Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, 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("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.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: | \(48.1817325796\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-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 | ||||||||
\(3\) | −2.67063 | −1.54189 | −0.770946 | − | 0.636901i | \(-0.780216\pi\) | ||||
−0.770946 | + | 0.636901i | \(0.780216\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.15601 | 1.41141 | 0.705705 | − | 0.708506i | \(-0.250631\pi\) | ||||
0.705705 | + | 0.708506i | \(0.250631\pi\) | |||||||
\(6\) | 2.67063 | 1.09028 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 4.13228 | 1.37743 | ||||||||
\(10\) | −3.15601 | −0.998017 | ||||||||
\(11\) | 3.01631 | 0.909452 | 0.454726 | − | 0.890632i | \(-0.349737\pi\) | ||||
0.454726 | + | 0.890632i | \(0.349737\pi\) | |||||||
\(12\) | −2.67063 | −0.770946 | ||||||||
\(13\) | −4.63033 | −1.28422 | −0.642112 | − | 0.766611i | \(-0.721941\pi\) | ||||
−0.642112 | + | 0.766611i | \(0.721941\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −8.42854 | −2.17624 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.60020 | −1.60078 | −0.800392 | − | 0.599477i | \(-0.795375\pi\) | ||||
−0.800392 | + | 0.599477i | \(0.795375\pi\) | |||||||
\(18\) | −4.13228 | −0.973989 | ||||||||
\(19\) | −4.22204 | −0.968603 | −0.484302 | − | 0.874901i | \(-0.660926\pi\) | ||||
−0.484302 | + | 0.874901i | \(0.660926\pi\) | |||||||
\(20\) | 3.15601 | 0.705705 | ||||||||
\(21\) | 2.67063 | 0.582780 | ||||||||
\(22\) | −3.01631 | −0.643079 | ||||||||
\(23\) | −0.524979 | −0.109466 | −0.0547328 | − | 0.998501i | \(-0.517431\pi\) | ||||
−0.0547328 | + | 0.998501i | \(0.517431\pi\) | |||||||
\(24\) | 2.67063 | 0.545141 | ||||||||
\(25\) | 4.96038 | 0.992076 | ||||||||
\(26\) | 4.63033 | 0.908083 | ||||||||
\(27\) | −3.02392 | −0.581953 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −9.21317 | −1.71084 | −0.855421 | − | 0.517933i | \(-0.826702\pi\) | ||||
−0.855421 | + | 0.517933i | \(0.826702\pi\) | |||||||
\(30\) | 8.42854 | 1.53883 | ||||||||
\(31\) | 1.00489 | 0.180484 | 0.0902419 | − | 0.995920i | \(-0.471236\pi\) | ||||
0.0902419 | + | 0.995920i | \(0.471236\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −8.05546 | −1.40228 | ||||||||
\(34\) | 6.60020 | 1.13192 | ||||||||
\(35\) | −3.15601 | −0.533463 | ||||||||
\(36\) | 4.13228 | 0.688714 | ||||||||
\(37\) | −8.56493 | −1.40807 | −0.704033 | − | 0.710168i | \(-0.748619\pi\) | ||||
−0.704033 | + | 0.710168i | \(0.748619\pi\) | |||||||
\(38\) | 4.22204 | 0.684906 | ||||||||
\(39\) | 12.3659 | 1.98013 | ||||||||
\(40\) | −3.15601 | −0.499009 | ||||||||
\(41\) | 6.31163 | 0.985711 | 0.492855 | − | 0.870111i | \(-0.335953\pi\) | ||||
0.492855 | + | 0.870111i | \(0.335953\pi\) | |||||||
\(42\) | −2.67063 | −0.412088 | ||||||||
\(43\) | −11.7000 | −1.78423 | −0.892116 | − | 0.451807i | \(-0.850780\pi\) | ||||
−0.892116 | + | 0.451807i | \(0.850780\pi\) | |||||||
\(44\) | 3.01631 | 0.454726 | ||||||||
\(45\) | 13.0415 | 1.94411 | ||||||||
\(46\) | 0.524979 | 0.0774039 | ||||||||
\(47\) | −7.89697 | −1.15189 | −0.575946 | − | 0.817488i | \(-0.695366\pi\) | ||||
−0.575946 | + | 0.817488i | \(0.695366\pi\) | |||||||
\(48\) | −2.67063 | −0.385473 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −4.96038 | −0.701504 | ||||||||
\(51\) | 17.6267 | 2.46823 | ||||||||
\(52\) | −4.63033 | −0.642112 | ||||||||
\(53\) | 0.831758 | 0.114251 | 0.0571254 | − | 0.998367i | \(-0.481807\pi\) | ||||
0.0571254 | + | 0.998367i | \(0.481807\pi\) | |||||||
\(54\) | 3.02392 | 0.411503 | ||||||||
\(55\) | 9.51949 | 1.28361 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 11.2755 | 1.49348 | ||||||||
\(58\) | 9.21317 | 1.20975 | ||||||||
\(59\) | −2.18079 | −0.283914 | −0.141957 | − | 0.989873i | \(-0.545340\pi\) | ||||
−0.141957 | + | 0.989873i | \(0.545340\pi\) | |||||||
\(60\) | −8.42854 | −1.08812 | ||||||||
\(61\) | −1.29727 | −0.166098 | −0.0830490 | − | 0.996545i | \(-0.526466\pi\) | ||||
−0.0830490 | + | 0.996545i | \(0.526466\pi\) | |||||||
\(62\) | −1.00489 | −0.127621 | ||||||||
\(63\) | −4.13228 | −0.520619 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −14.6134 | −1.81256 | ||||||||
\(66\) | 8.05546 | 0.991558 | ||||||||
\(67\) | 8.28511 | 1.01219 | 0.506093 | − | 0.862479i | \(-0.331089\pi\) | ||||
0.506093 | + | 0.862479i | \(0.331089\pi\) | |||||||
\(68\) | −6.60020 | −0.800392 | ||||||||
\(69\) | 1.40203 | 0.168784 | ||||||||
\(70\) | 3.15601 | 0.377215 | ||||||||
\(71\) | 14.0501 | 1.66744 | 0.833720 | − | 0.552188i | \(-0.186207\pi\) | ||||
0.833720 | + | 0.552188i | \(0.186207\pi\) | |||||||
\(72\) | −4.13228 | −0.486994 | ||||||||
\(73\) | 16.6288 | 1.94625 | 0.973127 | − | 0.230270i | \(-0.0739610\pi\) | ||||
0.973127 | + | 0.230270i | \(0.0739610\pi\) | |||||||
\(74\) | 8.56493 | 0.995652 | ||||||||
\(75\) | −13.2474 | −1.52967 | ||||||||
\(76\) | −4.22204 | −0.484302 | ||||||||
\(77\) | −3.01631 | −0.343740 | ||||||||
\(78\) | −12.3659 | −1.40017 | ||||||||
\(79\) | 16.4102 | 1.84629 | 0.923145 | − | 0.384453i | \(-0.125610\pi\) | ||||
0.923145 | + | 0.384453i | \(0.125610\pi\) | |||||||
\(80\) | 3.15601 | 0.352852 | ||||||||
\(81\) | −4.32108 | −0.480120 | ||||||||
\(82\) | −6.31163 | −0.697003 | ||||||||
\(83\) | 7.07919 | 0.777042 | 0.388521 | − | 0.921440i | \(-0.372986\pi\) | ||||
0.388521 | + | 0.921440i | \(0.372986\pi\) | |||||||
\(84\) | 2.67063 | 0.291390 | ||||||||
\(85\) | −20.8303 | −2.25936 | ||||||||
\(86\) | 11.7000 | 1.26164 | ||||||||
\(87\) | 24.6050 | 2.63793 | ||||||||
\(88\) | −3.01631 | −0.321540 | ||||||||
\(89\) | 14.0832 | 1.49282 | 0.746408 | − | 0.665489i | \(-0.231777\pi\) | ||||
0.746408 | + | 0.665489i | \(0.231777\pi\) | |||||||
\(90\) | −13.0415 | −1.37470 | ||||||||
\(91\) | 4.63033 | 0.485391 | ||||||||
\(92\) | −0.524979 | −0.0547328 | ||||||||
\(93\) | −2.68370 | −0.278286 | ||||||||
\(94\) | 7.89697 | 0.814511 | ||||||||
\(95\) | −13.3248 | −1.36710 | ||||||||
\(96\) | 2.67063 | 0.272570 | ||||||||
\(97\) | 14.9874 | 1.52174 | 0.760868 | − | 0.648907i | \(-0.224773\pi\) | ||||
0.760868 | + | 0.648907i | \(0.224773\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 12.4642 | 1.25270 | ||||||||
\(100\) | 4.96038 | 0.496038 | ||||||||
\(101\) | −0.171171 | −0.0170322 | −0.00851608 | − | 0.999964i | \(-0.502711\pi\) | ||||
−0.00851608 | + | 0.999964i | \(0.502711\pi\) | |||||||
\(102\) | −17.6267 | −1.74530 | ||||||||
\(103\) | 11.0002 | 1.08388 | 0.541941 | − | 0.840417i | \(-0.317690\pi\) | ||||
0.541941 | + | 0.840417i | \(0.317690\pi\) | |||||||
\(104\) | 4.63033 | 0.454042 | ||||||||
\(105\) | 8.42854 | 0.822541 | ||||||||
\(106\) | −0.831758 | −0.0807875 | ||||||||
\(107\) | −16.3738 | −1.58292 | −0.791458 | − | 0.611223i | \(-0.790678\pi\) | ||||
−0.791458 | + | 0.611223i | \(0.790678\pi\) | |||||||
\(108\) | −3.02392 | −0.290977 | ||||||||
\(109\) | −10.6488 | −1.01997 | −0.509984 | − | 0.860184i | \(-0.670349\pi\) | ||||
−0.509984 | + | 0.860184i | \(0.670349\pi\) | |||||||
\(110\) | −9.51949 | −0.907648 | ||||||||
\(111\) | 22.8738 | 2.17108 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −17.2274 | −1.62062 | −0.810308 | − | 0.586005i | \(-0.800700\pi\) | ||||
−0.810308 | + | 0.586005i | \(0.800700\pi\) | |||||||
\(114\) | −11.2755 | −1.05605 | ||||||||
\(115\) | −1.65684 | −0.154501 | ||||||||
\(116\) | −9.21317 | −0.855421 | ||||||||
\(117\) | −19.1339 | −1.76893 | ||||||||
\(118\) | 2.18079 | 0.200758 | ||||||||
\(119\) | 6.60020 | 0.605039 | ||||||||
\(120\) | 8.42854 | 0.769417 | ||||||||
\(121\) | −1.90188 | −0.172898 | ||||||||
\(122\) | 1.29727 | 0.117449 | ||||||||
\(123\) | −16.8561 | −1.51986 | ||||||||
\(124\) | 1.00489 | 0.0902419 | ||||||||
\(125\) | −0.125039 | −0.0111839 | ||||||||
\(126\) | 4.13228 | 0.368133 | ||||||||
\(127\) | 12.3826 | 1.09878 | 0.549389 | − | 0.835567i | \(-0.314861\pi\) | ||||
0.549389 | + | 0.835567i | \(0.314861\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 31.2464 | 2.75109 | ||||||||
\(130\) | 14.6134 | 1.28168 | ||||||||
\(131\) | 11.2346 | 0.981574 | 0.490787 | − | 0.871280i | \(-0.336709\pi\) | ||||
0.490787 | + | 0.871280i | \(0.336709\pi\) | |||||||
\(132\) | −8.05546 | −0.701138 | ||||||||
\(133\) | 4.22204 | 0.366098 | ||||||||
\(134\) | −8.28511 | −0.715724 | ||||||||
\(135\) | −9.54350 | −0.821374 | ||||||||
\(136\) | 6.60020 | 0.565962 | ||||||||
\(137\) | 7.05090 | 0.602399 | 0.301200 | − | 0.953561i | \(-0.402613\pi\) | ||||
0.301200 | + | 0.953561i | \(0.402613\pi\) | |||||||
\(138\) | −1.40203 | −0.119348 | ||||||||
\(139\) | 19.2723 | 1.63465 | 0.817325 | − | 0.576176i | \(-0.195456\pi\) | ||||
0.817325 | + | 0.576176i | \(0.195456\pi\) | |||||||
\(140\) | −3.15601 | −0.266731 | ||||||||
\(141\) | 21.0899 | 1.77609 | ||||||||
\(142\) | −14.0501 | −1.17906 | ||||||||
\(143\) | −13.9665 | −1.16794 | ||||||||
\(144\) | 4.13228 | 0.344357 | ||||||||
\(145\) | −29.0768 | −2.41470 | ||||||||
\(146\) | −16.6288 | −1.37621 | ||||||||
\(147\) | −2.67063 | −0.220270 | ||||||||
\(148\) | −8.56493 | −0.704033 | ||||||||
\(149\) | −16.3469 | −1.33919 | −0.669595 | − | 0.742726i | \(-0.733532\pi\) | ||||
−0.669595 | + | 0.742726i | \(0.733532\pi\) | |||||||
\(150\) | 13.2474 | 1.08164 | ||||||||
\(151\) | −4.57648 | −0.372429 | −0.186214 | − | 0.982509i | \(-0.559622\pi\) | ||||
−0.186214 | + | 0.982509i | \(0.559622\pi\) | |||||||
\(152\) | 4.22204 | 0.342453 | ||||||||
\(153\) | −27.2739 | −2.20496 | ||||||||
\(154\) | 3.01631 | 0.243061 | ||||||||
\(155\) | 3.17144 | 0.254736 | ||||||||
\(156\) | 12.3659 | 0.990066 | ||||||||
\(157\) | −7.67641 | −0.612644 | −0.306322 | − | 0.951928i | \(-0.599099\pi\) | ||||
−0.306322 | + | 0.951928i | \(0.599099\pi\) | |||||||
\(158\) | −16.4102 | −1.30552 | ||||||||
\(159\) | −2.22132 | −0.176162 | ||||||||
\(160\) | −3.15601 | −0.249504 | ||||||||
\(161\) | 0.524979 | 0.0413741 | ||||||||
\(162\) | 4.32108 | 0.339496 | ||||||||
\(163\) | 1.14467 | 0.0896571 | 0.0448286 | − | 0.998995i | \(-0.485726\pi\) | ||||
0.0448286 | + | 0.998995i | \(0.485726\pi\) | |||||||
\(164\) | 6.31163 | 0.492855 | ||||||||
\(165\) | −25.4231 | −1.97918 | ||||||||
\(166\) | −7.07919 | −0.549452 | ||||||||
\(167\) | 20.8699 | 1.61496 | 0.807482 | − | 0.589892i | \(-0.200830\pi\) | ||||
0.807482 | + | 0.589892i | \(0.200830\pi\) | |||||||
\(168\) | −2.67063 | −0.206044 | ||||||||
\(169\) | 8.43999 | 0.649230 | ||||||||
\(170\) | 20.8303 | 1.59761 | ||||||||
\(171\) | −17.4467 | −1.33418 | ||||||||
\(172\) | −11.7000 | −0.892116 | ||||||||
\(173\) | 9.07022 | 0.689596 | 0.344798 | − | 0.938677i | \(-0.387947\pi\) | ||||
0.344798 | + | 0.938677i | \(0.387947\pi\) | |||||||
\(174\) | −24.6050 | −1.86530 | ||||||||
\(175\) | −4.96038 | −0.374970 | ||||||||
\(176\) | 3.01631 | 0.227363 | ||||||||
\(177\) | 5.82409 | 0.437765 | ||||||||
\(178\) | −14.0832 | −1.05558 | ||||||||
\(179\) | 4.01486 | 0.300085 | 0.150042 | − | 0.988680i | \(-0.452059\pi\) | ||||
0.150042 | + | 0.988680i | \(0.452059\pi\) | |||||||
\(180\) | 13.0415 | 0.972057 | ||||||||
\(181\) | 5.69222 | 0.423100 | 0.211550 | − | 0.977367i | \(-0.432149\pi\) | ||||
0.211550 | + | 0.977367i | \(0.432149\pi\) | |||||||
\(182\) | −4.63033 | −0.343223 | ||||||||
\(183\) | 3.46452 | 0.256105 | ||||||||
\(184\) | 0.524979 | 0.0387020 | ||||||||
\(185\) | −27.0310 | −1.98736 | ||||||||
\(186\) | 2.68370 | 0.196778 | ||||||||
\(187\) | −19.9082 | −1.45583 | ||||||||
\(188\) | −7.89697 | −0.575946 | ||||||||
\(189\) | 3.02392 | 0.219958 | ||||||||
\(190\) | 13.3248 | 0.966683 | ||||||||
\(191\) | −7.41957 | −0.536861 | −0.268431 | − | 0.963299i | \(-0.586505\pi\) | ||||
−0.268431 | + | 0.963299i | \(0.586505\pi\) | |||||||
\(192\) | −2.67063 | −0.192736 | ||||||||
\(193\) | −2.64434 | −0.190344 | −0.0951720 | − | 0.995461i | \(-0.530340\pi\) | ||||
−0.0951720 | + | 0.995461i | \(0.530340\pi\) | |||||||
\(194\) | −14.9874 | −1.07603 | ||||||||
\(195\) | 39.0269 | 2.79478 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 2.48654 | 0.177158 | 0.0885792 | − | 0.996069i | \(-0.471767\pi\) | ||||
0.0885792 | + | 0.996069i | \(0.471767\pi\) | |||||||
\(198\) | −12.4642 | −0.885796 | ||||||||
\(199\) | 7.21010 | 0.511111 | 0.255555 | − | 0.966794i | \(-0.417742\pi\) | ||||
0.255555 | + | 0.966794i | \(0.417742\pi\) | |||||||
\(200\) | −4.96038 | −0.350752 | ||||||||
\(201\) | −22.1265 | −1.56068 | ||||||||
\(202\) | 0.171171 | 0.0120436 | ||||||||
\(203\) | 9.21317 | 0.646638 | ||||||||
\(204\) | 17.6267 | 1.23412 | ||||||||
\(205\) | 19.9195 | 1.39124 | ||||||||
\(206\) | −11.0002 | −0.766420 | ||||||||
\(207\) | −2.16936 | −0.150781 | ||||||||
\(208\) | −4.63033 | −0.321056 | ||||||||
\(209\) | −12.7350 | −0.880898 | ||||||||
\(210\) | −8.42854 | −0.581624 | ||||||||
\(211\) | −14.2028 | −0.977760 | −0.488880 | − | 0.872351i | \(-0.662594\pi\) | ||||
−0.488880 | + | 0.872351i | \(0.662594\pi\) | |||||||
\(212\) | 0.831758 | 0.0571254 | ||||||||
\(213\) | −37.5226 | −2.57101 | ||||||||
\(214\) | 16.3738 | 1.11929 | ||||||||
\(215\) | −36.9252 | −2.51828 | ||||||||
\(216\) | 3.02392 | 0.205751 | ||||||||
\(217\) | −1.00489 | −0.0682164 | ||||||||
\(218\) | 10.6488 | 0.721226 | ||||||||
\(219\) | −44.4094 | −3.00091 | ||||||||
\(220\) | 9.51949 | 0.641804 | ||||||||
\(221\) | 30.5611 | 2.05576 | ||||||||
\(222\) | −22.8738 | −1.53519 | ||||||||
\(223\) | −6.07525 | −0.406829 | −0.203414 | − | 0.979093i | \(-0.565204\pi\) | ||||
−0.203414 | + | 0.979093i | \(0.565204\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 20.4977 | 1.36651 | ||||||||
\(226\) | 17.2274 | 1.14595 | ||||||||
\(227\) | 26.8622 | 1.78291 | 0.891455 | − | 0.453109i | \(-0.149685\pi\) | ||||
0.891455 | + | 0.453109i | \(0.149685\pi\) | |||||||
\(228\) | 11.2755 | 0.746740 | ||||||||
\(229\) | 15.0402 | 0.993886 | 0.496943 | − | 0.867783i | \(-0.334456\pi\) | ||||
0.496943 | + | 0.867783i | \(0.334456\pi\) | |||||||
\(230\) | 1.65684 | 0.109249 | ||||||||
\(231\) | 8.05546 | 0.530010 | ||||||||
\(232\) | 9.21317 | 0.604874 | ||||||||
\(233\) | −24.5638 | −1.60923 | −0.804613 | − | 0.593800i | \(-0.797627\pi\) | ||||
−0.804613 | + | 0.593800i | \(0.797627\pi\) | |||||||
\(234\) | 19.1339 | 1.25082 | ||||||||
\(235\) | −24.9229 | −1.62579 | ||||||||
\(236\) | −2.18079 | −0.141957 | ||||||||
\(237\) | −43.8256 | −2.84678 | ||||||||
\(238\) | −6.60020 | −0.427827 | ||||||||
\(239\) | −6.35840 | −0.411291 | −0.205645 | − | 0.978627i | \(-0.565929\pi\) | ||||
−0.205645 | + | 0.978627i | \(0.565929\pi\) | |||||||
\(240\) | −8.42854 | −0.544060 | ||||||||
\(241\) | −5.51971 | −0.355556 | −0.177778 | − | 0.984071i | \(-0.556891\pi\) | ||||
−0.177778 | + | 0.984071i | \(0.556891\pi\) | |||||||
\(242\) | 1.90188 | 0.122257 | ||||||||
\(243\) | 20.6118 | 1.32225 | ||||||||
\(244\) | −1.29727 | −0.0830490 | ||||||||
\(245\) | 3.15601 | 0.201630 | ||||||||
\(246\) | 16.8561 | 1.07470 | ||||||||
\(247\) | 19.5495 | 1.24390 | ||||||||
\(248\) | −1.00489 | −0.0638106 | ||||||||
\(249\) | −18.9059 | −1.19811 | ||||||||
\(250\) | 0.125039 | 0.00790819 | ||||||||
\(251\) | 5.28603 | 0.333652 | 0.166826 | − | 0.985986i | \(-0.446648\pi\) | ||||
0.166826 | + | 0.985986i | \(0.446648\pi\) | |||||||
\(252\) | −4.13228 | −0.260309 | ||||||||
\(253\) | −1.58350 | −0.0995537 | ||||||||
\(254\) | −12.3826 | −0.776953 | ||||||||
\(255\) | 55.6300 | 3.48369 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.39010 | −0.398603 | −0.199302 | − | 0.979938i | \(-0.563867\pi\) | ||||
−0.199302 | + | 0.979938i | \(0.563867\pi\) | |||||||
\(258\) | −31.2464 | −1.94531 | ||||||||
\(259\) | 8.56493 | 0.532199 | ||||||||
\(260\) | −14.6134 | −0.906282 | ||||||||
\(261\) | −38.0714 | −2.35656 | ||||||||
\(262\) | −11.2346 | −0.694077 | ||||||||
\(263\) | −2.48872 | −0.153461 | −0.0767304 | − | 0.997052i | \(-0.524448\pi\) | ||||
−0.0767304 | + | 0.997052i | \(0.524448\pi\) | |||||||
\(264\) | 8.05546 | 0.495779 | ||||||||
\(265\) | 2.62504 | 0.161255 | ||||||||
\(266\) | −4.22204 | −0.258870 | ||||||||
\(267\) | −37.6111 | −2.30176 | ||||||||
\(268\) | 8.28511 | 0.506093 | ||||||||
\(269\) | −1.04689 | −0.0638299 | −0.0319150 | − | 0.999491i | \(-0.510161\pi\) | ||||
−0.0319150 | + | 0.999491i | \(0.510161\pi\) | |||||||
\(270\) | 9.54350 | 0.580799 | ||||||||
\(271\) | −6.47317 | −0.393217 | −0.196609 | − | 0.980482i | \(-0.562993\pi\) | ||||
−0.196609 | + | 0.980482i | \(0.562993\pi\) | |||||||
\(272\) | −6.60020 | −0.400196 | ||||||||
\(273\) | −12.3659 | −0.748420 | ||||||||
\(274\) | −7.05090 | −0.425961 | ||||||||
\(275\) | 14.9620 | 0.902245 | ||||||||
\(276\) | 1.40203 | 0.0843921 | ||||||||
\(277\) | 5.18131 | 0.311315 | 0.155657 | − | 0.987811i | \(-0.450250\pi\) | ||||
0.155657 | + | 0.987811i | \(0.450250\pi\) | |||||||
\(278\) | −19.2723 | −1.15587 | ||||||||
\(279\) | 4.15250 | 0.248603 | ||||||||
\(280\) | 3.15601 | 0.188607 | ||||||||
\(281\) | 0.340066 | 0.0202867 | 0.0101433 | − | 0.999949i | \(-0.496771\pi\) | ||||
0.0101433 | + | 0.999949i | \(0.496771\pi\) | |||||||
\(282\) | −21.0899 | −1.25589 | ||||||||
\(283\) | −20.1181 | −1.19590 | −0.597948 | − | 0.801535i | \(-0.704017\pi\) | ||||
−0.597948 | + | 0.801535i | \(0.704017\pi\) | |||||||
\(284\) | 14.0501 | 0.833720 | ||||||||
\(285\) | 35.5857 | 2.10791 | ||||||||
\(286\) | 13.9665 | 0.825857 | ||||||||
\(287\) | −6.31163 | −0.372564 | ||||||||
\(288\) | −4.13228 | −0.243497 | ||||||||
\(289\) | 26.5626 | 1.56251 | ||||||||
\(290\) | 29.0768 | 1.70745 | ||||||||
\(291\) | −40.0257 | −2.34635 | ||||||||
\(292\) | 16.6288 | 0.973127 | ||||||||
\(293\) | 13.9830 | 0.816893 | 0.408447 | − | 0.912782i | \(-0.366071\pi\) | ||||
0.408447 | + | 0.912782i | \(0.366071\pi\) | |||||||
\(294\) | 2.67063 | 0.155755 | ||||||||
\(295\) | −6.88258 | −0.400720 | ||||||||
\(296\) | 8.56493 | 0.497826 | ||||||||
\(297\) | −9.12107 | −0.529258 | ||||||||
\(298\) | 16.3469 | 0.946950 | ||||||||
\(299\) | 2.43083 | 0.140578 | ||||||||
\(300\) | −13.2474 | −0.764837 | ||||||||
\(301\) | 11.7000 | 0.674376 | ||||||||
\(302\) | 4.57648 | 0.263347 | ||||||||
\(303\) | 0.457135 | 0.0262617 | ||||||||
\(304\) | −4.22204 | −0.242151 | ||||||||
\(305\) | −4.09418 | −0.234432 | ||||||||
\(306\) | 27.2739 | 1.55915 | ||||||||
\(307\) | 28.6630 | 1.63588 | 0.817941 | − | 0.575302i | \(-0.195115\pi\) | ||||
0.817941 | + | 0.575302i | \(0.195115\pi\) | |||||||
\(308\) | −3.01631 | −0.171870 | ||||||||
\(309\) | −29.3775 | −1.67123 | ||||||||
\(310\) | −3.17144 | −0.180126 | ||||||||
\(311\) | 10.8244 | 0.613793 | 0.306897 | − | 0.951743i | \(-0.400709\pi\) | ||||
0.306897 | + | 0.951743i | \(0.400709\pi\) | |||||||
\(312\) | −12.3659 | −0.700083 | ||||||||
\(313\) | −13.5622 | −0.766579 | −0.383289 | − | 0.923628i | \(-0.625209\pi\) | ||||
−0.383289 | + | 0.923628i | \(0.625209\pi\) | |||||||
\(314\) | 7.67641 | 0.433205 | ||||||||
\(315\) | −13.0415 | −0.734806 | ||||||||
\(316\) | 16.4102 | 0.923145 | ||||||||
\(317\) | 12.4644 | 0.700070 | 0.350035 | − | 0.936737i | \(-0.386170\pi\) | ||||
0.350035 | + | 0.936737i | \(0.386170\pi\) | |||||||
\(318\) | 2.22132 | 0.124566 | ||||||||
\(319\) | −27.7898 | −1.55593 | ||||||||
\(320\) | 3.15601 | 0.176426 | ||||||||
\(321\) | 43.7285 | 2.44069 | ||||||||
\(322\) | −0.524979 | −0.0292559 | ||||||||
\(323\) | 27.8663 | 1.55052 | ||||||||
\(324\) | −4.32108 | −0.240060 | ||||||||
\(325\) | −22.9682 | −1.27405 | ||||||||
\(326\) | −1.14467 | −0.0633972 | ||||||||
\(327\) | 28.4390 | 1.57268 | ||||||||
\(328\) | −6.31163 | −0.348501 | ||||||||
\(329\) | 7.89697 | 0.435374 | ||||||||
\(330\) | 25.4231 | 1.39949 | ||||||||
\(331\) | 7.39253 | 0.406330 | 0.203165 | − | 0.979144i | \(-0.434877\pi\) | ||||
0.203165 | + | 0.979144i | \(0.434877\pi\) | |||||||
\(332\) | 7.07919 | 0.388521 | ||||||||
\(333\) | −35.3927 | −1.93951 | ||||||||
\(334\) | −20.8699 | −1.14195 | ||||||||
\(335\) | 26.1479 | 1.42861 | ||||||||
\(336\) | 2.67063 | 0.145695 | ||||||||
\(337\) | 30.2671 | 1.64876 | 0.824378 | − | 0.566040i | \(-0.191525\pi\) | ||||
0.824378 | + | 0.566040i | \(0.191525\pi\) | |||||||
\(338\) | −8.43999 | −0.459075 | ||||||||
\(339\) | 46.0080 | 2.49881 | ||||||||
\(340\) | −20.8303 | −1.12968 | ||||||||
\(341\) | 3.03106 | 0.164141 | ||||||||
\(342\) | 17.4467 | 0.943409 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 11.7000 | 0.630821 | ||||||||
\(345\) | 4.42480 | 0.238223 | ||||||||
\(346\) | −9.07022 | −0.487618 | ||||||||
\(347\) | 22.4200 | 1.20357 | 0.601786 | − | 0.798658i | \(-0.294456\pi\) | ||||
0.601786 | + | 0.798658i | \(0.294456\pi\) | |||||||
\(348\) | 24.6050 | 1.31897 | ||||||||
\(349\) | −14.1699 | −0.758500 | −0.379250 | − | 0.925294i | \(-0.623818\pi\) | ||||
−0.379250 | + | 0.925294i | \(0.623818\pi\) | |||||||
\(350\) | 4.96038 | 0.265143 | ||||||||
\(351\) | 14.0017 | 0.747358 | ||||||||
\(352\) | −3.01631 | −0.160770 | ||||||||
\(353\) | −9.44344 | −0.502624 | −0.251312 | − | 0.967906i | \(-0.580862\pi\) | ||||
−0.251312 | + | 0.967906i | \(0.580862\pi\) | |||||||
\(354\) | −5.82409 | −0.309547 | ||||||||
\(355\) | 44.3422 | 2.35344 | ||||||||
\(356\) | 14.0832 | 0.746408 | ||||||||
\(357\) | −17.6267 | −0.932905 | ||||||||
\(358\) | −4.01486 | −0.212192 | ||||||||
\(359\) | 2.00815 | 0.105986 | 0.0529929 | − | 0.998595i | \(-0.483124\pi\) | ||||
0.0529929 | + | 0.998595i | \(0.483124\pi\) | |||||||
\(360\) | −13.0415 | −0.687348 | ||||||||
\(361\) | −1.17434 | −0.0618076 | ||||||||
\(362\) | −5.69222 | −0.299177 | ||||||||
\(363\) | 5.07922 | 0.266590 | ||||||||
\(364\) | 4.63033 | 0.242695 | ||||||||
\(365\) | 52.4806 | 2.74696 | ||||||||
\(366\) | −3.46452 | −0.181094 | ||||||||
\(367\) | 14.7871 | 0.771881 | 0.385940 | − | 0.922524i | \(-0.373877\pi\) | ||||
0.385940 | + | 0.922524i | \(0.373877\pi\) | |||||||
\(368\) | −0.524979 | −0.0273664 | ||||||||
\(369\) | 26.0814 | 1.35775 | ||||||||
\(370\) | 27.0310 | 1.40527 | ||||||||
\(371\) | −0.831758 | −0.0431827 | ||||||||
\(372\) | −2.68370 | −0.139143 | ||||||||
\(373\) | 30.6145 | 1.58516 | 0.792579 | − | 0.609769i | \(-0.208738\pi\) | ||||
0.792579 | + | 0.609769i | \(0.208738\pi\) | |||||||
\(374\) | 19.9082 | 1.02943 | ||||||||
\(375\) | 0.333934 | 0.0172443 | ||||||||
\(376\) | 7.89697 | 0.407255 | ||||||||
\(377\) | 42.6600 | 2.19710 | ||||||||
\(378\) | −3.02392 | −0.155534 | ||||||||
\(379\) | 10.7563 | 0.552512 | 0.276256 | − | 0.961084i | \(-0.410906\pi\) | ||||
0.276256 | + | 0.961084i | \(0.410906\pi\) | |||||||
\(380\) | −13.3248 | −0.683548 | ||||||||
\(381\) | −33.0694 | −1.69420 | ||||||||
\(382\) | 7.41957 | 0.379618 | ||||||||
\(383\) | −1.45941 | −0.0745723 | −0.0372862 | − | 0.999305i | \(-0.511871\pi\) | ||||
−0.0372862 | + | 0.999305i | \(0.511871\pi\) | |||||||
\(384\) | 2.67063 | 0.136285 | ||||||||
\(385\) | −9.51949 | −0.485158 | ||||||||
\(386\) | 2.64434 | 0.134594 | ||||||||
\(387\) | −48.3477 | −2.45765 | ||||||||
\(388\) | 14.9874 | 0.760868 | ||||||||
\(389\) | 4.73759 | 0.240205 | 0.120103 | − | 0.992761i | \(-0.461678\pi\) | ||||
0.120103 | + | 0.992761i | \(0.461678\pi\) | |||||||
\(390\) | −39.0269 | −1.97621 | ||||||||
\(391\) | 3.46496 | 0.175231 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −30.0036 | −1.51348 | ||||||||
\(394\) | −2.48654 | −0.125270 | ||||||||
\(395\) | 51.7906 | 2.60587 | ||||||||
\(396\) | 12.4642 | 0.626352 | ||||||||
\(397\) | −16.7995 | −0.843143 | −0.421572 | − | 0.906795i | \(-0.638521\pi\) | ||||
−0.421572 | + | 0.906795i | \(0.638521\pi\) | |||||||
\(398\) | −7.21010 | −0.361410 | ||||||||
\(399\) | −11.2755 | −0.564483 | ||||||||
\(400\) | 4.96038 | 0.248019 | ||||||||
\(401\) | −2.31347 | −0.115529 | −0.0577647 | − | 0.998330i | \(-0.518397\pi\) | ||||
−0.0577647 | + | 0.998330i | \(0.518397\pi\) | |||||||
\(402\) | 22.1265 | 1.10357 | ||||||||
\(403\) | −4.65298 | −0.231781 | ||||||||
\(404\) | −0.171171 | −0.00851608 | ||||||||
\(405\) | −13.6374 | −0.677646 | ||||||||
\(406\) | −9.21317 | −0.457242 | ||||||||
\(407\) | −25.8345 | −1.28057 | ||||||||
\(408\) | −17.6267 | −0.872652 | ||||||||
\(409\) | −11.6520 | −0.576152 | −0.288076 | − | 0.957608i | \(-0.593016\pi\) | ||||
−0.288076 | + | 0.957608i | \(0.593016\pi\) | |||||||
\(410\) | −19.9195 | −0.983756 | ||||||||
\(411\) | −18.8304 | −0.928834 | ||||||||
\(412\) | 11.0002 | 0.541941 | ||||||||
\(413\) | 2.18079 | 0.107310 | ||||||||
\(414\) | 2.16936 | 0.106618 | ||||||||
\(415\) | 22.3420 | 1.09672 | ||||||||
\(416\) | 4.63033 | 0.227021 | ||||||||
\(417\) | −51.4691 | −2.52045 | ||||||||
\(418\) | 12.7350 | 0.622889 | ||||||||
\(419\) | −31.2631 | −1.52730 | −0.763652 | − | 0.645628i | \(-0.776596\pi\) | ||||
−0.763652 | + | 0.645628i | \(0.776596\pi\) | |||||||
\(420\) | 8.42854 | 0.411271 | ||||||||
\(421\) | 24.4387 | 1.19107 | 0.595534 | − | 0.803330i | \(-0.296941\pi\) | ||||
0.595534 | + | 0.803330i | \(0.296941\pi\) | |||||||
\(422\) | 14.2028 | 0.691381 | ||||||||
\(423\) | −32.6325 | −1.58665 | ||||||||
\(424\) | −0.831758 | −0.0403938 | ||||||||
\(425\) | −32.7395 | −1.58810 | ||||||||
\(426\) | 37.5226 | 1.81798 | ||||||||
\(427\) | 1.29727 | 0.0627791 | ||||||||
\(428\) | −16.3738 | −0.791458 | ||||||||
\(429\) | 37.2995 | 1.80083 | ||||||||
\(430\) | 36.9252 | 1.78069 | ||||||||
\(431\) | 1.00000 | 0.0481683 | ||||||||
\(432\) | −3.02392 | −0.145488 | ||||||||
\(433\) | −25.2393 | −1.21292 | −0.606462 | − | 0.795112i | \(-0.707412\pi\) | ||||
−0.606462 | + | 0.795112i | \(0.707412\pi\) | |||||||
\(434\) | 1.00489 | 0.0482363 | ||||||||
\(435\) | 77.6535 | 3.72320 | ||||||||
\(436\) | −10.6488 | −0.509984 | ||||||||
\(437\) | 2.21648 | 0.106029 | ||||||||
\(438\) | 44.4094 | 2.12196 | ||||||||
\(439\) | 12.9214 | 0.616706 | 0.308353 | − | 0.951272i | \(-0.400222\pi\) | ||||
0.308353 | + | 0.951272i | \(0.400222\pi\) | |||||||
\(440\) | −9.51949 | −0.453824 | ||||||||
\(441\) | 4.13228 | 0.196775 | ||||||||
\(442\) | −30.5611 | −1.45364 | ||||||||
\(443\) | 3.93412 | 0.186916 | 0.0934578 | − | 0.995623i | \(-0.470208\pi\) | ||||
0.0934578 | + | 0.995623i | \(0.470208\pi\) | |||||||
\(444\) | 22.8738 | 1.08554 | ||||||||
\(445\) | 44.4467 | 2.10697 | ||||||||
\(446\) | 6.07525 | 0.287671 | ||||||||
\(447\) | 43.6566 | 2.06488 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 31.8219 | 1.50177 | 0.750883 | − | 0.660435i | \(-0.229628\pi\) | ||||
0.750883 | + | 0.660435i | \(0.229628\pi\) | |||||||
\(450\) | −20.4977 | −0.966271 | ||||||||
\(451\) | 19.0378 | 0.896456 | ||||||||
\(452\) | −17.2274 | −0.810308 | ||||||||
\(453\) | 12.2221 | 0.574245 | ||||||||
\(454\) | −26.8622 | −1.26071 | ||||||||
\(455\) | 14.6134 | 0.685085 | ||||||||
\(456\) | −11.2755 | −0.528025 | ||||||||
\(457\) | −15.1960 | −0.710838 | −0.355419 | − | 0.934707i | \(-0.615662\pi\) | ||||
−0.355419 | + | 0.934707i | \(0.615662\pi\) | |||||||
\(458\) | −15.0402 | −0.702784 | ||||||||
\(459\) | 19.9585 | 0.931581 | ||||||||
\(460\) | −1.65684 | −0.0772504 | ||||||||
\(461\) | −5.80779 | −0.270496 | −0.135248 | − | 0.990812i | \(-0.543183\pi\) | ||||
−0.135248 | + | 0.990812i | \(0.543183\pi\) | |||||||
\(462\) | −8.05546 | −0.374774 | ||||||||
\(463\) | 21.0429 | 0.977948 | 0.488974 | − | 0.872298i | \(-0.337371\pi\) | ||||
0.488974 | + | 0.872298i | \(0.337371\pi\) | |||||||
\(464\) | −9.21317 | −0.427711 | ||||||||
\(465\) | −8.46976 | −0.392776 | ||||||||
\(466\) | 24.5638 | 1.13789 | ||||||||
\(467\) | 25.8605 | 1.19668 | 0.598341 | − | 0.801241i | \(-0.295827\pi\) | ||||
0.598341 | + | 0.801241i | \(0.295827\pi\) | |||||||
\(468\) | −19.1339 | −0.884463 | ||||||||
\(469\) | −8.28511 | −0.382571 | ||||||||
\(470\) | 24.9229 | 1.14961 | ||||||||
\(471\) | 20.5009 | 0.944631 | ||||||||
\(472\) | 2.18079 | 0.100379 | ||||||||
\(473\) | −35.2908 | −1.62267 | ||||||||
\(474\) | 43.8256 | 2.01298 | ||||||||
\(475\) | −20.9429 | −0.960928 | ||||||||
\(476\) | 6.60020 | 0.302520 | ||||||||
\(477\) | 3.43706 | 0.157372 | ||||||||
\(478\) | 6.35840 | 0.290826 | ||||||||
\(479\) | −21.8365 | −0.997733 | −0.498866 | − | 0.866679i | \(-0.666250\pi\) | ||||
−0.498866 | + | 0.866679i | \(0.666250\pi\) | |||||||
\(480\) | 8.42854 | 0.384708 | ||||||||
\(481\) | 39.6585 | 1.80827 | ||||||||
\(482\) | 5.51971 | 0.251416 | ||||||||
\(483\) | −1.40203 | −0.0637944 | ||||||||
\(484\) | −1.90188 | −0.0864490 | ||||||||
\(485\) | 47.3002 | 2.14779 | ||||||||
\(486\) | −20.6118 | −0.934969 | ||||||||
\(487\) | −31.9434 | −1.44749 | −0.723746 | − | 0.690066i | \(-0.757581\pi\) | ||||
−0.723746 | + | 0.690066i | \(0.757581\pi\) | |||||||
\(488\) | 1.29727 | 0.0587245 | ||||||||
\(489\) | −3.05698 | −0.138242 | ||||||||
\(490\) | −3.15601 | −0.142574 | ||||||||
\(491\) | 4.08024 | 0.184139 | 0.0920694 | − | 0.995753i | \(-0.470652\pi\) | ||||
0.0920694 | + | 0.995753i | \(0.470652\pi\) | |||||||
\(492\) | −16.8561 | −0.759929 | ||||||||
\(493\) | 60.8087 | 2.73869 | ||||||||
\(494\) | −19.5495 | −0.879572 | ||||||||
\(495\) | 39.3373 | 1.76808 | ||||||||
\(496\) | 1.00489 | 0.0451209 | ||||||||
\(497\) | −14.0501 | −0.630233 | ||||||||
\(498\) | 18.9059 | 0.847195 | ||||||||
\(499\) | 43.4544 | 1.94529 | 0.972644 | − | 0.232302i | \(-0.0746257\pi\) | ||||
0.972644 | + | 0.232302i | \(0.0746257\pi\) | |||||||
\(500\) | −0.125039 | −0.00559193 | ||||||||
\(501\) | −55.7360 | −2.49010 | ||||||||
\(502\) | −5.28603 | −0.235927 | ||||||||
\(503\) | −1.47723 | −0.0658665 | −0.0329333 | − | 0.999458i | \(-0.510485\pi\) | ||||
−0.0329333 | + | 0.999458i | \(0.510485\pi\) | |||||||
\(504\) | 4.13228 | 0.184067 | ||||||||
\(505\) | −0.540217 | −0.0240393 | ||||||||
\(506\) | 1.58350 | 0.0703951 | ||||||||
\(507\) | −22.5401 | −1.00104 | ||||||||
\(508\) | 12.3826 | 0.549389 | ||||||||
\(509\) | −12.5665 | −0.557000 | −0.278500 | − | 0.960436i | \(-0.589837\pi\) | ||||
−0.278500 | + | 0.960436i | \(0.589837\pi\) | |||||||
\(510\) | −55.6300 | −2.46334 | ||||||||
\(511\) | −16.6288 | −0.735615 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 12.7671 | 0.563682 | ||||||||
\(514\) | 6.39010 | 0.281855 | ||||||||
\(515\) | 34.7167 | 1.52980 | ||||||||
\(516\) | 31.2464 | 1.37555 | ||||||||
\(517\) | −23.8197 | −1.04759 | ||||||||
\(518\) | −8.56493 | −0.376321 | ||||||||
\(519\) | −24.2232 | −1.06328 | ||||||||
\(520\) | 14.6134 | 0.640838 | ||||||||
\(521\) | −0.365819 | −0.0160268 | −0.00801340 | − | 0.999968i | \(-0.502551\pi\) | ||||
−0.00801340 | + | 0.999968i | \(0.502551\pi\) | |||||||
\(522\) | 38.0714 | 1.66634 | ||||||||
\(523\) | −24.9640 | −1.09160 | −0.545800 | − | 0.837915i | \(-0.683774\pi\) | ||||
−0.545800 | + | 0.837915i | \(0.683774\pi\) | |||||||
\(524\) | 11.2346 | 0.490787 | ||||||||
\(525\) | 13.2474 | 0.578162 | ||||||||
\(526\) | 2.48872 | 0.108513 | ||||||||
\(527\) | −6.63248 | −0.288915 | ||||||||
\(528\) | −8.05546 | −0.350569 | ||||||||
\(529\) | −22.7244 | −0.988017 | ||||||||
\(530\) | −2.62504 | −0.114024 | ||||||||
\(531\) | −9.01164 | −0.391072 | ||||||||
\(532\) | 4.22204 | 0.183049 | ||||||||
\(533\) | −29.2249 | −1.26587 | ||||||||
\(534\) | 37.6111 | 1.62759 | ||||||||
\(535\) | −51.6759 | −2.23414 | ||||||||
\(536\) | −8.28511 | −0.357862 | ||||||||
\(537\) | −10.7222 | −0.462698 | ||||||||
\(538\) | 1.04689 | 0.0451346 | ||||||||
\(539\) | 3.01631 | 0.129922 | ||||||||
\(540\) | −9.54350 | −0.410687 | ||||||||
\(541\) | −40.6148 | −1.74617 | −0.873083 | − | 0.487571i | \(-0.837883\pi\) | ||||
−0.873083 | + | 0.487571i | \(0.837883\pi\) | |||||||
\(542\) | 6.47317 | 0.278046 | ||||||||
\(543\) | −15.2018 | −0.652374 | ||||||||
\(544\) | 6.60020 | 0.282981 | ||||||||
\(545\) | −33.6076 | −1.43959 | ||||||||
\(546\) | 12.3659 | 0.529213 | ||||||||
\(547\) | −13.5048 | −0.577422 | −0.288711 | − | 0.957416i | \(-0.593227\pi\) | ||||
−0.288711 | + | 0.957416i | \(0.593227\pi\) | |||||||
\(548\) | 7.05090 | 0.301200 | ||||||||
\(549\) | −5.36068 | −0.228788 | ||||||||
\(550\) | −14.9620 | −0.637984 | ||||||||
\(551\) | 38.8984 | 1.65713 | ||||||||
\(552\) | −1.40203 | −0.0596742 | ||||||||
\(553\) | −16.4102 | −0.697832 | ||||||||
\(554\) | −5.18131 | −0.220133 | ||||||||
\(555\) | 72.1898 | 3.06429 | ||||||||
\(556\) | 19.2723 | 0.817325 | ||||||||
\(557\) | 9.82915 | 0.416474 | 0.208237 | − | 0.978078i | \(-0.433227\pi\) | ||||
0.208237 | + | 0.978078i | \(0.433227\pi\) | |||||||
\(558\) | −4.15250 | −0.175789 | ||||||||
\(559\) | 54.1748 | 2.29135 | ||||||||
\(560\) | −3.15601 | −0.133366 | ||||||||
\(561\) | 53.1676 | 2.24474 | ||||||||
\(562\) | −0.340066 | −0.0143448 | ||||||||
\(563\) | 1.12295 | 0.0473267 | 0.0236634 | − | 0.999720i | \(-0.492467\pi\) | ||||
0.0236634 | + | 0.999720i | \(0.492467\pi\) | |||||||
\(564\) | 21.0899 | 0.888046 | ||||||||
\(565\) | −54.3697 | −2.28735 | ||||||||
\(566\) | 20.1181 | 0.845626 | ||||||||
\(567\) | 4.32108 | 0.181468 | ||||||||
\(568\) | −14.0501 | −0.589529 | ||||||||
\(569\) | −30.7579 | −1.28944 | −0.644719 | − | 0.764420i | \(-0.723026\pi\) | ||||
−0.644719 | + | 0.764420i | \(0.723026\pi\) | |||||||
\(570\) | −35.5857 | −1.49052 | ||||||||
\(571\) | 3.90203 | 0.163295 | 0.0816474 | − | 0.996661i | \(-0.473982\pi\) | ||||
0.0816474 | + | 0.996661i | \(0.473982\pi\) | |||||||
\(572\) | −13.9665 | −0.583969 | ||||||||
\(573\) | 19.8150 | 0.827782 | ||||||||
\(574\) | 6.31163 | 0.263442 | ||||||||
\(575\) | −2.60409 | −0.108598 | ||||||||
\(576\) | 4.13228 | 0.172179 | ||||||||
\(577\) | 4.41862 | 0.183949 | 0.0919747 | − | 0.995761i | \(-0.470682\pi\) | ||||
0.0919747 | + | 0.995761i | \(0.470682\pi\) | |||||||
\(578\) | −26.5626 | −1.10486 | ||||||||
\(579\) | 7.06207 | 0.293490 | ||||||||
\(580\) | −29.0768 | −1.20735 | ||||||||
\(581\) | −7.07919 | −0.293694 | ||||||||
\(582\) | 40.0257 | 1.65912 | ||||||||
\(583\) | 2.50884 | 0.103906 | ||||||||
\(584\) | −16.6288 | −0.688105 | ||||||||
\(585\) | −60.3866 | −2.49668 | ||||||||
\(586\) | −13.9830 | −0.577631 | ||||||||
\(587\) | −22.3402 | −0.922080 | −0.461040 | − | 0.887379i | \(-0.652524\pi\) | ||||
−0.461040 | + | 0.887379i | \(0.652524\pi\) | |||||||
\(588\) | −2.67063 | −0.110135 | ||||||||
\(589\) | −4.24269 | −0.174817 | ||||||||
\(590\) | 6.88258 | 0.283352 | ||||||||
\(591\) | −6.64063 | −0.273159 | ||||||||
\(592\) | −8.56493 | −0.352016 | ||||||||
\(593\) | 22.0369 | 0.904948 | 0.452474 | − | 0.891778i | \(-0.350542\pi\) | ||||
0.452474 | + | 0.891778i | \(0.350542\pi\) | |||||||
\(594\) | 9.12107 | 0.374242 | ||||||||
\(595\) | 20.8303 | 0.853958 | ||||||||
\(596\) | −16.3469 | −0.669595 | ||||||||
\(597\) | −19.2555 | −0.788077 | ||||||||
\(598\) | −2.43083 | −0.0994039 | ||||||||
\(599\) | −20.8130 | −0.850397 | −0.425199 | − | 0.905100i | \(-0.639796\pi\) | ||||
−0.425199 | + | 0.905100i | \(0.639796\pi\) | |||||||
\(600\) | 13.2474 | 0.540821 | ||||||||
\(601\) | 36.2110 | 1.47708 | 0.738540 | − | 0.674210i | \(-0.235516\pi\) | ||||
0.738540 | + | 0.674210i | \(0.235516\pi\) | |||||||
\(602\) | −11.7000 | −0.476856 | ||||||||
\(603\) | 34.2364 | 1.39421 | ||||||||
\(604\) | −4.57648 | −0.186214 | ||||||||
\(605\) | −6.00234 | −0.244030 | ||||||||
\(606\) | −0.457135 | −0.0185698 | ||||||||
\(607\) | 30.2052 | 1.22599 | 0.612995 | − | 0.790087i | \(-0.289965\pi\) | ||||
0.612995 | + | 0.790087i | \(0.289965\pi\) | |||||||
\(608\) | 4.22204 | 0.171226 | ||||||||
\(609\) | −24.6050 | −0.997045 | ||||||||
\(610\) | 4.09418 | 0.165769 | ||||||||
\(611\) | 36.5656 | 1.47929 | ||||||||
\(612\) | −27.2739 | −1.10248 | ||||||||
\(613\) | −43.0840 | −1.74014 | −0.870072 | − | 0.492924i | \(-0.835928\pi\) | ||||
−0.870072 | + | 0.492924i | \(0.835928\pi\) | |||||||
\(614\) | −28.6630 | −1.15674 | ||||||||
\(615\) | −53.1978 | −2.14514 | ||||||||
\(616\) | 3.01631 | 0.121531 | ||||||||
\(617\) | 13.6269 | 0.548597 | 0.274298 | − | 0.961645i | \(-0.411554\pi\) | ||||
0.274298 | + | 0.961645i | \(0.411554\pi\) | |||||||
\(618\) | 29.3775 | 1.18174 | ||||||||
\(619\) | 6.17501 | 0.248195 | 0.124097 | − | 0.992270i | \(-0.460396\pi\) | ||||
0.124097 | + | 0.992270i | \(0.460396\pi\) | |||||||
\(620\) | 3.17144 | 0.127368 | ||||||||
\(621\) | 1.58749 | 0.0637039 | ||||||||
\(622\) | −10.8244 | −0.434017 | ||||||||
\(623\) | −14.0832 | −0.564231 | ||||||||
\(624\) | 12.3659 | 0.495033 | ||||||||
\(625\) | −25.1965 | −1.00786 | ||||||||
\(626\) | 13.5622 | 0.542053 | ||||||||
\(627\) | 34.0105 | 1.35825 | ||||||||
\(628\) | −7.67641 | −0.306322 | ||||||||
\(629\) | 56.5302 | 2.25401 | ||||||||
\(630\) | 13.0415 | 0.519587 | ||||||||
\(631\) | 23.9546 | 0.953619 | 0.476809 | − | 0.879007i | \(-0.341793\pi\) | ||||
0.476809 | + | 0.879007i | \(0.341793\pi\) | |||||||
\(632\) | −16.4102 | −0.652762 | ||||||||
\(633\) | 37.9305 | 1.50760 | ||||||||
\(634\) | −12.4644 | −0.495024 | ||||||||
\(635\) | 39.0796 | 1.55083 | ||||||||
\(636\) | −2.22132 | −0.0880812 | ||||||||
\(637\) | −4.63033 | −0.183460 | ||||||||
\(638\) | 27.7898 | 1.10021 | ||||||||
\(639\) | 58.0590 | 2.29678 | ||||||||
\(640\) | −3.15601 | −0.124752 | ||||||||
\(641\) | 11.3253 | 0.447321 | 0.223661 | − | 0.974667i | \(-0.428199\pi\) | ||||
0.223661 | + | 0.974667i | \(0.428199\pi\) | |||||||
\(642\) | −43.7285 | −1.72583 | ||||||||
\(643\) | −37.7847 | −1.49008 | −0.745042 | − | 0.667018i | \(-0.767571\pi\) | ||||
−0.745042 | + | 0.667018i | \(0.767571\pi\) | |||||||
\(644\) | 0.524979 | 0.0206871 | ||||||||
\(645\) | 98.6138 | 3.88291 | ||||||||
\(646\) | −27.8663 | −1.09639 | ||||||||
\(647\) | 23.2338 | 0.913415 | 0.456707 | − | 0.889617i | \(-0.349029\pi\) | ||||
0.456707 | + | 0.889617i | \(0.349029\pi\) | |||||||
\(648\) | 4.32108 | 0.169748 | ||||||||
\(649\) | −6.57793 | −0.258206 | ||||||||
\(650\) | 22.9682 | 0.900887 | ||||||||
\(651\) | 2.68370 | 0.105182 | ||||||||
\(652\) | 1.14467 | 0.0448286 | ||||||||
\(653\) | 43.7520 | 1.71215 | 0.856074 | − | 0.516853i | \(-0.172897\pi\) | ||||
0.856074 | + | 0.516853i | \(0.172897\pi\) | |||||||
\(654\) | −28.4390 | −1.11205 | ||||||||
\(655\) | 35.4565 | 1.38540 | ||||||||
\(656\) | 6.31163 | 0.246428 | ||||||||
\(657\) | 68.7149 | 2.68082 | ||||||||
\(658\) | −7.89697 | −0.307856 | ||||||||
\(659\) | −41.2372 | −1.60637 | −0.803186 | − | 0.595728i | \(-0.796864\pi\) | ||||
−0.803186 | + | 0.595728i | \(0.796864\pi\) | |||||||
\(660\) | −25.4231 | −0.989592 | ||||||||
\(661\) | −13.4403 | −0.522766 | −0.261383 | − | 0.965235i | \(-0.584179\pi\) | ||||
−0.261383 | + | 0.965235i | \(0.584179\pi\) | |||||||
\(662\) | −7.39253 | −0.287319 | ||||||||
\(663\) | −81.6176 | −3.16976 | ||||||||
\(664\) | −7.07919 | −0.274726 | ||||||||
\(665\) | 13.3248 | 0.516714 | ||||||||
\(666\) | 35.3927 | 1.37144 | ||||||||
\(667\) | 4.83672 | 0.187278 | ||||||||
\(668\) | 20.8699 | 0.807482 | ||||||||
\(669\) | 16.2248 | 0.627286 | ||||||||
\(670\) | −26.1479 | −1.01018 | ||||||||
\(671\) | −3.91296 | −0.151058 | ||||||||
\(672\) | −2.67063 | −0.103022 | ||||||||
\(673\) | 27.4599 | 1.05850 | 0.529251 | − | 0.848465i | \(-0.322473\pi\) | ||||
0.529251 | + | 0.848465i | \(0.322473\pi\) | |||||||
\(674\) | −30.2671 | −1.16585 | ||||||||
\(675\) | −14.9998 | −0.577342 | ||||||||
\(676\) | 8.43999 | 0.324615 | ||||||||
\(677\) | 39.3655 | 1.51294 | 0.756469 | − | 0.654030i | \(-0.226923\pi\) | ||||
0.756469 | + | 0.654030i | \(0.226923\pi\) | |||||||
\(678\) | −46.0080 | −1.76693 | ||||||||
\(679\) | −14.9874 | −0.575162 | ||||||||
\(680\) | 20.8303 | 0.798805 | ||||||||
\(681\) | −71.7392 | −2.74905 | ||||||||
\(682\) | −3.03106 | −0.116065 | ||||||||
\(683\) | −32.4141 | −1.24029 | −0.620146 | − | 0.784487i | \(-0.712927\pi\) | ||||
−0.620146 | + | 0.784487i | \(0.712927\pi\) | |||||||
\(684\) | −17.4467 | −0.667091 | ||||||||
\(685\) | 22.2527 | 0.850232 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −40.1669 | −1.53246 | ||||||||
\(688\) | −11.7000 | −0.446058 | ||||||||
\(689\) | −3.85132 | −0.146724 | ||||||||
\(690\) | −4.42480 | −0.168449 | ||||||||
\(691\) | −15.0473 | −0.572427 | −0.286213 | − | 0.958166i | \(-0.592397\pi\) | ||||
−0.286213 | + | 0.958166i | \(0.592397\pi\) | |||||||
\(692\) | 9.07022 | 0.344798 | ||||||||
\(693\) | −12.4642 | −0.473478 | ||||||||
\(694\) | −22.4200 | −0.851053 | ||||||||
\(695\) | 60.8234 | 2.30716 | ||||||||
\(696\) | −24.6050 | −0.932650 | ||||||||
\(697\) | −41.6580 | −1.57791 | ||||||||
\(698\) | 14.1699 | 0.536340 | ||||||||
\(699\) | 65.6008 | 2.48125 | ||||||||
\(700\) | −4.96038 | −0.187485 | ||||||||
\(701\) | 17.8235 | 0.673186 | 0.336593 | − | 0.941650i | \(-0.390725\pi\) | ||||
0.336593 | + | 0.941650i | \(0.390725\pi\) | |||||||
\(702\) | −14.0017 | −0.528462 | ||||||||
\(703\) | 36.1615 | 1.36386 | ||||||||
\(704\) | 3.01631 | 0.113681 | ||||||||
\(705\) | 66.5600 | 2.50679 | ||||||||
\(706\) | 9.44344 | 0.355409 | ||||||||
\(707\) | 0.171171 | 0.00643755 | ||||||||
\(708\) | 5.82409 | 0.218883 | ||||||||
\(709\) | 42.6540 | 1.60190 | 0.800952 | − | 0.598728i | \(-0.204327\pi\) | ||||
0.800952 | + | 0.598728i | \(0.204327\pi\) | |||||||
\(710\) | −44.3422 | −1.66413 | ||||||||
\(711\) | 67.8115 | 2.54313 | ||||||||
\(712\) | −14.0832 | −0.527790 | ||||||||
\(713\) | −0.527547 | −0.0197568 | ||||||||
\(714\) | 17.6267 | 0.659663 | ||||||||
\(715\) | −44.0784 | −1.64844 | ||||||||
\(716\) | 4.01486 | 0.150042 | ||||||||
\(717\) | 16.9809 | 0.634165 | ||||||||
\(718\) | −2.00815 | −0.0749433 | ||||||||
\(719\) | −16.0627 | −0.599038 | −0.299519 | − | 0.954090i | \(-0.596826\pi\) | ||||
−0.299519 | + | 0.954090i | \(0.596826\pi\) | |||||||
\(720\) | 13.0415 | 0.486029 | ||||||||
\(721\) | −11.0002 | −0.409669 | ||||||||
\(722\) | 1.17434 | 0.0437046 | ||||||||
\(723\) | 14.7411 | 0.548229 | ||||||||
\(724\) | 5.69222 | 0.211550 | ||||||||
\(725\) | −45.7008 | −1.69729 | ||||||||
\(726\) | −5.07922 | −0.188507 | ||||||||
\(727\) | −9.33177 | −0.346096 | −0.173048 | − | 0.984913i | \(-0.555362\pi\) | ||||
−0.173048 | + | 0.984913i | \(0.555362\pi\) | |||||||
\(728\) | −4.63033 | −0.171612 | ||||||||
\(729\) | −42.0833 | −1.55864 | ||||||||
\(730\) | −52.4806 | −1.94239 | ||||||||
\(731\) | 77.2222 | 2.85617 | ||||||||
\(732\) | 3.46452 | 0.128053 | ||||||||
\(733\) | 44.0899 | 1.62850 | 0.814248 | − | 0.580517i | \(-0.197149\pi\) | ||||
0.814248 | + | 0.580517i | \(0.197149\pi\) | |||||||
\(734\) | −14.7871 | −0.545802 | ||||||||
\(735\) | −8.42854 | −0.310891 | ||||||||
\(736\) | 0.524979 | 0.0193510 | ||||||||
\(737\) | 24.9904 | 0.920535 | ||||||||
\(738\) | −26.0814 | −0.960071 | ||||||||
\(739\) | 37.6307 | 1.38427 | 0.692134 | − | 0.721769i | \(-0.256670\pi\) | ||||
0.692134 | + | 0.721769i | \(0.256670\pi\) | |||||||
\(740\) | −27.0310 | −0.993678 | ||||||||
\(741\) | −52.2095 | −1.91796 | ||||||||
\(742\) | 0.831758 | 0.0305348 | ||||||||
\(743\) | 16.9980 | 0.623597 | 0.311799 | − | 0.950148i | \(-0.399069\pi\) | ||||
0.311799 | + | 0.950148i | \(0.399069\pi\) | |||||||
\(744\) | 2.68370 | 0.0983891 | ||||||||
\(745\) | −51.5909 | −1.89015 | ||||||||
\(746\) | −30.6145 | −1.12088 | ||||||||
\(747\) | 29.2532 | 1.07032 | ||||||||
\(748\) | −19.9082 | −0.727917 | ||||||||
\(749\) | 16.3738 | 0.598286 | ||||||||
\(750\) | −0.333934 | −0.0121936 | ||||||||
\(751\) | 24.0331 | 0.876981 | 0.438491 | − | 0.898736i | \(-0.355513\pi\) | ||||
0.438491 | + | 0.898736i | \(0.355513\pi\) | |||||||
\(752\) | −7.89697 | −0.287973 | ||||||||
\(753\) | −14.1171 | −0.514454 | ||||||||
\(754\) | −42.6600 | −1.55359 | ||||||||
\(755\) | −14.4434 | −0.525650 | ||||||||
\(756\) | 3.02392 | 0.109979 | ||||||||
\(757\) | 9.02734 | 0.328104 | 0.164052 | − | 0.986452i | \(-0.447543\pi\) | ||||
0.164052 | + | 0.986452i | \(0.447543\pi\) | |||||||
\(758\) | −10.7563 | −0.390685 | ||||||||
\(759\) | 4.22894 | 0.153501 | ||||||||
\(760\) | 13.3248 | 0.483341 | ||||||||
\(761\) | −42.4388 | −1.53841 | −0.769203 | − | 0.639005i | \(-0.779346\pi\) | ||||
−0.769203 | + | 0.639005i | \(0.779346\pi\) | |||||||
\(762\) | 33.0694 | 1.19798 | ||||||||
\(763\) | 10.6488 | 0.385512 | ||||||||
\(764\) | −7.41957 | −0.268431 | ||||||||
\(765\) | −86.0766 | −3.11211 | ||||||||
\(766\) | 1.45941 | 0.0527306 | ||||||||
\(767\) | 10.0978 | 0.364610 | ||||||||
\(768\) | −2.67063 | −0.0963682 | ||||||||
\(769\) | −39.2468 | −1.41528 | −0.707639 | − | 0.706575i | \(-0.750239\pi\) | ||||
−0.707639 | + | 0.706575i | \(0.750239\pi\) | |||||||
\(770\) | 9.51949 | 0.343059 | ||||||||
\(771\) | 17.0656 | 0.614603 | ||||||||
\(772\) | −2.64434 | −0.0951720 | ||||||||
\(773\) | 13.2797 | 0.477638 | 0.238819 | − | 0.971064i | \(-0.423240\pi\) | ||||
0.238819 | + | 0.971064i | \(0.423240\pi\) | |||||||
\(774\) | 48.3477 | 1.73782 | ||||||||
\(775\) | 4.98464 | 0.179054 | ||||||||
\(776\) | −14.9874 | −0.538015 | ||||||||
\(777\) | −22.8738 | −0.820592 | ||||||||
\(778\) | −4.73759 | −0.169851 | ||||||||
\(779\) | −26.6480 | −0.954763 | ||||||||
\(780\) | 39.0269 | 1.39739 | ||||||||
\(781\) | 42.3794 | 1.51645 | ||||||||
\(782\) | −3.46496 | −0.123907 | ||||||||
\(783\) | 27.8599 | 0.995630 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −24.2268 | −0.864692 | ||||||||
\(786\) | 30.0036 | 1.07019 | ||||||||
\(787\) | −30.6190 | −1.09145 | −0.545725 | − | 0.837964i | \(-0.683746\pi\) | ||||
−0.545725 | + | 0.837964i | \(0.683746\pi\) | |||||||
\(788\) | 2.48654 | 0.0885792 | ||||||||
\(789\) | 6.64645 | 0.236620 | ||||||||
\(790\) | −51.7906 | −1.84263 | ||||||||
\(791\) | 17.2274 | 0.612535 | ||||||||
\(792\) | −12.4642 | −0.442898 | ||||||||
\(793\) | 6.00678 | 0.213307 | ||||||||
\(794\) | 16.7995 | 0.596192 | ||||||||
\(795\) | −7.01051 | −0.248637 | ||||||||
\(796\) | 7.21010 | 0.255555 | ||||||||
\(797\) | 2.40628 | 0.0852348 | 0.0426174 | − | 0.999091i | \(-0.486430\pi\) | ||||
0.0426174 | + | 0.999091i | \(0.486430\pi\) | |||||||
\(798\) | 11.2755 | 0.399150 | ||||||||
\(799\) | 52.1216 | 1.84393 | ||||||||
\(800\) | −4.96038 | −0.175376 | ||||||||
\(801\) | 58.1958 | 2.05625 | ||||||||
\(802\) | 2.31347 | 0.0816916 | ||||||||
\(803\) | 50.1576 | 1.77002 | ||||||||
\(804\) | −22.1265 | −0.780341 | ||||||||
\(805\) | 1.65684 | 0.0583958 | ||||||||
\(806\) | 4.65298 | 0.163894 | ||||||||
\(807\) | 2.79586 | 0.0984188 | ||||||||
\(808\) | 0.171171 | 0.00602178 | ||||||||
\(809\) | 20.3487 | 0.715421 | 0.357711 | − | 0.933833i | \(-0.383557\pi\) | ||||
0.357711 | + | 0.933833i | \(0.383557\pi\) | |||||||
\(810\) | 13.6374 | 0.479168 | ||||||||
\(811\) | −13.6894 | −0.480700 | −0.240350 | − | 0.970686i | \(-0.577262\pi\) | ||||
−0.240350 | + | 0.970686i | \(0.577262\pi\) | |||||||
\(812\) | 9.21317 | 0.323319 | ||||||||
\(813\) | 17.2875 | 0.606298 | ||||||||
\(814\) | 25.8345 | 0.905498 | ||||||||
\(815\) | 3.61257 | 0.126543 | ||||||||
\(816\) | 17.6267 | 0.617058 | ||||||||
\(817\) | 49.3979 | 1.72821 | ||||||||
\(818\) | 11.6520 | 0.407401 | ||||||||
\(819\) | 19.1339 | 0.668591 | ||||||||
\(820\) | 19.9195 | 0.695621 | ||||||||
\(821\) | 27.8882 | 0.973306 | 0.486653 | − | 0.873595i | \(-0.338218\pi\) | ||||
0.486653 | + | 0.873595i | \(0.338218\pi\) | |||||||
\(822\) | 18.8304 | 0.656785 | ||||||||
\(823\) | 36.9433 | 1.28776 | 0.643881 | − | 0.765126i | \(-0.277323\pi\) | ||||
0.643881 | + | 0.765126i | \(0.277323\pi\) | |||||||
\(824\) | −11.0002 | −0.383210 | ||||||||
\(825\) | −39.9581 | −1.39116 | ||||||||
\(826\) | −2.18079 | −0.0758793 | ||||||||
\(827\) | −47.4353 | −1.64949 | −0.824743 | − | 0.565507i | \(-0.808681\pi\) | ||||
−0.824743 | + | 0.565507i | \(0.808681\pi\) | |||||||
\(828\) | −2.16936 | −0.0753905 | ||||||||
\(829\) | −42.0991 | −1.46216 | −0.731081 | − | 0.682291i | \(-0.760984\pi\) | ||||
−0.731081 | + | 0.682291i | \(0.760984\pi\) | |||||||
\(830\) | −22.3420 | −0.775502 | ||||||||
\(831\) | −13.8374 | −0.480013 | ||||||||
\(832\) | −4.63033 | −0.160528 | ||||||||
\(833\) | −6.60020 | −0.228683 | ||||||||
\(834\) | 51.4691 | 1.78223 | ||||||||
\(835\) | 65.8657 | 2.27938 | ||||||||
\(836\) | −12.7350 | −0.440449 | ||||||||
\(837\) | −3.03871 | −0.105033 | ||||||||
\(838\) | 31.2631 | 1.07997 | ||||||||
\(839\) | 48.2754 | 1.66665 | 0.833326 | − | 0.552782i | \(-0.186434\pi\) | ||||
0.833326 | + | 0.552782i | \(0.186434\pi\) | |||||||
\(840\) | −8.42854 | −0.290812 | ||||||||
\(841\) | 55.8824 | 1.92698 | ||||||||
\(842\) | −24.4387 | −0.842212 | ||||||||
\(843\) | −0.908192 | −0.0312798 | ||||||||
\(844\) | −14.2028 | −0.488880 | ||||||||
\(845\) | 26.6367 | 0.916329 | ||||||||
\(846\) | 32.6325 | 1.12193 | ||||||||
\(847\) | 1.90188 | 0.0653493 | ||||||||
\(848\) | 0.831758 | 0.0285627 | ||||||||
\(849\) | 53.7280 | 1.84394 | ||||||||
\(850\) | 32.7395 | 1.12296 | ||||||||
\(851\) | 4.49640 | 0.154135 | ||||||||
\(852\) | −37.5226 | −1.28550 | ||||||||
\(853\) | −11.2223 | −0.384246 | −0.192123 | − | 0.981371i | \(-0.561537\pi\) | ||||
−0.192123 | + | 0.981371i | \(0.561537\pi\) | |||||||
\(854\) | −1.29727 | −0.0443916 | ||||||||
\(855\) | −55.0619 | −1.88308 | ||||||||
\(856\) | 16.3738 | 0.559646 | ||||||||
\(857\) | 39.1309 | 1.33669 | 0.668343 | − | 0.743853i | \(-0.267004\pi\) | ||||
0.668343 | + | 0.743853i | \(0.267004\pi\) | |||||||
\(858\) | −37.2995 | −1.27338 | ||||||||
\(859\) | 2.68444 | 0.0915917 | 0.0457959 | − | 0.998951i | \(-0.485418\pi\) | ||||
0.0457959 | + | 0.998951i | \(0.485418\pi\) | |||||||
\(860\) | −36.9252 | −1.25914 | ||||||||
\(861\) | 16.8561 | 0.574453 | ||||||||
\(862\) | −1.00000 | −0.0340601 | ||||||||
\(863\) | −50.4232 | −1.71643 | −0.858213 | − | 0.513294i | \(-0.828425\pi\) | ||||
−0.858213 | + | 0.513294i | \(0.828425\pi\) | |||||||
\(864\) | 3.02392 | 0.102876 | ||||||||
\(865\) | 28.6257 | 0.973302 | ||||||||
\(866\) | 25.2393 | 0.857667 | ||||||||
\(867\) | −70.9390 | −2.40922 | ||||||||
\(868\) | −1.00489 | −0.0341082 | ||||||||
\(869\) | 49.4982 | 1.67911 | ||||||||
\(870\) | −77.6535 | −2.63270 | ||||||||
\(871\) | −38.3628 | −1.29987 | ||||||||
\(872\) | 10.6488 | 0.360613 | ||||||||
\(873\) | 61.9320 | 2.09608 | ||||||||
\(874\) | −2.21648 | −0.0749737 | ||||||||
\(875\) | 0.125039 | 0.00422710 | ||||||||
\(876\) | −44.4094 | −1.50046 | ||||||||
\(877\) | −41.8989 | −1.41483 | −0.707413 | − | 0.706800i | \(-0.750138\pi\) | ||||
−0.707413 | + | 0.706800i | \(0.750138\pi\) | |||||||
\(878\) | −12.9214 | −0.436077 | ||||||||
\(879\) | −37.3434 | −1.25956 | ||||||||
\(880\) | 9.51949 | 0.320902 | ||||||||
\(881\) | −28.5652 | −0.962385 | −0.481192 | − | 0.876615i | \(-0.659796\pi\) | ||||
−0.481192 | + | 0.876615i | \(0.659796\pi\) | |||||||
\(882\) | −4.13228 | −0.139141 | ||||||||
\(883\) | −46.3681 | −1.56041 | −0.780206 | − | 0.625523i | \(-0.784886\pi\) | ||||
−0.780206 | + | 0.625523i | \(0.784886\pi\) | |||||||
\(884\) | 30.5611 | 1.02788 | ||||||||
\(885\) | 18.3809 | 0.617866 | ||||||||
\(886\) | −3.93412 | −0.132169 | ||||||||
\(887\) | 41.9775 | 1.40947 | 0.704733 | − | 0.709472i | \(-0.251067\pi\) | ||||
0.704733 | + | 0.709472i | \(0.251067\pi\) | |||||||
\(888\) | −22.8738 | −0.767594 | ||||||||
\(889\) | −12.3826 | −0.415299 | ||||||||
\(890\) | −44.4467 | −1.48986 | ||||||||
\(891\) | −13.0337 | −0.436646 | ||||||||
\(892\) | −6.07525 | −0.203414 | ||||||||
\(893\) | 33.3414 | 1.11573 | ||||||||
\(894\) | −43.6566 | −1.46009 | ||||||||
\(895\) | 12.6709 | 0.423542 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −6.49185 | −0.216757 | ||||||||
\(898\) | −31.8219 | −1.06191 | ||||||||
\(899\) | −9.25823 | −0.308779 | ||||||||
\(900\) | 20.4977 | 0.683257 | ||||||||
\(901\) | −5.48977 | −0.182891 | ||||||||
\(902\) | −19.0378 | −0.633890 | ||||||||
\(903\) | −31.2464 | −1.03981 | ||||||||
\(904\) | 17.2274 | 0.572974 | ||||||||
\(905\) | 17.9647 | 0.597167 | ||||||||
\(906\) | −12.2221 | −0.406052 | ||||||||
\(907\) | −34.6891 | −1.15183 | −0.575917 | − | 0.817508i | \(-0.695355\pi\) | ||||
−0.575917 | + | 0.817508i | \(0.695355\pi\) | |||||||
\(908\) | 26.8622 | 0.891455 | ||||||||
\(909\) | −0.707327 | −0.0234606 | ||||||||
\(910\) | −14.6134 | −0.484428 | ||||||||
\(911\) | 59.0097 | 1.95508 | 0.977540 | − | 0.210750i | \(-0.0675906\pi\) | ||||
0.977540 | + | 0.210750i | \(0.0675906\pi\) | |||||||
\(912\) | 11.2755 | 0.373370 | ||||||||
\(913\) | 21.3530 | 0.706682 | ||||||||
\(914\) | 15.1960 | 0.502638 | ||||||||
\(915\) | 10.9341 | 0.361469 | ||||||||
\(916\) | 15.0402 | 0.496943 | ||||||||
\(917\) | −11.2346 | −0.371000 | ||||||||
\(918\) | −19.9585 | −0.658727 | ||||||||
\(919\) | 3.70958 | 0.122368 | 0.0611839 | − | 0.998127i | \(-0.480512\pi\) | ||||
0.0611839 | + | 0.998127i | \(0.480512\pi\) | |||||||
\(920\) | 1.65684 | 0.0546243 | ||||||||
\(921\) | −76.5483 | −2.52235 | ||||||||
\(922\) | 5.80779 | 0.191270 | ||||||||
\(923\) | −65.0566 | −2.14136 | ||||||||
\(924\) | 8.05546 | 0.265005 | ||||||||
\(925\) | −42.4853 | −1.39691 | ||||||||
\(926\) | −21.0429 | −0.691514 | ||||||||
\(927\) | 45.4559 | 1.49297 | ||||||||
\(928\) | 9.21317 | 0.302437 | ||||||||
\(929\) | 35.6276 | 1.16891 | 0.584453 | − | 0.811428i | \(-0.301309\pi\) | ||||
0.584453 | + | 0.811428i | \(0.301309\pi\) | |||||||
\(930\) | 8.46976 | 0.277734 | ||||||||
\(931\) | −4.22204 | −0.138372 | ||||||||
\(932\) | −24.5638 | −0.804613 | ||||||||
\(933\) | −28.9079 | −0.946402 | ||||||||
\(934\) | −25.8605 | −0.846182 | ||||||||
\(935\) | −62.8306 | −2.05478 | ||||||||
\(936\) | 19.1339 | 0.625410 | ||||||||
\(937\) | −22.5160 | −0.735567 | −0.367783 | − | 0.929911i | \(-0.619883\pi\) | ||||
−0.367783 | + | 0.929911i | \(0.619883\pi\) | |||||||
\(938\) | 8.28511 | 0.270518 | ||||||||
\(939\) | 36.2196 | 1.18198 | ||||||||
\(940\) | −24.9229 | −0.812896 | ||||||||
\(941\) | −36.3844 | −1.18610 | −0.593049 | − | 0.805166i | \(-0.702076\pi\) | ||||
−0.593049 | + | 0.805166i | \(0.702076\pi\) | |||||||
\(942\) | −20.5009 | −0.667955 | ||||||||
\(943\) | −3.31347 | −0.107901 | ||||||||
\(944\) | −2.18079 | −0.0709786 | ||||||||
\(945\) | 9.54350 | 0.310450 | ||||||||
\(946\) | 35.2908 | 1.14740 | ||||||||
\(947\) | −44.9617 | −1.46106 | −0.730530 | − | 0.682881i | \(-0.760727\pi\) | ||||
−0.730530 | + | 0.682881i | \(0.760727\pi\) | |||||||
\(948\) | −43.8256 | −1.42339 | ||||||||
\(949\) | −76.9969 | −2.49942 | ||||||||
\(950\) | 20.9429 | 0.679479 | ||||||||
\(951\) | −33.2878 | −1.07943 | ||||||||
\(952\) | −6.60020 | −0.213914 | ||||||||
\(953\) | 6.43848 | 0.208563 | 0.104281 | − | 0.994548i | \(-0.466746\pi\) | ||||
0.104281 | + | 0.994548i | \(0.466746\pi\) | |||||||
\(954\) | −3.43706 | −0.111279 | ||||||||
\(955\) | −23.4162 | −0.757731 | ||||||||
\(956\) | −6.35840 | −0.205645 | ||||||||
\(957\) | 74.2163 | 2.39907 | ||||||||
\(958\) | 21.8365 | 0.705504 | ||||||||
\(959\) | −7.05090 | −0.227685 | ||||||||
\(960\) | −8.42854 | −0.272030 | ||||||||
\(961\) | −29.9902 | −0.967426 | ||||||||
\(962\) | −39.6585 | −1.27864 | ||||||||
\(963\) | −67.6613 | −2.18035 | ||||||||
\(964\) | −5.51971 | −0.177778 | ||||||||
\(965\) | −8.34557 | −0.268653 | ||||||||
\(966\) | 1.40203 | 0.0451095 | ||||||||
\(967\) | 58.5436 | 1.88263 | 0.941317 | − | 0.337523i | \(-0.109589\pi\) | ||||
0.941317 | + | 0.337523i | \(0.109589\pi\) | |||||||
\(968\) | 1.90188 | 0.0611287 | ||||||||
\(969\) | −74.4208 | −2.39074 | ||||||||
\(970\) | −47.3002 | −1.51872 | ||||||||
\(971\) | −11.2801 | −0.361995 | −0.180998 | − | 0.983484i | \(-0.557933\pi\) | ||||
−0.180998 | + | 0.983484i | \(0.557933\pi\) | |||||||
\(972\) | 20.6118 | 0.661123 | ||||||||
\(973\) | −19.2723 | −0.617840 | ||||||||
\(974\) | 31.9434 | 1.02353 | ||||||||
\(975\) | 61.3397 | 1.96444 | ||||||||
\(976\) | −1.29727 | −0.0415245 | ||||||||
\(977\) | 33.9580 | 1.08641 | 0.543206 | − | 0.839599i | \(-0.317210\pi\) | ||||
0.543206 | + | 0.839599i | \(0.317210\pi\) | |||||||
\(978\) | 3.05698 | 0.0977515 | ||||||||
\(979\) | 42.4793 | 1.35764 | ||||||||
\(980\) | 3.15601 | 0.100815 | ||||||||
\(981\) | −44.0038 | −1.40493 | ||||||||
\(982\) | −4.08024 | −0.130206 | ||||||||
\(983\) | 44.3483 | 1.41449 | 0.707246 | − | 0.706967i | \(-0.249937\pi\) | ||||
0.707246 | + | 0.706967i | \(0.249937\pi\) | |||||||
\(984\) | 16.8561 | 0.537351 | ||||||||
\(985\) | 7.84753 | 0.250043 | ||||||||
\(986\) | −60.8087 | −1.93654 | ||||||||
\(987\) | −21.0899 | −0.671300 | ||||||||
\(988\) | 19.5495 | 0.621952 | ||||||||
\(989\) | 6.14225 | 0.195312 | ||||||||
\(990\) | −39.3373 | −1.25022 | ||||||||
\(991\) | −11.4795 | −0.364657 | −0.182329 | − | 0.983238i | \(-0.558363\pi\) | ||||
−0.182329 | + | 0.983238i | \(0.558363\pi\) | |||||||
\(992\) | −1.00489 | −0.0319053 | ||||||||
\(993\) | −19.7427 | −0.626517 | ||||||||
\(994\) | 14.0501 | 0.445642 | ||||||||
\(995\) | 22.7551 | 0.721386 | ||||||||
\(996\) | −18.9059 | −0.599057 | ||||||||
\(997\) | −18.1121 | −0.573615 | −0.286808 | − | 0.957988i | \(-0.592594\pi\) | ||||
−0.286808 | + | 0.957988i | \(0.592594\pi\) | |||||||
\(998\) | −43.4544 | −1.37553 | ||||||||
\(999\) | 25.8996 | 0.819428 |
(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 | 6034.2.a.n.1.2 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.n.1.2 | ✓ | 24 | 1.1 | even | 1 | trivial |