Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(0\) |
Dimension: | \(47\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 | ||||||||
\(3\) | −1.46195 | −0.844056 | −0.422028 | − | 0.906583i | \(-0.638682\pi\) | ||||
−0.422028 | + | 0.906583i | \(0.638682\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.14418 | 0.958908 | 0.479454 | − | 0.877567i | \(-0.340835\pi\) | ||||
0.479454 | + | 0.877567i | \(0.340835\pi\) | |||||||
\(6\) | −1.46195 | −0.596838 | ||||||||
\(7\) | 2.84565 | 1.07556 | 0.537778 | − | 0.843087i | \(-0.319264\pi\) | ||||
0.537778 | + | 0.843087i | \(0.319264\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.862709 | −0.287570 | ||||||||
\(10\) | 2.14418 | 0.678050 | ||||||||
\(11\) | −4.14345 | −1.24930 | −0.624649 | − | 0.780905i | \(-0.714758\pi\) | ||||
−0.624649 | + | 0.780905i | \(0.714758\pi\) | |||||||
\(12\) | −1.46195 | −0.422028 | ||||||||
\(13\) | 5.72765 | 1.58856 | 0.794282 | − | 0.607549i | \(-0.207847\pi\) | ||||
0.794282 | + | 0.607549i | \(0.207847\pi\) | |||||||
\(14\) | 2.84565 | 0.760533 | ||||||||
\(15\) | −3.13468 | −0.809372 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.828433 | 0.200925 | 0.100462 | − | 0.994941i | \(-0.467968\pi\) | ||||
0.100462 | + | 0.994941i | \(0.467968\pi\) | |||||||
\(18\) | −0.862709 | −0.203343 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 2.14418 | 0.479454 | ||||||||
\(21\) | −4.16019 | −0.907829 | ||||||||
\(22\) | −4.14345 | −0.883388 | ||||||||
\(23\) | 4.11173 | 0.857355 | 0.428678 | − | 0.903458i | \(-0.358980\pi\) | ||||
0.428678 | + | 0.903458i | \(0.358980\pi\) | |||||||
\(24\) | −1.46195 | −0.298419 | ||||||||
\(25\) | −0.402477 | −0.0804955 | ||||||||
\(26\) | 5.72765 | 1.12328 | ||||||||
\(27\) | 5.64708 | 1.08678 | ||||||||
\(28\) | 2.84565 | 0.537778 | ||||||||
\(29\) | 5.07697 | 0.942770 | 0.471385 | − | 0.881928i | \(-0.343754\pi\) | ||||
0.471385 | + | 0.881928i | \(0.343754\pi\) | |||||||
\(30\) | −3.13468 | −0.572312 | ||||||||
\(31\) | 3.20401 | 0.575456 | 0.287728 | − | 0.957712i | \(-0.407100\pi\) | ||||
0.287728 | + | 0.957712i | \(0.407100\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 6.05751 | 1.05448 | ||||||||
\(34\) | 0.828433 | 0.142075 | ||||||||
\(35\) | 6.10160 | 1.03136 | ||||||||
\(36\) | −0.862709 | −0.143785 | ||||||||
\(37\) | −1.30300 | −0.214211 | −0.107106 | − | 0.994248i | \(-0.534158\pi\) | ||||
−0.107106 | + | 0.994248i | \(0.534158\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −8.37352 | −1.34084 | ||||||||
\(40\) | 2.14418 | 0.339025 | ||||||||
\(41\) | −9.49007 | −1.48210 | −0.741050 | − | 0.671450i | \(-0.765672\pi\) | ||||
−0.741050 | + | 0.671450i | \(0.765672\pi\) | |||||||
\(42\) | −4.16019 | −0.641932 | ||||||||
\(43\) | 1.76733 | 0.269515 | 0.134758 | − | 0.990879i | \(-0.456974\pi\) | ||||
0.134758 | + | 0.990879i | \(0.456974\pi\) | |||||||
\(44\) | −4.14345 | −0.624649 | ||||||||
\(45\) | −1.84981 | −0.275753 | ||||||||
\(46\) | 4.11173 | 0.606242 | ||||||||
\(47\) | 6.02255 | 0.878479 | 0.439239 | − | 0.898370i | \(-0.355248\pi\) | ||||
0.439239 | + | 0.898370i | \(0.355248\pi\) | |||||||
\(48\) | −1.46195 | −0.211014 | ||||||||
\(49\) | 1.09774 | 0.156820 | ||||||||
\(50\) | −0.402477 | −0.0569189 | ||||||||
\(51\) | −1.21113 | −0.169592 | ||||||||
\(52\) | 5.72765 | 0.794282 | ||||||||
\(53\) | −9.71241 | −1.33410 | −0.667051 | − | 0.745012i | \(-0.732444\pi\) | ||||
−0.667051 | + | 0.745012i | \(0.732444\pi\) | |||||||
\(54\) | 5.64708 | 0.768470 | ||||||||
\(55\) | −8.88433 | −1.19796 | ||||||||
\(56\) | 2.84565 | 0.380266 | ||||||||
\(57\) | 1.46195 | 0.193640 | ||||||||
\(58\) | 5.07697 | 0.666639 | ||||||||
\(59\) | −1.16819 | −0.152086 | −0.0760430 | − | 0.997105i | \(-0.524229\pi\) | ||||
−0.0760430 | + | 0.997105i | \(0.524229\pi\) | |||||||
\(60\) | −3.13468 | −0.404686 | ||||||||
\(61\) | −0.741864 | −0.0949860 | −0.0474930 | − | 0.998872i | \(-0.515123\pi\) | ||||
−0.0474930 | + | 0.998872i | \(0.515123\pi\) | |||||||
\(62\) | 3.20401 | 0.406909 | ||||||||
\(63\) | −2.45497 | −0.309297 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 12.2811 | 1.52329 | ||||||||
\(66\) | 6.05751 | 0.745628 | ||||||||
\(67\) | 12.6141 | 1.54106 | 0.770528 | − | 0.637406i | \(-0.219992\pi\) | ||||
0.770528 | + | 0.637406i | \(0.219992\pi\) | |||||||
\(68\) | 0.828433 | 0.100462 | ||||||||
\(69\) | −6.01113 | −0.723656 | ||||||||
\(70\) | 6.10160 | 0.729281 | ||||||||
\(71\) | 1.20025 | 0.142444 | 0.0712219 | − | 0.997460i | \(-0.477310\pi\) | ||||
0.0712219 | + | 0.997460i | \(0.477310\pi\) | |||||||
\(72\) | −0.862709 | −0.101671 | ||||||||
\(73\) | 14.2635 | 1.66942 | 0.834710 | − | 0.550690i | \(-0.185635\pi\) | ||||
0.834710 | + | 0.550690i | \(0.185635\pi\) | |||||||
\(74\) | −1.30300 | −0.151470 | ||||||||
\(75\) | 0.588401 | 0.0679427 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −11.7908 | −1.34369 | ||||||||
\(78\) | −8.37352 | −0.948115 | ||||||||
\(79\) | 0.0154584 | 0.00173920 | 0.000869600 | − | 1.00000i | \(-0.499723\pi\) | ||||
0.000869600 | 1.00000i | \(0.499723\pi\) | ||||||||
\(80\) | 2.14418 | 0.239727 | ||||||||
\(81\) | −5.66760 | −0.629734 | ||||||||
\(82\) | −9.49007 | −1.04800 | ||||||||
\(83\) | 5.25605 | 0.576926 | 0.288463 | − | 0.957491i | \(-0.406856\pi\) | ||||
0.288463 | + | 0.957491i | \(0.406856\pi\) | |||||||
\(84\) | −4.16019 | −0.453914 | ||||||||
\(85\) | 1.77631 | 0.192668 | ||||||||
\(86\) | 1.76733 | 0.190576 | ||||||||
\(87\) | −7.42227 | −0.795750 | ||||||||
\(88\) | −4.14345 | −0.441694 | ||||||||
\(89\) | 15.8470 | 1.67978 | 0.839888 | − | 0.542759i | \(-0.182620\pi\) | ||||
0.839888 | + | 0.542759i | \(0.182620\pi\) | |||||||
\(90\) | −1.84981 | −0.194987 | ||||||||
\(91\) | 16.2989 | 1.70859 | ||||||||
\(92\) | 4.11173 | 0.428678 | ||||||||
\(93\) | −4.68409 | −0.485717 | ||||||||
\(94\) | 6.02255 | 0.621178 | ||||||||
\(95\) | −2.14418 | −0.219989 | ||||||||
\(96\) | −1.46195 | −0.149209 | ||||||||
\(97\) | −9.00620 | −0.914441 | −0.457221 | − | 0.889353i | \(-0.651155\pi\) | ||||
−0.457221 | + | 0.889353i | \(0.651155\pi\) | |||||||
\(98\) | 1.09774 | 0.110888 | ||||||||
\(99\) | 3.57460 | 0.359261 | ||||||||
\(100\) | −0.402477 | −0.0402477 | ||||||||
\(101\) | 9.96408 | 0.991464 | 0.495732 | − | 0.868476i | \(-0.334900\pi\) | ||||
0.495732 | + | 0.868476i | \(0.334900\pi\) | |||||||
\(102\) | −1.21113 | −0.119919 | ||||||||
\(103\) | −7.91932 | −0.780313 | −0.390157 | − | 0.920748i | \(-0.627579\pi\) | ||||
−0.390157 | + | 0.920748i | \(0.627579\pi\) | |||||||
\(104\) | 5.72765 | 0.561642 | ||||||||
\(105\) | −8.92022 | −0.870524 | ||||||||
\(106\) | −9.71241 | −0.943353 | ||||||||
\(107\) | −19.5270 | −1.88775 | −0.943875 | − | 0.330302i | \(-0.892849\pi\) | ||||
−0.943875 | + | 0.330302i | \(0.892849\pi\) | |||||||
\(108\) | 5.64708 | 0.543390 | ||||||||
\(109\) | 2.14391 | 0.205349 | 0.102674 | − | 0.994715i | \(-0.467260\pi\) | ||||
0.102674 | + | 0.994715i | \(0.467260\pi\) | |||||||
\(110\) | −8.88433 | −0.847087 | ||||||||
\(111\) | 1.90491 | 0.180806 | ||||||||
\(112\) | 2.84565 | 0.268889 | ||||||||
\(113\) | 17.2207 | 1.61999 | 0.809993 | − | 0.586440i | \(-0.199471\pi\) | ||||
0.809993 | + | 0.586440i | \(0.199471\pi\) | |||||||
\(114\) | 1.46195 | 0.136924 | ||||||||
\(115\) | 8.81631 | 0.822125 | ||||||||
\(116\) | 5.07697 | 0.471385 | ||||||||
\(117\) | −4.94130 | −0.456823 | ||||||||
\(118\) | −1.16819 | −0.107541 | ||||||||
\(119\) | 2.35743 | 0.216106 | ||||||||
\(120\) | −3.13468 | −0.286156 | ||||||||
\(121\) | 6.16822 | 0.560747 | ||||||||
\(122\) | −0.741864 | −0.0671652 | ||||||||
\(123\) | 13.8740 | 1.25097 | ||||||||
\(124\) | 3.20401 | 0.287728 | ||||||||
\(125\) | −11.5839 | −1.03610 | ||||||||
\(126\) | −2.45497 | −0.218706 | ||||||||
\(127\) | −0.744794 | −0.0660897 | −0.0330449 | − | 0.999454i | \(-0.510520\pi\) | ||||
−0.0330449 | + | 0.999454i | \(0.510520\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −2.58374 | −0.227486 | ||||||||
\(130\) | 12.2811 | 1.07713 | ||||||||
\(131\) | 0.775074 | 0.0677185 | 0.0338592 | − | 0.999427i | \(-0.489220\pi\) | ||||
0.0338592 | + | 0.999427i | \(0.489220\pi\) | |||||||
\(132\) | 6.05751 | 0.527239 | ||||||||
\(133\) | −2.84565 | −0.246749 | ||||||||
\(134\) | 12.6141 | 1.08969 | ||||||||
\(135\) | 12.1084 | 1.04212 | ||||||||
\(136\) | 0.828433 | 0.0710376 | ||||||||
\(137\) | −10.8225 | −0.924630 | −0.462315 | − | 0.886716i | \(-0.652981\pi\) | ||||
−0.462315 | + | 0.886716i | \(0.652981\pi\) | |||||||
\(138\) | −6.01113 | −0.511702 | ||||||||
\(139\) | −5.75291 | −0.487955 | −0.243978 | − | 0.969781i | \(-0.578452\pi\) | ||||
−0.243978 | + | 0.969781i | \(0.578452\pi\) | |||||||
\(140\) | 6.10160 | 0.515679 | ||||||||
\(141\) | −8.80465 | −0.741485 | ||||||||
\(142\) | 1.20025 | 0.100723 | ||||||||
\(143\) | −23.7323 | −1.98459 | ||||||||
\(144\) | −0.862709 | −0.0718925 | ||||||||
\(145\) | 10.8860 | 0.904030 | ||||||||
\(146\) | 14.2635 | 1.18046 | ||||||||
\(147\) | −1.60484 | −0.132365 | ||||||||
\(148\) | −1.30300 | −0.107106 | ||||||||
\(149\) | 17.6403 | 1.44515 | 0.722574 | − | 0.691294i | \(-0.242959\pi\) | ||||
0.722574 | + | 0.691294i | \(0.242959\pi\) | |||||||
\(150\) | 0.588401 | 0.0480427 | ||||||||
\(151\) | −11.6954 | −0.951755 | −0.475877 | − | 0.879512i | \(-0.657869\pi\) | ||||
−0.475877 | + | 0.879512i | \(0.657869\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −0.714697 | −0.0577798 | ||||||||
\(154\) | −11.7908 | −0.950132 | ||||||||
\(155\) | 6.86997 | 0.551810 | ||||||||
\(156\) | −8.37352 | −0.670418 | ||||||||
\(157\) | 19.0859 | 1.52322 | 0.761611 | − | 0.648034i | \(-0.224409\pi\) | ||||
0.761611 | + | 0.648034i | \(0.224409\pi\) | |||||||
\(158\) | 0.0154584 | 0.00122980 | ||||||||
\(159\) | 14.1990 | 1.12606 | ||||||||
\(160\) | 2.14418 | 0.169513 | ||||||||
\(161\) | 11.7006 | 0.922133 | ||||||||
\(162\) | −5.66760 | −0.445289 | ||||||||
\(163\) | −4.38341 | −0.343335 | −0.171668 | − | 0.985155i | \(-0.554916\pi\) | ||||
−0.171668 | + | 0.985155i | \(0.554916\pi\) | |||||||
\(164\) | −9.49007 | −0.741050 | ||||||||
\(165\) | 12.9884 | 1.01115 | ||||||||
\(166\) | 5.25605 | 0.407948 | ||||||||
\(167\) | 12.6831 | 0.981444 | 0.490722 | − | 0.871316i | \(-0.336733\pi\) | ||||
0.490722 | + | 0.871316i | \(0.336733\pi\) | |||||||
\(168\) | −4.16019 | −0.320966 | ||||||||
\(169\) | 19.8060 | 1.52354 | ||||||||
\(170\) | 1.77631 | 0.136237 | ||||||||
\(171\) | 0.862709 | 0.0659730 | ||||||||
\(172\) | 1.76733 | 0.134758 | ||||||||
\(173\) | 14.5957 | 1.10969 | 0.554846 | − | 0.831953i | \(-0.312777\pi\) | ||||
0.554846 | + | 0.831953i | \(0.312777\pi\) | |||||||
\(174\) | −7.42227 | −0.562681 | ||||||||
\(175\) | −1.14531 | −0.0865774 | ||||||||
\(176\) | −4.14345 | −0.312325 | ||||||||
\(177\) | 1.70784 | 0.128369 | ||||||||
\(178\) | 15.8470 | 1.18778 | ||||||||
\(179\) | −7.01955 | −0.524666 | −0.262333 | − | 0.964977i | \(-0.584492\pi\) | ||||
−0.262333 | + | 0.964977i | \(0.584492\pi\) | |||||||
\(180\) | −1.84981 | −0.137877 | ||||||||
\(181\) | 6.98602 | 0.519267 | 0.259633 | − | 0.965707i | \(-0.416398\pi\) | ||||
0.259633 | + | 0.965707i | \(0.416398\pi\) | |||||||
\(182\) | 16.2989 | 1.20815 | ||||||||
\(183\) | 1.08457 | 0.0801735 | ||||||||
\(184\) | 4.11173 | 0.303121 | ||||||||
\(185\) | −2.79386 | −0.205409 | ||||||||
\(186\) | −4.68409 | −0.343454 | ||||||||
\(187\) | −3.43258 | −0.251015 | ||||||||
\(188\) | 6.02255 | 0.439239 | ||||||||
\(189\) | 16.0696 | 1.16889 | ||||||||
\(190\) | −2.14418 | −0.155555 | ||||||||
\(191\) | −4.48856 | −0.324781 | −0.162391 | − | 0.986727i | \(-0.551920\pi\) | ||||
−0.162391 | + | 0.986727i | \(0.551920\pi\) | |||||||
\(192\) | −1.46195 | −0.105507 | ||||||||
\(193\) | 15.3315 | 1.10358 | 0.551791 | − | 0.833982i | \(-0.313945\pi\) | ||||
0.551791 | + | 0.833982i | \(0.313945\pi\) | |||||||
\(194\) | −9.00620 | −0.646608 | ||||||||
\(195\) | −17.9544 | −1.28574 | ||||||||
\(196\) | 1.09774 | 0.0784099 | ||||||||
\(197\) | −14.0812 | −1.00325 | −0.501623 | − | 0.865086i | \(-0.667264\pi\) | ||||
−0.501623 | + | 0.865086i | \(0.667264\pi\) | |||||||
\(198\) | 3.57460 | 0.254036 | ||||||||
\(199\) | −7.77841 | −0.551397 | −0.275699 | − | 0.961244i | \(-0.588909\pi\) | ||||
−0.275699 | + | 0.961244i | \(0.588909\pi\) | |||||||
\(200\) | −0.402477 | −0.0284595 | ||||||||
\(201\) | −18.4411 | −1.30074 | ||||||||
\(202\) | 9.96408 | 0.701071 | ||||||||
\(203\) | 14.4473 | 1.01400 | ||||||||
\(204\) | −1.21113 | −0.0847958 | ||||||||
\(205\) | −20.3484 | −1.42120 | ||||||||
\(206\) | −7.91932 | −0.551765 | ||||||||
\(207\) | −3.54723 | −0.246549 | ||||||||
\(208\) | 5.72765 | 0.397141 | ||||||||
\(209\) | 4.14345 | 0.286609 | ||||||||
\(210\) | −8.92022 | −0.615554 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | −9.71241 | −0.667051 | ||||||||
\(213\) | −1.75471 | −0.120231 | ||||||||
\(214\) | −19.5270 | −1.33484 | ||||||||
\(215\) | 3.78948 | 0.258440 | ||||||||
\(216\) | 5.64708 | 0.384235 | ||||||||
\(217\) | 9.11749 | 0.618935 | ||||||||
\(218\) | 2.14391 | 0.145204 | ||||||||
\(219\) | −20.8525 | −1.40908 | ||||||||
\(220\) | −8.88433 | −0.598981 | ||||||||
\(221\) | 4.74497 | 0.319182 | ||||||||
\(222\) | 1.90491 | 0.127849 | ||||||||
\(223\) | −25.6890 | −1.72026 | −0.860130 | − | 0.510075i | \(-0.829618\pi\) | ||||
−0.860130 | + | 0.510075i | \(0.829618\pi\) | |||||||
\(224\) | 2.84565 | 0.190133 | ||||||||
\(225\) | 0.347221 | 0.0231481 | ||||||||
\(226\) | 17.2207 | 1.14550 | ||||||||
\(227\) | −0.630959 | −0.0418782 | −0.0209391 | − | 0.999781i | \(-0.506666\pi\) | ||||
−0.0209391 | + | 0.999781i | \(0.506666\pi\) | |||||||
\(228\) | 1.46195 | 0.0968198 | ||||||||
\(229\) | 15.0811 | 0.996588 | 0.498294 | − | 0.867008i | \(-0.333960\pi\) | ||||
0.498294 | + | 0.867008i | \(0.333960\pi\) | |||||||
\(230\) | 8.81631 | 0.581330 | ||||||||
\(231\) | 17.2376 | 1.13415 | ||||||||
\(232\) | 5.07697 | 0.333320 | ||||||||
\(233\) | 9.27718 | 0.607768 | 0.303884 | − | 0.952709i | \(-0.401716\pi\) | ||||
0.303884 | + | 0.952709i | \(0.401716\pi\) | |||||||
\(234\) | −4.94130 | −0.323023 | ||||||||
\(235\) | 12.9134 | 0.842380 | ||||||||
\(236\) | −1.16819 | −0.0760430 | ||||||||
\(237\) | −0.0225993 | −0.00146798 | ||||||||
\(238\) | 2.35743 | 0.152810 | ||||||||
\(239\) | −3.55667 | −0.230062 | −0.115031 | − | 0.993362i | \(-0.536697\pi\) | ||||
−0.115031 | + | 0.993362i | \(0.536697\pi\) | |||||||
\(240\) | −3.13468 | −0.202343 | ||||||||
\(241\) | 22.0482 | 1.42025 | 0.710125 | − | 0.704075i | \(-0.248638\pi\) | ||||
0.710125 | + | 0.704075i | \(0.248638\pi\) | |||||||
\(242\) | 6.16822 | 0.396508 | ||||||||
\(243\) | −8.65550 | −0.555250 | ||||||||
\(244\) | −0.741864 | −0.0474930 | ||||||||
\(245\) | 2.35375 | 0.150376 | ||||||||
\(246\) | 13.8740 | 0.884573 | ||||||||
\(247\) | −5.72765 | −0.364442 | ||||||||
\(248\) | 3.20401 | 0.203455 | ||||||||
\(249\) | −7.68406 | −0.486958 | ||||||||
\(250\) | −11.5839 | −0.732630 | ||||||||
\(251\) | −20.7095 | −1.30717 | −0.653587 | − | 0.756851i | \(-0.726737\pi\) | ||||
−0.653587 | + | 0.756851i | \(0.726737\pi\) | |||||||
\(252\) | −2.45497 | −0.154649 | ||||||||
\(253\) | −17.0368 | −1.07109 | ||||||||
\(254\) | −0.744794 | −0.0467325 | ||||||||
\(255\) | −2.59688 | −0.162623 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 27.8267 | 1.73578 | 0.867891 | − | 0.496754i | \(-0.165475\pi\) | ||||
0.867891 | + | 0.496754i | \(0.165475\pi\) | |||||||
\(258\) | −2.58374 | −0.160857 | ||||||||
\(259\) | −3.70787 | −0.230396 | ||||||||
\(260\) | 12.2811 | 0.761643 | ||||||||
\(261\) | −4.37995 | −0.271112 | ||||||||
\(262\) | 0.775074 | 0.0478842 | ||||||||
\(263\) | −25.6234 | −1.58001 | −0.790003 | − | 0.613103i | \(-0.789921\pi\) | ||||
−0.790003 | + | 0.613103i | \(0.789921\pi\) | |||||||
\(264\) | 6.05751 | 0.372814 | ||||||||
\(265\) | −20.8252 | −1.27928 | ||||||||
\(266\) | −2.84565 | −0.174478 | ||||||||
\(267\) | −23.1675 | −1.41783 | ||||||||
\(268\) | 12.6141 | 0.770528 | ||||||||
\(269\) | −13.2302 | −0.806658 | −0.403329 | − | 0.915055i | \(-0.632147\pi\) | ||||
−0.403329 | + | 0.915055i | \(0.632147\pi\) | |||||||
\(270\) | 12.1084 | 0.736892 | ||||||||
\(271\) | 16.9638 | 1.03048 | 0.515240 | − | 0.857046i | \(-0.327703\pi\) | ||||
0.515240 | + | 0.857046i | \(0.327703\pi\) | |||||||
\(272\) | 0.828433 | 0.0502311 | ||||||||
\(273\) | −23.8281 | −1.44214 | ||||||||
\(274\) | −10.8225 | −0.653812 | ||||||||
\(275\) | 1.66765 | 0.100563 | ||||||||
\(276\) | −6.01113 | −0.361828 | ||||||||
\(277\) | −5.90568 | −0.354838 | −0.177419 | − | 0.984135i | \(-0.556775\pi\) | ||||
−0.177419 | + | 0.984135i | \(0.556775\pi\) | |||||||
\(278\) | −5.75291 | −0.345037 | ||||||||
\(279\) | −2.76413 | −0.165484 | ||||||||
\(280\) | 6.10160 | 0.364640 | ||||||||
\(281\) | −20.4261 | −1.21852 | −0.609261 | − | 0.792970i | \(-0.708534\pi\) | ||||
−0.609261 | + | 0.792970i | \(0.708534\pi\) | |||||||
\(282\) | −8.80465 | −0.524309 | ||||||||
\(283\) | 4.60453 | 0.273711 | 0.136855 | − | 0.990591i | \(-0.456300\pi\) | ||||
0.136855 | + | 0.990591i | \(0.456300\pi\) | |||||||
\(284\) | 1.20025 | 0.0712219 | ||||||||
\(285\) | 3.13468 | 0.185683 | ||||||||
\(286\) | −23.7323 | −1.40332 | ||||||||
\(287\) | −27.0054 | −1.59408 | ||||||||
\(288\) | −0.862709 | −0.0508356 | ||||||||
\(289\) | −16.3137 | −0.959629 | ||||||||
\(290\) | 10.8860 | 0.639245 | ||||||||
\(291\) | 13.1666 | 0.771839 | ||||||||
\(292\) | 14.2635 | 0.834710 | ||||||||
\(293\) | −16.3422 | −0.954723 | −0.477362 | − | 0.878707i | \(-0.658407\pi\) | ||||
−0.477362 | + | 0.878707i | \(0.658407\pi\) | |||||||
\(294\) | −1.60484 | −0.0935959 | ||||||||
\(295\) | −2.50482 | −0.145836 | ||||||||
\(296\) | −1.30300 | −0.0757351 | ||||||||
\(297\) | −23.3984 | −1.35771 | ||||||||
\(298\) | 17.6403 | 1.02187 | ||||||||
\(299\) | 23.5506 | 1.36196 | ||||||||
\(300\) | 0.588401 | 0.0339713 | ||||||||
\(301\) | 5.02920 | 0.289879 | ||||||||
\(302\) | −11.6954 | −0.672992 | ||||||||
\(303\) | −14.5670 | −0.836851 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −1.59069 | −0.0910828 | ||||||||
\(306\) | −0.714697 | −0.0408565 | ||||||||
\(307\) | 4.35094 | 0.248321 | 0.124161 | − | 0.992262i | \(-0.460376\pi\) | ||||
0.124161 | + | 0.992262i | \(0.460376\pi\) | |||||||
\(308\) | −11.7908 | −0.671845 | ||||||||
\(309\) | 11.5776 | 0.658628 | ||||||||
\(310\) | 6.86997 | 0.390188 | ||||||||
\(311\) | −1.44045 | −0.0816803 | −0.0408402 | − | 0.999166i | \(-0.513003\pi\) | ||||
−0.0408402 | + | 0.999166i | \(0.513003\pi\) | |||||||
\(312\) | −8.37352 | −0.474057 | ||||||||
\(313\) | 17.9598 | 1.01515 | 0.507575 | − | 0.861608i | \(-0.330542\pi\) | ||||
0.507575 | + | 0.861608i | \(0.330542\pi\) | |||||||
\(314\) | 19.0859 | 1.07708 | ||||||||
\(315\) | −5.26391 | −0.296588 | ||||||||
\(316\) | 0.0154584 | 0.000869600 0 | ||||||||
\(317\) | 4.35186 | 0.244425 | 0.122212 | − | 0.992504i | \(-0.461001\pi\) | ||||
0.122212 | + | 0.992504i | \(0.461001\pi\) | |||||||
\(318\) | 14.1990 | 0.796242 | ||||||||
\(319\) | −21.0362 | −1.17780 | ||||||||
\(320\) | 2.14418 | 0.119863 | ||||||||
\(321\) | 28.5475 | 1.59337 | ||||||||
\(322\) | 11.7006 | 0.652047 | ||||||||
\(323\) | −0.828433 | −0.0460953 | ||||||||
\(324\) | −5.66760 | −0.314867 | ||||||||
\(325\) | −2.30525 | −0.127872 | ||||||||
\(326\) | −4.38341 | −0.242775 | ||||||||
\(327\) | −3.13428 | −0.173326 | ||||||||
\(328\) | −9.49007 | −0.524001 | ||||||||
\(329\) | 17.1381 | 0.944853 | ||||||||
\(330\) | 12.9884 | 0.714989 | ||||||||
\(331\) | 11.8181 | 0.649582 | 0.324791 | − | 0.945786i | \(-0.394706\pi\) | ||||
0.324791 | + | 0.945786i | \(0.394706\pi\) | |||||||
\(332\) | 5.25605 | 0.288463 | ||||||||
\(333\) | 1.12411 | 0.0616007 | ||||||||
\(334\) | 12.6831 | 0.693986 | ||||||||
\(335\) | 27.0469 | 1.47773 | ||||||||
\(336\) | −4.16019 | −0.226957 | ||||||||
\(337\) | −19.4839 | −1.06135 | −0.530677 | − | 0.847574i | \(-0.678062\pi\) | ||||
−0.530677 | + | 0.847574i | \(0.678062\pi\) | |||||||
\(338\) | 19.8060 | 1.07730 | ||||||||
\(339\) | −25.1757 | −1.36736 | ||||||||
\(340\) | 1.77631 | 0.0963341 | ||||||||
\(341\) | −13.2757 | −0.718917 | ||||||||
\(342\) | 0.862709 | 0.0466500 | ||||||||
\(343\) | −16.7958 | −0.906887 | ||||||||
\(344\) | 1.76733 | 0.0952880 | ||||||||
\(345\) | −12.8890 | −0.693919 | ||||||||
\(346\) | 14.5957 | 0.784671 | ||||||||
\(347\) | 10.4554 | 0.561274 | 0.280637 | − | 0.959814i | \(-0.409454\pi\) | ||||
0.280637 | + | 0.959814i | \(0.409454\pi\) | |||||||
\(348\) | −7.42227 | −0.397875 | ||||||||
\(349\) | 30.9932 | 1.65903 | 0.829515 | − | 0.558485i | \(-0.188617\pi\) | ||||
0.829515 | + | 0.558485i | \(0.188617\pi\) | |||||||
\(350\) | −1.14531 | −0.0612194 | ||||||||
\(351\) | 32.3445 | 1.72642 | ||||||||
\(352\) | −4.14345 | −0.220847 | ||||||||
\(353\) | 31.9801 | 1.70213 | 0.851064 | − | 0.525061i | \(-0.175958\pi\) | ||||
0.851064 | + | 0.525061i | \(0.175958\pi\) | |||||||
\(354\) | 1.70784 | 0.0907706 | ||||||||
\(355\) | 2.57356 | 0.136590 | ||||||||
\(356\) | 15.8470 | 0.839888 | ||||||||
\(357\) | −3.44644 | −0.182405 | ||||||||
\(358\) | −7.01955 | −0.370995 | ||||||||
\(359\) | 11.4813 | 0.605958 | 0.302979 | − | 0.952997i | \(-0.402019\pi\) | ||||
0.302979 | + | 0.952997i | \(0.402019\pi\) | |||||||
\(360\) | −1.84981 | −0.0974934 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 6.98602 | 0.367177 | ||||||||
\(363\) | −9.01761 | −0.473302 | ||||||||
\(364\) | 16.2989 | 0.854295 | ||||||||
\(365\) | 30.5836 | 1.60082 | ||||||||
\(366\) | 1.08457 | 0.0566912 | ||||||||
\(367\) | 4.21857 | 0.220207 | 0.110104 | − | 0.993920i | \(-0.464882\pi\) | ||||
0.110104 | + | 0.993920i | \(0.464882\pi\) | |||||||
\(368\) | 4.11173 | 0.214339 | ||||||||
\(369\) | 8.18717 | 0.426207 | ||||||||
\(370\) | −2.79386 | −0.145246 | ||||||||
\(371\) | −27.6381 | −1.43490 | ||||||||
\(372\) | −4.68409 | −0.242859 | ||||||||
\(373\) | 18.0156 | 0.932812 | 0.466406 | − | 0.884571i | \(-0.345549\pi\) | ||||
0.466406 | + | 0.884571i | \(0.345549\pi\) | |||||||
\(374\) | −3.43258 | −0.177494 | ||||||||
\(375\) | 16.9351 | 0.874523 | ||||||||
\(376\) | 6.02255 | 0.310589 | ||||||||
\(377\) | 29.0791 | 1.49765 | ||||||||
\(378\) | 16.0696 | 0.826532 | ||||||||
\(379\) | 11.2182 | 0.576242 | 0.288121 | − | 0.957594i | \(-0.406970\pi\) | ||||
0.288121 | + | 0.957594i | \(0.406970\pi\) | |||||||
\(380\) | −2.14418 | −0.109994 | ||||||||
\(381\) | 1.08885 | 0.0557834 | ||||||||
\(382\) | −4.48856 | −0.229655 | ||||||||
\(383\) | −1.60731 | −0.0821299 | −0.0410650 | − | 0.999156i | \(-0.513075\pi\) | ||||
−0.0410650 | + | 0.999156i | \(0.513075\pi\) | |||||||
\(384\) | −1.46195 | −0.0746047 | ||||||||
\(385\) | −25.2817 | −1.28848 | ||||||||
\(386\) | 15.3315 | 0.780351 | ||||||||
\(387\) | −1.52469 | −0.0775044 | ||||||||
\(388\) | −9.00620 | −0.457221 | ||||||||
\(389\) | −17.5609 | −0.890375 | −0.445187 | − | 0.895437i | \(-0.646863\pi\) | ||||
−0.445187 | + | 0.895437i | \(0.646863\pi\) | |||||||
\(390\) | −17.9544 | −0.909155 | ||||||||
\(391\) | 3.40629 | 0.172264 | ||||||||
\(392\) | 1.09774 | 0.0554442 | ||||||||
\(393\) | −1.13312 | −0.0571582 | ||||||||
\(394\) | −14.0812 | −0.709402 | ||||||||
\(395\) | 0.0331455 | 0.00166773 | ||||||||
\(396\) | 3.57460 | 0.179630 | ||||||||
\(397\) | −0.150873 | −0.00757208 | −0.00378604 | − | 0.999993i | \(-0.501205\pi\) | ||||
−0.00378604 | + | 0.999993i | \(0.501205\pi\) | |||||||
\(398\) | −7.77841 | −0.389897 | ||||||||
\(399\) | 4.16019 | 0.208270 | ||||||||
\(400\) | −0.402477 | −0.0201239 | ||||||||
\(401\) | −5.06306 | −0.252837 | −0.126418 | − | 0.991977i | \(-0.540348\pi\) | ||||
−0.126418 | + | 0.991977i | \(0.540348\pi\) | |||||||
\(402\) | −18.4411 | −0.919760 | ||||||||
\(403\) | 18.3514 | 0.914149 | ||||||||
\(404\) | 9.96408 | 0.495732 | ||||||||
\(405\) | −12.1524 | −0.603857 | ||||||||
\(406\) | 14.4473 | 0.717007 | ||||||||
\(407\) | 5.39891 | 0.267614 | ||||||||
\(408\) | −1.21113 | −0.0599597 | ||||||||
\(409\) | 29.5594 | 1.46162 | 0.730809 | − | 0.682581i | \(-0.239143\pi\) | ||||
0.730809 | + | 0.682581i | \(0.239143\pi\) | |||||||
\(410\) | −20.3484 | −1.00494 | ||||||||
\(411\) | 15.8219 | 0.780439 | ||||||||
\(412\) | −7.91932 | −0.390157 | ||||||||
\(413\) | −3.32427 | −0.163577 | ||||||||
\(414\) | −3.54723 | −0.174337 | ||||||||
\(415\) | 11.2699 | 0.553219 | ||||||||
\(416\) | 5.72765 | 0.280821 | ||||||||
\(417\) | 8.41045 | 0.411862 | ||||||||
\(418\) | 4.14345 | 0.202663 | ||||||||
\(419\) | −10.8629 | −0.530687 | −0.265343 | − | 0.964154i | \(-0.585485\pi\) | ||||
−0.265343 | + | 0.964154i | \(0.585485\pi\) | |||||||
\(420\) | −8.92022 | −0.435262 | ||||||||
\(421\) | 20.9345 | 1.02029 | 0.510143 | − | 0.860090i | \(-0.329593\pi\) | ||||
0.510143 | + | 0.860090i | \(0.329593\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | −5.19571 | −0.252624 | ||||||||
\(424\) | −9.71241 | −0.471676 | ||||||||
\(425\) | −0.333426 | −0.0161735 | ||||||||
\(426\) | −1.75471 | −0.0850158 | ||||||||
\(427\) | −2.11109 | −0.102163 | ||||||||
\(428\) | −19.5270 | −0.943875 | ||||||||
\(429\) | 34.6953 | 1.67511 | ||||||||
\(430\) | 3.78948 | 0.182745 | ||||||||
\(431\) | −24.5708 | −1.18353 | −0.591767 | − | 0.806109i | \(-0.701569\pi\) | ||||
−0.591767 | + | 0.806109i | \(0.701569\pi\) | |||||||
\(432\) | 5.64708 | 0.271695 | ||||||||
\(433\) | −10.2969 | −0.494836 | −0.247418 | − | 0.968909i | \(-0.579582\pi\) | ||||
−0.247418 | + | 0.968909i | \(0.579582\pi\) | |||||||
\(434\) | 9.11749 | 0.437653 | ||||||||
\(435\) | −15.9147 | −0.763051 | ||||||||
\(436\) | 2.14391 | 0.102674 | ||||||||
\(437\) | −4.11173 | −0.196691 | ||||||||
\(438\) | −20.8525 | −0.996372 | ||||||||
\(439\) | 23.3441 | 1.11415 | 0.557077 | − | 0.830461i | \(-0.311923\pi\) | ||||
0.557077 | + | 0.830461i | \(0.311923\pi\) | |||||||
\(440\) | −8.88433 | −0.423544 | ||||||||
\(441\) | −0.947029 | −0.0450966 | ||||||||
\(442\) | 4.74497 | 0.225695 | ||||||||
\(443\) | −35.5818 | −1.69054 | −0.845271 | − | 0.534338i | \(-0.820561\pi\) | ||||
−0.845271 | + | 0.534338i | \(0.820561\pi\) | |||||||
\(444\) | 1.90491 | 0.0904031 | ||||||||
\(445\) | 33.9788 | 1.61075 | ||||||||
\(446\) | −25.6890 | −1.21641 | ||||||||
\(447\) | −25.7892 | −1.21979 | ||||||||
\(448\) | 2.84565 | 0.134444 | ||||||||
\(449\) | 25.6489 | 1.21045 | 0.605223 | − | 0.796056i | \(-0.293084\pi\) | ||||
0.605223 | + | 0.796056i | \(0.293084\pi\) | |||||||
\(450\) | 0.347221 | 0.0163682 | ||||||||
\(451\) | 39.3217 | 1.85159 | ||||||||
\(452\) | 17.2207 | 0.809993 | ||||||||
\(453\) | 17.0980 | 0.803334 | ||||||||
\(454\) | −0.630959 | −0.0296124 | ||||||||
\(455\) | 34.9478 | 1.63838 | ||||||||
\(456\) | 1.46195 | 0.0684620 | ||||||||
\(457\) | −24.8873 | −1.16418 | −0.582090 | − | 0.813124i | \(-0.697765\pi\) | ||||
−0.582090 | + | 0.813124i | \(0.697765\pi\) | |||||||
\(458\) | 15.0811 | 0.704694 | ||||||||
\(459\) | 4.67823 | 0.218361 | ||||||||
\(460\) | 8.81631 | 0.411062 | ||||||||
\(461\) | 18.8711 | 0.878915 | 0.439457 | − | 0.898263i | \(-0.355171\pi\) | ||||
0.439457 | + | 0.898263i | \(0.355171\pi\) | |||||||
\(462\) | 17.2376 | 0.801965 | ||||||||
\(463\) | −4.38457 | −0.203768 | −0.101884 | − | 0.994796i | \(-0.532487\pi\) | ||||
−0.101884 | + | 0.994796i | \(0.532487\pi\) | |||||||
\(464\) | 5.07697 | 0.235692 | ||||||||
\(465\) | −10.0435 | −0.465758 | ||||||||
\(466\) | 9.27718 | 0.429757 | ||||||||
\(467\) | −9.98957 | −0.462262 | −0.231131 | − | 0.972923i | \(-0.574243\pi\) | ||||
−0.231131 | + | 0.972923i | \(0.574243\pi\) | |||||||
\(468\) | −4.94130 | −0.228412 | ||||||||
\(469\) | 35.8953 | 1.65749 | ||||||||
\(470\) | 12.9134 | 0.595653 | ||||||||
\(471\) | −27.9026 | −1.28568 | ||||||||
\(472\) | −1.16819 | −0.0537705 | ||||||||
\(473\) | −7.32285 | −0.336705 | ||||||||
\(474\) | −0.0225993 | −0.00103802 | ||||||||
\(475\) | 0.402477 | 0.0184669 | ||||||||
\(476\) | 2.35743 | 0.108053 | ||||||||
\(477\) | 8.37899 | 0.383648 | ||||||||
\(478\) | −3.55667 | −0.162678 | ||||||||
\(479\) | 40.2855 | 1.84069 | 0.920346 | − | 0.391106i | \(-0.127907\pi\) | ||||
0.920346 | + | 0.391106i | \(0.127907\pi\) | |||||||
\(480\) | −3.13468 | −0.143078 | ||||||||
\(481\) | −7.46311 | −0.340288 | ||||||||
\(482\) | 22.0482 | 1.00427 | ||||||||
\(483\) | −17.1056 | −0.778332 | ||||||||
\(484\) | 6.16822 | 0.280374 | ||||||||
\(485\) | −19.3109 | −0.876865 | ||||||||
\(486\) | −8.65550 | −0.392621 | ||||||||
\(487\) | 14.0124 | 0.634964 | 0.317482 | − | 0.948264i | \(-0.397163\pi\) | ||||
0.317482 | + | 0.948264i | \(0.397163\pi\) | |||||||
\(488\) | −0.741864 | −0.0335826 | ||||||||
\(489\) | 6.40832 | 0.289794 | ||||||||
\(490\) | 2.35375 | 0.106332 | ||||||||
\(491\) | −12.7909 | −0.577243 | −0.288622 | − | 0.957443i | \(-0.593197\pi\) | ||||
−0.288622 | + | 0.957443i | \(0.593197\pi\) | |||||||
\(492\) | 13.8740 | 0.625487 | ||||||||
\(493\) | 4.20593 | 0.189426 | ||||||||
\(494\) | −5.72765 | −0.257699 | ||||||||
\(495\) | 7.66459 | 0.344498 | ||||||||
\(496\) | 3.20401 | 0.143864 | ||||||||
\(497\) | 3.41550 | 0.153206 | ||||||||
\(498\) | −7.68406 | −0.344331 | ||||||||
\(499\) | 2.40267 | 0.107558 | 0.0537791 | − | 0.998553i | \(-0.482873\pi\) | ||||
0.0537791 | + | 0.998553i | \(0.482873\pi\) | |||||||
\(500\) | −11.5839 | −0.518048 | ||||||||
\(501\) | −18.5420 | −0.828394 | ||||||||
\(502\) | −20.7095 | −0.924312 | ||||||||
\(503\) | −32.3328 | −1.44165 | −0.720824 | − | 0.693118i | \(-0.756237\pi\) | ||||
−0.720824 | + | 0.693118i | \(0.756237\pi\) | |||||||
\(504\) | −2.45497 | −0.109353 | ||||||||
\(505\) | 21.3648 | 0.950722 | ||||||||
\(506\) | −17.0368 | −0.757377 | ||||||||
\(507\) | −28.9553 | −1.28595 | ||||||||
\(508\) | −0.744794 | −0.0330449 | ||||||||
\(509\) | 30.9450 | 1.37161 | 0.685807 | − | 0.727783i | \(-0.259449\pi\) | ||||
0.685807 | + | 0.727783i | \(0.259449\pi\) | |||||||
\(510\) | −2.59688 | −0.114992 | ||||||||
\(511\) | 40.5890 | 1.79555 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −5.64708 | −0.249325 | ||||||||
\(514\) | 27.8267 | 1.22738 | ||||||||
\(515\) | −16.9805 | −0.748249 | ||||||||
\(516\) | −2.58374 | −0.113743 | ||||||||
\(517\) | −24.9542 | −1.09748 | ||||||||
\(518\) | −3.70787 | −0.162915 | ||||||||
\(519\) | −21.3382 | −0.936642 | ||||||||
\(520\) | 12.2811 | 0.538563 | ||||||||
\(521\) | 27.0458 | 1.18490 | 0.592450 | − | 0.805608i | \(-0.298161\pi\) | ||||
0.592450 | + | 0.805608i | \(0.298161\pi\) | |||||||
\(522\) | −4.37995 | −0.191705 | ||||||||
\(523\) | −12.6584 | −0.553514 | −0.276757 | − | 0.960940i | \(-0.589260\pi\) | ||||
−0.276757 | + | 0.960940i | \(0.589260\pi\) | |||||||
\(524\) | 0.775074 | 0.0338592 | ||||||||
\(525\) | 1.67438 | 0.0730761 | ||||||||
\(526\) | −25.6234 | −1.11723 | ||||||||
\(527\) | 2.65430 | 0.115623 | ||||||||
\(528\) | 6.05751 | 0.263619 | ||||||||
\(529\) | −6.09367 | −0.264942 | ||||||||
\(530\) | −20.8252 | −0.904588 | ||||||||
\(531\) | 1.00781 | 0.0437353 | ||||||||
\(532\) | −2.84565 | −0.123375 | ||||||||
\(533\) | −54.3558 | −2.35441 | ||||||||
\(534\) | −23.1675 | −1.00255 | ||||||||
\(535\) | −41.8696 | −1.81018 | ||||||||
\(536\) | 12.6141 | 0.544846 | ||||||||
\(537\) | 10.2622 | 0.442847 | ||||||||
\(538\) | −13.2302 | −0.570393 | ||||||||
\(539\) | −4.54843 | −0.195915 | ||||||||
\(540\) | 12.1084 | 0.521061 | ||||||||
\(541\) | 12.2683 | 0.527455 | 0.263727 | − | 0.964597i | \(-0.415048\pi\) | ||||
0.263727 | + | 0.964597i | \(0.415048\pi\) | |||||||
\(542\) | 16.9638 | 0.728660 | ||||||||
\(543\) | −10.2132 | −0.438290 | ||||||||
\(544\) | 0.828433 | 0.0355188 | ||||||||
\(545\) | 4.59693 | 0.196911 | ||||||||
\(546\) | −23.8281 | −1.01975 | ||||||||
\(547\) | −15.9475 | −0.681867 | −0.340933 | − | 0.940087i | \(-0.610743\pi\) | ||||
−0.340933 | + | 0.940087i | \(0.610743\pi\) | |||||||
\(548\) | −10.8225 | −0.462315 | ||||||||
\(549\) | 0.640013 | 0.0273151 | ||||||||
\(550\) | 1.66765 | 0.0711087 | ||||||||
\(551\) | −5.07697 | −0.216286 | ||||||||
\(552\) | −6.01113 | −0.255851 | ||||||||
\(553\) | 0.0439891 | 0.00187061 | ||||||||
\(554\) | −5.90568 | −0.250908 | ||||||||
\(555\) | 4.08448 | 0.173377 | ||||||||
\(556\) | −5.75291 | −0.243978 | ||||||||
\(557\) | −4.10858 | −0.174086 | −0.0870431 | − | 0.996205i | \(-0.527742\pi\) | ||||
−0.0870431 | + | 0.996205i | \(0.527742\pi\) | |||||||
\(558\) | −2.76413 | −0.117015 | ||||||||
\(559\) | 10.1226 | 0.428142 | ||||||||
\(560\) | 6.10160 | 0.257840 | ||||||||
\(561\) | 5.01824 | 0.211870 | ||||||||
\(562\) | −20.4261 | −0.861625 | ||||||||
\(563\) | 19.4469 | 0.819591 | 0.409796 | − | 0.912177i | \(-0.365600\pi\) | ||||
0.409796 | + | 0.912177i | \(0.365600\pi\) | |||||||
\(564\) | −8.80465 | −0.370743 | ||||||||
\(565\) | 36.9243 | 1.55342 | ||||||||
\(566\) | 4.60453 | 0.193543 | ||||||||
\(567\) | −16.1280 | −0.677314 | ||||||||
\(568\) | 1.20025 | 0.0503615 | ||||||||
\(569\) | −27.9325 | −1.17099 | −0.585496 | − | 0.810675i | \(-0.699100\pi\) | ||||
−0.585496 | + | 0.810675i | \(0.699100\pi\) | |||||||
\(570\) | 3.13468 | 0.131297 | ||||||||
\(571\) | 40.9053 | 1.71184 | 0.855918 | − | 0.517112i | \(-0.172993\pi\) | ||||
0.855918 | + | 0.517112i | \(0.172993\pi\) | |||||||
\(572\) | −23.7323 | −0.992296 | ||||||||
\(573\) | 6.56204 | 0.274133 | ||||||||
\(574\) | −27.0054 | −1.12719 | ||||||||
\(575\) | −1.65488 | −0.0690132 | ||||||||
\(576\) | −0.862709 | −0.0359462 | ||||||||
\(577\) | 29.0254 | 1.20834 | 0.604172 | − | 0.796854i | \(-0.293504\pi\) | ||||
0.604172 | + | 0.796854i | \(0.293504\pi\) | |||||||
\(578\) | −16.3137 | −0.678560 | ||||||||
\(579\) | −22.4138 | −0.931485 | ||||||||
\(580\) | 10.8860 | 0.452015 | ||||||||
\(581\) | 14.9569 | 0.620516 | ||||||||
\(582\) | 13.1666 | 0.545773 | ||||||||
\(583\) | 40.2429 | 1.66669 | ||||||||
\(584\) | 14.2635 | 0.590229 | ||||||||
\(585\) | −10.5950 | −0.438051 | ||||||||
\(586\) | −16.3422 | −0.675091 | ||||||||
\(587\) | −36.9891 | −1.52670 | −0.763351 | − | 0.645984i | \(-0.776447\pi\) | ||||
−0.763351 | + | 0.645984i | \(0.776447\pi\) | |||||||
\(588\) | −1.60484 | −0.0661823 | ||||||||
\(589\) | −3.20401 | −0.132019 | ||||||||
\(590\) | −2.50482 | −0.103122 | ||||||||
\(591\) | 20.5860 | 0.846796 | ||||||||
\(592\) | −1.30300 | −0.0535528 | ||||||||
\(593\) | 14.0042 | 0.575084 | 0.287542 | − | 0.957768i | \(-0.407162\pi\) | ||||
0.287542 | + | 0.957768i | \(0.407162\pi\) | |||||||
\(594\) | −23.3984 | −0.960049 | ||||||||
\(595\) | 5.05477 | 0.207225 | ||||||||
\(596\) | 17.6403 | 0.722574 | ||||||||
\(597\) | 11.3716 | 0.465410 | ||||||||
\(598\) | 23.5506 | 0.963054 | ||||||||
\(599\) | −21.9668 | −0.897540 | −0.448770 | − | 0.893647i | \(-0.648138\pi\) | ||||
−0.448770 | + | 0.893647i | \(0.648138\pi\) | |||||||
\(600\) | 0.588401 | 0.0240214 | ||||||||
\(601\) | −0.402585 | −0.0164218 | −0.00821089 | − | 0.999966i | \(-0.502614\pi\) | ||||
−0.00821089 | + | 0.999966i | \(0.502614\pi\) | |||||||
\(602\) | 5.02920 | 0.204975 | ||||||||
\(603\) | −10.8823 | −0.443161 | ||||||||
\(604\) | −11.6954 | −0.475877 | ||||||||
\(605\) | 13.2258 | 0.537705 | ||||||||
\(606\) | −14.5670 | −0.591743 | ||||||||
\(607\) | −17.8165 | −0.723150 | −0.361575 | − | 0.932343i | \(-0.617761\pi\) | ||||
−0.361575 | + | 0.932343i | \(0.617761\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −21.1212 | −0.855874 | ||||||||
\(610\) | −1.59069 | −0.0644053 | ||||||||
\(611\) | 34.4950 | 1.39552 | ||||||||
\(612\) | −0.714697 | −0.0288899 | ||||||||
\(613\) | 0.241320 | 0.00974684 | 0.00487342 | − | 0.999988i | \(-0.498449\pi\) | ||||
0.00487342 | + | 0.999988i | \(0.498449\pi\) | |||||||
\(614\) | 4.35094 | 0.175590 | ||||||||
\(615\) | 29.7484 | 1.19957 | ||||||||
\(616\) | −11.7908 | −0.475066 | ||||||||
\(617\) | −22.2070 | −0.894020 | −0.447010 | − | 0.894529i | \(-0.647511\pi\) | ||||
−0.447010 | + | 0.894529i | \(0.647511\pi\) | |||||||
\(618\) | 11.5776 | 0.465720 | ||||||||
\(619\) | −43.9613 | −1.76695 | −0.883476 | − | 0.468476i | \(-0.844803\pi\) | ||||
−0.883476 | + | 0.468476i | \(0.844803\pi\) | |||||||
\(620\) | 6.86997 | 0.275905 | ||||||||
\(621\) | 23.2193 | 0.931757 | ||||||||
\(622\) | −1.44045 | −0.0577567 | ||||||||
\(623\) | 45.0950 | 1.80669 | ||||||||
\(624\) | −8.37352 | −0.335209 | ||||||||
\(625\) | −22.8256 | −0.913025 | ||||||||
\(626\) | 17.9598 | 0.717819 | ||||||||
\(627\) | −6.05751 | −0.241914 | ||||||||
\(628\) | 19.0859 | 0.761611 | ||||||||
\(629\) | −1.07945 | −0.0430403 | ||||||||
\(630\) | −5.26391 | −0.209719 | ||||||||
\(631\) | 17.9004 | 0.712603 | 0.356301 | − | 0.934371i | \(-0.384038\pi\) | ||||
0.356301 | + | 0.934371i | \(0.384038\pi\) | |||||||
\(632\) | 0.0154584 | 0.000614900 0 | ||||||||
\(633\) | 1.46195 | 0.0581072 | ||||||||
\(634\) | 4.35186 | 0.172834 | ||||||||
\(635\) | −1.59697 | −0.0633740 | ||||||||
\(636\) | 14.1990 | 0.563028 | ||||||||
\(637\) | 6.28746 | 0.249118 | ||||||||
\(638\) | −21.0362 | −0.832831 | ||||||||
\(639\) | −1.03547 | −0.0409625 | ||||||||
\(640\) | 2.14418 | 0.0847563 | ||||||||
\(641\) | 19.7232 | 0.779021 | 0.389511 | − | 0.921022i | \(-0.372644\pi\) | ||||
0.389511 | + | 0.921022i | \(0.372644\pi\) | |||||||
\(642\) | 28.5475 | 1.12668 | ||||||||
\(643\) | 29.3895 | 1.15901 | 0.579505 | − | 0.814969i | \(-0.303246\pi\) | ||||
0.579505 | + | 0.814969i | \(0.303246\pi\) | |||||||
\(644\) | 11.7006 | 0.461067 | ||||||||
\(645\) | −5.54002 | −0.218138 | ||||||||
\(646\) | −0.828433 | −0.0325943 | ||||||||
\(647\) | −18.7284 | −0.736290 | −0.368145 | − | 0.929768i | \(-0.620007\pi\) | ||||
−0.368145 | + | 0.929768i | \(0.620007\pi\) | |||||||
\(648\) | −5.66760 | −0.222645 | ||||||||
\(649\) | 4.84036 | 0.190001 | ||||||||
\(650\) | −2.30525 | −0.0904193 | ||||||||
\(651\) | −13.3293 | −0.522416 | ||||||||
\(652\) | −4.38341 | −0.171668 | ||||||||
\(653\) | −28.2590 | −1.10586 | −0.552930 | − | 0.833228i | \(-0.686490\pi\) | ||||
−0.552930 | + | 0.833228i | \(0.686490\pi\) | |||||||
\(654\) | −3.13428 | −0.122560 | ||||||||
\(655\) | 1.66190 | 0.0649358 | ||||||||
\(656\) | −9.49007 | −0.370525 | ||||||||
\(657\) | −12.3053 | −0.480075 | ||||||||
\(658\) | 17.1381 | 0.668112 | ||||||||
\(659\) | −14.9519 | −0.582442 | −0.291221 | − | 0.956656i | \(-0.594061\pi\) | ||||
−0.291221 | + | 0.956656i | \(0.594061\pi\) | |||||||
\(660\) | 12.9884 | 0.505574 | ||||||||
\(661\) | 33.3340 | 1.29654 | 0.648272 | − | 0.761409i | \(-0.275492\pi\) | ||||
0.648272 | + | 0.761409i | \(0.275492\pi\) | |||||||
\(662\) | 11.8181 | 0.459324 | ||||||||
\(663\) | −6.93690 | −0.269407 | ||||||||
\(664\) | 5.25605 | 0.203974 | ||||||||
\(665\) | −6.10160 | −0.236610 | ||||||||
\(666\) | 1.12411 | 0.0435583 | ||||||||
\(667\) | 20.8751 | 0.808289 | ||||||||
\(668\) | 12.6831 | 0.490722 | ||||||||
\(669\) | 37.5559 | 1.45200 | ||||||||
\(670\) | 27.0469 | 1.04491 | ||||||||
\(671\) | 3.07388 | 0.118666 | ||||||||
\(672\) | −4.16019 | −0.160483 | ||||||||
\(673\) | −15.6909 | −0.604839 | −0.302419 | − | 0.953175i | \(-0.597794\pi\) | ||||
−0.302419 | + | 0.953175i | \(0.597794\pi\) | |||||||
\(674\) | −19.4839 | −0.750490 | ||||||||
\(675\) | −2.27282 | −0.0874809 | ||||||||
\(676\) | 19.8060 | 0.761768 | ||||||||
\(677\) | 2.12121 | 0.0815246 | 0.0407623 | − | 0.999169i | \(-0.487021\pi\) | ||||
0.0407623 | + | 0.999169i | \(0.487021\pi\) | |||||||
\(678\) | −25.1757 | −0.966868 | ||||||||
\(679\) | −25.6285 | −0.983532 | ||||||||
\(680\) | 1.77631 | 0.0681185 | ||||||||
\(681\) | 0.922429 | 0.0353476 | ||||||||
\(682\) | −13.2757 | −0.508351 | ||||||||
\(683\) | 44.9510 | 1.72000 | 0.860001 | − | 0.510293i | \(-0.170463\pi\) | ||||
0.860001 | + | 0.510293i | \(0.170463\pi\) | |||||||
\(684\) | 0.862709 | 0.0329865 | ||||||||
\(685\) | −23.2055 | −0.886635 | ||||||||
\(686\) | −16.7958 | −0.641266 | ||||||||
\(687\) | −22.0478 | −0.841176 | ||||||||
\(688\) | 1.76733 | 0.0673788 | ||||||||
\(689\) | −55.6293 | −2.11931 | ||||||||
\(690\) | −12.8890 | −0.490675 | ||||||||
\(691\) | −30.8647 | −1.17415 | −0.587074 | − | 0.809534i | \(-0.699720\pi\) | ||||
−0.587074 | + | 0.809534i | \(0.699720\pi\) | |||||||
\(692\) | 14.5957 | 0.554846 | ||||||||
\(693\) | 10.1721 | 0.386405 | ||||||||
\(694\) | 10.4554 | 0.396880 | ||||||||
\(695\) | −12.3353 | −0.467904 | ||||||||
\(696\) | −7.42227 | −0.281340 | ||||||||
\(697\) | −7.86189 | −0.297790 | ||||||||
\(698\) | 30.9932 | 1.17311 | ||||||||
\(699\) | −13.5628 | −0.512990 | ||||||||
\(700\) | −1.14531 | −0.0432887 | ||||||||
\(701\) | −13.8059 | −0.521441 | −0.260721 | − | 0.965414i | \(-0.583960\pi\) | ||||
−0.260721 | + | 0.965414i | \(0.583960\pi\) | |||||||
\(702\) | 32.3445 | 1.22076 | ||||||||
\(703\) | 1.30300 | 0.0491434 | ||||||||
\(704\) | −4.14345 | −0.156162 | ||||||||
\(705\) | −18.8788 | −0.711016 | ||||||||
\(706\) | 31.9801 | 1.20359 | ||||||||
\(707\) | 28.3543 | 1.06637 | ||||||||
\(708\) | 1.70784 | 0.0641845 | ||||||||
\(709\) | 38.8522 | 1.45913 | 0.729563 | − | 0.683914i | \(-0.239724\pi\) | ||||
0.729563 | + | 0.683914i | \(0.239724\pi\) | |||||||
\(710\) | 2.57356 | 0.0965841 | ||||||||
\(711\) | −0.0133361 | −0.000500142 0 | ||||||||
\(712\) | 15.8470 | 0.593891 | ||||||||
\(713\) | 13.1740 | 0.493370 | ||||||||
\(714\) | −3.44644 | −0.128980 | ||||||||
\(715\) | −50.8863 | −1.90304 | ||||||||
\(716\) | −7.01955 | −0.262333 | ||||||||
\(717\) | 5.19967 | 0.194185 | ||||||||
\(718\) | 11.4813 | 0.428477 | ||||||||
\(719\) | −5.04037 | −0.187974 | −0.0939870 | − | 0.995573i | \(-0.529961\pi\) | ||||
−0.0939870 | + | 0.995573i | \(0.529961\pi\) | |||||||
\(720\) | −1.84981 | −0.0689383 | ||||||||
\(721\) | −22.5356 | −0.839271 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −32.2333 | −1.19877 | ||||||||
\(724\) | 6.98602 | 0.259633 | ||||||||
\(725\) | −2.04337 | −0.0758887 | ||||||||
\(726\) | −9.01761 | −0.334675 | ||||||||
\(727\) | 21.3845 | 0.793106 | 0.396553 | − | 0.918012i | \(-0.370206\pi\) | ||||
0.396553 | + | 0.918012i | \(0.370206\pi\) | |||||||
\(728\) | 16.2989 | 0.604077 | ||||||||
\(729\) | 29.6567 | 1.09840 | ||||||||
\(730\) | 30.5836 | 1.13195 | ||||||||
\(731\) | 1.46411 | 0.0541522 | ||||||||
\(732\) | 1.08457 | 0.0400867 | ||||||||
\(733\) | 38.8646 | 1.43550 | 0.717748 | − | 0.696303i | \(-0.245173\pi\) | ||||
0.717748 | + | 0.696303i | \(0.245173\pi\) | |||||||
\(734\) | 4.21857 | 0.155710 | ||||||||
\(735\) | −3.44106 | −0.126926 | ||||||||
\(736\) | 4.11173 | 0.151560 | ||||||||
\(737\) | −52.2659 | −1.92524 | ||||||||
\(738\) | 8.18717 | 0.301374 | ||||||||
\(739\) | −13.4327 | −0.494129 | −0.247064 | − | 0.968999i | \(-0.579466\pi\) | ||||
−0.247064 | + | 0.968999i | \(0.579466\pi\) | |||||||
\(740\) | −2.79386 | −0.102704 | ||||||||
\(741\) | 8.37352 | 0.307609 | ||||||||
\(742\) | −27.6381 | −1.01463 | ||||||||
\(743\) | 2.75446 | 0.101051 | 0.0505257 | − | 0.998723i | \(-0.483910\pi\) | ||||
0.0505257 | + | 0.998723i | \(0.483910\pi\) | |||||||
\(744\) | −4.68409 | −0.171727 | ||||||||
\(745\) | 37.8240 | 1.38576 | ||||||||
\(746\) | 18.0156 | 0.659598 | ||||||||
\(747\) | −4.53444 | −0.165906 | ||||||||
\(748\) | −3.43258 | −0.125507 | ||||||||
\(749\) | −55.5672 | −2.03038 | ||||||||
\(750\) | 16.9351 | 0.618381 | ||||||||
\(751\) | 33.9990 | 1.24064 | 0.620320 | − | 0.784349i | \(-0.287003\pi\) | ||||
0.620320 | + | 0.784349i | \(0.287003\pi\) | |||||||
\(752\) | 6.02255 | 0.219620 | ||||||||
\(753\) | 30.2763 | 1.10333 | ||||||||
\(754\) | 29.0791 | 1.05900 | ||||||||
\(755\) | −25.0770 | −0.912645 | ||||||||
\(756\) | 16.0696 | 0.584447 | ||||||||
\(757\) | −22.4250 | −0.815049 | −0.407524 | − | 0.913194i | \(-0.633608\pi\) | ||||
−0.407524 | + | 0.913194i | \(0.633608\pi\) | |||||||
\(758\) | 11.2182 | 0.407464 | ||||||||
\(759\) | 24.9069 | 0.904062 | ||||||||
\(760\) | −2.14418 | −0.0777777 | ||||||||
\(761\) | −38.2175 | −1.38538 | −0.692691 | − | 0.721235i | \(-0.743575\pi\) | ||||
−0.692691 | + | 0.721235i | \(0.743575\pi\) | |||||||
\(762\) | 1.08885 | 0.0394448 | ||||||||
\(763\) | 6.10081 | 0.220864 | ||||||||
\(764\) | −4.48856 | −0.162391 | ||||||||
\(765\) | −1.53244 | −0.0554055 | ||||||||
\(766\) | −1.60731 | −0.0580746 | ||||||||
\(767\) | −6.69101 | −0.241598 | ||||||||
\(768\) | −1.46195 | −0.0527535 | ||||||||
\(769\) | −18.3195 | −0.660618 | −0.330309 | − | 0.943873i | \(-0.607153\pi\) | ||||
−0.330309 | + | 0.943873i | \(0.607153\pi\) | |||||||
\(770\) | −25.2817 | −0.911090 | ||||||||
\(771\) | −40.6812 | −1.46510 | ||||||||
\(772\) | 15.3315 | 0.551791 | ||||||||
\(773\) | −12.4872 | −0.449133 | −0.224566 | − | 0.974459i | \(-0.572097\pi\) | ||||
−0.224566 | + | 0.974459i | \(0.572097\pi\) | |||||||
\(774\) | −1.52469 | −0.0548039 | ||||||||
\(775\) | −1.28954 | −0.0463216 | ||||||||
\(776\) | −9.00620 | −0.323304 | ||||||||
\(777\) | 5.42072 | 0.194467 | ||||||||
\(778\) | −17.5609 | −0.629590 | ||||||||
\(779\) | 9.49007 | 0.340017 | ||||||||
\(780\) | −17.9544 | −0.642870 | ||||||||
\(781\) | −4.97319 | −0.177955 | ||||||||
\(782\) | 3.40629 | 0.121809 | ||||||||
\(783\) | 28.6701 | 1.02458 | ||||||||
\(784\) | 1.09774 | 0.0392049 | ||||||||
\(785\) | 40.9237 | 1.46063 | ||||||||
\(786\) | −1.13312 | −0.0404169 | ||||||||
\(787\) | 33.3598 | 1.18915 | 0.594575 | − | 0.804040i | \(-0.297320\pi\) | ||||
0.594575 | + | 0.804040i | \(0.297320\pi\) | |||||||
\(788\) | −14.0812 | −0.501623 | ||||||||
\(789\) | 37.4600 | 1.33361 | ||||||||
\(790\) | 0.0331455 | 0.00117927 | ||||||||
\(791\) | 49.0041 | 1.74238 | ||||||||
\(792\) | 3.57460 | 0.127018 | ||||||||
\(793\) | −4.24914 | −0.150891 | ||||||||
\(794\) | −0.150873 | −0.00535427 | ||||||||
\(795\) | 30.4453 | 1.07978 | ||||||||
\(796\) | −7.77841 | −0.275699 | ||||||||
\(797\) | −19.1245 | −0.677424 | −0.338712 | − | 0.940890i | \(-0.609991\pi\) | ||||
−0.338712 | + | 0.940890i | \(0.609991\pi\) | |||||||
\(798\) | 4.16019 | 0.147269 | ||||||||
\(799\) | 4.98928 | 0.176508 | ||||||||
\(800\) | −0.402477 | −0.0142297 | ||||||||
\(801\) | −13.6713 | −0.483053 | ||||||||
\(802\) | −5.06306 | −0.178783 | ||||||||
\(803\) | −59.1003 | −2.08560 | ||||||||
\(804\) | −18.4411 | −0.650369 | ||||||||
\(805\) | 25.0881 | 0.884241 | ||||||||
\(806\) | 18.3514 | 0.646401 | ||||||||
\(807\) | 19.3418 | 0.680864 | ||||||||
\(808\) | 9.96408 | 0.350535 | ||||||||
\(809\) | −49.0298 | −1.72380 | −0.861898 | − | 0.507081i | \(-0.830725\pi\) | ||||
−0.861898 | + | 0.507081i | \(0.830725\pi\) | |||||||
\(810\) | −12.1524 | −0.426991 | ||||||||
\(811\) | 9.58531 | 0.336586 | 0.168293 | − | 0.985737i | \(-0.446175\pi\) | ||||
0.168293 | + | 0.985737i | \(0.446175\pi\) | |||||||
\(812\) | 14.4473 | 0.507001 | ||||||||
\(813\) | −24.8003 | −0.869783 | ||||||||
\(814\) | 5.39891 | 0.189232 | ||||||||
\(815\) | −9.39884 | −0.329227 | ||||||||
\(816\) | −1.21113 | −0.0423979 | ||||||||
\(817\) | −1.76733 | −0.0618310 | ||||||||
\(818\) | 29.5594 | 1.03352 | ||||||||
\(819\) | −14.0612 | −0.491339 | ||||||||
\(820\) | −20.3484 | −0.710599 | ||||||||
\(821\) | 25.8400 | 0.901823 | 0.450912 | − | 0.892569i | \(-0.351099\pi\) | ||||
0.450912 | + | 0.892569i | \(0.351099\pi\) | |||||||
\(822\) | 15.8219 | 0.551854 | ||||||||
\(823\) | −22.3393 | −0.778700 | −0.389350 | − | 0.921090i | \(-0.627300\pi\) | ||||
−0.389350 | + | 0.921090i | \(0.627300\pi\) | |||||||
\(824\) | −7.91932 | −0.275882 | ||||||||
\(825\) | −2.43801 | −0.0848807 | ||||||||
\(826\) | −3.32427 | −0.115666 | ||||||||
\(827\) | 12.8864 | 0.448104 | 0.224052 | − | 0.974577i | \(-0.428072\pi\) | ||||
0.224052 | + | 0.974577i | \(0.428072\pi\) | |||||||
\(828\) | −3.54723 | −0.123275 | ||||||||
\(829\) | 17.9879 | 0.624747 | 0.312374 | − | 0.949959i | \(-0.398876\pi\) | ||||
0.312374 | + | 0.949959i | \(0.398876\pi\) | |||||||
\(830\) | 11.2699 | 0.391185 | ||||||||
\(831\) | 8.63379 | 0.299503 | ||||||||
\(832\) | 5.72765 | 0.198571 | ||||||||
\(833\) | 0.909403 | 0.0315089 | ||||||||
\(834\) | 8.41045 | 0.291230 | ||||||||
\(835\) | 27.1948 | 0.941115 | ||||||||
\(836\) | 4.14345 | 0.143304 | ||||||||
\(837\) | 18.0933 | 0.625395 | ||||||||
\(838\) | −10.8629 | −0.375252 | ||||||||
\(839\) | 15.2591 | 0.526802 | 0.263401 | − | 0.964686i | \(-0.415156\pi\) | ||||
0.263401 | + | 0.964686i | \(0.415156\pi\) | |||||||
\(840\) | −8.92022 | −0.307777 | ||||||||
\(841\) | −3.22436 | −0.111185 | ||||||||
\(842\) | 20.9345 | 0.721450 | ||||||||
\(843\) | 29.8619 | 1.02850 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | 42.4676 | 1.46093 | ||||||||
\(846\) | −5.19571 | −0.178632 | ||||||||
\(847\) | 17.5526 | 0.603115 | ||||||||
\(848\) | −9.71241 | −0.333526 | ||||||||
\(849\) | −6.73158 | −0.231027 | ||||||||
\(850\) | −0.333426 | −0.0114364 | ||||||||
\(851\) | −5.35757 | −0.183655 | ||||||||
\(852\) | −1.75471 | −0.0601153 | ||||||||
\(853\) | 20.0870 | 0.687764 | 0.343882 | − | 0.939013i | \(-0.388258\pi\) | ||||
0.343882 | + | 0.939013i | \(0.388258\pi\) | |||||||
\(854\) | −2.11109 | −0.0722399 | ||||||||
\(855\) | 1.84981 | 0.0632621 | ||||||||
\(856\) | −19.5270 | −0.667421 | ||||||||
\(857\) | −49.4204 | −1.68817 | −0.844085 | − | 0.536210i | \(-0.819856\pi\) | ||||
−0.844085 | + | 0.536210i | \(0.819856\pi\) | |||||||
\(858\) | 34.6953 | 1.18448 | ||||||||
\(859\) | −14.5429 | −0.496198 | −0.248099 | − | 0.968735i | \(-0.579806\pi\) | ||||
−0.248099 | + | 0.968735i | \(0.579806\pi\) | |||||||
\(860\) | 3.78948 | 0.129220 | ||||||||
\(861\) | 39.4805 | 1.34549 | ||||||||
\(862\) | −24.5708 | −0.836884 | ||||||||
\(863\) | −4.16415 | −0.141749 | −0.0708747 | − | 0.997485i | \(-0.522579\pi\) | ||||
−0.0708747 | + | 0.997485i | \(0.522579\pi\) | |||||||
\(864\) | 5.64708 | 0.192118 | ||||||||
\(865\) | 31.2959 | 1.06409 | ||||||||
\(866\) | −10.2969 | −0.349902 | ||||||||
\(867\) | 23.8498 | 0.809981 | ||||||||
\(868\) | 9.11749 | 0.309468 | ||||||||
\(869\) | −0.0640510 | −0.00217278 | ||||||||
\(870\) | −15.9147 | −0.539559 | ||||||||
\(871\) | 72.2491 | 2.44807 | ||||||||
\(872\) | 2.14391 | 0.0726018 | ||||||||
\(873\) | 7.76973 | 0.262966 | ||||||||
\(874\) | −4.11173 | −0.139081 | ||||||||
\(875\) | −32.9638 | −1.11438 | ||||||||
\(876\) | −20.8525 | −0.704542 | ||||||||
\(877\) | −17.1129 | −0.577860 | −0.288930 | − | 0.957350i | \(-0.593300\pi\) | ||||
−0.288930 | + | 0.957350i | \(0.593300\pi\) | |||||||
\(878\) | 23.3441 | 0.787826 | ||||||||
\(879\) | 23.8915 | 0.805840 | ||||||||
\(880\) | −8.88433 | −0.299491 | ||||||||
\(881\) | 33.3241 | 1.12272 | 0.561358 | − | 0.827573i | \(-0.310279\pi\) | ||||
0.561358 | + | 0.827573i | \(0.310279\pi\) | |||||||
\(882\) | −0.947029 | −0.0318881 | ||||||||
\(883\) | −14.1100 | −0.474839 | −0.237420 | − | 0.971407i | \(-0.576302\pi\) | ||||
−0.237420 | + | 0.971407i | \(0.576302\pi\) | |||||||
\(884\) | 4.74497 | 0.159591 | ||||||||
\(885\) | 3.66192 | 0.123094 | ||||||||
\(886\) | −35.5818 | −1.19539 | ||||||||
\(887\) | −2.02756 | −0.0680787 | −0.0340394 | − | 0.999420i | \(-0.510837\pi\) | ||||
−0.0340394 | + | 0.999420i | \(0.510837\pi\) | |||||||
\(888\) | 1.90491 | 0.0639247 | ||||||||
\(889\) | −2.11942 | −0.0710832 | ||||||||
\(890\) | 33.9788 | 1.13897 | ||||||||
\(891\) | 23.4835 | 0.786726 | ||||||||
\(892\) | −25.6890 | −0.860130 | ||||||||
\(893\) | −6.02255 | −0.201537 | ||||||||
\(894\) | −25.7892 | −0.862518 | ||||||||
\(895\) | −15.0512 | −0.503106 | ||||||||
\(896\) | 2.84565 | 0.0950666 | ||||||||
\(897\) | −34.4297 | −1.14957 | ||||||||
\(898\) | 25.6489 | 0.855915 | ||||||||
\(899\) | 16.2666 | 0.542523 | ||||||||
\(900\) | 0.347221 | 0.0115740 | ||||||||
\(901\) | −8.04608 | −0.268054 | ||||||||
\(902\) | 39.3217 | 1.30927 | ||||||||
\(903\) | −7.35243 | −0.244674 | ||||||||
\(904\) | 17.2207 | 0.572751 | ||||||||
\(905\) | 14.9793 | 0.497929 | ||||||||
\(906\) | 17.0980 | 0.568043 | ||||||||
\(907\) | −24.9178 | −0.827383 | −0.413692 | − | 0.910417i | \(-0.635761\pi\) | ||||
−0.413692 | + | 0.910417i | \(0.635761\pi\) | |||||||
\(908\) | −0.630959 | −0.0209391 | ||||||||
\(909\) | −8.59611 | −0.285115 | ||||||||
\(910\) | 34.9478 | 1.15851 | ||||||||
\(911\) | −10.1240 | −0.335423 | −0.167712 | − | 0.985836i | \(-0.553638\pi\) | ||||
−0.167712 | + | 0.985836i | \(0.553638\pi\) | |||||||
\(912\) | 1.46195 | 0.0484099 | ||||||||
\(913\) | −21.7782 | −0.720753 | ||||||||
\(914\) | −24.8873 | −0.823199 | ||||||||
\(915\) | 2.32551 | 0.0768790 | ||||||||
\(916\) | 15.0811 | 0.498294 | ||||||||
\(917\) | 2.20559 | 0.0728350 | ||||||||
\(918\) | 4.67823 | 0.154404 | ||||||||
\(919\) | 15.2836 | 0.504160 | 0.252080 | − | 0.967706i | \(-0.418885\pi\) | ||||
0.252080 | + | 0.967706i | \(0.418885\pi\) | |||||||
\(920\) | 8.81631 | 0.290665 | ||||||||
\(921\) | −6.36084 | −0.209597 | ||||||||
\(922\) | 18.8711 | 0.621486 | ||||||||
\(923\) | 6.87463 | 0.226281 | ||||||||
\(924\) | 17.2376 | 0.567075 | ||||||||
\(925\) | 0.524427 | 0.0172430 | ||||||||
\(926\) | −4.38457 | −0.144086 | ||||||||
\(927\) | 6.83207 | 0.224395 | ||||||||
\(928\) | 5.07697 | 0.166660 | ||||||||
\(929\) | 28.5284 | 0.935985 | 0.467993 | − | 0.883732i | \(-0.344977\pi\) | ||||
0.467993 | + | 0.883732i | \(0.344977\pi\) | |||||||
\(930\) | −10.0435 | −0.329341 | ||||||||
\(931\) | −1.09774 | −0.0359769 | ||||||||
\(932\) | 9.27718 | 0.303884 | ||||||||
\(933\) | 2.10586 | 0.0689427 | ||||||||
\(934\) | −9.98957 | −0.326869 | ||||||||
\(935\) | −7.36007 | −0.240700 | ||||||||
\(936\) | −4.94130 | −0.161511 | ||||||||
\(937\) | −50.1429 | −1.63810 | −0.819048 | − | 0.573725i | \(-0.805498\pi\) | ||||
−0.819048 | + | 0.573725i | \(0.805498\pi\) | |||||||
\(938\) | 35.8953 | 1.17202 | ||||||||
\(939\) | −26.2563 | −0.856843 | ||||||||
\(940\) | 12.9134 | 0.421190 | ||||||||
\(941\) | −19.0410 | −0.620720 | −0.310360 | − | 0.950619i | \(-0.600450\pi\) | ||||
−0.310360 | + | 0.950619i | \(0.600450\pi\) | |||||||
\(942\) | −27.9026 | −0.909116 | ||||||||
\(943\) | −39.0206 | −1.27069 | ||||||||
\(944\) | −1.16819 | −0.0380215 | ||||||||
\(945\) | 34.4562 | 1.12086 | ||||||||
\(946\) | −7.32285 | −0.238086 | ||||||||
\(947\) | −51.1006 | −1.66054 | −0.830272 | − | 0.557358i | \(-0.811815\pi\) | ||||
−0.830272 | + | 0.557358i | \(0.811815\pi\) | |||||||
\(948\) | −0.0225993 | −0.000733991 0 | ||||||||
\(949\) | 81.6965 | 2.65198 | ||||||||
\(950\) | 0.402477 | 0.0130581 | ||||||||
\(951\) | −6.36219 | −0.206308 | ||||||||
\(952\) | 2.35743 | 0.0764048 | ||||||||
\(953\) | −30.2817 | −0.980922 | −0.490461 | − | 0.871463i | \(-0.663172\pi\) | ||||
−0.490461 | + | 0.871463i | \(0.663172\pi\) | |||||||
\(954\) | 8.37899 | 0.271280 | ||||||||
\(955\) | −9.62430 | −0.311435 | ||||||||
\(956\) | −3.55667 | −0.115031 | ||||||||
\(957\) | 30.7538 | 0.994130 | ||||||||
\(958\) | 40.2855 | 1.30157 | ||||||||
\(959\) | −30.7971 | −0.994491 | ||||||||
\(960\) | −3.13468 | −0.101171 | ||||||||
\(961\) | −20.7344 | −0.668850 | ||||||||
\(962\) | −7.46311 | −0.240620 | ||||||||
\(963\) | 16.8462 | 0.542860 | ||||||||
\(964\) | 22.0482 | 0.710125 | ||||||||
\(965\) | 32.8735 | 1.05823 | ||||||||
\(966\) | −17.1056 | −0.550364 | ||||||||
\(967\) | −19.5173 | −0.627635 | −0.313818 | − | 0.949483i | \(-0.601608\pi\) | ||||
−0.313818 | + | 0.949483i | \(0.601608\pi\) | |||||||
\(968\) | 6.16822 | 0.198254 | ||||||||
\(969\) | 1.21113 | 0.0389070 | ||||||||
\(970\) | −19.3109 | −0.620037 | ||||||||
\(971\) | −22.1916 | −0.712163 | −0.356081 | − | 0.934455i | \(-0.615887\pi\) | ||||
−0.356081 | + | 0.934455i | \(0.615887\pi\) | |||||||
\(972\) | −8.65550 | −0.277625 | ||||||||
\(973\) | −16.3708 | −0.524823 | ||||||||
\(974\) | 14.0124 | 0.448988 | ||||||||
\(975\) | 3.37015 | 0.107931 | ||||||||
\(976\) | −0.741864 | −0.0237465 | ||||||||
\(977\) | 25.5094 | 0.816118 | 0.408059 | − | 0.912956i | \(-0.366206\pi\) | ||||
0.408059 | + | 0.912956i | \(0.366206\pi\) | |||||||
\(978\) | 6.40832 | 0.204915 | ||||||||
\(979\) | −65.6612 | −2.09854 | ||||||||
\(980\) | 2.35375 | 0.0751879 | ||||||||
\(981\) | −1.84957 | −0.0590522 | ||||||||
\(982\) | −12.7909 | −0.408173 | ||||||||
\(983\) | −4.81931 | −0.153712 | −0.0768560 | − | 0.997042i | \(-0.524488\pi\) | ||||
−0.0768560 | + | 0.997042i | \(0.524488\pi\) | |||||||
\(984\) | 13.8740 | 0.442286 | ||||||||
\(985\) | −30.1928 | −0.962021 | ||||||||
\(986\) | 4.20593 | 0.133944 | ||||||||
\(987\) | −25.0550 | −0.797509 | ||||||||
\(988\) | −5.72765 | −0.182221 | ||||||||
\(989\) | 7.26678 | 0.231070 | ||||||||
\(990\) | 7.66459 | 0.243597 | ||||||||
\(991\) | 21.3126 | 0.677016 | 0.338508 | − | 0.940963i | \(-0.390078\pi\) | ||||
0.338508 | + | 0.940963i | \(0.390078\pi\) | |||||||
\(992\) | 3.20401 | 0.101727 | ||||||||
\(993\) | −17.2775 | −0.548283 | ||||||||
\(994\) | 3.41550 | 0.108333 | ||||||||
\(995\) | −16.6783 | −0.528739 | ||||||||
\(996\) | −7.68406 | −0.243479 | ||||||||
\(997\) | −51.5769 | −1.63346 | −0.816728 | − | 0.577023i | \(-0.804214\pi\) | ||||
−0.816728 | + | 0.577023i | \(0.804214\pi\) | |||||||
\(998\) | 2.40267 | 0.0760552 | ||||||||
\(999\) | −7.35812 | −0.232801 |
(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 | 8018.2.a.j.1.13 | ✓ | 47 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.j.1.13 | ✓ | 47 | 1.1 | even | 1 | trivial |