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: | \(48\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.26 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.188504 | 0.133293 | 0.0666463 | − | 0.997777i | \(-0.478770\pi\) | ||||
0.0666463 | + | 0.997777i | \(0.478770\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.96447 | −0.982233 | ||||||||
\(5\) | 3.42459 | 1.53152 | 0.765762 | − | 0.643123i | \(-0.222362\pi\) | ||||
0.765762 | + | 0.643123i | \(0.222362\pi\) | |||||||
\(6\) | −0.188504 | −0.0769565 | ||||||||
\(7\) | 1.78425 | 0.674382 | 0.337191 | − | 0.941436i | \(-0.390523\pi\) | ||||
0.337191 | + | 0.941436i | \(0.390523\pi\) | |||||||
\(8\) | −0.747318 | −0.264217 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.645550 | 0.204141 | ||||||||
\(11\) | 3.14859 | 0.949334 | 0.474667 | − | 0.880165i | \(-0.342568\pi\) | ||||
0.474667 | + | 0.880165i | \(0.342568\pi\) | |||||||
\(12\) | 1.96447 | 0.567093 | ||||||||
\(13\) | −5.35980 | −1.48654 | −0.743271 | − | 0.668991i | \(-0.766727\pi\) | ||||
−0.743271 | + | 0.668991i | \(0.766727\pi\) | |||||||
\(14\) | 0.336338 | 0.0898901 | ||||||||
\(15\) | −3.42459 | −0.884226 | ||||||||
\(16\) | 3.78806 | 0.947015 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0.188504 | 0.0444308 | ||||||||
\(19\) | −0.832236 | −0.190928 | −0.0954640 | − | 0.995433i | \(-0.530433\pi\) | ||||
−0.0954640 | + | 0.995433i | \(0.530433\pi\) | |||||||
\(20\) | −6.72750 | −1.50431 | ||||||||
\(21\) | −1.78425 | −0.389355 | ||||||||
\(22\) | 0.593521 | 0.126539 | ||||||||
\(23\) | −4.73322 | −0.986945 | −0.493472 | − | 0.869761i | \(-0.664273\pi\) | ||||
−0.493472 | + | 0.869761i | \(0.664273\pi\) | |||||||
\(24\) | 0.747318 | 0.152546 | ||||||||
\(25\) | 6.72784 | 1.34557 | ||||||||
\(26\) | −1.01034 | −0.198145 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −3.50509 | −0.662400 | ||||||||
\(29\) | 1.69187 | 0.314172 | 0.157086 | − | 0.987585i | \(-0.449790\pi\) | ||||
0.157086 | + | 0.987585i | \(0.449790\pi\) | |||||||
\(30\) | −0.645550 | −0.117861 | ||||||||
\(31\) | 5.10521 | 0.916923 | 0.458462 | − | 0.888714i | \(-0.348401\pi\) | ||||
0.458462 | + | 0.888714i | \(0.348401\pi\) | |||||||
\(32\) | 2.20870 | 0.390447 | ||||||||
\(33\) | −3.14859 | −0.548098 | ||||||||
\(34\) | −0.188504 | −0.0323282 | ||||||||
\(35\) | 6.11032 | 1.03283 | ||||||||
\(36\) | −1.96447 | −0.327411 | ||||||||
\(37\) | −3.43992 | −0.565519 | −0.282760 | − | 0.959191i | \(-0.591250\pi\) | ||||
−0.282760 | + | 0.959191i | \(0.591250\pi\) | |||||||
\(38\) | −0.156880 | −0.0254493 | ||||||||
\(39\) | 5.35980 | 0.858255 | ||||||||
\(40\) | −2.55926 | −0.404655 | ||||||||
\(41\) | −6.02983 | −0.941702 | −0.470851 | − | 0.882213i | \(-0.656053\pi\) | ||||
−0.470851 | + | 0.882213i | \(0.656053\pi\) | |||||||
\(42\) | −0.336338 | −0.0518981 | ||||||||
\(43\) | −10.8902 | −1.66074 | −0.830372 | − | 0.557209i | \(-0.811872\pi\) | ||||
−0.830372 | + | 0.557209i | \(0.811872\pi\) | |||||||
\(44\) | −6.18529 | −0.932468 | ||||||||
\(45\) | 3.42459 | 0.510508 | ||||||||
\(46\) | −0.892232 | −0.131552 | ||||||||
\(47\) | −4.41038 | −0.643320 | −0.321660 | − | 0.946855i | \(-0.604241\pi\) | ||||
−0.321660 | + | 0.946855i | \(0.604241\pi\) | |||||||
\(48\) | −3.78806 | −0.546759 | ||||||||
\(49\) | −3.81646 | −0.545209 | ||||||||
\(50\) | 1.26823 | 0.179354 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 10.5291 | 1.46013 | ||||||||
\(53\) | 8.72542 | 1.19853 | 0.599264 | − | 0.800551i | \(-0.295460\pi\) | ||||
0.599264 | + | 0.800551i | \(0.295460\pi\) | |||||||
\(54\) | −0.188504 | −0.0256522 | ||||||||
\(55\) | 10.7826 | 1.45393 | ||||||||
\(56\) | −1.33340 | −0.178183 | ||||||||
\(57\) | 0.832236 | 0.110232 | ||||||||
\(58\) | 0.318924 | 0.0418768 | ||||||||
\(59\) | 4.56892 | 0.594823 | 0.297411 | − | 0.954749i | \(-0.403877\pi\) | ||||
0.297411 | + | 0.954749i | \(0.403877\pi\) | |||||||
\(60\) | 6.72750 | 0.868516 | ||||||||
\(61\) | −1.80853 | −0.231558 | −0.115779 | − | 0.993275i | \(-0.536936\pi\) | ||||
−0.115779 | + | 0.993275i | \(0.536936\pi\) | |||||||
\(62\) | 0.962354 | 0.122219 | ||||||||
\(63\) | 1.78425 | 0.224794 | ||||||||
\(64\) | −7.15977 | −0.894971 | ||||||||
\(65\) | −18.3551 | −2.27668 | ||||||||
\(66\) | −0.593521 | −0.0730574 | ||||||||
\(67\) | −12.6074 | −1.54024 | −0.770119 | − | 0.637900i | \(-0.779803\pi\) | ||||
−0.770119 | + | 0.637900i | \(0.779803\pi\) | |||||||
\(68\) | 1.96447 | 0.238227 | ||||||||
\(69\) | 4.73322 | 0.569813 | ||||||||
\(70\) | 1.15182 | 0.137669 | ||||||||
\(71\) | −3.53152 | −0.419114 | −0.209557 | − | 0.977796i | \(-0.567202\pi\) | ||||
−0.209557 | + | 0.977796i | \(0.567202\pi\) | |||||||
\(72\) | −0.747318 | −0.0880723 | ||||||||
\(73\) | −9.39859 | −1.10002 | −0.550011 | − | 0.835158i | \(-0.685376\pi\) | ||||
−0.550011 | + | 0.835158i | \(0.685376\pi\) | |||||||
\(74\) | −0.648439 | −0.0753795 | ||||||||
\(75\) | −6.72784 | −0.776865 | ||||||||
\(76\) | 1.63490 | 0.187536 | ||||||||
\(77\) | 5.61786 | 0.640214 | ||||||||
\(78\) | 1.01034 | 0.114399 | ||||||||
\(79\) | −6.65430 | −0.748667 | −0.374334 | − | 0.927294i | \(-0.622129\pi\) | ||||
−0.374334 | + | 0.927294i | \(0.622129\pi\) | |||||||
\(80\) | 12.9726 | 1.45038 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.13665 | −0.125522 | ||||||||
\(83\) | −12.3936 | −1.36037 | −0.680186 | − | 0.733040i | \(-0.738101\pi\) | ||||
−0.680186 | + | 0.733040i | \(0.738101\pi\) | |||||||
\(84\) | 3.50509 | 0.382437 | ||||||||
\(85\) | −3.42459 | −0.371449 | ||||||||
\(86\) | −2.05285 | −0.221365 | ||||||||
\(87\) | −1.69187 | −0.181387 | ||||||||
\(88\) | −2.35300 | −0.250830 | ||||||||
\(89\) | −11.5838 | −1.22788 | −0.613941 | − | 0.789352i | \(-0.710417\pi\) | ||||
−0.613941 | + | 0.789352i | \(0.710417\pi\) | |||||||
\(90\) | 0.645550 | 0.0680469 | ||||||||
\(91\) | −9.56321 | −1.00250 | ||||||||
\(92\) | 9.29825 | 0.969410 | ||||||||
\(93\) | −5.10521 | −0.529386 | ||||||||
\(94\) | −0.831374 | −0.0857497 | ||||||||
\(95\) | −2.85007 | −0.292411 | ||||||||
\(96\) | −2.20870 | −0.225425 | ||||||||
\(97\) | 6.57626 | 0.667718 | 0.333859 | − | 0.942623i | \(-0.391649\pi\) | ||||
0.333859 | + | 0.942623i | \(0.391649\pi\) | |||||||
\(98\) | −0.719419 | −0.0726723 | ||||||||
\(99\) | 3.14859 | 0.316445 | ||||||||
\(100\) | −13.2166 | −1.32166 | ||||||||
\(101\) | 11.9878 | 1.19283 | 0.596415 | − | 0.802676i | \(-0.296591\pi\) | ||||
0.596415 | + | 0.802676i | \(0.296591\pi\) | |||||||
\(102\) | 0.188504 | 0.0186647 | ||||||||
\(103\) | 19.0602 | 1.87806 | 0.939028 | − | 0.343841i | \(-0.111728\pi\) | ||||
0.939028 | + | 0.343841i | \(0.111728\pi\) | |||||||
\(104\) | 4.00548 | 0.392769 | ||||||||
\(105\) | −6.11032 | −0.596306 | ||||||||
\(106\) | 1.64478 | 0.159755 | ||||||||
\(107\) | −6.96116 | −0.672961 | −0.336481 | − | 0.941690i | \(-0.609237\pi\) | ||||
−0.336481 | + | 0.941690i | \(0.609237\pi\) | |||||||
\(108\) | 1.96447 | 0.189031 | ||||||||
\(109\) | 1.39644 | 0.133755 | 0.0668775 | − | 0.997761i | \(-0.478696\pi\) | ||||
0.0668775 | + | 0.997761i | \(0.478696\pi\) | |||||||
\(110\) | 2.03257 | 0.193798 | ||||||||
\(111\) | 3.43992 | 0.326503 | ||||||||
\(112\) | 6.75884 | 0.638650 | ||||||||
\(113\) | −7.84851 | −0.738326 | −0.369163 | − | 0.929365i | \(-0.620356\pi\) | ||||
−0.369163 | + | 0.929365i | \(0.620356\pi\) | |||||||
\(114\) | 0.156880 | 0.0146932 | ||||||||
\(115\) | −16.2094 | −1.51153 | ||||||||
\(116\) | −3.32362 | −0.308590 | ||||||||
\(117\) | −5.35980 | −0.495514 | ||||||||
\(118\) | 0.861260 | 0.0792854 | ||||||||
\(119\) | −1.78425 | −0.163562 | ||||||||
\(120\) | 2.55926 | 0.233628 | ||||||||
\(121\) | −1.08641 | −0.0987643 | ||||||||
\(122\) | −0.340915 | −0.0308649 | ||||||||
\(123\) | 6.02983 | 0.543692 | ||||||||
\(124\) | −10.0290 | −0.900633 | ||||||||
\(125\) | 5.91716 | 0.529247 | ||||||||
\(126\) | 0.336338 | 0.0299634 | ||||||||
\(127\) | 16.7200 | 1.48366 | 0.741830 | − | 0.670588i | \(-0.233958\pi\) | ||||
0.741830 | + | 0.670588i | \(0.233958\pi\) | |||||||
\(128\) | −5.76705 | −0.509740 | ||||||||
\(129\) | 10.8902 | 0.958832 | ||||||||
\(130\) | −3.46002 | −0.303464 | ||||||||
\(131\) | −10.0844 | −0.881081 | −0.440540 | − | 0.897733i | \(-0.645213\pi\) | ||||
−0.440540 | + | 0.897733i | \(0.645213\pi\) | |||||||
\(132\) | 6.18529 | 0.538360 | ||||||||
\(133\) | −1.48492 | −0.128758 | ||||||||
\(134\) | −2.37655 | −0.205302 | ||||||||
\(135\) | −3.42459 | −0.294742 | ||||||||
\(136\) | 0.747318 | 0.0640820 | ||||||||
\(137\) | 9.89827 | 0.845666 | 0.422833 | − | 0.906208i | \(-0.361036\pi\) | ||||
0.422833 | + | 0.906208i | \(0.361036\pi\) | |||||||
\(138\) | 0.892232 | 0.0759518 | ||||||||
\(139\) | 10.0127 | 0.849266 | 0.424633 | − | 0.905365i | \(-0.360403\pi\) | ||||
0.424633 | + | 0.905365i | \(0.360403\pi\) | |||||||
\(140\) | −12.0035 | −1.01448 | ||||||||
\(141\) | 4.41038 | 0.371421 | ||||||||
\(142\) | −0.665706 | −0.0558648 | ||||||||
\(143\) | −16.8758 | −1.41122 | ||||||||
\(144\) | 3.78806 | 0.315672 | ||||||||
\(145\) | 5.79396 | 0.481162 | ||||||||
\(146\) | −1.77167 | −0.146625 | ||||||||
\(147\) | 3.81646 | 0.314776 | ||||||||
\(148\) | 6.75760 | 0.555472 | ||||||||
\(149\) | −21.4950 | −1.76094 | −0.880471 | − | 0.474100i | \(-0.842774\pi\) | ||||
−0.880471 | + | 0.474100i | \(0.842774\pi\) | |||||||
\(150\) | −1.26823 | −0.103550 | ||||||||
\(151\) | 6.89040 | 0.560733 | 0.280366 | − | 0.959893i | \(-0.409544\pi\) | ||||
0.280366 | + | 0.959893i | \(0.409544\pi\) | |||||||
\(152\) | 0.621945 | 0.0504464 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 1.05899 | 0.0853357 | ||||||||
\(155\) | 17.4833 | 1.40429 | ||||||||
\(156\) | −10.5291 | −0.843007 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | −1.25436 | −0.0997917 | ||||||||
\(159\) | −8.72542 | −0.691971 | ||||||||
\(160\) | 7.56390 | 0.597979 | ||||||||
\(161\) | −8.44524 | −0.665578 | ||||||||
\(162\) | 0.188504 | 0.0148103 | ||||||||
\(163\) | 13.3271 | 1.04386 | 0.521931 | − | 0.852988i | \(-0.325212\pi\) | ||||
0.521931 | + | 0.852988i | \(0.325212\pi\) | |||||||
\(164\) | 11.8454 | 0.924971 | ||||||||
\(165\) | −10.7826 | −0.839426 | ||||||||
\(166\) | −2.33624 | −0.181327 | ||||||||
\(167\) | −21.9521 | −1.69871 | −0.849353 | − | 0.527825i | \(-0.823008\pi\) | ||||
−0.849353 | + | 0.527825i | \(0.823008\pi\) | |||||||
\(168\) | 1.33340 | 0.102874 | ||||||||
\(169\) | 15.7275 | 1.20981 | ||||||||
\(170\) | −0.645550 | −0.0495114 | ||||||||
\(171\) | −0.832236 | −0.0636427 | ||||||||
\(172\) | 21.3935 | 1.63124 | ||||||||
\(173\) | −9.46456 | −0.719577 | −0.359789 | − | 0.933034i | \(-0.617151\pi\) | ||||
−0.359789 | + | 0.933034i | \(0.617151\pi\) | |||||||
\(174\) | −0.318924 | −0.0241776 | ||||||||
\(175\) | 12.0041 | 0.907427 | ||||||||
\(176\) | 11.9270 | 0.899034 | ||||||||
\(177\) | −4.56892 | −0.343421 | ||||||||
\(178\) | −2.18360 | −0.163667 | ||||||||
\(179\) | −6.28826 | −0.470007 | −0.235003 | − | 0.971995i | \(-0.575510\pi\) | ||||
−0.235003 | + | 0.971995i | \(0.575510\pi\) | |||||||
\(180\) | −6.72750 | −0.501438 | ||||||||
\(181\) | 22.2200 | 1.65160 | 0.825799 | − | 0.563964i | \(-0.190724\pi\) | ||||
0.825799 | + | 0.563964i | \(0.190724\pi\) | |||||||
\(182\) | −1.80270 | −0.133625 | ||||||||
\(183\) | 1.80853 | 0.133690 | ||||||||
\(184\) | 3.53722 | 0.260767 | ||||||||
\(185\) | −11.7803 | −0.866107 | ||||||||
\(186\) | −0.962354 | −0.0705632 | ||||||||
\(187\) | −3.14859 | −0.230247 | ||||||||
\(188\) | 8.66404 | 0.631890 | ||||||||
\(189\) | −1.78425 | −0.129785 | ||||||||
\(190\) | −0.537250 | −0.0389762 | ||||||||
\(191\) | 13.2135 | 0.956096 | 0.478048 | − | 0.878334i | \(-0.341345\pi\) | ||||
0.478048 | + | 0.878334i | \(0.341345\pi\) | |||||||
\(192\) | 7.15977 | 0.516712 | ||||||||
\(193\) | −16.1579 | −1.16307 | −0.581536 | − | 0.813521i | \(-0.697548\pi\) | ||||
−0.581536 | + | 0.813521i | \(0.697548\pi\) | |||||||
\(194\) | 1.23965 | 0.0890018 | ||||||||
\(195\) | 18.3551 | 1.31444 | ||||||||
\(196\) | 7.49731 | 0.535522 | ||||||||
\(197\) | 22.5229 | 1.60469 | 0.802345 | − | 0.596861i | \(-0.203586\pi\) | ||||
0.802345 | + | 0.596861i | \(0.203586\pi\) | |||||||
\(198\) | 0.593521 | 0.0421797 | ||||||||
\(199\) | −14.3787 | −1.01928 | −0.509641 | − | 0.860387i | \(-0.670222\pi\) | ||||
−0.509641 | + | 0.860387i | \(0.670222\pi\) | |||||||
\(200\) | −5.02784 | −0.355522 | ||||||||
\(201\) | 12.6074 | 0.889257 | ||||||||
\(202\) | 2.25975 | 0.158995 | ||||||||
\(203\) | 3.01871 | 0.211872 | ||||||||
\(204\) | −1.96447 | −0.137540 | ||||||||
\(205\) | −20.6497 | −1.44224 | ||||||||
\(206\) | 3.59292 | 0.250331 | ||||||||
\(207\) | −4.73322 | −0.328982 | ||||||||
\(208\) | −20.3032 | −1.40778 | ||||||||
\(209\) | −2.62037 | −0.181255 | ||||||||
\(210\) | −1.15182 | −0.0794832 | ||||||||
\(211\) | 17.9288 | 1.23427 | 0.617136 | − | 0.786856i | \(-0.288293\pi\) | ||||
0.617136 | + | 0.786856i | \(0.288293\pi\) | |||||||
\(212\) | −17.1408 | −1.17723 | ||||||||
\(213\) | 3.53152 | 0.241976 | ||||||||
\(214\) | −1.31221 | −0.0897007 | ||||||||
\(215\) | −37.2946 | −2.54347 | ||||||||
\(216\) | 0.747318 | 0.0508486 | ||||||||
\(217\) | 9.10896 | 0.618357 | ||||||||
\(218\) | 0.263235 | 0.0178285 | ||||||||
\(219\) | 9.39859 | 0.635098 | ||||||||
\(220\) | −21.1821 | −1.42810 | ||||||||
\(221\) | 5.35980 | 0.360539 | ||||||||
\(222\) | 0.648439 | 0.0435204 | ||||||||
\(223\) | −23.8723 | −1.59861 | −0.799304 | − | 0.600926i | \(-0.794798\pi\) | ||||
−0.799304 | + | 0.600926i | \(0.794798\pi\) | |||||||
\(224\) | 3.94087 | 0.263310 | ||||||||
\(225\) | 6.72784 | 0.448523 | ||||||||
\(226\) | −1.47948 | −0.0984133 | ||||||||
\(227\) | 1.00897 | 0.0669675 | 0.0334837 | − | 0.999439i | \(-0.489340\pi\) | ||||
0.0334837 | + | 0.999439i | \(0.489340\pi\) | |||||||
\(228\) | −1.63490 | −0.108274 | ||||||||
\(229\) | −22.1200 | −1.46173 | −0.730866 | − | 0.682521i | \(-0.760884\pi\) | ||||
−0.730866 | + | 0.682521i | \(0.760884\pi\) | |||||||
\(230\) | −3.05553 | −0.201476 | ||||||||
\(231\) | −5.61786 | −0.369628 | ||||||||
\(232\) | −1.26436 | −0.0830095 | ||||||||
\(233\) | 24.2251 | 1.58704 | 0.793521 | − | 0.608543i | \(-0.208246\pi\) | ||||
0.793521 | + | 0.608543i | \(0.208246\pi\) | |||||||
\(234\) | −1.01034 | −0.0660483 | ||||||||
\(235\) | −15.1038 | −0.985260 | ||||||||
\(236\) | −8.97549 | −0.584255 | ||||||||
\(237\) | 6.65430 | 0.432243 | ||||||||
\(238\) | −0.336338 | −0.0218015 | ||||||||
\(239\) | 1.48328 | 0.0959451 | 0.0479726 | − | 0.998849i | \(-0.484724\pi\) | ||||
0.0479726 | + | 0.998849i | \(0.484724\pi\) | |||||||
\(240\) | −12.9726 | −0.837376 | ||||||||
\(241\) | 24.7453 | 1.59398 | 0.796992 | − | 0.603989i | \(-0.206423\pi\) | ||||
0.796992 | + | 0.603989i | \(0.206423\pi\) | |||||||
\(242\) | −0.204792 | −0.0131645 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 3.55279 | 0.227444 | ||||||||
\(245\) | −13.0698 | −0.835001 | ||||||||
\(246\) | 1.13665 | 0.0724701 | ||||||||
\(247\) | 4.46062 | 0.283823 | ||||||||
\(248\) | −3.81522 | −0.242267 | ||||||||
\(249\) | 12.3936 | 0.785411 | ||||||||
\(250\) | 1.11541 | 0.0705447 | ||||||||
\(251\) | −0.828587 | −0.0523000 | −0.0261500 | − | 0.999658i | \(-0.508325\pi\) | ||||
−0.0261500 | + | 0.999658i | \(0.508325\pi\) | |||||||
\(252\) | −3.50509 | −0.220800 | ||||||||
\(253\) | −14.9030 | −0.936941 | ||||||||
\(254\) | 3.15179 | 0.197761 | ||||||||
\(255\) | 3.42459 | 0.214456 | ||||||||
\(256\) | 13.2324 | 0.827027 | ||||||||
\(257\) | 1.47420 | 0.0919581 | 0.0459790 | − | 0.998942i | \(-0.485359\pi\) | ||||
0.0459790 | + | 0.998942i | \(0.485359\pi\) | |||||||
\(258\) | 2.05285 | 0.127805 | ||||||||
\(259\) | −6.13767 | −0.381376 | ||||||||
\(260\) | 36.0581 | 2.23623 | ||||||||
\(261\) | 1.69187 | 0.104724 | ||||||||
\(262\) | −1.90096 | −0.117441 | ||||||||
\(263\) | −10.6460 | −0.656458 | −0.328229 | − | 0.944598i | \(-0.606452\pi\) | ||||
−0.328229 | + | 0.944598i | \(0.606452\pi\) | |||||||
\(264\) | 2.35300 | 0.144817 | ||||||||
\(265\) | 29.8810 | 1.83558 | ||||||||
\(266\) | −0.279913 | −0.0171625 | ||||||||
\(267\) | 11.5838 | 0.708918 | ||||||||
\(268\) | 24.7668 | 1.51287 | ||||||||
\(269\) | 13.6965 | 0.835093 | 0.417547 | − | 0.908656i | \(-0.362890\pi\) | ||||
0.417547 | + | 0.908656i | \(0.362890\pi\) | |||||||
\(270\) | −0.645550 | −0.0392869 | ||||||||
\(271\) | 4.94456 | 0.300361 | 0.150180 | − | 0.988659i | \(-0.452015\pi\) | ||||
0.150180 | + | 0.988659i | \(0.452015\pi\) | |||||||
\(272\) | −3.78806 | −0.229685 | ||||||||
\(273\) | 9.56321 | 0.578792 | ||||||||
\(274\) | 1.86586 | 0.112721 | ||||||||
\(275\) | 21.1832 | 1.27739 | ||||||||
\(276\) | −9.29825 | −0.559689 | ||||||||
\(277\) | −7.90270 | −0.474827 | −0.237414 | − | 0.971409i | \(-0.576300\pi\) | ||||
−0.237414 | + | 0.971409i | \(0.576300\pi\) | |||||||
\(278\) | 1.88744 | 0.113201 | ||||||||
\(279\) | 5.10521 | 0.305641 | ||||||||
\(280\) | −4.56635 | −0.272892 | ||||||||
\(281\) | −18.4923 | −1.10316 | −0.551579 | − | 0.834122i | \(-0.685975\pi\) | ||||
−0.551579 | + | 0.834122i | \(0.685975\pi\) | |||||||
\(282\) | 0.831374 | 0.0495076 | ||||||||
\(283\) | 31.6209 | 1.87967 | 0.939834 | − | 0.341632i | \(-0.110980\pi\) | ||||
0.939834 | + | 0.341632i | \(0.110980\pi\) | |||||||
\(284\) | 6.93755 | 0.411668 | ||||||||
\(285\) | 2.85007 | 0.168824 | ||||||||
\(286\) | −3.18116 | −0.188106 | ||||||||
\(287\) | −10.7587 | −0.635067 | ||||||||
\(288\) | 2.20870 | 0.130149 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 1.09219 | 0.0641353 | ||||||||
\(291\) | −6.57626 | −0.385507 | ||||||||
\(292\) | 18.4632 | 1.08048 | ||||||||
\(293\) | −24.1591 | −1.41139 | −0.705694 | − | 0.708517i | \(-0.749365\pi\) | ||||
−0.705694 | + | 0.708517i | \(0.749365\pi\) | |||||||
\(294\) | 0.719419 | 0.0419573 | ||||||||
\(295\) | 15.6467 | 0.910986 | ||||||||
\(296\) | 2.57071 | 0.149420 | ||||||||
\(297\) | −3.14859 | −0.182699 | ||||||||
\(298\) | −4.05190 | −0.234720 | ||||||||
\(299\) | 25.3691 | 1.46713 | ||||||||
\(300\) | 13.2166 | 0.763062 | ||||||||
\(301\) | −19.4309 | −1.11998 | ||||||||
\(302\) | 1.29887 | 0.0747415 | ||||||||
\(303\) | −11.9878 | −0.688681 | ||||||||
\(304\) | −3.15256 | −0.180812 | ||||||||
\(305\) | −6.19347 | −0.354637 | ||||||||
\(306\) | −0.188504 | −0.0107761 | ||||||||
\(307\) | −29.0744 | −1.65937 | −0.829683 | − | 0.558235i | \(-0.811479\pi\) | ||||
−0.829683 | + | 0.558235i | \(0.811479\pi\) | |||||||
\(308\) | −11.0361 | −0.628839 | ||||||||
\(309\) | −19.0602 | −1.08430 | ||||||||
\(310\) | 3.29567 | 0.187182 | ||||||||
\(311\) | −2.85818 | −0.162072 | −0.0810361 | − | 0.996711i | \(-0.525823\pi\) | ||||
−0.0810361 | + | 0.996711i | \(0.525823\pi\) | |||||||
\(312\) | −4.00548 | −0.226765 | ||||||||
\(313\) | −14.6211 | −0.826431 | −0.413215 | − | 0.910633i | \(-0.635594\pi\) | ||||
−0.413215 | + | 0.910633i | \(0.635594\pi\) | |||||||
\(314\) | −0.188504 | −0.0106379 | ||||||||
\(315\) | 6.11032 | 0.344278 | ||||||||
\(316\) | 13.0721 | 0.735366 | ||||||||
\(317\) | −26.4706 | −1.48674 | −0.743368 | − | 0.668883i | \(-0.766773\pi\) | ||||
−0.743368 | + | 0.668883i | \(0.766773\pi\) | |||||||
\(318\) | −1.64478 | −0.0922345 | ||||||||
\(319\) | 5.32699 | 0.298254 | ||||||||
\(320\) | −24.5193 | −1.37067 | ||||||||
\(321\) | 6.96116 | 0.388534 | ||||||||
\(322\) | −1.59196 | −0.0887166 | ||||||||
\(323\) | 0.832236 | 0.0463069 | ||||||||
\(324\) | −1.96447 | −0.109137 | ||||||||
\(325\) | −36.0599 | −2.00024 | ||||||||
\(326\) | 2.51222 | 0.139139 | ||||||||
\(327\) | −1.39644 | −0.0772234 | ||||||||
\(328\) | 4.50620 | 0.248814 | ||||||||
\(329\) | −7.86920 | −0.433843 | ||||||||
\(330\) | −2.03257 | −0.111889 | ||||||||
\(331\) | 23.1563 | 1.27278 | 0.636391 | − | 0.771366i | \(-0.280426\pi\) | ||||
0.636391 | + | 0.771366i | \(0.280426\pi\) | |||||||
\(332\) | 24.3468 | 1.33620 | ||||||||
\(333\) | −3.43992 | −0.188506 | ||||||||
\(334\) | −4.13807 | −0.226425 | ||||||||
\(335\) | −43.1752 | −2.35891 | ||||||||
\(336\) | −6.75884 | −0.368725 | ||||||||
\(337\) | 24.3828 | 1.32822 | 0.664109 | − | 0.747636i | \(-0.268811\pi\) | ||||
0.664109 | + | 0.747636i | \(0.268811\pi\) | |||||||
\(338\) | 2.96469 | 0.161258 | ||||||||
\(339\) | 7.84851 | 0.426273 | ||||||||
\(340\) | 6.72750 | 0.364850 | ||||||||
\(341\) | 16.0742 | 0.870467 | ||||||||
\(342\) | −0.156880 | −0.00848310 | ||||||||
\(343\) | −19.2992 | −1.04206 | ||||||||
\(344\) | 8.13847 | 0.438797 | ||||||||
\(345\) | 16.2094 | 0.872683 | ||||||||
\(346\) | −1.78411 | −0.0959143 | ||||||||
\(347\) | −17.2409 | −0.925541 | −0.462770 | − | 0.886478i | \(-0.653145\pi\) | ||||
−0.462770 | + | 0.886478i | \(0.653145\pi\) | |||||||
\(348\) | 3.32362 | 0.178165 | ||||||||
\(349\) | 28.6472 | 1.53345 | 0.766725 | − | 0.641976i | \(-0.221885\pi\) | ||||
0.766725 | + | 0.641976i | \(0.221885\pi\) | |||||||
\(350\) | 2.26283 | 0.120953 | ||||||||
\(351\) | 5.35980 | 0.286085 | ||||||||
\(352\) | 6.95428 | 0.370665 | ||||||||
\(353\) | −2.04573 | −0.108883 | −0.0544416 | − | 0.998517i | \(-0.517338\pi\) | ||||
−0.0544416 | + | 0.998517i | \(0.517338\pi\) | |||||||
\(354\) | −0.861260 | −0.0457755 | ||||||||
\(355\) | −12.0940 | −0.641884 | ||||||||
\(356\) | 22.7560 | 1.20607 | ||||||||
\(357\) | 1.78425 | 0.0944324 | ||||||||
\(358\) | −1.18536 | −0.0626484 | ||||||||
\(359\) | 23.6854 | 1.25007 | 0.625033 | − | 0.780598i | \(-0.285085\pi\) | ||||
0.625033 | + | 0.780598i | \(0.285085\pi\) | |||||||
\(360\) | −2.55926 | −0.134885 | ||||||||
\(361\) | −18.3074 | −0.963546 | ||||||||
\(362\) | 4.18856 | 0.220146 | ||||||||
\(363\) | 1.08641 | 0.0570216 | ||||||||
\(364\) | 18.7866 | 0.984686 | ||||||||
\(365\) | −32.1863 | −1.68471 | ||||||||
\(366\) | 0.340915 | 0.0178199 | ||||||||
\(367\) | −2.56356 | −0.133817 | −0.0669084 | − | 0.997759i | \(-0.521314\pi\) | ||||
−0.0669084 | + | 0.997759i | \(0.521314\pi\) | |||||||
\(368\) | −17.9297 | −0.934652 | ||||||||
\(369\) | −6.02983 | −0.313901 | ||||||||
\(370\) | −2.22064 | −0.115446 | ||||||||
\(371\) | 15.5683 | 0.808266 | ||||||||
\(372\) | 10.0290 | 0.519980 | ||||||||
\(373\) | −35.0637 | −1.81553 | −0.907764 | − | 0.419482i | \(-0.862212\pi\) | ||||
−0.907764 | + | 0.419482i | \(0.862212\pi\) | |||||||
\(374\) | −0.593521 | −0.0306903 | ||||||||
\(375\) | −5.91716 | −0.305561 | ||||||||
\(376\) | 3.29595 | 0.169976 | ||||||||
\(377\) | −9.06808 | −0.467030 | ||||||||
\(378\) | −0.336338 | −0.0172994 | ||||||||
\(379\) | −11.2334 | −0.577022 | −0.288511 | − | 0.957477i | \(-0.593160\pi\) | ||||
−0.288511 | + | 0.957477i | \(0.593160\pi\) | |||||||
\(380\) | 5.59887 | 0.287216 | ||||||||
\(381\) | −16.7200 | −0.856592 | ||||||||
\(382\) | 2.49080 | 0.127440 | ||||||||
\(383\) | −14.7874 | −0.755603 | −0.377801 | − | 0.925887i | \(-0.623320\pi\) | ||||
−0.377801 | + | 0.925887i | \(0.623320\pi\) | |||||||
\(384\) | 5.76705 | 0.294298 | ||||||||
\(385\) | 19.2389 | 0.980504 | ||||||||
\(386\) | −3.04583 | −0.155029 | ||||||||
\(387\) | −10.8902 | −0.553582 | ||||||||
\(388\) | −12.9188 | −0.655855 | ||||||||
\(389\) | −36.9250 | −1.87217 | −0.936086 | − | 0.351772i | \(-0.885579\pi\) | ||||
−0.936086 | + | 0.351772i | \(0.885579\pi\) | |||||||
\(390\) | 3.46002 | 0.175205 | ||||||||
\(391\) | 4.73322 | 0.239369 | ||||||||
\(392\) | 2.85211 | 0.144053 | ||||||||
\(393\) | 10.0844 | 0.508692 | ||||||||
\(394\) | 4.24566 | 0.213893 | ||||||||
\(395\) | −22.7883 | −1.14660 | ||||||||
\(396\) | −6.18529 | −0.310823 | ||||||||
\(397\) | 4.10526 | 0.206037 | 0.103018 | − | 0.994679i | \(-0.467150\pi\) | ||||
0.103018 | + | 0.994679i | \(0.467150\pi\) | |||||||
\(398\) | −2.71045 | −0.135863 | ||||||||
\(399\) | 1.48492 | 0.0743387 | ||||||||
\(400\) | 25.4855 | 1.27427 | ||||||||
\(401\) | −24.6512 | −1.23102 | −0.615510 | − | 0.788129i | \(-0.711050\pi\) | ||||
−0.615510 | + | 0.788129i | \(0.711050\pi\) | |||||||
\(402\) | 2.37655 | 0.118531 | ||||||||
\(403\) | −27.3629 | −1.36304 | ||||||||
\(404\) | −23.5496 | −1.17164 | ||||||||
\(405\) | 3.42459 | 0.170169 | ||||||||
\(406\) | 0.569039 | 0.0282409 | ||||||||
\(407\) | −10.8309 | −0.536867 | ||||||||
\(408\) | −0.747318 | −0.0369978 | ||||||||
\(409\) | −4.01280 | −0.198420 | −0.0992102 | − | 0.995066i | \(-0.531632\pi\) | ||||
−0.0992102 | + | 0.995066i | \(0.531632\pi\) | |||||||
\(410\) | −3.89256 | −0.192240 | ||||||||
\(411\) | −9.89827 | −0.488245 | ||||||||
\(412\) | −37.4431 | −1.84469 | ||||||||
\(413\) | 8.15208 | 0.401138 | ||||||||
\(414\) | −0.892232 | −0.0438508 | ||||||||
\(415\) | −42.4430 | −2.08344 | ||||||||
\(416\) | −11.8382 | −0.580415 | ||||||||
\(417\) | −10.0127 | −0.490324 | ||||||||
\(418\) | −0.493950 | −0.0241599 | ||||||||
\(419\) | −4.91641 | −0.240182 | −0.120091 | − | 0.992763i | \(-0.538319\pi\) | ||||
−0.120091 | + | 0.992763i | \(0.538319\pi\) | |||||||
\(420\) | 12.0035 | 0.585712 | ||||||||
\(421\) | −31.4007 | −1.53038 | −0.765189 | − | 0.643806i | \(-0.777354\pi\) | ||||
−0.765189 | + | 0.643806i | \(0.777354\pi\) | |||||||
\(422\) | 3.37966 | 0.164519 | ||||||||
\(423\) | −4.41038 | −0.214440 | ||||||||
\(424\) | −6.52066 | −0.316671 | ||||||||
\(425\) | −6.72784 | −0.326348 | ||||||||
\(426\) | 0.665706 | 0.0322536 | ||||||||
\(427\) | −3.22686 | −0.156159 | ||||||||
\(428\) | 13.6750 | 0.661005 | ||||||||
\(429\) | 16.8758 | 0.814771 | ||||||||
\(430\) | −7.03019 | −0.339026 | ||||||||
\(431\) | 23.4265 | 1.12842 | 0.564208 | − | 0.825633i | \(-0.309182\pi\) | ||||
0.564208 | + | 0.825633i | \(0.309182\pi\) | |||||||
\(432\) | −3.78806 | −0.182253 | ||||||||
\(433\) | −25.6687 | −1.23356 | −0.616781 | − | 0.787135i | \(-0.711563\pi\) | ||||
−0.616781 | + | 0.787135i | \(0.711563\pi\) | |||||||
\(434\) | 1.71708 | 0.0824223 | ||||||||
\(435\) | −5.79396 | −0.277799 | ||||||||
\(436\) | −2.74326 | −0.131378 | ||||||||
\(437\) | 3.93916 | 0.188435 | ||||||||
\(438\) | 1.77167 | 0.0846538 | ||||||||
\(439\) | −22.5823 | −1.07779 | −0.538897 | − | 0.842372i | \(-0.681159\pi\) | ||||
−0.538897 | + | 0.842372i | \(0.681159\pi\) | |||||||
\(440\) | −8.05805 | −0.384153 | ||||||||
\(441\) | −3.81646 | −0.181736 | ||||||||
\(442\) | 1.01034 | 0.0480572 | ||||||||
\(443\) | −19.7356 | −0.937668 | −0.468834 | − | 0.883286i | \(-0.655326\pi\) | ||||
−0.468834 | + | 0.883286i | \(0.655326\pi\) | |||||||
\(444\) | −6.75760 | −0.320702 | ||||||||
\(445\) | −39.6699 | −1.88053 | ||||||||
\(446\) | −4.50003 | −0.213083 | ||||||||
\(447\) | 21.4950 | 1.01668 | ||||||||
\(448\) | −12.7748 | −0.603553 | ||||||||
\(449\) | 33.9785 | 1.60354 | 0.801772 | − | 0.597630i | \(-0.203891\pi\) | ||||
0.801772 | + | 0.597630i | \(0.203891\pi\) | |||||||
\(450\) | 1.26823 | 0.0597848 | ||||||||
\(451\) | −18.9855 | −0.893990 | ||||||||
\(452\) | 15.4181 | 0.725208 | ||||||||
\(453\) | −6.89040 | −0.323739 | ||||||||
\(454\) | 0.190194 | 0.00892627 | ||||||||
\(455\) | −32.7501 | −1.53535 | ||||||||
\(456\) | −0.621945 | −0.0291253 | ||||||||
\(457\) | −5.72640 | −0.267870 | −0.133935 | − | 0.990990i | \(-0.542761\pi\) | ||||
−0.133935 | + | 0.990990i | \(0.542761\pi\) | |||||||
\(458\) | −4.16971 | −0.194838 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 31.8427 | 1.48468 | ||||||||
\(461\) | 13.4590 | 0.626847 | 0.313424 | − | 0.949613i | \(-0.398524\pi\) | ||||
0.313424 | + | 0.949613i | \(0.398524\pi\) | |||||||
\(462\) | −1.05899 | −0.0492686 | ||||||||
\(463\) | 0.923415 | 0.0429148 | 0.0214574 | − | 0.999770i | \(-0.493169\pi\) | ||||
0.0214574 | + | 0.999770i | \(0.493169\pi\) | |||||||
\(464\) | 6.40890 | 0.297526 | ||||||||
\(465\) | −17.4833 | −0.810768 | ||||||||
\(466\) | 4.56654 | 0.211541 | ||||||||
\(467\) | 30.3393 | 1.40394 | 0.701969 | − | 0.712208i | \(-0.252305\pi\) | ||||
0.701969 | + | 0.712208i | \(0.252305\pi\) | |||||||
\(468\) | 10.5291 | 0.486710 | ||||||||
\(469\) | −22.4947 | −1.03871 | ||||||||
\(470\) | −2.84712 | −0.131328 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | −3.41444 | −0.157162 | ||||||||
\(473\) | −34.2888 | −1.57660 | ||||||||
\(474\) | 1.25436 | 0.0576148 | ||||||||
\(475\) | −5.59916 | −0.256907 | ||||||||
\(476\) | 3.50509 | 0.160656 | ||||||||
\(477\) | 8.72542 | 0.399509 | ||||||||
\(478\) | 0.279604 | 0.0127888 | ||||||||
\(479\) | 10.2457 | 0.468137 | 0.234069 | − | 0.972220i | \(-0.424796\pi\) | ||||
0.234069 | + | 0.972220i | \(0.424796\pi\) | |||||||
\(480\) | −7.56390 | −0.345243 | ||||||||
\(481\) | 18.4373 | 0.840668 | ||||||||
\(482\) | 4.66459 | 0.212466 | ||||||||
\(483\) | 8.44524 | 0.384272 | ||||||||
\(484\) | 2.13421 | 0.0970095 | ||||||||
\(485\) | 22.5210 | 1.02263 | ||||||||
\(486\) | −0.188504 | −0.00855072 | ||||||||
\(487\) | −17.2746 | −0.782788 | −0.391394 | − | 0.920223i | \(-0.628007\pi\) | ||||
−0.391394 | + | 0.920223i | \(0.628007\pi\) | |||||||
\(488\) | 1.35154 | 0.0611815 | ||||||||
\(489\) | −13.3271 | −0.602674 | ||||||||
\(490\) | −2.46372 | −0.111299 | ||||||||
\(491\) | −14.2036 | −0.641000 | −0.320500 | − | 0.947248i | \(-0.603851\pi\) | ||||
−0.320500 | + | 0.947248i | \(0.603851\pi\) | |||||||
\(492\) | −11.8454 | −0.534032 | ||||||||
\(493\) | −1.69187 | −0.0761979 | ||||||||
\(494\) | 0.840845 | 0.0378314 | ||||||||
\(495\) | 10.7826 | 0.484643 | ||||||||
\(496\) | 19.3389 | 0.868340 | ||||||||
\(497\) | −6.30111 | −0.282643 | ||||||||
\(498\) | 2.33624 | 0.104689 | ||||||||
\(499\) | −11.8923 | −0.532372 | −0.266186 | − | 0.963922i | \(-0.585764\pi\) | ||||
−0.266186 | + | 0.963922i | \(0.585764\pi\) | |||||||
\(500\) | −11.6241 | −0.519844 | ||||||||
\(501\) | 21.9521 | 0.980749 | ||||||||
\(502\) | −0.156192 | −0.00697119 | ||||||||
\(503\) | −21.7496 | −0.969765 | −0.484883 | − | 0.874579i | \(-0.661138\pi\) | ||||
−0.484883 | + | 0.874579i | \(0.661138\pi\) | |||||||
\(504\) | −1.33340 | −0.0593944 | ||||||||
\(505\) | 41.0533 | 1.82685 | ||||||||
\(506\) | −2.80927 | −0.124887 | ||||||||
\(507\) | −15.7275 | −0.698482 | ||||||||
\(508\) | −32.8459 | −1.45730 | ||||||||
\(509\) | −25.2949 | −1.12118 | −0.560589 | − | 0.828094i | \(-0.689425\pi\) | ||||
−0.560589 | + | 0.828094i | \(0.689425\pi\) | |||||||
\(510\) | 0.645550 | 0.0285854 | ||||||||
\(511\) | −16.7694 | −0.741835 | ||||||||
\(512\) | 14.0285 | 0.619976 | ||||||||
\(513\) | 0.832236 | 0.0367441 | ||||||||
\(514\) | 0.277893 | 0.0122573 | ||||||||
\(515\) | 65.2734 | 2.87629 | ||||||||
\(516\) | −21.3935 | −0.941796 | ||||||||
\(517\) | −13.8865 | −0.610725 | ||||||||
\(518\) | −1.15698 | −0.0508346 | ||||||||
\(519\) | 9.46456 | 0.415448 | ||||||||
\(520\) | 13.7171 | 0.601536 | ||||||||
\(521\) | −2.57071 | −0.112625 | −0.0563124 | − | 0.998413i | \(-0.517934\pi\) | ||||
−0.0563124 | + | 0.998413i | \(0.517934\pi\) | |||||||
\(522\) | 0.318924 | 0.0139589 | ||||||||
\(523\) | 38.7582 | 1.69478 | 0.847390 | − | 0.530971i | \(-0.178173\pi\) | ||||
0.847390 | + | 0.530971i | \(0.178173\pi\) | |||||||
\(524\) | 19.8105 | 0.865427 | ||||||||
\(525\) | −12.0041 | −0.523904 | ||||||||
\(526\) | −2.00681 | −0.0875009 | ||||||||
\(527\) | −5.10521 | −0.222387 | ||||||||
\(528\) | −11.9270 | −0.519057 | ||||||||
\(529\) | −0.596618 | −0.0259399 | ||||||||
\(530\) | 5.63269 | 0.244669 | ||||||||
\(531\) | 4.56892 | 0.198274 | ||||||||
\(532\) | 2.91707 | 0.126471 | ||||||||
\(533\) | 32.3187 | 1.39988 | ||||||||
\(534\) | 2.18360 | 0.0944935 | ||||||||
\(535\) | −23.8392 | −1.03066 | ||||||||
\(536\) | 9.42174 | 0.406957 | ||||||||
\(537\) | 6.28826 | 0.271358 | ||||||||
\(538\) | 2.58185 | 0.111312 | ||||||||
\(539\) | −12.0165 | −0.517585 | ||||||||
\(540\) | 6.72750 | 0.289505 | ||||||||
\(541\) | 1.12159 | 0.0482209 | 0.0241104 | − | 0.999709i | \(-0.492325\pi\) | ||||
0.0241104 | + | 0.999709i | \(0.492325\pi\) | |||||||
\(542\) | 0.932070 | 0.0400358 | ||||||||
\(543\) | −22.2200 | −0.953551 | ||||||||
\(544\) | −2.20870 | −0.0946973 | ||||||||
\(545\) | 4.78225 | 0.204849 | ||||||||
\(546\) | 1.80270 | 0.0771486 | ||||||||
\(547\) | −10.5264 | −0.450075 | −0.225037 | − | 0.974350i | \(-0.572250\pi\) | ||||
−0.225037 | + | 0.974350i | \(0.572250\pi\) | |||||||
\(548\) | −19.4448 | −0.830641 | ||||||||
\(549\) | −1.80853 | −0.0771860 | ||||||||
\(550\) | 3.99312 | 0.170267 | ||||||||
\(551\) | −1.40803 | −0.0599843 | ||||||||
\(552\) | −3.53722 | −0.150554 | ||||||||
\(553\) | −11.8729 | −0.504888 | ||||||||
\(554\) | −1.48969 | −0.0632909 | ||||||||
\(555\) | 11.7803 | 0.500047 | ||||||||
\(556\) | −19.6696 | −0.834178 | ||||||||
\(557\) | −15.7987 | −0.669412 | −0.334706 | − | 0.942323i | \(-0.608637\pi\) | ||||
−0.334706 | + | 0.942323i | \(0.608637\pi\) | |||||||
\(558\) | 0.962354 | 0.0407397 | ||||||||
\(559\) | 58.3695 | 2.46877 | ||||||||
\(560\) | 23.1463 | 0.978108 | ||||||||
\(561\) | 3.14859 | 0.132933 | ||||||||
\(562\) | −3.48588 | −0.147043 | ||||||||
\(563\) | 8.36938 | 0.352727 | 0.176364 | − | 0.984325i | \(-0.443567\pi\) | ||||
0.176364 | + | 0.984325i | \(0.443567\pi\) | |||||||
\(564\) | −8.66404 | −0.364822 | ||||||||
\(565\) | −26.8780 | −1.13076 | ||||||||
\(566\) | 5.96067 | 0.250546 | ||||||||
\(567\) | 1.78425 | 0.0749313 | ||||||||
\(568\) | 2.63917 | 0.110737 | ||||||||
\(569\) | 45.0689 | 1.88939 | 0.944693 | − | 0.327955i | \(-0.106360\pi\) | ||||
0.944693 | + | 0.327955i | \(0.106360\pi\) | |||||||
\(570\) | 0.537250 | 0.0225029 | ||||||||
\(571\) | 38.0004 | 1.59027 | 0.795135 | − | 0.606433i | \(-0.207400\pi\) | ||||
0.795135 | + | 0.606433i | \(0.207400\pi\) | |||||||
\(572\) | 33.1519 | 1.38615 | ||||||||
\(573\) | −13.2135 | −0.552002 | ||||||||
\(574\) | −2.02806 | −0.0846497 | ||||||||
\(575\) | −31.8444 | −1.32800 | ||||||||
\(576\) | −7.15977 | −0.298324 | ||||||||
\(577\) | 26.9205 | 1.12071 | 0.560357 | − | 0.828251i | \(-0.310664\pi\) | ||||
0.560357 | + | 0.828251i | \(0.310664\pi\) | |||||||
\(578\) | 0.188504 | 0.00784074 | ||||||||
\(579\) | 16.1579 | 0.671499 | ||||||||
\(580\) | −11.3820 | −0.472613 | ||||||||
\(581\) | −22.1132 | −0.917410 | ||||||||
\(582\) | −1.23965 | −0.0513852 | ||||||||
\(583\) | 27.4727 | 1.13780 | ||||||||
\(584\) | 7.02373 | 0.290644 | ||||||||
\(585\) | −18.3551 | −0.758892 | ||||||||
\(586\) | −4.55408 | −0.188127 | ||||||||
\(587\) | −4.31654 | −0.178163 | −0.0890814 | − | 0.996024i | \(-0.528393\pi\) | ||||
−0.0890814 | + | 0.996024i | \(0.528393\pi\) | |||||||
\(588\) | −7.49731 | −0.309184 | ||||||||
\(589\) | −4.24874 | −0.175066 | ||||||||
\(590\) | 2.94947 | 0.121428 | ||||||||
\(591\) | −22.5229 | −0.926468 | ||||||||
\(592\) | −13.0306 | −0.535555 | ||||||||
\(593\) | 19.4764 | 0.799799 | 0.399899 | − | 0.916559i | \(-0.369045\pi\) | ||||
0.399899 | + | 0.916559i | \(0.369045\pi\) | |||||||
\(594\) | −0.593521 | −0.0243525 | ||||||||
\(595\) | −6.11032 | −0.250499 | ||||||||
\(596\) | 42.2263 | 1.72966 | ||||||||
\(597\) | 14.3787 | 0.588482 | ||||||||
\(598\) | 4.78218 | 0.195558 | ||||||||
\(599\) | −3.16468 | −0.129305 | −0.0646526 | − | 0.997908i | \(-0.520594\pi\) | ||||
−0.0646526 | + | 0.997908i | \(0.520594\pi\) | |||||||
\(600\) | 5.02784 | 0.205261 | ||||||||
\(601\) | 19.2069 | 0.783466 | 0.391733 | − | 0.920079i | \(-0.371876\pi\) | ||||
0.391733 | + | 0.920079i | \(0.371876\pi\) | |||||||
\(602\) | −3.66280 | −0.149285 | ||||||||
\(603\) | −12.6074 | −0.513413 | ||||||||
\(604\) | −13.5360 | −0.550770 | ||||||||
\(605\) | −3.72050 | −0.151260 | ||||||||
\(606\) | −2.25975 | −0.0917960 | ||||||||
\(607\) | −0.150792 | −0.00612045 | −0.00306023 | − | 0.999995i | \(-0.500974\pi\) | ||||
−0.00306023 | + | 0.999995i | \(0.500974\pi\) | |||||||
\(608\) | −1.83816 | −0.0745473 | ||||||||
\(609\) | −3.01871 | −0.122324 | ||||||||
\(610\) | −1.16749 | −0.0472704 | ||||||||
\(611\) | 23.6387 | 0.956321 | ||||||||
\(612\) | 1.96447 | 0.0794088 | ||||||||
\(613\) | −27.8618 | −1.12533 | −0.562664 | − | 0.826686i | \(-0.690223\pi\) | ||||
−0.562664 | + | 0.826686i | \(0.690223\pi\) | |||||||
\(614\) | −5.48065 | −0.221181 | ||||||||
\(615\) | 20.6497 | 0.832678 | ||||||||
\(616\) | −4.19833 | −0.169155 | ||||||||
\(617\) | −16.6285 | −0.669439 | −0.334720 | − | 0.942318i | \(-0.608642\pi\) | ||||
−0.334720 | + | 0.942318i | \(0.608642\pi\) | |||||||
\(618\) | −3.59292 | −0.144529 | ||||||||
\(619\) | −23.0207 | −0.925279 | −0.462640 | − | 0.886546i | \(-0.653098\pi\) | ||||
−0.462640 | + | 0.886546i | \(0.653098\pi\) | |||||||
\(620\) | −34.3453 | −1.37934 | ||||||||
\(621\) | 4.73322 | 0.189938 | ||||||||
\(622\) | −0.538778 | −0.0216030 | ||||||||
\(623\) | −20.6684 | −0.828062 | ||||||||
\(624\) | 20.3032 | 0.812780 | ||||||||
\(625\) | −13.3753 | −0.535013 | ||||||||
\(626\) | −2.75613 | −0.110157 | ||||||||
\(627\) | 2.62037 | 0.104647 | ||||||||
\(628\) | 1.96447 | 0.0783907 | ||||||||
\(629\) | 3.43992 | 0.137159 | ||||||||
\(630\) | 1.15182 | 0.0458896 | ||||||||
\(631\) | −27.3793 | −1.08995 | −0.544976 | − | 0.838452i | \(-0.683461\pi\) | ||||
−0.544976 | + | 0.838452i | \(0.683461\pi\) | |||||||
\(632\) | 4.97288 | 0.197810 | ||||||||
\(633\) | −17.9288 | −0.712607 | ||||||||
\(634\) | −4.98981 | −0.198171 | ||||||||
\(635\) | 57.2592 | 2.27226 | ||||||||
\(636\) | 17.1408 | 0.679677 | ||||||||
\(637\) | 20.4555 | 0.810476 | ||||||||
\(638\) | 1.00416 | 0.0397551 | ||||||||
\(639\) | −3.53152 | −0.139705 | ||||||||
\(640\) | −19.7498 | −0.780679 | ||||||||
\(641\) | −7.49037 | −0.295852 | −0.147926 | − | 0.988998i | \(-0.547260\pi\) | ||||
−0.147926 | + | 0.988998i | \(0.547260\pi\) | |||||||
\(642\) | 1.31221 | 0.0517887 | ||||||||
\(643\) | 11.1091 | 0.438099 | 0.219049 | − | 0.975714i | \(-0.429704\pi\) | ||||
0.219049 | + | 0.975714i | \(0.429704\pi\) | |||||||
\(644\) | 16.5904 | 0.653753 | ||||||||
\(645\) | 37.2946 | 1.46847 | ||||||||
\(646\) | 0.156880 | 0.00617236 | ||||||||
\(647\) | −6.63118 | −0.260698 | −0.130349 | − | 0.991468i | \(-0.541610\pi\) | ||||
−0.130349 | + | 0.991468i | \(0.541610\pi\) | |||||||
\(648\) | −0.747318 | −0.0293574 | ||||||||
\(649\) | 14.3856 | 0.564686 | ||||||||
\(650\) | −6.79744 | −0.266618 | ||||||||
\(651\) | −9.10896 | −0.357008 | ||||||||
\(652\) | −26.1807 | −1.02532 | ||||||||
\(653\) | −41.0044 | −1.60462 | −0.802312 | − | 0.596904i | \(-0.796397\pi\) | ||||
−0.802312 | + | 0.596904i | \(0.796397\pi\) | |||||||
\(654\) | −0.263235 | −0.0102933 | ||||||||
\(655\) | −34.5351 | −1.34940 | ||||||||
\(656\) | −22.8414 | −0.891806 | ||||||||
\(657\) | −9.39859 | −0.366674 | ||||||||
\(658\) | −1.48338 | −0.0578281 | ||||||||
\(659\) | 40.5473 | 1.57950 | 0.789750 | − | 0.613429i | \(-0.210210\pi\) | ||||
0.789750 | + | 0.613429i | \(0.210210\pi\) | |||||||
\(660\) | 21.1821 | 0.824512 | ||||||||
\(661\) | −45.5368 | −1.77118 | −0.885588 | − | 0.464472i | \(-0.846244\pi\) | ||||
−0.885588 | + | 0.464472i | \(0.846244\pi\) | |||||||
\(662\) | 4.36505 | 0.169652 | ||||||||
\(663\) | −5.35980 | −0.208157 | ||||||||
\(664\) | 9.26194 | 0.359433 | ||||||||
\(665\) | −5.08523 | −0.197197 | ||||||||
\(666\) | −0.648439 | −0.0251265 | ||||||||
\(667\) | −8.00798 | −0.310070 | ||||||||
\(668\) | 43.1242 | 1.66853 | ||||||||
\(669\) | 23.8723 | 0.922957 | ||||||||
\(670\) | −8.13871 | −0.314426 | ||||||||
\(671\) | −5.69430 | −0.219826 | ||||||||
\(672\) | −3.94087 | −0.152022 | ||||||||
\(673\) | −33.3132 | −1.28413 | −0.642064 | − | 0.766651i | \(-0.721922\pi\) | ||||
−0.642064 | + | 0.766651i | \(0.721922\pi\) | |||||||
\(674\) | 4.59626 | 0.177041 | ||||||||
\(675\) | −6.72784 | −0.258955 | ||||||||
\(676\) | −30.8961 | −1.18831 | ||||||||
\(677\) | 37.5805 | 1.44434 | 0.722168 | − | 0.691718i | \(-0.243146\pi\) | ||||
0.722168 | + | 0.691718i | \(0.243146\pi\) | |||||||
\(678\) | 1.47948 | 0.0568189 | ||||||||
\(679\) | 11.7337 | 0.450297 | ||||||||
\(680\) | 2.55926 | 0.0981432 | ||||||||
\(681\) | −1.00897 | −0.0386637 | ||||||||
\(682\) | 3.03005 | 0.116027 | ||||||||
\(683\) | −35.3950 | −1.35435 | −0.677175 | − | 0.735822i | \(-0.736796\pi\) | ||||
−0.677175 | + | 0.735822i | \(0.736796\pi\) | |||||||
\(684\) | 1.63490 | 0.0625120 | ||||||||
\(685\) | 33.8975 | 1.29516 | ||||||||
\(686\) | −3.63799 | −0.138899 | ||||||||
\(687\) | 22.1200 | 0.843931 | ||||||||
\(688\) | −41.2529 | −1.57275 | ||||||||
\(689\) | −46.7665 | −1.78166 | ||||||||
\(690\) | 3.05553 | 0.116322 | ||||||||
\(691\) | −46.2849 | −1.76076 | −0.880380 | − | 0.474270i | \(-0.842712\pi\) | ||||
−0.880380 | + | 0.474270i | \(0.842712\pi\) | |||||||
\(692\) | 18.5928 | 0.706793 | ||||||||
\(693\) | 5.61786 | 0.213405 | ||||||||
\(694\) | −3.24998 | −0.123368 | ||||||||
\(695\) | 34.2894 | 1.30067 | ||||||||
\(696\) | 1.26436 | 0.0479256 | ||||||||
\(697\) | 6.02983 | 0.228396 | ||||||||
\(698\) | 5.40011 | 0.204397 | ||||||||
\(699\) | −24.2251 | −0.916279 | ||||||||
\(700\) | −23.5817 | −0.891305 | ||||||||
\(701\) | 15.6870 | 0.592491 | 0.296246 | − | 0.955112i | \(-0.404265\pi\) | ||||
0.296246 | + | 0.955112i | \(0.404265\pi\) | |||||||
\(702\) | 1.01034 | 0.0381330 | ||||||||
\(703\) | 2.86283 | 0.107973 | ||||||||
\(704\) | −22.5432 | −0.849627 | ||||||||
\(705\) | 15.1038 | 0.568840 | ||||||||
\(706\) | −0.385629 | −0.0145133 | ||||||||
\(707\) | 21.3892 | 0.804423 | ||||||||
\(708\) | 8.97549 | 0.337320 | ||||||||
\(709\) | 29.0503 | 1.09101 | 0.545504 | − | 0.838108i | \(-0.316338\pi\) | ||||
0.545504 | + | 0.838108i | \(0.316338\pi\) | |||||||
\(710\) | −2.27977 | −0.0855584 | ||||||||
\(711\) | −6.65430 | −0.249556 | ||||||||
\(712\) | 8.65679 | 0.324427 | ||||||||
\(713\) | −24.1641 | −0.904953 | ||||||||
\(714\) | 0.336338 | 0.0125871 | ||||||||
\(715\) | −57.7927 | −2.16133 | ||||||||
\(716\) | 12.3531 | 0.461656 | ||||||||
\(717\) | −1.48328 | −0.0553939 | ||||||||
\(718\) | 4.46479 | 0.166625 | ||||||||
\(719\) | −1.82416 | −0.0680299 | −0.0340149 | − | 0.999421i | \(-0.510829\pi\) | ||||
−0.0340149 | + | 0.999421i | \(0.510829\pi\) | |||||||
\(720\) | 12.9726 | 0.483459 | ||||||||
\(721\) | 34.0081 | 1.26653 | ||||||||
\(722\) | −3.45102 | −0.128434 | ||||||||
\(723\) | −24.7453 | −0.920288 | ||||||||
\(724\) | −43.6504 | −1.62225 | ||||||||
\(725\) | 11.3826 | 0.422740 | ||||||||
\(726\) | 0.204792 | 0.00760055 | ||||||||
\(727\) | 23.5960 | 0.875126 | 0.437563 | − | 0.899188i | \(-0.355842\pi\) | ||||
0.437563 | + | 0.899188i | \(0.355842\pi\) | |||||||
\(728\) | 7.14676 | 0.264877 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −6.06726 | −0.224559 | ||||||||
\(731\) | 10.8902 | 0.402790 | ||||||||
\(732\) | −3.55279 | −0.131315 | ||||||||
\(733\) | −39.2461 | −1.44959 | −0.724794 | − | 0.688965i | \(-0.758065\pi\) | ||||
−0.724794 | + | 0.688965i | \(0.758065\pi\) | |||||||
\(734\) | −0.483242 | −0.0178368 | ||||||||
\(735\) | 13.0698 | 0.482088 | ||||||||
\(736\) | −10.4543 | −0.385350 | ||||||||
\(737\) | −39.6955 | −1.46220 | ||||||||
\(738\) | −1.13665 | −0.0418406 | ||||||||
\(739\) | 5.52386 | 0.203198 | 0.101599 | − | 0.994825i | \(-0.467604\pi\) | ||||
0.101599 | + | 0.994825i | \(0.467604\pi\) | |||||||
\(740\) | 23.1421 | 0.850719 | ||||||||
\(741\) | −4.46062 | −0.163865 | ||||||||
\(742\) | 2.93469 | 0.107736 | ||||||||
\(743\) | −27.3105 | −1.00193 | −0.500963 | − | 0.865469i | \(-0.667021\pi\) | ||||
−0.500963 | + | 0.865469i | \(0.667021\pi\) | |||||||
\(744\) | 3.81522 | 0.139873 | ||||||||
\(745\) | −73.6118 | −2.69693 | ||||||||
\(746\) | −6.60964 | −0.241996 | ||||||||
\(747\) | −12.3936 | −0.453457 | ||||||||
\(748\) | 6.18529 | 0.226157 | ||||||||
\(749\) | −12.4204 | −0.453833 | ||||||||
\(750\) | −1.11541 | −0.0407290 | ||||||||
\(751\) | −12.9932 | −0.474128 | −0.237064 | − | 0.971494i | \(-0.576185\pi\) | ||||
−0.237064 | + | 0.971494i | \(0.576185\pi\) | |||||||
\(752\) | −16.7068 | −0.609233 | ||||||||
\(753\) | 0.828587 | 0.0301954 | ||||||||
\(754\) | −1.70937 | −0.0622516 | ||||||||
\(755\) | 23.5968 | 0.858776 | ||||||||
\(756\) | 3.50509 | 0.127479 | ||||||||
\(757\) | 11.3433 | 0.412279 | 0.206140 | − | 0.978523i | \(-0.433910\pi\) | ||||
0.206140 | + | 0.978523i | \(0.433910\pi\) | |||||||
\(758\) | −2.11755 | −0.0769128 | ||||||||
\(759\) | 14.9030 | 0.540943 | ||||||||
\(760\) | 2.12991 | 0.0772600 | ||||||||
\(761\) | −28.1484 | −1.02038 | −0.510189 | − | 0.860063i | \(-0.670424\pi\) | ||||
−0.510189 | + | 0.860063i | \(0.670424\pi\) | |||||||
\(762\) | −3.15179 | −0.114177 | ||||||||
\(763\) | 2.49160 | 0.0902019 | ||||||||
\(764\) | −25.9575 | −0.939109 | ||||||||
\(765\) | −3.42459 | −0.123816 | ||||||||
\(766\) | −2.78749 | −0.100716 | ||||||||
\(767\) | −24.4885 | −0.884229 | ||||||||
\(768\) | −13.2324 | −0.477484 | ||||||||
\(769\) | −38.0823 | −1.37328 | −0.686642 | − | 0.726996i | \(-0.740916\pi\) | ||||
−0.686642 | + | 0.726996i | \(0.740916\pi\) | |||||||
\(770\) | 3.62661 | 0.130694 | ||||||||
\(771\) | −1.47420 | −0.0530920 | ||||||||
\(772\) | 31.7416 | 1.14241 | ||||||||
\(773\) | 42.7696 | 1.53832 | 0.769158 | − | 0.639059i | \(-0.220676\pi\) | ||||
0.769158 | + | 0.639059i | \(0.220676\pi\) | |||||||
\(774\) | −2.05285 | −0.0737883 | ||||||||
\(775\) | 34.3471 | 1.23378 | ||||||||
\(776\) | −4.91456 | −0.176422 | ||||||||
\(777\) | 6.13767 | 0.220188 | ||||||||
\(778\) | −6.96051 | −0.249546 | ||||||||
\(779\) | 5.01825 | 0.179797 | ||||||||
\(780\) | −36.0581 | −1.29109 | ||||||||
\(781\) | −11.1193 | −0.397880 | ||||||||
\(782\) | 0.892232 | 0.0319061 | ||||||||
\(783\) | −1.69187 | −0.0604624 | ||||||||
\(784\) | −14.4570 | −0.516321 | ||||||||
\(785\) | −3.42459 | −0.122229 | ||||||||
\(786\) | 1.90096 | 0.0678049 | ||||||||
\(787\) | 42.9371 | 1.53054 | 0.765271 | − | 0.643709i | \(-0.222605\pi\) | ||||
0.765271 | + | 0.643709i | \(0.222605\pi\) | |||||||
\(788\) | −44.2455 | −1.57618 | ||||||||
\(789\) | 10.6460 | 0.379006 | ||||||||
\(790\) | −4.29568 | −0.152834 | ||||||||
\(791\) | −14.0037 | −0.497914 | ||||||||
\(792\) | −2.35300 | −0.0836100 | ||||||||
\(793\) | 9.69334 | 0.344221 | ||||||||
\(794\) | 0.773858 | 0.0274632 | ||||||||
\(795\) | −29.8810 | −1.05977 | ||||||||
\(796\) | 28.2465 | 1.00117 | ||||||||
\(797\) | −25.7429 | −0.911862 | −0.455931 | − | 0.890015i | \(-0.650694\pi\) | ||||
−0.455931 | + | 0.890015i | \(0.650694\pi\) | |||||||
\(798\) | 0.279913 | 0.00990880 | ||||||||
\(799\) | 4.41038 | 0.156028 | ||||||||
\(800\) | 14.8598 | 0.525373 | ||||||||
\(801\) | −11.5838 | −0.409294 | ||||||||
\(802\) | −4.64685 | −0.164086 | ||||||||
\(803\) | −29.5923 | −1.04429 | ||||||||
\(804\) | −24.7668 | −0.873458 | ||||||||
\(805\) | −28.9215 | −1.01935 | ||||||||
\(806\) | −5.15802 | −0.181684 | ||||||||
\(807\) | −13.6965 | −0.482141 | ||||||||
\(808\) | −8.95869 | −0.315166 | ||||||||
\(809\) | 31.5271 | 1.10843 | 0.554216 | − | 0.832373i | \(-0.313018\pi\) | ||||
0.554216 | + | 0.832373i | \(0.313018\pi\) | |||||||
\(810\) | 0.645550 | 0.0226823 | ||||||||
\(811\) | 52.5422 | 1.84501 | 0.922503 | − | 0.385991i | \(-0.126140\pi\) | ||||
0.922503 | + | 0.385991i | \(0.126140\pi\) | |||||||
\(812\) | −5.93015 | −0.208108 | ||||||||
\(813\) | −4.94456 | −0.173413 | ||||||||
\(814\) | −2.04167 | −0.0715603 | ||||||||
\(815\) | 45.6400 | 1.59870 | ||||||||
\(816\) | 3.78806 | 0.132609 | ||||||||
\(817\) | 9.06325 | 0.317083 | ||||||||
\(818\) | −0.756430 | −0.0264480 | ||||||||
\(819\) | −9.56321 | −0.334166 | ||||||||
\(820\) | 40.5657 | 1.41662 | ||||||||
\(821\) | 5.39941 | 0.188441 | 0.0942203 | − | 0.995551i | \(-0.469964\pi\) | ||||
0.0942203 | + | 0.995551i | \(0.469964\pi\) | |||||||
\(822\) | −1.86586 | −0.0650795 | ||||||||
\(823\) | 51.6915 | 1.80185 | 0.900926 | − | 0.433972i | \(-0.142888\pi\) | ||||
0.900926 | + | 0.433972i | \(0.142888\pi\) | |||||||
\(824\) | −14.2440 | −0.496214 | ||||||||
\(825\) | −21.1832 | −0.737504 | ||||||||
\(826\) | 1.53670 | 0.0534687 | ||||||||
\(827\) | 33.7956 | 1.17519 | 0.587594 | − | 0.809156i | \(-0.300075\pi\) | ||||
0.587594 | + | 0.809156i | \(0.300075\pi\) | |||||||
\(828\) | 9.29825 | 0.323137 | ||||||||
\(829\) | −46.8907 | −1.62858 | −0.814291 | − | 0.580456i | \(-0.802874\pi\) | ||||
−0.814291 | + | 0.580456i | \(0.802874\pi\) | |||||||
\(830\) | −8.00067 | −0.277707 | ||||||||
\(831\) | 7.90270 | 0.274142 | ||||||||
\(832\) | 38.3749 | 1.33041 | ||||||||
\(833\) | 3.81646 | 0.132233 | ||||||||
\(834\) | −1.88744 | −0.0653566 | ||||||||
\(835\) | −75.1771 | −2.60161 | ||||||||
\(836\) | 5.14762 | 0.178034 | ||||||||
\(837\) | −5.10521 | −0.176462 | ||||||||
\(838\) | −0.926763 | −0.0320145 | ||||||||
\(839\) | 34.8732 | 1.20396 | 0.601978 | − | 0.798513i | \(-0.294380\pi\) | ||||
0.601978 | + | 0.798513i | \(0.294380\pi\) | |||||||
\(840\) | 4.56635 | 0.157554 | ||||||||
\(841\) | −26.1376 | −0.901296 | ||||||||
\(842\) | −5.91916 | −0.203988 | ||||||||
\(843\) | 18.4923 | 0.636909 | ||||||||
\(844\) | −35.2206 | −1.21234 | ||||||||
\(845\) | 53.8602 | 1.85285 | ||||||||
\(846\) | −0.831374 | −0.0285832 | ||||||||
\(847\) | −1.93842 | −0.0666049 | ||||||||
\(848\) | 33.0524 | 1.13502 | ||||||||
\(849\) | −31.6209 | −1.08523 | ||||||||
\(850\) | −1.26823 | −0.0434998 | ||||||||
\(851\) | 16.2819 | 0.558136 | ||||||||
\(852\) | −6.93755 | −0.237677 | ||||||||
\(853\) | 8.22003 | 0.281449 | 0.140724 | − | 0.990049i | \(-0.455057\pi\) | ||||
0.140724 | + | 0.990049i | \(0.455057\pi\) | |||||||
\(854\) | −0.608276 | −0.0208148 | ||||||||
\(855\) | −2.85007 | −0.0974704 | ||||||||
\(856\) | 5.20220 | 0.177808 | ||||||||
\(857\) | 1.09505 | 0.0374063 | 0.0187031 | − | 0.999825i | \(-0.494046\pi\) | ||||
0.0187031 | + | 0.999825i | \(0.494046\pi\) | |||||||
\(858\) | 3.18116 | 0.108603 | ||||||||
\(859\) | 28.4147 | 0.969498 | 0.484749 | − | 0.874653i | \(-0.338911\pi\) | ||||
0.484749 | + | 0.874653i | \(0.338911\pi\) | |||||||
\(860\) | 73.2640 | 2.49828 | ||||||||
\(861\) | 10.7587 | 0.366656 | ||||||||
\(862\) | 4.41599 | 0.150409 | ||||||||
\(863\) | −40.7980 | −1.38878 | −0.694389 | − | 0.719600i | \(-0.744325\pi\) | ||||
−0.694389 | + | 0.719600i | \(0.744325\pi\) | |||||||
\(864\) | −2.20870 | −0.0751415 | ||||||||
\(865\) | −32.4123 | −1.10205 | ||||||||
\(866\) | −4.83866 | −0.164425 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −17.8943 | −0.607370 | ||||||||
\(869\) | −20.9516 | −0.710735 | ||||||||
\(870\) | −1.09219 | −0.0370285 | ||||||||
\(871\) | 67.5731 | 2.28963 | ||||||||
\(872\) | −1.04359 | −0.0353403 | ||||||||
\(873\) | 6.57626 | 0.222573 | ||||||||
\(874\) | 0.742547 | 0.0251170 | ||||||||
\(875\) | 10.5577 | 0.356915 | ||||||||
\(876\) | −18.4632 | −0.623814 | ||||||||
\(877\) | 36.9166 | 1.24658 | 0.623292 | − | 0.781989i | \(-0.285795\pi\) | ||||
0.623292 | + | 0.781989i | \(0.285795\pi\) | |||||||
\(878\) | −4.25685 | −0.143662 | ||||||||
\(879\) | 24.1591 | 0.814865 | ||||||||
\(880\) | 40.8452 | 1.37689 | ||||||||
\(881\) | −13.0274 | −0.438905 | −0.219452 | − | 0.975623i | \(-0.570427\pi\) | ||||
−0.219452 | + | 0.975623i | \(0.570427\pi\) | |||||||
\(882\) | −0.719419 | −0.0242241 | ||||||||
\(883\) | 35.8333 | 1.20589 | 0.602943 | − | 0.797784i | \(-0.293994\pi\) | ||||
0.602943 | + | 0.797784i | \(0.293994\pi\) | |||||||
\(884\) | −10.5291 | −0.354134 | ||||||||
\(885\) | −15.6467 | −0.525958 | ||||||||
\(886\) | −3.72025 | −0.124984 | ||||||||
\(887\) | −18.0952 | −0.607576 | −0.303788 | − | 0.952740i | \(-0.598252\pi\) | ||||
−0.303788 | + | 0.952740i | \(0.598252\pi\) | |||||||
\(888\) | −2.57071 | −0.0862675 | ||||||||
\(889\) | 29.8326 | 1.00055 | ||||||||
\(890\) | −7.47793 | −0.250661 | ||||||||
\(891\) | 3.14859 | 0.105482 | ||||||||
\(892\) | 46.8964 | 1.57021 | ||||||||
\(893\) | 3.67048 | 0.122828 | ||||||||
\(894\) | 4.05190 | 0.135516 | ||||||||
\(895\) | −21.5347 | −0.719827 | ||||||||
\(896\) | −10.2898 | −0.343759 | ||||||||
\(897\) | −25.3691 | −0.847050 | ||||||||
\(898\) | 6.40509 | 0.213740 | ||||||||
\(899\) | 8.63735 | 0.288072 | ||||||||
\(900\) | −13.2166 | −0.440554 | ||||||||
\(901\) | −8.72542 | −0.290686 | ||||||||
\(902\) | −3.57884 | −0.119162 | ||||||||
\(903\) | 19.4309 | 0.646619 | ||||||||
\(904\) | 5.86533 | 0.195078 | ||||||||
\(905\) | 76.0944 | 2.52946 | ||||||||
\(906\) | −1.29887 | −0.0431520 | ||||||||
\(907\) | 8.08629 | 0.268501 | 0.134250 | − | 0.990947i | \(-0.457137\pi\) | ||||
0.134250 | + | 0.990947i | \(0.457137\pi\) | |||||||
\(908\) | −1.98208 | −0.0657777 | ||||||||
\(909\) | 11.9878 | 0.397610 | ||||||||
\(910\) | −6.17353 | −0.204651 | ||||||||
\(911\) | −6.91168 | −0.228994 | −0.114497 | − | 0.993424i | \(-0.536526\pi\) | ||||
−0.114497 | + | 0.993424i | \(0.536526\pi\) | |||||||
\(912\) | 3.15256 | 0.104392 | ||||||||
\(913\) | −39.0222 | −1.29145 | ||||||||
\(914\) | −1.07945 | −0.0357050 | ||||||||
\(915\) | 6.19347 | 0.204750 | ||||||||
\(916\) | 43.4540 | 1.43576 | ||||||||
\(917\) | −17.9931 | −0.594185 | ||||||||
\(918\) | 0.188504 | 0.00622156 | ||||||||
\(919\) | −27.0744 | −0.893103 | −0.446552 | − | 0.894758i | \(-0.647348\pi\) | ||||
−0.446552 | + | 0.894758i | \(0.647348\pi\) | |||||||
\(920\) | 12.1135 | 0.399372 | ||||||||
\(921\) | 29.0744 | 0.958035 | ||||||||
\(922\) | 2.53707 | 0.0835541 | ||||||||
\(923\) | 18.9283 | 0.623031 | ||||||||
\(924\) | 11.0361 | 0.363061 | ||||||||
\(925\) | −23.1432 | −0.760945 | ||||||||
\(926\) | 0.174068 | 0.00572022 | ||||||||
\(927\) | 19.0602 | 0.626019 | ||||||||
\(928\) | 3.73683 | 0.122667 | ||||||||
\(929\) | −3.69474 | −0.121220 | −0.0606102 | − | 0.998162i | \(-0.519305\pi\) | ||||
−0.0606102 | + | 0.998162i | \(0.519305\pi\) | |||||||
\(930\) | −3.29567 | −0.108069 | ||||||||
\(931\) | 3.17620 | 0.104096 | ||||||||
\(932\) | −47.5895 | −1.55884 | ||||||||
\(933\) | 2.85818 | 0.0935725 | ||||||||
\(934\) | 5.71909 | 0.187134 | ||||||||
\(935\) | −10.7826 | −0.352630 | ||||||||
\(936\) | 4.00548 | 0.130923 | ||||||||
\(937\) | 13.7223 | 0.448288 | 0.224144 | − | 0.974556i | \(-0.428041\pi\) | ||||
0.224144 | + | 0.974556i | \(0.428041\pi\) | |||||||
\(938\) | −4.24035 | −0.138452 | ||||||||
\(939\) | 14.6211 | 0.477140 | ||||||||
\(940\) | 29.6708 | 0.967755 | ||||||||
\(941\) | 9.84849 | 0.321052 | 0.160526 | − | 0.987032i | \(-0.448681\pi\) | ||||
0.160526 | + | 0.987032i | \(0.448681\pi\) | |||||||
\(942\) | 0.188504 | 0.00614180 | ||||||||
\(943\) | 28.5405 | 0.929408 | ||||||||
\(944\) | 17.3073 | 0.563306 | ||||||||
\(945\) | −6.11032 | −0.198769 | ||||||||
\(946\) | −6.46359 | −0.210149 | ||||||||
\(947\) | −4.23259 | −0.137541 | −0.0687704 | − | 0.997633i | \(-0.521908\pi\) | ||||
−0.0687704 | + | 0.997633i | \(0.521908\pi\) | |||||||
\(948\) | −13.0721 | −0.424564 | ||||||||
\(949\) | 50.3746 | 1.63523 | ||||||||
\(950\) | −1.05546 | −0.0342438 | ||||||||
\(951\) | 26.4706 | 0.858367 | ||||||||
\(952\) | 1.33340 | 0.0432158 | ||||||||
\(953\) | −19.1966 | −0.621840 | −0.310920 | − | 0.950436i | \(-0.600637\pi\) | ||||
−0.310920 | + | 0.950436i | \(0.600637\pi\) | |||||||
\(954\) | 1.64478 | 0.0532516 | ||||||||
\(955\) | 45.2509 | 1.46428 | ||||||||
\(956\) | −2.91384 | −0.0942405 | ||||||||
\(957\) | −5.32699 | −0.172197 | ||||||||
\(958\) | 1.93135 | 0.0623992 | ||||||||
\(959\) | 17.6610 | 0.570302 | ||||||||
\(960\) | 24.5193 | 0.791357 | ||||||||
\(961\) | −4.93679 | −0.159251 | ||||||||
\(962\) | 3.47550 | 0.112055 | ||||||||
\(963\) | −6.96116 | −0.224320 | ||||||||
\(964\) | −48.6113 | −1.56566 | ||||||||
\(965\) | −55.3342 | −1.78127 | ||||||||
\(966\) | 1.59196 | 0.0512205 | ||||||||
\(967\) | −7.35773 | −0.236609 | −0.118304 | − | 0.992977i | \(-0.537746\pi\) | ||||
−0.118304 | + | 0.992977i | \(0.537746\pi\) | |||||||
\(968\) | 0.811892 | 0.0260952 | ||||||||
\(969\) | −0.832236 | −0.0267353 | ||||||||
\(970\) | 4.24530 | 0.136309 | ||||||||
\(971\) | 23.9232 | 0.767731 | 0.383866 | − | 0.923389i | \(-0.374593\pi\) | ||||
0.383866 | + | 0.923389i | \(0.374593\pi\) | |||||||
\(972\) | 1.96447 | 0.0630103 | ||||||||
\(973\) | 17.8651 | 0.572730 | ||||||||
\(974\) | −3.25634 | −0.104340 | ||||||||
\(975\) | 36.0599 | 1.15484 | ||||||||
\(976\) | −6.85080 | −0.219289 | ||||||||
\(977\) | 0.958442 | 0.0306633 | 0.0153316 | − | 0.999882i | \(-0.495120\pi\) | ||||
0.0153316 | + | 0.999882i | \(0.495120\pi\) | |||||||
\(978\) | −2.51222 | −0.0803319 | ||||||||
\(979\) | −36.4726 | −1.16567 | ||||||||
\(980\) | 25.6752 | 0.820166 | ||||||||
\(981\) | 1.39644 | 0.0445850 | ||||||||
\(982\) | −2.67744 | −0.0854406 | ||||||||
\(983\) | 41.4620 | 1.32243 | 0.661216 | − | 0.750196i | \(-0.270041\pi\) | ||||
0.661216 | + | 0.750196i | \(0.270041\pi\) | |||||||
\(984\) | −4.50620 | −0.143653 | ||||||||
\(985\) | 77.1317 | 2.45762 | ||||||||
\(986\) | −0.318924 | −0.0101566 | ||||||||
\(987\) | 7.86920 | 0.250480 | ||||||||
\(988\) | −8.76274 | −0.278780 | ||||||||
\(989\) | 51.5459 | 1.63906 | ||||||||
\(990\) | 2.03257 | 0.0645993 | ||||||||
\(991\) | 10.7114 | 0.340259 | 0.170130 | − | 0.985422i | \(-0.445581\pi\) | ||||
0.170130 | + | 0.985422i | \(0.445581\pi\) | |||||||
\(992\) | 11.2759 | 0.358010 | ||||||||
\(993\) | −23.1563 | −0.734842 | ||||||||
\(994\) | −1.18778 | −0.0376742 | ||||||||
\(995\) | −49.2413 | −1.56105 | ||||||||
\(996\) | −24.3468 | −0.771457 | ||||||||
\(997\) | −24.1247 | −0.764037 | −0.382018 | − | 0.924155i | \(-0.624771\pi\) | ||||
−0.382018 | + | 0.924155i | \(0.624771\pi\) | |||||||
\(998\) | −2.24175 | −0.0709612 | ||||||||
\(999\) | 3.43992 | 0.108834 |
(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.f.1.26 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.f.1.26 | ✓ | 48 | 1.1 | even | 1 | trivial |