Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1232,2,Mod(815,1232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1232, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1232.815");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1232 = 2^{4} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1232.be (of order \(6\), degree \(2\), 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: | \(9.83756952902\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1167.2 | ||
Character | \(\chi\) | \(=\) | 1232.1167 |
Dual form | 1232.2.be.b.815.2 |
$q$-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 \(\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times\).
\(n\) | \(309\) | \(353\) | \(463\) | \(673\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −1.51694 | − | 2.62742i | −0.875808 | − | 1.51694i | −0.855899 | − | 0.517142i | \(-0.826996\pi\) |
−0.0199086 | − | 0.999802i | \(-0.506338\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.766106 | − | 0.442311i | −0.342613 | − | 0.197808i | 0.318814 | − | 0.947817i | \(-0.396715\pi\) |
−0.661427 | + | 0.750010i | \(0.730049\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.296809 | − | 2.62905i | 0.112183 | − | 0.993688i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.10224 | + | 5.37323i | −1.03408 | + | 1.79108i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.866025 | − | 0.500000i | 0.261116 | − | 0.150756i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.80526i | 1.61009i | 0.593215 | + | 0.805044i | \(0.297858\pi\) | ||||
−0.593215 | + | 0.805044i | \(0.702142\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.68385i | 0.692966i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.576630 | + | 0.332917i | −0.139853 | + | 0.0807443i | −0.568294 | − | 0.822826i | \(-0.692396\pi\) |
0.428441 | + | 0.903570i | \(0.359063\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.71630 | + | 6.43682i | −0.852577 | + | 1.47671i | 0.0262969 | + | 0.999654i | \(0.491628\pi\) |
−0.878874 | + | 0.477053i | \(0.841705\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.35787 | + | 3.20828i | −1.60562 | + | 0.700104i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.96659 | − | 1.71276i | −0.618577 | − | 0.357135i | 0.157738 | − | 0.987481i | \(-0.449580\pi\) |
−0.776315 | + | 0.630346i | \(0.782913\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.10872 | − | 3.65241i | −0.421744 | − | 0.730483i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 9.72202 | 1.87100 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.57738 | −0.292912 | −0.146456 | − | 0.989217i | \(-0.546787\pi\) | ||||
−0.146456 | + | 0.989217i | \(0.546787\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.72783 | + | 4.72475i | 0.489933 | + | 0.848590i | 0.999933 | − | 0.0115851i | \(-0.00368774\pi\) |
−0.509999 | + | 0.860175i | \(0.670354\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.62742 | − | 1.51694i | −0.457376 | − | 0.264066i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.39025 | + | 1.88285i | −0.234994 | + | 0.318259i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.867604 | + | 1.50273i | −0.142633 | + | 0.247048i | −0.928487 | − | 0.371364i | \(-0.878890\pi\) |
0.785854 | + | 0.618412i | \(0.212224\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 15.2529 | − | 8.80625i | 2.44241 | − | 1.41013i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.51870i | 0.393355i | 0.980468 | + | 0.196678i | \(0.0630152\pi\) | ||||
−0.980468 | + | 0.196678i | \(0.936985\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.40277i | 0.671416i | 0.941966 | + | 0.335708i | \(0.108976\pi\) | ||||
−0.941966 | + | 0.335708i | \(0.891024\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.75329 | − | 2.74431i | 0.708578 | − | 0.409098i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.68759 | − | 4.65504i | 0.392025 | − | 0.679008i | −0.600691 | − | 0.799481i | \(-0.705108\pi\) |
0.992717 | + | 0.120473i | \(0.0384412\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.82381 | − | 1.56065i | −0.974830 | − | 0.222950i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.74943 | + | 1.01003i | 0.244969 | + | 0.141433i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.74837 | + | 9.95647i | 0.789600 | + | 1.36763i | 0.926212 | + | 0.377002i | \(0.123045\pi\) |
−0.136613 | + | 0.990625i | \(0.543622\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.884623 | −0.119282 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 22.5497 | 2.98678 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.50282 | + | 2.60295i | 0.195650 | + | 0.338876i | 0.947113 | − | 0.320899i | \(-0.103985\pi\) |
−0.751463 | + | 0.659775i | \(0.770652\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.33095 | − | 1.34578i | −0.298448 | − | 0.172309i | 0.343298 | − | 0.939227i | \(-0.388456\pi\) |
−0.641745 | + | 0.766918i | \(0.721789\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 13.2057 | + | 9.75077i | 1.66377 | + | 1.22848i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.56773 | − | 4.44744i | 0.318488 | − | 0.551637i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.18079 | − | 4.14583i | 0.877273 | − | 0.506494i | 0.00751450 | − | 0.999972i | \(-0.497608\pi\) |
0.869758 | + | 0.493478i | \(0.164275\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.3927i | 1.25113i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 11.9263i | − | 1.41539i | −0.706517 | − | 0.707696i | \(-0.749735\pi\) | ||
0.706517 | − | 0.707696i | \(-0.250265\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.43070 | + | 1.40336i | −0.284492 | + | 0.164251i | −0.635455 | − | 0.772138i | \(-0.719188\pi\) |
0.350963 | + | 0.936389i | \(0.385854\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.39762 | + | 11.0810i | −0.738734 | + | 1.27952i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.05748 | − | 2.42523i | −0.120511 | − | 0.276380i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.4260 | − | 6.01945i | −1.17302 | − | 0.677241i | −0.218628 | − | 0.975808i | \(-0.570158\pi\) |
−0.954389 | + | 0.298567i | \(0.903491\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.44105 | − | 9.42418i | −0.604561 | − | 1.04713i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.1174 | −1.33006 | −0.665030 | − | 0.746816i | \(-0.731581\pi\) | ||||
−0.665030 | + | 0.746816i | \(0.731581\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.589012 | 0.0638874 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.39279 | + | 4.14444i | 0.256534 | + | 0.444331i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.6907 | + | 6.74965i | 1.23922 | + | 0.715462i | 0.968934 | − | 0.247319i | \(-0.0795497\pi\) |
0.270282 | + | 0.962781i | \(0.412883\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.2623 | + | 1.72305i | 1.59992 | + | 0.180625i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.27594 | − | 14.3344i | 0.858175 | − | 1.48640i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.69416 | − | 3.28752i | 0.584208 | − | 0.337293i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.764589i | 0.0776322i | 0.999246 | + | 0.0388161i | \(0.0123587\pi\) | ||||
−0.999246 | + | 0.0388161i | \(0.987641\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.20448i | 0.623573i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.5487 | + | 7.82233i | −1.34814 | + | 0.778351i | −0.987987 | − | 0.154540i | \(-0.950610\pi\) |
−0.360158 | + | 0.932891i | \(0.617277\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.31722 | + | 7.47765i | −0.425389 | + | 0.736795i | −0.996457 | − | 0.0841079i | \(-0.973196\pi\) |
0.571068 | + | 0.820903i | \(0.306529\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.05597 | + | 0.796590i | 0.688592 | + | 0.0777392i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.9765 | + | 6.33727i | 1.06113 | + | 0.612647i | 0.925746 | − | 0.378146i | \(-0.123438\pi\) |
0.135389 | + | 0.990793i | \(0.456772\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.08695 | − | 12.2750i | −0.678806 | − | 1.17573i | −0.975341 | − | 0.220705i | \(-0.929164\pi\) |
0.296534 | − | 0.955022i | \(-0.404169\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.26442 | 0.499677 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.3199 | 1.62932 | 0.814660 | − | 0.579938i | \(-0.196923\pi\) | ||||
0.814660 | + | 0.579938i | \(0.196923\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.51515 | + | 2.62431i | 0.141288 | + | 0.244718i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −31.1930 | − | 18.0093i | −2.88379 | − | 1.66496i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.704107 | + | 1.61480i | 0.0645454 | + | 0.148029i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | − | 0.866025i | 0.0454545 | − | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.61770 | − | 3.82073i | 0.596698 | − | 0.344504i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.15396i | 0.729312i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.06788i | − | 0.183495i | −0.995782 | − | 0.0917475i | \(-0.970755\pi\) | ||
0.995782 | − | 0.0917475i | \(-0.0292453\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.5679 | − | 6.67876i | 1.01850 | − | 0.588032i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.82744 | + | 17.0216i | −0.858627 | + | 1.48719i | 0.0146114 | + | 0.999893i | \(0.495349\pi\) |
−0.873239 | + | 0.487293i | \(0.837984\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.8197 | + | 11.6808i | 1.37174 | + | 1.01286i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.44810 | − | 4.30016i | −0.641030 | − | 0.370099i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.58725 | + | 16.6056i | 0.819094 | + | 1.41871i | 0.906350 | + | 0.422527i | \(0.138857\pi\) |
−0.0872558 | + | 0.996186i | \(0.527810\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.06327 | −0.0901857 | −0.0450928 | − | 0.998983i | \(-0.514358\pi\) | ||||
−0.0450928 | + | 0.998983i | \(0.514358\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.3077 | −1.37336 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.90263 | + | 5.02750i | 0.242730 | + | 0.420421i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.20844 | + | 0.697692i | 0.100355 | + | 0.0579402i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.25084 | + | 20.2965i | 0.515561 | + | 1.67402i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.96461 | − | 5.13486i | 0.242871 | − | 0.420664i | −0.718660 | − | 0.695362i | \(-0.755244\pi\) |
0.961531 | + | 0.274697i | \(0.0885776\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.7645 | + | 10.2563i | −1.44565 | + | 0.834648i | −0.998218 | − | 0.0596695i | \(-0.980995\pi\) |
−0.447434 | + | 0.894317i | \(0.647662\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 4.13116i | − | 0.333984i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 4.82621i | − | 0.387650i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.431120 | + | 0.248907i | −0.0344071 | + | 0.0198650i | −0.517105 | − | 0.855922i | \(-0.672990\pi\) |
0.482698 | + | 0.875787i | \(0.339657\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 17.4399 | − | 30.2068i | 1.38308 | − | 2.39556i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.38345 | + | 7.29095i | −0.424275 | + | 0.574607i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.6100 | − | 11.3218i | −1.53597 | − | 0.886795i | −0.999068 | − | 0.0431533i | \(-0.986260\pi\) |
−0.536906 | − | 0.843642i | \(-0.680407\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.34192 | + | 2.32428i | 0.104469 | + | 0.180945i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.3679 | 1.11182 | 0.555910 | − | 0.831242i | \(-0.312370\pi\) | ||||
0.555910 | + | 0.831242i | \(0.312370\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −20.7010 | −1.59238 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −23.0577 | − | 39.9371i | −1.76327 | − | 3.05407i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.00943 | − | 5.20160i | −0.684974 | − | 0.395470i | 0.116752 | − | 0.993161i | \(-0.462752\pi\) |
−0.801727 | + | 0.597691i | \(0.796085\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.2283 | + | 4.45986i | −0.773184 | + | 0.337134i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.55938 | − | 7.89707i | 0.342704 | − | 0.593580i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.25927 | − | 3.03644i | 0.393096 | − | 0.226954i | −0.290404 | − | 0.956904i | \(-0.593790\pi\) |
0.683501 | + | 0.729950i | \(0.260457\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.68994i | 0.422930i | 0.977386 | + | 0.211465i | \(0.0678234\pi\) | ||||
−0.977386 | + | 0.211465i | \(0.932177\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.16586i | 0.603638i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.32935 | − | 0.767502i | 0.0977359 | − | 0.0564279i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.332917 | + | 0.576630i | −0.0243453 | + | 0.0421673i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.88559 | − | 25.5597i | 0.209895 | − | 1.85919i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.2687 | − | 11.7021i | −1.46659 | − | 0.846737i | −0.467290 | − | 0.884104i | \(-0.654770\pi\) |
−0.999302 | + | 0.0373671i | \(0.988103\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.38111 | + | 5.85625i | 0.243377 | + | 0.421542i | 0.961674 | − | 0.274195i | \(-0.0884113\pi\) |
−0.718297 | + | 0.695737i | \(0.755078\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −15.5804 | −1.11574 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.5300 | 1.10647 | 0.553235 | − | 0.833025i | \(-0.313393\pi\) | ||||
0.553235 | + | 0.833025i | \(0.313393\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.68811 | − | 9.85209i | −0.403219 | − | 0.698396i | 0.590893 | − | 0.806750i | \(-0.298775\pi\) |
−0.994112 | + | 0.108354i | \(0.965442\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −21.7857 | − | 12.5780i | −1.53665 | − | 0.887182i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.468180 | + | 4.14700i | −0.0328598 | + | 0.291063i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.11405 | − | 1.92959i | 0.0778086 | − | 0.134769i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 18.4061 | − | 10.6268i | 1.27932 | − | 0.738613i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.43260i | 0.514124i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.9893i | 1.23843i | 0.785221 | + | 0.619216i | \(0.212550\pi\) | ||||
−0.785221 | + | 0.619216i | \(0.787450\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −31.3355 | + | 18.0915i | −2.14707 | + | 1.23961i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.94740 | − | 3.37299i | 0.132811 | − | 0.230036i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.2312 | − | 5.76926i | 0.898195 | − | 0.391643i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.37447 | + | 4.25765i | 0.498320 | + | 0.287705i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.93267 | − | 3.34748i | −0.130005 | − | 0.225176i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.8373 | −1.26144 | −0.630719 | − | 0.776011i | \(-0.717240\pi\) | ||||
−0.630719 | + | 0.776011i | \(0.717240\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 26.1670 | 1.74447 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.2362 | − | 19.4618i | −0.745776 | − | 1.29172i | −0.949831 | − | 0.312763i | \(-0.898746\pi\) |
0.204055 | − | 0.978959i | \(-0.434588\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.92762 | − | 1.69026i | −0.193463 | − | 0.111696i | 0.400140 | − | 0.916454i | \(-0.368962\pi\) |
−0.593603 | + | 0.804758i | \(0.702295\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.76797 | + | 6.45739i | −0.313709 | + | 0.424865i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.64816 | + | 2.85470i | −0.107975 | + | 0.187018i | −0.914950 | − | 0.403568i | \(-0.867770\pi\) |
0.806975 | + | 0.590586i | \(0.201103\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.11796 | + | 2.37750i | −0.268626 | + | 0.155091i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 36.5247i | 2.37253i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 0.172767i | − | 0.0111754i | −0.999984 | − | 0.00558768i | \(-0.998221\pi\) | ||
0.999984 | − | 0.00558768i | \(-0.00177862\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.0433 | + | 10.4173i | −1.16227 | + | 0.671039i | −0.951848 | − | 0.306571i | \(-0.900818\pi\) |
−0.210425 | + | 0.977610i | \(0.567485\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.92451 | + | 3.33334i | −0.123457 | + | 0.213834i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.53746 | + | 4.21387i | 0.289888 | + | 0.269214i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −37.3674 | − | 21.5741i | −2.37763 | − | 1.37273i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 18.3815 | + | 31.8376i | 1.16488 | + | 2.01763i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.8033 | 1.31309 | 0.656547 | − | 0.754285i | \(-0.272016\pi\) | ||||
0.656547 | + | 0.754285i | \(0.272016\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.42552 | −0.215361 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.893499 | − | 1.54759i | −0.0559531 | − | 0.0969136i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.3974 | − | 10.0444i | −1.08522 | − | 0.626554i | −0.152922 | − | 0.988238i | \(-0.548868\pi\) |
−0.932301 | + | 0.361685i | \(0.882202\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.69325 | + | 2.72700i | 0.229487 | + | 0.169447i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.89340 | − | 8.47562i | 0.302894 | − | 0.524628i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.2700 | + | 12.8576i | −1.37323 | + | 0.792833i | −0.991333 | − | 0.131374i | \(-0.958061\pi\) |
−0.381893 | + | 0.924206i | \(0.624728\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 10.1703i | − | 0.624755i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 40.9554i | − | 2.50643i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.98673 | + | 1.72439i | −0.182104 | + | 0.105138i | −0.588281 | − | 0.808657i | \(-0.700195\pi\) |
0.406177 | + | 0.913794i | \(0.366862\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.47499 | + | 12.9471i | −0.454073 | + | 0.786478i | −0.998634 | − | 0.0522430i | \(-0.983363\pi\) |
0.544561 | + | 0.838721i | \(0.316696\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −18.6249 | − | 42.7143i | −1.12723 | − | 2.58519i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.65241 | − | 2.10872i | −0.220249 | − | 0.127161i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.0238068 | − | 0.0412346i | −0.00143041 | − | 0.00247755i | 0.865309 | − | 0.501238i | \(-0.167122\pi\) |
−0.866740 | + | 0.498761i | \(0.833789\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −33.8496 | −2.02652 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.28214 | −0.255451 | −0.127725 | − | 0.991810i | \(-0.540768\pi\) | ||||
−0.127725 | + | 0.991810i | \(0.540768\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.18207 | + | 12.4397i | 0.426930 | + | 0.739464i | 0.996598 | − | 0.0824104i | \(-0.0262618\pi\) |
−0.569669 | + | 0.821874i | \(0.692928\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −17.2754 | − | 9.97398i | −1.02331 | − | 0.590807i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.62179 | + | 0.747573i | 0.390872 | + | 0.0441279i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.27833 | + | 14.3385i | −0.486961 | + | 0.843441i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.00890 | − | 1.15984i | 0.117764 | − | 0.0679909i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 3.11780i | − | 0.182144i | −0.995844 | − | 0.0910718i | \(-0.970971\pi\) | ||
0.995844 | − | 0.0910718i | \(-0.0290293\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 2.65885i | − | 0.154804i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.41952 | − | 4.86101i | 0.488550 | − | 0.282065i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.94302 | − | 17.2218i | 0.575020 | − | 0.995963i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.5751 | + | 1.30678i | 0.667178 | + | 0.0753217i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 41.1052 | + | 23.7321i | 2.36143 | + | 1.36337i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.19050 | + | 2.06201i | 0.0681680 | + | 0.118070i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.167901 | −0.00958260 | −0.00479130 | − | 0.999989i | \(-0.501525\pi\) | ||||
−0.00479130 | + | 0.999989i | \(0.501525\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 26.1959 | 1.49024 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.91505 | + | 10.2452i | 0.335412 | + | 0.580950i | 0.983564 | − | 0.180561i | \(-0.0577913\pi\) |
−0.648152 | + | 0.761511i | \(0.724458\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.0325 | + | 13.8751i | 1.35839 | + | 0.784270i | 0.989407 | − | 0.145165i | \(-0.0463713\pi\) |
0.368987 | + | 0.929434i | \(0.379705\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.80411 | − | 13.3112i | −0.327025 | − | 0.749999i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.6861 | + | 27.1692i | −0.881021 | + | 1.52597i | −0.0308132 | + | 0.999525i | \(0.509810\pi\) |
−0.850208 | + | 0.526448i | \(0.823524\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.36605 | + | 0.788689i | −0.0764841 | + | 0.0441581i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 38.4531i | − | 2.14624i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4.94888i | − | 0.275363i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.2032 | − | 12.2417i | 1.17614 | − | 0.679046i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −21.5010 | + | 37.2408i | −1.18901 | + | 2.05942i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.4406 | − | 8.44747i | −0.630743 | − | 0.465724i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.16861 | + | 0.674694i | 0.0642323 | + | 0.0370846i | 0.531772 | − | 0.846887i | \(-0.321526\pi\) |
−0.467540 | + | 0.883972i | \(0.654860\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.38303 | − | 9.32368i | −0.294988 | − | 0.510934i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.33499 | −0.400753 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.3720 | 1.54552 | 0.772759 | − | 0.634699i | \(-0.218876\pi\) | ||||
0.772759 | + | 0.634699i | \(0.218876\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −26.2733 | − | 45.5068i | −1.42697 | − | 2.47159i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.72475 | + | 2.72783i | 0.255859 | + | 0.147720i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.12840 | + | 17.4769i | −0.330903 | + | 0.943665i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.59679 | − | 7.96187i | 0.247483 | − | 0.428653i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.5343 | + | 7.23669i | −0.672878 | + | 0.388486i | −0.797166 | − | 0.603760i | \(-0.793669\pi\) |
0.124288 | + | 0.992246i | \(0.460335\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 5.72848i | − | 0.306639i | −0.988177 | − | 0.153319i | \(-0.951004\pi\) | ||
0.988177 | − | 0.153319i | \(-0.0489963\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 56.4388i | 3.01248i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.7869 | − | 7.38254i | 0.680580 | − | 0.392933i | −0.119494 | − | 0.992835i | \(-0.538127\pi\) |
0.800073 | + | 0.599902i | \(0.204794\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.27514 | + | 9.13681i | −0.279975 | + | 0.484931i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.17468 | − | 4.29955i | 0.168022 | − | 0.227556i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.5098 | + | 6.64517i | 0.607462 | + | 0.350719i | 0.771972 | − | 0.635657i | \(-0.219271\pi\) |
−0.164509 | + | 0.986376i | \(0.552604\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.1218 | − | 31.3878i | −0.953777 | − | 1.65199i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.03389 | −0.159238 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.48290 | 0.129961 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.6619 | + | 30.5914i | 0.921945 | + | 1.59686i | 0.796402 | + | 0.604768i | \(0.206734\pi\) |
0.125544 | + | 0.992088i | \(0.459932\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −13.5336 | − | 7.81361i | −0.704530 | − | 0.406760i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 27.8822 | − | 12.1576i | 1.44757 | − | 0.631190i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.10727 | + | 7.11401i | −0.212667 | + | 0.368349i | −0.952548 | − | 0.304388i | \(-0.901548\pi\) |
0.739882 | + | 0.672737i | \(0.234881\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 21.4239 | − | 12.3691i | 1.10633 | − | 0.638738i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 9.15708i | − | 0.471614i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.9059i | 0.765665i | 0.923818 | + | 0.382832i | \(0.125051\pi\) | ||||
−0.923818 | + | 0.382832i | \(0.874949\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.43321 | + | 3.13686i | −0.278352 | + | 0.160706i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.12686 | − | 14.0761i | 0.415263 | − | 0.719257i | −0.580193 | − | 0.814479i | \(-0.697023\pi\) |
0.995456 | + | 0.0952221i | \(0.0303561\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.262564 | + | 2.32572i | −0.0133815 | + | 0.118530i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −23.6571 | − | 13.6584i | −1.20256 | − | 0.694298i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.2874 | − | 24.7465i | −0.724399 | − | 1.25470i | −0.959221 | − | 0.282657i | \(-0.908784\pi\) |
0.234822 | − | 0.972038i | \(-0.424549\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.28083 | 0.115347 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 59.6307 | 3.00797 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.32495 | + | 9.22308i | 0.267927 | + | 0.464063i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.7044 | − | 9.64428i | −0.838369 | − | 0.484033i | 0.0183405 | − | 0.999832i | \(-0.494162\pi\) |
−0.856709 | + | 0.515799i | \(0.827495\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.69295 | − | 59.2842i | 0.335066 | − | 2.96792i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.9815 | − | 20.7526i | 0.598327 | − | 1.03633i | −0.394741 | − | 0.918792i | \(-0.629166\pi\) |
0.993068 | − | 0.117541i | \(-0.0375010\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −27.4284 | + | 15.8358i | −1.36630 | + | 0.788836i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.62656i | 0.478347i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.73521i | 0.0860110i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.33938 | − | 0.773291i | 0.0662280 | − | 0.0382368i | −0.466520 | − | 0.884510i | \(-0.654493\pi\) |
0.532748 | + | 0.846274i | \(0.321159\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 29.0867 | − | 50.3796i | 1.43474 | − | 2.48504i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.28935 | − | 3.17840i | 0.358685 | − | 0.156399i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.28323 | + | 5.35968i | 0.455696 | + | 0.263096i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.61293 | + | 2.79367i | 0.0789854 | + | 0.136807i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.6341 | −1.69199 | −0.845993 | − | 0.533194i | \(-0.820992\pi\) | ||||
−0.845993 | + | 0.533194i | \(0.820992\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.57711 | −0.369286 | −0.184643 | − | 0.982806i | \(-0.559113\pi\) | ||||
−0.184643 | + | 0.982806i | \(0.559113\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 16.6751 | + | 28.8821i | 0.810771 | + | 1.40430i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.43190 | + | 1.40406i | 0.117965 | + | 0.0681069i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.22996 | + | 5.72875i | −0.204702 | + | 0.277234i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.80625 | − | 15.2529i | 0.425170 | − | 0.736415i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.19894 | + | 0.692206i | −0.0577507 | + | 0.0333424i | −0.528597 | − | 0.848873i | \(-0.677282\pi\) |
0.470847 | + | 0.882215i | \(0.343949\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.4764i | 0.743747i | 0.928284 | + | 0.371873i | \(0.121284\pi\) | ||||
−0.928284 | + | 0.371873i | \(0.878716\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 4.23344i | − | 0.202978i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.0495 | − | 12.7303i | 1.05477 | − | 0.608971i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.92086 | − | 13.7193i | 0.378042 | − | 0.654788i | −0.612735 | − | 0.790288i | \(-0.709931\pi\) |
0.990777 | + | 0.135500i | \(0.0432641\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 29.5548 | − | 31.8244i | 1.40737 | − | 1.51545i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.66477 | + | 5.00260i | 0.411675 | + | 0.237681i | 0.691509 | − | 0.722368i | \(-0.256946\pi\) |
−0.279834 | + | 0.960048i | \(0.590279\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.97090 | − | 10.3419i | −0.283048 | − | 0.490253i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17.9886 | −0.850832 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.3617 | 1.38567 | 0.692833 | − | 0.721098i | \(-0.256362\pi\) | ||||
0.692833 | + | 0.721098i | \(0.256362\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.25935 | + | 2.18126i | 0.0593005 | + | 0.102711i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 53.8954 | + | 31.1165i | 2.53223 | + | 1.46198i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.9304 | − | 8.07073i | −0.512426 | − | 0.378362i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.91450 | + | 8.51217i | −0.229891 | + | 0.398182i | −0.957776 | − | 0.287517i | \(-0.907170\pi\) |
0.727885 | + | 0.685699i | \(0.240504\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.60601 | + | 3.23663i | −0.261666 | + | 0.151073i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.8901i | 1.34554i | 0.739850 | + | 0.672772i | \(0.234897\pi\) | ||||
−0.739850 | + | 0.672772i | \(0.765103\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.9310i | 0.786849i | 0.919357 | + | 0.393425i | \(0.128710\pi\) | ||||
−0.919357 | + | 0.393425i | \(0.871290\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.6805 | + | 7.32109i | −0.588044 | + | 0.339507i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.8677 | − | 36.1439i | 0.965641 | − | 1.67254i | 0.257757 | − | 0.966210i | \(-0.417016\pi\) |
0.707883 | − | 0.706329i | \(-0.249650\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.76827 | − | 20.1092i | −0.404881 | − | 0.928555i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.30797 | + | 0.755157i | 0.0602681 | + | 0.0347958i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.20138 | + | 3.81291i | 0.101220 | + | 0.175318i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.3466 | 1.43828 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −71.3313 | −3.26604 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.64784 | − | 14.9785i | −0.395130 | − | 0.684385i | 0.597988 | − | 0.801505i | \(-0.295967\pi\) |
−0.993118 | + | 0.117120i | \(0.962634\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.72375 | − | 5.03666i | −0.397769 | − | 0.229652i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 27.3228 | + | 3.08463i | 1.24323 | + | 0.140356i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.338186 | − | 0.585756i | 0.0153562 | − | 0.0265978i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.53520 | + | 4.35045i | −0.341452 | + | 0.197138i | −0.660914 | − | 0.750462i | \(-0.729831\pi\) |
0.319462 | + | 0.947599i | \(0.396498\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 68.6984i | 3.10665i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.84010i | 0.263560i | 0.991279 | + | 0.131780i | \(0.0420692\pi\) | ||||
−0.991279 | + | 0.131780i | \(0.957931\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.909563 | − | 0.525136i | 0.0409647 | − | 0.0236510i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.74431 | − | 4.75329i | 0.123348 | − | 0.213644i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −31.3548 | − | 3.53984i | −1.40646 | − | 0.158783i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.6340 | + | 9.02630i | 0.699875 | + | 0.404073i | 0.807301 | − | 0.590140i | \(-0.200928\pi\) |
−0.107426 | + | 0.994213i | \(0.534261\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.7953 | − | 37.7505i | −0.973742 | − | 1.68657i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.4279 | 0.598721 | 0.299360 | − | 0.954140i | \(-0.403227\pi\) | ||||
0.299360 | + | 0.954140i | \(0.403227\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.8396 | 0.615855 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 31.4023 | + | 54.3903i | 1.39462 | + | 2.41556i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.2618 | + | 11.1208i | 0.853766 | + | 0.492922i | 0.861920 | − | 0.507045i | \(-0.169262\pi\) |
−0.00815390 | + | 0.999967i | \(0.502595\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.96806 | + | 6.80696i | 0.131299 | + | 0.301122i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −36.1300 | + | 62.5789i | −1.59518 | + | 2.76293i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.61490 | − | 3.81911i | 0.291487 | − | 0.168290i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 5.37518i | − | 0.236400i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 31.5621i | 1.38542i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.0494 | + | 10.4208i | −0.790757 | + | 0.456544i | −0.840229 | − | 0.542232i | \(-0.817579\pi\) |
0.0494720 | + | 0.998776i | \(0.484246\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.45030 | + | 7.70815i | −0.194598 | + | 0.337054i | −0.946769 | − | 0.321915i | \(-0.895674\pi\) |
0.752171 | + | 0.658968i | \(0.229007\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 27.2337 | + | 20.1086i | 1.18857 | + | 0.877612i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.14590 | − | 1.81629i | −0.137038 | − | 0.0791187i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.63289 | − | 9.75646i | −0.244908 | − | 0.424194i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.6484 | −0.809271 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.6217 | −0.633336 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.60609 | − | 9.71003i | −0.242372 | − | 0.419801i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.9560 | − | 9.21223i | −0.688554 | − | 0.397537i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.68992 | + | 2.06034i | −0.288155 | + | 0.0887451i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.1631 | + | 19.3351i | −0.479941 | + | 0.831282i | −0.999735 | − | 0.0230096i | \(-0.992675\pi\) |
0.519794 | + | 0.854291i | \(0.326009\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.9499 | − | 8.63132i | 0.641561 | − | 0.370405i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.5385i | 0.537092i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 7.46203i | − | 0.319053i | −0.987194 | − | 0.159527i | \(-0.949003\pi\) | ||
0.987194 | − | 0.159527i | \(-0.0509968\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.4623 | − | 8.34983i | 0.617237 | − | 0.356362i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.86201 | − | 10.1533i | 0.249730 | − | 0.432545i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.9200 | + | 25.6238i | −0.804559 | + | 1.08964i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.03311 | − | 2.32851i | −0.171196 | − | 0.0988399i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.6505 | − | 25.3754i | −0.620760 | − | 1.07519i | −0.989344 | − | 0.145594i | \(-0.953491\pi\) |
0.368584 | − | 0.929594i | \(-0.379843\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.5592 | −1.08104 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.02007 | 0.0852873 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.6343 | + | 37.4717i | 0.911777 | + | 1.57924i | 0.811552 | + | 0.584280i | \(0.198623\pi\) |
0.100225 | + | 0.994965i | \(0.468044\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.2689 | − | 7.66080i | −0.558226 | − | 0.322292i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −26.3916 | + | 11.5076i | −1.10834 | + | 0.483274i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.33795 | + | 9.24560i | −0.223778 | + | 0.387596i | −0.955952 | − | 0.293522i | \(-0.905173\pi\) |
0.732174 | + | 0.681118i | \(0.238506\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.01939 | + | 5.20735i | −0.377450 | + | 0.217921i | −0.676708 | − | 0.736251i | \(-0.736594\pi\) |
0.299258 | + | 0.954172i | \(0.403261\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 71.0060i | 2.96632i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.4469i | 0.602479i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.9407 | + | 15.5542i | −1.12155 | + | 0.647530i | −0.941797 | − | 0.336181i | \(-0.890864\pi\) |
−0.179757 | + | 0.983711i | \(0.557531\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.2579 | − | 17.7672i | 0.426304 | − | 0.738380i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.59656 | + | 31.8573i | −0.149211 | + | 1.32166i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.95647 | + | 5.74837i | 0.412355 | + | 0.238073i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.9314 | + | 27.5940i | 0.658683 | + | 1.14087i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.80480 | 0.157041 | 0.0785205 | − | 0.996913i | \(-0.474980\pi\) | ||||
0.0785205 | + | 0.996913i | \(0.474980\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −40.5498 | −1.67082 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23.5582 | − | 40.8040i | −0.969055 | − | 1.67845i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.8184 | + | 19.5250i | 1.38875 | + | 0.801797i | 0.993175 | − | 0.116635i | \(-0.0372108\pi\) |
0.395579 | + | 0.918432i | \(0.370544\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.174824 | − | 1.54854i | 0.00716710 | − | 0.0634841i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17.2571 | + | 29.8901i | −0.706285 | + | 1.22332i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.54063 | + | 3.19888i | −0.226384 | + | 0.130703i | −0.608903 | − | 0.793245i | \(-0.708390\pi\) |
0.382519 | + | 0.923948i | \(0.375057\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 15.4619i | − | 0.630703i | −0.948975 | − | 0.315352i | \(-0.897878\pi\) | ||
0.948975 | − | 0.315352i | \(-0.102122\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 51.4454i | 2.09502i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.766106 | + | 0.442311i | −0.0311466 | + | 0.0179825i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.8652 | − | 20.5512i | 0.481595 | − | 0.834146i | −0.518182 | − | 0.855270i | \(-0.673391\pi\) |
0.999777 | + | 0.0211239i | \(0.00672446\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.6061 | − | 5.06067i | 0.470305 | − | 0.205069i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 27.0237 | + | 15.6021i | 1.09326 | + | 0.631195i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.97371 | − | 13.8109i | −0.322055 | − | 0.557816i | 0.658857 | − | 0.752268i | \(-0.271040\pi\) |
−0.980912 | + | 0.194452i | \(0.937707\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.75981 | −0.272582 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.58440 | −0.104044 | −0.0520220 | − | 0.998646i | \(-0.516567\pi\) | ||||
−0.0520220 | + | 0.998646i | \(0.516567\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.96976 | − | 8.60788i | −0.199751 | − | 0.345980i | 0.748696 | − | 0.662913i | \(-0.230680\pi\) |
−0.948448 | + | 0.316933i | \(0.897347\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −28.8413 | − | 16.6515i | −1.15736 | − | 0.668202i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.2151 | − | 28.7322i | 0.849965 | − | 1.15113i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.93702 | + | 12.0153i | −0.277481 | + | 0.480611i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 19.5286 | − | 11.2748i | 0.779897 | − | 0.450274i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.15536i | − | 0.0460673i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 47.4180i | − | 1.88768i | −0.330400 | − | 0.943841i | \(-0.607184\pi\) | ||
0.330400 | − | 0.943841i | \(-0.392816\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 47.2654 | − | 27.2887i | 1.87863 | − | 1.08463i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.914649 | + | 1.58422i | −0.0362967 | + | 0.0628678i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.05998 | − | 39.6140i | 0.358970 | − | 1.56956i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 64.0828 | + | 36.9982i | 2.53508 | + | 1.46363i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.22066 | − | 9.04245i | −0.206204 | − | 0.357155i | 0.744312 | − | 0.667832i | \(-0.232778\pi\) |
−0.950516 | + | 0.310677i | \(0.899444\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.45741 | −0.372964 | −0.186482 | − | 0.982458i | \(-0.559709\pi\) | ||||
−0.186482 | + | 0.982458i | \(0.559709\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.8164 | −0.465269 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.92768 | − | 3.33884i | −0.0757848 | − | 0.131263i | 0.825642 | − | 0.564194i | \(-0.190813\pi\) |
−0.901427 | + | 0.432931i | \(0.857480\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.60295 | + | 1.50282i | 0.102175 | + | 0.0589907i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −35.2294 | − | 26.0124i | −1.38075 | − | 1.01951i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.9036 | − | 31.0100i | 0.700624 | − | 1.21352i | −0.267624 | − | 0.963523i | \(-0.586239\pi\) |
0.968248 | − | 0.249992i | \(-0.0804281\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.0577 | − | 8.69357i | 0.588354 | − | 0.339686i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 17.4143i | − | 0.679396i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 33.1431i | − | 1.29107i | −0.763730 | − | 0.645536i | \(-0.776634\pi\) | ||
0.763730 | − | 0.645536i | \(-0.223366\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.97837 | − | 5.18366i | 0.349218 | − | 0.201621i | −0.315123 | − | 0.949051i | \(-0.602046\pi\) |
0.664341 | + | 0.747430i | \(0.268712\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.86351 | + | 10.1559i | −0.227720 | + | 0.394422i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.95298 | − | 15.9460i | −0.269625 | − | 0.618359i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.67943 | + | 2.70167i | 0.181188 | + | 0.104609i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 28.5751 | + | 49.4936i | 1.10478 | + | 1.91353i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.69155 | −0.103906 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.15602 | 0.314392 | 0.157196 | − | 0.987567i | \(-0.449755\pi\) | ||||
0.157196 | + | 0.987567i | \(0.449755\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −20.5010 | − | 35.5088i | −0.789085 | − | 1.36674i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.0530 | − | 8.69088i | −0.578536 | − | 0.334018i | 0.182016 | − | 0.983296i | \(-0.441738\pi\) |
−0.760551 | + | 0.649278i | \(0.775071\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.01014 | + | 0.226937i | 0.0771422 | + | 0.00870904i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −34.0895 | + | 59.0448i | −1.30631 | + | 2.26260i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.2478 | + | 11.6901i | −0.774760 | + | 0.447308i | −0.834570 | − | 0.550902i | \(-0.814284\pi\) |
0.0598101 | + | 0.998210i | \(0.480950\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 16.9622i | − | 0.648093i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.2561i | 0.391296i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −57.7999 | + | 33.3708i | −2.20200 | + | 1.27133i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.64879 | − | 8.05194i | 0.176848 | − | 0.306310i | −0.763951 | − | 0.645274i | \(-0.776743\pi\) |
0.940799 | + | 0.338964i | \(0.110076\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 16.3119 | + | 1.84155i | 0.619637 | + | 0.0699545i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.814580 | + | 0.470298i | 0.0308988 | + | 0.0178394i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.838519 | − | 1.45236i | −0.0317612 | − | 0.0550120i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.0007 | 0.378260 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.6125 | 0.665216 | 0.332608 | − | 0.943065i | \(-0.392071\pi\) | ||||
0.332608 | + | 0.943065i | \(0.392071\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.44855 | − | 11.1692i | −0.243212 | − | 0.421255i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.4934 | + | 7.21308i | 0.470529 | + | 0.271660i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.5439 | + | 37.9419i | 0.622199 | + | 1.42695i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.3032 | − | 29.9701i | 0.649837 | − | 1.12555i | −0.333325 | − | 0.942812i | \(-0.608171\pi\) |
0.983162 | − | 0.182738i | \(-0.0584962\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 64.6879 | − | 37.3476i | 2.42598 | − | 1.40064i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 18.6885i | − | 0.699890i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 5.13546i | − | 0.192055i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.453932 | + | 0.262078i | −0.0169524 | + | 0.00978747i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.622685 | − | 1.07852i | 0.0232222 | − | 0.0402221i | −0.854181 | − | 0.519976i | \(-0.825941\pi\) |
0.877403 | + | 0.479754i | \(0.159274\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.3777 | + | 13.5696i | 0.684422 | + | 0.505360i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 54.7414 | + | 31.6050i | 2.03586 | + | 1.17540i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.32625 | + | 5.76123i | 0.123534 | + | 0.213967i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.8198 | −1.62519 | −0.812594 | − | 0.582830i | \(-0.801945\pi\) | ||||
−0.812594 | + | 0.582830i | \(0.801945\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.9688 | −0.776624 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.46576 | − | 2.53877i | −0.0542130 | − | 0.0938997i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.5120 | − | 14.7293i | −0.942307 | − | 0.544041i | −0.0516240 | − | 0.998667i | \(-0.516440\pi\) |
−0.890683 | + | 0.454626i | \(0.849773\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.18855 | − | 18.3141i | 0.154497 | − | 0.675524i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.14583 | − | 7.18079i | 0.152714 | − | 0.264508i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.8977 | + | 20.1482i | −1.28373 | + | 0.741164i | −0.977529 | − | 0.210801i | \(-0.932393\pi\) |
−0.306205 | + | 0.951966i | \(0.599059\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 130.907i | 4.80897i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 16.0426i | − | 0.588546i | −0.955721 | − | 0.294273i | \(-0.904923\pi\) | ||
0.955721 | − | 0.294273i | \(-0.0950775\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.54242 | + | 2.62257i | −0.166421 | + | 0.0960834i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 37.5912 | − | 65.1098i | 1.37539 | − | 2.38224i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.9189 | − | 26.9767i | 0.727821 | − | 0.985708i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.7121 | + | 13.1128i | 0.828776 | + | 0.478494i | 0.853434 | − | 0.521202i | \(-0.174516\pi\) |
−0.0246571 | + | 0.999696i | \(0.507849\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −31.5575 | − | 54.6591i | −1.15002 | − | 1.99189i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.1459 | 0.660399 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.0555 | 1.38315 | 0.691576 | − | 0.722303i | \(-0.256917\pi\) | ||||
0.691576 | + | 0.722303i | \(0.256917\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.19633 | + | 9.00030i | 0.188615 | + | 0.326690i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.47387 | + | 2.58299i | 0.162178 | + | 0.0936332i | 0.578892 | − | 0.815404i | \(-0.303485\pi\) |
−0.416715 | + | 0.909037i | \(0.636819\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −34.3749 | + | 14.9886i | −1.24446 | + | 0.542624i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.82726 | + | 3.16490i | −0.0660646 | + | 0.114427i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.1108 | + | 8.72423i | −0.545620 | + | 0.315014i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 53.5221i | − | 1.93006i | −0.262143 | − | 0.965029i | \(-0.584429\pi\) | ||
0.262143 | − | 0.965029i | \(-0.415571\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 60.9473i | 2.19496i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −33.9926 | + | 19.6256i | −1.22263 | + | 0.705885i | −0.965478 | − | 0.260486i | \(-0.916117\pi\) |
−0.257152 | + | 0.966371i | \(0.582784\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.5045 | − | 19.9263i | 0.413253 | − | 0.715776i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.56253 | − | 13.8404i | 0.0560554 | − | 0.496523i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.2124 | − | 9.36025i | −0.580870 | − | 0.335366i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.96315 | − | 10.3285i | −0.213378 | − | 0.369582i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15.3353 | −0.548039 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.440378 | 0.0157178 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.1109 | + | 33.1010i | 0.681229 | + | 1.17992i | 0.974606 | + | 0.223927i | \(0.0718877\pi\) |
−0.293377 | + | 0.955997i | \(0.594779\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 67.5646 | + | 39.0085i | 2.40537 | + | 1.38874i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.14071 | − | 45.5349i | 0.182783 | − | 1.61904i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.81257 | − | 13.5318i | 0.277432 | − | 0.480527i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −26.7216 | + | 15.4277i | −0.947719 | + | 0.547166i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 43.7129i | − | 1.54839i | −0.632946 | − | 0.774196i | \(-0.718155\pi\) | ||
0.632946 | − | 0.774196i | \(-0.281845\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.57898i | 0.126615i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −72.5349 | + | 41.8781i | −2.56290 | + | 1.47969i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.40336 | + | 2.43070i | −0.0495237 | + | 0.0857775i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.34916 | − | 3.20448i | 0.259024 | − | 0.112943i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.06140 | + | 5.23160i | 0.318976 | + | 0.184161i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.24769 | + | 5.62516i | 0.114183 | + | 0.197770i | 0.917453 | − | 0.397845i | \(-0.130242\pi\) |
−0.803270 | + | 0.595615i | \(0.796908\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.692067 | −0.0243018 | −0.0121509 | − | 0.999926i | \(-0.503868\pi\) | ||||
−0.0121509 | + | 0.999926i | \(0.503868\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 45.3566 | 1.59072 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.0156 | + | 17.3475i | 0.350830 | + | 0.607655i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28.3398 | − | 16.3620i | −0.991485 | − | 0.572434i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −56.6057 | + | 76.6626i | −1.97796 | + | 2.67881i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.09226 | − | 3.62391i | 0.0730205 | − | 0.126475i | −0.827203 | − | 0.561903i | \(-0.810069\pi\) |
0.900224 | + | 0.435428i | \(0.143403\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.168118 | + | 0.0970628i | −0.00586022 | + | 0.00338340i | −0.502927 | − | 0.864329i | \(-0.667744\pi\) |
0.497067 | + | 0.867712i | \(0.334410\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.7952i | 0.445473i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.3697i | 1.22992i | 0.788557 | + | 0.614962i | \(0.210829\pi\) | ||||
−0.788557 | + | 0.614962i | \(0.789171\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.3542 | − | 11.7515i | 0.706930 | − | 0.408146i | −0.102993 | − | 0.994682i | \(-0.532842\pi\) |
0.809923 | + | 0.586536i | \(0.199509\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.0722272 | + | 0.125101i | −0.00250553 | + | 0.00433971i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.45438 | − | 1.37185i | 0.154335 | − | 0.0475316i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.0073 | − | 6.35508i | −0.380924 | − | 0.219927i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 26.5201 | + | 45.9341i | 0.916668 | + | 1.58771i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.7473 | 0.647228 | 0.323614 | − | 0.946189i | \(-0.395102\pi\) | ||||
0.323614 | + | 0.946189i | \(0.395102\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.5119 | −0.914203 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.49576 | + | 11.2510i | 0.223726 | + | 0.387505i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15.8592 | + | 9.15629i | 0.545571 | + | 0.314986i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.12842 | − | 1.57157i | −0.0731334 | − | 0.0539998i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21.7896 | − | 37.7407i | 0.747817 | − | 1.29526i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.14765 | − | 2.97200i | 0.176459 | − | 0.101879i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.3087i | 0.558400i | 0.960233 | + | 0.279200i | \(0.0900693\pi\) | ||||
−0.960233 | + | 0.279200i | \(0.909931\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 40.7947i | 1.39515i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 38.2423 | − | 22.0792i | 1.30633 | − | 0.754212i | 0.324851 | − | 0.945765i | \(-0.394686\pi\) |
0.981482 | + | 0.191554i | \(0.0613526\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.3337 | + | 23.0946i | −0.454939 | + | 0.787978i | −0.998685 | − | 0.0512722i | \(-0.983672\pi\) |
0.543745 | + | 0.839250i | \(0.317006\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.08069 | − | 18.5323i | −0.275389 | − | 0.631578i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.1977 | + | 5.88767i | 0.347135 | + | 0.200418i | 0.663423 | − | 0.748245i | \(-0.269103\pi\) |
−0.316288 | + | 0.948663i | \(0.602436\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.60145 | + | 7.96995i | 0.156454 | + | 0.270986i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 50.2311 | 1.70594 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.0389 | −0.408392 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.0676 | + | 41.6863i | 0.815499 | + | 1.41249i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.10831 | − | 2.37194i | −0.139045 | − | 0.0802779i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 21.4372 | + | 2.42017i | 0.724709 | + | 0.0818167i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.95390 | − | 8.58041i | 0.167281 | − | 0.289740i | −0.770182 | − | 0.637825i | \(-0.779834\pi\) |
0.937463 | + | 0.348085i | \(0.113168\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.19178 | + | 4.72952i | −0.276302 | + | 0.159523i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 48.3702i | − | 1.62963i | −0.579718 | − | 0.814817i | \(-0.696837\pi\) | ||
0.579718 | − | 0.814817i | \(-0.303163\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.3911i | 0.585256i | 0.956226 | + | 0.292628i | \(0.0945297\pi\) | ||||
−0.956226 | + | 0.292628i | \(0.905470\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.98593 | + | 4.03333i | −0.234829 | + | 0.135579i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.4880 | + | 30.2900i | −0.587189 | + | 1.01704i | 0.407410 | + | 0.913245i | \(0.366432\pi\) |
−0.994599 | + | 0.103795i | \(0.966901\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.43657 | − | 0.613767i | −0.182337 | − | 0.0205851i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.42418 | − | 5.44105i | −0.315722 | − | 0.182282i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 19.9758 | + | 34.5991i | 0.668464 | + | 1.15781i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.37221 | −0.179573 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −60.3320 | −2.01443 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.30282 | − | 7.45271i | −0.143507 | − | 0.248562i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.62937 | − | 3.82747i | −0.220856 | − | 0.127511i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14.1253 | − | 32.3950i | −0.470061 | − | 1.07804i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.51672 | − | 4.35910i | 0.0836588 | − | 0.144901i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.9486 | + | 16.7135i | −0.961222 | + | 0.554962i | −0.896549 | − | 0.442945i | \(-0.853934\pi\) |
−0.0646732 | + | 0.997906i | \(0.520601\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 97.0670i | − | 3.21951i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.5057i | 0.513727i | 0.966448 | + | 0.256864i | \(0.0826891\pi\) | ||||
−0.966448 | + | 0.256864i | \(0.917311\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.4940 | + | 6.05872i | −0.347301 | + | 0.200514i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.61185 | − | 6.25591i | 0.119404 | − | 0.206814i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 41.8338 | + | 30.8890i | 1.38147 | + | 1.02004i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.20611 | + | 4.16045i | 0.237708 | + | 0.137241i | 0.614123 | − | 0.789211i | \(-0.289510\pi\) |
−0.376415 | + | 0.926451i | \(0.622843\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.254696 | + | 0.441146i | 0.00839252 | + | 0.0145363i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 69.2352 | 2.27891 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.31814 | 0.240619 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −26.7861 | − | 46.3949i | −0.879771 | − | 1.52381i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.9341 | + | 12.0863i | 0.686826 | + | 0.396539i | 0.802422 | − | 0.596757i | \(-0.203544\pi\) |
−0.115596 | + | 0.993296i | \(0.536878\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 35.4049 | − | 38.1238i | 1.16035 | − | 1.24946i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.9456 | − | 31.0827i | 0.587512 | − | 1.01760i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.510100 | − | 0.294506i | 0.0166820 | − | 0.00963138i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 39.4466i | − | 1.28866i | −0.764746 | − | 0.644332i | \(-0.777135\pi\) | ||
0.764746 | − | 0.644332i | \(-0.222865\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 84.1913i | − | 2.74748i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.7952 | + | 16.0476i | −0.906099 | + | 0.523136i | −0.879174 | − | 0.476501i | \(-0.841905\pi\) |
−0.0269249 | + | 0.999637i | \(0.508571\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.31393 | − | 7.47195i | 0.140481 | − | 0.243320i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.5160 | + | 18.3051i | −0.439676 | + | 0.595465i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.1997 | − | 16.2811i | −0.916368 | − | 0.529065i | −0.0338936 | − | 0.999425i | \(-0.510791\pi\) |
−0.882475 | + | 0.470360i | \(0.844124\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.14689 | − | 14.1108i | −0.264459 | − | 0.458057i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 95.1799 | 3.08642 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.32173 | 0.107601 | 0.0538006 | − | 0.998552i | \(-0.482866\pi\) | ||||
0.0538006 | + | 0.998552i | \(0.482866\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.3520 | + | 17.9302i | 0.334982 | + | 0.580206i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.14444 | + | 2.39279i | 0.133971 | + | 0.0773480i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 46.5026 | − | 20.2767i | 1.50165 | − | 0.654768i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.617844 | − | 1.07014i | 0.0199305 | − | 0.0345206i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −68.1032 | + | 39.3194i | −2.19460 | + | 1.26705i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 5.98201i | − | 0.192568i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 51.0144i | − | 1.64051i | −0.571997 | − | 0.820256i | \(-0.693831\pi\) | ||
0.571997 | − | 0.820256i | \(-0.306169\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13.0028 | + | 7.50718i | −0.417710 | + | 0.241165i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.58697 | + | 6.21281i | −0.115111 | + | 0.199379i | −0.917824 | − | 0.396987i | \(-0.870056\pi\) |
0.802713 | + | 0.596366i | \(0.203389\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.315589 | + | 2.79540i | −0.0101173 | + | 0.0896164i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −64.3281 | − | 37.1398i | −2.06015 | − | 1.18943i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.72080 | − | 16.8369i | −0.310996 | − | 0.538661i | 0.667582 | − | 0.744536i | \(-0.267329\pi\) |
−0.978578 | + | 0.205875i | \(0.933996\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.4993 | 0.431440 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 87.9416 | 2.80776 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.06343 | − | 7.03806i | −0.129603 | − | 0.224479i | 0.793920 | − | 0.608023i | \(-0.208037\pi\) |
−0.923523 | + | 0.383543i | \(0.874704\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.8977 | − | 6.86911i | −0.379091 | − | 0.218868i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.84027 | + | 42.8737i | −0.154068 | + | 1.36469i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.54090 | − | 13.0612i | 0.239787 | − | 0.415322i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.27614 | + | 4.77823i | −0.262900 | + | 0.151785i | −0.625657 | − | 0.780098i | \(-0.715169\pi\) |
0.362757 | + | 0.931884i | \(0.381836\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 4.09389i | − | 0.129916i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.0637i | 0.319039i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.9012 | − | 6.29382i | 0.345245 | − | 0.199327i | −0.317344 | − | 0.948310i | \(-0.602791\pi\) |
0.662589 | + | 0.748983i | \(0.269458\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.43486 | + | 14.6096i | −0.266867 | + | 0.462228i |
(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 | 1232.2.be.b.1167.2 | yes | 28 | |
4.3 | odd | 2 | 1232.2.be.c.1167.13 | yes | 28 | ||
7.3 | odd | 6 | 1232.2.be.c.815.13 | yes | 28 | ||
28.3 | even | 6 | inner | 1232.2.be.b.815.2 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1232.2.be.b.815.2 | ✓ | 28 | 28.3 | even | 6 | inner | |
1232.2.be.b.1167.2 | yes | 28 | 1.1 | even | 1 | trivial | |
1232.2.be.c.815.13 | yes | 28 | 7.3 | odd | 6 | ||
1232.2.be.c.1167.13 | yes | 28 | 4.3 | odd | 2 |