Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8019,2,Mod(1,8019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8019, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8019 = 3^{6} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8019.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0320373809\) |
Analytic rank: | \(0\) |
Dimension: | \(51\) |
Twist minimal: | no (minimal twist has level 297) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.98291 | −1.40213 | −0.701065 | − | 0.713097i | \(-0.747292\pi\) | ||||
−0.701065 | + | 0.713097i | \(0.747292\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.93194 | 0.965970 | ||||||||
\(5\) | 0.594867 | 0.266033 | 0.133016 | − | 0.991114i | \(-0.457534\pi\) | ||||
0.133016 | + | 0.991114i | \(0.457534\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.24839 | −0.471849 | −0.235924 | − | 0.971771i | \(-0.575812\pi\) | ||||
−0.235924 | + | 0.971771i | \(0.575812\pi\) | |||||||
\(8\) | 0.134957 | 0.0477144 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.17957 | −0.373013 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.57436 | 1.54605 | 0.773024 | − | 0.634377i | \(-0.218743\pi\) | ||||
0.773024 | + | 0.634377i | \(0.218743\pi\) | |||||||
\(14\) | 2.47546 | 0.661594 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.13149 | −1.03287 | ||||||||
\(17\) | 6.43369 | 1.56040 | 0.780199 | − | 0.625531i | \(-0.215118\pi\) | ||||
0.780199 | + | 0.625531i | \(0.215118\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.69526 | 1.30658 | 0.653291 | − | 0.757107i | \(-0.273388\pi\) | ||||
0.653291 | + | 0.757107i | \(0.273388\pi\) | |||||||
\(20\) | 1.14925 | 0.256980 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.98291 | −0.422758 | ||||||||
\(23\) | −9.13802 | −1.90541 | −0.952704 | − | 0.303899i | \(-0.901711\pi\) | ||||
−0.952704 | + | 0.303899i | \(0.901711\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.64613 | −0.929227 | ||||||||
\(26\) | −11.0535 | −2.16776 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.41182 | −0.455792 | ||||||||
\(29\) | 2.60888 | 0.484457 | 0.242229 | − | 0.970219i | \(-0.422122\pi\) | ||||
0.242229 | + | 0.970219i | \(0.422122\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.60529 | −0.647529 | −0.323765 | − | 0.946138i | \(-0.604949\pi\) | ||||
−0.323765 | + | 0.946138i | \(0.604949\pi\) | |||||||
\(32\) | 7.92246 | 1.40051 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −12.7574 | −2.18788 | ||||||||
\(35\) | −0.742629 | −0.125527 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.88375 | 1.29608 | 0.648040 | − | 0.761606i | \(-0.275589\pi\) | ||||
0.648040 | + | 0.761606i | \(0.275589\pi\) | |||||||
\(38\) | −11.2932 | −1.83200 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.0802814 | 0.0126936 | ||||||||
\(41\) | −2.17028 | −0.338942 | −0.169471 | − | 0.985535i | \(-0.554206\pi\) | ||||
−0.169471 | + | 0.985535i | \(0.554206\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.71494 | 0.871521 | 0.435760 | − | 0.900063i | \(-0.356479\pi\) | ||||
0.435760 | + | 0.900063i | \(0.356479\pi\) | |||||||
\(44\) | 1.93194 | 0.291251 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 18.1199 | 2.67163 | ||||||||
\(47\) | −0.711651 | −0.103805 | −0.0519024 | − | 0.998652i | \(-0.516528\pi\) | ||||
−0.0519024 | + | 0.998652i | \(0.516528\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.44151 | −0.777359 | ||||||||
\(50\) | 9.21287 | 1.30290 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10.7693 | 1.49344 | ||||||||
\(53\) | 7.07446 | 0.971751 | 0.485876 | − | 0.874028i | \(-0.338501\pi\) | ||||
0.485876 | + | 0.874028i | \(0.338501\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.594867 | 0.0802119 | ||||||||
\(56\) | −0.168479 | −0.0225140 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.17319 | −0.679273 | ||||||||
\(59\) | −2.32477 | −0.302660 | −0.151330 | − | 0.988483i | \(-0.548356\pi\) | ||||
−0.151330 | + | 0.988483i | \(0.548356\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.0099 | 1.79379 | 0.896894 | − | 0.442246i | \(-0.145818\pi\) | ||||
0.896894 | + | 0.442246i | \(0.145818\pi\) | |||||||
\(62\) | 7.14897 | 0.907920 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.44657 | −0.930821 | ||||||||
\(65\) | 3.31600 | 0.411299 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.9152 | 1.45567 | 0.727835 | − | 0.685752i | \(-0.240527\pi\) | ||||
0.727835 | + | 0.685752i | \(0.240527\pi\) | |||||||
\(68\) | 12.4295 | 1.50730 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.47257 | 0.176006 | ||||||||
\(71\) | 1.19258 | 0.141534 | 0.0707669 | − | 0.997493i | \(-0.477455\pi\) | ||||
0.0707669 | + | 0.997493i | \(0.477455\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.74213 | 1.02319 | 0.511594 | − | 0.859227i | \(-0.329055\pi\) | ||||
0.511594 | + | 0.859227i | \(0.329055\pi\) | |||||||
\(74\) | −15.6328 | −1.81727 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.0029 | 1.26212 | ||||||||
\(77\) | −1.24839 | −0.142268 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.98017 | 0.447804 | 0.223902 | − | 0.974612i | \(-0.428120\pi\) | ||||
0.223902 | + | 0.974612i | \(0.428120\pi\) | |||||||
\(80\) | −2.45769 | −0.274778 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.30348 | 0.475240 | ||||||||
\(83\) | −1.78700 | −0.196149 | −0.0980744 | − | 0.995179i | \(-0.531268\pi\) | ||||
−0.0980744 | + | 0.995179i | \(0.531268\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.82719 | 0.415117 | ||||||||
\(86\) | −11.3322 | −1.22199 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.134957 | 0.0143864 | ||||||||
\(89\) | 6.84126 | 0.725172 | 0.362586 | − | 0.931950i | \(-0.381894\pi\) | ||||
0.362586 | + | 0.931950i | \(0.381894\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.95900 | −0.729501 | ||||||||
\(92\) | −17.6541 | −1.84057 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.41114 | 0.145548 | ||||||||
\(95\) | 3.38792 | 0.347594 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.93852 | 0.501431 | 0.250716 | − | 0.968061i | \(-0.419334\pi\) | ||||
0.250716 | + | 0.968061i | \(0.419334\pi\) | |||||||
\(98\) | 10.7900 | 1.08996 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.97605 | −0.897605 | ||||||||
\(101\) | −2.44844 | −0.243629 | −0.121814 | − | 0.992553i | \(-0.538871\pi\) | ||||
−0.121814 | + | 0.992553i | \(0.538871\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.42683 | 0.830320 | 0.415160 | − | 0.909748i | \(-0.363726\pi\) | ||||
0.415160 | + | 0.909748i | \(0.363726\pi\) | |||||||
\(104\) | 0.752297 | 0.0737688 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.0280 | −1.36252 | ||||||||
\(107\) | −11.4829 | −1.11009 | −0.555046 | − | 0.831820i | \(-0.687299\pi\) | ||||
−0.555046 | + | 0.831820i | \(0.687299\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.0761 | −1.34825 | −0.674123 | − | 0.738619i | \(-0.735478\pi\) | ||||
−0.674123 | + | 0.738619i | \(0.735478\pi\) | |||||||
\(110\) | −1.17957 | −0.112468 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.15773 | 0.487359 | ||||||||
\(113\) | −14.0724 | −1.32382 | −0.661909 | − | 0.749585i | \(-0.730253\pi\) | ||||
−0.661909 | + | 0.749585i | \(0.730253\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.43591 | −0.506901 | ||||||||
\(116\) | 5.04021 | 0.467971 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.60982 | 0.424368 | ||||||||
\(119\) | −8.03178 | −0.736272 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −27.7805 | −2.51512 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.96520 | −0.625494 | ||||||||
\(125\) | −5.73817 | −0.513237 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.69300 | 0.593907 | 0.296954 | − | 0.954892i | \(-0.404029\pi\) | ||||
0.296954 | + | 0.954892i | \(0.404029\pi\) | |||||||
\(128\) | −1.07903 | −0.0953736 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.57534 | −0.576695 | ||||||||
\(131\) | 16.4880 | 1.44057 | 0.720283 | − | 0.693681i | \(-0.244012\pi\) | ||||
0.720283 | + | 0.693681i | \(0.244012\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.10993 | −0.616509 | ||||||||
\(134\) | −23.6268 | −2.04104 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.868270 | 0.0744535 | ||||||||
\(137\) | −16.4149 | −1.40242 | −0.701210 | − | 0.712955i | \(-0.747357\pi\) | ||||
−0.701210 | + | 0.712955i | \(0.747357\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.0455 | −0.936871 | −0.468436 | − | 0.883498i | \(-0.655182\pi\) | ||||
−0.468436 | + | 0.883498i | \(0.655182\pi\) | |||||||
\(140\) | −1.43471 | −0.121256 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.36479 | −0.198449 | ||||||||
\(143\) | 5.57436 | 0.466151 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.55194 | 0.128882 | ||||||||
\(146\) | −17.3349 | −1.43464 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 15.2309 | 1.25198 | ||||||||
\(149\) | 1.23552 | 0.101217 | 0.0506087 | − | 0.998719i | \(-0.483884\pi\) | ||||
0.0506087 | + | 0.998719i | \(0.483884\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.75905 | −0.305907 | −0.152954 | − | 0.988233i | \(-0.548879\pi\) | ||||
−0.152954 | + | 0.988233i | \(0.548879\pi\) | |||||||
\(152\) | 0.768614 | 0.0623429 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.47546 | 0.199478 | ||||||||
\(155\) | −2.14467 | −0.172264 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.6451 | 1.72746 | 0.863732 | − | 0.503951i | \(-0.168121\pi\) | ||||
0.863732 | + | 0.503951i | \(0.168121\pi\) | |||||||
\(158\) | −7.89232 | −0.627879 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.71281 | 0.372581 | ||||||||
\(161\) | 11.4079 | 0.899065 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.99715 | −0.156429 | −0.0782143 | − | 0.996937i | \(-0.524922\pi\) | ||||
−0.0782143 | + | 0.996937i | \(0.524922\pi\) | |||||||
\(164\) | −4.19286 | −0.327407 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.54346 | 0.275026 | ||||||||
\(167\) | −11.7227 | −0.907131 | −0.453565 | − | 0.891223i | \(-0.649848\pi\) | ||||
−0.453565 | + | 0.891223i | \(0.649848\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.0734 | 1.39026 | ||||||||
\(170\) | −7.58898 | −0.582048 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.0409 | 0.841863 | ||||||||
\(173\) | 0.690170 | 0.0524727 | 0.0262363 | − | 0.999656i | \(-0.491648\pi\) | ||||
0.0262363 | + | 0.999656i | \(0.491648\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.80021 | 0.438454 | ||||||||
\(176\) | −4.13149 | −0.311423 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.5656 | −1.01679 | ||||||||
\(179\) | −2.20803 | −0.165036 | −0.0825180 | − | 0.996590i | \(-0.526296\pi\) | ||||
−0.0825180 | + | 0.996590i | \(0.526296\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.13288 | −0.381524 | −0.190762 | − | 0.981636i | \(-0.561096\pi\) | ||||
−0.190762 | + | 0.981636i | \(0.561096\pi\) | |||||||
\(182\) | 13.7991 | 1.02286 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.23324 | −0.0909155 | ||||||||
\(185\) | 4.68978 | 0.344800 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.43369 | 0.470478 | ||||||||
\(188\) | −1.37487 | −0.100272 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.71796 | −0.487372 | ||||||||
\(191\) | −16.2003 | −1.17222 | −0.586108 | − | 0.810233i | \(-0.699341\pi\) | ||||
−0.586108 | + | 0.810233i | \(0.699341\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.18408 | −0.301177 | −0.150588 | − | 0.988597i | \(-0.548117\pi\) | ||||
−0.150588 | + | 0.988597i | \(0.548117\pi\) | |||||||
\(194\) | −9.79266 | −0.703072 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −10.5127 | −0.750905 | ||||||||
\(197\) | −8.93397 | −0.636519 | −0.318259 | − | 0.948004i | \(-0.603098\pi\) | ||||
−0.318259 | + | 0.948004i | \(0.603098\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.3429 | −1.15852 | −0.579260 | − | 0.815143i | \(-0.696659\pi\) | ||||
−0.579260 | + | 0.815143i | \(0.696659\pi\) | |||||||
\(200\) | −0.627027 | −0.0443375 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.85504 | 0.341599 | ||||||||
\(203\) | −3.25692 | −0.228591 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.29103 | −0.0901695 | ||||||||
\(206\) | −16.7097 | −1.16422 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −23.0304 | −1.59687 | ||||||||
\(209\) | 5.69526 | 0.393949 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.4820 | 0.721614 | 0.360807 | − | 0.932641i | \(-0.382501\pi\) | ||||
0.360807 | + | 0.932641i | \(0.382501\pi\) | |||||||
\(212\) | 13.6674 | 0.938683 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 22.7695 | 1.55649 | ||||||||
\(215\) | 3.39963 | 0.231853 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.50082 | 0.305536 | ||||||||
\(218\) | 27.9117 | 1.89042 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.14925 | 0.0774823 | ||||||||
\(221\) | 35.8637 | 2.41245 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.78584 | 0.588343 | 0.294172 | − | 0.955753i | \(-0.404956\pi\) | ||||
0.294172 | + | 0.955753i | \(0.404956\pi\) | |||||||
\(224\) | −9.89036 | −0.660828 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 27.9043 | 1.85616 | ||||||||
\(227\) | −24.7854 | −1.64507 | −0.822534 | − | 0.568716i | \(-0.807440\pi\) | ||||
−0.822534 | + | 0.568716i | \(0.807440\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.96533 | −0.262037 | −0.131018 | − | 0.991380i | \(-0.541825\pi\) | ||||
−0.131018 | + | 0.991380i | \(0.541825\pi\) | |||||||
\(230\) | 10.7789 | 0.710741 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.352087 | 0.0231156 | ||||||||
\(233\) | 14.0587 | 0.921014 | 0.460507 | − | 0.887656i | \(-0.347668\pi\) | ||||
0.460507 | + | 0.887656i | \(0.347668\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.423338 | −0.0276155 | ||||||||
\(236\) | −4.49132 | −0.292360 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 15.9263 | 1.03235 | ||||||||
\(239\) | 10.5509 | 0.682482 | 0.341241 | − | 0.939976i | \(-0.389153\pi\) | ||||
0.341241 | + | 0.939976i | \(0.389153\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.8998 | 0.702115 | 0.351058 | − | 0.936354i | \(-0.385822\pi\) | ||||
0.351058 | + | 0.936354i | \(0.385822\pi\) | |||||||
\(242\) | −1.98291 | −0.127466 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 27.0663 | 1.73275 | ||||||||
\(245\) | −3.23698 | −0.206803 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 31.7474 | 2.02004 | ||||||||
\(248\) | −0.486558 | −0.0308965 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.3783 | 0.719626 | ||||||||
\(251\) | −27.9276 | −1.76277 | −0.881386 | − | 0.472396i | \(-0.843389\pi\) | ||||
−0.881386 | + | 0.472396i | \(0.843389\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.13802 | −0.574502 | ||||||||
\(254\) | −13.2716 | −0.832736 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 17.0328 | 1.06455 | ||||||||
\(257\) | 9.73742 | 0.607404 | 0.303702 | − | 0.952767i | \(-0.401777\pi\) | ||||
0.303702 | + | 0.952767i | \(0.401777\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.84203 | −0.611554 | ||||||||
\(260\) | 6.40632 | 0.397303 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −32.6943 | −2.01986 | ||||||||
\(263\) | −19.1008 | −1.17781 | −0.588903 | − | 0.808203i | \(-0.700440\pi\) | ||||
−0.588903 | + | 0.808203i | \(0.700440\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.20836 | 0.258518 | ||||||||
\(266\) | 14.0984 | 0.864427 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 23.0194 | 1.40613 | ||||||||
\(269\) | 29.3520 | 1.78962 | 0.894812 | − | 0.446443i | \(-0.147309\pi\) | ||||
0.894812 | + | 0.446443i | \(0.147309\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.62696 | 0.281068 | 0.140534 | − | 0.990076i | \(-0.455118\pi\) | ||||
0.140534 | + | 0.990076i | \(0.455118\pi\) | |||||||
\(272\) | −26.5807 | −1.61169 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 32.5493 | 1.96638 | ||||||||
\(275\) | −4.64613 | −0.280172 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.69788 | −0.582689 | −0.291345 | − | 0.956618i | \(-0.594103\pi\) | ||||
−0.291345 | + | 0.956618i | \(0.594103\pi\) | |||||||
\(278\) | 21.9024 | 1.31362 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.100223 | −0.00598946 | ||||||||
\(281\) | 29.7691 | 1.77588 | 0.887939 | − | 0.459961i | \(-0.152137\pi\) | ||||
0.887939 | + | 0.459961i | \(0.152137\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.61235 | 0.452507 | 0.226254 | − | 0.974068i | \(-0.427352\pi\) | ||||
0.226254 | + | 0.974068i | \(0.427352\pi\) | |||||||
\(284\) | 2.30400 | 0.136717 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −11.0535 | −0.653605 | ||||||||
\(287\) | 2.70937 | 0.159929 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.3923 | 1.43484 | ||||||||
\(290\) | −3.07736 | −0.180709 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 16.8893 | 0.988370 | ||||||||
\(293\) | 4.81805 | 0.281473 | 0.140737 | − | 0.990047i | \(-0.455053\pi\) | ||||
0.140737 | + | 0.990047i | \(0.455053\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.38293 | −0.0805174 | ||||||||
\(296\) | 1.06397 | 0.0618418 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.44992 | −0.141920 | ||||||||
\(299\) | −50.9386 | −2.94585 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.13451 | −0.411226 | ||||||||
\(302\) | 7.45387 | 0.428922 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −23.5299 | −1.34953 | ||||||||
\(305\) | 8.33405 | 0.477206 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.01933 | 0.172322 | 0.0861611 | − | 0.996281i | \(-0.472540\pi\) | ||||
0.0861611 | + | 0.996281i | \(0.472540\pi\) | |||||||
\(308\) | −2.41182 | −0.137426 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.25269 | 0.241536 | ||||||||
\(311\) | −5.14190 | −0.291570 | −0.145785 | − | 0.989316i | \(-0.546571\pi\) | ||||
−0.145785 | + | 0.989316i | \(0.546571\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.0431 | 0.737242 | 0.368621 | − | 0.929580i | \(-0.379830\pi\) | ||||
0.368621 | + | 0.929580i | \(0.379830\pi\) | |||||||
\(314\) | −42.9203 | −2.42213 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.68944 | 0.432565 | ||||||||
\(317\) | −3.51382 | −0.197356 | −0.0986778 | − | 0.995119i | \(-0.531461\pi\) | ||||
−0.0986778 | + | 0.995119i | \(0.531461\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.60888 | 0.146069 | ||||||||
\(320\) | −4.42972 | −0.247629 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −22.6208 | −1.26061 | ||||||||
\(323\) | 36.6415 | 2.03879 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −25.8992 | −1.43663 | ||||||||
\(326\) | 3.96016 | 0.219333 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.292895 | −0.0161724 | ||||||||
\(329\) | 0.888421 | 0.0489802 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.6654 | −1.02594 | −0.512972 | − | 0.858405i | \(-0.671456\pi\) | ||||
−0.512972 | + | 0.858405i | \(0.671456\pi\) | |||||||
\(332\) | −3.45238 | −0.189474 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 23.2451 | 1.27192 | ||||||||
\(335\) | 7.08795 | 0.387256 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.5844 | 1.06683 | 0.533415 | − | 0.845853i | \(-0.320908\pi\) | ||||
0.533415 | + | 0.845853i | \(0.320908\pi\) | |||||||
\(338\) | −35.8380 | −1.94933 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.39390 | 0.400990 | ||||||||
\(341\) | −3.60529 | −0.195237 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.5319 | 0.838645 | ||||||||
\(344\) | 0.771271 | 0.0415841 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.36855 | −0.0735735 | ||||||||
\(347\) | −0.135314 | −0.00726404 | −0.00363202 | − | 0.999993i | \(-0.501156\pi\) | ||||
−0.00363202 | + | 0.999993i | \(0.501156\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.0131 | 0.696578 | 0.348289 | − | 0.937387i | \(-0.386763\pi\) | ||||
0.348289 | + | 0.937387i | \(0.386763\pi\) | |||||||
\(350\) | −11.5013 | −0.614770 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.92246 | 0.422269 | ||||||||
\(353\) | 11.6510 | 0.620123 | 0.310061 | − | 0.950717i | \(-0.399650\pi\) | ||||
0.310061 | + | 0.950717i | \(0.399650\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.709430 | 0.0376526 | ||||||||
\(356\) | 13.2169 | 0.700494 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.37833 | 0.231402 | ||||||||
\(359\) | 8.81094 | 0.465024 | 0.232512 | − | 0.972594i | \(-0.425306\pi\) | ||||
0.232512 | + | 0.972594i | \(0.425306\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.4360 | 0.707158 | ||||||||
\(362\) | 10.1780 | 0.534946 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −13.4444 | −0.704676 | ||||||||
\(365\) | 5.20041 | 0.272202 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.7508 | −1.23978 | −0.619890 | − | 0.784689i | \(-0.712823\pi\) | ||||
−0.619890 | + | 0.784689i | \(0.712823\pi\) | |||||||
\(368\) | 37.7536 | 1.96804 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −9.29943 | −0.483454 | ||||||||
\(371\) | −8.83171 | −0.458520 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −34.2810 | −1.77500 | −0.887501 | − | 0.460806i | \(-0.847561\pi\) | ||||
−0.887501 | + | 0.460806i | \(0.847561\pi\) | |||||||
\(374\) | −12.7574 | −0.659671 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.0960421 | −0.00495299 | ||||||||
\(377\) | 14.5428 | 0.748994 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.6242 | −0.905295 | −0.452647 | − | 0.891690i | \(-0.649520\pi\) | ||||
−0.452647 | + | 0.891690i | \(0.649520\pi\) | |||||||
\(380\) | 6.54527 | 0.335765 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 32.1239 | 1.64360 | ||||||||
\(383\) | 20.4485 | 1.04487 | 0.522436 | − | 0.852679i | \(-0.325024\pi\) | ||||
0.522436 | + | 0.852679i | \(0.325024\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.742629 | −0.0378479 | ||||||||
\(386\) | 8.29667 | 0.422289 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.54093 | 0.484367 | ||||||||
\(389\) | −23.5354 | −1.19329 | −0.596646 | − | 0.802505i | \(-0.703500\pi\) | ||||
−0.596646 | + | 0.802505i | \(0.703500\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −58.7911 | −2.97320 | ||||||||
\(392\) | −0.734369 | −0.0370912 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 17.7153 | 0.892482 | ||||||||
\(395\) | 2.36767 | 0.119130 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.4452 | −1.22687 | −0.613436 | − | 0.789745i | \(-0.710213\pi\) | ||||
−0.613436 | + | 0.789745i | \(0.710213\pi\) | |||||||
\(398\) | 32.4066 | 1.62440 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.1954 | 0.959772 | ||||||||
\(401\) | −23.6966 | −1.18335 | −0.591676 | − | 0.806176i | \(-0.701533\pi\) | ||||
−0.591676 | + | 0.806176i | \(0.701533\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.0972 | −1.00111 | ||||||||
\(404\) | −4.73023 | −0.235338 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.45818 | 0.320514 | ||||||||
\(407\) | 7.88375 | 0.390783 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.9971 | −1.58216 | −0.791078 | − | 0.611715i | \(-0.790480\pi\) | ||||
−0.791078 | + | 0.611715i | \(0.790480\pi\) | |||||||
\(410\) | 2.56000 | 0.126429 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 16.2801 | 0.802064 | ||||||||
\(413\) | 2.90223 | 0.142810 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.06303 | −0.0521820 | ||||||||
\(416\) | 44.1626 | 2.16525 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −11.2932 | −0.552369 | ||||||||
\(419\) | 22.6536 | 1.10670 | 0.553351 | − | 0.832948i | \(-0.313349\pi\) | ||||
0.553351 | + | 0.832948i | \(0.313349\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.2685 | 0.500455 | 0.250227 | − | 0.968187i | \(-0.419495\pi\) | ||||
0.250227 | + | 0.968187i | \(0.419495\pi\) | |||||||
\(422\) | −20.7850 | −1.01180 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.954746 | 0.0463666 | ||||||||
\(425\) | −29.8918 | −1.44996 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.4899 | −0.846397 | ||||||||
\(428\) | −22.1842 | −1.07232 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.74117 | −0.325088 | ||||||||
\(431\) | 1.01829 | 0.0490493 | 0.0245246 | − | 0.999699i | \(-0.492193\pi\) | ||||
0.0245246 | + | 0.999699i | \(0.492193\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.1760 | −0.873481 | −0.436740 | − | 0.899588i | \(-0.643867\pi\) | ||||
−0.436740 | + | 0.899588i | \(0.643867\pi\) | |||||||
\(434\) | −8.92474 | −0.428401 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −27.1942 | −1.30237 | ||||||||
\(437\) | −52.0434 | −2.48957 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.2984 | 0.634696 | 0.317348 | − | 0.948309i | \(-0.397208\pi\) | ||||
0.317348 | + | 0.948309i | \(0.397208\pi\) | |||||||
\(440\) | 0.0802814 | 0.00382726 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −71.1145 | −3.38257 | ||||||||
\(443\) | 16.5205 | 0.784912 | 0.392456 | − | 0.919771i | \(-0.371626\pi\) | ||||
0.392456 | + | 0.919771i | \(0.371626\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.06964 | 0.192919 | ||||||||
\(446\) | −17.4216 | −0.824934 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9.29626 | 0.439207 | ||||||||
\(449\) | −8.93629 | −0.421730 | −0.210865 | − | 0.977515i | \(-0.567628\pi\) | ||||
−0.210865 | + | 0.977515i | \(0.567628\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.17028 | −0.102195 | ||||||||
\(452\) | −27.1870 | −1.27877 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 49.1473 | 2.30660 | ||||||||
\(455\) | −4.13968 | −0.194071 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.0746 | 1.17294 | 0.586471 | − | 0.809970i | \(-0.300517\pi\) | ||||
0.586471 | + | 0.809970i | \(0.300517\pi\) | |||||||
\(458\) | 7.86290 | 0.367409 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −10.5018 | −0.489651 | ||||||||
\(461\) | 30.7120 | 1.43040 | 0.715201 | − | 0.698919i | \(-0.246335\pi\) | ||||
0.715201 | + | 0.698919i | \(0.246335\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.0716 | 1.58344 | 0.791721 | − | 0.610883i | \(-0.209185\pi\) | ||||
0.791721 | + | 0.610883i | \(0.209185\pi\) | |||||||
\(464\) | −10.7786 | −0.500382 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −27.8771 | −1.29138 | ||||||||
\(467\) | −26.6921 | −1.23516 | −0.617582 | − | 0.786506i | \(-0.711888\pi\) | ||||
−0.617582 | + | 0.786506i | \(0.711888\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.8748 | −0.686857 | ||||||||
\(470\) | 0.839441 | 0.0387205 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.313744 | −0.0144412 | ||||||||
\(473\) | 5.71494 | 0.262773 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −26.4609 | −1.21411 | ||||||||
\(476\) | −15.5169 | −0.711217 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −20.9215 | −0.956928 | ||||||||
\(479\) | 19.6602 | 0.898298 | 0.449149 | − | 0.893457i | \(-0.351727\pi\) | ||||
0.449149 | + | 0.893457i | \(0.351727\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 43.9468 | 2.00380 | ||||||||
\(482\) | −21.6133 | −0.984458 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.93194 | 0.0878155 | ||||||||
\(485\) | 2.93777 | 0.133397 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.2757 | 0.465638 | 0.232819 | − | 0.972520i | \(-0.425205\pi\) | ||||
0.232819 | + | 0.972520i | \(0.425205\pi\) | |||||||
\(488\) | 1.89074 | 0.0855896 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.41864 | 0.289965 | ||||||||
\(491\) | 22.5795 | 1.01900 | 0.509499 | − | 0.860471i | \(-0.329831\pi\) | ||||
0.509499 | + | 0.860471i | \(0.329831\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.7847 | 0.755946 | ||||||||
\(494\) | −62.9523 | −2.83236 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14.8952 | 0.668815 | ||||||||
\(497\) | −1.48882 | −0.0667826 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.34717 | 0.328905 | 0.164452 | − | 0.986385i | \(-0.447414\pi\) | ||||
0.164452 | + | 0.986385i | \(0.447414\pi\) | |||||||
\(500\) | −11.0858 | −0.495772 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 55.3779 | 2.47164 | ||||||||
\(503\) | 20.5595 | 0.916703 | 0.458351 | − | 0.888771i | \(-0.348440\pi\) | ||||
0.458351 | + | 0.888771i | \(0.348440\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.45650 | −0.0648132 | ||||||||
\(506\) | 18.1199 | 0.805527 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.9305 | 0.573697 | ||||||||
\(509\) | −5.37046 | −0.238042 | −0.119021 | − | 0.992892i | \(-0.537976\pi\) | ||||
−0.119021 | + | 0.992892i | \(0.537976\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.9136 | −0.482790 | ||||||||
\(512\) | −31.6164 | −1.39726 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −19.3084 | −0.851659 | ||||||||
\(515\) | 5.01284 | 0.220892 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.711651 | −0.0312984 | ||||||||
\(518\) | 19.5159 | 0.857479 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.447517 | 0.0196249 | ||||||||
\(521\) | 4.19741 | 0.183892 | 0.0919460 | − | 0.995764i | \(-0.470691\pi\) | ||||
0.0919460 | + | 0.995764i | \(0.470691\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.88046 | −0.169681 | −0.0848404 | − | 0.996395i | \(-0.527038\pi\) | ||||
−0.0848404 | + | 0.996395i | \(0.527038\pi\) | |||||||
\(524\) | 31.8539 | 1.39154 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 37.8752 | 1.65144 | ||||||||
\(527\) | −23.1953 | −1.01040 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 60.5034 | 2.63058 | ||||||||
\(530\) | −8.34481 | −0.362475 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −13.7360 | −0.595530 | ||||||||
\(533\) | −12.0979 | −0.524020 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.83079 | −0.295321 | ||||||||
\(536\) | 1.60803 | 0.0694565 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −58.2025 | −2.50929 | ||||||||
\(539\) | −5.44151 | −0.234382 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.8963 | 1.32834 | 0.664168 | − | 0.747583i | \(-0.268786\pi\) | ||||
0.664168 | + | 0.747583i | \(0.268786\pi\) | |||||||
\(542\) | −9.17485 | −0.394094 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 50.9706 | 2.18535 | ||||||||
\(545\) | −8.37342 | −0.358678 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.3226 | −0.441362 | −0.220681 | − | 0.975346i | \(-0.570828\pi\) | ||||
−0.220681 | + | 0.975346i | \(0.570828\pi\) | |||||||
\(548\) | −31.7126 | −1.35470 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.21287 | 0.392838 | ||||||||
\(551\) | 14.8583 | 0.632984 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.96882 | −0.211296 | ||||||||
\(554\) | 19.2300 | 0.817006 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −21.3393 | −0.904990 | ||||||||
\(557\) | −1.71110 | −0.0725018 | −0.0362509 | − | 0.999343i | \(-0.511542\pi\) | ||||
−0.0362509 | + | 0.999343i | \(0.511542\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.8571 | 1.34741 | ||||||||
\(560\) | 3.06816 | 0.129654 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −59.0296 | −2.49001 | ||||||||
\(563\) | −24.2136 | −1.02048 | −0.510241 | − | 0.860031i | \(-0.670444\pi\) | ||||
−0.510241 | + | 0.860031i | \(0.670444\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.37119 | −0.352179 | ||||||||
\(566\) | −15.0946 | −0.634474 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.160947 | 0.00675321 | ||||||||
\(569\) | −11.0133 | −0.461700 | −0.230850 | − | 0.972989i | \(-0.574151\pi\) | ||||
−0.230850 | + | 0.972989i | \(0.574151\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.6779 | −0.907193 | −0.453596 | − | 0.891207i | \(-0.649859\pi\) | ||||
−0.453596 | + | 0.891207i | \(0.649859\pi\) | |||||||
\(572\) | 10.7693 | 0.450288 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.37245 | −0.224242 | ||||||||
\(575\) | 42.4564 | 1.77056 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.7494 | −1.44663 | −0.723317 | − | 0.690516i | \(-0.757384\pi\) | ||||
−0.723317 | + | 0.690516i | \(0.757384\pi\) | |||||||
\(578\) | −48.3678 | −2.01184 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.99825 | 0.124496 | ||||||||
\(581\) | 2.23088 | 0.0925526 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.07446 | 0.292994 | ||||||||
\(584\) | 1.17981 | 0.0488209 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.55376 | −0.394662 | ||||||||
\(587\) | 9.57384 | 0.395155 | 0.197577 | − | 0.980287i | \(-0.436693\pi\) | ||||
0.197577 | + | 0.980287i | \(0.436693\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.5331 | −0.846050 | ||||||||
\(590\) | 2.74223 | 0.112896 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −32.5716 | −1.33869 | ||||||||
\(593\) | −12.1826 | −0.500281 | −0.250141 | − | 0.968210i | \(-0.580477\pi\) | ||||
−0.250141 | + | 0.968210i | \(0.580477\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.77784 | −0.195872 | ||||||||
\(596\) | 2.38694 | 0.0977729 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 101.007 | 4.13047 | ||||||||
\(599\) | 15.6022 | 0.637488 | 0.318744 | − | 0.947841i | \(-0.396739\pi\) | ||||
0.318744 | + | 0.947841i | \(0.396739\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.6560 | 0.801784 | 0.400892 | − | 0.916125i | \(-0.368700\pi\) | ||||
0.400892 | + | 0.916125i | \(0.368700\pi\) | |||||||
\(602\) | 14.1471 | 0.576593 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.26227 | −0.295497 | ||||||||
\(605\) | 0.594867 | 0.0241848 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.7220 | 0.556959 | 0.278479 | − | 0.960442i | \(-0.410170\pi\) | ||||
0.278479 | + | 0.960442i | \(0.410170\pi\) | |||||||
\(608\) | 45.1205 | 1.82988 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −16.5257 | −0.669105 | ||||||||
\(611\) | −3.96699 | −0.160487 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.1817 | −1.09786 | −0.548929 | − | 0.835869i | \(-0.684964\pi\) | ||||
−0.548929 | + | 0.835869i | \(0.684964\pi\) | |||||||
\(614\) | −5.98706 | −0.241618 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.168479 | −0.00678823 | ||||||||
\(617\) | 2.87522 | 0.115752 | 0.0578759 | − | 0.998324i | \(-0.481567\pi\) | ||||
0.0578759 | + | 0.998324i | \(0.481567\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.7754 | 1.51832 | 0.759161 | − | 0.650903i | \(-0.225609\pi\) | ||||
0.759161 | + | 0.650903i | \(0.225609\pi\) | |||||||
\(620\) | −4.14337 | −0.166402 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.1959 | 0.408820 | ||||||||
\(623\) | −8.54059 | −0.342172 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.8172 | 0.792689 | ||||||||
\(626\) | −25.8634 | −1.03371 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 41.8170 | 1.66868 | ||||||||
\(629\) | 50.7216 | 2.02240 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.3497 | −1.48687 | −0.743435 | − | 0.668808i | \(-0.766805\pi\) | ||||
−0.743435 | + | 0.668808i | \(0.766805\pi\) | |||||||
\(632\) | 0.537151 | 0.0213667 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.96759 | 0.276718 | ||||||||
\(635\) | 3.98144 | 0.157999 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −30.3329 | −1.20183 | ||||||||
\(638\) | −5.17319 | −0.204808 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.641879 | −0.0253725 | ||||||||
\(641\) | 39.0718 | 1.54324 | 0.771621 | − | 0.636082i | \(-0.219446\pi\) | ||||
0.771621 | + | 0.636082i | \(0.219446\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.62560 | −0.300724 | −0.150362 | − | 0.988631i | \(-0.548044\pi\) | ||||
−0.150362 | + | 0.988631i | \(0.548044\pi\) | |||||||
\(644\) | 22.0393 | 0.868470 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −72.6569 | −2.85865 | ||||||||
\(647\) | 0.837635 | 0.0329308 | 0.0164654 | − | 0.999864i | \(-0.494759\pi\) | ||||
0.0164654 | + | 0.999864i | \(0.494759\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.32477 | −0.0912553 | ||||||||
\(650\) | 51.3558 | 2.01434 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.85837 | −0.151105 | ||||||||
\(653\) | 37.3531 | 1.46174 | 0.730869 | − | 0.682517i | \(-0.239115\pi\) | ||||
0.730869 | + | 0.682517i | \(0.239115\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.80818 | 0.383237 | ||||||||
\(656\) | 8.96651 | 0.350083 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.76166 | −0.0686767 | ||||||||
\(659\) | 45.0815 | 1.75613 | 0.878063 | − | 0.478546i | \(-0.158836\pi\) | ||||
0.878063 | + | 0.478546i | \(0.158836\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.1438 | 1.25025 | 0.625124 | − | 0.780526i | \(-0.285049\pi\) | ||||
0.625124 | + | 0.780526i | \(0.285049\pi\) | |||||||
\(662\) | 37.0119 | 1.43851 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.241168 | −0.00935913 | ||||||||
\(665\) | −4.22947 | −0.164012 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.8400 | −0.923089 | ||||||||
\(668\) | −22.6476 | −0.876261 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −14.0548 | −0.542983 | ||||||||
\(671\) | 14.0099 | 0.540847 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.37561 | 0.361403 | 0.180702 | − | 0.983538i | \(-0.442163\pi\) | ||||
0.180702 | + | 0.983538i | \(0.442163\pi\) | |||||||
\(674\) | −38.8342 | −1.49584 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 34.9168 | 1.34295 | ||||||||
\(677\) | 10.0639 | 0.386785 | 0.193393 | − | 0.981121i | \(-0.438051\pi\) | ||||
0.193393 | + | 0.981121i | \(0.438051\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.16523 | −0.236600 | ||||||||
\(680\) | 0.516505 | 0.0198071 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7.14897 | 0.273748 | ||||||||
\(683\) | −4.40902 | −0.168706 | −0.0843532 | − | 0.996436i | \(-0.526882\pi\) | ||||
−0.0843532 | + | 0.996436i | \(0.526882\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.76469 | −0.373090 | ||||||||
\(686\) | −30.7984 | −1.17589 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −23.6112 | −0.900169 | ||||||||
\(689\) | 39.4355 | 1.50237 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.7064 | 0.445333 | 0.222667 | − | 0.974895i | \(-0.428524\pi\) | ||||
0.222667 | + | 0.974895i | \(0.428524\pi\) | |||||||
\(692\) | 1.33337 | 0.0506870 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.268316 | 0.0101851 | ||||||||
\(695\) | −6.57063 | −0.249238 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.9629 | −0.528884 | ||||||||
\(698\) | −25.8039 | −0.976693 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 11.2057 | 0.423534 | ||||||||
\(701\) | 13.3602 | 0.504608 | 0.252304 | − | 0.967648i | \(-0.418812\pi\) | ||||
0.252304 | + | 0.967648i | \(0.418812\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 44.9000 | 1.69344 | ||||||||
\(704\) | −7.44657 | −0.280653 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23.1030 | −0.869493 | ||||||||
\(707\) | 3.05662 | 0.114956 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.9680 | −0.487025 | −0.243513 | − | 0.969898i | \(-0.578300\pi\) | ||||
−0.243513 | + | 0.969898i | \(0.578300\pi\) | |||||||
\(710\) | −1.40674 | −0.0527939 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.923274 | 0.0346012 | ||||||||
\(713\) | 32.9452 | 1.23381 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.31600 | 0.124011 | ||||||||
\(716\) | −4.26578 | −0.159420 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −17.4713 | −0.652024 | ||||||||
\(719\) | −10.8533 | −0.404760 | −0.202380 | − | 0.979307i | \(-0.564868\pi\) | ||||
−0.202380 | + | 0.979307i | \(0.564868\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.5200 | −0.391785 | ||||||||
\(722\) | −26.6424 | −0.991528 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.91642 | −0.368541 | ||||||||
\(725\) | −12.1212 | −0.450171 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.40864 | 0.126419 | 0.0632097 | − | 0.998000i | \(-0.479866\pi\) | ||||
0.0632097 | + | 0.998000i | \(0.479866\pi\) | |||||||
\(728\) | −0.939164 | −0.0348077 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10.3119 | −0.381662 | ||||||||
\(731\) | 36.7682 | 1.35992 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.53306 | 0.130497 | 0.0652484 | − | 0.997869i | \(-0.479216\pi\) | ||||
0.0652484 | + | 0.997869i | \(0.479216\pi\) | |||||||
\(734\) | 47.0957 | 1.73833 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −72.3956 | −2.66854 | ||||||||
\(737\) | 11.9152 | 0.438901 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.6120 | −1.08930 | −0.544648 | − | 0.838665i | \(-0.683337\pi\) | ||||
−0.544648 | + | 0.838665i | \(0.683337\pi\) | |||||||
\(740\) | 9.06038 | 0.333066 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 17.5125 | 0.642905 | ||||||||
\(743\) | 12.6382 | 0.463651 | 0.231825 | − | 0.972757i | \(-0.425530\pi\) | ||||
0.231825 | + | 0.972757i | \(0.425530\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.734968 | 0.0269271 | ||||||||
\(746\) | 67.9762 | 2.48878 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 12.4295 | 0.454467 | ||||||||
\(749\) | 14.3352 | 0.523796 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.2466 | 1.54160 | 0.770799 | − | 0.637078i | \(-0.219857\pi\) | ||||
0.770799 | + | 0.637078i | \(0.219857\pi\) | |||||||
\(752\) | 2.94018 | 0.107217 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −28.8372 | −1.05019 | ||||||||
\(755\) | −2.23614 | −0.0813814 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.3409 | 1.06641 | 0.533207 | − | 0.845985i | \(-0.320987\pi\) | ||||
0.533207 | + | 0.845985i | \(0.320987\pi\) | |||||||
\(758\) | 34.9473 | 1.26934 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.457223 | 0.0165852 | ||||||||
\(761\) | −43.2228 | −1.56683 | −0.783413 | − | 0.621501i | \(-0.786523\pi\) | ||||
−0.783413 | + | 0.621501i | \(0.786523\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.5725 | 0.636169 | ||||||||
\(764\) | −31.2981 | −1.13233 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −40.5476 | −1.46505 | ||||||||
\(767\) | −12.9591 | −0.467926 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.3541 | 1.49127 | 0.745633 | − | 0.666357i | \(-0.232147\pi\) | ||||
0.745633 | + | 0.666357i | \(0.232147\pi\) | |||||||
\(770\) | 1.47257 | 0.0530677 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.08340 | −0.290928 | ||||||||
\(773\) | 8.38159 | 0.301465 | 0.150732 | − | 0.988575i | \(-0.451837\pi\) | ||||
0.150732 | + | 0.988575i | \(0.451837\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.7507 | 0.601701 | ||||||||
\(776\) | 0.666487 | 0.0239255 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 46.6686 | 1.67315 | ||||||||
\(779\) | −12.3603 | −0.442855 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.19258 | 0.0426740 | ||||||||
\(782\) | 116.578 | 4.16881 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 22.4815 | 0.802912 | ||||||||
\(785\) | 12.8759 | 0.459562 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.6487 | −1.30638 | −0.653192 | − | 0.757192i | \(-0.726570\pi\) | ||||
−0.653192 | + | 0.757192i | \(0.726570\pi\) | |||||||
\(788\) | −17.2599 | −0.614858 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.69488 | −0.167036 | ||||||||
\(791\) | 17.5679 | 0.624642 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 78.0963 | 2.77328 | ||||||||
\(794\) | 48.4727 | 1.72023 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −31.5736 | −1.11910 | ||||||||
\(797\) | 23.0271 | 0.815663 | 0.407831 | − | 0.913057i | \(-0.366285\pi\) | ||||
0.407831 | + | 0.913057i | \(0.366285\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.57854 | −0.161977 | ||||||||
\(800\) | −36.8088 | −1.30139 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 46.9882 | 1.65921 | ||||||||
\(803\) | 8.74213 | 0.308503 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.78616 | 0.239181 | ||||||||
\(806\) | 39.8509 | 1.40369 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.330433 | −0.0116246 | ||||||||
\(809\) | 31.8739 | 1.12063 | 0.560314 | − | 0.828280i | \(-0.310680\pi\) | ||||
0.560314 | + | 0.828280i | \(0.310680\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.6519 | −1.18168 | −0.590838 | − | 0.806790i | \(-0.701203\pi\) | ||||
−0.590838 | + | 0.806790i | \(0.701203\pi\) | |||||||
\(812\) | −6.29217 | −0.220812 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −15.6328 | −0.547929 | ||||||||
\(815\) | −1.18804 | −0.0416151 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 32.5481 | 1.13871 | ||||||||
\(818\) | 63.4475 | 2.21839 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.49420 | −0.0871011 | ||||||||
\(821\) | 25.8678 | 0.902793 | 0.451397 | − | 0.892323i | \(-0.350926\pi\) | ||||
0.451397 | + | 0.892323i | \(0.350926\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −49.3280 | −1.71947 | −0.859733 | − | 0.510744i | \(-0.829370\pi\) | ||||
−0.859733 | + | 0.510744i | \(0.829370\pi\) | |||||||
\(824\) | 1.13726 | 0.0396182 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.75488 | −0.200238 | ||||||||
\(827\) | 29.8291 | 1.03726 | 0.518630 | − | 0.854999i | \(-0.326442\pi\) | ||||
0.518630 | + | 0.854999i | \(0.326442\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.3449 | −0.914995 | −0.457498 | − | 0.889211i | \(-0.651254\pi\) | ||||
−0.457498 | + | 0.889211i | \(0.651254\pi\) | |||||||
\(830\) | 2.10789 | 0.0731659 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −41.5098 | −1.43909 | ||||||||
\(833\) | −35.0090 | −1.21299 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.97346 | −0.241326 | ||||||||
\(836\) | 11.0029 | 0.380543 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −44.9201 | −1.55174 | ||||||||
\(839\) | 37.0520 | 1.27918 | 0.639589 | − | 0.768717i | \(-0.279105\pi\) | ||||
0.639589 | + | 0.768717i | \(0.279105\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.1937 | −0.765301 | ||||||||
\(842\) | −20.3615 | −0.701703 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 20.2507 | 0.697057 | ||||||||
\(845\) | 10.7513 | 0.369856 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.24839 | −0.0428953 | ||||||||
\(848\) | −29.2280 | −1.00369 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 59.2727 | 2.03304 | ||||||||
\(851\) | −72.0418 | −2.46956 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.6609 | −0.707416 | −0.353708 | − | 0.935356i | \(-0.615079\pi\) | ||||
−0.353708 | + | 0.935356i | \(0.615079\pi\) | |||||||
\(854\) | 34.6810 | 1.18676 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.54969 | −0.0529674 | ||||||||
\(857\) | −23.3980 | −0.799260 | −0.399630 | − | 0.916676i | \(-0.630861\pi\) | ||||
−0.399630 | + | 0.916676i | \(0.630861\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.03073 | 0.274005 | 0.137003 | − | 0.990571i | \(-0.456253\pi\) | ||||
0.137003 | + | 0.990571i | \(0.456253\pi\) | |||||||
\(860\) | 6.56789 | 0.223963 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.01918 | −0.0687735 | ||||||||
\(863\) | −41.1668 | −1.40133 | −0.700667 | − | 0.713489i | \(-0.747114\pi\) | ||||
−0.700667 | + | 0.713489i | \(0.747114\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.410560 | 0.0139594 | ||||||||
\(866\) | 36.0413 | 1.22473 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.69532 | 0.295138 | ||||||||
\(869\) | 3.98017 | 0.135018 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 66.4194 | 2.25054 | ||||||||
\(872\) | −1.89967 | −0.0643308 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 103.197 | 3.49071 | ||||||||
\(875\) | 7.16350 | 0.242170 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.4484 | 0.791797 | 0.395898 | − | 0.918294i | \(-0.370433\pi\) | ||||
0.395898 | + | 0.918294i | \(0.370433\pi\) | |||||||
\(878\) | −26.3695 | −0.889926 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.45769 | −0.0828486 | ||||||||
\(881\) | 9.12961 | 0.307584 | 0.153792 | − | 0.988103i | \(-0.450851\pi\) | ||||
0.153792 | + | 0.988103i | \(0.450851\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.3941 | 1.49398 | 0.746990 | − | 0.664835i | \(-0.231498\pi\) | ||||
0.746990 | + | 0.664835i | \(0.231498\pi\) | |||||||
\(884\) | 69.2864 | 2.33035 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −32.7587 | −1.10055 | ||||||||
\(887\) | −1.16604 | −0.0391518 | −0.0195759 | − | 0.999808i | \(-0.506232\pi\) | ||||
−0.0195759 | + | 0.999808i | \(0.506232\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.35550 | −0.280234 | ||||||||
\(890\) | −8.06974 | −0.270498 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16.9737 | 0.568322 | ||||||||
\(893\) | −4.05304 | −0.135630 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.31349 | −0.0439050 | ||||||||
\(896\) | 1.34705 | 0.0450019 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 17.7199 | 0.591320 | ||||||||
\(899\) | −9.40578 | −0.313700 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 45.5148 | 1.51632 | ||||||||
\(902\) | 4.30348 | 0.143290 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.89916 | −0.0631652 | ||||||||
\(905\) | −3.05338 | −0.101498 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.4121 | 0.445340 | 0.222670 | − | 0.974894i | \(-0.428523\pi\) | ||||
0.222670 | + | 0.974894i | \(0.428523\pi\) | |||||||
\(908\) | −47.8840 | −1.58909 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8.20862 | 0.272113 | ||||||||
\(911\) | −15.5787 | −0.516145 | −0.258073 | − | 0.966126i | \(-0.583087\pi\) | ||||
−0.258073 | + | 0.966126i | \(0.583087\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.78700 | −0.0591411 | ||||||||
\(914\) | −49.7208 | −1.64462 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.66078 | −0.253119 | ||||||||
\(917\) | −20.5836 | −0.679729 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.7124 | −0.485316 | −0.242658 | − | 0.970112i | \(-0.578019\pi\) | ||||
−0.242658 | + | 0.970112i | \(0.578019\pi\) | |||||||
\(920\) | −0.733613 | −0.0241865 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −60.8992 | −2.00561 | ||||||||
\(923\) | 6.64789 | 0.218818 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36.6290 | −1.20435 | ||||||||
\(926\) | −67.5610 | −2.22019 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 20.6688 | 0.678486 | ||||||||
\(929\) | −19.4271 | −0.637382 | −0.318691 | − | 0.947859i | \(-0.603243\pi\) | ||||
−0.318691 | + | 0.947859i | \(0.603243\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30.9908 | −1.01568 | ||||||||
\(932\) | 27.1605 | 0.889672 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 52.9282 | 1.73186 | ||||||||
\(935\) | 3.82719 | 0.125162 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.3590 | 0.893779 | 0.446889 | − | 0.894589i | \(-0.352532\pi\) | ||||
0.446889 | + | 0.894589i | \(0.352532\pi\) | |||||||
\(938\) | 29.4955 | 0.963063 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.817863 | −0.0266757 | ||||||||
\(941\) | −0.136616 | −0.00445356 | −0.00222678 | − | 0.999998i | \(-0.500709\pi\) | ||||
−0.00222678 | + | 0.999998i | \(0.500709\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.8321 | 0.645822 | ||||||||
\(944\) | 9.60477 | 0.312609 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.3322 | −0.368443 | ||||||||
\(947\) | 33.7242 | 1.09589 | 0.547945 | − | 0.836514i | \(-0.315410\pi\) | ||||
0.547945 | + | 0.836514i | \(0.315410\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 48.7317 | 1.58190 | ||||||||
\(950\) | 52.4697 | 1.70234 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.08394 | −0.0351308 | ||||||||
\(953\) | 4.05681 | 0.131413 | 0.0657065 | − | 0.997839i | \(-0.479070\pi\) | ||||
0.0657065 | + | 0.997839i | \(0.479070\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.63706 | −0.311848 | ||||||||
\(956\) | 20.3837 | 0.659257 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −38.9845 | −1.25953 | ||||||||
\(959\) | 20.4923 | 0.661730 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.0019 | −0.580706 | ||||||||
\(962\) | −87.1427 | −2.80959 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 21.0577 | 0.678223 | ||||||||
\(965\) | −2.48897 | −0.0801229 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.7505 | 1.34261 | 0.671303 | − | 0.741183i | \(-0.265735\pi\) | ||||
0.671303 | + | 0.741183i | \(0.265735\pi\) | |||||||
\(968\) | 0.134957 | 0.00433768 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.82533 | −0.187040 | ||||||||
\(971\) | 0.681779 | 0.0218793 | 0.0109397 | − | 0.999940i | \(-0.496518\pi\) | ||||
0.0109397 | + | 0.999940i | \(0.496518\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.7892 | 0.442062 | ||||||||
\(974\) | −20.3759 | −0.652886 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −57.8819 | −1.85275 | ||||||||
\(977\) | −13.8474 | −0.443018 | −0.221509 | − | 0.975158i | \(-0.571098\pi\) | ||||
−0.221509 | + | 0.975158i | \(0.571098\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.84126 | 0.218648 | ||||||||
\(980\) | −6.25364 | −0.199765 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −44.7732 | −1.42877 | ||||||||
\(983\) | 14.5944 | 0.465488 | 0.232744 | − | 0.972538i | \(-0.425230\pi\) | ||||
0.232744 | + | 0.972538i | \(0.425230\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.31452 | −0.169335 | ||||||||
\(986\) | −33.2827 | −1.05994 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 61.3341 | 1.95130 | ||||||||
\(989\) | −52.2233 | −1.66060 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.4979 | −0.492306 | −0.246153 | − | 0.969231i | \(-0.579167\pi\) | ||||
−0.246153 | + | 0.969231i | \(0.579167\pi\) | |||||||
\(992\) | −28.5628 | −0.906869 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.95219 | 0.0936379 | ||||||||
\(995\) | −9.72188 | −0.308204 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.92781 | 0.156065 | 0.0780326 | − | 0.996951i | \(-0.475136\pi\) | ||||
0.0780326 | + | 0.996951i | \(0.475136\pi\) | |||||||
\(998\) | −14.5688 | −0.461167 | ||||||||
\(999\) | 0 | 0 |
(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 | 8019.2.a.l.1.9 | 51 | ||
3.2 | odd | 2 | 8019.2.a.k.1.43 | 51 | |||
27.4 | even | 9 | 297.2.j.c.232.3 | ✓ | 102 | ||
27.7 | even | 9 | 297.2.j.c.265.3 | yes | 102 | ||
27.20 | odd | 18 | 891.2.j.c.199.15 | 102 | |||
27.23 | odd | 18 | 891.2.j.c.694.15 | 102 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
297.2.j.c.232.3 | ✓ | 102 | 27.4 | even | 9 | ||
297.2.j.c.265.3 | yes | 102 | 27.7 | even | 9 | ||
891.2.j.c.199.15 | 102 | 27.20 | odd | 18 | |||
891.2.j.c.694.15 | 102 | 27.23 | odd | 18 | |||
8019.2.a.k.1.43 | 51 | 3.2 | odd | 2 | |||
8019.2.a.l.1.9 | 51 | 1.1 | even | 1 | trivial |