Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4006,2,Mod(1,4006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4006, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4006 = 2 \cdot 2003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4006.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: | \(31.9880710497\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 4006.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −3.34571 | −1.93165 | −0.965823 | − | 0.259203i | \(-0.916540\pi\) | ||||
−0.965823 | + | 0.259203i | \(0.916540\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.64453 | −1.62988 | −0.814942 | − | 0.579543i | \(-0.803231\pi\) | ||||
−0.814942 | + | 0.579543i | \(0.803231\pi\) | |||||||
\(6\) | 3.34571 | 1.36588 | ||||||||
\(7\) | 5.09237 | 1.92473 | 0.962367 | − | 0.271753i | \(-0.0876035\pi\) | ||||
0.962367 | + | 0.271753i | \(0.0876035\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 8.19376 | 2.73125 | ||||||||
\(10\) | 3.64453 | 1.15250 | ||||||||
\(11\) | −0.225781 | −0.0680756 | −0.0340378 | − | 0.999421i | \(-0.510837\pi\) | ||||
−0.0340378 | + | 0.999421i | \(0.510837\pi\) | |||||||
\(12\) | −3.34571 | −0.965823 | ||||||||
\(13\) | −4.05580 | −1.12488 | −0.562439 | − | 0.826839i | \(-0.690137\pi\) | ||||
−0.562439 | + | 0.826839i | \(0.690137\pi\) | |||||||
\(14\) | −5.09237 | −1.36099 | ||||||||
\(15\) | 12.1935 | 3.14836 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.866411 | 0.210136 | 0.105068 | − | 0.994465i | \(-0.466494\pi\) | ||||
0.105068 | + | 0.994465i | \(0.466494\pi\) | |||||||
\(18\) | −8.19376 | −1.93129 | ||||||||
\(19\) | −0.400561 | −0.0918950 | −0.0459475 | − | 0.998944i | \(-0.514631\pi\) | ||||
−0.0459475 | + | 0.998944i | \(0.514631\pi\) | |||||||
\(20\) | −3.64453 | −0.814942 | ||||||||
\(21\) | −17.0376 | −3.71790 | ||||||||
\(22\) | 0.225781 | 0.0481368 | ||||||||
\(23\) | 2.97729 | 0.620808 | 0.310404 | − | 0.950605i | \(-0.399536\pi\) | ||||
0.310404 | + | 0.950605i | \(0.399536\pi\) | |||||||
\(24\) | 3.34571 | 0.682940 | ||||||||
\(25\) | 8.28261 | 1.65652 | ||||||||
\(26\) | 4.05580 | 0.795409 | ||||||||
\(27\) | −17.3768 | −3.34417 | ||||||||
\(28\) | 5.09237 | 0.962367 | ||||||||
\(29\) | −2.19058 | −0.406780 | −0.203390 | − | 0.979098i | \(-0.565196\pi\) | ||||
−0.203390 | + | 0.979098i | \(0.565196\pi\) | |||||||
\(30\) | −12.1935 | −2.22623 | ||||||||
\(31\) | −9.28273 | −1.66723 | −0.833614 | − | 0.552348i | \(-0.813732\pi\) | ||||
−0.833614 | + | 0.552348i | \(0.813732\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.755399 | 0.131498 | ||||||||
\(34\) | −0.866411 | −0.148588 | ||||||||
\(35\) | −18.5593 | −3.13709 | ||||||||
\(36\) | 8.19376 | 1.36563 | ||||||||
\(37\) | 5.14177 | 0.845301 | 0.422651 | − | 0.906293i | \(-0.361100\pi\) | ||||
0.422651 | + | 0.906293i | \(0.361100\pi\) | |||||||
\(38\) | 0.400561 | 0.0649796 | ||||||||
\(39\) | 13.5695 | 2.17287 | ||||||||
\(40\) | 3.64453 | 0.576251 | ||||||||
\(41\) | −4.50642 | −0.703785 | −0.351892 | − | 0.936040i | \(-0.614462\pi\) | ||||
−0.351892 | + | 0.936040i | \(0.614462\pi\) | |||||||
\(42\) | 17.0376 | 2.62895 | ||||||||
\(43\) | 5.90255 | 0.900131 | 0.450065 | − | 0.892996i | \(-0.351401\pi\) | ||||
0.450065 | + | 0.892996i | \(0.351401\pi\) | |||||||
\(44\) | −0.225781 | −0.0340378 | ||||||||
\(45\) | −29.8624 | −4.45163 | ||||||||
\(46\) | −2.97729 | −0.438977 | ||||||||
\(47\) | −12.4279 | −1.81280 | −0.906400 | − | 0.422421i | \(-0.861180\pi\) | ||||
−0.906400 | + | 0.422421i | \(0.861180\pi\) | |||||||
\(48\) | −3.34571 | −0.482911 | ||||||||
\(49\) | 18.9322 | 2.70460 | ||||||||
\(50\) | −8.28261 | −1.17134 | ||||||||
\(51\) | −2.89876 | −0.405907 | ||||||||
\(52\) | −4.05580 | −0.562439 | ||||||||
\(53\) | −1.83001 | −0.251371 | −0.125685 | − | 0.992070i | \(-0.540113\pi\) | ||||
−0.125685 | + | 0.992070i | \(0.540113\pi\) | |||||||
\(54\) | 17.3768 | 2.36469 | ||||||||
\(55\) | 0.822867 | 0.110955 | ||||||||
\(56\) | −5.09237 | −0.680496 | ||||||||
\(57\) | 1.34016 | 0.177509 | ||||||||
\(58\) | 2.19058 | 0.287637 | ||||||||
\(59\) | 9.30416 | 1.21130 | 0.605650 | − | 0.795732i | \(-0.292913\pi\) | ||||
0.605650 | + | 0.795732i | \(0.292913\pi\) | |||||||
\(60\) | 12.1935 | 1.57418 | ||||||||
\(61\) | −0.790477 | −0.101210 | −0.0506051 | − | 0.998719i | \(-0.516115\pi\) | ||||
−0.0506051 | + | 0.998719i | \(0.516115\pi\) | |||||||
\(62\) | 9.28273 | 1.17891 | ||||||||
\(63\) | 41.7257 | 5.25694 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 14.7815 | 1.83342 | ||||||||
\(66\) | −0.755399 | −0.0929831 | ||||||||
\(67\) | −4.08274 | −0.498786 | −0.249393 | − | 0.968402i | \(-0.580231\pi\) | ||||
−0.249393 | + | 0.968402i | \(0.580231\pi\) | |||||||
\(68\) | 0.866411 | 0.105068 | ||||||||
\(69\) | −9.96114 | −1.19918 | ||||||||
\(70\) | 18.5593 | 2.21826 | ||||||||
\(71\) | −9.99418 | −1.18609 | −0.593046 | − | 0.805169i | \(-0.702075\pi\) | ||||
−0.593046 | + | 0.805169i | \(0.702075\pi\) | |||||||
\(72\) | −8.19376 | −0.965644 | ||||||||
\(73\) | 9.29518 | 1.08792 | 0.543960 | − | 0.839111i | \(-0.316925\pi\) | ||||
0.543960 | + | 0.839111i | \(0.316925\pi\) | |||||||
\(74\) | −5.14177 | −0.597718 | ||||||||
\(75\) | −27.7112 | −3.19981 | ||||||||
\(76\) | −0.400561 | −0.0459475 | ||||||||
\(77\) | −1.14976 | −0.131028 | ||||||||
\(78\) | −13.5695 | −1.53645 | ||||||||
\(79\) | 8.02468 | 0.902847 | 0.451424 | − | 0.892310i | \(-0.350916\pi\) | ||||
0.451424 | + | 0.892310i | \(0.350916\pi\) | |||||||
\(80\) | −3.64453 | −0.407471 | ||||||||
\(81\) | 33.5565 | 3.72850 | ||||||||
\(82\) | 4.50642 | 0.497651 | ||||||||
\(83\) | 3.91707 | 0.429954 | 0.214977 | − | 0.976619i | \(-0.431032\pi\) | ||||
0.214977 | + | 0.976619i | \(0.431032\pi\) | |||||||
\(84\) | −17.0376 | −1.85895 | ||||||||
\(85\) | −3.15766 | −0.342496 | ||||||||
\(86\) | −5.90255 | −0.636488 | ||||||||
\(87\) | 7.32903 | 0.785754 | ||||||||
\(88\) | 0.225781 | 0.0240684 | ||||||||
\(89\) | −12.6557 | −1.34150 | −0.670748 | − | 0.741685i | \(-0.734027\pi\) | ||||
−0.670748 | + | 0.741685i | \(0.734027\pi\) | |||||||
\(90\) | 29.8624 | 3.14778 | ||||||||
\(91\) | −20.6536 | −2.16509 | ||||||||
\(92\) | 2.97729 | 0.310404 | ||||||||
\(93\) | 31.0573 | 3.22049 | ||||||||
\(94\) | 12.4279 | 1.28184 | ||||||||
\(95\) | 1.45986 | 0.149778 | ||||||||
\(96\) | 3.34571 | 0.341470 | ||||||||
\(97\) | 10.1195 | 1.02748 | 0.513738 | − | 0.857947i | \(-0.328260\pi\) | ||||
0.513738 | + | 0.857947i | \(0.328260\pi\) | |||||||
\(98\) | −18.9322 | −1.91244 | ||||||||
\(99\) | −1.85000 | −0.185932 | ||||||||
\(100\) | 8.28261 | 0.828261 | ||||||||
\(101\) | 15.5250 | 1.54480 | 0.772399 | − | 0.635138i | \(-0.219057\pi\) | ||||
0.772399 | + | 0.635138i | \(0.219057\pi\) | |||||||
\(102\) | 2.89876 | 0.287020 | ||||||||
\(103\) | 12.2172 | 1.20379 | 0.601896 | − | 0.798574i | \(-0.294412\pi\) | ||||
0.601896 | + | 0.798574i | \(0.294412\pi\) | |||||||
\(104\) | 4.05580 | 0.397704 | ||||||||
\(105\) | 62.0940 | 6.05975 | ||||||||
\(106\) | 1.83001 | 0.177746 | ||||||||
\(107\) | −1.19286 | −0.115318 | −0.0576591 | − | 0.998336i | \(-0.518364\pi\) | ||||
−0.0576591 | + | 0.998336i | \(0.518364\pi\) | |||||||
\(108\) | −17.3768 | −1.67209 | ||||||||
\(109\) | −4.15216 | −0.397705 | −0.198853 | − | 0.980029i | \(-0.563722\pi\) | ||||
−0.198853 | + | 0.980029i | \(0.563722\pi\) | |||||||
\(110\) | −0.822867 | −0.0784573 | ||||||||
\(111\) | −17.2028 | −1.63282 | ||||||||
\(112\) | 5.09237 | 0.481183 | ||||||||
\(113\) | 10.4021 | 0.978551 | 0.489276 | − | 0.872129i | \(-0.337261\pi\) | ||||
0.489276 | + | 0.872129i | \(0.337261\pi\) | |||||||
\(114\) | −1.34016 | −0.125518 | ||||||||
\(115\) | −10.8508 | −1.01184 | ||||||||
\(116\) | −2.19058 | −0.203390 | ||||||||
\(117\) | −33.2323 | −3.07233 | ||||||||
\(118\) | −9.30416 | −0.856518 | ||||||||
\(119\) | 4.41208 | 0.404455 | ||||||||
\(120\) | −12.1935 | −1.11311 | ||||||||
\(121\) | −10.9490 | −0.995366 | ||||||||
\(122\) | 0.790477 | 0.0715664 | ||||||||
\(123\) | 15.0772 | 1.35946 | ||||||||
\(124\) | −9.28273 | −0.833614 | ||||||||
\(125\) | −11.9636 | −1.07005 | ||||||||
\(126\) | −41.7257 | −3.71722 | ||||||||
\(127\) | 4.03373 | 0.357935 | 0.178968 | − | 0.983855i | \(-0.442724\pi\) | ||||
0.178968 | + | 0.983855i | \(0.442724\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −19.7482 | −1.73873 | ||||||||
\(130\) | −14.7815 | −1.29642 | ||||||||
\(131\) | −0.688921 | −0.0601913 | −0.0300957 | − | 0.999547i | \(-0.509581\pi\) | ||||
−0.0300957 | + | 0.999547i | \(0.509581\pi\) | |||||||
\(132\) | 0.755399 | 0.0657490 | ||||||||
\(133\) | −2.03980 | −0.176873 | ||||||||
\(134\) | 4.08274 | 0.352695 | ||||||||
\(135\) | 63.3304 | 5.45061 | ||||||||
\(136\) | −0.866411 | −0.0742941 | ||||||||
\(137\) | 14.0944 | 1.20417 | 0.602084 | − | 0.798432i | \(-0.294337\pi\) | ||||
0.602084 | + | 0.798432i | \(0.294337\pi\) | |||||||
\(138\) | 9.96114 | 0.847949 | ||||||||
\(139\) | 11.0608 | 0.938169 | 0.469084 | − | 0.883153i | \(-0.344584\pi\) | ||||
0.469084 | + | 0.883153i | \(0.344584\pi\) | |||||||
\(140\) | −18.5593 | −1.56855 | ||||||||
\(141\) | 41.5802 | 3.50169 | ||||||||
\(142\) | 9.99418 | 0.838693 | ||||||||
\(143\) | 0.915725 | 0.0765768 | ||||||||
\(144\) | 8.19376 | 0.682814 | ||||||||
\(145\) | 7.98362 | 0.663004 | ||||||||
\(146\) | −9.29518 | −0.769275 | ||||||||
\(147\) | −63.3416 | −5.22433 | ||||||||
\(148\) | 5.14177 | 0.422651 | ||||||||
\(149\) | −9.28809 | −0.760910 | −0.380455 | − | 0.924799i | \(-0.624233\pi\) | ||||
−0.380455 | + | 0.924799i | \(0.624233\pi\) | |||||||
\(150\) | 27.7112 | 2.26261 | ||||||||
\(151\) | 0.175333 | 0.0142684 | 0.00713421 | − | 0.999975i | \(-0.497729\pi\) | ||||
0.00713421 | + | 0.999975i | \(0.497729\pi\) | |||||||
\(152\) | 0.400561 | 0.0324898 | ||||||||
\(153\) | 7.09917 | 0.573934 | ||||||||
\(154\) | 1.14976 | 0.0926504 | ||||||||
\(155\) | 33.8312 | 2.71739 | ||||||||
\(156\) | 13.5695 | 1.08643 | ||||||||
\(157\) | −16.2661 | −1.29817 | −0.649087 | − | 0.760714i | \(-0.724849\pi\) | ||||
−0.649087 | + | 0.760714i | \(0.724849\pi\) | |||||||
\(158\) | −8.02468 | −0.638409 | ||||||||
\(159\) | 6.12267 | 0.485559 | ||||||||
\(160\) | 3.64453 | 0.288125 | ||||||||
\(161\) | 15.1614 | 1.19489 | ||||||||
\(162\) | −33.5565 | −2.63645 | ||||||||
\(163\) | 12.4851 | 0.977908 | 0.488954 | − | 0.872310i | \(-0.337379\pi\) | ||||
0.488954 | + | 0.872310i | \(0.337379\pi\) | |||||||
\(164\) | −4.50642 | −0.351892 | ||||||||
\(165\) | −2.75307 | −0.214327 | ||||||||
\(166\) | −3.91707 | −0.304024 | ||||||||
\(167\) | −16.5947 | −1.28413 | −0.642067 | − | 0.766649i | \(-0.721923\pi\) | ||||
−0.642067 | + | 0.766649i | \(0.721923\pi\) | |||||||
\(168\) | 17.0376 | 1.31448 | ||||||||
\(169\) | 3.44955 | 0.265350 | ||||||||
\(170\) | 3.15766 | 0.242182 | ||||||||
\(171\) | −3.28210 | −0.250989 | ||||||||
\(172\) | 5.90255 | 0.450065 | ||||||||
\(173\) | −11.0918 | −0.843294 | −0.421647 | − | 0.906760i | \(-0.638548\pi\) | ||||
−0.421647 | + | 0.906760i | \(0.638548\pi\) | |||||||
\(174\) | −7.32903 | −0.555612 | ||||||||
\(175\) | 42.1781 | 3.18836 | ||||||||
\(176\) | −0.225781 | −0.0170189 | ||||||||
\(177\) | −31.1290 | −2.33980 | ||||||||
\(178\) | 12.6557 | 0.948581 | ||||||||
\(179\) | 18.2533 | 1.36431 | 0.682156 | − | 0.731207i | \(-0.261042\pi\) | ||||
0.682156 | + | 0.731207i | \(0.261042\pi\) | |||||||
\(180\) | −29.8624 | −2.22581 | ||||||||
\(181\) | −25.5293 | −1.89758 | −0.948789 | − | 0.315912i | \(-0.897690\pi\) | ||||
−0.948789 | + | 0.315912i | \(0.897690\pi\) | |||||||
\(182\) | 20.6536 | 1.53095 | ||||||||
\(183\) | 2.64471 | 0.195502 | ||||||||
\(184\) | −2.97729 | −0.219489 | ||||||||
\(185\) | −18.7393 | −1.37774 | ||||||||
\(186\) | −31.0573 | −2.27723 | ||||||||
\(187\) | −0.195619 | −0.0143051 | ||||||||
\(188\) | −12.4279 | −0.906400 | ||||||||
\(189\) | −88.4892 | −6.43664 | ||||||||
\(190\) | −1.45986 | −0.105909 | ||||||||
\(191\) | 4.04315 | 0.292552 | 0.146276 | − | 0.989244i | \(-0.453271\pi\) | ||||
0.146276 | + | 0.989244i | \(0.453271\pi\) | |||||||
\(192\) | −3.34571 | −0.241456 | ||||||||
\(193\) | −3.19342 | −0.229867 | −0.114934 | − | 0.993373i | \(-0.536666\pi\) | ||||
−0.114934 | + | 0.993373i | \(0.536666\pi\) | |||||||
\(194\) | −10.1195 | −0.726535 | ||||||||
\(195\) | −49.4546 | −3.54152 | ||||||||
\(196\) | 18.9322 | 1.35230 | ||||||||
\(197\) | −6.83509 | −0.486980 | −0.243490 | − | 0.969903i | \(-0.578292\pi\) | ||||
−0.243490 | + | 0.969903i | \(0.578292\pi\) | |||||||
\(198\) | 1.85000 | 0.131474 | ||||||||
\(199\) | −25.4649 | −1.80516 | −0.902578 | − | 0.430527i | \(-0.858328\pi\) | ||||
−0.902578 | + | 0.430527i | \(0.858328\pi\) | |||||||
\(200\) | −8.28261 | −0.585669 | ||||||||
\(201\) | 13.6597 | 0.963479 | ||||||||
\(202\) | −15.5250 | −1.09234 | ||||||||
\(203\) | −11.1552 | −0.782943 | ||||||||
\(204\) | −2.89876 | −0.202954 | ||||||||
\(205\) | 16.4238 | 1.14709 | ||||||||
\(206\) | −12.2172 | −0.851210 | ||||||||
\(207\) | 24.3952 | 1.69558 | ||||||||
\(208\) | −4.05580 | −0.281219 | ||||||||
\(209\) | 0.0904392 | 0.00625581 | ||||||||
\(210\) | −62.0940 | −4.28489 | ||||||||
\(211\) | −16.3806 | −1.12769 | −0.563845 | − | 0.825881i | \(-0.690678\pi\) | ||||
−0.563845 | + | 0.825881i | \(0.690678\pi\) | |||||||
\(212\) | −1.83001 | −0.125685 | ||||||||
\(213\) | 33.4376 | 2.29111 | ||||||||
\(214\) | 1.19286 | 0.0815423 | ||||||||
\(215\) | −21.5120 | −1.46711 | ||||||||
\(216\) | 17.3768 | 1.18234 | ||||||||
\(217\) | −47.2711 | −3.20897 | ||||||||
\(218\) | 4.15216 | 0.281220 | ||||||||
\(219\) | −31.0990 | −2.10147 | ||||||||
\(220\) | 0.822867 | 0.0554777 | ||||||||
\(221\) | −3.51399 | −0.236377 | ||||||||
\(222\) | 17.2028 | 1.15458 | ||||||||
\(223\) | 6.01176 | 0.402577 | 0.201288 | − | 0.979532i | \(-0.435487\pi\) | ||||
0.201288 | + | 0.979532i | \(0.435487\pi\) | |||||||
\(224\) | −5.09237 | −0.340248 | ||||||||
\(225\) | 67.8657 | 4.52438 | ||||||||
\(226\) | −10.4021 | −0.691940 | ||||||||
\(227\) | 6.55876 | 0.435320 | 0.217660 | − | 0.976025i | \(-0.430158\pi\) | ||||
0.217660 | + | 0.976025i | \(0.430158\pi\) | |||||||
\(228\) | 1.34016 | 0.0887543 | ||||||||
\(229\) | 28.6438 | 1.89284 | 0.946418 | − | 0.322945i | \(-0.104673\pi\) | ||||
0.946418 | + | 0.322945i | \(0.104673\pi\) | |||||||
\(230\) | 10.8508 | 0.715482 | ||||||||
\(231\) | 3.84677 | 0.253099 | ||||||||
\(232\) | 2.19058 | 0.143818 | ||||||||
\(233\) | −1.09835 | −0.0719551 | −0.0359776 | − | 0.999353i | \(-0.511454\pi\) | ||||
−0.0359776 | + | 0.999353i | \(0.511454\pi\) | |||||||
\(234\) | 33.2323 | 2.17246 | ||||||||
\(235\) | 45.2940 | 2.95465 | ||||||||
\(236\) | 9.30416 | 0.605650 | ||||||||
\(237\) | −26.8482 | −1.74398 | ||||||||
\(238\) | −4.41208 | −0.285993 | ||||||||
\(239\) | −21.8676 | −1.41450 | −0.707249 | − | 0.706964i | \(-0.750064\pi\) | ||||
−0.707249 | + | 0.706964i | \(0.750064\pi\) | |||||||
\(240\) | 12.1935 | 0.787089 | ||||||||
\(241\) | −20.6562 | −1.33058 | −0.665291 | − | 0.746584i | \(-0.731693\pi\) | ||||
−0.665291 | + | 0.746584i | \(0.731693\pi\) | |||||||
\(242\) | 10.9490 | 0.703830 | ||||||||
\(243\) | −60.1397 | −3.85797 | ||||||||
\(244\) | −0.790477 | −0.0506051 | ||||||||
\(245\) | −68.9990 | −4.40818 | ||||||||
\(246\) | −15.0772 | −0.961285 | ||||||||
\(247\) | 1.62460 | 0.103371 | ||||||||
\(248\) | 9.28273 | 0.589454 | ||||||||
\(249\) | −13.1054 | −0.830520 | ||||||||
\(250\) | 11.9636 | 0.756642 | ||||||||
\(251\) | 12.0655 | 0.761569 | 0.380784 | − | 0.924664i | \(-0.375654\pi\) | ||||
0.380784 | + | 0.924664i | \(0.375654\pi\) | |||||||
\(252\) | 41.7257 | 2.62847 | ||||||||
\(253\) | −0.672216 | −0.0422619 | ||||||||
\(254\) | −4.03373 | −0.253099 | ||||||||
\(255\) | 10.5646 | 0.661582 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 29.6448 | 1.84919 | 0.924597 | − | 0.380948i | \(-0.124402\pi\) | ||||
0.924597 | + | 0.380948i | \(0.124402\pi\) | |||||||
\(258\) | 19.7482 | 1.22947 | ||||||||
\(259\) | 26.1838 | 1.62698 | ||||||||
\(260\) | 14.7815 | 0.916710 | ||||||||
\(261\) | −17.9491 | −1.11102 | ||||||||
\(262\) | 0.688921 | 0.0425617 | ||||||||
\(263\) | −25.3004 | −1.56009 | −0.780043 | − | 0.625725i | \(-0.784803\pi\) | ||||
−0.780043 | + | 0.625725i | \(0.784803\pi\) | |||||||
\(264\) | −0.755399 | −0.0464916 | ||||||||
\(265\) | 6.66952 | 0.409705 | ||||||||
\(266\) | 2.03980 | 0.125068 | ||||||||
\(267\) | 42.3421 | 2.59130 | ||||||||
\(268\) | −4.08274 | −0.249393 | ||||||||
\(269\) | −13.3561 | −0.814336 | −0.407168 | − | 0.913353i | \(-0.633484\pi\) | ||||
−0.407168 | + | 0.913353i | \(0.633484\pi\) | |||||||
\(270\) | −63.3304 | −3.85416 | ||||||||
\(271\) | −4.66595 | −0.283436 | −0.141718 | − | 0.989907i | \(-0.545263\pi\) | ||||
−0.141718 | + | 0.989907i | \(0.545263\pi\) | |||||||
\(272\) | 0.866411 | 0.0525339 | ||||||||
\(273\) | 69.1011 | 4.18219 | ||||||||
\(274\) | −14.0944 | −0.851476 | ||||||||
\(275\) | −1.87006 | −0.112769 | ||||||||
\(276\) | −9.96114 | −0.599590 | ||||||||
\(277\) | 9.79161 | 0.588321 | 0.294160 | − | 0.955756i | \(-0.404960\pi\) | ||||
0.294160 | + | 0.955756i | \(0.404960\pi\) | |||||||
\(278\) | −11.0608 | −0.663386 | ||||||||
\(279\) | −76.0605 | −4.55362 | ||||||||
\(280\) | 18.5593 | 1.10913 | ||||||||
\(281\) | −18.8851 | −1.12659 | −0.563294 | − | 0.826256i | \(-0.690466\pi\) | ||||
−0.563294 | + | 0.826256i | \(0.690466\pi\) | |||||||
\(282\) | −41.5802 | −2.47607 | ||||||||
\(283\) | −16.2713 | −0.967226 | −0.483613 | − | 0.875282i | \(-0.660676\pi\) | ||||
−0.483613 | + | 0.875282i | \(0.660676\pi\) | |||||||
\(284\) | −9.99418 | −0.593046 | ||||||||
\(285\) | −4.88426 | −0.289318 | ||||||||
\(286\) | −0.915725 | −0.0541480 | ||||||||
\(287\) | −22.9484 | −1.35460 | ||||||||
\(288\) | −8.19376 | −0.482822 | ||||||||
\(289\) | −16.2493 | −0.955843 | ||||||||
\(290\) | −7.98362 | −0.468814 | ||||||||
\(291\) | −33.8568 | −1.98472 | ||||||||
\(292\) | 9.29518 | 0.543960 | ||||||||
\(293\) | −0.296281 | −0.0173089 | −0.00865447 | − | 0.999963i | \(-0.502755\pi\) | ||||
−0.00865447 | + | 0.999963i | \(0.502755\pi\) | |||||||
\(294\) | 63.3416 | 3.69416 | ||||||||
\(295\) | −33.9093 | −1.97428 | ||||||||
\(296\) | −5.14177 | −0.298859 | ||||||||
\(297\) | 3.92336 | 0.227657 | ||||||||
\(298\) | 9.28809 | 0.538045 | ||||||||
\(299\) | −12.0753 | −0.698333 | ||||||||
\(300\) | −27.7112 | −1.59991 | ||||||||
\(301\) | 30.0580 | 1.73251 | ||||||||
\(302\) | −0.175333 | −0.0100893 | ||||||||
\(303\) | −51.9422 | −2.98400 | ||||||||
\(304\) | −0.400561 | −0.0229738 | ||||||||
\(305\) | 2.88092 | 0.164961 | ||||||||
\(306\) | −7.09917 | −0.405832 | ||||||||
\(307\) | 33.7428 | 1.92580 | 0.962902 | − | 0.269852i | \(-0.0869748\pi\) | ||||
0.962902 | + | 0.269852i | \(0.0869748\pi\) | |||||||
\(308\) | −1.14976 | −0.0655138 | ||||||||
\(309\) | −40.8751 | −2.32530 | ||||||||
\(310\) | −33.8312 | −1.92148 | ||||||||
\(311\) | 29.1852 | 1.65494 | 0.827470 | − | 0.561510i | \(-0.189779\pi\) | ||||
0.827470 | + | 0.561510i | \(0.189779\pi\) | |||||||
\(312\) | −13.5695 | −0.768224 | ||||||||
\(313\) | −14.9698 | −0.846141 | −0.423070 | − | 0.906097i | \(-0.639048\pi\) | ||||
−0.423070 | + | 0.906097i | \(0.639048\pi\) | |||||||
\(314\) | 16.2661 | 0.917947 | ||||||||
\(315\) | −152.070 | −8.56820 | ||||||||
\(316\) | 8.02468 | 0.451424 | ||||||||
\(317\) | −13.0581 | −0.733415 | −0.366707 | − | 0.930336i | \(-0.619515\pi\) | ||||
−0.366707 | + | 0.930336i | \(0.619515\pi\) | |||||||
\(318\) | −6.12267 | −0.343342 | ||||||||
\(319\) | 0.494591 | 0.0276918 | ||||||||
\(320\) | −3.64453 | −0.203735 | ||||||||
\(321\) | 3.99097 | 0.222754 | ||||||||
\(322\) | −15.1614 | −0.844914 | ||||||||
\(323\) | −0.347051 | −0.0193104 | ||||||||
\(324\) | 33.5565 | 1.86425 | ||||||||
\(325\) | −33.5926 | −1.86338 | ||||||||
\(326\) | −12.4851 | −0.691485 | ||||||||
\(327\) | 13.8919 | 0.768226 | ||||||||
\(328\) | 4.50642 | 0.248826 | ||||||||
\(329\) | −63.2876 | −3.48916 | ||||||||
\(330\) | 2.75307 | 0.151552 | ||||||||
\(331\) | −25.7235 | −1.41389 | −0.706946 | − | 0.707267i | \(-0.749928\pi\) | ||||
−0.706946 | + | 0.707267i | \(0.749928\pi\) | |||||||
\(332\) | 3.91707 | 0.214977 | ||||||||
\(333\) | 42.1304 | 2.30873 | ||||||||
\(334\) | 16.5947 | 0.908019 | ||||||||
\(335\) | 14.8797 | 0.812964 | ||||||||
\(336\) | −17.0376 | −0.929476 | ||||||||
\(337\) | 24.5965 | 1.33986 | 0.669928 | − | 0.742426i | \(-0.266325\pi\) | ||||
0.669928 | + | 0.742426i | \(0.266325\pi\) | |||||||
\(338\) | −3.44955 | −0.187631 | ||||||||
\(339\) | −34.8025 | −1.89021 | ||||||||
\(340\) | −3.15766 | −0.171248 | ||||||||
\(341\) | 2.09587 | 0.113498 | ||||||||
\(342\) | 3.28210 | 0.177476 | ||||||||
\(343\) | 60.7631 | 3.28090 | ||||||||
\(344\) | −5.90255 | −0.318244 | ||||||||
\(345\) | 36.3037 | 1.95452 | ||||||||
\(346\) | 11.0918 | 0.596299 | ||||||||
\(347\) | 16.7055 | 0.896797 | 0.448399 | − | 0.893834i | \(-0.351995\pi\) | ||||
0.448399 | + | 0.893834i | \(0.351995\pi\) | |||||||
\(348\) | 7.32903 | 0.392877 | ||||||||
\(349\) | 14.6391 | 0.783615 | 0.391807 | − | 0.920047i | \(-0.371850\pi\) | ||||
0.391807 | + | 0.920047i | \(0.371850\pi\) | |||||||
\(350\) | −42.1781 | −2.25451 | ||||||||
\(351\) | 70.4770 | 3.76178 | ||||||||
\(352\) | 0.225781 | 0.0120342 | ||||||||
\(353\) | −26.0658 | −1.38734 | −0.693670 | − | 0.720293i | \(-0.744007\pi\) | ||||
−0.693670 | + | 0.720293i | \(0.744007\pi\) | |||||||
\(354\) | 31.1290 | 1.65449 | ||||||||
\(355\) | 36.4241 | 1.93319 | ||||||||
\(356\) | −12.6557 | −0.670748 | ||||||||
\(357\) | −14.7615 | −0.781264 | ||||||||
\(358\) | −18.2533 | −0.964714 | ||||||||
\(359\) | 1.94679 | 0.102748 | 0.0513738 | − | 0.998679i | \(-0.483640\pi\) | ||||
0.0513738 | + | 0.998679i | \(0.483640\pi\) | |||||||
\(360\) | 29.8624 | 1.57389 | ||||||||
\(361\) | −18.8396 | −0.991555 | ||||||||
\(362\) | 25.5293 | 1.34179 | ||||||||
\(363\) | 36.6322 | 1.92269 | ||||||||
\(364\) | −20.6536 | −1.08255 | ||||||||
\(365\) | −33.8766 | −1.77318 | ||||||||
\(366\) | −2.64471 | −0.138241 | ||||||||
\(367\) | 10.8315 | 0.565401 | 0.282700 | − | 0.959208i | \(-0.408770\pi\) | ||||
0.282700 | + | 0.959208i | \(0.408770\pi\) | |||||||
\(368\) | 2.97729 | 0.155202 | ||||||||
\(369\) | −36.9246 | −1.92222 | ||||||||
\(370\) | 18.7393 | 0.974211 | ||||||||
\(371\) | −9.31907 | −0.483822 | ||||||||
\(372\) | 31.0573 | 1.61025 | ||||||||
\(373\) | −36.4854 | −1.88914 | −0.944571 | − | 0.328307i | \(-0.893522\pi\) | ||||
−0.944571 | + | 0.328307i | \(0.893522\pi\) | |||||||
\(374\) | 0.195619 | 0.0101152 | ||||||||
\(375\) | 40.0266 | 2.06696 | ||||||||
\(376\) | 12.4279 | 0.640921 | ||||||||
\(377\) | 8.88455 | 0.457577 | ||||||||
\(378\) | 88.4892 | 4.55139 | ||||||||
\(379\) | −16.7914 | −0.862518 | −0.431259 | − | 0.902228i | \(-0.641930\pi\) | ||||
−0.431259 | + | 0.902228i | \(0.641930\pi\) | |||||||
\(380\) | 1.45986 | 0.0748891 | ||||||||
\(381\) | −13.4957 | −0.691405 | ||||||||
\(382\) | −4.04315 | −0.206866 | ||||||||
\(383\) | −10.2072 | −0.521563 | −0.260782 | − | 0.965398i | \(-0.583980\pi\) | ||||
−0.260782 | + | 0.965398i | \(0.583980\pi\) | |||||||
\(384\) | 3.34571 | 0.170735 | ||||||||
\(385\) | 4.19034 | 0.213560 | ||||||||
\(386\) | 3.19342 | 0.162541 | ||||||||
\(387\) | 48.3641 | 2.45849 | ||||||||
\(388\) | 10.1195 | 0.513738 | ||||||||
\(389\) | 19.7850 | 1.00314 | 0.501569 | − | 0.865118i | \(-0.332757\pi\) | ||||
0.501569 | + | 0.865118i | \(0.332757\pi\) | |||||||
\(390\) | 49.4546 | 2.50423 | ||||||||
\(391\) | 2.57956 | 0.130454 | ||||||||
\(392\) | −18.9322 | −0.956221 | ||||||||
\(393\) | 2.30493 | 0.116268 | ||||||||
\(394\) | 6.83509 | 0.344347 | ||||||||
\(395\) | −29.2462 | −1.47154 | ||||||||
\(396\) | −1.85000 | −0.0929660 | ||||||||
\(397\) | −6.55430 | −0.328951 | −0.164476 | − | 0.986381i | \(-0.552593\pi\) | ||||
−0.164476 | + | 0.986381i | \(0.552593\pi\) | |||||||
\(398\) | 25.4649 | 1.27644 | ||||||||
\(399\) | 6.82459 | 0.341657 | ||||||||
\(400\) | 8.28261 | 0.414130 | ||||||||
\(401\) | −17.7763 | −0.887707 | −0.443854 | − | 0.896099i | \(-0.646389\pi\) | ||||
−0.443854 | + | 0.896099i | \(0.646389\pi\) | |||||||
\(402\) | −13.6597 | −0.681282 | ||||||||
\(403\) | 37.6489 | 1.87543 | ||||||||
\(404\) | 15.5250 | 0.772399 | ||||||||
\(405\) | −122.298 | −6.07702 | ||||||||
\(406\) | 11.1552 | 0.553624 | ||||||||
\(407\) | −1.16091 | −0.0575444 | ||||||||
\(408\) | 2.89876 | 0.143510 | ||||||||
\(409\) | 28.7471 | 1.42145 | 0.710726 | − | 0.703469i | \(-0.248366\pi\) | ||||
0.710726 | + | 0.703469i | \(0.248366\pi\) | |||||||
\(410\) | −16.4238 | −0.811113 | ||||||||
\(411\) | −47.1559 | −2.32603 | ||||||||
\(412\) | 12.2172 | 0.601896 | ||||||||
\(413\) | 47.3802 | 2.33143 | ||||||||
\(414\) | −24.3952 | −1.19896 | ||||||||
\(415\) | −14.2759 | −0.700776 | ||||||||
\(416\) | 4.05580 | 0.198852 | ||||||||
\(417\) | −37.0064 | −1.81221 | ||||||||
\(418\) | −0.0904392 | −0.00442353 | ||||||||
\(419\) | 25.2111 | 1.23164 | 0.615821 | − | 0.787886i | \(-0.288824\pi\) | ||||
0.615821 | + | 0.787886i | \(0.288824\pi\) | |||||||
\(420\) | 62.0940 | 3.02988 | ||||||||
\(421\) | −12.9193 | −0.629648 | −0.314824 | − | 0.949150i | \(-0.601946\pi\) | ||||
−0.314824 | + | 0.949150i | \(0.601946\pi\) | |||||||
\(422\) | 16.3806 | 0.797397 | ||||||||
\(423\) | −101.832 | −4.95122 | ||||||||
\(424\) | 1.83001 | 0.0888730 | ||||||||
\(425\) | 7.17614 | 0.348094 | ||||||||
\(426\) | −33.4376 | −1.62006 | ||||||||
\(427\) | −4.02540 | −0.194803 | ||||||||
\(428\) | −1.19286 | −0.0576591 | ||||||||
\(429\) | −3.06375 | −0.147919 | ||||||||
\(430\) | 21.5120 | 1.03740 | ||||||||
\(431\) | −14.8705 | −0.716286 | −0.358143 | − | 0.933667i | \(-0.616590\pi\) | ||||
−0.358143 | + | 0.933667i | \(0.616590\pi\) | |||||||
\(432\) | −17.3768 | −0.836043 | ||||||||
\(433\) | 15.3636 | 0.738328 | 0.369164 | − | 0.929364i | \(-0.379644\pi\) | ||||
0.369164 | + | 0.929364i | \(0.379644\pi\) | |||||||
\(434\) | 47.2711 | 2.26908 | ||||||||
\(435\) | −26.7109 | −1.28069 | ||||||||
\(436\) | −4.15216 | −0.198853 | ||||||||
\(437\) | −1.19259 | −0.0570491 | ||||||||
\(438\) | 31.0990 | 1.48597 | ||||||||
\(439\) | 33.0583 | 1.57779 | 0.788894 | − | 0.614530i | \(-0.210654\pi\) | ||||
0.788894 | + | 0.614530i | \(0.210654\pi\) | |||||||
\(440\) | −0.822867 | −0.0392287 | ||||||||
\(441\) | 155.126 | 7.38695 | ||||||||
\(442\) | 3.51399 | 0.167144 | ||||||||
\(443\) | −3.60408 | −0.171235 | −0.0856175 | − | 0.996328i | \(-0.527286\pi\) | ||||
−0.0856175 | + | 0.996328i | \(0.527286\pi\) | |||||||
\(444\) | −17.2028 | −0.816411 | ||||||||
\(445\) | 46.1239 | 2.18648 | ||||||||
\(446\) | −6.01176 | −0.284665 | ||||||||
\(447\) | 31.0753 | 1.46981 | ||||||||
\(448\) | 5.09237 | 0.240592 | ||||||||
\(449\) | −2.73595 | −0.129118 | −0.0645588 | − | 0.997914i | \(-0.520564\pi\) | ||||
−0.0645588 | + | 0.997914i | \(0.520564\pi\) | |||||||
\(450\) | −67.8657 | −3.19922 | ||||||||
\(451\) | 1.01747 | 0.0479106 | ||||||||
\(452\) | 10.4021 | 0.489276 | ||||||||
\(453\) | −0.586614 | −0.0275615 | ||||||||
\(454\) | −6.55876 | −0.307818 | ||||||||
\(455\) | 75.2728 | 3.52885 | ||||||||
\(456\) | −1.34016 | −0.0627588 | ||||||||
\(457\) | −5.07560 | −0.237426 | −0.118713 | − | 0.992929i | \(-0.537877\pi\) | ||||
−0.118713 | + | 0.992929i | \(0.537877\pi\) | |||||||
\(458\) | −28.6438 | −1.33844 | ||||||||
\(459\) | −15.0555 | −0.702729 | ||||||||
\(460\) | −10.8508 | −0.505922 | ||||||||
\(461\) | 25.3870 | 1.18239 | 0.591195 | − | 0.806528i | \(-0.298656\pi\) | ||||
0.591195 | + | 0.806528i | \(0.298656\pi\) | |||||||
\(462\) | −3.84677 | −0.178968 | ||||||||
\(463\) | 17.4199 | 0.809572 | 0.404786 | − | 0.914411i | \(-0.367346\pi\) | ||||
0.404786 | + | 0.914411i | \(0.367346\pi\) | |||||||
\(464\) | −2.19058 | −0.101695 | ||||||||
\(465\) | −113.189 | −5.24903 | ||||||||
\(466\) | 1.09835 | 0.0508800 | ||||||||
\(467\) | 34.1750 | 1.58143 | 0.790715 | − | 0.612185i | \(-0.209709\pi\) | ||||
0.790715 | + | 0.612185i | \(0.209709\pi\) | |||||||
\(468\) | −33.2323 | −1.53616 | ||||||||
\(469\) | −20.7908 | −0.960031 | ||||||||
\(470\) | −45.2940 | −2.08925 | ||||||||
\(471\) | 54.4215 | 2.50761 | ||||||||
\(472\) | −9.30416 | −0.428259 | ||||||||
\(473\) | −1.33269 | −0.0612770 | ||||||||
\(474\) | 26.8482 | 1.23318 | ||||||||
\(475\) | −3.31769 | −0.152226 | ||||||||
\(476\) | 4.41208 | 0.202227 | ||||||||
\(477\) | −14.9946 | −0.686558 | ||||||||
\(478\) | 21.8676 | 1.00020 | ||||||||
\(479\) | −43.0987 | −1.96923 | −0.984615 | − | 0.174740i | \(-0.944092\pi\) | ||||
−0.984615 | + | 0.174740i | \(0.944092\pi\) | |||||||
\(480\) | −12.1935 | −0.556556 | ||||||||
\(481\) | −20.8540 | −0.950860 | ||||||||
\(482\) | 20.6562 | 0.940864 | ||||||||
\(483\) | −50.7258 | −2.30810 | ||||||||
\(484\) | −10.9490 | −0.497683 | ||||||||
\(485\) | −36.8807 | −1.67467 | ||||||||
\(486\) | 60.1397 | 2.72799 | ||||||||
\(487\) | 20.2072 | 0.915674 | 0.457837 | − | 0.889036i | \(-0.348624\pi\) | ||||
0.457837 | + | 0.889036i | \(0.348624\pi\) | |||||||
\(488\) | 0.790477 | 0.0357832 | ||||||||
\(489\) | −41.7715 | −1.88897 | ||||||||
\(490\) | 68.9990 | 3.11706 | ||||||||
\(491\) | 8.40833 | 0.379463 | 0.189731 | − | 0.981836i | \(-0.439238\pi\) | ||||
0.189731 | + | 0.981836i | \(0.439238\pi\) | |||||||
\(492\) | 15.0772 | 0.679731 | ||||||||
\(493\) | −1.89794 | −0.0854789 | ||||||||
\(494\) | −1.62460 | −0.0730941 | ||||||||
\(495\) | 6.74238 | 0.303047 | ||||||||
\(496\) | −9.28273 | −0.416807 | ||||||||
\(497\) | −50.8941 | −2.28291 | ||||||||
\(498\) | 13.1054 | 0.587266 | ||||||||
\(499\) | 12.9379 | 0.579180 | 0.289590 | − | 0.957151i | \(-0.406481\pi\) | ||||
0.289590 | + | 0.957151i | \(0.406481\pi\) | |||||||
\(500\) | −11.9636 | −0.535027 | ||||||||
\(501\) | 55.5209 | 2.48049 | ||||||||
\(502\) | −12.0655 | −0.538511 | ||||||||
\(503\) | 13.0734 | 0.582912 | 0.291456 | − | 0.956584i | \(-0.405860\pi\) | ||||
0.291456 | + | 0.956584i | \(0.405860\pi\) | |||||||
\(504\) | −41.7257 | −1.85861 | ||||||||
\(505\) | −56.5814 | −2.51784 | ||||||||
\(506\) | 0.672216 | 0.0298837 | ||||||||
\(507\) | −11.5412 | −0.512562 | ||||||||
\(508\) | 4.03373 | 0.178968 | ||||||||
\(509\) | −24.1204 | −1.06912 | −0.534560 | − | 0.845131i | \(-0.679523\pi\) | ||||
−0.534560 | + | 0.845131i | \(0.679523\pi\) | |||||||
\(510\) | −10.5646 | −0.467809 | ||||||||
\(511\) | 47.3345 | 2.09395 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 6.96048 | 0.307313 | ||||||||
\(514\) | −29.6448 | −1.30758 | ||||||||
\(515\) | −44.5258 | −1.96204 | ||||||||
\(516\) | −19.7482 | −0.869367 | ||||||||
\(517\) | 2.80599 | 0.123408 | ||||||||
\(518\) | −26.1838 | −1.15045 | ||||||||
\(519\) | 37.1099 | 1.62894 | ||||||||
\(520\) | −14.7815 | −0.648212 | ||||||||
\(521\) | −19.2528 | −0.843482 | −0.421741 | − | 0.906716i | \(-0.638581\pi\) | ||||
−0.421741 | + | 0.906716i | \(0.638581\pi\) | |||||||
\(522\) | 17.9491 | 0.785609 | ||||||||
\(523\) | −1.14698 | −0.0501538 | −0.0250769 | − | 0.999686i | \(-0.507983\pi\) | ||||
−0.0250769 | + | 0.999686i | \(0.507983\pi\) | |||||||
\(524\) | −0.688921 | −0.0300957 | ||||||||
\(525\) | −141.116 | −6.15879 | ||||||||
\(526\) | 25.3004 | 1.10315 | ||||||||
\(527\) | −8.04266 | −0.350344 | ||||||||
\(528\) | 0.755399 | 0.0328745 | ||||||||
\(529\) | −14.1358 | −0.614598 | ||||||||
\(530\) | −6.66952 | −0.289705 | ||||||||
\(531\) | 76.2361 | 3.30837 | ||||||||
\(532\) | −2.03980 | −0.0884367 | ||||||||
\(533\) | 18.2772 | 0.791672 | ||||||||
\(534\) | −42.3421 | −1.83232 | ||||||||
\(535\) | 4.34742 | 0.187955 | ||||||||
\(536\) | 4.08274 | 0.176348 | ||||||||
\(537\) | −61.0701 | −2.63537 | ||||||||
\(538\) | 13.3561 | 0.575822 | ||||||||
\(539\) | −4.27454 | −0.184117 | ||||||||
\(540\) | 63.3304 | 2.72531 | ||||||||
\(541\) | −6.64322 | −0.285614 | −0.142807 | − | 0.989751i | \(-0.545613\pi\) | ||||
−0.142807 | + | 0.989751i | \(0.545613\pi\) | |||||||
\(542\) | 4.66595 | 0.200420 | ||||||||
\(543\) | 85.4136 | 3.66545 | ||||||||
\(544\) | −0.866411 | −0.0371471 | ||||||||
\(545\) | 15.1327 | 0.648213 | ||||||||
\(546\) | −69.1011 | −2.95725 | ||||||||
\(547\) | 37.3406 | 1.59657 | 0.798283 | − | 0.602282i | \(-0.205742\pi\) | ||||
0.798283 | + | 0.602282i | \(0.205742\pi\) | |||||||
\(548\) | 14.0944 | 0.602084 | ||||||||
\(549\) | −6.47698 | −0.276431 | ||||||||
\(550\) | 1.87006 | 0.0797396 | ||||||||
\(551\) | 0.877459 | 0.0373810 | ||||||||
\(552\) | 9.96114 | 0.423974 | ||||||||
\(553\) | 40.8646 | 1.73774 | ||||||||
\(554\) | −9.79161 | −0.416006 | ||||||||
\(555\) | 62.6963 | 2.66131 | ||||||||
\(556\) | 11.0608 | 0.469084 | ||||||||
\(557\) | −36.5932 | −1.55050 | −0.775252 | − | 0.631652i | \(-0.782377\pi\) | ||||
−0.775252 | + | 0.631652i | \(0.782377\pi\) | |||||||
\(558\) | 76.0605 | 3.21990 | ||||||||
\(559\) | −23.9396 | −1.01254 | ||||||||
\(560\) | −18.5593 | −0.784273 | ||||||||
\(561\) | 0.654486 | 0.0276324 | ||||||||
\(562\) | 18.8851 | 0.796618 | ||||||||
\(563\) | 4.53101 | 0.190959 | 0.0954797 | − | 0.995431i | \(-0.469562\pi\) | ||||
0.0954797 | + | 0.995431i | \(0.469562\pi\) | |||||||
\(564\) | 41.5802 | 1.75084 | ||||||||
\(565\) | −37.9109 | −1.59492 | ||||||||
\(566\) | 16.2713 | 0.683932 | ||||||||
\(567\) | 170.882 | 7.17637 | ||||||||
\(568\) | 9.99418 | 0.419347 | ||||||||
\(569\) | −9.92421 | −0.416044 | −0.208022 | − | 0.978124i | \(-0.566703\pi\) | ||||
−0.208022 | + | 0.978124i | \(0.566703\pi\) | |||||||
\(570\) | 4.88426 | 0.204579 | ||||||||
\(571\) | 14.5818 | 0.610229 | 0.305115 | − | 0.952316i | \(-0.401305\pi\) | ||||
0.305115 | + | 0.952316i | \(0.401305\pi\) | |||||||
\(572\) | 0.915725 | 0.0382884 | ||||||||
\(573\) | −13.5272 | −0.565108 | ||||||||
\(574\) | 22.9484 | 0.957846 | ||||||||
\(575\) | 24.6597 | 1.02838 | ||||||||
\(576\) | 8.19376 | 0.341407 | ||||||||
\(577\) | −26.4842 | −1.10255 | −0.551275 | − | 0.834324i | \(-0.685859\pi\) | ||||
−0.551275 | + | 0.834324i | \(0.685859\pi\) | |||||||
\(578\) | 16.2493 | 0.675883 | ||||||||
\(579\) | 10.6842 | 0.444022 | ||||||||
\(580\) | 7.98362 | 0.331502 | ||||||||
\(581\) | 19.9472 | 0.827548 | ||||||||
\(582\) | 33.8568 | 1.40341 | ||||||||
\(583\) | 0.413182 | 0.0171122 | ||||||||
\(584\) | −9.29518 | −0.384637 | ||||||||
\(585\) | 121.116 | 5.00754 | ||||||||
\(586\) | 0.296281 | 0.0122393 | ||||||||
\(587\) | −26.0865 | −1.07671 | −0.538353 | − | 0.842720i | \(-0.680953\pi\) | ||||
−0.538353 | + | 0.842720i | \(0.680953\pi\) | |||||||
\(588\) | −63.3416 | −2.61216 | ||||||||
\(589\) | 3.71830 | 0.153210 | ||||||||
\(590\) | 33.9093 | 1.39602 | ||||||||
\(591\) | 22.8682 | 0.940673 | ||||||||
\(592\) | 5.14177 | 0.211325 | ||||||||
\(593\) | −14.6531 | −0.601730 | −0.300865 | − | 0.953667i | \(-0.597275\pi\) | ||||
−0.300865 | + | 0.953667i | \(0.597275\pi\) | |||||||
\(594\) | −3.92336 | −0.160978 | ||||||||
\(595\) | −16.0800 | −0.659215 | ||||||||
\(596\) | −9.28809 | −0.380455 | ||||||||
\(597\) | 85.1980 | 3.48692 | ||||||||
\(598\) | 12.0753 | 0.493796 | ||||||||
\(599\) | −2.09562 | −0.0856249 | −0.0428125 | − | 0.999083i | \(-0.513632\pi\) | ||||
−0.0428125 | + | 0.999083i | \(0.513632\pi\) | |||||||
\(600\) | 27.7112 | 1.13130 | ||||||||
\(601\) | 17.1605 | 0.699990 | 0.349995 | − | 0.936752i | \(-0.386183\pi\) | ||||
0.349995 | + | 0.936752i | \(0.386183\pi\) | |||||||
\(602\) | −30.0580 | −1.22507 | ||||||||
\(603\) | −33.4530 | −1.36231 | ||||||||
\(604\) | 0.175333 | 0.00713421 | ||||||||
\(605\) | 39.9041 | 1.62233 | ||||||||
\(606\) | 51.9422 | 2.11001 | ||||||||
\(607\) | 22.1521 | 0.899126 | 0.449563 | − | 0.893249i | \(-0.351580\pi\) | ||||
0.449563 | + | 0.893249i | \(0.351580\pi\) | |||||||
\(608\) | 0.400561 | 0.0162449 | ||||||||
\(609\) | 37.3221 | 1.51237 | ||||||||
\(610\) | −2.88092 | −0.116645 | ||||||||
\(611\) | 50.4052 | 2.03918 | ||||||||
\(612\) | 7.09917 | 0.286967 | ||||||||
\(613\) | −13.3345 | −0.538576 | −0.269288 | − | 0.963060i | \(-0.586788\pi\) | ||||
−0.269288 | + | 0.963060i | \(0.586788\pi\) | |||||||
\(614\) | −33.7428 | −1.36175 | ||||||||
\(615\) | −54.9492 | −2.21577 | ||||||||
\(616\) | 1.14976 | 0.0463252 | ||||||||
\(617\) | 8.10512 | 0.326300 | 0.163150 | − | 0.986601i | \(-0.447835\pi\) | ||||
0.163150 | + | 0.986601i | \(0.447835\pi\) | |||||||
\(618\) | 40.8751 | 1.64424 | ||||||||
\(619\) | −24.3681 | −0.979436 | −0.489718 | − | 0.871881i | \(-0.662900\pi\) | ||||
−0.489718 | + | 0.871881i | \(0.662900\pi\) | |||||||
\(620\) | 33.8312 | 1.35869 | ||||||||
\(621\) | −51.7358 | −2.07609 | ||||||||
\(622\) | −29.1852 | −1.17022 | ||||||||
\(623\) | −64.4472 | −2.58202 | ||||||||
\(624\) | 13.5695 | 0.543216 | ||||||||
\(625\) | 2.18853 | 0.0875412 | ||||||||
\(626\) | 14.9698 | 0.598312 | ||||||||
\(627\) | −0.302583 | −0.0120840 | ||||||||
\(628\) | −16.2661 | −0.649087 | ||||||||
\(629\) | 4.45488 | 0.177628 | ||||||||
\(630\) | 152.070 | 6.05863 | ||||||||
\(631\) | −28.1349 | −1.12003 | −0.560017 | − | 0.828481i | \(-0.689205\pi\) | ||||
−0.560017 | + | 0.828481i | \(0.689205\pi\) | |||||||
\(632\) | −8.02468 | −0.319205 | ||||||||
\(633\) | 54.8048 | 2.17830 | ||||||||
\(634\) | 13.0581 | 0.518602 | ||||||||
\(635\) | −14.7010 | −0.583393 | ||||||||
\(636\) | 6.12267 | 0.242780 | ||||||||
\(637\) | −76.7853 | −3.04234 | ||||||||
\(638\) | −0.494591 | −0.0195811 | ||||||||
\(639\) | −81.8900 | −3.23952 | ||||||||
\(640\) | 3.64453 | 0.144063 | ||||||||
\(641\) | −28.2380 | −1.11533 | −0.557667 | − | 0.830065i | \(-0.688303\pi\) | ||||
−0.557667 | + | 0.830065i | \(0.688303\pi\) | |||||||
\(642\) | −3.99097 | −0.157511 | ||||||||
\(643\) | −46.6720 | −1.84057 | −0.920283 | − | 0.391254i | \(-0.872041\pi\) | ||||
−0.920283 | + | 0.391254i | \(0.872041\pi\) | |||||||
\(644\) | 15.1614 | 0.597445 | ||||||||
\(645\) | 71.9730 | 2.83393 | ||||||||
\(646\) | 0.347051 | 0.0136545 | ||||||||
\(647\) | −16.3500 | −0.642786 | −0.321393 | − | 0.946946i | \(-0.604151\pi\) | ||||
−0.321393 | + | 0.946946i | \(0.604151\pi\) | |||||||
\(648\) | −33.5565 | −1.31822 | ||||||||
\(649\) | −2.10071 | −0.0824600 | ||||||||
\(650\) | 33.5926 | 1.31761 | ||||||||
\(651\) | 158.155 | 6.19859 | ||||||||
\(652\) | 12.4851 | 0.488954 | ||||||||
\(653\) | −30.5874 | −1.19698 | −0.598488 | − | 0.801131i | \(-0.704232\pi\) | ||||
−0.598488 | + | 0.801131i | \(0.704232\pi\) | |||||||
\(654\) | −13.8919 | −0.543218 | ||||||||
\(655\) | 2.51079 | 0.0981048 | ||||||||
\(656\) | −4.50642 | −0.175946 | ||||||||
\(657\) | 76.1626 | 2.97138 | ||||||||
\(658\) | 63.2876 | 2.46721 | ||||||||
\(659\) | 3.71700 | 0.144794 | 0.0723970 | − | 0.997376i | \(-0.476935\pi\) | ||||
0.0723970 | + | 0.997376i | \(0.476935\pi\) | |||||||
\(660\) | −2.75307 | −0.107163 | ||||||||
\(661\) | 23.6062 | 0.918175 | 0.459088 | − | 0.888391i | \(-0.348176\pi\) | ||||
0.459088 | + | 0.888391i | \(0.348176\pi\) | |||||||
\(662\) | 25.7235 | 0.999773 | ||||||||
\(663\) | 11.7568 | 0.456596 | ||||||||
\(664\) | −3.91707 | −0.152012 | ||||||||
\(665\) | 7.43413 | 0.288283 | ||||||||
\(666\) | −42.1304 | −1.63252 | ||||||||
\(667\) | −6.52198 | −0.252532 | ||||||||
\(668\) | −16.5947 | −0.642067 | ||||||||
\(669\) | −20.1136 | −0.777636 | ||||||||
\(670\) | −14.8797 | −0.574852 | ||||||||
\(671\) | 0.178475 | 0.00688995 | ||||||||
\(672\) | 17.0376 | 0.657239 | ||||||||
\(673\) | 5.20959 | 0.200815 | 0.100408 | − | 0.994946i | \(-0.467985\pi\) | ||||
0.100408 | + | 0.994946i | \(0.467985\pi\) | |||||||
\(674\) | −24.5965 | −0.947421 | ||||||||
\(675\) | −143.925 | −5.53969 | ||||||||
\(676\) | 3.44955 | 0.132675 | ||||||||
\(677\) | −46.6202 | −1.79176 | −0.895880 | − | 0.444297i | \(-0.853453\pi\) | ||||
−0.895880 | + | 0.444297i | \(0.853453\pi\) | |||||||
\(678\) | 34.8025 | 1.33658 | ||||||||
\(679\) | 51.5320 | 1.97762 | ||||||||
\(680\) | 3.15766 | 0.121091 | ||||||||
\(681\) | −21.9437 | −0.840885 | ||||||||
\(682\) | −2.09587 | −0.0802549 | ||||||||
\(683\) | −4.70304 | −0.179957 | −0.0899785 | − | 0.995944i | \(-0.528680\pi\) | ||||
−0.0899785 | + | 0.995944i | \(0.528680\pi\) | |||||||
\(684\) | −3.28210 | −0.125494 | ||||||||
\(685\) | −51.3676 | −1.96266 | ||||||||
\(686\) | −60.7631 | −2.31995 | ||||||||
\(687\) | −95.8338 | −3.65629 | ||||||||
\(688\) | 5.90255 | 0.225033 | ||||||||
\(689\) | 7.42215 | 0.282761 | ||||||||
\(690\) | −36.3037 | −1.38206 | ||||||||
\(691\) | −28.6239 | −1.08891 | −0.544453 | − | 0.838791i | \(-0.683263\pi\) | ||||
−0.544453 | + | 0.838791i | \(0.683263\pi\) | |||||||
\(692\) | −11.0918 | −0.421647 | ||||||||
\(693\) | −9.42088 | −0.357870 | ||||||||
\(694\) | −16.7055 | −0.634131 | ||||||||
\(695\) | −40.3116 | −1.52911 | ||||||||
\(696\) | −7.32903 | −0.277806 | ||||||||
\(697\) | −3.90441 | −0.147890 | ||||||||
\(698\) | −14.6391 | −0.554099 | ||||||||
\(699\) | 3.67475 | 0.138992 | ||||||||
\(700\) | 42.1781 | 1.59418 | ||||||||
\(701\) | −29.2768 | −1.10577 | −0.552884 | − | 0.833258i | \(-0.686473\pi\) | ||||
−0.552884 | + | 0.833258i | \(0.686473\pi\) | |||||||
\(702\) | −70.4770 | −2.65998 | ||||||||
\(703\) | −2.05959 | −0.0776790 | ||||||||
\(704\) | −0.225781 | −0.00850946 | ||||||||
\(705\) | −151.540 | −5.70734 | ||||||||
\(706\) | 26.0658 | 0.980998 | ||||||||
\(707\) | 79.0591 | 2.97332 | ||||||||
\(708\) | −31.1290 | −1.16990 | ||||||||
\(709\) | −38.6355 | −1.45099 | −0.725494 | − | 0.688228i | \(-0.758389\pi\) | ||||
−0.725494 | + | 0.688228i | \(0.758389\pi\) | |||||||
\(710\) | −36.4241 | −1.36697 | ||||||||
\(711\) | 65.7524 | 2.46591 | ||||||||
\(712\) | 12.6557 | 0.474291 | ||||||||
\(713\) | −27.6374 | −1.03503 | ||||||||
\(714\) | 14.7615 | 0.552437 | ||||||||
\(715\) | −3.33739 | −0.124811 | ||||||||
\(716\) | 18.2533 | 0.682156 | ||||||||
\(717\) | 73.1626 | 2.73231 | ||||||||
\(718\) | −1.94679 | −0.0726536 | ||||||||
\(719\) | −19.8083 | −0.738723 | −0.369362 | − | 0.929286i | \(-0.620424\pi\) | ||||
−0.369362 | + | 0.929286i | \(0.620424\pi\) | |||||||
\(720\) | −29.8624 | −1.11291 | ||||||||
\(721\) | 62.2143 | 2.31698 | ||||||||
\(722\) | 18.8396 | 0.701135 | ||||||||
\(723\) | 69.1096 | 2.57021 | ||||||||
\(724\) | −25.5293 | −0.948789 | ||||||||
\(725\) | −18.1437 | −0.673839 | ||||||||
\(726\) | −36.6322 | −1.35955 | ||||||||
\(727\) | −30.8120 | −1.14275 | −0.571377 | − | 0.820688i | \(-0.693590\pi\) | ||||
−0.571377 | + | 0.820688i | \(0.693590\pi\) | |||||||
\(728\) | 20.6536 | 0.765475 | ||||||||
\(729\) | 100.541 | 3.72373 | ||||||||
\(730\) | 33.8766 | 1.25383 | ||||||||
\(731\) | 5.11404 | 0.189149 | ||||||||
\(732\) | 2.64471 | 0.0977512 | ||||||||
\(733\) | 19.6630 | 0.726270 | 0.363135 | − | 0.931736i | \(-0.381706\pi\) | ||||
0.363135 | + | 0.931736i | \(0.381706\pi\) | |||||||
\(734\) | −10.8315 | −0.399799 | ||||||||
\(735\) | 230.851 | 8.51505 | ||||||||
\(736\) | −2.97729 | −0.109744 | ||||||||
\(737\) | 0.921807 | 0.0339552 | ||||||||
\(738\) | 36.9246 | 1.35921 | ||||||||
\(739\) | −50.5270 | −1.85867 | −0.929333 | − | 0.369243i | \(-0.879617\pi\) | ||||
−0.929333 | + | 0.369243i | \(0.879617\pi\) | |||||||
\(740\) | −18.7393 | −0.688871 | ||||||||
\(741\) | −5.43543 | −0.199675 | ||||||||
\(742\) | 9.31907 | 0.342114 | ||||||||
\(743\) | 1.93521 | 0.0709958 | 0.0354979 | − | 0.999370i | \(-0.488698\pi\) | ||||
0.0354979 | + | 0.999370i | \(0.488698\pi\) | |||||||
\(744\) | −31.0573 | −1.13862 | ||||||||
\(745\) | 33.8507 | 1.24020 | ||||||||
\(746\) | 36.4854 | 1.33583 | ||||||||
\(747\) | 32.0956 | 1.17432 | ||||||||
\(748\) | −0.195619 | −0.00715256 | ||||||||
\(749\) | −6.07449 | −0.221957 | ||||||||
\(750\) | −40.0266 | −1.46156 | ||||||||
\(751\) | −39.4628 | −1.44002 | −0.720010 | − | 0.693964i | \(-0.755863\pi\) | ||||
−0.720010 | + | 0.693964i | \(0.755863\pi\) | |||||||
\(752\) | −12.4279 | −0.453200 | ||||||||
\(753\) | −40.3677 | −1.47108 | ||||||||
\(754\) | −8.88455 | −0.323556 | ||||||||
\(755\) | −0.639007 | −0.0232559 | ||||||||
\(756\) | −88.4892 | −3.21832 | ||||||||
\(757\) | −10.6029 | −0.385369 | −0.192685 | − | 0.981261i | \(-0.561719\pi\) | ||||
−0.192685 | + | 0.981261i | \(0.561719\pi\) | |||||||
\(758\) | 16.7914 | 0.609892 | ||||||||
\(759\) | 2.24904 | 0.0816350 | ||||||||
\(760\) | −1.45986 | −0.0529546 | ||||||||
\(761\) | 3.73082 | 0.135242 | 0.0676211 | − | 0.997711i | \(-0.478459\pi\) | ||||
0.0676211 | + | 0.997711i | \(0.478459\pi\) | |||||||
\(762\) | 13.4957 | 0.488897 | ||||||||
\(763\) | −21.1443 | −0.765477 | ||||||||
\(764\) | 4.04315 | 0.146276 | ||||||||
\(765\) | −25.8731 | −0.935445 | ||||||||
\(766\) | 10.2072 | 0.368801 | ||||||||
\(767\) | −37.7359 | −1.36256 | ||||||||
\(768\) | −3.34571 | −0.120728 | ||||||||
\(769\) | −42.7266 | −1.54076 | −0.770380 | − | 0.637585i | \(-0.779934\pi\) | ||||
−0.770380 | + | 0.637585i | \(0.779934\pi\) | |||||||
\(770\) | −4.19034 | −0.151009 | ||||||||
\(771\) | −99.1829 | −3.57199 | ||||||||
\(772\) | −3.19342 | −0.114934 | ||||||||
\(773\) | −6.58701 | −0.236918 | −0.118459 | − | 0.992959i | \(-0.537795\pi\) | ||||
−0.118459 | + | 0.992959i | \(0.537795\pi\) | |||||||
\(774\) | −48.3641 | −1.73841 | ||||||||
\(775\) | −76.8852 | −2.76180 | ||||||||
\(776\) | −10.1195 | −0.363267 | ||||||||
\(777\) | −87.6032 | −3.14275 | ||||||||
\(778\) | −19.7850 | −0.709325 | ||||||||
\(779\) | 1.80510 | 0.0646743 | ||||||||
\(780\) | −49.4546 | −1.77076 | ||||||||
\(781\) | 2.25650 | 0.0807439 | ||||||||
\(782\) | −2.57956 | −0.0922447 | ||||||||
\(783\) | 38.0652 | 1.36034 | ||||||||
\(784\) | 18.9322 | 0.676150 | ||||||||
\(785\) | 59.2822 | 2.11587 | ||||||||
\(786\) | −2.30493 | −0.0822141 | ||||||||
\(787\) | −16.4679 | −0.587017 | −0.293508 | − | 0.955957i | \(-0.594823\pi\) | ||||
−0.293508 | + | 0.955957i | \(0.594823\pi\) | |||||||
\(788\) | −6.83509 | −0.243490 | ||||||||
\(789\) | 84.6476 | 3.01354 | ||||||||
\(790\) | 29.2462 | 1.04053 | ||||||||
\(791\) | 52.9715 | 1.88345 | ||||||||
\(792\) | 1.85000 | 0.0657369 | ||||||||
\(793\) | 3.20602 | 0.113849 | ||||||||
\(794\) | 6.55430 | 0.232604 | ||||||||
\(795\) | −22.3143 | −0.791405 | ||||||||
\(796\) | −25.4649 | −0.902578 | ||||||||
\(797\) | −16.4052 | −0.581102 | −0.290551 | − | 0.956859i | \(-0.593839\pi\) | ||||
−0.290551 | + | 0.956859i | \(0.593839\pi\) | |||||||
\(798\) | −6.82459 | −0.241588 | ||||||||
\(799\) | −10.7677 | −0.380934 | ||||||||
\(800\) | −8.28261 | −0.292834 | ||||||||
\(801\) | −103.697 | −3.66397 | ||||||||
\(802\) | 17.7763 | 0.627704 | ||||||||
\(803\) | −2.09868 | −0.0740608 | ||||||||
\(804\) | 13.6597 | 0.481739 | ||||||||
\(805\) | −55.2564 | −1.94753 | ||||||||
\(806\) | −37.6489 | −1.32613 | ||||||||
\(807\) | 44.6856 | 1.57301 | ||||||||
\(808\) | −15.5250 | −0.546168 | ||||||||
\(809\) | −15.5536 | −0.546837 | −0.273419 | − | 0.961895i | \(-0.588154\pi\) | ||||
−0.273419 | + | 0.961895i | \(0.588154\pi\) | |||||||
\(810\) | 122.298 | 4.29710 | ||||||||
\(811\) | 0.0117685 | 0.000413248 0 | 0.000206624 | − | 1.00000i | \(-0.499934\pi\) | ||||
0.000206624 | 1.00000i | \(0.499934\pi\) | ||||||||
\(812\) | −11.1552 | −0.391471 | ||||||||
\(813\) | 15.6109 | 0.547499 | ||||||||
\(814\) | 1.16091 | 0.0406900 | ||||||||
\(815\) | −45.5023 | −1.59388 | ||||||||
\(816\) | −2.89876 | −0.101477 | ||||||||
\(817\) | −2.36433 | −0.0827175 | ||||||||
\(818\) | −28.7471 | −1.00512 | ||||||||
\(819\) | −169.231 | −5.91341 | ||||||||
\(820\) | 16.4238 | 0.573544 | ||||||||
\(821\) | −0.271600 | −0.00947891 | −0.00473945 | − | 0.999989i | \(-0.501509\pi\) | ||||
−0.00473945 | + | 0.999989i | \(0.501509\pi\) | |||||||
\(822\) | 47.1559 | 1.64475 | ||||||||
\(823\) | −36.1856 | −1.26135 | −0.630676 | − | 0.776046i | \(-0.717222\pi\) | ||||
−0.630676 | + | 0.776046i | \(0.717222\pi\) | |||||||
\(824\) | −12.2172 | −0.425605 | ||||||||
\(825\) | 6.25667 | 0.217829 | ||||||||
\(826\) | −47.3802 | −1.64857 | ||||||||
\(827\) | 25.2701 | 0.878729 | 0.439365 | − | 0.898309i | \(-0.355204\pi\) | ||||
0.439365 | + | 0.898309i | \(0.355204\pi\) | |||||||
\(828\) | 24.3952 | 0.847792 | ||||||||
\(829\) | −54.8501 | −1.90502 | −0.952512 | − | 0.304502i | \(-0.901510\pi\) | ||||
−0.952512 | + | 0.304502i | \(0.901510\pi\) | |||||||
\(830\) | 14.2759 | 0.495523 | ||||||||
\(831\) | −32.7599 | −1.13643 | ||||||||
\(832\) | −4.05580 | −0.140610 | ||||||||
\(833\) | 16.4031 | 0.568333 | ||||||||
\(834\) | 37.0064 | 1.28143 | ||||||||
\(835\) | 60.4798 | 2.09299 | ||||||||
\(836\) | 0.0904392 | 0.00312791 | ||||||||
\(837\) | 161.304 | 5.57549 | ||||||||
\(838\) | −25.2111 | −0.870903 | ||||||||
\(839\) | 46.3934 | 1.60168 | 0.800839 | − | 0.598879i | \(-0.204387\pi\) | ||||
0.800839 | + | 0.598879i | \(0.204387\pi\) | |||||||
\(840\) | −62.0940 | −2.14245 | ||||||||
\(841\) | −24.2014 | −0.834530 | ||||||||
\(842\) | 12.9193 | 0.445228 | ||||||||
\(843\) | 63.1839 | 2.17617 | ||||||||
\(844\) | −16.3806 | −0.563845 | ||||||||
\(845\) | −12.5720 | −0.432490 | ||||||||
\(846\) | 101.832 | 3.50104 | ||||||||
\(847\) | −55.7564 | −1.91581 | ||||||||
\(848\) | −1.83001 | −0.0628427 | ||||||||
\(849\) | 54.4389 | 1.86834 | ||||||||
\(850\) | −7.17614 | −0.246140 | ||||||||
\(851\) | 15.3085 | 0.524769 | ||||||||
\(852\) | 33.4376 | 1.14555 | ||||||||
\(853\) | −54.4289 | −1.86361 | −0.931806 | − | 0.362957i | \(-0.881767\pi\) | ||||
−0.931806 | + | 0.362957i | \(0.881767\pi\) | |||||||
\(854\) | 4.02540 | 0.137746 | ||||||||
\(855\) | 11.9617 | 0.409082 | ||||||||
\(856\) | 1.19286 | 0.0407712 | ||||||||
\(857\) | 41.7559 | 1.42635 | 0.713177 | − | 0.700984i | \(-0.247255\pi\) | ||||
0.713177 | + | 0.700984i | \(0.247255\pi\) | |||||||
\(858\) | 3.06375 | 0.104595 | ||||||||
\(859\) | −13.7299 | −0.468460 | −0.234230 | − | 0.972181i | \(-0.575257\pi\) | ||||
−0.234230 | + | 0.972181i | \(0.575257\pi\) | |||||||
\(860\) | −21.5120 | −0.733554 | ||||||||
\(861\) | 76.7785 | 2.61660 | ||||||||
\(862\) | 14.8705 | 0.506490 | ||||||||
\(863\) | 25.7327 | 0.875950 | 0.437975 | − | 0.898987i | \(-0.355696\pi\) | ||||
0.437975 | + | 0.898987i | \(0.355696\pi\) | |||||||
\(864\) | 17.3768 | 0.591171 | ||||||||
\(865\) | 40.4244 | 1.37447 | ||||||||
\(866\) | −15.3636 | −0.522077 | ||||||||
\(867\) | 54.3655 | 1.84635 | ||||||||
\(868\) | −47.2711 | −1.60448 | ||||||||
\(869\) | −1.81182 | −0.0614619 | ||||||||
\(870\) | 26.7109 | 0.905583 | ||||||||
\(871\) | 16.5588 | 0.561074 | ||||||||
\(872\) | 4.15216 | 0.140610 | ||||||||
\(873\) | 82.9165 | 2.80630 | ||||||||
\(874\) | 1.19259 | 0.0403398 | ||||||||
\(875\) | −60.9228 | −2.05957 | ||||||||
\(876\) | −31.0990 | −1.05074 | ||||||||
\(877\) | −39.9849 | −1.35019 | −0.675097 | − | 0.737729i | \(-0.735898\pi\) | ||||
−0.675097 | + | 0.737729i | \(0.735898\pi\) | |||||||
\(878\) | −33.0583 | −1.11566 | ||||||||
\(879\) | 0.991271 | 0.0334348 | ||||||||
\(880\) | 0.822867 | 0.0277388 | ||||||||
\(881\) | 36.3809 | 1.22570 | 0.612852 | − | 0.790198i | \(-0.290022\pi\) | ||||
0.612852 | + | 0.790198i | \(0.290022\pi\) | |||||||
\(882\) | −155.126 | −5.22336 | ||||||||
\(883\) | −12.8491 | −0.432408 | −0.216204 | − | 0.976348i | \(-0.569368\pi\) | ||||
−0.216204 | + | 0.976348i | \(0.569368\pi\) | |||||||
\(884\) | −3.51399 | −0.118188 | ||||||||
\(885\) | 113.451 | 3.81360 | ||||||||
\(886\) | 3.60408 | 0.121081 | ||||||||
\(887\) | −23.9722 | −0.804909 | −0.402455 | − | 0.915440i | \(-0.631843\pi\) | ||||
−0.402455 | + | 0.915440i | \(0.631843\pi\) | |||||||
\(888\) | 17.2028 | 0.577290 | ||||||||
\(889\) | 20.5412 | 0.688931 | ||||||||
\(890\) | −46.1239 | −1.54608 | ||||||||
\(891\) | −7.57643 | −0.253820 | ||||||||
\(892\) | 6.01176 | 0.201288 | ||||||||
\(893\) | 4.97814 | 0.166587 | ||||||||
\(894\) | −31.0753 | −1.03931 | ||||||||
\(895\) | −66.5246 | −2.22367 | ||||||||
\(896\) | −5.09237 | −0.170124 | ||||||||
\(897\) | 40.4004 | 1.34893 | ||||||||
\(898\) | 2.73595 | 0.0912999 | ||||||||
\(899\) | 20.3345 | 0.678194 | ||||||||
\(900\) | 67.8657 | 2.26219 | ||||||||
\(901\) | −1.58554 | −0.0528219 | ||||||||
\(902\) | −1.01747 | −0.0338779 | ||||||||
\(903\) | −100.565 | −3.34660 | ||||||||
\(904\) | −10.4021 | −0.345970 | ||||||||
\(905\) | 93.0423 | 3.09283 | ||||||||
\(906\) | 0.586614 | 0.0194889 | ||||||||
\(907\) | 30.7286 | 1.02033 | 0.510164 | − | 0.860077i | \(-0.329585\pi\) | ||||
0.510164 | + | 0.860077i | \(0.329585\pi\) | |||||||
\(908\) | 6.55876 | 0.217660 | ||||||||
\(909\) | 127.208 | 4.21924 | ||||||||
\(910\) | −75.2728 | −2.49527 | ||||||||
\(911\) | 33.0407 | 1.09469 | 0.547343 | − | 0.836908i | \(-0.315639\pi\) | ||||
0.547343 | + | 0.836908i | \(0.315639\pi\) | |||||||
\(912\) | 1.34016 | 0.0443772 | ||||||||
\(913\) | −0.884402 | −0.0292694 | ||||||||
\(914\) | 5.07560 | 0.167886 | ||||||||
\(915\) | −9.63871 | −0.318646 | ||||||||
\(916\) | 28.6438 | 0.946418 | ||||||||
\(917\) | −3.50824 | −0.115852 | ||||||||
\(918\) | 15.0555 | 0.496905 | ||||||||
\(919\) | −11.4572 | −0.377937 | −0.188968 | − | 0.981983i | \(-0.560514\pi\) | ||||
−0.188968 | + | 0.981983i | \(0.560514\pi\) | |||||||
\(920\) | 10.8508 | 0.357741 | ||||||||
\(921\) | −112.894 | −3.71997 | ||||||||
\(922\) | −25.3870 | −0.836077 | ||||||||
\(923\) | 40.5345 | 1.33421 | ||||||||
\(924\) | 3.84677 | 0.126549 | ||||||||
\(925\) | 42.5872 | 1.40026 | ||||||||
\(926\) | −17.4199 | −0.572454 | ||||||||
\(927\) | 100.105 | 3.28786 | ||||||||
\(928\) | 2.19058 | 0.0719092 | ||||||||
\(929\) | −29.4185 | −0.965189 | −0.482595 | − | 0.875844i | \(-0.660306\pi\) | ||||
−0.482595 | + | 0.875844i | \(0.660306\pi\) | |||||||
\(930\) | 113.189 | 3.71162 | ||||||||
\(931\) | −7.58350 | −0.248539 | ||||||||
\(932\) | −1.09835 | −0.0359776 | ||||||||
\(933\) | −97.6451 | −3.19676 | ||||||||
\(934\) | −34.1750 | −1.11824 | ||||||||
\(935\) | 0.712941 | 0.0233157 | ||||||||
\(936\) | 33.2323 | 1.08623 | ||||||||
\(937\) | −28.8733 | −0.943250 | −0.471625 | − | 0.881799i | \(-0.656332\pi\) | ||||
−0.471625 | + | 0.881799i | \(0.656332\pi\) | |||||||
\(938\) | 20.7908 | 0.678844 | ||||||||
\(939\) | 50.0845 | 1.63444 | ||||||||
\(940\) | 45.2940 | 1.47733 | ||||||||
\(941\) | −15.2362 | −0.496686 | −0.248343 | − | 0.968672i | \(-0.579886\pi\) | ||||
−0.248343 | + | 0.968672i | \(0.579886\pi\) | |||||||
\(942\) | −54.4215 | −1.77315 | ||||||||
\(943\) | −13.4169 | −0.436915 | ||||||||
\(944\) | 9.30416 | 0.302825 | ||||||||
\(945\) | 322.501 | 10.4910 | ||||||||
\(946\) | 1.33269 | 0.0433294 | ||||||||
\(947\) | −17.6980 | −0.575109 | −0.287555 | − | 0.957764i | \(-0.592842\pi\) | ||||
−0.287555 | + | 0.957764i | \(0.592842\pi\) | |||||||
\(948\) | −26.8482 | −0.871990 | ||||||||
\(949\) | −37.6995 | −1.22378 | ||||||||
\(950\) | 3.31769 | 0.107640 | ||||||||
\(951\) | 43.6885 | 1.41670 | ||||||||
\(952\) | −4.41208 | −0.142996 | ||||||||
\(953\) | 22.6190 | 0.732700 | 0.366350 | − | 0.930477i | \(-0.380607\pi\) | ||||
0.366350 | + | 0.930477i | \(0.380607\pi\) | |||||||
\(954\) | 14.9946 | 0.485470 | ||||||||
\(955\) | −14.7354 | −0.476826 | ||||||||
\(956\) | −21.8676 | −0.707249 | ||||||||
\(957\) | −1.65476 | −0.0534907 | ||||||||
\(958\) | 43.0987 | 1.39246 | ||||||||
\(959\) | 71.7740 | 2.31770 | ||||||||
\(960\) | 12.1935 | 0.393545 | ||||||||
\(961\) | 55.1691 | 1.77965 | ||||||||
\(962\) | 20.8540 | 0.672360 | ||||||||
\(963\) | −9.77403 | −0.314964 | ||||||||
\(964\) | −20.6562 | −0.665291 | ||||||||
\(965\) | 11.6385 | 0.374657 | ||||||||
\(966\) | 50.7258 | 1.63208 | ||||||||
\(967\) | 41.7973 | 1.34411 | 0.672056 | − | 0.740501i | \(-0.265412\pi\) | ||||
0.672056 | + | 0.740501i | \(0.265412\pi\) | |||||||
\(968\) | 10.9490 | 0.351915 | ||||||||
\(969\) | 1.16113 | 0.0373009 | ||||||||
\(970\) | 36.8807 | 1.18417 | ||||||||
\(971\) | −22.8917 | −0.734628 | −0.367314 | − | 0.930097i | \(-0.619723\pi\) | ||||
−0.367314 | + | 0.930097i | \(0.619723\pi\) | |||||||
\(972\) | −60.1397 | −1.92898 | ||||||||
\(973\) | 56.3259 | 1.80573 | ||||||||
\(974\) | −20.2072 | −0.647479 | ||||||||
\(975\) | 112.391 | 3.59940 | ||||||||
\(976\) | −0.790477 | −0.0253026 | ||||||||
\(977\) | −4.39443 | −0.140590 | −0.0702951 | − | 0.997526i | \(-0.522394\pi\) | ||||
−0.0702951 | + | 0.997526i | \(0.522394\pi\) | |||||||
\(978\) | 41.7715 | 1.33570 | ||||||||
\(979\) | 2.85741 | 0.0913232 | ||||||||
\(980\) | −68.9990 | −2.20409 | ||||||||
\(981\) | −34.0219 | −1.08623 | ||||||||
\(982\) | −8.40833 | −0.268321 | ||||||||
\(983\) | 19.7597 | 0.630237 | 0.315118 | − | 0.949052i | \(-0.397956\pi\) | ||||
0.315118 | + | 0.949052i | \(0.397956\pi\) | |||||||
\(984\) | −15.0772 | −0.480643 | ||||||||
\(985\) | 24.9107 | 0.793721 | ||||||||
\(986\) | 1.89794 | 0.0604427 | ||||||||
\(987\) | 211.742 | 6.73981 | ||||||||
\(988\) | 1.62460 | 0.0516853 | ||||||||
\(989\) | 17.5736 | 0.558808 | ||||||||
\(990\) | −6.74238 | −0.214287 | ||||||||
\(991\) | −34.6916 | −1.10202 | −0.551008 | − | 0.834500i | \(-0.685757\pi\) | ||||
−0.551008 | + | 0.834500i | \(0.685757\pi\) | |||||||
\(992\) | 9.28273 | 0.294727 | ||||||||
\(993\) | 86.0634 | 2.73114 | ||||||||
\(994\) | 50.8941 | 1.61426 | ||||||||
\(995\) | 92.8075 | 2.94219 | ||||||||
\(996\) | −13.1054 | −0.415260 | ||||||||
\(997\) | 21.8229 | 0.691138 | 0.345569 | − | 0.938393i | \(-0.387686\pi\) | ||||
0.345569 | + | 0.938393i | \(0.387686\pi\) | |||||||
\(998\) | −12.9379 | −0.409542 | ||||||||
\(999\) | −89.3475 | −2.82683 |
(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 | 4006.2.a.g.1.1 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4006.2.a.g.1.1 | ✓ | 40 | 1.1 | even | 1 | trivial |