Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 27 x^{12} + 78 x^{11} + 273 x^{10} - 750 x^{9} - 1306 x^{8} + 3378 x^{7} + 2996 x^{6} - 7275 x^{5} - 2804 x^{4} + 6417 x^{3} + 538 x^{2} - 1032 x - 128 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.528665\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-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 | ||||||||
\(3\) | −0.528665 | −0.305225 | −0.152612 | − | 0.988286i | \(-0.548769\pi\) | ||||
−0.152612 | + | 0.988286i | \(0.548769\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.933973 | 0.417685 | 0.208843 | − | 0.977949i | \(-0.433030\pi\) | ||||
0.208843 | + | 0.977949i | \(0.433030\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.72051 | −0.906838 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.493759 | −0.127488 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.372048 | 0.0902349 | 0.0451175 | − | 0.998982i | \(-0.485634\pi\) | ||||
0.0451175 | + | 0.998982i | \(0.485634\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.48213 | −0.798855 | −0.399427 | − | 0.916765i | \(-0.630791\pi\) | ||||
−0.399427 | + | 0.916765i | \(0.630791\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.528665 | −0.115364 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.94271 | −1.03063 | −0.515314 | − | 0.857002i | \(-0.672325\pi\) | ||||
−0.515314 | + | 0.857002i | \(0.672325\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.12769 | −0.825539 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.02424 | 0.582014 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.77261 | 1.81473 | 0.907364 | − | 0.420346i | \(-0.138091\pi\) | ||||
0.907364 | + | 0.420346i | \(0.138091\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.42408 | 1.51301 | 0.756505 | − | 0.653988i | \(-0.226905\pi\) | ||||
0.756505 | + | 0.653988i | \(0.226905\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.528665 | 0.0920288 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.933973 | 0.157870 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.32225 | −0.381776 | −0.190888 | − | 0.981612i | \(-0.561137\pi\) | ||||
−0.190888 | + | 0.981612i | \(0.561137\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.528665 | 0.0846541 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.25828 | 1.28973 | 0.644864 | − | 0.764298i | \(-0.276914\pi\) | ||||
0.644864 | + | 0.764298i | \(0.276914\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.29298 | 0.197178 | 0.0985890 | − | 0.995128i | \(-0.468567\pi\) | ||||
0.0985890 | + | 0.995128i | \(0.468567\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.54089 | −0.378773 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.0753 | 1.46964 | 0.734819 | − | 0.678263i | \(-0.237267\pi\) | ||||
0.734819 | + | 0.678263i | \(0.237267\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.196689 | −0.0275419 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.68137 | 0.230954 | 0.115477 | − | 0.993310i | \(-0.463160\pi\) | ||||
0.115477 | + | 0.993310i | \(0.463160\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.933973 | −0.125937 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.84088 | 0.243830 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.7033 | 1.78401 | 0.892007 | − | 0.452022i | \(-0.149297\pi\) | ||||
0.892007 | + | 0.452022i | \(0.149297\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.52555 | −0.835511 | −0.417755 | − | 0.908560i | \(-0.637183\pi\) | ||||
−0.417755 | + | 0.908560i | \(0.637183\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.72051 | −0.342752 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.933973 | −0.115845 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.1966 | −1.73439 | −0.867194 | − | 0.497970i | \(-0.834079\pi\) | ||||
−0.867194 | + | 0.497970i | \(0.834079\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.61304 | 0.314573 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.57695 | −1.13658 | −0.568288 | − | 0.822830i | \(-0.692394\pi\) | ||||
−0.568288 | + | 0.822830i | \(0.692394\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.18018 | −0.372212 | −0.186106 | − | 0.982530i | \(-0.559587\pi\) | ||||
−0.186106 | + | 0.982530i | \(0.559587\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.18217 | 0.251975 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −17.5913 | −1.97918 | −0.989590 | − | 0.143917i | \(-0.954030\pi\) | ||||
−0.989590 | + | 0.143917i | \(0.954030\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.56273 | 0.729193 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.45504 | −0.269476 | −0.134738 | − | 0.990881i | \(-0.543019\pi\) | ||||
−0.134738 | + | 0.990881i | \(0.543019\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.347483 | 0.0376898 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.16644 | −0.553900 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.5225 | −1.11538 | −0.557690 | − | 0.830049i | \(-0.688312\pi\) | ||||
−0.557690 | + | 0.830049i | \(0.688312\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.45352 | −0.461808 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.25221 | −0.333670 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.79736 | −0.690167 | −0.345083 | − | 0.938572i | \(-0.612149\pi\) | ||||
−0.345083 | + | 0.938572i | \(0.612149\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.72051 | 0.273422 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.58580 | 0.655311 | 0.327656 | − | 0.944797i | \(-0.393741\pi\) | ||||
0.327656 | + | 0.944797i | \(0.393741\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.4920 | −1.42794 | −0.713968 | − | 0.700178i | \(-0.753104\pi\) | ||||
−0.713968 | + | 0.700178i | \(0.753104\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.493759 | −0.0481859 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.5657 | −1.40811 | −0.704057 | − | 0.710143i | \(-0.748630\pi\) | ||||
−0.704057 | + | 0.710143i | \(0.748630\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.6628 | −1.30866 | −0.654331 | − | 0.756208i | \(-0.727050\pi\) | ||||
−0.654331 | + | 0.756208i | \(0.727050\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.22769 | 0.116527 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.72536 | 0.914885 | 0.457443 | − | 0.889239i | \(-0.348766\pi\) | ||||
0.457443 | + | 0.889239i | \(0.348766\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.61636 | −0.430478 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.72051 | 0.251512 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.372048 | 0.0341056 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.36586 | −0.393657 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.52502 | −0.762501 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.48189 | −0.486439 | −0.243219 | − | 0.969971i | \(-0.578204\pi\) | ||||
−0.243219 | + | 0.969971i | \(0.578204\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.683555 | −0.0601836 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.957619 | 0.0836675 | 0.0418338 | − | 0.999125i | \(-0.486680\pi\) | ||||
0.0418338 | + | 0.999125i | \(0.486680\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.48213 | −0.301939 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.82455 | 0.243099 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.243329 | 0.0207890 | 0.0103945 | − | 0.999946i | \(-0.496691\pi\) | ||||
0.0103945 | + | 0.999946i | \(0.496691\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.71861 | 0.400227 | 0.200114 | − | 0.979773i | \(-0.435869\pi\) | ||||
0.200114 | + | 0.979773i | \(0.435869\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.32648 | −0.448570 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.12735 | 0.757985 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.528665 | −0.0436036 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.74561 | 0.552622 | 0.276311 | − | 0.961068i | \(-0.410888\pi\) | ||||
0.276311 | + | 0.961068i | \(0.410888\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.4337 | 1.50011 | 0.750055 | − | 0.661375i | \(-0.230027\pi\) | ||||
0.750055 | + | 0.661375i | \(0.230027\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.01216 | −0.0818285 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.86786 | 0.631962 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.8281 | −1.34303 | −0.671514 | − | 0.740992i | \(-0.734356\pi\) | ||||
−0.671514 | + | 0.740992i | \(0.734356\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.888883 | −0.0704930 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.94271 | −0.389540 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.5879 | 1.61257 | 0.806286 | − | 0.591526i | \(-0.201474\pi\) | ||||
0.806286 | + | 0.591526i | \(0.201474\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.493759 | 0.0384391 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.9427 | −1.69798 | −0.848988 | − | 0.528412i | \(-0.822788\pi\) | ||||
−0.848988 | + | 0.528412i | \(0.822788\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.47317 | 0.724432 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −21.7997 | −1.65740 | −0.828699 | − | 0.559695i | \(-0.810918\pi\) | ||||
−0.828699 | + | 0.559695i | \(0.810918\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.12769 | −0.312024 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.24444 | −0.544525 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.1571 | −1.58136 | −0.790678 | − | 0.612232i | \(-0.790272\pi\) | ||||
−0.790678 | + | 0.612232i | \(0.790272\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.29825 | 0.616804 | 0.308402 | − | 0.951256i | \(-0.400206\pi\) | ||||
0.308402 | + | 0.951256i | \(0.400206\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.44983 | 0.255019 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.16892 | −0.159462 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.372048 | −0.0272069 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.02424 | 0.219981 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.0851 | −1.59802 | −0.799010 | − | 0.601318i | \(-0.794643\pi\) | ||||
−0.799010 | + | 0.601318i | \(0.794643\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.950189 | 0.0683961 | 0.0341981 | − | 0.999415i | \(-0.489112\pi\) | ||||
0.0341981 | + | 0.999415i | \(0.489112\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.493759 | 0.0353588 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.17415 | −0.582384 | −0.291192 | − | 0.956665i | \(-0.594052\pi\) | ||||
−0.291192 | + | 0.956665i | \(0.594052\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.1537 | 1.64132 | 0.820661 | − | 0.571415i | \(-0.193605\pi\) | ||||
0.820661 | + | 0.571415i | \(0.193605\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.50523 | 0.529378 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.77261 | 0.685903 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.71301 | 0.538700 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 13.4467 | 0.934612 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.48213 | 0.240864 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.8345 | −1.02125 | −0.510626 | − | 0.859803i | \(-0.670586\pi\) | ||||
−0.510626 | + | 0.859803i | \(0.670586\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.06300 | 0.346911 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.20761 | 0.0823584 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.42408 | 0.571864 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.68125 | 0.113608 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.372048 | −0.0250267 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.33295 | −0.624980 | −0.312490 | − | 0.949921i | \(-0.601163\pi\) | ||||
−0.312490 | + | 0.949921i | \(0.601163\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.2294 | 0.748630 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.2598 | −1.54381 | −0.771903 | − | 0.635740i | \(-0.780695\pi\) | ||||
−0.771903 | + | 0.635740i | \(0.780695\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.74296 | 0.511669 | 0.255834 | − | 0.966721i | \(-0.417650\pi\) | ||||
0.255834 | + | 0.966721i | \(0.417650\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.528665 | 0.0347836 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.7728 | 1.42638 | 0.713191 | − | 0.700969i | \(-0.247249\pi\) | ||||
0.713191 | + | 0.700969i | \(0.247249\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.41009 | 0.613846 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.29992 | 0.604095 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.83967 | 0.313052 | 0.156526 | − | 0.987674i | \(-0.449971\pi\) | ||||
0.156526 | + | 0.987674i | \(0.449971\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.09112 | 0.134701 | 0.0673505 | − | 0.997729i | \(-0.478545\pi\) | ||||
0.0673505 | + | 0.997729i | \(0.478545\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.5422 | −0.804582 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.933973 | 0.0596693 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.48213 | 0.221562 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.29790 | 0.0822508 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.95974 | −0.565534 | −0.282767 | − | 0.959189i | \(-0.591252\pi\) | ||||
−0.282767 | + | 0.959189i | \(0.591252\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.94271 | 0.310746 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.183702 | −0.0115039 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.7700 | −1.48273 | −0.741367 | − | 0.671100i | \(-0.765822\pi\) | ||||
−0.741367 | + | 0.671100i | \(0.765822\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.32225 | −0.144298 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −26.5865 | −1.64566 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.2435 | −1.18660 | −0.593302 | − | 0.804980i | \(-0.702176\pi\) | ||||
−0.593302 | + | 0.804980i | \(0.702176\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.57036 | 0.0964662 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.56286 | 0.340442 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.525897 | 0.0320645 | 0.0160322 | − | 0.999871i | \(-0.494897\pi\) | ||||
0.0160322 | + | 0.999871i | \(0.494897\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.6902 | −1.31759 | −0.658793 | − | 0.752324i | \(-0.728933\pi\) | ||||
−0.658793 | + | 0.752324i | \(0.728933\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.528665 | 0.0319963 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.12769 | 0.248909 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.69386 | −0.402195 | −0.201097 | − | 0.979571i | \(-0.564451\pi\) | ||||
−0.201097 | + | 0.979571i | \(0.564451\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −22.9178 | −1.37205 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.55903 | 0.0930040 | 0.0465020 | − | 0.998918i | \(-0.485193\pi\) | ||||
0.0465020 | + | 0.998918i | \(0.485193\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.3182 | 0.851126 | 0.425563 | − | 0.904929i | \(-0.360076\pi\) | ||||
0.425563 | + | 0.904929i | \(0.360076\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.71933 | 0.101844 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.25828 | 0.487471 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8616 | −0.991858 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.59352 | 0.210656 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.51062 | 0.497196 | 0.248598 | − | 0.968607i | \(-0.420030\pi\) | ||||
0.248598 | + | 0.968607i | \(0.420030\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.7985 | 0.745156 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.02424 | −0.175484 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.94271 | 0.285845 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.29298 | 0.0745263 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.48168 | −0.200017 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.09468 | −0.348981 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.1322 | −0.806567 | −0.403283 | − | 0.915075i | \(-0.632131\pi\) | ||||
−0.403283 | + | 0.915075i | \(0.632131\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.66140 | 0.435842 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.41608 | −0.533937 | −0.266968 | − | 0.963705i | \(-0.586022\pi\) | ||||
−0.266968 | + | 0.963705i | \(0.586022\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.9266 | 1.18284 | 0.591421 | − | 0.806363i | \(-0.298567\pi\) | ||||
0.591421 | + | 0.806363i | \(0.298567\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.54089 | −0.143163 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.0936 | 1.57789 | 0.788946 | − | 0.614463i | \(-0.210627\pi\) | ||||
0.788946 | + | 0.614463i | \(0.210627\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.77261 | −0.547161 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.70035 | 0.429792 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.29552 | −0.0720846 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.12769 | 0.228963 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.22306 | 0.399436 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.0753 | 0.555471 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.69656 | 0.532971 | 0.266486 | − | 0.963839i | \(-0.414138\pi\) | ||||
0.266486 | + | 0.963839i | \(0.414138\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.31771 | 0.346209 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.2592 | −0.724428 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.12736 | −0.497199 | −0.248599 | − | 0.968606i | \(-0.579970\pi\) | ||||
−0.248599 | + | 0.968606i | \(0.579970\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.14146 | −0.279246 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.42408 | −0.456190 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.44051 | 0.131393 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.8688 | −0.690833 | −0.345416 | − | 0.938450i | \(-0.612262\pi\) | ||||
−0.345416 | + | 0.938450i | \(0.612262\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.9680 | 1.17592 | 0.587960 | − | 0.808890i | \(-0.299931\pi\) | ||||
0.587960 | + | 0.808890i | \(0.299931\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.02424 | −0.161422 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.6928 | 0.888466 | 0.444233 | − | 0.895911i | \(-0.353476\pi\) | ||||
0.444233 | + | 0.895911i | \(0.353476\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.94461 | −0.474731 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.196689 | −0.0104099 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.2966 | −1.44066 | −0.720330 | − | 0.693632i | \(-0.756010\pi\) | ||||
−0.720330 | + | 0.693632i | \(0.756010\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.87480 | −0.361831 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.528665 | −0.0277477 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.97020 | −0.155468 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.0514 | −0.785675 | −0.392838 | − | 0.919608i | \(-0.628507\pi\) | ||||
−0.392838 | + | 0.919608i | \(0.628507\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −22.4668 | −1.16957 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.68137 | 0.0872925 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.2726 | −0.687231 | −0.343616 | − | 0.939110i | \(-0.611652\pi\) | ||||
−0.343616 | + | 0.939110i | \(0.611652\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.50688 | 0.232734 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.77261 | −0.503315 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.1865 | −0.677347 | −0.338674 | − | 0.940904i | \(-0.609978\pi\) | ||||
−0.338674 | + | 0.940904i | \(0.609978\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.89808 | 0.148473 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.569479 | 0.0290990 | 0.0145495 | − | 0.999894i | \(-0.495369\pi\) | ||||
0.0145495 | + | 0.999894i | \(0.495369\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.933973 | −0.0475997 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.51758 | −0.178808 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.68298 | 0.490946 | 0.245473 | − | 0.969403i | \(-0.421057\pi\) | ||||
0.245473 | + | 0.969403i | \(0.421057\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.83893 | −0.0929986 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.506260 | −0.0255374 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.4298 | −0.826674 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.6845 | −0.736992 | −0.368496 | − | 0.929629i | \(-0.620127\pi\) | ||||
−0.368496 | + | 0.929629i | \(0.620127\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.84088 | 0.0921592 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.6342 | 1.08036 | 0.540180 | − | 0.841549i | \(-0.318356\pi\) | ||||
0.540180 | + | 0.841549i | \(0.318356\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.42408 | −0.419634 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.12941 | 0.304573 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.32225 | 0.115110 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.7570 | 0.531900 | 0.265950 | − | 0.963987i | \(-0.414314\pi\) | ||||
0.265950 | + | 0.963987i | \(0.414314\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.128640 | −0.00634533 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.7033 | 0.674294 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.29294 | −0.112556 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.49456 | −0.122159 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.90107 | −0.141726 | −0.0708632 | − | 0.997486i | \(-0.522575\pi\) | ||||
−0.0708632 | + | 0.997486i | \(0.522575\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.8475 | −1.84457 | −0.922286 | − | 0.386508i | \(-0.873681\pi\) | ||||
−0.922286 | + | 0.386508i | \(0.873681\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −27.4101 | −1.33272 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.53570 | −0.0744925 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.52555 | −0.315793 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.528665 | −0.0255242 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.1454 | −1.11487 | −0.557437 | − | 0.830219i | \(-0.688215\pi\) | ||||
−0.557437 | + | 0.830219i | \(0.688215\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.68155 | 0.273038 | 0.136519 | − | 0.990637i | \(-0.456409\pi\) | ||||
0.136519 | + | 0.990637i | \(0.456409\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.82531 | −0.231356 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17.2112 | 0.823321 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.7782 | 1.08714 | 0.543571 | − | 0.839363i | \(-0.317072\pi\) | ||||
0.543571 | + | 0.839363i | \(0.317072\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.72051 | −0.129548 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.60012 | −0.123535 | −0.0617676 | − | 0.998091i | \(-0.519674\pi\) | ||||
−0.0617676 | + | 0.998091i | \(0.519674\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.82770 | −0.465878 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.56617 | −0.168674 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.5119 | −0.920825 | −0.460413 | − | 0.887705i | \(-0.652299\pi\) | ||||
−0.460413 | + | 0.887705i | \(0.652299\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.25828 | −0.388867 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.74523 | −0.457871 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.933973 | −0.0437853 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.6042 | 1.10416 | 0.552079 | − | 0.833792i | \(-0.313835\pi\) | ||||
0.552079 | + | 0.833792i | \(0.313835\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.12516 | 0.0525180 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.54946 | 0.0721656 | 0.0360828 | − | 0.999349i | \(-0.488512\pi\) | ||||
0.0360828 | + | 0.999349i | \(0.488512\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.7272 | 0.870325 | 0.435163 | − | 0.900352i | \(-0.356691\pi\) | ||||
0.435163 | + | 0.900352i | \(0.356691\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.15946 | −0.192891 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.95315 | −0.321753 | −0.160877 | − | 0.986975i | \(-0.551432\pi\) | ||||
−0.160877 | + | 0.986975i | \(0.551432\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.1966 | −0.655537 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.89642 | 0.409925 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.29298 | −0.0594514 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.3732 | 0.659486 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.57420 | −0.209438 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.436792 | −0.0199575 | −0.00997877 | − | 0.999950i | \(-0.503176\pi\) | ||||
−0.00997877 | + | 0.999950i | \(0.503176\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.32225 | 0.105886 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.61304 | 0.118897 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.34855 | −0.288273 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.0384 | 0.862710 | 0.431355 | − | 0.902182i | \(-0.358036\pi\) | ||||
0.431355 | + | 0.902182i | \(0.358036\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.8841 | −0.492197 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.83175 | −0.398571 | −0.199286 | − | 0.979941i | \(-0.563862\pi\) | ||||
−0.199286 | + | 0.979941i | \(0.563862\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.63588 | 0.163752 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.54089 | 0.114204 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.57695 | −0.429585 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.14601 | 0.275133 | 0.137567 | − | 0.990493i | \(-0.456072\pi\) | ||||
0.137567 | + | 0.990493i | \(0.456072\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.6003 | 0.518265 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.98619 | −0.266911 | −0.133455 | − | 0.991055i | \(-0.542607\pi\) | ||||
−0.133455 | + | 0.991055i | \(0.542607\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.15095 | 0.273714 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.528665 | −0.0234788 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 29.5736 | 1.31083 | 0.655413 | − | 0.755271i | \(-0.272495\pi\) | ||||
0.655413 | + | 0.755271i | \(0.272495\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.18018 | −0.140683 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.5308 | −0.464945 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.5351 | −0.596428 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.0753 | −0.443113 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.5247 | 0.505879 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.2021 | 1.58604 | 0.793022 | − | 0.609194i | \(-0.208507\pi\) | ||||
0.793022 | + | 0.609194i | \(0.208507\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.45323 | 0.369634 | 0.184817 | − | 0.982773i | \(-0.440831\pi\) | ||||
0.184817 | + | 0.982773i | \(0.440831\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.18217 | 0.0952376 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.13417 | 0.136526 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.43042 | 0.0621922 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −37.2799 | −1.61781 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.25828 | −0.357706 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.6039 | −0.588149 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.1850 | 0.482669 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.8656 | 1.75695 | 0.878475 | − | 0.477788i | \(-0.158561\pi\) | ||||
0.878475 | + | 0.477788i | \(0.158561\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.38699 | −0.188264 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.7607 | −0.546609 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.0400 | −1.11339 | −0.556694 | − | 0.830718i | \(-0.687930\pi\) | ||||
−0.556694 | + | 0.830718i | \(0.687930\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 17.7528 | 0.757673 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −34.0295 | −1.44970 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.5913 | −0.748060 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.14663 | 0.0486718 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.33403 | −0.268381 | −0.134191 | − | 0.990956i | \(-0.542843\pi\) | ||||
−0.134191 | + | 0.990956i | \(0.542843\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.29298 | −0.0546873 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.196689 | 0.00830421 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.4713 | 1.19992 | 0.599961 | − | 0.800030i | \(-0.295183\pi\) | ||||
0.599961 | + | 0.800030i | \(0.295183\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.08322 | 0.382134 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.56273 | 0.275609 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.9445 | 0.500739 | 0.250370 | − | 0.968150i | \(-0.419448\pi\) | ||||
0.250370 | + | 0.968150i | \(0.419448\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.2488 | 0.554445 | 0.277222 | − | 0.960806i | \(-0.410586\pi\) | ||||
0.277222 | + | 0.960806i | \(0.410586\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.6756 | 0.487755 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.4020 | 0.850823 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.14213 | −0.172439 | −0.0862195 | − | 0.996276i | \(-0.527479\pi\) | ||||
−0.0862195 | + | 0.996276i | \(0.527479\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.502332 | −0.0208762 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.45504 | −0.101852 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.68137 | −0.0696353 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.54089 | 0.105053 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.4677 | −0.720969 | −0.360484 | − | 0.932765i | \(-0.617389\pi\) | ||||
−0.360484 | + | 0.932765i | \(0.617389\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29.3337 | −1.20868 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.32139 | 0.177758 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −29.2995 | −1.20319 | −0.601593 | − | 0.798803i | \(-0.705467\pi\) | ||||
−0.601593 | + | 0.798803i | \(0.705467\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.347483 | 0.0142454 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.2406 | −0.500972 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.9878 | 0.734960 | 0.367480 | − | 0.930031i | \(-0.380221\pi\) | ||||
0.367480 | + | 0.930031i | \(0.380221\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.2872 | 0.582786 | 0.291393 | − | 0.956603i | \(-0.405881\pi\) | ||||
0.291393 | + | 0.956603i | \(0.405881\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 38.6220 | 1.57281 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.933973 | 0.0379714 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.7899 | 1.20913 | 0.604567 | − | 0.796555i | \(-0.293346\pi\) | ||||
0.604567 | + | 0.796555i | \(0.293346\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.16644 | −0.209355 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.0753 | −0.407604 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.0152 | 0.848797 | 0.424399 | − | 0.905475i | \(-0.360485\pi\) | ||||
0.424399 | + | 0.905475i | \(0.360485\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.07760 | −0.164425 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.66609 | −0.147591 | −0.0737956 | − | 0.997273i | \(-0.523511\pi\) | ||||
−0.0737956 | + | 0.997273i | \(0.523511\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.1426 | 1.01057 | 0.505284 | − | 0.862953i | \(-0.331388\pi\) | ||||
0.505284 | + | 0.862953i | \(0.331388\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.9479 | −0.599840 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.5225 | −0.421574 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.6763 | 0.507054 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.84088 | −0.0735176 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.863989 | −0.0344495 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.5222 | −1.01602 | −0.508010 | − | 0.861351i | \(-0.669619\pi\) | ||||
−0.508010 | + | 0.861351i | \(0.669619\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.84250 | 0.311712 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.11993 | −0.203178 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 26.0542 | 1.03069 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.9750 | 1.14444 | 0.572221 | − | 0.820099i | \(-0.306082\pi\) | ||||
0.572221 | + | 0.820099i | \(0.306082\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.5369 | −1.32257 | −0.661283 | − | 0.750137i | \(-0.729988\pi\) | ||||
−0.661283 | + | 0.750137i | \(0.729988\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.638421 | −0.0251378 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −40.8038 | −1.60416 | −0.802082 | − | 0.597214i | \(-0.796274\pi\) | ||||
−0.802082 | + | 0.597214i | \(0.796274\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.7033 | −0.537900 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.45352 | −0.174547 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.3615 | 0.562010 | 0.281005 | − | 0.959706i | \(-0.409332\pi\) | ||||
0.281005 | + | 0.959706i | \(0.409332\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.894390 | 0.0349467 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.65173 | 0.337536 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.65171 | −0.220159 | −0.110080 | − | 0.993923i | \(-0.535111\pi\) | ||||
−0.110080 | + | 0.993923i | \(0.535111\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.1044 | 1.05424 | 0.527120 | − | 0.849791i | \(-0.323272\pi\) | ||||
0.527120 | + | 0.849791i | \(0.323272\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.196689 | 0.00763876 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.25221 | −0.126115 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −48.3032 | −1.87031 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.93400 | 0.190760 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.52555 | 0.251916 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.3336 | 1.36201 | 0.681005 | − | 0.732279i | \(-0.261543\pi\) | ||||
0.681005 | + | 0.732279i | \(0.261543\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.4831 | −0.480476 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.97653 | 0.383429 | 0.191715 | − | 0.981451i | \(-0.438595\pi\) | ||||
0.191715 | + | 0.981451i | \(0.438595\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.79736 | −0.260859 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.2966 | 0.471208 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −51.3730 | −1.96573 | −0.982866 | − | 0.184322i | \(-0.940991\pi\) | ||||
−0.982866 | + | 0.184322i | \(0.940991\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.227263 | 0.00868327 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.09343 | −0.156174 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.68137 | −0.0640552 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.3730 | −0.927193 | −0.463596 | − | 0.886046i | \(-0.653441\pi\) | ||||
−0.463596 | + | 0.886046i | \(0.653441\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.72051 | 0.103344 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.40705 | 0.167169 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.07248 | 0.116378 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.5105 | −0.435367 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.4248 | −0.809204 | −0.404602 | − | 0.914493i | \(-0.632590\pi\) | ||||
−0.404602 | + | 0.914493i | \(0.632590\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.08637 | 0.304983 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.97478 | −0.187361 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.58580 | 0.247684 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −39.5345 | −1.48475 | −0.742374 | − | 0.669985i | \(-0.766300\pi\) | ||||
−0.742374 | + | 0.669985i | \(0.766300\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 47.8575 | 1.79479 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −41.6378 | −1.55935 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.933973 | 0.0349286 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.55856 | −0.0955512 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −42.5602 | −1.58723 | −0.793614 | − | 0.608422i | \(-0.791803\pi\) | ||||
−0.793614 | + | 0.608422i | \(0.791803\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.4920 | −0.539709 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.10550 | −0.0411141 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −40.3384 | −1.49813 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.0575 | 0.558453 | 0.279226 | − | 0.960225i | \(-0.409922\pi\) | ||||
0.279226 | + | 0.960225i | \(0.409922\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0576 | −0.483614 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.481052 | 0.0177923 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.2906 | −0.860257 | −0.430129 | − | 0.902768i | \(-0.641532\pi\) | ||||
−0.430129 | + | 0.902768i | \(0.641532\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.493759 | −0.0182126 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.1966 | 0.522938 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.9234 | −1.32146 | −0.660732 | − | 0.750622i | \(-0.729754\pi\) | ||||
−0.660732 | + | 0.750622i | \(0.729754\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.84088 | −0.0676264 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.4649 | 0.824157 | 0.412079 | − | 0.911148i | \(-0.364803\pi\) | ||||
0.412079 | + | 0.911148i | \(0.364803\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.30021 | 0.230822 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.67898 | 0.244371 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.5657 | −0.532217 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.1213 | −0.697746 | −0.348873 | − | 0.937170i | \(-0.613436\pi\) | ||||
−0.348873 | + | 0.937170i | \(0.613436\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.73670 | 0.172615 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.2165 | 0.626574 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.6307 | −1.33136 | −0.665682 | − | 0.746235i | \(-0.731859\pi\) | ||||
−0.665682 | + | 0.746235i | \(0.731859\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.61304 | −0.0948473 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.79570 | −0.355094 | −0.177547 | − | 0.984112i | \(-0.556816\pi\) | ||||
−0.177547 | + | 0.984112i | \(0.556816\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.6628 | −0.494628 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.945332 | −0.0341785 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.7033 | −0.494796 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.1550 | −0.762868 | −0.381434 | − | 0.924396i | \(-0.624570\pi\) | ||||
−0.381434 | + | 0.924396i | \(0.624570\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.5664 | 0.452567 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.22490 | −0.115992 | −0.0579958 | − | 0.998317i | \(-0.518471\pi\) | ||||
−0.0579958 | + | 0.998317i | \(0.518471\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −34.7721 | −1.24905 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.22769 | 0.0440432 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −28.7564 | −1.03030 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.57695 | 0.342690 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 29.5547 | 1.05620 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.7170 | −0.560963 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.35097 | 0.0481568 | 0.0240784 | − | 0.999710i | \(-0.492335\pi\) | ||||
0.0240784 | + | 0.999710i | \(0.492335\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.1734 | 0.362181 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.72536 | 0.345794 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.52555 | 0.231729 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.830192 | −0.0294439 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −56.0012 | −1.98366 | −0.991832 | − | 0.127552i | \(-0.959288\pi\) | ||||
−0.991832 | + | 0.127552i | \(0.959288\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.74851 | 0.132613 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 28.6265 | 1.01147 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.18018 | 0.112226 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.61636 | −0.162705 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.278023 | −0.00978688 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.3551 | −0.539858 | −0.269929 | − | 0.962880i | \(-0.587000\pi\) | ||||
−0.269929 | + | 0.962880i | \(0.587000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.51841 | 0.158663 | 0.0793313 | − | 0.996848i | \(-0.474721\pi\) | ||||
0.0793313 | + | 0.996848i | \(0.474721\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.4669 | 0.402160 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.2286 | 0.673547 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.50233 | −0.157517 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.72051 | 0.0950624 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.6419 | −0.406306 | −0.203153 | − | 0.979147i | \(-0.565119\pi\) | ||||
−0.203153 | + | 0.979147i | \(0.565119\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.9212 | 0.554979 | 0.277489 | − | 0.960729i | \(-0.410498\pi\) | ||||
0.277489 | + | 0.960729i | \(0.410498\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.18217 | −0.0759733 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.89577 | 0.309336 | 0.154668 | − | 0.987966i | \(-0.450569\pi\) | ||||
0.154668 | + | 0.987966i | \(0.450569\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −44.7425 | −1.55397 | −0.776986 | − | 0.629517i | \(-0.783253\pi\) | ||||
−0.776986 | + | 0.629517i | \(0.783253\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.53881 | 0.122760 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.372048 | 0.0128907 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20.4939 | −0.709220 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 25.4764 | 0.880594 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.1279 | 0.660369 | 0.330185 | − | 0.943916i | \(-0.392889\pi\) | ||||
0.330185 | + | 0.943916i | \(0.392889\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 66.5039 | 2.29324 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.824205 | −0.0283871 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.933973 | 0.0321296 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.56951 | −0.259785 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.4782 | 0.393468 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.64029 | 0.0561624 | 0.0280812 | − | 0.999606i | \(-0.491060\pi\) | ||||
0.0280812 | + | 0.999606i | \(0.491060\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.84768 | 0.302584 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.1131 | −0.516255 | −0.258127 | − | 0.966111i | \(-0.583105\pi\) | ||||
−0.258127 | + | 0.966111i | \(0.583105\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.23148 | −0.314974 | −0.157487 | − | 0.987521i | \(-0.550339\pi\) | ||||
−0.157487 | + | 0.987521i | \(0.550339\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.36586 | −0.148788 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.5560 | 1.04014 | 0.520068 | − | 0.854125i | \(-0.325906\pi\) | ||||
0.520068 | + | 0.854125i | \(0.325906\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.3603 | −0.692270 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.91413 | 0.302740 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.5913 | 0.596745 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.1966 | 0.481033 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.4923 | 0.625869 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.52502 | −0.288198 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −50.5110 | −1.70564 | −0.852818 | − | 0.522208i | \(-0.825109\pi\) | ||||
−0.852818 | + | 0.522208i | \(0.825109\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.49927 | −0.151757 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.7308 | −0.563674 | −0.281837 | − | 0.959462i | \(-0.590944\pi\) | ||||
−0.281837 | + | 0.959462i | \(0.590944\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.82152 | −0.195910 | −0.0979549 | − | 0.995191i | \(-0.531230\pi\) | ||||
−0.0979549 | + | 0.995191i | \(0.531230\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.76611 | −0.227440 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.2498 | −0.411308 | −0.205654 | − | 0.978625i | \(-0.565932\pi\) | ||||
−0.205654 | + | 0.978625i | \(0.565932\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.48189 | −0.183857 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.56273 | −0.219860 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −35.0836 | −1.17403 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.7602 | −0.660509 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.61304 | −0.0872469 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 82.3253 | 2.74570 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.625552 | 0.0208401 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.683555 | −0.0227473 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.75033 | 0.257630 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.3906 | −1.10872 | −0.554359 | − | 0.832278i | \(-0.687036\pi\) | ||||
−0.554359 | + | 0.832278i | \(0.687036\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −17.9167 | −0.594261 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.2936 | −1.06993 | −0.534967 | − | 0.844873i | \(-0.679676\pi\) | ||||
−0.534967 | + | 0.844873i | \(0.679676\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.45504 | 0.0812501 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.22205 | 0.106518 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.957619 | 0.0316234 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −56.0214 | −1.84798 | −0.923988 | − | 0.382422i | \(-0.875090\pi\) | ||||
−0.923988 | + | 0.382422i | \(0.875090\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.47119 | 0.246184 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.57695 | 0.315229 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.58554 | 0.315171 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 39.4256 | 1.29491 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.4649 | −0.343342 | −0.171671 | − | 0.985154i | \(-0.554917\pi\) | ||||
−0.171671 | + | 0.985154i | \(0.554917\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.48213 | −0.114122 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.97795 | 0.162971 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.347483 | −0.0113639 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.9879 | 0.783649 | 0.391824 | − | 0.920040i | \(-0.371844\pi\) | ||||
0.391824 | + | 0.920040i | \(0.371844\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.0632 | −0.361033 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.65798 | −0.314841 | −0.157421 | − | 0.987532i | \(-0.550318\pi\) | ||||
−0.157421 | + | 0.987532i | \(0.550318\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −40.8183 | −1.32923 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.82455 | 0.0918827 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.0206 | 0.813060 | 0.406530 | − | 0.913637i | \(-0.366739\pi\) | ||||
0.406530 | + | 0.913637i | \(0.366739\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.18018 | 0.103233 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.8521 | −0.481612 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.74580 | 0.283304 | 0.141652 | − | 0.989917i | \(-0.454759\pi\) | ||||
0.141652 | + | 0.989917i | \(0.454759\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.6269 | −0.667469 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.16644 | 0.167007 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.243329 | 0.00785752 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 39.9652 | 1.28920 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 39.6261 | 1.27693 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.887451 | 0.0285681 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.2746 | 1.55241 | 0.776203 | − | 0.630482i | \(-0.217143\pi\) | ||||
0.776203 | + | 0.630482i | \(0.217143\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.684895 | 0.0220020 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −58.9239 | −1.89096 | −0.945479 | − | 0.325682i | \(-0.894406\pi\) | ||||
−0.945479 | + | 0.325682i | \(0.894406\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.71861 | 0.151272 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.18217 | −0.0698853 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26.7961 | 0.857284 | 0.428642 | − | 0.903475i | \(-0.358992\pi\) | ||||
0.428642 | + | 0.903475i | \(0.358992\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.5225 | 0.336300 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 37.1699 | 1.18674 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.6014 | 0.816557 | 0.408279 | − | 0.912857i | \(-0.366129\pi\) | ||||
0.408279 | + | 0.912857i | \(0.366129\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.63444 | −0.243253 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.32648 | −0.169544 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.39084 | −0.203217 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.0898 | 1.17820 | 0.589098 | − | 0.808061i | \(-0.299483\pi\) | ||||
0.589098 | + | 0.808061i | \(0.299483\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.12623 | −0.162676 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.6249 | 0.685556 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.24256 | −0.0393524 | −0.0196762 | − | 0.999806i | \(-0.506264\pi\) | ||||
−0.0196762 | + | 0.999806i | \(0.506264\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.02303 | −0.222199 |
(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 | 8008.2.a.y.1.7 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.y.1.7 | ✓ | 14 | 1.1 | even | 1 | trivial |