LMFDB - Embedded newform 1089.2.e.p.364.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1089,2,Mod(364,1089)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1089, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1089.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1089 = 3^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1089.e (of order $3$, 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:	$8.69570878012$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			364.7
Character	$\chi$	$=$	1089.364
Dual form			1089.2.e.p.727.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.338834 - 0.586878i) q^{2} +(0.461570 - 1.66942i) q^{3} +(0.770383 - 1.33434i) q^{4} +(-0.145397 + 0.251836i) q^{5} +(-1.13614 + 0.294770i) q^{6} +(-1.67774 - 2.90594i) q^{7} -2.39947 q^{8} +(-2.57391 - 1.54111i) q^{9} +O(q^{10})$	\(q+(-0.338834 - 0.586878i) q^{2} +(0.461570 - 1.66942i) q^{3} +(0.770383 - 1.33434i) q^{4} +(-0.145397 + 0.251836i) q^{5} +(-1.13614 + 0.294770i) q^{6} +(-1.67774 - 2.90594i) q^{7} -2.39947 q^{8} +(-2.57391 - 1.54111i) q^{9} +0.197063 q^{10} +(-1.87199 - 1.90198i) q^{12} +(-2.09336 + 3.62580i) q^{13} +(-1.13695 + 1.96926i) q^{14} +(0.353308 + 0.358969i) q^{15} +(-0.727744 - 1.26049i) q^{16} +3.48327 q^{17} +(-0.0323148 + 2.03275i) q^{18} -6.07908 q^{19} +(0.224023 + 0.388020i) q^{20} +(-5.62562 + 1.45956i) q^{21} +(3.34545 - 5.79449i) q^{23} +(-1.10752 + 4.00571i) q^{24} +(2.45772 + 4.25689i) q^{25} +2.83720 q^{26} +(-3.76079 + 3.58559i) q^{27} -5.17002 q^{28} +(0.829864 + 1.43737i) q^{29} +(0.0909583 - 0.328980i) q^{30} +(-0.981505 + 1.70002i) q^{31} +(-2.89263 + 5.01019i) q^{32} +(-1.18025 - 2.04426i) q^{34} +0.975759 q^{35} +(-4.03926 + 2.24723i) q^{36} -2.53648 q^{37} +(2.05980 + 3.56768i) q^{38} +(5.08674 + 5.16825i) q^{39} +(0.348876 - 0.604271i) q^{40} +(3.24317 - 5.61734i) q^{41} +(2.76274 + 2.80701i) q^{42} +(-0.0247979 - 0.0429513i) q^{43} +(0.762345 - 0.424128i) q^{45} -4.53422 q^{46} +(-0.674704 - 1.16862i) q^{47} +(-2.44019 + 0.633103i) q^{48} +(-2.12965 + 3.68867i) q^{49} +(1.66552 - 2.88476i) q^{50} +(1.60778 - 5.81503i) q^{51} +(3.22537 + 5.58651i) q^{52} -1.87766 q^{53} +(3.37859 + 0.992204i) q^{54} +(4.02569 + 6.97270i) q^{56} +(-2.80592 + 10.1485i) q^{57} +(0.562373 - 0.974058i) q^{58} +(7.28706 - 12.6216i) q^{59} +(0.751169 - 0.194890i) q^{60} +(-1.92957 - 3.34212i) q^{61} +1.33027 q^{62} +(-0.160007 + 10.0652i) q^{63} +1.00952 q^{64} +(-0.608737 - 1.05436i) q^{65} +(4.46764 - 7.73818i) q^{67} +(2.68345 - 4.64788i) q^{68} +(-8.12926 - 8.25952i) q^{69} +(-0.330621 - 0.572652i) q^{70} -11.1283 q^{71} +(6.17600 + 3.69783i) q^{72} +1.25869 q^{73} +(0.859446 + 1.48860i) q^{74} +(8.24094 - 2.13810i) q^{75} +(-4.68321 + 8.11157i) q^{76} +(1.30957 - 4.73648i) q^{78} +(-1.05357 - 1.82483i) q^{79} +0.423248 q^{80} +(4.24998 + 7.93333i) q^{81} -4.39559 q^{82} +(-4.68763 - 8.11922i) q^{83} +(-2.38633 + 8.63092i) q^{84} +(-0.506459 + 0.877212i) q^{85} +(-0.0168048 + 0.0291068i) q^{86} +(2.78260 - 0.721943i) q^{87} -8.41413 q^{89} +(-0.507220 - 0.303694i) q^{90} +14.0485 q^{91} +(-5.15456 - 8.92795i) q^{92} +(2.38500 + 2.42322i) q^{93} +(-0.457226 + 0.791938i) q^{94} +(0.883882 - 1.53093i) q^{95} +(7.02894 + 7.14157i) q^{96} +(-0.491742 - 0.851722i) q^{97} +2.88640 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 2 q^{2} + 9 q^{3} - 12 q^{4} + q^{5} - q^{6} - q^{7} - 12 q^{8} - q^{9}+O(q^{10}) $ 36 * q + 2 * q^2 + 9 * q^3 - 12 * q^4 + q^5 - q^6 - q^7 - 12 * q^8 - q^9	$ 36 q + 2 q^{2} + 9 q^{3} - 12 q^{4} + q^{5} - q^{6} - q^{7} - 12 q^{8} - q^{9} - 4 q^{10} - 8 q^{12} - 3 q^{13} - 5 q^{15} + 8 q^{16} - 40 q^{17} + 17 q^{18} - 6 q^{19} + 5 q^{20} - 8 q^{21} + 10 q^{23} - 57 q^{24} - 7 q^{25} + 4 q^{26} - 9 q^{27} + 38 q^{28} + 21 q^{29} + 12 q^{30} - 6 q^{31} + 9 q^{32} + 4 q^{34} - 76 q^{35} - 65 q^{36} + 14 q^{37} - 13 q^{38} + 42 q^{39} + 20 q^{41} + 18 q^{42} - 4 q^{43} + 20 q^{45} + 16 q^{46} - 7 q^{47} + 10 q^{48} - 7 q^{49} + 25 q^{50} - 4 q^{51} + 19 q^{52} + 62 q^{53} + 17 q^{54} + 57 q^{56} - 18 q^{57} - 12 q^{58} + 12 q^{59} + 11 q^{60} + 16 q^{61} - 38 q^{62} + 5 q^{63} - 32 q^{64} + 42 q^{65} + 5 q^{67} + 51 q^{68} + 31 q^{69} - 8 q^{70} + 26 q^{71} + 51 q^{72} + 9 q^{74} - 16 q^{75} + 8 q^{76} - 32 q^{78} + 2 q^{79} + 92 q^{80} + 47 q^{81} - 68 q^{82} + 36 q^{83} + 60 q^{84} - 25 q^{85} - 26 q^{86} - 60 q^{87} - 28 q^{89} + 163 q^{90} - 30 q^{91} + 15 q^{92} - 39 q^{93} - 4 q^{94} + 64 q^{95} - 21 q^{96} + 16 q^{97} - 164 q^{98}+O(q^{100}) $ 36 * q + 2 * q^2 + 9 * q^3 - 12 * q^4 + q^5 - q^6 - q^7 - 12 * q^8 - q^9 - 4 * q^10 - 8 * q^12 - 3 * q^13 - 5 * q^15 + 8 * q^16 - 40 * q^17 + 17 * q^18 - 6 * q^19 + 5 * q^20 - 8 * q^21 + 10 * q^23 - 57 * q^24 - 7 * q^25 + 4 * q^26 - 9 * q^27 + 38 * q^28 + 21 * q^29 + 12 * q^30 - 6 * q^31 + 9 * q^32 + 4 * q^34 - 76 * q^35 - 65 * q^36 + 14 * q^37 - 13 * q^38 + 42 * q^39 + 20 * q^41 + 18 * q^42 - 4 * q^43 + 20 * q^45 + 16 * q^46 - 7 * q^47 + 10 * q^48 - 7 * q^49 + 25 * q^50 - 4 * q^51 + 19 * q^52 + 62 * q^53 + 17 * q^54 + 57 * q^56 - 18 * q^57 - 12 * q^58 + 12 * q^59 + 11 * q^60 + 16 * q^61 - 38 * q^62 + 5 * q^63 - 32 * q^64 + 42 * q^65 + 5 * q^67 + 51 * q^68 + 31 * q^69 - 8 * q^70 + 26 * q^71 + 51 * q^72 + 9 * q^74 - 16 * q^75 + 8 * q^76 - 32 * q^78 + 2 * q^79 + 92 * q^80 + 47 * q^81 - 68 * q^82 + 36 * q^83 + 60 * q^84 - 25 * q^85 - 26 * q^86 - 60 * q^87 - 28 * q^89 + 163 * q^90 - 30 * q^91 + 15 * q^92 - 39 * q^93 - 4 * q^94 + 64 * q^95 - 21 * q^96 + 16 * q^97 - 164 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times$.

$n$	$244$	$848$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.338834	−	0.586878i	−0.239592	−	0.414986i	0.721005	−	0.692930i	$-0.243680\pi$
$2$	−0.338834	−	0.586878i	−0.239592	−	0.414986i	−0.960597	+	0.277944i	$0.910347\pi$
$3$	0.461570	−	1.66942i	0.266488	−	0.963838i
$3$	0.461570	−	1.66942i	0.266488	−	0.963838i
$4$	0.770383	−	1.33434i	0.385191	−	0.667171i
$5$	−0.145397	+	0.251836i	−0.0650237	+	0.112624i	−0.896705	−	0.442630i	$-0.854046\pi$
$5$	−0.145397	+	0.251836i	−0.0650237	+	0.112624i	0.831681	+	0.555254i	$0.187379\pi$
$6$	−1.13614	+	0.294770i	−0.463827	+	0.120339i
$7$	−1.67774	−	2.90594i	−0.634128	−	1.09834i	−0.986699	−	0.162557i	$-0.948026\pi$
$7$	−1.67774	−	2.90594i	−0.634128	−	1.09834i	0.352571	−	0.935785i	$-0.385307\pi$
$8$	−2.39947			−0.848339
$9$	−2.57391	−	1.54111i	−0.857968	−	0.513702i
$10$	0.197063			0.0623166
$11$		0			0
$11$		0			0
$12$	−1.87199	−	1.90198i	−0.540396	−	0.549055i
$13$	−2.09336	+	3.62580i	−0.580593	+	1.00562i	0.414817	+	0.909905i	$0.363846\pi$
$13$	−2.09336	+	3.62580i	−0.580593	+	1.00562i	−0.995409	+	0.0957108i	$0.969488\pi$
$14$	−1.13695	+	1.96926i	−0.303864	+	0.526308i
$15$	0.353308	+	0.358969i	0.0912236	+	0.0926853i
$16$	−0.727744	−	1.26049i	−0.181936	−	0.315122i
$17$	3.48327			0.844818			0.422409	−	0.906405i	$-0.361185\pi$
$17$	3.48327			0.844818			0.422409	+	0.906405i	$0.361185\pi$
$18$	−0.0323148	+	2.03275i	−0.00761667	+	0.479124i
$19$	−6.07908			−1.39464			−0.697318	−	0.716762i	$-0.745623\pi$
$19$	−6.07908			−1.39464			−0.697318	+	0.716762i	$0.745623\pi$
$20$	0.224023	+	0.388020i	0.0500931	+	0.0867638i
$21$	−5.62562	+	1.45956i	−1.22761	+	0.318502i
$22$		0			0
$23$	3.34545	−	5.79449i	0.697575	−	1.20824i	−0.271730	−	0.962374i	$-0.587596\pi$
$23$	3.34545	−	5.79449i	0.697575	−	1.20824i	0.969305	−	0.245862i	$-0.0790709\pi$
$24$	−1.10752	+	4.00571i	−0.226072	+	0.817662i
$25$	2.45772	+	4.25689i	0.491544	+	0.851379i
$26$	2.83720			0.556422
$27$	−3.76079	+	3.58559i	−0.723764	+	0.690047i
$28$	−5.17002			−0.977042
$29$	0.829864	+	1.43737i	0.154102	+	0.266912i	0.932732	−	0.360571i	$-0.117418\pi$
$29$	0.829864	+	1.43737i	0.154102	+	0.266912i	−0.778630	+	0.627484i	$0.784085\pi$
$30$	0.0909583	−	0.328980i	0.0166066	−	0.0600632i
$31$	−0.981505	+	1.70002i	−0.176284	+	0.305332i	−0.940605	−	0.339504i	$-0.889741\pi$
$31$	−0.981505	+	1.70002i	−0.176284	+	0.305332i	0.764321	+	0.644836i	$0.223074\pi$
$32$	−2.89263	+	5.01019i	−0.511350	+	0.885685i
$33$		0			0
$34$	−1.18025	−	2.04426i	−0.202412	−	0.350587i
$35$	0.975759			0.164933
$36$	−4.03926	+	2.24723i	−0.673209	+	0.374538i
$37$	−2.53648			−0.416995			−0.208497	−	0.978023i	$-0.566857\pi$
$37$	−2.53648			−0.416995			−0.208497	+	0.978023i	$0.566857\pi$
$38$	2.05980	+	3.56768i	0.334144	+	0.578754i
$39$	5.08674	+	5.16825i	0.814530	+	0.827582i
$40$	0.348876	−	0.604271i	0.0551622	−	0.0955437i
$41$	3.24317	−	5.61734i	0.506499	−	0.877281i	−0.493473	−	0.869761i	$-0.664273\pi$
$41$	3.24317	−	5.61734i	0.506499	−	0.877281i	0.999972	−	0.00752028i	$-0.00239380\pi$
$42$	2.76274	+	2.80701i	0.426300	+	0.433130i
$43$	−0.0247979	−	0.0429513i	−0.00378165	−	0.00655001i	0.864128	−	0.503271i	$-0.167870\pi$
$43$	−0.0247979	−	0.0429513i	−0.00378165	−	0.00655001i	−0.867910	+	0.496721i	$0.834537\pi$
$44$		0			0
$45$	0.762345	−	0.424128i	0.113644	−	0.0632253i
$46$	−4.53422			−0.668534
$47$	−0.674704	−	1.16862i	−0.0984157	−	0.170461i	0.812613	−	0.582803i	$-0.198044\pi$
$47$	−0.674704	−	1.16862i	−0.0984157	−	0.170461i	−0.911029	+	0.412342i	$0.864711\pi$
$48$	−2.44019	+	0.633103i	−0.352211	+	0.0913806i
$49$	−2.12965	+	3.68867i	−0.304236	+	0.526952i
$50$	1.66552	−	2.88476i	0.235540	−	0.407967i
$51$	1.60778	−	5.81503i	0.225134	−	0.814267i
$52$	3.22537	+	5.58651i	0.447278	+	0.774709i
$53$	−1.87766			−0.257916			−0.128958	−	0.991650i	$-0.541163\pi$
$53$	−1.87766			−0.257916			−0.128958	+	0.991650i	$0.541163\pi$
$54$	3.37859	+	0.992204i	0.459768	+	0.135022i
$55$		0			0
$56$	4.02569	+	6.97270i	0.537955	+	0.931766i
$57$	−2.80592	+	10.1485i	−0.371653	+	1.34420i
$58$	0.562373	−	0.974058i	0.0738432	−	0.127900i
$59$	7.28706	−	12.6216i	0.948694	−	1.64319i	0.200515	−	0.979691i	$-0.435739\pi$
$59$	7.28706	−	12.6216i	0.948694	−	1.64319i	0.748180	−	0.663496i	$-0.230928\pi$
$60$	0.751169	−	0.194890i	0.0969755	−	0.0251602i
$61$	−1.92957	−	3.34212i	−0.247056	−	0.427914i	0.715651	−	0.698458i	$-0.246130\pi$
$61$	−1.92957	−	3.34212i	−0.247056	−	0.427914i	−0.962708	+	0.270544i	$0.912797\pi$
$62$	1.33027			0.168945
$63$	−0.160007	+	10.0652i	−0.0201590	+	1.26810i
$64$	1.00952			0.126190
$65$	−0.608737	−	1.05436i	−0.0755046	−	0.130778i
$66$		0			0
$67$	4.46764	−	7.73818i	0.545809	−	0.945369i	−0.452746	−	0.891639i	$-0.649556\pi$
$67$	4.46764	−	7.73818i	0.545809	−	0.945369i	0.998556	−	0.0537300i	$-0.0171110\pi$
$68$	2.68345	−	4.64788i	0.325416	−	0.563638i
$69$	−8.12926	−	8.25952i	−0.978648	−	0.994330i
$70$	−0.330621	−	0.572652i	−0.0395167	−	0.0684450i
$71$	−11.1283			−1.32068			−0.660340	−	0.750967i	$-0.729588\pi$
$71$	−11.1283			−1.32068			−0.660340	+	0.750967i	$0.729588\pi$
$72$	6.17600	+	3.69783i	0.727848	+	0.435794i
$73$	1.25869			0.147318			0.0736591	−	0.997283i	$-0.476532\pi$
$73$	1.25869			0.147318			0.0736591	+	0.997283i	$0.476532\pi$
$74$	0.859446	+	1.48860i	0.0999086	+	0.173047i
$75$	8.24094	−	2.13810i	0.951582	−	0.246887i
$76$	−4.68321	+	8.11157i	−0.537202	+	0.930460i
$77$		0			0
$78$	1.30957	−	4.73648i	0.148280	−	0.536300i
$79$	−1.05357	−	1.82483i	−0.118535	−	0.205309i	0.800652	−	0.599130i	$-0.204487\pi$
$79$	−1.05357	−	1.82483i	−0.118535	−	0.205309i	−0.919188	+	0.393820i	$0.871153\pi$
$80$	0.423248			0.0473206
$81$	4.24998	+	7.93333i	0.472220	+	0.881481i
$82$	−4.39559			−0.485412
$83$	−4.68763	−	8.11922i	−0.514535	−	0.891200i	−0.999858	−	0.0168653i	$-0.994631\pi$
$83$	−4.68763	−	8.11922i	−0.514535	−	0.891200i	0.485323	−	0.874335i	$-0.338702\pi$
$84$	−2.38633	+	8.63092i	−0.260370	+	0.941710i
$85$	−0.506459	+	0.877212i	−0.0549332	+	0.0951470i
$86$	−0.0168048	+	0.0291068i	−0.00181211	+	0.00313866i
$87$	2.78260	−	0.721943i	0.298326	−	0.0774004i
$88$		0			0
$89$	−8.41413			−0.891896			−0.445948	−	0.895059i	$-0.647133\pi$
$89$	−8.41413			−0.891896			−0.445948	+	0.895059i	$0.647133\pi$
$90$	−0.507220	−	0.303694i	−0.0534657	−	0.0320122i
$91$	14.0485			1.47268
$92$	−5.15456	−	8.92795i	−0.537400	−	0.930803i
$93$	2.38500	+	2.42322i	0.247313	+	0.251276i
$94$	−0.457226	+	0.791938i	−0.0471593	+	0.0816822i
$95$	0.883882	−	1.53093i	0.0906844	−	0.157070i
$96$	7.02894	+	7.14157i	0.717388	+	0.728883i
$97$	−0.491742	−	0.851722i	−0.0499288	−	0.0864793i	0.839981	−	0.542616i	$-0.182566\pi$
$97$	−0.491742	−	0.851722i	−0.0499288	−	0.0864793i	−0.889910	+	0.456137i	$0.849233\pi$
$98$	2.88640			0.291570
$99$		0			0
$100$	7.57354			0.757354
$101$	1.95582	+	3.38758i	0.194611	+	0.337077i	0.946773	−	0.321902i	$-0.104322\pi$
$101$	1.95582	+	3.38758i	0.194611	+	0.337077i	−0.752162	+	0.658979i	$0.770989\pi$
$102$	−3.95749	+	1.02676i	−0.391850	+	0.101665i
$103$	−7.73117	+	13.3908i	−0.761775	+	1.31943i	0.180160	+	0.983637i	$0.442338\pi$
$103$	−7.73117	+	13.3908i	−0.761775	+	1.31943i	−0.941935	+	0.335795i	$0.890995\pi$
$104$	5.02294	−	8.69998i	0.492539	−	0.853103i
$105$	0.450381	−	1.62895i	0.0439527	−	0.158969i
$106$	0.636215	+	1.10196i	0.0617946	+	0.107031i
$107$	6.26446			0.605609			0.302804	−	0.953053i	$-0.402077\pi$
$107$	6.26446			0.605609			0.302804	+	0.953053i	$0.402077\pi$
$108$	1.88716	+	7.78045i	0.181592	+	0.748675i
$109$	3.09153			0.296115			0.148057	−	0.988979i	$-0.452698\pi$
$109$	3.09153			0.296115			0.148057	+	0.988979i	$0.452698\pi$
$110$		0			0
$111$	−1.17076	+	4.23444i	−0.111124	+	0.401915i
$112$	−2.44194	+	4.22956i	−0.230741	+	0.399656i
$113$	−7.97205	+	13.8080i	−0.749948	+	1.29895i	0.197899	+	0.980222i	$0.436588\pi$
$113$	−7.97205	+	13.8080i	−0.749948	+	1.29895i	−0.947847	+	0.318725i	$0.896745\pi$
$114$	6.90669	−	1.79193i	0.646870	−	0.167830i
$115$	0.972840	+	1.68501i	0.0907178	+	0.157128i
$116$	2.55725			0.237435
$117$	10.9758	−	6.10638i	1.01472	−	0.564535i
$118$	−9.87642			−0.909199
$119$	−5.84404	−	10.1222i	−0.535722	−	0.927898i
$120$	−0.847750	−	0.861333i	−0.0773886	−	0.0786286i
$121$		0			0
$122$	−1.30761	+	2.26485i	−0.118385	+	0.205050i
$123$	−7.88073	−	8.00701i	−0.710582	−	0.721968i
$124$	1.51227	+	2.61933i	0.135806	+	0.235222i
$125$	−2.88336			−0.257895
$126$	5.96126	−	3.31653i	0.531071	−	0.295460i
$127$	−18.5061			−1.64215			−0.821075	−	0.570821i	$-0.806625\pi$
$127$	−18.5061			−1.64215			−0.821075	+	0.570821i	$0.806625\pi$
$128$	5.44321	+	9.42791i	0.481116	+	0.833318i
$129$	−0.0831496	+	0.0215731i	−0.00732092	+	0.00189940i
$130$	−0.412522	+	0.714509i	−0.0361806	+	0.0626666i
$131$	0.432321	−	0.748803i	0.0377721	−	0.0654232i	−0.846521	−	0.532355i	$-0.821307\pi$
$131$	0.432321	−	0.748803i	0.0377721	−	0.0654232i	0.884293	+	0.466932i	$0.154641\pi$
$132$		0			0
$133$	10.1991	+	17.6654i	0.884377	+	1.53179i
$134$	−6.05516			−0.523086
$135$	−0.356171	−	1.46844i	−0.0306543	−	0.126383i
$136$	−8.35799			−0.716692
$137$	6.18908	+	10.7198i	0.528769	+	0.915855i	0.999437	+	0.0335444i	$0.0106795\pi$
$137$	6.18908	+	10.7198i	0.528769	+	0.915855i	−0.470668	+	0.882310i	$0.655987\pi$
$138$	−2.09286	+	7.56950i	−0.178156	+	0.644358i
$139$	0.332985	−	0.576746i	0.0282434	−	0.0489190i	−0.851558	−	0.524260i	$-0.824342\pi$
$139$	0.332985	−	0.576746i	0.0282434	−	0.0489190i	0.879802	+	0.475341i	$0.157675\pi$
$140$	0.751707	−	1.30200i	0.0635309	−	0.110039i
$141$	−2.26234	+	0.586961i	−0.190523	+	0.0494310i
$142$	3.77063	+	6.53093i	0.316425	+	0.548063i
$143$		0			0
$144$	−0.0694052	+	4.36591i	−0.00578377	+	0.363826i
$145$	−0.482640			−0.0400811
$146$	−0.426487	−	0.738697i	−0.0352963	−	0.0611350i
$147$	5.17494	+	5.25786i	0.426822	+	0.433661i
$148$	−1.95406	+	3.38453i	−0.160623	+	0.278207i
$149$	6.02662	−	10.4384i	0.493720	−	0.855148i	−0.506254	−	0.862384i	$-0.668970\pi$
$149$	6.02662	−	10.4384i	0.493720	−	0.855148i	0.999974	+	0.00723647i	$0.00230346\pi$
$150$	−4.04712	−	4.11197i	−0.330446	−	0.335741i
$151$	−10.2525	−	17.7578i	−0.834333	−	1.44511i	−0.894572	−	0.446924i	$-0.852519\pi$
$151$	−10.2525	−	17.7578i	−0.834333	−	1.44511i	0.0602386	−	0.998184i	$-0.480814\pi$
$152$	14.5865			1.18312
$153$	−8.96561	−	5.36810i	−0.724827	−	0.433985i
$154$		0			0
$155$	−0.285417	−	0.494356i	−0.0229252	−	0.0397076i
$156$	10.8149	−	2.80592i	0.865888	−	0.224654i
$157$	4.22762	−	7.32245i	0.337401	−	0.584395i	−0.646542	−	0.762878i	$-0.723786\pi$
$157$	4.22762	−	7.32245i	0.337401	−	0.584395i	0.983943	+	0.178483i	$0.0571190\pi$
$158$	−0.713969	+	1.23663i	−0.0568003	+	0.0983811i
$159$	−0.866671	+	3.13459i	−0.0687315	+	0.248589i
$160$	−0.841163	−	1.45694i	−0.0664998	−	0.115181i
$161$	−22.4513			−1.76941
$162$	3.21586	−	5.18230i	0.252662	−	0.407160i
$163$	−23.2731			−1.82289			−0.911446	−	0.411419i	$-0.865033\pi$
$163$	−23.2731			−1.82289			−0.911446	+	0.411419i	$0.865033\pi$
$164$	−4.99697	−	8.65500i	−0.390198	−	0.675842i
$165$		0			0
$166$	−3.17666	+	5.50214i	−0.246557	+	0.427049i
$167$	9.78866	−	16.9545i	0.757469	−	1.31198i	−0.186668	−	0.982423i	$-0.559769\pi$
$167$	9.78866	−	16.9545i	0.757469	−	1.31198i	0.944137	−	0.329553i	$-0.106898\pi$
$168$	13.4985	−	3.50216i	1.04143	−	0.270198i
$169$	−2.26428	−	3.92185i	−0.174176	−	0.301681i
$170$	0.686422			0.0526462
$171$	15.6470	+	9.36851i	1.19655	+	0.716428i
$172$	−0.0764156			−0.00582664
$173$	−8.95509	−	15.5107i	−0.680843	−	1.17925i	−0.974724	−	0.223413i	$-0.928280\pi$
$173$	−8.95509	−	15.5107i	−0.680843	−	1.17925i	0.293881	−	0.955842i	$-0.405053\pi$
$174$	−1.36653	−	1.38843i	−0.103597	−	0.105257i
$175$	8.24685	−	14.2840i	0.623403	−	1.07977i
$176$		0			0
$177$	−17.7071	−	17.9909i	−1.33095	−	1.35228i
$178$	2.85100	+	4.93807i	0.213691	+	0.370124i
$179$	9.44944			0.706284			0.353142	−	0.935570i	$-0.385113\pi$
$179$	9.44944			0.706284			0.353142	+	0.935570i	$0.385113\pi$
$180$	0.0213652	−	1.34397i	0.00159247	−	0.100174i
$181$	11.0798			0.823555			0.411777	−	0.911284i	$-0.364908\pi$
$181$	11.0798			0.823555			0.411777	+	0.911284i	$0.364908\pi$
$182$	−4.76010	−	8.24474i	−0.352842	−	0.611141i
$183$	−6.47002	+	1.67864i	−0.478277	+	0.124088i
$184$	−8.02730	+	13.9037i	−0.591780	+	1.02499i
$185$	0.368797	−	0.638776i	0.0271145	−	0.0469637i
$186$	0.614014	−	2.22078i	0.0450217	−	0.162835i
$187$		0			0
$188$	−2.07912			−0.151636
$189$	16.7292	+	4.91292i	1.21687	+	0.357362i
$190$	−1.19796			−0.0869090
$191$	2.26860	+	3.92932i	0.164150	+	0.284316i	0.936353	−	0.351060i	$-0.114179\pi$
$191$	2.26860	+	3.92932i	0.164150	+	0.284316i	−0.772203	+	0.635376i	$0.780845\pi$
$192$	0.465965	−	1.68531i	0.0336282	−	0.121627i
$193$	−6.74928	+	11.6901i	−0.485824	+	0.841471i	−0.999867	−	0.0162928i	$-0.994814\pi$
$193$	−6.74928	+	11.6901i	−0.485824	+	0.841471i	0.514044	+	0.857764i	$0.328147\pi$
$194$	−0.333238	+	0.577185i	−0.0239251	+	0.0414395i
$195$	−2.04115	+	0.529573i	−0.146170	+	0.0379235i
$196$	3.28129	+	5.68337i	0.234378	+	0.405955i
$197$	1.70047			0.121153			0.0605766	−	0.998164i	$-0.480706\pi$
$197$	1.70047			0.121153			0.0605766	+	0.998164i	$0.480706\pi$
$198$		0			0
$199$	−10.1442			−0.719105			−0.359552	−	0.933125i	$-0.617071\pi$
$199$	−10.1442			−0.719105			−0.359552	+	0.933125i	$0.617071\pi$
$200$	−5.89721	−	10.2143i	−0.416996	−	0.722258i
$201$	−10.8561	−	11.0301i	−0.765732	−	0.778001i
$202$	1.32540	−	2.29566i	0.0932547	−	0.161522i
$203$	2.78460	−	4.82307i	0.195441	−	0.338513i
$204$	−6.52064	−	6.62512i	−0.456536	−	0.463851i
$205$	0.943098	+	1.63349i	0.0658688	+	0.114088i
$206$	10.4783			0.730061
$207$	−17.5408	+	9.75878i	−1.21917	+	0.678282i
$208$	6.09371			0.422523
$209$		0			0
$210$	−1.10860	+	0.287624i	−0.0765006	+	0.0198480i
$211$	5.33769	−	9.24514i	0.367461	−	0.636462i	−0.621707	−	0.783250i	$-0.713560\pi$
$211$	5.33769	−	9.24514i	0.367461	−	0.636462i	0.989168	+	0.146788i	$0.0468937\pi$
$212$	−1.44651	+	2.50544i	−0.0993470	+	0.172074i
$213$	−5.13647	+	18.5777i	−0.351945	+	1.27292i
$214$	−2.12262	−	3.67648i	−0.145099	−	0.251319i
$215$	0.0144222			0.000983588
$216$	9.02388	−	8.60350i	0.613998	−	0.585394i
$217$	6.58686			0.447145
$218$	−1.04752	−	1.81435i	−0.0709467	−	0.122883i
$219$	0.580973	−	2.10128i	0.0392585	−	0.141991i
$220$		0			0
$221$	−7.29173	+	12.6296i	−0.490495	+	0.849562i
$222$	2.88180	−	0.747678i	0.193414	−	0.0501809i
$223$	−1.41869	−	2.45725i	−0.0950028	−	0.164550i	0.814607	−	0.580013i	$-0.196953\pi$
$223$	−1.41869	−	2.45725i	−0.0950028	−	0.164550i	−0.909610	+	0.415464i	$0.863619\pi$
$224$	19.4124			1.29705
$225$	0.234394	−	14.7445i	0.0156262	−	0.982963i
$226$	10.8048			0.718726
$227$	−3.24294	−	5.61693i	−0.215241	−	0.372809i	0.738106	−	0.674685i	$-0.235720\pi$
$227$	−3.24294	−	5.61693i	−0.215241	−	0.372809i	−0.953347	+	0.301876i	$0.902387\pi$
$228$	11.3800	+	11.5623i	0.753656	+	0.765732i
$229$	12.8202	−	22.2052i	0.847181	−	1.46736i	−0.0365331	−	0.999332i	$-0.511631\pi$
$229$	12.8202	−	22.2052i	0.847181	−	1.46736i	0.883714	−	0.468028i	$-0.155035\pi$
$230$	0.659263	−	1.14188i	0.0434705	−	0.0752932i
$231$		0			0
$232$	−1.99123	−	3.44891i	−0.130731	−	0.226432i
$233$	−0.649882			−0.0425752			−0.0212876	−	0.999773i	$-0.506777\pi$
$233$	−0.649882			−0.0425752			−0.0212876	+	0.999773i	$0.506777\pi$
$234$	−7.30270	−	4.37244i	−0.477392	−	0.285835i
$235$	0.392401			0.0255974
$236$	−11.2276	−	19.4469i	−0.730858	−	1.26588i
$237$	−3.53270	+	0.916554i	−0.229473	+	0.0595366i
$238$	−3.96032	+	6.85948i	−0.256710	+	0.444634i
$239$	8.46729	−	14.6658i	0.547703	−	0.948650i	−0.450728	−	0.892661i	$-0.648836\pi$
$239$	8.46729	−	14.6658i	0.547703	−	0.948650i	0.998431	−	0.0559887i	$-0.0178311\pi$
$240$	0.195359	−	0.706578i	0.0126104	−	0.0456094i
$241$	−12.2496	−	21.2170i	−0.789069	−	1.36671i	−0.926538	−	0.376201i	$-0.877230\pi$
$241$	−12.2496	−	21.2170i	−0.789069	−	1.36671i	0.137469	−	0.990506i	$-0.456103\pi$
$242$		0			0
$243$	15.2057	−	3.43319i	0.975446	−	0.220240i
$244$	−5.94603			−0.380656
$245$	−0.619292	−	1.07264i	−0.0395651	−	0.0685288i
$246$	−2.02888	+	7.33808i	−0.129356	+	0.467859i
$247$	12.7257	−	22.0415i	0.809715	−	1.40247i
$248$	2.35509	−	4.07913i	0.149548	−	0.259025i
$249$	−15.7180	+	4.07802i	−0.996090	+	0.258434i
$250$	0.976981	+	1.69218i	0.0617897	+	0.107023i
$251$	17.8710			1.12801			0.564005	−	0.825771i	$-0.309260\pi$
$251$	17.8710			1.12801			0.564005	+	0.825771i	$0.309260\pi$
$252$	13.3071	+	7.96755i	0.838271	+	0.501909i
$253$		0			0
$254$	6.27050	+	10.8608i	0.393446	+	0.681468i
$255$	1.23067	+	1.25039i	0.0770673	+	0.0783022i
$256$	4.69821	−	8.13755i	0.293638	−	0.508597i
$257$	0.623376	−	1.07972i	0.0388851	−	0.0673510i	−0.845928	−	0.533297i	$-0.820953\pi$
$257$	0.623376	−	1.07972i	0.0388851	−	0.0673510i	0.884813	+	0.465946i	$0.154286\pi$
$258$	0.0408347	+	0.0414890i	0.00254226	+	0.00258299i
$259$	4.25556	+	7.37085i	0.264428	+	0.458002i
$260$	−1.87584			−0.116335
$261$	0.0791445	−	4.97855i	0.00489892	−	0.308165i
$262$	−0.585941			−0.0361996
$263$	8.39035	+	14.5325i	0.517371	+	0.896113i	0.999796	+	0.0201758i	$0.00642261\pi$
$263$	8.39035	+	14.5325i	0.517371	+	0.896113i	−0.482425	+	0.875937i	$0.660244\pi$
$264$		0			0
$265$	0.273006	−	0.472861i	0.0167707	−	0.0290476i
$266$	6.91164	−	11.9713i	0.423780	−	0.734008i
$267$	−3.88371	+	14.0467i	−0.237679	+	0.859643i
$268$	−6.88359	−	11.9227i	−0.420482	−	0.728296i
$269$	21.9703			1.33955			0.669777	−	0.742563i	$-0.266390\pi$
$269$	21.9703			1.33955			0.669777	+	0.742563i	$0.266390\pi$
$270$	−0.741111	+	0.706586i	−0.0451026	+	0.0430014i
$271$	10.1083			0.614037			0.307018	−	0.951704i	$-0.400669\pi$
$271$	10.1083			0.614037			0.307018	+	0.951704i	$0.400669\pi$
$272$	−2.53493	−	4.39063i	−0.153703	−	0.266221i
$273$	6.48436	−	23.4527i	0.392451	−	1.41942i
$274$	4.19415	−	7.26448i	0.253378	−	0.438863i
$275$		0			0
$276$	−17.2837	+	4.48422i	−1.04035	+	0.269919i
$277$	−3.88655	−	6.73171i	−0.233520	−	0.404469i	0.725321	−	0.688411i	$-0.241691\pi$
$277$	−3.88655	−	6.73171i	−0.233520	−	0.404469i	−0.958842	+	0.283941i	$0.908358\pi$
$278$	−0.451306			−0.0270676
$279$	5.14621	−	2.86308i	0.308095	−	0.171408i
$280$	−2.34130			−0.139919
$281$	16.1452	+	27.9643i	0.963142	+	1.66821i	0.714527	+	0.699608i	$0.246642\pi$
$281$	16.1452	+	27.9643i	0.963142	+	1.66821i	0.248615	+	0.968602i	$0.420025\pi$
$282$	1.11103	+	1.12884i	0.0661611	+	0.0672212i
$283$	6.26153	−	10.8453i	0.372209	−	0.644685i	−0.617696	−	0.786417i	$-0.711934\pi$
$283$	6.26153	−	10.8453i	0.372209	−	0.644685i	0.989905	+	0.141732i	$0.0452671\pi$
$284$	−8.57301	+	14.8489i	−0.508715	+	0.881120i
$285$	−2.14778	−	2.18220i	−0.127224	−	0.129262i
$286$		0			0
$287$	−21.7649			−1.28474
$288$	15.1666	−	8.43790i	0.893701	−	0.497208i
$289$	−4.86682			−0.286283
$290$	0.163535	+	0.283251i	0.00960311	+	0.0166331i
$291$	−1.64885	+	0.427793i	−0.0966575	+	0.0250776i
$292$	0.969671	−	1.67952i	0.0567457	−	0.0982865i
$293$	9.19219	−	15.9213i	0.537013	−	0.930134i	−0.462050	−	0.886854i	$-0.652886\pi$
$293$	9.19219	−	15.9213i	0.537013	−	0.930134i	0.999063	−	0.0432803i	$-0.0137809\pi$
$294$	1.33228	−	4.81860i	0.0776999	−	0.281026i
$295$	2.11904	+	3.67028i	0.123375	+	0.213692i
$296$	6.08619			0.353753
$297$		0			0
$298$	−8.16810			−0.473166
$299$	14.0064	+	24.2599i	0.810014	+	1.40299i
$300$	3.49572	−	12.6434i	0.201826	−	0.729966i
$301$	−0.0832092	+	0.144123i	−0.00479610	+	0.00830709i
$302$	−6.94777	+	12.0339i	−0.399799	+	0.692473i
$303$	6.55803	−	1.70147i	0.376749	−	0.0977470i
$304$	4.42401	+	7.66261i	0.253734	+	0.439481i
$305$	1.12222			0.0642581
$306$	−0.112561	+	7.08062i	−0.00643469	+	0.404772i
$307$	8.42389			0.480777			0.240388	−	0.970677i	$-0.422725\pi$
$307$	8.42389			0.480777			0.240388	+	0.970677i	$0.422725\pi$
$308$		0			0
$309$	18.7863	+	19.0873i	1.06872	+	1.08584i
$310$	−0.193418	+	0.335010i	−0.0109854	+	0.0190273i
$311$	−5.65168	+	9.78899i	−0.320477	+	0.555083i	−0.980587	−	0.196087i	$-0.937177\pi$
$311$	−5.65168	+	9.78899i	−0.320477	+	0.555083i	0.660109	+	0.751170i	$0.270510\pi$
$312$	−12.2055	−	12.4010i	−0.690998	−	0.702070i
$313$	−3.05532	−	5.29197i	−0.172697	−	0.299120i	0.766665	−	0.642047i	$-0.221915\pi$
$313$	−3.05532	−	5.29197i	−0.172697	−	0.299120i	−0.939362	+	0.342928i	$0.888581\pi$
$314$	−5.72985			−0.323354
$315$	−2.51151	−	1.50375i	−0.141508	−	0.0847266i
$316$	−3.24660			−0.182635
$317$	0.414288	+	0.717568i	0.0232687	+	0.0403026i	0.877425	−	0.479713i	$-0.159259\pi$
$317$	0.414288	+	0.717568i	0.0232687	+	0.0403026i	−0.854157	+	0.520016i	$0.825926\pi$
$318$	2.13328	−	0.553477i	0.119629	−	0.0310375i
$319$		0			0
$320$	−0.146782	+	0.254234i	−0.00820535	+	0.0142121i
$321$	2.89149	−	10.4580i	0.161387	−	0.583709i
$322$	7.60726	+	13.1762i	0.423936	+	0.734278i
$323$	−21.1751			−1.17821
$324$	13.8599	+	0.440775i	0.769993	+	0.0244875i
$325$	−20.5795			−1.14155
$326$	7.88574	+	13.6585i	0.436751	+	0.756474i
$327$	1.42696	−	5.16105i	0.0789110	−	0.285407i
$328$	−7.78188	+	13.4786i	−0.429683	+	0.744232i
$329$	−2.26396	+	3.92130i	−0.124816	+	0.216188i
$330$		0			0
$331$	−4.09227	−	7.08802i	−0.224931	−	0.389593i	0.731367	−	0.681984i	$-0.238882\pi$
$331$	−4.09227	−	7.08802i	−0.224931	−	0.389593i	−0.956299	+	0.292391i	$0.905549\pi$
$332$	−14.4451			−0.792777
$333$	6.52866	+	3.90899i	0.357768	+	0.214211i
$334$	−13.2669			−0.725935
$335$	1.29917	+	2.25022i	0.0709811	+	0.122943i
$336$	5.93377	+	6.02885i	0.323714	+	0.328901i
$337$	1.25242	−	2.16926i	0.0682239	−	0.118167i	−0.829896	−	0.557919i	$-0.811600\pi$
$337$	1.25242	−	2.16926i	0.0682239	−	0.118167i	0.898120	+	0.439751i	$0.144933\pi$
$338$	−1.53443	+	2.65772i	−0.0834622	+	0.144561i
$339$	19.3716	+	19.6820i	1.05212	+	1.06898i
$340$	0.780334	+	1.35158i	0.0423195	+	0.0732996i
$341$		0			0
$342$	0.196444	−	12.3572i	0.0106225	−	0.668203i
$343$	−9.19637			−0.496558
$344$	0.0595018	+	0.103060i	0.00320812	+	0.00555663i
$345$	3.26202	−	0.846326i	0.175621	−	0.0455646i
$346$	−6.06858	+	10.5111i	−0.326249	+	0.565080i
$347$	15.7632	−	27.3027i	0.846213	−	1.46568i	−0.0383501	−	0.999264i	$-0.512210\pi$
$347$	15.7632	−	27.3027i	0.846213	−	1.46568i	0.884563	−	0.466420i	$-0.154456\pi$
$348$	1.18035	−	4.26912i	0.0632735	−	0.228849i
$349$	4.37596	+	7.57939i	0.234240	+	0.405715i	0.959052	−	0.283232i	$-0.0914065\pi$
$349$	4.37596	+	7.57939i	0.234240	+	0.405715i	−0.724812	+	0.688947i	$0.758073\pi$
$350$	−11.1773			−0.597450
$351$	−5.12796	−	21.1418i	−0.273711	−	1.12847i
$352$		0			0
$353$	−0.219931	−	0.380932i	−0.0117058	−	0.0202750i	0.860113	−	0.510103i	$-0.170393\pi$
$353$	−0.219931	−	0.380932i	−0.0117058	−	0.0202750i	−0.871819	+	0.489828i	$0.837059\pi$
$354$	−4.55867	+	16.4879i	−0.242290	+	0.876320i
$355$	1.61802	−	2.80249i	0.0858755	−	0.148741i
$356$	−6.48210	+	11.2273i	−0.343550	+	0.595047i
$357$	−19.5956	+	5.08404i	−1.03711	+	0.269076i
$358$	−3.20179	−	5.54567i	−0.169220	−	0.293098i
$359$	16.7381			0.883404			0.441702	−	0.897162i	$-0.354375\pi$
$359$	16.7381			0.883404			0.441702	+	0.897162i	$0.354375\pi$
$360$	−1.82922	+	1.01768i	−0.0964084	+	0.0536365i
$361$	17.9552			0.945009
$362$	−3.75422	−	6.50249i	−0.197317	−	0.341763i
$363$		0			0
$364$	10.8227	−	18.7455i	0.567263	−	0.982529i
$365$	−0.183010	+	0.316983i	−0.00957918	+	0.0165916i
$366$	3.17742	+	3.22833i	0.166086	+	0.168748i
$367$	7.37439	+	12.7728i	0.384940	+	0.666735i	0.991761	−	0.128103i	$-0.0408888\pi$
$367$	7.37439	+	12.7728i	0.384940	+	0.666735i	−0.606821	+	0.794839i	$0.707556\pi$
$368$	−9.73853			−0.507656
$369$	−17.0045	+	9.46043i	−0.885221	+	0.492490i
$370$	−0.499845			−0.0259857
$371$	3.15023	+	5.45636i	0.163552	+	0.283280i
$372$	5.07077	−	1.31560i	0.262907	−	0.0682108i
$373$	−11.8254	+	20.4822i	−0.612296	+	1.06053i	0.378556	+	0.925578i	$0.376421\pi$
$373$	−11.8254	+	20.4822i	−0.612296	+	1.06053i	−0.990852	+	0.134950i	$0.956913\pi$
$374$		0			0
$375$	−1.33087	+	4.81353i	−0.0687260	+	0.248569i
$376$	1.61893	+	2.80407i	0.0834899	+	0.144609i
$377$	−6.94880			−0.357882
$378$	−2.78513	−	11.4826i	−0.143252	−	0.590603i
$379$	−11.4766			−0.589514			−0.294757	−	0.955572i	$-0.595239\pi$
$379$	−11.4766			−0.589514			−0.294757	+	0.955572i	$0.595239\pi$
$380$	−1.36185	−	2.35880i	−0.0698617	−	0.121004i
$381$	−8.54186	+	30.8944i	−0.437613	+	1.58277i
$382$	1.53736	−	2.66278i	0.0786580	−	0.136240i
$383$	3.96434	−	6.86643i	0.202568	−	0.350858i	−0.746787	−	0.665063i	$-0.768405\pi$
$383$	3.96434	−	6.86643i	0.202568	−	0.350858i	0.949355	+	0.314205i	$0.101738\pi$
$384$	18.2515	−	4.73534i	0.931395	−	0.241649i
$385$		0			0
$386$	9.14755			0.465598
$387$	−0.00236499	+	0.148769i	−0.000120219	+	0.00756235i
$388$	−1.51532			−0.0769286
$389$	−4.52549	−	7.83839i	−0.229452	−	0.397422i	0.728194	−	0.685371i	$-0.240360\pi$
$389$	−4.52549	−	7.83839i	−0.229452	−	0.397422i	−0.957646	+	0.287949i	$0.907027\pi$
$390$	1.00241	+	1.01847i	0.0507588	+	0.0515721i
$391$	11.6531	−	20.1838i	0.589324	−	1.02074i
$392$	5.11003	−	8.85083i	0.258095	−	0.447034i
$393$	−1.05052	−	1.06735i	−0.0529916	−	0.0538407i
$394$	−0.576176	−	0.997966i	−0.0290273	−	0.0502768i
$395$	0.612743			0.0308305
$396$		0			0
$397$	5.38182			0.270106			0.135053	−	0.990838i	$-0.456880\pi$
$397$	5.38182			0.270106			0.135053	+	0.990838i	$0.456880\pi$
$398$	3.43721	+	5.95342i	0.172292	+	0.298418i
$399$	34.1986	−	8.87277i	1.71207	−	0.444194i
$400$	3.57718	−	6.19586i	0.178859	−	0.309793i
$401$	7.83416	−	13.5692i	0.391219	−	0.677611i	−0.601392	−	0.798954i	$-0.705387\pi$
$401$	7.83416	−	13.5692i	0.391219	−	0.677611i	0.992611	+	0.121343i	$0.0387201\pi$
$402$	−2.79488	+	10.1086i	−0.139396	+	0.504171i
$403$	−4.10928	−	7.11748i	−0.204698	−	0.354547i
$404$	6.02692			0.299850
$405$	−2.61583	−	0.0831892i	−0.129982	−	0.00413370i
$406$	−3.77407			−0.187304
$407$		0			0
$408$	−3.85780	+	13.9530i	−0.190990	+	0.690775i
$409$	11.3706	−	19.6945i	0.562242	−	0.973832i	−0.435058	−	0.900402i	$-0.643272\pi$
$409$	11.3706	−	19.6945i	0.562242	−	0.973832i	0.997300	−	0.0734296i	$-0.0233944\pi$
$410$	0.639108	−	1.10697i	0.0315633	−	0.0546692i
$411$	20.7525	−	5.38421i	1.02365	−	0.265584i
$412$	11.9119	+	20.6320i	0.586858	+	1.01647i
$413$	−48.9033			−2.40637
$414$	11.6706	+	6.98771i	0.573581	+	0.343427i
$415$	2.72628			0.133828
$416$	−12.1106	−	20.9762i	−0.593773	−	1.02844i
$417$	−0.809134	−	0.822099i	−0.0396235	−	0.0402584i
$418$		0			0
$419$	19.5131	−	33.7978i	0.953279	−	1.65113i	0.215022	−	0.976609i	$-0.431018\pi$
$419$	19.5131	−	33.7978i	0.953279	−	1.65113i	0.738257	−	0.674519i	$-0.235649\pi$
$420$	−1.82661	−	1.85588i	−0.0891293	−	0.0905575i
$421$	−12.0938	−	20.9470i	−0.589414	−	1.02090i	−0.994309	−	0.106532i	$-0.966025\pi$
$421$	−12.0938	−	20.9470i	−0.589414	−	1.02090i	0.404895	−	0.914363i	$-0.367308\pi$
$422$	−7.23436			−0.352163
$423$	−0.0643468	+	4.04771i	−0.00312865	+	0.196807i
$424$	4.50537			0.218800
$425$	8.56090	+	14.8279i	0.415265	+	0.719260i
$426$	12.6433	−	3.28028i	0.612568	−	0.158930i
$427$	−6.47465	+	11.2144i	−0.313330	+	0.542704i
$428$	4.82603	−	8.35894i	0.233275	−	0.404044i
$429$		0			0
$430$	−0.00488675	−	0.00846409i	−0.000235660	−	0.000408175i
$431$	−12.2455			−0.589844			−0.294922	−	0.955521i	$-0.595294\pi$
$431$	−12.2455			−0.589844			−0.294922	+	0.955521i	$0.595294\pi$
$432$	7.25649	+	2.13104i	0.349128	+	0.102530i
$433$	−7.13183			−0.342734			−0.171367	−	0.985207i	$-0.554818\pi$
$433$	−7.13183			−0.342734			−0.171367	+	0.985207i	$0.554818\pi$
$434$	−2.23185	−	3.86568i	−0.107132	−	0.185559i
$435$	−0.222772	+	0.805728i	−0.0106811	+	0.0386317i
$436$	2.38166	−	4.12515i	0.114061	−	0.197559i
$437$	−20.3373	+	35.2252i	−0.972863	+	1.68505i
$438$	−1.43005	+	0.371024i	−0.0683303	+	0.0177282i
$439$	9.59720	+	16.6228i	0.458049	+	0.793365i	0.998858	−	0.0477810i	$-0.0152150\pi$
$439$	9.59720	+	16.6228i	0.458049	+	0.793365i	−0.540808	+	0.841146i	$0.681882\pi$
$440$		0			0
$441$	11.1662	−	6.21225i	0.531721	−	0.295822i
$442$	9.88275			0.470075
$443$	4.82527	+	8.35762i	0.229256	+	0.397083i	0.957588	−	0.288142i	$-0.0930375\pi$
$443$	4.82527	+	8.35762i	0.229256	+	0.397083i	−0.728332	+	0.685224i	$0.759704\pi$
$444$	4.74826	+	4.82434i	0.225342	+	0.228953i
$445$	1.22339	−	2.11898i	0.0579944	−	0.100449i
$446$	−0.961405	+	1.66520i	−0.0455238	+	0.0788496i
$447$	−14.6444	−	14.8790i	−0.692654	−	0.703753i
$448$	−1.69372	−	2.93361i	−0.0800207	−	0.138600i
$449$	−15.3818			−0.725912			−0.362956	−	0.931806i	$-0.618233\pi$
$449$	−15.3818			−0.725912			−0.362956	+	0.931806i	$0.618233\pi$
$450$	−8.73262	+	4.85837i	−0.411660	+	0.229026i
$451$		0			0
$452$	12.2831	+	21.2749i	0.577747	+	1.00069i
$453$	−34.3774	+	8.91916i	−1.61519	+	0.419059i
$454$	−2.19764	+	3.80642i	−0.103140	+	0.178644i
$455$	−2.04261	+	3.53791i	−0.0957591	+	0.165860i
$456$	6.73271	−	24.3510i	0.315288	−	1.14034i
$457$	9.54887	+	16.5391i	0.446678	+	0.773668i	0.998167	−	0.0605134i	$-0.0192738\pi$
$457$	9.54887	+	16.5391i	0.446678	+	0.773668i	−0.551490	+	0.834182i	$0.685940\pi$
$458$	−17.3757			−0.811911
$459$	−13.0999	+	12.4896i	−0.611449	+	0.582964i
$460$	2.99784			0.139775
$461$	−4.18590	−	7.25020i	−0.194957	−	0.337675i	0.751929	−	0.659244i	$-0.229123\pi$
$461$	−4.18590	−	7.25020i	−0.194957	−	0.337675i	−0.946886	+	0.321568i	$0.895790\pi$
$462$		0			0
$463$	−14.1298	+	24.4735i	−0.656665	+	1.13738i	0.324808	+	0.945780i	$0.394700\pi$
$463$	−14.1298	+	24.4735i	−0.656665	+	1.13738i	−0.981474	+	0.191598i	$0.938633\pi$
$464$	1.20786	−	2.09207i	0.0560733	−	0.0971218i
$465$	−0.957026	+	0.248299i	−0.0443810	+	0.0115146i
$466$	0.220202	+	0.381402i	0.0102007	+	0.0176681i
$467$	−8.22408			−0.380565			−0.190282	−	0.981729i	$-0.560940\pi$
$467$	−8.22408			−0.380565			−0.190282	+	0.981729i	$0.560940\pi$
$468$	0.307605	−	19.3498i	0.0142190	−	0.894444i
$469$	−29.9822			−1.38445
$470$	−0.132959	−	0.230292i	−0.00613294	−	0.0106226i
$471$	−10.2729	−	10.4375i	−0.473349	−	0.480934i
$472$	−17.4850	+	30.2850i	−0.804815	+	1.39398i
$473$		0			0
$474$	1.73491	+	1.76270i	0.0796868	+	0.0809637i
$475$	−14.9407	−	25.8780i	−0.685525	−	1.18736i
$476$	−18.0086			−0.825422
$477$	4.83291	+	2.89367i	0.221284	+	0.132492i
$478$	−11.4760			−0.524901
$479$	15.2111	+	26.3463i	0.695012	+	1.20380i	0.970177	+	0.242398i	$0.0779341\pi$
$479$	15.2111	+	26.3463i	0.695012	+	1.20380i	−0.275165	+	0.961397i	$0.588733\pi$
$480$	−2.82049	+	0.731773i	−0.128737	+	0.0334007i
$481$	5.30975	−	9.19677i	0.242104	−	0.419336i
$482$	−8.30120	+	14.3781i	−0.378109	+	0.654905i
$483$	−10.3628	+	37.4805i	−0.471525	+	1.70542i
$484$		0			0
$485$	0.285992			0.0129862
$486$	−7.16708	−	7.76061i	−0.325105	−	0.352028i
$487$	−22.2893			−1.01002			−0.505012	−	0.863112i	$-0.668512\pi$
$487$	−22.2893			−1.01002			−0.505012	+	0.863112i	$0.668512\pi$
$488$	4.62994	+	8.01929i	0.209588	+	0.363016i
$489$	−10.7422	+	38.8526i	−0.485779	+	1.75697i
$490$	−0.419675	+	0.726898i	−0.0189590	+	0.0328379i
$491$	16.1829	−	28.0296i	0.730325	−	1.26496i	−0.226419	−	0.974030i	$-0.572702\pi$
$491$	16.1829	−	28.0296i	0.730325	−	1.26496i	0.956744	−	0.290930i	$-0.0939647\pi$
$492$	−16.7553	+	4.34713i	−0.755386	+	0.195984i
$493$	2.89064	+	5.00674i	0.130188	+	0.225492i
$494$	−17.2476			−0.776005
$495$		0			0
$496$	2.85714			0.128289
$497$	18.6704	+	32.3380i	0.837480	+	1.45056i
$498$	7.71911	+	7.84280i	0.345902	+	0.351444i
$499$	−0.130887	+	0.226703i	−0.00585931	+	0.0101486i	−0.868940	−	0.494917i	$-0.835198\pi$
$499$	−0.130887	+	0.226703i	−0.00585931	+	0.0101486i	0.863081	+	0.505066i	$0.168532\pi$
$500$	−2.22129	+	3.84738i	−0.0993391	+	0.172060i
$501$	−23.7859	−	24.1670i	−1.06268	−	1.07970i
$502$	−6.05532	−	10.4881i	−0.270262	−	0.468108i
$503$	−18.0436			−0.804525			−0.402263	−	0.915524i	$-0.631776\pi$
$503$	−18.0436			−0.804525			−0.402263	+	0.915524i	$0.631776\pi$
$504$	0.383932	−	24.1511i	0.0171017	−	1.07577i
$505$	−1.13748			−0.0506174
$506$		0			0
$507$	−7.59233	+	1.96982i	−0.337187	+	0.0874828i
$508$	−14.2568	+	24.6934i	−0.632542	+	1.09559i
$509$	2.12639	−	3.68302i	0.0942506	−	0.163247i	−0.815045	−	0.579398i	$-0.803288\pi$
$509$	2.12639	−	3.68302i	0.0942506	−	0.163247i	0.909296	+	0.416151i	$0.136621\pi$
$510$	0.316832	−	1.14593i	0.0140296	−	0.0507424i
$511$	−2.11176	−	3.65767i	−0.0934186	−	0.161806i
$512$	15.4052			0.680819
$513$	22.8621	−	21.7971i	1.00939	−	0.962365i
$514$	−0.844884			−0.0372662
$515$	−2.24818	−	3.89397i	−0.0990668	−	0.171589i
$516$	−0.0352712	+	0.127570i	−0.00155273	+	0.00561593i
$517$		0			0
$518$	2.88386	−	4.99500i	0.126710	−	0.219468i
$519$	−30.0272	+	7.79051i	−1.31805	+	0.341965i
$520$	1.46064	+	2.52991i	0.0640535	+	0.110944i
$521$	13.7326			0.601635			0.300817	−	0.953682i	$-0.402741\pi$
$521$	13.7326			0.601635			0.300817	+	0.953682i	$0.402741\pi$
$522$	−2.94862	+	1.64046i	−0.129058	+	0.0718009i
$523$	26.0362			1.13849			0.569243	−	0.822170i	$-0.307236\pi$
$523$	26.0362			1.13849			0.569243	+	0.822170i	$0.307236\pi$
$524$	−0.666106	−	1.15373i	−0.0290990	−	0.0504009i
$525$	−20.0394	−	20.3605i	−0.874590	−	0.888604i
$526$	5.68588	−	9.84823i	0.247916	−	0.429403i
$527$	−3.41885	+	5.92162i	−0.148927	+	0.257950i
$528$		0			0
$529$	−10.8841	−	18.8518i	−0.473222	−	0.819644i
$530$	−0.370016			−0.0160725
$531$	−38.2074	+	21.2566i	−1.65806	+	0.922456i
$532$	31.4289			1.36262
$533$	13.5782	+	23.5182i	0.588139	+	1.01869i
$534$	9.55963	−	2.48023i	0.413686	−	0.107330i
$535$	−0.910837	+	1.57762i	−0.0393789	+	0.0682063i
$536$	−10.7200	+	18.5675i	−0.463031	+	0.801994i
$537$	4.36158	−	15.7751i	0.188216	−	0.680744i
$538$	−7.44430	−	12.8939i	−0.320946	−	0.555895i
$539$		0			0
$540$	−2.23378	−	0.656004i	−0.0961268	−	0.0282299i
$541$	15.1235			0.650211			0.325106	−	0.945678i	$-0.394600\pi$
$541$	15.1235			0.650211			0.325106	+	0.945678i	$0.394600\pi$
$542$	−3.42505	−	5.93236i	−0.147118	−	0.254816i
$543$	5.11411	−	18.4968i	0.219467	−	0.793774i
$544$	−10.0758	+	17.4519i	−0.431998	+	0.748242i
$545$	−0.449500	+	0.778557i	−0.0192545	+	0.0333497i
$546$	−15.9610	+	4.14107i	−0.683069	+	0.177221i
$547$	11.1215	+	19.2630i	0.475521	+	0.823627i	0.999607	−	0.0280389i	$-0.00892622\pi$
$547$	11.1215	+	19.2630i	0.475521	+	0.823627i	−0.524086	+	0.851665i	$0.675593\pi$
$548$	19.0718			0.814709
$549$	−0.184024	+	11.5760i	−0.00785395	+	0.494050i
$550$		0			0
$551$	−5.04481	−	8.73786i	−0.214916	−	0.372245i
$552$	19.5059	+	19.8184i	0.830226	+	0.843529i
$553$	−3.53523	+	6.12320i	−0.150333	+	0.260385i
$554$	−2.63380	+	4.56187i	−0.111899	+	0.193815i
$555$	−0.896157	−	0.910517i	−0.0380398	−	0.0386493i
$556$	−0.513051	−	0.888630i	−0.0217582	−	0.0376863i
$557$	−35.8076			−1.51722			−0.758609	−	0.651546i	$-0.774121\pi$
$557$	−35.8076			−1.51722			−0.758609	+	0.651546i	$0.774121\pi$
$558$	−3.42399	−	2.05009i	−0.144949	−	0.0867872i
$559$	0.207644			0.00878239
$560$	−0.710102	−	1.22993i	−0.0300073	−	0.0519742i
$561$		0			0
$562$	10.9411	−	18.9505i	0.461522	−	0.799380i
$563$	−16.8060	+	29.1089i	−0.708289	+	1.22679i	0.257202	+	0.966358i	$0.417199\pi$
$563$	−16.8060	+	29.1089i	−0.708289	+	1.22679i	−0.965491	+	0.260435i	$0.916134\pi$
$564$	−0.959661	+	3.47092i	−0.0404090	+	0.146152i
$565$	−2.31823	−	4.01530i	−0.0975288	−	0.168925i
$566$	−8.48648			−0.356713
$567$	15.9234	−	25.6603i	0.668719	−	1.07763i
$568$	26.7019			1.12039
$569$	11.3739	+	19.7001i	0.476817	+	0.825872i	0.999647	−	0.0265652i	$-0.00845695\pi$
$569$	11.3739	+	19.7001i	0.476817	+	0.825872i	−0.522830	+	0.852437i	$0.675124\pi$
$570$	−0.552942	+	1.99989i	−0.0231602	+	0.0837663i
$571$	17.6597	−	30.5875i	0.739035	−	1.28005i	−0.213895	−	0.976857i	$-0.568615\pi$
$571$	17.6597	−	30.5875i	0.739035	−	1.28005i	0.952930	−	0.303190i	$-0.0980517\pi$
$572$		0			0
$573$	7.60679	−	1.97357i	0.317778	−	0.0824472i
$574$	7.37468	+	12.7733i	0.307813	+	0.533148i
$575$	32.8887			1.37155
$576$	−2.59841	−	1.55578i	−0.108267	−	0.0648242i
$577$	29.5174			1.22883			0.614413	−	0.788984i	$-0.289393\pi$
$577$	29.5174			1.22883			0.614413	+	0.788984i	$0.289393\pi$
$578$	1.64904	+	2.85623i	0.0685912	+	0.118803i
$579$	16.4004	+	16.6632i	0.681576	+	0.692497i
$580$	−0.371818	+	0.644007i	−0.0154389	+	0.0267409i
$581$	−15.7293	+	27.2440i	−0.652561	+	1.13027i
$582$	0.809750	+	0.822725i	0.0335652	+	0.0341031i
$583$		0			0
$584$	−3.02018			−0.124976
$585$	−0.0580555	+	3.65196i	−0.00240030	+	0.150990i
$586$	−12.4585			−0.514657
$587$	16.5389	+	28.6462i	0.682632	+	1.18235i	0.974175	+	0.225796i	$0.0724983\pi$
$587$	16.5389	+	28.6462i	0.682632	+	1.18235i	−0.291542	+	0.956558i	$0.594168\pi$
$588$	11.0025	−	2.85457i	0.453734	−	0.117721i
$589$	5.96664	−	10.3345i	0.245851	−	0.425827i
$590$	1.43601	−	2.48724i	0.0591195	−	0.102398i
$591$	0.784884	−	2.83878i	0.0322858	−	0.116772i
$592$	1.84591	+	3.19720i	0.0758663	+	0.131404i
$593$	−9.74358			−0.400121			−0.200060	−	0.979784i	$-0.564114\pi$
$593$	−9.74358			−0.400121			−0.200060	+	0.979784i	$0.564114\pi$
$594$		0			0
$595$	3.39883			0.139339
$596$	−9.28561	−	16.0831i	−0.380353	−	0.658791i
$597$	−4.68227	+	16.9349i	−0.191633	+	0.693101i
$598$	9.49173	−	16.4402i	0.388146	−	0.672288i
$599$	−13.9289	+	24.1256i	−0.569120	+	0.985744i	0.427533	+	0.904000i	$0.359383\pi$
$599$	−13.9289	+	24.1256i	−0.569120	+	0.985744i	−0.996653	+	0.0817449i	$0.973951\pi$
$600$	−19.7739	+	5.13030i	−0.807264	+	0.209444i
$601$	10.6596	+	18.4630i	0.434815	+	0.753122i	0.997281	−	0.0736992i	$-0.0234805\pi$
$601$	10.6596	+	18.4630i	0.434815	+	0.753122i	−0.562466	+	0.826821i	$0.690147\pi$
$602$	0.112777			0.00459643
$603$	−23.4247	+	13.0322i	−0.953926	+	0.530714i
$604$	−31.5933			−1.28551
$605$		0			0
$606$	−3.22064	−	3.27225i	−0.130830	−	0.132926i
$607$	−9.57155	+	16.5784i	−0.388497	+	0.672897i	−0.992248	−	0.124277i	$-0.960339\pi$
$607$	−9.57155	+	16.5784i	−0.388497	+	0.672897i	0.603750	+	0.797173i	$0.293672\pi$
$608$	17.5845	−	30.4573i	0.713148	−	1.23521i
$609$	−6.76642	−	6.87484i	−0.274189	−	0.278583i
$610$	−0.380246	−	0.658606i	−0.0153957	−	0.0266662i
$611$	5.64959			0.228558
$612$	−14.0698	+	7.82770i	−0.568739	+	0.316416i
$613$	6.05388			0.244514			0.122257	−	0.992498i	$-0.460987\pi$
$613$	6.05388			0.244514			0.122257	+	0.992498i	$0.460987\pi$
$614$	−2.85430	−	4.94380i	−0.115190	−	0.199515i
$615$	3.16229	−	0.820451i	0.127516	−	0.0330838i
$616$		0			0
$617$	15.1632	−	26.2634i	0.610448	−	1.05733i	−0.380717	−	0.924692i	$-0.624323\pi$
$617$	15.1632	−	26.2634i	0.610448	−	1.05733i	0.991165	−	0.132635i	$-0.0423438\pi$
$618$	4.83649	−	17.4927i	0.194552	−	0.703661i
$619$	2.33034	+	4.03627i	0.0936642	+	0.162231i	0.909050	−	0.416686i	$-0.136809\pi$
$619$	2.33034	+	4.03627i	0.0936642	+	0.162231i	−0.815386	+	0.578918i	$0.803475\pi$
$620$	−0.879520			−0.0353224
$621$	8.19515	+	33.7873i	0.328860	+	1.35584i
$622$	7.65993			0.307135
$623$	14.1168	+	24.4509i	0.565576	+	0.979606i
$624$	2.81268	−	10.1729i	0.112597	−	0.407243i
$625$	−11.8694	+	20.5583i	−0.474775	+	0.822334i
$626$	−2.07050	+	3.58620i	−0.0827536	+	0.143334i
$627$		0			0
$628$	−6.51377	−	11.2822i	−0.259928	−	0.450208i
$629$	−8.83525			−0.352284
$630$	−0.0315314	+	1.98347i	−0.00125624	+	0.0790234i
$631$	49.0740			1.95360			0.976802	−	0.214146i	$-0.0686968\pi$
$631$	49.0740			1.95360			0.976802	+	0.214146i	$0.0686968\pi$
$632$	2.52800	+	4.37862i	0.100558	+	0.174172i
$633$	−12.9703	−	13.1781i	−0.515522	−	0.523783i
$634$	0.280750	−	0.486273i	0.0111500	−	0.0193124i
$635$	2.69074	−	4.66049i	0.106779	−	0.184946i
$636$	3.51495	+	3.57127i	0.139377	+	0.141610i
$637$	−8.91624	−	15.4434i	−0.353274	−	0.611889i
$638$		0			0
$639$	28.6431	+	17.1498i	1.13310	+	0.678437i
$640$	−3.16571			−0.125136
$641$	−14.3613	−	24.8746i	−0.567239	−	0.982487i	−0.996837	−	0.0794670i	$-0.974678\pi$
$641$	−14.3613	−	24.8746i	−0.567239	−	0.982487i	0.429598	−	0.903020i	$-0.358655\pi$
$642$	−7.11731	+	1.84658i	−0.280898	+	0.0728786i
$643$	−6.51054	+	11.2766i	−0.256751	+	0.444705i	−0.965370	−	0.260886i	$-0.915985\pi$
$643$	−6.51054	+	11.2766i	−0.256751	+	0.444705i	0.708619	+	0.705591i	$0.249319\pi$
$644$	−17.2961	+	29.9576i	−0.681560	+	1.18050i
$645$	0.00665687	−	0.0240767i	0.000262114	−	0.000948020i
$646$	7.17484	+	12.4272i	0.282290	+	0.488941i
$647$	36.6127			1.43939			0.719696	−	0.694289i	$-0.244281\pi$
$647$	36.6127			1.43939			0.719696	+	0.694289i	$0.244281\pi$
$648$	−10.1977	−	19.0357i	−0.400603	−	0.747795i
$649$		0			0
$650$	6.97305	+	12.0777i	0.273506	+	0.473726i
$651$	3.04030	−	10.9962i	0.119159	−	0.430976i
$652$	−17.9292	+	31.0543i	−0.702162	+	1.21618i
$653$	5.83469	−	10.1060i	0.228329	−	0.395478i	−0.728984	−	0.684531i	$-0.760007\pi$
$653$	5.83469	−	10.1060i	0.228329	−	0.395478i	0.957313	+	0.289053i	$0.0933404\pi$
$654$	−3.51241	+	0.911290i	−0.137346	+	0.0356343i
$655$	0.125717	+	0.217748i	0.00491216	+	0.00850811i
$656$	−9.44080			−0.368601
$657$	−3.23974	−	1.93977i	−0.126394	−	0.0756778i
$658$	3.06843			0.119620
$659$	19.8661	+	34.4091i	0.773873	+	1.34039i	0.935426	+	0.353523i	$0.115016\pi$
$659$	19.8661	+	34.4091i	0.773873	+	1.34039i	−0.161553	+	0.986864i	$0.551650\pi$
$660$		0			0
$661$	−10.7410	+	18.6039i	−0.417775	+	0.723607i	−0.995715	−	0.0924716i	$-0.970523\pi$
$661$	−10.7410	+	18.6039i	−0.417775	+	0.723607i	0.577940	+	0.816079i	$0.303857\pi$
$662$	−2.77320	+	4.80333i	−0.107784	+	0.186687i
$663$	17.7185	+	18.0024i	0.688129	+	0.699156i
$664$	11.2478	+	19.4818i	0.436500	+	0.756040i
$665$	−5.93171			−0.230022
$666$	0.0819658	−	5.15603i	0.00317611	−	0.199792i
$667$	11.1051			0.429990
$668$	−15.0820	−	26.1228i	−0.583541	−	1.01072i
$669$	−4.75700	+	1.23420i	−0.183916	+	0.0477168i
$670$	0.880405	−	1.52491i	0.0340130	−	0.0589123i
$671$		0			0
$672$	8.96019	−	32.4074i	0.345647	−	1.25014i
$673$	10.2554	+	17.7629i	0.395316	+	0.684708i	0.993141	−	0.116919i	$-0.0373017\pi$
$673$	10.2554	+	17.7629i	0.395316	+	0.684708i	−0.597825	+	0.801626i	$0.703968\pi$
$674$	−1.69746			−0.0653836
$675$	−24.5064	−	7.19690i	−0.943254	−	0.277009i
$676$	−6.97745			−0.268364
$677$	−0.591492	−	1.02450i	−0.0227329	−	0.0393745i	0.854435	−	0.519558i	$-0.173903\pi$
$677$	−0.591492	−	1.02450i	−0.0227329	−	0.0393745i	−0.877168	+	0.480184i	$0.840570\pi$
$678$	4.98719	−	18.0378i	0.191532	−	0.692736i
$679$	−1.65003	+	2.85794i	−0.0633225	+	0.109678i
$680$	1.21523	−	2.10484i	0.0466020	−	0.0807170i
$681$	−10.8738	+	2.82120i	−0.416687	+	0.108109i
$682$		0			0
$683$	−6.06013			−0.231884			−0.115942	−	0.993256i	$-0.536989\pi$
$683$	−6.06013			−0.231884			−0.115942	+	0.993256i	$0.536989\pi$
$684$	24.5549	−	13.6611i	0.938882	−	0.522344i
$685$	−3.59951			−0.137530
$686$	3.11605	+	5.39715i	0.118971	+	0.206064i
$687$	−31.1523	−	31.6515i	−1.18853	−	1.20758i
$688$	−0.0360931	+	0.0625151i	−0.00137604	+	0.00238336i
$689$	3.93061	−	6.80801i	0.149744	−	0.259364i
$690$	−1.60197	−	1.62764i	−0.0609861	−	0.0619633i
$691$	−21.4146	−	37.0912i	−0.814650	−	1.41101i	−0.909579	−	0.415531i	$-0.863596\pi$
$691$	−21.4146	−	37.0912i	−0.814650	−	1.41101i	0.0949295	−	0.995484i	$-0.469737\pi$
$692$	−27.5954			−1.04902
$693$		0			0
$694$	−21.3645			−0.810984
$695$	0.0968302	+	0.167715i	0.00367298	+	0.00636179i
$696$	−6.67676	+	1.73228i	−0.253082	+	0.0656618i
$697$	11.2969	−	19.5667i	0.427899	−	0.741143i
$698$	2.96545	−	5.13631i	0.112244	−	0.194412i
$699$	−0.299966	+	1.08492i	−0.0113458	+	0.0410356i
$700$	−12.7065	−	22.0082i	−0.480259	−	0.831833i
$701$	−3.89209			−0.147002			−0.0735011	−	0.997295i	$-0.523417\pi$
$701$	−3.89209			−0.147002			−0.0735011	+	0.997295i	$0.523417\pi$
$702$	−10.6701	+	10.1731i	−0.402718	+	0.383957i
$703$	15.4195			0.581556
$704$		0			0
$705$	0.181121	−	0.655081i	0.00682140	−	0.0246718i
$706$	−0.149041	+	0.258146i	−0.00560922	+	0.00971545i
$707$	6.56273	−	11.3670i	0.246817	−	0.427499i
$708$	−37.6473	+	9.76753i	−1.41487	+	0.367086i
$709$	−11.0746	−	19.1818i	−0.415917	−	0.720389i	0.579608	−	0.814896i	$-0.303206\pi$
$709$	−11.0746	−	19.1818i	−0.415917	−	0.720389i	−0.995524	+	0.0945071i	$0.969873\pi$
$710$	−2.19296			−0.0823004
$711$	−0.100479	+	6.32060i	−0.00376826	+	0.237041i
$712$	20.1894			0.756630
$713$	6.56716	+	11.3746i	0.245942	+	0.425984i
$714$	9.62336	+	9.77756i	0.360145	+	0.365916i
$715$		0			0
$716$	7.27968	−	12.6088i	0.272054	−	0.471212i
$717$	−20.5750	−	20.9047i	−0.768389	−	0.780701i
$718$	−5.67145	−	9.82323i	−0.211657	−	0.366600i
$719$	−37.5592			−1.40072			−0.700362	−	0.713788i	$-0.746978\pi$
$719$	−37.5592			−1.40072			−0.700362	+	0.713788i	$0.746978\pi$
$720$	−1.08940	−	0.652271i	−0.0405996	−	0.0243087i
$721$	51.8837			1.93225
$722$	−6.08383	−	10.5375i	−0.226417	−	0.392165i
$723$	−41.0741	+	10.6566i	−1.52756	+	0.396324i
$724$	8.53568	−	14.7842i	0.317226	−	0.549452i
$725$	−4.07914	+	7.06529i	−0.151496	+	0.262398i
$726$		0			0
$727$	14.2388	+	24.6624i	0.528090	+	0.914678i	0.999464	+	0.0327447i	$0.0104248\pi$
$727$	14.2388	+	24.6624i	0.528090	+	0.914678i	−0.471374	+	0.881933i	$0.656242\pi$
$728$	−33.7088			−1.24933
$729$	1.28707	−	26.9693i	0.0476691	−	0.998863i
$730$	0.248040			0.00918038
$731$	−0.0863780	−	0.149611i	−0.00319481	−	0.00553356i
$732$	−2.74451	+	9.92641i	−0.101440	+	0.366891i
$733$	−7.94821	+	13.7667i	−0.293574	+	0.508485i	−0.974652	−	0.223726i	$-0.928178\pi$
$733$	−7.94821	+	13.7667i	−0.293574	+	0.508485i	0.681078	+	0.732211i	$0.261511\pi$
$734$	4.99739	−	8.65574i	0.184457	−	0.319489i
$735$	−2.07654	+	0.538755i	−0.0765943	+	0.0198723i
$736$	19.3543	+	33.5227i	0.713411	+	1.23566i
$737$		0			0
$738$	11.3138	+	6.77408i	0.416468	+	0.249357i
$739$	36.3058			1.33553			0.667766	−	0.744371i	$-0.267251\pi$
$739$	36.3058			1.33553			0.667766	+	0.744371i	$0.267251\pi$
$740$	−0.568230	−	0.984204i	−0.0208886	−	0.0361801i
$741$	−30.9227	−	31.4182i	−1.13597	−	1.15418i
$742$	2.13481	−	3.69760i	0.0783714	−	0.135743i
$743$	−20.9153	+	36.2264i	−0.767308	+	1.32902i	0.171710	+	0.985148i	$0.445071\pi$
$743$	−20.9153	+	36.2264i	−0.767308	+	1.32902i	−0.939018	+	0.343869i	$0.888262\pi$
$744$	−5.72273	−	5.81443i	−0.209806	−	0.213167i
$745$	1.75251	+	3.03544i	0.0642070	+	0.111210i
$746$	16.0274			0.586805
$747$	−0.447062	+	28.1223i	−0.0163571	+	1.02894i
$748$		0			0
$749$	−10.5102	−	18.2041i	−0.384033	−	0.665165i
$750$	3.27590	−	0.849928i	0.119619	−	0.0310350i
$751$	−8.99786	+	15.5848i	−0.328337	+	0.568696i	−0.982182	−	0.187933i	$-0.939821\pi$
$751$	−8.99786	+	15.5848i	−0.328337	+	0.568696i	0.653845	+	0.756628i	$0.273155\pi$
$752$	−0.982023	+	1.70091i	−0.0358107	+	0.0620260i
$753$	8.24874	−	29.8342i	0.300601	−	1.08722i
$754$	2.35449	+	4.07810i	0.0857456	+	0.148516i
$755$	5.96272			0.217006
$756$	19.4434	−	18.5376i	0.707148	−	0.674205i
$757$	27.2640			0.990928			0.495464	−	0.868628i	$-0.334998\pi$
$757$	27.2640			0.990928			0.495464	+	0.868628i	$0.334998\pi$
$758$	3.88867	+	6.73538i	0.141243	+	0.244640i
$759$		0			0
$760$	−2.12084	+	3.67341i	−0.0769311	+	0.133249i
$761$	0.262219	−	0.454176i	0.00950543	−	0.0164639i	−0.861234	−	0.508209i	$-0.830308\pi$
$761$	0.262219	−	0.454176i	0.00950543	−	0.0164639i	0.870739	+	0.491745i	$0.163641\pi$
$762$	21.0255	−	5.45504i	0.761674	−	0.197615i
$763$	−5.18679	−	8.98379i	−0.187775	−	0.325235i
$764$	6.99075			0.252916
$765$	2.65545	−	1.47735i	0.0960082	−	0.0534139i
$766$	−5.37301			−0.194135
$767$	30.5088	+	52.8428i	1.10161	+	1.90804i
$768$	−11.4164	−	11.5993i	−0.411954	−	0.418555i
$769$	0.597250	−	1.03447i	0.0215374	−	0.0373038i	−0.855056	−	0.518536i	$-0.826477\pi$
$769$	0.597250	−	1.03447i	0.0215374	−	0.0373038i	0.876593	+	0.481232i	$0.159811\pi$
$770$		0			0
$771$	−1.51477	−	1.53904i	−0.0545530	−	0.0554272i
$772$	10.3991	+	18.0117i	0.374270	+	0.648255i
$773$	28.6486			1.03042			0.515209	−	0.857065i	$-0.327714\pi$
$773$	28.6486			1.03042			0.515209	+	0.857065i	$0.327714\pi$
$774$	0.0881106	−	0.0490200i	0.00316707	−	0.00176199i
$775$	−9.64906			−0.346604
$776$	1.17992	+	2.04368i	0.0423566	+	0.0733638i
$777$	14.2693	−	3.70214i	0.511907	−	0.132814i
$778$	−3.06679	+	5.31183i	−0.109950	+	0.190438i
$779$	−19.7155	+	34.1482i	−0.706381	+	1.22349i
$780$	−0.865833	+	3.13156i	−0.0310018	+	0.112128i
$781$		0			0
$782$	−15.7939			−0.564789
$783$	−8.27475	−	2.43008i	−0.295715	−	0.0868439i
$784$	6.19936			0.221406
$785$	1.22937	+	2.12933i	0.0438781	+	0.0759990i
$786$	−0.270453	+	0.978180i	−0.00964675	+	0.0348905i
$787$	−5.75380	+	9.96587i	−0.205101	+	0.355245i	−0.950165	−	0.311748i	$-0.899086\pi$
$787$	−5.75380	+	9.96587i	−0.205101	+	0.355245i	0.745064	+	0.666993i	$0.232419\pi$
$788$	1.31001	−	2.26900i	0.0466671	−	0.0808298i
$789$	28.1336	−	7.29921i	1.00158	−	0.259859i
$790$	−0.207619	−	0.359606i	−0.00738673	−	0.0127942i
$791$	53.5003			1.90225
$792$		0			0
$793$	16.1571			0.573756
$794$	−1.82354	−	3.15847i	−0.0647152	−	0.112090i
$795$	−0.663390	−	0.674020i	−0.0235280	−	0.0239050i
$796$	−7.81493	+	13.5359i	−0.276993	+	0.479766i
$797$	−0.670392	+	1.16115i	−0.0237465	+	0.0411301i	−0.877654	−	0.479294i	$-0.840893\pi$
$797$	−0.670392	+	1.16115i	−0.0237465	+	0.0411301i	0.853908	+	0.520424i	$0.174226\pi$
$798$	−16.7949	−	17.0640i	−0.594533	−	0.604059i
$799$	−2.35018	−	4.07063i	−0.0831433	−	0.144008i
$800$	−28.4371			−1.00540
$801$	21.6572	+	12.9671i	0.765218	+	0.458169i
$802$	−10.6179			−0.374932
$803$		0			0
$804$	−23.0813	+	5.98840i	−0.814013	+	0.211195i
$805$	3.26435	−	5.65403i	0.115053	−	0.199278i
$806$	−2.78473	+	4.82329i	−0.0980879	+	0.169893i
$807$	10.1408	−	36.6776i	0.356975	−	1.29111i
$808$	−4.69292	−	8.12838i	−0.165096	−	0.285955i
$809$	−29.7375			−1.04551			−0.522757	−	0.852482i	$-0.675096\pi$
$809$	−29.7375			−1.04551			−0.522757	+	0.852482i	$0.675096\pi$
$810$	0.837511	+	1.56336i	0.0294272	+	0.0549309i
$811$	28.5904			1.00395			0.501973	−	0.864883i	$-0.332608\pi$
$811$	28.5904			1.00395			0.501973	+	0.864883i	$0.332608\pi$
$812$	−4.29041	−	7.43121i	−0.150564	−	0.260784i
$813$	4.66570	−	16.8750i	0.163633	−	0.591832i
$814$		0			0
$815$	3.38385	−	5.86101i	0.118531	−	0.205302i
$816$	−8.49983	+	2.20527i	−0.297554	+	0.0771999i
$817$	0.150749	+	0.261104i	0.00527403	+	0.00913488i
$818$	−15.4111			−0.538835
$819$	−36.1594	−	21.6502i	−1.26351	−	0.756519i
$820$	2.90619			0.101488
$821$	7.76988	+	13.4578i	0.271171	+	0.469681i	0.969162	−	0.246425i	$-0.0792559\pi$
$821$	7.76988	+	13.4578i	0.271171	+	0.469681i	−0.697991	+	0.716106i	$0.745923\pi$
$822$	−10.1915	−	10.3548i	−0.355471	−	0.361167i
$823$	20.2888	−	35.1413i	0.707225	−	1.22495i	−0.258658	−	0.965969i	$-0.583280\pi$
$823$	20.2888	−	35.1413i	0.707225	−	1.22495i	0.965883	−	0.258980i	$-0.0833865\pi$
$824$	18.5507	−	32.1307i	0.646244	−	1.11933i
$825$		0			0
$826$	16.5701	+	28.7003i	0.576548	+	0.998610i
$827$	−2.54353			−0.0884472			−0.0442236	−	0.999022i	$-0.514081\pi$
$827$	−2.54353			−0.0884472			−0.0442236	+	0.999022i	$0.514081\pi$
$828$	−0.491592	+	30.9234i	−0.0170840	+	1.07466i
$829$	−14.3710			−0.499127			−0.249564	−	0.968358i	$-0.580287\pi$
$829$	−14.3710			−0.499127			−0.249564	+	0.968358i	$0.580287\pi$
$830$	−0.923757	−	1.59999i	−0.0320641	−	0.0555366i
$831$	−13.0319	+	3.38112i	−0.452073	+	0.117290i
$832$	−2.11329	+	3.66032i	−0.0732651	+	0.126899i
$833$	−7.41816	+	12.8486i	−0.257024	+	0.445178i
$834$	−0.208310	+	0.753419i	−0.00721318	+	0.0260888i
$835$	2.84649	+	4.93027i	0.0985069	+	0.170619i
$836$		0			0
$837$	−2.40433	−	9.91268i	−0.0831059	−	0.342632i
$838$	−26.4469			−0.913593
$839$	−18.7905	−	32.5461i	−0.648721	−	1.12362i	−0.983429	−	0.181296i	$-0.941971\pi$
$839$	−18.7905	−	32.5461i	−0.648721	−	1.12362i	0.334708	−	0.942322i	$-0.391362\pi$
$840$	−1.08067	+	3.90861i	−0.0372868	+	0.134860i
$841$	13.1227	−	22.7291i	0.452505	−	0.783762i
$842$	−8.19557	+	14.1951i	−0.282438	+	0.489197i
$843$	54.1362	−	14.0456i	1.86455	−	0.483755i
$844$	−8.22412	−	14.2446i	−0.283086	−	0.490319i
$845$	1.31688			0.0453022
$846$	2.39732	−	1.33374i	0.0824215	−	0.0458549i
$847$		0			0
$848$	1.36645	+	2.36677i	0.0469242	+	0.0812751i
$849$	−15.2152	−	15.4590i	−0.522183	−	0.530550i
$850$	5.80146	−	10.0484i	0.198988	−	0.344658i
$851$	−8.48567	+	14.6976i	−0.290885	+	0.503828i
$852$	20.8319	+	21.1657i	0.713690	+	0.725126i
$853$	−17.5579	−	30.4111i	−0.601170	−	1.04126i	−0.992644	−	0.121068i	$-0.961368\pi$
$853$	−17.5579	−	30.4111i	−0.601170	−	1.04126i	0.391474	−	0.920189i	$-0.371965\pi$
$854$	8.77534			0.300286
$855$	−4.63435	+	2.57831i	−0.158492	+	0.0881763i
$856$	−15.0314			−0.513762
$857$	−14.5051	−	25.1236i	−0.495486	−	0.858206i	0.504501	−	0.863411i	$-0.331677\pi$
$857$	−14.5051	−	25.1236i	−0.495486	−	0.858206i	−0.999986	+	0.00520496i	$0.998343\pi$
$858$		0			0
$859$	1.95891	−	3.39292i	0.0668370	−	0.115765i	−0.830670	−	0.556764i	$-0.812043\pi$
$859$	1.95891	−	3.39292i	0.0668370	−	0.115765i	0.897507	+	0.440999i	$0.145376\pi$
$860$	0.0111106	−	0.0192442i	0.000378869	−	0.000656221i
$861$	−10.0460	+	36.3346i	−0.342367	+	1.23828i
$862$	4.14919	+	7.18661i	0.141322	+	0.244777i
$863$	−15.5259			−0.528507			−0.264253	−	0.964453i	$-0.585126\pi$
$863$	−15.5259			−0.528507			−0.264253	+	0.964453i	$0.585126\pi$
$864$	−7.08591	−	29.2141i	−0.241067	−	0.993883i
$865$	5.20819			0.177084
$866$	2.41651	+	4.18551i	0.0821163	+	0.142230i
$867$	−2.24638	+	8.12475i	−0.0762910	+	0.275931i
$868$	5.07440	−	8.78912i	0.172236	−	0.298322i
$869$		0			0
$870$	0.548347	−	0.142268i	0.0185907	−	0.00482333i
$871$	18.7047	+	32.3975i	0.633786	+	1.09775i
$872$	−7.41801			−0.251206
$873$	−0.0468976	+	2.95008i	−0.00158724	+	0.0998451i
$874$	27.5639			0.932361
$875$	4.83754	+	8.37886i	0.163539	+	0.283257i
$876$	−2.35625	−	2.39400i	−0.0796102	−	0.0808858i
$877$	17.0122	−	29.4659i	0.574460	−	0.994994i	−0.421640	−	0.906763i	$-0.638545\pi$
$877$	17.0122	−	29.4659i	0.574460	−	0.994994i	0.996100	−	0.0882306i	$-0.0281212\pi$
$878$	6.50372	−	11.2648i	0.219490	−	0.380168i
$879$	−22.3365	−	22.6944i	−0.753392	−	0.765464i
$880$		0			0
$881$	−24.8513			−0.837261			−0.418630	−	0.908157i	$-0.637490\pi$
$881$	−24.8513			−0.837261			−0.418630	+	0.908157i	$0.637490\pi$
$882$	−7.42931	−	4.44825i	−0.250158	−	0.149780i
$883$	23.5034			0.790952			0.395476	−	0.918476i	$-0.370580\pi$
$883$	23.5034			0.790952			0.395476	+	0.918476i	$0.370580\pi$
$884$	11.2348	+	19.4593i	0.377869	+	0.654488i
$885$	7.10532	−	1.84347i	0.238843	−	0.0619674i
$886$	3.26994	−	5.66370i	0.109856	−	0.190276i
$887$	−18.9872	+	32.8867i	−0.637527	+	1.10423i	0.348447	+	0.937328i	$0.386709\pi$
$887$	−18.9872	+	32.8867i	−0.637527	+	1.10423i	−0.985974	+	0.166900i	$0.946624\pi$
$888$	2.80921	−	10.1604i	0.0942708	−	0.340961i
$889$	31.0485	+	53.7775i	1.04133	+	1.80364i
$890$	−1.65811			−0.0555800
$891$		0			0
$892$	−4.37175			−0.146377
$893$	4.10158	+	7.10414i	0.137254	+	0.237731i
$894$	−3.77016	+	13.6360i	−0.126093	+	0.456055i
$895$	−1.37392	+	2.37971i	−0.0459252	+	0.0795448i
$896$	18.2646	−	31.6353i	0.610178	−	1.05686i
$897$	46.9648	−	12.1850i	1.56811	−	0.406844i
$898$	5.21189	+	9.02725i	0.173923	+	0.301243i
$899$	−3.25806			−0.108662
$900$	−19.4936	−	11.6716i	−0.649785	−	0.389054i
$901$	−6.54039			−0.217892
$902$		0			0
$903$	0.202194	+	0.205434i	0.00672859	+	0.00683640i
$904$	19.1287	−	33.1318i	0.636210	−	1.10195i
$905$	−1.61097	+	2.79029i	−0.0535506	+	0.0927523i
$906$	16.8827	+	17.1532i	0.560890	+	0.569877i
$907$	9.17576	+	15.8929i	0.304676	+	0.527715i	0.977189	−	0.212371i	$-0.0681184\pi$
$907$	9.17576	+	15.8929i	0.304676	+	0.527715i	−0.672513	+	0.740085i	$0.734785\pi$
$908$	−9.99321			−0.331636
$909$	0.186527	−	11.7334i	0.00618672	−	0.389173i
$910$	2.76843			0.0917725
$911$	−1.05480	−	1.82697i	−0.0349472	−	0.0605303i	0.848023	−	0.529960i	$-0.177793\pi$
$911$	−1.05480	−	1.82697i	−0.0349472	−	0.0605303i	−0.882970	+	0.469429i	$0.844460\pi$
$912$	14.8341	−	3.84868i	0.491206	−	0.127443i
$913$		0			0
$914$	6.47097	−	11.2081i	0.214041	−	0.370730i
$915$	0.517983	−	1.87345i	0.0171240	−	0.0619344i
$916$	−19.7529	−	34.2130i	−0.652653	−	1.13043i
$917$	−2.90130			−0.0958093
$918$	11.7685	+	3.45612i	0.388420	+	0.114069i
$919$	11.0435			0.364290			0.182145	−	0.983272i	$-0.441696\pi$
$919$	11.0435			0.364290			0.182145	+	0.983272i	$0.441696\pi$
$920$	−2.33430	−	4.04312i	−0.0769595	−	0.133298i
$921$	3.88822	−	14.0630i	0.128121	−	0.463391i
$922$	−2.83666	+	4.91323i	−0.0934203	+	0.161809i
$923$	23.2954	−	40.3488i	0.766777	−	1.32810i
$924$		0			0
$925$	−6.23395	−	10.7975i	−0.204971	−	0.355020i
$926$	19.1506			0.629327
$927$	40.5359	−	22.5520i	1.33137	−	0.740706i
$928$	−9.60197			−0.315200
$929$	−7.77092	−	13.4596i	−0.254956	−	0.441596i	0.709928	−	0.704275i	$-0.248728\pi$
$929$	−7.77092	−	13.4596i	−0.254956	−	0.441596i	−0.964884	+	0.262678i	$0.915394\pi$
$930$	0.469995	+	0.477526i	0.0154117	+	0.0156587i
$931$	12.9463	−	22.4237i	0.424298	−	0.734906i
$932$	−0.500658	+	0.867165i	−0.0163996	+	0.0284049i
$933$	13.7333	+	13.9533i	0.449607	+	0.456811i
$934$	2.78660	+	4.82653i	0.0911803	+	0.157929i
$935$		0			0
$936$	−26.3362	+	14.6520i	−0.860825	+	0.478917i
$937$	22.4663			0.733941			0.366971	−	0.930232i	$-0.380395\pi$
$937$	22.4663			0.733941			0.366971	+	0.930232i	$0.380395\pi$
$938$	10.1590	+	17.5959i	0.331704	+	0.574527i
$939$	−10.2448	+	2.65799i	−0.334325	+	0.0867401i
$940$	0.302299	−	0.523597i	0.00985990	−	0.0170778i
$941$	2.60544	−	4.51276i	0.0849350	−	0.147112i	−0.820429	−	0.571749i	$-0.806265\pi$
$941$	2.60544	−	4.51276i	0.0849350	−	0.147112i	0.905364	+	0.424637i	$0.139598\pi$
$942$	−2.64473	+	9.56550i	−0.0861699	+	0.311661i
$943$	−21.6998	−	37.5851i	−0.706642	−	1.22394i
$944$	−21.2124			−0.690406
$945$	−3.66962	+	3.49867i	−0.119373	+	0.113812i
$946$		0			0
$947$	8.81080	+	15.2608i	0.286312	+	0.495908i	0.972927	−	0.231114i	$-0.0742371\pi$
$947$	8.81080	+	15.2608i	0.286312	+	0.495908i	−0.686614	+	0.727022i	$0.740904\pi$
$948$	−1.49853	+	5.41992i	−0.0486701	+	0.176031i
$949$	−2.63488	+	4.56375i	−0.0855319	+	0.148146i
$950$	−10.1248	+	17.5367i	−0.328493	+	0.568966i
$951$	1.38914	−	0.360411i	0.0450460	−	0.0116871i
$952$	14.0226	+	24.2878i	0.454474	+	0.787172i
$953$	−46.6714			−1.51183			−0.755917	−	0.654667i	$-0.772809\pi$
$953$	−46.6714			−1.51183			−0.755917	+	0.654667i	$0.772809\pi$
$954$	0.0606761	−	3.81681i	0.00196446	−	0.123574i
$955$	−1.31939			−0.0426945
$956$	−13.0461	−	22.5965i	−0.421941	−	0.730823i
$957$		0			0
$958$	10.3081	−	17.8541i	0.333039	−	0.576840i
$959$	20.7674	−	35.9702i	0.670614	−	1.16154i
$960$	0.356672	+	0.362387i	0.0115115	+	0.0116960i
$961$	13.5733	+	23.5096i	0.437848	+	0.758375i
$962$	−7.19651			−0.232025
$963$	−16.1241	−	9.65421i	−0.519593	−	0.311103i
$964$	−37.7476			−1.21577
$965$	−1.96266	−	3.39942i	−0.0631801	−	0.109431i
$966$	25.5078	−	6.61796i	0.820699	−	0.212929i
$967$	0.286105	−	0.495548i	0.00920051	−	0.0159357i	−0.861388	−	0.507947i	$-0.830405\pi$
$967$	0.286105	−	0.495548i	0.00920051	−	0.0159357i	0.870589	+	0.492011i	$0.163738\pi$
$968$		0			0
$969$	−9.77379	+	35.3500i	−0.313979	+	1.13561i
$970$	−0.0969039	−	0.167843i	−0.00311140	−	0.00538910i
$971$	37.1703			1.19285			0.596426	−	0.802668i	$-0.296587\pi$
$971$	37.1703			1.19285			0.596426	+	0.802668i	$0.296587\pi$
$972$	7.13315	−	22.9345i	0.228796	−	0.735623i
$973$	−2.23465			−0.0716397
$974$	7.55238	+	13.0811i	0.241994	+	0.419146i
$975$	−9.49890	+	34.3558i	−0.304208	+	1.10027i
$976$	−2.80847	+	4.86441i	−0.0898968	+	0.155706i
$977$	8.02404	−	13.8980i	0.256712	−	0.444638i	−0.708647	−	0.705563i	$-0.750694\pi$
$977$	8.02404	−	13.8980i	0.256712	−	0.444638i	0.965359	+	0.260925i	$0.0840275\pi$
$978$	26.4416	−	6.86022i	0.845508	−	0.219366i
$979$		0			0
$980$	−1.90837			−0.0609605
$981$	−7.95730	−	4.76438i	−0.254057	−	0.152115i
$982$	−21.9333			−0.699920
$983$	−22.9464	−	39.7443i	−0.731877	−	1.26765i	−0.956080	−	0.293105i	$-0.905311\pi$
$983$	−22.9464	−	39.7443i	−0.731877	−	1.26765i	0.224203	−	0.974542i	$-0.428022\pi$
$984$	18.9095	+	19.2125i	0.602814	+	0.612473i
$985$	−0.247243	+	0.428238i	−0.00787782	+	0.0136448i
$986$	1.95890	−	3.39291i	0.0623840	−	0.108052i
$987$	5.50130	+	5.58945i	0.175108	+	0.177914i
$988$	−19.6073	−	33.9608i	−0.623791	−	1.08044i
$989$	−0.331841			−0.0105519
$990$		0			0
$991$	−28.3187			−0.899573			−0.449786	−	0.893136i	$-0.648500\pi$
$991$	−28.3187			−0.899573			−0.449786	+	0.893136i	$0.648500\pi$
$992$	−5.67827	−	9.83505i	−0.180285	−	0.312263i
$993$	−13.7217	+	3.56008i	−0.435446	+	0.112976i
$994$	12.6523	−	21.9145i	0.401307	−	0.695084i
$995$	1.47494	−	2.55468i	0.0467589	−	0.0809887i
$996$	−6.66743	+	24.1149i	−0.211265	+	0.764109i
$997$	17.5735	+	30.4382i	0.556558	+	0.963987i	0.997780	+	0.0665894i	$0.0212117\pi$
$997$	17.5735	+	30.4382i	0.556558	+	0.963987i	−0.441222	+	0.897398i	$0.645455\pi$
$998$	0.177396			0.00561538
$999$	9.53916	−	9.09478i	0.301806	−	0.287746i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1089.2.e.p.364.7		36
9.4	even	3		9801.2.a.cm.1.12		18
9.5	odd	6		9801.2.a.cp.1.7		18
9.7	even	3	inner	1089.2.e.p.727.7		36
11.3	even	5		99.2.m.b.31.4	yes	72
11.4	even	5		99.2.m.b.49.6	yes	72
11.10	odd	2		1089.2.e.o.364.12		36
33.14	odd	10		297.2.n.b.64.6		72
33.26	odd	10		297.2.n.b.280.4		72
99.4	even	15		891.2.f.f.82.6		36
99.14	odd	30		891.2.f.e.163.4		36
99.25	even	15		99.2.m.b.97.6	yes	72
99.32	even	6		9801.2.a.cn.1.12		18
99.43	odd	6		1089.2.e.o.727.12		36
99.47	odd	30		297.2.n.b.262.4		72
99.58	even	15		891.2.f.f.163.6		36
99.59	odd	30		891.2.f.e.82.4		36
99.70	even	15		99.2.m.b.16.4	✓	72
99.76	odd	6		9801.2.a.co.1.7		18
99.92	odd	30		297.2.n.b.181.6		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.16.4	✓	72	99.70	even	15
99.2.m.b.31.4	yes	72	11.3	even	5
99.2.m.b.49.6	yes	72	11.4	even	5
99.2.m.b.97.6	yes	72	99.25	even	15
297.2.n.b.64.6		72	33.14	odd	10
297.2.n.b.181.6		72	99.92	odd	30
297.2.n.b.262.4		72	99.47	odd	30
297.2.n.b.280.4		72	33.26	odd	10
891.2.f.e.82.4		36	99.59	odd	30
891.2.f.e.163.4		36	99.14	odd	30
891.2.f.f.82.6		36	99.4	even	15
891.2.f.f.163.6		36	99.58	even	15
1089.2.e.o.364.12		36	11.10	odd	2
1089.2.e.o.727.12		36	99.43	odd	6
1089.2.e.p.364.7		36	1.1	even	1	trivial
1089.2.e.p.727.7		36	9.7	even	3	inner
9801.2.a.cm.1.12		18	9.4	even	3
9801.2.a.cn.1.12		18	99.32	even	6
9801.2.a.co.1.7		18	99.76	odd	6
9801.2.a.cp.1.7		18	9.5	odd	6

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:	\( N \)	\(=\)	\( 1089 = 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1089.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.338834 - 0.586878i) q^{2} +(0.461570 - 1.66942i) q^{3} +(0.770383 - 1.33434i) q^{4} +(-0.145397 + 0.251836i) q^{5} +(-1.13614 + 0.294770i) q^{6} +(-1.67774 - 2.90594i) q^{7} -2.39947 q^{8} +(-2.57391 - 1.54111i) q^{9} +O(q^{10})\)	\(q+(-0.338834 - 0.586878i) q^{2} +(0.461570 - 1.66942i) q^{3} +(0.770383 - 1.33434i) q^{4} +(-0.145397 + 0.251836i) q^{5} +(-1.13614 + 0.294770i) q^{6} +(-1.67774 - 2.90594i) q^{7} -2.39947 q^{8} +(-2.57391 - 1.54111i) q^{9} +0.197063 q^{10} +(-1.87199 - 1.90198i) q^{12} +(-2.09336 + 3.62580i) q^{13} +(-1.13695 + 1.96926i) q^{14} +(0.353308 + 0.358969i) q^{15} +(-0.727744 - 1.26049i) q^{16} +3.48327 q^{17} +(-0.0323148 + 2.03275i) q^{18} -6.07908 q^{19} +(0.224023 + 0.388020i) q^{20} +(-5.62562 + 1.45956i) q^{21} +(3.34545 - 5.79449i) q^{23} +(-1.10752 + 4.00571i) q^{24} +(2.45772 + 4.25689i) q^{25} +2.83720 q^{26} +(-3.76079 + 3.58559i) q^{27} -5.17002 q^{28} +(0.829864 + 1.43737i) q^{29} +(0.0909583 - 0.328980i) q^{30} +(-0.981505 + 1.70002i) q^{31} +(-2.89263 + 5.01019i) q^{32} +(-1.18025 - 2.04426i) q^{34} +0.975759 q^{35} +(-4.03926 + 2.24723i) q^{36} -2.53648 q^{37} +(2.05980 + 3.56768i) q^{38} +(5.08674 + 5.16825i) q^{39} +(0.348876 - 0.604271i) q^{40} +(3.24317 - 5.61734i) q^{41} +(2.76274 + 2.80701i) q^{42} +(-0.0247979 - 0.0429513i) q^{43} +(0.762345 - 0.424128i) q^{45} -4.53422 q^{46} +(-0.674704 - 1.16862i) q^{47} +(-2.44019 + 0.633103i) q^{48} +(-2.12965 + 3.68867i) q^{49} +(1.66552 - 2.88476i) q^{50} +(1.60778 - 5.81503i) q^{51} +(3.22537 + 5.58651i) q^{52} -1.87766 q^{53} +(3.37859 + 0.992204i) q^{54} +(4.02569 + 6.97270i) q^{56} +(-2.80592 + 10.1485i) q^{57} +(0.562373 - 0.974058i) q^{58} +(7.28706 - 12.6216i) q^{59} +(0.751169 - 0.194890i) q^{60} +(-1.92957 - 3.34212i) q^{61} +1.33027 q^{62} +(-0.160007 + 10.0652i) q^{63} +1.00952 q^{64} +(-0.608737 - 1.05436i) q^{65} +(4.46764 - 7.73818i) q^{67} +(2.68345 - 4.64788i) q^{68} +(-8.12926 - 8.25952i) q^{69} +(-0.330621 - 0.572652i) q^{70} -11.1283 q^{71} +(6.17600 + 3.69783i) q^{72} +1.25869 q^{73} +(0.859446 + 1.48860i) q^{74} +(8.24094 - 2.13810i) q^{75} +(-4.68321 + 8.11157i) q^{76} +(1.30957 - 4.73648i) q^{78} +(-1.05357 - 1.82483i) q^{79} +0.423248 q^{80} +(4.24998 + 7.93333i) q^{81} -4.39559 q^{82} +(-4.68763 - 8.11922i) q^{83} +(-2.38633 + 8.63092i) q^{84} +(-0.506459 + 0.877212i) q^{85} +(-0.0168048 + 0.0291068i) q^{86} +(2.78260 - 0.721943i) q^{87} -8.41413 q^{89} +(-0.507220 - 0.303694i) q^{90} +14.0485 q^{91} +(-5.15456 - 8.92795i) q^{92} +(2.38500 + 2.42322i) q^{93} +(-0.457226 + 0.791938i) q^{94} +(0.883882 - 1.53093i) q^{95} +(7.02894 + 7.14157i) q^{96} +(-0.491742 - 0.851722i) q^{97} +2.88640 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} + 9 q^{3} - 12 q^{4} + q^{5} - q^{6} - q^{7} - 12 q^{8} - q^{9}+O(q^{10}) \) 36 * q + 2 * q^2 + 9 * q^3 - 12 * q^4 + q^5 - q^6 - q^7 - 12 * q^8 - q^9	\( 36 q + 2 q^{2} + 9 q^{3} - 12 q^{4} + q^{5} - q^{6} - q^{7} - 12 q^{8} - q^{9} - 4 q^{10} - 8 q^{12} - 3 q^{13} - 5 q^{15} + 8 q^{16} - 40 q^{17} + 17 q^{18} - 6 q^{19} + 5 q^{20} - 8 q^{21} + 10 q^{23} - 57 q^{24} - 7 q^{25} + 4 q^{26} - 9 q^{27} + 38 q^{28} + 21 q^{29} + 12 q^{30} - 6 q^{31} + 9 q^{32} + 4 q^{34} - 76 q^{35} - 65 q^{36} + 14 q^{37} - 13 q^{38} + 42 q^{39} + 20 q^{41} + 18 q^{42} - 4 q^{43} + 20 q^{45} + 16 q^{46} - 7 q^{47} + 10 q^{48} - 7 q^{49} + 25 q^{50} - 4 q^{51} + 19 q^{52} + 62 q^{53} + 17 q^{54} + 57 q^{56} - 18 q^{57} - 12 q^{58} + 12 q^{59} + 11 q^{60} + 16 q^{61} - 38 q^{62} + 5 q^{63} - 32 q^{64} + 42 q^{65} + 5 q^{67} + 51 q^{68} + 31 q^{69} - 8 q^{70} + 26 q^{71} + 51 q^{72} + 9 q^{74} - 16 q^{75} + 8 q^{76} - 32 q^{78} + 2 q^{79} + 92 q^{80} + 47 q^{81} - 68 q^{82} + 36 q^{83} + 60 q^{84} - 25 q^{85} - 26 q^{86} - 60 q^{87} - 28 q^{89} + 163 q^{90} - 30 q^{91} + 15 q^{92} - 39 q^{93} - 4 q^{94} + 64 q^{95} - 21 q^{96} + 16 q^{97} - 164 q^{98}+O(q^{100}) \) 36 * q + 2 * q^2 + 9 * q^3 - 12 * q^4 + q^5 - q^6 - q^7 - 12 * q^8 - q^9 - 4 * q^10 - 8 * q^12 - 3 * q^13 - 5 * q^15 + 8 * q^16 - 40 * q^17 + 17 * q^18 - 6 * q^19 + 5 * q^20 - 8 * q^21 + 10 * q^23 - 57 * q^24 - 7 * q^25 + 4 * q^26 - 9 * q^27 + 38 * q^28 + 21 * q^29 + 12 * q^30 - 6 * q^31 + 9 * q^32 + 4 * q^34 - 76 * q^35 - 65 * q^36 + 14 * q^37 - 13 * q^38 + 42 * q^39 + 20 * q^41 + 18 * q^42 - 4 * q^43 + 20 * q^45 + 16 * q^46 - 7 * q^47 + 10 * q^48 - 7 * q^49 + 25 * q^50 - 4 * q^51 + 19 * q^52 + 62 * q^53 + 17 * q^54 + 57 * q^56 - 18 * q^57 - 12 * q^58 + 12 * q^59 + 11 * q^60 + 16 * q^61 - 38 * q^62 + 5 * q^63 - 32 * q^64 + 42 * q^65 + 5 * q^67 + 51 * q^68 + 31 * q^69 - 8 * q^70 + 26 * q^71 + 51 * q^72 + 9 * q^74 - 16 * q^75 + 8 * q^76 - 32 * q^78 + 2 * q^79 + 92 * q^80 + 47 * q^81 - 68 * q^82 + 36 * q^83 + 60 * q^84 - 25 * q^85 - 26 * q^86 - 60 * q^87 - 28 * q^89 + 163 * q^90 - 30 * q^91 + 15 * q^92 - 39 * q^93 - 4 * q^94 + 64 * q^95 - 21 * q^96 + 16 * q^97 - 164 * q^98

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