Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, 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("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2077082653\) |
Analytic rank: | \(1\) |
Dimension: | \(74\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.02657 | −1.43300 | −0.716501 | − | 0.697586i | \(-0.754258\pi\) | ||||
−0.716501 | + | 0.697586i | \(0.754258\pi\) | |||||||
\(3\) | 2.55915 | 1.47753 | 0.738763 | − | 0.673965i | \(-0.235410\pi\) | ||||
0.738763 | + | 0.673965i | \(0.235410\pi\) | |||||||
\(4\) | 2.10699 | 1.05350 | ||||||||
\(5\) | −3.25953 | −1.45771 | −0.728853 | − | 0.684670i | \(-0.759946\pi\) | ||||
−0.728853 | + | 0.684670i | \(0.759946\pi\) | |||||||
\(6\) | −5.18630 | −2.11730 | ||||||||
\(7\) | 3.04044 | 1.14918 | 0.574589 | − | 0.818442i | \(-0.305162\pi\) | ||||
0.574589 | + | 0.818442i | \(0.305162\pi\) | |||||||
\(8\) | −0.216828 | −0.0766604 | ||||||||
\(9\) | 3.54925 | 1.18308 | ||||||||
\(10\) | 6.60567 | 2.08890 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 5.39211 | 1.55657 | ||||||||
\(13\) | 2.88993 | 0.801521 | 0.400761 | − | 0.916183i | \(-0.368746\pi\) | ||||
0.400761 | + | 0.916183i | \(0.368746\pi\) | |||||||
\(14\) | −6.16167 | −1.64678 | ||||||||
\(15\) | −8.34163 | −2.15380 | ||||||||
\(16\) | −3.77457 | −0.943642 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −7.19282 | −1.69536 | ||||||||
\(19\) | 8.33818 | 1.91291 | 0.956455 | − | 0.291879i | \(-0.0942804\pi\) | ||||
0.956455 | + | 0.291879i | \(0.0942804\pi\) | |||||||
\(20\) | −6.86781 | −1.53569 | ||||||||
\(21\) | 7.78094 | 1.69794 | ||||||||
\(22\) | 2.02657 | 0.432067 | ||||||||
\(23\) | −8.73652 | −1.82169 | −0.910846 | − | 0.412747i | \(-0.864569\pi\) | ||||
−0.910846 | + | 0.412747i | \(0.864569\pi\) | |||||||
\(24\) | −0.554897 | −0.113268 | ||||||||
\(25\) | 5.62454 | 1.12491 | ||||||||
\(26\) | −5.85664 | −1.14858 | ||||||||
\(27\) | 1.40562 | 0.270512 | ||||||||
\(28\) | 6.40618 | 1.21065 | ||||||||
\(29\) | −3.91827 | −0.727604 | −0.363802 | − | 0.931476i | \(-0.618522\pi\) | ||||
−0.363802 | + | 0.931476i | \(0.618522\pi\) | |||||||
\(30\) | 16.9049 | 3.08640 | ||||||||
\(31\) | 3.01615 | 0.541716 | 0.270858 | − | 0.962619i | \(-0.412693\pi\) | ||||
0.270858 | + | 0.962619i | \(0.412693\pi\) | |||||||
\(32\) | 8.08309 | 1.42890 | ||||||||
\(33\) | −2.55915 | −0.445491 | ||||||||
\(34\) | 2.02657 | 0.347554 | ||||||||
\(35\) | −9.91041 | −1.67516 | ||||||||
\(36\) | 7.47825 | 1.24638 | ||||||||
\(37\) | −6.85881 | −1.12758 | −0.563791 | − | 0.825917i | \(-0.690658\pi\) | ||||
−0.563791 | + | 0.825917i | \(0.690658\pi\) | |||||||
\(38\) | −16.8979 | −2.74121 | ||||||||
\(39\) | 7.39576 | 1.18427 | ||||||||
\(40\) | 0.706759 | 0.111748 | ||||||||
\(41\) | −0.0237582 | −0.00371040 | −0.00185520 | − | 0.999998i | \(-0.500591\pi\) | ||||
−0.00185520 | + | 0.999998i | \(0.500591\pi\) | |||||||
\(42\) | −15.7686 | −2.43315 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | −2.10699 | −0.317641 | ||||||||
\(45\) | −11.5689 | −1.72459 | ||||||||
\(46\) | 17.7052 | 2.61049 | ||||||||
\(47\) | −9.03774 | −1.31829 | −0.659145 | − | 0.752016i | \(-0.729082\pi\) | ||||
−0.659145 | + | 0.752016i | \(0.729082\pi\) | |||||||
\(48\) | −9.65969 | −1.39426 | ||||||||
\(49\) | 2.24427 | 0.320610 | ||||||||
\(50\) | −11.3985 | −1.61200 | ||||||||
\(51\) | −2.55915 | −0.358353 | ||||||||
\(52\) | 6.08905 | 0.844400 | ||||||||
\(53\) | −8.62071 | −1.18415 | −0.592073 | − | 0.805885i | \(-0.701690\pi\) | ||||
−0.592073 | + | 0.805885i | \(0.701690\pi\) | |||||||
\(54\) | −2.84860 | −0.387645 | ||||||||
\(55\) | 3.25953 | 0.439515 | ||||||||
\(56\) | −0.659254 | −0.0880965 | ||||||||
\(57\) | 21.3387 | 2.82638 | ||||||||
\(58\) | 7.94065 | 1.04266 | ||||||||
\(59\) | −0.122360 | −0.0159300 | −0.00796499 | − | 0.999968i | \(-0.502535\pi\) | ||||
−0.00796499 | + | 0.999968i | \(0.502535\pi\) | |||||||
\(60\) | −17.5758 | −2.26902 | ||||||||
\(61\) | −10.5942 | −1.35644 | −0.678222 | − | 0.734857i | \(-0.737249\pi\) | ||||
−0.678222 | + | 0.734857i | \(0.737249\pi\) | |||||||
\(62\) | −6.11244 | −0.776281 | ||||||||
\(63\) | 10.7913 | 1.35957 | ||||||||
\(64\) | −8.83182 | −1.10398 | ||||||||
\(65\) | −9.41980 | −1.16838 | ||||||||
\(66\) | 5.18630 | 0.638390 | ||||||||
\(67\) | 7.28490 | 0.889992 | 0.444996 | − | 0.895532i | \(-0.353205\pi\) | ||||
0.444996 | + | 0.895532i | \(0.353205\pi\) | |||||||
\(68\) | −2.10699 | −0.255510 | ||||||||
\(69\) | −22.3581 | −2.69160 | ||||||||
\(70\) | 20.0841 | 2.40051 | ||||||||
\(71\) | −12.8719 | −1.52761 | −0.763807 | − | 0.645444i | \(-0.776672\pi\) | ||||
−0.763807 | + | 0.645444i | \(0.776672\pi\) | |||||||
\(72\) | −0.769579 | −0.0906958 | ||||||||
\(73\) | 7.70920 | 0.902293 | 0.451147 | − | 0.892450i | \(-0.351015\pi\) | ||||
0.451147 | + | 0.892450i | \(0.351015\pi\) | |||||||
\(74\) | 13.8999 | 1.61583 | ||||||||
\(75\) | 14.3941 | 1.66208 | ||||||||
\(76\) | 17.5685 | 2.01524 | ||||||||
\(77\) | −3.04044 | −0.346490 | ||||||||
\(78\) | −14.9880 | −1.69706 | ||||||||
\(79\) | 4.18057 | 0.470351 | 0.235175 | − | 0.971953i | \(-0.424434\pi\) | ||||
0.235175 | + | 0.971953i | \(0.424434\pi\) | |||||||
\(80\) | 12.3033 | 1.37555 | ||||||||
\(81\) | −7.05056 | −0.783395 | ||||||||
\(82\) | 0.0481476 | 0.00531702 | ||||||||
\(83\) | 16.9950 | 1.86544 | 0.932722 | − | 0.360597i | \(-0.117427\pi\) | ||||
0.932722 | + | 0.360597i | \(0.117427\pi\) | |||||||
\(84\) | 16.3944 | 1.78877 | ||||||||
\(85\) | 3.25953 | 0.353546 | ||||||||
\(86\) | 2.02657 | 0.218531 | ||||||||
\(87\) | −10.0274 | −1.07505 | ||||||||
\(88\) | 0.216828 | 0.0231140 | ||||||||
\(89\) | −5.32663 | −0.564622 | −0.282311 | − | 0.959323i | \(-0.591101\pi\) | ||||
−0.282311 | + | 0.959323i | \(0.591101\pi\) | |||||||
\(90\) | 23.4452 | 2.47134 | ||||||||
\(91\) | 8.78665 | 0.921091 | ||||||||
\(92\) | −18.4078 | −1.91914 | ||||||||
\(93\) | 7.71878 | 0.800400 | ||||||||
\(94\) | 18.3156 | 1.88911 | ||||||||
\(95\) | −27.1786 | −2.78846 | ||||||||
\(96\) | 20.6858 | 2.11124 | ||||||||
\(97\) | −11.9933 | −1.21773 | −0.608866 | − | 0.793273i | \(-0.708375\pi\) | ||||
−0.608866 | + | 0.793273i | \(0.708375\pi\) | |||||||
\(98\) | −4.54818 | −0.459435 | ||||||||
\(99\) | −3.54925 | −0.356713 | ||||||||
\(100\) | 11.8509 | 1.18509 | ||||||||
\(101\) | −5.03944 | −0.501443 | −0.250722 | − | 0.968059i | \(-0.580668\pi\) | ||||
−0.250722 | + | 0.968059i | \(0.580668\pi\) | |||||||
\(102\) | 5.18630 | 0.513521 | ||||||||
\(103\) | −4.65680 | −0.458848 | −0.229424 | − | 0.973327i | \(-0.573684\pi\) | ||||
−0.229424 | + | 0.973327i | \(0.573684\pi\) | |||||||
\(104\) | −0.626618 | −0.0614450 | ||||||||
\(105\) | −25.3622 | −2.47510 | ||||||||
\(106\) | 17.4705 | 1.69688 | ||||||||
\(107\) | −1.54468 | −0.149330 | −0.0746650 | − | 0.997209i | \(-0.523789\pi\) | ||||
−0.0746650 | + | 0.997209i | \(0.523789\pi\) | |||||||
\(108\) | 2.96164 | 0.284984 | ||||||||
\(109\) | −10.0344 | −0.961122 | −0.480561 | − | 0.876961i | \(-0.659567\pi\) | ||||
−0.480561 | + | 0.876961i | \(0.659567\pi\) | |||||||
\(110\) | −6.60567 | −0.629826 | ||||||||
\(111\) | −17.5527 | −1.66603 | ||||||||
\(112\) | −11.4763 | −1.08441 | ||||||||
\(113\) | −5.65748 | −0.532211 | −0.266106 | − | 0.963944i | \(-0.585737\pi\) | ||||
−0.266106 | + | 0.963944i | \(0.585737\pi\) | |||||||
\(114\) | −43.2444 | −4.05020 | ||||||||
\(115\) | 28.4770 | 2.65549 | ||||||||
\(116\) | −8.25577 | −0.766529 | ||||||||
\(117\) | 10.2571 | 0.948268 | ||||||||
\(118\) | 0.247972 | 0.0228277 | ||||||||
\(119\) | −3.04044 | −0.278717 | ||||||||
\(120\) | 1.80870 | 0.165111 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 21.4698 | 1.94379 | ||||||||
\(123\) | −0.0608008 | −0.00548222 | ||||||||
\(124\) | 6.35500 | 0.570696 | ||||||||
\(125\) | −2.03572 | −0.182080 | ||||||||
\(126\) | −21.8693 | −1.94827 | ||||||||
\(127\) | −15.5405 | −1.37900 | −0.689498 | − | 0.724288i | \(-0.742169\pi\) | ||||
−0.689498 | + | 0.724288i | \(0.742169\pi\) | |||||||
\(128\) | 1.73215 | 0.153101 | ||||||||
\(129\) | −2.55915 | −0.225321 | ||||||||
\(130\) | 19.0899 | 1.67430 | ||||||||
\(131\) | 19.7013 | 1.72131 | 0.860656 | − | 0.509187i | \(-0.170054\pi\) | ||||
0.860656 | + | 0.509187i | \(0.170054\pi\) | |||||||
\(132\) | −5.39211 | −0.469323 | ||||||||
\(133\) | 25.3517 | 2.19827 | ||||||||
\(134\) | −14.7634 | −1.27536 | ||||||||
\(135\) | −4.58167 | −0.394328 | ||||||||
\(136\) | 0.216828 | 0.0185929 | ||||||||
\(137\) | 19.4702 | 1.66345 | 0.831726 | − | 0.555187i | \(-0.187353\pi\) | ||||
0.831726 | + | 0.555187i | \(0.187353\pi\) | |||||||
\(138\) | 45.3103 | 3.85707 | ||||||||
\(139\) | −20.2447 | −1.71714 | −0.858568 | − | 0.512700i | \(-0.828645\pi\) | ||||
−0.858568 | + | 0.512700i | \(0.828645\pi\) | |||||||
\(140\) | −20.8812 | −1.76478 | ||||||||
\(141\) | −23.1289 | −1.94781 | ||||||||
\(142\) | 26.0859 | 2.18908 | ||||||||
\(143\) | −2.88993 | −0.241668 | ||||||||
\(144\) | −13.3969 | −1.11641 | ||||||||
\(145\) | 12.7717 | 1.06063 | ||||||||
\(146\) | −15.6232 | −1.29299 | ||||||||
\(147\) | 5.74343 | 0.473710 | ||||||||
\(148\) | −14.4515 | −1.18790 | ||||||||
\(149\) | −10.4035 | −0.852289 | −0.426144 | − | 0.904655i | \(-0.640128\pi\) | ||||
−0.426144 | + | 0.904655i | \(0.640128\pi\) | |||||||
\(150\) | −29.1706 | −2.38177 | ||||||||
\(151\) | −5.40587 | −0.439923 | −0.219962 | − | 0.975509i | \(-0.570593\pi\) | ||||
−0.219962 | + | 0.975509i | \(0.570593\pi\) | |||||||
\(152\) | −1.80796 | −0.146645 | ||||||||
\(153\) | −3.54925 | −0.286940 | ||||||||
\(154\) | 6.16167 | 0.496521 | ||||||||
\(155\) | −9.83123 | −0.789664 | ||||||||
\(156\) | 15.5828 | 1.24762 | ||||||||
\(157\) | −8.06075 | −0.643318 | −0.321659 | − | 0.946856i | \(-0.604240\pi\) | ||||
−0.321659 | + | 0.946856i | \(0.604240\pi\) | |||||||
\(158\) | −8.47222 | −0.674014 | ||||||||
\(159\) | −22.0617 | −1.74961 | ||||||||
\(160\) | −26.3471 | −2.08292 | ||||||||
\(161\) | −26.5629 | −2.09345 | ||||||||
\(162\) | 14.2885 | 1.12261 | ||||||||
\(163\) | −0.640726 | −0.0501855 | −0.0250927 | − | 0.999685i | \(-0.507988\pi\) | ||||
−0.0250927 | + | 0.999685i | \(0.507988\pi\) | |||||||
\(164\) | −0.0500583 | −0.00390890 | ||||||||
\(165\) | 8.34163 | 0.649395 | ||||||||
\(166\) | −34.4416 | −2.67319 | ||||||||
\(167\) | 12.5146 | 0.968407 | 0.484203 | − | 0.874955i | \(-0.339109\pi\) | ||||
0.484203 | + | 0.874955i | \(0.339109\pi\) | |||||||
\(168\) | −1.68713 | −0.130165 | ||||||||
\(169\) | −4.64833 | −0.357564 | ||||||||
\(170\) | −6.60567 | −0.506632 | ||||||||
\(171\) | 29.5943 | 2.26314 | ||||||||
\(172\) | −2.10699 | −0.160657 | ||||||||
\(173\) | 7.81461 | 0.594134 | 0.297067 | − | 0.954857i | \(-0.403992\pi\) | ||||
0.297067 | + | 0.954857i | \(0.403992\pi\) | |||||||
\(174\) | 20.3213 | 1.54056 | ||||||||
\(175\) | 17.1011 | 1.29272 | ||||||||
\(176\) | 3.77457 | 0.284519 | ||||||||
\(177\) | −0.313139 | −0.0235370 | ||||||||
\(178\) | 10.7948 | 0.809104 | ||||||||
\(179\) | 9.75957 | 0.729465 | 0.364732 | − | 0.931112i | \(-0.381160\pi\) | ||||
0.364732 | + | 0.931112i | \(0.381160\pi\) | |||||||
\(180\) | −24.3756 | −1.81685 | ||||||||
\(181\) | 15.9816 | 1.18790 | 0.593950 | − | 0.804502i | \(-0.297568\pi\) | ||||
0.593950 | + | 0.804502i | \(0.297568\pi\) | |||||||
\(182\) | −17.8068 | −1.31993 | ||||||||
\(183\) | −27.1121 | −2.00418 | ||||||||
\(184\) | 1.89433 | 0.139652 | ||||||||
\(185\) | 22.3565 | 1.64368 | ||||||||
\(186\) | −15.6427 | −1.14698 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | −19.0425 | −1.38881 | ||||||||
\(189\) | 4.27371 | 0.310867 | ||||||||
\(190\) | 55.0793 | 3.99587 | ||||||||
\(191\) | 9.77118 | 0.707018 | 0.353509 | − | 0.935431i | \(-0.384988\pi\) | ||||
0.353509 | + | 0.935431i | \(0.384988\pi\) | |||||||
\(192\) | −22.6020 | −1.63116 | ||||||||
\(193\) | −10.5506 | −0.759450 | −0.379725 | − | 0.925099i | \(-0.623981\pi\) | ||||
−0.379725 | + | 0.925099i | \(0.623981\pi\) | |||||||
\(194\) | 24.3052 | 1.74501 | ||||||||
\(195\) | −24.1067 | −1.72632 | ||||||||
\(196\) | 4.72866 | 0.337762 | ||||||||
\(197\) | −7.72618 | −0.550467 | −0.275234 | − | 0.961377i | \(-0.588755\pi\) | ||||
−0.275234 | + | 0.961377i | \(0.588755\pi\) | |||||||
\(198\) | 7.19282 | 0.511171 | ||||||||
\(199\) | −9.46948 | −0.671273 | −0.335637 | − | 0.941992i | \(-0.608951\pi\) | ||||
−0.335637 | + | 0.941992i | \(0.608951\pi\) | |||||||
\(200\) | −1.21956 | −0.0862360 | ||||||||
\(201\) | 18.6432 | 1.31499 | ||||||||
\(202\) | 10.2128 | 0.718570 | ||||||||
\(203\) | −11.9133 | −0.836147 | ||||||||
\(204\) | −5.39211 | −0.377523 | ||||||||
\(205\) | 0.0774405 | 0.00540868 | ||||||||
\(206\) | 9.43734 | 0.657531 | ||||||||
\(207\) | −31.0081 | −2.15521 | ||||||||
\(208\) | −10.9082 | −0.756349 | ||||||||
\(209\) | −8.33818 | −0.576764 | ||||||||
\(210\) | 51.3984 | 3.54682 | ||||||||
\(211\) | 12.9206 | 0.889494 | 0.444747 | − | 0.895656i | \(-0.353294\pi\) | ||||
0.444747 | + | 0.895656i | \(0.353294\pi\) | |||||||
\(212\) | −18.1638 | −1.24749 | ||||||||
\(213\) | −32.9412 | −2.25709 | ||||||||
\(214\) | 3.13041 | 0.213990 | ||||||||
\(215\) | 3.25953 | 0.222298 | ||||||||
\(216\) | −0.304779 | −0.0207376 | ||||||||
\(217\) | 9.17042 | 0.622529 | ||||||||
\(218\) | 20.3354 | 1.37729 | ||||||||
\(219\) | 19.7290 | 1.33316 | ||||||||
\(220\) | 6.86781 | 0.463028 | ||||||||
\(221\) | −2.88993 | −0.194397 | ||||||||
\(222\) | 35.5719 | 2.38743 | ||||||||
\(223\) | 8.74127 | 0.585359 | 0.292679 | − | 0.956211i | \(-0.405453\pi\) | ||||
0.292679 | + | 0.956211i | \(0.405453\pi\) | |||||||
\(224\) | 24.5761 | 1.64206 | ||||||||
\(225\) | 19.9629 | 1.33086 | ||||||||
\(226\) | 11.4653 | 0.762660 | ||||||||
\(227\) | 14.6266 | 0.970799 | 0.485399 | − | 0.874293i | \(-0.338674\pi\) | ||||
0.485399 | + | 0.874293i | \(0.338674\pi\) | |||||||
\(228\) | 44.9604 | 2.97758 | ||||||||
\(229\) | −13.0833 | −0.864568 | −0.432284 | − | 0.901738i | \(-0.642292\pi\) | ||||
−0.432284 | + | 0.901738i | \(0.642292\pi\) | |||||||
\(230\) | −57.7106 | −3.80533 | ||||||||
\(231\) | −7.78094 | −0.511948 | ||||||||
\(232\) | 0.849592 | 0.0557785 | ||||||||
\(233\) | 28.7731 | 1.88499 | 0.942494 | − | 0.334223i | \(-0.108474\pi\) | ||||
0.942494 | + | 0.334223i | \(0.108474\pi\) | |||||||
\(234\) | −20.7867 | −1.35887 | ||||||||
\(235\) | 29.4588 | 1.92168 | ||||||||
\(236\) | −0.257813 | −0.0167822 | ||||||||
\(237\) | 10.6987 | 0.694956 | ||||||||
\(238\) | 6.16167 | 0.399402 | ||||||||
\(239\) | 19.9574 | 1.29094 | 0.645470 | − | 0.763786i | \(-0.276662\pi\) | ||||
0.645470 | + | 0.763786i | \(0.276662\pi\) | |||||||
\(240\) | 31.4861 | 2.03242 | ||||||||
\(241\) | 10.9302 | 0.704075 | 0.352038 | − | 0.935986i | \(-0.385489\pi\) | ||||
0.352038 | + | 0.935986i | \(0.385489\pi\) | |||||||
\(242\) | −2.02657 | −0.130273 | ||||||||
\(243\) | −22.2603 | −1.42800 | ||||||||
\(244\) | −22.3218 | −1.42901 | ||||||||
\(245\) | −7.31527 | −0.467355 | ||||||||
\(246\) | 0.123217 | 0.00785604 | ||||||||
\(247\) | 24.0967 | 1.53324 | ||||||||
\(248\) | −0.653987 | −0.0415282 | ||||||||
\(249\) | 43.4928 | 2.75624 | ||||||||
\(250\) | 4.12552 | 0.260921 | ||||||||
\(251\) | −17.9686 | −1.13417 | −0.567084 | − | 0.823660i | \(-0.691929\pi\) | ||||
−0.567084 | + | 0.823660i | \(0.691929\pi\) | |||||||
\(252\) | 22.7372 | 1.43231 | ||||||||
\(253\) | 8.73652 | 0.549261 | ||||||||
\(254\) | 31.4939 | 1.97610 | ||||||||
\(255\) | 8.34163 | 0.522373 | ||||||||
\(256\) | 14.1533 | 0.884583 | ||||||||
\(257\) | −24.5411 | −1.53083 | −0.765416 | − | 0.643535i | \(-0.777467\pi\) | ||||
−0.765416 | + | 0.643535i | \(0.777467\pi\) | |||||||
\(258\) | 5.18630 | 0.322885 | ||||||||
\(259\) | −20.8538 | −1.29579 | ||||||||
\(260\) | −19.8475 | −1.23089 | ||||||||
\(261\) | −13.9069 | −0.860818 | ||||||||
\(262\) | −39.9261 | −2.46664 | ||||||||
\(263\) | −13.9072 | −0.857554 | −0.428777 | − | 0.903410i | \(-0.641055\pi\) | ||||
−0.428777 | + | 0.903410i | \(0.641055\pi\) | |||||||
\(264\) | 0.554897 | 0.0341515 | ||||||||
\(265\) | 28.0995 | 1.72614 | ||||||||
\(266\) | −51.3771 | −3.15013 | ||||||||
\(267\) | −13.6317 | −0.834243 | ||||||||
\(268\) | 15.3492 | 0.937604 | ||||||||
\(269\) | −14.7066 | −0.896674 | −0.448337 | − | 0.893865i | \(-0.647984\pi\) | ||||
−0.448337 | + | 0.893865i | \(0.647984\pi\) | |||||||
\(270\) | 9.28509 | 0.565073 | ||||||||
\(271\) | 19.4408 | 1.18095 | 0.590473 | − | 0.807058i | \(-0.298941\pi\) | ||||
0.590473 | + | 0.807058i | \(0.298941\pi\) | |||||||
\(272\) | 3.77457 | 0.228867 | ||||||||
\(273\) | 22.4864 | 1.36094 | ||||||||
\(274\) | −39.4578 | −2.38373 | ||||||||
\(275\) | −5.62454 | −0.339173 | ||||||||
\(276\) | −47.1083 | −2.83559 | ||||||||
\(277\) | 6.22571 | 0.374067 | 0.187033 | − | 0.982354i | \(-0.440113\pi\) | ||||
0.187033 | + | 0.982354i | \(0.440113\pi\) | |||||||
\(278\) | 41.0274 | 2.46066 | ||||||||
\(279\) | 10.7051 | 0.640896 | ||||||||
\(280\) | 2.14886 | 0.128419 | ||||||||
\(281\) | 6.24993 | 0.372839 | 0.186420 | − | 0.982470i | \(-0.440312\pi\) | ||||
0.186420 | + | 0.982470i | \(0.440312\pi\) | |||||||
\(282\) | 46.8725 | 2.79121 | ||||||||
\(283\) | −29.9267 | −1.77896 | −0.889480 | − | 0.456974i | \(-0.848933\pi\) | ||||
−0.889480 | + | 0.456974i | \(0.848933\pi\) | |||||||
\(284\) | −27.1210 | −1.60934 | ||||||||
\(285\) | −69.5541 | −4.12003 | ||||||||
\(286\) | 5.85664 | 0.346311 | ||||||||
\(287\) | −0.0722353 | −0.00426391 | ||||||||
\(288\) | 28.6889 | 1.69051 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −25.8828 | −1.51989 | ||||||||
\(291\) | −30.6926 | −1.79923 | ||||||||
\(292\) | 16.2432 | 0.950563 | ||||||||
\(293\) | 20.5015 | 1.19771 | 0.598856 | − | 0.800857i | \(-0.295622\pi\) | ||||
0.598856 | + | 0.800857i | \(0.295622\pi\) | |||||||
\(294\) | −11.6395 | −0.678828 | ||||||||
\(295\) | 0.398838 | 0.0232212 | ||||||||
\(296\) | 1.48719 | 0.0864409 | ||||||||
\(297\) | −1.40562 | −0.0815626 | ||||||||
\(298\) | 21.0835 | 1.22133 | ||||||||
\(299\) | −25.2479 | −1.46012 | ||||||||
\(300\) | 30.3282 | 1.75100 | ||||||||
\(301\) | −3.04044 | −0.175248 | ||||||||
\(302\) | 10.9554 | 0.630411 | ||||||||
\(303\) | −12.8967 | −0.740896 | ||||||||
\(304\) | −31.4730 | −1.80510 | ||||||||
\(305\) | 34.5320 | 1.97730 | ||||||||
\(306\) | 7.19282 | 0.411186 | ||||||||
\(307\) | −29.0408 | −1.65744 | −0.828722 | − | 0.559660i | \(-0.810932\pi\) | ||||
−0.828722 | + | 0.559660i | \(0.810932\pi\) | |||||||
\(308\) | −6.40618 | −0.365026 | ||||||||
\(309\) | −11.9175 | −0.677960 | ||||||||
\(310\) | 19.9237 | 1.13159 | ||||||||
\(311\) | 21.4914 | 1.21867 | 0.609334 | − | 0.792914i | \(-0.291437\pi\) | ||||
0.609334 | + | 0.792914i | \(0.291437\pi\) | |||||||
\(312\) | −1.60361 | −0.0907866 | ||||||||
\(313\) | −14.4809 | −0.818508 | −0.409254 | − | 0.912420i | \(-0.634211\pi\) | ||||
−0.409254 | + | 0.912420i | \(0.634211\pi\) | |||||||
\(314\) | 16.3357 | 0.921876 | ||||||||
\(315\) | −35.1745 | −1.98186 | ||||||||
\(316\) | 8.80843 | 0.495513 | ||||||||
\(317\) | 6.57217 | 0.369130 | 0.184565 | − | 0.982820i | \(-0.440912\pi\) | ||||
0.184565 | + | 0.982820i | \(0.440912\pi\) | |||||||
\(318\) | 44.7096 | 2.50719 | ||||||||
\(319\) | 3.91827 | 0.219381 | ||||||||
\(320\) | 28.7876 | 1.60928 | ||||||||
\(321\) | −3.95307 | −0.220639 | ||||||||
\(322\) | 53.8316 | 2.99992 | ||||||||
\(323\) | −8.33818 | −0.463949 | ||||||||
\(324\) | −14.8555 | −0.825304 | ||||||||
\(325\) | 16.2545 | 0.901638 | ||||||||
\(326\) | 1.29848 | 0.0719159 | ||||||||
\(327\) | −25.6796 | −1.42008 | ||||||||
\(328\) | 0.00515145 | 0.000284441 0 | ||||||||
\(329\) | −27.4787 | −1.51495 | ||||||||
\(330\) | −16.9049 | −0.930585 | ||||||||
\(331\) | −32.9573 | −1.81150 | −0.905749 | − | 0.423815i | \(-0.860691\pi\) | ||||
−0.905749 | + | 0.423815i | \(0.860691\pi\) | |||||||
\(332\) | 35.8083 | 1.96524 | ||||||||
\(333\) | −24.3437 | −1.33403 | ||||||||
\(334\) | −25.3617 | −1.38773 | ||||||||
\(335\) | −23.7454 | −1.29735 | ||||||||
\(336\) | −29.3697 | −1.60225 | ||||||||
\(337\) | −1.17969 | −0.0642617 | −0.0321309 | − | 0.999484i | \(-0.510229\pi\) | ||||
−0.0321309 | + | 0.999484i | \(0.510229\pi\) | |||||||
\(338\) | 9.42016 | 0.512389 | ||||||||
\(339\) | −14.4784 | −0.786356 | ||||||||
\(340\) | 6.86781 | 0.372459 | ||||||||
\(341\) | −3.01615 | −0.163334 | ||||||||
\(342\) | −59.9750 | −3.24308 | ||||||||
\(343\) | −14.4595 | −0.780740 | ||||||||
\(344\) | 0.216828 | 0.0116906 | ||||||||
\(345\) | 72.8769 | 3.92356 | ||||||||
\(346\) | −15.8369 | −0.851395 | ||||||||
\(347\) | 2.02485 | 0.108700 | 0.0543498 | − | 0.998522i | \(-0.482691\pi\) | ||||
0.0543498 | + | 0.998522i | \(0.482691\pi\) | |||||||
\(348\) | −21.1278 | −1.13257 | ||||||||
\(349\) | −22.7080 | −1.21553 | −0.607767 | − | 0.794116i | \(-0.707934\pi\) | ||||
−0.607767 | + | 0.794116i | \(0.707934\pi\) | |||||||
\(350\) | −34.6566 | −1.85247 | ||||||||
\(351\) | 4.06215 | 0.216821 | ||||||||
\(352\) | −8.08309 | −0.430830 | ||||||||
\(353\) | −4.34326 | −0.231168 | −0.115584 | − | 0.993298i | \(-0.536874\pi\) | ||||
−0.115584 | + | 0.993298i | \(0.536874\pi\) | |||||||
\(354\) | 0.634598 | 0.0337285 | ||||||||
\(355\) | 41.9564 | 2.22681 | ||||||||
\(356\) | −11.2232 | −0.594827 | ||||||||
\(357\) | −7.78094 | −0.411811 | ||||||||
\(358\) | −19.7785 | −1.04532 | ||||||||
\(359\) | −33.4108 | −1.76336 | −0.881678 | − | 0.471851i | \(-0.843586\pi\) | ||||
−0.881678 | + | 0.471851i | \(0.843586\pi\) | |||||||
\(360\) | 2.50847 | 0.132208 | ||||||||
\(361\) | 50.5253 | 2.65923 | ||||||||
\(362\) | −32.3878 | −1.70226 | ||||||||
\(363\) | 2.55915 | 0.134321 | ||||||||
\(364\) | 18.5134 | 0.970366 | ||||||||
\(365\) | −25.1284 | −1.31528 | ||||||||
\(366\) | 54.9446 | 2.87200 | ||||||||
\(367\) | 35.4437 | 1.85014 | 0.925072 | − | 0.379792i | \(-0.124004\pi\) | ||||
0.925072 | + | 0.379792i | \(0.124004\pi\) | |||||||
\(368\) | 32.9766 | 1.71902 | ||||||||
\(369\) | −0.0843238 | −0.00438972 | ||||||||
\(370\) | −45.3071 | −2.35540 | ||||||||
\(371\) | −26.2107 | −1.36079 | ||||||||
\(372\) | 16.2634 | 0.843219 | ||||||||
\(373\) | −7.24223 | −0.374988 | −0.187494 | − | 0.982266i | \(-0.560037\pi\) | ||||
−0.187494 | + | 0.982266i | \(0.560037\pi\) | |||||||
\(374\) | −2.02657 | −0.104792 | ||||||||
\(375\) | −5.20970 | −0.269028 | ||||||||
\(376\) | 1.95964 | 0.101061 | ||||||||
\(377\) | −11.3235 | −0.583190 | ||||||||
\(378\) | −8.66099 | −0.445473 | ||||||||
\(379\) | −21.3275 | −1.09552 | −0.547761 | − | 0.836635i | \(-0.684520\pi\) | ||||
−0.547761 | + | 0.836635i | \(0.684520\pi\) | |||||||
\(380\) | −57.2651 | −2.93764 | ||||||||
\(381\) | −39.7704 | −2.03750 | ||||||||
\(382\) | −19.8020 | −1.01316 | ||||||||
\(383\) | 12.6202 | 0.644860 | 0.322430 | − | 0.946593i | \(-0.395500\pi\) | ||||
0.322430 | + | 0.946593i | \(0.395500\pi\) | |||||||
\(384\) | 4.43282 | 0.226211 | ||||||||
\(385\) | 9.91041 | 0.505081 | ||||||||
\(386\) | 21.3816 | 1.08829 | ||||||||
\(387\) | −3.54925 | −0.180419 | ||||||||
\(388\) | −25.2697 | −1.28288 | ||||||||
\(389\) | −16.2467 | −0.823740 | −0.411870 | − | 0.911243i | \(-0.635124\pi\) | ||||
−0.411870 | + | 0.911243i | \(0.635124\pi\) | |||||||
\(390\) | 48.8540 | 2.47382 | ||||||||
\(391\) | 8.73652 | 0.441825 | ||||||||
\(392\) | −0.486622 | −0.0245781 | ||||||||
\(393\) | 50.4186 | 2.54328 | ||||||||
\(394\) | 15.6577 | 0.788821 | ||||||||
\(395\) | −13.6267 | −0.685633 | ||||||||
\(396\) | −7.47825 | −0.375796 | ||||||||
\(397\) | −21.3689 | −1.07247 | −0.536237 | − | 0.844067i | \(-0.680155\pi\) | ||||
−0.536237 | + | 0.844067i | \(0.680155\pi\) | |||||||
\(398\) | 19.1906 | 0.961937 | ||||||||
\(399\) | 64.8789 | 3.24801 | ||||||||
\(400\) | −21.2302 | −1.06151 | ||||||||
\(401\) | −12.1090 | −0.604696 | −0.302348 | − | 0.953198i | \(-0.597770\pi\) | ||||
−0.302348 | + | 0.953198i | \(0.597770\pi\) | |||||||
\(402\) | −37.7817 | −1.88438 | ||||||||
\(403\) | 8.71645 | 0.434197 | ||||||||
\(404\) | −10.6181 | −0.528269 | ||||||||
\(405\) | 22.9815 | 1.14196 | ||||||||
\(406\) | 24.1431 | 1.19820 | ||||||||
\(407\) | 6.85881 | 0.339979 | ||||||||
\(408\) | 0.554897 | 0.0274715 | ||||||||
\(409\) | −3.75547 | −0.185696 | −0.0928481 | − | 0.995680i | \(-0.529597\pi\) | ||||
−0.0928481 | + | 0.995680i | \(0.529597\pi\) | |||||||
\(410\) | −0.156939 | −0.00775065 | ||||||||
\(411\) | 49.8272 | 2.45779 | ||||||||
\(412\) | −9.81184 | −0.483395 | ||||||||
\(413\) | −0.372030 | −0.0183064 | ||||||||
\(414\) | 62.8402 | 3.08843 | ||||||||
\(415\) | −55.3957 | −2.71927 | ||||||||
\(416\) | 23.3595 | 1.14530 | ||||||||
\(417\) | −51.8093 | −2.53711 | ||||||||
\(418\) | 16.8979 | 0.826505 | ||||||||
\(419\) | 2.39542 | 0.117024 | 0.0585119 | − | 0.998287i | \(-0.481364\pi\) | ||||
0.0585119 | + | 0.998287i | \(0.481364\pi\) | |||||||
\(420\) | −53.4380 | −2.60751 | ||||||||
\(421\) | −6.31668 | −0.307856 | −0.153928 | − | 0.988082i | \(-0.549192\pi\) | ||||
−0.153928 | + | 0.988082i | \(0.549192\pi\) | |||||||
\(422\) | −26.1846 | −1.27465 | ||||||||
\(423\) | −32.0772 | −1.55965 | ||||||||
\(424\) | 1.86921 | 0.0907771 | ||||||||
\(425\) | −5.62454 | −0.272830 | ||||||||
\(426\) | 66.7576 | 3.23442 | ||||||||
\(427\) | −32.2109 | −1.55880 | ||||||||
\(428\) | −3.25463 | −0.157319 | ||||||||
\(429\) | −7.39576 | −0.357071 | ||||||||
\(430\) | −6.60567 | −0.318554 | ||||||||
\(431\) | −12.2055 | −0.587919 | −0.293959 | − | 0.955818i | \(-0.594973\pi\) | ||||
−0.293959 | + | 0.955818i | \(0.594973\pi\) | |||||||
\(432\) | −5.30562 | −0.255267 | ||||||||
\(433\) | −19.3230 | −0.928604 | −0.464302 | − | 0.885677i | \(-0.653695\pi\) | ||||
−0.464302 | + | 0.885677i | \(0.653695\pi\) | |||||||
\(434\) | −18.5845 | −0.892085 | ||||||||
\(435\) | 32.6848 | 1.56711 | ||||||||
\(436\) | −21.1424 | −1.01254 | ||||||||
\(437\) | −72.8467 | −3.48473 | ||||||||
\(438\) | −39.9822 | −1.91043 | ||||||||
\(439\) | −28.4308 | −1.35693 | −0.678464 | − | 0.734633i | \(-0.737354\pi\) | ||||
−0.678464 | + | 0.734633i | \(0.737354\pi\) | |||||||
\(440\) | −0.706759 | −0.0336934 | ||||||||
\(441\) | 7.96549 | 0.379309 | ||||||||
\(442\) | 5.85664 | 0.278572 | ||||||||
\(443\) | −16.3248 | −0.775613 | −0.387807 | − | 0.921741i | \(-0.626767\pi\) | ||||
−0.387807 | + | 0.921741i | \(0.626767\pi\) | |||||||
\(444\) | −36.9835 | −1.75516 | ||||||||
\(445\) | 17.3623 | 0.823053 | ||||||||
\(446\) | −17.7148 | −0.838821 | ||||||||
\(447\) | −26.6241 | −1.25928 | ||||||||
\(448\) | −26.8526 | −1.26867 | ||||||||
\(449\) | −5.19775 | −0.245297 | −0.122648 | − | 0.992450i | \(-0.539139\pi\) | ||||
−0.122648 | + | 0.992450i | \(0.539139\pi\) | |||||||
\(450\) | −40.4563 | −1.90713 | ||||||||
\(451\) | 0.0237582 | 0.00111873 | ||||||||
\(452\) | −11.9203 | −0.560683 | ||||||||
\(453\) | −13.8344 | −0.649998 | ||||||||
\(454\) | −29.6418 | −1.39116 | ||||||||
\(455\) | −28.6403 | −1.34268 | ||||||||
\(456\) | −4.62683 | −0.216671 | ||||||||
\(457\) | 23.7406 | 1.11054 | 0.555270 | − | 0.831670i | \(-0.312615\pi\) | ||||
0.555270 | + | 0.831670i | \(0.312615\pi\) | |||||||
\(458\) | 26.5142 | 1.23893 | ||||||||
\(459\) | −1.40562 | −0.0656089 | ||||||||
\(460\) | 60.0008 | 2.79755 | ||||||||
\(461\) | −29.6074 | −1.37896 | −0.689478 | − | 0.724307i | \(-0.742160\pi\) | ||||
−0.689478 | + | 0.724307i | \(0.742160\pi\) | |||||||
\(462\) | 15.7686 | 0.733623 | ||||||||
\(463\) | 33.5579 | 1.55957 | 0.779784 | − | 0.626049i | \(-0.215329\pi\) | ||||
0.779784 | + | 0.626049i | \(0.215329\pi\) | |||||||
\(464\) | 14.7898 | 0.686598 | ||||||||
\(465\) | −25.1596 | −1.16675 | ||||||||
\(466\) | −58.3107 | −2.70119 | ||||||||
\(467\) | −15.7475 | −0.728706 | −0.364353 | − | 0.931261i | \(-0.618710\pi\) | ||||
−0.364353 | + | 0.931261i | \(0.618710\pi\) | |||||||
\(468\) | 21.6116 | 0.998996 | ||||||||
\(469\) | 22.1493 | 1.02276 | ||||||||
\(470\) | −59.7004 | −2.75377 | ||||||||
\(471\) | −20.6287 | −0.950519 | ||||||||
\(472\) | 0.0265312 | 0.00122120 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | −21.6817 | −0.995873 | ||||||||
\(475\) | 46.8985 | 2.15185 | ||||||||
\(476\) | −6.40618 | −0.293627 | ||||||||
\(477\) | −30.5971 | −1.40094 | ||||||||
\(478\) | −40.4452 | −1.84992 | ||||||||
\(479\) | 25.1894 | 1.15093 | 0.575467 | − | 0.817825i | \(-0.304820\pi\) | ||||
0.575467 | + | 0.817825i | \(0.304820\pi\) | |||||||
\(480\) | −67.4261 | −3.07757 | ||||||||
\(481\) | −19.8215 | −0.903781 | ||||||||
\(482\) | −22.1508 | −1.00894 | ||||||||
\(483\) | −67.9784 | −3.09312 | ||||||||
\(484\) | 2.10699 | 0.0957724 | ||||||||
\(485\) | 39.0924 | 1.77510 | ||||||||
\(486\) | 45.1121 | 2.04633 | ||||||||
\(487\) | −38.0696 | −1.72510 | −0.862548 | − | 0.505974i | \(-0.831133\pi\) | ||||
−0.862548 | + | 0.505974i | \(0.831133\pi\) | |||||||
\(488\) | 2.29712 | 0.103986 | ||||||||
\(489\) | −1.63971 | −0.0741504 | ||||||||
\(490\) | 14.8249 | 0.669722 | ||||||||
\(491\) | 37.2898 | 1.68286 | 0.841432 | − | 0.540363i | \(-0.181713\pi\) | ||||
0.841432 | + | 0.540363i | \(0.181713\pi\) | |||||||
\(492\) | −0.128107 | −0.00577550 | ||||||||
\(493\) | 3.91827 | 0.176470 | ||||||||
\(494\) | −48.8338 | −2.19714 | ||||||||
\(495\) | 11.5689 | 0.519984 | ||||||||
\(496\) | −11.3847 | −0.511186 | ||||||||
\(497\) | −39.1363 | −1.75550 | ||||||||
\(498\) | −88.1412 | −3.94970 | ||||||||
\(499\) | 30.5469 | 1.36747 | 0.683734 | − | 0.729731i | \(-0.260355\pi\) | ||||
0.683734 | + | 0.729731i | \(0.260355\pi\) | |||||||
\(500\) | −4.28924 | −0.191821 | ||||||||
\(501\) | 32.0267 | 1.43085 | ||||||||
\(502\) | 36.4147 | 1.62527 | ||||||||
\(503\) | 36.7018 | 1.63645 | 0.818226 | − | 0.574896i | \(-0.194958\pi\) | ||||
0.818226 | + | 0.574896i | \(0.194958\pi\) | |||||||
\(504\) | −2.33986 | −0.104226 | ||||||||
\(505\) | 16.4262 | 0.730957 | ||||||||
\(506\) | −17.7052 | −0.787092 | ||||||||
\(507\) | −11.8958 | −0.528310 | ||||||||
\(508\) | −32.7437 | −1.45277 | ||||||||
\(509\) | 20.8694 | 0.925019 | 0.462510 | − | 0.886614i | \(-0.346949\pi\) | ||||
0.462510 | + | 0.886614i | \(0.346949\pi\) | |||||||
\(510\) | −16.9049 | −0.748562 | ||||||||
\(511\) | 23.4393 | 1.03690 | ||||||||
\(512\) | −32.1470 | −1.42071 | ||||||||
\(513\) | 11.7203 | 0.517466 | ||||||||
\(514\) | 49.7343 | 2.19369 | ||||||||
\(515\) | 15.1790 | 0.668866 | ||||||||
\(516\) | −5.39211 | −0.237375 | ||||||||
\(517\) | 9.03774 | 0.397479 | ||||||||
\(518\) | 42.2617 | 1.85687 | ||||||||
\(519\) | 19.9988 | 0.877849 | ||||||||
\(520\) | 2.04248 | 0.0895687 | ||||||||
\(521\) | 11.1934 | 0.490393 | 0.245196 | − | 0.969473i | \(-0.421148\pi\) | ||||
0.245196 | + | 0.969473i | \(0.421148\pi\) | |||||||
\(522\) | 28.1834 | 1.23355 | ||||||||
\(523\) | −4.44012 | −0.194153 | −0.0970764 | − | 0.995277i | \(-0.530949\pi\) | ||||
−0.0970764 | + | 0.995277i | \(0.530949\pi\) | |||||||
\(524\) | 41.5105 | 1.81340 | ||||||||
\(525\) | 43.7642 | 1.91003 | ||||||||
\(526\) | 28.1839 | 1.22888 | ||||||||
\(527\) | −3.01615 | −0.131386 | ||||||||
\(528\) | 9.65969 | 0.420384 | ||||||||
\(529\) | 53.3268 | 2.31856 | ||||||||
\(530\) | −56.9456 | −2.47356 | ||||||||
\(531\) | −0.434288 | −0.0188465 | ||||||||
\(532\) | 53.4159 | 2.31587 | ||||||||
\(533\) | −0.0686594 | −0.00297397 | ||||||||
\(534\) | 27.6255 | 1.19547 | ||||||||
\(535\) | 5.03493 | 0.217679 | ||||||||
\(536\) | −1.57957 | −0.0682272 | ||||||||
\(537\) | 24.9762 | 1.07780 | ||||||||
\(538\) | 29.8039 | 1.28494 | ||||||||
\(539\) | −2.24427 | −0.0966676 | ||||||||
\(540\) | −9.65355 | −0.415423 | ||||||||
\(541\) | −1.88172 | −0.0809016 | −0.0404508 | − | 0.999182i | \(-0.512879\pi\) | ||||
−0.0404508 | + | 0.999182i | \(0.512879\pi\) | |||||||
\(542\) | −39.3982 | −1.69230 | ||||||||
\(543\) | 40.8992 | 1.75515 | ||||||||
\(544\) | −8.08309 | −0.346560 | ||||||||
\(545\) | 32.7075 | 1.40103 | ||||||||
\(546\) | −45.5702 | −1.95022 | ||||||||
\(547\) | −12.5095 | −0.534867 | −0.267433 | − | 0.963576i | \(-0.586176\pi\) | ||||
−0.267433 | + | 0.963576i | \(0.586176\pi\) | |||||||
\(548\) | 41.0236 | 1.75244 | ||||||||
\(549\) | −37.6014 | −1.60479 | ||||||||
\(550\) | 11.3985 | 0.486035 | ||||||||
\(551\) | −32.6713 | −1.39184 | ||||||||
\(552\) | 4.84787 | 0.206339 | ||||||||
\(553\) | 12.7108 | 0.540517 | ||||||||
\(554\) | −12.6169 | −0.536039 | ||||||||
\(555\) | 57.2137 | 2.42859 | ||||||||
\(556\) | −42.6555 | −1.80900 | ||||||||
\(557\) | 38.7431 | 1.64160 | 0.820798 | − | 0.571219i | \(-0.193529\pi\) | ||||
0.820798 | + | 0.571219i | \(0.193529\pi\) | |||||||
\(558\) | −21.6946 | −0.918406 | ||||||||
\(559\) | −2.88993 | −0.122231 | ||||||||
\(560\) | 37.4075 | 1.58076 | ||||||||
\(561\) | 2.55915 | 0.108047 | ||||||||
\(562\) | −12.6659 | −0.534280 | ||||||||
\(563\) | 32.2774 | 1.36033 | 0.680166 | − | 0.733058i | \(-0.261908\pi\) | ||||
0.680166 | + | 0.733058i | \(0.261908\pi\) | |||||||
\(564\) | −48.7325 | −2.05201 | ||||||||
\(565\) | 18.4407 | 0.775808 | ||||||||
\(566\) | 60.6487 | 2.54925 | ||||||||
\(567\) | −21.4368 | −0.900261 | ||||||||
\(568\) | 2.79100 | 0.117108 | ||||||||
\(569\) | −42.4634 | −1.78016 | −0.890080 | − | 0.455804i | \(-0.849352\pi\) | ||||
−0.890080 | + | 0.455804i | \(0.849352\pi\) | |||||||
\(570\) | 140.956 | 5.90401 | ||||||||
\(571\) | −8.99550 | −0.376450 | −0.188225 | − | 0.982126i | \(-0.560273\pi\) | ||||
−0.188225 | + | 0.982126i | \(0.560273\pi\) | |||||||
\(572\) | −6.08905 | −0.254596 | ||||||||
\(573\) | 25.0059 | 1.04464 | ||||||||
\(574\) | 0.146390 | 0.00611020 | ||||||||
\(575\) | −49.1390 | −2.04924 | ||||||||
\(576\) | −31.3464 | −1.30610 | ||||||||
\(577\) | −9.92261 | −0.413084 | −0.206542 | − | 0.978438i | \(-0.566221\pi\) | ||||
−0.206542 | + | 0.978438i | \(0.566221\pi\) | |||||||
\(578\) | −2.02657 | −0.0842943 | ||||||||
\(579\) | −27.0006 | −1.12211 | ||||||||
\(580\) | 26.9099 | 1.11737 | ||||||||
\(581\) | 51.6723 | 2.14373 | ||||||||
\(582\) | 62.2007 | 2.57830 | ||||||||
\(583\) | 8.62071 | 0.357033 | ||||||||
\(584\) | −1.67157 | −0.0691702 | ||||||||
\(585\) | −33.4333 | −1.38230 | ||||||||
\(586\) | −41.5478 | −1.71632 | ||||||||
\(587\) | 13.0553 | 0.538848 | 0.269424 | − | 0.963022i | \(-0.413167\pi\) | ||||
0.269424 | + | 0.963022i | \(0.413167\pi\) | |||||||
\(588\) | 12.1014 | 0.499052 | ||||||||
\(589\) | 25.1492 | 1.03626 | ||||||||
\(590\) | −0.808273 | −0.0332761 | ||||||||
\(591\) | −19.7725 | −0.813330 | ||||||||
\(592\) | 25.8891 | 1.06403 | ||||||||
\(593\) | 26.0149 | 1.06830 | 0.534152 | − | 0.845388i | \(-0.320631\pi\) | ||||
0.534152 | + | 0.845388i | \(0.320631\pi\) | |||||||
\(594\) | 2.84860 | 0.116879 | ||||||||
\(595\) | 9.91041 | 0.406287 | ||||||||
\(596\) | −21.9201 | −0.897883 | ||||||||
\(597\) | −24.2338 | −0.991824 | ||||||||
\(598\) | 51.1667 | 2.09236 | ||||||||
\(599\) | 11.8208 | 0.482983 | 0.241491 | − | 0.970403i | \(-0.422363\pi\) | ||||
0.241491 | + | 0.970403i | \(0.422363\pi\) | |||||||
\(600\) | −3.12104 | −0.127416 | ||||||||
\(601\) | −11.5228 | −0.470025 | −0.235013 | − | 0.971992i | \(-0.575513\pi\) | ||||
−0.235013 | + | 0.971992i | \(0.575513\pi\) | |||||||
\(602\) | 6.16167 | 0.251131 | ||||||||
\(603\) | 25.8560 | 1.05294 | ||||||||
\(604\) | −11.3901 | −0.463458 | ||||||||
\(605\) | −3.25953 | −0.132519 | ||||||||
\(606\) | 26.1361 | 1.06171 | ||||||||
\(607\) | −14.9968 | −0.608702 | −0.304351 | − | 0.952560i | \(-0.598440\pi\) | ||||
−0.304351 | + | 0.952560i | \(0.598440\pi\) | |||||||
\(608\) | 67.3983 | 2.73336 | ||||||||
\(609\) | −30.4878 | −1.23543 | ||||||||
\(610\) | −69.9816 | −2.83347 | ||||||||
\(611\) | −26.1184 | −1.05664 | ||||||||
\(612\) | −7.47825 | −0.302290 | ||||||||
\(613\) | 4.65850 | 0.188155 | 0.0940774 | − | 0.995565i | \(-0.470010\pi\) | ||||
0.0940774 | + | 0.995565i | \(0.470010\pi\) | |||||||
\(614\) | 58.8532 | 2.37512 | ||||||||
\(615\) | 0.198182 | 0.00799147 | ||||||||
\(616\) | 0.659254 | 0.0265621 | ||||||||
\(617\) | −1.47789 | −0.0594977 | −0.0297488 | − | 0.999557i | \(-0.509471\pi\) | ||||
−0.0297488 | + | 0.999557i | \(0.509471\pi\) | |||||||
\(618\) | 24.1516 | 0.971519 | ||||||||
\(619\) | 4.34496 | 0.174639 | 0.0873194 | − | 0.996180i | \(-0.472170\pi\) | ||||
0.0873194 | + | 0.996180i | \(0.472170\pi\) | |||||||
\(620\) | −20.7143 | −0.831908 | ||||||||
\(621\) | −12.2803 | −0.492790 | ||||||||
\(622\) | −43.5540 | −1.74635 | ||||||||
\(623\) | −16.1953 | −0.648851 | ||||||||
\(624\) | −27.9158 | −1.11753 | ||||||||
\(625\) | −21.4872 | −0.859489 | ||||||||
\(626\) | 29.3466 | 1.17292 | ||||||||
\(627\) | −21.3387 | −0.852185 | ||||||||
\(628\) | −16.9839 | −0.677733 | ||||||||
\(629\) | 6.85881 | 0.273479 | ||||||||
\(630\) | 71.2837 | 2.84001 | ||||||||
\(631\) | 16.5213 | 0.657701 | 0.328851 | − | 0.944382i | \(-0.393339\pi\) | ||||
0.328851 | + | 0.944382i | \(0.393339\pi\) | |||||||
\(632\) | −0.906466 | −0.0360573 | ||||||||
\(633\) | 33.0659 | 1.31425 | ||||||||
\(634\) | −13.3190 | −0.528964 | ||||||||
\(635\) | 50.6547 | 2.01017 | ||||||||
\(636\) | −46.4838 | −1.84320 | ||||||||
\(637\) | 6.48578 | 0.256976 | ||||||||
\(638\) | −7.94065 | −0.314374 | ||||||||
\(639\) | −45.6857 | −1.80730 | ||||||||
\(640\) | −5.64598 | −0.223177 | ||||||||
\(641\) | 18.5618 | 0.733147 | 0.366573 | − | 0.930389i | \(-0.380531\pi\) | ||||
0.366573 | + | 0.930389i | \(0.380531\pi\) | |||||||
\(642\) | 8.01118 | 0.316176 | ||||||||
\(643\) | −48.2244 | −1.90179 | −0.950893 | − | 0.309521i | \(-0.899831\pi\) | ||||
−0.950893 | + | 0.309521i | \(0.899831\pi\) | |||||||
\(644\) | −55.9678 | −2.20544 | ||||||||
\(645\) | 8.34163 | 0.328451 | ||||||||
\(646\) | 16.8979 | 0.664840 | ||||||||
\(647\) | −22.1623 | −0.871290 | −0.435645 | − | 0.900119i | \(-0.643480\pi\) | ||||
−0.435645 | + | 0.900119i | \(0.643480\pi\) | |||||||
\(648\) | 1.52876 | 0.0600554 | ||||||||
\(649\) | 0.122360 | 0.00480307 | ||||||||
\(650\) | −32.9409 | −1.29205 | ||||||||
\(651\) | 23.4685 | 0.919802 | ||||||||
\(652\) | −1.35000 | −0.0528702 | ||||||||
\(653\) | −18.3901 | −0.719659 | −0.359830 | − | 0.933018i | \(-0.617165\pi\) | ||||
−0.359830 | + | 0.933018i | \(0.617165\pi\) | |||||||
\(654\) | 52.0415 | 2.03498 | ||||||||
\(655\) | −64.2171 | −2.50917 | ||||||||
\(656\) | 0.0896768 | 0.00350129 | ||||||||
\(657\) | 27.3619 | 1.06749 | ||||||||
\(658\) | 55.6876 | 2.17093 | ||||||||
\(659\) | 0.399685 | 0.0155695 | 0.00778477 | − | 0.999970i | \(-0.497522\pi\) | ||||
0.00778477 | + | 0.999970i | \(0.497522\pi\) | |||||||
\(660\) | 17.5758 | 0.684135 | ||||||||
\(661\) | 1.07879 | 0.0419601 | 0.0209800 | − | 0.999780i | \(-0.493321\pi\) | ||||
0.0209800 | + | 0.999780i | \(0.493321\pi\) | |||||||
\(662\) | 66.7903 | 2.59588 | ||||||||
\(663\) | −7.39576 | −0.287227 | ||||||||
\(664\) | −3.68500 | −0.143006 | ||||||||
\(665\) | −82.6348 | −3.20444 | ||||||||
\(666\) | 49.3342 | 1.91166 | ||||||||
\(667\) | 34.2321 | 1.32547 | ||||||||
\(668\) | 26.3681 | 1.02021 | ||||||||
\(669\) | 22.3702 | 0.864883 | ||||||||
\(670\) | 48.1217 | 1.85910 | ||||||||
\(671\) | 10.5942 | 0.408983 | ||||||||
\(672\) | 62.8940 | 2.42619 | ||||||||
\(673\) | 9.36242 | 0.360895 | 0.180447 | − | 0.983585i | \(-0.442245\pi\) | ||||
0.180447 | + | 0.983585i | \(0.442245\pi\) | |||||||
\(674\) | 2.39072 | 0.0920872 | ||||||||
\(675\) | 7.90599 | 0.304302 | ||||||||
\(676\) | −9.79399 | −0.376692 | ||||||||
\(677\) | −31.4519 | −1.20880 | −0.604398 | − | 0.796683i | \(-0.706586\pi\) | ||||
−0.604398 | + | 0.796683i | \(0.706586\pi\) | |||||||
\(678\) | 29.3414 | 1.12685 | ||||||||
\(679\) | −36.4648 | −1.39939 | ||||||||
\(680\) | −0.706759 | −0.0271030 | ||||||||
\(681\) | 37.4316 | 1.43438 | ||||||||
\(682\) | 6.11244 | 0.234058 | ||||||||
\(683\) | −14.4700 | −0.553681 | −0.276840 | − | 0.960916i | \(-0.589287\pi\) | ||||
−0.276840 | + | 0.960916i | \(0.589287\pi\) | |||||||
\(684\) | 62.3550 | 2.38420 | ||||||||
\(685\) | −63.4637 | −2.42482 | ||||||||
\(686\) | 29.3032 | 1.11880 | ||||||||
\(687\) | −33.4821 | −1.27742 | ||||||||
\(688\) | 3.77457 | 0.143904 | ||||||||
\(689\) | −24.9132 | −0.949118 | ||||||||
\(690\) | −147.690 | −5.62247 | ||||||||
\(691\) | 16.6530 | 0.633509 | 0.316755 | − | 0.948508i | \(-0.397407\pi\) | ||||
0.316755 | + | 0.948508i | \(0.397407\pi\) | |||||||
\(692\) | 16.4653 | 0.625918 | ||||||||
\(693\) | −10.7913 | −0.409927 | ||||||||
\(694\) | −4.10350 | −0.155767 | ||||||||
\(695\) | 65.9883 | 2.50308 | ||||||||
\(696\) | 2.17423 | 0.0824142 | ||||||||
\(697\) | 0.0237582 | 0.000899905 0 | ||||||||
\(698\) | 46.0195 | 1.74186 | ||||||||
\(699\) | 73.6347 | 2.78512 | ||||||||
\(700\) | 36.0319 | 1.36188 | ||||||||
\(701\) | −51.1165 | −1.93065 | −0.965323 | − | 0.261060i | \(-0.915928\pi\) | ||||
−0.965323 | + | 0.261060i | \(0.915928\pi\) | |||||||
\(702\) | −8.23224 | −0.310706 | ||||||||
\(703\) | −57.1901 | −2.15696 | ||||||||
\(704\) | 8.83182 | 0.332862 | ||||||||
\(705\) | 75.3895 | 2.83933 | ||||||||
\(706\) | 8.80192 | 0.331265 | ||||||||
\(707\) | −15.3221 | −0.576248 | ||||||||
\(708\) | −0.659781 | −0.0247961 | ||||||||
\(709\) | −7.14979 | −0.268516 | −0.134258 | − | 0.990946i | \(-0.542865\pi\) | ||||
−0.134258 | + | 0.990946i | \(0.542865\pi\) | |||||||
\(710\) | −85.0276 | −3.19103 | ||||||||
\(711\) | 14.8379 | 0.556465 | ||||||||
\(712\) | 1.15496 | 0.0432841 | ||||||||
\(713\) | −26.3507 | −0.986840 | ||||||||
\(714\) | 15.7686 | 0.590126 | ||||||||
\(715\) | 9.41980 | 0.352281 | ||||||||
\(716\) | 20.5633 | 0.768488 | ||||||||
\(717\) | 51.0741 | 1.90740 | ||||||||
\(718\) | 67.7094 | 2.52689 | ||||||||
\(719\) | −18.3003 | −0.682486 | −0.341243 | − | 0.939975i | \(-0.610848\pi\) | ||||
−0.341243 | + | 0.939975i | \(0.610848\pi\) | |||||||
\(720\) | 43.6676 | 1.62740 | ||||||||
\(721\) | −14.1587 | −0.527298 | ||||||||
\(722\) | −102.393 | −3.81068 | ||||||||
\(723\) | 27.9720 | 1.04029 | ||||||||
\(724\) | 33.6730 | 1.25145 | ||||||||
\(725\) | −22.0385 | −0.818488 | ||||||||
\(726\) | −5.18630 | −0.192482 | ||||||||
\(727\) | 32.9511 | 1.22209 | 0.611045 | − | 0.791596i | \(-0.290749\pi\) | ||||
0.611045 | + | 0.791596i | \(0.290749\pi\) | |||||||
\(728\) | −1.90519 | −0.0706112 | ||||||||
\(729\) | −35.8158 | −1.32651 | ||||||||
\(730\) | 50.9244 | 1.88480 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | −57.1250 | −2.11140 | ||||||||
\(733\) | −21.3433 | −0.788331 | −0.394166 | − | 0.919039i | \(-0.628966\pi\) | ||||
−0.394166 | + | 0.919039i | \(0.628966\pi\) | |||||||
\(734\) | −71.8291 | −2.65126 | ||||||||
\(735\) | −18.7209 | −0.690530 | ||||||||
\(736\) | −70.6181 | −2.60302 | ||||||||
\(737\) | −7.28490 | −0.268343 | ||||||||
\(738\) | 0.170888 | 0.00629048 | ||||||||
\(739\) | 38.9036 | 1.43109 | 0.715546 | − | 0.698566i | \(-0.246178\pi\) | ||||
0.715546 | + | 0.698566i | \(0.246178\pi\) | |||||||
\(740\) | 47.1050 | 1.73162 | ||||||||
\(741\) | 61.6672 | 2.26540 | ||||||||
\(742\) | 53.1179 | 1.95002 | ||||||||
\(743\) | −33.5357 | −1.23031 | −0.615154 | − | 0.788407i | \(-0.710906\pi\) | ||||
−0.615154 | + | 0.788407i | \(0.710906\pi\) | |||||||
\(744\) | −1.67365 | −0.0613590 | ||||||||
\(745\) | 33.9106 | 1.24239 | ||||||||
\(746\) | 14.6769 | 0.537359 | ||||||||
\(747\) | 60.3196 | 2.20698 | ||||||||
\(748\) | 2.10699 | 0.0770393 | ||||||||
\(749\) | −4.69651 | −0.171607 | ||||||||
\(750\) | 10.5578 | 0.385518 | ||||||||
\(751\) | 47.6710 | 1.73954 | 0.869770 | − | 0.493457i | \(-0.164267\pi\) | ||||
0.869770 | + | 0.493457i | \(0.164267\pi\) | |||||||
\(752\) | 34.1136 | 1.24399 | ||||||||
\(753\) | −45.9844 | −1.67576 | ||||||||
\(754\) | 22.9479 | 0.835713 | ||||||||
\(755\) | 17.6206 | 0.641279 | ||||||||
\(756\) | 9.00468 | 0.327497 | ||||||||
\(757\) | −14.6980 | −0.534208 | −0.267104 | − | 0.963668i | \(-0.586067\pi\) | ||||
−0.267104 | + | 0.963668i | \(0.586067\pi\) | |||||||
\(758\) | 43.2218 | 1.56989 | ||||||||
\(759\) | 22.3581 | 0.811547 | ||||||||
\(760\) | 5.89309 | 0.213765 | ||||||||
\(761\) | 20.2590 | 0.734387 | 0.367194 | − | 0.930145i | \(-0.380319\pi\) | ||||
0.367194 | + | 0.930145i | \(0.380319\pi\) | |||||||
\(762\) | 80.5977 | 2.91975 | ||||||||
\(763\) | −30.5090 | −1.10450 | ||||||||
\(764\) | 20.5878 | 0.744841 | ||||||||
\(765\) | 11.5689 | 0.418275 | ||||||||
\(766\) | −25.5757 | −0.924087 | ||||||||
\(767\) | −0.353613 | −0.0127682 | ||||||||
\(768\) | 36.2205 | 1.30699 | ||||||||
\(769\) | −12.8221 | −0.462377 | −0.231189 | − | 0.972909i | \(-0.574261\pi\) | ||||
−0.231189 | + | 0.972909i | \(0.574261\pi\) | |||||||
\(770\) | −20.0841 | −0.723782 | ||||||||
\(771\) | −62.8044 | −2.26185 | ||||||||
\(772\) | −22.2301 | −0.800077 | ||||||||
\(773\) | −9.45325 | −0.340010 | −0.170005 | − | 0.985443i | \(-0.554378\pi\) | ||||
−0.170005 | + | 0.985443i | \(0.554378\pi\) | |||||||
\(774\) | 7.19282 | 0.258540 | ||||||||
\(775\) | 16.9645 | 0.609381 | ||||||||
\(776\) | 2.60048 | 0.0933518 | ||||||||
\(777\) | −53.3680 | −1.91457 | ||||||||
\(778\) | 32.9251 | 1.18042 | ||||||||
\(779\) | −0.198100 | −0.00709767 | ||||||||
\(780\) | −50.7926 | −1.81867 | ||||||||
\(781\) | 12.8719 | 0.460593 | ||||||||
\(782\) | −17.7052 | −0.633136 | ||||||||
\(783\) | −5.50761 | −0.196826 | ||||||||
\(784\) | −8.47115 | −0.302541 | ||||||||
\(785\) | 26.2743 | 0.937768 | ||||||||
\(786\) | −102.177 | −3.64453 | ||||||||
\(787\) | −12.2613 | −0.437069 | −0.218535 | − | 0.975829i | \(-0.570128\pi\) | ||||
−0.218535 | + | 0.975829i | \(0.570128\pi\) | |||||||
\(788\) | −16.2790 | −0.579915 | ||||||||
\(789\) | −35.5906 | −1.26706 | ||||||||
\(790\) | 27.6155 | 0.982514 | ||||||||
\(791\) | −17.2012 | −0.611605 | ||||||||
\(792\) | 0.769579 | 0.0273458 | ||||||||
\(793\) | −30.6164 | −1.08722 | ||||||||
\(794\) | 43.3056 | 1.53686 | ||||||||
\(795\) | 71.9108 | 2.55041 | ||||||||
\(796\) | −19.9521 | −0.707184 | ||||||||
\(797\) | −12.4030 | −0.439336 | −0.219668 | − | 0.975575i | \(-0.570497\pi\) | ||||
−0.219668 | + | 0.975575i | \(0.570497\pi\) | |||||||
\(798\) | −131.482 | −4.65441 | ||||||||
\(799\) | 9.03774 | 0.319732 | ||||||||
\(800\) | 45.4637 | 1.60738 | ||||||||
\(801\) | −18.9056 | −0.667995 | ||||||||
\(802\) | 24.5398 | 0.866531 | ||||||||
\(803\) | −7.70920 | −0.272052 | ||||||||
\(804\) | 39.2810 | 1.38533 | ||||||||
\(805\) | 86.5825 | 3.05163 | ||||||||
\(806\) | −17.6645 | −0.622206 | ||||||||
\(807\) | −37.6363 | −1.32486 | ||||||||
\(808\) | 1.09269 | 0.0384409 | ||||||||
\(809\) | −24.3665 | −0.856682 | −0.428341 | − | 0.903617i | \(-0.640902\pi\) | ||||
−0.428341 | + | 0.903617i | \(0.640902\pi\) | |||||||
\(810\) | −46.5737 | −1.63643 | ||||||||
\(811\) | −7.92032 | −0.278120 | −0.139060 | − | 0.990284i | \(-0.544408\pi\) | ||||
−0.139060 | + | 0.990284i | \(0.544408\pi\) | |||||||
\(812\) | −25.1012 | −0.880878 | ||||||||
\(813\) | 49.7520 | 1.74488 | ||||||||
\(814\) | −13.8999 | −0.487191 | ||||||||
\(815\) | 2.08846 | 0.0731557 | ||||||||
\(816\) | 9.65969 | 0.338157 | ||||||||
\(817\) | −8.33818 | −0.291716 | ||||||||
\(818\) | 7.61074 | 0.266103 | ||||||||
\(819\) | 31.1860 | 1.08973 | ||||||||
\(820\) | 0.163167 | 0.00569803 | ||||||||
\(821\) | 35.5010 | 1.23900 | 0.619498 | − | 0.784999i | \(-0.287336\pi\) | ||||
0.619498 | + | 0.784999i | \(0.287336\pi\) | |||||||
\(822\) | −100.978 | −3.52203 | ||||||||
\(823\) | −27.2380 | −0.949456 | −0.474728 | − | 0.880132i | \(-0.657454\pi\) | ||||
−0.474728 | + | 0.880132i | \(0.657454\pi\) | |||||||
\(824\) | 1.00973 | 0.0351755 | ||||||||
\(825\) | −14.3941 | −0.501137 | ||||||||
\(826\) | 0.753944 | 0.0262331 | ||||||||
\(827\) | −26.3329 | −0.915686 | −0.457843 | − | 0.889033i | \(-0.651378\pi\) | ||||
−0.457843 | + | 0.889033i | \(0.651378\pi\) | |||||||
\(828\) | −65.3339 | −2.27051 | ||||||||
\(829\) | 13.4609 | 0.467517 | 0.233759 | − | 0.972295i | \(-0.424897\pi\) | ||||
0.233759 | + | 0.972295i | \(0.424897\pi\) | |||||||
\(830\) | 112.263 | 3.89672 | ||||||||
\(831\) | 15.9325 | 0.552694 | ||||||||
\(832\) | −25.5233 | −0.884862 | ||||||||
\(833\) | −2.24427 | −0.0777594 | ||||||||
\(834\) | 104.995 | 3.63569 | ||||||||
\(835\) | −40.7916 | −1.41165 | ||||||||
\(836\) | −17.5685 | −0.607619 | ||||||||
\(837\) | 4.23957 | 0.146541 | ||||||||
\(838\) | −4.85449 | −0.167695 | ||||||||
\(839\) | −42.8477 | −1.47927 | −0.739634 | − | 0.673010i | \(-0.765001\pi\) | ||||
−0.739634 | + | 0.673010i | \(0.765001\pi\) | |||||||
\(840\) | 5.49925 | 0.189742 | ||||||||
\(841\) | −13.6472 | −0.470592 | ||||||||
\(842\) | 12.8012 | 0.441159 | ||||||||
\(843\) | 15.9945 | 0.550880 | ||||||||
\(844\) | 27.2237 | 0.937078 | ||||||||
\(845\) | 15.1514 | 0.521223 | ||||||||
\(846\) | 65.0068 | 2.23498 | ||||||||
\(847\) | 3.04044 | 0.104471 | ||||||||
\(848\) | 32.5394 | 1.11741 | ||||||||
\(849\) | −76.5870 | −2.62846 | ||||||||
\(850\) | 11.3985 | 0.390967 | ||||||||
\(851\) | 59.9222 | 2.05411 | ||||||||
\(852\) | −69.4068 | −2.37784 | ||||||||
\(853\) | −31.6409 | −1.08336 | −0.541682 | − | 0.840584i | \(-0.682212\pi\) | ||||
−0.541682 | + | 0.840584i | \(0.682212\pi\) | |||||||
\(854\) | 65.2778 | 2.23376 | ||||||||
\(855\) | −96.4636 | −3.29899 | ||||||||
\(856\) | 0.334931 | 0.0114477 | ||||||||
\(857\) | 30.0257 | 1.02566 | 0.512829 | − | 0.858491i | \(-0.328598\pi\) | ||||
0.512829 | + | 0.858491i | \(0.328598\pi\) | |||||||
\(858\) | 14.9880 | 0.511683 | ||||||||
\(859\) | −3.70446 | −0.126395 | −0.0631974 | − | 0.998001i | \(-0.520130\pi\) | ||||
−0.0631974 | + | 0.998001i | \(0.520130\pi\) | |||||||
\(860\) | 6.86781 | 0.234190 | ||||||||
\(861\) | −0.184861 | −0.00630005 | ||||||||
\(862\) | 24.7353 | 0.842489 | ||||||||
\(863\) | −17.9681 | −0.611643 | −0.305821 | − | 0.952089i | \(-0.598931\pi\) | ||||
−0.305821 | + | 0.952089i | \(0.598931\pi\) | |||||||
\(864\) | 11.3618 | 0.386536 | ||||||||
\(865\) | −25.4720 | −0.866073 | ||||||||
\(866\) | 39.1594 | 1.33069 | ||||||||
\(867\) | 2.55915 | 0.0869133 | ||||||||
\(868\) | 19.3220 | 0.655832 | ||||||||
\(869\) | −4.18057 | −0.141816 | ||||||||
\(870\) | −66.2380 | −2.24568 | ||||||||
\(871\) | 21.0528 | 0.713348 | ||||||||
\(872\) | 2.17574 | 0.0736800 | ||||||||
\(873\) | −42.5672 | −1.44068 | ||||||||
\(874\) | 147.629 | 4.99363 | ||||||||
\(875\) | −6.18947 | −0.209242 | ||||||||
\(876\) | 41.5689 | 1.40448 | ||||||||
\(877\) | −32.7033 | −1.10431 | −0.552157 | − | 0.833740i | \(-0.686195\pi\) | ||||
−0.552157 | + | 0.833740i | \(0.686195\pi\) | |||||||
\(878\) | 57.6171 | 1.94448 | ||||||||
\(879\) | 52.4665 | 1.76965 | ||||||||
\(880\) | −12.3033 | −0.414745 | ||||||||
\(881\) | −35.1116 | −1.18294 | −0.591471 | − | 0.806327i | \(-0.701452\pi\) | ||||
−0.591471 | + | 0.806327i | \(0.701452\pi\) | |||||||
\(882\) | −16.1426 | −0.543551 | ||||||||
\(883\) | 13.4576 | 0.452884 | 0.226442 | − | 0.974025i | \(-0.427291\pi\) | ||||
0.226442 | + | 0.974025i | \(0.427291\pi\) | |||||||
\(884\) | −6.08905 | −0.204797 | ||||||||
\(885\) | 1.02069 | 0.0343100 | ||||||||
\(886\) | 33.0833 | 1.11146 | ||||||||
\(887\) | 13.2888 | 0.446196 | 0.223098 | − | 0.974796i | \(-0.428383\pi\) | ||||
0.223098 | + | 0.974796i | \(0.428383\pi\) | |||||||
\(888\) | 3.80593 | 0.127719 | ||||||||
\(889\) | −47.2499 | −1.58471 | ||||||||
\(890\) | −35.1860 | −1.17944 | ||||||||
\(891\) | 7.05056 | 0.236203 | ||||||||
\(892\) | 18.4178 | 0.616674 | ||||||||
\(893\) | −75.3584 | −2.52177 | ||||||||
\(894\) | 53.9557 | 1.80455 | ||||||||
\(895\) | −31.8116 | −1.06335 | ||||||||
\(896\) | 5.26648 | 0.175941 | ||||||||
\(897\) | −64.6132 | −2.15737 | ||||||||
\(898\) | 10.5336 | 0.351511 | ||||||||
\(899\) | −11.8181 | −0.394155 | ||||||||
\(900\) | 42.0617 | 1.40206 | ||||||||
\(901\) | 8.62071 | 0.287197 | ||||||||
\(902\) | −0.0481476 | −0.00160314 | ||||||||
\(903\) | −7.78094 | −0.258934 | ||||||||
\(904\) | 1.22670 | 0.0407995 | ||||||||
\(905\) | −52.0924 | −1.73161 | ||||||||
\(906\) | 28.0365 | 0.931449 | ||||||||
\(907\) | 12.4164 | 0.412278 | 0.206139 | − | 0.978523i | \(-0.433910\pi\) | ||||
0.206139 | + | 0.978523i | \(0.433910\pi\) | |||||||
\(908\) | 30.8181 | 1.02273 | ||||||||
\(909\) | −17.8863 | −0.593250 | ||||||||
\(910\) | 58.0417 | 1.92406 | ||||||||
\(911\) | 26.6922 | 0.884350 | 0.442175 | − | 0.896929i | \(-0.354207\pi\) | ||||
0.442175 | + | 0.896929i | \(0.354207\pi\) | |||||||
\(912\) | −80.5443 | −2.66709 | ||||||||
\(913\) | −16.9950 | −0.562452 | ||||||||
\(914\) | −48.1121 | −1.59141 | ||||||||
\(915\) | 88.3727 | 2.92151 | ||||||||
\(916\) | −27.5664 | −0.910819 | ||||||||
\(917\) | 59.9007 | 1.97809 | ||||||||
\(918\) | 2.84860 | 0.0940177 | ||||||||
\(919\) | 26.1594 | 0.862919 | 0.431460 | − | 0.902132i | \(-0.357999\pi\) | ||||
0.431460 | + | 0.902132i | \(0.357999\pi\) | |||||||
\(920\) | −6.17462 | −0.203571 | ||||||||
\(921\) | −74.3197 | −2.44892 | ||||||||
\(922\) | 60.0016 | 1.97605 | ||||||||
\(923\) | −37.1989 | −1.22442 | ||||||||
\(924\) | −16.3944 | −0.539336 | ||||||||
\(925\) | −38.5777 | −1.26843 | ||||||||
\(926\) | −68.0075 | −2.23487 | ||||||||
\(927\) | −16.5282 | −0.542856 | ||||||||
\(928\) | −31.6717 | −1.03968 | ||||||||
\(929\) | −13.1967 | −0.432970 | −0.216485 | − | 0.976286i | \(-0.569459\pi\) | ||||
−0.216485 | + | 0.976286i | \(0.569459\pi\) | |||||||
\(930\) | 50.9877 | 1.67195 | ||||||||
\(931\) | 18.7131 | 0.613298 | ||||||||
\(932\) | 60.6247 | 1.98583 | ||||||||
\(933\) | 54.9999 | 1.80061 | ||||||||
\(934\) | 31.9134 | 1.04424 | ||||||||
\(935\) | −3.25953 | −0.106598 | ||||||||
\(936\) | −2.22403 | −0.0726946 | ||||||||
\(937\) | 48.6401 | 1.58900 | 0.794502 | − | 0.607262i | \(-0.207732\pi\) | ||||
0.794502 | + | 0.607262i | \(0.207732\pi\) | |||||||
\(938\) | −44.8871 | −1.46562 | ||||||||
\(939\) | −37.0588 | −1.20937 | ||||||||
\(940\) | 62.0695 | 2.02448 | ||||||||
\(941\) | 12.1121 | 0.394843 | 0.197421 | − | 0.980319i | \(-0.436743\pi\) | ||||
0.197421 | + | 0.980319i | \(0.436743\pi\) | |||||||
\(942\) | 41.8055 | 1.36210 | ||||||||
\(943\) | 0.207564 | 0.00675921 | ||||||||
\(944\) | 0.461858 | 0.0150322 | ||||||||
\(945\) | −13.9303 | −0.453153 | ||||||||
\(946\) | −2.02657 | −0.0658895 | ||||||||
\(947\) | −3.07767 | −0.100011 | −0.0500054 | − | 0.998749i | \(-0.515924\pi\) | ||||
−0.0500054 | + | 0.998749i | \(0.515924\pi\) | |||||||
\(948\) | 22.5421 | 0.732133 | ||||||||
\(949\) | 22.2790 | 0.723207 | ||||||||
\(950\) | −95.0431 | −3.08361 | ||||||||
\(951\) | 16.8192 | 0.545399 | ||||||||
\(952\) | 0.659254 | 0.0213665 | ||||||||
\(953\) | −28.4517 | −0.921640 | −0.460820 | − | 0.887494i | \(-0.652445\pi\) | ||||
−0.460820 | + | 0.887494i | \(0.652445\pi\) | |||||||
\(954\) | 62.0072 | 2.00756 | ||||||||
\(955\) | −31.8495 | −1.03062 | ||||||||
\(956\) | 42.0502 | 1.36000 | ||||||||
\(957\) | 10.0274 | 0.324141 | ||||||||
\(958\) | −51.0482 | −1.64929 | ||||||||
\(959\) | 59.1980 | 1.91160 | ||||||||
\(960\) | 73.6718 | 2.37775 | ||||||||
\(961\) | −21.9028 | −0.706543 | ||||||||
\(962\) | 40.1696 | 1.29512 | ||||||||
\(963\) | −5.48246 | −0.176670 | ||||||||
\(964\) | 23.0298 | 0.741741 | ||||||||
\(965\) | 34.3900 | 1.10705 | ||||||||
\(966\) | 137.763 | 4.43245 | ||||||||
\(967\) | 1.29759 | 0.0417277 | 0.0208639 | − | 0.999782i | \(-0.493358\pi\) | ||||
0.0208639 | + | 0.999782i | \(0.493358\pi\) | |||||||
\(968\) | −0.216828 | −0.00696913 | ||||||||
\(969\) | −21.3387 | −0.685497 | ||||||||
\(970\) | −79.2236 | −2.54372 | ||||||||
\(971\) | 47.7571 | 1.53260 | 0.766299 | − | 0.642484i | \(-0.222096\pi\) | ||||
0.766299 | + | 0.642484i | \(0.222096\pi\) | |||||||
\(972\) | −46.9023 | −1.50439 | ||||||||
\(973\) | −61.5529 | −1.97329 | ||||||||
\(974\) | 77.1507 | 2.47207 | ||||||||
\(975\) | 41.5978 | 1.33219 | ||||||||
\(976\) | 39.9884 | 1.28000 | ||||||||
\(977\) | −56.4776 | −1.80688 | −0.903440 | − | 0.428715i | \(-0.858967\pi\) | ||||
−0.903440 | + | 0.428715i | \(0.858967\pi\) | |||||||
\(978\) | 3.32300 | 0.106258 | ||||||||
\(979\) | 5.32663 | 0.170240 | ||||||||
\(980\) | −15.4132 | −0.492357 | ||||||||
\(981\) | −35.6147 | −1.13709 | ||||||||
\(982\) | −75.5704 | −2.41155 | ||||||||
\(983\) | 30.5986 | 0.975942 | 0.487971 | − | 0.872860i | \(-0.337737\pi\) | ||||
0.487971 | + | 0.872860i | \(0.337737\pi\) | |||||||
\(984\) | 0.0131833 | 0.000420269 0 | ||||||||
\(985\) | 25.1837 | 0.802420 | ||||||||
\(986\) | −7.94065 | −0.252882 | ||||||||
\(987\) | −70.3222 | −2.23838 | ||||||||
\(988\) | 50.7717 | 1.61526 | ||||||||
\(989\) | 8.73652 | 0.277805 | ||||||||
\(990\) | −23.4452 | −0.745138 | ||||||||
\(991\) | −13.2983 | −0.422435 | −0.211218 | − | 0.977439i | \(-0.567743\pi\) | ||||
−0.211218 | + | 0.977439i | \(0.567743\pi\) | |||||||
\(992\) | 24.3798 | 0.774059 | ||||||||
\(993\) | −84.3427 | −2.67654 | ||||||||
\(994\) | 79.3124 | 2.51564 | ||||||||
\(995\) | 30.8661 | 0.978520 | ||||||||
\(996\) | 91.6390 | 2.90369 | ||||||||
\(997\) | 40.6832 | 1.28845 | 0.644224 | − | 0.764837i | \(-0.277180\pi\) | ||||
0.644224 | + | 0.764837i | \(0.277180\pi\) | |||||||
\(998\) | −61.9055 | −1.95958 | ||||||||
\(999\) | −9.64091 | −0.305025 |
(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 | 8041.2.a.h.1.14 | ✓ | 74 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.h.1.14 | ✓ | 74 | 1.1 | even | 1 | trivial |