Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, 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("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.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: | \(32.0759064919\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.48812 | −1.05226 | −0.526130 | − | 0.850404i | \(-0.676357\pi\) | ||||
−0.526130 | + | 0.850404i | \(0.676357\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.214502 | 0.107251 | ||||||||
\(5\) | −3.58678 | −1.60406 | −0.802029 | − | 0.597285i | \(-0.796246\pi\) | ||||
−0.802029 | + | 0.597285i | \(0.796246\pi\) | |||||||
\(6\) | −1.48812 | −0.607523 | ||||||||
\(7\) | 0.0236485 | 0.00893829 | 0.00446915 | − | 0.999990i | \(-0.498577\pi\) | ||||
0.00446915 | + | 0.999990i | \(0.498577\pi\) | |||||||
\(8\) | 2.65704 | 0.939404 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 5.33757 | 1.68789 | ||||||||
\(11\) | −3.71531 | −1.12021 | −0.560104 | − | 0.828422i | \(-0.689239\pi\) | ||||
−0.560104 | + | 0.828422i | \(0.689239\pi\) | |||||||
\(12\) | 0.214502 | 0.0619214 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −0.0351918 | −0.00940541 | ||||||||
\(15\) | −3.58678 | −0.926103 | ||||||||
\(16\) | −4.38299 | −1.09575 | ||||||||
\(17\) | 2.38483 | 0.578405 | 0.289203 | − | 0.957268i | \(-0.406610\pi\) | ||||
0.289203 | + | 0.957268i | \(0.406610\pi\) | |||||||
\(18\) | −1.48812 | −0.350753 | ||||||||
\(19\) | 1.67761 | 0.384869 | 0.192435 | − | 0.981310i | \(-0.438362\pi\) | ||||
0.192435 | + | 0.981310i | \(0.438362\pi\) | |||||||
\(20\) | −0.769373 | −0.172037 | ||||||||
\(21\) | 0.0236485 | 0.00516053 | ||||||||
\(22\) | 5.52883 | 1.17875 | ||||||||
\(23\) | −5.50028 | −1.14689 | −0.573443 | − | 0.819245i | \(-0.694393\pi\) | ||||
−0.573443 | + | 0.819245i | \(0.694393\pi\) | |||||||
\(24\) | 2.65704 | 0.542365 | ||||||||
\(25\) | 7.86502 | 1.57300 | ||||||||
\(26\) | 1.48812 | 0.291844 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.00507265 | 0.000958641 0 | ||||||||
\(29\) | −1.60562 | −0.298156 | −0.149078 | − | 0.988825i | \(-0.547631\pi\) | ||||
−0.149078 | + | 0.988825i | \(0.547631\pi\) | |||||||
\(30\) | 5.33757 | 0.974502 | ||||||||
\(31\) | 2.89038 | 0.519127 | 0.259563 | − | 0.965726i | \(-0.416421\pi\) | ||||
0.259563 | + | 0.965726i | \(0.416421\pi\) | |||||||
\(32\) | 1.20835 | 0.213608 | ||||||||
\(33\) | −3.71531 | −0.646753 | ||||||||
\(34\) | −3.54891 | −0.608633 | ||||||||
\(35\) | −0.0848220 | −0.0143375 | ||||||||
\(36\) | 0.214502 | 0.0357504 | ||||||||
\(37\) | −3.51029 | −0.577089 | −0.288544 | − | 0.957467i | \(-0.593171\pi\) | ||||
−0.288544 | + | 0.957467i | \(0.593171\pi\) | |||||||
\(38\) | −2.49648 | −0.404983 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −9.53021 | −1.50686 | ||||||||
\(41\) | −6.74954 | −1.05410 | −0.527051 | − | 0.849834i | \(-0.676702\pi\) | ||||
−0.527051 | + | 0.849834i | \(0.676702\pi\) | |||||||
\(42\) | −0.0351918 | −0.00543021 | ||||||||
\(43\) | −0.758748 | −0.115708 | −0.0578540 | − | 0.998325i | \(-0.518426\pi\) | ||||
−0.0578540 | + | 0.998325i | \(0.518426\pi\) | |||||||
\(44\) | −0.796942 | −0.120144 | ||||||||
\(45\) | −3.58678 | −0.534686 | ||||||||
\(46\) | 8.18507 | 1.20682 | ||||||||
\(47\) | −4.08640 | −0.596063 | −0.298032 | − | 0.954556i | \(-0.596330\pi\) | ||||
−0.298032 | + | 0.954556i | \(0.596330\pi\) | |||||||
\(48\) | −4.38299 | −0.632631 | ||||||||
\(49\) | −6.99944 | −0.999920 | ||||||||
\(50\) | −11.7041 | −1.65521 | ||||||||
\(51\) | 2.38483 | 0.333942 | ||||||||
\(52\) | −0.214502 | −0.0297461 | ||||||||
\(53\) | 7.86931 | 1.08093 | 0.540466 | − | 0.841366i | \(-0.318248\pi\) | ||||
0.540466 | + | 0.841366i | \(0.318248\pi\) | |||||||
\(54\) | −1.48812 | −0.202508 | ||||||||
\(55\) | 13.3260 | 1.79688 | ||||||||
\(56\) | 0.0628349 | 0.00839667 | ||||||||
\(57\) | 1.67761 | 0.222204 | ||||||||
\(58\) | 2.38936 | 0.313738 | ||||||||
\(59\) | −10.6800 | −1.39042 | −0.695209 | − | 0.718807i | \(-0.744688\pi\) | ||||
−0.695209 | + | 0.718807i | \(0.744688\pi\) | |||||||
\(60\) | −0.769373 | −0.0993256 | ||||||||
\(61\) | −5.42985 | −0.695221 | −0.347611 | − | 0.937639i | \(-0.613007\pi\) | ||||
−0.347611 | + | 0.937639i | \(0.613007\pi\) | |||||||
\(62\) | −4.30123 | −0.546256 | ||||||||
\(63\) | 0.0236485 | 0.00297943 | ||||||||
\(64\) | 6.96782 | 0.870977 | ||||||||
\(65\) | 3.58678 | 0.444886 | ||||||||
\(66\) | 5.52883 | 0.680552 | ||||||||
\(67\) | −9.67812 | −1.18237 | −0.591185 | − | 0.806536i | \(-0.701340\pi\) | ||||
−0.591185 | + | 0.806536i | \(0.701340\pi\) | |||||||
\(68\) | 0.511550 | 0.0620346 | ||||||||
\(69\) | −5.50028 | −0.662156 | ||||||||
\(70\) | 0.126225 | 0.0150868 | ||||||||
\(71\) | −2.86157 | −0.339606 | −0.169803 | − | 0.985478i | \(-0.554313\pi\) | ||||
−0.169803 | + | 0.985478i | \(0.554313\pi\) | |||||||
\(72\) | 2.65704 | 0.313135 | ||||||||
\(73\) | 15.1910 | 1.77797 | 0.888986 | − | 0.457935i | \(-0.151411\pi\) | ||||
0.888986 | + | 0.457935i | \(0.151411\pi\) | |||||||
\(74\) | 5.22374 | 0.607247 | ||||||||
\(75\) | 7.86502 | 0.908174 | ||||||||
\(76\) | 0.359850 | 0.0412776 | ||||||||
\(77\) | −0.0878616 | −0.0100128 | ||||||||
\(78\) | 1.48812 | 0.168496 | ||||||||
\(79\) | 16.7621 | 1.88589 | 0.942945 | − | 0.332950i | \(-0.108044\pi\) | ||||
0.942945 | + | 0.332950i | \(0.108044\pi\) | |||||||
\(80\) | 15.7208 | 1.75764 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.0441 | 1.10919 | ||||||||
\(83\) | −4.59132 | −0.503963 | −0.251982 | − | 0.967732i | \(-0.581082\pi\) | ||||
−0.251982 | + | 0.967732i | \(0.581082\pi\) | |||||||
\(84\) | 0.00507265 | 0.000553472 0 | ||||||||
\(85\) | −8.55385 | −0.927796 | ||||||||
\(86\) | 1.12911 | 0.121755 | ||||||||
\(87\) | −1.60562 | −0.172141 | ||||||||
\(88\) | −9.87172 | −1.05233 | ||||||||
\(89\) | 9.99536 | 1.05951 | 0.529753 | − | 0.848152i | \(-0.322285\pi\) | ||||
0.529753 | + | 0.848152i | \(0.322285\pi\) | |||||||
\(90\) | 5.33757 | 0.562629 | ||||||||
\(91\) | −0.0236485 | −0.00247904 | ||||||||
\(92\) | −1.17982 | −0.123005 | ||||||||
\(93\) | 2.89038 | 0.299718 | ||||||||
\(94\) | 6.08106 | 0.627214 | ||||||||
\(95\) | −6.01721 | −0.617353 | ||||||||
\(96\) | 1.20835 | 0.123327 | ||||||||
\(97\) | −3.56186 | −0.361653 | −0.180826 | − | 0.983515i | \(-0.557877\pi\) | ||||
−0.180826 | + | 0.983515i | \(0.557877\pi\) | |||||||
\(98\) | 10.4160 | 1.05218 | ||||||||
\(99\) | −3.71531 | −0.373403 | ||||||||
\(100\) | 1.68706 | 0.168706 | ||||||||
\(101\) | 1.85275 | 0.184356 | 0.0921779 | − | 0.995743i | \(-0.470617\pi\) | ||||
0.0921779 | + | 0.995743i | \(0.470617\pi\) | |||||||
\(102\) | −3.54891 | −0.351394 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −2.65704 | −0.260544 | ||||||||
\(105\) | −0.0848220 | −0.00827778 | ||||||||
\(106\) | −11.7105 | −1.13742 | ||||||||
\(107\) | −1.21058 | −0.117031 | −0.0585155 | − | 0.998287i | \(-0.518637\pi\) | ||||
−0.0585155 | + | 0.998287i | \(0.518637\pi\) | |||||||
\(108\) | 0.214502 | 0.0206405 | ||||||||
\(109\) | −9.25070 | −0.886057 | −0.443028 | − | 0.896508i | \(-0.646096\pi\) | ||||
−0.443028 | + | 0.896508i | \(0.646096\pi\) | |||||||
\(110\) | −19.8307 | −1.89079 | ||||||||
\(111\) | −3.51029 | −0.333182 | ||||||||
\(112\) | −0.103651 | −0.00979412 | ||||||||
\(113\) | −12.0437 | −1.13297 | −0.566487 | − | 0.824070i | \(-0.691698\pi\) | ||||
−0.566487 | + | 0.824070i | \(0.691698\pi\) | |||||||
\(114\) | −2.49648 | −0.233817 | ||||||||
\(115\) | 19.7283 | 1.83967 | ||||||||
\(116\) | −0.344409 | −0.0319776 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 15.8931 | 1.46308 | ||||||||
\(119\) | 0.0563975 | 0.00516995 | ||||||||
\(120\) | −9.53021 | −0.869985 | ||||||||
\(121\) | 2.80355 | 0.254868 | ||||||||
\(122\) | 8.08027 | 0.731553 | ||||||||
\(123\) | −6.74954 | −0.608586 | ||||||||
\(124\) | 0.619992 | 0.0556769 | ||||||||
\(125\) | −10.2762 | −0.919130 | ||||||||
\(126\) | −0.0351918 | −0.00313514 | ||||||||
\(127\) | 1.60892 | 0.142769 | 0.0713845 | − | 0.997449i | \(-0.477258\pi\) | ||||
0.0713845 | + | 0.997449i | \(0.477258\pi\) | |||||||
\(128\) | −12.7856 | −1.13010 | ||||||||
\(129\) | −0.758748 | −0.0668040 | ||||||||
\(130\) | −5.33757 | −0.468135 | ||||||||
\(131\) | 5.67616 | 0.495928 | 0.247964 | − | 0.968769i | \(-0.420238\pi\) | ||||
0.247964 | + | 0.968769i | \(0.420238\pi\) | |||||||
\(132\) | −0.796942 | −0.0693649 | ||||||||
\(133\) | 0.0396729 | 0.00344007 | ||||||||
\(134\) | 14.4022 | 1.24416 | ||||||||
\(135\) | −3.58678 | −0.308701 | ||||||||
\(136\) | 6.33657 | 0.543356 | ||||||||
\(137\) | −13.8157 | −1.18035 | −0.590176 | − | 0.807275i | \(-0.700942\pi\) | ||||
−0.590176 | + | 0.807275i | \(0.700942\pi\) | |||||||
\(138\) | 8.18507 | 0.696760 | ||||||||
\(139\) | 13.2348 | 1.12256 | 0.561280 | − | 0.827626i | \(-0.310309\pi\) | ||||
0.561280 | + | 0.827626i | \(0.310309\pi\) | |||||||
\(140\) | −0.0181945 | −0.00153772 | ||||||||
\(141\) | −4.08640 | −0.344137 | ||||||||
\(142\) | 4.25836 | 0.357354 | ||||||||
\(143\) | 3.71531 | 0.310690 | ||||||||
\(144\) | −4.38299 | −0.365249 | ||||||||
\(145\) | 5.75902 | 0.478260 | ||||||||
\(146\) | −22.6060 | −1.87089 | ||||||||
\(147\) | −6.99944 | −0.577304 | ||||||||
\(148\) | −0.752965 | −0.0618934 | ||||||||
\(149\) | −3.91884 | −0.321044 | −0.160522 | − | 0.987032i | \(-0.551318\pi\) | ||||
−0.160522 | + | 0.987032i | \(0.551318\pi\) | |||||||
\(150\) | −11.7041 | −0.955635 | ||||||||
\(151\) | 21.0997 | 1.71707 | 0.858534 | − | 0.512756i | \(-0.171376\pi\) | ||||
0.858534 | + | 0.512756i | \(0.171376\pi\) | |||||||
\(152\) | 4.45746 | 0.361548 | ||||||||
\(153\) | 2.38483 | 0.192802 | ||||||||
\(154\) | 0.130749 | 0.0105360 | ||||||||
\(155\) | −10.3672 | −0.832710 | ||||||||
\(156\) | −0.214502 | −0.0171739 | ||||||||
\(157\) | 9.31170 | 0.743155 | 0.371577 | − | 0.928402i | \(-0.378817\pi\) | ||||
0.371577 | + | 0.928402i | \(0.378817\pi\) | |||||||
\(158\) | −24.9441 | −1.98445 | ||||||||
\(159\) | 7.86931 | 0.624077 | ||||||||
\(160\) | −4.33409 | −0.342640 | ||||||||
\(161\) | −0.130073 | −0.0102512 | ||||||||
\(162\) | −1.48812 | −0.116918 | ||||||||
\(163\) | −3.01766 | −0.236361 | −0.118181 | − | 0.992992i | \(-0.537706\pi\) | ||||
−0.118181 | + | 0.992992i | \(0.537706\pi\) | |||||||
\(164\) | −1.44779 | −0.113053 | ||||||||
\(165\) | 13.3260 | 1.03743 | ||||||||
\(166\) | 6.83244 | 0.530300 | ||||||||
\(167\) | 21.5065 | 1.66422 | 0.832111 | − | 0.554608i | \(-0.187132\pi\) | ||||
0.832111 | + | 0.554608i | \(0.187132\pi\) | |||||||
\(168\) | 0.0628349 | 0.00484782 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 12.7292 | 0.976282 | ||||||||
\(171\) | 1.67761 | 0.128290 | ||||||||
\(172\) | −0.162753 | −0.0124098 | ||||||||
\(173\) | 18.3177 | 1.39267 | 0.696334 | − | 0.717718i | \(-0.254813\pi\) | ||||
0.696334 | + | 0.717718i | \(0.254813\pi\) | |||||||
\(174\) | 2.38936 | 0.181137 | ||||||||
\(175\) | 0.185996 | 0.0140600 | ||||||||
\(176\) | 16.2842 | 1.22747 | ||||||||
\(177\) | −10.6800 | −0.802759 | ||||||||
\(178\) | −14.8743 | −1.11488 | ||||||||
\(179\) | 0.253741 | 0.0189655 | 0.00948273 | − | 0.999955i | \(-0.496982\pi\) | ||||
0.00948273 | + | 0.999955i | \(0.496982\pi\) | |||||||
\(180\) | −0.769373 | −0.0573456 | ||||||||
\(181\) | −15.1376 | −1.12517 | −0.562584 | − | 0.826740i | \(-0.690193\pi\) | ||||
−0.562584 | + | 0.826740i | \(0.690193\pi\) | |||||||
\(182\) | 0.0351918 | 0.00260859 | ||||||||
\(183\) | −5.42985 | −0.401386 | ||||||||
\(184\) | −14.6144 | −1.07739 | ||||||||
\(185\) | 12.5907 | 0.925684 | ||||||||
\(186\) | −4.30123 | −0.315381 | ||||||||
\(187\) | −8.86037 | −0.647935 | ||||||||
\(188\) | −0.876542 | −0.0639284 | ||||||||
\(189\) | 0.0236485 | 0.00172018 | ||||||||
\(190\) | 8.95434 | 0.649616 | ||||||||
\(191\) | 10.3023 | 0.745448 | 0.372724 | − | 0.927942i | \(-0.378424\pi\) | ||||
0.372724 | + | 0.927942i | \(0.378424\pi\) | |||||||
\(192\) | 6.96782 | 0.502859 | ||||||||
\(193\) | 6.08382 | 0.437923 | 0.218962 | − | 0.975733i | \(-0.429733\pi\) | ||||
0.218962 | + | 0.975733i | \(0.429733\pi\) | |||||||
\(194\) | 5.30048 | 0.380553 | ||||||||
\(195\) | 3.58678 | 0.256855 | ||||||||
\(196\) | −1.50139 | −0.107242 | ||||||||
\(197\) | −15.6327 | −1.11379 | −0.556893 | − | 0.830584i | \(-0.688007\pi\) | ||||
−0.556893 | + | 0.830584i | \(0.688007\pi\) | |||||||
\(198\) | 5.52883 | 0.392917 | ||||||||
\(199\) | 17.8911 | 1.26827 | 0.634134 | − | 0.773223i | \(-0.281357\pi\) | ||||
0.634134 | + | 0.773223i | \(0.281357\pi\) | |||||||
\(200\) | 20.8976 | 1.47769 | ||||||||
\(201\) | −9.67812 | −0.682642 | ||||||||
\(202\) | −2.75712 | −0.193990 | ||||||||
\(203\) | −0.0379705 | −0.00266501 | ||||||||
\(204\) | 0.511550 | 0.0358157 | ||||||||
\(205\) | 24.2091 | 1.69084 | ||||||||
\(206\) | 1.48812 | 0.103682 | ||||||||
\(207\) | −5.50028 | −0.382296 | ||||||||
\(208\) | 4.38299 | 0.303906 | ||||||||
\(209\) | −6.23283 | −0.431134 | ||||||||
\(210\) | 0.126225 | 0.00871038 | ||||||||
\(211\) | 3.09757 | 0.213245 | 0.106623 | − | 0.994300i | \(-0.465996\pi\) | ||||
0.106623 | + | 0.994300i | \(0.465996\pi\) | |||||||
\(212\) | 1.68798 | 0.115931 | ||||||||
\(213\) | −2.86157 | −0.196071 | ||||||||
\(214\) | 1.80148 | 0.123147 | ||||||||
\(215\) | 2.72146 | 0.185602 | ||||||||
\(216\) | 2.65704 | 0.180788 | ||||||||
\(217\) | 0.0683530 | 0.00464011 | ||||||||
\(218\) | 13.7662 | 0.932362 | ||||||||
\(219\) | 15.1910 | 1.02651 | ||||||||
\(220\) | 2.85846 | 0.192717 | ||||||||
\(221\) | −2.38483 | −0.160421 | ||||||||
\(222\) | 5.22374 | 0.350594 | ||||||||
\(223\) | 9.20720 | 0.616560 | 0.308280 | − | 0.951296i | \(-0.400247\pi\) | ||||
0.308280 | + | 0.951296i | \(0.400247\pi\) | |||||||
\(224\) | 0.0285757 | 0.00190929 | ||||||||
\(225\) | 7.86502 | 0.524334 | ||||||||
\(226\) | 17.9225 | 1.19218 | ||||||||
\(227\) | −16.1094 | −1.06922 | −0.534610 | − | 0.845099i | \(-0.679541\pi\) | ||||
−0.534610 | + | 0.845099i | \(0.679541\pi\) | |||||||
\(228\) | 0.359850 | 0.0238317 | ||||||||
\(229\) | 29.8683 | 1.97375 | 0.986875 | − | 0.161485i | \(-0.0516284\pi\) | ||||
0.986875 | + | 0.161485i | \(0.0516284\pi\) | |||||||
\(230\) | −29.3581 | −1.93581 | ||||||||
\(231\) | −0.0878616 | −0.00578087 | ||||||||
\(232\) | −4.26619 | −0.280089 | ||||||||
\(233\) | 28.5167 | 1.86819 | 0.934094 | − | 0.357027i | \(-0.116210\pi\) | ||||
0.934094 | + | 0.357027i | \(0.116210\pi\) | |||||||
\(234\) | 1.48812 | 0.0972815 | ||||||||
\(235\) | 14.6570 | 0.956120 | ||||||||
\(236\) | −2.29088 | −0.149124 | ||||||||
\(237\) | 16.7621 | 1.08882 | ||||||||
\(238\) | −0.0839263 | −0.00544014 | ||||||||
\(239\) | 5.57306 | 0.360491 | 0.180246 | − | 0.983622i | \(-0.442311\pi\) | ||||
0.180246 | + | 0.983622i | \(0.442311\pi\) | |||||||
\(240\) | 15.7208 | 1.01478 | ||||||||
\(241\) | 5.03224 | 0.324155 | 0.162078 | − | 0.986778i | \(-0.448181\pi\) | ||||
0.162078 | + | 0.986778i | \(0.448181\pi\) | |||||||
\(242\) | −4.17202 | −0.268187 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.16471 | −0.0745632 | ||||||||
\(245\) | 25.1055 | 1.60393 | ||||||||
\(246\) | 10.0441 | 0.640390 | ||||||||
\(247\) | −1.67761 | −0.106744 | ||||||||
\(248\) | 7.67983 | 0.487670 | ||||||||
\(249\) | −4.59132 | −0.290963 | ||||||||
\(250\) | 15.2922 | 0.967164 | ||||||||
\(251\) | −4.32041 | −0.272702 | −0.136351 | − | 0.990661i | \(-0.543537\pi\) | ||||
−0.136351 | + | 0.990661i | \(0.543537\pi\) | |||||||
\(252\) | 0.00507265 | 0.000319547 0 | ||||||||
\(253\) | 20.4352 | 1.28475 | ||||||||
\(254\) | −2.39427 | −0.150230 | ||||||||
\(255\) | −8.55385 | −0.535663 | ||||||||
\(256\) | 5.09095 | 0.318184 | ||||||||
\(257\) | 25.6635 | 1.60084 | 0.800422 | − | 0.599436i | \(-0.204609\pi\) | ||||
0.800422 | + | 0.599436i | \(0.204609\pi\) | |||||||
\(258\) | 1.12911 | 0.0702952 | ||||||||
\(259\) | −0.0830132 | −0.00515819 | ||||||||
\(260\) | 0.769373 | 0.0477145 | ||||||||
\(261\) | −1.60562 | −0.0993855 | ||||||||
\(262\) | −8.44681 | −0.521846 | ||||||||
\(263\) | −10.3901 | −0.640683 | −0.320341 | − | 0.947302i | \(-0.603798\pi\) | ||||
−0.320341 | + | 0.947302i | \(0.603798\pi\) | |||||||
\(264\) | −9.87172 | −0.607562 | ||||||||
\(265\) | −28.2255 | −1.73388 | ||||||||
\(266\) | −0.0590380 | −0.00361985 | ||||||||
\(267\) | 9.99536 | 0.611706 | ||||||||
\(268\) | −2.07598 | −0.126810 | ||||||||
\(269\) | −6.11062 | −0.372571 | −0.186285 | − | 0.982496i | \(-0.559645\pi\) | ||||
−0.186285 | + | 0.982496i | \(0.559645\pi\) | |||||||
\(270\) | 5.33757 | 0.324834 | ||||||||
\(271\) | 6.66920 | 0.405125 | 0.202562 | − | 0.979269i | \(-0.435073\pi\) | ||||
0.202562 | + | 0.979269i | \(0.435073\pi\) | |||||||
\(272\) | −10.4527 | −0.633786 | ||||||||
\(273\) | −0.0236485 | −0.00143127 | ||||||||
\(274\) | 20.5594 | 1.24204 | ||||||||
\(275\) | −29.2210 | −1.76209 | ||||||||
\(276\) | −1.17982 | −0.0710169 | ||||||||
\(277\) | 31.3374 | 1.88288 | 0.941442 | − | 0.337174i | \(-0.109471\pi\) | ||||
0.941442 | + | 0.337174i | \(0.109471\pi\) | |||||||
\(278\) | −19.6949 | −1.18122 | ||||||||
\(279\) | 2.89038 | 0.173042 | ||||||||
\(280\) | −0.225375 | −0.0134687 | ||||||||
\(281\) | −29.0071 | −1.73042 | −0.865210 | − | 0.501410i | \(-0.832815\pi\) | ||||
−0.865210 | + | 0.501410i | \(0.832815\pi\) | |||||||
\(282\) | 6.08106 | 0.362122 | ||||||||
\(283\) | −8.88428 | −0.528116 | −0.264058 | − | 0.964507i | \(-0.585061\pi\) | ||||
−0.264058 | + | 0.964507i | \(0.585061\pi\) | |||||||
\(284\) | −0.613813 | −0.0364231 | ||||||||
\(285\) | −6.01721 | −0.356429 | ||||||||
\(286\) | −5.52883 | −0.326927 | ||||||||
\(287\) | −0.159617 | −0.00942186 | ||||||||
\(288\) | 1.20835 | 0.0712027 | ||||||||
\(289\) | −11.3126 | −0.665447 | ||||||||
\(290\) | −8.57011 | −0.503254 | ||||||||
\(291\) | −3.56186 | −0.208800 | ||||||||
\(292\) | 3.25850 | 0.190689 | ||||||||
\(293\) | −10.7899 | −0.630355 | −0.315178 | − | 0.949033i | \(-0.602064\pi\) | ||||
−0.315178 | + | 0.949033i | \(0.602064\pi\) | |||||||
\(294\) | 10.4160 | 0.607474 | ||||||||
\(295\) | 38.3069 | 2.23031 | ||||||||
\(296\) | −9.32697 | −0.542119 | ||||||||
\(297\) | −3.71531 | −0.215584 | ||||||||
\(298\) | 5.83171 | 0.337822 | ||||||||
\(299\) | 5.50028 | 0.318089 | ||||||||
\(300\) | 1.68706 | 0.0974026 | ||||||||
\(301\) | −0.0179432 | −0.00103423 | ||||||||
\(302\) | −31.3989 | −1.80680 | ||||||||
\(303\) | 1.85275 | 0.106438 | ||||||||
\(304\) | −7.35294 | −0.421720 | ||||||||
\(305\) | 19.4757 | 1.11518 | ||||||||
\(306\) | −3.54891 | −0.202878 | ||||||||
\(307\) | −15.7118 | −0.896722 | −0.448361 | − | 0.893853i | \(-0.647992\pi\) | ||||
−0.448361 | + | 0.893853i | \(0.647992\pi\) | |||||||
\(308\) | −0.0188465 | −0.00107388 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 15.4276 | 0.876227 | ||||||||
\(311\) | 10.8175 | 0.613405 | 0.306703 | − | 0.951805i | \(-0.400774\pi\) | ||||
0.306703 | + | 0.951805i | \(0.400774\pi\) | |||||||
\(312\) | −2.65704 | −0.150425 | ||||||||
\(313\) | −11.1508 | −0.630283 | −0.315142 | − | 0.949045i | \(-0.602052\pi\) | ||||
−0.315142 | + | 0.949045i | \(0.602052\pi\) | |||||||
\(314\) | −13.8569 | −0.781992 | ||||||||
\(315\) | −0.0848220 | −0.00477918 | ||||||||
\(316\) | 3.59552 | 0.202264 | ||||||||
\(317\) | 11.1229 | 0.624727 | 0.312363 | − | 0.949963i | \(-0.398879\pi\) | ||||
0.312363 | + | 0.949963i | \(0.398879\pi\) | |||||||
\(318\) | −11.7105 | −0.656691 | ||||||||
\(319\) | 5.96539 | 0.333998 | ||||||||
\(320\) | −24.9920 | −1.39710 | ||||||||
\(321\) | −1.21058 | −0.0675678 | ||||||||
\(322\) | 0.193565 | 0.0107869 | ||||||||
\(323\) | 4.00080 | 0.222610 | ||||||||
\(324\) | 0.214502 | 0.0119168 | ||||||||
\(325\) | −7.86502 | −0.436273 | ||||||||
\(326\) | 4.49064 | 0.248713 | ||||||||
\(327\) | −9.25070 | −0.511565 | ||||||||
\(328\) | −17.9338 | −0.990227 | ||||||||
\(329\) | −0.0966373 | −0.00532779 | ||||||||
\(330\) | −19.8307 | −1.09165 | ||||||||
\(331\) | 6.81134 | 0.374385 | 0.187193 | − | 0.982323i | \(-0.440061\pi\) | ||||
0.187193 | + | 0.982323i | \(0.440061\pi\) | |||||||
\(332\) | −0.984848 | −0.0540506 | ||||||||
\(333\) | −3.51029 | −0.192363 | ||||||||
\(334\) | −32.0043 | −1.75120 | ||||||||
\(335\) | 34.7133 | 1.89659 | ||||||||
\(336\) | −0.103651 | −0.00565464 | ||||||||
\(337\) | 7.54055 | 0.410760 | 0.205380 | − | 0.978682i | \(-0.434157\pi\) | ||||
0.205380 | + | 0.978682i | \(0.434157\pi\) | |||||||
\(338\) | −1.48812 | −0.0809431 | ||||||||
\(339\) | −12.0437 | −0.654123 | ||||||||
\(340\) | −1.83482 | −0.0995071 | ||||||||
\(341\) | −10.7386 | −0.581530 | ||||||||
\(342\) | −2.49648 | −0.134994 | ||||||||
\(343\) | −0.331066 | −0.0178759 | ||||||||
\(344\) | −2.01602 | −0.108696 | ||||||||
\(345\) | 19.7283 | 1.06214 | ||||||||
\(346\) | −27.2589 | −1.46545 | ||||||||
\(347\) | −0.978400 | −0.0525233 | −0.0262616 | − | 0.999655i | \(-0.508360\pi\) | ||||
−0.0262616 | + | 0.999655i | \(0.508360\pi\) | |||||||
\(348\) | −0.344409 | −0.0184623 | ||||||||
\(349\) | 1.21341 | 0.0649522 | 0.0324761 | − | 0.999473i | \(-0.489661\pi\) | ||||
0.0324761 | + | 0.999473i | \(0.489661\pi\) | |||||||
\(350\) | −0.276784 | −0.0147947 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −4.48940 | −0.239286 | ||||||||
\(353\) | −5.19525 | −0.276515 | −0.138258 | − | 0.990396i | \(-0.544150\pi\) | ||||
−0.138258 | + | 0.990396i | \(0.544150\pi\) | |||||||
\(354\) | 15.8931 | 0.844711 | ||||||||
\(355\) | 10.2638 | 0.544747 | ||||||||
\(356\) | 2.14402 | 0.113633 | ||||||||
\(357\) | 0.0563975 | 0.00298487 | ||||||||
\(358\) | −0.377597 | −0.0199566 | ||||||||
\(359\) | 36.8307 | 1.94385 | 0.971925 | − | 0.235291i | \(-0.0756042\pi\) | ||||
0.971925 | + | 0.235291i | \(0.0756042\pi\) | |||||||
\(360\) | −9.53021 | −0.502286 | ||||||||
\(361\) | −16.1856 | −0.851876 | ||||||||
\(362\) | 22.5266 | 1.18397 | ||||||||
\(363\) | 2.80355 | 0.147148 | ||||||||
\(364\) | −0.00507265 | −0.000265879 0 | ||||||||
\(365\) | −54.4868 | −2.85197 | ||||||||
\(366\) | 8.08027 | 0.422363 | ||||||||
\(367\) | 22.8942 | 1.19507 | 0.597534 | − | 0.801844i | \(-0.296147\pi\) | ||||
0.597534 | + | 0.801844i | \(0.296147\pi\) | |||||||
\(368\) | 24.1077 | 1.25670 | ||||||||
\(369\) | −6.74954 | −0.351367 | ||||||||
\(370\) | −18.7364 | −0.974060 | ||||||||
\(371\) | 0.186097 | 0.00966169 | ||||||||
\(372\) | 0.619992 | 0.0321451 | ||||||||
\(373\) | 25.3139 | 1.31070 | 0.655351 | − | 0.755324i | \(-0.272521\pi\) | ||||
0.655351 | + | 0.755324i | \(0.272521\pi\) | |||||||
\(374\) | 13.1853 | 0.681796 | ||||||||
\(375\) | −10.2762 | −0.530660 | ||||||||
\(376\) | −10.8577 | −0.559944 | ||||||||
\(377\) | 1.60562 | 0.0826937 | ||||||||
\(378\) | −0.0351918 | −0.00181007 | ||||||||
\(379\) | 8.48624 | 0.435909 | 0.217955 | − | 0.975959i | \(-0.430062\pi\) | ||||
0.217955 | + | 0.975959i | \(0.430062\pi\) | |||||||
\(380\) | −1.29070 | −0.0662117 | ||||||||
\(381\) | 1.60892 | 0.0824277 | ||||||||
\(382\) | −15.3311 | −0.784405 | ||||||||
\(383\) | −3.24774 | −0.165952 | −0.0829759 | − | 0.996552i | \(-0.526442\pi\) | ||||
−0.0829759 | + | 0.996552i | \(0.526442\pi\) | |||||||
\(384\) | −12.7856 | −0.652465 | ||||||||
\(385\) | 0.315140 | 0.0160610 | ||||||||
\(386\) | −9.05346 | −0.460809 | ||||||||
\(387\) | −0.758748 | −0.0385693 | ||||||||
\(388\) | −0.764028 | −0.0387876 | ||||||||
\(389\) | 19.8931 | 1.00862 | 0.504311 | − | 0.863522i | \(-0.331746\pi\) | ||||
0.504311 | + | 0.863522i | \(0.331746\pi\) | |||||||
\(390\) | −5.33757 | −0.270278 | ||||||||
\(391\) | −13.1172 | −0.663365 | ||||||||
\(392\) | −18.5978 | −0.939329 | ||||||||
\(393\) | 5.67616 | 0.286324 | ||||||||
\(394\) | 23.2634 | 1.17199 | ||||||||
\(395\) | −60.1222 | −3.02508 | ||||||||
\(396\) | −0.796942 | −0.0400479 | ||||||||
\(397\) | −11.7640 | −0.590421 | −0.295210 | − | 0.955432i | \(-0.595390\pi\) | ||||
−0.295210 | + | 0.955432i | \(0.595390\pi\) | |||||||
\(398\) | −26.6241 | −1.33455 | ||||||||
\(399\) | 0.0396729 | 0.00198613 | ||||||||
\(400\) | −34.4723 | −1.72362 | ||||||||
\(401\) | 16.2212 | 0.810050 | 0.405025 | − | 0.914306i | \(-0.367263\pi\) | ||||
0.405025 | + | 0.914306i | \(0.367263\pi\) | |||||||
\(402\) | 14.4022 | 0.718317 | ||||||||
\(403\) | −2.89038 | −0.143980 | ||||||||
\(404\) | 0.397419 | 0.0197723 | ||||||||
\(405\) | −3.58678 | −0.178229 | ||||||||
\(406\) | 0.0565047 | 0.00280428 | ||||||||
\(407\) | 13.0418 | 0.646460 | ||||||||
\(408\) | 6.33657 | 0.313707 | ||||||||
\(409\) | 29.6167 | 1.46445 | 0.732227 | − | 0.681061i | \(-0.238481\pi\) | ||||
0.732227 | + | 0.681061i | \(0.238481\pi\) | |||||||
\(410\) | −36.0261 | −1.77920 | ||||||||
\(411\) | −13.8157 | −0.681476 | ||||||||
\(412\) | −0.214502 | −0.0105678 | ||||||||
\(413\) | −0.252566 | −0.0124280 | ||||||||
\(414\) | 8.18507 | 0.402274 | ||||||||
\(415\) | 16.4681 | 0.808386 | ||||||||
\(416\) | −1.20835 | −0.0592442 | ||||||||
\(417\) | 13.2348 | 0.648110 | ||||||||
\(418\) | 9.27521 | 0.453665 | ||||||||
\(419\) | 8.22298 | 0.401719 | 0.200859 | − | 0.979620i | \(-0.435627\pi\) | ||||
0.200859 | + | 0.979620i | \(0.435627\pi\) | |||||||
\(420\) | −0.0181945 | −0.000887801 0 | ||||||||
\(421\) | −30.6539 | −1.49398 | −0.746989 | − | 0.664836i | \(-0.768501\pi\) | ||||
−0.746989 | + | 0.664836i | \(0.768501\pi\) | |||||||
\(422\) | −4.60955 | −0.224389 | ||||||||
\(423\) | −4.08640 | −0.198688 | ||||||||
\(424\) | 20.9090 | 1.01543 | ||||||||
\(425\) | 18.7567 | 0.909833 | ||||||||
\(426\) | 4.25836 | 0.206318 | ||||||||
\(427\) | −0.128408 | −0.00621409 | ||||||||
\(428\) | −0.259671 | −0.0125517 | ||||||||
\(429\) | 3.71531 | 0.179377 | ||||||||
\(430\) | −4.04987 | −0.195302 | ||||||||
\(431\) | 21.8734 | 1.05361 | 0.526803 | − | 0.849987i | \(-0.323391\pi\) | ||||
0.526803 | + | 0.849987i | \(0.323391\pi\) | |||||||
\(432\) | −4.38299 | −0.210877 | ||||||||
\(433\) | 11.9588 | 0.574704 | 0.287352 | − | 0.957825i | \(-0.407225\pi\) | ||||
0.287352 | + | 0.957825i | \(0.407225\pi\) | |||||||
\(434\) | −0.101718 | −0.00488260 | ||||||||
\(435\) | 5.75902 | 0.276124 | ||||||||
\(436\) | −1.98430 | −0.0950305 | ||||||||
\(437\) | −9.22730 | −0.441402 | ||||||||
\(438\) | −22.6060 | −1.08016 | ||||||||
\(439\) | −16.6422 | −0.794290 | −0.397145 | − | 0.917756i | \(-0.629999\pi\) | ||||
−0.397145 | + | 0.917756i | \(0.629999\pi\) | |||||||
\(440\) | 35.4077 | 1.68800 | ||||||||
\(441\) | −6.99944 | −0.333307 | ||||||||
\(442\) | 3.54891 | 0.168804 | ||||||||
\(443\) | 12.2352 | 0.581312 | 0.290656 | − | 0.956828i | \(-0.406126\pi\) | ||||
0.290656 | + | 0.956828i | \(0.406126\pi\) | |||||||
\(444\) | −0.752965 | −0.0357342 | ||||||||
\(445\) | −35.8512 | −1.69951 | ||||||||
\(446\) | −13.7014 | −0.648781 | ||||||||
\(447\) | −3.91884 | −0.185355 | ||||||||
\(448\) | 0.164778 | 0.00778505 | ||||||||
\(449\) | −29.8011 | −1.40640 | −0.703200 | − | 0.710992i | \(-0.748246\pi\) | ||||
−0.703200 | + | 0.710992i | \(0.748246\pi\) | |||||||
\(450\) | −11.7041 | −0.551736 | ||||||||
\(451\) | 25.0767 | 1.18081 | ||||||||
\(452\) | −2.58340 | −0.121513 | ||||||||
\(453\) | 21.0997 | 0.991350 | ||||||||
\(454\) | 23.9727 | 1.12510 | ||||||||
\(455\) | 0.0848220 | 0.00397652 | ||||||||
\(456\) | 4.45746 | 0.208740 | ||||||||
\(457\) | 6.28598 | 0.294046 | 0.147023 | − | 0.989133i | \(-0.453031\pi\) | ||||
0.147023 | + | 0.989133i | \(0.453031\pi\) | |||||||
\(458\) | −44.4476 | −2.07690 | ||||||||
\(459\) | 2.38483 | 0.111314 | ||||||||
\(460\) | 4.23176 | 0.197307 | ||||||||
\(461\) | −11.7732 | −0.548332 | −0.274166 | − | 0.961682i | \(-0.588402\pi\) | ||||
−0.274166 | + | 0.961682i | \(0.588402\pi\) | |||||||
\(462\) | 0.130749 | 0.00608297 | ||||||||
\(463\) | −25.6663 | −1.19281 | −0.596406 | − | 0.802683i | \(-0.703405\pi\) | ||||
−0.596406 | + | 0.802683i | \(0.703405\pi\) | |||||||
\(464\) | 7.03743 | 0.326704 | ||||||||
\(465\) | −10.3672 | −0.480765 | ||||||||
\(466\) | −42.4362 | −1.96582 | ||||||||
\(467\) | 27.1923 | 1.25831 | 0.629155 | − | 0.777280i | \(-0.283401\pi\) | ||||
0.629155 | + | 0.777280i | \(0.283401\pi\) | |||||||
\(468\) | −0.214502 | −0.00991536 | ||||||||
\(469\) | −0.228873 | −0.0105684 | ||||||||
\(470\) | −21.8115 | −1.00609 | ||||||||
\(471\) | 9.31170 | 0.429060 | ||||||||
\(472\) | −28.3772 | −1.30616 | ||||||||
\(473\) | 2.81898 | 0.129617 | ||||||||
\(474\) | −24.9441 | −1.14572 | ||||||||
\(475\) | 13.1944 | 0.605401 | ||||||||
\(476\) | 0.0120974 | 0.000554483 0 | ||||||||
\(477\) | 7.86931 | 0.360311 | ||||||||
\(478\) | −8.29339 | −0.379331 | ||||||||
\(479\) | 19.4778 | 0.889963 | 0.444981 | − | 0.895540i | \(-0.353210\pi\) | ||||
0.444981 | + | 0.895540i | \(0.353210\pi\) | |||||||
\(480\) | −4.33409 | −0.197823 | ||||||||
\(481\) | 3.51029 | 0.160056 | ||||||||
\(482\) | −7.48858 | −0.341096 | ||||||||
\(483\) | −0.130073 | −0.00591854 | ||||||||
\(484\) | 0.601367 | 0.0273349 | ||||||||
\(485\) | 12.7756 | 0.580112 | ||||||||
\(486\) | −1.48812 | −0.0675025 | ||||||||
\(487\) | −35.5437 | −1.61064 | −0.805319 | − | 0.592841i | \(-0.798006\pi\) | ||||
−0.805319 | + | 0.592841i | \(0.798006\pi\) | |||||||
\(488\) | −14.4273 | −0.653094 | ||||||||
\(489\) | −3.01766 | −0.136463 | ||||||||
\(490\) | −37.3600 | −1.68775 | ||||||||
\(491\) | 25.9533 | 1.17126 | 0.585628 | − | 0.810580i | \(-0.300848\pi\) | ||||
0.585628 | + | 0.810580i | \(0.300848\pi\) | |||||||
\(492\) | −1.44779 | −0.0652714 | ||||||||
\(493\) | −3.82913 | −0.172455 | ||||||||
\(494\) | 2.49648 | 0.112322 | ||||||||
\(495\) | 13.3260 | 0.598960 | ||||||||
\(496\) | −12.6685 | −0.568832 | ||||||||
\(497\) | −0.0676718 | −0.00303550 | ||||||||
\(498\) | 6.83244 | 0.306169 | ||||||||
\(499\) | 14.5179 | 0.649911 | 0.324955 | − | 0.945729i | \(-0.394651\pi\) | ||||
0.324955 | + | 0.945729i | \(0.394651\pi\) | |||||||
\(500\) | −2.20426 | −0.0985777 | ||||||||
\(501\) | 21.5065 | 0.960840 | ||||||||
\(502\) | 6.42929 | 0.286953 | ||||||||
\(503\) | 16.4003 | 0.731254 | 0.365627 | − | 0.930761i | \(-0.380855\pi\) | ||||
0.365627 | + | 0.930761i | \(0.380855\pi\) | |||||||
\(504\) | 0.0628349 | 0.00279889 | ||||||||
\(505\) | −6.64542 | −0.295717 | ||||||||
\(506\) | −30.4101 | −1.35189 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0.345118 | 0.0153121 | ||||||||
\(509\) | −0.273378 | −0.0121172 | −0.00605862 | − | 0.999982i | \(-0.501929\pi\) | ||||
−0.00605862 | + | 0.999982i | \(0.501929\pi\) | |||||||
\(510\) | 12.7292 | 0.563657 | ||||||||
\(511\) | 0.359244 | 0.0158920 | ||||||||
\(512\) | 17.9954 | 0.795290 | ||||||||
\(513\) | 1.67761 | 0.0740681 | ||||||||
\(514\) | −38.1904 | −1.68450 | ||||||||
\(515\) | 3.58678 | 0.158053 | ||||||||
\(516\) | −0.162753 | −0.00716480 | ||||||||
\(517\) | 15.1823 | 0.667715 | ||||||||
\(518\) | 0.123534 | 0.00542775 | ||||||||
\(519\) | 18.3177 | 0.804057 | ||||||||
\(520\) | 9.53021 | 0.417927 | ||||||||
\(521\) | 25.0865 | 1.09906 | 0.549529 | − | 0.835475i | \(-0.314807\pi\) | ||||
0.549529 | + | 0.835475i | \(0.314807\pi\) | |||||||
\(522\) | 2.38936 | 0.104579 | ||||||||
\(523\) | −38.2574 | −1.67288 | −0.836440 | − | 0.548058i | \(-0.815367\pi\) | ||||
−0.836440 | + | 0.548058i | \(0.815367\pi\) | |||||||
\(524\) | 1.21755 | 0.0531888 | ||||||||
\(525\) | 0.185996 | 0.00811752 | ||||||||
\(526\) | 15.4618 | 0.674165 | ||||||||
\(527\) | 6.89304 | 0.300266 | ||||||||
\(528\) | 16.2842 | 0.708678 | ||||||||
\(529\) | 7.25305 | 0.315350 | ||||||||
\(530\) | 42.0029 | 1.82449 | ||||||||
\(531\) | −10.6800 | −0.463473 | ||||||||
\(532\) | 0.00850992 | 0.000368952 0 | ||||||||
\(533\) | 6.74954 | 0.292355 | ||||||||
\(534\) | −14.8743 | −0.643674 | ||||||||
\(535\) | 4.34208 | 0.187724 | ||||||||
\(536\) | −25.7151 | −1.11072 | ||||||||
\(537\) | 0.253741 | 0.0109497 | ||||||||
\(538\) | 9.09333 | 0.392041 | ||||||||
\(539\) | 26.0051 | 1.12012 | ||||||||
\(540\) | −0.769373 | −0.0331085 | ||||||||
\(541\) | 20.3560 | 0.875172 | 0.437586 | − | 0.899177i | \(-0.355834\pi\) | ||||
0.437586 | + | 0.899177i | \(0.355834\pi\) | |||||||
\(542\) | −9.92457 | −0.426297 | ||||||||
\(543\) | −15.1376 | −0.649616 | ||||||||
\(544\) | 2.88170 | 0.123552 | ||||||||
\(545\) | 33.1803 | 1.42129 | ||||||||
\(546\) | 0.0351918 | 0.00150607 | ||||||||
\(547\) | 19.4491 | 0.831584 | 0.415792 | − | 0.909460i | \(-0.363505\pi\) | ||||
0.415792 | + | 0.909460i | \(0.363505\pi\) | |||||||
\(548\) | −2.96349 | −0.126594 | ||||||||
\(549\) | −5.42985 | −0.231740 | ||||||||
\(550\) | 43.4844 | 1.85418 | ||||||||
\(551\) | −2.69360 | −0.114751 | ||||||||
\(552\) | −14.6144 | −0.622032 | ||||||||
\(553\) | 0.396400 | 0.0168566 | ||||||||
\(554\) | −46.6339 | −1.98128 | ||||||||
\(555\) | 12.5907 | 0.534444 | ||||||||
\(556\) | 2.83889 | 0.120396 | ||||||||
\(557\) | 4.82681 | 0.204518 | 0.102259 | − | 0.994758i | \(-0.467393\pi\) | ||||
0.102259 | + | 0.994758i | \(0.467393\pi\) | |||||||
\(558\) | −4.30123 | −0.182085 | ||||||||
\(559\) | 0.758748 | 0.0320916 | ||||||||
\(560\) | 0.371774 | 0.0157103 | ||||||||
\(561\) | −8.86037 | −0.374085 | ||||||||
\(562\) | 43.1661 | 1.82085 | ||||||||
\(563\) | −20.8748 | −0.879768 | −0.439884 | − | 0.898055i | \(-0.644980\pi\) | ||||
−0.439884 | + | 0.898055i | \(0.644980\pi\) | |||||||
\(564\) | −0.876542 | −0.0369091 | ||||||||
\(565\) | 43.1981 | 1.81736 | ||||||||
\(566\) | 13.2209 | 0.555715 | ||||||||
\(567\) | 0.0236485 | 0.000993144 0 | ||||||||
\(568\) | −7.60329 | −0.319027 | ||||||||
\(569\) | 7.59511 | 0.318404 | 0.159202 | − | 0.987246i | \(-0.449108\pi\) | ||||
0.159202 | + | 0.987246i | \(0.449108\pi\) | |||||||
\(570\) | 8.95434 | 0.375056 | ||||||||
\(571\) | 21.5156 | 0.900401 | 0.450200 | − | 0.892928i | \(-0.351353\pi\) | ||||
0.450200 | + | 0.892928i | \(0.351353\pi\) | |||||||
\(572\) | 0.796942 | 0.0333218 | ||||||||
\(573\) | 10.3023 | 0.430384 | ||||||||
\(574\) | 0.237529 | 0.00991425 | ||||||||
\(575\) | −43.2598 | −1.80406 | ||||||||
\(576\) | 6.96782 | 0.290326 | ||||||||
\(577\) | 5.99567 | 0.249603 | 0.124801 | − | 0.992182i | \(-0.460171\pi\) | ||||
0.124801 | + | 0.992182i | \(0.460171\pi\) | |||||||
\(578\) | 16.8345 | 0.700224 | ||||||||
\(579\) | 6.08382 | 0.252835 | ||||||||
\(580\) | 1.23532 | 0.0512939 | ||||||||
\(581\) | −0.108578 | −0.00450457 | ||||||||
\(582\) | 5.30048 | 0.219712 | ||||||||
\(583\) | −29.2369 | −1.21087 | ||||||||
\(584\) | 40.3630 | 1.67023 | ||||||||
\(585\) | 3.58678 | 0.148295 | ||||||||
\(586\) | 16.0567 | 0.663297 | ||||||||
\(587\) | −12.3136 | −0.508237 | −0.254118 | − | 0.967173i | \(-0.581785\pi\) | ||||
−0.254118 | + | 0.967173i | \(0.581785\pi\) | |||||||
\(588\) | −1.50139 | −0.0619165 | ||||||||
\(589\) | 4.84891 | 0.199796 | ||||||||
\(590\) | −57.0052 | −2.34687 | ||||||||
\(591\) | −15.6327 | −0.643045 | ||||||||
\(592\) | 15.3856 | 0.632344 | ||||||||
\(593\) | −33.3943 | −1.37134 | −0.685671 | − | 0.727912i | \(-0.740491\pi\) | ||||
−0.685671 | + | 0.727912i | \(0.740491\pi\) | |||||||
\(594\) | 5.52883 | 0.226851 | ||||||||
\(595\) | −0.202286 | −0.00829291 | ||||||||
\(596\) | −0.840601 | −0.0344323 | ||||||||
\(597\) | 17.8911 | 0.732235 | ||||||||
\(598\) | −8.18507 | −0.334713 | ||||||||
\(599\) | −30.9686 | −1.26534 | −0.632672 | − | 0.774420i | \(-0.718042\pi\) | ||||
−0.632672 | + | 0.774420i | \(0.718042\pi\) | |||||||
\(600\) | 20.8976 | 0.853142 | ||||||||
\(601\) | 31.0693 | 1.26734 | 0.633672 | − | 0.773601i | \(-0.281547\pi\) | ||||
0.633672 | + | 0.773601i | \(0.281547\pi\) | |||||||
\(602\) | 0.0267017 | 0.00108828 | ||||||||
\(603\) | −9.67812 | −0.394124 | ||||||||
\(604\) | 4.52593 | 0.184157 | ||||||||
\(605\) | −10.0557 | −0.408823 | ||||||||
\(606\) | −2.75712 | −0.112000 | ||||||||
\(607\) | −5.04927 | −0.204944 | −0.102472 | − | 0.994736i | \(-0.532675\pi\) | ||||
−0.102472 | + | 0.994736i | \(0.532675\pi\) | |||||||
\(608\) | 2.02714 | 0.0822112 | ||||||||
\(609\) | −0.0379705 | −0.00153864 | ||||||||
\(610\) | −28.9822 | −1.17345 | ||||||||
\(611\) | 4.08640 | 0.165318 | ||||||||
\(612\) | 0.511550 | 0.0206782 | ||||||||
\(613\) | 17.5767 | 0.709915 | 0.354958 | − | 0.934882i | \(-0.384495\pi\) | ||||
0.354958 | + | 0.934882i | \(0.384495\pi\) | |||||||
\(614\) | 23.3811 | 0.943584 | ||||||||
\(615\) | 24.2091 | 0.976207 | ||||||||
\(616\) | −0.233451 | −0.00940602 | ||||||||
\(617\) | 1.63595 | 0.0658608 | 0.0329304 | − | 0.999458i | \(-0.489516\pi\) | ||||
0.0329304 | + | 0.999458i | \(0.489516\pi\) | |||||||
\(618\) | 1.48812 | 0.0598610 | ||||||||
\(619\) | 0.779525 | 0.0313318 | 0.0156659 | − | 0.999877i | \(-0.495013\pi\) | ||||
0.0156659 | + | 0.999877i | \(0.495013\pi\) | |||||||
\(620\) | −2.22378 | −0.0893090 | ||||||||
\(621\) | −5.50028 | −0.220719 | ||||||||
\(622\) | −16.0978 | −0.645462 | ||||||||
\(623\) | 0.236375 | 0.00947017 | ||||||||
\(624\) | 4.38299 | 0.175460 | ||||||||
\(625\) | −2.46661 | −0.0986645 | ||||||||
\(626\) | 16.5938 | 0.663222 | ||||||||
\(627\) | −6.23283 | −0.248915 | ||||||||
\(628\) | 1.99738 | 0.0797041 | ||||||||
\(629\) | −8.37144 | −0.333791 | ||||||||
\(630\) | 0.126225 | 0.00502894 | ||||||||
\(631\) | −23.5978 | −0.939412 | −0.469706 | − | 0.882823i | \(-0.655640\pi\) | ||||
−0.469706 | + | 0.882823i | \(0.655640\pi\) | |||||||
\(632\) | 44.5376 | 1.77161 | ||||||||
\(633\) | 3.09757 | 0.123117 | ||||||||
\(634\) | −16.5523 | −0.657375 | ||||||||
\(635\) | −5.77086 | −0.229010 | ||||||||
\(636\) | 1.68798 | 0.0669329 | ||||||||
\(637\) | 6.99944 | 0.277328 | ||||||||
\(638\) | −8.87721 | −0.351452 | ||||||||
\(639\) | −2.86157 | −0.113202 | ||||||||
\(640\) | 45.8594 | 1.81275 | ||||||||
\(641\) | −38.6884 | −1.52810 | −0.764051 | − | 0.645156i | \(-0.776792\pi\) | ||||
−0.764051 | + | 0.645156i | \(0.776792\pi\) | |||||||
\(642\) | 1.80148 | 0.0710989 | ||||||||
\(643\) | −23.2538 | −0.917039 | −0.458519 | − | 0.888684i | \(-0.651620\pi\) | ||||
−0.458519 | + | 0.888684i | \(0.651620\pi\) | |||||||
\(644\) | −0.0279010 | −0.00109945 | ||||||||
\(645\) | 2.72146 | 0.107158 | ||||||||
\(646\) | −5.95367 | −0.234244 | ||||||||
\(647\) | 14.5221 | 0.570924 | 0.285462 | − | 0.958390i | \(-0.407853\pi\) | ||||
0.285462 | + | 0.958390i | \(0.407853\pi\) | |||||||
\(648\) | 2.65704 | 0.104378 | ||||||||
\(649\) | 39.6796 | 1.55756 | ||||||||
\(650\) | 11.7041 | 0.459072 | ||||||||
\(651\) | 0.0683530 | 0.00267897 | ||||||||
\(652\) | −0.647294 | −0.0253500 | ||||||||
\(653\) | −0.348559 | −0.0136402 | −0.00682008 | − | 0.999977i | \(-0.502171\pi\) | ||||
−0.00682008 | + | 0.999977i | \(0.502171\pi\) | |||||||
\(654\) | 13.7662 | 0.538299 | ||||||||
\(655\) | −20.3592 | −0.795498 | ||||||||
\(656\) | 29.5832 | 1.15503 | ||||||||
\(657\) | 15.1910 | 0.592657 | ||||||||
\(658\) | 0.143808 | 0.00560622 | ||||||||
\(659\) | −11.2477 | −0.438148 | −0.219074 | − | 0.975708i | \(-0.570304\pi\) | ||||
−0.219074 | + | 0.975708i | \(0.570304\pi\) | |||||||
\(660\) | 2.85846 | 0.111265 | ||||||||
\(661\) | 36.4348 | 1.41715 | 0.708574 | − | 0.705637i | \(-0.249339\pi\) | ||||
0.708574 | + | 0.705637i | \(0.249339\pi\) | |||||||
\(662\) | −10.1361 | −0.393951 | ||||||||
\(663\) | −2.38483 | −0.0926189 | ||||||||
\(664\) | −12.1993 | −0.473425 | ||||||||
\(665\) | −0.142298 | −0.00551808 | ||||||||
\(666\) | 5.22374 | 0.202416 | ||||||||
\(667\) | 8.83136 | 0.341952 | ||||||||
\(668\) | 4.61319 | 0.178490 | ||||||||
\(669\) | 9.20720 | 0.355971 | ||||||||
\(670\) | −51.6576 | −1.99571 | ||||||||
\(671\) | 20.1736 | 0.778793 | ||||||||
\(672\) | 0.0285757 | 0.00110233 | ||||||||
\(673\) | −43.6019 | −1.68073 | −0.840366 | − | 0.542020i | \(-0.817660\pi\) | ||||
−0.840366 | + | 0.542020i | \(0.817660\pi\) | |||||||
\(674\) | −11.2212 | −0.432226 | ||||||||
\(675\) | 7.86502 | 0.302725 | ||||||||
\(676\) | 0.214502 | 0.00825008 | ||||||||
\(677\) | 20.9648 | 0.805741 | 0.402871 | − | 0.915257i | \(-0.368012\pi\) | ||||
0.402871 | + | 0.915257i | \(0.368012\pi\) | |||||||
\(678\) | 17.9225 | 0.688308 | ||||||||
\(679\) | −0.0842328 | −0.00323256 | ||||||||
\(680\) | −22.7279 | −0.871575 | ||||||||
\(681\) | −16.1094 | −0.617314 | ||||||||
\(682\) | 15.9804 | 0.611921 | ||||||||
\(683\) | 12.3760 | 0.473554 | 0.236777 | − | 0.971564i | \(-0.423909\pi\) | ||||
0.236777 | + | 0.971564i | \(0.423909\pi\) | |||||||
\(684\) | 0.359850 | 0.0137592 | ||||||||
\(685\) | 49.5538 | 1.89335 | ||||||||
\(686\) | 0.492666 | 0.0188101 | ||||||||
\(687\) | 29.8683 | 1.13955 | ||||||||
\(688\) | 3.32559 | 0.126787 | ||||||||
\(689\) | −7.86931 | −0.299797 | ||||||||
\(690\) | −29.3581 | −1.11764 | ||||||||
\(691\) | −32.3780 | −1.23172 | −0.615859 | − | 0.787857i | \(-0.711191\pi\) | ||||
−0.615859 | + | 0.787857i | \(0.711191\pi\) | |||||||
\(692\) | 3.92918 | 0.149365 | ||||||||
\(693\) | −0.0878616 | −0.00333758 | ||||||||
\(694\) | 1.45598 | 0.0552681 | ||||||||
\(695\) | −47.4703 | −1.80065 | ||||||||
\(696\) | −4.26619 | −0.161710 | ||||||||
\(697\) | −16.0965 | −0.609698 | ||||||||
\(698\) | −1.80570 | −0.0683466 | ||||||||
\(699\) | 28.5167 | 1.07860 | ||||||||
\(700\) | 0.0398965 | 0.00150795 | ||||||||
\(701\) | 33.1812 | 1.25324 | 0.626618 | − | 0.779327i | \(-0.284439\pi\) | ||||
0.626618 | + | 0.779327i | \(0.284439\pi\) | |||||||
\(702\) | 1.48812 | 0.0561655 | ||||||||
\(703\) | −5.88889 | −0.222104 | ||||||||
\(704\) | −25.8876 | −0.975676 | ||||||||
\(705\) | 14.6570 | 0.552016 | ||||||||
\(706\) | 7.73115 | 0.290966 | ||||||||
\(707\) | 0.0438148 | 0.00164783 | ||||||||
\(708\) | −2.29088 | −0.0860967 | ||||||||
\(709\) | 48.9104 | 1.83687 | 0.918434 | − | 0.395575i | \(-0.129455\pi\) | ||||
0.918434 | + | 0.395575i | \(0.129455\pi\) | |||||||
\(710\) | −15.2738 | −0.573216 | ||||||||
\(711\) | 16.7621 | 0.628630 | ||||||||
\(712\) | 26.5580 | 0.995304 | ||||||||
\(713\) | −15.8979 | −0.595380 | ||||||||
\(714\) | −0.0839263 | −0.00314086 | ||||||||
\(715\) | −13.3260 | −0.498365 | ||||||||
\(716\) | 0.0544279 | 0.00203407 | ||||||||
\(717\) | 5.57306 | 0.208130 | ||||||||
\(718\) | −54.8085 | −2.04544 | ||||||||
\(719\) | −50.7176 | −1.89145 | −0.945725 | − | 0.324969i | \(-0.894646\pi\) | ||||
−0.945725 | + | 0.324969i | \(0.894646\pi\) | |||||||
\(720\) | 15.7208 | 0.585881 | ||||||||
\(721\) | −0.0236485 | −0.000880716 0 | ||||||||
\(722\) | 24.0862 | 0.896395 | ||||||||
\(723\) | 5.03224 | 0.187151 | ||||||||
\(724\) | −3.24705 | −0.120676 | ||||||||
\(725\) | −12.6282 | −0.469001 | ||||||||
\(726\) | −4.17202 | −0.154838 | ||||||||
\(727\) | 17.6824 | 0.655805 | 0.327903 | − | 0.944712i | \(-0.393658\pi\) | ||||
0.327903 | + | 0.944712i | \(0.393658\pi\) | |||||||
\(728\) | −0.0628349 | −0.00232882 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 81.0829 | 3.00101 | ||||||||
\(731\) | −1.80948 | −0.0669261 | ||||||||
\(732\) | −1.16471 | −0.0430491 | ||||||||
\(733\) | −15.0161 | −0.554632 | −0.277316 | − | 0.960779i | \(-0.589445\pi\) | ||||
−0.277316 | + | 0.960779i | \(0.589445\pi\) | |||||||
\(734\) | −34.0693 | −1.25752 | ||||||||
\(735\) | 25.1055 | 0.926030 | ||||||||
\(736\) | −6.64626 | −0.244984 | ||||||||
\(737\) | 35.9572 | 1.32450 | ||||||||
\(738\) | 10.0441 | 0.369730 | ||||||||
\(739\) | 28.7271 | 1.05674 | 0.528372 | − | 0.849013i | \(-0.322803\pi\) | ||||
0.528372 | + | 0.849013i | \(0.322803\pi\) | |||||||
\(740\) | 2.70072 | 0.0992806 | ||||||||
\(741\) | −1.67761 | −0.0616284 | ||||||||
\(742\) | −0.276935 | −0.0101666 | ||||||||
\(743\) | 50.5855 | 1.85580 | 0.927900 | − | 0.372829i | \(-0.121612\pi\) | ||||
0.927900 | + | 0.372829i | \(0.121612\pi\) | |||||||
\(744\) | 7.67983 | 0.281556 | ||||||||
\(745\) | 14.0560 | 0.514974 | ||||||||
\(746\) | −37.6701 | −1.37920 | ||||||||
\(747\) | −4.59132 | −0.167988 | ||||||||
\(748\) | −1.90057 | −0.0694917 | ||||||||
\(749\) | −0.0286283 | −0.00104606 | ||||||||
\(750\) | 15.2922 | 0.558392 | ||||||||
\(751\) | −25.9645 | −0.947457 | −0.473728 | − | 0.880671i | \(-0.657092\pi\) | ||||
−0.473728 | + | 0.880671i | \(0.657092\pi\) | |||||||
\(752\) | 17.9107 | 0.653135 | ||||||||
\(753\) | −4.32041 | −0.157444 | ||||||||
\(754\) | −2.38936 | −0.0870153 | ||||||||
\(755\) | −75.6800 | −2.75428 | ||||||||
\(756\) | 0.00507265 | 0.000184491 0 | ||||||||
\(757\) | 34.2130 | 1.24349 | 0.621746 | − | 0.783219i | \(-0.286423\pi\) | ||||
0.621746 | + | 0.783219i | \(0.286423\pi\) | |||||||
\(758\) | −12.6286 | −0.458690 | ||||||||
\(759\) | 20.4352 | 0.741753 | ||||||||
\(760\) | −15.9879 | −0.579944 | ||||||||
\(761\) | 51.7887 | 1.87734 | 0.938670 | − | 0.344816i | \(-0.112059\pi\) | ||||
0.938670 | + | 0.344816i | \(0.112059\pi\) | |||||||
\(762\) | −2.39427 | −0.0867354 | ||||||||
\(763\) | −0.218765 | −0.00791983 | ||||||||
\(764\) | 2.20986 | 0.0799501 | ||||||||
\(765\) | −8.55385 | −0.309265 | ||||||||
\(766\) | 4.83303 | 0.174624 | ||||||||
\(767\) | 10.6800 | 0.385633 | ||||||||
\(768\) | 5.09095 | 0.183704 | ||||||||
\(769\) | −11.0760 | −0.399409 | −0.199705 | − | 0.979856i | \(-0.563998\pi\) | ||||
−0.199705 | + | 0.979856i | \(0.563998\pi\) | |||||||
\(770\) | −0.468967 | −0.0169004 | ||||||||
\(771\) | 25.6635 | 0.924248 | ||||||||
\(772\) | 1.30499 | 0.0469677 | ||||||||
\(773\) | −20.8839 | −0.751143 | −0.375571 | − | 0.926794i | \(-0.622553\pi\) | ||||
−0.375571 | + | 0.926794i | \(0.622553\pi\) | |||||||
\(774\) | 1.12911 | 0.0405849 | ||||||||
\(775\) | 22.7328 | 0.816588 | ||||||||
\(776\) | −9.46400 | −0.339738 | ||||||||
\(777\) | −0.0830132 | −0.00297808 | ||||||||
\(778\) | −29.6034 | −1.06133 | ||||||||
\(779\) | −11.3231 | −0.405691 | ||||||||
\(780\) | 0.769373 | 0.0275480 | ||||||||
\(781\) | 10.6316 | 0.380429 | ||||||||
\(782\) | 19.5200 | 0.698033 | ||||||||
\(783\) | −1.60562 | −0.0573802 | ||||||||
\(784\) | 30.6785 | 1.09566 | ||||||||
\(785\) | −33.3991 | −1.19206 | ||||||||
\(786\) | −8.44681 | −0.301288 | ||||||||
\(787\) | −2.13144 | −0.0759775 | −0.0379888 | − | 0.999278i | \(-0.512095\pi\) | ||||
−0.0379888 | + | 0.999278i | \(0.512095\pi\) | |||||||
\(788\) | −3.35326 | −0.119455 | ||||||||
\(789\) | −10.3901 | −0.369898 | ||||||||
\(790\) | 89.4691 | 3.18317 | ||||||||
\(791\) | −0.284815 | −0.0101269 | ||||||||
\(792\) | −9.87172 | −0.350776 | ||||||||
\(793\) | 5.42985 | 0.192820 | ||||||||
\(794\) | 17.5063 | 0.621276 | ||||||||
\(795\) | −28.2255 | −1.00106 | ||||||||
\(796\) | 3.83768 | 0.136023 | ||||||||
\(797\) | −55.9046 | −1.98024 | −0.990121 | − | 0.140214i | \(-0.955221\pi\) | ||||
−0.990121 | + | 0.140214i | \(0.955221\pi\) | |||||||
\(798\) | −0.0590380 | −0.00208992 | ||||||||
\(799\) | −9.74536 | −0.344766 | ||||||||
\(800\) | 9.50369 | 0.336006 | ||||||||
\(801\) | 9.99536 | 0.353169 | ||||||||
\(802\) | −24.1392 | −0.852383 | ||||||||
\(803\) | −56.4393 | −1.99170 | ||||||||
\(804\) | −2.07598 | −0.0732141 | ||||||||
\(805\) | 0.466545 | 0.0164435 | ||||||||
\(806\) | 4.30123 | 0.151504 | ||||||||
\(807\) | −6.11062 | −0.215104 | ||||||||
\(808\) | 4.92283 | 0.173184 | ||||||||
\(809\) | −20.7727 | −0.730330 | −0.365165 | − | 0.930943i | \(-0.618987\pi\) | ||||
−0.365165 | + | 0.930943i | \(0.618987\pi\) | |||||||
\(810\) | 5.33757 | 0.187543 | ||||||||
\(811\) | 27.3891 | 0.961762 | 0.480881 | − | 0.876786i | \(-0.340317\pi\) | ||||
0.480881 | + | 0.876786i | \(0.340317\pi\) | |||||||
\(812\) | −0.00814476 | −0.000285825 0 | ||||||||
\(813\) | 6.66920 | 0.233899 | ||||||||
\(814\) | −19.4078 | −0.680244 | ||||||||
\(815\) | 10.8237 | 0.379137 | ||||||||
\(816\) | −10.4527 | −0.365917 | ||||||||
\(817\) | −1.27288 | −0.0445324 | ||||||||
\(818\) | −44.0733 | −1.54099 | ||||||||
\(819\) | −0.0236485 | −0.000826345 0 | ||||||||
\(820\) | 5.19291 | 0.181344 | ||||||||
\(821\) | −8.56521 | −0.298928 | −0.149464 | − | 0.988767i | \(-0.547755\pi\) | ||||
−0.149464 | + | 0.988767i | \(0.547755\pi\) | |||||||
\(822\) | 20.5594 | 0.717090 | ||||||||
\(823\) | −4.04383 | −0.140959 | −0.0704794 | − | 0.997513i | \(-0.522453\pi\) | ||||
−0.0704794 | + | 0.997513i | \(0.522453\pi\) | |||||||
\(824\) | −2.65704 | −0.0925622 | ||||||||
\(825\) | −29.2210 | −1.01734 | ||||||||
\(826\) | 0.375849 | 0.0130775 | ||||||||
\(827\) | 26.2429 | 0.912555 | 0.456278 | − | 0.889837i | \(-0.349182\pi\) | ||||
0.456278 | + | 0.889837i | \(0.349182\pi\) | |||||||
\(828\) | −1.17982 | −0.0410016 | ||||||||
\(829\) | 9.21308 | 0.319984 | 0.159992 | − | 0.987118i | \(-0.448853\pi\) | ||||
0.159992 | + | 0.987118i | \(0.448853\pi\) | |||||||
\(830\) | −24.5065 | −0.850633 | ||||||||
\(831\) | 31.3374 | 1.08708 | ||||||||
\(832\) | −6.96782 | −0.241566 | ||||||||
\(833\) | −16.6924 | −0.578359 | ||||||||
\(834\) | −19.6949 | −0.681980 | ||||||||
\(835\) | −77.1392 | −2.66951 | ||||||||
\(836\) | −1.33696 | −0.0462396 | ||||||||
\(837\) | 2.89038 | 0.0999060 | ||||||||
\(838\) | −12.2368 | −0.422712 | ||||||||
\(839\) | −52.0976 | −1.79861 | −0.899304 | − | 0.437325i | \(-0.855926\pi\) | ||||
−0.899304 | + | 0.437325i | \(0.855926\pi\) | |||||||
\(840\) | −0.225375 | −0.00777618 | ||||||||
\(841\) | −26.4220 | −0.911103 | ||||||||
\(842\) | 45.6166 | 1.57205 | ||||||||
\(843\) | −29.0071 | −0.999059 | ||||||||
\(844\) | 0.664434 | 0.0228708 | ||||||||
\(845\) | −3.58678 | −0.123389 | ||||||||
\(846\) | 6.08106 | 0.209071 | ||||||||
\(847\) | 0.0662997 | 0.00227809 | ||||||||
\(848\) | −34.4911 | −1.18443 | ||||||||
\(849\) | −8.88428 | −0.304908 | ||||||||
\(850\) | −27.9122 | −0.957381 | ||||||||
\(851\) | 19.3076 | 0.661855 | ||||||||
\(852\) | −0.613813 | −0.0210289 | ||||||||
\(853\) | 16.5563 | 0.566878 | 0.283439 | − | 0.958990i | \(-0.408525\pi\) | ||||
0.283439 | + | 0.958990i | \(0.408525\pi\) | |||||||
\(854\) | 0.191086 | 0.00653884 | ||||||||
\(855\) | −6.01721 | −0.205784 | ||||||||
\(856\) | −3.21655 | −0.109939 | ||||||||
\(857\) | 2.19005 | 0.0748108 | 0.0374054 | − | 0.999300i | \(-0.488091\pi\) | ||||
0.0374054 | + | 0.999300i | \(0.488091\pi\) | |||||||
\(858\) | −5.52883 | −0.188751 | ||||||||
\(859\) | −35.4959 | −1.21110 | −0.605552 | − | 0.795805i | \(-0.707048\pi\) | ||||
−0.605552 | + | 0.795805i | \(0.707048\pi\) | |||||||
\(860\) | 0.583760 | 0.0199060 | ||||||||
\(861\) | −0.159617 | −0.00543972 | ||||||||
\(862\) | −32.5503 | −1.10867 | ||||||||
\(863\) | 0.00343611 | 0.000116967 0 | 5.84833e−5 | − | 1.00000i | \(-0.499981\pi\) | ||||
5.84833e−5 | 1.00000i | \(0.499981\pi\) | ||||||||
\(864\) | 1.20835 | 0.0411089 | ||||||||
\(865\) | −65.7015 | −2.23392 | ||||||||
\(866\) | −17.7962 | −0.604738 | ||||||||
\(867\) | −11.3126 | −0.384196 | ||||||||
\(868\) | 0.0146619 | 0.000497656 0 | ||||||||
\(869\) | −62.2766 | −2.11259 | ||||||||
\(870\) | −8.57011 | −0.290554 | ||||||||
\(871\) | 9.67812 | 0.327931 | ||||||||
\(872\) | −24.5794 | −0.832365 | ||||||||
\(873\) | −3.56186 | −0.120551 | ||||||||
\(874\) | 13.7313 | 0.464469 | ||||||||
\(875\) | −0.243016 | −0.00821545 | ||||||||
\(876\) | 3.25850 | 0.110095 | ||||||||
\(877\) | 31.7336 | 1.07157 | 0.535784 | − | 0.844355i | \(-0.320016\pi\) | ||||
0.535784 | + | 0.844355i | \(0.320016\pi\) | |||||||
\(878\) | 24.7656 | 0.835800 | ||||||||
\(879\) | −10.7899 | −0.363936 | ||||||||
\(880\) | −58.4079 | −1.96893 | ||||||||
\(881\) | 33.8906 | 1.14180 | 0.570901 | − | 0.821019i | \(-0.306594\pi\) | ||||
0.570901 | + | 0.821019i | \(0.306594\pi\) | |||||||
\(882\) | 10.4160 | 0.350725 | ||||||||
\(883\) | −14.9095 | −0.501744 | −0.250872 | − | 0.968020i | \(-0.580717\pi\) | ||||
−0.250872 | + | 0.968020i | \(0.580717\pi\) | |||||||
\(884\) | −0.511550 | −0.0172053 | ||||||||
\(885\) | 38.3069 | 1.28767 | ||||||||
\(886\) | −18.2075 | −0.611692 | ||||||||
\(887\) | 5.81841 | 0.195363 | 0.0976815 | − | 0.995218i | \(-0.468857\pi\) | ||||
0.0976815 | + | 0.995218i | \(0.468857\pi\) | |||||||
\(888\) | −9.32697 | −0.312993 | ||||||||
\(889\) | 0.0380487 | 0.00127611 | ||||||||
\(890\) | 53.3509 | 1.78832 | ||||||||
\(891\) | −3.71531 | −0.124468 | ||||||||
\(892\) | 1.97496 | 0.0661267 | ||||||||
\(893\) | −6.85538 | −0.229407 | ||||||||
\(894\) | 5.83171 | 0.195042 | ||||||||
\(895\) | −0.910113 | −0.0304217 | ||||||||
\(896\) | −0.302361 | −0.0101012 | ||||||||
\(897\) | 5.50028 | 0.183649 | ||||||||
\(898\) | 44.3476 | 1.47990 | ||||||||
\(899\) | −4.64085 | −0.154781 | ||||||||
\(900\) | 1.68706 | 0.0562354 | ||||||||
\(901\) | 18.7669 | 0.625217 | ||||||||
\(902\) | −37.3171 | −1.24252 | ||||||||
\(903\) | −0.0179432 | −0.000597114 0 | ||||||||
\(904\) | −32.0005 | −1.06432 | ||||||||
\(905\) | 54.2953 | 1.80484 | ||||||||
\(906\) | −31.3989 | −1.04316 | ||||||||
\(907\) | −11.9288 | −0.396090 | −0.198045 | − | 0.980193i | \(-0.563459\pi\) | ||||
−0.198045 | + | 0.980193i | \(0.563459\pi\) | |||||||
\(908\) | −3.45550 | −0.114675 | ||||||||
\(909\) | 1.85275 | 0.0614519 | ||||||||
\(910\) | −0.126225 | −0.00418433 | ||||||||
\(911\) | −38.6204 | −1.27955 | −0.639775 | − | 0.768562i | \(-0.720973\pi\) | ||||
−0.639775 | + | 0.768562i | \(0.720973\pi\) | |||||||
\(912\) | −7.35294 | −0.243480 | ||||||||
\(913\) | 17.0582 | 0.564544 | ||||||||
\(914\) | −9.35429 | −0.309412 | ||||||||
\(915\) | 19.4757 | 0.643847 | ||||||||
\(916\) | 6.40680 | 0.211687 | ||||||||
\(917\) | 0.134233 | 0.00443275 | ||||||||
\(918\) | −3.54891 | −0.117131 | ||||||||
\(919\) | −28.0457 | −0.925142 | −0.462571 | − | 0.886582i | \(-0.653073\pi\) | ||||
−0.462571 | + | 0.886582i | \(0.653073\pi\) | |||||||
\(920\) | 52.4188 | 1.72820 | ||||||||
\(921\) | −15.7118 | −0.517723 | ||||||||
\(922\) | 17.5199 | 0.576988 | ||||||||
\(923\) | 2.86157 | 0.0941897 | ||||||||
\(924\) | −0.0188465 | −0.000620004 0 | ||||||||
\(925\) | −27.6085 | −0.907762 | ||||||||
\(926\) | 38.1945 | 1.25515 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | −1.94015 | −0.0636886 | ||||||||
\(929\) | 28.3527 | 0.930221 | 0.465110 | − | 0.885253i | \(-0.346015\pi\) | ||||
0.465110 | + | 0.885253i | \(0.346015\pi\) | |||||||
\(930\) | 15.4276 | 0.505890 | ||||||||
\(931\) | −11.7423 | −0.384839 | ||||||||
\(932\) | 6.11688 | 0.200365 | ||||||||
\(933\) | 10.8175 | 0.354150 | ||||||||
\(934\) | −40.4654 | −1.32407 | ||||||||
\(935\) | 31.7802 | 1.03932 | ||||||||
\(936\) | −2.65704 | −0.0868479 | ||||||||
\(937\) | 2.23335 | 0.0729605 | 0.0364803 | − | 0.999334i | \(-0.488385\pi\) | ||||
0.0364803 | + | 0.999334i | \(0.488385\pi\) | |||||||
\(938\) | 0.340591 | 0.0111207 | ||||||||
\(939\) | −11.1508 | −0.363894 | ||||||||
\(940\) | 3.14397 | 0.102545 | ||||||||
\(941\) | 21.9982 | 0.717122 | 0.358561 | − | 0.933506i | \(-0.383268\pi\) | ||||
0.358561 | + | 0.933506i | \(0.383268\pi\) | |||||||
\(942\) | −13.8569 | −0.451483 | ||||||||
\(943\) | 37.1243 | 1.20893 | ||||||||
\(944\) | 46.8104 | 1.52355 | ||||||||
\(945\) | −0.0848220 | −0.00275926 | ||||||||
\(946\) | −4.19499 | −0.136391 | ||||||||
\(947\) | 1.67200 | 0.0543327 | 0.0271663 | − | 0.999631i | \(-0.491352\pi\) | ||||
0.0271663 | + | 0.999631i | \(0.491352\pi\) | |||||||
\(948\) | 3.59552 | 0.116777 | ||||||||
\(949\) | −15.1910 | −0.493121 | ||||||||
\(950\) | −19.6349 | −0.637039 | ||||||||
\(951\) | 11.1229 | 0.360686 | ||||||||
\(952\) | 0.149850 | 0.00485668 | ||||||||
\(953\) | 31.1056 | 1.00761 | 0.503805 | − | 0.863818i | \(-0.331933\pi\) | ||||
0.503805 | + | 0.863818i | \(0.331933\pi\) | |||||||
\(954\) | −11.7105 | −0.379141 | ||||||||
\(955\) | −36.9521 | −1.19574 | ||||||||
\(956\) | 1.19543 | 0.0386631 | ||||||||
\(957\) | 5.96539 | 0.192834 | ||||||||
\(958\) | −28.9853 | −0.936472 | ||||||||
\(959\) | −0.326720 | −0.0105503 | ||||||||
\(960\) | −24.9920 | −0.806615 | ||||||||
\(961\) | −22.6457 | −0.730507 | ||||||||
\(962\) | −5.22374 | −0.168420 | ||||||||
\(963\) | −1.21058 | −0.0390103 | ||||||||
\(964\) | 1.07943 | 0.0347660 | ||||||||
\(965\) | −21.8214 | −0.702454 | ||||||||
\(966\) | 0.193565 | 0.00622784 | ||||||||
\(967\) | −35.1720 | −1.13105 | −0.565527 | − | 0.824730i | \(-0.691327\pi\) | ||||
−0.565527 | + | 0.824730i | \(0.691327\pi\) | |||||||
\(968\) | 7.44913 | 0.239424 | ||||||||
\(969\) | 4.00080 | 0.128524 | ||||||||
\(970\) | −19.0117 | −0.610428 | ||||||||
\(971\) | −26.7524 | −0.858524 | −0.429262 | − | 0.903180i | \(-0.641226\pi\) | ||||
−0.429262 | + | 0.903180i | \(0.641226\pi\) | |||||||
\(972\) | 0.214502 | 0.00688016 | ||||||||
\(973\) | 0.312983 | 0.0100338 | ||||||||
\(974\) | 52.8933 | 1.69481 | ||||||||
\(975\) | −7.86502 | −0.251882 | ||||||||
\(976\) | 23.7990 | 0.761787 | ||||||||
\(977\) | −11.5874 | −0.370715 | −0.185357 | − | 0.982671i | \(-0.559344\pi\) | ||||
−0.185357 | + | 0.982671i | \(0.559344\pi\) | |||||||
\(978\) | 4.49064 | 0.143595 | ||||||||
\(979\) | −37.1359 | −1.18687 | ||||||||
\(980\) | 5.38518 | 0.172023 | ||||||||
\(981\) | −9.25070 | −0.295352 | ||||||||
\(982\) | −38.6216 | −1.23247 | ||||||||
\(983\) | 0.844719 | 0.0269424 | 0.0134712 | − | 0.999909i | \(-0.495712\pi\) | ||||
0.0134712 | + | 0.999909i | \(0.495712\pi\) | |||||||
\(984\) | −17.9338 | −0.571708 | ||||||||
\(985\) | 56.0712 | 1.78658 | ||||||||
\(986\) | 5.69820 | 0.181468 | ||||||||
\(987\) | −0.0966373 | −0.00307600 | ||||||||
\(988\) | −0.359850 | −0.0114484 | ||||||||
\(989\) | 4.17332 | 0.132704 | ||||||||
\(990\) | −19.8307 | −0.630262 | ||||||||
\(991\) | 45.4221 | 1.44288 | 0.721440 | − | 0.692477i | \(-0.243481\pi\) | ||||
0.721440 | + | 0.692477i | \(0.243481\pi\) | |||||||
\(992\) | 3.49258 | 0.110890 | ||||||||
\(993\) | 6.81134 | 0.216151 | ||||||||
\(994\) | 0.100704 | 0.00319413 | ||||||||
\(995\) | −64.1716 | −2.03438 | ||||||||
\(996\) | −0.984848 | −0.0312061 | ||||||||
\(997\) | −27.0049 | −0.855254 | −0.427627 | − | 0.903955i | \(-0.640650\pi\) | ||||
−0.427627 | + | 0.903955i | \(0.640650\pi\) | |||||||
\(998\) | −21.6044 | −0.683875 | ||||||||
\(999\) | −3.51029 | −0.111061 |
(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 | 4017.2.a.l.1.9 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.l.1.9 | ✓ | 32 | 1.1 | even | 1 | trivial |