
\(553\) | 5.95085 | 0.253056 | ||||||||
\(554\) | −21.8027 | −0.926309 | ||||||||
\(555\) | 26.3025 | 1.11648 | ||||||||
\(556\) | 45.3223 | 1.92209 | ||||||||
\(557\) | −28.1065 | −1.19091 | −0.595455 | − | 0.803388i | \(-0.703028\pi\) | ||||
−0.595455 | + | 0.803388i | \(0.703028\pi\) | |||||||
\(558\) | −10.4600 | −0.442807 | ||||||||
\(559\) | 23.4493 | 0.991800 | ||||||||
\(560\) | −16.2481 | −0.686607 | ||||||||
\(561\) | −36.4893 | −1.54058 | ||||||||
\(562\) | 9.75882 | 0.411651 | ||||||||
\(563\) | 2.93732 | 0.123793 | 0.0618966 | − | 0.998083i | \(-0.480285\pi\) | ||||
0.0618966 | + | 0.998083i | \(0.480285\pi\) | |||||||
\(564\) | 122.626 | 5.16347 | ||||||||
\(565\) | 17.1921 | 0.723277 | ||||||||
\(566\) | −26.7531 | −1.12452 | ||||||||
\(567\) | 7.20137 | 0.302429 | ||||||||
\(568\) | −13.2838 | −0.557377 | ||||||||
\(569\) | 10.0156 | 0.419874 | 0.209937 | − | 0.977715i | \(-0.432674\pi\) | ||||
0.209937 | + | 0.977715i | \(0.432674\pi\) | |||||||
\(570\) | −26.3534 | −1.10382 | ||||||||
\(571\) | 19.7007 | 0.824447 | 0.412224 | − | 0.911083i | \(-0.364752\pi\) | ||||
0.412224 | + | 0.911083i | \(0.364752\pi\) | |||||||
\(572\) | −76.1158 | −3.18256 | ||||||||
\(573\) | −19.0402 | −0.795414 | ||||||||
\(574\) | 30.3816 | 1.26810 | ||||||||
\(575\) | −0.395409 | −0.0164897 | ||||||||
\(576\) | −3.15896 | −0.131623 | ||||||||
\(577\) | −10.4580 | −0.435372 | −0.217686 | − | 0.976019i | \(-0.569851\pi\) | ||||
−0.217686 | + | 0.976019i | \(0.569851\pi\) | |||||||
\(578\) | 23.9358 | 0.995598 | ||||||||
\(579\) | −39.7663 | −1.65263 | ||||||||
\(580\) | 17.6021 | 0.730887 | ||||||||
\(581\) | 17.0570 | 0.707645 | ||||||||
\(582\) | 68.0774 | 2.82190 | ||||||||
\(583\) | −57.2799 | −2.37229 | ||||||||
\(584\) | 67.9684 | 2.81255 | ||||||||
\(585\) | 27.0204 | 1.11715 | ||||||||
\(586\) | −59.8596 | −2.47278 | ||||||||
\(587\) | −2.33653 | −0.0964388 | −0.0482194 | − | 0.998837i | \(-0.515355\pi\) | ||||
−0.0482194 | + | 0.998837i | \(0.515355\pi\) | |||||||
\(588\) | −67.8503 | −2.79810 | ||||||||
\(589\) | 2.04070 | 0.0840855 | ||||||||
\(590\) | −43.3884 | −1.78627 | ||||||||
\(591\) | −36.6092 | −1.50590 | ||||||||
\(592\) | 30.7512 | 1.26387 | ||||||||
\(593\) | 37.4259 | 1.53690 | 0.768449 | − | 0.639911i | \(-0.221029\pi\) | ||||
0.768449 | + | 0.639911i | \(0.221029\pi\) | |||||||
\(594\) | 18.4363 | 0.756450 | ||||||||
\(595\) | −6.47931 | −0.265626 | ||||||||
\(596\) | 10.7699 | 0.441152 | ||||||||
\(597\) | −12.7620 | −0.522313 | ||||||||
\(598\) | 10.2727 | 0.420083 | ||||||||
\(599\) | −10.6432 | −0.434869 | −0.217434 | − | 0.976075i | \(-0.569769\pi\) | ||||
−0.217434 | + | 0.976075i | \(0.569769\pi\) | |||||||
\(600\) | −5.13809 | −0.209762 | ||||||||
\(601\) | 23.1478 | 0.944217 | 0.472108 | − | 0.881541i | \(-0.343493\pi\) | ||||
0.472108 | + | 0.881541i | \(0.343493\pi\) | |||||||
\(602\) | 18.4067 | 0.750201 | ||||||||
\(603\) | −53.9889 | −2.19860 | ||||||||
\(604\) | 80.4086 | 3.27178 | ||||||||
\(605\) | 36.5549 | 1.48617 | ||||||||
\(606\) | −88.2067 | −3.58315 | ||||||||
\(607\) | −31.5986 | −1.28255 | −0.641273 | − | 0.767313i | \(-0.721593\pi\) | ||||
−0.641273 | + | 0.767313i | \(0.721593\pi\) | |||||||
\(608\) | −8.93754 | −0.362465 | ||||||||
\(609\) | −4.47660 | −0.181401 | ||||||||
\(610\) | 5.99748 | 0.242831 | ||||||||
\(611\) | 35.5536 | 1.43835 | ||||||||
\(612\) | 43.4490 | 1.75632 | ||||||||
\(613\) | 41.8023 | 1.68838 | 0.844190 | − | 0.536045i | \(-0.180082\pi\) | ||||
0.844190 | + | 0.536045i | \(0.180082\pi\) | |||||||
\(614\) | −2.49349 | −0.100629 | ||||||||
\(615\) | 69.2112 | 2.79086 | ||||||||
\(616\) | −32.8943 | −1.32535 | ||||||||
\(617\) | −43.4379 | −1.74874 | −0.874372 | − | 0.485256i | \(-0.838727\pi\) | ||||
−0.874372 | + | 0.485256i | \(0.838727\pi\) | |||||||
\(618\) | −36.3681 | −1.46294 | ||||||||
\(619\) | −43.6686 | −1.75519 | −0.877594 | − | 0.479405i | \(-0.840852\pi\) | ||||
−0.877594 | + | 0.479405i | \(0.840852\pi\) | |||||||
\(620\) | 11.9191 | 0.478684 | ||||||||
\(621\) | −1.71665 | −0.0688869 | ||||||||
\(622\) | 46.6446 | 1.87028 | ||||||||
\(623\) | 6.41112 | 0.256856 | ||||||||
\(624\) | 58.3050 | 2.33407 | ||||||||
\(625\) | −26.5095 | −1.06038 | ||||||||
\(626\) | −40.4696 | −1.61749 | ||||||||
\(627\) | −23.3035 | −0.930651 | ||||||||
\(628\) | 44.3293 | 1.76893 | ||||||||
\(629\) | 12.2628 | 0.488949 | ||||||||
\(630\) | 21.2098 | 0.845020 | ||||||||
\(631\) | −24.9021 | −0.991336 | −0.495668 | − | 0.868512i | \(-0.665077\pi\) | ||||
−0.495668 | + | 0.868512i | \(0.665077\pi\) | |||||||
\(632\) | 36.2864 | 1.44340 | ||||||||
\(633\) | 22.9282 | 0.911315 | ||||||||
\(634\) | −64.5761 | −2.56465 | ||||||||
\(635\) | −29.4118 | −1.16717 | ||||||||
\(636\) | 125.883 | 4.99158 | ||||||||
\(637\) | −19.6723 | −0.779444 | ||||||||
\(638\) | 22.5605 | 0.893181 | ||||||||
\(639\) | 7.57396 | 0.299621 | ||||||||
\(640\) | 28.6793 | 1.13365 | ||||||||
\(641\) | −48.4140 | −1.91224 | −0.956119 | − | 0.292978i | \(-0.905354\pi\) | ||||
−0.956119 | + | 0.292978i | \(0.905354\pi\) | |||||||
\(642\) | −32.5992 | −1.28659 | ||||||||
\(643\) | −49.5208 | −1.95291 | −0.976456 | − | 0.215718i | \(-0.930791\pi\) | ||||
−0.976456 | + | 0.215718i | \(0.930791\pi\) | |||||||
\(644\) | 5.56326 | 0.219223 | ||||||||
\(645\) | 41.9316 | 1.65106 | ||||||||
\(646\) | −12.2865 | −0.483406 | ||||||||
\(647\) | 44.5616 | 1.75190 | 0.875948 | − | 0.482406i | \(-0.160237\pi\) | ||||
0.875948 | + | 0.482406i | \(0.160237\pi\) | |||||||
\(648\) | 43.9117 | 1.72502 | ||||||||
\(649\) | −38.3670 | −1.50604 | ||||||||
\(650\) | −2.70586 | −0.106132 | ||||||||
\(651\) | −3.03130 | −0.118806 | ||||||||
\(652\) | 59.8793 | 2.34505 | ||||||||
\(653\) | 23.0276 | 0.901141 | 0.450571 | − | 0.892741i | \(-0.351221\pi\) | ||||
0.450571 | + | 0.892741i | \(0.351221\pi\) | |||||||
\(654\) | −81.8383 | −3.20013 | ||||||||
\(655\) | 29.6927 | 1.16019 | ||||||||
\(656\) | 80.9173 | 3.15929 | ||||||||
\(657\) | −38.7532 | −1.51191 | ||||||||
\(658\) | 27.9081 | 1.08797 | ||||||||
\(659\) | −22.2955 | −0.868510 | −0.434255 | − | 0.900790i | \(-0.642988\pi\) | ||||
−0.434255 | + | 0.900790i | \(0.642988\pi\) | |||||||
\(660\) | −136.109 | −5.29803 | ||||||||
\(661\) | 46.4407 | 1.80634 | 0.903168 | − | 0.429288i | \(-0.141236\pi\) | ||||
0.903168 | + | 0.429288i | \(0.141236\pi\) | |||||||
\(662\) | 17.3015 | 0.672441 | ||||||||
\(663\) | 23.2505 | 0.902975 | ||||||||
\(664\) | 104.009 | 4.03631 | ||||||||
\(665\) | −4.13794 | −0.160462 | ||||||||
\(666\) | −40.1418 | −1.55546 | ||||||||
\(667\) | −2.10067 | −0.0813384 | ||||||||
\(668\) | −13.0222 | −0.503843 | ||||||||
\(669\) | −8.71109 | −0.336790 | ||||||||
\(670\) | 89.1701 | 3.44494 | ||||||||
\(671\) | 5.30337 | 0.204734 | ||||||||
\(672\) | 13.2760 | 0.512134 | ||||||||
\(673\) | 5.74251 | 0.221357 | 0.110679 | − | 0.993856i | \(-0.464698\pi\) | ||||
0.110679 | + | 0.993856i | \(0.464698\pi\) | |||||||
\(674\) | −53.9833 | −2.07936 | ||||||||
\(675\) | 0.452170 | 0.0174040 | ||||||||
\(676\) | −9.34896 | −0.359575 | ||||||||
\(677\) | −3.41592 | −0.131285 | −0.0656423 | − | 0.997843i | \(-0.520910\pi\) | ||||
−0.0656423 | + | 0.997843i | \(0.520910\pi\) | |||||||
\(678\) | −48.4260 | −1.85979 | ||||||||
\(679\) | 10.6893 | 0.410218 | ||||||||
\(680\) | −39.5088 | −1.51509 | ||||||||
\(681\) | 65.5929 | 2.51353 | ||||||||
\(682\) | 15.2767 | 0.584976 | ||||||||
\(683\) | −32.6551 | −1.24951 | −0.624756 | − | 0.780820i | \(-0.714802\pi\) | ||||
−0.624756 | + | 0.780820i | \(0.714802\pi\) | |||||||
\(684\) | 27.7482 | 1.06098 | ||||||||
\(685\) | −30.3342 | −1.15901 | ||||||||
\(686\) | −33.5820 | −1.28217 | ||||||||
\(687\) | 44.4144 | 1.69451 | ||||||||
\(688\) | 49.0238 | 1.86901 | ||||||||
\(689\) | 36.4980 | 1.39046 | ||||||||
\(690\) | 18.3695 | 0.699315 | ||||||||
\(691\) | −13.1401 | −0.499873 | −0.249936 | − | 0.968262i | \(-0.580410\pi\) | ||||
−0.249936 | + | 0.968262i | \(0.580410\pi\) | |||||||
\(692\) | 25.8565 | 0.982918 | ||||||||
\(693\) | 18.7552 | 0.712449 | ||||||||
\(694\) | 0.305236 | 0.0115866 | ||||||||
\(695\) | 23.4978 | 0.891321 | ||||||||
\(696\) | −27.2969 | −1.03469 | ||||||||
\(697\) | 32.2677 | 1.22223 | ||||||||
\(698\) | 23.7383 | 0.898507 | ||||||||
\(699\) | 20.6133 | 0.779668 | ||||||||
\(700\) | −1.46538 | −0.0553860 | ||||||||
\(701\) | −21.7553 | −0.821686 | −0.410843 | − | 0.911706i | \(-0.634766\pi\) | ||||
−0.410843 | + | 0.911706i | \(0.634766\pi\) | |||||||
\(702\) | −11.7474 | −0.443376 | ||||||||
\(703\) | 7.83148 | 0.295370 | ||||||||
\(704\) | 4.61363 | 0.173883 | ||||||||
\(705\) | 63.5764 | 2.39443 | ||||||||
\(706\) | 77.1871 | 2.90497 | ||||||||
\(707\) | −13.8500 | −0.520881 | ||||||||
\(708\) | 84.3183 | 3.16888 | ||||||||
\(709\) | 9.15783 | 0.343930 | 0.171965 | − | 0.985103i | \(-0.444988\pi\) | ||||
0.171965 | + | 0.985103i | \(0.444988\pi\) | |||||||
\(710\) | −12.5094 | −0.469471 | ||||||||
\(711\) | −20.6892 | −0.775907 | ||||||||
\(712\) | 39.0930 | 1.46507 | ||||||||
\(713\) | −1.42246 | −0.0532714 | ||||||||
\(714\) | 18.2507 | 0.683014 | ||||||||
\(715\) | −39.4629 | −1.47583 | ||||||||
\(716\) | −12.1343 | −0.453481 | ||||||||
\(717\) | 53.4447 | 1.99593 | ||||||||
\(718\) | 53.6181 | 2.00101 | ||||||||
\(719\) | −27.5086 | −1.02590 | −0.512948 | − | 0.858419i | \(-0.671447\pi\) | ||||
−0.512948 | + | 0.858419i | \(0.671447\pi\) | |||||||
\(720\) | 56.4895 | 2.10524 | ||||||||
\(721\) | −5.71041 | −0.212667 | ||||||||
\(722\) | 40.4071 | 1.50380 | ||||||||
\(723\) | 17.3890 | 0.646706 | ||||||||
\(724\) | 25.8307 | 0.959989 | ||||||||
\(725\) | 0.553322 | 0.0205499 | ||||||||
\(726\) | −102.966 | −3.82144 | ||||||||
\(727\) | −3.14110 | −0.116497 | −0.0582485 | − | 0.998302i | \(-0.518552\pi\) | ||||
−0.0582485 | + | 0.998302i | \(0.518552\pi\) | |||||||
\(728\) | 20.9598 | 0.776823 | ||||||||
\(729\) | −35.7924 | −1.32564 | ||||||||
\(730\) | 64.0062 | 2.36898 | ||||||||
\(731\) | 19.5494 | 0.723060 | ||||||||
\(732\) | −11.6551 | −0.430785 | ||||||||
\(733\) | 19.5963 | 0.723807 | 0.361903 | − | 0.932216i | \(-0.382127\pi\) | ||||
0.361903 | + | 0.932216i | \(0.382127\pi\) | |||||||
\(734\) | 15.6684 | 0.578331 | ||||||||
\(735\) | −35.1776 | −1.29755 | ||||||||
\(736\) | 6.22986 | 0.229636 | ||||||||
\(737\) | 78.8502 | 2.90449 | ||||||||
\(738\) | −105.627 | −3.88819 | ||||||||
\(739\) | 30.4179 | 1.11894 | 0.559470 | − | 0.828851i | \(-0.311005\pi\) | ||||
0.559470 | + | 0.828851i | \(0.311005\pi\) | |||||||
\(740\) | 45.7415 | 1.68149 | ||||||||
\(741\) | 14.8487 | 0.545480 | ||||||||
\(742\) | 28.6494 | 1.05175 | ||||||||
\(743\) | 20.0776 | 0.736575 | 0.368288 | − | 0.929712i | \(-0.379944\pi\) | ||||
0.368288 | + | 0.929712i | \(0.379944\pi\) | |||||||
\(744\) | −18.4839 | −0.677654 | ||||||||
\(745\) | 5.58375 | 0.204573 | ||||||||
\(746\) | −56.6977 | −2.07585 | ||||||||
\(747\) | −59.3020 | −2.16975 | ||||||||
\(748\) | −63.4568 | −2.32021 | ||||||||
\(749\) | −5.11862 | −0.187030 | ||||||||
\(750\) | 70.1256 | 2.56063 | ||||||||
\(751\) | −6.34154 | −0.231406 | −0.115703 | − | 0.993284i | \(-0.536912\pi\) | ||||
−0.115703 | + | 0.993284i | \(0.536912\pi\) | |||||||
\(752\) | 74.3295 | 2.71052 | ||||||||
\(753\) | 0.882078 | 0.0321447 | ||||||||
\(754\) | −14.3753 | −0.523517 | ||||||||
\(755\) | 41.6886 | 1.51720 | ||||||||
\(756\) | −6.36187 | −0.231379 | ||||||||
\(757\) | −17.4100 | −0.632776 | −0.316388 | − | 0.948630i | \(-0.602470\pi\) | ||||
−0.316388 | + | 0.948630i | \(0.602470\pi\) | |||||||
\(758\) | 52.9790 | 1.92428 | ||||||||
\(759\) | 16.2435 | 0.589603 | ||||||||
\(760\) | −25.2319 | −0.915256 | ||||||||
\(761\) | −38.5466 | −1.39731 | −0.698656 | − | 0.715458i | \(-0.746218\pi\) | ||||
−0.698656 | + | 0.715458i | \(0.746218\pi\) | |||||||
\(762\) | 82.8460 | 3.00119 | ||||||||
\(763\) | −12.8500 | −0.465202 | ||||||||
\(764\) | −33.1118 | −1.19794 | ||||||||
\(765\) | 22.5265 | 0.814449 | ||||||||
\(766\) | −17.1833 | −0.620857 | ||||||||
\(767\) | 24.4470 | 0.882728 | ||||||||
\(768\) | −76.2256 | −2.75055 | ||||||||
\(769\) | −47.3557 | −1.70769 | −0.853845 | − | 0.520527i | \(-0.825735\pi\) | ||||
−0.853845 | + | 0.520527i | \(0.825735\pi\) | |||||||
\(770\) | −30.9767 | −1.11632 | ||||||||
\(771\) | 14.4556 | 0.520607 | ||||||||
\(772\) | −69.1556 | −2.48896 | ||||||||
\(773\) | 52.2686 | 1.87997 | 0.939986 | − | 0.341213i | \(-0.110838\pi\) | ||||
0.939986 | + | 0.341213i | \(0.110838\pi\) | |||||||
\(774\) | −63.9943 | −2.30023 | ||||||||
\(775\) | 0.374678 | 0.0134588 | ||||||||
\(776\) | 65.1801 | 2.33983 | ||||||||
\(777\) | −11.6331 | −0.417334 | ||||||||
\(778\) | −36.1885 | −1.29742 | ||||||||
\(779\) | 20.6074 | 0.738336 | ||||||||
\(780\) | 86.7269 | 3.10532 | ||||||||
\(781\) | −11.0617 | −0.395818 | ||||||||
\(782\) | 8.56424 | 0.306257 | ||||||||
\(783\) | 2.40222 | 0.0858485 | ||||||||
\(784\) | −41.1274 | −1.46884 | ||||||||
\(785\) | 22.9830 | 0.820297 | ||||||||
\(786\) | −83.6371 | −2.98324 | ||||||||
\(787\) | 26.1883 | 0.933511 | 0.466756 | − | 0.884386i | \(-0.345423\pi\) | ||||
0.466756 | + | 0.884386i | \(0.345423\pi\) | |||||||
\(788\) | −63.6653 | −2.26798 | ||||||||
\(789\) | 58.9697 | 2.09938 | ||||||||
\(790\) | 34.1711 | 1.21575 | ||||||||
\(791\) | −7.60371 | −0.270357 | ||||||||
\(792\) | 114.363 | 4.06372 | ||||||||
\(793\) | −3.37924 | −0.120000 | ||||||||
\(794\) | 39.9018 | 1.41606 | ||||||||
\(795\) | 65.2651 | 2.31472 | ||||||||
\(796\) | −22.1938 | −0.786637 | ||||||||
\(797\) | −11.0850 | −0.392650 | −0.196325 | − | 0.980539i | \(-0.562901\pi\) | ||||
−0.196325 | + | 0.980539i | \(0.562901\pi\) | |||||||
\(798\) | 11.6556 | 0.412603 | ||||||||
\(799\) | 29.6406 | 1.04861 | ||||||||
\(800\) | −1.64096 | −0.0580167 | ||||||||
\(801\) | −22.2895 | −0.787559 | ||||||||
\(802\) | −52.6747 | −1.86001 | ||||||||
\(803\) | 56.5986 | 1.99732 | ||||||||
\(804\) | −173.287 | −6.11138 | ||||||||
\(805\) | 2.88433 | 0.101659 | ||||||||
\(806\) | −9.73414 | −0.342870 | ||||||||
\(807\) | 66.4654 | 2.33969 | ||||||||
\(808\) | −84.4528 | −2.97104 | ||||||||
\(809\) | 17.3132 | 0.608698 | 0.304349 | − | 0.952561i | \(-0.401561\pi\) | ||||
0.304349 | + | 0.952561i | \(0.401561\pi\) | |||||||
\(810\) | 41.3519 | 1.45296 | ||||||||
\(811\) | −22.9372 | −0.805435 | −0.402717 | − | 0.915324i | \(-0.631934\pi\) | ||||
−0.402717 | + | 0.915324i | \(0.631934\pi\) | |||||||
\(812\) | −7.78504 | −0.273201 | ||||||||
\(813\) | −6.52147 | −0.228718 | ||||||||
\(814\) | 58.6267 | 2.05487 | ||||||||
\(815\) | 31.0450 | 1.08746 | ||||||||
\(816\) | 48.6082 | 1.70163 | ||||||||
\(817\) | 12.4850 | 0.436795 | ||||||||
\(818\) | −12.0785 | −0.422315 | ||||||||
\(819\) | −11.9505 | −0.417586 | ||||||||
\(820\) | 120.362 | 4.20322 | ||||||||
\(821\) | 23.9003 | 0.834128 | 0.417064 | − | 0.908877i | \(-0.363059\pi\) | ||||
0.417064 | + | 0.908877i | \(0.363059\pi\) | |||||||
\(822\) | 85.4440 | 2.98020 | ||||||||
\(823\) | −34.0190 | −1.18583 | −0.592913 | − | 0.805266i | \(-0.702022\pi\) | ||||
−0.592913 | + | 0.805266i | \(0.702022\pi\) | |||||||
\(824\) | −34.8203 | −1.21302 | ||||||||
\(825\) | −4.27859 | −0.148961 | ||||||||
\(826\) | 19.1898 | 0.667699 | ||||||||
\(827\) | −12.0353 | −0.418509 | −0.209254 | − | 0.977861i | \(-0.567104\pi\) | ||||
−0.209254 | + | 0.977861i | \(0.567104\pi\) | |||||||
\(828\) | −19.3417 | −0.672171 | ||||||||
\(829\) | −18.0819 | −0.628012 | −0.314006 | − | 0.949421i | \(-0.601671\pi\) | ||||
−0.314006 | + | 0.949421i | \(0.601671\pi\) | |||||||
\(830\) | 97.9454 | 3.39974 | ||||||||
\(831\) | 21.9671 | 0.762031 | ||||||||
\(832\) | −2.93975 | −0.101917 | ||||||||
\(833\) | −16.4005 | −0.568245 | ||||||||
\(834\) | −66.1876 | −2.29189 | ||||||||
\(835\) | −6.75147 | −0.233644 | ||||||||
\(836\) | −40.5259 | −1.40162 | ||||||||
\(837\) | 1.62665 | 0.0562253 | ||||||||
\(838\) | −50.4930 | −1.74425 | ||||||||
\(839\) | 41.2960 | 1.42570 | 0.712848 | − | 0.701318i | \(-0.247405\pi\) | ||||
0.712848 | + | 0.701318i | \(0.247405\pi\) | |||||||
\(840\) | 37.4800 | 1.29318 | ||||||||
\(841\) | −26.0604 | −0.898634 | ||||||||
\(842\) | −25.2452 | −0.870007 | ||||||||
\(843\) | −9.83240 | −0.338646 | ||||||||
\(844\) | 39.8733 | 1.37250 | ||||||||
\(845\) | −4.84706 | −0.166744 | ||||||||
\(846\) | −97.0277 | −3.33588 | ||||||||
\(847\) | −16.1675 | −0.555521 | ||||||||
\(848\) | 76.3038 | 2.62028 | ||||||||
\(849\) | 26.9549 | 0.925089 | ||||||||
\(850\) | −2.25584 | −0.0773747 | ||||||||
\(851\) | −5.45889 | −0.187128 | ||||||||
\(852\) | 24.3100 | 0.832848 | ||||||||
\(853\) | 3.23885 | 0.110896 | 0.0554480 | − | 0.998462i | \(-0.482341\pi\) | ||||
0.0554480 | + | 0.998462i | \(0.482341\pi\) | |||||||
\(854\) | −2.65256 | −0.0907688 | ||||||||
\(855\) | 14.3863 | 0.492002 | ||||||||
\(856\) | −31.2118 | −1.06680 | ||||||||
\(857\) | −18.3234 | −0.625916 | −0.312958 | − | 0.949767i | \(-0.601320\pi\) | ||||
−0.312958 | + | 0.949767i | \(0.601320\pi\) | |||||||
\(858\) | 111.158 | 3.79486 | ||||||||
\(859\) | −33.9225 | −1.15742 | −0.578711 | − | 0.815533i | \(-0.696444\pi\) | ||||
−0.578711 | + | 0.815533i | \(0.696444\pi\) | |||||||
\(860\) | 72.9213 | 2.48660 | ||||||||
\(861\) | −30.6107 | −1.04321 | ||||||||
\(862\) | 68.8809 | 2.34609 | ||||||||
\(863\) | −51.0173 | −1.73665 | −0.868325 | − | 0.495995i | \(-0.834803\pi\) | ||||
−0.868325 | + | 0.495995i | \(0.834803\pi\) | |||||||
\(864\) | −7.12415 | −0.242369 | ||||||||
\(865\) | 13.4056 | 0.455803 | ||||||||
\(866\) | −66.2684 | −2.25189 | ||||||||
\(867\) | −24.1163 | −0.819032 | ||||||||
\(868\) | −5.27159 | −0.178929 | ||||||||
\(869\) | 30.2164 | 1.02502 | ||||||||
\(870\) | −25.7057 | −0.871503 | ||||||||
\(871\) | −50.2424 | −1.70240 | ||||||||
\(872\) | −78.3554 | −2.65345 | ||||||||
\(873\) | −37.1634 | −1.25779 | ||||||||
\(874\) | 5.46945 | 0.185007 | ||||||||
\(875\) | 11.0109 | 0.372237 | ||||||||
\(876\) | −124.386 | −4.20260 | ||||||||
\(877\) | −11.6024 | −0.391785 | −0.195893 | − | 0.980625i | \(-0.562760\pi\) | ||||
−0.195893 | + | 0.980625i | \(0.562760\pi\) | |||||||
\(878\) | 58.0206 | 1.95810 | ||||||||
\(879\) | 60.3110 | 2.03424 | ||||||||
\(880\) | −82.5024 | −2.78115 | ||||||||
\(881\) | −25.3671 | −0.854638 | −0.427319 | − | 0.904101i | \(-0.640542\pi\) | ||||
−0.427319 | + | 0.904101i | \(0.640542\pi\) | |||||||
\(882\) | 53.6867 | 1.80772 | ||||||||
\(883\) | −43.4063 | −1.46074 | −0.730369 | − | 0.683053i | \(-0.760652\pi\) | ||||
−0.730369 | + | 0.683053i | \(0.760652\pi\) | |||||||
\(884\) | 40.4338 | 1.35994 | ||||||||
\(885\) | 43.7156 | 1.46948 | ||||||||
\(886\) | 69.0065 | 2.31832 | ||||||||
\(887\) | 16.8270 | 0.564996 | 0.282498 | − | 0.959268i | \(-0.408837\pi\) | ||||
0.282498 | + | 0.959268i | \(0.408837\pi\) | |||||||
\(888\) | −70.9348 | −2.38042 | ||||||||
\(889\) | 13.0082 | 0.436282 | ||||||||
\(890\) | 36.8141 | 1.23401 | ||||||||
\(891\) | 36.5662 | 1.22501 | ||||||||
\(892\) | −15.1490 | −0.507227 | ||||||||
\(893\) | 18.9297 | 0.633457 | ||||||||
\(894\) | −15.7281 | −0.526026 | ||||||||
\(895\) | −6.29115 | −0.210290 | ||||||||
\(896\) | −12.6843 | −0.423751 | ||||||||
\(897\) | −10.3502 | −0.345582 | ||||||||
\(898\) | −54.0088 | −1.80230 | ||||||||
\(899\) | 1.99054 | 0.0663881 | ||||||||
\(900\) | 5.09465 | 0.169822 | ||||||||
\(901\) | 30.4279 | 1.01370 | ||||||||
\(902\) | 154.268 | 5.13655 | ||||||||
\(903\) | −18.5455 | −0.617155 | ||||||||
\(904\) | −46.3651 | −1.54208 | ||||||||
\(905\) | 13.3922 | 0.445170 | ||||||||
\(906\) | −117.427 | −3.90124 | ||||||||
\(907\) | −38.1979 | −1.26834 | −0.634170 | − | 0.773193i | \(-0.718658\pi\) | ||||
−0.634170 | + | 0.773193i | \(0.718658\pi\) | |||||||
\(908\) | 114.070 | 3.78553 | ||||||||
\(909\) | 48.1520 | 1.59710 | ||||||||
\(910\) | 19.7380 | 0.654308 | ||||||||
\(911\) | 28.1937 | 0.934099 | 0.467049 | − | 0.884231i | \(-0.345317\pi\) | ||||
0.467049 | + | 0.884231i | \(0.345317\pi\) | |||||||
\(912\) | 31.0431 | 1.02794 | ||||||||
\(913\) | 86.6099 | 2.86637 | ||||||||
\(914\) | 63.2739 | 2.09292 | ||||||||
\(915\) | −6.04270 | −0.199766 | ||||||||
\(916\) | 77.2389 | 2.55204 | ||||||||
\(917\) | −13.1324 | −0.433672 | ||||||||
\(918\) | −9.79363 | −0.323238 | ||||||||
\(919\) | −51.2018 | −1.68899 | −0.844496 | − | 0.535561i | \(-0.820100\pi\) | ||||
−0.844496 | + | 0.535561i | \(0.820100\pi\) | |||||||
\(920\) | 17.5877 | 0.579850 | ||||||||
\(921\) | 2.51229 | 0.0827829 | ||||||||
\(922\) | −73.3262 | −2.41487 | ||||||||
\(923\) | 7.04837 | 0.232000 | ||||||||
\(924\) | 60.1982 | 1.98037 | ||||||||
\(925\) | 1.43788 | 0.0472773 | ||||||||
\(926\) | −27.7857 | −0.913096 | ||||||||
\(927\) | 19.8533 | 0.652068 | ||||||||
\(928\) | −8.71785 | −0.286177 | ||||||||
\(929\) | −28.4086 | −0.932056 | −0.466028 | − | 0.884770i | \(-0.654315\pi\) | ||||
−0.466028 | + | 0.884770i | \(0.654315\pi\) | |||||||
\(930\) | −17.4064 | −0.570779 | ||||||||
\(931\) | −10.4740 | −0.343272 | ||||||||
\(932\) | 35.8477 | 1.17423 | ||||||||
\(933\) | −46.9964 | −1.53859 | ||||||||
\(934\) | −56.0578 | −1.83427 | ||||||||
\(935\) | −32.8998 | −1.07594 | ||||||||
\(936\) | −72.8707 | −2.38185 | ||||||||
\(937\) | 14.7153 | 0.480728 | 0.240364 | − | 0.970683i | \(-0.422733\pi\) | ||||
0.240364 | + | 0.970683i | \(0.422733\pi\) | |||||||
\(938\) | −39.4381 | −1.28770 | ||||||||
\(939\) | 40.7747 | 1.33063 | ||||||||
\(940\) | 110.563 | 3.60616 | ||||||||
\(941\) | 18.2326 | 0.594365 | 0.297183 | − | 0.954821i | \(-0.403953\pi\) | ||||
0.297183 | + | 0.954821i | \(0.403953\pi\) | |||||||
\(942\) | −64.7375 | −2.10926 | ||||||||
\(943\) | −14.3643 | −0.467765 | ||||||||
\(944\) | 51.1095 | 1.66347 | ||||||||
\(945\) | −3.29837 | −0.107296 | ||||||||
\(946\) | 93.4630 | 3.03875 | ||||||||
\(947\) | −40.5452 | −1.31754 | −0.658771 | − | 0.752343i | \(-0.728924\pi\) | ||||
−0.658771 | + | 0.752343i | \(0.728924\pi\) | |||||||
\(948\) | −66.4059 | −2.15676 | ||||||||
\(949\) | −36.0639 | −1.17068 | ||||||||
\(950\) | −1.44067 | −0.0467414 | ||||||||
\(951\) | 65.0631 | 2.10981 | ||||||||
\(952\) | 17.4739 | 0.566334 | ||||||||
\(953\) | 1.49813 | 0.0485291 | 0.0242645 | − | 0.999706i | \(-0.492276\pi\) | ||||
0.0242645 | + | 0.999706i | \(0.492276\pi\) | |||||||
\(954\) | −99.6050 | −3.22483 | ||||||||
\(955\) | −17.1671 | −0.555516 | ||||||||
\(956\) | 92.9430 | 3.00599 | ||||||||
\(957\) | −22.7307 | −0.734778 | ||||||||
\(958\) | 57.8201 | 1.86808 | ||||||||
\(959\) | 13.4162 | 0.433231 | ||||||||
\(960\) | −5.25680 | −0.169663 | ||||||||
\(961\) | −29.6521 | −0.956520 | ||||||||
\(962\) | −37.3562 | −1.20441 | ||||||||
\(963\) | 17.7959 | 0.573463 | ||||||||
\(964\) | 30.2405 | 0.973980 | ||||||||
\(965\) | −35.8544 | −1.15419 | ||||||||
\(966\) | −8.12445 | −0.261400 | ||||||||
\(967\) | −25.7047 | −0.826607 | −0.413303 | − | 0.910593i | \(-0.635625\pi\) | ||||
−0.413303 | + | 0.910593i | \(0.635625\pi\) | |||||||
\(968\) | −98.5843 | −3.16862 | ||||||||
\(969\) | 12.3792 | 0.397676 | ||||||||
\(970\) | 61.3805 | 1.97081 | ||||||||
\(971\) | 41.8327 | 1.34247 | 0.671237 | − | 0.741243i | \(-0.265763\pi\) | ||||
0.671237 | + | 0.741243i | \(0.265763\pi\) | |||||||
\(972\) | −99.0650 | −3.17751 | ||||||||
\(973\) | −10.3926 | −0.333171 | ||||||||
\(974\) | 95.0816 | 3.04661 | ||||||||
\(975\) | 2.72626 | 0.0873102 | ||||||||
\(976\) | −7.06474 | −0.226137 | ||||||||
\(977\) | −19.4714 | −0.622945 | −0.311472 | − | 0.950255i | \(-0.600822\pi\) | ||||
−0.311472 | + | 0.950255i | \(0.600822\pi\) | |||||||
\(978\) | −87.4462 | −2.79622 | ||||||||
\(979\) | 32.5535 | 1.04041 | ||||||||
\(980\) | −61.1757 | −1.95419 | ||||||||
\(981\) | 44.6755 | 1.42638 | ||||||||
\(982\) | 73.3680 | 2.34127 | ||||||||
\(983\) | 28.5364 | 0.910170 | 0.455085 | − | 0.890448i | \(-0.349609\pi\) | ||||
0.455085 | + | 0.890448i | \(0.349609\pi\) | |||||||
\(984\) | −186.654 | −5.95033 | ||||||||
\(985\) | −33.0079 | −1.05172 | ||||||||
\(986\) | −11.9845 | −0.381664 | ||||||||
\(987\) | −28.1185 | −0.895023 | ||||||||
\(988\) | 25.8226 | 0.821527 | ||||||||
\(989\) | −8.70259 | −0.276726 | ||||||||
\(990\) | 107.696 | 3.42282 | ||||||||
\(991\) | 21.2895 | 0.676284 | 0.338142 | − | 0.941095i | \(-0.390202\pi\) | ||||
0.338142 | + | 0.941095i | \(0.390202\pi\) | |||||||
\(992\) | −5.90324 | −0.187428 | ||||||||
\(993\) | −17.4319 | −0.553186 | ||||||||
\(994\) | 5.53267 | 0.175486 | ||||||||
\(995\) | −11.5066 | −0.364783 | ||||||||
\(996\) | −190.341 | −6.03118 | ||||||||
\(997\) | 24.2323 | 0.767445 | 0.383722 | − | 0.923448i | \(-0.374642\pi\) | ||||
0.383722 | + | 0.923448i | \(0.374642\pi\) | |||||||
\(998\) | −91.7365 | −2.90387 | ||||||||
\(999\) | 6.24251 | 0.197504 |
(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 | 6007.2.a.c.1.12 | ✓ | 261 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6007.2.a.c.1.12 | ✓ | 261 | 1.1 | even | 1 | trivial |