Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3680,2,Mod(1,3680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3680.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3680 = 2^{5} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3680.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: | \(29.3849479438\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.876604.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 9x^{3} + 8x^{2} + 18x - 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.60527\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3680.1 |
$q$-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 | ||||||||
\(3\) | −0.352411 | −0.203465 | −0.101732 | − | 0.994812i | \(-0.532439\pi\) | ||||
−0.101732 | + | 0.994812i | \(0.532439\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.95190 | 1.49368 | 0.746840 | − | 0.665004i | \(-0.231570\pi\) | ||||
0.746840 | + | 0.665004i | \(0.231570\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.87581 | −0.958602 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.63905 | 1.70024 | 0.850118 | − | 0.526592i | \(-0.176530\pi\) | ||||
0.850118 | + | 0.526592i | \(0.176530\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.53457 | 0.702963 | 0.351481 | − | 0.936195i | \(-0.385678\pi\) | ||||
0.351481 | + | 0.936195i | \(0.385678\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.352411 | −0.0909922 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.26403 | 0.306573 | 0.153286 | − | 0.988182i | \(-0.451014\pi\) | ||||
0.153286 | + | 0.988182i | \(0.451014\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.83349 | −1.56771 | −0.783855 | − | 0.620944i | \(-0.786749\pi\) | ||||
−0.783855 | + | 0.620944i | \(0.786749\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.39270 | −0.303911 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.07070 | 0.398506 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.69701 | 1.42930 | 0.714650 | − | 0.699483i | \(-0.246586\pi\) | ||||
0.714650 | + | 0.699483i | \(0.246586\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.04028 | 1.62368 | 0.811842 | − | 0.583878i | \(-0.198465\pi\) | ||||
0.811842 | + | 0.583878i | \(0.198465\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.98726 | −0.345938 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.95190 | 0.667994 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.90308 | −0.477263 | −0.238632 | − | 0.971110i | \(-0.576699\pi\) | ||||
−0.238632 | + | 0.971110i | \(0.576699\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.893211 | −0.143028 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.188663 | 0.0294643 | 0.0147321 | − | 0.999891i | \(-0.495310\pi\) | ||||
0.0147321 | + | 0.999891i | \(0.495310\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.97692 | −0.453976 | −0.226988 | − | 0.973898i | \(-0.572888\pi\) | ||||
−0.226988 | + | 0.973898i | \(0.572888\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.87581 | −0.428700 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.82698 | 0.704088 | 0.352044 | − | 0.935984i | \(-0.385487\pi\) | ||||
0.352044 | + | 0.935984i | \(0.385487\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.61755 | 1.23108 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.445459 | −0.0623767 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.328956 | 0.0451856 | 0.0225928 | − | 0.999745i | \(-0.492808\pi\) | ||||
0.0225928 | + | 0.999745i | \(0.492808\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.63905 | 0.760369 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.40820 | 0.318974 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.966221 | 0.125791 | 0.0628957 | − | 0.998020i | \(-0.479966\pi\) | ||||
0.0628957 | + | 0.998020i | \(0.479966\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.31009 | 0.167740 | 0.0838700 | − | 0.996477i | \(-0.473272\pi\) | ||||
0.0838700 | + | 0.996477i | \(0.473272\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11.3649 | −1.43184 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.53457 | 0.314375 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.94987 | −0.482553 | −0.241277 | − | 0.970456i | \(-0.577566\pi\) | ||||
−0.241277 | + | 0.970456i | \(0.577566\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.352411 | 0.0424253 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.69365 | −0.913068 | −0.456534 | − | 0.889706i | \(-0.650909\pi\) | ||||
−0.456534 | + | 0.889706i | \(0.650909\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.617173 | 0.0722346 | 0.0361173 | − | 0.999348i | \(-0.488501\pi\) | ||||
0.0361173 | + | 0.999348i | \(0.488501\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.352411 | −0.0406929 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 22.2850 | 2.53961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.1828 | −1.70819 | −0.854097 | − | 0.520114i | \(-0.825889\pi\) | ||||
−0.854097 | + | 0.520114i | \(0.825889\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.89768 | 0.877520 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.30673 | 0.143432 | 0.0717161 | − | 0.997425i | \(-0.477152\pi\) | ||||
0.0717161 | + | 0.997425i | \(0.477152\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.26403 | 0.137103 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.71251 | −0.290812 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.3242 | −1.83636 | −0.918178 | − | 0.396167i | \(-0.870340\pi\) | ||||
−0.918178 | + | 0.396167i | \(0.870340\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.0164 | 1.05000 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.18590 | −0.330362 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.83349 | −0.701101 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.26476 | 0.839159 | 0.419580 | − | 0.907718i | \(-0.362177\pi\) | ||||
0.419580 | + | 0.907718i | \(0.362177\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −16.2168 | −1.62985 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.8545 | 1.77659 | 0.888296 | − | 0.459271i | \(-0.151889\pi\) | ||||
0.888296 | + | 0.459271i | \(0.151889\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.0624 | −1.77974 | −0.889872 | − | 0.456210i | \(-0.849207\pi\) | ||||
−0.889872 | + | 0.456210i | \(0.849207\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.39270 | −0.135913 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.7747 | −1.23498 | −0.617488 | − | 0.786580i | \(-0.711850\pi\) | ||||
−0.617488 | + | 0.786580i | \(0.711850\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.7596 | 1.41372 | 0.706859 | − | 0.707355i | \(-0.250112\pi\) | ||||
0.706859 | + | 0.707355i | \(0.250112\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.02308 | 0.0971062 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.11666 | −0.857623 | −0.428812 | − | 0.903394i | \(-0.641068\pi\) | ||||
−0.428812 | + | 0.903394i | \(0.641068\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.28893 | −0.673862 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.99533 | 0.457921 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.7989 | 1.89081 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.0664871 | −0.00599494 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.87377 | 0.343742 | 0.171871 | − | 0.985120i | \(-0.445019\pi\) | ||||
0.171871 | + | 0.985120i | \(0.445019\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.04910 | 0.0923682 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.55488 | 0.223221 | 0.111610 | − | 0.993752i | \(-0.464399\pi\) | ||||
0.111610 | + | 0.993752i | \(0.464399\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −27.0053 | −2.34166 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.07070 | 0.178217 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.37778 | 0.288583 | 0.144292 | − | 0.989535i | \(-0.453910\pi\) | ||||
0.144292 | + | 0.989535i | \(0.453910\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.41965 | 0.120413 | 0.0602064 | − | 0.998186i | \(-0.480824\pi\) | ||||
0.0602064 | + | 0.998186i | \(0.480824\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.70108 | −0.143257 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.2926 | 1.19520 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.69701 | 0.639202 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.03692 | −0.250481 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.3961 | 1.09745 | 0.548724 | − | 0.836004i | \(-0.315114\pi\) | ||||
0.548724 | + | 0.836004i | \(0.315114\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.6090 | −1.10749 | −0.553743 | − | 0.832688i | \(-0.686801\pi\) | ||||
−0.553743 | + | 0.832688i | \(0.686801\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.63511 | −0.293881 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.04028 | 0.726133 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.8029 | 1.58045 | 0.790223 | − | 0.612819i | \(-0.209965\pi\) | ||||
0.790223 | + | 0.612819i | \(0.209965\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.115928 | −0.00919367 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.95190 | −0.311454 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.4606 | 1.60260 | 0.801300 | − | 0.598263i | \(-0.204142\pi\) | ||||
0.801300 | + | 0.598263i | \(0.204142\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.98726 | −0.154708 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.1227 | −1.55714 | −0.778569 | − | 0.627559i | \(-0.784054\pi\) | ||||
−0.778569 | + | 0.627559i | \(0.784054\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.57596 | −0.505843 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 19.6518 | 1.50281 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 24.2937 | 1.84702 | 0.923509 | − | 0.383576i | \(-0.125308\pi\) | ||||
0.923509 | + | 0.383576i | \(0.125308\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.95190 | 0.298736 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.340507 | −0.0255941 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.3672 | 1.14860 | 0.574299 | − | 0.818645i | \(-0.305275\pi\) | ||||
0.574299 | + | 0.818645i | \(0.305275\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0440 | −1.04388 | −0.521942 | − | 0.852981i | \(-0.674792\pi\) | ||||
−0.521942 | + | 0.852981i | \(0.674792\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.461691 | −0.0341292 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.90308 | −0.213439 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.12793 | 0.521246 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.18321 | 0.595241 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.51098 | 0.181688 | 0.0908441 | − | 0.995865i | \(-0.471044\pi\) | ||||
0.0908441 | + | 0.995865i | \(0.471044\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.6016 | 1.33897 | 0.669484 | − | 0.742826i | \(-0.266515\pi\) | ||||
0.669484 | + | 0.742826i | \(0.266515\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.893211 | −0.0639641 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.8033 | −1.26843 | −0.634216 | − | 0.773156i | \(-0.718677\pi\) | ||||
−0.634216 | + | 0.773156i | \(0.718677\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.14740 | 0.648442 | 0.324221 | − | 0.945981i | \(-0.394898\pi\) | ||||
0.324221 | + | 0.945981i | \(0.394898\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.39198 | 0.0981826 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 30.4179 | 2.13491 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.188663 | 0.0131768 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.87581 | 0.199882 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −38.5344 | −2.66548 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.6161 | 1.28159 | 0.640793 | − | 0.767714i | \(-0.278606\pi\) | ||||
0.640793 | + | 0.767714i | \(0.278606\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.71133 | 0.185777 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.97692 | −0.203024 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 35.7263 | 2.42526 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.217499 | −0.0146972 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.20377 | 0.215509 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.7475 | 1.05453 | 0.527267 | − | 0.849700i | \(-0.323217\pi\) | ||||
0.527267 | + | 0.849700i | \(0.323217\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.87581 | −0.191720 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.28041 | −0.0849835 | −0.0424918 | − | 0.999097i | \(-0.513530\pi\) | ||||
−0.0424918 | + | 0.999097i | \(0.513530\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.257424 | −0.0170110 | −0.00850552 | − | 0.999964i | \(-0.502707\pi\) | ||||
−0.00850552 | + | 0.999964i | \(0.502707\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.85348 | −0.516721 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.2036 | 0.799483 | 0.399741 | − | 0.916628i | \(-0.369100\pi\) | ||||
0.399741 | + | 0.916628i | \(0.369100\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.82698 | 0.314878 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.35057 | 0.347557 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.31120 | −0.472922 | −0.236461 | − | 0.971641i | \(-0.575988\pi\) | ||||
−0.236461 | + | 0.971641i | \(0.575988\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.7293 | −0.755548 | −0.377774 | − | 0.925898i | \(-0.623310\pi\) | ||||
−0.377774 | + | 0.925898i | \(0.623310\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.99533 | −0.577051 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.61755 | 0.550555 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.3199 | −1.10204 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.460506 | −0.0291834 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.21099 | −0.392034 | −0.196017 | − | 0.980600i | \(-0.562801\pi\) | ||||
−0.196017 | + | 0.980600i | \(0.562801\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.63905 | −0.354524 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.445459 | −0.0278957 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.0382 | 1.68660 | 0.843300 | − | 0.537443i | \(-0.180610\pi\) | ||||
0.843300 | + | 0.537443i | \(0.180610\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.4727 | −0.712878 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −22.1351 | −1.37013 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.3100 | −1.37569 | −0.687846 | − | 0.725857i | \(-0.741444\pi\) | ||||
−0.687846 | + | 0.725857i | \(0.741444\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.328956 | 0.0202076 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.10523 | 0.373634 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.2720 | −0.870178 | −0.435089 | − | 0.900387i | \(-0.643283\pi\) | ||||
−0.435089 | + | 0.900387i | \(0.643283\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.0785 | −1.09819 | −0.549096 | − | 0.835759i | \(-0.685028\pi\) | ||||
−0.549096 | + | 0.835759i | \(0.685028\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.52988 | −0.213638 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.63905 | 0.340047 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.97476 | 0.298905 | 0.149452 | − | 0.988769i | \(-0.452249\pi\) | ||||
0.149452 | + | 0.988769i | \(0.452249\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −25.9981 | −1.55647 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.15895 | −0.307757 | −0.153878 | − | 0.988090i | \(-0.549176\pi\) | ||||
−0.153878 | + | 0.988090i | \(0.549176\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.8800 | 0.706193 | 0.353096 | − | 0.935587i | \(-0.385129\pi\) | ||||
0.353096 | + | 0.935587i | \(0.385129\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.40820 | 0.142649 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.745580 | 0.0440102 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.4022 | −0.906013 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.91259 | −0.170739 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.0075 | −1.40253 | −0.701266 | − | 0.712900i | \(-0.747381\pi\) | ||||
−0.701266 | + | 0.712900i | \(0.747381\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.966221 | 0.0562556 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.6768 | 0.677555 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.53457 | −0.146578 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.7645 | −0.678095 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.29214 | −0.361474 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.31009 | 0.0750156 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.8389 | 1.18934 | 0.594669 | − | 0.803971i | \(-0.297283\pi\) | ||||
0.594669 | + | 0.803971i | \(0.297283\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.36540 | 0.362115 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.6092 | 1.33875 | 0.669376 | − | 0.742924i | \(-0.266562\pi\) | ||||
0.669376 | + | 0.742924i | \(0.266562\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.7933 | 0.892692 | 0.446346 | − | 0.894861i | \(-0.352725\pi\) | ||||
0.446346 | + | 0.894861i | \(0.352725\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11.3649 | −0.640340 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −32.3058 | −1.81447 | −0.907236 | − | 0.420621i | \(-0.861812\pi\) | ||||
−0.907236 | + | 0.420621i | \(0.861812\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 43.4038 | 2.43015 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.50194 | 0.251274 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.63774 | −0.480617 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.53457 | 0.140593 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.20146 | −0.287642 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.0758 | 1.05168 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.4140 | −0.792265 | −0.396132 | − | 0.918193i | \(-0.629648\pi\) | ||||
−0.396132 | + | 0.918193i | \(0.629648\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.34869 | 0.457506 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.94987 | −0.215804 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.34929 | 0.509288 | 0.254644 | − | 0.967035i | \(-0.418042\pi\) | ||||
0.254644 | + | 0.967035i | \(0.418042\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.21281 | 0.174496 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 50.9786 | 2.76065 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.39240 | 0.345157 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.352411 | 0.0189732 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.13655 | 0.0610133 | 0.0305067 | − | 0.999535i | \(-0.490288\pi\) | ||||
0.0305067 | + | 0.999535i | \(0.490288\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.75535 | −0.468663 | −0.234332 | − | 0.972157i | \(-0.575290\pi\) | ||||
−0.234332 | + | 0.972157i | \(0.575290\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.24833 | 0.280135 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.1257 | 1.17763 | 0.588815 | − | 0.808268i | \(-0.299595\pi\) | ||||
0.588815 | + | 0.808268i | \(0.299595\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.69365 | −0.408336 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.76041 | −0.0931708 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.55850 | 0.451700 | 0.225850 | − | 0.974162i | \(-0.427484\pi\) | ||||
0.225850 | + | 0.974162i | \(0.427484\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.6965 | 1.45771 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.32975 | −0.384712 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.617173 | 0.0323043 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.4672 | −0.650784 | −0.325392 | − | 0.945579i | \(-0.605496\pi\) | ||||
−0.325392 | + | 0.945579i | \(0.605496\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.542559 | −0.0282445 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.30000 | 0.0674928 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.6684 | 0.914837 | 0.457418 | − | 0.889252i | \(-0.348774\pi\) | ||||
0.457418 | + | 0.889252i | \(0.348774\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.352411 | −0.0181984 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.5086 | 1.00474 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.67680 | 0.342964 | 0.171482 | − | 0.985187i | \(-0.445144\pi\) | ||||
0.171482 | + | 0.985187i | \(0.445144\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.36516 | −0.0699393 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.27134 | −0.218256 | −0.109128 | − | 0.994028i | \(-0.534806\pi\) | ||||
−0.109128 | + | 0.994028i | \(0.534806\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 22.2850 | 1.13575 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.56105 | 0.435183 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.4378 | −0.732023 | −0.366011 | − | 0.930610i | \(-0.619277\pi\) | ||||
−0.366011 | + | 0.930610i | \(0.619277\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.26403 | −0.0639248 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.900369 | −0.0454176 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.1828 | −0.763927 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.49861 | 0.476722 | 0.238361 | − | 0.971177i | \(-0.423390\pi\) | ||||
0.238361 | + | 0.971177i | \(0.423390\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.51697 | 0.476444 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.6884 | −1.58244 | −0.791221 | − | 0.611530i | \(-0.790554\pi\) | ||||
−0.791221 | + | 0.611530i | \(0.790554\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.9132 | 1.14139 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.89768 | 0.392439 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.3706 | −0.811461 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.2552 | −1.29824 | −0.649119 | − | 0.760687i | \(-0.724862\pi\) | ||||
−0.649119 | + | 0.760687i | \(0.724862\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.19037 | −0.0587165 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.81841 | 0.187892 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.30673 | 0.0641448 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.500299 | −0.0244998 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.3855 | 1.24016 | 0.620082 | − | 0.784537i | \(-0.287099\pi\) | ||||
0.620082 | + | 0.784537i | \(0.287099\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.2678 | 0.792846 | 0.396423 | − | 0.918068i | \(-0.370251\pi\) | ||||
0.396423 | + | 0.918068i | \(0.370251\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.8815 | −0.674940 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.26403 | 0.0613145 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.17736 | 0.250550 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.03686 | −0.243182 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.2534 | −1.07191 | −0.535953 | − | 0.844248i | \(-0.680048\pi\) | ||||
−0.535953 | + | 0.844248i | \(0.680048\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.72589 | 0.323226 | 0.161613 | − | 0.986854i | \(-0.448330\pi\) | ||||
0.161613 | + | 0.986854i | \(0.448330\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.71251 | −0.130055 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.83349 | 0.326890 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.3391 | −0.541188 | −0.270594 | − | 0.962694i | \(-0.587220\pi\) | ||||
−0.270594 | + | 0.962694i | \(0.587220\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −24.7824 | −1.18011 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.39714 | 0.303937 | 0.151969 | − | 0.988385i | \(-0.451439\pi\) | ||||
0.151969 | + | 0.988385i | \(0.451439\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17.3242 | −0.821244 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.72092 | −0.223292 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.84945 | 0.417631 | 0.208816 | − | 0.977955i | \(-0.433039\pi\) | ||||
0.208816 | + | 0.977955i | \(0.433039\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.06388 | 0.0500962 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.79597 | 0.225334 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.0164 | 0.469575 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.8347 | 1.34883 | 0.674415 | − | 0.738353i | \(-0.264396\pi\) | ||||
0.674415 | + | 0.738353i | \(0.264396\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.61743 | 0.122171 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.5500 | −1.32970 | −0.664852 | − | 0.746975i | \(-0.731505\pi\) | ||||
−0.664852 | + | 0.746975i | \(0.731505\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.4923 | 1.27768 | 0.638838 | − | 0.769341i | \(-0.279415\pi\) | ||||
0.638838 | + | 0.769341i | \(0.279415\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.18590 | −0.147742 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −34.0356 | −1.57498 | −0.787490 | − | 0.616327i | \(-0.788620\pi\) | ||||
−0.787490 | + | 0.616327i | \(0.788620\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.6095 | −0.720780 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.97878 | −0.321565 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.7870 | −0.771867 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.83349 | −0.313542 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.946014 | −0.0433150 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.53712 | −0.344380 | −0.172190 | − | 0.985064i | \(-0.555084\pi\) | ||||
−0.172190 | + | 0.985064i | \(0.555084\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.35805 | −0.335498 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.39270 | 0.0633698 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.26476 | 0.375283 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.6238 | 1.11581 | 0.557906 | − | 0.829904i | \(-0.311605\pi\) | ||||
0.557906 | + | 0.829904i | \(0.311605\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.21056 | −0.326073 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.0638 | 0.634692 | 0.317346 | − | 0.948310i | \(-0.397208\pi\) | ||||
0.317346 | + | 0.948310i | \(0.397208\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.72927 | 0.438184 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −16.2168 | −0.728891 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −30.4046 | −1.36383 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.5470 | −1.18841 | −0.594204 | − | 0.804315i | \(-0.702533\pi\) | ||||
−0.594204 | + | 0.804315i | \(0.702533\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.09145 | 0.316823 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −36.3219 | −1.61952 | −0.809758 | − | 0.586764i | \(-0.800401\pi\) | ||||
−0.809758 | + | 0.586764i | \(0.800401\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.8545 | 0.794516 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.31744 | 0.102921 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.72157 | 0.0763074 | 0.0381537 | − | 0.999272i | \(-0.487852\pi\) | ||||
0.0381537 | + | 0.999272i | \(0.487852\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.43901 | 0.107895 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −14.1501 | −0.624742 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −18.0624 | −0.795926 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.2196 | 1.19712 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.56139 | −0.375803 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −45.2230 | −1.98126 | −0.990629 | − | 0.136582i | \(-0.956388\pi\) | ||||
−0.990629 | + | 0.136582i | \(0.956388\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.2150 | 1.19003 | 0.595013 | − | 0.803716i | \(-0.297147\pi\) | ||||
0.595013 | + | 0.803716i | \(0.297147\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.39270 | −0.0607822 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.4272 | 0.497777 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.77867 | −0.120584 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.478180 | 0.0207123 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.7747 | −0.552298 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.41558 | −0.233699 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 48.5948 | 2.09313 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.81174 | −0.249866 | −0.124933 | − | 0.992165i | \(-0.539872\pi\) | ||||
−0.124933 | + | 0.992165i | \(0.539872\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.94927 | 0.212394 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.7596 | 0.632234 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.4942 | 1.09005 | 0.545027 | − | 0.838419i | \(-0.316519\pi\) | ||||
0.545027 | + | 0.838419i | \(0.316519\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.76757 | −0.160796 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −52.5974 | −2.24073 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −60.0008 | −2.55149 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.02308 | 0.0434272 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.522188 | −0.0221258 | −0.0110629 | − | 0.999939i | \(-0.503522\pi\) | ||||
−0.0110629 | + | 0.999939i | \(0.503522\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.54521 | −0.319129 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.51196 | −0.106055 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.8837 | −0.964432 | −0.482216 | − | 0.876052i | \(-0.660168\pi\) | ||||
−0.482216 | + | 0.876052i | \(0.660168\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.11666 | −0.383541 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 31.2109 | 1.31073 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.19530 | −0.0920319 | −0.0460159 | − | 0.998941i | \(-0.514652\pi\) | ||||
−0.0460159 | + | 0.998941i | \(0.514652\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.5189 | 0.774991 | 0.387495 | − | 0.921872i | \(-0.373340\pi\) | ||||
0.387495 | + | 0.921872i | \(0.373340\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.884898 | −0.0369671 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.5975 | −1.27379 | −0.636895 | − | 0.770951i | \(-0.719781\pi\) | ||||
−0.636895 | + | 0.770951i | \(0.719781\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.55540 | −0.272433 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.16407 | 0.214242 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.85500 | 0.0768262 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.28893 | −0.301360 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.0369 | −0.579365 | −0.289683 | − | 0.957123i | \(-0.593550\pi\) | ||||
−0.289683 | + | 0.957123i | \(0.593550\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −61.7767 | −2.54546 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.27408 | 0.258081 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.1236 | −0.826376 | −0.413188 | − | 0.910646i | \(-0.635585\pi\) | ||||
−0.413188 | + | 0.910646i | \(0.635585\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.99533 | 0.204789 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.22365 | −0.131935 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.1489 | 1.43615 | 0.718073 | − | 0.695968i | \(-0.245025\pi\) | ||||
0.718073 | + | 0.695968i | \(0.245025\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.1732 | −0.537346 | −0.268673 | − | 0.963231i | \(-0.586585\pi\) | ||||
−0.268673 | + | 0.963231i | \(0.586585\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.3591 | 0.462577 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20.7989 | 0.845594 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.4291 | −1.35685 | −0.678423 | − | 0.734672i | \(-0.737336\pi\) | ||||
−0.678423 | + | 0.734672i | \(0.737336\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.7196 | −0.434380 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.2343 | 0.494947 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.1013 | −0.731103 | −0.365551 | − | 0.930791i | \(-0.619120\pi\) | ||||
−0.365551 | + | 0.930791i | \(0.619120\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.0664871 | −0.00268102 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.09327 | 0.164789 | 0.0823944 | − | 0.996600i | \(-0.473743\pi\) | ||||
0.0823944 | + | 0.996600i | \(0.473743\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.9861 | −1.20525 | −0.602623 | − | 0.798026i | \(-0.705878\pi\) | ||||
−0.602623 | + | 0.798026i | \(0.705878\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.07070 | −0.0830943 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −68.4634 | −2.74293 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.5799 | 0.542331 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.66958 | −0.146316 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.5829 | −1.49615 | −0.748077 | − | 0.663612i | \(-0.769022\pi\) | ||||
−0.748077 | + | 0.663612i | \(0.769022\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.56053 | −0.260758 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.87377 | 0.153726 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.8418 | 0.865403 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 22.1254 | 0.875269 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.9195 | 1.14225 | 0.571126 | − | 0.820863i | \(-0.306507\pi\) | ||||
0.571126 | + | 0.820863i | \(0.306507\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.05771 | −0.160020 | −0.0800102 | − | 0.996794i | \(-0.525495\pi\) | ||||
−0.0800102 | + | 0.996794i | \(0.525495\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.04910 | 0.0413083 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.81376 | 0.110621 | 0.0553103 | − | 0.998469i | \(-0.482385\pi\) | ||||
0.0553103 | + | 0.998469i | \(0.482385\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.44857 | 0.213875 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.5904 | −0.493455 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.7672 | 0.930083 | 0.465041 | − | 0.885289i | \(-0.346039\pi\) | ||||
0.465041 | + | 0.885289i | \(0.346039\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.55488 | 0.0998275 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.77487 | −0.0692443 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.2518 | −0.866807 | −0.433403 | − | 0.901200i | \(-0.642687\pi\) | ||||
−0.433403 | + | 0.901200i | \(0.642687\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.0505 | 1.75226 | 0.876131 | − | 0.482074i | \(-0.160116\pi\) | ||||
0.876131 | + | 0.482074i | \(0.160116\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.12905 | −0.0438485 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −27.0053 | −1.04722 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.69701 | −0.298029 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.54961 | −0.214560 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.38767 | 0.285198 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −38.8944 | −1.49927 | −0.749635 | − | 0.661851i | \(-0.769771\pi\) | ||||
−0.749635 | + | 0.661851i | \(0.769771\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.07070 | 0.0797013 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.7421 | 1.18151 | 0.590757 | − | 0.806849i | \(-0.298829\pi\) | ||||
0.590757 | + | 0.806849i | \(0.298829\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.6616 | 1.25344 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.451229 | 0.0172911 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −50.7299 | −1.94113 | −0.970564 | − | 0.240844i | \(-0.922576\pi\) | ||||
−0.970564 | + | 0.240844i | \(0.922576\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.37778 | 0.129058 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.0907190 | 0.00346114 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.833762 | 0.0317638 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.3810 | −0.432954 | −0.216477 | − | 0.976288i | \(-0.569457\pi\) | ||||
−0.216477 | + | 0.976288i | \(0.569457\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −64.0873 | −2.43447 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.41965 | 0.0538503 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.238476 | 0.00903294 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.30068 | −0.162667 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.38246 | −0.0522149 | −0.0261074 | − | 0.999659i | \(-0.508311\pi\) | ||||
−0.0261074 | + | 0.999659i | \(0.508311\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.8382 | 0.748210 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.70108 | −0.0640665 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 70.5594 | 2.65366 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.4080 | −1.32978 | −0.664888 | − | 0.746944i | \(-0.731521\pi\) | ||||
−0.664888 | + | 0.746944i | \(0.731521\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 43.6627 | 1.63748 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.04028 | −0.338561 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.2926 | 0.534511 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.57655 | 0.0962230 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.0867 | 0.376169 | 0.188085 | − | 0.982153i | \(-0.439772\pi\) | ||||
0.188085 | + | 0.982153i | \(0.439772\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −71.3810 | −2.65837 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.13352 | 0.153727 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.69701 | 0.285860 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.4646 | −0.499374 | −0.249687 | − | 0.968327i | \(-0.580328\pi\) | ||||
−0.249687 | + | 0.968327i | \(0.580328\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.5230 | −0.760111 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.76292 | −0.139177 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.2923 | 0.712577 | 0.356289 | − | 0.934376i | \(-0.384042\pi\) | ||||
0.356289 | + | 0.934376i | \(0.384042\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.03692 | −0.112019 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.2735 | −0.820455 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −41.9597 | −1.54351 | −0.771756 | − | 0.635918i | \(-0.780621\pi\) | ||||
−0.771756 | + | 0.635918i | \(0.780621\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.10374 | 0.224227 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.2397 | 0.962640 | 0.481320 | − | 0.876545i | \(-0.340157\pi\) | ||||
0.481320 | + | 0.876545i | \(0.340157\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.3961 | 0.490794 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.75790 | −0.137494 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −50.4844 | −1.84466 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −43.8563 | −1.60034 | −0.800170 | − | 0.599773i | \(-0.795258\pi\) | ||||
−0.800170 | + | 0.599773i | \(0.795258\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.18882 | 0.0797652 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.6090 | −0.495283 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.2435 | 0.953835 | 0.476918 | − | 0.878948i | \(-0.341754\pi\) | ||||
0.476918 | + | 0.878948i | \(0.341754\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.98726 | 0.0721331 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −45.7738 | −1.65930 | −0.829650 | − | 0.558283i | \(-0.811460\pi\) | ||||
−0.829650 | + | 0.558283i | \(0.811460\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 58.3287 | 2.11164 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.63511 | −0.131428 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.44895 | 0.0884266 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.7930 | 0.966181 | 0.483091 | − | 0.875570i | \(-0.339514\pi\) | ||||
0.483091 | + | 0.875570i | \(0.339514\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.52858 | −0.343164 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −40.8103 | −1.46784 | −0.733922 | − | 0.679234i | \(-0.762312\pi\) | ||||
−0.733922 | + | 0.679234i | \(0.762312\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.04028 | 0.324737 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.04311 | 0.145046 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.28923 | −0.0461914 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −43.3849 | −1.55243 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15.9382 | 0.569585 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.8029 | 0.706797 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.34419 | 0.261792 | 0.130896 | − | 0.991396i | \(-0.458215\pi\) | ||||
0.130896 | + | 0.991396i | \(0.458215\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.86228 | 0.279905 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −36.0282 | −1.28101 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.32052 | 0.117915 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.115928 | −0.00411154 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.62790 | −0.128507 | −0.0642535 | − | 0.997934i | \(-0.520467\pi\) | ||||
−0.0642535 | + | 0.997934i | \(0.520467\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.10146 | 0.215854 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 49.8209 | 1.76034 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.48027 | 0.122816 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.95190 | −0.139286 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.02961 | 0.177051 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.82493 | 0.310268 | 0.155134 | − | 0.987893i | \(-0.450419\pi\) | ||||
0.155134 | + | 0.987893i | \(0.450419\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.9422 | −0.630035 | −0.315018 | − | 0.949086i | \(-0.602010\pi\) | ||||
−0.315018 | + | 0.949086i | \(0.602010\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.37108 | 0.223443 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.4606 | 0.716705 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.3428 | 0.711703 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −28.8052 | −1.00653 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.7051 | −1.35082 | −0.675409 | − | 0.737444i | \(-0.736033\pi\) | ||||
−0.675409 | + | 0.737444i | \(0.736033\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.7406 | −0.897259 | −0.448630 | − | 0.893718i | \(-0.648088\pi\) | ||||
−0.448630 | + | 0.893718i | \(0.648088\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.98726 | −0.0691876 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 54.3061 | 1.88841 | 0.944205 | − | 0.329359i | \(-0.106833\pi\) | ||||
0.944205 | + | 0.329359i | \(0.106833\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.6143 | 1.54952 | 0.774759 | − | 0.632257i | \(-0.217871\pi\) | ||||
0.774759 | + | 0.632257i | \(0.217871\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.75316 | −0.0608165 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.8929 | 0.377415 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20.1227 | −0.696373 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.7197 | 0.647048 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.1843 | −0.903984 | −0.451992 | − | 0.892022i | \(-0.649286\pi\) | ||||
−0.451992 | + | 0.892022i | \(0.649286\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30.2440 | 1.04290 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.81807 | 0.0626177 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.57596 | −0.226220 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 82.1951 | 2.82426 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.18665 | −0.143685 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.90308 | 0.0995163 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.97182 | 0.307189 | 0.153595 | − | 0.988134i | \(-0.450915\pi\) | ||||
0.153595 | + | 0.988134i | \(0.450915\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 19.6518 | 0.672077 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.25709 | 0.247898 | 0.123949 | − | 0.992289i | \(-0.460444\pi\) | ||||
0.123949 | + | 0.992289i | \(0.460444\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.9010 | −1.19081 | −0.595403 | − | 0.803427i | \(-0.703007\pi\) | ||||
−0.595403 | + | 0.803427i | \(0.703007\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.262751 | −0.00895452 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.7663 | 0.536690 | 0.268345 | − | 0.963323i | \(-0.413523\pi\) | ||||
0.268345 | + | 0.963323i | \(0.413523\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.2937 | 0.826012 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.42792 | 0.184342 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −85.6163 | −2.90433 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.0112 | −0.339217 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −23.7679 | −0.804420 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.95190 | 0.133599 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.07478 | −0.103828 | −0.0519139 | − | 0.998652i | \(-0.516532\pi\) | ||||
−0.0519139 | + | 0.998652i | \(0.516532\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.46051 | 0.285366 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.27798 | 0.278892 | 0.139446 | − | 0.990230i | \(-0.455468\pi\) | ||||
0.139446 | + | 0.990230i | \(0.455468\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.5521 | 0.388758 | 0.194379 | − | 0.980927i | \(-0.437731\pi\) | ||||
0.194379 | + | 0.980927i | \(0.437731\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.340507 | −0.0114460 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −44.6832 | −1.50031 | −0.750157 | − | 0.661260i | \(-0.770022\pi\) | ||||
−0.750157 | + | 0.661260i | \(0.770022\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.3088 | 0.513440 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 44.5354 | 1.49199 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −32.9851 | −1.10380 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.3672 | 0.513669 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.893211 | 0.0298234 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 69.5832 | 2.32073 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.415811 | 0.0138527 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.14595 | 0.137968 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.0440 | −0.466839 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.55427 | −0.184426 | −0.0922132 | − | 0.995739i | \(-0.529394\pi\) | ||||
−0.0922132 | + | 0.995739i | \(0.529394\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −51.3462 | −1.70304 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.1325 | 0.435100 | 0.217550 | − | 0.976049i | \(-0.430193\pi\) | ||||
0.217550 | + | 0.976049i | \(0.430193\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.36871 | 0.243869 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.461691 | −0.0152630 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.0966 | 0.333421 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.5417 | −0.413712 | −0.206856 | − | 0.978371i | \(-0.566323\pi\) | ||||
−0.206856 | + | 0.978371i | \(0.566323\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.34386 | −0.241988 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −19.5001 | −0.641853 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.90308 | −0.0954527 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 51.9441 | 1.70607 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.24051 | −0.270362 | −0.135181 | − | 0.990821i | \(-0.543162\pi\) | ||||
−0.135181 | + | 0.990821i | \(0.543162\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −58.8879 | −1.92997 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.32013 | −0.272389 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.12793 | 0.233108 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.4798 | 0.375030 | 0.187515 | − | 0.982262i | \(-0.439957\pi\) | ||||
0.187515 | + | 0.982262i | \(0.439957\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.56575 | −0.181631 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.3769 | −0.925061 | −0.462531 | − | 0.886603i | \(-0.653058\pi\) | ||||
−0.462531 | + | 0.886603i | \(0.653058\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.188663 | −0.00614373 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.18321 | 0.266200 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.88882 | −0.256352 | −0.128176 | − | 0.991751i | \(-0.540912\pi\) | ||||
−0.128176 | + | 0.991751i | \(0.540912\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.56427 | 0.0507783 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.3849 | 0.369181 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.20245 | −0.298096 | −0.149048 | − | 0.988830i | \(-0.547621\pi\) | ||||
−0.149048 | + | 0.988830i | \(0.547621\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.51098 | 0.0812534 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −15.2960 | −0.494449 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.3487 | 0.431051 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 50.7267 | 1.63635 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 36.7375 | 1.18385 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18.6016 | 0.598805 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.6278 | −0.631186 | −0.315593 | − | 0.948895i | \(-0.602203\pi\) | ||||
−0.315593 | + | 0.948895i | \(0.602203\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.04404 | 0.0977886 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.09502 | 0.227690 | 0.113845 | − | 0.993499i | \(-0.463683\pi\) | ||||
0.113845 | + | 0.993499i | \(0.463683\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.61031 | 0.179858 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.893211 | −0.0286056 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.5255 | 1.29652 | 0.648262 | − | 0.761417i | \(-0.275496\pi\) | ||||
0.648262 | + | 0.761417i | \(0.275496\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −97.6917 | −3.12224 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −42.4459 | −1.35519 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −48.8845 | −1.55917 | −0.779587 | − | 0.626294i | \(-0.784571\pi\) | ||||
−0.779587 | + | 0.626294i | \(0.784571\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.8033 | −0.567260 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.72251 | −0.213980 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.97692 | 0.0946606 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.9031 | 1.42639 | 0.713197 | − | 0.700963i | \(-0.247246\pi\) | ||||
0.713197 | + | 0.700963i | \(0.247246\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.07965 | 0.161198 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.14740 | 0.289992 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 55.6027 | 1.76096 | 0.880478 | − | 0.474087i | \(-0.157222\pi\) | ||||
0.880478 | + | 0.474087i | \(0.157222\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.01141 | −0.190192 |
(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 | 3680.2.a.ba.1.3 | yes | 5 | |
4.3 | odd | 2 | 3680.2.a.x.1.3 | ✓ | 5 | ||
8.3 | odd | 2 | 7360.2.a.cq.1.3 | 5 | |||
8.5 | even | 2 | 7360.2.a.cl.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3680.2.a.x.1.3 | ✓ | 5 | 4.3 | odd | 2 | ||
3680.2.a.ba.1.3 | yes | 5 | 1.1 | even | 1 | trivial | |
7360.2.a.cl.1.3 | 5 | 8.5 | even | 2 | |||
7360.2.a.cq.1.3 | 5 | 8.3 | odd | 2 |