Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, 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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(0\) |
Dimension: | \(49\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.90482 | −1.67710 | −0.838550 | − | 0.544825i | \(-0.816596\pi\) | ||||
−0.838550 | + | 0.544825i | \(0.816596\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.52511 | −1.57648 | −0.788239 | − | 0.615369i | \(-0.789007\pi\) | ||||
−0.788239 | + | 0.615369i | \(0.789007\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.26846 | 1.23536 | 0.617681 | − | 0.786429i | \(-0.288072\pi\) | ||||
0.617681 | + | 0.786429i | \(0.288072\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.43799 | 1.81266 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.64760 | −1.40131 | −0.700653 | − | 0.713502i | \(-0.747108\pi\) | ||||
−0.700653 | + | 0.713502i | \(0.747108\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.0450431 | −0.0124927 | −0.00624635 | − | 0.999980i | \(-0.501988\pi\) | ||||
−0.00624635 | + | 0.999980i | \(0.501988\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10.2398 | 2.64391 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.09573 | −1.23590 | −0.617948 | − | 0.786219i | \(-0.712036\pi\) | ||||
−0.617948 | + | 0.786219i | \(0.712036\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.40802 | 0.552439 | 0.276219 | − | 0.961095i | \(-0.410918\pi\) | ||||
0.276219 | + | 0.961095i | \(0.410918\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9.49429 | −2.07182 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.86095 | −0.388036 | −0.194018 | − | 0.980998i | \(-0.562152\pi\) | ||||
−0.194018 | + | 0.980998i | \(0.562152\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.42643 | 1.48529 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.08191 | −1.36291 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.84468 | −0.342548 | −0.171274 | − | 0.985223i | \(-0.554788\pi\) | ||||
−0.171274 | + | 0.985223i | \(0.554788\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.76774 | −0.676705 | −0.338353 | − | 0.941019i | \(-0.609870\pi\) | ||||
−0.338353 | + | 0.941019i | \(0.609870\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 13.5005 | 2.35013 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −11.5217 | −1.94752 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.39868 | 1.38073 | 0.690367 | − | 0.723459i | \(-0.257449\pi\) | ||||
0.690367 | + | 0.723459i | \(0.257449\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.130842 | 0.0209515 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.06429 | 0.478561 | 0.239281 | − | 0.970950i | \(-0.423088\pi\) | ||||
0.239281 | + | 0.970950i | \(0.423088\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.51254 | −1.14565 | −0.572826 | − | 0.819677i | \(-0.694153\pi\) | ||||
−0.572826 | + | 0.819677i | \(0.694153\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −19.1695 | −2.85762 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.33898 | 1.21637 | 0.608183 | − | 0.793797i | \(-0.291899\pi\) | ||||
0.608183 | + | 0.793797i | \(0.291899\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.68283 | 0.526119 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.8022 | 2.07272 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.2994 | −1.41473 | −0.707365 | − | 0.706848i | \(-0.750116\pi\) | ||||
−0.707365 | + | 0.706848i | \(0.750116\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.3833 | 2.20913 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.99488 | −0.926495 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.35032 | −0.305985 | −0.152993 | − | 0.988227i | \(-0.548891\pi\) | ||||
−0.152993 | + | 0.988227i | \(0.548891\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.15473 | −0.403922 | −0.201961 | − | 0.979394i | \(-0.564731\pi\) | ||||
−0.201961 | + | 0.979394i | \(0.564731\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 17.7738 | 2.23929 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.158782 | 0.0196945 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.89025 | −0.841778 | −0.420889 | − | 0.907112i | \(-0.638282\pi\) | ||||
−0.420889 | + | 0.907112i | \(0.638282\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.40574 | 0.650775 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.257052 | −0.0305065 | −0.0152532 | − | 0.999884i | \(-0.504855\pi\) | ||||
−0.0152532 | + | 0.999884i | \(0.504855\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.34373 | −0.859519 | −0.429759 | − | 0.902943i | \(-0.641402\pi\) | ||||
−0.429759 | + | 0.902943i | \(0.641402\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −21.5725 | −2.49097 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −15.1905 | −1.73112 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.04528 | −0.905165 | −0.452582 | − | 0.891723i | \(-0.649497\pi\) | ||||
−0.452582 | + | 0.891723i | \(0.649497\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.25773 | 0.473081 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.16290 | 0.456938 | 0.228469 | − | 0.973551i | \(-0.426628\pi\) | ||||
0.228469 | + | 0.973551i | \(0.426628\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.9630 | 1.94836 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.35846 | 0.574487 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.10488 | −0.435117 | −0.217558 | − | 0.976047i | \(-0.569809\pi\) | ||||
−0.217558 | + | 0.976047i | \(0.569809\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.147221 | −0.0154330 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.9446 | 1.13490 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.48856 | −0.870908 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.27541 | −0.738706 | −0.369353 | − | 0.929289i | \(-0.620421\pi\) | ||||
−0.369353 | + | 0.929289i | \(0.620421\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −25.2736 | −2.54009 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.1900 | −1.51147 | −0.755733 | − | 0.654880i | \(-0.772719\pi\) | ||||
−0.755733 | + | 0.654880i | \(0.772719\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.19234 | 0.117485 | 0.0587424 | − | 0.998273i | \(-0.481291\pi\) | ||||
0.0587424 | + | 0.998273i | \(0.481291\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 33.4685 | 3.26619 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.3674 | −1.29227 | −0.646137 | − | 0.763222i | \(-0.723616\pi\) | ||||
−0.646137 | + | 0.763222i | \(0.723616\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.2854 | −1.08094 | −0.540472 | − | 0.841362i | \(-0.681754\pi\) | ||||
−0.540472 | + | 0.841362i | \(0.681754\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −24.3967 | −2.31563 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.36482 | −0.410607 | −0.205304 | − | 0.978698i | \(-0.565818\pi\) | ||||
−0.205304 | + | 0.978698i | \(0.565818\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.56008 | 0.611730 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.244944 | −0.0226450 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.6552 | −1.52678 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.6002 | 0.963657 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.90120 | −0.802595 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.55344 | −0.765043 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.38340 | −0.122757 | −0.0613784 | − | 0.998115i | \(-0.519550\pi\) | ||||
−0.0613784 | + | 0.998115i | \(0.519550\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 21.8226 | 1.92137 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.57506 | 0.749207 | 0.374603 | − | 0.927185i | \(-0.377779\pi\) | ||||
0.374603 | + | 0.927185i | \(0.377779\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.87053 | 0.682462 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 24.9646 | 2.14861 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.35232 | −0.628151 | −0.314076 | − | 0.949398i | \(-0.601695\pi\) | ||||
−0.314076 | + | 0.949398i | \(0.601695\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.46826 | 0.803088 | 0.401544 | − | 0.915840i | \(-0.368474\pi\) | ||||
0.401544 | + | 0.915840i | \(0.368474\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −24.2233 | −2.03997 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.209342 | 0.0175061 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.50270 | 0.540020 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.6980 | −0.882353 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.2018 | −0.999611 | −0.499805 | − | 0.866138i | \(-0.666595\pi\) | ||||
−0.499805 | + | 0.866138i | \(0.666595\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.8095 | 1.61207 | 0.806036 | − | 0.591867i | \(-0.201609\pi\) | ||||
0.806036 | + | 0.591867i | \(0.201609\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −27.7105 | −2.24026 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.2817 | 1.06681 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.8024 | −1.66021 | −0.830107 | − | 0.557604i | \(-0.811721\pi\) | ||||
−0.830107 | + | 0.557604i | \(0.811721\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 29.9179 | 2.37264 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.08246 | −0.479365 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.72139 | −0.213156 | −0.106578 | − | 0.994304i | \(-0.533989\pi\) | ||||
−0.106578 | + | 0.994304i | \(0.533989\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −47.5907 | −3.70493 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.1603 | 1.56005 | 0.780026 | − | 0.625748i | \(-0.215206\pi\) | ||||
0.780026 | + | 0.625748i | \(0.215206\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9980 | −0.999844 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.0948 | 1.00138 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.5453 | 1.63806 | 0.819029 | − | 0.573752i | \(-0.194512\pi\) | ||||
0.819029 | + | 0.573752i | \(0.194512\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 24.2730 | 1.83487 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.82725 | 0.513168 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.69574 | −0.276233 | −0.138116 | − | 0.990416i | \(-0.544105\pi\) | ||||
−0.138116 | + | 0.990416i | \(0.544105\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.18186 | 0.533823 | 0.266912 | − | 0.963721i | \(-0.413997\pi\) | ||||
0.266912 | + | 0.963721i | \(0.413997\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.16392 | 0.677417 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −29.6063 | −2.17670 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 23.6829 | 1.73187 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −23.1469 | −1.68369 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.01302 | 0.579802 | 0.289901 | − | 0.957057i | \(-0.406378\pi\) | ||||
0.289901 | + | 0.957057i | \(0.406378\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.26269 | 0.522780 | 0.261390 | − | 0.965233i | \(-0.415819\pi\) | ||||
0.261390 | + | 0.965233i | \(0.415819\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.461233 | −0.0330296 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.29301 | 0.234617 | 0.117309 | − | 0.993095i | \(-0.462573\pi\) | ||||
0.117309 | + | 0.993095i | \(0.462573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.31505 | −0.376774 | −0.188387 | − | 0.982095i | \(-0.560326\pi\) | ||||
−0.188387 | + | 0.982095i | \(0.560326\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 20.0150 | 1.41175 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.02926 | −0.423171 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.8020 | −0.754442 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.1198 | −0.703378 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.1915 | −0.774135 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.7288 | 1.01397 | 0.506985 | − | 0.861955i | \(-0.330760\pi\) | ||||
0.506985 | + | 0.861955i | \(0.330760\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.746691 | 0.0511624 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 26.4826 | 1.80610 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.3147 | −0.835976 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 21.3322 | 1.44150 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.229527 | 0.0154397 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.17168 | 0.480251 | 0.240126 | − | 0.970742i | \(-0.422811\pi\) | ||||
0.240126 | + | 0.970742i | \(0.422811\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 40.3848 | 2.69232 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.3297 | −1.15021 | −0.575107 | − | 0.818079i | \(-0.695039\pi\) | ||||
−0.575107 | + | 0.818079i | \(0.695039\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.11565 | −0.0737241 | −0.0368621 | − | 0.999320i | \(-0.511736\pi\) | ||||
−0.0368621 | + | 0.999320i | \(0.511736\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 44.1257 | 2.90326 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.9785 | −0.719228 | −0.359614 | − | 0.933101i | \(-0.617092\pi\) | ||||
−0.359614 | + | 0.933101i | \(0.617092\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −29.3959 | −1.91758 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 23.3701 | 1.51805 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.70638 | −0.175061 | −0.0875307 | − | 0.996162i | \(-0.527898\pi\) | ||||
−0.0875307 | + | 0.996162i | \(0.527898\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.4495 | 1.25285 | 0.626427 | − | 0.779480i | \(-0.284517\pi\) | ||||
0.626427 | + | 0.779480i | \(0.284517\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.87779 | 0.569510 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.9824 | −0.829415 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.108465 | −0.00690145 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.0925 | −0.766330 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.1612 | 1.90376 | 0.951880 | − | 0.306472i | \(-0.0991486\pi\) | ||||
0.951880 | + | 0.306472i | \(0.0991486\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.64898 | 0.543757 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −52.1794 | −3.26760 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −27.6829 | −1.72681 | −0.863405 | − | 0.504511i | \(-0.831673\pi\) | ||||
−0.863405 | + | 0.504511i | \(0.831673\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 27.4507 | 1.70571 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.0313 | −0.620924 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.5189 | −0.833612 | −0.416806 | − | 0.908995i | \(-0.636851\pi\) | ||||
−0.416806 | + | 0.908995i | \(0.636851\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 36.3065 | 2.23029 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.9239 | 0.729734 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.19352 | 0.560539 | 0.280269 | − | 0.959921i | \(-0.409576\pi\) | ||||
0.280269 | + | 0.959921i | \(0.409576\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.8199 | 1.68994 | 0.844968 | − | 0.534817i | \(-0.179619\pi\) | ||||
0.844968 | + | 0.534817i | \(0.179619\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.427652 | 0.0258827 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −34.5151 | −2.08134 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.4555 | 1.58956 | 0.794778 | − | 0.606900i | \(-0.207587\pi\) | ||||
0.794778 | + | 0.606900i | \(0.207587\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −20.4889 | −1.22664 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.5284 | −1.10531 | −0.552657 | − | 0.833409i | \(-0.686386\pi\) | ||||
−0.552657 | + | 0.833409i | \(0.686386\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.5921 | 1.22407 | 0.612037 | − | 0.790829i | \(-0.290350\pi\) | ||||
0.612037 | + | 0.790829i | \(0.290350\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 24.6578 | 1.46060 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.0155 | 0.591196 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.96646 | 0.527439 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.1338 | 1.23888 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.1527 | 1.29417 | 0.647086 | − | 0.762417i | \(-0.275987\pi\) | ||||
0.647086 | + | 0.762417i | \(0.275987\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.28514 | 0.482379 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 32.9139 | 1.90986 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.0838231 | 0.00484762 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −24.5544 | −1.41529 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 44.1244 | 2.53488 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.1208 | 0.636774 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.00131 | 0.0571477 | 0.0285739 | − | 0.999592i | \(-0.490903\pi\) | ||||
0.0285739 | + | 0.999592i | \(0.490903\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.46354 | −0.197034 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.6042 | −0.771426 | −0.385713 | − | 0.922619i | \(-0.626044\pi\) | ||||
−0.385713 | + | 0.922619i | \(0.626044\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.02662 | −0.114551 | −0.0572757 | − | 0.998358i | \(-0.518241\pi\) | ||||
−0.0572757 | + | 0.998358i | \(0.518241\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −62.6548 | −3.53020 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.59531 | 0.0896018 | 0.0448009 | − | 0.998996i | \(-0.485735\pi\) | ||||
0.0448009 | + | 0.998996i | \(0.485735\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.57334 | 0.480015 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 38.8299 | 2.16727 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.2706 | −0.682757 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.334509 | −0.0185552 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 32.7820 | 1.81285 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 27.2556 | 1.50265 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.0047 | −0.769771 | −0.384885 | − | 0.922964i | \(-0.625759\pi\) | ||||
−0.384885 | + | 0.922964i | \(0.625759\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 45.6719 | 2.50280 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 24.2889 | 1.32705 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.50883 | 0.463505 | 0.231753 | − | 0.972775i | \(-0.425554\pi\) | ||||
0.231753 | + | 0.972775i | \(0.425554\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.6790 | 0.688629 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.5109 | 0.948271 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.8420 | −0.585415 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −19.0559 | −1.02593 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 36.0884 | 1.93733 | 0.968663 | − | 0.248380i | \(-0.0798982\pi\) | ||||
0.968663 | + | 0.248380i | \(0.0798982\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.88702 | −0.208067 | −0.104034 | − | 0.994574i | \(-0.533175\pi\) | ||||
−0.104034 | + | 0.994574i | \(0.533175\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.318991 | 0.0170265 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.59663 | 0.191429 | 0.0957147 | − | 0.995409i | \(-0.469486\pi\) | ||||
0.0957147 | + | 0.995409i | \(0.469486\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.906138 | 0.0480928 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 48.3803 | 2.56056 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.1587 | −1.59172 | −0.795859 | − | 0.605483i | \(-0.792980\pi\) | ||||
−0.795859 | + | 0.605483i | \(0.792980\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.2014 | −0.694811 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −30.7918 | −1.61615 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 25.8875 | 1.35501 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.1574 | 1.57421 | 0.787103 | − | 0.616822i | \(-0.211580\pi\) | ||||
0.787103 | + | 0.616822i | \(0.211580\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.6635 | 0.867470 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −33.6631 | −1.74770 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.3686 | 0.951090 | 0.475545 | − | 0.879691i | \(-0.342251\pi\) | ||||
0.475545 | + | 0.879691i | \(0.342251\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 24.8462 | 1.28305 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.0830900 | 0.00427935 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.0624 | −1.49283 | −0.746417 | − | 0.665478i | \(-0.768228\pi\) | ||||
−0.746417 | + | 0.665478i | \(0.768228\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.01853 | 0.205875 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.0563 | −0.667147 | −0.333574 | − | 0.942724i | \(-0.608255\pi\) | ||||
−0.333574 | + | 0.942724i | \(0.608255\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 53.5483 | 2.72907 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −40.8531 | −2.07668 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.3178 | −0.624539 | −0.312270 | − | 0.949993i | \(-0.601089\pi\) | ||||
−0.312270 | + | 0.949993i | \(0.601089\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.48292 | 0.479572 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −24.9090 | −1.25649 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 28.3605 | 1.42697 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.08564 | −0.405807 | −0.202903 | − | 0.979199i | \(-0.565038\pi\) | ||||
−0.202903 | + | 0.979199i | \(0.565038\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −22.8625 | −1.14456 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.80321 | 0.0900482 | 0.0450241 | − | 0.998986i | \(-0.485664\pi\) | ||||
0.0450241 | + | 0.998986i | \(0.485664\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.169710 | 0.00845388 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −15.0090 | −0.745803 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −39.0337 | −1.93483 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −36.4847 | −1.80405 | −0.902025 | − | 0.431683i | \(-0.857920\pi\) | ||||
−0.902025 | + | 0.431683i | \(0.857920\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.3572 | 1.05347 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.68192 | −0.378002 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.6747 | −0.720353 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −27.5036 | −1.34686 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −35.4041 | −1.72960 | −0.864801 | − | 0.502115i | \(-0.832555\pi\) | ||||
−0.864801 | + | 0.502115i | \(0.832555\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.3305 | −0.649689 | −0.324844 | − | 0.945767i | \(-0.605312\pi\) | ||||
−0.324844 | + | 0.945767i | \(0.605312\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 45.3473 | 2.20486 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −37.8431 | −1.83566 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.3111 | −0.498989 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.608102 | −0.0293595 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.2799 | 1.60304 | 0.801519 | − | 0.597969i | \(-0.204025\pi\) | ||||
0.801519 | + | 0.597969i | \(0.204025\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.0058 | 0.576962 | 0.288481 | − | 0.957486i | \(-0.406850\pi\) | ||||
0.288481 | + | 0.957486i | \(0.406850\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −18.8892 | −0.905667 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.48122 | −0.214366 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.6186 | 1.22271 | 0.611355 | − | 0.791357i | \(-0.290625\pi\) | ||||
0.611355 | + | 0.791357i | \(0.290625\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.0272 | 0.953675 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.67532 | −0.0795968 | −0.0397984 | − | 0.999208i | \(-0.512672\pi\) | ||||
−0.0397984 | + | 0.999208i | \(0.512672\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.4702 | 0.685952 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 35.4441 | 1.67645 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.7593 | 0.602148 | 0.301074 | − | 0.953601i | \(-0.402655\pi\) | ||||
0.301074 | + | 0.953601i | \(0.402655\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.2416 | −0.670610 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −57.5429 | −2.70360 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.518973 | 0.0243298 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.2083 | 1.27275 | 0.636376 | − | 0.771379i | \(-0.280433\pi\) | ||||
0.636376 | + | 0.771379i | \(0.280433\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 36.0875 | 1.68442 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.7155 | 1.33741 | 0.668706 | − | 0.743527i | \(-0.266848\pi\) | ||||
0.668706 | + | 0.743527i | \(0.266848\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.6857 | 1.14724 | 0.573621 | − | 0.819121i | \(-0.305538\pi\) | ||||
0.573621 | + | 0.819121i | \(0.305538\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −38.5810 | −1.78915 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.8583 | 1.42795 | 0.713975 | − | 0.700171i | \(-0.246893\pi\) | ||||
0.713975 | + | 0.700171i | \(0.246893\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.5205 | −1.03990 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 60.4273 | 2.78434 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 34.9153 | 1.60541 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17.8830 | 0.820530 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −56.0079 | −2.56443 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 33.3513 | 1.52386 | 0.761929 | − | 0.647660i | \(-0.224252\pi\) | ||||
0.761929 | + | 0.647660i | \(0.224252\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.378302 | −0.0172491 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 17.6684 | 0.803942 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 25.6467 | 1.16455 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.4361 | −1.24325 | −0.621624 | − | 0.783316i | \(-0.713527\pi\) | ||||
−0.621624 | + | 0.783316i | \(0.713527\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.90515 | 0.357483 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.6578 | 1.60921 | 0.804607 | − | 0.593807i | \(-0.202376\pi\) | ||||
0.804607 | + | 0.593807i | \(0.202376\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.39998 | 0.423354 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 89.0923 | 4.00440 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.840165 | −0.0376865 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.08748 | 0.317279 | 0.158640 | − | 0.987337i | \(-0.449289\pi\) | ||||
0.158640 | + | 0.987337i | \(0.449289\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −58.5621 | −2.61636 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 28.9768 | 1.29201 | 0.646006 | − | 0.763332i | \(-0.276438\pi\) | ||||
0.646006 | + | 0.763332i | \(0.276438\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 53.5467 | 2.38280 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 37.7568 | 1.67684 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.75520 | −0.0777978 | −0.0388989 | − | 0.999243i | \(-0.512385\pi\) | ||||
−0.0388989 | + | 0.999243i | \(0.512385\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.0027 | −1.06182 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −17.0534 | −0.752927 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.20314 | −0.185212 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −38.7563 | −1.70450 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −62.5852 | −2.74719 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.6076 | 1.34094 | 0.670472 | − | 0.741935i | \(-0.266092\pi\) | ||||
0.670472 | + | 0.741935i | \(0.266092\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.6993 | 1.25493 | 0.627465 | − | 0.778644i | \(-0.284092\pi\) | ||||
0.627465 | + | 0.778644i | \(0.284092\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −70.5087 | −3.07725 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.1994 | 0.836337 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.5368 | −0.849428 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.7810 | −0.554648 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.138025 | −0.00597852 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 47.1216 | 2.03724 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.7355 | 0.463270 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17.1163 | −0.737253 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.12633 | 0.306385 | 0.153192 | − | 0.988196i | \(-0.451045\pi\) | ||||
0.153192 | + | 0.988196i | \(0.451045\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −20.8620 | −0.895275 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 39.7823 | 1.70409 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.08335 | −0.302862 | −0.151431 | − | 0.988468i | \(-0.548388\pi\) | ||||
−0.151431 | + | 0.988468i | \(0.548388\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −17.1554 | −0.732173 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.44203 | −0.189237 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −26.2957 | −1.11821 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 86.0010 | 3.65054 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.5666 | −0.701951 | −0.350976 | − | 0.936385i | \(-0.614150\pi\) | ||||
−0.350976 | + | 0.936385i | \(0.614150\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.338388 | 0.0143123 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −68.7947 | −2.90451 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.909317 | 0.0383231 | 0.0191616 | − | 0.999816i | \(-0.493900\pi\) | ||||
0.0191616 | + | 0.999816i | \(0.493900\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.3865 | 0.647314 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 13.9162 | 0.584427 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.63794 | −0.278277 | −0.139138 | − | 0.990273i | \(-0.544433\pi\) | ||||
−0.139138 | + | 0.990273i | \(0.544433\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.2806 | 0.974263 | 0.487131 | − | 0.873329i | \(-0.338043\pi\) | ||||
0.487131 | + | 0.873329i | \(0.338043\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −23.2764 | −0.972385 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.8202 | −0.576344 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.44482 | 0.0601485 | 0.0300742 | − | 0.999548i | \(-0.490426\pi\) | ||||
0.0300742 | + | 0.999548i | \(0.490426\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −21.0968 | −0.876754 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.6063 | 0.564484 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 47.8675 | 1.98247 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.863454 | 0.0356994 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.2366 | −0.546334 | −0.273167 | − | 0.961967i | \(-0.588071\pi\) | ||||
−0.273167 | + | 0.961967i | \(0.588071\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.07280 | −0.373838 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.56561 | −0.393477 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −40.3145 | −1.65552 | −0.827758 | − | 0.561085i | \(-0.810384\pi\) | ||||
−0.827758 | + | 0.561085i | \(0.810384\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 58.7114 | 2.40693 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.4393 | 0.631887 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −34.6587 | −1.41612 | −0.708058 | − | 0.706155i | \(-0.750428\pi\) | ||||
−0.708058 | + | 0.706155i | \(0.750428\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.9913 | 1.46812 | 0.734059 | − | 0.679086i | \(-0.237624\pi\) | ||||
0.734059 | + | 0.679086i | \(0.237624\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −37.4691 | −1.52586 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −37.3670 | −1.51918 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.3487 | −1.27241 | −0.636203 | − | 0.771522i | \(-0.719496\pi\) | ||||
−0.636203 | + | 0.771522i | \(0.719496\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17.5139 | 0.709700 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.375613 | −0.0151957 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.1047 | 1.17553 | 0.587764 | − | 0.809033i | \(-0.300009\pi\) | ||||
0.587764 | + | 0.809033i | \(0.300009\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 31.3778 | 1.26527 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.1416 | 0.851129 | 0.425565 | − | 0.904928i | \(-0.360076\pi\) | ||||
0.425565 | + | 0.904928i | \(0.360076\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.7431 | −0.833737 | −0.416868 | − | 0.908967i | \(-0.636872\pi\) | ||||
−0.416868 | + | 0.908967i | \(0.636872\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.1791 | 0.528860 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.4166 | −0.537526 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.98029 | −0.279212 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 32.5094 | 1.29830 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −42.7974 | −1.70644 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.6048 | −0.740645 | −0.370323 | − | 0.928903i | \(-0.620753\pi\) | ||||
−0.370323 | + | 0.928903i | \(0.620753\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −42.7845 | −1.70053 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.87664 | 0.193524 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.165886 | −0.00657264 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.39785 | −0.0552979 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.403031 | −0.0159188 | −0.00795938 | − | 0.999968i | \(-0.502534\pi\) | ||||
−0.00795938 | + | 0.999968i | \(0.502534\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.77077 | −0.148705 | −0.0743523 | − | 0.997232i | \(-0.523689\pi\) | ||||
−0.0743523 | + | 0.997232i | \(0.523689\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −76.9271 | −3.02900 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.56734 | −0.336817 | −0.168408 | − | 0.985717i | \(-0.553863\pi\) | ||||
−0.168408 | + | 0.985717i | \(0.553863\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.9233 | 0.428779 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 35.7720 | 1.40201 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.9154 | 0.740215 | 0.370108 | − | 0.928989i | \(-0.379321\pi\) | ||||
0.370108 | + | 0.928989i | \(0.379321\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −30.2281 | −1.18111 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −39.9351 | −1.55802 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.31655 | −0.0512856 | −0.0256428 | − | 0.999671i | \(-0.508163\pi\) | ||||
−0.0256428 | + | 0.999671i | \(0.508163\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.986571 | −0.0383732 | −0.0191866 | − | 0.999816i | \(-0.506108\pi\) | ||||
−0.0191866 | + | 0.999816i | \(0.506108\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.666736 | −0.0258939 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −27.7445 | −1.07589 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.43286 | 0.132921 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.8324 | −0.805429 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.6619 | 0.566018 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.2168 | 1.31896 | 0.659480 | − | 0.751722i | \(-0.270777\pi\) | ||||
0.659480 | + | 0.751722i | \(0.270777\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −52.5933 | −2.02432 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.9512 | −0.689922 | −0.344961 | − | 0.938617i | \(-0.612108\pi\) | ||||
−0.344961 | + | 0.938617i | \(0.612108\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −23.7794 | −0.912569 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 50.3397 | 1.92902 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.19391 | −0.160476 | −0.0802378 | − | 0.996776i | \(-0.525568\pi\) | ||||
−0.0802378 | + | 0.996776i | \(0.525568\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25.9178 | 0.990267 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.24076 | 0.123643 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.463916 | 0.0176738 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.1107 | 1.33567 | 0.667837 | − | 0.744307i | \(-0.267220\pi\) | ||||
0.667837 | + | 0.744307i | \(0.267220\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −82.6058 | −3.13793 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −33.3767 | −1.26605 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.6148 | −0.591452 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 31.8907 | 1.20622 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.1149 | −0.835269 | −0.417634 | − | 0.908615i | \(-0.637141\pi\) | ||||
−0.417634 | + | 0.908615i | \(0.637141\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.2242 | 0.762771 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 85.3897 | 3.21596 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −49.6481 | −1.86721 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.6284 | −0.399157 | −0.199579 | − | 0.979882i | \(-0.563957\pi\) | ||||
−0.199579 | + | 0.979882i | \(0.563957\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −43.7501 | −1.64076 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.01159 | 0.262586 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.737956 | −0.0275980 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.86156 | 0.293595 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.9050 | 0.928798 | 0.464399 | − | 0.885626i | \(-0.346270\pi\) | ||||
0.464399 | + | 0.885626i | \(0.346270\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.89712 | 0.145136 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −56.4974 | −2.10116 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.6994 | −0.508782 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.2334 | −1.04712 | −0.523560 | − | 0.851989i | \(-0.675396\pi\) | ||||
−0.523560 | + | 0.851989i | \(0.675396\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −38.5616 | −1.42821 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 38.2819 | 1.41591 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.8385 | 0.880494 | 0.440247 | − | 0.897877i | \(-0.354891\pi\) | ||||
0.440247 | + | 0.897877i | \(0.354891\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 37.7115 | 1.39101 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 32.0232 | 1.17959 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −45.0849 | −1.65847 | −0.829237 | − | 0.558897i | \(-0.811225\pi\) | ||||
−0.829237 | + | 0.558897i | \(0.811225\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.315071 | 0.0115744 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.9612 | 1.42935 | 0.714673 | − | 0.699458i | \(-0.246575\pi\) | ||||
0.714673 | + | 0.699458i | \(0.246575\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 43.0128 | 1.57587 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 22.6378 | 0.828274 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −43.6908 | −1.59643 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.00000 | 0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −87.6129 | −3.19279 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −69.8306 | −2.54140 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −51.1309 | −1.85839 | −0.929193 | − | 0.369596i | \(-0.879496\pi\) | ||||
−0.929193 | + | 0.369596i | \(0.879496\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −25.1237 | −0.911934 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −42.8507 | −1.55334 | −0.776669 | − | 0.629909i | \(-0.783092\pi\) | ||||
−0.776669 | + | 0.629909i | \(0.783092\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −36.8859 | −1.33536 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 97.6827 | 3.53172 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.105865 | 0.00382258 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.1534 | 0.510383 | 0.255192 | − | 0.966891i | \(-0.417861\pi\) | ||||
0.255192 | + | 0.966891i | \(0.417861\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 80.4138 | 2.89603 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.5119 | −1.09744 | −0.548719 | − | 0.836007i | \(-0.684884\pi\) | ||||
−0.548719 | + | 0.836007i | \(0.684884\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27.9808 | −1.00510 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −79.7395 | −2.86064 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.37888 | 0.264376 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.19468 | 0.0427489 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 13.0639 | 0.466864 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 73.3309 | 2.61729 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.6189 | −1.09145 | −0.545724 | − | 0.837965i | \(-0.683745\pi\) | ||||
−0.545724 | + | 0.837965i | \(0.683745\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 39.2701 | 1.39805 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.2662 | −0.507249 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.142099 | 0.00504607 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −105.464 | −3.74042 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.7125 | −0.946205 | −0.473102 | − | 0.881007i | \(-0.656866\pi\) | ||||
−0.473102 | + | 0.881007i | \(0.656866\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −42.4932 | −1.50330 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.3223 | −0.788719 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 34.1308 | 1.20445 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.4413 | 0.755708 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.7055 | −0.940079 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 42.2289 | 1.48469 | 0.742344 | − | 0.670019i | \(-0.233714\pi\) | ||||
0.742344 | + | 0.670019i | \(0.233714\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.145146 | 0.00509676 | 0.00254838 | − | 0.999997i | \(-0.499189\pi\) | ||||
0.00254838 | + | 0.999997i | \(0.499189\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −80.8117 | −2.83419 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.59321 | 0.336035 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.0904 | −0.632903 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.800588 | −0.0279748 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.8853 | 0.449699 | 0.224849 | − | 0.974394i | \(-0.427811\pi\) | ||||
0.224849 | + | 0.974394i | \(0.427811\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.4979 | 1.27224 | 0.636119 | − | 0.771591i | \(-0.280539\pi\) | ||||
0.636119 | + | 0.771591i | \(0.280539\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 100.260 | 3.49061 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42.0933 | 1.46373 | 0.731865 | − | 0.681450i | \(-0.238650\pi\) | ||||
0.731865 | + | 0.681450i | \(0.238650\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.364644 | 0.0126646 | 0.00633231 | − | 0.999980i | \(-0.497984\pi\) | ||||
0.00633231 | + | 0.999980i | \(0.497984\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −76.8485 | −2.66584 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.7667 | −0.650228 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −71.0674 | −2.45939 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 26.6828 | 0.922292 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −44.1110 | −1.52288 | −0.761441 | − | 0.648235i | \(-0.775508\pi\) | ||||
−0.761441 | + | 0.648235i | \(0.775508\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.5972 | −0.882661 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 53.8218 | 1.85372 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 45.8193 | 1.57623 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 34.6464 | 1.19046 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −59.8164 | −2.05289 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.6296 | −0.535774 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36.0779 | −1.23528 | −0.617642 | − | 0.786459i | \(-0.711912\pi\) | ||||
−0.617642 | + | 0.786459i | \(0.711912\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −46.1607 | −1.57866 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −35.9596 | −1.22836 | −0.614178 | − | 0.789167i | \(-0.710512\pi\) | ||||
−0.614178 | + | 0.789167i | \(0.710512\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.2381 | 0.349320 | 0.174660 | − | 0.984629i | \(-0.444117\pi\) | ||||
0.174660 | + | 0.984629i | \(0.444117\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −29.0932 | −0.991495 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.23190 | 0.246177 | 0.123088 | − | 0.992396i | \(-0.460720\pi\) | ||||
0.123088 | + | 0.992396i | \(0.460720\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −75.9496 | −2.58237 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −26.0460 | −0.884567 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37.3913 | 1.26841 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.310358 | 0.0105161 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −39.5636 | −1.33902 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −27.9566 | −0.945105 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.7751 | 0.431384 | 0.215692 | − | 0.976461i | \(-0.430799\pi\) | ||||
0.215692 | + | 0.976461i | \(0.430799\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −64.3495 | −2.17046 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.3509 | −0.550877 | −0.275438 | − | 0.961319i | \(-0.588823\pi\) | ||||
−0.275438 | + | 0.961319i | \(0.588823\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.72647 | −0.0581004 | −0.0290502 | − | 0.999578i | \(-0.509248\pi\) | ||||
−0.0290502 | + | 0.999578i | \(0.509248\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −24.0668 | −0.808998 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.878493 | 0.0294969 | 0.0147485 | − | 0.999891i | \(-0.495305\pi\) | ||||
0.0147485 | + | 0.999891i | \(0.495305\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.52159 | −0.151649 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −19.7883 | −0.662931 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 20.0805 | 0.671968 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.0279 | 0.435475 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.243491 | −0.00812993 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.95026 | 0.231804 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 52.4829 | 1.74846 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 71.3263 | 2.37359 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −25.3169 | −0.841561 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.1660 | 1.03485 | 0.517426 | − | 0.855728i | \(-0.326890\pi\) | ||||
0.517426 | + | 0.855728i | \(0.326890\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −82.6033 | −2.73978 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.5934 | −1.34492 | −0.672459 | − | 0.740134i | \(-0.734762\pi\) | ||||
−0.672459 | + | 0.740134i | \(0.734762\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.3475 | −0.640310 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −32.3039 | −1.06793 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 28.0273 | 0.925541 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53.3539 | 1.75998 | 0.879992 | − | 0.474989i | \(-0.157548\pi\) | ||||
0.879992 | + | 0.474989i | \(0.157548\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.90862 | −0.0958424 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.0115784 | 0.000381108 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 62.3722 | 2.05079 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.48393 | 0.212960 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32.1988 | 1.05641 | 0.528205 | − | 0.849117i | \(-0.322865\pi\) | ||||
0.528205 | + | 0.849117i | \(0.322865\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.86834 | 0.290648 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 39.5179 | 1.29376 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −83.4850 | −2.73025 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.7175 | 1.68954 | 0.844768 | − | 0.535133i | \(-0.179739\pi\) | ||||
0.844768 | + | 0.535133i | \(0.179739\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.88697 | 0.192114 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.72993 | −0.154191 | −0.0770956 | − | 0.997024i | \(-0.524565\pi\) | ||||
−0.0770956 | + | 0.997024i | \(0.524565\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.70250 | −0.185699 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 81.5956 | 2.65431 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.94001 | 0.193024 | 0.0965122 | − | 0.995332i | \(-0.469231\pi\) | ||||
0.0965122 | + | 0.995332i | \(0.469231\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.330784 | 0.0107377 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.63410 | −0.150271 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.894420 | −0.0289731 | −0.0144865 | − | 0.999895i | \(-0.504611\pi\) | ||||
−0.0144865 | + | 0.999895i | \(0.504611\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −28.2468 | −0.914045 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −24.9040 | −0.805032 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24.0308 | −0.775994 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.8042 | −0.542070 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −72.6916 | −2.34246 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −25.6018 | −0.824152 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.6760 | 0.922157 | 0.461078 | − | 0.887359i | \(-0.347463\pi\) | ||||
0.461078 | + | 0.887359i | \(0.347463\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 35.6440 | 1.14505 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.8305 | 0.411751 | 0.205875 | − | 0.978578i | \(-0.433996\pi\) | ||||
0.205875 | + | 0.978578i | \(0.433996\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.9466 | 0.992104 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.971689 | 0.0311190 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 53.2446 | 1.70344 | 0.851722 | − | 0.523994i | \(-0.175559\pi\) | ||||
0.851722 | + | 0.523994i | \(0.175559\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.0779 | 0.609731 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −61.3698 | −1.95939 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.3312 | 0.393306 | 0.196653 | − | 0.980473i | \(-0.436993\pi\) | ||||
0.196653 | + | 0.980473i | \(0.436993\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.6082 | −0.369869 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −79.1727 | −2.52010 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.9805 | 0.444554 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −53.4595 | −1.69820 | −0.849099 | − | 0.528233i | \(-0.822855\pi\) | ||||
−0.849099 | + | 0.528233i | \(0.822855\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 40.6813 | 1.29098 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.7362 | 0.593976 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45.7533 | 1.44902 | 0.724511 | − | 0.689264i | \(-0.242066\pi\) | ||||
0.724511 | + | 0.689264i | \(0.242066\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −59.4787 | −1.88182 |
(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 | 6008.2.a.d.1.3 | ✓ | 49 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.d.1.3 | ✓ | 49 | 1.1 | even | 1 | trivial |