Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4011,2,Mod(1,4011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4011, 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("4011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4011 = 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4011.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0279962507\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 4011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.75611 | −1.94887 | −0.974433 | − | 0.224677i | \(-0.927867\pi\) | ||||
−0.974433 | + | 0.224677i | \(0.927867\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.59616 | 2.79808 | ||||||||
\(5\) | −2.11611 | −0.946354 | −0.473177 | − | 0.880967i | \(-0.656893\pi\) | ||||
−0.473177 | + | 0.880967i | \(0.656893\pi\) | |||||||
\(6\) | 2.75611 | 1.12518 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −9.91144 | −3.50422 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 5.83224 | 1.84432 | ||||||||
\(11\) | −2.18663 | −0.659295 | −0.329648 | − | 0.944104i | \(-0.606930\pi\) | ||||
−0.329648 | + | 0.944104i | \(0.606930\pi\) | |||||||
\(12\) | −5.59616 | −1.61547 | ||||||||
\(13\) | −3.28792 | −0.911905 | −0.455953 | − | 0.890004i | \(-0.650701\pi\) | ||||
−0.455953 | + | 0.890004i | \(0.650701\pi\) | |||||||
\(14\) | −2.75611 | −0.736602 | ||||||||
\(15\) | 2.11611 | 0.546378 | ||||||||
\(16\) | 16.1247 | 4.03118 | ||||||||
\(17\) | 4.46735 | 1.08349 | 0.541746 | − | 0.840542i | \(-0.317764\pi\) | ||||
0.541746 | + | 0.840542i | \(0.317764\pi\) | |||||||
\(18\) | −2.75611 | −0.649622 | ||||||||
\(19\) | 3.35498 | 0.769684 | 0.384842 | − | 0.922982i | \(-0.374256\pi\) | ||||
0.384842 | + | 0.922982i | \(0.374256\pi\) | |||||||
\(20\) | −11.8421 | −2.64798 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 6.02661 | 1.28488 | ||||||||
\(23\) | −9.54424 | −1.99011 | −0.995056 | − | 0.0993165i | \(-0.968334\pi\) | ||||
−0.995056 | + | 0.0993165i | \(0.968334\pi\) | |||||||
\(24\) | 9.91144 | 2.02316 | ||||||||
\(25\) | −0.522072 | −0.104414 | ||||||||
\(26\) | 9.06188 | 1.77718 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 5.59616 | 1.05758 | ||||||||
\(29\) | 8.29783 | 1.54087 | 0.770434 | − | 0.637520i | \(-0.220040\pi\) | ||||
0.770434 | + | 0.637520i | \(0.220040\pi\) | |||||||
\(30\) | −5.83224 | −1.06482 | ||||||||
\(31\) | −8.23902 | −1.47977 | −0.739886 | − | 0.672732i | \(-0.765121\pi\) | ||||
−0.739886 | + | 0.672732i | \(0.765121\pi\) | |||||||
\(32\) | −24.6187 | −4.35201 | ||||||||
\(33\) | 2.18663 | 0.380644 | ||||||||
\(34\) | −12.3125 | −2.11158 | ||||||||
\(35\) | −2.11611 | −0.357688 | ||||||||
\(36\) | 5.59616 | 0.932694 | ||||||||
\(37\) | 9.18971 | 1.51078 | 0.755389 | − | 0.655276i | \(-0.227448\pi\) | ||||
0.755389 | + | 0.655276i | \(0.227448\pi\) | |||||||
\(38\) | −9.24669 | −1.50001 | ||||||||
\(39\) | 3.28792 | 0.526489 | ||||||||
\(40\) | 20.9737 | 3.31623 | ||||||||
\(41\) | 2.51603 | 0.392938 | 0.196469 | − | 0.980510i | \(-0.437053\pi\) | ||||
0.196469 | + | 0.980510i | \(0.437053\pi\) | |||||||
\(42\) | 2.75611 | 0.425278 | ||||||||
\(43\) | −0.997412 | −0.152104 | −0.0760519 | − | 0.997104i | \(-0.524231\pi\) | ||||
−0.0760519 | + | 0.997104i | \(0.524231\pi\) | |||||||
\(44\) | −12.2368 | −1.84476 | ||||||||
\(45\) | −2.11611 | −0.315451 | ||||||||
\(46\) | 26.3050 | 3.87846 | ||||||||
\(47\) | −4.66122 | −0.679909 | −0.339954 | − | 0.940442i | \(-0.610412\pi\) | ||||
−0.339954 | + | 0.940442i | \(0.610412\pi\) | |||||||
\(48\) | −16.1247 | −2.32740 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.43889 | 0.203490 | ||||||||
\(51\) | −4.46735 | −0.625554 | ||||||||
\(52\) | −18.3997 | −2.55158 | ||||||||
\(53\) | −10.9605 | −1.50554 | −0.752770 | − | 0.658284i | \(-0.771283\pi\) | ||||
−0.752770 | + | 0.658284i | \(0.771283\pi\) | |||||||
\(54\) | 2.75611 | 0.375060 | ||||||||
\(55\) | 4.62716 | 0.623926 | ||||||||
\(56\) | −9.91144 | −1.32447 | ||||||||
\(57\) | −3.35498 | −0.444377 | ||||||||
\(58\) | −22.8698 | −3.00295 | ||||||||
\(59\) | −8.79911 | −1.14555 | −0.572773 | − | 0.819714i | \(-0.694133\pi\) | ||||
−0.572773 | + | 0.819714i | \(0.694133\pi\) | |||||||
\(60\) | 11.8421 | 1.52881 | ||||||||
\(61\) | −6.53065 | −0.836164 | −0.418082 | − | 0.908409i | \(-0.637298\pi\) | ||||
−0.418082 | + | 0.908409i | \(0.637298\pi\) | |||||||
\(62\) | 22.7077 | 2.88388 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 35.6025 | 4.45031 | ||||||||
\(65\) | 6.95761 | 0.862985 | ||||||||
\(66\) | −6.02661 | −0.741825 | ||||||||
\(67\) | −12.9550 | −1.58271 | −0.791354 | − | 0.611358i | \(-0.790623\pi\) | ||||
−0.791354 | + | 0.611358i | \(0.790623\pi\) | |||||||
\(68\) | 25.0000 | 3.03170 | ||||||||
\(69\) | 9.54424 | 1.14899 | ||||||||
\(70\) | 5.83224 | 0.697087 | ||||||||
\(71\) | 3.16272 | 0.375345 | 0.187673 | − | 0.982232i | \(-0.439906\pi\) | ||||
0.187673 | + | 0.982232i | \(0.439906\pi\) | |||||||
\(72\) | −9.91144 | −1.16807 | ||||||||
\(73\) | 12.3345 | 1.44364 | 0.721822 | − | 0.692079i | \(-0.243305\pi\) | ||||
0.721822 | + | 0.692079i | \(0.243305\pi\) | |||||||
\(74\) | −25.3279 | −2.94431 | ||||||||
\(75\) | 0.522072 | 0.0602837 | ||||||||
\(76\) | 18.7750 | 2.15364 | ||||||||
\(77\) | −2.18663 | −0.249190 | ||||||||
\(78\) | −9.06188 | −1.02606 | ||||||||
\(79\) | 15.3503 | 1.72704 | 0.863521 | − | 0.504313i | \(-0.168254\pi\) | ||||
0.863521 | + | 0.504313i | \(0.168254\pi\) | |||||||
\(80\) | −34.1217 | −3.81492 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.93446 | −0.765783 | ||||||||
\(83\) | 14.1553 | 1.55375 | 0.776873 | − | 0.629657i | \(-0.216805\pi\) | ||||
0.776873 | + | 0.629657i | \(0.216805\pi\) | |||||||
\(84\) | −5.59616 | −0.610592 | ||||||||
\(85\) | −9.45341 | −1.02537 | ||||||||
\(86\) | 2.74898 | 0.296430 | ||||||||
\(87\) | −8.29783 | −0.889620 | ||||||||
\(88\) | 21.6727 | 2.31032 | ||||||||
\(89\) | 3.19891 | 0.339084 | 0.169542 | − | 0.985523i | \(-0.445771\pi\) | ||||
0.169542 | + | 0.985523i | \(0.445771\pi\) | |||||||
\(90\) | 5.83224 | 0.614773 | ||||||||
\(91\) | −3.28792 | −0.344668 | ||||||||
\(92\) | −53.4111 | −5.56850 | ||||||||
\(93\) | 8.23902 | 0.854347 | ||||||||
\(94\) | 12.8469 | 1.32505 | ||||||||
\(95\) | −7.09950 | −0.728393 | ||||||||
\(96\) | 24.6187 | 2.51263 | ||||||||
\(97\) | 1.77027 | 0.179744 | 0.0898720 | − | 0.995953i | \(-0.471354\pi\) | ||||
0.0898720 | + | 0.995953i | \(0.471354\pi\) | |||||||
\(98\) | −2.75611 | −0.278410 | ||||||||
\(99\) | −2.18663 | −0.219765 | ||||||||
\(100\) | −2.92160 | −0.292160 | ||||||||
\(101\) | −11.6006 | −1.15430 | −0.577152 | − | 0.816637i | \(-0.695836\pi\) | ||||
−0.577152 | + | 0.816637i | \(0.695836\pi\) | |||||||
\(102\) | 12.3125 | 1.21912 | ||||||||
\(103\) | −11.1441 | −1.09806 | −0.549030 | − | 0.835803i | \(-0.685003\pi\) | ||||
−0.549030 | + | 0.835803i | \(0.685003\pi\) | |||||||
\(104\) | 32.5880 | 3.19552 | ||||||||
\(105\) | 2.11611 | 0.206511 | ||||||||
\(106\) | 30.2084 | 2.93410 | ||||||||
\(107\) | −8.51950 | −0.823611 | −0.411806 | − | 0.911272i | \(-0.635102\pi\) | ||||
−0.411806 | + | 0.911272i | \(0.635102\pi\) | |||||||
\(108\) | −5.59616 | −0.538491 | ||||||||
\(109\) | 12.1672 | 1.16541 | 0.582703 | − | 0.812685i | \(-0.301995\pi\) | ||||
0.582703 | + | 0.812685i | \(0.301995\pi\) | |||||||
\(110\) | −12.7530 | −1.21595 | ||||||||
\(111\) | −9.18971 | −0.872249 | ||||||||
\(112\) | 16.1247 | 1.52364 | ||||||||
\(113\) | 1.00573 | 0.0946110 | 0.0473055 | − | 0.998880i | \(-0.484937\pi\) | ||||
0.0473055 | + | 0.998880i | \(0.484937\pi\) | |||||||
\(114\) | 9.24669 | 0.866032 | ||||||||
\(115\) | 20.1967 | 1.88335 | ||||||||
\(116\) | 46.4360 | 4.31147 | ||||||||
\(117\) | −3.28792 | −0.303968 | ||||||||
\(118\) | 24.2514 | 2.23252 | ||||||||
\(119\) | 4.46735 | 0.409521 | ||||||||
\(120\) | −20.9737 | −1.91463 | ||||||||
\(121\) | −6.21863 | −0.565330 | ||||||||
\(122\) | 17.9992 | 1.62957 | ||||||||
\(123\) | −2.51603 | −0.226863 | ||||||||
\(124\) | −46.1069 | −4.14052 | ||||||||
\(125\) | 11.6853 | 1.04517 | ||||||||
\(126\) | −2.75611 | −0.245534 | ||||||||
\(127\) | −20.2374 | −1.79578 | −0.897888 | − | 0.440224i | \(-0.854899\pi\) | ||||
−0.897888 | + | 0.440224i | \(0.854899\pi\) | |||||||
\(128\) | −48.8871 | −4.32105 | ||||||||
\(129\) | 0.997412 | 0.0878172 | ||||||||
\(130\) | −19.1760 | −1.68184 | ||||||||
\(131\) | 6.57730 | 0.574661 | 0.287331 | − | 0.957831i | \(-0.407232\pi\) | ||||
0.287331 | + | 0.957831i | \(0.407232\pi\) | |||||||
\(132\) | 12.2368 | 1.06507 | ||||||||
\(133\) | 3.35498 | 0.290913 | ||||||||
\(134\) | 35.7055 | 3.08449 | ||||||||
\(135\) | 2.11611 | 0.182126 | ||||||||
\(136\) | −44.2778 | −3.79679 | ||||||||
\(137\) | −11.5417 | −0.986072 | −0.493036 | − | 0.870009i | \(-0.664113\pi\) | ||||
−0.493036 | + | 0.870009i | \(0.664113\pi\) | |||||||
\(138\) | −26.3050 | −2.23923 | ||||||||
\(139\) | −4.37972 | −0.371483 | −0.185741 | − | 0.982599i | \(-0.559469\pi\) | ||||
−0.185741 | + | 0.982599i | \(0.559469\pi\) | |||||||
\(140\) | −11.8421 | −1.00084 | ||||||||
\(141\) | 4.66122 | 0.392546 | ||||||||
\(142\) | −8.71681 | −0.731498 | ||||||||
\(143\) | 7.18948 | 0.601215 | ||||||||
\(144\) | 16.1247 | 1.34373 | ||||||||
\(145\) | −17.5591 | −1.45821 | ||||||||
\(146\) | −33.9953 | −2.81347 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 51.4271 | 4.22728 | ||||||||
\(149\) | 21.7290 | 1.78011 | 0.890053 | − | 0.455857i | \(-0.150667\pi\) | ||||
0.890053 | + | 0.455857i | \(0.150667\pi\) | |||||||
\(150\) | −1.43889 | −0.117485 | ||||||||
\(151\) | −11.5335 | −0.938583 | −0.469291 | − | 0.883043i | \(-0.655491\pi\) | ||||
−0.469291 | + | 0.883043i | \(0.655491\pi\) | |||||||
\(152\) | −33.2526 | −2.69714 | ||||||||
\(153\) | 4.46735 | 0.361164 | ||||||||
\(154\) | 6.02661 | 0.485638 | ||||||||
\(155\) | 17.4347 | 1.40039 | ||||||||
\(156\) | 18.3997 | 1.47316 | ||||||||
\(157\) | 10.7752 | 0.859956 | 0.429978 | − | 0.902839i | \(-0.358521\pi\) | ||||
0.429978 | + | 0.902839i | \(0.358521\pi\) | |||||||
\(158\) | −42.3071 | −3.36577 | ||||||||
\(159\) | 10.9605 | 0.869224 | ||||||||
\(160\) | 52.0959 | 4.11854 | ||||||||
\(161\) | −9.54424 | −0.752192 | ||||||||
\(162\) | −2.75611 | −0.216541 | ||||||||
\(163\) | −4.59452 | −0.359870 | −0.179935 | − | 0.983678i | \(-0.557589\pi\) | ||||
−0.179935 | + | 0.983678i | \(0.557589\pi\) | |||||||
\(164\) | 14.0801 | 1.09947 | ||||||||
\(165\) | −4.62716 | −0.360224 | ||||||||
\(166\) | −39.0136 | −3.02805 | ||||||||
\(167\) | 16.7510 | 1.29623 | 0.648116 | − | 0.761541i | \(-0.275557\pi\) | ||||
0.648116 | + | 0.761541i | \(0.275557\pi\) | |||||||
\(168\) | 9.91144 | 0.764684 | ||||||||
\(169\) | −2.18958 | −0.168429 | ||||||||
\(170\) | 26.0547 | 1.99830 | ||||||||
\(171\) | 3.35498 | 0.256561 | ||||||||
\(172\) | −5.58168 | −0.425599 | ||||||||
\(173\) | −10.6292 | −0.808122 | −0.404061 | − | 0.914732i | \(-0.632402\pi\) | ||||
−0.404061 | + | 0.914732i | \(0.632402\pi\) | |||||||
\(174\) | 22.8698 | 1.73375 | ||||||||
\(175\) | −0.522072 | −0.0394650 | ||||||||
\(176\) | −35.2589 | −2.65774 | ||||||||
\(177\) | 8.79911 | 0.661382 | ||||||||
\(178\) | −8.81655 | −0.660829 | ||||||||
\(179\) | −19.0567 | −1.42436 | −0.712182 | − | 0.701995i | \(-0.752293\pi\) | ||||
−0.712182 | + | 0.701995i | \(0.752293\pi\) | |||||||
\(180\) | −11.8421 | −0.882658 | ||||||||
\(181\) | 13.1844 | 0.979992 | 0.489996 | − | 0.871725i | \(-0.336998\pi\) | ||||
0.489996 | + | 0.871725i | \(0.336998\pi\) | |||||||
\(182\) | 9.06188 | 0.671711 | ||||||||
\(183\) | 6.53065 | 0.482760 | ||||||||
\(184\) | 94.5971 | 6.97379 | ||||||||
\(185\) | −19.4464 | −1.42973 | ||||||||
\(186\) | −22.7077 | −1.66501 | ||||||||
\(187\) | −9.76846 | −0.714341 | ||||||||
\(188\) | −26.0850 | −1.90244 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 19.5670 | 1.41954 | ||||||||
\(191\) | −1.00000 | −0.0723575 | ||||||||
\(192\) | −35.6025 | −2.56939 | ||||||||
\(193\) | −11.2526 | −0.809978 | −0.404989 | − | 0.914321i | \(-0.632725\pi\) | ||||
−0.404989 | + | 0.914321i | \(0.632725\pi\) | |||||||
\(194\) | −4.87907 | −0.350297 | ||||||||
\(195\) | −6.95761 | −0.498245 | ||||||||
\(196\) | 5.59616 | 0.399726 | ||||||||
\(197\) | 1.88628 | 0.134392 | 0.0671960 | − | 0.997740i | \(-0.478595\pi\) | ||||
0.0671960 | + | 0.997740i | \(0.478595\pi\) | |||||||
\(198\) | 6.02661 | 0.428293 | ||||||||
\(199\) | −4.43674 | −0.314512 | −0.157256 | − | 0.987558i | \(-0.550265\pi\) | ||||
−0.157256 | + | 0.987558i | \(0.550265\pi\) | |||||||
\(200\) | 5.17449 | 0.365891 | ||||||||
\(201\) | 12.9550 | 0.913777 | ||||||||
\(202\) | 31.9726 | 2.24958 | ||||||||
\(203\) | 8.29783 | 0.582393 | ||||||||
\(204\) | −25.0000 | −1.75035 | ||||||||
\(205\) | −5.32420 | −0.371858 | ||||||||
\(206\) | 30.7144 | 2.13997 | ||||||||
\(207\) | −9.54424 | −0.663371 | ||||||||
\(208\) | −53.0168 | −3.67605 | ||||||||
\(209\) | −7.33611 | −0.507449 | ||||||||
\(210\) | −5.83224 | −0.402463 | ||||||||
\(211\) | −21.0358 | −1.44816 | −0.724082 | − | 0.689714i | \(-0.757736\pi\) | ||||
−0.724082 | + | 0.689714i | \(0.757736\pi\) | |||||||
\(212\) | −61.3367 | −4.21262 | ||||||||
\(213\) | −3.16272 | −0.216706 | ||||||||
\(214\) | 23.4807 | 1.60511 | ||||||||
\(215\) | 2.11063 | 0.143944 | ||||||||
\(216\) | 9.91144 | 0.674388 | ||||||||
\(217\) | −8.23902 | −0.559301 | ||||||||
\(218\) | −33.5342 | −2.27122 | ||||||||
\(219\) | −12.3345 | −0.833488 | ||||||||
\(220\) | 25.8944 | 1.74580 | ||||||||
\(221\) | −14.6883 | −0.988041 | ||||||||
\(222\) | 25.3279 | 1.69990 | ||||||||
\(223\) | 0.748847 | 0.0501465 | 0.0250733 | − | 0.999686i | \(-0.492018\pi\) | ||||
0.0250733 | + | 0.999686i | \(0.492018\pi\) | |||||||
\(224\) | −24.6187 | −1.64491 | ||||||||
\(225\) | −0.522072 | −0.0348048 | ||||||||
\(226\) | −2.77190 | −0.184384 | ||||||||
\(227\) | 15.5627 | 1.03293 | 0.516467 | − | 0.856307i | \(-0.327247\pi\) | ||||
0.516467 | + | 0.856307i | \(0.327247\pi\) | |||||||
\(228\) | −18.7750 | −1.24340 | ||||||||
\(229\) | 0.522483 | 0.0345266 | 0.0172633 | − | 0.999851i | \(-0.494505\pi\) | ||||
0.0172633 | + | 0.999851i | \(0.494505\pi\) | |||||||
\(230\) | −55.6643 | −3.67040 | ||||||||
\(231\) | 2.18663 | 0.143870 | ||||||||
\(232\) | −82.2434 | −5.39954 | ||||||||
\(233\) | 10.4341 | 0.683558 | 0.341779 | − | 0.939780i | \(-0.388971\pi\) | ||||
0.341779 | + | 0.939780i | \(0.388971\pi\) | |||||||
\(234\) | 9.06188 | 0.592394 | ||||||||
\(235\) | 9.86366 | 0.643434 | ||||||||
\(236\) | −49.2413 | −3.20533 | ||||||||
\(237\) | −15.3503 | −0.997108 | ||||||||
\(238\) | −12.3125 | −0.798102 | ||||||||
\(239\) | −10.9384 | −0.707548 | −0.353774 | − | 0.935331i | \(-0.615102\pi\) | ||||
−0.353774 | + | 0.935331i | \(0.615102\pi\) | |||||||
\(240\) | 34.1217 | 2.20255 | ||||||||
\(241\) | −23.2504 | −1.49769 | −0.748844 | − | 0.662747i | \(-0.769391\pi\) | ||||
−0.748844 | + | 0.662747i | \(0.769391\pi\) | |||||||
\(242\) | 17.1392 | 1.10175 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −36.5466 | −2.33966 | ||||||||
\(245\) | −2.11611 | −0.135193 | ||||||||
\(246\) | 6.93446 | 0.442125 | ||||||||
\(247\) | −11.0309 | −0.701879 | ||||||||
\(248\) | 81.6606 | 5.18545 | ||||||||
\(249\) | −14.1553 | −0.897056 | ||||||||
\(250\) | −32.2061 | −2.03689 | ||||||||
\(251\) | −16.0351 | −1.01213 | −0.506063 | − | 0.862496i | \(-0.668900\pi\) | ||||
−0.506063 | + | 0.862496i | \(0.668900\pi\) | |||||||
\(252\) | 5.59616 | 0.352525 | ||||||||
\(253\) | 20.8698 | 1.31207 | ||||||||
\(254\) | 55.7765 | 3.49973 | ||||||||
\(255\) | 9.45341 | 0.591995 | ||||||||
\(256\) | 63.5335 | 3.97084 | ||||||||
\(257\) | −13.3950 | −0.835559 | −0.417779 | − | 0.908549i | \(-0.637191\pi\) | ||||
−0.417779 | + | 0.908549i | \(0.637191\pi\) | |||||||
\(258\) | −2.74898 | −0.171144 | ||||||||
\(259\) | 9.18971 | 0.571021 | ||||||||
\(260\) | 38.9359 | 2.41470 | ||||||||
\(261\) | 8.29783 | 0.513623 | ||||||||
\(262\) | −18.1278 | −1.11994 | ||||||||
\(263\) | 23.0822 | 1.42331 | 0.711655 | − | 0.702529i | \(-0.247946\pi\) | ||||
0.711655 | + | 0.702529i | \(0.247946\pi\) | |||||||
\(264\) | −21.6727 | −1.33386 | ||||||||
\(265\) | 23.1936 | 1.42477 | ||||||||
\(266\) | −9.24669 | −0.566951 | ||||||||
\(267\) | −3.19891 | −0.195770 | ||||||||
\(268\) | −72.4984 | −4.42855 | ||||||||
\(269\) | 17.1973 | 1.04854 | 0.524269 | − | 0.851553i | \(-0.324339\pi\) | ||||
0.524269 | + | 0.851553i | \(0.324339\pi\) | |||||||
\(270\) | −5.83224 | −0.354939 | ||||||||
\(271\) | 16.8486 | 1.02348 | 0.511741 | − | 0.859140i | \(-0.329001\pi\) | ||||
0.511741 | + | 0.859140i | \(0.329001\pi\) | |||||||
\(272\) | 72.0348 | 4.36775 | ||||||||
\(273\) | 3.28792 | 0.198994 | ||||||||
\(274\) | 31.8102 | 1.92172 | ||||||||
\(275\) | 1.14158 | 0.0688399 | ||||||||
\(276\) | 53.4111 | 3.21497 | ||||||||
\(277\) | 21.0004 | 1.26179 | 0.630895 | − | 0.775868i | \(-0.282688\pi\) | ||||
0.630895 | + | 0.775868i | \(0.282688\pi\) | |||||||
\(278\) | 12.0710 | 0.723970 | ||||||||
\(279\) | −8.23902 | −0.493257 | ||||||||
\(280\) | 20.9737 | 1.25342 | ||||||||
\(281\) | 4.70943 | 0.280941 | 0.140471 | − | 0.990085i | \(-0.455138\pi\) | ||||
0.140471 | + | 0.990085i | \(0.455138\pi\) | |||||||
\(282\) | −12.8469 | −0.765019 | ||||||||
\(283\) | 2.32384 | 0.138138 | 0.0690689 | − | 0.997612i | \(-0.477997\pi\) | ||||
0.0690689 | + | 0.997612i | \(0.477997\pi\) | |||||||
\(284\) | 17.6991 | 1.05025 | ||||||||
\(285\) | 7.09950 | 0.420538 | ||||||||
\(286\) | −19.8150 | −1.17169 | ||||||||
\(287\) | 2.51603 | 0.148517 | ||||||||
\(288\) | −24.6187 | −1.45067 | ||||||||
\(289\) | 2.95721 | 0.173953 | ||||||||
\(290\) | 48.3949 | 2.84185 | ||||||||
\(291\) | −1.77027 | −0.103775 | ||||||||
\(292\) | 69.0259 | 4.03943 | ||||||||
\(293\) | 15.4114 | 0.900344 | 0.450172 | − | 0.892942i | \(-0.351363\pi\) | ||||
0.450172 | + | 0.892942i | \(0.351363\pi\) | |||||||
\(294\) | 2.75611 | 0.160740 | ||||||||
\(295\) | 18.6199 | 1.08409 | ||||||||
\(296\) | −91.0832 | −5.29410 | ||||||||
\(297\) | 2.18663 | 0.126881 | ||||||||
\(298\) | −59.8875 | −3.46919 | ||||||||
\(299\) | 31.3807 | 1.81479 | ||||||||
\(300\) | 2.92160 | 0.168679 | ||||||||
\(301\) | −0.997412 | −0.0574899 | ||||||||
\(302\) | 31.7876 | 1.82917 | ||||||||
\(303\) | 11.6006 | 0.666438 | ||||||||
\(304\) | 54.0980 | 3.10274 | ||||||||
\(305\) | 13.8196 | 0.791307 | ||||||||
\(306\) | −12.3125 | −0.703860 | ||||||||
\(307\) | −8.63781 | −0.492986 | −0.246493 | − | 0.969145i | \(-0.579278\pi\) | ||||
−0.246493 | + | 0.969145i | \(0.579278\pi\) | |||||||
\(308\) | −12.2368 | −0.697254 | ||||||||
\(309\) | 11.1441 | 0.633965 | ||||||||
\(310\) | −48.0520 | −2.72917 | ||||||||
\(311\) | 16.3592 | 0.927645 | 0.463822 | − | 0.885928i | \(-0.346478\pi\) | ||||
0.463822 | + | 0.885928i | \(0.346478\pi\) | |||||||
\(312\) | −32.5880 | −1.84493 | ||||||||
\(313\) | −13.9498 | −0.788490 | −0.394245 | − | 0.919005i | \(-0.628994\pi\) | ||||
−0.394245 | + | 0.919005i | \(0.628994\pi\) | |||||||
\(314\) | −29.6977 | −1.67594 | ||||||||
\(315\) | −2.11611 | −0.119229 | ||||||||
\(316\) | 85.9027 | 4.83240 | ||||||||
\(317\) | 3.09494 | 0.173829 | 0.0869146 | − | 0.996216i | \(-0.472299\pi\) | ||||
0.0869146 | + | 0.996216i | \(0.472299\pi\) | |||||||
\(318\) | −30.2084 | −1.69400 | ||||||||
\(319\) | −18.1443 | −1.01589 | ||||||||
\(320\) | −75.3388 | −4.21157 | ||||||||
\(321\) | 8.51950 | 0.475512 | ||||||||
\(322\) | 26.3050 | 1.46592 | ||||||||
\(323\) | 14.9878 | 0.833946 | ||||||||
\(324\) | 5.59616 | 0.310898 | ||||||||
\(325\) | 1.71653 | 0.0952161 | ||||||||
\(326\) | 12.6630 | 0.701339 | ||||||||
\(327\) | −12.1672 | −0.672848 | ||||||||
\(328\) | −24.9375 | −1.37694 | ||||||||
\(329\) | −4.66122 | −0.256981 | ||||||||
\(330\) | 12.7530 | 0.702029 | ||||||||
\(331\) | 21.1056 | 1.16007 | 0.580034 | − | 0.814592i | \(-0.303039\pi\) | ||||
0.580034 | + | 0.814592i | \(0.303039\pi\) | |||||||
\(332\) | 79.2154 | 4.34751 | ||||||||
\(333\) | 9.18971 | 0.503593 | ||||||||
\(334\) | −46.1677 | −2.52618 | ||||||||
\(335\) | 27.4143 | 1.49780 | ||||||||
\(336\) | −16.1247 | −0.879676 | ||||||||
\(337\) | −11.4890 | −0.625848 | −0.312924 | − | 0.949778i | \(-0.601309\pi\) | ||||
−0.312924 | + | 0.949778i | \(0.601309\pi\) | |||||||
\(338\) | 6.03473 | 0.328246 | ||||||||
\(339\) | −1.00573 | −0.0546237 | ||||||||
\(340\) | −52.9028 | −2.86906 | ||||||||
\(341\) | 18.0157 | 0.975607 | ||||||||
\(342\) | −9.24669 | −0.500004 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 9.88578 | 0.533006 | ||||||||
\(345\) | −20.1967 | −1.08735 | ||||||||
\(346\) | 29.2952 | 1.57492 | ||||||||
\(347\) | 12.4995 | 0.671009 | 0.335505 | − | 0.942039i | \(-0.391093\pi\) | ||||
0.335505 | + | 0.942039i | \(0.391093\pi\) | |||||||
\(348\) | −46.4360 | −2.48923 | ||||||||
\(349\) | 20.6103 | 1.10325 | 0.551623 | − | 0.834093i | \(-0.314009\pi\) | ||||
0.551623 | + | 0.834093i | \(0.314009\pi\) | |||||||
\(350\) | 1.43889 | 0.0769119 | ||||||||
\(351\) | 3.28792 | 0.175496 | ||||||||
\(352\) | 53.8321 | 2.86926 | ||||||||
\(353\) | −27.9988 | −1.49023 | −0.745114 | − | 0.666937i | \(-0.767605\pi\) | ||||
−0.745114 | + | 0.666937i | \(0.767605\pi\) | |||||||
\(354\) | −24.2514 | −1.28894 | ||||||||
\(355\) | −6.69266 | −0.355210 | ||||||||
\(356\) | 17.9016 | 0.948784 | ||||||||
\(357\) | −4.46735 | −0.236437 | ||||||||
\(358\) | 52.5224 | 2.77589 | ||||||||
\(359\) | 15.2709 | 0.805969 | 0.402984 | − | 0.915207i | \(-0.367973\pi\) | ||||
0.402984 | + | 0.915207i | \(0.367973\pi\) | |||||||
\(360\) | 20.9737 | 1.10541 | ||||||||
\(361\) | −7.74414 | −0.407586 | ||||||||
\(362\) | −36.3378 | −1.90987 | ||||||||
\(363\) | 6.21863 | 0.326393 | ||||||||
\(364\) | −18.3997 | −0.964408 | ||||||||
\(365\) | −26.1012 | −1.36620 | ||||||||
\(366\) | −17.9992 | −0.940834 | ||||||||
\(367\) | 6.35567 | 0.331763 | 0.165882 | − | 0.986146i | \(-0.446953\pi\) | ||||
0.165882 | + | 0.986146i | \(0.446953\pi\) | |||||||
\(368\) | −153.898 | −8.02250 | ||||||||
\(369\) | 2.51603 | 0.130979 | ||||||||
\(370\) | 53.5966 | 2.78636 | ||||||||
\(371\) | −10.9605 | −0.569040 | ||||||||
\(372\) | 46.1069 | 2.39053 | ||||||||
\(373\) | −9.44285 | −0.488932 | −0.244466 | − | 0.969658i | \(-0.578613\pi\) | ||||
−0.244466 | + | 0.969658i | \(0.578613\pi\) | |||||||
\(374\) | 26.9230 | 1.39215 | ||||||||
\(375\) | −11.6853 | −0.603427 | ||||||||
\(376\) | 46.1994 | 2.38255 | ||||||||
\(377\) | −27.2826 | −1.40512 | ||||||||
\(378\) | 2.75611 | 0.141759 | ||||||||
\(379\) | 24.2886 | 1.24762 | 0.623810 | − | 0.781576i | \(-0.285584\pi\) | ||||
0.623810 | + | 0.781576i | \(0.285584\pi\) | |||||||
\(380\) | −39.7300 | −2.03810 | ||||||||
\(381\) | 20.2374 | 1.03679 | ||||||||
\(382\) | 2.75611 | 0.141015 | ||||||||
\(383\) | 28.9024 | 1.47684 | 0.738422 | − | 0.674338i | \(-0.235571\pi\) | ||||
0.738422 | + | 0.674338i | \(0.235571\pi\) | |||||||
\(384\) | 48.8871 | 2.49476 | ||||||||
\(385\) | 4.62716 | 0.235822 | ||||||||
\(386\) | 31.0134 | 1.57854 | ||||||||
\(387\) | −0.997412 | −0.0507013 | ||||||||
\(388\) | 9.90674 | 0.502938 | ||||||||
\(389\) | 27.3709 | 1.38776 | 0.693880 | − | 0.720091i | \(-0.255900\pi\) | ||||
0.693880 | + | 0.720091i | \(0.255900\pi\) | |||||||
\(390\) | 19.1760 | 0.971012 | ||||||||
\(391\) | −42.6375 | −2.15627 | ||||||||
\(392\) | −9.91144 | −0.500603 | ||||||||
\(393\) | −6.57730 | −0.331781 | ||||||||
\(394\) | −5.19881 | −0.261912 | ||||||||
\(395\) | −32.4829 | −1.63439 | ||||||||
\(396\) | −12.2368 | −0.614921 | ||||||||
\(397\) | −28.2806 | −1.41936 | −0.709681 | − | 0.704523i | \(-0.751161\pi\) | ||||
−0.709681 | + | 0.704523i | \(0.751161\pi\) | |||||||
\(398\) | 12.2282 | 0.612943 | ||||||||
\(399\) | −3.35498 | −0.167959 | ||||||||
\(400\) | −8.41827 | −0.420914 | ||||||||
\(401\) | −6.18517 | −0.308873 | −0.154436 | − | 0.988003i | \(-0.549356\pi\) | ||||
−0.154436 | + | 0.988003i | \(0.549356\pi\) | |||||||
\(402\) | −35.7055 | −1.78083 | ||||||||
\(403\) | 27.0893 | 1.34941 | ||||||||
\(404\) | −64.9189 | −3.22984 | ||||||||
\(405\) | −2.11611 | −0.105150 | ||||||||
\(406\) | −22.8698 | −1.13501 | ||||||||
\(407\) | −20.0945 | −0.996049 | ||||||||
\(408\) | 44.2778 | 2.19208 | ||||||||
\(409\) | 36.8706 | 1.82313 | 0.911567 | − | 0.411151i | \(-0.134873\pi\) | ||||
0.911567 | + | 0.411151i | \(0.134873\pi\) | |||||||
\(410\) | 14.6741 | 0.724702 | ||||||||
\(411\) | 11.5417 | 0.569309 | ||||||||
\(412\) | −62.3642 | −3.07246 | ||||||||
\(413\) | −8.79911 | −0.432976 | ||||||||
\(414\) | 26.3050 | 1.29282 | ||||||||
\(415\) | −29.9542 | −1.47039 | ||||||||
\(416\) | 80.9443 | 3.96862 | ||||||||
\(417\) | 4.37972 | 0.214476 | ||||||||
\(418\) | 20.2191 | 0.988951 | ||||||||
\(419\) | −4.46489 | −0.218124 | −0.109062 | − | 0.994035i | \(-0.534785\pi\) | ||||
−0.109062 | + | 0.994035i | \(0.534785\pi\) | |||||||
\(420\) | 11.8421 | 0.577836 | ||||||||
\(421\) | 14.6840 | 0.715653 | 0.357826 | − | 0.933788i | \(-0.383518\pi\) | ||||
0.357826 | + | 0.933788i | \(0.383518\pi\) | |||||||
\(422\) | 57.9771 | 2.82228 | ||||||||
\(423\) | −4.66122 | −0.226636 | ||||||||
\(424\) | 108.634 | 5.27574 | ||||||||
\(425\) | −2.33228 | −0.113132 | ||||||||
\(426\) | 8.71681 | 0.422331 | ||||||||
\(427\) | −6.53065 | −0.316040 | ||||||||
\(428\) | −47.6765 | −2.30453 | ||||||||
\(429\) | −7.18948 | −0.347111 | ||||||||
\(430\) | −5.81715 | −0.280528 | ||||||||
\(431\) | 6.71719 | 0.323556 | 0.161778 | − | 0.986827i | \(-0.448277\pi\) | ||||
0.161778 | + | 0.986827i | \(0.448277\pi\) | |||||||
\(432\) | −16.1247 | −0.775801 | ||||||||
\(433\) | 29.0923 | 1.39809 | 0.699043 | − | 0.715080i | \(-0.253610\pi\) | ||||
0.699043 | + | 0.715080i | \(0.253610\pi\) | |||||||
\(434\) | 22.7077 | 1.09000 | ||||||||
\(435\) | 17.5591 | 0.841896 | ||||||||
\(436\) | 68.0896 | 3.26090 | ||||||||
\(437\) | −32.0207 | −1.53176 | ||||||||
\(438\) | 33.9953 | 1.62436 | ||||||||
\(439\) | 22.6122 | 1.07922 | 0.539610 | − | 0.841915i | \(-0.318572\pi\) | ||||
0.539610 | + | 0.841915i | \(0.318572\pi\) | |||||||
\(440\) | −45.8618 | −2.18638 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 40.4826 | 1.92556 | ||||||||
\(443\) | 20.4059 | 0.969513 | 0.484756 | − | 0.874649i | \(-0.338908\pi\) | ||||
0.484756 | + | 0.874649i | \(0.338908\pi\) | |||||||
\(444\) | −51.4271 | −2.44062 | ||||||||
\(445\) | −6.76925 | −0.320893 | ||||||||
\(446\) | −2.06391 | −0.0977289 | ||||||||
\(447\) | −21.7290 | −1.02774 | ||||||||
\(448\) | 35.6025 | 1.68206 | ||||||||
\(449\) | 27.1454 | 1.28107 | 0.640536 | − | 0.767928i | \(-0.278712\pi\) | ||||
0.640536 | + | 0.767928i | \(0.278712\pi\) | |||||||
\(450\) | 1.43889 | 0.0678300 | ||||||||
\(451\) | −5.50164 | −0.259062 | ||||||||
\(452\) | 5.62822 | 0.264729 | ||||||||
\(453\) | 11.5335 | 0.541891 | ||||||||
\(454\) | −42.8927 | −2.01305 | ||||||||
\(455\) | 6.95761 | 0.326178 | ||||||||
\(456\) | 33.2526 | 1.55720 | ||||||||
\(457\) | −14.8386 | −0.694120 | −0.347060 | − | 0.937843i | \(-0.612820\pi\) | ||||
−0.347060 | + | 0.937843i | \(0.612820\pi\) | |||||||
\(458\) | −1.44002 | −0.0672878 | ||||||||
\(459\) | −4.46735 | −0.208518 | ||||||||
\(460\) | 113.024 | 5.26977 | ||||||||
\(461\) | 27.6469 | 1.28765 | 0.643823 | − | 0.765175i | \(-0.277347\pi\) | ||||
0.643823 | + | 0.765175i | \(0.277347\pi\) | |||||||
\(462\) | −6.02661 | −0.280383 | ||||||||
\(463\) | 22.4006 | 1.04105 | 0.520523 | − | 0.853848i | \(-0.325737\pi\) | ||||
0.520523 | + | 0.853848i | \(0.325737\pi\) | |||||||
\(464\) | 133.800 | 6.21152 | ||||||||
\(465\) | −17.4347 | −0.808514 | ||||||||
\(466\) | −28.7574 | −1.33216 | ||||||||
\(467\) | −30.0050 | −1.38846 | −0.694232 | − | 0.719751i | \(-0.744256\pi\) | ||||
−0.694232 | + | 0.719751i | \(0.744256\pi\) | |||||||
\(468\) | −18.3997 | −0.850528 | ||||||||
\(469\) | −12.9550 | −0.598207 | ||||||||
\(470\) | −27.1854 | −1.25397 | ||||||||
\(471\) | −10.7752 | −0.496496 | ||||||||
\(472\) | 87.2118 | 4.01425 | ||||||||
\(473\) | 2.18097 | 0.100281 | ||||||||
\(474\) | 42.3071 | 1.94323 | ||||||||
\(475\) | −1.75154 | −0.0803662 | ||||||||
\(476\) | 25.0000 | 1.14587 | ||||||||
\(477\) | −10.9605 | −0.501846 | ||||||||
\(478\) | 30.1476 | 1.37892 | ||||||||
\(479\) | 27.7495 | 1.26791 | 0.633954 | − | 0.773370i | \(-0.281431\pi\) | ||||
0.633954 | + | 0.773370i | \(0.281431\pi\) | |||||||
\(480\) | −52.0959 | −2.37784 | ||||||||
\(481\) | −30.2150 | −1.37769 | ||||||||
\(482\) | 64.0806 | 2.91879 | ||||||||
\(483\) | 9.54424 | 0.434278 | ||||||||
\(484\) | −34.8005 | −1.58184 | ||||||||
\(485\) | −3.74609 | −0.170101 | ||||||||
\(486\) | 2.75611 | 0.125020 | ||||||||
\(487\) | 22.7088 | 1.02903 | 0.514517 | − | 0.857480i | \(-0.327971\pi\) | ||||
0.514517 | + | 0.857480i | \(0.327971\pi\) | |||||||
\(488\) | 64.7281 | 2.93010 | ||||||||
\(489\) | 4.59452 | 0.207771 | ||||||||
\(490\) | 5.83224 | 0.263474 | ||||||||
\(491\) | 21.1753 | 0.955629 | 0.477815 | − | 0.878461i | \(-0.341429\pi\) | ||||
0.477815 | + | 0.878461i | \(0.341429\pi\) | |||||||
\(492\) | −14.0801 | −0.634780 | ||||||||
\(493\) | 37.0693 | 1.66952 | ||||||||
\(494\) | 30.4024 | 1.36787 | ||||||||
\(495\) | 4.62716 | 0.207975 | ||||||||
\(496\) | −132.852 | −5.96523 | ||||||||
\(497\) | 3.16272 | 0.141867 | ||||||||
\(498\) | 39.0136 | 1.74824 | ||||||||
\(499\) | 22.9663 | 1.02811 | 0.514057 | − | 0.857756i | \(-0.328142\pi\) | ||||
0.514057 | + | 0.857756i | \(0.328142\pi\) | |||||||
\(500\) | 65.3930 | 2.92446 | ||||||||
\(501\) | −16.7510 | −0.748380 | ||||||||
\(502\) | 44.1946 | 1.97250 | ||||||||
\(503\) | 28.2489 | 1.25956 | 0.629779 | − | 0.776774i | \(-0.283145\pi\) | ||||
0.629779 | + | 0.776774i | \(0.283145\pi\) | |||||||
\(504\) | −9.91144 | −0.441490 | ||||||||
\(505\) | 24.5482 | 1.09238 | ||||||||
\(506\) | −57.5195 | −2.55705 | ||||||||
\(507\) | 2.18958 | 0.0972427 | ||||||||
\(508\) | −113.252 | −5.02473 | ||||||||
\(509\) | 13.8796 | 0.615204 | 0.307602 | − | 0.951515i | \(-0.400474\pi\) | ||||
0.307602 | + | 0.951515i | \(0.400474\pi\) | |||||||
\(510\) | −26.0547 | −1.15372 | ||||||||
\(511\) | 12.3345 | 0.545646 | ||||||||
\(512\) | −77.3312 | −3.41759 | ||||||||
\(513\) | −3.35498 | −0.148126 | ||||||||
\(514\) | 36.9182 | 1.62839 | ||||||||
\(515\) | 23.5821 | 1.03915 | ||||||||
\(516\) | 5.58168 | 0.245720 | ||||||||
\(517\) | 10.1924 | 0.448261 | ||||||||
\(518\) | −25.3279 | −1.11284 | ||||||||
\(519\) | 10.6292 | 0.466569 | ||||||||
\(520\) | −68.9599 | −3.02409 | ||||||||
\(521\) | 8.69891 | 0.381106 | 0.190553 | − | 0.981677i | \(-0.438972\pi\) | ||||
0.190553 | + | 0.981677i | \(0.438972\pi\) | |||||||
\(522\) | −22.8698 | −1.00098 | ||||||||
\(523\) | 4.21749 | 0.184418 | 0.0922090 | − | 0.995740i | \(-0.470607\pi\) | ||||
0.0922090 | + | 0.995740i | \(0.470607\pi\) | |||||||
\(524\) | 36.8076 | 1.60795 | ||||||||
\(525\) | 0.522072 | 0.0227851 | ||||||||
\(526\) | −63.6172 | −2.77384 | ||||||||
\(527\) | −36.8066 | −1.60332 | ||||||||
\(528\) | 35.2589 | 1.53445 | ||||||||
\(529\) | 68.0925 | 2.96054 | ||||||||
\(530\) | −63.9243 | −2.77669 | ||||||||
\(531\) | −8.79911 | −0.381849 | ||||||||
\(532\) | 18.7750 | 0.813999 | ||||||||
\(533\) | −8.27250 | −0.358322 | ||||||||
\(534\) | 8.81655 | 0.381530 | ||||||||
\(535\) | 18.0282 | 0.779428 | ||||||||
\(536\) | 128.403 | 5.54616 | ||||||||
\(537\) | 19.0567 | 0.822356 | ||||||||
\(538\) | −47.3977 | −2.04346 | ||||||||
\(539\) | −2.18663 | −0.0941850 | ||||||||
\(540\) | 11.8421 | 0.509603 | ||||||||
\(541\) | −37.6038 | −1.61671 | −0.808356 | − | 0.588694i | \(-0.799642\pi\) | ||||
−0.808356 | + | 0.588694i | \(0.799642\pi\) | |||||||
\(542\) | −46.4368 | −1.99463 | ||||||||
\(543\) | −13.1844 | −0.565799 | ||||||||
\(544\) | −109.980 | −4.71537 | ||||||||
\(545\) | −25.7471 | −1.10289 | ||||||||
\(546\) | −9.06188 | −0.387813 | ||||||||
\(547\) | 27.0576 | 1.15690 | 0.578449 | − | 0.815719i | \(-0.303658\pi\) | ||||
0.578449 | + | 0.815719i | \(0.303658\pi\) | |||||||
\(548\) | −64.5891 | −2.75911 | ||||||||
\(549\) | −6.53065 | −0.278721 | ||||||||
\(550\) | −3.14633 | −0.134160 | ||||||||
\(551\) | 27.8390 | 1.18598 | ||||||||
\(552\) | −94.5971 | −4.02632 | ||||||||
\(553\) | 15.3503 | 0.652761 | ||||||||
\(554\) | −57.8794 | −2.45906 | ||||||||
\(555\) | 19.4464 | 0.825456 | ||||||||
\(556\) | −24.5096 | −1.03944 | ||||||||
\(557\) | −7.29845 | −0.309245 | −0.154623 | − | 0.987974i | \(-0.549416\pi\) | ||||
−0.154623 | + | 0.987974i | \(0.549416\pi\) | |||||||
\(558\) | 22.7077 | 0.961293 | ||||||||
\(559\) | 3.27941 | 0.138704 | ||||||||
\(560\) | −34.1217 | −1.44191 | ||||||||
\(561\) | 9.76846 | 0.412425 | ||||||||
\(562\) | −12.9797 | −0.547517 | ||||||||
\(563\) | 4.33188 | 0.182567 | 0.0912836 | − | 0.995825i | \(-0.470903\pi\) | ||||
0.0912836 | + | 0.995825i | \(0.470903\pi\) | |||||||
\(564\) | 26.0850 | 1.09837 | ||||||||
\(565\) | −2.12823 | −0.0895355 | ||||||||
\(566\) | −6.40476 | −0.269212 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −31.3471 | −1.31529 | ||||||||
\(569\) | −31.9664 | −1.34010 | −0.670052 | − | 0.742315i | \(-0.733728\pi\) | ||||
−0.670052 | + | 0.742315i | \(0.733728\pi\) | |||||||
\(570\) | −19.5670 | −0.819573 | ||||||||
\(571\) | 4.09939 | 0.171554 | 0.0857772 | − | 0.996314i | \(-0.472663\pi\) | ||||
0.0857772 | + | 0.996314i | \(0.472663\pi\) | |||||||
\(572\) | 40.2335 | 1.68225 | ||||||||
\(573\) | 1.00000 | 0.0417756 | ||||||||
\(574\) | −6.93446 | −0.289439 | ||||||||
\(575\) | 4.98278 | 0.207796 | ||||||||
\(576\) | 35.6025 | 1.48344 | ||||||||
\(577\) | −16.9228 | −0.704506 | −0.352253 | − | 0.935905i | \(-0.614584\pi\) | ||||
−0.352253 | + | 0.935905i | \(0.614584\pi\) | |||||||
\(578\) | −8.15040 | −0.339012 | ||||||||
\(579\) | 11.2526 | 0.467641 | ||||||||
\(580\) | −98.2637 | −4.08018 | ||||||||
\(581\) | 14.1553 | 0.587261 | ||||||||
\(582\) | 4.87907 | 0.202244 | ||||||||
\(583\) | 23.9666 | 0.992595 | ||||||||
\(584\) | −122.253 | −5.05885 | ||||||||
\(585\) | 6.95761 | 0.287662 | ||||||||
\(586\) | −42.4756 | −1.75465 | ||||||||
\(587\) | 33.9789 | 1.40246 | 0.701230 | − | 0.712936i | \(-0.252635\pi\) | ||||
0.701230 | + | 0.712936i | \(0.252635\pi\) | |||||||
\(588\) | −5.59616 | −0.230782 | ||||||||
\(589\) | −27.6417 | −1.13896 | ||||||||
\(590\) | −51.3186 | −2.11275 | ||||||||
\(591\) | −1.88628 | −0.0775913 | ||||||||
\(592\) | 148.181 | 6.09022 | ||||||||
\(593\) | −16.3383 | −0.670934 | −0.335467 | − | 0.942052i | \(-0.608894\pi\) | ||||
−0.335467 | + | 0.942052i | \(0.608894\pi\) | |||||||
\(594\) | −6.02661 | −0.247275 | ||||||||
\(595\) | −9.45341 | −0.387552 | ||||||||
\(596\) | 121.599 | 4.98088 | ||||||||
\(597\) | 4.43674 | 0.181584 | ||||||||
\(598\) | −86.4888 | −3.53679 | ||||||||
\(599\) | −23.1694 | −0.946676 | −0.473338 | − | 0.880881i | \(-0.656951\pi\) | ||||
−0.473338 | + | 0.880881i | \(0.656951\pi\) | |||||||
\(600\) | −5.17449 | −0.211248 | ||||||||
\(601\) | 19.7009 | 0.803616 | 0.401808 | − | 0.915724i | \(-0.368382\pi\) | ||||
0.401808 | + | 0.915724i | \(0.368382\pi\) | |||||||
\(602\) | 2.74898 | 0.112040 | ||||||||
\(603\) | −12.9550 | −0.527569 | ||||||||
\(604\) | −64.5433 | −2.62623 | ||||||||
\(605\) | 13.1593 | 0.535002 | ||||||||
\(606\) | −31.9726 | −1.29880 | ||||||||
\(607\) | −0.246448 | −0.0100030 | −0.00500151 | − | 0.999987i | \(-0.501592\pi\) | ||||
−0.00500151 | + | 0.999987i | \(0.501592\pi\) | |||||||
\(608\) | −82.5951 | −3.34967 | ||||||||
\(609\) | −8.29783 | −0.336245 | ||||||||
\(610\) | −38.0884 | −1.54215 | ||||||||
\(611\) | 15.3257 | 0.620012 | ||||||||
\(612\) | 25.0000 | 1.01057 | ||||||||
\(613\) | −0.975068 | −0.0393826 | −0.0196913 | − | 0.999806i | \(-0.506268\pi\) | ||||
−0.0196913 | + | 0.999806i | \(0.506268\pi\) | |||||||
\(614\) | 23.8068 | 0.960763 | ||||||||
\(615\) | 5.32420 | 0.214692 | ||||||||
\(616\) | 21.6727 | 0.873218 | ||||||||
\(617\) | 4.85140 | 0.195310 | 0.0976551 | − | 0.995220i | \(-0.468866\pi\) | ||||
0.0976551 | + | 0.995220i | \(0.468866\pi\) | |||||||
\(618\) | −30.7144 | −1.23551 | ||||||||
\(619\) | 31.0996 | 1.25000 | 0.624999 | − | 0.780625i | \(-0.285099\pi\) | ||||
0.624999 | + | 0.780625i | \(0.285099\pi\) | |||||||
\(620\) | 97.5674 | 3.91840 | ||||||||
\(621\) | 9.54424 | 0.382997 | ||||||||
\(622\) | −45.0878 | −1.80786 | ||||||||
\(623\) | 3.19891 | 0.128162 | ||||||||
\(624\) | 53.0168 | 2.12237 | ||||||||
\(625\) | −22.1171 | −0.884683 | ||||||||
\(626\) | 38.4473 | 1.53666 | ||||||||
\(627\) | 7.33611 | 0.292976 | ||||||||
\(628\) | 60.2999 | 2.40623 | ||||||||
\(629\) | 41.0536 | 1.63692 | ||||||||
\(630\) | 5.83224 | 0.232362 | ||||||||
\(631\) | 11.8055 | 0.469970 | 0.234985 | − | 0.971999i | \(-0.424496\pi\) | ||||
0.234985 | + | 0.971999i | \(0.424496\pi\) | |||||||
\(632\) | −152.143 | −6.05194 | ||||||||
\(633\) | 21.0358 | 0.836098 | ||||||||
\(634\) | −8.53001 | −0.338770 | ||||||||
\(635\) | 42.8245 | 1.69944 | ||||||||
\(636\) | 61.3367 | 2.43216 | ||||||||
\(637\) | −3.28792 | −0.130272 | ||||||||
\(638\) | 50.0078 | 1.97983 | ||||||||
\(639\) | 3.16272 | 0.125115 | ||||||||
\(640\) | 103.451 | 4.08924 | ||||||||
\(641\) | −28.5668 | −1.12832 | −0.564160 | − | 0.825665i | \(-0.690800\pi\) | ||||
−0.564160 | + | 0.825665i | \(0.690800\pi\) | |||||||
\(642\) | −23.4807 | −0.926710 | ||||||||
\(643\) | −41.9476 | −1.65425 | −0.827125 | − | 0.562018i | \(-0.810025\pi\) | ||||
−0.827125 | + | 0.562018i | \(0.810025\pi\) | |||||||
\(644\) | −53.4111 | −2.10469 | ||||||||
\(645\) | −2.11063 | −0.0831061 | ||||||||
\(646\) | −41.3082 | −1.62525 | ||||||||
\(647\) | 6.49160 | 0.255211 | 0.127606 | − | 0.991825i | \(-0.459271\pi\) | ||||
0.127606 | + | 0.991825i | \(0.459271\pi\) | |||||||
\(648\) | −9.91144 | −0.389358 | ||||||||
\(649\) | 19.2404 | 0.755253 | ||||||||
\(650\) | −4.73096 | −0.185563 | ||||||||
\(651\) | 8.23902 | 0.322913 | ||||||||
\(652\) | −25.7117 | −1.00695 | ||||||||
\(653\) | 43.1943 | 1.69032 | 0.845162 | − | 0.534510i | \(-0.179504\pi\) | ||||
0.845162 | + | 0.534510i | \(0.179504\pi\) | |||||||
\(654\) | 33.5342 | 1.31129 | ||||||||
\(655\) | −13.9183 | −0.543833 | ||||||||
\(656\) | 40.5703 | 1.58400 | ||||||||
\(657\) | 12.3345 | 0.481215 | ||||||||
\(658\) | 12.8469 | 0.500823 | ||||||||
\(659\) | 3.79415 | 0.147799 | 0.0738996 | − | 0.997266i | \(-0.476456\pi\) | ||||
0.0738996 | + | 0.997266i | \(0.476456\pi\) | |||||||
\(660\) | −25.8944 | −1.00794 | ||||||||
\(661\) | 18.8678 | 0.733873 | 0.366937 | − | 0.930246i | \(-0.380407\pi\) | ||||
0.366937 | + | 0.930246i | \(0.380407\pi\) | |||||||
\(662\) | −58.1694 | −2.26082 | ||||||||
\(663\) | 14.6883 | 0.570446 | ||||||||
\(664\) | −140.299 | −5.44467 | ||||||||
\(665\) | −7.09950 | −0.275307 | ||||||||
\(666\) | −25.3279 | −0.981436 | ||||||||
\(667\) | −79.1965 | −3.06650 | ||||||||
\(668\) | 93.7414 | 3.62696 | ||||||||
\(669\) | −0.748847 | −0.0289521 | ||||||||
\(670\) | −75.5569 | −2.91902 | ||||||||
\(671\) | 14.2801 | 0.551279 | ||||||||
\(672\) | 24.6187 | 0.949687 | ||||||||
\(673\) | −19.9481 | −0.768942 | −0.384471 | − | 0.923137i | \(-0.625616\pi\) | ||||
−0.384471 | + | 0.923137i | \(0.625616\pi\) | |||||||
\(674\) | 31.6651 | 1.21969 | ||||||||
\(675\) | 0.522072 | 0.0200946 | ||||||||
\(676\) | −12.2532 | −0.471279 | ||||||||
\(677\) | 23.5173 | 0.903842 | 0.451921 | − | 0.892058i | \(-0.350739\pi\) | ||||
0.451921 | + | 0.892058i | \(0.350739\pi\) | |||||||
\(678\) | 2.77190 | 0.106454 | ||||||||
\(679\) | 1.77027 | 0.0679368 | ||||||||
\(680\) | 93.6969 | 3.59311 | ||||||||
\(681\) | −15.5627 | −0.596365 | ||||||||
\(682\) | −49.6534 | −1.90133 | ||||||||
\(683\) | 2.22738 | 0.0852284 | 0.0426142 | − | 0.999092i | \(-0.486431\pi\) | ||||
0.0426142 | + | 0.999092i | \(0.486431\pi\) | |||||||
\(684\) | 18.7750 | 0.717880 | ||||||||
\(685\) | 24.4235 | 0.933173 | ||||||||
\(686\) | −2.75611 | −0.105229 | ||||||||
\(687\) | −0.522483 | −0.0199340 | ||||||||
\(688\) | −16.0830 | −0.613158 | ||||||||
\(689\) | 36.0372 | 1.37291 | ||||||||
\(690\) | 55.6643 | 2.11911 | ||||||||
\(691\) | 36.2540 | 1.37917 | 0.689584 | − | 0.724206i | \(-0.257793\pi\) | ||||
0.689584 | + | 0.724206i | \(0.257793\pi\) | |||||||
\(692\) | −59.4827 | −2.26119 | ||||||||
\(693\) | −2.18663 | −0.0830634 | ||||||||
\(694\) | −34.4501 | −1.30771 | ||||||||
\(695\) | 9.26797 | 0.351554 | ||||||||
\(696\) | 82.2434 | 3.11743 | ||||||||
\(697\) | 11.2400 | 0.425745 | ||||||||
\(698\) | −56.8044 | −2.15008 | ||||||||
\(699\) | −10.4341 | −0.394652 | ||||||||
\(700\) | −2.92160 | −0.110426 | ||||||||
\(701\) | −25.6133 | −0.967401 | −0.483700 | − | 0.875234i | \(-0.660708\pi\) | ||||
−0.483700 | + | 0.875234i | \(0.660708\pi\) | |||||||
\(702\) | −9.06188 | −0.342019 | ||||||||
\(703\) | 30.8312 | 1.16282 | ||||||||
\(704\) | −77.8496 | −2.93407 | ||||||||
\(705\) | −9.86366 | −0.371487 | ||||||||
\(706\) | 77.1680 | 2.90426 | ||||||||
\(707\) | −11.6006 | −0.436286 | ||||||||
\(708\) | 49.2413 | 1.85060 | ||||||||
\(709\) | 29.3825 | 1.10348 | 0.551741 | − | 0.834015i | \(-0.313964\pi\) | ||||
0.551741 | + | 0.834015i | \(0.313964\pi\) | |||||||
\(710\) | 18.4457 | 0.692256 | ||||||||
\(711\) | 15.3503 | 0.575681 | ||||||||
\(712\) | −31.7058 | −1.18822 | ||||||||
\(713\) | 78.6352 | 2.94491 | ||||||||
\(714\) | 12.3125 | 0.460785 | ||||||||
\(715\) | −15.2137 | −0.568962 | ||||||||
\(716\) | −106.644 | −3.98548 | ||||||||
\(717\) | 10.9384 | 0.408503 | ||||||||
\(718\) | −42.0884 | −1.57073 | ||||||||
\(719\) | −31.9567 | −1.19179 | −0.595893 | − | 0.803064i | \(-0.703202\pi\) | ||||
−0.595893 | + | 0.803064i | \(0.703202\pi\) | |||||||
\(720\) | −34.1217 | −1.27164 | ||||||||
\(721\) | −11.1441 | −0.415028 | ||||||||
\(722\) | 21.3437 | 0.794332 | ||||||||
\(723\) | 23.2504 | 0.864690 | ||||||||
\(724\) | 73.7823 | 2.74210 | ||||||||
\(725\) | −4.33207 | −0.160889 | ||||||||
\(726\) | −17.1392 | −0.636097 | ||||||||
\(727\) | −10.1572 | −0.376708 | −0.188354 | − | 0.982101i | \(-0.560315\pi\) | ||||
−0.188354 | + | 0.982101i | \(0.560315\pi\) | |||||||
\(728\) | 32.5880 | 1.20779 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 71.9378 | 2.66254 | ||||||||
\(731\) | −4.45579 | −0.164803 | ||||||||
\(732\) | 36.5466 | 1.35080 | ||||||||
\(733\) | 10.9492 | 0.404419 | 0.202210 | − | 0.979342i | \(-0.435188\pi\) | ||||
0.202210 | + | 0.979342i | \(0.435188\pi\) | |||||||
\(734\) | −17.5169 | −0.646562 | ||||||||
\(735\) | 2.11611 | 0.0780539 | ||||||||
\(736\) | 234.967 | 8.66099 | ||||||||
\(737\) | 28.3279 | 1.04347 | ||||||||
\(738\) | −6.93446 | −0.255261 | ||||||||
\(739\) | −31.9795 | −1.17638 | −0.588192 | − | 0.808721i | \(-0.700160\pi\) | ||||
−0.588192 | + | 0.808721i | \(0.700160\pi\) | |||||||
\(740\) | −108.826 | −4.00051 | ||||||||
\(741\) | 11.0309 | 0.405230 | ||||||||
\(742\) | 30.2084 | 1.10898 | ||||||||
\(743\) | −38.1901 | −1.40106 | −0.700530 | − | 0.713623i | \(-0.747053\pi\) | ||||
−0.700530 | + | 0.713623i | \(0.747053\pi\) | |||||||
\(744\) | −81.6606 | −2.99382 | ||||||||
\(745\) | −45.9809 | −1.68461 | ||||||||
\(746\) | 26.0256 | 0.952863 | ||||||||
\(747\) | 14.1553 | 0.517916 | ||||||||
\(748\) | −54.6659 | −1.99878 | ||||||||
\(749\) | −8.51950 | −0.311296 | ||||||||
\(750\) | 32.2061 | 1.17600 | ||||||||
\(751\) | −2.92633 | −0.106783 | −0.0533916 | − | 0.998574i | \(-0.517003\pi\) | ||||
−0.0533916 | + | 0.998574i | \(0.517003\pi\) | |||||||
\(752\) | −75.1609 | −2.74084 | ||||||||
\(753\) | 16.0351 | 0.584351 | ||||||||
\(754\) | 75.1939 | 2.73840 | ||||||||
\(755\) | 24.4062 | 0.888231 | ||||||||
\(756\) | −5.59616 | −0.203531 | ||||||||
\(757\) | 18.6454 | 0.677678 | 0.338839 | − | 0.940844i | \(-0.389966\pi\) | ||||
0.338839 | + | 0.940844i | \(0.389966\pi\) | |||||||
\(758\) | −66.9420 | −2.43144 | ||||||||
\(759\) | −20.8698 | −0.757525 | ||||||||
\(760\) | 70.3663 | 2.55245 | ||||||||
\(761\) | 18.0874 | 0.655669 | 0.327835 | − | 0.944735i | \(-0.393681\pi\) | ||||
0.327835 | + | 0.944735i | \(0.393681\pi\) | |||||||
\(762\) | −55.7765 | −2.02057 | ||||||||
\(763\) | 12.1672 | 0.440482 | ||||||||
\(764\) | −5.59616 | −0.202462 | ||||||||
\(765\) | −9.45341 | −0.341789 | ||||||||
\(766\) | −79.6584 | −2.87817 | ||||||||
\(767\) | 28.9308 | 1.04463 | ||||||||
\(768\) | −63.5335 | −2.29257 | ||||||||
\(769\) | −28.1402 | −1.01476 | −0.507381 | − | 0.861722i | \(-0.669386\pi\) | ||||
−0.507381 | + | 0.861722i | \(0.669386\pi\) | |||||||
\(770\) | −12.7530 | −0.459586 | ||||||||
\(771\) | 13.3950 | 0.482410 | ||||||||
\(772\) | −62.9713 | −2.26639 | ||||||||
\(773\) | −23.5799 | −0.848109 | −0.424055 | − | 0.905637i | \(-0.639394\pi\) | ||||
−0.424055 | + | 0.905637i | \(0.639394\pi\) | |||||||
\(774\) | 2.74898 | 0.0988100 | ||||||||
\(775\) | 4.30137 | 0.154510 | ||||||||
\(776\) | −17.5459 | −0.629863 | ||||||||
\(777\) | −9.18971 | −0.329679 | ||||||||
\(778\) | −75.4373 | −2.70456 | ||||||||
\(779\) | 8.44122 | 0.302438 | ||||||||
\(780\) | −38.9359 | −1.39413 | ||||||||
\(781\) | −6.91570 | −0.247463 | ||||||||
\(782\) | 117.514 | 4.20228 | ||||||||
\(783\) | −8.29783 | −0.296540 | ||||||||
\(784\) | 16.1247 | 0.575883 | ||||||||
\(785\) | −22.8016 | −0.813823 | ||||||||
\(786\) | 18.1278 | 0.646596 | ||||||||
\(787\) | 25.1308 | 0.895818 | 0.447909 | − | 0.894079i | \(-0.352169\pi\) | ||||
0.447909 | + | 0.894079i | \(0.352169\pi\) | |||||||
\(788\) | 10.5559 | 0.376040 | ||||||||
\(789\) | −23.0822 | −0.821749 | ||||||||
\(790\) | 89.5266 | 3.18521 | ||||||||
\(791\) | 1.00573 | 0.0357596 | ||||||||
\(792\) | 21.6727 | 0.770106 | ||||||||
\(793\) | 21.4723 | 0.762502 | ||||||||
\(794\) | 77.9445 | 2.76615 | ||||||||
\(795\) | −23.1936 | −0.822593 | ||||||||
\(796\) | −24.8287 | −0.880032 | ||||||||
\(797\) | 50.6636 | 1.79460 | 0.897299 | − | 0.441423i | \(-0.145526\pi\) | ||||
0.897299 | + | 0.441423i | \(0.145526\pi\) | |||||||
\(798\) | 9.24669 | 0.327329 | ||||||||
\(799\) | −20.8233 | −0.736675 | ||||||||
\(800\) | 12.8527 | 0.454413 | ||||||||
\(801\) | 3.19891 | 0.113028 | ||||||||
\(802\) | 17.0470 | 0.601952 | ||||||||
\(803\) | −26.9710 | −0.951787 | ||||||||
\(804\) | 72.4984 | 2.55682 | ||||||||
\(805\) | 20.1967 | 0.711839 | ||||||||
\(806\) | −74.6611 | −2.62982 | ||||||||
\(807\) | −17.1973 | −0.605374 | ||||||||
\(808\) | 114.979 | 4.04494 | ||||||||
\(809\) | −31.8629 | −1.12024 | −0.560120 | − | 0.828411i | \(-0.689245\pi\) | ||||
−0.560120 | + | 0.828411i | \(0.689245\pi\) | |||||||
\(810\) | 5.83224 | 0.204924 | ||||||||
\(811\) | 22.1827 | 0.778940 | 0.389470 | − | 0.921039i | \(-0.372658\pi\) | ||||
0.389470 | + | 0.921039i | \(0.372658\pi\) | |||||||
\(812\) | 46.4360 | 1.62958 | ||||||||
\(813\) | −16.8486 | −0.590908 | ||||||||
\(814\) | 55.3828 | 1.94117 | ||||||||
\(815\) | 9.72251 | 0.340565 | ||||||||
\(816\) | −72.0348 | −2.52172 | ||||||||
\(817\) | −3.34629 | −0.117072 | ||||||||
\(818\) | −101.620 | −3.55305 | ||||||||
\(819\) | −3.28792 | −0.114889 | ||||||||
\(820\) | −29.7951 | −1.04049 | ||||||||
\(821\) | 3.32613 | 0.116083 | 0.0580414 | − | 0.998314i | \(-0.481514\pi\) | ||||
0.0580414 | + | 0.998314i | \(0.481514\pi\) | |||||||
\(822\) | −31.8102 | −1.10951 | ||||||||
\(823\) | −45.2666 | −1.57789 | −0.788947 | − | 0.614461i | \(-0.789373\pi\) | ||||
−0.788947 | + | 0.614461i | \(0.789373\pi\) | |||||||
\(824\) | 110.454 | 3.84785 | ||||||||
\(825\) | −1.14158 | −0.0397448 | ||||||||
\(826\) | 24.2514 | 0.843813 | ||||||||
\(827\) | 12.6262 | 0.439056 | 0.219528 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219528 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(828\) | −53.4111 | −1.85617 | ||||||||
\(829\) | −18.4456 | −0.640642 | −0.320321 | − | 0.947309i | \(-0.603791\pi\) | ||||
−0.320321 | + | 0.947309i | \(0.603791\pi\) | |||||||
\(830\) | 82.5572 | 2.86560 | ||||||||
\(831\) | −21.0004 | −0.728495 | ||||||||
\(832\) | −117.058 | −4.05826 | ||||||||
\(833\) | 4.46735 | 0.154784 | ||||||||
\(834\) | −12.0710 | −0.417984 | ||||||||
\(835\) | −35.4470 | −1.22669 | ||||||||
\(836\) | −41.0540 | −1.41988 | ||||||||
\(837\) | 8.23902 | 0.284782 | ||||||||
\(838\) | 12.3057 | 0.425095 | ||||||||
\(839\) | 32.2901 | 1.11478 | 0.557389 | − | 0.830251i | \(-0.311803\pi\) | ||||
0.557389 | + | 0.830251i | \(0.311803\pi\) | |||||||
\(840\) | −20.9737 | −0.723662 | ||||||||
\(841\) | 39.8539 | 1.37427 | ||||||||
\(842\) | −40.4707 | −1.39471 | ||||||||
\(843\) | −4.70943 | −0.162201 | ||||||||
\(844\) | −117.720 | −4.05208 | ||||||||
\(845\) | 4.63340 | 0.159394 | ||||||||
\(846\) | 12.8469 | 0.441684 | ||||||||
\(847\) | −6.21863 | −0.213675 | ||||||||
\(848\) | −176.735 | −6.06910 | ||||||||
\(849\) | −2.32384 | −0.0797538 | ||||||||
\(850\) | 6.42803 | 0.220480 | ||||||||
\(851\) | −87.7088 | −3.00662 | ||||||||
\(852\) | −17.6991 | −0.606360 | ||||||||
\(853\) | 40.5710 | 1.38912 | 0.694562 | − | 0.719433i | \(-0.255598\pi\) | ||||
0.694562 | + | 0.719433i | \(0.255598\pi\) | |||||||
\(854\) | 17.9992 | 0.615921 | ||||||||
\(855\) | −7.09950 | −0.242798 | ||||||||
\(856\) | 84.4405 | 2.88612 | ||||||||
\(857\) | −10.9171 | −0.372923 | −0.186461 | − | 0.982462i | \(-0.559702\pi\) | ||||
−0.186461 | + | 0.982462i | \(0.559702\pi\) | |||||||
\(858\) | 19.8150 | 0.676474 | ||||||||
\(859\) | 29.2631 | 0.998443 | 0.499221 | − | 0.866475i | \(-0.333619\pi\) | ||||
0.499221 | + | 0.866475i | \(0.333619\pi\) | |||||||
\(860\) | 11.8115 | 0.402767 | ||||||||
\(861\) | −2.51603 | −0.0857461 | ||||||||
\(862\) | −18.5134 | −0.630567 | ||||||||
\(863\) | −9.14629 | −0.311343 | −0.155672 | − | 0.987809i | \(-0.549754\pi\) | ||||
−0.155672 | + | 0.987809i | \(0.549754\pi\) | |||||||
\(864\) | 24.6187 | 0.837545 | ||||||||
\(865\) | 22.4925 | 0.764769 | ||||||||
\(866\) | −80.1816 | −2.72468 | ||||||||
\(867\) | −2.95721 | −0.100432 | ||||||||
\(868\) | −46.1069 | −1.56497 | ||||||||
\(869\) | −33.5655 | −1.13863 | ||||||||
\(870\) | −48.3949 | −1.64074 | ||||||||
\(871\) | 42.5951 | 1.44328 | ||||||||
\(872\) | −120.594 | −4.08384 | ||||||||
\(873\) | 1.77027 | 0.0599147 | ||||||||
\(874\) | 88.2527 | 2.98519 | ||||||||
\(875\) | 11.6853 | 0.395036 | ||||||||
\(876\) | −69.0259 | −2.33217 | ||||||||
\(877\) | 27.4597 | 0.927247 | 0.463624 | − | 0.886032i | \(-0.346549\pi\) | ||||
0.463624 | + | 0.886032i | \(0.346549\pi\) | |||||||
\(878\) | −62.3217 | −2.10326 | ||||||||
\(879\) | −15.4114 | −0.519814 | ||||||||
\(880\) | 74.6117 | 2.51516 | ||||||||
\(881\) | −8.62776 | −0.290677 | −0.145338 | − | 0.989382i | \(-0.546427\pi\) | ||||
−0.145338 | + | 0.989382i | \(0.546427\pi\) | |||||||
\(882\) | −2.75611 | −0.0928032 | ||||||||
\(883\) | −30.6920 | −1.03287 | −0.516434 | − | 0.856327i | \(-0.672741\pi\) | ||||
−0.516434 | + | 0.856327i | \(0.672741\pi\) | |||||||
\(884\) | −82.1981 | −2.76462 | ||||||||
\(885\) | −18.6199 | −0.625901 | ||||||||
\(886\) | −56.2409 | −1.88945 | ||||||||
\(887\) | 12.4362 | 0.417566 | 0.208783 | − | 0.977962i | \(-0.433050\pi\) | ||||
0.208783 | + | 0.977962i | \(0.433050\pi\) | |||||||
\(888\) | 91.0832 | 3.05655 | ||||||||
\(889\) | −20.2374 | −0.678739 | ||||||||
\(890\) | 18.6568 | 0.625378 | ||||||||
\(891\) | −2.18663 | −0.0732550 | ||||||||
\(892\) | 4.19067 | 0.140314 | ||||||||
\(893\) | −15.6383 | −0.523315 | ||||||||
\(894\) | 59.8875 | 2.00294 | ||||||||
\(895\) | 40.3261 | 1.34795 | ||||||||
\(896\) | −48.8871 | −1.63320 | ||||||||
\(897\) | −31.3807 | −1.04777 | ||||||||
\(898\) | −74.8159 | −2.49664 | ||||||||
\(899\) | −68.3660 | −2.28013 | ||||||||
\(900\) | −2.92160 | −0.0973867 | ||||||||
\(901\) | −48.9643 | −1.63124 | ||||||||
\(902\) | 15.1631 | 0.504877 | ||||||||
\(903\) | 0.997412 | 0.0331918 | ||||||||
\(904\) | −9.96822 | −0.331538 | ||||||||
\(905\) | −27.8998 | −0.927419 | ||||||||
\(906\) | −31.7876 | −1.05607 | ||||||||
\(907\) | −30.8690 | −1.02499 | −0.512494 | − | 0.858691i | \(-0.671278\pi\) | ||||
−0.512494 | + | 0.858691i | \(0.671278\pi\) | |||||||
\(908\) | 87.0916 | 2.89024 | ||||||||
\(909\) | −11.6006 | −0.384768 | ||||||||
\(910\) | −19.1760 | −0.635677 | ||||||||
\(911\) | −4.15241 | −0.137575 | −0.0687877 | − | 0.997631i | \(-0.521913\pi\) | ||||
−0.0687877 | + | 0.997631i | \(0.521913\pi\) | |||||||
\(912\) | −54.0980 | −1.79137 | ||||||||
\(913\) | −30.9525 | −1.02438 | ||||||||
\(914\) | 40.8969 | 1.35275 | ||||||||
\(915\) | −13.8196 | −0.456861 | ||||||||
\(916\) | 2.92390 | 0.0966084 | ||||||||
\(917\) | 6.57730 | 0.217201 | ||||||||
\(918\) | 12.3125 | 0.406374 | ||||||||
\(919\) | −48.2362 | −1.59116 | −0.795582 | − | 0.605846i | \(-0.792835\pi\) | ||||
−0.795582 | + | 0.605846i | \(0.792835\pi\) | |||||||
\(920\) | −200.178 | −6.59968 | ||||||||
\(921\) | 8.63781 | 0.284625 | ||||||||
\(922\) | −76.1981 | −2.50945 | ||||||||
\(923\) | −10.3988 | −0.342279 | ||||||||
\(924\) | 12.2368 | 0.402560 | ||||||||
\(925\) | −4.79769 | −0.157747 | ||||||||
\(926\) | −61.7387 | −2.02886 | ||||||||
\(927\) | −11.1441 | −0.366020 | ||||||||
\(928\) | −204.282 | −6.70587 | ||||||||
\(929\) | −36.6577 | −1.20270 | −0.601350 | − | 0.798986i | \(-0.705370\pi\) | ||||
−0.601350 | + | 0.798986i | \(0.705370\pi\) | |||||||
\(930\) | 48.0520 | 1.57569 | ||||||||
\(931\) | 3.35498 | 0.109955 | ||||||||
\(932\) | 58.3907 | 1.91265 | ||||||||
\(933\) | −16.3592 | −0.535576 | ||||||||
\(934\) | 82.6971 | 2.70593 | ||||||||
\(935\) | 20.6712 | 0.676019 | ||||||||
\(936\) | 32.5880 | 1.06517 | ||||||||
\(937\) | 16.6817 | 0.544967 | 0.272483 | − | 0.962160i | \(-0.412155\pi\) | ||||
0.272483 | + | 0.962160i | \(0.412155\pi\) | |||||||
\(938\) | 35.7055 | 1.16583 | ||||||||
\(939\) | 13.9498 | 0.455235 | ||||||||
\(940\) | 55.1987 | 1.80038 | ||||||||
\(941\) | 32.4898 | 1.05914 | 0.529569 | − | 0.848267i | \(-0.322354\pi\) | ||||
0.529569 | + | 0.848267i | \(0.322354\pi\) | |||||||
\(942\) | 29.6977 | 0.967604 | ||||||||
\(943\) | −24.0136 | −0.781990 | ||||||||
\(944\) | −141.883 | −4.61791 | ||||||||
\(945\) | 2.11611 | 0.0688371 | ||||||||
\(946\) | −6.01102 | −0.195435 | ||||||||
\(947\) | −14.4960 | −0.471056 | −0.235528 | − | 0.971868i | \(-0.575682\pi\) | ||||
−0.235528 | + | 0.971868i | \(0.575682\pi\) | |||||||
\(948\) | −85.9027 | −2.78999 | ||||||||
\(949\) | −40.5548 | −1.31647 | ||||||||
\(950\) | 4.82744 | 0.156623 | ||||||||
\(951\) | −3.09494 | −0.100360 | ||||||||
\(952\) | −44.2778 | −1.43505 | ||||||||
\(953\) | 8.71306 | 0.282244 | 0.141122 | − | 0.989992i | \(-0.454929\pi\) | ||||
0.141122 | + | 0.989992i | \(0.454929\pi\) | |||||||
\(954\) | 30.2084 | 0.978032 | ||||||||
\(955\) | 2.11611 | 0.0684758 | ||||||||
\(956\) | −61.2133 | −1.97978 | ||||||||
\(957\) | 18.1443 | 0.586522 | ||||||||
\(958\) | −76.4809 | −2.47099 | ||||||||
\(959\) | −11.5417 | −0.372700 | ||||||||
\(960\) | 75.3388 | 2.43155 | ||||||||
\(961\) | 36.8815 | 1.18973 | ||||||||
\(962\) | 83.2761 | 2.68493 | ||||||||
\(963\) | −8.51950 | −0.274537 | ||||||||
\(964\) | −130.113 | −4.19065 | ||||||||
\(965\) | 23.8117 | 0.766526 | ||||||||
\(966\) | −26.3050 | −0.846350 | ||||||||
\(967\) | 40.9388 | 1.31650 | 0.658252 | − | 0.752798i | \(-0.271296\pi\) | ||||
0.658252 | + | 0.752798i | \(0.271296\pi\) | |||||||
\(968\) | 61.6355 | 1.98104 | ||||||||
\(969\) | −14.9878 | −0.481479 | ||||||||
\(970\) | 10.3247 | 0.331505 | ||||||||
\(971\) | −17.1882 | −0.551595 | −0.275798 | − | 0.961216i | \(-0.588942\pi\) | ||||
−0.275798 | + | 0.961216i | \(0.588942\pi\) | |||||||
\(972\) | −5.59616 | −0.179497 | ||||||||
\(973\) | −4.37972 | −0.140407 | ||||||||
\(974\) | −62.5880 | −2.00545 | ||||||||
\(975\) | −1.71653 | −0.0549730 | ||||||||
\(976\) | −105.305 | −3.37073 | ||||||||
\(977\) | 45.0128 | 1.44009 | 0.720043 | − | 0.693929i | \(-0.244122\pi\) | ||||
0.720043 | + | 0.693929i | \(0.244122\pi\) | |||||||
\(978\) | −12.6630 | −0.404918 | ||||||||
\(979\) | −6.99484 | −0.223556 | ||||||||
\(980\) | −11.8421 | −0.378282 | ||||||||
\(981\) | 12.1672 | 0.388469 | ||||||||
\(982\) | −58.3616 | −1.86239 | ||||||||
\(983\) | 2.46244 | 0.0785397 | 0.0392699 | − | 0.999229i | \(-0.487497\pi\) | ||||
0.0392699 | + | 0.999229i | \(0.487497\pi\) | |||||||
\(984\) | 24.9375 | 0.794977 | ||||||||
\(985\) | −3.99158 | −0.127182 | ||||||||
\(986\) | −102.167 | −3.25367 | ||||||||
\(987\) | 4.66122 | 0.148368 | ||||||||
\(988\) | −61.7307 | −1.96391 | ||||||||
\(989\) | 9.51954 | 0.302704 | ||||||||
\(990\) | −12.7530 | −0.405317 | ||||||||
\(991\) | −17.5912 | −0.558803 | −0.279401 | − | 0.960174i | \(-0.590136\pi\) | ||||
−0.279401 | + | 0.960174i | \(0.590136\pi\) | |||||||
\(992\) | 202.834 | 6.43998 | ||||||||
\(993\) | −21.1056 | −0.669766 | ||||||||
\(994\) | −8.71681 | −0.276480 | ||||||||
\(995\) | 9.38865 | 0.297640 | ||||||||
\(996\) | −79.2154 | −2.51004 | ||||||||
\(997\) | 54.0681 | 1.71235 | 0.856177 | − | 0.516683i | \(-0.172833\pi\) | ||||
0.856177 | + | 0.516683i | \(0.172833\pi\) | |||||||
\(998\) | −63.2978 | −2.00366 | ||||||||
\(999\) | −9.18971 | −0.290750 |
(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 | 4011.2.a.l.1.2 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4011.2.a.l.1.2 | ✓ | 28 | 1.1 | even | 1 | trivial |