Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.45922 | −1.73893 | −0.869464 | − | 0.493996i | \(-0.835536\pi\) | ||||
−0.869464 | + | 0.493996i | \(0.835536\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.04774 | 2.02387 | ||||||||
\(5\) | 2.82362 | 1.26276 | 0.631381 | − | 0.775473i | \(-0.282488\pi\) | ||||
0.631381 | + | 0.775473i | \(0.282488\pi\) | |||||||
\(6\) | −2.45922 | −1.00397 | ||||||||
\(7\) | 4.27749 | 1.61674 | 0.808370 | − | 0.588675i | \(-0.200350\pi\) | ||||
0.808370 | + | 0.588675i | \(0.200350\pi\) | |||||||
\(8\) | −5.03584 | −1.78044 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −6.94390 | −2.19585 | ||||||||
\(11\) | −3.19677 | −0.963862 | −0.481931 | − | 0.876209i | \(-0.660064\pi\) | ||||
−0.481931 | + | 0.876209i | \(0.660064\pi\) | |||||||
\(12\) | 4.04774 | 1.16848 | ||||||||
\(13\) | 0.537035 | 0.148947 | 0.0744734 | − | 0.997223i | \(-0.476272\pi\) | ||||
0.0744734 | + | 0.997223i | \(0.476272\pi\) | |||||||
\(14\) | −10.5193 | −2.81139 | ||||||||
\(15\) | 2.82362 | 0.729056 | ||||||||
\(16\) | 4.28873 | 1.07218 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −2.45922 | −0.579643 | ||||||||
\(19\) | −4.65843 | −1.06872 | −0.534358 | − | 0.845258i | \(-0.679447\pi\) | ||||
−0.534358 | + | 0.845258i | \(0.679447\pi\) | |||||||
\(20\) | 11.4293 | 2.55567 | ||||||||
\(21\) | 4.27749 | 0.933425 | ||||||||
\(22\) | 7.86155 | 1.67609 | ||||||||
\(23\) | −1.04489 | −0.217875 | −0.108938 | − | 0.994049i | \(-0.534745\pi\) | ||||
−0.108938 | + | 0.994049i | \(0.534745\pi\) | |||||||
\(24\) | −5.03584 | −1.02794 | ||||||||
\(25\) | 2.97284 | 0.594568 | ||||||||
\(26\) | −1.32068 | −0.259008 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 17.3142 | 3.27207 | ||||||||
\(29\) | −9.34609 | −1.73553 | −0.867763 | − | 0.496979i | \(-0.834443\pi\) | ||||
−0.867763 | + | 0.496979i | \(0.834443\pi\) | |||||||
\(30\) | −6.94390 | −1.26778 | ||||||||
\(31\) | −8.67933 | −1.55885 | −0.779427 | − | 0.626493i | \(-0.784490\pi\) | ||||
−0.779427 | + | 0.626493i | \(0.784490\pi\) | |||||||
\(32\) | −0.475238 | −0.0840110 | ||||||||
\(33\) | −3.19677 | −0.556486 | ||||||||
\(34\) | 2.45922 | 0.421752 | ||||||||
\(35\) | 12.0780 | 2.04156 | ||||||||
\(36\) | 4.04774 | 0.674624 | ||||||||
\(37\) | −5.77798 | −0.949893 | −0.474947 | − | 0.880015i | \(-0.657533\pi\) | ||||
−0.474947 | + | 0.880015i | \(0.657533\pi\) | |||||||
\(38\) | 11.4561 | 1.85842 | ||||||||
\(39\) | 0.537035 | 0.0859944 | ||||||||
\(40\) | −14.2193 | −2.24827 | ||||||||
\(41\) | −7.18874 | −1.12269 | −0.561347 | − | 0.827581i | \(-0.689717\pi\) | ||||
−0.561347 | + | 0.827581i | \(0.689717\pi\) | |||||||
\(42\) | −10.5193 | −1.62316 | ||||||||
\(43\) | −1.84695 | −0.281657 | −0.140828 | − | 0.990034i | \(-0.544977\pi\) | ||||
−0.140828 | + | 0.990034i | \(0.544977\pi\) | |||||||
\(44\) | −12.9397 | −1.95073 | ||||||||
\(45\) | 2.82362 | 0.420921 | ||||||||
\(46\) | 2.56962 | 0.378869 | ||||||||
\(47\) | −9.23665 | −1.34730 | −0.673652 | − | 0.739048i | \(-0.735275\pi\) | ||||
−0.673652 | + | 0.739048i | \(0.735275\pi\) | |||||||
\(48\) | 4.28873 | 0.619025 | ||||||||
\(49\) | 11.2969 | 1.61385 | ||||||||
\(50\) | −7.31086 | −1.03391 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 2.17378 | 0.301449 | ||||||||
\(53\) | 1.01554 | 0.139496 | 0.0697478 | − | 0.997565i | \(-0.477781\pi\) | ||||
0.0697478 | + | 0.997565i | \(0.477781\pi\) | |||||||
\(54\) | −2.45922 | −0.334657 | ||||||||
\(55\) | −9.02647 | −1.21713 | ||||||||
\(56\) | −21.5408 | −2.87850 | ||||||||
\(57\) | −4.65843 | −0.617023 | ||||||||
\(58\) | 22.9840 | 3.01795 | ||||||||
\(59\) | −13.4723 | −1.75394 | −0.876969 | − | 0.480547i | \(-0.840438\pi\) | ||||
−0.876969 | + | 0.480547i | \(0.840438\pi\) | |||||||
\(60\) | 11.4293 | 1.47552 | ||||||||
\(61\) | 2.60984 | 0.334156 | 0.167078 | − | 0.985944i | \(-0.446567\pi\) | ||||
0.167078 | + | 0.985944i | \(0.446567\pi\) | |||||||
\(62\) | 21.3443 | 2.71073 | ||||||||
\(63\) | 4.27749 | 0.538913 | ||||||||
\(64\) | −7.40875 | −0.926094 | ||||||||
\(65\) | 1.51638 | 0.188084 | ||||||||
\(66\) | 7.86155 | 0.967689 | ||||||||
\(67\) | 2.87750 | 0.351543 | 0.175771 | − | 0.984431i | \(-0.443758\pi\) | ||||
0.175771 | + | 0.984431i | \(0.443758\pi\) | |||||||
\(68\) | −4.04774 | −0.490861 | ||||||||
\(69\) | −1.04489 | −0.125790 | ||||||||
\(70\) | −29.7025 | −3.55012 | ||||||||
\(71\) | 15.8287 | 1.87852 | 0.939262 | − | 0.343200i | \(-0.111511\pi\) | ||||
0.939262 | + | 0.343200i | \(0.111511\pi\) | |||||||
\(72\) | −5.03584 | −0.593479 | ||||||||
\(73\) | 9.34396 | 1.09363 | 0.546814 | − | 0.837254i | \(-0.315840\pi\) | ||||
0.546814 | + | 0.837254i | \(0.315840\pi\) | |||||||
\(74\) | 14.2093 | 1.65180 | ||||||||
\(75\) | 2.97284 | 0.343274 | ||||||||
\(76\) | −18.8561 | −2.16294 | ||||||||
\(77\) | −13.6742 | −1.55831 | ||||||||
\(78\) | −1.32068 | −0.149538 | ||||||||
\(79\) | 3.82203 | 0.430012 | 0.215006 | − | 0.976613i | \(-0.431023\pi\) | ||||
0.215006 | + | 0.976613i | \(0.431023\pi\) | |||||||
\(80\) | 12.1098 | 1.35391 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 17.6787 | 1.95228 | ||||||||
\(83\) | −6.64544 | −0.729432 | −0.364716 | − | 0.931119i | \(-0.618834\pi\) | ||||
−0.364716 | + | 0.931119i | \(0.618834\pi\) | |||||||
\(84\) | 17.3142 | 1.88913 | ||||||||
\(85\) | −2.82362 | −0.306265 | ||||||||
\(86\) | 4.54204 | 0.489781 | ||||||||
\(87\) | −9.34609 | −1.00201 | ||||||||
\(88\) | 16.0984 | 1.71610 | ||||||||
\(89\) | −8.76855 | −0.929464 | −0.464732 | − | 0.885451i | \(-0.653849\pi\) | ||||
−0.464732 | + | 0.885451i | \(0.653849\pi\) | |||||||
\(90\) | −6.94390 | −0.731951 | ||||||||
\(91\) | 2.29716 | 0.240808 | ||||||||
\(92\) | −4.22946 | −0.440951 | ||||||||
\(93\) | −8.67933 | −0.900005 | ||||||||
\(94\) | 22.7149 | 2.34287 | ||||||||
\(95\) | −13.1536 | −1.34953 | ||||||||
\(96\) | −0.475238 | −0.0485038 | ||||||||
\(97\) | 14.0107 | 1.42257 | 0.711285 | − | 0.702904i | \(-0.248114\pi\) | ||||
0.711285 | + | 0.702904i | \(0.248114\pi\) | |||||||
\(98\) | −27.7816 | −2.80636 | ||||||||
\(99\) | −3.19677 | −0.321287 | ||||||||
\(100\) | 12.0333 | 1.20333 | ||||||||
\(101\) | −6.64364 | −0.661067 | −0.330534 | − | 0.943794i | \(-0.607229\pi\) | ||||
−0.330534 | + | 0.943794i | \(0.607229\pi\) | |||||||
\(102\) | 2.45922 | 0.243499 | ||||||||
\(103\) | 13.7755 | 1.35734 | 0.678669 | − | 0.734444i | \(-0.262557\pi\) | ||||
0.678669 | + | 0.734444i | \(0.262557\pi\) | |||||||
\(104\) | −2.70442 | −0.265190 | ||||||||
\(105\) | 12.0780 | 1.17869 | ||||||||
\(106\) | −2.49744 | −0.242573 | ||||||||
\(107\) | 4.18323 | 0.404408 | 0.202204 | − | 0.979343i | \(-0.435190\pi\) | ||||
0.202204 | + | 0.979343i | \(0.435190\pi\) | |||||||
\(108\) | 4.04774 | 0.389494 | ||||||||
\(109\) | −6.51227 | −0.623763 | −0.311881 | − | 0.950121i | \(-0.600959\pi\) | ||||
−0.311881 | + | 0.950121i | \(0.600959\pi\) | |||||||
\(110\) | 22.1980 | 2.11650 | ||||||||
\(111\) | −5.77798 | −0.548421 | ||||||||
\(112\) | 18.3450 | 1.73344 | ||||||||
\(113\) | 2.08121 | 0.195783 | 0.0978917 | − | 0.995197i | \(-0.468790\pi\) | ||||
0.0978917 | + | 0.995197i | \(0.468790\pi\) | |||||||
\(114\) | 11.4561 | 1.07296 | ||||||||
\(115\) | −2.95038 | −0.275125 | ||||||||
\(116\) | −37.8306 | −3.51248 | ||||||||
\(117\) | 0.537035 | 0.0496489 | ||||||||
\(118\) | 33.1312 | 3.04997 | ||||||||
\(119\) | −4.27749 | −0.392117 | ||||||||
\(120\) | −14.2193 | −1.29804 | ||||||||
\(121\) | −0.780666 | −0.0709696 | ||||||||
\(122\) | −6.41816 | −0.581073 | ||||||||
\(123\) | −7.18874 | −0.648187 | ||||||||
\(124\) | −35.1317 | −3.15492 | ||||||||
\(125\) | −5.72393 | −0.511964 | ||||||||
\(126\) | −10.5193 | −0.937131 | ||||||||
\(127\) | −21.3532 | −1.89479 | −0.947395 | − | 0.320066i | \(-0.896295\pi\) | ||||
−0.947395 | + | 0.320066i | \(0.896295\pi\) | |||||||
\(128\) | 19.1702 | 1.69442 | ||||||||
\(129\) | −1.84695 | −0.162615 | ||||||||
\(130\) | −3.72912 | −0.327065 | ||||||||
\(131\) | −10.0499 | −0.878062 | −0.439031 | − | 0.898472i | \(-0.644678\pi\) | ||||
−0.439031 | + | 0.898472i | \(0.644678\pi\) | |||||||
\(132\) | −12.9397 | −1.12626 | ||||||||
\(133\) | −19.9264 | −1.72784 | ||||||||
\(134\) | −7.07640 | −0.611308 | ||||||||
\(135\) | 2.82362 | 0.243019 | ||||||||
\(136\) | 5.03584 | 0.431820 | ||||||||
\(137\) | −17.8050 | −1.52118 | −0.760592 | − | 0.649230i | \(-0.775091\pi\) | ||||
−0.760592 | + | 0.649230i | \(0.775091\pi\) | |||||||
\(138\) | 2.56962 | 0.218740 | ||||||||
\(139\) | −3.67569 | −0.311768 | −0.155884 | − | 0.987775i | \(-0.549823\pi\) | ||||
−0.155884 | + | 0.987775i | \(0.549823\pi\) | |||||||
\(140\) | 48.8887 | 4.13185 | ||||||||
\(141\) | −9.23665 | −0.777867 | ||||||||
\(142\) | −38.9263 | −3.26662 | ||||||||
\(143\) | −1.71678 | −0.143564 | ||||||||
\(144\) | 4.28873 | 0.357394 | ||||||||
\(145\) | −26.3898 | −2.19156 | ||||||||
\(146\) | −22.9788 | −1.90174 | ||||||||
\(147\) | 11.2969 | 0.931755 | ||||||||
\(148\) | −23.3878 | −1.92246 | ||||||||
\(149\) | −10.0174 | −0.820653 | −0.410327 | − | 0.911939i | \(-0.634585\pi\) | ||||
−0.410327 | + | 0.911939i | \(0.634585\pi\) | |||||||
\(150\) | −7.31086 | −0.596929 | ||||||||
\(151\) | 6.73957 | 0.548458 | 0.274229 | − | 0.961664i | \(-0.411577\pi\) | ||||
0.274229 | + | 0.961664i | \(0.411577\pi\) | |||||||
\(152\) | 23.4591 | 1.90278 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 33.6277 | 2.70980 | ||||||||
\(155\) | −24.5072 | −1.96846 | ||||||||
\(156\) | 2.17378 | 0.174042 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | −9.39920 | −0.747760 | ||||||||
\(159\) | 1.01554 | 0.0805378 | ||||||||
\(160\) | −1.34189 | −0.106086 | ||||||||
\(161\) | −4.46952 | −0.352247 | ||||||||
\(162\) | −2.45922 | −0.193214 | ||||||||
\(163\) | 19.2725 | 1.50954 | 0.754768 | − | 0.655991i | \(-0.227749\pi\) | ||||
0.754768 | + | 0.655991i | \(0.227749\pi\) | |||||||
\(164\) | −29.0982 | −2.27219 | ||||||||
\(165\) | −9.02647 | −0.702710 | ||||||||
\(166\) | 16.3426 | 1.26843 | ||||||||
\(167\) | 12.3806 | 0.958042 | 0.479021 | − | 0.877804i | \(-0.340992\pi\) | ||||
0.479021 | + | 0.877804i | \(0.340992\pi\) | |||||||
\(168\) | −21.5408 | −1.66191 | ||||||||
\(169\) | −12.7116 | −0.977815 | ||||||||
\(170\) | 6.94390 | 0.532572 | ||||||||
\(171\) | −4.65843 | −0.356239 | ||||||||
\(172\) | −7.47596 | −0.570037 | ||||||||
\(173\) | 7.04944 | 0.535959 | 0.267979 | − | 0.963425i | \(-0.413644\pi\) | ||||
0.267979 | + | 0.963425i | \(0.413644\pi\) | |||||||
\(174\) | 22.9840 | 1.74242 | ||||||||
\(175\) | 12.7163 | 0.961262 | ||||||||
\(176\) | −13.7101 | −1.03344 | ||||||||
\(177\) | −13.4723 | −1.01264 | ||||||||
\(178\) | 21.5637 | 1.61627 | ||||||||
\(179\) | −5.87911 | −0.439425 | −0.219713 | − | 0.975565i | \(-0.570512\pi\) | ||||
−0.219713 | + | 0.975565i | \(0.570512\pi\) | |||||||
\(180\) | 11.4293 | 0.851889 | ||||||||
\(181\) | −7.34617 | −0.546036 | −0.273018 | − | 0.962009i | \(-0.588022\pi\) | ||||
−0.273018 | + | 0.962009i | \(0.588022\pi\) | |||||||
\(182\) | −5.64922 | −0.418748 | ||||||||
\(183\) | 2.60984 | 0.192925 | ||||||||
\(184\) | 5.26191 | 0.387913 | ||||||||
\(185\) | −16.3148 | −1.19949 | ||||||||
\(186\) | 21.3443 | 1.56504 | ||||||||
\(187\) | 3.19677 | 0.233771 | ||||||||
\(188\) | −37.3876 | −2.72677 | ||||||||
\(189\) | 4.27749 | 0.311142 | ||||||||
\(190\) | 32.3476 | 2.34674 | ||||||||
\(191\) | 4.92504 | 0.356363 | 0.178182 | − | 0.983998i | \(-0.442979\pi\) | ||||
0.178182 | + | 0.983998i | \(0.442979\pi\) | |||||||
\(192\) | −7.40875 | −0.534681 | ||||||||
\(193\) | 17.1994 | 1.23804 | 0.619019 | − | 0.785376i | \(-0.287530\pi\) | ||||
0.619019 | + | 0.785376i | \(0.287530\pi\) | |||||||
\(194\) | −34.4553 | −2.47375 | ||||||||
\(195\) | 1.51638 | 0.108591 | ||||||||
\(196\) | 45.7270 | 3.26622 | ||||||||
\(197\) | 21.1151 | 1.50439 | 0.752194 | − | 0.658942i | \(-0.228996\pi\) | ||||
0.752194 | + | 0.658942i | \(0.228996\pi\) | |||||||
\(198\) | 7.86155 | 0.558696 | ||||||||
\(199\) | −23.9759 | −1.69961 | −0.849804 | − | 0.527098i | \(-0.823280\pi\) | ||||
−0.849804 | + | 0.527098i | \(0.823280\pi\) | |||||||
\(200\) | −14.9708 | −1.05859 | ||||||||
\(201\) | 2.87750 | 0.202963 | ||||||||
\(202\) | 16.3382 | 1.14955 | ||||||||
\(203\) | −39.9778 | −2.80589 | ||||||||
\(204\) | −4.04774 | −0.283399 | ||||||||
\(205\) | −20.2983 | −1.41769 | ||||||||
\(206\) | −33.8769 | −2.36031 | ||||||||
\(207\) | −1.04489 | −0.0726251 | ||||||||
\(208\) | 2.30320 | 0.159698 | ||||||||
\(209\) | 14.8919 | 1.03009 | ||||||||
\(210\) | −29.7025 | −2.04966 | ||||||||
\(211\) | 12.1321 | 0.835209 | 0.417605 | − | 0.908629i | \(-0.362870\pi\) | ||||
0.417605 | + | 0.908629i | \(0.362870\pi\) | |||||||
\(212\) | 4.11066 | 0.282321 | ||||||||
\(213\) | 15.8287 | 1.08457 | ||||||||
\(214\) | −10.2875 | −0.703236 | ||||||||
\(215\) | −5.21508 | −0.355665 | ||||||||
\(216\) | −5.03584 | −0.342645 | ||||||||
\(217\) | −37.1258 | −2.52026 | ||||||||
\(218\) | 16.0151 | 1.08468 | ||||||||
\(219\) | 9.34396 | 0.631407 | ||||||||
\(220\) | −36.5368 | −2.46331 | ||||||||
\(221\) | −0.537035 | −0.0361249 | ||||||||
\(222\) | 14.2093 | 0.953665 | ||||||||
\(223\) | −1.74290 | −0.116713 | −0.0583566 | − | 0.998296i | \(-0.518586\pi\) | ||||
−0.0583566 | + | 0.998296i | \(0.518586\pi\) | |||||||
\(224\) | −2.03283 | −0.135824 | ||||||||
\(225\) | 2.97284 | 0.198189 | ||||||||
\(226\) | −5.11813 | −0.340453 | ||||||||
\(227\) | 19.2034 | 1.27458 | 0.637288 | − | 0.770625i | \(-0.280056\pi\) | ||||
0.637288 | + | 0.770625i | \(0.280056\pi\) | |||||||
\(228\) | −18.8561 | −1.24878 | ||||||||
\(229\) | −26.5978 | −1.75763 | −0.878816 | − | 0.477161i | \(-0.841666\pi\) | ||||
−0.878816 | + | 0.477161i | \(0.841666\pi\) | |||||||
\(230\) | 7.25563 | 0.478422 | ||||||||
\(231\) | −13.6742 | −0.899693 | ||||||||
\(232\) | 47.0654 | 3.09000 | ||||||||
\(233\) | −21.9668 | −1.43909 | −0.719546 | − | 0.694445i | \(-0.755650\pi\) | ||||
−0.719546 | + | 0.694445i | \(0.755650\pi\) | |||||||
\(234\) | −1.32068 | −0.0863359 | ||||||||
\(235\) | −26.0808 | −1.70133 | ||||||||
\(236\) | −54.5322 | −3.54974 | ||||||||
\(237\) | 3.82203 | 0.248268 | ||||||||
\(238\) | 10.5193 | 0.681863 | ||||||||
\(239\) | 6.77243 | 0.438072 | 0.219036 | − | 0.975717i | \(-0.429709\pi\) | ||||
0.219036 | + | 0.975717i | \(0.429709\pi\) | |||||||
\(240\) | 12.1098 | 0.781682 | ||||||||
\(241\) | −30.3120 | −1.95257 | −0.976285 | − | 0.216491i | \(-0.930539\pi\) | ||||
−0.976285 | + | 0.216491i | \(0.930539\pi\) | |||||||
\(242\) | 1.91983 | 0.123411 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 10.5640 | 0.676289 | ||||||||
\(245\) | 31.8983 | 2.03790 | ||||||||
\(246\) | 17.6787 | 1.12715 | ||||||||
\(247\) | −2.50174 | −0.159182 | ||||||||
\(248\) | 43.7077 | 2.77544 | ||||||||
\(249\) | −6.64544 | −0.421138 | ||||||||
\(250\) | 14.0764 | 0.890268 | ||||||||
\(251\) | −15.2650 | −0.963516 | −0.481758 | − | 0.876304i | \(-0.660002\pi\) | ||||
−0.481758 | + | 0.876304i | \(0.660002\pi\) | |||||||
\(252\) | 17.3142 | 1.09069 | ||||||||
\(253\) | 3.34028 | 0.210002 | ||||||||
\(254\) | 52.5121 | 3.29490 | ||||||||
\(255\) | −2.82362 | −0.176822 | ||||||||
\(256\) | −32.3261 | −2.02038 | ||||||||
\(257\) | −16.7718 | −1.04620 | −0.523098 | − | 0.852273i | \(-0.675224\pi\) | ||||
−0.523098 | + | 0.852273i | \(0.675224\pi\) | |||||||
\(258\) | 4.54204 | 0.282775 | ||||||||
\(259\) | −24.7152 | −1.53573 | ||||||||
\(260\) | 6.13793 | 0.380658 | ||||||||
\(261\) | −9.34609 | −0.578508 | ||||||||
\(262\) | 24.7148 | 1.52689 | ||||||||
\(263\) | 0.183039 | 0.0112867 | 0.00564335 | − | 0.999984i | \(-0.498204\pi\) | ||||
0.00564335 | + | 0.999984i | \(0.498204\pi\) | |||||||
\(264\) | 16.0984 | 0.990789 | ||||||||
\(265\) | 2.86751 | 0.176150 | ||||||||
\(266\) | 49.0032 | 3.00458 | ||||||||
\(267\) | −8.76855 | −0.536626 | ||||||||
\(268\) | 11.6474 | 0.711478 | ||||||||
\(269\) | 24.3485 | 1.48455 | 0.742277 | − | 0.670093i | \(-0.233746\pi\) | ||||
0.742277 | + | 0.670093i | \(0.233746\pi\) | |||||||
\(270\) | −6.94390 | −0.422592 | ||||||||
\(271\) | 9.97250 | 0.605786 | 0.302893 | − | 0.953025i | \(-0.402047\pi\) | ||||
0.302893 | + | 0.953025i | \(0.402047\pi\) | |||||||
\(272\) | −4.28873 | −0.260043 | ||||||||
\(273\) | 2.29716 | 0.139031 | ||||||||
\(274\) | 43.7863 | 2.64523 | ||||||||
\(275\) | −9.50349 | −0.573082 | ||||||||
\(276\) | −4.22946 | −0.254583 | ||||||||
\(277\) | 21.7960 | 1.30959 | 0.654797 | − | 0.755805i | \(-0.272754\pi\) | ||||
0.654797 | + | 0.755805i | \(0.272754\pi\) | |||||||
\(278\) | 9.03930 | 0.542141 | ||||||||
\(279\) | −8.67933 | −0.519618 | ||||||||
\(280\) | −60.8230 | −3.63487 | ||||||||
\(281\) | −21.6113 | −1.28922 | −0.644610 | − | 0.764511i | \(-0.722980\pi\) | ||||
−0.644610 | + | 0.764511i | \(0.722980\pi\) | |||||||
\(282\) | 22.7149 | 1.35265 | ||||||||
\(283\) | 17.0175 | 1.01159 | 0.505794 | − | 0.862655i | \(-0.331200\pi\) | ||||
0.505794 | + | 0.862655i | \(0.331200\pi\) | |||||||
\(284\) | 64.0706 | 3.80189 | ||||||||
\(285\) | −13.1536 | −0.779154 | ||||||||
\(286\) | 4.22193 | 0.249648 | ||||||||
\(287\) | −30.7498 | −1.81510 | ||||||||
\(288\) | −0.475238 | −0.0280037 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 64.8983 | 3.81096 | ||||||||
\(291\) | 14.0107 | 0.821321 | ||||||||
\(292\) | 37.8220 | 2.21336 | ||||||||
\(293\) | 28.3764 | 1.65776 | 0.828882 | − | 0.559423i | \(-0.188977\pi\) | ||||
0.828882 | + | 0.559423i | \(0.188977\pi\) | |||||||
\(294\) | −27.7816 | −1.62025 | ||||||||
\(295\) | −38.0405 | −2.21481 | ||||||||
\(296\) | 29.0970 | 1.69123 | ||||||||
\(297\) | −3.19677 | −0.185495 | ||||||||
\(298\) | 24.6348 | 1.42706 | ||||||||
\(299\) | −0.561144 | −0.0324518 | ||||||||
\(300\) | 12.0333 | 0.694743 | ||||||||
\(301\) | −7.90029 | −0.455365 | ||||||||
\(302\) | −16.5741 | −0.953730 | ||||||||
\(303\) | −6.64364 | −0.381667 | ||||||||
\(304\) | −19.9787 | −1.14586 | ||||||||
\(305\) | 7.36921 | 0.421960 | ||||||||
\(306\) | 2.45922 | 0.140584 | ||||||||
\(307\) | 24.9877 | 1.42612 | 0.713061 | − | 0.701102i | \(-0.247308\pi\) | ||||
0.713061 | + | 0.701102i | \(0.247308\pi\) | |||||||
\(308\) | −55.3494 | −3.15383 | ||||||||
\(309\) | 13.7755 | 0.783660 | ||||||||
\(310\) | 60.2684 | 3.42301 | ||||||||
\(311\) | −17.7126 | −1.00439 | −0.502195 | − | 0.864754i | \(-0.667474\pi\) | ||||
−0.502195 | + | 0.864754i | \(0.667474\pi\) | |||||||
\(312\) | −2.70442 | −0.153108 | ||||||||
\(313\) | −11.4673 | −0.648170 | −0.324085 | − | 0.946028i | \(-0.605056\pi\) | ||||
−0.324085 | + | 0.946028i | \(0.605056\pi\) | |||||||
\(314\) | −2.45922 | −0.138782 | ||||||||
\(315\) | 12.0780 | 0.680519 | ||||||||
\(316\) | 15.4706 | 0.870289 | ||||||||
\(317\) | −12.4978 | −0.701945 | −0.350972 | − | 0.936386i | \(-0.614149\pi\) | ||||
−0.350972 | + | 0.936386i | \(0.614149\pi\) | |||||||
\(318\) | −2.49744 | −0.140049 | ||||||||
\(319\) | 29.8773 | 1.67281 | ||||||||
\(320\) | −20.9195 | −1.16944 | ||||||||
\(321\) | 4.18323 | 0.233485 | ||||||||
\(322\) | 10.9915 | 0.612533 | ||||||||
\(323\) | 4.65843 | 0.259202 | ||||||||
\(324\) | 4.04774 | 0.224875 | ||||||||
\(325\) | 1.59652 | 0.0885590 | ||||||||
\(326\) | −47.3952 | −2.62498 | ||||||||
\(327\) | −6.51227 | −0.360129 | ||||||||
\(328\) | 36.2014 | 1.99889 | ||||||||
\(329\) | −39.5097 | −2.17824 | ||||||||
\(330\) | 22.1980 | 1.22196 | ||||||||
\(331\) | −13.3860 | −0.735761 | −0.367880 | − | 0.929873i | \(-0.619916\pi\) | ||||
−0.367880 | + | 0.929873i | \(0.619916\pi\) | |||||||
\(332\) | −26.8990 | −1.47628 | ||||||||
\(333\) | −5.77798 | −0.316631 | ||||||||
\(334\) | −30.4466 | −1.66597 | ||||||||
\(335\) | 8.12498 | 0.443915 | ||||||||
\(336\) | 18.3450 | 1.00080 | ||||||||
\(337\) | 4.76598 | 0.259620 | 0.129810 | − | 0.991539i | \(-0.458563\pi\) | ||||
0.129810 | + | 0.991539i | \(0.458563\pi\) | |||||||
\(338\) | 31.2606 | 1.70035 | ||||||||
\(339\) | 2.08121 | 0.113036 | ||||||||
\(340\) | −11.4293 | −0.619840 | ||||||||
\(341\) | 27.7458 | 1.50252 | ||||||||
\(342\) | 11.4561 | 0.619473 | ||||||||
\(343\) | 18.3801 | 0.992430 | ||||||||
\(344\) | 9.30092 | 0.501472 | ||||||||
\(345\) | −2.95038 | −0.158843 | ||||||||
\(346\) | −17.3361 | −0.931994 | ||||||||
\(347\) | 16.1440 | 0.866655 | 0.433328 | − | 0.901236i | \(-0.357339\pi\) | ||||
0.433328 | + | 0.901236i | \(0.357339\pi\) | |||||||
\(348\) | −37.8306 | −2.02793 | ||||||||
\(349\) | 21.8287 | 1.16847 | 0.584233 | − | 0.811586i | \(-0.301395\pi\) | ||||
0.584233 | + | 0.811586i | \(0.301395\pi\) | |||||||
\(350\) | −31.2721 | −1.67157 | ||||||||
\(351\) | 0.537035 | 0.0286648 | ||||||||
\(352\) | 1.51923 | 0.0809750 | ||||||||
\(353\) | 14.9000 | 0.793048 | 0.396524 | − | 0.918024i | \(-0.370216\pi\) | ||||
0.396524 | + | 0.918024i | \(0.370216\pi\) | |||||||
\(354\) | 33.1312 | 1.76090 | ||||||||
\(355\) | 44.6944 | 2.37213 | ||||||||
\(356\) | −35.4928 | −1.88112 | ||||||||
\(357\) | −4.27749 | −0.226389 | ||||||||
\(358\) | 14.4580 | 0.764129 | ||||||||
\(359\) | 2.36781 | 0.124968 | 0.0624840 | − | 0.998046i | \(-0.480098\pi\) | ||||
0.0624840 | + | 0.998046i | \(0.480098\pi\) | |||||||
\(360\) | −14.2193 | −0.749423 | ||||||||
\(361\) | 2.70092 | 0.142154 | ||||||||
\(362\) | 18.0658 | 0.949518 | ||||||||
\(363\) | −0.780666 | −0.0409743 | ||||||||
\(364\) | 9.29832 | 0.487364 | ||||||||
\(365\) | 26.3838 | 1.38099 | ||||||||
\(366\) | −6.41816 | −0.335483 | ||||||||
\(367\) | 25.2616 | 1.31865 | 0.659323 | − | 0.751859i | \(-0.270843\pi\) | ||||
0.659323 | + | 0.751859i | \(0.270843\pi\) | |||||||
\(368\) | −4.48126 | −0.233602 | ||||||||
\(369\) | −7.18874 | −0.374231 | ||||||||
\(370\) | 40.1217 | 2.08583 | ||||||||
\(371\) | 4.34398 | 0.225528 | ||||||||
\(372\) | −35.1317 | −1.82149 | ||||||||
\(373\) | 13.1367 | 0.680192 | 0.340096 | − | 0.940391i | \(-0.389540\pi\) | ||||
0.340096 | + | 0.940391i | \(0.389540\pi\) | |||||||
\(374\) | −7.86155 | −0.406511 | ||||||||
\(375\) | −5.72393 | −0.295582 | ||||||||
\(376\) | 46.5143 | 2.39879 | ||||||||
\(377\) | −5.01918 | −0.258501 | ||||||||
\(378\) | −10.5193 | −0.541053 | ||||||||
\(379\) | 25.3983 | 1.30462 | 0.652312 | − | 0.757950i | \(-0.273799\pi\) | ||||
0.652312 | + | 0.757950i | \(0.273799\pi\) | |||||||
\(380\) | −53.2425 | −2.73128 | ||||||||
\(381\) | −21.3532 | −1.09396 | ||||||||
\(382\) | −12.1117 | −0.619690 | ||||||||
\(383\) | 1.68455 | 0.0860763 | 0.0430381 | − | 0.999073i | \(-0.486296\pi\) | ||||
0.0430381 | + | 0.999073i | \(0.486296\pi\) | |||||||
\(384\) | 19.1702 | 0.978275 | ||||||||
\(385\) | −38.6106 | −1.96778 | ||||||||
\(386\) | −42.2970 | −2.15286 | ||||||||
\(387\) | −1.84695 | −0.0938855 | ||||||||
\(388\) | 56.7116 | 2.87910 | ||||||||
\(389\) | 19.6316 | 0.995362 | 0.497681 | − | 0.867360i | \(-0.334185\pi\) | ||||
0.497681 | + | 0.867360i | \(0.334185\pi\) | |||||||
\(390\) | −3.72912 | −0.188831 | ||||||||
\(391\) | 1.04489 | 0.0528425 | ||||||||
\(392\) | −56.8895 | −2.87335 | ||||||||
\(393\) | −10.0499 | −0.506949 | ||||||||
\(394\) | −51.9266 | −2.61602 | ||||||||
\(395\) | 10.7920 | 0.543003 | ||||||||
\(396\) | −12.9397 | −0.650244 | ||||||||
\(397\) | 1.42929 | 0.0717343 | 0.0358671 | − | 0.999357i | \(-0.488581\pi\) | ||||
0.0358671 | + | 0.999357i | \(0.488581\pi\) | |||||||
\(398\) | 58.9620 | 2.95550 | ||||||||
\(399\) | −19.9264 | −0.997566 | ||||||||
\(400\) | 12.7497 | 0.637486 | ||||||||
\(401\) | 23.8472 | 1.19087 | 0.595436 | − | 0.803403i | \(-0.296979\pi\) | ||||
0.595436 | + | 0.803403i | \(0.296979\pi\) | |||||||
\(402\) | −7.07640 | −0.352939 | ||||||||
\(403\) | −4.66110 | −0.232186 | ||||||||
\(404\) | −26.8918 | −1.33792 | ||||||||
\(405\) | 2.82362 | 0.140307 | ||||||||
\(406\) | 98.3141 | 4.87924 | ||||||||
\(407\) | 18.4709 | 0.915566 | ||||||||
\(408\) | 5.03584 | 0.249311 | ||||||||
\(409\) | −5.93584 | −0.293509 | −0.146754 | − | 0.989173i | \(-0.546883\pi\) | ||||
−0.146754 | + | 0.989173i | \(0.546883\pi\) | |||||||
\(410\) | 49.9179 | 2.46527 | ||||||||
\(411\) | −17.8050 | −0.878256 | ||||||||
\(412\) | 55.7596 | 2.74708 | ||||||||
\(413\) | −57.6274 | −2.83566 | ||||||||
\(414\) | 2.56962 | 0.126290 | ||||||||
\(415\) | −18.7642 | −0.921099 | ||||||||
\(416\) | −0.255219 | −0.0125132 | ||||||||
\(417\) | −3.67569 | −0.179999 | ||||||||
\(418\) | −36.6224 | −1.79126 | ||||||||
\(419\) | −30.5487 | −1.49240 | −0.746201 | − | 0.665721i | \(-0.768124\pi\) | ||||
−0.746201 | + | 0.665721i | \(0.768124\pi\) | |||||||
\(420\) | 48.8887 | 2.38552 | ||||||||
\(421\) | 35.7120 | 1.74049 | 0.870247 | − | 0.492615i | \(-0.163959\pi\) | ||||
0.870247 | + | 0.492615i | \(0.163959\pi\) | |||||||
\(422\) | −29.8355 | −1.45237 | ||||||||
\(423\) | −9.23665 | −0.449102 | ||||||||
\(424\) | −5.11411 | −0.248363 | ||||||||
\(425\) | −2.97284 | −0.144204 | ||||||||
\(426\) | −38.9263 | −1.88598 | ||||||||
\(427\) | 11.1636 | 0.540243 | ||||||||
\(428\) | 16.9326 | 0.818469 | ||||||||
\(429\) | −1.71678 | −0.0828868 | ||||||||
\(430\) | 12.8250 | 0.618476 | ||||||||
\(431\) | 10.4534 | 0.503521 | 0.251761 | − | 0.967790i | \(-0.418990\pi\) | ||||
0.251761 | + | 0.967790i | \(0.418990\pi\) | |||||||
\(432\) | 4.28873 | 0.206342 | ||||||||
\(433\) | −27.6875 | −1.33057 | −0.665287 | − | 0.746587i | \(-0.731691\pi\) | ||||
−0.665287 | + | 0.746587i | \(0.731691\pi\) | |||||||
\(434\) | 91.3003 | 4.38255 | ||||||||
\(435\) | −26.3898 | −1.26530 | ||||||||
\(436\) | −26.3600 | −1.26241 | ||||||||
\(437\) | 4.86755 | 0.232847 | ||||||||
\(438\) | −22.9788 | −1.09797 | ||||||||
\(439\) | 1.74863 | 0.0834576 | 0.0417288 | − | 0.999129i | \(-0.486713\pi\) | ||||
0.0417288 | + | 0.999129i | \(0.486713\pi\) | |||||||
\(440\) | 45.4558 | 2.16702 | ||||||||
\(441\) | 11.2969 | 0.537949 | ||||||||
\(442\) | 1.32068 | 0.0628186 | ||||||||
\(443\) | 27.4503 | 1.30421 | 0.652103 | − | 0.758131i | \(-0.273887\pi\) | ||||
0.652103 | + | 0.758131i | \(0.273887\pi\) | |||||||
\(444\) | −23.3878 | −1.10993 | ||||||||
\(445\) | −24.7591 | −1.17369 | ||||||||
\(446\) | 4.28617 | 0.202956 | ||||||||
\(447\) | −10.0174 | −0.473804 | ||||||||
\(448\) | −31.6909 | −1.49725 | ||||||||
\(449\) | 20.4193 | 0.963648 | 0.481824 | − | 0.876268i | \(-0.339975\pi\) | ||||
0.481824 | + | 0.876268i | \(0.339975\pi\) | |||||||
\(450\) | −7.31086 | −0.344637 | ||||||||
\(451\) | 22.9808 | 1.08212 | ||||||||
\(452\) | 8.42418 | 0.396240 | ||||||||
\(453\) | 6.73957 | 0.316653 | ||||||||
\(454\) | −47.2254 | −2.21640 | ||||||||
\(455\) | 6.48632 | 0.304083 | ||||||||
\(456\) | 23.4591 | 1.09857 | ||||||||
\(457\) | 7.15108 | 0.334514 | 0.167257 | − | 0.985913i | \(-0.446509\pi\) | ||||
0.167257 | + | 0.985913i | \(0.446509\pi\) | |||||||
\(458\) | 65.4097 | 3.05639 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −11.9424 | −0.556817 | ||||||||
\(461\) | −14.6639 | −0.682968 | −0.341484 | − | 0.939888i | \(-0.610929\pi\) | ||||
−0.341484 | + | 0.939888i | \(0.610929\pi\) | |||||||
\(462\) | 33.6277 | 1.56450 | ||||||||
\(463\) | −5.56437 | −0.258598 | −0.129299 | − | 0.991606i | \(-0.541273\pi\) | ||||
−0.129299 | + | 0.991606i | \(0.541273\pi\) | |||||||
\(464\) | −40.0829 | −1.86080 | ||||||||
\(465\) | −24.5072 | −1.13649 | ||||||||
\(466\) | 54.0210 | 2.50248 | ||||||||
\(467\) | −31.6309 | −1.46370 | −0.731852 | − | 0.681464i | \(-0.761344\pi\) | ||||
−0.731852 | + | 0.681464i | \(0.761344\pi\) | |||||||
\(468\) | 2.17378 | 0.100483 | ||||||||
\(469\) | 12.3085 | 0.568353 | ||||||||
\(470\) | 64.1384 | 2.95848 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 67.8441 | 3.12278 | ||||||||
\(473\) | 5.90426 | 0.271478 | ||||||||
\(474\) | −9.39920 | −0.431720 | ||||||||
\(475\) | −13.8488 | −0.635425 | ||||||||
\(476\) | −17.3142 | −0.793594 | ||||||||
\(477\) | 1.01554 | 0.0464985 | ||||||||
\(478\) | −16.6549 | −0.761776 | ||||||||
\(479\) | −41.2334 | −1.88400 | −0.942000 | − | 0.335613i | \(-0.891057\pi\) | ||||
−0.942000 | + | 0.335613i | \(0.891057\pi\) | |||||||
\(480\) | −1.34189 | −0.0612487 | ||||||||
\(481\) | −3.10298 | −0.141484 | ||||||||
\(482\) | 74.5438 | 3.39538 | ||||||||
\(483\) | −4.46952 | −0.203370 | ||||||||
\(484\) | −3.15993 | −0.143633 | ||||||||
\(485\) | 39.5609 | 1.79637 | ||||||||
\(486\) | −2.45922 | −0.111552 | ||||||||
\(487\) | −23.0766 | −1.04570 | −0.522850 | − | 0.852425i | \(-0.675131\pi\) | ||||
−0.522850 | + | 0.852425i | \(0.675131\pi\) | |||||||
\(488\) | −13.1427 | −0.594944 | ||||||||
\(489\) | 19.2725 | 0.871531 | ||||||||
\(490\) | −78.4447 | −3.54377 | ||||||||
\(491\) | −42.4561 | −1.91602 | −0.958008 | − | 0.286743i | \(-0.907428\pi\) | ||||
−0.958008 | + | 0.286743i | \(0.907428\pi\) | |||||||
\(492\) | −29.0982 | −1.31185 | ||||||||
\(493\) | 9.34609 | 0.420927 | ||||||||
\(494\) | 6.15231 | 0.276806 | ||||||||
\(495\) | −9.02647 | −0.405710 | ||||||||
\(496\) | −37.2233 | −1.67138 | ||||||||
\(497\) | 67.7073 | 3.03709 | ||||||||
\(498\) | 16.3426 | 0.732328 | ||||||||
\(499\) | −0.302886 | −0.0135590 | −0.00677952 | − | 0.999977i | \(-0.502158\pi\) | ||||
−0.00677952 | + | 0.999977i | \(0.502158\pi\) | |||||||
\(500\) | −23.1690 | −1.03615 | ||||||||
\(501\) | 12.3806 | 0.553126 | ||||||||
\(502\) | 37.5398 | 1.67548 | ||||||||
\(503\) | −35.0804 | −1.56416 | −0.782078 | − | 0.623181i | \(-0.785840\pi\) | ||||
−0.782078 | + | 0.623181i | \(0.785840\pi\) | |||||||
\(504\) | −21.5408 | −0.959502 | ||||||||
\(505\) | −18.7591 | −0.834771 | ||||||||
\(506\) | −8.21447 | −0.365178 | ||||||||
\(507\) | −12.7116 | −0.564542 | ||||||||
\(508\) | −86.4323 | −3.83481 | ||||||||
\(509\) | 26.1299 | 1.15819 | 0.579093 | − | 0.815262i | \(-0.303407\pi\) | ||||
0.579093 | + | 0.815262i | \(0.303407\pi\) | |||||||
\(510\) | 6.94390 | 0.307481 | ||||||||
\(511\) | 39.9687 | 1.76811 | ||||||||
\(512\) | 41.1566 | 1.81888 | ||||||||
\(513\) | −4.65843 | −0.205674 | ||||||||
\(514\) | 41.2454 | 1.81926 | ||||||||
\(515\) | 38.8968 | 1.71400 | ||||||||
\(516\) | −7.47596 | −0.329111 | ||||||||
\(517\) | 29.5275 | 1.29862 | ||||||||
\(518\) | 60.7801 | 2.67052 | ||||||||
\(519\) | 7.04944 | 0.309436 | ||||||||
\(520\) | −7.63627 | −0.334872 | ||||||||
\(521\) | 12.5119 | 0.548156 | 0.274078 | − | 0.961707i | \(-0.411627\pi\) | ||||
0.274078 | + | 0.961707i | \(0.411627\pi\) | |||||||
\(522\) | 22.9840 | 1.00598 | ||||||||
\(523\) | 1.35910 | 0.0594294 | 0.0297147 | − | 0.999558i | \(-0.490540\pi\) | ||||
0.0297147 | + | 0.999558i | \(0.490540\pi\) | |||||||
\(524\) | −40.6793 | −1.77708 | ||||||||
\(525\) | 12.7163 | 0.554985 | ||||||||
\(526\) | −0.450133 | −0.0196267 | ||||||||
\(527\) | 8.67933 | 0.378078 | ||||||||
\(528\) | −13.7101 | −0.596655 | ||||||||
\(529\) | −21.9082 | −0.952530 | ||||||||
\(530\) | −7.05183 | −0.306312 | ||||||||
\(531\) | −13.4723 | −0.584646 | ||||||||
\(532\) | −80.6568 | −3.49692 | ||||||||
\(533\) | −3.86061 | −0.167221 | ||||||||
\(534\) | 21.5637 | 0.933155 | ||||||||
\(535\) | 11.8118 | 0.510671 | ||||||||
\(536\) | −14.4906 | −0.625900 | ||||||||
\(537\) | −5.87911 | −0.253702 | ||||||||
\(538\) | −59.8782 | −2.58153 | ||||||||
\(539\) | −36.1137 | −1.55553 | ||||||||
\(540\) | 11.4293 | 0.491838 | ||||||||
\(541\) | 3.94295 | 0.169520 | 0.0847602 | − | 0.996401i | \(-0.472988\pi\) | ||||
0.0847602 | + | 0.996401i | \(0.472988\pi\) | |||||||
\(542\) | −24.5245 | −1.05342 | ||||||||
\(543\) | −7.34617 | −0.315254 | ||||||||
\(544\) | 0.475238 | 0.0203757 | ||||||||
\(545\) | −18.3882 | −0.787664 | ||||||||
\(546\) | −5.64922 | −0.241764 | ||||||||
\(547\) | 26.5602 | 1.13563 | 0.567816 | − | 0.823155i | \(-0.307788\pi\) | ||||
0.567816 | + | 0.823155i | \(0.307788\pi\) | |||||||
\(548\) | −72.0701 | −3.07868 | ||||||||
\(549\) | 2.60984 | 0.111385 | ||||||||
\(550\) | 23.3711 | 0.996548 | ||||||||
\(551\) | 43.5381 | 1.85478 | ||||||||
\(552\) | 5.26191 | 0.223962 | ||||||||
\(553\) | 16.3487 | 0.695218 | ||||||||
\(554\) | −53.6010 | −2.27729 | ||||||||
\(555\) | −16.3148 | −0.692526 | ||||||||
\(556\) | −14.8782 | −0.630977 | ||||||||
\(557\) | −19.3734 | −0.820878 | −0.410439 | − | 0.911888i | \(-0.634625\pi\) | ||||
−0.410439 | + | 0.911888i | \(0.634625\pi\) | |||||||
\(558\) | 21.3443 | 0.903578 | ||||||||
\(559\) | −0.991875 | −0.0419518 | ||||||||
\(560\) | 51.7994 | 2.18892 | ||||||||
\(561\) | 3.19677 | 0.134968 | ||||||||
\(562\) | 53.1468 | 2.24186 | ||||||||
\(563\) | 38.3610 | 1.61672 | 0.808361 | − | 0.588687i | \(-0.200355\pi\) | ||||
0.808361 | + | 0.588687i | \(0.200355\pi\) | |||||||
\(564\) | −37.3876 | −1.57430 | ||||||||
\(565\) | 5.87654 | 0.247228 | ||||||||
\(566\) | −41.8498 | −1.75908 | ||||||||
\(567\) | 4.27749 | 0.179638 | ||||||||
\(568\) | −79.7110 | −3.34460 | ||||||||
\(569\) | 23.8214 | 0.998644 | 0.499322 | − | 0.866417i | \(-0.333583\pi\) | ||||
0.499322 | + | 0.866417i | \(0.333583\pi\) | |||||||
\(570\) | 32.3476 | 1.35489 | ||||||||
\(571\) | −8.73348 | −0.365485 | −0.182742 | − | 0.983161i | \(-0.558497\pi\) | ||||
−0.182742 | + | 0.983161i | \(0.558497\pi\) | |||||||
\(572\) | −6.94907 | −0.290555 | ||||||||
\(573\) | 4.92504 | 0.205746 | ||||||||
\(574\) | 75.6204 | 3.15633 | ||||||||
\(575\) | −3.10630 | −0.129542 | ||||||||
\(576\) | −7.40875 | −0.308698 | ||||||||
\(577\) | 3.02177 | 0.125798 | 0.0628989 | − | 0.998020i | \(-0.479965\pi\) | ||||
0.0628989 | + | 0.998020i | \(0.479965\pi\) | |||||||
\(578\) | −2.45922 | −0.102290 | ||||||||
\(579\) | 17.1994 | 0.714782 | ||||||||
\(580\) | −106.819 | −4.43543 | ||||||||
\(581\) | −28.4258 | −1.17930 | ||||||||
\(582\) | −34.4553 | −1.42822 | ||||||||
\(583\) | −3.24646 | −0.134455 | ||||||||
\(584\) | −47.0547 | −1.94714 | ||||||||
\(585\) | 1.51638 | 0.0626948 | ||||||||
\(586\) | −69.7836 | −2.88273 | ||||||||
\(587\) | 10.9557 | 0.452191 | 0.226096 | − | 0.974105i | \(-0.427404\pi\) | ||||
0.226096 | + | 0.974105i | \(0.427404\pi\) | |||||||
\(588\) | 45.7270 | 1.88575 | ||||||||
\(589\) | 40.4320 | 1.66597 | ||||||||
\(590\) | 93.5499 | 3.85139 | ||||||||
\(591\) | 21.1151 | 0.868559 | ||||||||
\(592\) | −24.7802 | −1.01846 | ||||||||
\(593\) | −14.0083 | −0.575252 | −0.287626 | − | 0.957743i | \(-0.592866\pi\) | ||||
−0.287626 | + | 0.957743i | \(0.592866\pi\) | |||||||
\(594\) | 7.86155 | 0.322563 | ||||||||
\(595\) | −12.0780 | −0.495150 | ||||||||
\(596\) | −40.5477 | −1.66090 | ||||||||
\(597\) | −23.9759 | −0.981269 | ||||||||
\(598\) | 1.37997 | 0.0564313 | ||||||||
\(599\) | 40.0636 | 1.63696 | 0.818478 | − | 0.574538i | \(-0.194818\pi\) | ||||
0.818478 | + | 0.574538i | \(0.194818\pi\) | |||||||
\(600\) | −14.9708 | −0.611178 | ||||||||
\(601\) | 38.9751 | 1.58983 | 0.794914 | − | 0.606722i | \(-0.207516\pi\) | ||||
0.794914 | + | 0.606722i | \(0.207516\pi\) | |||||||
\(602\) | 19.4285 | 0.791848 | ||||||||
\(603\) | 2.87750 | 0.117181 | ||||||||
\(604\) | 27.2800 | 1.11001 | ||||||||
\(605\) | −2.20430 | −0.0896177 | ||||||||
\(606\) | 16.3382 | 0.663692 | ||||||||
\(607\) | 15.6268 | 0.634274 | 0.317137 | − | 0.948380i | \(-0.397279\pi\) | ||||
0.317137 | + | 0.948380i | \(0.397279\pi\) | |||||||
\(608\) | 2.21386 | 0.0897839 | ||||||||
\(609\) | −39.9778 | −1.61998 | ||||||||
\(610\) | −18.1225 | −0.733757 | ||||||||
\(611\) | −4.96041 | −0.200677 | ||||||||
\(612\) | −4.04774 | −0.163620 | ||||||||
\(613\) | −25.0999 | −1.01378 | −0.506889 | − | 0.862012i | \(-0.669204\pi\) | ||||
−0.506889 | + | 0.862012i | \(0.669204\pi\) | |||||||
\(614\) | −61.4501 | −2.47992 | ||||||||
\(615\) | −20.2983 | −0.818506 | ||||||||
\(616\) | 68.8608 | 2.77448 | ||||||||
\(617\) | −40.7679 | −1.64125 | −0.820626 | − | 0.571465i | \(-0.806375\pi\) | ||||
−0.820626 | + | 0.571465i | \(0.806375\pi\) | |||||||
\(618\) | −33.8769 | −1.36273 | ||||||||
\(619\) | 28.8748 | 1.16058 | 0.580288 | − | 0.814411i | \(-0.302940\pi\) | ||||
0.580288 | + | 0.814411i | \(0.302940\pi\) | |||||||
\(620\) | −99.1986 | −3.98391 | ||||||||
\(621\) | −1.04489 | −0.0419301 | ||||||||
\(622\) | 43.5592 | 1.74656 | ||||||||
\(623\) | −37.5074 | −1.50270 | ||||||||
\(624\) | 2.30320 | 0.0922018 | ||||||||
\(625\) | −31.0264 | −1.24106 | ||||||||
\(626\) | 28.2005 | 1.12712 | ||||||||
\(627\) | 14.8919 | 0.594726 | ||||||||
\(628\) | 4.04774 | 0.161522 | ||||||||
\(629\) | 5.77798 | 0.230383 | ||||||||
\(630\) | −29.7025 | −1.18337 | ||||||||
\(631\) | −42.3304 | −1.68515 | −0.842573 | − | 0.538582i | \(-0.818960\pi\) | ||||
−0.842573 | + | 0.538582i | \(0.818960\pi\) | |||||||
\(632\) | −19.2471 | −0.765610 | ||||||||
\(633\) | 12.1321 | 0.482208 | ||||||||
\(634\) | 30.7347 | 1.22063 | ||||||||
\(635\) | −60.2934 | −2.39267 | ||||||||
\(636\) | 4.11066 | 0.162998 | ||||||||
\(637\) | 6.06685 | 0.240377 | ||||||||
\(638\) | −73.4747 | −2.90889 | ||||||||
\(639\) | 15.8287 | 0.626175 | ||||||||
\(640\) | 54.1294 | 2.13965 | ||||||||
\(641\) | −32.0473 | −1.26579 | −0.632896 | − | 0.774237i | \(-0.718134\pi\) | ||||
−0.632896 | + | 0.774237i | \(0.718134\pi\) | |||||||
\(642\) | −10.2875 | −0.406013 | ||||||||
\(643\) | 23.8842 | 0.941900 | 0.470950 | − | 0.882160i | \(-0.343911\pi\) | ||||
0.470950 | + | 0.882160i | \(0.343911\pi\) | |||||||
\(644\) | −18.0915 | −0.712903 | ||||||||
\(645\) | −5.21508 | −0.205343 | ||||||||
\(646\) | −11.4561 | −0.450733 | ||||||||
\(647\) | 47.7991 | 1.87918 | 0.939588 | − | 0.342307i | \(-0.111208\pi\) | ||||
0.939588 | + | 0.342307i | \(0.111208\pi\) | |||||||
\(648\) | −5.03584 | −0.197826 | ||||||||
\(649\) | 43.0677 | 1.69055 | ||||||||
\(650\) | −3.92619 | −0.153998 | ||||||||
\(651\) | −37.1258 | −1.45507 | ||||||||
\(652\) | 78.0100 | 3.05511 | ||||||||
\(653\) | −26.5989 | −1.04090 | −0.520448 | − | 0.853893i | \(-0.674235\pi\) | ||||
−0.520448 | + | 0.853893i | \(0.674235\pi\) | |||||||
\(654\) | 16.0151 | 0.626239 | ||||||||
\(655\) | −28.3771 | −1.10878 | ||||||||
\(656\) | −30.8306 | −1.20373 | ||||||||
\(657\) | 9.34396 | 0.364543 | ||||||||
\(658\) | 97.1629 | 3.78780 | ||||||||
\(659\) | 6.41364 | 0.249840 | 0.124920 | − | 0.992167i | \(-0.460133\pi\) | ||||
0.124920 | + | 0.992167i | \(0.460133\pi\) | |||||||
\(660\) | −36.5368 | −1.42219 | ||||||||
\(661\) | 28.3451 | 1.10250 | 0.551249 | − | 0.834341i | \(-0.314152\pi\) | ||||
0.551249 | + | 0.834341i | \(0.314152\pi\) | |||||||
\(662\) | 32.9190 | 1.27943 | ||||||||
\(663\) | −0.537035 | −0.0208567 | ||||||||
\(664\) | 33.4654 | 1.29871 | ||||||||
\(665\) | −56.2645 | −2.18185 | ||||||||
\(666\) | 14.2093 | 0.550599 | ||||||||
\(667\) | 9.76566 | 0.378128 | ||||||||
\(668\) | 50.1136 | 1.93895 | ||||||||
\(669\) | −1.74290 | −0.0673844 | ||||||||
\(670\) | −19.9811 | −0.771936 | ||||||||
\(671\) | −8.34306 | −0.322080 | ||||||||
\(672\) | −2.03283 | −0.0784180 | ||||||||
\(673\) | 38.9978 | 1.50326 | 0.751628 | − | 0.659587i | \(-0.229269\pi\) | ||||
0.751628 | + | 0.659587i | \(0.229269\pi\) | |||||||
\(674\) | −11.7206 | −0.451460 | ||||||||
\(675\) | 2.97284 | 0.114425 | ||||||||
\(676\) | −51.4533 | −1.97897 | ||||||||
\(677\) | −18.1078 | −0.695939 | −0.347970 | − | 0.937506i | \(-0.613129\pi\) | ||||
−0.347970 | + | 0.937506i | \(0.613129\pi\) | |||||||
\(678\) | −5.11813 | −0.196561 | ||||||||
\(679\) | 59.9306 | 2.29992 | ||||||||
\(680\) | 14.2193 | 0.545286 | ||||||||
\(681\) | 19.2034 | 0.735877 | ||||||||
\(682\) | −68.2330 | −2.61278 | ||||||||
\(683\) | 16.1734 | 0.618858 | 0.309429 | − | 0.950923i | \(-0.399862\pi\) | ||||
0.309429 | + | 0.950923i | \(0.399862\pi\) | |||||||
\(684\) | −18.8561 | −0.720981 | ||||||||
\(685\) | −50.2746 | −1.92089 | ||||||||
\(686\) | −45.2006 | −1.72577 | ||||||||
\(687\) | −26.5978 | −1.01477 | ||||||||
\(688\) | −7.92106 | −0.301987 | ||||||||
\(689\) | 0.545382 | 0.0207774 | ||||||||
\(690\) | 7.25563 | 0.276217 | ||||||||
\(691\) | 7.42506 | 0.282462 | 0.141231 | − | 0.989977i | \(-0.454894\pi\) | ||||
0.141231 | + | 0.989977i | \(0.454894\pi\) | |||||||
\(692\) | 28.5343 | 1.08471 | ||||||||
\(693\) | −13.6742 | −0.519438 | ||||||||
\(694\) | −39.7016 | −1.50705 | ||||||||
\(695\) | −10.3787 | −0.393688 | ||||||||
\(696\) | 47.0654 | 1.78401 | ||||||||
\(697\) | 7.18874 | 0.272293 | ||||||||
\(698\) | −53.6816 | −2.03188 | ||||||||
\(699\) | −21.9668 | −0.830860 | ||||||||
\(700\) | 51.4723 | 1.94547 | ||||||||
\(701\) | 22.5837 | 0.852973 | 0.426486 | − | 0.904494i | \(-0.359751\pi\) | ||||
0.426486 | + | 0.904494i | \(0.359751\pi\) | |||||||
\(702\) | −1.32068 | −0.0498460 | ||||||||
\(703\) | 26.9163 | 1.01517 | ||||||||
\(704\) | 23.6841 | 0.892627 | ||||||||
\(705\) | −26.0808 | −0.982261 | ||||||||
\(706\) | −36.6424 | −1.37905 | ||||||||
\(707\) | −28.4181 | −1.06877 | ||||||||
\(708\) | −54.5322 | −2.04945 | ||||||||
\(709\) | −37.6548 | −1.41416 | −0.707078 | − | 0.707136i | \(-0.749987\pi\) | ||||
−0.707078 | + | 0.707136i | \(0.749987\pi\) | |||||||
\(710\) | −109.913 | −4.12496 | ||||||||
\(711\) | 3.82203 | 0.143337 | ||||||||
\(712\) | 44.1570 | 1.65485 | ||||||||
\(713\) | 9.06897 | 0.339636 | ||||||||
\(714\) | 10.5193 | 0.393674 | ||||||||
\(715\) | −4.84753 | −0.181287 | ||||||||
\(716\) | −23.7971 | −0.889340 | ||||||||
\(717\) | 6.77243 | 0.252921 | ||||||||
\(718\) | −5.82294 | −0.217310 | ||||||||
\(719\) | 20.4295 | 0.761893 | 0.380947 | − | 0.924597i | \(-0.375598\pi\) | ||||
0.380947 | + | 0.924597i | \(0.375598\pi\) | |||||||
\(720\) | 12.1098 | 0.451304 | ||||||||
\(721\) | 58.9245 | 2.19446 | ||||||||
\(722\) | −6.64216 | −0.247195 | ||||||||
\(723\) | −30.3120 | −1.12732 | ||||||||
\(724\) | −29.7354 | −1.10511 | ||||||||
\(725\) | −27.7844 | −1.03189 | ||||||||
\(726\) | 1.91983 | 0.0712514 | ||||||||
\(727\) | 30.0043 | 1.11280 | 0.556399 | − | 0.830915i | \(-0.312183\pi\) | ||||
0.556399 | + | 0.830915i | \(0.312183\pi\) | |||||||
\(728\) | −11.5681 | −0.428744 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −64.8835 | −2.40145 | ||||||||
\(731\) | 1.84695 | 0.0683118 | ||||||||
\(732\) | 10.5640 | 0.390455 | ||||||||
\(733\) | −30.3144 | −1.11969 | −0.559844 | − | 0.828598i | \(-0.689139\pi\) | ||||
−0.559844 | + | 0.828598i | \(0.689139\pi\) | |||||||
\(734\) | −62.1238 | −2.29303 | ||||||||
\(735\) | 31.8983 | 1.17658 | ||||||||
\(736\) | 0.496573 | 0.0183039 | ||||||||
\(737\) | −9.19871 | −0.338839 | ||||||||
\(738\) | 17.6787 | 0.650761 | ||||||||
\(739\) | −11.8085 | −0.434383 | −0.217192 | − | 0.976129i | \(-0.569690\pi\) | ||||
−0.217192 | + | 0.976129i | \(0.569690\pi\) | |||||||
\(740\) | −66.0382 | −2.42761 | ||||||||
\(741\) | −2.50174 | −0.0919036 | ||||||||
\(742\) | −10.6828 | −0.392177 | ||||||||
\(743\) | −33.4717 | −1.22796 | −0.613978 | − | 0.789323i | \(-0.710432\pi\) | ||||
−0.613978 | + | 0.789323i | \(0.710432\pi\) | |||||||
\(744\) | 43.7077 | 1.60240 | ||||||||
\(745\) | −28.2852 | −1.03629 | ||||||||
\(746\) | −32.3060 | −1.18281 | ||||||||
\(747\) | −6.64544 | −0.243144 | ||||||||
\(748\) | 12.9397 | 0.473122 | ||||||||
\(749\) | 17.8937 | 0.653822 | ||||||||
\(750\) | 14.0764 | 0.513997 | ||||||||
\(751\) | 3.84339 | 0.140247 | 0.0701237 | − | 0.997538i | \(-0.477661\pi\) | ||||
0.0701237 | + | 0.997538i | \(0.477661\pi\) | |||||||
\(752\) | −39.6135 | −1.44456 | ||||||||
\(753\) | −15.2650 | −0.556286 | ||||||||
\(754\) | 12.3432 | 0.449514 | ||||||||
\(755\) | 19.0300 | 0.692573 | ||||||||
\(756\) | 17.3142 | 0.629711 | ||||||||
\(757\) | −43.3583 | −1.57588 | −0.787942 | − | 0.615749i | \(-0.788853\pi\) | ||||
−0.787942 | + | 0.615749i | \(0.788853\pi\) | |||||||
\(758\) | −62.4600 | −2.26865 | ||||||||
\(759\) | 3.34028 | 0.121245 | ||||||||
\(760\) | 66.2396 | 2.40276 | ||||||||
\(761\) | 22.0285 | 0.798532 | 0.399266 | − | 0.916835i | \(-0.369265\pi\) | ||||
0.399266 | + | 0.916835i | \(0.369265\pi\) | |||||||
\(762\) | 52.5121 | 1.90231 | ||||||||
\(763\) | −27.8562 | −1.00846 | ||||||||
\(764\) | 19.9353 | 0.721233 | ||||||||
\(765\) | −2.82362 | −0.102088 | ||||||||
\(766\) | −4.14266 | −0.149680 | ||||||||
\(767\) | −7.23507 | −0.261243 | ||||||||
\(768\) | −32.3261 | −1.16647 | ||||||||
\(769\) | −22.4708 | −0.810318 | −0.405159 | − | 0.914246i | \(-0.632784\pi\) | ||||
−0.405159 | + | 0.914246i | \(0.632784\pi\) | |||||||
\(770\) | 94.9519 | 3.42183 | ||||||||
\(771\) | −16.7718 | −0.604021 | ||||||||
\(772\) | 69.6186 | 2.50563 | ||||||||
\(773\) | −3.44582 | −0.123938 | −0.0619688 | − | 0.998078i | \(-0.519738\pi\) | ||||
−0.0619688 | + | 0.998078i | \(0.519738\pi\) | |||||||
\(774\) | 4.54204 | 0.163260 | ||||||||
\(775\) | −25.8023 | −0.926845 | ||||||||
\(776\) | −70.5556 | −2.53280 | ||||||||
\(777\) | −24.7152 | −0.886654 | ||||||||
\(778\) | −48.2784 | −1.73086 | ||||||||
\(779\) | 33.4882 | 1.19984 | ||||||||
\(780\) | 6.13793 | 0.219773 | ||||||||
\(781\) | −50.6008 | −1.81064 | ||||||||
\(782\) | −2.56962 | −0.0918893 | ||||||||
\(783\) | −9.34609 | −0.334002 | ||||||||
\(784\) | 48.4495 | 1.73034 | ||||||||
\(785\) | 2.82362 | 0.100779 | ||||||||
\(786\) | 24.7148 | 0.881548 | ||||||||
\(787\) | −1.35257 | −0.0482140 | −0.0241070 | − | 0.999709i | \(-0.507674\pi\) | ||||
−0.0241070 | + | 0.999709i | \(0.507674\pi\) | |||||||
\(788\) | 85.4685 | 3.04469 | ||||||||
\(789\) | 0.183039 | 0.00651637 | ||||||||
\(790\) | −26.5398 | −0.944243 | ||||||||
\(791\) | 8.90234 | 0.316531 | ||||||||
\(792\) | 16.0984 | 0.572032 | ||||||||
\(793\) | 1.40158 | 0.0497714 | ||||||||
\(794\) | −3.51494 | −0.124741 | ||||||||
\(795\) | 2.86751 | 0.101700 | ||||||||
\(796\) | −97.0484 | −3.43979 | ||||||||
\(797\) | 4.65406 | 0.164855 | 0.0824277 | − | 0.996597i | \(-0.473733\pi\) | ||||
0.0824277 | + | 0.996597i | \(0.473733\pi\) | |||||||
\(798\) | 49.0032 | 1.73470 | ||||||||
\(799\) | 9.23665 | 0.326769 | ||||||||
\(800\) | −1.41281 | −0.0499503 | ||||||||
\(801\) | −8.76855 | −0.309821 | ||||||||
\(802\) | −58.6454 | −2.07084 | ||||||||
\(803\) | −29.8705 | −1.05411 | ||||||||
\(804\) | 11.6474 | 0.410772 | ||||||||
\(805\) | −12.6202 | −0.444805 | ||||||||
\(806\) | 11.4627 | 0.403755 | ||||||||
\(807\) | 24.3485 | 0.857108 | ||||||||
\(808\) | 33.4563 | 1.17699 | ||||||||
\(809\) | −15.3152 | −0.538453 | −0.269226 | − | 0.963077i | \(-0.586768\pi\) | ||||
−0.269226 | + | 0.963077i | \(0.586768\pi\) | |||||||
\(810\) | −6.94390 | −0.243984 | ||||||||
\(811\) | 44.6870 | 1.56917 | 0.784587 | − | 0.620019i | \(-0.212875\pi\) | ||||
0.784587 | + | 0.620019i | \(0.212875\pi\) | |||||||
\(812\) | −161.820 | −5.67876 | ||||||||
\(813\) | 9.97250 | 0.349751 | ||||||||
\(814\) | −45.4238 | −1.59210 | ||||||||
\(815\) | 54.4182 | 1.90619 | ||||||||
\(816\) | −4.28873 | −0.150136 | ||||||||
\(817\) | 8.60386 | 0.301011 | ||||||||
\(818\) | 14.5975 | 0.510390 | ||||||||
\(819\) | 2.29716 | 0.0802693 | ||||||||
\(820\) | −82.1623 | −2.86923 | ||||||||
\(821\) | 41.2781 | 1.44062 | 0.720308 | − | 0.693654i | \(-0.244000\pi\) | ||||
0.720308 | + | 0.693654i | \(0.244000\pi\) | |||||||
\(822\) | 43.7863 | 1.52722 | ||||||||
\(823\) | −10.1629 | −0.354256 | −0.177128 | − | 0.984188i | \(-0.556681\pi\) | ||||
−0.177128 | + | 0.984188i | \(0.556681\pi\) | |||||||
\(824\) | −69.3711 | −2.41666 | ||||||||
\(825\) | −9.50349 | −0.330869 | ||||||||
\(826\) | 141.718 | 4.93101 | ||||||||
\(827\) | 3.91567 | 0.136161 | 0.0680807 | − | 0.997680i | \(-0.478312\pi\) | ||||
0.0680807 | + | 0.997680i | \(0.478312\pi\) | |||||||
\(828\) | −4.22946 | −0.146984 | ||||||||
\(829\) | −27.7387 | −0.963406 | −0.481703 | − | 0.876334i | \(-0.659982\pi\) | ||||
−0.481703 | + | 0.876334i | \(0.659982\pi\) | |||||||
\(830\) | 46.1452 | 1.60172 | ||||||||
\(831\) | 21.7960 | 0.756094 | ||||||||
\(832\) | −3.97876 | −0.137939 | ||||||||
\(833\) | −11.2969 | −0.391415 | ||||||||
\(834\) | 9.03930 | 0.313005 | ||||||||
\(835\) | 34.9582 | 1.20978 | ||||||||
\(836\) | 60.2786 | 2.08478 | ||||||||
\(837\) | −8.67933 | −0.300002 | ||||||||
\(838\) | 75.1259 | 2.59518 | ||||||||
\(839\) | 15.5886 | 0.538177 | 0.269089 | − | 0.963115i | \(-0.413278\pi\) | ||||
0.269089 | + | 0.963115i | \(0.413278\pi\) | |||||||
\(840\) | −60.8230 | −2.09859 | ||||||||
\(841\) | 58.3494 | 2.01205 | ||||||||
\(842\) | −87.8234 | −3.02659 | ||||||||
\(843\) | −21.6113 | −0.744332 | ||||||||
\(844\) | 49.1077 | 1.69036 | ||||||||
\(845\) | −35.8927 | −1.23475 | ||||||||
\(846\) | 22.7149 | 0.780955 | ||||||||
\(847\) | −3.33929 | −0.114739 | ||||||||
\(848\) | 4.35539 | 0.149565 | ||||||||
\(849\) | 17.0175 | 0.584040 | ||||||||
\(850\) | 7.31086 | 0.250760 | ||||||||
\(851\) | 6.03737 | 0.206958 | ||||||||
\(852\) | 64.0706 | 2.19502 | ||||||||
\(853\) | 21.3620 | 0.731422 | 0.365711 | − | 0.930728i | \(-0.380826\pi\) | ||||
0.365711 | + | 0.930728i | \(0.380826\pi\) | |||||||
\(854\) | −27.4536 | −0.939444 | ||||||||
\(855\) | −13.1536 | −0.449845 | ||||||||
\(856\) | −21.0661 | −0.720023 | ||||||||
\(857\) | 25.8274 | 0.882249 | 0.441124 | − | 0.897446i | \(-0.354580\pi\) | ||||
0.441124 | + | 0.897446i | \(0.354580\pi\) | |||||||
\(858\) | 4.22193 | 0.144134 | ||||||||
\(859\) | 27.5648 | 0.940498 | 0.470249 | − | 0.882534i | \(-0.344164\pi\) | ||||
0.470249 | + | 0.882534i | \(0.344164\pi\) | |||||||
\(860\) | −21.1093 | −0.719821 | ||||||||
\(861\) | −30.7498 | −1.04795 | ||||||||
\(862\) | −25.7071 | −0.875587 | ||||||||
\(863\) | −16.4001 | −0.558267 | −0.279134 | − | 0.960252i | \(-0.590047\pi\) | ||||
−0.279134 | + | 0.960252i | \(0.590047\pi\) | |||||||
\(864\) | −0.475238 | −0.0161679 | ||||||||
\(865\) | 19.9049 | 0.676789 | ||||||||
\(866\) | 68.0895 | 2.31377 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −150.276 | −5.10068 | ||||||||
\(869\) | −12.2182 | −0.414472 | ||||||||
\(870\) | 64.8983 | 2.20026 | ||||||||
\(871\) | 1.54532 | 0.0523612 | ||||||||
\(872\) | 32.7948 | 1.11057 | ||||||||
\(873\) | 14.0107 | 0.474190 | ||||||||
\(874\) | −11.9704 | −0.404904 | ||||||||
\(875\) | −24.4841 | −0.827712 | ||||||||
\(876\) | 37.8220 | 1.27789 | ||||||||
\(877\) | −7.63702 | −0.257884 | −0.128942 | − | 0.991652i | \(-0.541158\pi\) | ||||
−0.128942 | + | 0.991652i | \(0.541158\pi\) | |||||||
\(878\) | −4.30026 | −0.145127 | ||||||||
\(879\) | 28.3764 | 0.957111 | ||||||||
\(880\) | −38.7121 | −1.30498 | ||||||||
\(881\) | 10.2482 | 0.345272 | 0.172636 | − | 0.984986i | \(-0.444772\pi\) | ||||
0.172636 | + | 0.984986i | \(0.444772\pi\) | |||||||
\(882\) | −27.7816 | −0.935455 | ||||||||
\(883\) | −35.9183 | −1.20875 | −0.604373 | − | 0.796702i | \(-0.706576\pi\) | ||||
−0.604373 | + | 0.796702i | \(0.706576\pi\) | |||||||
\(884\) | −2.17378 | −0.0731121 | ||||||||
\(885\) | −38.0405 | −1.27872 | ||||||||
\(886\) | −67.5063 | −2.26792 | ||||||||
\(887\) | 12.9928 | 0.436255 | 0.218128 | − | 0.975920i | \(-0.430005\pi\) | ||||
0.218128 | + | 0.975920i | \(0.430005\pi\) | |||||||
\(888\) | 29.0970 | 0.976430 | ||||||||
\(889\) | −91.3381 | −3.06338 | ||||||||
\(890\) | 60.8879 | 2.04097 | ||||||||
\(891\) | −3.19677 | −0.107096 | ||||||||
\(892\) | −7.05481 | −0.236213 | ||||||||
\(893\) | 43.0283 | 1.43989 | ||||||||
\(894\) | 24.6348 | 0.823912 | ||||||||
\(895\) | −16.6004 | −0.554889 | ||||||||
\(896\) | 82.0003 | 2.73944 | ||||||||
\(897\) | −0.561144 | −0.0187361 | ||||||||
\(898\) | −50.2155 | −1.67571 | ||||||||
\(899\) | 81.1178 | 2.70543 | ||||||||
\(900\) | 12.0333 | 0.401110 | ||||||||
\(901\) | −1.01554 | −0.0338326 | ||||||||
\(902\) | −56.5146 | −1.88173 | ||||||||
\(903\) | −7.90029 | −0.262905 | ||||||||
\(904\) | −10.4806 | −0.348580 | ||||||||
\(905\) | −20.7428 | −0.689514 | ||||||||
\(906\) | −16.5741 | −0.550636 | ||||||||
\(907\) | 37.2800 | 1.23786 | 0.618931 | − | 0.785445i | \(-0.287566\pi\) | ||||
0.618931 | + | 0.785445i | \(0.287566\pi\) | |||||||
\(908\) | 77.7306 | 2.57958 | ||||||||
\(909\) | −6.64364 | −0.220356 | ||||||||
\(910\) | −15.9513 | −0.528779 | ||||||||
\(911\) | 52.0471 | 1.72440 | 0.862199 | − | 0.506570i | \(-0.169087\pi\) | ||||
0.862199 | + | 0.506570i | \(0.169087\pi\) | |||||||
\(912\) | −19.9787 | −0.661562 | ||||||||
\(913\) | 21.2439 | 0.703072 | ||||||||
\(914\) | −17.5861 | −0.581695 | ||||||||
\(915\) | 7.36921 | 0.243618 | ||||||||
\(916\) | −107.661 | −3.55722 | ||||||||
\(917\) | −42.9883 | −1.41960 | ||||||||
\(918\) | 2.45922 | 0.0811662 | ||||||||
\(919\) | −23.8943 | −0.788199 | −0.394099 | − | 0.919068i | \(-0.628943\pi\) | ||||
−0.394099 | + | 0.919068i | \(0.628943\pi\) | |||||||
\(920\) | 14.8577 | 0.489842 | ||||||||
\(921\) | 24.9877 | 0.823372 | ||||||||
\(922\) | 36.0618 | 1.18763 | ||||||||
\(923\) | 8.50058 | 0.279800 | ||||||||
\(924\) | −55.3494 | −1.82086 | ||||||||
\(925\) | −17.1770 | −0.564777 | ||||||||
\(926\) | 13.6840 | 0.449684 | ||||||||
\(927\) | 13.7755 | 0.452446 | ||||||||
\(928\) | 4.44162 | 0.145803 | ||||||||
\(929\) | −6.87302 | −0.225497 | −0.112748 | − | 0.993624i | \(-0.535965\pi\) | ||||
−0.112748 | + | 0.993624i | \(0.535965\pi\) | |||||||
\(930\) | 60.2684 | 1.97628 | ||||||||
\(931\) | −52.6259 | −1.72474 | ||||||||
\(932\) | −88.9158 | −2.91254 | ||||||||
\(933\) | −17.7126 | −0.579885 | ||||||||
\(934\) | 77.7872 | 2.54527 | ||||||||
\(935\) | 9.02647 | 0.295197 | ||||||||
\(936\) | −2.70442 | −0.0883968 | ||||||||
\(937\) | −25.3647 | −0.828627 | −0.414314 | − | 0.910134i | \(-0.635978\pi\) | ||||
−0.414314 | + | 0.910134i | \(0.635978\pi\) | |||||||
\(938\) | −30.2692 | −0.988326 | ||||||||
\(939\) | −11.4673 | −0.374221 | ||||||||
\(940\) | −105.568 | −3.44326 | ||||||||
\(941\) | −13.6757 | −0.445816 | −0.222908 | − | 0.974839i | \(-0.571555\pi\) | ||||
−0.222908 | + | 0.974839i | \(0.571555\pi\) | |||||||
\(942\) | −2.45922 | −0.0801256 | ||||||||
\(943\) | 7.51147 | 0.244607 | ||||||||
\(944\) | −57.7789 | −1.88054 | ||||||||
\(945\) | 12.0780 | 0.392898 | ||||||||
\(946\) | −14.5198 | −0.472081 | ||||||||
\(947\) | 31.5260 | 1.02446 | 0.512229 | − | 0.858849i | \(-0.328820\pi\) | ||||
0.512229 | + | 0.858849i | \(0.328820\pi\) | |||||||
\(948\) | 15.4706 | 0.502462 | ||||||||
\(949\) | 5.01804 | 0.162892 | ||||||||
\(950\) | 34.0571 | 1.10496 | ||||||||
\(951\) | −12.4978 | −0.405268 | ||||||||
\(952\) | 21.5408 | 0.698140 | ||||||||
\(953\) | −38.7891 | −1.25650 | −0.628251 | − | 0.778010i | \(-0.716229\pi\) | ||||
−0.628251 | + | 0.778010i | \(0.716229\pi\) | |||||||
\(954\) | −2.49744 | −0.0808576 | ||||||||
\(955\) | 13.9064 | 0.450002 | ||||||||
\(956\) | 27.4131 | 0.886602 | ||||||||
\(957\) | 29.8773 | 0.965796 | ||||||||
\(958\) | 101.402 | 3.27614 | ||||||||
\(959\) | −76.1607 | −2.45936 | ||||||||
\(960\) | −20.9195 | −0.675174 | ||||||||
\(961\) | 44.3308 | 1.43003 | ||||||||
\(962\) | 7.63089 | 0.246030 | ||||||||
\(963\) | 4.18323 | 0.134803 | ||||||||
\(964\) | −122.695 | −3.95175 | ||||||||
\(965\) | 48.5645 | 1.56335 | ||||||||
\(966\) | 10.9915 | 0.353646 | ||||||||
\(967\) | −40.2174 | −1.29330 | −0.646652 | − | 0.762785i | \(-0.723831\pi\) | ||||
−0.646652 | + | 0.762785i | \(0.723831\pi\) | |||||||
\(968\) | 3.93131 | 0.126357 | ||||||||
\(969\) | 4.65843 | 0.149650 | ||||||||
\(970\) | −97.2887 | −3.12375 | ||||||||
\(971\) | −22.2842 | −0.715135 | −0.357567 | − | 0.933887i | \(-0.616394\pi\) | ||||
−0.357567 | + | 0.933887i | \(0.616394\pi\) | |||||||
\(972\) | 4.04774 | 0.129831 | ||||||||
\(973\) | −15.7227 | −0.504047 | ||||||||
\(974\) | 56.7503 | 1.81840 | ||||||||
\(975\) | 1.59652 | 0.0511296 | ||||||||
\(976\) | 11.1929 | 0.358276 | ||||||||
\(977\) | −16.9512 | −0.542317 | −0.271159 | − | 0.962535i | \(-0.587407\pi\) | ||||
−0.271159 | + | 0.962535i | \(0.587407\pi\) | |||||||
\(978\) | −47.3952 | −1.51553 | ||||||||
\(979\) | 28.0310 | 0.895875 | ||||||||
\(980\) | 129.116 | 4.12446 | ||||||||
\(981\) | −6.51227 | −0.207921 | ||||||||
\(982\) | 104.409 | 3.33181 | ||||||||
\(983\) | −14.5140 | −0.462926 | −0.231463 | − | 0.972844i | \(-0.574351\pi\) | ||||
−0.231463 | + | 0.972844i | \(0.574351\pi\) | |||||||
\(984\) | 36.2014 | 1.15406 | ||||||||
\(985\) | 59.6210 | 1.89968 | ||||||||
\(986\) | −22.9840 | −0.731961 | ||||||||
\(987\) | −39.5097 | −1.25761 | ||||||||
\(988\) | −10.1264 | −0.322163 | ||||||||
\(989\) | 1.92986 | 0.0613660 | ||||||||
\(990\) | 22.1980 | 0.705500 | ||||||||
\(991\) | −37.5055 | −1.19140 | −0.595701 | − | 0.803206i | \(-0.703126\pi\) | ||||
−0.595701 | + | 0.803206i | \(0.703126\pi\) | |||||||
\(992\) | 4.12475 | 0.130961 | ||||||||
\(993\) | −13.3860 | −0.424792 | ||||||||
\(994\) | −166.507 | −5.28127 | ||||||||
\(995\) | −67.6990 | −2.14620 | ||||||||
\(996\) | −26.8990 | −0.852328 | ||||||||
\(997\) | −7.72403 | −0.244623 | −0.122311 | − | 0.992492i | \(-0.539031\pi\) | ||||
−0.122311 | + | 0.992492i | \(0.539031\pi\) | |||||||
\(998\) | 0.744862 | 0.0235782 | ||||||||
\(999\) | −5.77798 | −0.182807 |
(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 | 8007.2.a.e.1.5 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.e.1.5 | ✓ | 46 | 1.1 | even | 1 | trivial |