Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6036,2,Mod(1,6036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6036, 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("6036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6036 = 2^{2} \cdot 3 \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6036.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: | \(48.1977026600\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6036.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.63100 | 0.729405 | 0.364702 | − | 0.931124i | \(-0.381171\pi\) | ||||
0.364702 | + | 0.931124i | \(0.381171\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.968844 | 0.366188 | 0.183094 | − | 0.983095i | \(-0.441389\pi\) | ||||
0.183094 | + | 0.983095i | \(0.441389\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.515879 | −0.155543 | −0.0777717 | − | 0.996971i | \(-0.524781\pi\) | ||||
−0.0777717 | + | 0.996971i | \(0.524781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.41601 | 0.670081 | 0.335040 | − | 0.942204i | \(-0.391250\pi\) | ||||
0.335040 | + | 0.942204i | \(0.391250\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.63100 | 0.421122 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.72683 | 0.661353 | 0.330677 | − | 0.943744i | \(-0.392723\pi\) | ||||
0.330677 | + | 0.943744i | \(0.392723\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.28783 | 0.754281 | 0.377140 | − | 0.926156i | \(-0.376907\pi\) | ||||
0.377140 | + | 0.926156i | \(0.376907\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.968844 | 0.211419 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.42636 | 0.505932 | 0.252966 | − | 0.967475i | \(-0.418594\pi\) | ||||
0.252966 | + | 0.967475i | \(0.418594\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.33984 | −0.467969 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.20663 | 0.409760 | 0.204880 | − | 0.978787i | \(-0.434320\pi\) | ||||
0.204880 | + | 0.978787i | \(0.434320\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.45143 | −1.15871 | −0.579355 | − | 0.815075i | \(-0.696696\pi\) | ||||
−0.579355 | + | 0.815075i | \(0.696696\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.515879 | −0.0898031 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.58018 | 0.267100 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.93597 | 0.811468 | 0.405734 | − | 0.913991i | \(-0.367016\pi\) | ||||
0.405734 | + | 0.913991i | \(0.367016\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.41601 | 0.386871 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.19804 | −0.187103 | −0.0935515 | − | 0.995614i | \(-0.529822\pi\) | ||||
−0.0935515 | + | 0.995614i | \(0.529822\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.4640 | 1.74825 | 0.874125 | − | 0.485701i | \(-0.161436\pi\) | ||||
0.874125 | + | 0.485701i | \(0.161436\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.63100 | 0.243135 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.331760 | 0.0483921 | 0.0241961 | − | 0.999707i | \(-0.492297\pi\) | ||||
0.0241961 | + | 0.999707i | \(0.492297\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.06134 | −0.865906 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.72683 | 0.381833 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.641025 | 0.0880516 | 0.0440258 | − | 0.999030i | \(-0.485982\pi\) | ||||
0.0440258 | + | 0.999030i | \(0.485982\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.841398 | −0.113454 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.28783 | 0.435484 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.73990 | −0.356705 | −0.178352 | − | 0.983967i | \(-0.557077\pi\) | ||||
−0.178352 | + | 0.983967i | \(0.557077\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.89119 | 0.498215 | 0.249108 | − | 0.968476i | \(-0.419863\pi\) | ||||
0.249108 | + | 0.968476i | \(0.419863\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.968844 | 0.122063 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.94051 | 0.488760 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.15669 | 0.629990 | 0.314995 | − | 0.949093i | \(-0.397997\pi\) | ||||
0.314995 | + | 0.949093i | \(0.397997\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.42636 | 0.292100 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.21702 | −0.144433 | −0.0722167 | − | 0.997389i | \(-0.523007\pi\) | ||||
−0.0722167 | + | 0.997389i | \(0.523007\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.96885 | 0.464518 | 0.232259 | − | 0.972654i | \(-0.425388\pi\) | ||||
0.232259 | + | 0.972654i | \(0.425388\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.33984 | −0.270182 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.499806 | −0.0569582 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.3007 | −1.72147 | −0.860733 | − | 0.509057i | \(-0.829994\pi\) | ||||
−0.860733 | + | 0.509057i | \(0.829994\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.12065 | 0.891357 | 0.445679 | − | 0.895193i | \(-0.352962\pi\) | ||||
0.445679 | + | 0.895193i | \(0.352962\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.44746 | 0.482394 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.20663 | 0.236575 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.00258 | −0.212273 | −0.106136 | − | 0.994352i | \(-0.533848\pi\) | ||||
−0.106136 | + | 0.994352i | \(0.533848\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.34074 | 0.245376 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.45143 | −0.668982 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.36245 | 0.550176 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.76692 | −0.382472 | −0.191236 | − | 0.981544i | \(-0.561250\pi\) | ||||
−0.191236 | + | 0.981544i | \(0.561250\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.515879 | −0.0518478 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.2846 | 1.71988 | 0.859942 | − | 0.510392i | \(-0.170500\pi\) | ||||
0.859942 | + | 0.510392i | \(0.170500\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.0176 | −1.47973 | −0.739865 | − | 0.672755i | \(-0.765111\pi\) | ||||
−0.739865 | + | 0.672755i | \(0.765111\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.58018 | 0.154210 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.951772 | −0.0920113 | −0.0460056 | − | 0.998941i | \(-0.514649\pi\) | ||||
−0.0460056 | + | 0.998941i | \(0.514649\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.4449 | 1.09623 | 0.548113 | − | 0.836404i | \(-0.315346\pi\) | ||||
0.548113 | + | 0.836404i | \(0.315346\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.93597 | 0.468501 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.51785 | −0.895364 | −0.447682 | − | 0.894193i | \(-0.647750\pi\) | ||||
−0.447682 | + | 0.894193i | \(0.647750\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.95740 | 0.369029 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.41601 | 0.223360 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.64187 | 0.242180 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7339 | −0.975806 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.19804 | −0.108024 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.9713 | −1.07074 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.15260 | 0.545955 | 0.272978 | − | 0.962020i | \(-0.411992\pi\) | ||||
0.272978 | + | 0.962020i | \(0.411992\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.4640 | 1.00935 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.3869 | −1.34436 | −0.672180 | − | 0.740388i | \(-0.734642\pi\) | ||||
−0.672180 | + | 0.740388i | \(0.734642\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.18540 | 0.276209 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.63100 | 0.140374 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.39887 | 0.803000 | 0.401500 | − | 0.915859i | \(-0.368489\pi\) | ||||
0.401500 | + | 0.915859i | \(0.368489\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.9337 | 1.43629 | 0.718147 | − | 0.695891i | \(-0.244990\pi\) | ||||
0.718147 | + | 0.695891i | \(0.244990\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.331760 | 0.0279392 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.24637 | −0.104227 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.59900 | 0.298881 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.06134 | −0.499931 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.33872 | 0.683135 | 0.341567 | − | 0.939857i | \(-0.389042\pi\) | ||||
0.341567 | + | 0.939857i | \(0.389042\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.79467 | −0.390185 | −0.195092 | − | 0.980785i | \(-0.562501\pi\) | ||||
−0.195092 | + | 0.980785i | \(0.562501\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.72683 | 0.220451 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.5223 | −0.845169 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.8380 | 0.944772 | 0.472386 | − | 0.881392i | \(-0.343393\pi\) | ||||
0.472386 | + | 0.881392i | \(0.343393\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.641025 | 0.0508366 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.35077 | 0.185266 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.32206 | 0.103552 | 0.0517760 | − | 0.998659i | \(-0.483512\pi\) | ||||
0.0517760 | + | 0.998659i | \(0.483512\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.841398 | −0.0655028 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.3543 | 0.801237 | 0.400619 | − | 0.916245i | \(-0.368795\pi\) | ||||
0.400619 | + | 0.916245i | \(0.368795\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.16289 | −0.550991 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.28783 | 0.251427 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 25.5438 | 1.94206 | 0.971030 | − | 0.238960i | \(-0.0768064\pi\) | ||||
0.971030 | + | 0.238960i | \(0.0768064\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.26694 | −0.171365 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.73990 | −0.205943 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.50943 | −0.710768 | −0.355384 | − | 0.934720i | \(-0.615650\pi\) | ||||
−0.355384 | + | 0.934720i | \(0.615650\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.6579 | −1.46116 | −0.730581 | − | 0.682826i | \(-0.760751\pi\) | ||||
−0.730581 | + | 0.682826i | \(0.760751\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.89119 | 0.287645 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.05056 | 0.591889 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.40672 | −0.102869 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.968844 | 0.0704730 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.5726 | 1.85037 | 0.925185 | − | 0.379516i | \(-0.123910\pi\) | ||||
0.925185 | + | 0.379516i | \(0.123910\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.47283 | −0.106017 | −0.0530085 | − | 0.998594i | \(-0.516881\pi\) | ||||
−0.0530085 | + | 0.998594i | \(0.516881\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.94051 | 0.282186 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.5426 | 1.17861 | 0.589307 | − | 0.807909i | \(-0.299401\pi\) | ||||
0.589307 | + | 0.807909i | \(0.299401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.3063 | −1.01415 | −0.507073 | − | 0.861903i | \(-0.669273\pi\) | ||||
−0.507073 | + | 0.861903i | \(0.669273\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.15669 | 0.363725 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.13788 | 0.150049 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.95401 | −0.136474 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.42636 | 0.168644 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.69613 | −0.117323 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.517844 | −0.0356499 | −0.0178249 | − | 0.999841i | \(-0.505674\pi\) | ||||
−0.0178249 | + | 0.999841i | \(0.505674\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.21702 | −0.0833887 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.6978 | 1.27518 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.25043 | −0.424307 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.96885 | 0.268190 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.58805 | 0.443160 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.28956 | 0.153321 | 0.0766603 | − | 0.997057i | \(-0.475574\pi\) | ||||
0.0766603 | + | 0.997057i | \(0.475574\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.33984 | −0.155990 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.05886 | 0.0702791 | 0.0351395 | − | 0.999382i | \(-0.488812\pi\) | ||||
0.0351395 | + | 0.999382i | \(0.488812\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.23606 | −0.0816810 | −0.0408405 | − | 0.999166i | \(-0.513004\pi\) | ||||
−0.0408405 | + | 0.999166i | \(0.513004\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.499806 | −0.0328848 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.8090 | 1.29773 | 0.648864 | − | 0.760904i | \(-0.275244\pi\) | ||||
0.648864 | + | 0.760904i | \(0.275244\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.541100 | 0.0352974 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.3007 | −0.993889 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.2624 | −1.76346 | −0.881730 | − | 0.471754i | \(-0.843621\pi\) | ||||
−0.881730 | + | 0.471754i | \(0.843621\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.3465 | 1.05297 | 0.526486 | − | 0.850184i | \(-0.323509\pi\) | ||||
0.526486 | + | 0.850184i | \(0.323509\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.88604 | −0.631596 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.94344 | 0.505429 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.12065 | 0.514625 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.02322 | −0.253943 | −0.126972 | − | 0.991906i | \(-0.540526\pi\) | ||||
−0.126972 | + | 0.991906i | \(0.540526\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.25171 | −0.0786944 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.44746 | 0.278511 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.96131 | −0.184721 | −0.0923607 | − | 0.995726i | \(-0.529441\pi\) | ||||
−0.0923607 | + | 0.995726i | \(0.529441\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.78218 | 0.297150 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.20663 | 0.136587 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.5063 | −1.20281 | −0.601405 | − | 0.798945i | \(-0.705392\pi\) | ||||
−0.601405 | + | 0.798945i | \(0.705392\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.04551 | 0.0642252 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.00258 | −0.122556 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.2657 | −1.11368 | −0.556840 | − | 0.830620i | \(-0.687986\pi\) | ||||
−0.556840 | + | 0.830620i | \(0.687986\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.41708 | −0.450556 | −0.225278 | − | 0.974295i | \(-0.572329\pi\) | ||||
−0.225278 | + | 0.974295i | \(0.572329\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.34074 | 0.141668 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.20708 | 0.0727895 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.9772 | 1.26040 | 0.630199 | − | 0.776434i | \(-0.282973\pi\) | ||||
0.630199 | + | 0.776434i | \(0.282973\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.45143 | −0.386237 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.11739 | −0.245623 | −0.122812 | − | 0.992430i | \(-0.539191\pi\) | ||||
−0.122812 | + | 0.992430i | \(0.539191\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.4094 | 1.80765 | 0.903827 | − | 0.427899i | \(-0.140746\pi\) | ||||
0.903827 | + | 0.427899i | \(0.140746\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.36245 | 0.317644 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.16072 | −0.0685149 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.56440 | −0.562612 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.76692 | −0.220821 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.8666 | −0.634834 | −0.317417 | − | 0.948286i | \(-0.602815\pi\) | ||||
−0.317417 | + | 0.948286i | \(0.602815\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.46877 | −0.260182 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.515879 | −0.0299344 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.86212 | 0.339015 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.1069 | 0.640189 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.2846 | 0.992976 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.34652 | 0.363401 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.21688 | −0.526035 | −0.263018 | − | 0.964791i | \(-0.584718\pi\) | ||||
−0.263018 | + | 0.964791i | \(0.584718\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.0176 | −0.854322 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.0405 | −1.30651 | −0.653254 | − | 0.757138i | \(-0.726597\pi\) | ||||
−0.653254 | + | 0.757138i | \(0.726597\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.5492 | 1.16151 | 0.580754 | − | 0.814079i | \(-0.302758\pi\) | ||||
0.580754 | + | 0.814079i | \(0.302758\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.58018 | 0.0890332 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −31.5199 | −1.77034 | −0.885168 | − | 0.465272i | \(-0.845957\pi\) | ||||
−0.885168 | + | 0.465272i | \(0.845957\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.13835 | −0.0637355 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.951772 | −0.0531227 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.96536 | 0.498846 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.65309 | −0.313577 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.4449 | 0.632906 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.321423 | 0.0177206 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.0690 | −0.828269 | −0.414134 | − | 0.910216i | \(-0.635916\pi\) | ||||
−0.414134 | + | 0.910216i | \(0.635916\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.93597 | 0.270489 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.41056 | 0.459518 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.4681 | −1.11497 | −0.557484 | − | 0.830187i | \(-0.688233\pi\) | ||||
−0.557484 | + | 0.830187i | \(0.688233\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.51785 | −0.516939 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.32816 | 0.180230 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.6544 | −0.683273 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.95740 | 0.213059 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.01798 | 0.323062 | 0.161531 | − | 0.986868i | \(-0.448357\pi\) | ||||
0.161531 | + | 0.986868i | \(0.448357\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −31.2949 | −1.67518 | −0.837588 | − | 0.546302i | \(-0.816035\pi\) | ||||
−0.837588 | + | 0.546302i | \(0.816035\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.41601 | 0.128957 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.87028 | 0.472117 | 0.236059 | − | 0.971739i | \(-0.424144\pi\) | ||||
0.236059 | + | 0.971739i | \(0.424144\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.98495 | −0.105350 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.64187 | 0.139823 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.8386 | 0.783153 | 0.391577 | − | 0.920146i | \(-0.371930\pi\) | ||||
0.391577 | + | 0.920146i | \(0.371930\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.19015 | −0.431061 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.7339 | −0.563382 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.47318 | 0.338822 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.3018 | 1.32074 | 0.660371 | − | 0.750940i | \(-0.270399\pi\) | ||||
0.660371 | + | 0.750940i | \(0.270399\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.19804 | −0.0623676 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.621053 | 0.0322435 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.48742 | −0.284128 | −0.142064 | − | 0.989857i | \(-0.545374\pi\) | ||||
−0.142064 | + | 0.989857i | \(0.545374\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.9713 | −0.618194 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.33123 | 0.274573 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.7359 | −0.756931 | −0.378466 | − | 0.925615i | \(-0.623548\pi\) | ||||
−0.378466 | + | 0.925615i | \(0.623548\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.15260 | 0.315207 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.872601 | −0.0445878 | −0.0222939 | − | 0.999751i | \(-0.507097\pi\) | ||||
−0.0222939 | + | 0.999751i | \(0.507097\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.815184 | −0.0415456 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.4640 | 0.582750 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.8903 | −0.907074 | −0.453537 | − | 0.891237i | \(-0.649838\pi\) | ||||
−0.453537 | + | 0.891237i | \(0.649838\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.61628 | 0.334600 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.3869 | −0.776167 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −24.9555 | −1.25565 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.9980 | 0.702540 | 0.351270 | − | 0.936274i | \(-0.385750\pi\) | ||||
0.351270 | + | 0.936274i | \(0.385750\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.18540 | 0.159469 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.4831 | 1.07282 | 0.536408 | − | 0.843959i | \(-0.319781\pi\) | ||||
0.536408 | + | 0.843959i | \(0.319781\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.5867 | −0.776430 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.63100 | 0.0810450 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.54636 | −0.126219 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.4490 | 1.55505 | 0.777526 | − | 0.628851i | \(-0.216475\pi\) | ||||
0.777526 | + | 0.628851i | \(0.216475\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.39887 | 0.463612 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.65453 | −0.130621 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.2448 | 0.650160 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.9337 | 0.829245 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.1679 | 1.42494 | 0.712472 | − | 0.701700i | \(-0.247575\pi\) | ||||
0.712472 | + | 0.701700i | \(0.247575\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.4349 | 1.04467 | 0.522335 | − | 0.852740i | \(-0.325061\pi\) | ||||
0.522335 | + | 0.852740i | \(0.325061\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.331760 | 0.0161307 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.38036 | −0.309493 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.76995 | 0.182441 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.24637 | −0.0601753 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.7575 | −0.903518 | −0.451759 | − | 0.892140i | \(-0.649203\pi\) | ||||
−0.451759 | + | 0.892140i | \(0.649203\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.7762 | −0.517871 | −0.258936 | − | 0.965895i | \(-0.583372\pi\) | ||||
−0.258936 | + | 0.965895i | \(0.583372\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.59900 | 0.172559 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.97748 | 0.381615 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.4831 | −1.45488 | −0.727439 | − | 0.686172i | \(-0.759290\pi\) | ||||
−0.727439 | + | 0.686172i | \(0.759290\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.06134 | −0.288635 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.25081 | 0.439519 | 0.219760 | − | 0.975554i | \(-0.429473\pi\) | ||||
0.219760 | + | 0.975554i | \(0.429473\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.26620 | −0.154833 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.33872 | 0.394408 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.1903 | 1.28319 | 0.641595 | − | 0.767044i | \(-0.278273\pi\) | ||||
0.641595 | + | 0.767044i | \(0.278273\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.618046 | 0.0291026 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.79467 | −0.225273 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.81774 | 0.178978 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.2266 | 1.36716 | 0.683582 | − | 0.729873i | \(-0.260421\pi\) | ||||
0.683582 | + | 0.729873i | \(0.260421\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.72683 | 0.127278 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.8966 | 1.57872 | 0.789362 | − | 0.613928i | \(-0.210412\pi\) | ||||
0.789362 | + | 0.613928i | \(0.210412\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.31649 | −0.432974 | −0.216487 | − | 0.976285i | \(-0.569460\pi\) | ||||
−0.216487 | + | 0.976285i | \(0.569460\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10.5223 | −0.487959 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.8899 | 1.10549 | 0.552746 | − | 0.833350i | \(-0.313580\pi\) | ||||
0.552746 | + | 0.833350i | \(0.313580\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.99603 | 0.230695 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.8380 | 0.545464 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.91406 | −0.271929 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.69302 | −0.352980 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.641025 | 0.0293505 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.8883 | 1.22856 | 0.614280 | − | 0.789089i | \(-0.289447\pi\) | ||||
0.614280 | + | 0.789089i | \(0.289447\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.9254 | 0.543749 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.35077 | 0.106964 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.14383 | −0.278977 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.3484 | −1.46584 | −0.732922 | − | 0.680313i | \(-0.761844\pi\) | ||||
−0.732922 | + | 0.680313i | \(0.761844\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.32206 | 0.0597858 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.80300 | 0.0813683 | 0.0406842 | − | 0.999172i | \(-0.487046\pi\) | ||||
0.0406842 | + | 0.999172i | \(0.487046\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.01710 | 0.270996 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.841398 | −0.0378180 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.17910 | −0.0528899 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.4536 | −0.781331 | −0.390665 | − | 0.920533i | \(-0.627755\pi\) | ||||
−0.390665 | + | 0.920533i | \(0.627755\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.3543 | 0.462595 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 28.1912 | 1.25449 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.16289 | −0.318115 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.56123 | 0.113524 | 0.0567622 | − | 0.998388i | \(-0.481922\pi\) | ||||
0.0567622 | + | 0.998388i | \(0.481922\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.84519 | 0.170101 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.28783 | 0.145161 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −24.4937 | −1.07932 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.171148 | −0.00752708 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 25.5438 | 1.12125 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −34.3833 | −1.50636 | −0.753180 | − | 0.657815i | \(-0.771481\pi\) | ||||
−0.753180 | + | 0.657815i | \(0.771481\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.53194 | −0.198168 | −0.0990841 | − | 0.995079i | \(-0.531591\pi\) | ||||
−0.0990841 | + | 0.995079i | \(0.531591\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.26694 | −0.0989375 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.5920 | −0.766317 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.1128 | −0.744033 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.73990 | −0.118902 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.89449 | −0.125374 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.55234 | −0.0671135 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.50943 | −0.410362 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.12692 | 0.134686 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.1880 | 0.609990 | 0.304995 | − | 0.952354i | \(-0.401345\pi\) | ||||
0.304995 | + | 0.952354i | \(0.401345\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −19.6579 | −0.843602 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.6667 | 0.799593 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.72334 | 0.244712 | 0.122356 | − | 0.992486i | \(-0.460955\pi\) | ||||
0.122356 | + | 0.992486i | \(0.460955\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.89119 | 0.166072 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.25502 | 0.309074 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.8240 | −0.630381 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.05056 | 0.341727 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.8068 | 0.966354 | 0.483177 | − | 0.875523i | \(-0.339483\pi\) | ||||
0.483177 | + | 0.875523i | \(0.339483\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27.6973 | 1.17147 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.40672 | −0.0593916 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −40.5967 | −1.71095 | −0.855474 | − | 0.517846i | \(-0.826734\pi\) | ||||
−0.855474 | + | 0.517846i | \(0.826734\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.5236 | −0.653083 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.968844 | 0.0406876 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.6650 | 0.656709 | 0.328355 | − | 0.944554i | \(-0.393506\pi\) | ||||
0.328355 | + | 0.944554i | \(0.393506\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.1409 | −0.424382 | −0.212191 | − | 0.977228i | \(-0.568060\pi\) | ||||
−0.212191 | + | 0.977228i | \(0.568060\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 25.5726 | 1.06831 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.67731 | −0.236760 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.6203 | −1.52452 | −0.762262 | − | 0.647268i | \(-0.775911\pi\) | ||||
−0.762262 | + | 0.647268i | \(0.775911\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.47283 | −0.0612089 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.86764 | 0.326405 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.330692 | −0.0136958 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.94051 | 0.162920 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.5892 | 0.973629 | 0.486815 | − | 0.873505i | \(-0.338159\pi\) | ||||
0.486815 | + | 0.873505i | \(0.338159\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.2112 | −0.873993 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.5426 | 0.680473 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.5607 | −0.515807 | −0.257904 | − | 0.966171i | \(-0.583032\pi\) | ||||
−0.257904 | + | 0.966171i | \(0.583032\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.30889 | 0.176647 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.3063 | −0.585517 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.6640 | 0.476579 | 0.238290 | − | 0.971194i | \(-0.423413\pi\) | ||||
0.238290 | + | 0.971194i | \(0.423413\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.7716 | −1.54074 | −0.770368 | − | 0.637600i | \(-0.779927\pi\) | ||||
−0.770368 | + | 0.637600i | \(0.779927\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.15669 | 0.209997 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.5069 | −0.711758 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.7414 | 1.65364 | 0.826820 | − | 0.562466i | \(-0.190147\pi\) | ||||
0.826820 | + | 0.562466i | \(0.190147\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.13788 | 0.0866311 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.801535 | 0.0324266 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.2493 | −1.34293 | −0.671463 | − | 0.741038i | \(-0.734334\pi\) | ||||
−0.671463 | + | 0.741038i | \(0.734334\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.95401 | −0.0787932 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.3766 | 1.34369 | 0.671845 | − | 0.740692i | \(-0.265502\pi\) | ||||
0.671845 | + | 0.740692i | \(0.265502\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.2922 | −1.49890 | −0.749450 | − | 0.662060i | \(-0.769682\pi\) | ||||
−0.749450 | + | 0.662060i | \(0.769682\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.42636 | 0.0973666 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.94018 | −0.0777318 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.82591 | −0.313036 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.69613 | −0.0677367 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.4595 | 0.536667 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.5076 | −1.09506 | −0.547531 | − | 0.836786i | \(-0.684432\pi\) | ||||
−0.547531 | + | 0.836786i | \(0.684432\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.517844 | −0.0205825 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.0349 | 0.398222 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.6443 | −0.580227 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.21702 | −0.0481445 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.2903 | 0.761919 | 0.380960 | − | 0.924592i | \(-0.375594\pi\) | ||||
0.380960 | + | 0.924592i | \(0.375594\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.96618 | 0.156411 | 0.0782054 | − | 0.996937i | \(-0.475081\pi\) | ||||
0.0782054 | + | 0.996937i | \(0.475081\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18.6978 | 0.736227 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.30261 | 0.208467 | 0.104234 | − | 0.994553i | \(-0.466761\pi\) | ||||
0.104234 | + | 0.994553i | \(0.466761\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.41346 | 0.0554831 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.25043 | −0.244973 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.4881 | 0.566964 | 0.283482 | − | 0.958978i | \(-0.408510\pi\) | ||||
0.283482 | + | 0.958978i | \(0.408510\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25.0960 | −0.980583 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.96885 | 0.154839 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.48530 | 0.0968134 | 0.0484067 | − | 0.998828i | \(-0.484586\pi\) | ||||
0.0484067 | + | 0.998828i | \(0.484586\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.2394 | 1.52624 | 0.763118 | − | 0.646259i | \(-0.223667\pi\) | ||||
0.763118 | + | 0.646259i | \(0.223667\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.58805 | 0.255859 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.19538 | 0.201468 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.35408 | 0.207311 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.28956 | 0.0885197 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.00738 | −0.0774941 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.1037 | −0.890583 | −0.445292 | − | 0.895386i | \(-0.646900\pi\) | ||||
−0.445292 | + | 0.895386i | \(0.646900\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.33984 | −0.0900606 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.8791 | 0.418120 | 0.209060 | − | 0.977903i | \(-0.432960\pi\) | ||||
0.209060 | + | 0.977903i | \(0.432960\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.64955 | −0.140057 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.05886 | 0.0405756 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −41.8702 | −1.60212 | −0.801060 | − | 0.598585i | \(-0.795730\pi\) | ||||
−0.801060 | + | 0.598585i | \(0.795730\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.3295 | 0.585712 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.23606 | −0.0471586 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.54872 | 0.0590017 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.01647 | −0.0386685 | −0.0193343 | − | 0.999813i | \(-0.506155\pi\) | ||||
−0.0193343 | + | 0.999813i | \(0.506155\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.499806 | −0.0189861 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 27.6188 | 1.04764 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.26686 | −0.123741 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.8090 | 0.749244 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.0986 | −0.456960 | −0.228480 | − | 0.973549i | \(-0.573375\pi\) | ||||
−0.228480 | + | 0.973549i | \(0.573375\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.2286 | 0.612075 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.541100 | 0.0203790 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.7461 | 0.629802 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.29914 | 0.0487903 | 0.0243951 | − | 0.999702i | \(-0.492234\pi\) | ||||
0.0243951 | + | 0.999702i | \(0.492234\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.3007 | −0.573822 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.6535 | −0.586229 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.03283 | −0.0760235 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27.2624 | −1.01813 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.5339 | 0.392847 | 0.196424 | − | 0.980519i | \(-0.437067\pi\) | ||||
0.196424 | + | 0.980519i | \(0.437067\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.5497 | −0.541860 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.3465 | 0.607934 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.16316 | −0.191755 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.4128 | −1.23921 | −0.619606 | − | 0.784913i | \(-0.712708\pi\) | ||||
−0.619606 | + | 0.784913i | \(0.712708\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.2605 | 1.15621 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.0612 | −0.519363 | −0.259682 | − | 0.965694i | \(-0.583618\pi\) | ||||
−0.259682 | + | 0.965694i | \(0.583618\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.88604 | −0.364652 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.66023 | −0.0979909 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.47844 | 0.0543854 | 0.0271927 | − | 0.999630i | \(-0.491343\pi\) | ||||
0.0271927 | + | 0.999630i | \(0.491343\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.94344 | 0.291810 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 42.2574 | 1.55027 | 0.775137 | − | 0.631794i | \(-0.217681\pi\) | ||||
0.775137 | + | 0.631794i | \(0.217681\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.6004 | 0.498282 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.12065 | 0.297119 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.922118 | −0.0336935 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.772760 | 0.0281984 | 0.0140992 | − | 0.999901i | \(-0.495512\pi\) | ||||
0.0140992 | + | 0.999901i | \(0.495512\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.02322 | −0.146614 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.82010 | −0.284602 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.5047 | −0.454491 | −0.227246 | − | 0.973837i | \(-0.572972\pi\) | ||||
−0.227246 | + | 0.973837i | \(0.572972\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.25171 | −0.0454342 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.2830 | 1.13401 | 0.567004 | − | 0.823715i | \(-0.308103\pi\) | ||||
0.567004 | + | 0.823715i | \(0.308103\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.0884 | 0.401425 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.44746 | 0.160798 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.61963 | −0.239021 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.52132 | −0.163043 | −0.0815214 | − | 0.996672i | \(-0.525978\pi\) | ||||
−0.0815214 | + | 0.996672i | \(0.525978\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.96131 | −0.106649 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.2992 | −0.370435 | −0.185217 | − | 0.982698i | \(-0.559299\pi\) | ||||
−0.185217 | + | 0.982698i | \(0.559299\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.0953 | 0.542240 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.78218 | 0.171560 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.93897 | −0.141128 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.627835 | 0.0224657 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.20663 | 0.0788584 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.3077 | 0.689121 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −53.0205 | −1.88998 | −0.944988 | − | 0.327105i | \(-0.893927\pi\) | ||||
−0.944988 | + | 0.327105i | \(0.893927\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.5063 | −0.694442 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.22131 | −0.327872 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.40115 | 0.333845 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.04551 | 0.0370805 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.1890 | 1.24646 | 0.623229 | − | 0.782040i | \(-0.285821\pi\) | ||||
0.623229 | + | 0.782040i | \(0.285821\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.904652 | 0.0320043 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.00258 | −0.0707576 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.04745 | −0.0722528 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.83410 | 0.135134 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.2657 | −0.642984 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.4985 | 0.685530 | 0.342765 | − | 0.939421i | \(-0.388637\pi\) | ||||
0.342765 | + | 0.939421i | \(0.388637\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.8768 | −1.40026 | −0.700131 | − | 0.714014i | \(-0.746875\pi\) | ||||
−0.700131 | + | 0.714014i | \(0.746875\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.41708 | −0.260128 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.15629 | 0.0755314 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 37.6919 | 1.31867 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.34074 | 0.0817920 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.9774 | 0.662314 | 0.331157 | − | 0.943576i | \(-0.392561\pi\) | ||||
0.331157 | + | 0.943576i | \(0.392561\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.6289 | −0.509932 | −0.254966 | − | 0.966950i | \(-0.582064\pi\) | ||||
−0.254966 | + | 0.966950i | \(0.582064\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.20708 | 0.0420250 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −41.6729 | −1.44911 | −0.724554 | − | 0.689218i | \(-0.757954\pi\) | ||||
−0.724554 | + | 0.689218i | \(0.757954\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −56.2693 | −1.95431 | −0.977157 | − | 0.212518i | \(-0.931834\pi\) | ||||
−0.977157 | + | 0.212518i | \(0.931834\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.9772 | 0.727691 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16.5283 | −0.572670 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.8878 | 0.584426 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.45143 | −0.222994 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.9995 | −0.863079 | −0.431540 | − | 0.902094i | \(-0.642030\pi\) | ||||
−0.431540 | + | 0.902094i | \(0.642030\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.1308 | −0.832097 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.11739 | −0.141811 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.6827 | −0.401896 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.3994 | −0.357329 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 30.4094 | 1.04365 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.9765 | 0.410548 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −47.5546 | −1.62824 | −0.814119 | − | 0.580699i | \(-0.802779\pi\) | ||||
−0.814119 | + | 0.580699i | \(0.802779\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.36245 | 0.183392 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.1854 | −0.996956 | −0.498478 | − | 0.866902i | \(-0.666108\pi\) | ||||
−0.498478 | + | 0.866902i | \(0.666108\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.0652 | 0.479897 | 0.239949 | − | 0.970786i | \(-0.422869\pi\) | ||||
0.239949 | + | 0.970786i | \(0.422869\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.16072 | −0.0395571 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 47.2171 | 1.60729 | 0.803645 | − | 0.595109i | \(-0.202891\pi\) | ||||
0.803645 | + | 0.595109i | \(0.202891\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 41.6619 | 1.41655 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.56440 | −0.324824 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.89333 | 0.267763 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.4586 | 0.422144 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.76692 | −0.127491 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.5983 | −0.392094 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.3622 | −0.586279 | −0.293139 | − | 0.956070i | \(-0.594700\pi\) | ||||
−0.293139 | + | 0.956070i | \(0.594700\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.8666 | −0.366522 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.0490 | −0.944995 | −0.472497 | − | 0.881332i | \(-0.656647\pi\) | ||||
−0.472497 | + | 0.881332i | \(0.656647\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.61175 | 0.155198 | 0.0775989 | − | 0.996985i | \(-0.475275\pi\) | ||||
0.0775989 | + | 0.996985i | \(0.475275\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.46877 | −0.150216 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −55.7404 | −1.87158 | −0.935789 | − | 0.352560i | \(-0.885311\pi\) | ||||
−0.935789 | + | 0.352560i | \(0.885311\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.96091 | 0.199922 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.515879 | −0.0172826 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.09077 | 0.0365012 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.5099 | −0.518437 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.86212 | 0.195731 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14.2359 | −0.474794 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.74797 | 0.0582332 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.1069 | 0.369613 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −32.0620 | −1.06578 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.83474 | 0.226944 | 0.113472 | − | 0.993541i | \(-0.463803\pi\) | ||||
0.113472 | + | 0.993541i | \(0.463803\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.2846 | 0.573295 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.2339 | 0.537852 | 0.268926 | − | 0.963161i | \(-0.413331\pi\) | ||||
0.268926 | + | 0.963161i | \(0.413331\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.18928 | −0.138645 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.34652 | 0.209809 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.9075 | −0.492289 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.2132 | 0.468849 | 0.234425 | − | 0.972134i | \(-0.424679\pi\) | ||||
0.234425 | + | 0.972134i | \(0.424679\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.21688 | −0.303707 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.94033 | −0.0967821 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.5494 | −0.379742 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15.0176 | −0.493243 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.00736 | −0.197095 | −0.0985476 | − | 0.995132i | \(-0.531420\pi\) | ||||
−0.0985476 | + | 0.995132i | \(0.531420\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.9287 | −0.653136 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23.0405 | −0.754313 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.29435 | −0.0750333 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.6118 | −1.13072 | −0.565359 | − | 0.824845i | \(-0.691262\pi\) | ||||
−0.565359 | + | 0.824845i | \(0.691262\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.5492 | 0.670597 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.2853 | 1.05247 | 0.526236 | − | 0.850339i | \(-0.323603\pi\) | ||||
0.526236 | + | 0.850339i | \(0.323603\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.90689 | −0.0946613 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.58018 | 0.0514033 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.3810 | −1.01974 | −0.509872 | − | 0.860250i | \(-0.670307\pi\) | ||||
−0.509872 | + | 0.860250i | \(0.670307\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.58878 | 0.311265 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −31.5199 | −1.02210 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.3376 | 1.24188 | 0.620939 | − | 0.783859i | \(-0.286752\pi\) | ||||
0.620939 | + | 0.783859i | \(0.286752\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 41.7089 | 1.34967 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.13835 | −0.0367977 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.10604 | 0.294049 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.6209 | 0.342611 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.951772 | −0.0306704 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.40219 | −0.0773293 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.5213 | 0.756393 | 0.378196 | − | 0.925725i | \(-0.376544\pi\) | ||||
0.378196 | + | 0.925725i | \(0.376544\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.96536 | 0.288009 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.12179 | −0.196458 | −0.0982288 | − | 0.995164i | \(-0.531318\pi\) | ||||
−0.0982288 | + | 0.995164i | \(0.531318\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.4061 | 0.525954 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.65309 | −0.181044 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.8354 | −0.986512 | −0.493256 | − | 0.869884i | \(-0.664194\pi\) | ||||
−0.493256 | + | 0.869884i | \(0.664194\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.03309 | 0.0330176 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.4449 | 0.365409 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 48.4649 | 1.54579 | 0.772895 | − | 0.634534i | \(-0.218808\pi\) | ||||
0.772895 | + | 0.634534i | \(0.218808\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.9810 | 0.859687 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.321423 | 0.0102310 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.8159 | 0.884496 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54.5862 | −1.73399 | −0.866993 | − | 0.498320i | \(-0.833951\pi\) | ||||
−0.866993 | + | 0.498320i | \(0.833951\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15.0690 | −0.478201 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.3335 | −0.739723 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.47038 | −0.0465674 | −0.0232837 | − | 0.999729i | \(-0.507412\pi\) | ||||
−0.0232837 | + | 0.999729i | \(0.507412\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.93597 | 0.156167 |
(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 | 6036.2.a.h.1.14 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6036.2.a.h.1.14 | ✓ | 24 | 1.1 | even | 1 | trivial |