Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2077082653\) |
Analytic rank: | \(0\) |
Dimension: | \(78\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.05622 | −1.45397 | −0.726984 | − | 0.686655i | \(-0.759078\pi\) | ||||
−0.726984 | + | 0.686655i | \(0.759078\pi\) | |||||||
\(3\) | −3.10600 | −1.79325 | −0.896625 | − | 0.442790i | \(-0.853989\pi\) | ||||
−0.896625 | + | 0.442790i | \(0.853989\pi\) | |||||||
\(4\) | 2.22804 | 1.11402 | ||||||||
\(5\) | −2.37865 | −1.06377 | −0.531883 | − | 0.846818i | \(-0.678515\pi\) | ||||
−0.531883 | + | 0.846818i | \(0.678515\pi\) | |||||||
\(6\) | 6.38662 | 2.60733 | ||||||||
\(7\) | −3.40012 | −1.28512 | −0.642562 | − | 0.766233i | \(-0.722129\pi\) | ||||
−0.642562 | + | 0.766233i | \(0.722129\pi\) | |||||||
\(8\) | −0.468901 | −0.165781 | ||||||||
\(9\) | 6.64724 | 2.21575 | ||||||||
\(10\) | 4.89103 | 1.54668 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −6.92029 | −1.99772 | ||||||||
\(13\) | −5.45676 | −1.51343 | −0.756716 | − | 0.653743i | \(-0.773198\pi\) | ||||
−0.756716 | + | 0.653743i | \(0.773198\pi\) | |||||||
\(14\) | 6.99140 | 1.86853 | ||||||||
\(15\) | 7.38809 | 1.90760 | ||||||||
\(16\) | −3.49192 | −0.872979 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −13.6682 | −3.22162 | ||||||||
\(19\) | 1.95391 | 0.448257 | 0.224129 | − | 0.974560i | \(-0.428046\pi\) | ||||
0.224129 | + | 0.974560i | \(0.428046\pi\) | |||||||
\(20\) | −5.29973 | −1.18506 | ||||||||
\(21\) | 10.5608 | 2.30455 | ||||||||
\(22\) | −2.05622 | −0.438388 | ||||||||
\(23\) | −4.50873 | −0.940135 | −0.470068 | − | 0.882630i | \(-0.655770\pi\) | ||||
−0.470068 | + | 0.882630i | \(0.655770\pi\) | |||||||
\(24\) | 1.45641 | 0.297288 | ||||||||
\(25\) | 0.657984 | 0.131597 | ||||||||
\(26\) | 11.2203 | 2.20048 | ||||||||
\(27\) | −11.3283 | −2.18014 | ||||||||
\(28\) | −7.57561 | −1.43165 | ||||||||
\(29\) | 5.46615 | 1.01504 | 0.507520 | − | 0.861640i | \(-0.330563\pi\) | ||||
0.507520 | + | 0.861640i | \(0.330563\pi\) | |||||||
\(30\) | −15.1915 | −2.77358 | ||||||||
\(31\) | 6.68356 | 1.20040 | 0.600201 | − | 0.799849i | \(-0.295087\pi\) | ||||
0.600201 | + | 0.799849i | \(0.295087\pi\) | |||||||
\(32\) | 8.11795 | 1.43506 | ||||||||
\(33\) | −3.10600 | −0.540685 | ||||||||
\(34\) | 2.05622 | 0.352639 | ||||||||
\(35\) | 8.08770 | 1.36707 | ||||||||
\(36\) | 14.8103 | 2.46839 | ||||||||
\(37\) | 1.68237 | 0.276580 | 0.138290 | − | 0.990392i | \(-0.455839\pi\) | ||||
0.138290 | + | 0.990392i | \(0.455839\pi\) | |||||||
\(38\) | −4.01767 | −0.651751 | ||||||||
\(39\) | 16.9487 | 2.71396 | ||||||||
\(40\) | 1.11535 | 0.176353 | ||||||||
\(41\) | −8.75055 | −1.36661 | −0.683303 | − | 0.730135i | \(-0.739457\pi\) | ||||
−0.683303 | + | 0.730135i | \(0.739457\pi\) | |||||||
\(42\) | −21.7153 | −3.35074 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | 2.22804 | 0.335890 | ||||||||
\(45\) | −15.8115 | −2.35703 | ||||||||
\(46\) | 9.27094 | 1.36693 | ||||||||
\(47\) | −3.32091 | −0.484404 | −0.242202 | − | 0.970226i | \(-0.577870\pi\) | ||||
−0.242202 | + | 0.970226i | \(0.577870\pi\) | |||||||
\(48\) | 10.8459 | 1.56547 | ||||||||
\(49\) | 4.56082 | 0.651546 | ||||||||
\(50\) | −1.35296 | −0.191337 | ||||||||
\(51\) | 3.10600 | 0.434927 | ||||||||
\(52\) | −12.1579 | −1.68599 | ||||||||
\(53\) | −3.01462 | −0.414090 | −0.207045 | − | 0.978331i | \(-0.566385\pi\) | ||||
−0.207045 | + | 0.978331i | \(0.566385\pi\) | |||||||
\(54\) | 23.2935 | 3.16985 | ||||||||
\(55\) | −2.37865 | −0.320737 | ||||||||
\(56\) | 1.59432 | 0.213050 | ||||||||
\(57\) | −6.06884 | −0.803838 | ||||||||
\(58\) | −11.2396 | −1.47583 | ||||||||
\(59\) | 0.487630 | 0.0634840 | 0.0317420 | − | 0.999496i | \(-0.489895\pi\) | ||||
0.0317420 | + | 0.999496i | \(0.489895\pi\) | |||||||
\(60\) | 16.4610 | 2.12510 | ||||||||
\(61\) | 6.07482 | 0.777801 | 0.388900 | − | 0.921280i | \(-0.372855\pi\) | ||||
0.388900 | + | 0.921280i | \(0.372855\pi\) | |||||||
\(62\) | −13.7429 | −1.74535 | ||||||||
\(63\) | −22.6014 | −2.84751 | ||||||||
\(64\) | −9.70846 | −1.21356 | ||||||||
\(65\) | 12.9797 | 1.60994 | ||||||||
\(66\) | 6.38662 | 0.786139 | ||||||||
\(67\) | −0.331210 | −0.0404638 | −0.0202319 | − | 0.999795i | \(-0.506440\pi\) | ||||
−0.0202319 | + | 0.999795i | \(0.506440\pi\) | |||||||
\(68\) | −2.22804 | −0.270190 | ||||||||
\(69\) | 14.0041 | 1.68590 | ||||||||
\(70\) | −16.6301 | −1.98768 | ||||||||
\(71\) | −0.741187 | −0.0879627 | −0.0439813 | − | 0.999032i | \(-0.514004\pi\) | ||||
−0.0439813 | + | 0.999032i | \(0.514004\pi\) | |||||||
\(72\) | −3.11689 | −0.367330 | ||||||||
\(73\) | 11.8136 | 1.38268 | 0.691340 | − | 0.722530i | \(-0.257021\pi\) | ||||
0.691340 | + | 0.722530i | \(0.257021\pi\) | |||||||
\(74\) | −3.45933 | −0.402139 | ||||||||
\(75\) | −2.04370 | −0.235986 | ||||||||
\(76\) | 4.35339 | 0.499368 | ||||||||
\(77\) | −3.40012 | −0.387480 | ||||||||
\(78\) | −34.8502 | −3.94601 | ||||||||
\(79\) | 14.0142 | 1.57672 | 0.788362 | − | 0.615212i | \(-0.210929\pi\) | ||||
0.788362 | + | 0.615212i | \(0.210929\pi\) | |||||||
\(80\) | 8.30606 | 0.928645 | ||||||||
\(81\) | 15.2441 | 1.69379 | ||||||||
\(82\) | 17.9931 | 1.98700 | ||||||||
\(83\) | 2.19179 | 0.240580 | 0.120290 | − | 0.992739i | \(-0.461618\pi\) | ||||
0.120290 | + | 0.992739i | \(0.461618\pi\) | |||||||
\(84\) | 23.5298 | 2.56732 | ||||||||
\(85\) | 2.37865 | 0.258001 | ||||||||
\(86\) | 2.05622 | 0.221728 | ||||||||
\(87\) | −16.9779 | −1.82022 | ||||||||
\(88\) | −0.468901 | −0.0499850 | ||||||||
\(89\) | −4.14803 | −0.439691 | −0.219845 | − | 0.975535i | \(-0.570555\pi\) | ||||
−0.219845 | + | 0.975535i | \(0.570555\pi\) | |||||||
\(90\) | 32.5119 | 3.42705 | ||||||||
\(91\) | 18.5536 | 1.94495 | ||||||||
\(92\) | −10.0456 | −1.04733 | ||||||||
\(93\) | −20.7591 | −2.15262 | ||||||||
\(94\) | 6.82852 | 0.704308 | ||||||||
\(95\) | −4.64767 | −0.476841 | ||||||||
\(96\) | −25.2144 | −2.57343 | ||||||||
\(97\) | −1.97190 | −0.200216 | −0.100108 | − | 0.994977i | \(-0.531919\pi\) | ||||
−0.100108 | + | 0.994977i | \(0.531919\pi\) | |||||||
\(98\) | −9.37805 | −0.947326 | ||||||||
\(99\) | 6.64724 | 0.668073 | ||||||||
\(100\) | 1.46601 | 0.146601 | ||||||||
\(101\) | −13.2539 | −1.31881 | −0.659407 | − | 0.751786i | \(-0.729193\pi\) | ||||
−0.659407 | + | 0.751786i | \(0.729193\pi\) | |||||||
\(102\) | −6.38662 | −0.632370 | ||||||||
\(103\) | −17.7757 | −1.75149 | −0.875744 | − | 0.482776i | \(-0.839629\pi\) | ||||
−0.875744 | + | 0.482776i | \(0.839629\pi\) | |||||||
\(104\) | 2.55868 | 0.250899 | ||||||||
\(105\) | −25.1204 | −2.45150 | ||||||||
\(106\) | 6.19873 | 0.602074 | ||||||||
\(107\) | 11.8902 | 1.14947 | 0.574737 | − | 0.818338i | \(-0.305104\pi\) | ||||
0.574737 | + | 0.818338i | \(0.305104\pi\) | |||||||
\(108\) | −25.2400 | −2.42872 | ||||||||
\(109\) | −10.3027 | −0.986816 | −0.493408 | − | 0.869798i | \(-0.664249\pi\) | ||||
−0.493408 | + | 0.869798i | \(0.664249\pi\) | |||||||
\(110\) | 4.89103 | 0.466342 | ||||||||
\(111\) | −5.22545 | −0.495978 | ||||||||
\(112\) | 11.8729 | 1.12189 | ||||||||
\(113\) | 19.5391 | 1.83808 | 0.919040 | − | 0.394164i | \(-0.128966\pi\) | ||||
0.919040 | + | 0.394164i | \(0.128966\pi\) | |||||||
\(114\) | 12.4789 | 1.16875 | ||||||||
\(115\) | 10.7247 | 1.00008 | ||||||||
\(116\) | 12.1788 | 1.13077 | ||||||||
\(117\) | −36.2724 | −3.35338 | ||||||||
\(118\) | −1.00267 | −0.0923037 | ||||||||
\(119\) | 3.40012 | 0.311689 | ||||||||
\(120\) | −3.46428 | −0.316244 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −12.4912 | −1.13090 | ||||||||
\(123\) | 27.1792 | 2.45067 | ||||||||
\(124\) | 14.8912 | 1.33727 | ||||||||
\(125\) | 10.3281 | 0.923777 | ||||||||
\(126\) | 46.4735 | 4.14019 | ||||||||
\(127\) | 2.33243 | 0.206970 | 0.103485 | − | 0.994631i | \(-0.467001\pi\) | ||||
0.103485 | + | 0.994631i | \(0.467001\pi\) | |||||||
\(128\) | 3.72682 | 0.329408 | ||||||||
\(129\) | 3.10600 | 0.273468 | ||||||||
\(130\) | −26.6892 | −2.34080 | ||||||||
\(131\) | −11.7720 | −1.02852 | −0.514260 | − | 0.857634i | \(-0.671933\pi\) | ||||
−0.514260 | + | 0.857634i | \(0.671933\pi\) | |||||||
\(132\) | −6.92029 | −0.602334 | ||||||||
\(133\) | −6.64353 | −0.576067 | ||||||||
\(134\) | 0.681042 | 0.0588330 | ||||||||
\(135\) | 26.9461 | 2.31916 | ||||||||
\(136\) | 0.468901 | 0.0402079 | ||||||||
\(137\) | −0.629780 | −0.0538057 | −0.0269029 | − | 0.999638i | \(-0.508564\pi\) | ||||
−0.0269029 | + | 0.999638i | \(0.508564\pi\) | |||||||
\(138\) | −28.7955 | −2.45124 | ||||||||
\(139\) | −2.08107 | −0.176514 | −0.0882569 | − | 0.996098i | \(-0.528130\pi\) | ||||
−0.0882569 | + | 0.996098i | \(0.528130\pi\) | |||||||
\(140\) | 18.0197 | 1.52294 | ||||||||
\(141\) | 10.3147 | 0.868658 | ||||||||
\(142\) | 1.52404 | 0.127895 | ||||||||
\(143\) | −5.45676 | −0.456317 | ||||||||
\(144\) | −23.2116 | −1.93430 | ||||||||
\(145\) | −13.0021 | −1.07976 | ||||||||
\(146\) | −24.2914 | −2.01037 | ||||||||
\(147\) | −14.1659 | −1.16838 | ||||||||
\(148\) | 3.74839 | 0.308116 | ||||||||
\(149\) | 8.29557 | 0.679600 | 0.339800 | − | 0.940498i | \(-0.389641\pi\) | ||||
0.339800 | + | 0.940498i | \(0.389641\pi\) | |||||||
\(150\) | 4.20229 | 0.343116 | ||||||||
\(151\) | −5.92641 | −0.482285 | −0.241142 | − | 0.970490i | \(-0.577522\pi\) | ||||
−0.241142 | + | 0.970490i | \(0.577522\pi\) | |||||||
\(152\) | −0.916189 | −0.0743127 | ||||||||
\(153\) | −6.64724 | −0.537397 | ||||||||
\(154\) | 6.99140 | 0.563383 | ||||||||
\(155\) | −15.8979 | −1.27695 | ||||||||
\(156\) | 37.7624 | 3.02341 | ||||||||
\(157\) | 4.63271 | 0.369731 | 0.184865 | − | 0.982764i | \(-0.440815\pi\) | ||||
0.184865 | + | 0.982764i | \(0.440815\pi\) | |||||||
\(158\) | −28.8163 | −2.29250 | ||||||||
\(159\) | 9.36342 | 0.742568 | ||||||||
\(160\) | −19.3098 | −1.52657 | ||||||||
\(161\) | 15.3302 | 1.20819 | ||||||||
\(162\) | −31.3452 | −2.46271 | ||||||||
\(163\) | −15.7248 | −1.23166 | −0.615829 | − | 0.787880i | \(-0.711179\pi\) | ||||
−0.615829 | + | 0.787880i | \(0.711179\pi\) | |||||||
\(164\) | −19.4966 | −1.52243 | ||||||||
\(165\) | 7.38809 | 0.575162 | ||||||||
\(166\) | −4.50680 | −0.349796 | ||||||||
\(167\) | 5.67202 | 0.438914 | 0.219457 | − | 0.975622i | \(-0.429571\pi\) | ||||
0.219457 | + | 0.975622i | \(0.429571\pi\) | |||||||
\(168\) | −4.95195 | −0.382052 | ||||||||
\(169\) | 16.7762 | 1.29048 | ||||||||
\(170\) | −4.89103 | −0.375125 | ||||||||
\(171\) | 12.9881 | 0.993225 | ||||||||
\(172\) | −2.22804 | −0.169886 | ||||||||
\(173\) | −18.9204 | −1.43849 | −0.719244 | − | 0.694757i | \(-0.755512\pi\) | ||||
−0.719244 | + | 0.694757i | \(0.755512\pi\) | |||||||
\(174\) | 34.9102 | 2.64654 | ||||||||
\(175\) | −2.23723 | −0.169118 | ||||||||
\(176\) | −3.49192 | −0.263213 | ||||||||
\(177\) | −1.51458 | −0.113843 | ||||||||
\(178\) | 8.52927 | 0.639296 | ||||||||
\(179\) | −14.9099 | −1.11442 | −0.557210 | − | 0.830371i | \(-0.688128\pi\) | ||||
−0.557210 | + | 0.830371i | \(0.688128\pi\) | |||||||
\(180\) | −35.2286 | −2.62578 | ||||||||
\(181\) | 1.19021 | 0.0884672 | 0.0442336 | − | 0.999021i | \(-0.485915\pi\) | ||||
0.0442336 | + | 0.999021i | \(0.485915\pi\) | |||||||
\(182\) | −38.1504 | −2.82789 | ||||||||
\(183\) | −18.8684 | −1.39479 | ||||||||
\(184\) | 2.11415 | 0.155857 | ||||||||
\(185\) | −4.00178 | −0.294217 | ||||||||
\(186\) | 42.6853 | 3.12984 | ||||||||
\(187\) | −1.00000 | −0.0731272 | ||||||||
\(188\) | −7.39912 | −0.539636 | ||||||||
\(189\) | 38.5177 | 2.80175 | ||||||||
\(190\) | 9.55663 | 0.693311 | ||||||||
\(191\) | −11.6775 | −0.844955 | −0.422477 | − | 0.906374i | \(-0.638839\pi\) | ||||
−0.422477 | + | 0.906374i | \(0.638839\pi\) | |||||||
\(192\) | 30.1545 | 2.17621 | ||||||||
\(193\) | −16.3980 | −1.18035 | −0.590176 | − | 0.807274i | \(-0.700942\pi\) | ||||
−0.590176 | + | 0.807274i | \(0.700942\pi\) | |||||||
\(194\) | 4.05465 | 0.291107 | ||||||||
\(195\) | −40.3150 | −2.88702 | ||||||||
\(196\) | 10.1617 | 0.725835 | ||||||||
\(197\) | −6.90365 | −0.491864 | −0.245932 | − | 0.969287i | \(-0.579094\pi\) | ||||
−0.245932 | + | 0.969287i | \(0.579094\pi\) | |||||||
\(198\) | −13.6682 | −0.971356 | ||||||||
\(199\) | −24.5560 | −1.74073 | −0.870363 | − | 0.492411i | \(-0.836116\pi\) | ||||
−0.870363 | + | 0.492411i | \(0.836116\pi\) | |||||||
\(200\) | −0.308529 | −0.0218163 | ||||||||
\(201\) | 1.02874 | 0.0725617 | ||||||||
\(202\) | 27.2530 | 1.91751 | ||||||||
\(203\) | −18.5856 | −1.30445 | ||||||||
\(204\) | 6.92029 | 0.484517 | ||||||||
\(205\) | 20.8145 | 1.45375 | ||||||||
\(206\) | 36.5507 | 2.54661 | ||||||||
\(207\) | −29.9706 | −2.08310 | ||||||||
\(208\) | 19.0546 | 1.32120 | ||||||||
\(209\) | 1.95391 | 0.135155 | ||||||||
\(210\) | 51.6531 | 3.56440 | ||||||||
\(211\) | −26.0649 | −1.79438 | −0.897191 | − | 0.441642i | \(-0.854396\pi\) | ||||
−0.897191 | + | 0.441642i | \(0.854396\pi\) | |||||||
\(212\) | −6.71670 | −0.461305 | ||||||||
\(213\) | 2.30213 | 0.157739 | ||||||||
\(214\) | −24.4490 | −1.67130 | ||||||||
\(215\) | 2.37865 | 0.162223 | ||||||||
\(216\) | 5.31186 | 0.361426 | ||||||||
\(217\) | −22.7249 | −1.54267 | ||||||||
\(218\) | 21.1845 | 1.43480 | ||||||||
\(219\) | −36.6931 | −2.47949 | ||||||||
\(220\) | −5.29973 | −0.357308 | ||||||||
\(221\) | 5.45676 | 0.367061 | ||||||||
\(222\) | 10.7447 | 0.721135 | ||||||||
\(223\) | −11.1035 | −0.743543 | −0.371771 | − | 0.928324i | \(-0.621250\pi\) | ||||
−0.371771 | + | 0.928324i | \(0.621250\pi\) | |||||||
\(224\) | −27.6020 | −1.84424 | ||||||||
\(225\) | 4.37378 | 0.291585 | ||||||||
\(226\) | −40.1766 | −2.67251 | ||||||||
\(227\) | −0.650589 | −0.0431811 | −0.0215906 | − | 0.999767i | \(-0.506873\pi\) | ||||
−0.0215906 | + | 0.999767i | \(0.506873\pi\) | |||||||
\(228\) | −13.5216 | −0.895491 | ||||||||
\(229\) | −8.72696 | −0.576694 | −0.288347 | − | 0.957526i | \(-0.593106\pi\) | ||||
−0.288347 | + | 0.957526i | \(0.593106\pi\) | |||||||
\(230\) | −22.0523 | −1.45409 | ||||||||
\(231\) | 10.5608 | 0.694848 | ||||||||
\(232\) | −2.56308 | −0.168275 | ||||||||
\(233\) | −11.4269 | −0.748600 | −0.374300 | − | 0.927308i | \(-0.622117\pi\) | ||||
−0.374300 | + | 0.927308i | \(0.622117\pi\) | |||||||
\(234\) | 74.5840 | 4.87571 | ||||||||
\(235\) | 7.89929 | 0.515293 | ||||||||
\(236\) | 1.08646 | 0.0707225 | ||||||||
\(237\) | −43.5282 | −2.82746 | ||||||||
\(238\) | −6.99140 | −0.453185 | ||||||||
\(239\) | −6.82199 | −0.441278 | −0.220639 | − | 0.975356i | \(-0.570814\pi\) | ||||
−0.220639 | + | 0.975356i | \(0.570814\pi\) | |||||||
\(240\) | −25.7986 | −1.66529 | ||||||||
\(241\) | −19.5256 | −1.25775 | −0.628876 | − | 0.777505i | \(-0.716485\pi\) | ||||
−0.628876 | + | 0.777505i | \(0.716485\pi\) | |||||||
\(242\) | −2.05622 | −0.132179 | ||||||||
\(243\) | −13.3631 | −0.857245 | ||||||||
\(244\) | 13.5349 | 0.866486 | ||||||||
\(245\) | −10.8486 | −0.693092 | ||||||||
\(246\) | −55.8865 | −3.56319 | ||||||||
\(247\) | −10.6620 | −0.678407 | ||||||||
\(248\) | −3.13392 | −0.199004 | ||||||||
\(249\) | −6.80770 | −0.431421 | ||||||||
\(250\) | −21.2369 | −1.34314 | ||||||||
\(251\) | 12.0823 | 0.762626 | 0.381313 | − | 0.924446i | \(-0.375472\pi\) | ||||
0.381313 | + | 0.924446i | \(0.375472\pi\) | |||||||
\(252\) | −50.3569 | −3.17218 | ||||||||
\(253\) | −4.50873 | −0.283461 | ||||||||
\(254\) | −4.79599 | −0.300927 | ||||||||
\(255\) | −7.38809 | −0.462660 | ||||||||
\(256\) | 11.7538 | 0.734610 | ||||||||
\(257\) | 2.53783 | 0.158306 | 0.0791528 | − | 0.996862i | \(-0.474779\pi\) | ||||
0.0791528 | + | 0.996862i | \(0.474779\pi\) | |||||||
\(258\) | −6.38662 | −0.397614 | ||||||||
\(259\) | −5.72027 | −0.355440 | ||||||||
\(260\) | 28.9194 | 1.79350 | ||||||||
\(261\) | 36.3348 | 2.24907 | ||||||||
\(262\) | 24.2057 | 1.49544 | ||||||||
\(263\) | 15.5504 | 0.958880 | 0.479440 | − | 0.877575i | \(-0.340840\pi\) | ||||
0.479440 | + | 0.877575i | \(0.340840\pi\) | |||||||
\(264\) | 1.45641 | 0.0896356 | ||||||||
\(265\) | 7.17074 | 0.440495 | ||||||||
\(266\) | 13.6605 | 0.837582 | ||||||||
\(267\) | 12.8838 | 0.788476 | ||||||||
\(268\) | −0.737950 | −0.0450775 | ||||||||
\(269\) | 18.2485 | 1.11263 | 0.556314 | − | 0.830972i | \(-0.312215\pi\) | ||||
0.556314 | + | 0.830972i | \(0.312215\pi\) | |||||||
\(270\) | −55.4072 | −3.37198 | ||||||||
\(271\) | −0.581663 | −0.0353335 | −0.0176668 | − | 0.999844i | \(-0.505624\pi\) | ||||
−0.0176668 | + | 0.999844i | \(0.505624\pi\) | |||||||
\(272\) | 3.49192 | 0.211729 | ||||||||
\(273\) | −57.6276 | −3.48778 | ||||||||
\(274\) | 1.29497 | 0.0782317 | ||||||||
\(275\) | 0.657984 | 0.0396779 | ||||||||
\(276\) | 31.2017 | 1.87812 | ||||||||
\(277\) | −16.8074 | −1.00986 | −0.504929 | − | 0.863161i | \(-0.668481\pi\) | ||||
−0.504929 | + | 0.863161i | \(0.668481\pi\) | |||||||
\(278\) | 4.27913 | 0.256645 | ||||||||
\(279\) | 44.4272 | 2.65979 | ||||||||
\(280\) | −3.79233 | −0.226635 | ||||||||
\(281\) | −14.3817 | −0.857939 | −0.428969 | − | 0.903319i | \(-0.641123\pi\) | ||||
−0.428969 | + | 0.903319i | \(0.641123\pi\) | |||||||
\(282\) | −21.2094 | −1.26300 | ||||||||
\(283\) | −22.6885 | −1.34869 | −0.674346 | − | 0.738416i | \(-0.735574\pi\) | ||||
−0.674346 | + | 0.738416i | \(0.735574\pi\) | |||||||
\(284\) | −1.65139 | −0.0979922 | ||||||||
\(285\) | 14.4357 | 0.855095 | ||||||||
\(286\) | 11.2203 | 0.663470 | ||||||||
\(287\) | 29.7529 | 1.75626 | ||||||||
\(288\) | 53.9620 | 3.17974 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 26.7351 | 1.56994 | ||||||||
\(291\) | 6.12471 | 0.359037 | ||||||||
\(292\) | 26.3212 | 1.54033 | ||||||||
\(293\) | −18.1415 | −1.05984 | −0.529919 | − | 0.848048i | \(-0.677778\pi\) | ||||
−0.529919 | + | 0.848048i | \(0.677778\pi\) | |||||||
\(294\) | 29.1282 | 1.69879 | ||||||||
\(295\) | −1.15990 | −0.0675321 | ||||||||
\(296\) | −0.788865 | −0.0458519 | ||||||||
\(297\) | −11.3283 | −0.657336 | ||||||||
\(298\) | −17.0575 | −0.988116 | ||||||||
\(299\) | 24.6030 | 1.42283 | ||||||||
\(300\) | −4.55344 | −0.262893 | ||||||||
\(301\) | 3.40012 | 0.195980 | ||||||||
\(302\) | 12.1860 | 0.701226 | ||||||||
\(303\) | 41.1667 | 2.36496 | ||||||||
\(304\) | −6.82289 | −0.391319 | ||||||||
\(305\) | −14.4499 | −0.827397 | ||||||||
\(306\) | 13.6682 | 0.781358 | ||||||||
\(307\) | −10.1942 | −0.581811 | −0.290906 | − | 0.956752i | \(-0.593957\pi\) | ||||
−0.290906 | + | 0.956752i | \(0.593957\pi\) | |||||||
\(308\) | −7.57561 | −0.431660 | ||||||||
\(309\) | 55.2112 | 3.14086 | ||||||||
\(310\) | 32.6895 | 1.85664 | ||||||||
\(311\) | 7.16815 | 0.406469 | 0.203234 | − | 0.979130i | \(-0.434855\pi\) | ||||
0.203234 | + | 0.979130i | \(0.434855\pi\) | |||||||
\(312\) | −7.94725 | −0.449925 | ||||||||
\(313\) | −16.8453 | −0.952155 | −0.476078 | − | 0.879403i | \(-0.657942\pi\) | ||||
−0.476078 | + | 0.879403i | \(0.657942\pi\) | |||||||
\(314\) | −9.52588 | −0.537576 | ||||||||
\(315\) | 53.7609 | 3.02908 | ||||||||
\(316\) | 31.2243 | 1.75650 | ||||||||
\(317\) | −26.9650 | −1.51450 | −0.757252 | − | 0.653123i | \(-0.773459\pi\) | ||||
−0.757252 | + | 0.653123i | \(0.773459\pi\) | |||||||
\(318\) | −19.2533 | −1.07967 | ||||||||
\(319\) | 5.46615 | 0.306046 | ||||||||
\(320\) | 23.0930 | 1.29094 | ||||||||
\(321\) | −36.9311 | −2.06129 | ||||||||
\(322\) | −31.5223 | −1.75667 | ||||||||
\(323\) | −1.95391 | −0.108718 | ||||||||
\(324\) | 33.9644 | 1.88691 | ||||||||
\(325\) | −3.59046 | −0.199163 | ||||||||
\(326\) | 32.3336 | 1.79079 | ||||||||
\(327\) | 32.0001 | 1.76961 | ||||||||
\(328\) | 4.10314 | 0.226558 | ||||||||
\(329\) | 11.2915 | 0.622520 | ||||||||
\(330\) | −15.1915 | −0.836267 | ||||||||
\(331\) | −9.23332 | −0.507509 | −0.253755 | − | 0.967269i | \(-0.581666\pi\) | ||||
−0.253755 | + | 0.967269i | \(0.581666\pi\) | |||||||
\(332\) | 4.88340 | 0.268011 | ||||||||
\(333\) | 11.1831 | 0.612832 | ||||||||
\(334\) | −11.6629 | −0.638167 | ||||||||
\(335\) | 0.787834 | 0.0430440 | ||||||||
\(336\) | −36.8774 | −2.01182 | ||||||||
\(337\) | −17.0333 | −0.927862 | −0.463931 | − | 0.885871i | \(-0.653561\pi\) | ||||
−0.463931 | + | 0.885871i | \(0.653561\pi\) | |||||||
\(338\) | −34.4956 | −1.87631 | ||||||||
\(339\) | −60.6883 | −3.29614 | ||||||||
\(340\) | 5.29973 | 0.287418 | ||||||||
\(341\) | 6.68356 | 0.361935 | ||||||||
\(342\) | −26.7064 | −1.44412 | ||||||||
\(343\) | 8.29351 | 0.447807 | ||||||||
\(344\) | 0.468901 | 0.0252814 | ||||||||
\(345\) | −33.3109 | −1.79340 | ||||||||
\(346\) | 38.9044 | 2.09152 | ||||||||
\(347\) | 30.0576 | 1.61358 | 0.806788 | − | 0.590840i | \(-0.201204\pi\) | ||||
0.806788 | + | 0.590840i | \(0.201204\pi\) | |||||||
\(348\) | −37.8274 | −2.02776 | ||||||||
\(349\) | −19.3592 | −1.03627 | −0.518136 | − | 0.855298i | \(-0.673374\pi\) | ||||
−0.518136 | + | 0.855298i | \(0.673374\pi\) | |||||||
\(350\) | 4.60023 | 0.245892 | ||||||||
\(351\) | 61.8160 | 3.29949 | ||||||||
\(352\) | 8.11795 | 0.432688 | ||||||||
\(353\) | 3.49404 | 0.185969 | 0.0929846 | − | 0.995668i | \(-0.470359\pi\) | ||||
0.0929846 | + | 0.995668i | \(0.470359\pi\) | |||||||
\(354\) | 3.11431 | 0.165524 | ||||||||
\(355\) | 1.76303 | 0.0935717 | ||||||||
\(356\) | −9.24199 | −0.489824 | ||||||||
\(357\) | −10.5608 | −0.558936 | ||||||||
\(358\) | 30.6581 | 1.62033 | ||||||||
\(359\) | 1.53087 | 0.0807963 | 0.0403982 | − | 0.999184i | \(-0.487137\pi\) | ||||
0.0403982 | + | 0.999184i | \(0.487137\pi\) | |||||||
\(360\) | 7.41401 | 0.390752 | ||||||||
\(361\) | −15.1822 | −0.799065 | ||||||||
\(362\) | −2.44732 | −0.128628 | ||||||||
\(363\) | −3.10600 | −0.163023 | ||||||||
\(364\) | 41.3383 | 2.16671 | ||||||||
\(365\) | −28.1005 | −1.47085 | ||||||||
\(366\) | 38.7976 | 2.02798 | ||||||||
\(367\) | 33.8086 | 1.76479 | 0.882397 | − | 0.470505i | \(-0.155928\pi\) | ||||
0.882397 | + | 0.470505i | \(0.155928\pi\) | |||||||
\(368\) | 15.7441 | 0.820719 | ||||||||
\(369\) | −58.1670 | −3.02805 | ||||||||
\(370\) | 8.22854 | 0.427781 | ||||||||
\(371\) | 10.2501 | 0.532158 | ||||||||
\(372\) | −46.2522 | −2.39806 | ||||||||
\(373\) | 11.7615 | 0.608988 | 0.304494 | − | 0.952514i | \(-0.401513\pi\) | ||||
0.304494 | + | 0.952514i | \(0.401513\pi\) | |||||||
\(374\) | 2.05622 | 0.106325 | ||||||||
\(375\) | −32.0792 | −1.65656 | ||||||||
\(376\) | 1.55718 | 0.0803053 | ||||||||
\(377\) | −29.8275 | −1.53619 | ||||||||
\(378\) | −79.2008 | −4.07365 | ||||||||
\(379\) | 22.2130 | 1.14101 | 0.570504 | − | 0.821295i | \(-0.306748\pi\) | ||||
0.570504 | + | 0.821295i | \(0.306748\pi\) | |||||||
\(380\) | −10.3552 | −0.531210 | ||||||||
\(381\) | −7.24452 | −0.371148 | ||||||||
\(382\) | 24.0115 | 1.22854 | ||||||||
\(383\) | 25.4421 | 1.30003 | 0.650014 | − | 0.759922i | \(-0.274763\pi\) | ||||
0.650014 | + | 0.759922i | \(0.274763\pi\) | |||||||
\(384\) | −11.5755 | −0.590710 | ||||||||
\(385\) | 8.08770 | 0.412188 | ||||||||
\(386\) | 33.7179 | 1.71619 | ||||||||
\(387\) | −6.64724 | −0.337898 | ||||||||
\(388\) | −4.39347 | −0.223044 | ||||||||
\(389\) | 31.7725 | 1.61093 | 0.805464 | − | 0.592645i | \(-0.201916\pi\) | ||||
0.805464 | + | 0.592645i | \(0.201916\pi\) | |||||||
\(390\) | 82.8966 | 4.19763 | ||||||||
\(391\) | 4.50873 | 0.228016 | ||||||||
\(392\) | −2.13857 | −0.108014 | ||||||||
\(393\) | 36.5637 | 1.84439 | ||||||||
\(394\) | 14.1954 | 0.715155 | ||||||||
\(395\) | −33.3350 | −1.67726 | ||||||||
\(396\) | 14.8103 | 0.744246 | ||||||||
\(397\) | −15.0628 | −0.755981 | −0.377991 | − | 0.925809i | \(-0.623385\pi\) | ||||
−0.377991 | + | 0.925809i | \(0.623385\pi\) | |||||||
\(398\) | 50.4924 | 2.53096 | ||||||||
\(399\) | 20.6348 | 1.03303 | ||||||||
\(400\) | −2.29763 | −0.114881 | ||||||||
\(401\) | −1.42657 | −0.0712393 | −0.0356196 | − | 0.999365i | \(-0.511340\pi\) | ||||
−0.0356196 | + | 0.999365i | \(0.511340\pi\) | |||||||
\(402\) | −2.11532 | −0.105502 | ||||||||
\(403\) | −36.4706 | −1.81673 | ||||||||
\(404\) | −29.5303 | −1.46918 | ||||||||
\(405\) | −36.2603 | −1.80179 | ||||||||
\(406\) | 38.2160 | 1.89663 | ||||||||
\(407\) | 1.68237 | 0.0833921 | ||||||||
\(408\) | −1.45641 | −0.0721028 | ||||||||
\(409\) | −38.6806 | −1.91263 | −0.956316 | − | 0.292334i | \(-0.905568\pi\) | ||||
−0.956316 | + | 0.292334i | \(0.905568\pi\) | |||||||
\(410\) | −42.7992 | −2.11370 | ||||||||
\(411\) | 1.95610 | 0.0964871 | ||||||||
\(412\) | −39.6049 | −1.95119 | ||||||||
\(413\) | −1.65800 | −0.0815849 | ||||||||
\(414\) | 61.6262 | 3.02876 | ||||||||
\(415\) | −5.21351 | −0.255921 | ||||||||
\(416\) | −44.2977 | −2.17187 | ||||||||
\(417\) | 6.46379 | 0.316533 | ||||||||
\(418\) | −4.01767 | −0.196510 | ||||||||
\(419\) | −6.55337 | −0.320153 | −0.160076 | − | 0.987105i | \(-0.551174\pi\) | ||||
−0.160076 | + | 0.987105i | \(0.551174\pi\) | |||||||
\(420\) | −55.9693 | −2.73102 | ||||||||
\(421\) | −8.75754 | −0.426817 | −0.213408 | − | 0.976963i | \(-0.568456\pi\) | ||||
−0.213408 | + | 0.976963i | \(0.568456\pi\) | |||||||
\(422\) | 53.5952 | 2.60897 | ||||||||
\(423\) | −22.0749 | −1.07332 | ||||||||
\(424\) | 1.41356 | 0.0686485 | ||||||||
\(425\) | −0.657984 | −0.0319169 | ||||||||
\(426\) | −4.73368 | −0.229347 | ||||||||
\(427\) | −20.6551 | −0.999571 | ||||||||
\(428\) | 26.4919 | 1.28054 | ||||||||
\(429\) | 16.9487 | 0.818291 | ||||||||
\(430\) | −4.89103 | −0.235866 | ||||||||
\(431\) | 41.0193 | 1.97583 | 0.987915 | − | 0.154997i | \(-0.0495368\pi\) | ||||
0.987915 | + | 0.154997i | \(0.0495368\pi\) | |||||||
\(432\) | 39.5576 | 1.90322 | ||||||||
\(433\) | −23.2297 | −1.11635 | −0.558175 | − | 0.829724i | \(-0.688498\pi\) | ||||
−0.558175 | + | 0.829724i | \(0.688498\pi\) | |||||||
\(434\) | 46.7274 | 2.24299 | ||||||||
\(435\) | 40.3844 | 1.93629 | ||||||||
\(436\) | −22.9547 | −1.09933 | ||||||||
\(437\) | −8.80965 | −0.421423 | ||||||||
\(438\) | 75.4491 | 3.60510 | ||||||||
\(439\) | −5.15671 | −0.246116 | −0.123058 | − | 0.992399i | \(-0.539270\pi\) | ||||
−0.123058 | + | 0.992399i | \(0.539270\pi\) | |||||||
\(440\) | 1.11535 | 0.0531723 | ||||||||
\(441\) | 30.3169 | 1.44366 | ||||||||
\(442\) | −11.2203 | −0.533695 | ||||||||
\(443\) | −39.4287 | −1.87331 | −0.936657 | − | 0.350247i | \(-0.886098\pi\) | ||||
−0.936657 | + | 0.350247i | \(0.886098\pi\) | |||||||
\(444\) | −11.6425 | −0.552529 | ||||||||
\(445\) | 9.86673 | 0.467728 | ||||||||
\(446\) | 22.8312 | 1.08109 | ||||||||
\(447\) | −25.7661 | −1.21869 | ||||||||
\(448\) | 33.0099 | 1.55957 | ||||||||
\(449\) | −17.5279 | −0.827193 | −0.413597 | − | 0.910460i | \(-0.635728\pi\) | ||||
−0.413597 | + | 0.910460i | \(0.635728\pi\) | |||||||
\(450\) | −8.99345 | −0.423955 | ||||||||
\(451\) | −8.75055 | −0.412047 | ||||||||
\(452\) | 43.5338 | 2.04766 | ||||||||
\(453\) | 18.4074 | 0.864857 | ||||||||
\(454\) | 1.33775 | 0.0627839 | ||||||||
\(455\) | −44.1326 | −2.06897 | ||||||||
\(456\) | 2.84568 | 0.133261 | ||||||||
\(457\) | 9.57992 | 0.448130 | 0.224065 | − | 0.974574i | \(-0.428067\pi\) | ||||
0.224065 | + | 0.974574i | \(0.428067\pi\) | |||||||
\(458\) | 17.9446 | 0.838494 | ||||||||
\(459\) | 11.3283 | 0.528761 | ||||||||
\(460\) | 23.8951 | 1.11411 | ||||||||
\(461\) | −6.04114 | −0.281364 | −0.140682 | − | 0.990055i | \(-0.544929\pi\) | ||||
−0.140682 | + | 0.990055i | \(0.544929\pi\) | |||||||
\(462\) | −21.7153 | −1.01029 | ||||||||
\(463\) | 33.8178 | 1.57165 | 0.785823 | − | 0.618452i | \(-0.212240\pi\) | ||||
0.785823 | + | 0.618452i | \(0.212240\pi\) | |||||||
\(464\) | −19.0874 | −0.886108 | ||||||||
\(465\) | 49.3788 | 2.28988 | ||||||||
\(466\) | 23.4962 | 1.08844 | ||||||||
\(467\) | −1.06940 | −0.0494858 | −0.0247429 | − | 0.999694i | \(-0.507877\pi\) | ||||
−0.0247429 | + | 0.999694i | \(0.507877\pi\) | |||||||
\(468\) | −80.8163 | −3.73574 | ||||||||
\(469\) | 1.12616 | 0.0520010 | ||||||||
\(470\) | −16.2427 | −0.749219 | ||||||||
\(471\) | −14.3892 | −0.663020 | ||||||||
\(472\) | −0.228650 | −0.0105245 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | 89.5036 | 4.11103 | ||||||||
\(475\) | 1.28564 | 0.0589892 | ||||||||
\(476\) | 7.57561 | 0.347227 | ||||||||
\(477\) | −20.0389 | −0.917519 | ||||||||
\(478\) | 14.0275 | 0.641603 | ||||||||
\(479\) | −7.61412 | −0.347898 | −0.173949 | − | 0.984755i | \(-0.555653\pi\) | ||||
−0.173949 | + | 0.984755i | \(0.555653\pi\) | |||||||
\(480\) | 59.9762 | 2.73753 | ||||||||
\(481\) | −9.18030 | −0.418586 | ||||||||
\(482\) | 40.1489 | 1.82873 | ||||||||
\(483\) | −47.6157 | −2.16659 | ||||||||
\(484\) | 2.22804 | 0.101275 | ||||||||
\(485\) | 4.69046 | 0.212983 | ||||||||
\(486\) | 27.4775 | 1.24641 | ||||||||
\(487\) | 15.5730 | 0.705681 | 0.352841 | − | 0.935683i | \(-0.385216\pi\) | ||||
0.352841 | + | 0.935683i | \(0.385216\pi\) | |||||||
\(488\) | −2.84849 | −0.128945 | ||||||||
\(489\) | 48.8411 | 2.20867 | ||||||||
\(490\) | 22.3071 | 1.00773 | ||||||||
\(491\) | 26.4059 | 1.19168 | 0.595840 | − | 0.803103i | \(-0.296819\pi\) | ||||
0.595840 | + | 0.803103i | \(0.296819\pi\) | |||||||
\(492\) | 60.5564 | 2.73009 | ||||||||
\(493\) | −5.46615 | −0.246183 | ||||||||
\(494\) | 21.9234 | 0.986382 | ||||||||
\(495\) | −15.8115 | −0.710673 | ||||||||
\(496\) | −23.3384 | −1.04793 | ||||||||
\(497\) | 2.52012 | 0.113043 | ||||||||
\(498\) | 13.9981 | 0.627271 | ||||||||
\(499\) | 11.0078 | 0.492778 | 0.246389 | − | 0.969171i | \(-0.420756\pi\) | ||||
0.246389 | + | 0.969171i | \(0.420756\pi\) | |||||||
\(500\) | 23.0115 | 1.02911 | ||||||||
\(501\) | −17.6173 | −0.787083 | ||||||||
\(502\) | −24.8438 | −1.10883 | ||||||||
\(503\) | 36.9931 | 1.64944 | 0.824720 | − | 0.565541i | \(-0.191333\pi\) | ||||
0.824720 | + | 0.565541i | \(0.191333\pi\) | |||||||
\(504\) | 10.5978 | 0.472064 | ||||||||
\(505\) | 31.5264 | 1.40291 | ||||||||
\(506\) | 9.27094 | 0.412144 | ||||||||
\(507\) | −52.1069 | −2.31415 | ||||||||
\(508\) | 5.19674 | 0.230568 | ||||||||
\(509\) | −30.1261 | −1.33532 | −0.667658 | − | 0.744468i | \(-0.732703\pi\) | ||||
−0.667658 | + | 0.744468i | \(0.732703\pi\) | |||||||
\(510\) | 15.1915 | 0.672693 | ||||||||
\(511\) | −40.1677 | −1.77692 | ||||||||
\(512\) | −31.6219 | −1.39751 | ||||||||
\(513\) | −22.1345 | −0.977263 | ||||||||
\(514\) | −5.21834 | −0.230171 | ||||||||
\(515\) | 42.2821 | 1.86317 | ||||||||
\(516\) | 6.92029 | 0.304649 | ||||||||
\(517\) | −3.32091 | −0.146053 | ||||||||
\(518\) | 11.7621 | 0.516798 | ||||||||
\(519\) | 58.7667 | 2.57957 | ||||||||
\(520\) | −6.08620 | −0.266898 | ||||||||
\(521\) | 0.373711 | 0.0163726 | 0.00818628 | − | 0.999966i | \(-0.497394\pi\) | ||||
0.00818628 | + | 0.999966i | \(0.497394\pi\) | |||||||
\(522\) | −74.7124 | −3.27007 | ||||||||
\(523\) | 0.530468 | 0.0231957 | 0.0115979 | − | 0.999933i | \(-0.496308\pi\) | ||||
0.0115979 | + | 0.999933i | \(0.496308\pi\) | |||||||
\(524\) | −26.2284 | −1.14579 | ||||||||
\(525\) | 6.94882 | 0.303271 | ||||||||
\(526\) | −31.9751 | −1.39418 | ||||||||
\(527\) | −6.68356 | −0.291140 | ||||||||
\(528\) | 10.8459 | 0.472007 | ||||||||
\(529\) | −2.67136 | −0.116146 | ||||||||
\(530\) | −14.7446 | −0.640465 | ||||||||
\(531\) | 3.24139 | 0.140664 | ||||||||
\(532\) | −14.8020 | −0.641750 | ||||||||
\(533\) | 47.7497 | 2.06827 | ||||||||
\(534\) | −26.4919 | −1.14642 | ||||||||
\(535\) | −28.2828 | −1.22277 | ||||||||
\(536\) | 0.155305 | 0.00670815 | ||||||||
\(537\) | 46.3103 | 1.99843 | ||||||||
\(538\) | −37.5228 | −1.61772 | ||||||||
\(539\) | 4.56082 | 0.196448 | ||||||||
\(540\) | 60.0371 | 2.58359 | ||||||||
\(541\) | −44.6332 | −1.91893 | −0.959466 | − | 0.281825i | \(-0.909060\pi\) | ||||
−0.959466 | + | 0.281825i | \(0.909060\pi\) | |||||||
\(542\) | 1.19603 | 0.0513738 | ||||||||
\(543\) | −3.69678 | −0.158644 | ||||||||
\(544\) | −8.11795 | −0.348054 | ||||||||
\(545\) | 24.5064 | 1.04974 | ||||||||
\(546\) | 118.495 | 5.07112 | ||||||||
\(547\) | −15.6384 | −0.668652 | −0.334326 | − | 0.942458i | \(-0.608509\pi\) | ||||
−0.334326 | + | 0.942458i | \(0.608509\pi\) | |||||||
\(548\) | −1.40317 | −0.0599406 | ||||||||
\(549\) | 40.3808 | 1.72341 | ||||||||
\(550\) | −1.35296 | −0.0576904 | ||||||||
\(551\) | 10.6804 | 0.454999 | ||||||||
\(552\) | −6.56654 | −0.279490 | ||||||||
\(553\) | −47.6501 | −2.02629 | ||||||||
\(554\) | 34.5597 | 1.46830 | ||||||||
\(555\) | 12.4295 | 0.527604 | ||||||||
\(556\) | −4.63670 | −0.196640 | ||||||||
\(557\) | 7.85876 | 0.332986 | 0.166493 | − | 0.986043i | \(-0.446756\pi\) | ||||
0.166493 | + | 0.986043i | \(0.446756\pi\) | |||||||
\(558\) | −91.3521 | −3.86724 | ||||||||
\(559\) | 5.45676 | 0.230796 | ||||||||
\(560\) | −28.2416 | −1.19343 | ||||||||
\(561\) | 3.10600 | 0.131135 | ||||||||
\(562\) | 29.5719 | 1.24741 | ||||||||
\(563\) | −29.1530 | −1.22865 | −0.614326 | − | 0.789053i | \(-0.710572\pi\) | ||||
−0.614326 | + | 0.789053i | \(0.710572\pi\) | |||||||
\(564\) | 22.9817 | 0.967703 | ||||||||
\(565\) | −46.4766 | −1.95529 | ||||||||
\(566\) | 46.6526 | 1.96095 | ||||||||
\(567\) | −51.8317 | −2.17673 | ||||||||
\(568\) | 0.347543 | 0.0145826 | ||||||||
\(569\) | 5.28132 | 0.221404 | 0.110702 | − | 0.993854i | \(-0.464690\pi\) | ||||
0.110702 | + | 0.993854i | \(0.464690\pi\) | |||||||
\(570\) | −29.6829 | −1.24328 | ||||||||
\(571\) | −30.1706 | −1.26260 | −0.631301 | − | 0.775538i | \(-0.717479\pi\) | ||||
−0.631301 | + | 0.775538i | \(0.717479\pi\) | |||||||
\(572\) | −12.1579 | −0.508346 | ||||||||
\(573\) | 36.2703 | 1.51521 | ||||||||
\(574\) | −61.1786 | −2.55354 | ||||||||
\(575\) | −2.96667 | −0.123719 | ||||||||
\(576\) | −64.5344 | −2.68894 | ||||||||
\(577\) | 2.27433 | 0.0946816 | 0.0473408 | − | 0.998879i | \(-0.484925\pi\) | ||||
0.0473408 | + | 0.998879i | \(0.484925\pi\) | |||||||
\(578\) | −2.05622 | −0.0855275 | ||||||||
\(579\) | 50.9322 | 2.11667 | ||||||||
\(580\) | −28.9691 | −1.20288 | ||||||||
\(581\) | −7.45235 | −0.309176 | ||||||||
\(582\) | −12.5938 | −0.522028 | ||||||||
\(583\) | −3.01462 | −0.124853 | ||||||||
\(584\) | −5.53941 | −0.229222 | ||||||||
\(585\) | 86.2794 | 3.56721 | ||||||||
\(586\) | 37.3029 | 1.54097 | ||||||||
\(587\) | −40.2557 | −1.66153 | −0.830765 | − | 0.556623i | \(-0.812097\pi\) | ||||
−0.830765 | + | 0.556623i | \(0.812097\pi\) | |||||||
\(588\) | −31.5622 | −1.30160 | ||||||||
\(589\) | 13.0591 | 0.538089 | ||||||||
\(590\) | 2.38501 | 0.0981894 | ||||||||
\(591\) | 21.4427 | 0.882036 | ||||||||
\(592\) | −5.87471 | −0.241449 | ||||||||
\(593\) | 19.9104 | 0.817621 | 0.408811 | − | 0.912619i | \(-0.365944\pi\) | ||||
0.408811 | + | 0.912619i | \(0.365944\pi\) | |||||||
\(594\) | 23.2935 | 0.955745 | ||||||||
\(595\) | −8.08770 | −0.331563 | ||||||||
\(596\) | 18.4829 | 0.757088 | ||||||||
\(597\) | 76.2708 | 3.12156 | ||||||||
\(598\) | −50.5893 | −2.06875 | ||||||||
\(599\) | −1.50958 | −0.0616800 | −0.0308400 | − | 0.999524i | \(-0.509818\pi\) | ||||
−0.0308400 | + | 0.999524i | \(0.509818\pi\) | |||||||
\(600\) | 0.958292 | 0.0391221 | ||||||||
\(601\) | −38.6248 | −1.57554 | −0.787770 | − | 0.615970i | \(-0.788764\pi\) | ||||
−0.787770 | + | 0.615970i | \(0.788764\pi\) | |||||||
\(602\) | −6.99140 | −0.284948 | ||||||||
\(603\) | −2.20164 | −0.0896575 | ||||||||
\(604\) | −13.2043 | −0.537275 | ||||||||
\(605\) | −2.37865 | −0.0967059 | ||||||||
\(606\) | −84.6477 | −3.43858 | ||||||||
\(607\) | 24.9818 | 1.01398 | 0.506989 | − | 0.861952i | \(-0.330758\pi\) | ||||
0.506989 | + | 0.861952i | \(0.330758\pi\) | |||||||
\(608\) | 15.8617 | 0.643278 | ||||||||
\(609\) | 57.7268 | 2.33921 | ||||||||
\(610\) | 29.7121 | 1.20301 | ||||||||
\(611\) | 18.1214 | 0.733114 | ||||||||
\(612\) | −14.8103 | −0.598672 | ||||||||
\(613\) | 26.3188 | 1.06300 | 0.531502 | − | 0.847057i | \(-0.321628\pi\) | ||||
0.531502 | + | 0.847057i | \(0.321628\pi\) | |||||||
\(614\) | 20.9614 | 0.845934 | ||||||||
\(615\) | −64.6499 | −2.60694 | ||||||||
\(616\) | 1.59432 | 0.0642369 | ||||||||
\(617\) | −14.0481 | −0.565557 | −0.282778 | − | 0.959185i | \(-0.591256\pi\) | ||||
−0.282778 | + | 0.959185i | \(0.591256\pi\) | |||||||
\(618\) | −113.526 | −4.56670 | ||||||||
\(619\) | 33.6935 | 1.35426 | 0.677128 | − | 0.735865i | \(-0.263224\pi\) | ||||
0.677128 | + | 0.735865i | \(0.263224\pi\) | |||||||
\(620\) | −35.4211 | −1.42254 | ||||||||
\(621\) | 51.0764 | 2.04962 | ||||||||
\(622\) | −14.7393 | −0.590992 | ||||||||
\(623\) | 14.1038 | 0.565058 | ||||||||
\(624\) | −59.1835 | −2.36923 | ||||||||
\(625\) | −27.8570 | −1.11428 | ||||||||
\(626\) | 34.6377 | 1.38440 | ||||||||
\(627\) | −6.06884 | −0.242366 | ||||||||
\(628\) | 10.3219 | 0.411888 | ||||||||
\(629\) | −1.68237 | −0.0670806 | ||||||||
\(630\) | −110.544 | −4.40419 | ||||||||
\(631\) | 40.9122 | 1.62869 | 0.814344 | − | 0.580383i | \(-0.197097\pi\) | ||||
0.814344 | + | 0.580383i | \(0.197097\pi\) | |||||||
\(632\) | −6.57128 | −0.261392 | ||||||||
\(633\) | 80.9576 | 3.21778 | ||||||||
\(634\) | 55.4459 | 2.20204 | ||||||||
\(635\) | −5.54803 | −0.220167 | ||||||||
\(636\) | 20.8621 | 0.827235 | ||||||||
\(637\) | −24.8873 | −0.986071 | ||||||||
\(638\) | −11.2396 | −0.444980 | ||||||||
\(639\) | −4.92685 | −0.194903 | ||||||||
\(640\) | −8.86481 | −0.350412 | ||||||||
\(641\) | 1.50910 | 0.0596058 | 0.0298029 | − | 0.999556i | \(-0.490512\pi\) | ||||
0.0298029 | + | 0.999556i | \(0.490512\pi\) | |||||||
\(642\) | 75.9385 | 2.99705 | ||||||||
\(643\) | −7.99676 | −0.315361 | −0.157681 | − | 0.987490i | \(-0.550402\pi\) | ||||
−0.157681 | + | 0.987490i | \(0.550402\pi\) | |||||||
\(644\) | 34.1564 | 1.34595 | ||||||||
\(645\) | −7.38809 | −0.290906 | ||||||||
\(646\) | 4.01767 | 0.158073 | ||||||||
\(647\) | −7.66951 | −0.301520 | −0.150760 | − | 0.988570i | \(-0.548172\pi\) | ||||
−0.150760 | + | 0.988570i | \(0.548172\pi\) | |||||||
\(648\) | −7.14796 | −0.280798 | ||||||||
\(649\) | 0.487630 | 0.0191412 | ||||||||
\(650\) | 7.38278 | 0.289576 | ||||||||
\(651\) | 70.5836 | 2.76639 | ||||||||
\(652\) | −35.0354 | −1.37209 | ||||||||
\(653\) | 18.5430 | 0.725642 | 0.362821 | − | 0.931859i | \(-0.381814\pi\) | ||||
0.362821 | + | 0.931859i | \(0.381814\pi\) | |||||||
\(654\) | −65.7992 | −2.57295 | ||||||||
\(655\) | 28.0014 | 1.09410 | ||||||||
\(656\) | 30.5562 | 1.19302 | ||||||||
\(657\) | 78.5279 | 3.06367 | ||||||||
\(658\) | −23.2178 | −0.905124 | ||||||||
\(659\) | −17.0114 | −0.662668 | −0.331334 | − | 0.943513i | \(-0.607499\pi\) | ||||
−0.331334 | + | 0.943513i | \(0.607499\pi\) | |||||||
\(660\) | 16.4610 | 0.640742 | ||||||||
\(661\) | −35.7015 | −1.38863 | −0.694313 | − | 0.719673i | \(-0.744292\pi\) | ||||
−0.694313 | + | 0.719673i | \(0.744292\pi\) | |||||||
\(662\) | 18.9857 | 0.737902 | ||||||||
\(663\) | −16.9487 | −0.658233 | ||||||||
\(664\) | −1.02773 | −0.0398837 | ||||||||
\(665\) | 15.8026 | 0.612800 | ||||||||
\(666\) | −22.9950 | −0.891037 | ||||||||
\(667\) | −24.6454 | −0.954274 | ||||||||
\(668\) | 12.6375 | 0.488959 | ||||||||
\(669\) | 34.4874 | 1.33336 | ||||||||
\(670\) | −1.61996 | −0.0625845 | ||||||||
\(671\) | 6.07482 | 0.234516 | ||||||||
\(672\) | 85.7319 | 3.30718 | ||||||||
\(673\) | 18.6793 | 0.720036 | 0.360018 | − | 0.932945i | \(-0.382771\pi\) | ||||
0.360018 | + | 0.932945i | \(0.382771\pi\) | |||||||
\(674\) | 35.0242 | 1.34908 | ||||||||
\(675\) | −7.45386 | −0.286899 | ||||||||
\(676\) | 37.3781 | 1.43762 | ||||||||
\(677\) | 32.3805 | 1.24448 | 0.622242 | − | 0.782825i | \(-0.286222\pi\) | ||||
0.622242 | + | 0.782825i | \(0.286222\pi\) | |||||||
\(678\) | 124.789 | 4.79248 | ||||||||
\(679\) | 6.70469 | 0.257302 | ||||||||
\(680\) | −1.11535 | −0.0427718 | ||||||||
\(681\) | 2.02073 | 0.0774345 | ||||||||
\(682\) | −13.7429 | −0.526241 | ||||||||
\(683\) | 30.7170 | 1.17535 | 0.587676 | − | 0.809096i | \(-0.300043\pi\) | ||||
0.587676 | + | 0.809096i | \(0.300043\pi\) | |||||||
\(684\) | 28.9380 | 1.10647 | ||||||||
\(685\) | 1.49803 | 0.0572366 | ||||||||
\(686\) | −17.0533 | −0.651097 | ||||||||
\(687\) | 27.1060 | 1.03416 | ||||||||
\(688\) | 3.49192 | 0.133128 | ||||||||
\(689\) | 16.4501 | 0.626698 | ||||||||
\(690\) | 68.4946 | 2.60754 | ||||||||
\(691\) | −8.95350 | −0.340607 | −0.170304 | − | 0.985392i | \(-0.554475\pi\) | ||||
−0.170304 | + | 0.985392i | \(0.554475\pi\) | |||||||
\(692\) | −42.1553 | −1.60251 | ||||||||
\(693\) | −22.6014 | −0.858557 | ||||||||
\(694\) | −61.8050 | −2.34609 | ||||||||
\(695\) | 4.95013 | 0.187769 | ||||||||
\(696\) | 7.96093 | 0.301758 | ||||||||
\(697\) | 8.75055 | 0.331451 | ||||||||
\(698\) | 39.8067 | 1.50671 | ||||||||
\(699\) | 35.4919 | 1.34243 | ||||||||
\(700\) | −4.98463 | −0.188401 | ||||||||
\(701\) | −31.5969 | −1.19340 | −0.596699 | − | 0.802465i | \(-0.703521\pi\) | ||||
−0.596699 | + | 0.802465i | \(0.703521\pi\) | |||||||
\(702\) | −127.107 | −4.79735 | ||||||||
\(703\) | 3.28720 | 0.123979 | ||||||||
\(704\) | −9.70846 | −0.365901 | ||||||||
\(705\) | −24.5352 | −0.924049 | ||||||||
\(706\) | −7.18452 | −0.270393 | ||||||||
\(707\) | 45.0649 | 1.69484 | ||||||||
\(708\) | −3.37454 | −0.126823 | ||||||||
\(709\) | 1.13802 | 0.0427391 | 0.0213695 | − | 0.999772i | \(-0.493197\pi\) | ||||
0.0213695 | + | 0.999772i | \(0.493197\pi\) | |||||||
\(710\) | −3.62517 | −0.136050 | ||||||||
\(711\) | 93.1559 | 3.49362 | ||||||||
\(712\) | 1.94502 | 0.0728926 | ||||||||
\(713\) | −30.1344 | −1.12854 | ||||||||
\(714\) | 21.7153 | 0.812674 | ||||||||
\(715\) | 12.9797 | 0.485414 | ||||||||
\(716\) | −33.2199 | −1.24149 | ||||||||
\(717\) | 21.1891 | 0.791321 | ||||||||
\(718\) | −3.14781 | −0.117475 | ||||||||
\(719\) | 6.65675 | 0.248255 | 0.124127 | − | 0.992266i | \(-0.460387\pi\) | ||||
0.124127 | + | 0.992266i | \(0.460387\pi\) | |||||||
\(720\) | 55.2123 | 2.05764 | ||||||||
\(721\) | 60.4394 | 2.25088 | ||||||||
\(722\) | 31.2180 | 1.16181 | ||||||||
\(723\) | 60.6464 | 2.25547 | ||||||||
\(724\) | 2.65182 | 0.0985543 | ||||||||
\(725\) | 3.59664 | 0.133576 | ||||||||
\(726\) | 6.38662 | 0.237030 | ||||||||
\(727\) | −20.6180 | −0.764680 | −0.382340 | − | 0.924022i | \(-0.624882\pi\) | ||||
−0.382340 | + | 0.924022i | \(0.624882\pi\) | |||||||
\(728\) | −8.69981 | −0.322437 | ||||||||
\(729\) | −4.22636 | −0.156532 | ||||||||
\(730\) | 57.7808 | 2.13856 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | −42.0395 | −1.55383 | ||||||||
\(733\) | 10.2608 | 0.378990 | 0.189495 | − | 0.981882i | \(-0.439315\pi\) | ||||
0.189495 | + | 0.981882i | \(0.439315\pi\) | |||||||
\(734\) | −69.5179 | −2.56595 | ||||||||
\(735\) | 33.6958 | 1.24289 | ||||||||
\(736\) | −36.6016 | −1.34915 | ||||||||
\(737\) | −0.331210 | −0.0122003 | ||||||||
\(738\) | 119.604 | 4.40269 | ||||||||
\(739\) | −23.9256 | −0.880119 | −0.440059 | − | 0.897969i | \(-0.645043\pi\) | ||||
−0.440059 | + | 0.897969i | \(0.645043\pi\) | |||||||
\(740\) | −8.91612 | −0.327763 | ||||||||
\(741\) | 33.1162 | 1.21655 | ||||||||
\(742\) | −21.0764 | −0.773740 | ||||||||
\(743\) | 9.96762 | 0.365676 | 0.182838 | − | 0.983143i | \(-0.441472\pi\) | ||||
0.182838 | + | 0.983143i | \(0.441472\pi\) | |||||||
\(744\) | 9.73397 | 0.356865 | ||||||||
\(745\) | −19.7323 | −0.722935 | ||||||||
\(746\) | −24.1842 | −0.885448 | ||||||||
\(747\) | 14.5694 | 0.533065 | ||||||||
\(748\) | −2.22804 | −0.0814652 | ||||||||
\(749\) | −40.4283 | −1.47722 | ||||||||
\(750\) | 65.9619 | 2.40859 | ||||||||
\(751\) | 1.75348 | 0.0639855 | 0.0319927 | − | 0.999488i | \(-0.489815\pi\) | ||||
0.0319927 | + | 0.999488i | \(0.489815\pi\) | |||||||
\(752\) | 11.5963 | 0.422875 | ||||||||
\(753\) | −37.5275 | −1.36758 | ||||||||
\(754\) | 61.3318 | 2.23357 | ||||||||
\(755\) | 14.0969 | 0.513038 | ||||||||
\(756\) | 85.8189 | 3.12120 | ||||||||
\(757\) | −18.2790 | −0.664363 | −0.332181 | − | 0.943216i | \(-0.607785\pi\) | ||||
−0.332181 | + | 0.943216i | \(0.607785\pi\) | |||||||
\(758\) | −45.6749 | −1.65899 | ||||||||
\(759\) | 14.0041 | 0.508317 | ||||||||
\(760\) | 2.17929 | 0.0790513 | ||||||||
\(761\) | 2.52033 | 0.0913620 | 0.0456810 | − | 0.998956i | \(-0.485454\pi\) | ||||
0.0456810 | + | 0.998956i | \(0.485454\pi\) | |||||||
\(762\) | 14.8963 | 0.539637 | ||||||||
\(763\) | 35.0303 | 1.26818 | ||||||||
\(764\) | −26.0179 | −0.941296 | ||||||||
\(765\) | 15.8115 | 0.571665 | ||||||||
\(766\) | −52.3145 | −1.89020 | ||||||||
\(767\) | −2.66088 | −0.0960788 | ||||||||
\(768\) | −36.5072 | −1.31734 | ||||||||
\(769\) | −19.2276 | −0.693365 | −0.346683 | − | 0.937982i | \(-0.612692\pi\) | ||||
−0.346683 | + | 0.937982i | \(0.612692\pi\) | |||||||
\(770\) | −16.6301 | −0.599307 | ||||||||
\(771\) | −7.88251 | −0.283881 | ||||||||
\(772\) | −36.5354 | −1.31494 | ||||||||
\(773\) | 23.8924 | 0.859349 | 0.429674 | − | 0.902984i | \(-0.358628\pi\) | ||||
0.429674 | + | 0.902984i | \(0.358628\pi\) | |||||||
\(774\) | 13.6682 | 0.491293 | ||||||||
\(775\) | 4.39767 | 0.157969 | ||||||||
\(776\) | 0.924624 | 0.0331921 | ||||||||
\(777\) | 17.7672 | 0.637393 | ||||||||
\(778\) | −65.3311 | −2.34224 | ||||||||
\(779\) | −17.0978 | −0.612592 | ||||||||
\(780\) | −89.8235 | −3.21620 | ||||||||
\(781\) | −0.741187 | −0.0265218 | ||||||||
\(782\) | −9.27094 | −0.331528 | ||||||||
\(783\) | −61.9224 | −2.21292 | ||||||||
\(784\) | −15.9260 | −0.568786 | ||||||||
\(785\) | −11.0196 | −0.393307 | ||||||||
\(786\) | −75.1830 | −2.68169 | ||||||||
\(787\) | 5.71799 | 0.203824 | 0.101912 | − | 0.994793i | \(-0.467504\pi\) | ||||
0.101912 | + | 0.994793i | \(0.467504\pi\) | |||||||
\(788\) | −15.3816 | −0.547947 | ||||||||
\(789\) | −48.2996 | −1.71951 | ||||||||
\(790\) | 68.5440 | 2.43869 | ||||||||
\(791\) | −66.4352 | −2.36216 | ||||||||
\(792\) | −3.11689 | −0.110754 | ||||||||
\(793\) | −33.1488 | −1.17715 | ||||||||
\(794\) | 30.9725 | 1.09917 | ||||||||
\(795\) | −22.2723 | −0.789918 | ||||||||
\(796\) | −54.7116 | −1.93920 | ||||||||
\(797\) | −31.3544 | −1.11063 | −0.555315 | − | 0.831640i | \(-0.687402\pi\) | ||||
−0.555315 | + | 0.831640i | \(0.687402\pi\) | |||||||
\(798\) | −42.4297 | −1.50199 | ||||||||
\(799\) | 3.32091 | 0.117485 | ||||||||
\(800\) | 5.34148 | 0.188850 | ||||||||
\(801\) | −27.5730 | −0.974243 | ||||||||
\(802\) | 2.93333 | 0.103580 | ||||||||
\(803\) | 11.8136 | 0.416893 | ||||||||
\(804\) | 2.29207 | 0.0808352 | ||||||||
\(805\) | −36.4653 | −1.28523 | ||||||||
\(806\) | 74.9915 | 2.64146 | ||||||||
\(807\) | −56.6797 | −1.99522 | ||||||||
\(808\) | 6.21477 | 0.218635 | ||||||||
\(809\) | 24.5251 | 0.862258 | 0.431129 | − | 0.902290i | \(-0.358115\pi\) | ||||
0.431129 | + | 0.902290i | \(0.358115\pi\) | |||||||
\(810\) | 74.5592 | 2.61974 | ||||||||
\(811\) | −3.83856 | −0.134790 | −0.0673950 | − | 0.997726i | \(-0.521469\pi\) | ||||
−0.0673950 | + | 0.997726i | \(0.521469\pi\) | |||||||
\(812\) | −41.4094 | −1.45319 | ||||||||
\(813\) | 1.80665 | 0.0633618 | ||||||||
\(814\) | −3.45933 | −0.121249 | ||||||||
\(815\) | 37.4037 | 1.31020 | ||||||||
\(816\) | −10.8459 | −0.379682 | ||||||||
\(817\) | −1.95391 | −0.0683586 | ||||||||
\(818\) | 79.5358 | 2.78090 | ||||||||
\(819\) | 123.330 | 4.30952 | ||||||||
\(820\) | 46.3756 | 1.61951 | ||||||||
\(821\) | −22.8585 | −0.797765 | −0.398883 | − | 0.917002i | \(-0.630602\pi\) | ||||
−0.398883 | + | 0.917002i | \(0.630602\pi\) | |||||||
\(822\) | −4.02216 | −0.140289 | ||||||||
\(823\) | 5.16310 | 0.179974 | 0.0899872 | − | 0.995943i | \(-0.471317\pi\) | ||||
0.0899872 | + | 0.995943i | \(0.471317\pi\) | |||||||
\(824\) | 8.33502 | 0.290364 | ||||||||
\(825\) | −2.04370 | −0.0711525 | ||||||||
\(826\) | 3.40921 | 0.118622 | ||||||||
\(827\) | −7.46910 | −0.259726 | −0.129863 | − | 0.991532i | \(-0.541454\pi\) | ||||
−0.129863 | + | 0.991532i | \(0.541454\pi\) | |||||||
\(828\) | −66.7757 | −2.32062 | ||||||||
\(829\) | 14.9944 | 0.520777 | 0.260389 | − | 0.965504i | \(-0.416149\pi\) | ||||
0.260389 | + | 0.965504i | \(0.416149\pi\) | |||||||
\(830\) | 10.7201 | 0.372101 | ||||||||
\(831\) | 52.2037 | 1.81093 | ||||||||
\(832\) | 52.9767 | 1.83664 | ||||||||
\(833\) | −4.56082 | −0.158023 | ||||||||
\(834\) | −13.2910 | −0.460229 | ||||||||
\(835\) | −13.4918 | −0.466902 | ||||||||
\(836\) | 4.35339 | 0.150565 | ||||||||
\(837\) | −75.7135 | −2.61704 | ||||||||
\(838\) | 13.4752 | 0.465492 | ||||||||
\(839\) | −13.2047 | −0.455878 | −0.227939 | − | 0.973675i | \(-0.573199\pi\) | ||||
−0.227939 | + | 0.973675i | \(0.573199\pi\) | |||||||
\(840\) | 11.7790 | 0.406413 | ||||||||
\(841\) | 0.878821 | 0.0303042 | ||||||||
\(842\) | 18.0074 | 0.620577 | ||||||||
\(843\) | 44.6695 | 1.53850 | ||||||||
\(844\) | −58.0737 | −1.99898 | ||||||||
\(845\) | −39.9048 | −1.37277 | ||||||||
\(846\) | 45.3908 | 1.56057 | ||||||||
\(847\) | −3.40012 | −0.116830 | ||||||||
\(848\) | 10.5268 | 0.361492 | ||||||||
\(849\) | 70.4705 | 2.41854 | ||||||||
\(850\) | 1.35296 | 0.0464061 | ||||||||
\(851\) | −7.58536 | −0.260023 | ||||||||
\(852\) | 5.12923 | 0.175725 | ||||||||
\(853\) | −21.4738 | −0.735249 | −0.367625 | − | 0.929974i | \(-0.619829\pi\) | ||||
−0.367625 | + | 0.929974i | \(0.619829\pi\) | |||||||
\(854\) | 42.4715 | 1.45334 | ||||||||
\(855\) | −30.8942 | −1.05656 | ||||||||
\(856\) | −5.57534 | −0.190561 | ||||||||
\(857\) | −1.23096 | −0.0420488 | −0.0210244 | − | 0.999779i | \(-0.506693\pi\) | ||||
−0.0210244 | + | 0.999779i | \(0.506693\pi\) | |||||||
\(858\) | −34.8502 | −1.18977 | ||||||||
\(859\) | −46.7517 | −1.59515 | −0.797574 | − | 0.603221i | \(-0.793884\pi\) | ||||
−0.797574 | + | 0.603221i | \(0.793884\pi\) | |||||||
\(860\) | 5.29973 | 0.180719 | ||||||||
\(861\) | −92.4126 | −3.14941 | ||||||||
\(862\) | −84.3447 | −2.87279 | ||||||||
\(863\) | −31.2387 | −1.06338 | −0.531688 | − | 0.846940i | \(-0.678442\pi\) | ||||
−0.531688 | + | 0.846940i | \(0.678442\pi\) | |||||||
\(864\) | −91.9628 | −3.12864 | ||||||||
\(865\) | 45.0050 | 1.53021 | ||||||||
\(866\) | 47.7654 | 1.62313 | ||||||||
\(867\) | −3.10600 | −0.105485 | ||||||||
\(868\) | −50.6320 | −1.71856 | ||||||||
\(869\) | 14.0142 | 0.475400 | ||||||||
\(870\) | −83.0393 | −2.81530 | ||||||||
\(871\) | 1.80734 | 0.0612392 | ||||||||
\(872\) | 4.83092 | 0.163596 | ||||||||
\(873\) | −13.1077 | −0.443628 | ||||||||
\(874\) | 18.1146 | 0.612734 | ||||||||
\(875\) | −35.1169 | −1.18717 | ||||||||
\(876\) | −81.7537 | −2.76220 | ||||||||
\(877\) | 31.7235 | 1.07123 | 0.535613 | − | 0.844463i | \(-0.320080\pi\) | ||||
0.535613 | + | 0.844463i | \(0.320080\pi\) | |||||||
\(878\) | 10.6033 | 0.357845 | ||||||||
\(879\) | 56.3475 | 1.90055 | ||||||||
\(880\) | 8.30606 | 0.279997 | ||||||||
\(881\) | −10.8547 | −0.365706 | −0.182853 | − | 0.983140i | \(-0.558533\pi\) | ||||
−0.182853 | + | 0.983140i | \(0.558533\pi\) | |||||||
\(882\) | −62.3381 | −2.09903 | ||||||||
\(883\) | 24.7126 | 0.831646 | 0.415823 | − | 0.909445i | \(-0.363493\pi\) | ||||
0.415823 | + | 0.909445i | \(0.363493\pi\) | |||||||
\(884\) | 12.1579 | 0.408914 | ||||||||
\(885\) | 3.60266 | 0.121102 | ||||||||
\(886\) | 81.0741 | 2.72374 | ||||||||
\(887\) | 36.3601 | 1.22085 | 0.610426 | − | 0.792073i | \(-0.290998\pi\) | ||||
0.610426 | + | 0.792073i | \(0.290998\pi\) | |||||||
\(888\) | 2.45022 | 0.0822239 | ||||||||
\(889\) | −7.93054 | −0.265982 | ||||||||
\(890\) | −20.2882 | −0.680061 | ||||||||
\(891\) | 15.2441 | 0.510696 | ||||||||
\(892\) | −24.7390 | −0.828322 | ||||||||
\(893\) | −6.48875 | −0.217138 | ||||||||
\(894\) | 52.9807 | 1.77194 | ||||||||
\(895\) | 35.4655 | 1.18548 | ||||||||
\(896\) | −12.6716 | −0.423330 | ||||||||
\(897\) | −76.4171 | −2.55149 | ||||||||
\(898\) | 36.0412 | 1.20271 | ||||||||
\(899\) | 36.5333 | 1.21846 | ||||||||
\(900\) | 9.74495 | 0.324832 | ||||||||
\(901\) | 3.01462 | 0.100432 | ||||||||
\(902\) | 17.9931 | 0.599103 | ||||||||
\(903\) | −10.5608 | −0.351441 | ||||||||
\(904\) | −9.16188 | −0.304719 | ||||||||
\(905\) | −2.83108 | −0.0941084 | ||||||||
\(906\) | −37.8497 | −1.25747 | ||||||||
\(907\) | 42.7889 | 1.42078 | 0.710391 | − | 0.703808i | \(-0.248518\pi\) | ||||
0.710391 | + | 0.703808i | \(0.248518\pi\) | |||||||
\(908\) | −1.44954 | −0.0481046 | ||||||||
\(909\) | −88.1019 | −2.92216 | ||||||||
\(910\) | 90.7464 | 3.00821 | ||||||||
\(911\) | 9.40165 | 0.311491 | 0.155745 | − | 0.987797i | \(-0.450222\pi\) | ||||
0.155745 | + | 0.987797i | \(0.450222\pi\) | |||||||
\(912\) | 21.1919 | 0.701734 | ||||||||
\(913\) | 2.19179 | 0.0725377 | ||||||||
\(914\) | −19.6984 | −0.651566 | ||||||||
\(915\) | 44.8813 | 1.48373 | ||||||||
\(916\) | −19.4440 | −0.642449 | ||||||||
\(917\) | 40.0261 | 1.32178 | ||||||||
\(918\) | −23.2935 | −0.768801 | ||||||||
\(919\) | 24.0228 | 0.792437 | 0.396219 | − | 0.918156i | \(-0.370322\pi\) | ||||
0.396219 | + | 0.918156i | \(0.370322\pi\) | |||||||
\(920\) | −5.02882 | −0.165795 | ||||||||
\(921\) | 31.6631 | 1.04333 | ||||||||
\(922\) | 12.4219 | 0.409094 | ||||||||
\(923\) | 4.04448 | 0.133126 | ||||||||
\(924\) | 23.5298 | 0.774075 | ||||||||
\(925\) | 1.10697 | 0.0363971 | ||||||||
\(926\) | −69.5368 | −2.28512 | ||||||||
\(927\) | −118.159 | −3.88085 | ||||||||
\(928\) | 44.3740 | 1.45665 | ||||||||
\(929\) | 53.0682 | 1.74111 | 0.870556 | − | 0.492069i | \(-0.163759\pi\) | ||||
0.870556 | + | 0.492069i | \(0.163759\pi\) | |||||||
\(930\) | −101.534 | −3.32942 | ||||||||
\(931\) | 8.91143 | 0.292060 | ||||||||
\(932\) | −25.4596 | −0.833956 | ||||||||
\(933\) | −22.2643 | −0.728900 | ||||||||
\(934\) | 2.19891 | 0.0719507 | ||||||||
\(935\) | 2.37865 | 0.0777902 | ||||||||
\(936\) | 17.0081 | 0.555929 | ||||||||
\(937\) | 17.1710 | 0.560953 | 0.280476 | − | 0.959861i | \(-0.409508\pi\) | ||||
0.280476 | + | 0.959861i | \(0.409508\pi\) | |||||||
\(938\) | −2.31562 | −0.0756078 | ||||||||
\(939\) | 52.3216 | 1.70745 | ||||||||
\(940\) | 17.5999 | 0.574046 | ||||||||
\(941\) | 15.8365 | 0.516255 | 0.258127 | − | 0.966111i | \(-0.416895\pi\) | ||||
0.258127 | + | 0.966111i | \(0.416895\pi\) | |||||||
\(942\) | 29.5874 | 0.964009 | ||||||||
\(943\) | 39.4539 | 1.28480 | ||||||||
\(944\) | −1.70276 | −0.0554202 | ||||||||
\(945\) | −91.6202 | −2.98040 | ||||||||
\(946\) | 2.05622 | 0.0668535 | ||||||||
\(947\) | 47.4657 | 1.54243 | 0.771213 | − | 0.636577i | \(-0.219650\pi\) | ||||
0.771213 | + | 0.636577i | \(0.219650\pi\) | |||||||
\(948\) | −96.9826 | −3.14985 | ||||||||
\(949\) | −64.4640 | −2.09259 | ||||||||
\(950\) | −2.64356 | −0.0857684 | ||||||||
\(951\) | 83.7532 | 2.71588 | ||||||||
\(952\) | −1.59432 | −0.0516722 | ||||||||
\(953\) | −32.9572 | −1.06759 | −0.533795 | − | 0.845614i | \(-0.679234\pi\) | ||||
−0.533795 | + | 0.845614i | \(0.679234\pi\) | |||||||
\(954\) | 41.2044 | 1.33404 | ||||||||
\(955\) | 27.7767 | 0.898833 | ||||||||
\(956\) | −15.1997 | −0.491592 | ||||||||
\(957\) | −16.9779 | −0.548817 | ||||||||
\(958\) | 15.6563 | 0.505832 | ||||||||
\(959\) | 2.14133 | 0.0691470 | ||||||||
\(960\) | −71.7270 | −2.31498 | ||||||||
\(961\) | 13.6699 | 0.440966 | ||||||||
\(962\) | 18.8767 | 0.608610 | ||||||||
\(963\) | 79.0373 | 2.54694 | ||||||||
\(964\) | −43.5038 | −1.40116 | ||||||||
\(965\) | 39.0051 | 1.25562 | ||||||||
\(966\) | 97.9083 | 3.15015 | ||||||||
\(967\) | −13.3301 | −0.428666 | −0.214333 | − | 0.976761i | \(-0.568758\pi\) | ||||
−0.214333 | + | 0.976761i | \(0.568758\pi\) | |||||||
\(968\) | −0.468901 | −0.0150710 | ||||||||
\(969\) | 6.06884 | 0.194959 | ||||||||
\(970\) | −9.64461 | −0.309670 | ||||||||
\(971\) | 6.35365 | 0.203898 | 0.101949 | − | 0.994790i | \(-0.467492\pi\) | ||||
0.101949 | + | 0.994790i | \(0.467492\pi\) | |||||||
\(972\) | −29.7736 | −0.954988 | ||||||||
\(973\) | 7.07588 | 0.226842 | ||||||||
\(974\) | −32.0216 | −1.02604 | ||||||||
\(975\) | 11.1520 | 0.357149 | ||||||||
\(976\) | −21.2128 | −0.679004 | ||||||||
\(977\) | −22.9043 | −0.732772 | −0.366386 | − | 0.930463i | \(-0.619405\pi\) | ||||
−0.366386 | + | 0.930463i | \(0.619405\pi\) | |||||||
\(978\) | −100.428 | −3.21134 | ||||||||
\(979\) | −4.14803 | −0.132572 | ||||||||
\(980\) | −24.1711 | −0.772118 | ||||||||
\(981\) | −68.4843 | −2.18653 | ||||||||
\(982\) | −54.2963 | −1.73266 | ||||||||
\(983\) | 44.8318 | 1.42991 | 0.714956 | − | 0.699170i | \(-0.246447\pi\) | ||||
0.714956 | + | 0.699170i | \(0.246447\pi\) | |||||||
\(984\) | −12.7444 | −0.406275 | ||||||||
\(985\) | 16.4214 | 0.523228 | ||||||||
\(986\) | 11.2396 | 0.357942 | ||||||||
\(987\) | −35.0714 | −1.11633 | ||||||||
\(988\) | −23.7554 | −0.755759 | ||||||||
\(989\) | 4.50873 | 0.143369 | ||||||||
\(990\) | 32.5119 | 1.03329 | ||||||||
\(991\) | 15.1643 | 0.481710 | 0.240855 | − | 0.970561i | \(-0.422572\pi\) | ||||
0.240855 | + | 0.970561i | \(0.422572\pi\) | |||||||
\(992\) | 54.2568 | 1.72266 | ||||||||
\(993\) | 28.6787 | 0.910091 | ||||||||
\(994\) | −5.18193 | −0.164361 | ||||||||
\(995\) | 58.4101 | 1.85172 | ||||||||
\(996\) | −15.1678 | −0.480611 | ||||||||
\(997\) | 58.2846 | 1.84589 | 0.922946 | − | 0.384930i | \(-0.125774\pi\) | ||||
0.922946 | + | 0.384930i | \(0.125774\pi\) | |||||||
\(998\) | −22.6345 | −0.716483 | ||||||||
\(999\) | −19.0585 | −0.602983 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8041.2.a.i.1.12 | ✓ | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.i.1.12 | ✓ | 78 | 1.1 | even | 1 | trivial |