Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(49,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.q (of order \(3\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 456) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-0.173648 + 0.984808i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.49 |
Dual form | 912.2.q.k.577.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.53209 | + | 2.65366i | −0.685171 | + | 1.18675i | 0.288212 | + | 0.957567i | \(0.406939\pi\) |
−0.973383 | + | 0.229184i | \(0.926394\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.06418 | 0.780186 | 0.390093 | − | 0.920775i | \(-0.372443\pi\) | ||||
0.390093 | + | 0.920775i | \(0.372443\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.45336 | 1.94576 | 0.972881 | − | 0.231306i | \(-0.0742998\pi\) | ||||
0.972881 | + | 0.231306i | \(0.0742998\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.500000 | − | 0.866025i | −0.138675 | − | 0.240192i | 0.788320 | − | 0.615265i | \(-0.210951\pi\) |
−0.926995 | + | 0.375073i | \(0.877618\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.53209 | − | 2.65366i | −0.395584 | − | 0.685171i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.694593 | + | 1.20307i | −0.168463 | + | 0.291787i | −0.937880 | − | 0.346960i | \(-0.887214\pi\) |
0.769416 | + | 0.638748i | \(0.220547\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.75877 | + | 2.20718i | 0.862321 | + | 0.506362i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.03209 | + | 1.78763i | −0.225220 | + | 0.390093i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.53209 | + | 2.65366i | 0.319463 | + | 0.553325i | 0.980376 | − | 0.197137i | \(-0.0631643\pi\) |
−0.660913 | + | 0.750462i | \(0.729831\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.19459 | − | 3.80115i | −0.438919 | − | 0.760229i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.75877 | + | 3.04628i | 0.326595 | + | 0.565680i | 0.981834 | − | 0.189742i | \(-0.0607652\pi\) |
−0.655238 | + | 0.755422i | \(0.727432\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.45336 | −1.69787 | −0.848937 | − | 0.528494i | \(-0.822757\pi\) | ||||
−0.848937 | + | 0.528494i | \(0.822757\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.22668 | + | 5.58878i | −0.561693 | + | 0.972881i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.16250 | + | 5.47762i | −0.534561 | + | 0.925886i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.38919 | −0.392780 | −0.196390 | − | 0.980526i | \(-0.562922\pi\) | ||||
−0.196390 | + | 0.980526i | \(0.562922\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.06418 | + | 8.77141i | −0.790892 | + | 1.36986i | 0.134524 | + | 0.990910i | \(0.457050\pi\) |
−0.925415 | + | 0.378954i | \(0.876284\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.03209 | − | 5.25173i | 0.462389 | − | 0.800882i | −0.536690 | − | 0.843779i | \(-0.680326\pi\) |
0.999079 | + | 0.0428977i | \(0.0136590\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.06418 | 0.456781 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | − | 5.19615i | −0.437595 | − | 0.757937i | 0.559908 | − | 0.828554i | \(-0.310836\pi\) |
−0.997503 | + | 0.0706177i | \(0.977503\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.73917 | −0.391310 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.694593 | − | 1.20307i | −0.0972624 | − | 0.168463i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.29086 | + | 9.16404i | 0.726755 | + | 1.25878i | 0.958247 | + | 0.285941i | \(0.0923060\pi\) |
−0.231492 | + | 0.972837i | \(0.574361\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.88713 | + | 17.1250i | −1.33318 | + | 2.30914i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.79086 | + | 2.15160i | −0.502112 | + | 0.284986i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.59627 | + | 9.69302i | −0.728572 | + | 1.26192i | 0.228915 | + | 0.973446i | \(0.426482\pi\) |
−0.957487 | + | 0.288477i | \(0.906851\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.56418 | − | 4.44129i | −0.328309 | − | 0.568648i | 0.653867 | − | 0.756609i | \(-0.273146\pi\) |
−0.982177 | + | 0.187961i | \(0.939812\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.03209 | − | 1.78763i | −0.130031 | − | 0.225220i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.06418 | 0.380064 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.72668 | + | 2.99070i | 0.210948 | + | 0.365372i | 0.952011 | − | 0.306063i | \(-0.0990117\pi\) |
−0.741064 | + | 0.671435i | \(0.765678\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.06418 | −0.368884 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.36959 | − | 5.83629i | 0.399896 | − | 0.692640i | −0.593817 | − | 0.804600i | \(-0.702380\pi\) |
0.993713 | + | 0.111960i | \(0.0357128\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.56418 | − | 7.90539i | 0.534197 | − | 0.925256i | −0.465005 | − | 0.885308i | \(-0.653948\pi\) |
0.999202 | − | 0.0399477i | \(-0.0127191\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.38919 | 0.506819 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.3209 | 1.51806 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.790859 | + | 1.36981i | −0.0889786 | + | 0.154116i | −0.907080 | − | 0.420959i | \(-0.861694\pi\) |
0.818101 | + | 0.575075i | \(0.195027\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.6459 | 1.93689 | 0.968444 | − | 0.249230i | \(-0.0801774\pi\) | ||||
0.968444 | + | 0.249230i | \(0.0801774\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.12836 | − | 3.68642i | −0.230853 | − | 0.399848i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.51754 | −0.377120 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.22668 | − | 9.05288i | −0.554027 | − | 0.959603i | −0.997979 | − | 0.0635523i | \(-0.979757\pi\) |
0.443951 | − | 0.896051i | \(-0.353576\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.03209 | − | 1.78763i | −0.108192 | − | 0.187395i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.72668 | − | 8.18685i | 0.490134 | − | 0.848937i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.6159 | + | 6.59289i | −1.19176 | + | 0.676416i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.36959 | + | 5.83629i | −0.342130 | + | 0.592586i | −0.984828 | − | 0.173534i | \(-0.944481\pi\) |
0.642698 | + | 0.766119i | \(0.277815\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.22668 | − | 5.58878i | −0.324294 | − | 0.561693i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.305407 | − | 0.528981i | −0.0303892 | − | 0.0526356i | 0.850431 | − | 0.526087i | \(-0.176341\pi\) |
−0.880820 | + | 0.473451i | \(0.843008\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.0641778 | −0.00632362 | −0.00316181 | − | 0.999995i | \(-0.501006\pi\) | ||||
−0.00316181 | + | 0.999995i | \(0.501006\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.16250 | − | 5.47762i | −0.308629 | − | 0.534561i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.610815 | −0.0590497 | −0.0295248 | − | 0.999564i | \(-0.509399\pi\) | ||||
−0.0295248 | + | 0.999564i | \(0.509399\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.30541 | + | 3.99308i | −0.220818 | + | 0.382468i | −0.955057 | − | 0.296424i | \(-0.904206\pi\) |
0.734239 | + | 0.678891i | \(0.237539\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.19459 | − | 2.06910i | 0.113386 | − | 0.196390i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.4884 | 1.64517 | 0.822587 | − | 0.568639i | \(-0.192530\pi\) | ||||
0.822587 | + | 0.568639i | \(0.192530\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.38919 | −0.875546 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.500000 | + | 0.866025i | −0.0462250 | + | 0.0800641i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.43376 | + | 2.48335i | −0.131433 | + | 0.227648i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 30.6459 | 2.78599 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.06418 | − | 8.77141i | −0.456622 | − | 0.790892i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.87164 | −0.167405 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.06418 | + | 12.2355i | 0.626844 | + | 1.08573i | 0.988181 | + | 0.153291i | \(0.0489872\pi\) |
−0.361337 | + | 0.932435i | \(0.617679\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.03209 | + | 5.25173i | 0.266961 | + | 0.462389i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.75877 | − | 4.77833i | 0.241035 | − | 0.417485i | −0.719974 | − | 0.694001i | \(-0.755847\pi\) |
0.961009 | + | 0.276516i | \(0.0891798\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.75877 | + | 4.55601i | 0.672771 | + | 0.395056i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.53209 | + | 2.65366i | −0.131861 | + | 0.228390i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.88713 | − | 15.3930i | −0.759278 | − | 1.31511i | −0.943219 | − | 0.332171i | \(-0.892219\pi\) |
0.183941 | − | 0.982937i | \(-0.441115\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.48545 | − | 9.50108i | −0.465270 | − | 0.805871i | 0.533944 | − | 0.845520i | \(-0.320709\pi\) |
−0.999214 | + | 0.0396488i | \(0.987376\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.22668 | − | 5.58878i | −0.269829 | − | 0.467357i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.7784 | −0.895095 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.36959 | − | 2.37219i | 0.112961 | − | 0.195655i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.53209 | + | 11.3139i | −0.535130 | + | 0.926872i | 0.464027 | + | 0.885821i | \(0.346404\pi\) |
−0.999157 | + | 0.0410508i | \(0.986929\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.90673 | −0.399304 | −0.199652 | − | 0.979867i | \(-0.563981\pi\) | ||||
−0.199652 | + | 0.979867i | \(0.563981\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.38919 | 0.112309 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.4834 | − | 25.0860i | 1.16333 | − | 2.01495i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.86959 | + | 10.1664i | −0.468444 | + | 0.811369i | −0.999350 | − | 0.0360623i | \(-0.988519\pi\) |
0.530906 | + | 0.847431i | \(0.321852\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.5817 | −0.839185 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.16250 | + | 5.47762i | 0.249240 | + | 0.431697i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.4534 | 1.05375 | 0.526874 | − | 0.849943i | \(-0.323364\pi\) | ||||
0.526874 | + | 0.849943i | \(0.323364\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.88713 | − | 17.1250i | −0.769712 | − | 1.33318i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.98545 | + | 12.0992i | 0.540551 | + | 0.936261i | 0.998872 | + | 0.0474747i | \(0.0151173\pi\) |
−0.458322 | + | 0.888786i | \(0.651549\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0320889 | − | 4.35878i | 0.00245390 | − | 0.333324i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.75877 | + | 3.04628i | −0.133717 | + | 0.231604i | −0.925107 | − | 0.379708i | \(-0.876025\pi\) |
0.791390 | + | 0.611312i | \(0.209358\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.53003 | − | 7.84624i | −0.342438 | − | 0.593120i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.59627 | − | 9.69302i | −0.420641 | − | 0.728572i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.0642 | −0.826975 | −0.413488 | − | 0.910510i | \(-0.635690\pi\) | ||||
−0.413488 | + | 0.910510i | \(0.635690\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.7588 | − | 18.6347i | −0.799693 | − | 1.38511i | −0.919816 | − | 0.392350i | \(-0.871662\pi\) |
0.120123 | − | 0.992759i | \(-0.461671\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.12836 | 0.379099 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.66044 | − | 6.34008i | 0.269121 | − | 0.466132i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.48246 | + | 7.76385i | −0.327790 | + | 0.567749i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.06418 | 0.150147 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.2317 | 1.10213 | 0.551065 | − | 0.834462i | \(-0.314222\pi\) | ||||
0.551065 | + | 0.834462i | \(0.314222\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.13041 | + | 5.42204i | −0.225332 | + | 0.390287i | −0.956419 | − | 0.291998i | \(-0.905680\pi\) |
0.731087 | + | 0.682284i | \(0.239013\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.53209 | + | 2.65366i | −0.109715 | + | 0.190032i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.71007 | −0.478073 | −0.239036 | − | 0.971011i | \(-0.576832\pi\) | ||||
−0.239036 | + | 0.971011i | \(0.576832\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.4659 | − | 21.5915i | −0.883681 | − | 1.53058i | −0.847218 | − | 0.531245i | \(-0.821724\pi\) |
−0.0364626 | − | 0.999335i | \(-0.511609\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.45336 | −0.243581 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.63041 | + | 6.28806i | 0.254805 | + | 0.441336i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.5175 | − | 26.8772i | −1.08379 | − | 1.87718i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.53209 | − | 2.65366i | 0.106488 | − | 0.184442i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.2567 | + | 14.2437i | 1.67787 | + | 0.985260i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.48545 | − | 7.76903i | 0.308791 | − | 0.534842i | −0.669307 | − | 0.742986i | \(-0.733409\pi\) |
0.978098 | + | 0.208144i | \(0.0667422\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.36959 | + | 5.83629i | 0.230880 | + | 0.399896i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.29086 | + | 16.0922i | 0.633631 | + | 1.09748i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.5134 | −1.32466 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.56418 | + | 7.90539i | 0.308419 | + | 0.534197i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.38919 | 0.0934467 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.5692 | − | 21.7705i | 0.841698 | − | 1.45786i | −0.0467604 | − | 0.998906i | \(-0.514890\pi\) |
0.888458 | − | 0.458957i | \(-0.151777\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.19459 | + | 3.80115i | −0.146306 | + | 0.253410i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.8384 | 1.51584 | 0.757920 | − | 0.652348i | \(-0.226216\pi\) | ||||
0.757920 | + | 0.652348i | \(0.226216\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.03508 | −0.398809 | −0.199405 | − | 0.979917i | \(-0.563901\pi\) | ||||
−0.199405 | + | 0.979917i | \(0.563901\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.66044 | + | 11.5362i | −0.438225 | + | 0.759028i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.30541 | + | 3.99308i | −0.151032 | + | 0.261596i | −0.931607 | − | 0.363467i | \(-0.881593\pi\) |
0.780575 | + | 0.625062i | \(0.214926\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.3851 | 1.19931 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.790859 | − | 1.36981i | −0.0513718 | − | 0.0889786i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.36009 | −0.605454 | −0.302727 | − | 0.953077i | \(-0.597897\pi\) | ||||
−0.302727 | + | 0.953077i | \(0.597897\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.0817 | + | 17.4620i | 0.649421 | + | 1.12483i | 0.983261 | + | 0.182200i | \(0.0583218\pi\) |
−0.333841 | + | 0.942629i | \(0.608345\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.19665 | − | 7.26881i | 0.268114 | − | 0.464388i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0320889 | − | 4.35878i | 0.00204177 | − | 0.277343i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.82295 | + | 15.2818i | −0.559132 | + | 0.968444i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.06418 | + | 10.5035i | 0.382768 | + | 0.662973i | 0.991457 | − | 0.130436i | \(-0.0416377\pi\) |
−0.608689 | + | 0.793409i | \(0.708304\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.88713 | + | 17.1250i | 0.621598 | + | 1.07664i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.25671 | 0.266566 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.4192 | − | 26.7069i | −0.961824 | − | 1.66593i | −0.717916 | − | 0.696130i | \(-0.754904\pi\) |
−0.243909 | − | 0.969798i | \(-0.578430\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.93170 | −0.306441 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.75877 | − | 3.04628i | 0.108865 | − | 0.188560i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.24123 | + | 9.07808i | −0.323188 | + | 0.559778i | −0.981144 | − | 0.193278i | \(-0.938088\pi\) |
0.657956 | + | 0.753056i | \(0.271421\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −32.4243 | −1.99181 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.4534 | 0.639735 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.901674 | − | 1.56175i | 0.0549760 | − | 0.0952213i | −0.837228 | − | 0.546854i | \(-0.815825\pi\) |
0.892204 | + | 0.451633i | \(0.149158\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.1284 | − | 24.4710i | 0.858236 | − | 1.48651i | −0.0153732 | − | 0.999882i | \(-0.504894\pi\) |
0.873610 | − | 0.486627i | \(-0.161773\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.06418 | 0.124930 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.1625 | − | 24.5302i | −0.854031 | − | 1.47923i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.48246 | 0.389493 | 0.194747 | − | 0.980854i | \(-0.437612\pi\) | ||||
0.194747 | + | 0.980854i | \(0.437612\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.72668 | + | 8.18685i | 0.282979 | + | 0.490134i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.92127 | − | 5.05980i | −0.174269 | − | 0.301842i | 0.765639 | − | 0.643270i | \(-0.222423\pi\) |
−0.939908 | + | 0.341428i | \(0.889089\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.12836 | − | 14.0787i | 0.483181 | − | 0.836893i | −0.516633 | − | 0.856207i | \(-0.672815\pi\) |
0.999813 | + | 0.0193137i | \(0.00614812\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.0983261 | − | 13.3561i | 0.00582433 | − | 0.791146i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.4534 | + | 18.1058i | −0.617043 | + | 1.06875i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.53508 | + | 13.0511i | 0.443240 | + | 0.767714i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.36959 | − | 5.83629i | −0.197529 | − | 0.342130i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.2567 | 1.53393 | 0.766967 | − | 0.641687i | \(-0.221765\pi\) | ||||
0.766967 | + | 0.641687i | \(0.221765\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.1480 | − | 29.7011i | −0.998393 | − | 1.72927i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.45336 | 0.374462 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.53209 | − | 2.65366i | 0.0886030 | − | 0.153465i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.25877 | − | 10.8405i | 0.360750 | − | 0.624837i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.610815 | 0.0350904 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.7142 | 0.899792 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.14796 | − | 12.3806i | 0.407955 | − | 0.706599i | −0.586705 | − | 0.809801i | \(-0.699575\pi\) |
0.994661 | + | 0.103201i | \(0.0329086\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.0320889 | − | 0.0555796i | 0.00182547 | − | 0.00316181i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.2276 | −1.26041 | −0.630206 | − | 0.776428i | \(-0.717030\pi\) | ||||
−0.630206 | + | 0.776428i | \(0.717030\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.56624 | − | 2.71280i | −0.0885290 | − | 0.153337i | 0.818361 | − | 0.574705i | \(-0.194883\pi\) |
−0.906890 | + | 0.421368i | \(0.861550\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.32501 | 0.356374 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.04963 | + | 5.28211i | 0.171284 | + | 0.296673i | 0.938869 | − | 0.344274i | \(-0.111875\pi\) |
−0.767585 | + | 0.640947i | \(0.778542\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.3500 | + | 19.6588i | 0.635477 | + | 1.10068i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.305407 | − | 0.528981i | 0.0170462 | − | 0.0295248i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.26621 | + | 2.98897i | −0.293020 | + | 0.166311i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.19459 | + | 3.80115i | −0.121734 | + | 0.210850i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.30541 | − | 3.99308i | −0.127489 | − | 0.220818i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.19253 | − | 10.7258i | −0.341405 | − | 0.591332i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.93582 | 0.106402 | 0.0532012 | − | 0.998584i | \(-0.483058\pi\) | ||||
0.0532012 | + | 0.998584i | \(0.483058\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.19459 | + | 2.06910i | 0.0654633 | + | 0.113386i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.5817 | −0.578141 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.58378 | − | 6.20729i | 0.195221 | − | 0.338132i | −0.751752 | − | 0.659446i | \(-0.770791\pi\) |
0.946973 | + | 0.321313i | \(0.104124\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.74422 | + | 15.1454i | −0.474921 | + | 0.822587i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −61.0060 | −3.30366 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1034 | −1.08548 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.69459 | − | 8.13127i | 0.252748 | − | 0.437773i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.80840 | + | 8.32839i | −0.258128 | + | 0.447092i | −0.965741 | − | 0.259510i | \(-0.916439\pi\) |
0.707612 | + | 0.706601i | \(0.249772\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.5134 | 1.68687 | 0.843437 | − | 0.537227i | \(-0.180528\pi\) | ||||
0.843437 | + | 0.537227i | \(0.180528\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.500000 | − | 0.866025i | −0.0266880 | − | 0.0462250i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.8425 | −1.37546 | −0.687730 | − | 0.725967i | \(-0.741393\pi\) | ||||
−0.687730 | + | 0.725967i | \(0.741393\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.3250 | + | 17.8834i | 0.547995 | + | 0.949154i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.43376 | − | 2.48335i | −0.0758828 | − | 0.131433i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.1284 | − | 27.9351i | 0.851222 | − | 1.47436i | −0.0288840 | − | 0.999583i | \(-0.509195\pi\) |
0.880106 | − | 0.474777i | \(-0.157471\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.25671 | + | 16.5926i | 0.487195 | + | 0.873293i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.3229 | + | 26.5401i | −0.804246 | + | 1.39300i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.9855 | + | 24.2235i | 0.732032 | + | 1.26792i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.6334 | + | 25.3458i | 0.763858 | + | 1.32304i | 0.940848 | + | 0.338828i | \(0.110030\pi\) |
−0.176991 | + | 0.984213i | \(0.556636\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.1284 | 0.527261 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.9213 | + | 18.9162i | 0.567004 | + | 0.982080i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.03920 | 0.416254 | 0.208127 | − | 0.978102i | \(-0.433263\pi\) | ||||
0.208127 | + | 0.978102i | \(0.433263\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.935822 | − | 1.62089i | 0.0483257 | − | 0.0837025i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.75877 | − | 3.04628i | 0.0905813 | − | 0.156891i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.19253 | −0.420822 | −0.210411 | − | 0.977613i | \(-0.567480\pi\) | ||||
−0.210411 | + | 0.977613i | \(0.567480\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.1284 | −0.723818 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.74422 | + | 4.75313i | −0.140223 | + | 0.242874i | −0.927581 | − | 0.373623i | \(-0.878115\pi\) |
0.787357 | + | 0.616497i | \(0.211449\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20.4088 | + | 35.3491i | −1.04013 | + | 1.80155i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.06418 | −0.308259 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.22668 | − | 7.32083i | −0.214301 | − | 0.371181i | 0.738755 | − | 0.673974i | \(-0.235414\pi\) |
−0.953056 | + | 0.302793i | \(0.902081\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.25671 | −0.215271 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.75877 | + | 4.77833i | 0.139162 | + | 0.241035i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.42333 | − | 4.19734i | −0.121931 | − | 0.211191i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.5351 | + | 21.7114i | −0.629118 | + | 1.08966i | 0.358611 | + | 0.933487i | \(0.383250\pi\) |
−0.987729 | + | 0.156177i | \(0.950083\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.82501 | + | 4.44129i | −0.391740 | + | 0.222342i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.8726 | − | 22.2960i | 0.642826 | − | 1.11341i | −0.341973 | − | 0.939710i | \(-0.611095\pi\) |
0.984799 | − | 0.173697i | \(-0.0555715\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.72668 | + | 8.18685i | 0.235453 | + | 0.407816i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.53209 | − | 2.65366i | −0.0761301 | − | 0.131861i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.4183 | −0.764256 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.21213 | + | 5.56358i | 0.158830 | + | 0.275101i | 0.934447 | − | 0.356102i | \(-0.115895\pi\) |
−0.775617 | + | 0.631204i | \(0.782561\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.7743 | 0.876739 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.5517 | + | 20.0081i | −0.568421 | + | 0.984535i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −27.0351 | + | 46.8261i | −1.32710 | + | 2.29860i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.9709 | 0.537247 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.2668 | −0.794686 | −0.397343 | − | 0.917670i | \(-0.630068\pi\) | ||||
−0.397343 | + | 0.917670i | \(0.630068\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.7297 | − | 25.5125i | 0.717880 | − | 1.24341i | −0.243958 | − | 0.969786i | \(-0.578446\pi\) |
0.961838 | − | 0.273619i | \(-0.0882209\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.00000 | + | 5.19615i | −0.145865 | + | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.09739 | 0.295767 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.29292 | − | 9.16760i | −0.256142 | − | 0.443651i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.45336 | 0.311571 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.51754 | − | 14.7528i | −0.410276 | − | 0.710618i | 0.584644 | − | 0.811290i | \(-0.301234\pi\) |
−0.994920 | + | 0.100672i | \(0.967901\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.84049 | + | 11.8481i | 0.328733 | + | 0.569382i | 0.982261 | − | 0.187520i | \(-0.0600451\pi\) |
−0.653528 | + | 0.756903i | \(0.726712\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.38919 | − | 9.33434i | 0.258392 | − | 0.447547i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.0983261 | + | 13.3561i | −0.00470357 | + | 0.638908i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.707081 | − | 1.22470i | 0.0337471 | − | 0.0584518i | −0.848659 | − | 0.528941i | \(-0.822589\pi\) |
0.882406 | + | 0.470489i | \(0.155923\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.36959 | + | 2.37219i | 0.0652183 | + | 0.112961i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.369585 | + | 0.640140i | 0.0175595 | + | 0.0304140i | 0.874672 | − | 0.484716i | \(-0.161077\pi\) |
−0.857112 | + | 0.515130i | \(0.827744\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 32.0310 | 1.51841 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.53209 | − | 11.3139i | −0.308957 | − | 0.535130i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.51754 | 0.354775 | 0.177387 | − | 0.984141i | \(-0.443235\pi\) | ||||
0.177387 | + | 0.984141i | \(0.443235\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −32.6810 | + | 56.6051i | −1.53889 | + | 2.66543i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.45336 | − | 4.24935i | 0.115269 | − | 0.199652i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.32501 | 0.296521 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.6810 | −0.733525 | −0.366763 | − | 0.930315i | \(-0.619534\pi\) | ||||
−0.366763 | + | 0.930315i | \(0.619534\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.694593 | + | 1.20307i | −0.0324208 | + | 0.0561545i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.7442 | + | 18.6095i | −0.500408 | + | 0.866733i | 0.499592 | + | 0.866261i | \(0.333483\pi\) |
−1.00000 | 0.000471567i | \(0.999850\pi\) | ||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.62092 | 0.447122 | 0.223561 | − | 0.974690i | \(-0.428232\pi\) | ||||
0.223561 | + | 0.974690i | \(0.428232\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 14.4834 | + | 25.0860i | 0.671651 | + | 1.16333i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.87164 | −0.0866094 | −0.0433047 | − | 0.999062i | \(-0.513789\pi\) | ||||
−0.0433047 | + | 0.999062i | \(0.513789\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.56418 | + | 6.17334i | 0.164578 | + | 0.285058i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.86959 | − | 10.1664i | −0.270456 | − | 0.468444i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.5672 | − | 33.8913i | 0.899699 | − | 1.55833i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.140844 | − | 19.1315i | 0.00646237 | − | 0.877813i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.29086 | − | 9.16404i | 0.242252 | − | 0.419592i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.36959 | + | 5.83629i | 0.153960 | + | 0.266667i | 0.932680 | − | 0.360705i | \(-0.117464\pi\) |
−0.778720 | + | 0.627372i | \(0.784131\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.19459 | + | 2.06910i | 0.0544687 | + | 0.0943426i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.32501 | −0.287798 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.3250 | − | 17.8834i | −0.468834 | − | 0.812045i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.38507 | 0.108078 | 0.0540388 | − | 0.998539i | \(-0.482791\pi\) | ||||
0.0540388 | + | 0.998539i | \(0.482791\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.72668 | + | 11.6510i | −0.304191 | + | 0.526874i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.36959 | + | 9.30039i | −0.242326 | + | 0.419721i | −0.961376 | − | 0.275237i | \(-0.911244\pi\) |
0.719050 | + | 0.694958i | \(0.244577\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.88652 | −0.220078 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 19.7743 | 0.888787 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.95542 | − | 12.0471i | 0.311993 | − | 0.540388i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.2733 | − | 24.7221i | 0.638961 | − | 1.10671i | −0.346700 | − | 0.937976i | \(-0.612698\pi\) |
0.985661 | − | 0.168738i | \(-0.0539690\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.9709 | −0.624174 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.75877 | + | 3.04628i | 0.0784197 | + | 0.135827i | 0.902568 | − | 0.430547i | \(-0.141679\pi\) |
−0.824149 | + | 0.566374i | \(0.808346\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.87164 | 0.0832871 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.00000 | + | 10.3923i | 0.266469 | + | 0.461538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.61081 | − | 6.25411i | −0.160047 | − | 0.277209i | 0.774839 | − | 0.632159i | \(-0.217831\pi\) |
−0.934885 | + | 0.354950i | \(0.884498\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.42127 | − | 16.3181i | 0.416773 | − | 0.721871i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.75877 | + | 2.20718i | 0.165954 | + | 0.0974494i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.0983261 | − | 0.170306i | 0.00433276 | − | 0.00750457i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.3601 | − | 33.5327i | −0.851456 | − | 1.47476i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.75877 | − | 3.04628i | −0.0772015 | − | 0.133717i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.8075 | 0.736348 | 0.368174 | − | 0.929757i | \(-0.379983\pi\) | ||||
0.368174 | + | 0.929757i | \(0.379983\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.88413 | − | 6.72752i | −0.169841 | − | 0.294174i | 0.768523 | − | 0.639823i | \(-0.220992\pi\) |
−0.938364 | + | 0.345649i | \(0.887659\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.06006 | 0.395413 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.56624 | − | 11.3731i | 0.286030 | − | 0.495418i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.80541 | − | 11.7873i | 0.295887 | − | 0.512492i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.1925 | 0.485715 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.1284 | 0.438708 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.935822 | − | 1.62089i | 0.0404591 | − | 0.0700773i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.53209 | − | 9.58186i | 0.238727 | − | 0.413488i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17.6769 | −0.761396 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.1655 | + | 31.4636i | 0.780996 | + | 1.35272i | 0.931362 | + | 0.364094i | \(0.118621\pi\) |
−0.150367 | + | 0.988630i | \(0.548045\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.5175 | 0.923406 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.06418 | − | 12.2355i | −0.302596 | − | 0.524112i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.8105 | + | 27.3845i | 0.676006 | + | 1.17088i | 0.976174 | + | 0.216991i | \(0.0696242\pi\) |
−0.300167 | + | 0.953887i | \(0.597042\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.56418 | + | 4.44129i | −0.109436 | + | 0.189549i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.112874 | + | 15.3322i | −0.00480859 | + | 0.653173i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.63247 | + | 2.82753i | −0.0694199 | + | 0.120239i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.66044 | + | 6.34008i | 0.155377 | + | 0.269121i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.01960 | − | 3.49805i | −0.0855732 | − | 0.148217i | 0.820062 | − | 0.572275i | \(-0.193939\pi\) |
−0.905635 | + | 0.424057i | \(0.860605\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.06418 | −0.256487 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.48246 | − | 7.76385i | −0.189250 | − | 0.327790i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.61081 | 0.362903 | 0.181451 | − | 0.983400i | \(-0.441921\pi\) | ||||
0.181451 | + | 0.983400i | \(0.441921\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −26.7939 | + | 46.4083i | −1.12723 | + | 1.95241i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.03209 | + | 1.78763i | −0.0433437 | + | 0.0750734i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.6851 | −1.16062 | −0.580310 | − | 0.814396i | \(-0.697069\pi\) | ||||
−0.580310 | + | 0.814396i | \(0.697069\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.1533 | −1.01079 | −0.505393 | − | 0.862889i | \(-0.668652\pi\) | ||||
−0.505393 | + | 0.862889i | \(0.668652\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.61587 | + | 13.1911i | −0.318157 | + | 0.551065i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.72462 | − | 11.6474i | 0.280436 | − | 0.485730i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.8675 | 1.20177 | 0.600885 | − | 0.799335i | \(-0.294815\pi\) | ||||
0.600885 | + | 0.799335i | \(0.294815\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.13041 | − | 5.42204i | −0.130096 | − | 0.225332i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 36.4243 | 1.51113 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 34.1438 | + | 59.1389i | 1.41409 | + | 2.44928i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.53209 | − | 2.65366i | −0.0633441 | − | 0.109715i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.14290 | − | 8.90777i | 0.212270 | − | 0.367663i | −0.740154 | − | 0.672437i | \(-0.765248\pi\) |
0.952425 | + | 0.304774i | \(0.0985809\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −35.5330 | − | 20.8653i | −1.46411 | − | 0.859739i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.35504 | − | 5.81109i | 0.138008 | − | 0.239036i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.96585 | + | 13.7973i | 0.327118 | + | 0.566586i | 0.981939 | − | 0.189199i | \(-0.0605891\pi\) |
−0.654820 | + | 0.755784i | \(0.727256\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.39330 | − | 7.60943i | −0.180108 | − | 0.311956i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 24.9317 | 1.02039 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.03003 | − | 15.6405i | −0.368957 | − | 0.639052i | 0.620446 | − | 0.784249i | \(-0.286952\pi\) |
−0.989403 | + | 0.145197i | \(0.953618\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.86753 | −0.320923 | −0.160462 | − | 0.987042i | \(-0.551298\pi\) | ||||
−0.160462 | + | 0.987042i | \(0.551298\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.72668 | − | 2.99070i | 0.0703159 | − | 0.121791i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −46.9522 | + | 81.3237i | −1.90888 | + | 3.30628i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.2668 | 0.700838 | 0.350419 | − | 0.936593i | \(-0.386039\pi\) | ||||
0.350419 | + | 0.936593i | \(0.386039\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.26083 | −0.294224 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.00000 | + | 5.19615i | −0.121367 | + | 0.210214i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.7939 | − | 23.8917i | 0.557128 | − | 0.964975i | −0.440606 | − | 0.897701i | \(-0.645236\pi\) |
0.997735 | − | 0.0672742i | \(-0.0214302\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 31.0351 | 1.25146 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.24628 | − | 14.2830i | −0.331983 | − | 0.575011i | 0.650918 | − | 0.759148i | \(-0.274384\pi\) |
−0.982901 | + | 0.184137i | \(0.941051\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.4884 | −0.984274 | −0.492137 | − | 0.870518i | \(-0.663784\pi\) | ||||
−0.492137 | + | 0.870518i | \(0.663784\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.53209 | + | 2.65366i | 0.0614806 | + | 0.106488i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.7888 | − | 18.6867i | −0.432244 | − | 0.748669i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.8405 | − | 23.9724i | 0.553620 | − | 0.958897i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −24.4638 | + | 13.8851i | −0.976990 | + | 0.554516i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.65951 | − | 2.87436i | 0.0661690 | − | 0.114608i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.83544 | + | 17.0355i | 0.391543 | + | 0.678172i | 0.992653 | − | 0.120994i | \(-0.0386082\pi\) |
−0.601111 | + | 0.799166i | \(0.705275\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.48545 | + | 7.76903i | 0.178281 | + | 0.308791i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −43.2918 | −1.71798 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.36959 | + | 2.37219i | 0.0542649 | + | 0.0939896i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.73917 | −0.266597 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.06418 | + | 7.03936i | −0.160525 | + | 0.278038i | −0.935057 | − | 0.354497i | \(-0.884652\pi\) |
0.774532 | + | 0.632535i | \(0.217986\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.91921 | − | 6.78828i | 0.154559 | − | 0.267704i | −0.778340 | − | 0.627844i | \(-0.783938\pi\) |
0.932898 | + | 0.360140i | \(0.117271\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.5817 | −0.731654 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.7743 | 1.56369 | 0.781844 | − | 0.623475i | \(-0.214280\pi\) | ||||
0.781844 | + | 0.623475i | \(0.214280\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −36.1147 | + | 62.5526i | −1.41763 | + | 2.45540i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.75671 | − | 16.8991i | 0.382396 | − | 0.662329i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.94593 | 0.350081 | 0.175041 | − | 0.984561i | \(-0.443994\pi\) | ||||
0.175041 | + | 0.984561i | \(0.443994\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.45336 | + | 14.6417i | 0.330300 | + | 0.572097i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.12836 | −0.356131 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.93676 | − | 10.2828i | −0.231263 | − | 0.400560i | 0.726917 | − | 0.686725i | \(-0.240953\pi\) |
−0.958180 | + | 0.286166i | \(0.907619\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.9067 | − | 37.9436i | −0.852073 | − | 1.47583i | −0.879334 | − | 0.476205i | \(-0.842012\pi\) |
0.0272613 | − | 0.999628i | \(-0.491321\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.694593 | + | 1.20307i | −0.0269757 | + | 0.0467234i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −23.9772 | + | 13.6089i | −0.929796 | + | 0.527730i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.38919 | + | 9.33434i | −0.208670 | + | 0.361427i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.5692 | + | 21.7705i | 0.485955 | + | 0.841698i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.5476 | − | 28.6612i | −0.638812 | − | 1.10645i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.6810 | −1.45249 | −0.726247 | − | 0.687433i | \(-0.758737\pi\) | ||||
−0.726247 | + | 0.687433i | \(0.758737\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.19459 | − | 3.80115i | −0.0844699 | − | 0.146306i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −35.1052 | −1.34920 | −0.674602 | − | 0.738182i | \(-0.735685\pi\) | ||||
−0.674602 | + | 0.738182i | \(0.735685\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.95542 | + | 12.0471i | −0.266925 | + | 0.462327i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.4192 | + | 19.7787i | −0.437585 | + | 0.757920i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −37.6168 | −1.43937 | −0.719683 | − | 0.694302i | \(-0.755713\pi\) | ||||
−0.719683 | + | 0.694302i | \(0.755713\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 54.4635 | 2.08094 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.01754 | − | 5.22653i | 0.115126 | − | 0.199405i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.29086 | − | 9.16404i | 0.201566 | − | 0.349122i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.69997 | 0.102712 | 0.0513558 | − | 0.998680i | \(-0.483646\pi\) | ||||
0.0513558 | + | 0.998680i | \(0.483646\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.66044 | − | 11.5362i | −0.253009 | − | 0.438225i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 33.6168 | 1.27516 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.03508 | − | 12.1851i | −0.266473 | − | 0.461544i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.30541 | − | 3.99308i | −0.0871985 | − | 0.151032i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.8821 | − | 18.8483i | 0.411010 | − | 0.711891i | −0.583990 | − | 0.811761i | \(-0.698509\pi\) |
0.995000 | + | 0.0998700i | \(0.0318427\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.98040 | − | 5.27336i | −0.338702 | − | 0.198889i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.19253 | + | 15.9219i | −0.346211 | + | 0.599655i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.630415 | − | 1.09191i | −0.0237092 | − | 0.0410655i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.3033 | + | 23.0421i | 0.499618 | + | 0.865363i | 1.00000 | 0.000441366i | \(-0.000140491\pi\) | |
−0.500382 | + | 0.865805i | \(0.666807\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.58172 | 0.0593191 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14.4834 | − | 25.0860i | −0.542407 | − | 0.939477i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.7743 | 0.739515 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.68004 | − | 8.10608i | 0.174779 | − | 0.302727i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.81790 | + | 6.61279i | −0.142383 | + | 0.246615i | −0.928394 | − | 0.371598i | \(-0.878810\pi\) |
0.786010 | + | 0.618214i | \(0.212143\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.132474 | −0.00493360 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.1634 | −0.749886 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.71957 | − | 13.3707i | 0.286698 | − | 0.496575i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.3726 | − | 35.2863i | 0.755577 | − | 1.30870i | −0.189510 | − | 0.981879i | \(-0.560690\pi\) |
0.945087 | − | 0.326819i | \(-0.105977\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.21213 | + | 7.29563i | 0.155791 | + | 0.269839i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 48.4742 | 1.79044 | 0.895218 | − | 0.445628i | \(-0.147020\pi\) | ||||
0.895218 | + | 0.445628i | \(0.147020\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.19665 | + | 7.26881i | 0.154796 | + | 0.268114i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.1429 | + | 19.3001i | 0.410454 | + | 0.710927i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.30840 | + | 9.19442i | −0.195273 | + | 0.338222i | −0.946990 | − | 0.321263i | \(-0.895893\pi\) |
0.751717 | + | 0.659486i | \(0.229226\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.75877 | + | 2.20718i | 0.138082 | + | 0.0810828i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.7793 | − | 41.1870i | 0.872378 | − | 1.51100i | 0.0128483 | − | 0.999917i | \(-0.495910\pi\) |
0.859530 | − | 0.511086i | \(-0.170757\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.0155 | − | 34.6678i | −0.733311 | − | 1.27013i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.82295 | − | 15.2818i | −0.322815 | − | 0.559132i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.26083 | −0.0460697 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.96791 | − | 13.8008i | −0.290753 | − | 0.503599i | 0.683235 | − | 0.730199i | \(-0.260573\pi\) |
−0.973988 | + | 0.226599i | \(0.927239\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.1284 | −0.441982 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.51754 | − | 13.0208i | 0.273591 | − | 0.473874i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.17499 | − | 15.8916i | 0.333471 | − | 0.577588i | −0.649719 | − | 0.760174i | \(-0.725113\pi\) |
0.983190 | + | 0.182586i | \(0.0584468\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −19.7743 | −0.717760 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.7802 | −1.33328 | −0.666641 | − | 0.745379i | \(-0.732269\pi\) | ||||
−0.666641 | + | 0.745379i | \(0.732269\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.75877 | + | 8.24243i | −0.172279 | + | 0.298396i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.12836 | + | 3.68642i | −0.0769509 | + | 0.133283i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.1925 | 0.404139 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.0175 | − | 36.4034i | −0.757912 | − | 1.31274i | −0.943914 | − | 0.330193i | \(-0.892886\pi\) |
0.186002 | − | 0.982549i | \(-0.440447\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.8384 | 1.11062 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.9709 | − | 39.7868i | −0.826206 | − | 1.43103i | −0.900994 | − | 0.433831i | \(-0.857161\pi\) |
0.0747881 | − | 0.997199i | \(-0.476172\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.7463 | + | 35.9336i | 0.745228 | + | 1.29077i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.46585 | − | 4.27098i | 0.0884619 | − | 0.153221i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −38.3952 | + | 21.7922i | −1.37565 | + | 0.780786i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.7452 | − | 37.6637i | 0.778103 | − | 1.34771i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.75877 | + | 3.04628i | 0.0628533 | + | 0.108865i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.9855 | − | 31.1517i | −0.641928 | − | 1.11185i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.3250 | 0.617570 | 0.308785 | − | 0.951132i | \(-0.400078\pi\) | ||||
0.308785 | + | 0.951132i | \(0.400078\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.24123 | − | 9.07808i | −0.186593 | − | 0.323188i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 36.0993 | 1.28354 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.56418 | + | 4.44129i | −0.0910566 | + | 0.157715i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 16.2121 | − | 28.0802i | 0.574985 | − | 0.995903i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.8324 | −0.773345 | −0.386672 | − | 0.922217i | \(-0.626376\pi\) | ||||
−0.386672 | + | 0.922217i | \(0.626376\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.33511 | 0.294875 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.22668 | + | 9.05288i | −0.184676 | + | 0.319868i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 29.4543 | − | 51.0163i | 1.03942 | − | 1.80033i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19.3809 | −0.683089 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.901674 | + | 1.56175i | 0.0317404 | + | 0.0549760i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34.6709 | −1.21896 | −0.609482 | − | 0.792800i | \(-0.708622\pi\) | ||||
−0.609482 | + | 0.792800i | \(0.708622\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.4534 | − | 25.0340i | −0.507526 | − | 0.879061i | −0.999962 | − | 0.00871245i | \(-0.997227\pi\) |
0.492436 | − | 0.870349i | \(-0.336107\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.1284 | + | 24.4710i | 0.495503 | + | 0.858236i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.6117 | + | 35.7006i | −0.721998 | + | 1.25054i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.9884 | − | 13.0477i | 0.804264 | − | 0.456481i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.03209 | + | 1.78763i | −0.0360641 | + | 0.0624649i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.7588 | + | 23.8309i | 0.480184 | + | 0.831704i | 0.999742 | − | 0.0227319i | \(-0.00723641\pi\) |
−0.519557 | + | 0.854436i | \(0.673903\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.9709 | − | 38.0547i | −0.765858 | − | 1.32650i | −0.939792 | − | 0.341747i | \(-0.888981\pi\) |
0.173934 | − | 0.984757i | \(-0.444352\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 28.3250 | 0.986150 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.980400 | + | 1.69810i | 0.0340918 | + | 0.0590488i | 0.882568 | − | 0.470185i | \(-0.155813\pi\) |
−0.848476 | + | 0.529234i | \(0.822479\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.4284 | −0.362193 | −0.181096 | − | 0.983465i | \(-0.557965\pi\) | ||||
−0.181096 | + | 0.983465i | \(0.557965\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.24123 | + | 5.61397i | −0.112437 | + | 0.194747i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.90261 | − | 3.29541i | 0.0659214 | − | 0.114179i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −42.8093 | −1.48148 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.45336 | −0.326756 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.1976 | − | 28.0550i | 0.559203 | − | 0.968568i | −0.438360 | − | 0.898799i | \(-0.644441\pi\) |
0.997563 | − | 0.0697683i | \(-0.0222260\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.31345 | − | 14.3993i | 0.286671 | − | 0.496528i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.84255 | 0.201228 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.3851 | + | 31.8439i | 0.632466 | + | 1.09546i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 63.2586 | 2.17359 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.12836 | + | 14.0787i | 0.278964 | + | 0.483181i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.66044 | − | 6.34008i | −0.125478 | − | 0.217335i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.5838 | − | 25.2598i | 0.499339 | − | 0.864881i | −0.500661 | − | 0.865644i | \(-0.666910\pi\) |
1.00000 | 0.000763028i | \(0.000242879\pi\) | ||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.5175 | + | 6.76319i | 0.393892 | + | 0.231296i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.77837 | + | 13.4725i | −0.265704 | + | 0.460213i | −0.967748 | − | 0.251921i | \(-0.918938\pi\) |
0.702044 | + | 0.712134i | \(0.252271\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.0767 | + | 26.1136i | 0.514409 | + | 0.890983i | 0.999860 | + | 0.0167190i | \(0.00532208\pi\) |
−0.485451 | + | 0.874264i | \(0.661345\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.4534 | − | 18.1058i | −0.356250 | − | 0.617043i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.7351 | 0.671789 | 0.335894 | − | 0.941900i | \(-0.390961\pi\) | ||||
0.335894 | + | 0.941900i | \(0.390961\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.38919 | − | 9.33434i | −0.183238 | − | 0.317377i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.0702 | −0.511810 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.10370 | + | 8.83987i | −0.173131 | + | 0.299872i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.72668 | − | 2.99070i | 0.0585064 | − | 0.101336i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.73917 | 0.228086 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.86341 | −0.130607 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.32295 | − | 9.21962i | 0.179743 | − | 0.311324i | −0.762049 | − | 0.647519i | \(-0.775807\pi\) |
0.941793 | + | 0.336195i | \(0.109140\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.1284 | + | 22.7390i | −0.442808 | + | 0.766967i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.9709 | 1.34665 | 0.673327 | − | 0.739345i | \(-0.264865\pi\) | ||||
0.673327 | + | 0.739345i | \(0.264865\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.5496 | + | 25.2007i | 0.489634 | + | 0.848071i | 0.999929 | − | 0.0119285i | \(-0.00379705\pi\) |
−0.510295 | + | 0.860000i | \(0.670464\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 34.2959 | 1.15284 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.72462 | + | 16.8435i | 0.326521 | + | 0.565551i | 0.981819 | − | 0.189820i | \(-0.0607903\pi\) |
−0.655298 | + | 0.755370i | \(0.727457\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.5817 | + | 25.2563i | 0.489055 | + | 0.847068i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.22668 | + | 5.58878i | −0.108098 | + | 0.187231i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.192533 | − | 26.1527i | 0.00644288 | − | 0.875166i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.9513 | − | 29.3605i | 0.566620 | − | 0.981414i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.53209 | + | 2.65366i | 0.0511550 | + | 0.0886030i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16.6263 | − | 28.7976i | −0.554518 | − | 0.960453i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.7000 | −0.489727 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.25877 | + | 10.8405i | 0.208279 | + | 0.360750i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 65.9336 | 2.19171 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.778371 | − | 1.34818i | 0.0258454 | − | 0.0447655i | −0.852813 | − | 0.522216i | \(-0.825106\pi\) |
0.878659 | + | 0.477450i | \(0.158439\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.305407 | + | 0.528981i | −0.0101297 | + | 0.0175452i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.9418 | −1.45586 | −0.727929 | − | 0.685653i | \(-0.759517\pi\) | ||||
−0.727929 | + | 0.685653i | \(0.759517\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 113.875 | 3.76872 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.85710 | + | 13.6089i | −0.259748 | + | 0.449896i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.69459 | − | 9.86332i | 0.188052 | − | 0.325716i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43.4843 | −1.43442 | −0.717208 | − | 0.696859i | \(-0.754580\pi\) | ||||
−0.717208 | + | 0.696859i | \(0.754580\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.14796 | + | 12.3806i | 0.235533 | + | 0.407955i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.73917 | −0.221822 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.24329 | + | 9.08164i | 0.172398 | + | 0.298603i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.0320889 | + | 0.0555796i | 0.00105394 | + | 0.00182547i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.63547 | + | 14.9571i | −0.283320 | + | 0.490725i | −0.972201 | − | 0.234150i | \(-0.924769\pi\) |
0.688880 | + | 0.724875i | \(0.258103\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.2959 | − | 6.04584i | −0.337435 | − | 0.198144i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.1138 | − | 19.2497i | 0.363850 | − | 0.630206i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.7351 | − | 23.7898i | −0.449184 | − | 0.778010i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.6088 | − | 25.3031i | −0.477247 | − | 0.826616i | 0.522413 | − | 0.852693i | \(-0.325032\pi\) |
−0.999660 | + | 0.0260763i | \(0.991699\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.13247 | 0.102224 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.6459 | + | 23.6354i | 0.444844 | + | 0.770492i | 0.998041 | − | 0.0625584i | \(-0.0199260\pi\) |
−0.553198 | + | 0.833050i | \(0.686593\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31.0351 | −1.01064 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.16250 | + | 5.47762i | −0.102876 | + | 0.178187i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.6655 | + | 44.4539i | −0.834017 | + | 1.44456i | 0.0608120 | + | 0.998149i | \(0.480631\pi\) |
−0.894829 | + | 0.446410i | \(0.852702\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.12836 | −0.296319 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.09926 | −0.197782 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.5672 | − | 47.7477i | 0.892988 | − | 1.54670i | 0.0567134 | − | 0.998390i | \(-0.481938\pi\) |
0.836275 | − | 0.548311i | \(-0.184729\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.3364 | + | 40.4198i | −0.755147 | + | 1.30795i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −22.7000 | −0.733786 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.3446 | − | 31.7738i | −0.592378 | − | 1.02603i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 58.3661 | 1.88278 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.305407 | + | 0.528981i | 0.00984161 | + | 0.0170462i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.59215 | − | 16.6141i | −0.308782 | − | 0.534826i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.1759 | − | 43.6060i | 0.809603 | − | 1.40227i | −0.103536 | − | 0.994626i | \(-0.533016\pi\) |
0.913139 | − | 0.407648i | \(-0.133651\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.0445774 | − | 6.05515i | 0.00143203 | − | 0.194520i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.9959 | − | 48.4903i | 0.898431 | − | 1.55613i | 0.0689300 | − | 0.997621i | \(-0.478041\pi\) |
0.829501 | − | 0.558506i | \(-0.188625\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.3229 | − | 19.6119i | −0.362997 | − | 0.628729i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.19459 | − | 3.80115i | −0.0702832 | − | 0.121734i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.8283 | −0.474400 | −0.237200 | − | 0.971461i | \(-0.576230\pi\) | ||||
−0.237200 | + | 0.971461i | \(0.576230\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −33.7297 | − | 58.4215i | −1.07801 | − | 1.86716i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.61081 | 0.147212 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.41921 | − | 14.5825i | 0.268531 | − | 0.465110i | −0.699952 | − | 0.714190i | \(-0.746795\pi\) |
0.968483 | + | 0.249081i | \(0.0801284\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.2804 | − | 17.8062i | 0.327562 | − | 0.567354i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.3851 | 0.394221 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.5817 | 0.590864 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.2050 | − | 47.1205i | 0.864196 | − | 1.49683i | −0.00364729 | − | 0.999993i | \(-0.501161\pi\) |
0.867843 | − | 0.496838i | \(-0.165506\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.967911 | + | 1.67647i | −0.0307157 | + | 0.0532012i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 76.3952 | 2.42189 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.1614 | − | 47.0449i | −0.860209 | − | 1.48993i | −0.871726 | − | 0.489993i | \(-0.836999\pi\) |
0.0115170 | − | 0.999934i | \(-0.496334\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.38919 | −0.0755905 |
(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 | 912.2.q.k.49.1 | 6 | ||
3.2 | odd | 2 | 2736.2.s.x.1873.3 | 6 | |||
4.3 | odd | 2 | 456.2.q.f.49.1 | ✓ | 6 | ||
12.11 | even | 2 | 1368.2.s.j.505.3 | 6 | |||
19.7 | even | 3 | inner | 912.2.q.k.577.1 | 6 | ||
57.26 | odd | 6 | 2736.2.s.x.577.3 | 6 | |||
76.7 | odd | 6 | 456.2.q.f.121.1 | yes | 6 | ||
76.11 | odd | 6 | 8664.2.a.x.1.3 | 3 | |||
76.27 | even | 6 | 8664.2.a.z.1.3 | 3 | |||
228.83 | even | 6 | 1368.2.s.j.577.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.2.q.f.49.1 | ✓ | 6 | 4.3 | odd | 2 | ||
456.2.q.f.121.1 | yes | 6 | 76.7 | odd | 6 | ||
912.2.q.k.49.1 | 6 | 1.1 | even | 1 | trivial | ||
912.2.q.k.577.1 | 6 | 19.7 | even | 3 | inner | ||
1368.2.s.j.505.3 | 6 | 12.11 | even | 2 | |||
1368.2.s.j.577.3 | 6 | 228.83 | even | 6 | |||
2736.2.s.x.577.3 | 6 | 57.26 | odd | 6 | |||
2736.2.s.x.1873.3 | 6 | 3.2 | odd | 2 | |||
8664.2.a.x.1.3 | 3 | 76.11 | odd | 6 | |||
8664.2.a.z.1.3 | 3 | 76.27 | even | 6 |