LMFDB - Embedded newform 966.2.bf.a.11.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(11,966)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 44, 27]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("966.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.bf (of order $66$, degree $20$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$1280$
Relative dimension:	$64$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			11.19
Character	$\chi$	$=$	966.11
Dual form			966.2.bf.a.527.19

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.458227 + 0.888835i) q^{2} +(0.375913 - 1.69077i) q^{3} +(-0.580057 - 0.814576i) q^{4} +(3.10185 + 2.95761i) q^{5} +(1.33056 + 1.10888i) q^{6} +(-1.66460 - 2.05648i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-2.71738 - 1.27116i) q^{9} +O(q^{10})$	\(q+(-0.458227 + 0.888835i) q^{2} +(0.375913 - 1.69077i) q^{3} +(-0.580057 - 0.814576i) q^{4} +(3.10185 + 2.95761i) q^{5} +(1.33056 + 1.10888i) q^{6} +(-1.66460 - 2.05648i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-2.71738 - 1.27116i) q^{9} +(-4.05017 + 1.40178i) q^{10} +(-1.68441 + 0.868371i) q^{11} +(-1.59531 + 0.674531i) q^{12} +(2.57348 - 2.96996i) q^{13} +(2.59064 - 0.537222i) q^{14} +(6.16664 - 4.13270i) q^{15} +(-0.327068 + 0.945001i) q^{16} +(2.68416 + 0.256306i) q^{17} +(2.37503 - 1.83282i) q^{18} +(-0.679167 - 7.11256i) q^{19} +(0.609946 - 4.24227i) q^{20} +(-4.10277 + 2.04139i) q^{21} -1.89507i q^{22} +(3.21789 - 3.55600i) q^{23} +(0.131465 - 1.72705i) q^{24} +(0.636118 + 13.3538i) q^{25} +(1.46056 + 3.64831i) q^{26} +(-3.17073 + 4.11661i) q^{27} +(-0.709596 + 2.54882i) q^{28} +(8.55623 - 3.90750i) q^{29} +(0.847569 + 7.37484i) q^{30} +(2.31879 + 0.928305i) q^{31} +(-0.690079 - 0.723734i) q^{32} +(0.835023 + 3.17437i) q^{33} +(-1.45776 + 2.26833i) q^{34} +(0.918922 - 11.3021i) q^{35} +(0.540778 + 2.95086i) q^{36} +(0.693140 - 0.168154i) q^{37} +(6.63311 + 2.65550i) q^{38} +(-4.05410 - 5.46760i) q^{39} +(3.49119 + 2.48606i) q^{40} +(-0.240850 - 0.820259i) q^{41} +(0.0655365 - 4.58211i) q^{42} +(4.15923 + 0.598008i) q^{43} +(1.68441 + 0.868371i) q^{44} +(-4.66931 - 11.9799i) q^{45} +(1.68618 + 4.48963i) q^{46} +(-7.28725 + 4.20730i) q^{47} +(1.47483 + 0.908233i) q^{48} +(-1.45822 + 6.84643i) q^{49} +(-12.1608 - 5.55364i) q^{50} +(1.44236 - 4.44193i) q^{51} +(-3.91202 - 0.373553i) q^{52} +(-5.07801 + 0.978706i) q^{53} +(-2.20607 - 4.70460i) q^{54} +(-7.79307 - 2.28825i) q^{55} +(-1.94032 - 1.79865i) q^{56} +(-12.2810 - 1.52539i) q^{57} +(-0.447568 + 9.39560i) q^{58} +(6.59286 - 2.28181i) q^{59} +(-6.94340 - 2.62600i) q^{60} +(-5.11621 - 6.50579i) q^{61} +(-1.88764 + 1.63565i) q^{62} +(1.90923 + 7.70421i) q^{63} +(0.959493 - 0.281733i) q^{64} +(16.7665 - 1.60101i) q^{65} +(-3.20412 - 0.712381i) q^{66} +(12.8101 - 0.610222i) q^{67} +(-1.34818 - 2.33512i) q^{68} +(-4.80272 - 6.77745i) q^{69} +(9.62465 + 5.99570i) q^{70} +(2.84605 + 4.42854i) q^{71} +(-2.87063 - 0.871499i) q^{72} +(-1.84306 - 2.58821i) q^{73} +(-0.168154 + 0.693140i) q^{74} +(22.8172 + 3.94432i) q^{75} +(-5.39976 + 4.67892i) q^{76} +(4.58965 + 2.01845i) q^{77} +(6.71749 - 1.09803i) q^{78} +(0.248924 - 1.29154i) q^{79} +(-3.80946 + 1.96391i) q^{80} +(5.76830 + 6.90845i) q^{81} +(0.839439 + 0.161789i) q^{82} +(-11.9724 - 3.51540i) q^{83} +(4.04271 + 2.15789i) q^{84} +(7.56779 + 8.73370i) q^{85} +(-2.43740 + 3.42285i) q^{86} +(-3.39027 - 15.9355i) q^{87} +(-1.54368 + 1.09925i) q^{88} +(15.1603 - 6.06927i) q^{89} +(12.7877 + 1.33926i) q^{90} +(-10.3915 - 0.348525i) q^{91} +(-4.76320 - 0.558534i) q^{92} +(2.44121 - 3.57158i) q^{93} +(-0.400383 - 8.40507i) q^{94} +(18.9295 - 24.0708i) q^{95} +(-1.48307 + 0.894701i) q^{96} +(1.00139 + 3.41041i) q^{97} +(-5.41716 - 4.43333i) q^{98} +(5.68101 - 0.218545i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1280 q - 64 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) $ 1280 * q - 64 * q^4 - 8 * q^6 + 4 * q^9	$ 1280 q - 64 q^{4} - 8 q^{6} + 4 q^{9} + 64 q^{16} + 44 q^{18} - 132 q^{21} - 4 q^{24} + 72 q^{25} + 108 q^{27} + 44 q^{30} + 8 q^{36} + 44 q^{37} - 4 q^{39} - 88 q^{43} - 12 q^{46} + 60 q^{49} - 48 q^{54} + 96 q^{55} + 44 q^{58} - 176 q^{61} - 110 q^{63} + 128 q^{64} + 56 q^{69} - 120 q^{70} + 44 q^{72} + 40 q^{73} - 268 q^{75} + 16 q^{78} + 88 q^{79} + 8 q^{81} - 56 q^{82} - 22 q^{84} + 64 q^{85} - 42 q^{87} - 32 q^{93} + 8 q^{94} + 4 q^{96} + 132 q^{99}+O(q^{100}) $ 1280 * q - 64 * q^4 - 8 * q^6 + 4 * q^9 + 64 * q^16 + 44 * q^18 - 132 * q^21 - 4 * q^24 + 72 * q^25 + 108 * q^27 + 44 * q^30 + 8 * q^36 + 44 * q^37 - 4 * q^39 - 88 * q^43 - 12 * q^46 + 60 * q^49 - 48 * q^54 + 96 * q^55 + 44 * q^58 - 176 * q^61 - 110 * q^63 + 128 * q^64 + 56 * q^69 - 120 * q^70 + 44 * q^72 + 40 * q^73 - 268 * q^75 + 16 * q^78 + 88 * q^79 + 8 * q^81 - 56 * q^82 - 22 * q^84 + 64 * q^85 - 42 * q^87 - 32 * q^93 + 8 * q^94 + 4 * q^96 + 132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (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 $

$2$	−0.458227	+	0.888835i	−0.324015	+	0.628502i
$2$	−0.458227	+	0.888835i	−0.324015	+	0.628502i
$3$	0.375913	−	1.69077i	0.217033	−	0.976164i
$3$	0.375913	−	1.69077i	0.217033	−	0.976164i
$4$	−0.580057	−	0.814576i	−0.290028	−	0.407288i
$5$	3.10185	+	2.95761i	1.38719	+	1.32268i	0.890666	+	0.454658i	$0.150238\pi$
$5$	3.10185	+	2.95761i	1.38719	+	1.32268i	0.496522	+	0.868024i	$0.334610\pi$
$6$	1.33056	+	1.10888i	0.543199	+	0.452698i
$7$	−1.66460	−	2.05648i	−0.629160	−	0.777276i
$7$	−1.66460	−	2.05648i	−0.629160	−	0.777276i
$8$	0.989821	−	0.142315i	0.349955	−	0.0503159i
$9$	−2.71738	−	1.27116i	−0.905793	−	0.423720i
$10$	−4.05017	+	1.40178i	−1.28078	+	0.443281i
$11$	−1.68441	+	0.868371i	−0.507867	+	0.261824i	−0.693062	−	0.720878i	$-0.743739\pi$
$11$	−1.68441	+	0.868371i	−0.507867	+	0.261824i	0.185195	+	0.982702i	$0.440708\pi$
$12$	−1.59531	+	0.674531i	−0.460526	+	0.194720i
$13$	2.57348	−	2.96996i	0.713755	−	0.823718i	−0.276786	−	0.960932i	$-0.589269\pi$
$13$	2.57348	−	2.96996i	0.713755	−	0.823718i	0.990541	+	0.137214i	$0.0438148\pi$
$14$	2.59064	−	0.537222i	0.692376	−	0.143579i
$15$	6.16664	−	4.13270i	1.59222	−	1.06706i
$16$	−0.327068	+	0.945001i	−0.0817670	+	0.236250i
$17$	2.68416	+	0.256306i	0.651003	+	0.0621633i	0.415333	−	0.909670i	$-0.363665\pi$
$17$	2.68416	+	0.256306i	0.651003	+	0.0621633i	0.235671	+	0.971833i	$0.424271\pi$
$18$	2.37503	−	1.83282i	0.559799	−	0.432001i
$19$	−0.679167	−	7.11256i	−0.155812	−	1.63173i	−0.648280	−	0.761402i	$-0.724511\pi$
$19$	−0.679167	−	7.11256i	−0.155812	−	1.63173i	0.492468	−	0.870331i	$-0.336095\pi$
$20$	0.609946	−	4.24227i	0.136388	−	0.948601i
$21$	−4.10277	+	2.04139i	−0.895298	+	0.445468i
$22$		−	1.89507i		−	0.404030i
$23$	3.21789	−	3.55600i	0.670977	−	0.741478i
$23$	3.21789	−	3.55600i	0.670977	−	0.741478i
$24$	0.131465	−	1.72705i	0.0268352	−	0.352534i
$25$	0.636118	+	13.3538i	0.127224	+	2.67075i
$26$	1.46056	+	3.64831i	0.286440	+	0.715493i
$27$	−3.17073	+	4.11661i	−0.610208	+	0.792241i
$28$	−0.709596	+	2.54882i	−0.134101	+	0.481681i
$29$	8.55623	−	3.90750i	1.58885	−	0.725605i	0.592080	−	0.805879i	$-0.298307\pi$
$29$	8.55623	−	3.90750i	1.58885	−	0.725605i	0.996773	+	0.0802746i	$0.0255797\pi$
$30$	0.847569	+	7.37484i	0.154744	+	1.34646i
$31$	2.31879	+	0.928305i	0.416468	+	0.166729i	0.570426	−	0.821349i	$-0.306778\pi$
$31$	2.31879	+	0.928305i	0.416468	+	0.166729i	−0.153959	+	0.988077i	$0.549202\pi$
$32$	−0.690079	−	0.723734i	−0.121990	−	0.127939i
$33$	0.835023	+	3.17437i	0.145359	+	0.552586i
$34$	−1.45776	+	2.26833i	−0.250005	+	0.389015i
$35$	0.918922	−	11.3021i	0.155326	−	1.91041i
$36$	0.540778	+	2.95086i	0.0901297	+	0.491810i
$37$	0.693140	−	0.168154i	0.113952	−	0.0276443i	−0.178378	−	0.983962i	$-0.557085\pi$
$37$	0.693140	−	0.168154i	0.113952	−	0.0276443i	0.292329	+	0.956318i	$0.405570\pi$
$38$	6.63311	+	2.65550i	1.07603	+	0.430778i
$39$	−4.05410	−	5.46760i	−0.649175	−	0.875516i
$40$	3.49119	+	2.48606i	0.552005	+	0.393081i
$41$	−0.240850	−	0.820259i	−0.0376144	−	0.128103i	0.938545	−	0.345156i	$-0.112174\pi$
$41$	−0.240850	−	0.820259i	−0.0376144	−	0.128103i	−0.976160	+	0.217053i	$0.930356\pi$
$42$	0.0655365	−	4.58211i	0.0101125	−	0.707034i
$43$	4.15923	+	0.598008i	0.634277	+	0.0911953i	0.451951	−	0.892043i	$-0.350728\pi$
$43$	4.15923	+	0.598008i	0.634277	+	0.0911953i	0.182326	+	0.983238i	$0.441637\pi$
$44$	1.68441	+	0.868371i	0.253934	+	0.130912i
$45$	−4.66931	−	11.9799i	−0.696059	−	1.78586i
$46$	1.68618	+	4.48963i	0.248613	+	0.661960i
$47$	−7.28725	+	4.20730i	−1.06296	+	0.613698i	−0.926248	−	0.376914i	$-0.876985\pi$
$47$	−7.28725	+	4.20730i	−1.06296	+	0.613698i	−0.136707	+	0.990612i	$0.543652\pi$
$48$	1.47483	+	0.908233i	0.212873	+	0.131092i
$49$	−1.45822	+	6.84643i	−0.208317	+	0.978061i
$50$	−12.1608	−	5.55364i	−1.71979	−	0.785403i
$51$	1.44236	−	4.44193i	0.201971	−	0.621995i
$52$	−3.91202	−	0.373553i	−0.542500	−	0.0518024i
$53$	−5.07801	+	0.978706i	−0.697518	+	0.134436i	−0.525671	−	0.850688i	$-0.676186\pi$
$53$	−5.07801	+	0.978706i	−0.697518	+	0.134436i	−0.171847	+	0.985124i	$0.554974\pi$
$54$	−2.20607	−	4.70460i	−0.300209	−	0.640215i
$55$	−7.79307	−	2.28825i	−1.05082	−	0.308548i
$56$	−1.94032	−	1.79865i	−0.259287	−	0.240355i
$57$	−12.2810	−	1.52539i	−1.62666	−	0.202043i
$58$	−0.447568	+	9.39560i	−0.0587685	+	1.23370i
$59$	6.59286	−	2.28181i	0.858318	−	0.297067i	0.137763	−	0.990465i	$-0.456009\pi$
$59$	6.59286	−	2.28181i	0.858318	−	0.297067i	0.720554	+	0.693398i	$0.243887\pi$
$60$	−6.94340	−	2.62600i	−0.896389	−	0.339015i
$61$	−5.11621	−	6.50579i	−0.655063	−	0.832981i	0.339113	−	0.940746i	$-0.389873\pi$
$61$	−5.11621	−	6.50579i	−0.655063	−	0.832981i	−0.994176	+	0.107765i	$0.965631\pi$
$62$	−1.88764	+	1.63565i	−0.239731	+	0.207728i
$63$	1.90923	+	7.70421i	0.240541	+	0.970639i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	16.7665	−	1.60101i	2.07963	−	0.198581i
$66$	−3.20412	−	0.712381i	−0.394400	−	0.0876880i
$67$	12.8101	−	0.610222i	1.56501	−	0.0745505i	0.752930	−	0.658100i	$-0.228640\pi$
$67$	12.8101	−	0.610222i	1.56501	−	0.0745505i	0.812077	+	0.583550i	$0.198337\pi$
$68$	−1.34818	−	2.33512i	−0.163491	−	0.283175i
$69$	−4.80272	−	6.77745i	−0.578180	−	0.815909i
$70$	9.62465	+	5.99570i	1.15037	+	0.716623i
$71$	2.84605	+	4.42854i	0.337764	+	0.525571i	0.968039	−	0.250801i	$-0.0806941\pi$
$71$	2.84605	+	4.42854i	0.337764	+	0.525571i	−0.630275	+	0.776372i	$0.717058\pi$
$72$	−2.87063	−	0.871499i	−0.338306	−	0.102707i
$73$	−1.84306	−	2.58821i	−0.215714	−	0.302928i	0.692513	−	0.721405i	$-0.256503\pi$
$73$	−1.84306	−	2.58821i	−0.215714	−	0.302928i	−0.908227	+	0.418477i	$0.862564\pi$
$74$	−0.168154	+	0.693140i	−0.0195475	+	0.0805759i
$75$	22.8172	+	3.94432i	2.63470	+	0.455451i
$76$	−5.39976	+	4.67892i	−0.619395	+	0.536709i
$77$	4.58965	+	2.01845i	0.523039	+	0.230024i
$78$	6.71749	−	1.09803i	0.760606	−	0.124327i
$79$	0.248924	−	1.29154i	0.0280061	−	0.145309i	−0.965234	−	0.261387i	$-0.915820\pi$
$79$	0.248924	−	1.29154i	0.0280061	−	0.145309i	0.993240	+	0.116078i	$0.0370322\pi$
$80$	−3.80946	+	1.96391i	−0.425910	+	0.219572i
$81$	5.76830	+	6.90845i	0.640922	+	0.767606i
$82$	0.839439	+	0.161789i	0.0927005	+	0.0178666i
$83$	−11.9724	−	3.51540i	−1.31414	−	0.385865i	−0.451763	−	0.892138i	$-0.649205\pi$
$83$	−11.9724	−	3.51540i	−1.31414	−	0.385865i	−0.862373	+	0.506273i	$0.831023\pi$
$84$	4.04271	+	2.15789i	0.441096	+	0.235446i
$85$	7.56779	+	8.73370i	0.820842	+	0.947302i
$86$	−2.43740	+	3.42285i	−0.262832	+	0.369096i
$87$	−3.39027	−	15.9355i	−0.363475	−	1.70846i
$88$	−1.54368	+	1.09925i	−0.164557	+	0.117180i
$89$	15.1603	−	6.06927i	1.60699	−	0.643341i	0.617320	−	0.786712i	$-0.288218\pi$
$89$	15.1603	−	6.06927i	1.60699	−	0.643341i	0.989669	+	0.143371i	$0.0457941\pi$
$90$	12.7877	+	1.33926i	1.34795	+	0.141170i
$91$	−10.3915	−	0.348525i	−1.08932	−	0.0365353i
$92$	−4.76320	−	0.558534i	−0.496598	−	0.0582312i
$93$	2.44121	−	3.57158i	0.253142	−	0.370355i
$94$	−0.400383	−	8.40507i	−0.0412963	−	0.866916i
$95$	18.9295	−	24.0708i	1.94212	−	2.46961i
$96$	−1.48307	+	0.894701i	−0.151366	+	0.0913151i
$97$	1.00139	+	3.41041i	0.101675	+	0.346274i	0.994580	−	0.103971i	$-0.0331548\pi$
$97$	1.00139	+	3.41041i	0.101675	+	0.346274i	−0.892905	+	0.450245i	$0.851337\pi$
$98$	−5.41716	−	4.43333i	−0.547215	−	0.447834i
$99$	5.68101	−	0.218545i	0.570963	−	0.0219646i
$100$	10.5087	−	8.26410i	1.05087	−	0.826410i
$101$	−0.0739085	−	0.0775130i	−0.00735417	−	0.00771284i	0.720047	−	0.693926i	$-0.244120\pi$
$101$	−0.0739085	−	0.0775130i	−0.00735417	−	0.00771284i	−0.727401	+	0.686213i	$0.759272\pi$
$102$	3.28722	+	3.31743i	0.325483	+	0.328475i
$103$	6.86964	+	0.327241i	0.676885	+	0.0322440i	0.383210	−	0.923661i	$-0.374819\pi$
$103$	6.86964	+	0.327241i	0.676885	+	0.0322440i	0.293675	+	0.955905i	$0.405122\pi$
$104$	2.12462	−	3.30597i	0.208336	−	0.324177i
$105$	−18.7638	−	5.80229i	−1.83116	−	0.566245i
$106$	1.45697	−	4.96199i	0.141513	−	0.481951i
$107$	−9.71072	+	7.63660i	−0.938771	+	0.738258i	−0.965233	−	0.261392i	$-0.915818\pi$
$107$	−9.71072	+	7.63660i	−0.938771	+	0.738258i	0.0264618	+	0.999650i	$0.491576\pi$
$108$	5.19249	+	0.194936i	0.499648	+	0.0187577i
$109$	−0.598612	+	6.26895i	−0.0573367	+	0.600457i	0.920451	+	0.390858i	$0.127822\pi$
$109$	−0.598612	+	6.26895i	−0.0573367	+	0.600457i	−0.977788	+	0.209598i	$0.932784\pi$
$110$	5.60487	−	5.87822i	0.534403	−	0.560466i
$111$	−0.0237489	−	1.23515i	−0.00225415	−	0.117235i
$112$	2.48781	−	0.900439i	0.235076	−	0.0850835i
$113$	5.89039	−	3.78552i	0.554121	−	0.356112i	−0.233418	−	0.972376i	$-0.574991\pi$
$113$	5.89039	−	3.78552i	0.554121	−	0.356112i	0.787539	+	0.616264i	$0.211355\pi$
$114$	6.98329	−	10.2168i	0.654045	−	0.956891i
$115$	20.4987	−	1.51292i	1.91151	−	0.141081i
$116$	−8.14606	−	4.70313i	−0.756343	−	0.436675i
$117$	−10.7684	+	4.79919i	−0.995540	+	0.443685i
$118$	−0.992869	+	6.90556i	−0.0914010	+	0.635708i
$119$	−3.94096	−	5.94656i	−0.361267	−	0.545120i
$120$	5.51573	−	4.96824i	0.503515	−	0.453536i
$121$	−4.29747	+	6.03496i	−0.390679	+	0.548632i
$122$	8.12696	−	1.56634i	0.735780	−	0.141810i
$123$	−1.47740	+	0.0988748i	−0.133213	+	0.00891524i
$124$	−0.588858	−	2.42730i	−0.0528810	−	0.217978i
$125$	−23.4887	+	27.1074i	−2.10089	+	2.42456i
$126$	−7.72263	−	1.83328i	−0.687987	−	0.163321i
$127$	−11.6029	−	7.45676i	−1.02960	−	0.661681i	−0.0872029	−	0.996191i	$-0.527793\pi$
$127$	−11.6029	−	7.45676i	−1.02960	−	0.661681i	−0.942392	+	0.334510i	$0.891429\pi$
$128$	−0.189251	+	0.981929i	−0.0167276	+	0.0867911i
$129$	2.57460	−	6.80749i	0.226681	−	0.599366i
$130$	−6.25983	+	15.6363i	−0.549023	+	1.37139i
$131$	−0.0463112	−	0.0160285i	−0.00404623	−	0.00140041i	0.325044	−	0.945699i	$-0.394621\pi$
$131$	−0.0463112	−	0.0160285i	−0.00404623	−	0.00140041i	−0.329090	+	0.944298i	$0.606742\pi$
$132$	2.10140	−	2.52150i	0.182904	−	0.219469i
$133$	−13.4963	+	13.2363i	−1.17028	+	1.14773i
$134$	−5.32756	+	11.6657i	−0.460231	+	1.00777i
$135$	−22.0104	+	3.39131i	−1.89436	+	0.291878i
$136$	2.69331	−	0.128298i	0.230949	−	0.0110015i
$137$	−6.92651	+	11.9971i	−0.591772	+	1.02498i	0.402222	+	0.915542i	$0.368238\pi$
$137$	−6.92651	+	11.9971i	−0.591772	+	1.02498i	−0.993994	+	0.109436i	$0.965095\pi$
$138$	8.22477	−	1.16322i	0.700139	−	0.0990201i
$139$	−5.83436			−0.494864			−0.247432	−	0.968905i	$-0.579587\pi$
$139$	−5.83436			−0.494864			−0.247432	+	0.968905i	$0.579587\pi$
$140$	−9.73946	+	5.80734i	−0.823135	+	0.490810i
$141$	4.37419	+	13.9026i	0.368373	+	1.17081i
$142$	−5.24038	+	0.500395i	−0.439763	+	0.0419922i
$143$	−1.75576	+	7.23735i	−0.146824	+	0.605217i
$144$	2.09002	−	2.15217i	0.174168	−	0.179347i
$145$	38.0970	+	13.1855i	3.16378	+	1.09500i
$146$	3.14504	−	0.452188i	0.260285	−	0.0374233i
$147$	11.0275	+	5.03916i	0.909537	+	0.415623i
$148$	−0.539035	−	0.467076i	−0.0443084	−	0.0383934i
$149$	−0.0993599	+	2.08582i	−0.00813988	+	0.170877i	0.991137	+	0.132846i	$0.0424116\pi$
$149$	−0.0993599	+	2.08582i	−0.00813988	+	0.170877i	−0.999277	+	0.0380310i	$0.987891\pi$
$150$	−13.9613	+	18.4733i	−1.13993	+	1.50834i
$151$	−6.97348	−	20.1486i	−0.567494	−	1.63967i	−0.753747	−	0.657164i	$-0.771756\pi$
$151$	−6.97348	−	20.1486i	−0.567494	−	1.63967i	0.186253	−	0.982502i	$-0.440366\pi$
$152$	−1.68448	−	6.94351i	−0.136629	−	0.563193i
$153$	−6.96806	−	4.10847i	−0.563335	−	0.332150i
$154$	−3.89717	+	3.15453i	−0.314043	+	0.254199i
$155$	4.44699	+	9.73754i	0.357191	+	0.782138i
$156$	−2.10217	+	6.47389i	−0.168308	+	0.518326i
$157$	−6.04840	+	4.30705i	−0.482715	+	0.343740i	−0.795367	−	0.606128i	$-0.792722\pi$
$157$	−6.04840	+	4.30705i	−0.482715	+	0.343740i	0.312652	+	0.949868i	$0.398783\pi$
$158$	1.03390	+	0.813069i	0.0822528	+	0.0646843i
$159$	−0.254125	+	8.95364i	−0.0201534	+	0.710070i
$160$		−	4.28589i		−	0.338830i
$161$	−12.6694	−	0.698209i	−0.998485	−	0.0550266i
$162$	−8.78366	+	1.96144i	−0.690110	+	0.154105i
$163$	−9.95351	−	5.13139i	−0.779619	−	0.401922i	0.0219991	−	0.999758i	$-0.492997\pi$
$163$	−9.95351	−	5.13139i	−0.779619	−	0.401922i	−0.801618	+	0.597836i	$0.796027\pi$
$164$	−0.528456	+	0.671987i	−0.0412655	+	0.0524734i
$165$	−6.79841	+	12.3161i	−0.529256	+	0.958805i
$166$	8.61066	−	9.03060i	0.668317	−	0.700911i
$167$	6.17796	−	2.82138i	0.478065	−	0.218325i	−0.161783	−	0.986826i	$-0.551725\pi$
$167$	6.17796	−	2.82138i	0.478065	−	0.218325i	0.639848	+	0.768501i	$0.278997\pi$
$168$	−3.77049	+	2.60450i	−0.290900	+	0.200941i
$169$	−0.347738	−	2.41857i	−0.0267491	−	0.186044i
$170$	−11.2306	+	2.72451i	−0.861346	+	0.208960i
$171$	−7.19565	+	20.1909i	−0.550265	+	1.54403i
$172$	−1.92547	−	3.73489i	−0.146816	−	0.284783i
$173$	0.655092	+	0.0312059i	0.0498057	+	0.00237254i	0.0724700	−	0.997371i	$-0.476912\pi$
$173$	0.655092	+	0.0312059i	0.0498057	+	0.00237254i	−0.0226643	+	0.999743i	$0.507215\pi$
$174$	15.7175	+	4.28866i	1.19154	+	0.325122i
$175$	26.4028	−	23.5368i	1.99587	−	1.77922i
$176$	−0.269697	−	1.87578i	−0.0203291	−	0.141392i
$177$	−1.37967	−	12.0048i	−0.103702	−	0.902332i
$178$	−1.55227	+	16.2561i	−0.116348	+	1.21845i
$179$	−4.23859	−	1.02827i	−0.316807	−	0.0768565i	0.0742026	−	0.997243i	$-0.476359\pi$
$179$	−4.23859	−	1.02827i	−0.316807	−	0.0768565i	−0.391009	+	0.920387i	$0.627874\pi$
$180$	−7.05006	+	10.7525i	−0.525481	+	0.801445i
$181$	4.53798	+	0.652462i	0.337305	+	0.0484971i	0.308886	−	0.951099i	$-0.400044\pi$
$181$	4.53798	+	0.652462i	0.337305	+	0.0484971i	0.0284187	+	0.999596i	$0.490953\pi$
$182$	5.07143	−	9.07660i	0.375919	−	0.672803i
$183$	−12.9230	+	6.20470i	−0.955296	+	0.458665i
$184$	2.67907	−	3.97776i	0.197503	−	0.293245i
$185$	2.64735	+	1.52845i	0.194637	+	0.112374i
$186$	2.05592	+	3.80643i	0.150747	+	0.279101i
$187$	−4.74377	+	1.89912i	−0.346899	+	0.138877i
$188$	7.65419	+	3.49555i	0.558239	+	0.254939i
$189$	13.7437	−	0.331957i	0.999708	−	0.0241463i
$190$	12.7210	+	27.8551i	0.922877	+	2.02082i
$191$	−0.653713	+	1.88878i	−0.0473010	+	0.136667i	−0.966177	−	0.257878i	$-0.916977\pi$
$191$	−0.653713	+	1.88878i	−0.0473010	+	0.136667i	0.918876	+	0.394545i	$0.129098\pi$
$192$	−0.115658	−	1.72818i	−0.00834692	−	0.124721i
$193$	−4.20341	+	4.00795i	−0.302568	+	0.288498i	−0.826118	−	0.563497i	$-0.809456\pi$
$193$	−4.20341	+	4.00795i	−0.302568	+	0.288498i	0.523550	+	0.851995i	$0.324607\pi$
$194$	−3.49015	−	0.672672i	−0.250578	−	0.0482950i
$195$	3.59581	−	28.9501i	0.257502	−	2.07316i
$196$	6.42279	−	2.78349i	0.458770	−	0.198821i
$197$	−15.2659	−	13.2279i	−1.08765	−	0.942452i	−0.0890831	−	0.996024i	$-0.528394\pi$
$197$	−15.2659	−	13.2279i	−1.08765	−	0.942452i	−0.998564	+	0.0535726i	$0.982939\pi$
$198$	−2.40894	+	5.14962i	−0.171196	+	0.365968i
$199$	−9.26064	+	23.1320i	−0.656469	+	1.63978i	0.107250	+	0.994232i	$0.465795\pi$
$199$	−9.26064	+	23.1320i	−0.656469	+	1.63978i	−0.763719	+	0.645549i	$0.776629\pi$
$200$	2.53008	+	13.1273i	0.178904	+	0.928240i
$201$	3.78375	−	21.8883i	0.266885	−	1.54388i
$202$	0.102763	−	0.0301740i	0.00723039	−	0.00212303i
$203$	−22.2784	−	11.0913i	−1.56364	−	0.778456i
$204$	−4.45494	+	1.40166i	−0.311908	+	0.0981358i
$205$	1.67892	−	3.25666i	0.117261	−	0.227455i
$206$	−3.43871	+	5.95603i	−0.239587	+	0.414976i
$207$	−13.2645	+	5.57255i	−0.921946	+	0.387319i
$208$	1.96491	+	3.40332i	0.136242	+	0.235978i
$209$	7.32033	+	11.3907i	0.506358	+	0.787909i
$210$	13.7554	−	14.0192i	0.949209	−	0.967415i
$211$	−6.34131	+	13.8855i	−0.436554	+	0.955919i	0.555664	+	0.831407i	$0.312464\pi$
$211$	−6.34131	+	13.8855i	−0.436554	+	0.955919i	−0.992218	+	0.124512i	$0.960263\pi$
$212$	3.74277	+	3.56872i	0.257054	+	0.245101i
$213$	8.55749	−	3.14726i	0.586349	−	0.215647i
$214$	−2.33797	−	12.1305i	−0.159820	−	0.829226i
$215$	11.1326	+	14.1563i	0.759240	+	0.965452i
$216$	−2.55260	+	4.52595i	−0.173683	+	0.307952i
$217$	−1.95082	−	6.31381i	−0.132431	−	0.428609i
$218$	−5.29777	−	3.40467i	−0.358810	−	0.230593i
$219$	−5.06889	+	2.14324i	−0.342524	+	0.144827i
$220$	2.65647	+	7.67536i	0.179099	+	0.517473i
$221$	7.66884	−	7.31223i	0.515862	−	0.491873i
$222$	1.10873	+	0.544869i	0.0744128	+	0.0365692i
$223$	−8.28946	−	9.56655i	−0.555103	−	0.640623i	0.406961	−	0.913445i	$-0.366588\pi$
$223$	−8.28946	−	9.56655i	−0.555103	−	0.640623i	−0.962065	+	0.272822i	$0.912043\pi$
$224$	−0.339639	+	2.62386i	−0.0226931	+	0.175314i
$225$	15.2462	−	37.0958i	1.01641	−	2.47305i
$226$	0.665575	+	6.97022i	0.0442734	+	0.463652i
$227$	15.8502	+	12.4647i	1.05201	+	0.827314i	0.985364	−	0.170463i	$-0.0545262\pi$
$227$	15.8502	+	12.4647i	1.05201	+	0.827314i	0.0666508	+	0.997776i	$0.478769\pi$
$228$	5.88112	+	10.8886i	0.389487	+	0.721115i
$229$	−20.8122	+	12.0159i	−1.37531	+	0.794036i	−0.991591	−	0.129413i	$-0.958691\pi$
$229$	−20.8122	+	12.0159i	−1.37531	+	0.794036i	−0.383720	+	0.923449i	$0.625357\pi$
$230$	−8.04830	+	18.9132i	−0.530689	+	1.24710i
$231$	5.13804	−	7.00126i	0.338058	−	0.460649i
$232$	7.91305	−	5.08541i	0.519517	−	0.333873i
$233$	4.15845	+	10.3873i	0.272429	+	0.680495i	0.999985	−	0.00555378i	$-0.00176783\pi$
$233$	4.15845	+	10.3873i	0.272429	+	0.680495i	−0.727555	+	0.686049i	$0.759344\pi$
$234$	0.668685	−	11.7705i	0.0437133	−	0.769459i
$235$	−35.0475	−	8.50243i	−2.28625	−	0.554637i
$236$	−5.68295	−	4.04681i	−0.369928	−	0.263425i
$237$	−2.09012	−	0.906377i	−0.135768	−	0.0588755i
$238$	7.09136	−	0.777992i	0.459665	−	0.0504297i
$239$	−1.97046	+	6.71075i	−0.127458	+	0.434083i	−0.998352	−	0.0573887i	$-0.981723\pi$
$239$	−1.97046	+	6.71075i	−0.127458	+	0.434083i	0.870894	+	0.491471i	$0.163541\pi$
$240$	1.88849	+	7.17916i	0.121902	+	0.463413i
$241$	2.60990	+	5.06250i	0.168119	+	0.326104i	0.957811	−	0.287398i	$-0.0927903\pi$
$241$	2.60990	+	5.06250i	0.168119	+	0.326104i	−0.789693	+	0.613503i	$0.789760\pi$
$242$	−3.39487	−	6.58512i	−0.218230	−	0.423308i
$243$	13.8490	−	7.15587i	0.888411	−	0.459050i
$244$	−2.33177	+	7.94127i	−0.149276	+	0.508387i
$245$	−24.7722	+	16.9238i	−1.58264	+	1.08122i
$246$	0.589102	−	1.35848i	0.0375598	−	0.0866133i
$247$	−22.8718	−	16.2869i	−1.45530	−	1.03631i
$248$	2.42730	+	0.588858i	0.154134	+	0.0373925i
$249$	−10.4443	+	18.9210i	−0.661879	+	1.19907i
$250$	−13.3309	−	33.2989i	−0.843118	−	2.10601i
$251$	4.37816	−	2.81367i	0.276347	−	0.177597i	−0.395125	−	0.918627i	$-0.629299\pi$
$251$	4.37816	−	2.81367i	0.276347	−	0.177597i	0.671472	+	0.741030i	$0.265662\pi$
$252$	5.16820	−	6.02409i	0.325566	−	0.379482i
$253$	−2.33230	+	8.78408i	−0.146631	+	0.552250i
$254$	11.9446	−	6.89623i	0.749472	−	0.432708i
$255$	17.6115	−	9.51226i	1.10287	−	0.595681i
$256$	−0.786053	−	0.618159i	−0.0491283	−	0.0386349i
$257$	−2.07816	−	21.7634i	−0.129632	−	1.35757i	−0.792976	−	0.609252i	$-0.791470\pi$
$257$	−2.07816	−	21.7634i	−0.129632	−	1.35757i	0.663344	−	0.748314i	$-0.269136\pi$
$258$	4.87099	+	5.40777i	0.303255	+	0.336673i
$259$	−1.49961	−	1.14552i	−0.0931810	−	0.0711791i
$260$	−11.0297	−	12.7289i	−0.684031	−	0.789414i
$261$	−28.2176	−	0.258184i	−1.74663	−	0.0159812i
$262$	0.0354677	−	0.0338184i	0.00219120	−	0.00208930i
$263$	7.13012	+	20.6011i	0.439662	+	1.27032i	0.919544	+	0.392987i	$0.128558\pi$
$263$	7.13012	+	20.6011i	0.439662	+	1.27032i	−0.479882	+	0.877333i	$0.659321\pi$
$264$	1.27828	+	3.02322i	0.0786729	+	0.186066i
$265$	−18.6458	−	11.9830i	−1.14541	−	0.736107i
$266$	−5.58050	−	18.0612i	−0.342162	−	1.10740i
$267$	−4.56277	−	27.9140i	−0.279237	−	1.70831i
$268$	−7.92768	−	10.0809i	−0.484260	−	0.615787i
$269$	2.19216	+	11.3740i	0.133658	+	0.693486i	0.985499	+	0.169684i	$0.0542747\pi$
$269$	2.19216	+	11.3740i	0.133658	+	0.693486i	−0.851840	+	0.523802i	$0.824513\pi$
$270$	7.07144	−	21.1176i	0.430354	−	1.28518i
$271$	19.2951	+	18.3979i	1.17209	+	1.11759i	0.990964	+	0.134131i	$0.0428244\pi$
$271$	19.2951	+	18.3979i	1.17209	+	1.11759i	0.181131	+	0.983459i	$0.442024\pi$
$272$	−1.12011	+	2.45270i	−0.0679167	+	0.148717i
$273$	−4.49556	+	17.4385i	−0.272084	+	1.05543i
$274$	−7.48951	−	11.6539i	−0.452458	−	0.704038i
$275$	−12.6675	−	21.9407i	−0.763879	−	1.32308i
$276$	−2.73490	+	7.84349i	−0.164621	+	0.472123i
$277$	13.8163	−	23.9305i	0.830142	−	1.43785i	−0.0677841	−	0.997700i	$-0.521593\pi$
$277$	13.8163	−	23.9305i	0.830142	−	1.43785i	0.897926	−	0.440147i	$-0.145074\pi$
$278$	2.67346	−	5.18578i	0.160343	−	0.311023i
$279$	−5.12102	−	5.47012i	−0.306587	−	0.327487i
$280$	−0.698891	−	11.3179i	−0.0417667	−	0.676371i
$281$	7.32062	−	2.14953i	0.436712	−	0.128230i	−0.0559842	−	0.998432i	$-0.517830\pi$
$281$	7.32062	−	2.14953i	0.436712	−	0.128230i	0.492696	+	0.870202i	$0.336011\pi$
$282$	−14.3615	−	2.48262i	−0.855215	−	0.147838i
$283$	0.629592	+	3.26664i	0.0374254	+	0.194181i	0.995830	−	0.0912332i	$-0.0290809\pi$
$283$	0.629592	+	3.26664i	0.0374254	+	0.194181i	−0.958404	+	0.285414i	$0.907869\pi$
$284$	1.95651	−	4.88713i	0.116098	−	0.289998i
$285$	−33.5822	−	41.0538i	−1.98924	−	2.43182i
$286$	−5.62827	−	4.87693i	−0.332807	−	0.288379i
$287$	−1.28593	+	1.86070i	−0.0759059	+	0.109834i
$288$	0.955224	+	2.84386i	0.0562871	+	0.167576i
$289$	−9.55379	−	1.84134i	−0.561988	−	0.108314i
$290$	−29.1768	+	27.8200i	−1.71332	+	1.63365i
$291$	6.14263	−	0.411094i	0.360088	−	0.0240988i
$292$	−1.03922	+	3.00262i	−0.0608156	+	0.175715i
$293$	11.8607	+	25.9713i	0.692909	+	1.51726i	0.848362	+	0.529416i	$0.177589\pi$
$293$	11.8607	+	25.9713i	0.692909	+	1.51726i	−0.155453	+	0.987843i	$0.549684\pi$
$294$	−9.53210	+	7.49260i	−0.555923	+	0.436977i
$295$	27.1988	+	12.4213i	1.58357	+	0.723194i
$296$	0.662154	−	0.265086i	0.0384869	−	0.0154078i
$297$	1.76605	−	9.68741i	0.102477	−	0.562120i
$298$	−1.80842	−	1.04409i	−0.104759	−	0.0604827i
$299$	−2.27999	−	18.7083i	−0.131855	−	1.08193i
$300$	−10.0223	−	20.8743i	−0.578639	−	1.20518i
$301$	−5.69367	−	9.54882i	−0.328178	−	0.550385i
$302$	21.1042	+	3.03432i	1.21441	+	0.174606i
$303$	−0.158840	+	0.0958239i	−0.00912509	+	0.00550494i
$304$	6.94351	+	1.68448i	0.398237	+	0.0966114i
$305$	3.37186	−	35.3117i	0.193072	−	2.02194i
$306$	6.84471	−	4.31085i	0.391286	−	0.246435i
$307$	−0.496374	−	3.45235i	−0.0283295	−	0.197036i	0.970742	−	0.240126i	$-0.0771889\pi$
$307$	−0.496374	−	3.45235i	−0.0283295	−	0.197036i	−0.999071	+	0.0430900i	$0.986280\pi$
$308$	−1.01807	−	4.90944i	−0.0580101	−	0.279741i
$309$	3.13567	−	11.4919i	0.178382	−	0.653753i
$310$	−10.6928	−	0.509361i	−0.607310	−	0.0289298i
$311$	7.93590	+	15.3935i	0.450004	+	0.872886i	0.999306	+	0.0372615i	$0.0118634\pi$
$311$	7.93590	+	15.3935i	0.450004	+	0.872886i	−0.549302	+	0.835624i	$0.685106\pi$
$312$	−4.79095	−	4.83499i	−0.271234	−	0.273727i
$313$	−22.6584	+	5.49687i	−1.28073	+	0.310701i	−0.817701	−	0.575643i	$-0.804752\pi$
$313$	−22.6584	+	5.49687i	−1.28073	+	0.310701i	−0.463027	+	0.886344i	$0.653237\pi$
$314$	−1.05672	−	7.34964i	−0.0596341	−	0.414764i
$315$	−16.8639	+	29.5440i	−0.950171	+	1.66462i
$316$	−1.19645	+	0.546399i	−0.0673053	+	0.0307373i
$317$	1.45651	−	1.52755i	0.0818059	−	0.0857955i	−0.681559	−	0.731763i	$-0.738698\pi$
$317$	1.45651	−	1.52755i	0.0818059	−	0.0857955i	0.763365	+	0.645968i	$0.223546\pi$
$318$	−7.84186	−	4.32867i	−0.439750	−	0.242740i
$319$	−11.0190	+	14.0118i	−0.616946	+	0.784510i
$320$	3.80946	+	1.96391i	0.212955	+	0.109786i
$321$	9.26131	+	19.2892i	0.516916	+	1.07662i
$322$	6.42603	−	10.9410i	0.358108	−	0.609720i
$323$		−	19.2653i		−	1.07195i
$324$	2.28151	−	8.70601i	0.126751	−	0.483667i
$325$	41.2971	+	32.4764i	2.29075	+	1.80147i
$326$	9.12192	−	6.49569i	0.505217	−	0.359763i
$327$	10.3743	+	3.36869i	0.573700	+	0.186289i
$328$	−0.355133	−	0.777633i	−0.0196089	−	0.0429376i
$329$	20.7826	+	7.98262i	1.14578	+	0.440096i
$330$	−7.83175	−	11.6862i	−0.431124	−	0.643305i
$331$	5.57046	+	22.9618i	0.306180	+	1.26209i	0.892143	+	0.451754i	$0.149202\pi$
$331$	5.57046	+	22.9618i	0.306180	+	1.26209i	−0.585962	+	0.810338i	$0.699283\pi$
$332$	4.08109	+	11.7915i	0.223979	+	0.647144i
$333$	−2.09728	−	0.424154i	−0.114930	−	0.0232435i
$334$	−0.323163	+	6.78402i	−0.0176827	+	0.371205i
$335$	41.5399	+	35.9945i	2.26957	+	1.96659i
$336$	−0.587232	−	4.54479i	−0.0320362	−	0.247939i
$337$	−0.706071	+	0.101518i	−0.0384622	+	0.00553002i	−0.161519	−	0.986870i	$-0.551639\pi$
$337$	−0.706071	+	0.101518i	−0.0384622	+	0.00553002i	0.123057	+	0.992400i	$0.460730\pi$
$338$	2.30906	+	0.799172i	0.125596	+	0.0434692i
$339$	−4.18616	−	11.3823i	−0.227361	−	0.618202i
$340$	2.72451	−	11.2306i	0.147757	−	0.609064i
$341$	−4.71190	+	0.449932i	−0.255164	+	0.0243652i
$342$	−14.6491	−	15.6477i	−0.792133	−	0.846132i
$343$	16.5069	−	8.39777i	0.891288	−	0.453437i
$344$	4.20200			0.226557
$345$	5.14771	−	35.2272i	0.277143	−	1.89657i
$346$	−0.327917	+	0.567969i	−0.0176289	+	0.0305342i
$347$	−21.7442	+	1.03580i	−1.16729	+	0.0556048i	−0.622259	−	0.782812i	$-0.713785\pi$
$347$	−21.7442	+	1.03580i	−1.16729	+	0.0556048i	−0.545030	+	0.838416i	$0.683482\pi$
$348$	−11.0141	+	12.0051i	−0.590418	+	0.643542i
$349$	11.5661	−	25.3263i	0.619121	−	1.35569i	−0.297035	−	0.954867i	$-0.595998\pi$
$349$	11.5661	−	25.3263i	0.619121	−	1.35569i	0.916157	−	0.400820i	$-0.131275\pi$
$350$	8.82187	+	34.2530i	0.471549	+	1.83090i
$351$	4.06632	+	20.0109i	0.217044	+	1.06811i
$352$	1.79084	+	0.619817i	0.0954522	+	0.0330363i
$353$	5.66514	−	14.1508i	0.301525	−	0.753173i	−0.697795	−	0.716298i	$-0.745835\pi$
$353$	5.66514	−	14.1508i	0.301525	−	0.753173i	0.999320	−	0.0368755i	$-0.0117405\pi$
$354$	11.3025	+	4.27460i	0.600719	+	0.227192i
$355$	−4.26986	+	22.1541i	−0.226621	+	1.17582i
$356$	−13.7377	−	8.82870i	−0.728098	−	0.467920i
$357$	−11.5357	+	4.42785i	−0.610534	+	0.234347i
$358$	2.85620	−	3.29623i	0.150955	−	0.174211i
$359$	8.35959	+	34.4587i	0.441202	+	1.81866i	0.563436	+	0.826160i	$0.309479\pi$
$359$	8.35959	+	34.4587i	0.441202	+	1.81866i	−0.122233	+	0.992501i	$0.539006\pi$
$360$	−6.32669	−	11.1934i	−0.333446	−	0.589946i
$361$	−31.4706	+	6.06546i	−1.65635	+	0.319235i
$362$	−2.65935	+	3.73454i	−0.139772	+	0.196283i
$363$	8.58823	+	9.53464i	0.450765	+	0.500439i
$364$	5.74374	+	8.66681i	0.301054	+	0.454264i
$365$	1.93803	−	13.4793i	0.101441	−	0.705538i
$366$	0.406707	−	14.3296i	0.0212589	−	0.749020i
$367$	−3.53006	−	2.03808i	−0.184268	−	0.106387i	0.405029	−	0.914304i	$-0.367262\pi$
$367$	−3.53006	−	2.03808i	−0.184268	−	0.106387i	−0.589296	+	0.807917i	$0.700595\pi$
$368$	2.30796	+	4.20397i	0.120311	+	0.219147i
$369$	−0.388200	+	2.53511i	−0.0202089	+	0.131973i
$370$	−2.57162	+	1.65268i	−0.133692	+	0.0859188i
$371$	10.4655	+	8.81367i	0.543344	+	0.457583i
$372$	−4.32536	+	0.0831662i	−0.224260	+	0.00431197i
$373$	−6.16987	+	6.47077i	−0.319464	+	0.335044i	−0.863811	−	0.503816i	$-0.831929\pi$
$373$	−6.16987	+	6.47077i	−0.319464	+	0.335044i	0.544347	+	0.838860i	$0.316777\pi$
$374$	0.485717	−	5.08666i	0.0251158	−	0.263025i
$375$	37.0025	+	49.9039i	1.91080	+	2.57702i
$376$	−6.61432	+	5.20156i	−0.341108	+	0.268250i
$377$	10.4142	−	35.4675i	0.536359	−	1.82667i
$378$	−6.00268	+	12.3680i	−0.308745	+	0.636142i
$379$	3.74826	−	5.83241i	0.192535	−	0.299591i	−0.731542	−	0.681796i	$-0.761199\pi$
$379$	3.74826	−	5.83241i	0.192535	−	0.299591i	0.924077	+	0.382206i	$0.124835\pi$
$380$	−30.5877	−	1.45707i	−1.56911	−	0.0747461i
$381$	−16.9693	+	16.8148i	−0.869365	+	0.861447i
$382$	−1.37927	−	1.44653i	−0.0705694	−	0.0740110i
$383$	9.79820	−	7.70539i	0.500664	−	0.393727i	−0.335642	−	0.941990i	$-0.608953\pi$
$383$	9.79820	−	7.70539i	0.500664	−	0.393727i	0.836306	+	0.548263i	$0.184711\pi$
$384$	1.58907	+	0.689099i	0.0810919	+	0.0351654i
$385$	8.26660	+	19.8353i	0.421305	+	1.01090i
$386$	−1.63629	−	5.57269i	−0.0832850	−	0.283643i
$387$	−10.5421	−	6.91207i	−0.535883	−	0.351360i
$388$	2.19717	−	2.79393i	0.111545	−	0.141841i
$389$	1.02808	+	21.5821i	0.0521259	+	1.09426i	0.861758	+	0.507320i	$0.169364\pi$
$389$	1.02808	+	21.5821i	0.0521259	+	1.09426i	−0.809632	+	0.586938i	$0.800333\pi$
$390$	24.0842	+	16.4618i	1.21955	+	0.833575i
$391$	9.54875	−	8.72010i	0.482901	−	0.440995i
$392$	−0.469025	+	6.98427i	−0.0236894	+	0.352759i
$393$	−0.0445093	+	0.0722761i	−0.00224520	+	0.00364585i
$394$	18.7527	−	7.50744i	0.944746	−	0.378219i
$395$	4.59199	−	3.26994i	0.231048	−	0.164528i
$396$	−3.47333	−	4.50084i	−0.174541	−	0.226176i
$397$	−2.04481	+	2.87153i	−0.102626	+	0.144118i	−0.862695	−	0.505724i	$-0.831225\pi$
$397$	−2.04481	+	2.87153i	−0.102626	+	0.144118i	0.760069	+	0.649842i	$0.225165\pi$
$398$	−16.3170	−	18.8309i	−0.817899	−	0.943906i
$399$	17.3060	+	27.7947i	0.866383	+	1.39148i
$400$	−12.8274	−	3.76645i	−0.641368	−	0.188323i
$401$	−15.4764	−	2.98283i	−0.772855	−	0.148956i	−0.212448	−	0.977172i	$-0.568143\pi$
$401$	−15.4764	−	2.98283i	−0.772855	−	0.148956i	−0.560408	+	0.828217i	$0.689356\pi$
$402$	17.7213	+	13.3930i	0.883859	+	0.667980i
$403$	8.72440	−	4.49774i	0.434593	−	0.224048i
$404$	−0.0202691	+	0.105166i	−0.00100843	+	0.00523221i
$405$	−2.54008	+	38.4893i	−0.126218	+	1.91255i
$406$	20.0669	−	14.7195i	0.995903	−	0.730517i
$407$	−1.02151	+	0.885142i	−0.0506343	+	0.0438749i
$408$	0.795527	−	4.60199i	0.0393845	−	0.227832i
$409$	−2.06660	+	8.51866i	−0.102187	+	0.421221i	−0.999809	−	0.0195455i	$-0.993778\pi$
$409$	−2.06660	+	8.51866i	−0.102187	+	0.421221i	0.897622	+	0.440766i	$0.145293\pi$
$410$	2.12530	+	2.98457i	0.104961	+	0.147398i
$411$	17.6805	+	16.2210i	0.872113	+	0.800121i
$412$	−3.71822	−	5.78566i	−0.183183	−	0.285039i
$413$	−15.6670	−	9.75979i	−0.770922	−	0.480248i
$414$	1.12506	−	14.3434i	0.0552936	−	0.704942i
$415$	−26.7393	−	46.3137i	−1.31258	−	2.27345i
$416$	−3.92536	+	0.186988i	−0.192457	+	0.00916785i
$417$	−2.19321	+	9.86453i	−0.107402	+	0.483068i
$418$	−13.4788	+	1.28707i	−0.659269	+	0.0629526i
$419$	15.6694	−	4.60096i	0.765502	−	0.224772i	0.124405	−	0.992232i	$-0.460298\pi$
$419$	15.6694	−	4.60096i	0.765502	−	0.224772i	0.641097	+	0.767460i	$0.278480\pi$
$420$	6.15767	+	18.6502i	0.300463	+	0.910037i
$421$	2.75589	−	2.38799i	0.134314	−	0.116384i	−0.585113	−	0.810952i	$-0.698950\pi$
$421$	2.75589	−	2.38799i	0.134314	−	0.116384i	0.719427	+	0.694568i	$0.244404\pi$
$422$	−9.43619	−	11.9991i	−0.459347	−	0.584107i
$423$	25.1504	−	2.16956i	1.22285	−	0.105487i
$424$	−4.88704	+	1.69142i	−0.237336	+	0.0821427i
$425$	−1.71521	+	36.0066i	−0.0831997	+	1.74658i
$426$	−1.12387	+	9.04836i	−0.0544518	+	0.438394i
$427$	−4.86258	+	21.3509i	−0.235317	+	1.03324i
$428$	11.8534	+	3.48046i	0.572954	+	0.168234i
$429$	11.5766	+	5.68919i	0.558926	+	0.274677i
$430$	−17.6839	+	3.40829i	−0.852793	+	0.164362i
$431$	−25.8060	−	2.46417i	−1.24303	−	0.118695i	−0.547262	−	0.836961i	$-0.684330\pi$
$431$	−25.8060	−	2.46417i	−1.24303	−	0.118695i	−0.695768	+	0.718266i	$0.744936\pi$
$432$	−2.85315	−	4.34275i	−0.137272	−	0.208941i
$433$	2.99231	+	1.36654i	0.143801	+	0.0656718i	0.486016	−	0.873950i	$-0.338450\pi$
$433$	2.99231	+	1.36654i	0.143801	+	0.0656718i	−0.342215	+	0.939622i	$0.611177\pi$
$434$	6.50586	+	1.15919i	0.312291	+	0.0556431i
$435$	36.6147	−	59.4565i	1.75554	−	2.85072i
$436$	5.45377	−	3.14873i	0.261188	−	0.150797i
$437$	−27.4778	−	20.4723i	−1.31444	−	0.979325i
$438$	0.417715	−	5.48750i	0.0199592	−	0.262203i
$439$	4.25148	+	2.19179i	0.202912	+	0.104608i	0.556688	−	0.830722i	$-0.312072\pi$
$439$	4.25148	+	2.19179i	0.202912	+	0.104608i	−0.353776	+	0.935330i	$0.615102\pi$
$440$	−8.03940	−	1.15589i	−0.383263	−	0.0551049i
$441$	12.6654	−	16.7507i	0.603116	−	0.797653i
$442$	2.98530	+	10.1670i	0.141996	+	0.483595i
$443$	−0.866266	−	0.616865i	−0.0411575	−	0.0293081i	0.559293	−	0.828970i	$-0.311073\pi$
$443$	−0.866266	−	0.616865i	−0.0411575	−	0.0293081i	−0.600451	+	0.799662i	$0.705012\pi$
$444$	−0.992347	+	0.735802i	−0.0470947	+	0.0349196i
$445$	64.9755	+	26.0123i	3.08013	+	1.23310i
$446$	12.3015	−	2.98432i	0.582495	−	0.141312i
$447$	3.48928	+	0.952081i	0.165038	+	0.0450319i
$448$	−2.17655	−	1.50421i	−0.102832	−	0.0710670i
$449$	3.58621	−	5.58026i	0.169244	−	0.263349i	−0.746263	−	0.665651i	$-0.768154\pi$
$449$	3.58621	−	5.58026i	0.169244	−	0.263349i	0.915507	+	0.402303i	$0.131790\pi$
$450$	25.9859	+	30.5496i	1.22499	+	1.44012i
$451$	1.11798	+	1.17250i	0.0526435	+	0.0552109i
$452$	−6.50036	−	2.60235i	−0.305751	−	0.122404i
$453$	−36.6879	+	4.21643i	−1.72375	+	0.198105i
$454$	−18.3421	+	8.37655i	−0.860837	+	0.393131i
$455$	−31.2020	−	31.8149i	−1.46277	−	1.49151i
$456$	−12.3731	+	0.237904i	−0.579422	+	0.0111409i
$457$	12.3688	+	30.8958i	0.578589	+	1.44525i	0.872118	+	0.489296i	$0.162746\pi$
$457$	12.3688	+	30.8958i	0.578589	+	1.44525i	−0.293528	+	0.955950i	$0.594830\pi$
$458$	−1.14348	−	24.0047i	−0.0534315	−	1.12166i
$459$	−9.56585	+	10.2369i	−0.446496	+	0.477819i
$460$	−13.1228	−	15.8201i	−0.611853	−	0.737618i
$461$			7.26895i			0.338549i	0.985569	+	0.169274i	$0.0541424\pi$
$461$			7.26895i			0.338549i	−0.985569	+	0.169274i	$0.945858\pi$
$462$	3.86858	+	7.77503i	0.179983	+	0.361727i
$463$	−2.44283	+	16.9902i	−0.113528	+	0.789603i	0.850914	+	0.525306i	$0.176049\pi$
$463$	−2.44283	+	16.9902i	−0.113528	+	0.789603i	−0.964441	+	0.264297i	$0.914860\pi$
$464$	0.894122	+	9.36367i	0.0415086	+	0.434697i
$465$	18.1356	−	3.85835i	0.841018	−	0.178927i
$466$	−11.1381	−	1.06356i	−0.515963	−	0.0492685i
$467$	−11.2989	+	32.6461i	−0.522851	+	1.51068i	0.306455	+	0.951885i	$0.400857\pi$
$467$	−11.2989	+	32.6461i	−0.522851	+	1.51068i	−0.829306	+	0.558794i	$0.811264\pi$
$468$	10.1556	+	5.98789i	0.469443	+	0.276790i
$469$	−22.5787	−	25.3280i	−1.04259	−	1.16954i
$470$	23.6169	−	27.2554i	1.08937	−	1.25720i
$471$	5.00854	+	11.8455i	0.230781	+	0.545812i
$472$	6.20102	−	3.19685i	0.285425	−	0.147147i
$473$	−7.52513	+	2.60447i	−0.346006	+	0.119754i
$474$	1.76337	−	1.44244i	0.0809941	−	0.0662536i
$475$	94.5473	−	13.5939i	4.33813	−	0.623729i
$476$	−2.55794	+	6.65955i	−0.117243	+	0.305240i
$477$	15.0430	+	3.79545i	0.688770	+	0.173782i
$478$	−5.06184	−	4.82646i	−0.231523	−	0.220757i
$479$	9.36499	+	13.1513i	0.427897	+	0.600897i	0.971091	−	0.238710i	$-0.0767245\pi$
$479$	9.36499	+	13.1513i	0.427897	+	0.600897i	−0.543194	+	0.839607i	$0.682785\pi$
$480$	−7.24645	−	1.61112i	−0.330753	−	0.0735373i
$481$	1.28437	−	2.49134i	0.0585624	−	0.113595i
$482$	−5.69566			−0.259430
$483$	−5.94308	+	21.1584i	−0.270419	+	0.962743i
$484$	7.40871			0.336760
$485$	−6.98049	+	13.5403i	−0.316968	+	0.614832i
$486$	0.0144384	+	15.5885i	0.000654938	+	0.707106i
$487$	−11.7602	−	16.5149i	−0.532906	−	0.748362i	0.457096	−	0.889418i	$-0.348890\pi$
$487$	−11.7602	−	16.5149i	−0.532906	−	0.748362i	−0.990002	+	0.141056i	$0.954950\pi$
$488$	−5.99000	−	5.71145i	−0.271155	−	0.258545i
$489$	−12.4176	+	14.9001i	−0.561545	+	0.673806i
$490$	−3.69115	−	29.7733i	−0.166749	−	1.34502i
$491$	−15.2405	+	2.19125i	−0.687794	+	0.0988898i	−0.477346	−	0.878715i	$-0.658401\pi$
$491$	−15.2405	+	2.19125i	−0.687794	+	0.0988898i	−0.210448	+	0.977605i	$0.567492\pi$
$492$	0.937519	+	1.14610i	0.0422666	+	0.0516704i
$493$	23.9678	−	8.29533i	1.07945	−	0.373603i
$494$	24.9569	−	12.8662i	1.12286	−	0.578876i
$495$	18.2680	+	16.1243i	0.821085	+	0.724733i
$496$	−1.63565	+	1.88764i	−0.0734430	+	0.0847577i
$497$	4.36967	−	13.2246i	0.196006	−	0.593204i
$498$	−12.0318	−	17.9533i	−0.539157	−	0.804508i
$499$	−2.93783	+	8.48830i	−0.131515	+	0.379989i	−0.991462	−	0.130395i	$-0.958375\pi$
$499$	−2.93783	+	8.48830i	−0.131515	+	0.379989i	0.859947	+	0.510384i	$0.170497\pi$
$500$	35.7058	+	3.40949i	1.59681	+	0.152477i
$501$	−2.44792	−	11.5061i	−0.109365	−	0.514054i
$502$	0.494702	+	5.18076i	0.0220796	+	0.231229i
$503$	−0.264669	+	1.84081i	−0.0118010	+	0.0820778i	−0.994871	−	0.101154i	$-0.967747\pi$
$503$	−0.264669	+	1.84081i	−0.0118010	+	0.0820778i	0.983070	+	0.183231i	$0.0586558\pi$
$504$	2.98622	+	7.35408i	0.133017	+	0.327577i
$505$		−	0.459026i		−	0.0204264i
$506$	−6.73888	−	6.09813i	−0.299580	−	0.271095i
$507$	−4.21996	−	0.321228i	−0.187415	−	0.0142662i
$508$	0.656271	+	13.7768i	0.0291173	+	0.611248i
$509$	−6.97026	−	17.4109i	−0.308951	−	0.771724i	−0.998856	−	0.0478230i	$-0.984772\pi$
$509$	−6.97026	−	17.4109i	−0.308951	−	0.771724i	0.689904	−	0.723901i	$-0.257653\pi$
$510$	0.384791	+	20.0125i	0.0170388	+	0.886167i
$511$	−2.25465	+	8.09855i	−0.0997400	+	0.358259i
$512$	0.909632	−	0.415415i	0.0402004	−	0.0183589i
$513$	31.4331	+	19.7562i	1.38780	+	0.872256i
$514$	20.2964	+	8.12545i	0.895235	+	0.358398i
$515$	20.3407	+	21.3327i	0.896319	+	0.940033i
$516$	−7.03863	+	1.85153i	−0.309859	+	0.0815089i
$517$	8.62119	−	13.4148i	0.379160	−	0.589984i
$518$	1.70534	−	0.807995i	0.0749282	−	0.0355013i
$519$	0.299019	−	1.09588i	0.0131255	−	0.0481036i
$520$	16.3680	−	3.97083i	0.717784	−	0.174133i
$521$	8.54398	+	3.42049i	0.374318	+	0.149854i	0.551191	−	0.834379i	$-0.314174\pi$
$521$	8.54398	+	3.42049i	0.374318	+	0.149854i	−0.176872	+	0.984234i	$0.556598\pi$
$522$	13.1595	−	24.9625i	0.575977	−	1.09258i
$523$	−10.5720	−	7.52826i	−0.462280	−	0.329188i	0.325075	−	0.945688i	$-0.394610\pi$
$523$	−10.5720	−	7.52826i	−0.462280	−	0.329188i	−0.787355	+	0.616500i	$0.788550\pi$
$524$	0.0138067	+	0.0470214i	0.000603150	+	0.00205414i
$525$	−29.8701	−	53.4888i	−1.30364	−	2.33444i
$526$	−21.5782	−	3.10248i	−0.940855	−	0.135275i
$527$	5.98608	+	3.08604i	0.260758	+	0.134430i
$528$	−3.27289	−	0.249136i	−0.142434	−	0.0108422i
$529$	−2.29033	−	22.8857i	−0.0995794	−	0.995030i
$530$	19.1949	−	11.0822i	0.833773	−	0.481379i
$531$	−20.8159	−	2.18004i	−0.903332	−	0.0946056i
$532$	18.6106	+	3.31597i	0.806870	+	0.143766i
$533$	−3.05595	−	1.39561i	−0.132368	−	0.0604505i
$534$	26.9018	+	8.73541i	1.16415	+	0.378018i
$535$	−52.7072	−	5.03293i	−2.27873	−	0.217593i
$536$	12.5929	−	2.42708i	0.543931	−	0.104834i
$537$	−3.33190	+	6.77992i	−0.143782	+	0.292575i
$538$	−11.1141	−	3.26341i	−0.479164	−	0.140695i
$539$	−3.48902	−	12.7984i	−0.150283	−	0.551268i
$540$	15.5298	+	15.9620i	0.668296	+	0.686896i
$541$	0.156509	−	3.28552i	0.00672883	−	0.141255i	−0.993003	−	0.118091i	$-0.962323\pi$
$541$	0.156509	−	3.28552i	0.00672883	−	0.141255i	0.999732	−	0.0231649i	$-0.00737428\pi$
$542$	−25.1942	+	8.71980i	−1.08218	+	0.374547i
$543$	2.80904	−	7.42739i	0.120548	−	0.318740i
$544$	−1.66678	−	2.11949i	−0.0714627	−	0.0908722i
$545$	−20.3979	+	17.6749i	−0.873750	+	0.757109i
$546$	−13.4400	−	11.9866i	−0.575179	−	0.512979i
$547$	16.6303	−	4.88310i	0.711060	−	0.208786i	0.0938524	−	0.995586i	$-0.470082\pi$
$547$	16.6303	−	4.88310i	0.711060	−	0.208786i	0.617208	+	0.786800i	$0.288264\pi$
$548$	13.7903	−	1.31681i	0.589092	−	0.0562515i
$549$	5.63278	+	24.1822i	0.240401	+	1.03207i
$550$	25.3063	−	1.20549i	1.07906	−	0.0514022i
$551$	−33.6034	−	58.2029i	−1.43155	−	2.47953i
$552$	−5.71837	−	6.02497i	−0.243390	−	0.256440i
$553$	−3.07038	+	1.63799i	−0.130566	+	0.0696543i
$554$	14.9393	+	23.2460i	0.634711	+	0.987629i
$555$	3.57942	−	3.90148i	0.151938	−	0.165609i
$556$	3.38426	+	4.75253i	0.143525	+	0.201552i
$557$	4.59122	−	18.9252i	0.194536	−	0.801888i	−0.787979	−	0.615703i	$-0.788872\pi$
$557$	4.59122	−	18.9252i	0.194536	−	0.801888i	0.982515	−	0.186186i	$-0.0596126\pi$
$558$	7.20862	−	2.04519i	0.305165	−	0.0865798i
$559$	12.4798	−	10.8138i	0.527838	−	0.457374i
$560$	10.3800	+	4.56494i	0.438633	+	0.192904i
$561$	1.42772	+	8.73452i	0.0602786	+	0.368772i
$562$	−1.44393	+	7.49180i	−0.0609083	+	0.316023i
$563$	13.6164	−	7.01975i	0.573864	−	0.295847i	−0.146762	−	0.989172i	$-0.546885\pi$
$563$	13.6164	−	7.01975i	0.573864	−	0.295847i	0.720625	+	0.693325i	$0.243855\pi$
$564$	8.78746	−	11.6274i	0.370019	−	0.489603i
$565$	29.4672	+	5.67933i	1.23969	+	0.238931i
$566$	−3.19200	−	0.937255i	−0.134170	−	0.0393958i
$567$	4.60518	−	23.3622i	0.193399	−	0.981120i
$568$	3.44733	+	3.97843i	0.144647	+	0.166931i
$569$	21.8910	−	30.7416i	0.917718	−	1.28875i	−0.0394500	−	0.999222i	$-0.512561\pi$
$569$	21.8910	−	30.7416i	0.917718	−	1.28875i	0.957168	−	0.289533i	$-0.0935000\pi$
$570$	51.8784	−	11.0371i	2.17295	−	0.462295i
$571$	16.6741	−	11.8735i	0.697788	−	0.496892i	−0.175263	−	0.984522i	$-0.556078\pi$
$571$	16.6741	−	11.8735i	0.697788	−	0.496892i	0.873051	+	0.487629i	$0.162138\pi$
$572$	6.91381	−	2.76787i	0.289081	−	0.115731i
$573$	2.94775	+	1.81529i	0.123144	+	0.0758349i
$574$	−1.06461	−	1.99560i	−0.0444361	−	0.0832948i
$575$	49.5330	+	40.7089i	2.06567	+	1.69768i
$576$	−2.96543	−	0.454095i	−0.123560	−	0.0189206i
$577$	−1.91339	−	40.1671i	−0.0796556	−	1.67218i	−0.586355	−	0.810054i	$-0.699438\pi$
$577$	−1.91339	−	40.1671i	−0.0796556	−	1.67218i	0.506699	−	0.862123i	$-0.330866\pi$
$578$	6.01445	−	7.64800i	0.250168	−	0.318115i
$579$	5.19639	+	8.61363i	0.215954	+	0.357970i
$580$	−11.3578	−	38.6812i	−0.471608	−	1.60615i
$581$	12.6998	+	30.4726i	0.526878	+	1.26422i
$582$	−2.44932	+	5.64816i	−0.101528	+	0.234124i
$583$	7.70355	−	6.05814i	0.319048	−	0.250902i
$584$	−2.19264	−	2.29958i	−0.0907321	−	0.0951571i
$585$	−47.5961	−	16.9624i	−1.96786	−	0.701308i
$586$	−28.5191	−	1.35853i	−1.17811	−	0.0561204i
$587$	6.85334	−	10.6640i	0.282867	−	0.440150i	−0.670523	−	0.741888i	$-0.733930\pi$
$587$	6.85334	−	10.6640i	0.282867	−	0.440150i	0.953391	+	0.301738i	$0.0975668\pi$
$588$	−2.29183	−	11.9058i	−0.0945133	−	0.490986i
$589$	5.02778	−	17.1230i	0.207166	−	0.705543i
$590$	−23.5037	+	18.4835i	−0.967630	+	0.760953i
$591$	−28.1040	+	20.8384i	−1.15604	+	0.857179i
$592$	−0.0677983	+	0.710016i	−0.00278649	+	0.0291815i
$593$	20.8667	−	21.8844i	0.856893	−	0.898684i	−0.138901	−	0.990306i	$-0.544357\pi$
$593$	20.8667	−	21.8844i	0.856893	−	0.898684i	0.995794	+	0.0916227i	$0.0292054\pi$
$594$	7.80126	+	6.00876i	0.320090	+	0.246542i
$595$	5.36333	−	30.1011i	0.219875	−	1.23403i
$596$	1.75669	−	1.12896i	0.0719570	−	0.0462440i
$597$	35.6295	+	24.3532i	1.45822	+	0.996709i
$598$	17.6734	+	6.54611i	0.722717	+	0.267690i
$599$	−7.13448	−	4.11910i	−0.291507	−	0.168302i	0.347114	−	0.937823i	$-0.387162\pi$
$599$	−7.13448	−	4.11910i	−0.291507	−	0.168302i	−0.638621	+	0.769521i	$0.720495\pi$
$600$	23.1463	+	0.656945i	0.944943	+	0.0268197i
$601$	−2.98019	+	20.7276i	−0.121564	+	0.845498i	0.834220	+	0.551431i	$0.185918\pi$
$601$	−2.98019	+	20.7276i	−0.121564	+	0.845498i	−0.955785	+	0.294067i	$0.904991\pi$
$602$	11.0963	−	0.685211i	0.452252	−	0.0279271i
$603$	−35.5857	−	14.6255i	−1.44916	−	0.595598i
$604$	−12.3675	+	17.3677i	−0.503227	+	0.706683i
$605$	−31.1791	+	6.00929i	−1.26761	+	0.244312i
$606$	−0.0123872	−	0.185091i	−0.000503195	−	0.00751882i
$607$	−1.81613	−	7.48621i	−0.0737146	−	0.303856i	0.923005	−	0.384788i	$-0.125725\pi$
$607$	−1.81613	−	7.48621i	−0.0737146	−	0.303856i	−0.996720	+	0.0809322i	$0.974210\pi$
$608$	−4.67892	+	5.39976i	−0.189755	+	0.218989i
$609$	−27.1275	+	33.4982i	−1.09926	+	1.35742i
$610$	29.8412	+	19.1778i	1.20824	+	0.776485i
$611$	−6.25812	+	32.4702i	−0.253177	+	1.31360i
$612$	0.695210	+	8.05916i	0.0281022	+	0.325772i
$613$	0.808610	−	2.01981i	0.0326595	−	0.0815794i	−0.911142	−	0.412093i	$-0.864798\pi$
$613$	0.808610	−	2.01981i	0.0326595	−	0.0815794i	0.943801	+	0.330514i	$0.107222\pi$
$614$	3.29603	+	1.14077i	0.133017	+	0.0460376i
$615$	−4.87511	−	4.06288i	−0.196584	−	0.163831i
$616$	4.83019	+	1.34473i	0.194614	+	0.0541809i
$617$	10.4658	−	22.9168i	0.421336	−	0.922597i	−0.573318	−	0.819333i	$-0.694344\pi$
$617$	10.4658	−	22.9168i	0.421336	−	0.922597i	0.994654	−	0.103264i	$-0.0329287\pi$
$618$	8.77759	+	8.05301i	0.353087	+	0.323939i
$619$	−27.0265	+	1.28743i	−1.08629	+	0.0517463i	−0.583077	−	0.812417i	$-0.698151\pi$
$619$	−27.0265	+	1.28743i	−1.08629	+	0.0517463i	−0.503211	+	0.864164i	$0.667848\pi$
$620$	5.35246	−	9.27074i	0.214960	−	0.372322i
$621$	4.43559	+	24.5219i	0.177994	+	0.984032i
$622$	−17.3187			−0.694418
$623$	−37.7172	−	21.0740i	−1.51111	−	0.844310i
$624$	6.49285	−	2.04285i	0.259922	−	0.0817794i
$625$	−86.4895	+	8.25874i	−3.45958	+	0.330350i
$626$	5.49687	−	22.6584i	0.219699	−	0.905612i
$627$	22.0108	−	8.09508i	0.879025	−	0.323286i
$628$	7.01684	+	2.42855i	0.280002	+	0.0969097i
$629$	1.90359	−	0.273696i	0.0759013	−	0.0109130i
$630$	−18.5323	−	28.5271i	−0.738345	−	1.13655i
$631$	3.99351	+	3.46040i	0.158979	+	0.137756i	0.730718	−	0.682679i	$-0.239185\pi$
$631$	3.99351	+	3.46040i	0.158979	+	0.137756i	−0.571739	+	0.820436i	$0.693731\pi$
$632$	0.0625849	−	1.31382i	0.00248949	−	0.0522609i
$633$	21.0934	+	15.9414i	0.838387	+	0.633614i
$634$	0.690324	+	1.99456i	0.0274163	+	0.0792142i
$635$	−13.9364	−	57.4467i	−0.553050	−	2.27970i
$636$	7.44082	−	4.98661i	0.295048	−	0.197732i
$637$	16.5809	+	21.9500i	0.656959	+	0.869691i
$638$	−7.40499	−	16.2147i	−0.293166	−	0.641945i
$639$	−2.10441	−	15.6518i	−0.0832492	−	0.619176i
$640$	−3.49119	+	2.48606i	−0.138001	+	0.0982703i
$641$	−0.604574	−	0.475442i	−0.0238792	−	0.0187788i	0.606148	−	0.795352i	$-0.292714\pi$
$641$	−0.604574	−	0.475442i	−0.0238792	−	0.0187788i	−0.630027	+	0.776573i	$0.716956\pi$
$642$	−21.3887	−	0.607062i	−0.844147	−	0.0239588i
$643$			11.0801i			0.436957i	0.975842	+	0.218479i	$0.0701094\pi$
$643$			11.0801i			0.436957i	−0.975842	+	0.218479i	$0.929891\pi$
$644$	6.78020	+	10.7252i	0.267177	+	0.422630i
$645$	28.1199	−	13.5012i	1.10722	−	0.531608i
$646$	17.1237	+	8.82787i	0.673722	+	0.347328i
$647$	13.1946	−	16.7782i	0.518732	−	0.659621i	−0.454150	−	0.890925i	$-0.650057\pi$
$647$	13.1946	−	16.7782i	0.518732	−	0.659621i	0.972881	+	0.231304i	$0.0742993\pi$
$648$	6.69276	+	6.01722i	0.262917	+	0.236379i
$649$	−9.12359	+	9.56855i	−0.358132	+	0.375598i
$650$	−47.7896	+	21.8248i	−1.87446	+	0.856038i
$651$	−11.4085	+	0.924945i	−0.447135	+	0.0362515i
$652$	1.59369	+	11.0844i	0.0624139	+	0.434098i
$653$	31.7480	−	7.70197i	1.24239	−	0.301401i	0.439892	−	0.898051i	$-0.355017\pi$
$653$	31.7480	−	7.70197i	1.24239	−	0.301401i	0.802502	+	0.596649i	$0.203502\pi$
$654$	−7.74799	+	7.67743i	−0.302971	+	0.300211i
$655$	−0.0962444	−	0.186688i	−0.00376058	−	0.00729451i
$656$	0.853919	+	0.0406772i	0.0333399	+	0.00158818i
$657$	1.71825	+	9.37598i	0.0670355	+	0.365792i
$658$	−16.6184	+	14.8144i	−0.647852	+	0.577527i
$659$	−3.97368	−	27.6375i	−0.154793	−	1.07661i	−0.908044	−	0.418874i	$-0.862425\pi$
$659$	−3.97368	−	27.6375i	−0.154793	−	1.07661i	0.753252	−	0.657732i	$-0.228484\pi$
$660$	13.9758	−	1.60620i	0.544009	−	0.0625213i
$661$	1.21610	−	12.7356i	0.0473008	−	0.495356i	−0.940518	−	0.339745i	$-0.889659\pi$
$661$	1.21610	−	12.7356i	0.0473008	−	0.495356i	0.987818	−	0.155611i	$-0.0497347\pi$
$662$	−22.9618	−	5.57046i	−0.892434	−	0.216502i
$663$	−9.48045	−	15.7150i	−0.368190	−	0.610319i
$664$	−12.3508	−	1.77577i	−0.479303	−	0.0689134i
$665$	−81.0111	+	1.14014i	−3.14147	+	0.0442128i
$666$	1.33803	−	1.66977i	0.0518476	−	0.0647024i
$667$	13.6380	−	42.9999i	0.528064	−	1.66496i
$668$	−5.88180	−	3.39586i	−0.227574	−	0.131390i
$669$	−19.2909	+	10.4194i	−0.745830	+	0.402835i
$670$	−51.0279	+	20.4285i	−1.97138	+	0.789222i
$671$	14.2672	+	6.51561i	0.550779	+	0.251532i
$672$	4.30866	+	1.56059i	0.166210	+	0.0602012i
$673$	−6.59256	−	14.4357i	−0.254124	−	0.556455i	0.738975	−	0.673733i	$-0.235310\pi$
$673$	−6.59256	−	14.4357i	−0.254124	−	0.556455i	−0.993099	+	0.117278i	$0.962583\pi$
$674$	0.233308	−	0.674099i	0.00898669	−	0.0259653i
$675$	−56.9891	−	39.7225i	−2.19351	−	1.52892i
$676$	−1.76840	+	1.68617i	−0.0680155	+	0.0648527i
$677$	29.2780	+	5.64287i	1.12525	+	0.216873i	0.717728	−	0.696324i	$-0.245182\pi$
$677$	29.2780	+	5.64287i	1.12525	+	0.216873i	0.407518	+	0.913197i	$0.366394\pi$
$678$	12.0352	+	1.49486i	0.462209	+	0.0574098i
$679$	5.34653	−	7.73629i	0.205181	−	0.296892i
$680$	8.73370	+	7.56779i	0.334922	+	0.290212i
$681$	27.0332	−	22.1133i	1.03592	−	0.847385i
$682$	1.75920	−	4.39428i	0.0673634	−	0.168266i
$683$	0.739907	+	3.83900i	0.0283118	+	0.146895i	0.993334	−	0.115273i	$-0.0367744\pi$
$683$	0.739907	+	3.83900i	0.0283118	+	0.146895i	−0.965022	+	0.262169i	$0.915562\pi$
$684$	20.6209	−	5.85044i	0.788459	−	0.223697i
$685$	−56.9676	+	16.7272i	−2.17662	+	0.639113i
$686$	−0.0996569	+	18.5200i	−0.00380492	+	0.707097i
$687$	12.4926	+	39.7056i	0.476621	+	1.51486i
$688$	−1.92547	+	3.73489i	−0.0734079	+	0.142391i
$689$	−10.1615	+	17.6001i	−0.387120	+	0.670512i
$690$	28.9524	+	20.7175i	1.10220	+	0.788702i
$691$	6.57113	+	11.3815i	0.249978	+	0.432974i	0.963519	−	0.267639i	$-0.0862434\pi$
$691$	6.57113	+	11.3815i	0.249978	+	0.432974i	−0.713542	+	0.700613i	$0.752910\pi$
$692$	−0.354571	−	0.551723i	−0.0134788	−	0.0209734i
$693$	−9.90603	−	11.3191i	−0.376299	−	0.429977i
$694$	9.04311	−	19.8016i	0.343272	−	0.751660i
$695$	−18.0973	−	17.2557i	−0.686469	−	0.654547i
$696$	−5.62362	−	15.2908i	−0.213163	−	0.579596i
$697$	−0.436241	−	2.26343i	−0.0165238	−	0.0857336i
$698$	17.2110	+	21.8856i	0.651447	+	0.828382i
$699$	19.1257	−	3.12625i	0.723401	−	0.118246i
$700$	−34.4877	−	7.85443i	−1.30351	−	0.296869i
$701$	28.8829	+	18.5619i	1.09089	+	0.701073i	0.957048	−	0.289929i	$-0.0936318\pi$
$701$	28.8829	+	18.5619i	1.09089	+	0.701073i	0.133843	+	0.991003i	$0.457268\pi$
$702$	−19.6497	−	5.55526i	−0.741631	−	0.209670i
$703$	−1.66676	−	4.81579i	−0.0628631	−	0.181631i
$704$	−1.37153	+	1.30775i	−0.0516913	+	0.0492876i
$705$	−27.5504	+	56.0609i	−1.03761	+	2.11138i
$706$	9.98185	+	11.5197i	0.375672	+	0.433548i
$707$	−0.0363759	+	0.281020i	−0.00136806	+	0.0105688i
$708$	−8.97850	+	8.08729i	−0.337433	+	0.303939i
$709$	−2.53248	−	26.5214i	−0.0951095	−	0.996031i	−0.909497	−	0.415710i	$-0.863533\pi$
$709$	−2.53248	−	26.5214i	−0.0951095	−	0.996031i	0.814388	−	0.580321i	$-0.197073\pi$
$710$	−17.7348	−	13.9468i	−0.665576	−	0.523415i
$711$	−2.31817	+	3.19318i	−0.0869383	+	0.119754i
$712$	14.1422	−	8.16503i	0.530003	−	0.305997i
$713$	10.7627	−	5.25846i	0.403066	−	0.196931i
$714$	1.35033	−	12.2823i	0.0505349	−	0.459653i
$715$	−26.8513	+	17.2563i	−1.00418	+	0.645349i
$716$	1.62102	+	4.04911i	0.0605803	+	0.151322i
$717$	10.6056	+	5.85424i	0.396073	+	0.218630i
$718$	−34.4587	−	8.35959i	−1.28599	−	0.311977i
$719$	3.31649	+	2.36166i	0.123684	+	0.0880750i	0.640225	−	0.768188i	$-0.278841\pi$
$719$	3.31649	+	2.36166i	0.123684	+	0.0880750i	−0.516541	+	0.856263i	$0.672781\pi$
$720$	12.8482	−	0.494261i	0.478823	−	0.0184200i
$721$	−10.7622	−	14.6720i	−0.400806	−	0.546414i
$722$	9.02946	−	30.7515i	0.336042	−	1.14445i
$723$	9.54060	−	2.50967i	0.354819	−	0.0933358i
$724$	−2.10080	−	4.07499i	−0.0780758	−	0.151446i
$725$	57.6226	+	111.772i	2.14005	+	4.15112i
$726$	−12.4101	+	3.26450i	−0.460581	+	0.121157i
$727$	−8.38636	+	28.5613i	−0.311033	+	1.05928i	0.644551	+	0.764561i	$0.277044\pi$
$727$	−8.38636	+	28.5613i	−0.311033	+	1.05928i	−0.955584	+	0.294719i	$0.904774\pi$
$728$	−10.3353	+	1.13388i	−0.383052	+	0.0420245i
$729$	−6.89291	−	26.1053i	−0.255293	−	0.966864i
$730$	11.0928	+	7.89916i	0.410564	+	0.292361i
$731$	11.0108	+	2.67118i	0.407248	+	0.0987972i
$732$	12.5503	+	6.92769i	0.463872	+	0.256055i
$733$	2.62205	+	6.54957i	0.0968477	+	0.241914i	0.968878	−	0.247537i	$-0.0796213\pi$
$733$	2.62205	+	6.54957i	0.0968477	+	0.241914i	−0.872031	+	0.489451i	$0.837197\pi$
$734$	3.42908	−	2.20374i	0.126570	−	0.0813415i
$735$	19.3019	+	48.2459i	0.711962	+	1.77958i
$736$	−4.79420	+	0.125025i	−0.176717	+	0.00460848i
$737$	−21.0476	+	12.1518i	−0.775297	+	0.447618i
$738$	−2.07541	−	1.50670i	−0.0763970	−	0.0554625i
$739$	−12.0406	−	9.46886i	−0.442922	−	0.348318i	0.371657	−	0.928370i	$-0.378790\pi$
$739$	−12.0406	−	9.46886i	−0.442922	−	0.348318i	−0.814579	+	0.580052i	$0.803032\pi$
$740$	−0.290576	−	3.04305i	−0.0106818	−	0.111865i
$741$	−36.1352	+	32.5484i	−1.32746	+	1.19570i
$742$	−12.6295	+	5.26349i	−0.463643	+	0.193229i
$743$	7.60221	+	8.77342i	0.278898	+	0.321865i	0.877865	−	0.478908i	$-0.158967\pi$
$743$	7.60221	+	8.77342i	0.278898	+	0.321865i	−0.598967	+	0.800774i	$0.704422\pi$
$744$	1.90808	−	3.88265i	0.0699534	−	0.142345i
$745$	−6.47724	+	6.17603i	−0.237308	+	0.226272i
$746$	−2.92425	−	8.44908i	−0.107065	−	0.309343i
$747$	28.0648	+	24.7715i	1.02684	+	0.906340i
$748$	4.29864	+	2.76257i	0.157174	+	0.101009i
$749$	31.8690	+	7.25803i	1.16447	+	0.265202i
$750$	−61.3119	+	10.0219i	−2.23879	+	0.365948i
$751$	26.3950	+	33.5639i	0.963166	+	1.22476i	0.974398	+	0.224828i	$0.0721820\pi$
$751$	26.3950	+	33.5639i	0.963166	+	1.22476i	−0.0112327	+	0.999937i	$0.503576\pi$
$752$	−1.59247	−	8.26253i	−0.0580715	−	0.301304i
$753$	−3.11145	−	8.46013i	−0.113388	−	0.308304i
$754$	26.7527	+	25.5087i	0.974277	+	0.928971i
$755$	37.9608	−	83.1226i	1.38154	−	3.02514i
$756$	−8.24254	−	11.0027i	−0.299778	−	0.400166i
$757$	−13.3074	−	20.7068i	−0.483667	−	0.752601i	0.510566	−	0.859838i	$-0.329436\pi$
$757$	−13.3074	−	20.7068i	−0.483667	−	0.752601i	−0.994233	+	0.107238i	$0.965799\pi$
$758$	3.46650	+	6.00415i	0.125909	+	0.218081i
$759$	13.9751	+	7.24543i	0.507263	+	0.262992i
$760$	15.3112	−	26.5197i	0.555395	−	0.961972i
$761$	−7.51504	+	14.5771i	−0.272420	+	0.528421i	−0.984868	−	0.173303i	$-0.944556\pi$
$761$	−7.51504	+	14.5771i	−0.272420	+	0.528421i	0.712449	+	0.701724i	$0.247586\pi$
$762$	−7.16977	−	22.7879i	−0.259733	−	0.825519i
$763$	13.8884	−	9.20426i	0.502795	−	0.333217i
$764$	1.91775	−	0.563101i	0.0693816	−	0.0203723i
$765$	−9.46263	−	33.3526i	−0.342122	−	1.20587i
$766$	2.35903	+	12.2398i	0.0852351	+	0.442242i
$767$	10.1897	−	25.4527i	0.367930	−	0.919044i
$768$	−1.34065	+	1.09666i	−0.0483765	+	0.0395722i
$769$	12.4425	+	10.7815i	0.448688	+	0.388790i	0.849686	−	0.527289i	$-0.176791\pi$
$769$	12.4425	+	10.7815i	0.448688	+	0.388790i	−0.400999	+	0.916079i	$0.631337\pi$
$770$	−21.4183	−	1.74142i	−0.771862	−	0.0627564i
$771$	−37.5781	−	4.66748i	−1.35334	−	0.168095i
$772$	5.70300	+	1.09916i	0.205255	+	0.0395597i
$773$	−28.7846	+	27.4461i	−1.03531	+	0.987166i	−0.999925	−	0.0122077i	$-0.996114\pi$
$773$	−28.7846	+	27.4461i	−1.03531	+	0.987166i	−0.0353845	+	0.999374i	$0.511266\pi$
$774$	10.9743	−	6.20286i	0.394464	−	0.222957i
$775$	−10.9213	+	31.5551i	−0.392306	+	1.13349i
$776$	1.47654	+	3.23318i	0.0530049	+	0.116064i
$777$	−2.50053	+	2.10487i	−0.0897059	+	0.0755117i
$778$	−19.6541	−	8.97571i	−0.704632	−	0.321795i
$779$	−5.67056	+	2.27015i	−0.203169	+	0.0813366i
$780$	−25.6678	+	13.8636i	−0.919055	+	0.496398i
$781$	−8.63952	−	4.98803i	−0.309146	−	0.178486i
$782$	3.37525	+	12.4830i	0.120699	+	0.446393i
$783$	−11.0439	+	47.6123i	−0.394676	+	1.70152i
$784$	−5.99295	−	3.61726i	−0.214034	−	0.129188i
$785$	−31.4998	−	4.52898i	−1.12428	−	0.161646i
$786$	−0.0438462	−	0.0726803i	−0.00156394	−	0.00259242i
$787$	−5.53965	−	1.34390i	−0.197467	−	0.0479050i	0.135805	−	0.990736i	$-0.456638\pi$
$787$	−5.53965	−	1.34390i	−0.197467	−	0.0479050i	−0.333273	+	0.942831i	$0.608153\pi$
$788$	−1.92010	+	20.1082i	−0.0684006	+	0.716323i
$789$	37.5120	−	4.31114i	1.33546	−	0.153481i
$790$	0.802267	+	5.57989i	0.0285434	+	0.198524i
$791$	−17.5900	−	5.81209i	−0.625428	−	0.206654i
$792$	5.59208	−	1.02481i	0.198706	−	0.0364151i
$793$	−32.4884	−	1.54761i	−1.15370	−	0.0549573i
$794$	−1.61533	−	3.13331i	−0.0573260	−	0.111197i
$795$	−27.2696	+	27.0212i	−0.967153	+	0.958344i
$796$	24.2144	−	5.87436i	0.858258	−	0.208211i
$797$	−4.03546	−	28.0672i	−0.142943	−	0.994193i	−0.927417	−	0.374030i	$-0.877976\pi$
$797$	−4.03546	−	28.0672i	−0.142943	−	0.994193i	0.784473	−	0.620163i	$-0.212933\pi$
$798$	−32.6350	+	2.64588i	−1.15527	+	0.0936633i
$799$	−20.6385	+	9.42528i	−0.730137	+	0.333442i
$800$	9.22559	−	9.67552i	0.326174	−	0.342081i
$801$	−48.9113	−	2.77867i	−1.72820	−	0.0981795i
$802$	9.74295	−	12.3892i	0.344036	−	0.437477i
$803$	5.35199	+	2.75914i	0.188868	+	0.0973680i
$804$	−20.0245	+	9.61433i	−0.706210	+	0.339071i
$805$	−37.2334	−	39.6367i	−1.31230	−	1.39701i
$806$			9.81554i			0.345738i
$807$	20.0549	+	0.569203i	0.705965	+	0.0200369i
$808$	−0.0841875	−	0.0662058i	−0.00296171	−	0.00232911i
$809$	−14.5386	+	10.3529i	−0.511149	+	0.363987i	−0.806341	−	0.591450i	$-0.798556\pi$
$809$	−14.5386	+	10.3529i	−0.511149	+	0.363987i	0.295193	+	0.955438i	$0.404616\pi$
$810$	−33.0467	−	19.8945i	−1.16114	−	0.699023i
$811$	1.74380	+	3.81840i	0.0612332	+	0.134082i	0.937775	−	0.347244i	$-0.112883\pi$
$811$	1.74380	+	3.81840i	0.0612332	+	0.134082i	−0.876542	+	0.481326i	$0.840155\pi$
$812$	3.88804	+	24.5810i	0.136443	+	0.862625i
$813$	38.3597	−	25.7075i	1.34534	−	0.901603i
$814$	−0.318663	−	1.31355i	−0.0111691	−	0.0460399i
$815$	−15.6976	−	45.3554i	−0.549864	−	1.58873i
$816$	3.72588	+	2.81585i	0.130432	+	0.0985743i
$817$	1.42855	−	29.9889i	0.0499786	−	1.04918i
$818$	−6.62471	−	5.74035i	−0.231628	−	0.200707i
$819$	27.7945	+	14.1563i	0.971220	+	0.494661i
$820$	−3.62666	+	0.521436i	−0.126649	+	0.0182093i
$821$	−6.37576	−	2.20667i	−0.222516	−	0.0770134i	0.213536	−	0.976935i	$-0.431502\pi$
$821$	−6.37576	−	2.20667i	−0.222516	−	0.0770134i	−0.436051	+	0.899922i	$0.643623\pi$
$822$	−22.5194	+	8.28216i	−0.785455	+	0.288873i
$823$	−4.11977	+	16.9819i	−0.143606	+	0.591953i	0.853840	+	0.520535i	$0.174267\pi$
$823$	−4.11977	+	16.9819i	−0.143606	+	0.591953i	−0.997446	+	0.0714177i	$0.977248\pi$
$824$	6.84629	−	0.653741i	0.238502	−	0.0227741i
$825$	−41.8585	+	13.1700i	−1.45733	+	0.458519i
$826$	15.8539	−	9.45317i	0.551627	−	0.328918i
$827$	−3.11586			−0.108349			−0.0541746	−	0.998531i	$-0.517253\pi$
$827$	−3.11586			−0.108349			−0.0541746	+	0.998531i	$0.517253\pi$
$828$	12.2334	+	7.57254i	0.425141	+	0.263164i
$829$	−0.0970650	+	0.168122i	−0.00337121	+	0.00583910i	−0.867706	−	0.497078i	$-0.834406\pi$
$829$	−0.0970650	+	0.168122i	−0.00337121	+	0.00583910i	0.864335	+	0.502917i	$0.167740\pi$
$830$	53.4179	−	2.54461i	1.85416	−	0.0883247i
$831$	−35.2672	−	32.3559i	−1.22341	−	1.12242i
$832$	1.63250	−	3.57469i	0.0565969	−	0.123930i
$833$	−5.66886	+	18.0031i	−0.196414	+	0.623772i
$834$	−7.76296	−	6.46959i	−0.268809	−	0.224024i
$835$	27.5076	+	9.52048i	0.951941	+	0.329470i
$836$	5.03235	−	12.5702i	0.174047	−	0.434749i
$837$	−11.1737	+	6.60216i	−0.386221	+	0.228204i
$838$	−3.09065	+	16.0358i	−0.106765	+	0.553949i
$839$	3.31478	+	2.13028i	0.114439	+	0.0735453i	0.596608	−	0.802533i	$-0.296515\pi$
$839$	3.31478	+	2.13028i	0.114439	+	0.0735453i	−0.482169	+	0.876078i	$0.660151\pi$
$840$	−19.3986	−	3.07286i	−0.669314	−	0.106024i
$841$	38.9496	−	44.9502i	1.34309	−	1.55001i
$842$	0.859709	+	3.54377i	0.0296275	+	0.122126i
$843$	−0.882436	−	13.1855i	−0.0303927	−	0.454133i
$844$	14.9891	−	2.88892i	0.515947	−	0.0994407i
$845$	6.07456	−	8.53052i	0.208971	−	0.293459i
$846$	−9.59620	+	23.3487i	−0.329924	+	0.802745i
$847$	19.5643	−	1.20812i	0.672239	−	0.0415115i
$848$	0.735976	−	5.11883i	0.0252735	−	0.175781i
$849$	5.75979	+	0.163476i	0.197675	+	0.00561048i
$850$	−31.2180	−	18.0237i	−1.07077	−	0.618208i
$851$	1.63249	−	3.00591i	0.0559612	−	0.103041i
$852$	−7.52751	−	5.14514i	−0.257888	−	0.176269i
$853$	46.1790	−	29.6775i	1.58114	−	1.01614i	0.605749	−	0.795656i	$-0.292874\pi$
$853$	46.1790	−	29.6775i	1.58114	−	1.01614i	0.975391	−	0.220481i	$-0.0707628\pi$
$854$	−16.7493	−	14.1056i	−0.573148	−	0.482683i
$855$	−82.0364	+	41.3471i	−2.80559	+	1.41404i
$856$	−8.52508	+	8.94085i	−0.291381	+	0.305592i
$857$	0.439342	−	4.60100i	0.0150076	−	0.157167i	−0.984862	−	0.173343i	$-0.944543\pi$
$857$	0.439342	−	4.60100i	0.0150076	−	0.157167i	0.999869	+	0.0161759i	$0.00514917\pi$
$858$	−10.3615	+	7.68280i	−0.353735	+	0.262286i
$859$	6.61321	−	5.20069i	0.225640	−	0.177445i	−0.498939	−	0.866637i	$-0.666277\pi$
$859$	6.61321	−	5.20069i	0.225640	−	0.177445i	0.724579	+	0.689192i	$0.242034\pi$
$860$	5.07382	−	17.2798i	0.173016	−	0.589238i
$861$	2.66262	+	2.87366i	0.0907418	+	0.0979342i
$862$	14.0152	−	21.8081i	0.477360	−	0.742787i
$863$	−38.6053	−	1.83900i	−1.31414	−	0.0626002i	−0.621232	−	0.783626i	$-0.713368\pi$
$863$	−38.6053	−	1.83900i	−1.31414	−	0.0626002i	−0.692908	+	0.721026i	$0.743671\pi$
$864$	5.16738	−	0.546018i	0.175798	−	0.0185759i
$865$	1.93970	+	2.03430i	0.0659518	+	0.0691682i
$866$	−2.58579	+	2.03348i	−0.0878686	+	0.0691006i
$867$	−6.70467	+	15.4610i	−0.227702	+	0.525084i
$868$	−4.01149	+	5.25146i	−0.136159	+	0.178246i
$869$	0.702247	+	2.39163i	0.0238221	+	0.0811306i
$870$	36.0692	+	59.7890i	1.22286	+	2.02704i
$871$	31.1543	−	39.6160i	1.05562	−	1.34234i
$872$	0.299646	+	6.29033i	0.0101473	+	0.213018i
$873$	1.61403	−	10.5403i	0.0546266	−	0.356735i
$874$	30.7876	−	15.0423i	1.04141	−	0.508812i
$875$	94.8450	+	3.18105i	3.20635	+	0.107539i
$876$	4.68608	+	2.88580i	0.158328	+	0.0975021i
$877$	−48.2438	+	19.3139i	−1.62908	+	0.652184i	−0.992856	−	0.119322i	$-0.961928\pi$
$877$	−48.2438	+	19.3139i	−1.62908	+	0.652184i	−0.636222	+	0.771506i	$0.719504\pi$
$878$	−3.89628	+	2.77453i	−0.131493	+	0.0936358i
$879$	48.3700	−	10.2907i	1.63148	−	0.347097i
$880$	4.71126	−	6.61604i	0.158817	−	0.223027i
$881$	−14.6088	−	16.8594i	−0.492182	−	0.568009i	0.454265	−	0.890867i	$-0.349902\pi$
$881$	−14.6088	−	16.8594i	−0.492182	−	0.568009i	−0.946447	+	0.322858i	$0.895356\pi$
$882$	9.08499	+	18.9331i	0.305908	+	0.637511i
$883$	8.92845	+	2.62163i	0.300466	+	0.0882249i	0.428491	−	0.903546i	$-0.359045\pi$
$883$	8.92845	+	2.62163i	0.300466	+	0.0882249i	−0.128024	+	0.991771i	$0.540864\pi$
$884$	−10.4047	−	2.00535i	−0.349949	−	0.0674471i
$885$	31.2258	−	41.3174i	1.04964	−	1.38887i
$886$	0.945237	−	0.487304i	0.0317559	−	0.0163713i
$887$	4.93291	−	25.5944i	0.165631	−	0.859375i	−0.800107	−	0.599857i	$-0.795224\pi$
$887$	4.93291	−	25.5944i	0.165631	−	0.859375i	0.965738	−	0.259518i	$-0.0835637\pi$
$888$	−0.199287	−	1.21920i	−0.00668764	−	0.0409136i
$889$	3.97958	+	36.2737i	0.133471	+	1.21658i
$890$	−52.8941	+	45.8330i	−1.77301	+	1.53633i
$891$	−15.7153	−	6.62760i	−0.526481	−	0.222033i
$892$	−2.98432	+	12.3015i	−0.0999225	+	0.411886i
$893$	34.8739	+	48.9736i	1.16701	+	1.63884i
$894$	−2.44513	+	2.66513i	−0.0817772	+	0.0891353i
$895$	−10.1062	−	15.7256i	−0.337814	−	0.525649i
$896$	2.33434	−	1.24533i	0.0779850	−	0.0416034i
$897$	−32.4885	−	3.17777i	−1.08476	−	0.106103i
$898$	3.31663	+	5.74458i	0.110677	+	0.191699i
$899$	23.4675	−	1.11790i	0.782685	−	0.0372839i
$900$	−39.0610	+	9.09851i	−1.30203	+	0.303284i
$901$	−13.8810	+	1.32548i	−0.462444	+	0.0441580i
$902$	−1.55445	+	0.456427i	−0.0517574	+	0.0151974i
$903$	−18.2851	+	6.03714i	−0.608492	+	0.200903i
$904$	5.29170	−	4.58528i	0.175999	−	0.152504i
$905$	12.1464	+	15.4454i	0.403759	+	0.513422i
$906$	13.0637	−	34.5416i	0.434011	−	1.14757i
$907$	50.7953	−	17.5804i	1.68663	−	0.583748i	0.695725	−	0.718308i	$-0.255083\pi$
$907$	50.7953	−	17.5804i	1.68663	−	0.583748i	0.990905	+	0.134560i	$0.0429621\pi$
$908$	0.959456	−	20.1415i	0.0318407	−	0.668418i
$909$	0.102306	+	0.304582i	0.00339328	+	0.0101023i
$910$	42.5758	−	13.1550i	1.41137	−	0.436083i
$911$	53.3325	+	15.6598i	1.76699	+	0.518834i	0.993384	−	0.114838i	$-0.0366349\pi$
$911$	53.3325	+	15.6598i	1.76699	+	0.518834i	0.773602	+	0.633672i	$0.218453\pi$
$912$	5.45821	−	11.1066i	0.180739	−	0.367777i
$913$	23.2190	−	4.47509i	0.768436	−	0.148104i
$914$	−33.1290	−	3.16344i	−1.09581	−	0.104637i
$915$	−58.4363	−	18.9751i	−1.93184	−	0.627298i
$916$	21.8602	+	9.98321i	0.722281	+	0.329855i
$917$	0.0441274	+	0.121919i	0.00145721	+	0.00402612i
$918$	−4.71563	−	13.1933i	−0.155639	−	0.435444i
$919$	23.8754	−	13.7845i	0.787577	−	0.454708i	−0.0515321	−	0.998671i	$-0.516410\pi$
$919$	23.8754	−	13.7845i	0.787577	−	0.454708i	0.839109	+	0.543964i	$0.183077\pi$
$920$	20.0747	−	4.41479i	0.661844	−	0.145551i
$921$	−6.02372	−	0.458532i	−0.198488	−	0.0151091i
$922$	−6.46090	−	3.33083i	−0.212778	−	0.109695i
$923$	20.4768	+	2.94412i	0.674003	+	0.0969070i
$924$	−8.68341	−	0.124196i	−0.285663	−	0.00408576i
$925$	2.68640	+	9.14905i	0.0883284	+	0.300819i
$926$	−13.9821	−	9.95664i	−0.459482	−	0.327195i
$927$	−18.2514	−	9.62165i	−0.599456	−	0.316016i
$928$	−8.73247	−	3.49595i	−0.286657	−	0.114760i
$929$	−18.5490	+	4.49995i	−0.608574	+	0.147638i	−0.528191	−	0.849126i	$-0.677129\pi$
$929$	−18.5490	+	4.49995i	−0.608574	+	0.147638i	−0.0803830	+	0.996764i	$0.525614\pi$
$930$	−4.88077	+	17.8876i	−0.160047	+	0.586556i
$931$	49.6860	+	5.72178i	1.62839	+	0.187524i
$932$	6.04911	−	9.41260i	0.198145	−	0.308320i
$933$	29.0100	−	7.63114i	0.949745	−	0.249832i
$934$	−23.8395	−	25.0022i	−0.780053	−	0.818096i
$935$	−20.3313	−	8.13943i	−0.664905	−	0.266188i
$936$	−9.97581	+	6.28285i	−0.326070	+	0.205361i
$937$	22.1725	−	10.1258i	0.724345	−	0.330797i	−0.0188959	−	0.999821i	$-0.506015\pi$
$937$	22.1725	−	10.1258i	0.724345	−	0.330797i	0.743240	+	0.669024i	$0.233288\pi$
$938$	32.8586	−	8.46275i	1.07287	−	0.276319i
$939$	0.776340	+	40.3764i	0.0253349	+	1.31763i
$940$	13.4037	+	33.4807i	0.437179	+	1.09202i
$941$	2.79617	+	58.6987i	0.0911524	+	1.91352i	0.332529	+	0.943093i	$0.392098\pi$
$941$	2.79617	+	58.6987i	0.0911524	+	1.91352i	−0.241377	+	0.970431i	$0.577599\pi$
$942$	−12.8238	−	0.976158i	−0.417820	−	0.0318050i
$943$	−3.69187	−	1.78304i	−0.120224	−	0.0580638i
$944$			6.97657i			0.227068i
$945$	43.6127	+	39.6188i	1.41872	+	1.28880i
$946$	1.13327	−	7.88204i	0.0368457	−	0.256267i
$947$	4.84507	+	50.7399i	0.157444	+	1.64883i	0.636672	+	0.771135i	$0.280311\pi$
$947$	4.84507	+	50.7399i	0.157444	+	1.64883i	−0.479228	+	0.877690i	$0.659083\pi$
$948$	0.474073	+	2.22831i	0.0153972	+	0.0723721i
$949$	−12.4300	−	1.18692i	−0.403494	−	0.0385290i
$950$	−31.2414	+	90.2661i	−1.01360	+	2.92862i
$951$	−2.03520	−	3.03684i	−0.0659959	−	0.0984764i
$952$	−4.74713	−	5.32517i	−0.153855	−	0.172590i
$953$	−18.3152	+	21.1369i	−0.593287	+	0.684690i	−0.970407	−	0.241474i	$-0.922369\pi$
$953$	−18.3152	+	21.1369i	−0.593287	+	0.684690i	0.377120	+	0.926164i	$0.376915\pi$
$954$	−10.2666	+	11.6316i	−0.332394	+	0.376585i
$955$	−7.61399	+	3.92528i	−0.246383	+	0.127019i
$956$	6.60939	−	2.28753i	0.213763	−	0.0739841i
$957$	19.5485	+	23.8978i	0.631913	+	0.772505i
$958$	−15.9806	+	2.29767i	−0.516310	+	0.0742342i
$959$	36.2016	−	5.72609i	1.16901	−	0.184905i
$960$	4.75254	−	5.70264i	0.153387	−	0.184052i
$961$	−17.9207	−	17.0873i	−0.578087	−	0.551205i
$962$	1.62585	+	2.28319i	0.0524196	+	0.0736131i
$963$	36.0951	−	8.40764i	1.16315	−	0.270932i
$964$	2.60990	−	5.06250i	0.0840593	−	0.163052i
$965$	−24.8923			−0.801311
$966$	−16.0831	−	14.9778i	−0.517465	−	0.481902i
$967$	−49.5224			−1.59253			−0.796266	−	0.604947i	$-0.793194\pi$
$967$	−49.5224			−1.59253			−0.796266	+	0.604947i	$0.793194\pi$
$968$	−3.39487	+	6.58512i	−0.109115	+	0.211654i
$969$	−32.5731	−	7.24207i	−1.04640	−	0.232649i
$970$	−8.83642	−	12.4090i	−0.283720	−	0.398430i
$971$	14.4566	+	13.7844i	0.463935	+	0.442361i	0.885640	−	0.464372i	$-0.153720\pi$
$971$	14.4566	+	13.7844i	0.463935	+	0.442361i	−0.421705	+	0.906733i	$0.638568\pi$
$972$	−13.8622	−	7.13021i	−0.444630	−	0.228702i
$973$	9.71187	+	11.9982i	0.311348	+	0.384646i
$974$	20.0679	−	2.88532i	0.643016	−	0.0924518i
$975$	70.4341	−	57.6154i	2.25570	−	1.84517i
$976$	7.82132	−	2.70699i	0.250354	−	0.0866485i
$977$	−6.90688	+	3.56074i	−0.220971	+	0.113918i	−0.565158	−	0.824983i	$-0.691185\pi$
$977$	−6.90688	+	3.56074i	−0.220971	+	0.113918i	0.344187	+	0.938901i	$0.388154\pi$
$978$	−7.55365	−	17.8649i	−0.241539	−	0.571255i
$979$	−20.2657	+	23.3879i	−0.647695	+	0.747480i
$980$	28.1550	+	10.3621i	0.899378	+	0.331005i
$981$	9.59550	−	16.2742i	0.306361	−	0.519595i
$982$	5.03593	−	14.5504i	0.160703	−	0.464321i
$983$	−37.8105	−	3.61046i	−1.20597	−	0.115156i	−0.527350	−	0.849648i	$-0.676814\pi$
$983$	−37.8105	−	3.61046i	−1.20597	−	0.115156i	−0.678617	+	0.734493i	$0.737420\pi$
$984$	−1.44829	+	0.308125i	−0.0461699	+	0.00982266i
$985$	−8.22933	−	86.1814i	−0.262208	−	2.74597i
$986$	−3.60949	+	25.1045i	−0.114950	+	0.799492i
$987$	21.3092	−	32.1377i	0.678279	−	1.02295i
$988$			28.0782i			0.893286i
$989$	15.5105	−	12.8659i	0.493205	−	0.409113i
$990$	−22.7027	+	8.84866i	−0.721540	+	0.281229i
$991$	−0.530558	−	11.1378i	−0.0168537	−	0.353804i	−0.991505	−	0.130072i	$-0.958479\pi$
$991$	−0.530558	−	11.1378i	−0.0168537	−	0.353804i	0.974651	−	0.223732i	$-0.0718239\pi$
$992$	−0.928305	−	2.31879i	−0.0294737	−	0.0736218i
$993$	40.9170	−	0.786734i	1.29846	−	0.0249662i
$994$	9.75218	+	9.94377i	0.309320	+	0.315397i
$995$	−97.1403	+	44.3625i	−3.07955	+	1.40639i
$996$	21.4708	−	2.46758i	0.680330	−	0.0781882i
$997$	38.1144	+	15.2587i	1.20710	+	0.483248i	0.885949	−	0.463782i	$-0.153508\pi$
$997$	38.1144	+	15.2587i	1.20710	+	0.483248i	0.321146	+	0.947030i	$0.395932\pi$
$998$	−6.19851	−	6.50081i	−0.196211	−	0.205780i
$999$	−1.50554	+	3.38656i	−0.0476331	+	0.107146i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.bf.a.11.19	✓	1280
3.2	odd	2	inner	966.2.bf.a.11.38	yes	1280
7.2	even	3	inner	966.2.bf.a.149.55	yes	1280
21.2	odd	6	inner	966.2.bf.a.149.17	yes	1280
23.21	odd	22	inner	966.2.bf.a.389.17	yes	1280
69.44	even	22	inner	966.2.bf.a.389.55	yes	1280
161.44	odd	66	inner	966.2.bf.a.527.38	yes	1280
483.44	even	66	inner	966.2.bf.a.527.19	yes	1280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.bf.a.11.19	✓	1280	1.1	even	1	trivial
966.2.bf.a.11.38	yes	1280	3.2	odd	2	inner
966.2.bf.a.149.17	yes	1280	21.2	odd	6	inner
966.2.bf.a.149.55	yes	1280	7.2	even	3	inner
966.2.bf.a.389.17	yes	1280	23.21	odd	22	inner
966.2.bf.a.389.55	yes	1280	69.44	even	22	inner
966.2.bf.a.527.19	yes	1280	483.44	even	66	inner
966.2.bf.a.527.38	yes	1280	161.44	odd	66	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.bf (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.458227 + 0.888835i) q^{2} +(0.375913 - 1.69077i) q^{3} +(-0.580057 - 0.814576i) q^{4} +(3.10185 + 2.95761i) q^{5} +(1.33056 + 1.10888i) q^{6} +(-1.66460 - 2.05648i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-2.71738 - 1.27116i) q^{9} +O(q^{10})\)	\(q+(-0.458227 + 0.888835i) q^{2} +(0.375913 - 1.69077i) q^{3} +(-0.580057 - 0.814576i) q^{4} +(3.10185 + 2.95761i) q^{5} +(1.33056 + 1.10888i) q^{6} +(-1.66460 - 2.05648i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-2.71738 - 1.27116i) q^{9} +(-4.05017 + 1.40178i) q^{10} +(-1.68441 + 0.868371i) q^{11} +(-1.59531 + 0.674531i) q^{12} +(2.57348 - 2.96996i) q^{13} +(2.59064 - 0.537222i) q^{14} +(6.16664 - 4.13270i) q^{15} +(-0.327068 + 0.945001i) q^{16} +(2.68416 + 0.256306i) q^{17} +(2.37503 - 1.83282i) q^{18} +(-0.679167 - 7.11256i) q^{19} +(0.609946 - 4.24227i) q^{20} +(-4.10277 + 2.04139i) q^{21} -1.89507i q^{22} +(3.21789 - 3.55600i) q^{23} +(0.131465 - 1.72705i) q^{24} +(0.636118 + 13.3538i) q^{25} +(1.46056 + 3.64831i) q^{26} +(-3.17073 + 4.11661i) q^{27} +(-0.709596 + 2.54882i) q^{28} +(8.55623 - 3.90750i) q^{29} +(0.847569 + 7.37484i) q^{30} +(2.31879 + 0.928305i) q^{31} +(-0.690079 - 0.723734i) q^{32} +(0.835023 + 3.17437i) q^{33} +(-1.45776 + 2.26833i) q^{34} +(0.918922 - 11.3021i) q^{35} +(0.540778 + 2.95086i) q^{36} +(0.693140 - 0.168154i) q^{37} +(6.63311 + 2.65550i) q^{38} +(-4.05410 - 5.46760i) q^{39} +(3.49119 + 2.48606i) q^{40} +(-0.240850 - 0.820259i) q^{41} +(0.0655365 - 4.58211i) q^{42} +(4.15923 + 0.598008i) q^{43} +(1.68441 + 0.868371i) q^{44} +(-4.66931 - 11.9799i) q^{45} +(1.68618 + 4.48963i) q^{46} +(-7.28725 + 4.20730i) q^{47} +(1.47483 + 0.908233i) q^{48} +(-1.45822 + 6.84643i) q^{49} +(-12.1608 - 5.55364i) q^{50} +(1.44236 - 4.44193i) q^{51} +(-3.91202 - 0.373553i) q^{52} +(-5.07801 + 0.978706i) q^{53} +(-2.20607 - 4.70460i) q^{54} +(-7.79307 - 2.28825i) q^{55} +(-1.94032 - 1.79865i) q^{56} +(-12.2810 - 1.52539i) q^{57} +(-0.447568 + 9.39560i) q^{58} +(6.59286 - 2.28181i) q^{59} +(-6.94340 - 2.62600i) q^{60} +(-5.11621 - 6.50579i) q^{61} +(-1.88764 + 1.63565i) q^{62} +(1.90923 + 7.70421i) q^{63} +(0.959493 - 0.281733i) q^{64} +(16.7665 - 1.60101i) q^{65} +(-3.20412 - 0.712381i) q^{66} +(12.8101 - 0.610222i) q^{67} +(-1.34818 - 2.33512i) q^{68} +(-4.80272 - 6.77745i) q^{69} +(9.62465 + 5.99570i) q^{70} +(2.84605 + 4.42854i) q^{71} +(-2.87063 - 0.871499i) q^{72} +(-1.84306 - 2.58821i) q^{73} +(-0.168154 + 0.693140i) q^{74} +(22.8172 + 3.94432i) q^{75} +(-5.39976 + 4.67892i) q^{76} +(4.58965 + 2.01845i) q^{77} +(6.71749 - 1.09803i) q^{78} +(0.248924 - 1.29154i) q^{79} +(-3.80946 + 1.96391i) q^{80} +(5.76830 + 6.90845i) q^{81} +(0.839439 + 0.161789i) q^{82} +(-11.9724 - 3.51540i) q^{83} +(4.04271 + 2.15789i) q^{84} +(7.56779 + 8.73370i) q^{85} +(-2.43740 + 3.42285i) q^{86} +(-3.39027 - 15.9355i) q^{87} +(-1.54368 + 1.09925i) q^{88} +(15.1603 - 6.06927i) q^{89} +(12.7877 + 1.33926i) q^{90} +(-10.3915 - 0.348525i) q^{91} +(-4.76320 - 0.558534i) q^{92} +(2.44121 - 3.57158i) q^{93} +(-0.400383 - 8.40507i) q^{94} +(18.9295 - 24.0708i) q^{95} +(-1.48307 + 0.894701i) q^{96} +(1.00139 + 3.41041i) q^{97} +(-5.41716 - 4.43333i) q^{98} +(5.68101 - 0.218545i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1280 q - 64 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) \) 1280 * q - 64 * q^4 - 8 * q^6 + 4 * q^9	\( 1280 q - 64 q^{4} - 8 q^{6} + 4 q^{9} + 64 q^{16} + 44 q^{18} - 132 q^{21} - 4 q^{24} + 72 q^{25} + 108 q^{27} + 44 q^{30} + 8 q^{36} + 44 q^{37} - 4 q^{39} - 88 q^{43} - 12 q^{46} + 60 q^{49} - 48 q^{54} + 96 q^{55} + 44 q^{58} - 176 q^{61} - 110 q^{63} + 128 q^{64} + 56 q^{69} - 120 q^{70} + 44 q^{72} + 40 q^{73} - 268 q^{75} + 16 q^{78} + 88 q^{79} + 8 q^{81} - 56 q^{82} - 22 q^{84} + 64 q^{85} - 42 q^{87} - 32 q^{93} + 8 q^{94} + 4 q^{96} + 132 q^{99}+O(q^{100}) \) 1280 * q - 64 * q^4 - 8 * q^6 + 4 * q^9 + 64 * q^16 + 44 * q^18 - 132 * q^21 - 4 * q^24 + 72 * q^25 + 108 * q^27 + 44 * q^30 + 8 * q^36 + 44 * q^37 - 4 * q^39 - 88 * q^43 - 12 * q^46 + 60 * q^49 - 48 * q^54 + 96 * q^55 + 44 * q^58 - 176 * q^61 - 110 * q^63 + 128 * q^64 + 56 * q^69 - 120 * q^70 + 44 * q^72 + 40 * q^73 - 268 * q^75 + 16 * q^78 + 88 * q^79 + 8 * q^81 - 56 * q^82 - 22 * q^84 + 64 * q^85 - 42 * q^87 - 32 * q^93 + 8 * q^94 + 4 * q^96 + 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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