Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8045,2,Mod(1,8045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8045.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8045 = 5 \cdot 1609 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8045.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2396484261\) |
Analytic rank: | \(1\) |
Dimension: | \(127\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 8045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.26786 | −1.60362 | −0.801809 | − | 0.597581i | \(-0.796129\pi\) | ||||
−0.801809 | + | 0.597581i | \(0.796129\pi\) | |||||||
\(3\) | −1.17957 | −0.681025 | −0.340512 | − | 0.940240i | \(-0.610601\pi\) | ||||
−0.340512 | + | 0.940240i | \(0.610601\pi\) | |||||||
\(4\) | 3.14318 | 1.57159 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 2.67510 | 1.09210 | ||||||||
\(7\) | 2.15242 | 0.813539 | 0.406770 | − | 0.913531i | \(-0.366655\pi\) | ||||
0.406770 | + | 0.913531i | \(0.366655\pi\) | |||||||
\(8\) | −2.59257 | −0.916610 | ||||||||
\(9\) | −1.60862 | −0.536205 | ||||||||
\(10\) | −2.26786 | −0.717160 | ||||||||
\(11\) | 2.67641 | 0.806968 | 0.403484 | − | 0.914987i | \(-0.367799\pi\) | ||||
0.403484 | + | 0.914987i | \(0.367799\pi\) | |||||||
\(12\) | −3.70760 | −1.07029 | ||||||||
\(13\) | −0.871351 | −0.241669 | −0.120835 | − | 0.992673i | \(-0.538557\pi\) | ||||
−0.120835 | + | 0.992673i | \(0.538557\pi\) | |||||||
\(14\) | −4.88139 | −1.30461 | ||||||||
\(15\) | −1.17957 | −0.304563 | ||||||||
\(16\) | −0.406787 | −0.101697 | ||||||||
\(17\) | 1.87569 | 0.454921 | 0.227461 | − | 0.973787i | \(-0.426958\pi\) | ||||
0.227461 | + | 0.973787i | \(0.426958\pi\) | |||||||
\(18\) | 3.64811 | 0.859868 | ||||||||
\(19\) | 2.38854 | 0.547968 | 0.273984 | − | 0.961734i | \(-0.411658\pi\) | ||||
0.273984 | + | 0.961734i | \(0.411658\pi\) | |||||||
\(20\) | 3.14318 | 0.702836 | ||||||||
\(21\) | −2.53893 | −0.554040 | ||||||||
\(22\) | −6.06972 | −1.29407 | ||||||||
\(23\) | −6.26628 | −1.30661 | −0.653305 | − | 0.757095i | \(-0.726618\pi\) | ||||
−0.653305 | + | 0.757095i | \(0.726618\pi\) | |||||||
\(24\) | 3.05811 | 0.624234 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.97610 | 0.387545 | ||||||||
\(27\) | 5.43618 | 1.04619 | ||||||||
\(28\) | 6.76545 | 1.27855 | ||||||||
\(29\) | −4.67773 | −0.868632 | −0.434316 | − | 0.900761i | \(-0.643010\pi\) | ||||
−0.434316 | + | 0.900761i | \(0.643010\pi\) | |||||||
\(30\) | 2.67510 | 0.488403 | ||||||||
\(31\) | −1.14119 | −0.204964 | −0.102482 | − | 0.994735i | \(-0.532678\pi\) | ||||
−0.102482 | + | 0.994735i | \(0.532678\pi\) | |||||||
\(32\) | 6.10767 | 1.07969 | ||||||||
\(33\) | −3.15701 | −0.549565 | ||||||||
\(34\) | −4.25379 | −0.729519 | ||||||||
\(35\) | 2.15242 | 0.363826 | ||||||||
\(36\) | −5.05617 | −0.842695 | ||||||||
\(37\) | 4.20115 | 0.690665 | 0.345333 | − | 0.938480i | \(-0.387766\pi\) | ||||
0.345333 | + | 0.938480i | \(0.387766\pi\) | |||||||
\(38\) | −5.41687 | −0.878732 | ||||||||
\(39\) | 1.02782 | 0.164583 | ||||||||
\(40\) | −2.59257 | −0.409921 | ||||||||
\(41\) | 3.21088 | 0.501455 | 0.250727 | − | 0.968058i | \(-0.419330\pi\) | ||||
0.250727 | + | 0.968058i | \(0.419330\pi\) | |||||||
\(42\) | 5.75793 | 0.888468 | ||||||||
\(43\) | −6.74241 | −1.02821 | −0.514104 | − | 0.857728i | \(-0.671876\pi\) | ||||
−0.514104 | + | 0.857728i | \(0.671876\pi\) | |||||||
\(44\) | 8.41243 | 1.26822 | ||||||||
\(45\) | −1.60862 | −0.239798 | ||||||||
\(46\) | 14.2110 | 2.09530 | ||||||||
\(47\) | −3.44792 | −0.502931 | −0.251466 | − | 0.967866i | \(-0.580913\pi\) | ||||
−0.251466 | + | 0.967866i | \(0.580913\pi\) | |||||||
\(48\) | 0.479833 | 0.0692580 | ||||||||
\(49\) | −2.36708 | −0.338154 | ||||||||
\(50\) | −2.26786 | −0.320724 | ||||||||
\(51\) | −2.21250 | −0.309812 | ||||||||
\(52\) | −2.73881 | −0.379805 | ||||||||
\(53\) | 2.67159 | 0.366971 | 0.183485 | − | 0.983022i | \(-0.441262\pi\) | ||||
0.183485 | + | 0.983022i | \(0.441262\pi\) | |||||||
\(54\) | −12.3285 | −1.67769 | ||||||||
\(55\) | 2.67641 | 0.360887 | ||||||||
\(56\) | −5.58029 | −0.745698 | ||||||||
\(57\) | −2.81745 | −0.373180 | ||||||||
\(58\) | 10.6084 | 1.39295 | ||||||||
\(59\) | 10.8214 | 1.40882 | 0.704410 | − | 0.709793i | \(-0.251212\pi\) | ||||
0.704410 | + | 0.709793i | \(0.251212\pi\) | |||||||
\(60\) | −3.70760 | −0.478649 | ||||||||
\(61\) | 8.70416 | 1.11445 | 0.557226 | − | 0.830361i | \(-0.311866\pi\) | ||||
0.557226 | + | 0.830361i | \(0.311866\pi\) | |||||||
\(62\) | 2.58806 | 0.328684 | ||||||||
\(63\) | −3.46242 | −0.436224 | ||||||||
\(64\) | −13.0377 | −1.62972 | ||||||||
\(65\) | −0.871351 | −0.108078 | ||||||||
\(66\) | 7.15965 | 0.881292 | ||||||||
\(67\) | −4.63129 | −0.565802 | −0.282901 | − | 0.959149i | \(-0.591297\pi\) | ||||
−0.282901 | + | 0.959149i | \(0.591297\pi\) | |||||||
\(68\) | 5.89562 | 0.714949 | ||||||||
\(69\) | 7.39151 | 0.889834 | ||||||||
\(70\) | −4.88139 | −0.583437 | ||||||||
\(71\) | −8.76413 | −1.04011 | −0.520056 | − | 0.854132i | \(-0.674089\pi\) | ||||
−0.520056 | + | 0.854132i | \(0.674089\pi\) | |||||||
\(72\) | 4.17044 | 0.491491 | ||||||||
\(73\) | −7.75806 | −0.908012 | −0.454006 | − | 0.890999i | \(-0.650006\pi\) | ||||
−0.454006 | + | 0.890999i | \(0.650006\pi\) | |||||||
\(74\) | −9.52762 | −1.10756 | ||||||||
\(75\) | −1.17957 | −0.136205 | ||||||||
\(76\) | 7.50760 | 0.861181 | ||||||||
\(77\) | 5.76076 | 0.656500 | ||||||||
\(78\) | −2.33095 | −0.263928 | ||||||||
\(79\) | −1.66908 | −0.187786 | −0.0938928 | − | 0.995582i | \(-0.529931\pi\) | ||||
−0.0938928 | + | 0.995582i | \(0.529931\pi\) | |||||||
\(80\) | −0.406787 | −0.0454802 | ||||||||
\(81\) | −1.58650 | −0.176278 | ||||||||
\(82\) | −7.28181 | −0.804142 | ||||||||
\(83\) | −3.48575 | −0.382610 | −0.191305 | − | 0.981531i | \(-0.561272\pi\) | ||||
−0.191305 | + | 0.981531i | \(0.561272\pi\) | |||||||
\(84\) | −7.98031 | −0.870723 | ||||||||
\(85\) | 1.87569 | 0.203447 | ||||||||
\(86\) | 15.2908 | 1.64885 | ||||||||
\(87\) | 5.51770 | 0.591560 | ||||||||
\(88\) | −6.93877 | −0.739675 | ||||||||
\(89\) | −1.89909 | −0.201303 | −0.100651 | − | 0.994922i | \(-0.532093\pi\) | ||||
−0.100651 | + | 0.994922i | \(0.532093\pi\) | |||||||
\(90\) | 3.64811 | 0.384545 | ||||||||
\(91\) | −1.87552 | −0.196607 | ||||||||
\(92\) | −19.6960 | −2.05345 | ||||||||
\(93\) | 1.34611 | 0.139585 | ||||||||
\(94\) | 7.81940 | 0.806509 | ||||||||
\(95\) | 2.38854 | 0.245059 | ||||||||
\(96\) | −7.20442 | −0.735298 | ||||||||
\(97\) | −11.7240 | −1.19039 | −0.595196 | − | 0.803581i | \(-0.702926\pi\) | ||||
−0.595196 | + | 0.803581i | \(0.702926\pi\) | |||||||
\(98\) | 5.36820 | 0.542270 | ||||||||
\(99\) | −4.30532 | −0.432701 | ||||||||
\(100\) | 3.14318 | 0.314318 | ||||||||
\(101\) | 5.78568 | 0.575696 | 0.287848 | − | 0.957676i | \(-0.407060\pi\) | ||||
0.287848 | + | 0.957676i | \(0.407060\pi\) | |||||||
\(102\) | 5.01764 | 0.496821 | ||||||||
\(103\) | −19.2652 | −1.89826 | −0.949129 | − | 0.314887i | \(-0.898033\pi\) | ||||
−0.949129 | + | 0.314887i | \(0.898033\pi\) | |||||||
\(104\) | 2.25904 | 0.221517 | ||||||||
\(105\) | −2.53893 | −0.247774 | ||||||||
\(106\) | −6.05878 | −0.588480 | ||||||||
\(107\) | 12.7793 | 1.23542 | 0.617709 | − | 0.786407i | \(-0.288061\pi\) | ||||
0.617709 | + | 0.786407i | \(0.288061\pi\) | |||||||
\(108\) | 17.0869 | 1.64419 | ||||||||
\(109\) | 12.8600 | 1.23177 | 0.615883 | − | 0.787838i | \(-0.288799\pi\) | ||||
0.615883 | + | 0.787838i | \(0.288799\pi\) | |||||||
\(110\) | −6.06972 | −0.578725 | ||||||||
\(111\) | −4.95555 | −0.470360 | ||||||||
\(112\) | −0.875577 | −0.0827343 | ||||||||
\(113\) | −17.0935 | −1.60802 | −0.804008 | − | 0.594618i | \(-0.797303\pi\) | ||||
−0.804008 | + | 0.594618i | \(0.797303\pi\) | |||||||
\(114\) | 6.38957 | 0.598438 | ||||||||
\(115\) | −6.26628 | −0.584334 | ||||||||
\(116\) | −14.7029 | −1.36513 | ||||||||
\(117\) | 1.40167 | 0.129584 | ||||||||
\(118\) | −24.5413 | −2.25921 | ||||||||
\(119\) | 4.03727 | 0.370096 | ||||||||
\(120\) | 3.05811 | 0.279166 | ||||||||
\(121\) | −3.83683 | −0.348803 | ||||||||
\(122\) | −19.7398 | −1.78716 | ||||||||
\(123\) | −3.78745 | −0.341503 | ||||||||
\(124\) | −3.58697 | −0.322119 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 7.85228 | 0.699537 | ||||||||
\(127\) | 0.0825097 | 0.00732155 | 0.00366078 | − | 0.999993i | \(-0.498835\pi\) | ||||
0.00366078 | + | 0.999993i | \(0.498835\pi\) | |||||||
\(128\) | 17.3524 | 1.53375 | ||||||||
\(129\) | 7.95314 | 0.700235 | ||||||||
\(130\) | 1.97610 | 0.173315 | ||||||||
\(131\) | 14.3859 | 1.25690 | 0.628451 | − | 0.777849i | \(-0.283689\pi\) | ||||
0.628451 | + | 0.777849i | \(0.283689\pi\) | |||||||
\(132\) | −9.92305 | −0.863690 | ||||||||
\(133\) | 5.14114 | 0.445794 | ||||||||
\(134\) | 10.5031 | 0.907330 | ||||||||
\(135\) | 5.43618 | 0.467872 | ||||||||
\(136\) | −4.86284 | −0.416985 | ||||||||
\(137\) | 0.499890 | 0.0427085 | 0.0213542 | − | 0.999772i | \(-0.493202\pi\) | ||||
0.0213542 | + | 0.999772i | \(0.493202\pi\) | |||||||
\(138\) | −16.7629 | −1.42695 | ||||||||
\(139\) | 2.29988 | 0.195073 | 0.0975367 | − | 0.995232i | \(-0.468904\pi\) | ||||
0.0975367 | + | 0.995232i | \(0.468904\pi\) | |||||||
\(140\) | 6.76545 | 0.571785 | ||||||||
\(141\) | 4.06706 | 0.342509 | ||||||||
\(142\) | 19.8758 | 1.66794 | ||||||||
\(143\) | −2.33209 | −0.195019 | ||||||||
\(144\) | 0.654364 | 0.0545303 | ||||||||
\(145\) | −4.67773 | −0.388464 | ||||||||
\(146\) | 17.5942 | 1.45610 | ||||||||
\(147\) | 2.79213 | 0.230291 | ||||||||
\(148\) | 13.2050 | 1.08544 | ||||||||
\(149\) | −19.1682 | −1.57032 | −0.785158 | − | 0.619295i | \(-0.787418\pi\) | ||||
−0.785158 | + | 0.619295i | \(0.787418\pi\) | |||||||
\(150\) | 2.67510 | 0.218421 | ||||||||
\(151\) | −23.8297 | −1.93923 | −0.969615 | − | 0.244636i | \(-0.921332\pi\) | ||||
−0.969615 | + | 0.244636i | \(0.921332\pi\) | |||||||
\(152\) | −6.19244 | −0.502274 | ||||||||
\(153\) | −3.01726 | −0.243931 | ||||||||
\(154\) | −13.0646 | −1.05277 | ||||||||
\(155\) | −1.14119 | −0.0916626 | ||||||||
\(156\) | 3.23062 | 0.258657 | ||||||||
\(157\) | −2.47485 | −0.197515 | −0.0987574 | − | 0.995112i | \(-0.531487\pi\) | ||||
−0.0987574 | + | 0.995112i | \(0.531487\pi\) | |||||||
\(158\) | 3.78522 | 0.301136 | ||||||||
\(159\) | −3.15132 | −0.249916 | ||||||||
\(160\) | 6.10767 | 0.482853 | ||||||||
\(161\) | −13.4877 | −1.06298 | ||||||||
\(162\) | 3.59797 | 0.282683 | ||||||||
\(163\) | 13.9411 | 1.09195 | 0.545977 | − | 0.837800i | \(-0.316159\pi\) | ||||
0.545977 | + | 0.837800i | \(0.316159\pi\) | |||||||
\(164\) | 10.0924 | 0.788081 | ||||||||
\(165\) | −3.15701 | −0.245773 | ||||||||
\(166\) | 7.90517 | 0.613561 | ||||||||
\(167\) | −10.1364 | −0.784377 | −0.392188 | − | 0.919885i | \(-0.628282\pi\) | ||||
−0.392188 | + | 0.919885i | \(0.628282\pi\) | |||||||
\(168\) | 6.58234 | 0.507839 | ||||||||
\(169\) | −12.2407 | −0.941596 | ||||||||
\(170\) | −4.25379 | −0.326251 | ||||||||
\(171\) | −3.84224 | −0.293824 | ||||||||
\(172\) | −21.1926 | −1.61592 | ||||||||
\(173\) | 8.92803 | 0.678786 | 0.339393 | − | 0.940645i | \(-0.389778\pi\) | ||||
0.339393 | + | 0.940645i | \(0.389778\pi\) | |||||||
\(174\) | −12.5134 | −0.948635 | ||||||||
\(175\) | 2.15242 | 0.162708 | ||||||||
\(176\) | −1.08873 | −0.0820660 | ||||||||
\(177\) | −12.7645 | −0.959441 | ||||||||
\(178\) | 4.30686 | 0.322813 | ||||||||
\(179\) | −7.71860 | −0.576915 | −0.288458 | − | 0.957493i | \(-0.593142\pi\) | ||||
−0.288458 | + | 0.957493i | \(0.593142\pi\) | |||||||
\(180\) | −5.05617 | −0.376865 | ||||||||
\(181\) | −2.08498 | −0.154976 | −0.0774878 | − | 0.996993i | \(-0.524690\pi\) | ||||
−0.0774878 | + | 0.996993i | \(0.524690\pi\) | |||||||
\(182\) | 4.25340 | 0.315283 | ||||||||
\(183\) | −10.2672 | −0.758970 | ||||||||
\(184\) | 16.2457 | 1.19765 | ||||||||
\(185\) | 4.20115 | 0.308875 | ||||||||
\(186\) | −3.05279 | −0.223842 | ||||||||
\(187\) | 5.02011 | 0.367107 | ||||||||
\(188\) | −10.8374 | −0.790401 | ||||||||
\(189\) | 11.7010 | 0.851119 | ||||||||
\(190\) | −5.41687 | −0.392981 | ||||||||
\(191\) | −20.8169 | −1.50626 | −0.753129 | − | 0.657873i | \(-0.771456\pi\) | ||||
−0.753129 | + | 0.657873i | \(0.771456\pi\) | |||||||
\(192\) | 15.3789 | 1.10988 | ||||||||
\(193\) | −14.0844 | −1.01382 | −0.506909 | − | 0.862000i | \(-0.669212\pi\) | ||||
−0.506909 | + | 0.862000i | \(0.669212\pi\) | |||||||
\(194\) | 26.5884 | 1.90893 | ||||||||
\(195\) | 1.02782 | 0.0736037 | ||||||||
\(196\) | −7.44015 | −0.531440 | ||||||||
\(197\) | −26.7784 | −1.90788 | −0.953942 | − | 0.299991i | \(-0.903016\pi\) | ||||
−0.953942 | + | 0.299991i | \(0.903016\pi\) | |||||||
\(198\) | 9.76385 | 0.693886 | ||||||||
\(199\) | 26.5851 | 1.88457 | 0.942284 | − | 0.334816i | \(-0.108674\pi\) | ||||
0.942284 | + | 0.334816i | \(0.108674\pi\) | |||||||
\(200\) | −2.59257 | −0.183322 | ||||||||
\(201\) | 5.46293 | 0.385325 | ||||||||
\(202\) | −13.1211 | −0.923197 | ||||||||
\(203\) | −10.0684 | −0.706666 | ||||||||
\(204\) | −6.95429 | −0.486898 | ||||||||
\(205\) | 3.21088 | 0.224257 | ||||||||
\(206\) | 43.6908 | 3.04408 | ||||||||
\(207\) | 10.0800 | 0.700612 | ||||||||
\(208\) | 0.354454 | 0.0245770 | ||||||||
\(209\) | 6.39271 | 0.442193 | ||||||||
\(210\) | 5.75793 | 0.397335 | ||||||||
\(211\) | −6.53514 | −0.449898 | −0.224949 | − | 0.974371i | \(-0.572222\pi\) | ||||
−0.224949 | + | 0.974371i | \(0.572222\pi\) | |||||||
\(212\) | 8.39727 | 0.576727 | ||||||||
\(213\) | 10.3379 | 0.708341 | ||||||||
\(214\) | −28.9815 | −1.98114 | ||||||||
\(215\) | −6.74241 | −0.459829 | ||||||||
\(216\) | −14.0937 | −0.958952 | ||||||||
\(217\) | −2.45632 | −0.166746 | ||||||||
\(218\) | −29.1647 | −1.97528 | ||||||||
\(219\) | 9.15117 | 0.618379 | ||||||||
\(220\) | 8.41243 | 0.567166 | ||||||||
\(221\) | −1.63438 | −0.109940 | ||||||||
\(222\) | 11.2385 | 0.754278 | ||||||||
\(223\) | −25.5269 | −1.70941 | −0.854703 | − | 0.519118i | \(-0.826260\pi\) | ||||
−0.854703 | + | 0.519118i | \(0.826260\pi\) | |||||||
\(224\) | 13.1463 | 0.878372 | ||||||||
\(225\) | −1.60862 | −0.107241 | ||||||||
\(226\) | 38.7655 | 2.57864 | ||||||||
\(227\) | 18.7251 | 1.24283 | 0.621413 | − | 0.783483i | \(-0.286559\pi\) | ||||
0.621413 | + | 0.783483i | \(0.286559\pi\) | |||||||
\(228\) | −8.85574 | −0.586486 | ||||||||
\(229\) | 6.77749 | 0.447869 | 0.223935 | − | 0.974604i | \(-0.428110\pi\) | ||||
0.223935 | + | 0.974604i | \(0.428110\pi\) | |||||||
\(230\) | 14.2110 | 0.937048 | ||||||||
\(231\) | −6.79522 | −0.447093 | ||||||||
\(232\) | 12.1273 | 0.796197 | ||||||||
\(233\) | 18.7073 | 1.22556 | 0.612778 | − | 0.790255i | \(-0.290052\pi\) | ||||
0.612778 | + | 0.790255i | \(0.290052\pi\) | |||||||
\(234\) | −3.17879 | −0.207804 | ||||||||
\(235\) | −3.44792 | −0.224918 | ||||||||
\(236\) | 34.0134 | 2.21409 | ||||||||
\(237\) | 1.96879 | 0.127887 | ||||||||
\(238\) | −9.15596 | −0.593492 | ||||||||
\(239\) | 17.9729 | 1.16257 | 0.581284 | − | 0.813701i | \(-0.302551\pi\) | ||||
0.581284 | + | 0.813701i | \(0.302551\pi\) | |||||||
\(240\) | 0.479833 | 0.0309731 | ||||||||
\(241\) | 8.93184 | 0.575350 | 0.287675 | − | 0.957728i | \(-0.407118\pi\) | ||||
0.287675 | + | 0.957728i | \(0.407118\pi\) | |||||||
\(242\) | 8.70138 | 0.559346 | ||||||||
\(243\) | −14.4372 | −0.926144 | ||||||||
\(244\) | 27.3587 | 1.75146 | ||||||||
\(245\) | −2.36708 | −0.151227 | ||||||||
\(246\) | 8.58940 | 0.547640 | ||||||||
\(247\) | −2.08126 | −0.132427 | ||||||||
\(248\) | 2.95861 | 0.187872 | ||||||||
\(249\) | 4.11168 | 0.260567 | ||||||||
\(250\) | −2.26786 | −0.143432 | ||||||||
\(251\) | 26.6149 | 1.67992 | 0.839959 | − | 0.542650i | \(-0.182579\pi\) | ||||
0.839959 | + | 0.542650i | \(0.182579\pi\) | |||||||
\(252\) | −10.8830 | −0.685565 | ||||||||
\(253\) | −16.7711 | −1.05439 | ||||||||
\(254\) | −0.187120 | −0.0117410 | ||||||||
\(255\) | −2.21250 | −0.138552 | ||||||||
\(256\) | −13.2773 | −0.829832 | ||||||||
\(257\) | −29.3850 | −1.83299 | −0.916494 | − | 0.400049i | \(-0.868993\pi\) | ||||
−0.916494 | + | 0.400049i | \(0.868993\pi\) | |||||||
\(258\) | −18.0366 | −1.12291 | ||||||||
\(259\) | 9.04266 | 0.561883 | ||||||||
\(260\) | −2.73881 | −0.169854 | ||||||||
\(261\) | 7.52467 | 0.465765 | ||||||||
\(262\) | −32.6252 | −2.01559 | ||||||||
\(263\) | −21.1468 | −1.30397 | −0.651985 | − | 0.758232i | \(-0.726063\pi\) | ||||
−0.651985 | + | 0.758232i | \(0.726063\pi\) | |||||||
\(264\) | 8.18476 | 0.503737 | ||||||||
\(265\) | 2.67159 | 0.164114 | ||||||||
\(266\) | −11.6594 | −0.714883 | ||||||||
\(267\) | 2.24011 | 0.137092 | ||||||||
\(268\) | −14.5570 | −0.889209 | ||||||||
\(269\) | 6.64167 | 0.404950 | 0.202475 | − | 0.979287i | \(-0.435102\pi\) | ||||
0.202475 | + | 0.979287i | \(0.435102\pi\) | |||||||
\(270\) | −12.3285 | −0.750288 | ||||||||
\(271\) | 15.0187 | 0.912319 | 0.456160 | − | 0.889898i | \(-0.349225\pi\) | ||||
0.456160 | + | 0.889898i | \(0.349225\pi\) | |||||||
\(272\) | −0.763005 | −0.0462640 | ||||||||
\(273\) | 2.21230 | 0.133895 | ||||||||
\(274\) | −1.13368 | −0.0684880 | ||||||||
\(275\) | 2.67641 | 0.161394 | ||||||||
\(276\) | 23.2328 | 1.39845 | ||||||||
\(277\) | −9.85060 | −0.591865 | −0.295933 | − | 0.955209i | \(-0.595630\pi\) | ||||
−0.295933 | + | 0.955209i | \(0.595630\pi\) | |||||||
\(278\) | −5.21580 | −0.312823 | ||||||||
\(279\) | 1.83574 | 0.109903 | ||||||||
\(280\) | −5.58029 | −0.333486 | ||||||||
\(281\) | 27.2213 | 1.62389 | 0.811943 | − | 0.583736i | \(-0.198410\pi\) | ||||
0.811943 | + | 0.583736i | \(0.198410\pi\) | |||||||
\(282\) | −9.22352 | −0.549253 | ||||||||
\(283\) | −3.27407 | −0.194623 | −0.0973116 | − | 0.995254i | \(-0.531024\pi\) | ||||
−0.0973116 | + | 0.995254i | \(0.531024\pi\) | |||||||
\(284\) | −27.5472 | −1.63463 | ||||||||
\(285\) | −2.81745 | −0.166891 | ||||||||
\(286\) | 5.28885 | 0.312737 | ||||||||
\(287\) | 6.91116 | 0.407953 | ||||||||
\(288\) | −9.82489 | −0.578937 | ||||||||
\(289\) | −13.4818 | −0.793047 | ||||||||
\(290\) | 10.6084 | 0.622948 | ||||||||
\(291\) | 13.8293 | 0.810686 | ||||||||
\(292\) | −24.3850 | −1.42702 | ||||||||
\(293\) | 13.1616 | 0.768911 | 0.384455 | − | 0.923144i | \(-0.374389\pi\) | ||||
0.384455 | + | 0.923144i | \(0.374389\pi\) | |||||||
\(294\) | −6.33216 | −0.369299 | ||||||||
\(295\) | 10.8214 | 0.630043 | ||||||||
\(296\) | −10.8918 | −0.633071 | ||||||||
\(297\) | 14.5495 | 0.844245 | ||||||||
\(298\) | 43.4707 | 2.51819 | ||||||||
\(299\) | 5.46013 | 0.315768 | ||||||||
\(300\) | −3.70760 | −0.214058 | ||||||||
\(301\) | −14.5125 | −0.836488 | ||||||||
\(302\) | 54.0423 | 3.10978 | ||||||||
\(303\) | −6.82461 | −0.392063 | ||||||||
\(304\) | −0.971627 | −0.0557266 | ||||||||
\(305\) | 8.70416 | 0.498398 | ||||||||
\(306\) | 6.84272 | 0.391172 | ||||||||
\(307\) | 27.9742 | 1.59657 | 0.798285 | − | 0.602279i | \(-0.205741\pi\) | ||||
0.798285 | + | 0.602279i | \(0.205741\pi\) | |||||||
\(308\) | 18.1071 | 1.03175 | ||||||||
\(309\) | 22.7247 | 1.29276 | ||||||||
\(310\) | 2.58806 | 0.146992 | ||||||||
\(311\) | 27.0616 | 1.53452 | 0.767261 | − | 0.641335i | \(-0.221619\pi\) | ||||
0.767261 | + | 0.641335i | \(0.221619\pi\) | |||||||
\(312\) | −2.66469 | −0.150858 | ||||||||
\(313\) | −3.07038 | −0.173548 | −0.0867741 | − | 0.996228i | \(-0.527656\pi\) | ||||
−0.0867741 | + | 0.996228i | \(0.527656\pi\) | |||||||
\(314\) | 5.61261 | 0.316738 | ||||||||
\(315\) | −3.46242 | −0.195085 | ||||||||
\(316\) | −5.24620 | −0.295122 | ||||||||
\(317\) | 6.68029 | 0.375202 | 0.187601 | − | 0.982245i | \(-0.439929\pi\) | ||||
0.187601 | + | 0.982245i | \(0.439929\pi\) | |||||||
\(318\) | 7.14675 | 0.400770 | ||||||||
\(319\) | −12.5195 | −0.700958 | ||||||||
\(320\) | −13.0377 | −0.728832 | ||||||||
\(321\) | −15.0740 | −0.841349 | ||||||||
\(322\) | 30.5881 | 1.70461 | ||||||||
\(323\) | 4.48015 | 0.249282 | ||||||||
\(324\) | −4.98667 | −0.277037 | ||||||||
\(325\) | −0.871351 | −0.0483339 | ||||||||
\(326\) | −31.6165 | −1.75108 | ||||||||
\(327\) | −15.1693 | −0.838863 | ||||||||
\(328\) | −8.32441 | −0.459639 | ||||||||
\(329\) | −7.42138 | −0.409154 | ||||||||
\(330\) | 7.15965 | 0.394126 | ||||||||
\(331\) | −5.37572 | −0.295476 | −0.147738 | − | 0.989027i | \(-0.547199\pi\) | ||||
−0.147738 | + | 0.989027i | \(0.547199\pi\) | |||||||
\(332\) | −10.9563 | −0.601306 | ||||||||
\(333\) | −6.75805 | −0.370339 | ||||||||
\(334\) | 22.9879 | 1.25784 | ||||||||
\(335\) | −4.63129 | −0.253034 | ||||||||
\(336\) | 1.03280 | 0.0563441 | ||||||||
\(337\) | 8.61737 | 0.469418 | 0.234709 | − | 0.972066i | \(-0.424586\pi\) | ||||
0.234709 | + | 0.972066i | \(0.424586\pi\) | |||||||
\(338\) | 27.7603 | 1.50996 | ||||||||
\(339\) | 20.1629 | 1.09510 | ||||||||
\(340\) | 5.89562 | 0.319735 | ||||||||
\(341\) | −3.05429 | −0.165399 | ||||||||
\(342\) | 8.71366 | 0.471181 | ||||||||
\(343\) | −20.1619 | −1.08864 | ||||||||
\(344\) | 17.4802 | 0.942467 | ||||||||
\(345\) | 7.39151 | 0.397946 | ||||||||
\(346\) | −20.2475 | −1.08851 | ||||||||
\(347\) | −35.2905 | −1.89449 | −0.947247 | − | 0.320505i | \(-0.896148\pi\) | ||||
−0.947247 | + | 0.320505i | \(0.896148\pi\) | |||||||
\(348\) | 17.3431 | 0.929689 | ||||||||
\(349\) | 8.71790 | 0.466659 | 0.233329 | − | 0.972398i | \(-0.425038\pi\) | ||||
0.233329 | + | 0.972398i | \(0.425038\pi\) | |||||||
\(350\) | −4.88139 | −0.260921 | ||||||||
\(351\) | −4.73682 | −0.252833 | ||||||||
\(352\) | 16.3466 | 0.871278 | ||||||||
\(353\) | −9.15282 | −0.487155 | −0.243578 | − | 0.969881i | \(-0.578321\pi\) | ||||
−0.243578 | + | 0.969881i | \(0.578321\pi\) | |||||||
\(354\) | 28.9481 | 1.53858 | ||||||||
\(355\) | −8.76413 | −0.465152 | ||||||||
\(356\) | −5.96917 | −0.316366 | ||||||||
\(357\) | −4.76224 | −0.252044 | ||||||||
\(358\) | 17.5047 | 0.925151 | ||||||||
\(359\) | 27.5872 | 1.45600 | 0.727998 | − | 0.685579i | \(-0.240451\pi\) | ||||
0.727998 | + | 0.685579i | \(0.240451\pi\) | |||||||
\(360\) | 4.17044 | 0.219802 | ||||||||
\(361\) | −13.2949 | −0.699731 | ||||||||
\(362\) | 4.72844 | 0.248522 | ||||||||
\(363\) | 4.52581 | 0.237543 | ||||||||
\(364\) | −5.89508 | −0.308986 | ||||||||
\(365\) | −7.75806 | −0.406075 | ||||||||
\(366\) | 23.2844 | 1.21710 | ||||||||
\(367\) | −6.96519 | −0.363580 | −0.181790 | − | 0.983337i | \(-0.558189\pi\) | ||||
−0.181790 | + | 0.983337i | \(0.558189\pi\) | |||||||
\(368\) | 2.54904 | 0.132878 | ||||||||
\(369\) | −5.16507 | −0.268883 | ||||||||
\(370\) | −9.52762 | −0.495317 | ||||||||
\(371\) | 5.75038 | 0.298545 | ||||||||
\(372\) | 4.23107 | 0.219371 | ||||||||
\(373\) | −1.22195 | −0.0632701 | −0.0316351 | − | 0.999499i | \(-0.510071\pi\) | ||||
−0.0316351 | + | 0.999499i | \(0.510071\pi\) | |||||||
\(374\) | −11.3849 | −0.588699 | ||||||||
\(375\) | −1.17957 | −0.0609127 | ||||||||
\(376\) | 8.93897 | 0.460992 | ||||||||
\(377\) | 4.07594 | 0.209922 | ||||||||
\(378\) | −26.5361 | −1.36487 | ||||||||
\(379\) | −0.590855 | −0.0303502 | −0.0151751 | − | 0.999885i | \(-0.504831\pi\) | ||||
−0.0151751 | + | 0.999885i | \(0.504831\pi\) | |||||||
\(380\) | 7.50760 | 0.385132 | ||||||||
\(381\) | −0.0973259 | −0.00498616 | ||||||||
\(382\) | 47.2098 | 2.41546 | ||||||||
\(383\) | 11.6682 | 0.596217 | 0.298109 | − | 0.954532i | \(-0.403644\pi\) | ||||
0.298109 | + | 0.954532i | \(0.403644\pi\) | |||||||
\(384\) | −20.4684 | −1.04452 | ||||||||
\(385\) | 5.76076 | 0.293596 | ||||||||
\(386\) | 31.9414 | 1.62578 | ||||||||
\(387\) | 10.8460 | 0.551331 | ||||||||
\(388\) | −36.8506 | −1.87081 | ||||||||
\(389\) | −20.7143 | −1.05026 | −0.525129 | − | 0.851023i | \(-0.675983\pi\) | ||||
−0.525129 | + | 0.851023i | \(0.675983\pi\) | |||||||
\(390\) | −2.33095 | −0.118032 | ||||||||
\(391\) | −11.7536 | −0.594404 | ||||||||
\(392\) | 6.13681 | 0.309956 | ||||||||
\(393\) | −16.9692 | −0.855982 | ||||||||
\(394\) | 60.7297 | 3.05952 | ||||||||
\(395\) | −1.66908 | −0.0839803 | ||||||||
\(396\) | −13.5324 | −0.680028 | ||||||||
\(397\) | 10.2217 | 0.513013 | 0.256506 | − | 0.966543i | \(-0.417429\pi\) | ||||
0.256506 | + | 0.966543i | \(0.417429\pi\) | |||||||
\(398\) | −60.2912 | −3.02212 | ||||||||
\(399\) | −6.06433 | −0.303596 | ||||||||
\(400\) | −0.406787 | −0.0203393 | ||||||||
\(401\) | −24.8160 | −1.23925 | −0.619626 | − | 0.784897i | \(-0.712716\pi\) | ||||
−0.619626 | + | 0.784897i | \(0.712716\pi\) | |||||||
\(402\) | −12.3891 | −0.617914 | ||||||||
\(403\) | 0.994378 | 0.0495335 | ||||||||
\(404\) | 18.1854 | 0.904758 | ||||||||
\(405\) | −1.58650 | −0.0788340 | ||||||||
\(406\) | 22.8338 | 1.13322 | ||||||||
\(407\) | 11.2440 | 0.557345 | ||||||||
\(408\) | 5.73606 | 0.283977 | ||||||||
\(409\) | 21.5935 | 1.06773 | 0.533866 | − | 0.845569i | \(-0.320739\pi\) | ||||
0.533866 | + | 0.845569i | \(0.320739\pi\) | |||||||
\(410\) | −7.28181 | −0.359623 | ||||||||
\(411\) | −0.589655 | −0.0290855 | ||||||||
\(412\) | −60.5540 | −2.98328 | ||||||||
\(413\) | 23.2921 | 1.14613 | ||||||||
\(414\) | −22.8601 | −1.12351 | ||||||||
\(415\) | −3.48575 | −0.171109 | ||||||||
\(416\) | −5.32192 | −0.260929 | ||||||||
\(417\) | −2.71287 | −0.132850 | ||||||||
\(418\) | −14.4978 | −0.709108 | ||||||||
\(419\) | 9.24921 | 0.451853 | 0.225927 | − | 0.974144i | \(-0.427459\pi\) | ||||
0.225927 | + | 0.974144i | \(0.427459\pi\) | |||||||
\(420\) | −7.98031 | −0.389399 | ||||||||
\(421\) | 16.7295 | 0.815344 | 0.407672 | − | 0.913128i | \(-0.366341\pi\) | ||||
0.407672 | + | 0.913128i | \(0.366341\pi\) | |||||||
\(422\) | 14.8208 | 0.721464 | ||||||||
\(423\) | 5.54638 | 0.269674 | ||||||||
\(424\) | −6.92626 | −0.336369 | ||||||||
\(425\) | 1.87569 | 0.0909842 | ||||||||
\(426\) | −23.4449 | −1.13591 | ||||||||
\(427\) | 18.7350 | 0.906651 | ||||||||
\(428\) | 40.1675 | 1.94157 | ||||||||
\(429\) | 2.75087 | 0.132813 | ||||||||
\(430\) | 15.2908 | 0.737390 | ||||||||
\(431\) | 2.38773 | 0.115013 | 0.0575066 | − | 0.998345i | \(-0.481685\pi\) | ||||
0.0575066 | + | 0.998345i | \(0.481685\pi\) | |||||||
\(432\) | −2.21137 | −0.106394 | ||||||||
\(433\) | −24.0579 | −1.15615 | −0.578074 | − | 0.815984i | \(-0.696196\pi\) | ||||
−0.578074 | + | 0.815984i | \(0.696196\pi\) | |||||||
\(434\) | 5.57059 | 0.267397 | ||||||||
\(435\) | 5.51770 | 0.264554 | ||||||||
\(436\) | 40.4213 | 1.93583 | ||||||||
\(437\) | −14.9673 | −0.715981 | ||||||||
\(438\) | −20.7535 | −0.991643 | ||||||||
\(439\) | −24.5456 | −1.17150 | −0.585748 | − | 0.810493i | \(-0.699199\pi\) | ||||
−0.585748 | + | 0.810493i | \(0.699199\pi\) | |||||||
\(440\) | −6.93877 | −0.330793 | ||||||||
\(441\) | 3.80772 | 0.181320 | ||||||||
\(442\) | 3.70655 | 0.176302 | ||||||||
\(443\) | 27.4866 | 1.30593 | 0.652965 | − | 0.757388i | \(-0.273525\pi\) | ||||
0.652965 | + | 0.757388i | \(0.273525\pi\) | |||||||
\(444\) | −15.5762 | −0.739213 | ||||||||
\(445\) | −1.89909 | −0.0900254 | ||||||||
\(446\) | 57.8913 | 2.74123 | ||||||||
\(447\) | 22.6102 | 1.06942 | ||||||||
\(448\) | −28.0627 | −1.32584 | ||||||||
\(449\) | 0.815687 | 0.0384946 | 0.0192473 | − | 0.999815i | \(-0.493873\pi\) | ||||
0.0192473 | + | 0.999815i | \(0.493873\pi\) | |||||||
\(450\) | 3.64811 | 0.171974 | ||||||||
\(451\) | 8.59363 | 0.404658 | ||||||||
\(452\) | −53.7278 | −2.52714 | ||||||||
\(453\) | 28.1087 | 1.32066 | ||||||||
\(454\) | −42.4657 | −1.99302 | ||||||||
\(455\) | −1.87552 | −0.0879255 | ||||||||
\(456\) | 7.30442 | 0.342061 | ||||||||
\(457\) | 36.9412 | 1.72803 | 0.864017 | − | 0.503462i | \(-0.167941\pi\) | ||||
0.864017 | + | 0.503462i | \(0.167941\pi\) | |||||||
\(458\) | −15.3704 | −0.718211 | ||||||||
\(459\) | 10.1966 | 0.475936 | ||||||||
\(460\) | −19.6960 | −0.918333 | ||||||||
\(461\) | −20.5808 | −0.958545 | −0.479273 | − | 0.877666i | \(-0.659099\pi\) | ||||
−0.479273 | + | 0.877666i | \(0.659099\pi\) | |||||||
\(462\) | 15.4106 | 0.716966 | ||||||||
\(463\) | 26.8023 | 1.24561 | 0.622804 | − | 0.782378i | \(-0.285993\pi\) | ||||
0.622804 | + | 0.782378i | \(0.285993\pi\) | |||||||
\(464\) | 1.90284 | 0.0883370 | ||||||||
\(465\) | 1.34611 | 0.0624245 | ||||||||
\(466\) | −42.4255 | −1.96532 | ||||||||
\(467\) | −14.5415 | −0.672902 | −0.336451 | − | 0.941701i | \(-0.609227\pi\) | ||||
−0.336451 | + | 0.941701i | \(0.609227\pi\) | |||||||
\(468\) | 4.40570 | 0.203653 | ||||||||
\(469\) | −9.96849 | −0.460302 | ||||||||
\(470\) | 7.81940 | 0.360682 | ||||||||
\(471\) | 2.91926 | 0.134512 | ||||||||
\(472\) | −28.0551 | −1.29134 | ||||||||
\(473\) | −18.0455 | −0.829731 | ||||||||
\(474\) | −4.46494 | −0.205081 | ||||||||
\(475\) | 2.38854 | 0.109594 | ||||||||
\(476\) | 12.6899 | 0.581639 | ||||||||
\(477\) | −4.29756 | −0.196772 | ||||||||
\(478\) | −40.7599 | −1.86431 | ||||||||
\(479\) | 16.1558 | 0.738176 | 0.369088 | − | 0.929394i | \(-0.379670\pi\) | ||||
0.369088 | + | 0.929394i | \(0.379670\pi\) | |||||||
\(480\) | −7.20442 | −0.328835 | ||||||||
\(481\) | −3.66068 | −0.166913 | ||||||||
\(482\) | −20.2561 | −0.922642 | ||||||||
\(483\) | 15.9097 | 0.723914 | ||||||||
\(484\) | −12.0598 | −0.548175 | ||||||||
\(485\) | −11.7240 | −0.532359 | ||||||||
\(486\) | 32.7414 | 1.48518 | ||||||||
\(487\) | 13.5078 | 0.612098 | 0.306049 | − | 0.952016i | \(-0.400993\pi\) | ||||
0.306049 | + | 0.952016i | \(0.400993\pi\) | |||||||
\(488\) | −22.5661 | −1.02152 | ||||||||
\(489\) | −16.4445 | −0.743647 | ||||||||
\(490\) | 5.36820 | 0.242511 | ||||||||
\(491\) | 0.658614 | 0.0297228 | 0.0148614 | − | 0.999890i | \(-0.495269\pi\) | ||||
0.0148614 | + | 0.999890i | \(0.495269\pi\) | |||||||
\(492\) | −11.9046 | −0.536703 | ||||||||
\(493\) | −8.77395 | −0.395159 | ||||||||
\(494\) | 4.71999 | 0.212363 | ||||||||
\(495\) | −4.30532 | −0.193510 | ||||||||
\(496\) | 0.464221 | 0.0208442 | ||||||||
\(497\) | −18.8641 | −0.846171 | ||||||||
\(498\) | −9.32470 | −0.417850 | ||||||||
\(499\) | −32.4550 | −1.45289 | −0.726443 | − | 0.687226i | \(-0.758828\pi\) | ||||
−0.726443 | + | 0.687226i | \(0.758828\pi\) | |||||||
\(500\) | 3.14318 | 0.140567 | ||||||||
\(501\) | 11.9566 | 0.534180 | ||||||||
\(502\) | −60.3588 | −2.69395 | ||||||||
\(503\) | −1.91624 | −0.0854411 | −0.0427205 | − | 0.999087i | \(-0.513603\pi\) | ||||
−0.0427205 | + | 0.999087i | \(0.513603\pi\) | |||||||
\(504\) | 8.97655 | 0.399847 | ||||||||
\(505\) | 5.78568 | 0.257459 | ||||||||
\(506\) | 38.0346 | 1.69084 | ||||||||
\(507\) | 14.4388 | 0.641250 | ||||||||
\(508\) | 0.259343 | 0.0115065 | ||||||||
\(509\) | 30.6006 | 1.35635 | 0.678174 | − | 0.734902i | \(-0.262772\pi\) | ||||
0.678174 | + | 0.734902i | \(0.262772\pi\) | |||||||
\(510\) | 5.01764 | 0.222185 | ||||||||
\(511\) | −16.6986 | −0.738703 | ||||||||
\(512\) | −4.59376 | −0.203018 | ||||||||
\(513\) | 12.9845 | 0.573281 | ||||||||
\(514\) | 66.6411 | 2.93941 | ||||||||
\(515\) | −19.2652 | −0.848927 | ||||||||
\(516\) | 24.9982 | 1.10048 | ||||||||
\(517\) | −9.22805 | −0.405849 | ||||||||
\(518\) | −20.5075 | −0.901046 | ||||||||
\(519\) | −10.5312 | −0.462270 | ||||||||
\(520\) | 2.25904 | 0.0990652 | ||||||||
\(521\) | 6.69698 | 0.293400 | 0.146700 | − | 0.989181i | \(-0.453135\pi\) | ||||
0.146700 | + | 0.989181i | \(0.453135\pi\) | |||||||
\(522\) | −17.0649 | −0.746909 | ||||||||
\(523\) | 12.7692 | 0.558358 | 0.279179 | − | 0.960239i | \(-0.409938\pi\) | ||||
0.279179 | + | 0.960239i | \(0.409938\pi\) | |||||||
\(524\) | 45.2175 | 1.97533 | ||||||||
\(525\) | −2.53893 | −0.110808 | ||||||||
\(526\) | 47.9580 | 2.09107 | ||||||||
\(527\) | −2.14052 | −0.0932424 | ||||||||
\(528\) | 1.28423 | 0.0558890 | ||||||||
\(529\) | 16.2663 | 0.707230 | ||||||||
\(530\) | −6.05878 | −0.263176 | ||||||||
\(531\) | −17.4074 | −0.755417 | ||||||||
\(532\) | 16.1595 | 0.700605 | ||||||||
\(533\) | −2.79780 | −0.121186 | ||||||||
\(534\) | −5.08024 | −0.219844 | ||||||||
\(535\) | 12.7793 | 0.552495 | ||||||||
\(536\) | 12.0069 | 0.518620 | ||||||||
\(537\) | 9.10462 | 0.392893 | ||||||||
\(538\) | −15.0624 | −0.649385 | ||||||||
\(539\) | −6.33528 | −0.272880 | ||||||||
\(540\) | 17.0869 | 0.735303 | ||||||||
\(541\) | 16.8445 | 0.724201 | 0.362101 | − | 0.932139i | \(-0.382060\pi\) | ||||
0.362101 | + | 0.932139i | \(0.382060\pi\) | |||||||
\(542\) | −34.0602 | −1.46301 | ||||||||
\(543\) | 2.45938 | 0.105542 | ||||||||
\(544\) | 11.4561 | 0.491175 | ||||||||
\(545\) | 12.8600 | 0.550862 | ||||||||
\(546\) | −5.01718 | −0.214716 | ||||||||
\(547\) | −40.7302 | −1.74150 | −0.870748 | − | 0.491729i | \(-0.836365\pi\) | ||||
−0.870748 | + | 0.491729i | \(0.836365\pi\) | |||||||
\(548\) | 1.57124 | 0.0671202 | ||||||||
\(549\) | −14.0016 | −0.597576 | ||||||||
\(550\) | −6.06972 | −0.258814 | ||||||||
\(551\) | −11.1729 | −0.475983 | ||||||||
\(552\) | −19.1630 | −0.815631 | ||||||||
\(553\) | −3.59255 | −0.152771 | ||||||||
\(554\) | 22.3398 | 0.949125 | ||||||||
\(555\) | −4.95555 | −0.210351 | ||||||||
\(556\) | 7.22894 | 0.306575 | ||||||||
\(557\) | −12.6720 | −0.536929 | −0.268465 | − | 0.963290i | \(-0.586516\pi\) | ||||
−0.268465 | + | 0.963290i | \(0.586516\pi\) | |||||||
\(558\) | −4.16319 | −0.176242 | ||||||||
\(559\) | 5.87501 | 0.248486 | ||||||||
\(560\) | −0.875577 | −0.0369999 | ||||||||
\(561\) | −5.92157 | −0.250009 | ||||||||
\(562\) | −61.7340 | −2.60409 | ||||||||
\(563\) | −21.7518 | −0.916727 | −0.458364 | − | 0.888765i | \(-0.651564\pi\) | ||||
−0.458364 | + | 0.888765i | \(0.651564\pi\) | |||||||
\(564\) | 12.7835 | 0.538283 | ||||||||
\(565\) | −17.0935 | −0.719127 | ||||||||
\(566\) | 7.42512 | 0.312101 | ||||||||
\(567\) | −3.41483 | −0.143409 | ||||||||
\(568\) | 22.7216 | 0.953376 | ||||||||
\(569\) | −19.8873 | −0.833720 | −0.416860 | − | 0.908971i | \(-0.636869\pi\) | ||||
−0.416860 | + | 0.908971i | \(0.636869\pi\) | |||||||
\(570\) | 6.38957 | 0.267630 | ||||||||
\(571\) | −6.68180 | −0.279625 | −0.139812 | − | 0.990178i | \(-0.544650\pi\) | ||||
−0.139812 | + | 0.990178i | \(0.544650\pi\) | |||||||
\(572\) | −7.33018 | −0.306490 | ||||||||
\(573\) | 24.5550 | 1.02580 | ||||||||
\(574\) | −15.6735 | −0.654201 | ||||||||
\(575\) | −6.26628 | −0.261322 | ||||||||
\(576\) | 20.9727 | 0.873864 | ||||||||
\(577\) | −43.2384 | −1.80004 | −0.900020 | − | 0.435849i | \(-0.856448\pi\) | ||||
−0.900020 | + | 0.435849i | \(0.856448\pi\) | |||||||
\(578\) | 30.5748 | 1.27174 | ||||||||
\(579\) | 16.6135 | 0.690435 | ||||||||
\(580\) | −14.7029 | −0.610506 | ||||||||
\(581\) | −7.50280 | −0.311268 | ||||||||
\(582\) | −31.3628 | −1.30003 | ||||||||
\(583\) | 7.15026 | 0.296133 | ||||||||
\(584\) | 20.1133 | 0.832293 | ||||||||
\(585\) | 1.40167 | 0.0579519 | ||||||||
\(586\) | −29.8487 | −1.23304 | ||||||||
\(587\) | 14.9180 | 0.615731 | 0.307865 | − | 0.951430i | \(-0.400385\pi\) | ||||
0.307865 | + | 0.951430i | \(0.400385\pi\) | |||||||
\(588\) | 8.77618 | 0.361923 | ||||||||
\(589\) | −2.72578 | −0.112314 | ||||||||
\(590\) | −24.5413 | −1.01035 | ||||||||
\(591\) | 31.5870 | 1.29932 | ||||||||
\(592\) | −1.70897 | −0.0702384 | ||||||||
\(593\) | 8.39461 | 0.344725 | 0.172363 | − | 0.985034i | \(-0.444860\pi\) | ||||
0.172363 | + | 0.985034i | \(0.444860\pi\) | |||||||
\(594\) | −32.9961 | −1.35385 | ||||||||
\(595\) | 4.03727 | 0.165512 | ||||||||
\(596\) | −60.2489 | −2.46789 | ||||||||
\(597\) | −31.3590 | −1.28344 | ||||||||
\(598\) | −12.3828 | −0.506371 | ||||||||
\(599\) | 15.0159 | 0.613532 | 0.306766 | − | 0.951785i | \(-0.400753\pi\) | ||||
0.306766 | + | 0.951785i | \(0.400753\pi\) | |||||||
\(600\) | 3.05811 | 0.124847 | ||||||||
\(601\) | −30.3220 | −1.23686 | −0.618431 | − | 0.785839i | \(-0.712231\pi\) | ||||
−0.618431 | + | 0.785839i | \(0.712231\pi\) | |||||||
\(602\) | 32.9123 | 1.34141 | ||||||||
\(603\) | 7.44997 | 0.303386 | ||||||||
\(604\) | −74.9009 | −3.04767 | ||||||||
\(605\) | −3.83683 | −0.155989 | ||||||||
\(606\) | 15.4772 | 0.628720 | ||||||||
\(607\) | −24.5095 | −0.994808 | −0.497404 | − | 0.867519i | \(-0.665713\pi\) | ||||
−0.497404 | + | 0.867519i | \(0.665713\pi\) | |||||||
\(608\) | 14.5884 | 0.591638 | ||||||||
\(609\) | 11.8764 | 0.481257 | ||||||||
\(610\) | −19.7398 | −0.799241 | ||||||||
\(611\) | 3.00435 | 0.121543 | ||||||||
\(612\) | −9.48379 | −0.383360 | ||||||||
\(613\) | −10.6258 | −0.429171 | −0.214585 | − | 0.976705i | \(-0.568840\pi\) | ||||
−0.214585 | + | 0.976705i | \(0.568840\pi\) | |||||||
\(614\) | −63.4415 | −2.56029 | ||||||||
\(615\) | −3.78745 | −0.152725 | ||||||||
\(616\) | −14.9352 | −0.601755 | ||||||||
\(617\) | −0.813911 | −0.0327668 | −0.0163834 | − | 0.999866i | \(-0.505215\pi\) | ||||
−0.0163834 | + | 0.999866i | \(0.505215\pi\) | |||||||
\(618\) | −51.5363 | −2.07309 | ||||||||
\(619\) | −23.0166 | −0.925114 | −0.462557 | − | 0.886589i | \(-0.653068\pi\) | ||||
−0.462557 | + | 0.886589i | \(0.653068\pi\) | |||||||
\(620\) | −3.58697 | −0.144056 | ||||||||
\(621\) | −34.0647 | −1.36697 | ||||||||
\(622\) | −61.3718 | −2.46079 | ||||||||
\(623\) | −4.08764 | −0.163768 | ||||||||
\(624\) | −0.418103 | −0.0167375 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 6.96319 | 0.278305 | ||||||||
\(627\) | −7.54064 | −0.301144 | ||||||||
\(628\) | −7.77890 | −0.310412 | ||||||||
\(629\) | 7.88005 | 0.314198 | ||||||||
\(630\) | 7.85228 | 0.312842 | ||||||||
\(631\) | −35.2879 | −1.40479 | −0.702394 | − | 0.711788i | \(-0.747886\pi\) | ||||
−0.702394 | + | 0.711788i | \(0.747886\pi\) | |||||||
\(632\) | 4.32719 | 0.172126 | ||||||||
\(633\) | 7.70866 | 0.306392 | ||||||||
\(634\) | −15.1499 | −0.601681 | ||||||||
\(635\) | 0.0825097 | 0.00327430 | ||||||||
\(636\) | −9.90516 | −0.392765 | ||||||||
\(637\) | 2.06256 | 0.0817215 | ||||||||
\(638\) | 28.3925 | 1.12407 | ||||||||
\(639\) | 14.0981 | 0.557713 | ||||||||
\(640\) | 17.3524 | 0.685914 | ||||||||
\(641\) | 33.2214 | 1.31217 | 0.656083 | − | 0.754689i | \(-0.272212\pi\) | ||||
0.656083 | + | 0.754689i | \(0.272212\pi\) | |||||||
\(642\) | 34.1857 | 1.34920 | ||||||||
\(643\) | 10.6624 | 0.420484 | 0.210242 | − | 0.977649i | \(-0.432575\pi\) | ||||
0.210242 | + | 0.977649i | \(0.432575\pi\) | |||||||
\(644\) | −42.3942 | −1.67057 | ||||||||
\(645\) | 7.95314 | 0.313155 | ||||||||
\(646\) | −10.1603 | −0.399754 | ||||||||
\(647\) | −27.5899 | −1.08467 | −0.542335 | − | 0.840162i | \(-0.682460\pi\) | ||||
−0.542335 | + | 0.840162i | \(0.682460\pi\) | |||||||
\(648\) | 4.11312 | 0.161578 | ||||||||
\(649\) | 28.9624 | 1.13687 | ||||||||
\(650\) | 1.97610 | 0.0775090 | ||||||||
\(651\) | 2.89740 | 0.113558 | ||||||||
\(652\) | 43.8195 | 1.71610 | ||||||||
\(653\) | 27.0599 | 1.05893 | 0.529467 | − | 0.848330i | \(-0.322392\pi\) | ||||
0.529467 | + | 0.848330i | \(0.322392\pi\) | |||||||
\(654\) | 34.4018 | 1.34522 | ||||||||
\(655\) | 14.3859 | 0.562104 | ||||||||
\(656\) | −1.30614 | −0.0509963 | ||||||||
\(657\) | 12.4797 | 0.486881 | ||||||||
\(658\) | 16.8306 | 0.656127 | ||||||||
\(659\) | 4.50008 | 0.175298 | 0.0876492 | − | 0.996151i | \(-0.472065\pi\) | ||||
0.0876492 | + | 0.996151i | \(0.472065\pi\) | |||||||
\(660\) | −9.92305 | −0.386254 | ||||||||
\(661\) | −23.2858 | −0.905714 | −0.452857 | − | 0.891583i | \(-0.649595\pi\) | ||||
−0.452857 | + | 0.891583i | \(0.649595\pi\) | |||||||
\(662\) | 12.1914 | 0.473831 | ||||||||
\(663\) | 1.92787 | 0.0748722 | ||||||||
\(664\) | 9.03702 | 0.350705 | ||||||||
\(665\) | 5.14114 | 0.199365 | ||||||||
\(666\) | 15.3263 | 0.593881 | ||||||||
\(667\) | 29.3119 | 1.13496 | ||||||||
\(668\) | −31.8605 | −1.23272 | ||||||||
\(669\) | 30.1107 | 1.16415 | ||||||||
\(670\) | 10.5031 | 0.405770 | ||||||||
\(671\) | 23.2959 | 0.899328 | ||||||||
\(672\) | −15.5069 | −0.598193 | ||||||||
\(673\) | −7.90601 | −0.304754 | −0.152377 | − | 0.988322i | \(-0.548693\pi\) | ||||
−0.152377 | + | 0.988322i | \(0.548693\pi\) | |||||||
\(674\) | −19.5430 | −0.752767 | ||||||||
\(675\) | 5.43618 | 0.209239 | ||||||||
\(676\) | −38.4749 | −1.47980 | ||||||||
\(677\) | 31.5502 | 1.21257 | 0.606287 | − | 0.795246i | \(-0.292658\pi\) | ||||
0.606287 | + | 0.795246i | \(0.292658\pi\) | |||||||
\(678\) | −45.7266 | −1.75612 | ||||||||
\(679\) | −25.2350 | −0.968430 | ||||||||
\(680\) | −4.86284 | −0.186482 | ||||||||
\(681\) | −22.0875 | −0.846395 | ||||||||
\(682\) | 6.92670 | 0.265237 | ||||||||
\(683\) | −32.0048 | −1.22463 | −0.612315 | − | 0.790614i | \(-0.709762\pi\) | ||||
−0.612315 | + | 0.790614i | \(0.709762\pi\) | |||||||
\(684\) | −12.0769 | −0.461770 | ||||||||
\(685\) | 0.499890 | 0.0190998 | ||||||||
\(686\) | 45.7243 | 1.74576 | ||||||||
\(687\) | −7.99452 | −0.305010 | ||||||||
\(688\) | 2.74273 | 0.104565 | ||||||||
\(689\) | −2.32789 | −0.0886855 | ||||||||
\(690\) | −16.7629 | −0.638153 | ||||||||
\(691\) | −52.1096 | −1.98234 | −0.991170 | − | 0.132594i | \(-0.957669\pi\) | ||||
−0.991170 | + | 0.132594i | \(0.957669\pi\) | |||||||
\(692\) | 28.0624 | 1.06677 | ||||||||
\(693\) | −9.26686 | −0.352019 | ||||||||
\(694\) | 80.0339 | 3.03804 | ||||||||
\(695\) | 2.29988 | 0.0872395 | ||||||||
\(696\) | −14.3050 | −0.542230 | ||||||||
\(697\) | 6.02260 | 0.228122 | ||||||||
\(698\) | −19.7710 | −0.748342 | ||||||||
\(699\) | −22.0666 | −0.834634 | ||||||||
\(700\) | 6.76545 | 0.255710 | ||||||||
\(701\) | 18.5657 | 0.701218 | 0.350609 | − | 0.936522i | \(-0.385975\pi\) | ||||
0.350609 | + | 0.936522i | \(0.385975\pi\) | |||||||
\(702\) | 10.7424 | 0.405447 | ||||||||
\(703\) | 10.0346 | 0.378463 | ||||||||
\(704\) | −34.8943 | −1.31513 | ||||||||
\(705\) | 4.06706 | 0.153174 | ||||||||
\(706\) | 20.7573 | 0.781211 | ||||||||
\(707\) | 12.4532 | 0.468352 | ||||||||
\(708\) | −40.1212 | −1.50785 | ||||||||
\(709\) | −27.5543 | −1.03482 | −0.517411 | − | 0.855737i | \(-0.673104\pi\) | ||||
−0.517411 | + | 0.855737i | \(0.673104\pi\) | |||||||
\(710\) | 19.8758 | 0.745926 | ||||||||
\(711\) | 2.68490 | 0.100692 | ||||||||
\(712\) | 4.92351 | 0.184516 | ||||||||
\(713\) | 7.15102 | 0.267808 | ||||||||
\(714\) | 10.8001 | 0.404183 | ||||||||
\(715\) | −2.33209 | −0.0872153 | ||||||||
\(716\) | −24.2609 | −0.906673 | ||||||||
\(717\) | −21.2002 | −0.791737 | ||||||||
\(718\) | −62.5638 | −2.33486 | ||||||||
\(719\) | 3.70636 | 0.138224 | 0.0691119 | − | 0.997609i | \(-0.477983\pi\) | ||||
0.0691119 | + | 0.997609i | \(0.477983\pi\) | |||||||
\(720\) | 0.654364 | 0.0243867 | ||||||||
\(721\) | −41.4669 | −1.54431 | ||||||||
\(722\) | 30.1509 | 1.12210 | ||||||||
\(723\) | −10.5357 | −0.391828 | ||||||||
\(724\) | −6.55347 | −0.243558 | ||||||||
\(725\) | −4.67773 | −0.173726 | ||||||||
\(726\) | −10.2639 | −0.380929 | ||||||||
\(727\) | −24.7897 | −0.919399 | −0.459699 | − | 0.888075i | \(-0.652043\pi\) | ||||
−0.459699 | + | 0.888075i | \(0.652043\pi\) | |||||||
\(728\) | 4.86240 | 0.180212 | ||||||||
\(729\) | 21.7891 | 0.807005 | ||||||||
\(730\) | 17.5942 | 0.651190 | ||||||||
\(731\) | −12.6467 | −0.467754 | ||||||||
\(732\) | −32.2715 | −1.19279 | ||||||||
\(733\) | −48.2555 | −1.78236 | −0.891179 | − | 0.453651i | \(-0.850121\pi\) | ||||
−0.891179 | + | 0.453651i | \(0.850121\pi\) | |||||||
\(734\) | 15.7961 | 0.583043 | ||||||||
\(735\) | 2.79213 | 0.102989 | ||||||||
\(736\) | −38.2724 | −1.41074 | ||||||||
\(737\) | −12.3952 | −0.456584 | ||||||||
\(738\) | 11.7136 | 0.431185 | ||||||||
\(739\) | −1.74310 | −0.0641210 | −0.0320605 | − | 0.999486i | \(-0.510207\pi\) | ||||
−0.0320605 | + | 0.999486i | \(0.510207\pi\) | |||||||
\(740\) | 13.2050 | 0.485425 | ||||||||
\(741\) | 2.45499 | 0.0901862 | ||||||||
\(742\) | −13.0410 | −0.478752 | ||||||||
\(743\) | 17.9667 | 0.659136 | 0.329568 | − | 0.944132i | \(-0.393097\pi\) | ||||
0.329568 | + | 0.944132i | \(0.393097\pi\) | |||||||
\(744\) | −3.48989 | −0.127945 | ||||||||
\(745\) | −19.1682 | −0.702267 | ||||||||
\(746\) | 2.77121 | 0.101461 | ||||||||
\(747\) | 5.60723 | 0.205158 | ||||||||
\(748\) | 15.7791 | 0.576941 | ||||||||
\(749\) | 27.5063 | 1.00506 | ||||||||
\(750\) | 2.67510 | 0.0976807 | ||||||||
\(751\) | −45.2066 | −1.64961 | −0.824805 | − | 0.565417i | \(-0.808715\pi\) | ||||
−0.824805 | + | 0.565417i | \(0.808715\pi\) | |||||||
\(752\) | 1.40257 | 0.0511465 | ||||||||
\(753\) | −31.3941 | −1.14407 | ||||||||
\(754\) | −9.24366 | −0.336634 | ||||||||
\(755\) | −23.8297 | −0.867250 | ||||||||
\(756\) | 36.7782 | 1.33761 | ||||||||
\(757\) | −29.7522 | −1.08136 | −0.540682 | − | 0.841227i | \(-0.681834\pi\) | ||||
−0.540682 | + | 0.841227i | \(0.681834\pi\) | |||||||
\(758\) | 1.33998 | 0.0486701 | ||||||||
\(759\) | 19.7827 | 0.718067 | ||||||||
\(760\) | −6.19244 | −0.224624 | ||||||||
\(761\) | −10.7823 | −0.390857 | −0.195428 | − | 0.980718i | \(-0.562610\pi\) | ||||
−0.195428 | + | 0.980718i | \(0.562610\pi\) | |||||||
\(762\) | 0.220721 | 0.00799589 | ||||||||
\(763\) | 27.6802 | 1.00209 | ||||||||
\(764\) | −65.4312 | −2.36722 | ||||||||
\(765\) | −3.01726 | −0.109089 | ||||||||
\(766\) | −26.4618 | −0.956105 | ||||||||
\(767\) | −9.42920 | −0.340469 | ||||||||
\(768\) | 15.6615 | 0.565136 | ||||||||
\(769\) | 27.5402 | 0.993123 | 0.496562 | − | 0.868001i | \(-0.334596\pi\) | ||||
0.496562 | + | 0.868001i | \(0.334596\pi\) | |||||||
\(770\) | −13.0646 | −0.470815 | ||||||||
\(771\) | 34.6617 | 1.24831 | ||||||||
\(772\) | −44.2698 | −1.59331 | ||||||||
\(773\) | 25.1433 | 0.904340 | 0.452170 | − | 0.891932i | \(-0.350650\pi\) | ||||
0.452170 | + | 0.891932i | \(0.350650\pi\) | |||||||
\(774\) | −24.5971 | −0.884124 | ||||||||
\(775\) | −1.14119 | −0.0409928 | ||||||||
\(776\) | 30.3952 | 1.09113 | ||||||||
\(777\) | −10.6664 | −0.382656 | ||||||||
\(778\) | 46.9771 | 1.68421 | ||||||||
\(779\) | 7.66931 | 0.274781 | ||||||||
\(780\) | 3.23062 | 0.115675 | ||||||||
\(781\) | −23.4564 | −0.839336 | ||||||||
\(782\) | 26.6555 | 0.953197 | ||||||||
\(783\) | −25.4290 | −0.908757 | ||||||||
\(784\) | 0.962897 | 0.0343892 | ||||||||
\(785\) | −2.47485 | −0.0883313 | ||||||||
\(786\) | 38.4837 | 1.37267 | ||||||||
\(787\) | −22.0217 | −0.784990 | −0.392495 | − | 0.919754i | \(-0.628388\pi\) | ||||
−0.392495 | + | 0.919754i | \(0.628388\pi\) | |||||||
\(788\) | −84.1694 | −2.99841 | ||||||||
\(789\) | 24.9442 | 0.888035 | ||||||||
\(790\) | 3.78522 | 0.134672 | ||||||||
\(791\) | −36.7923 | −1.30818 | ||||||||
\(792\) | 11.1618 | 0.396618 | ||||||||
\(793\) | −7.58438 | −0.269329 | ||||||||
\(794\) | −23.1814 | −0.822676 | ||||||||
\(795\) | −3.15132 | −0.111766 | ||||||||
\(796\) | 83.5617 | 2.96177 | ||||||||
\(797\) | −8.79230 | −0.311439 | −0.155720 | − | 0.987801i | \(-0.549770\pi\) | ||||
−0.155720 | + | 0.987801i | \(0.549770\pi\) | |||||||
\(798\) | 13.7530 | 0.486853 | ||||||||
\(799\) | −6.46723 | −0.228794 | ||||||||
\(800\) | 6.10767 | 0.215939 | ||||||||
\(801\) | 3.05491 | 0.107940 | ||||||||
\(802\) | 56.2792 | 1.98729 | ||||||||
\(803\) | −20.7637 | −0.732737 | ||||||||
\(804\) | 17.1710 | 0.605573 | ||||||||
\(805\) | −13.4877 | −0.475378 | ||||||||
\(806\) | −2.25511 | −0.0794328 | ||||||||
\(807\) | −7.83431 | −0.275781 | ||||||||
\(808\) | −14.9997 | −0.527689 | ||||||||
\(809\) | −44.4529 | −1.56288 | −0.781441 | − | 0.623979i | \(-0.785515\pi\) | ||||
−0.781441 | + | 0.623979i | \(0.785515\pi\) | |||||||
\(810\) | 3.59797 | 0.126420 | ||||||||
\(811\) | 0.974230 | 0.0342098 | 0.0171049 | − | 0.999854i | \(-0.494555\pi\) | ||||
0.0171049 | + | 0.999854i | \(0.494555\pi\) | |||||||
\(812\) | −31.6469 | −1.11059 | ||||||||
\(813\) | −17.7156 | −0.621312 | ||||||||
\(814\) | −25.4998 | −0.893768 | ||||||||
\(815\) | 13.9411 | 0.488336 | ||||||||
\(816\) | 0.900017 | 0.0315069 | ||||||||
\(817\) | −16.1045 | −0.563426 | ||||||||
\(818\) | −48.9711 | −1.71223 | ||||||||
\(819\) | 3.01698 | 0.105422 | ||||||||
\(820\) | 10.0924 | 0.352441 | ||||||||
\(821\) | −20.7121 | −0.722859 | −0.361429 | − | 0.932399i | \(-0.617711\pi\) | ||||
−0.361429 | + | 0.932399i | \(0.617711\pi\) | |||||||
\(822\) | 1.33725 | 0.0466420 | ||||||||
\(823\) | −56.3089 | −1.96281 | −0.981403 | − | 0.191958i | \(-0.938516\pi\) | ||||
−0.981403 | + | 0.191958i | \(0.938516\pi\) | |||||||
\(824\) | 49.9463 | 1.73996 | ||||||||
\(825\) | −3.15701 | −0.109913 | ||||||||
\(826\) | −52.8232 | −1.83795 | ||||||||
\(827\) | −53.8747 | −1.87341 | −0.936703 | − | 0.350125i | \(-0.886139\pi\) | ||||
−0.936703 | + | 0.350125i | \(0.886139\pi\) | |||||||
\(828\) | 31.6834 | 1.10107 | ||||||||
\(829\) | 31.5772 | 1.09672 | 0.548360 | − | 0.836242i | \(-0.315252\pi\) | ||||
0.548360 | + | 0.836242i | \(0.315252\pi\) | |||||||
\(830\) | 7.90517 | 0.274393 | ||||||||
\(831\) | 11.6195 | 0.403075 | ||||||||
\(832\) | 11.3605 | 0.393853 | ||||||||
\(833\) | −4.43990 | −0.153833 | ||||||||
\(834\) | 6.15240 | 0.213040 | ||||||||
\(835\) | −10.1364 | −0.350784 | ||||||||
\(836\) | 20.0934 | 0.694946 | ||||||||
\(837\) | −6.20372 | −0.214432 | ||||||||
\(838\) | −20.9759 | −0.724600 | ||||||||
\(839\) | 4.52828 | 0.156334 | 0.0781668 | − | 0.996940i | \(-0.475093\pi\) | ||||
0.0781668 | + | 0.996940i | \(0.475093\pi\) | |||||||
\(840\) | 6.58234 | 0.227112 | ||||||||
\(841\) | −7.11889 | −0.245479 | ||||||||
\(842\) | −37.9401 | −1.30750 | ||||||||
\(843\) | −32.1094 | −1.10591 | ||||||||
\(844\) | −20.5411 | −0.707055 | ||||||||
\(845\) | −12.2407 | −0.421095 | ||||||||
\(846\) | −12.5784 | −0.432455 | ||||||||
\(847\) | −8.25848 | −0.283765 | ||||||||
\(848\) | −1.08677 | −0.0373197 | ||||||||
\(849\) | 3.86199 | 0.132543 | ||||||||
\(850\) | −4.25379 | −0.145904 | ||||||||
\(851\) | −26.3256 | −0.902431 | ||||||||
\(852\) | 32.4939 | 1.11322 | ||||||||
\(853\) | 45.3894 | 1.55410 | 0.777051 | − | 0.629438i | \(-0.216715\pi\) | ||||
0.777051 | + | 0.629438i | \(0.216715\pi\) | |||||||
\(854\) | −42.4883 | −1.45392 | ||||||||
\(855\) | −3.84224 | −0.131402 | ||||||||
\(856\) | −33.1311 | −1.13240 | ||||||||
\(857\) | 20.5039 | 0.700401 | 0.350201 | − | 0.936675i | \(-0.386113\pi\) | ||||
0.350201 | + | 0.936675i | \(0.386113\pi\) | |||||||
\(858\) | −6.23857 | −0.212981 | ||||||||
\(859\) | −8.72936 | −0.297842 | −0.148921 | − | 0.988849i | \(-0.547580\pi\) | ||||
−0.148921 | + | 0.988849i | \(0.547580\pi\) | |||||||
\(860\) | −21.1926 | −0.722662 | ||||||||
\(861\) | −8.15220 | −0.277826 | ||||||||
\(862\) | −5.41504 | −0.184437 | ||||||||
\(863\) | 4.08393 | 0.139019 | 0.0695094 | − | 0.997581i | \(-0.477857\pi\) | ||||
0.0695094 | + | 0.997581i | \(0.477857\pi\) | |||||||
\(864\) | 33.2024 | 1.12957 | ||||||||
\(865\) | 8.92803 | 0.303562 | ||||||||
\(866\) | 54.5599 | 1.85402 | ||||||||
\(867\) | 15.9027 | 0.540084 | ||||||||
\(868\) | −7.72066 | −0.262056 | ||||||||
\(869\) | −4.46713 | −0.151537 | ||||||||
\(870\) | −12.5134 | −0.424243 | ||||||||
\(871\) | 4.03548 | 0.136737 | ||||||||
\(872\) | −33.3404 | −1.12905 | ||||||||
\(873\) | 18.8594 | 0.638295 | ||||||||
\(874\) | 33.9436 | 1.14816 | ||||||||
\(875\) | 2.15242 | 0.0727651 | ||||||||
\(876\) | 28.7638 | 0.971837 | ||||||||
\(877\) | 27.5213 | 0.929330 | 0.464665 | − | 0.885487i | \(-0.346175\pi\) | ||||
0.464665 | + | 0.885487i | \(0.346175\pi\) | |||||||
\(878\) | 55.6659 | 1.87863 | ||||||||
\(879\) | −15.5251 | −0.523647 | ||||||||
\(880\) | −1.08873 | −0.0367010 | ||||||||
\(881\) | 4.35240 | 0.146636 | 0.0733180 | − | 0.997309i | \(-0.476641\pi\) | ||||
0.0733180 | + | 0.997309i | \(0.476641\pi\) | |||||||
\(882\) | −8.63538 | −0.290768 | ||||||||
\(883\) | −47.5253 | −1.59935 | −0.799677 | − | 0.600430i | \(-0.794996\pi\) | ||||
−0.799677 | + | 0.600430i | \(0.794996\pi\) | |||||||
\(884\) | −5.13716 | −0.172781 | ||||||||
\(885\) | −12.7645 | −0.429075 | ||||||||
\(886\) | −62.3358 | −2.09421 | ||||||||
\(887\) | 32.5618 | 1.09332 | 0.546658 | − | 0.837356i | \(-0.315900\pi\) | ||||
0.546658 | + | 0.837356i | \(0.315900\pi\) | |||||||
\(888\) | 12.8476 | 0.431137 | ||||||||
\(889\) | 0.177596 | 0.00595637 | ||||||||
\(890\) | 4.30686 | 0.144366 | ||||||||
\(891\) | −4.24614 | −0.142251 | ||||||||
\(892\) | −80.2355 | −2.68648 | ||||||||
\(893\) | −8.23550 | −0.275590 | ||||||||
\(894\) | −51.2766 | −1.71495 | ||||||||
\(895\) | −7.71860 | −0.258004 | ||||||||
\(896\) | 37.3497 | 1.24777 | ||||||||
\(897\) | −6.44061 | −0.215046 | ||||||||
\(898\) | −1.84986 | −0.0617307 | ||||||||
\(899\) | 5.33818 | 0.178038 | ||||||||
\(900\) | −5.05617 | −0.168539 | ||||||||
\(901\) | 5.01106 | 0.166943 | ||||||||
\(902\) | −19.4891 | −0.648917 | ||||||||
\(903\) | 17.1185 | 0.569669 | ||||||||
\(904\) | 44.3159 | 1.47392 | ||||||||
\(905\) | −2.08498 | −0.0693072 | ||||||||
\(906\) | −63.7466 | −2.11784 | ||||||||
\(907\) | −54.8562 | −1.82147 | −0.910735 | − | 0.412991i | \(-0.864484\pi\) | ||||
−0.910735 | + | 0.412991i | \(0.864484\pi\) | |||||||
\(908\) | 58.8562 | 1.95321 | ||||||||
\(909\) | −9.30694 | −0.308692 | ||||||||
\(910\) | 4.25340 | 0.140999 | ||||||||
\(911\) | −20.5620 | −0.681248 | −0.340624 | − | 0.940200i | \(-0.610638\pi\) | ||||
−0.340624 | + | 0.940200i | \(0.610638\pi\) | |||||||
\(912\) | 1.14610 | 0.0379512 | ||||||||
\(913\) | −9.32928 | −0.308754 | ||||||||
\(914\) | −83.7773 | −2.77111 | ||||||||
\(915\) | −10.2672 | −0.339422 | ||||||||
\(916\) | 21.3029 | 0.703867 | ||||||||
\(917\) | 30.9646 | 1.02254 | ||||||||
\(918\) | −23.1244 | −0.763219 | ||||||||
\(919\) | 15.6907 | 0.517588 | 0.258794 | − | 0.965932i | \(-0.416675\pi\) | ||||
0.258794 | + | 0.965932i | \(0.416675\pi\) | |||||||
\(920\) | 16.2457 | 0.535606 | ||||||||
\(921\) | −32.9975 | −1.08730 | ||||||||
\(922\) | 46.6744 | 1.53714 | ||||||||
\(923\) | 7.63664 | 0.251363 | ||||||||
\(924\) | −21.3586 | −0.702646 | ||||||||
\(925\) | 4.20115 | 0.138133 | ||||||||
\(926\) | −60.7838 | −1.99748 | ||||||||
\(927\) | 30.9903 | 1.01786 | ||||||||
\(928\) | −28.5700 | −0.937856 | ||||||||
\(929\) | 29.9859 | 0.983805 | 0.491903 | − | 0.870650i | \(-0.336302\pi\) | ||||
0.491903 | + | 0.870650i | \(0.336302\pi\) | |||||||
\(930\) | −3.05279 | −0.100105 | ||||||||
\(931\) | −5.65386 | −0.185298 | ||||||||
\(932\) | 58.8004 | 1.92607 | ||||||||
\(933\) | −31.9210 | −1.04505 | ||||||||
\(934\) | 32.9781 | 1.07908 | ||||||||
\(935\) | 5.02011 | 0.164175 | ||||||||
\(936\) | −3.63392 | −0.118778 | ||||||||
\(937\) | −23.8466 | −0.779035 | −0.389517 | − | 0.921019i | \(-0.627358\pi\) | ||||
−0.389517 | + | 0.921019i | \(0.627358\pi\) | |||||||
\(938\) | 22.6071 | 0.738149 | ||||||||
\(939\) | 3.62173 | 0.118191 | ||||||||
\(940\) | −10.8374 | −0.353478 | ||||||||
\(941\) | −33.0287 | −1.07671 | −0.538353 | − | 0.842719i | \(-0.680953\pi\) | ||||
−0.538353 | + | 0.842719i | \(0.680953\pi\) | |||||||
\(942\) | −6.62047 | −0.215706 | ||||||||
\(943\) | −20.1203 | −0.655206 | ||||||||
\(944\) | −4.40198 | −0.143272 | ||||||||
\(945\) | 11.7010 | 0.380632 | ||||||||
\(946\) | 40.9245 | 1.33057 | ||||||||
\(947\) | 48.5143 | 1.57650 | 0.788252 | − | 0.615353i | \(-0.210986\pi\) | ||||
0.788252 | + | 0.615353i | \(0.210986\pi\) | |||||||
\(948\) | 6.18826 | 0.200985 | ||||||||
\(949\) | 6.76000 | 0.219439 | ||||||||
\(950\) | −5.41687 | −0.175746 | ||||||||
\(951\) | −7.87986 | −0.255522 | ||||||||
\(952\) | −10.4669 | −0.339234 | ||||||||
\(953\) | −36.2788 | −1.17519 | −0.587593 | − | 0.809157i | \(-0.699924\pi\) | ||||
−0.587593 | + | 0.809157i | \(0.699924\pi\) | |||||||
\(954\) | 9.74625 | 0.315546 | ||||||||
\(955\) | −20.8169 | −0.673619 | ||||||||
\(956\) | 56.4919 | 1.82708 | ||||||||
\(957\) | 14.7676 | 0.477370 | ||||||||
\(958\) | −36.6390 | −1.18375 | ||||||||
\(959\) | 1.07597 | 0.0347450 | ||||||||
\(960\) | 15.3789 | 0.496353 | ||||||||
\(961\) | −29.6977 | −0.957990 | ||||||||
\(962\) | 8.30190 | 0.267664 | ||||||||
\(963\) | −20.5569 | −0.662437 | ||||||||
\(964\) | 28.0744 | 0.904214 | ||||||||
\(965\) | −14.0844 | −0.453393 | ||||||||
\(966\) | −36.0808 | −1.16088 | ||||||||
\(967\) | 46.4911 | 1.49505 | 0.747527 | − | 0.664232i | \(-0.231241\pi\) | ||||
0.747527 | + | 0.664232i | \(0.231241\pi\) | |||||||
\(968\) | 9.94723 | 0.319716 | ||||||||
\(969\) | −5.28465 | −0.169767 | ||||||||
\(970\) | 26.5884 | 0.853701 | ||||||||
\(971\) | −45.1256 | −1.44815 | −0.724074 | − | 0.689722i | \(-0.757733\pi\) | ||||
−0.724074 | + | 0.689722i | \(0.757733\pi\) | |||||||
\(972\) | −45.3786 | −1.45552 | ||||||||
\(973\) | 4.95031 | 0.158700 | ||||||||
\(974\) | −30.6338 | −0.981571 | ||||||||
\(975\) | 1.02782 | 0.0329166 | ||||||||
\(976\) | −3.54074 | −0.113336 | ||||||||
\(977\) | 0.557065 | 0.0178221 | 0.00891104 | − | 0.999960i | \(-0.497163\pi\) | ||||
0.00891104 | + | 0.999960i | \(0.497163\pi\) | |||||||
\(978\) | 37.2938 | 1.19253 | ||||||||
\(979\) | −5.08274 | −0.162445 | ||||||||
\(980\) | −7.44015 | −0.237667 | ||||||||
\(981\) | −20.6868 | −0.660480 | ||||||||
\(982\) | −1.49364 | −0.0476640 | ||||||||
\(983\) | 59.9611 | 1.91246 | 0.956231 | − | 0.292611i | \(-0.0945242\pi\) | ||||
0.956231 | + | 0.292611i | \(0.0945242\pi\) | |||||||
\(984\) | 9.81922 | 0.313025 | ||||||||
\(985\) | −26.7784 | −0.853232 | ||||||||
\(986\) | 19.8981 | 0.633684 | ||||||||
\(987\) | 8.75404 | 0.278644 | ||||||||
\(988\) | −6.54176 | −0.208121 | ||||||||
\(989\) | 42.2499 | 1.34347 | ||||||||
\(990\) | 9.76385 | 0.310315 | ||||||||
\(991\) | −16.0026 | −0.508338 | −0.254169 | − | 0.967160i | \(-0.581802\pi\) | ||||
−0.254169 | + | 0.967160i | \(0.581802\pi\) | |||||||
\(992\) | −6.97001 | −0.221298 | ||||||||
\(993\) | 6.34103 | 0.201227 | ||||||||
\(994\) | 42.7811 | 1.35693 | ||||||||
\(995\) | 26.5851 | 0.842804 | ||||||||
\(996\) | 12.9237 | 0.409504 | ||||||||
\(997\) | −23.9096 | −0.757224 | −0.378612 | − | 0.925555i | \(-0.623599\pi\) | ||||
−0.378612 | + | 0.925555i | \(0.623599\pi\) | |||||||
\(998\) | 73.6034 | 2.32987 | ||||||||
\(999\) | 22.8382 | 0.722570 |
(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 | 8045.2.a.c.1.18 | ✓ | 127 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8045.2.a.c.1.18 | ✓ | 127 | 1.1 | even | 1 | trivial |