LMFDB - Embedded newform 324.2.p.a.11.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(11,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([27, 13]))

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

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

chi := DirichletCharacter("324.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.p (of order $54$, degree $18$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$936$
Relative dimension:	$52$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			11.12
Character	$\chi$	$=$	324.11
Dual form			324.2.p.a.59.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09593 - 0.893834i) q^{2} +(0.138112 + 1.72654i) q^{3} +(0.402121 + 1.95916i) q^{4} +(-0.283509 + 2.42558i) q^{5} +(1.39188 - 2.01561i) q^{6} +(1.43973 + 2.86675i) q^{7} +(1.31047 - 2.50653i) q^{8} +(-2.96185 + 0.476909i) q^{9} +O(q^{10})$	\(q+(-1.09593 - 0.893834i) q^{2} +(0.138112 + 1.72654i) q^{3} +(0.402121 + 1.95916i) q^{4} +(-0.283509 + 2.42558i) q^{5} +(1.39188 - 2.01561i) q^{6} +(1.43973 + 2.86675i) q^{7} +(1.31047 - 2.50653i) q^{8} +(-2.96185 + 0.476909i) q^{9} +(2.47877 - 2.40485i) q^{10} +(1.56735 - 3.63353i) q^{11} +(-3.32702 + 0.964859i) q^{12} +(-6.41164 + 1.51959i) q^{13} +(0.984550 - 4.42864i) q^{14} +(-4.22700 - 0.154489i) q^{15} +(-3.67660 + 1.57564i) q^{16} +(-0.0431938 + 0.00761624i) q^{17} +(3.67226 + 2.12474i) q^{18} +(4.50470 + 0.794300i) q^{19} +(-4.86609 + 0.419936i) q^{20} +(-4.75070 + 2.88168i) q^{21} +(-4.96547 + 2.58114i) q^{22} +(-4.61035 - 2.31541i) q^{23} +(4.50860 + 1.91639i) q^{24} +(-0.937818 - 0.222267i) q^{25} +(8.38496 + 4.06558i) q^{26} +(-1.23247 - 5.04787i) q^{27} +(-5.03746 + 3.97345i) q^{28} +(-1.18331 + 0.354259i) q^{29} +(4.49440 + 3.94755i) q^{30} +(3.24150 + 4.92846i) q^{31} +(5.43765 + 1.55948i) q^{32} +(6.48988 + 2.20425i) q^{33} +(0.0541450 + 0.0302613i) q^{34} +(-7.36169 + 2.67944i) q^{35} +(-2.12536 - 5.61096i) q^{36} +(4.55219 + 1.65686i) q^{37} +(-4.22686 - 4.89695i) q^{38} +(-3.50914 - 10.8601i) q^{39} +(5.70824 + 3.88926i) q^{40} +(-0.981017 + 0.925542i) q^{41} +(7.78217 + 1.08821i) q^{42} +(-1.26027 + 0.938234i) q^{43} +(7.74891 + 1.60957i) q^{44} +(-0.317068 - 7.31940i) q^{45} +(2.98303 + 6.65841i) q^{46} +(5.76986 + 3.79489i) q^{47} +(-3.22817 - 6.13016i) q^{48} +(-1.96529 + 2.63985i) q^{49} +(0.829112 + 1.08184i) q^{50} +(-0.0191153 - 0.0735238i) q^{51} +(-5.55536 - 11.9504i) q^{52} +(-8.53190 + 4.92589i) q^{53} +(-3.16127 + 6.63373i) q^{54} +(8.36904 + 4.83187i) q^{55} +(9.07230 + 0.148041i) q^{56} +(-0.749236 + 7.88723i) q^{57} +(1.61347 + 0.669439i) q^{58} +(4.33789 + 10.0564i) q^{59} +(-1.39710 - 8.34348i) q^{60} +(-0.185066 + 3.17746i) q^{61} +(0.852772 - 8.29860i) q^{62} +(-5.63146 - 7.80425i) q^{63} +(-4.56536 - 6.56944i) q^{64} +(-1.86811 - 15.9827i) q^{65} +(-5.14221 - 8.21658i) q^{66} +(-1.14811 - 0.343723i) q^{67} +(-0.0322905 - 0.0815609i) q^{68} +(3.36089 - 8.27972i) q^{69} +(10.4629 + 3.64366i) q^{70} +(11.5777 - 9.71483i) q^{71} +(-2.68602 + 8.04893i) q^{72} +(-6.54463 - 5.49160i) q^{73} +(-3.50792 - 5.88471i) q^{74} +(0.254228 - 1.64987i) q^{75} +(0.255275 + 9.14482i) q^{76} +(12.6730 - 0.738116i) q^{77} +(-5.86131 + 15.0384i) q^{78} +(-1.32576 - 1.25079i) q^{79} +(-2.77948 - 9.36457i) q^{80} +(8.54512 - 2.82507i) q^{81} +(1.90241 - 0.137462i) q^{82} +(-5.72637 + 6.06959i) q^{83} +(-7.55603 - 8.14858i) q^{84} +(-0.00622792 - 0.106929i) q^{85} +(2.21979 + 0.0982318i) q^{86} +(-0.775070 - 1.99410i) q^{87} +(-7.05357 - 8.69022i) q^{88} +(1.91594 - 2.28333i) q^{89} +(-6.19485 + 8.30495i) q^{90} +(-13.5873 - 16.1927i) q^{91} +(2.68233 - 9.96348i) q^{92} +(-8.06147 + 6.27724i) q^{93} +(-2.93135 - 9.31623i) q^{94} +(-3.20376 + 10.7013i) q^{95} +(-1.94150 + 9.60368i) q^{96} +(17.9553 - 2.09867i) q^{97} +(4.51341 - 1.13644i) q^{98} +(-2.90939 + 11.5094i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{13}{54}\right)$

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 $

$2$	−1.09593	−	0.893834i	−0.774939	−	0.632036i
$2$	−1.09593	−	0.893834i	−0.774939	−	0.632036i
$3$	0.138112	+	1.72654i	0.0797388	+	0.996816i
$3$	0.138112	+	1.72654i	0.0797388	+	0.996816i
$4$	0.402121	+	1.95916i	0.201061	+	0.979579i
$5$	−0.283509	+	2.42558i	−0.126789	+	1.08475i	0.768682	+	0.639631i	$0.220913\pi$
$5$	−0.283509	+	2.42558i	−0.126789	+	1.08475i	−0.895471	+	0.445120i	$0.853161\pi$
$6$	1.39188	−	2.01561i	0.568231	−	0.822869i
$7$	1.43973	+	2.86675i	0.544168	+	1.08353i	0.982768	+	0.184846i	$0.0591785\pi$
$7$	1.43973	+	2.86675i	0.544168	+	1.08353i	−0.438599	+	0.898683i	$0.644525\pi$
$8$	1.31047	−	2.50653i	0.463320	−	0.886191i
$9$	−2.96185	+	0.476909i	−0.987283	+	0.158970i
$10$	2.47877	−	2.40485i	0.783856	−	0.760480i
$11$	1.56735	−	3.63353i	0.472574	−	1.09555i	−0.500642	−	0.865655i	$-0.666903\pi$
$11$	1.56735	−	3.63353i	0.472574	−	1.09555i	0.973216	−	0.229895i	$-0.0738382\pi$
$12$	−3.32702	+	0.964859i	−0.960427	+	0.278531i
$13$	−6.41164	+	1.51959i	−1.77827	+	0.421457i	−0.982820	−	0.184564i	$-0.940913\pi$
$13$	−6.41164	+	1.51959i	−1.77827	+	0.421457i	−0.795448	+	0.606022i	$0.792764\pi$
$14$	0.984550	−	4.42864i	0.263132	−	1.18360i
$15$	−4.22700	−	0.154489i	−1.09141	−	0.0398888i
$16$	−3.67660	+	1.57564i	−0.919149	+	0.393909i
$17$	−0.0431938	+	0.00761624i	−0.0104760	+	0.00184721i	−0.178884	−	0.983870i	$-0.557249\pi$
$17$	−0.0431938	+	0.00761624i	−0.0104760	+	0.00184721i	0.168408	+	0.985717i	$0.446137\pi$
$18$	3.67226	+	2.12474i	0.865559	+	0.500807i
$19$	4.50470	+	0.794300i	1.03345	+	0.182225i	0.664549	−	0.747244i	$-0.268624\pi$
$19$	4.50470	+	0.794300i	1.03345	+	0.182225i	0.368899	+	0.929469i	$0.379735\pi$
$20$	−4.86609	+	0.419936i	−1.08809	+	0.0939005i
$21$	−4.75070	+	2.88168i	−1.03669	+	0.628835i
$22$	−4.96547	+	2.58114i	−1.05864	+	0.550300i
$23$	−4.61035	−	2.31541i	−0.961325	−	0.482795i	−0.102313	−	0.994752i	$-0.532624\pi$
$23$	−4.61035	−	2.31541i	−0.961325	−	0.482795i	−0.859011	+	0.511957i	$0.828921\pi$
$24$	4.50860	+	1.91639i	0.920314	+	0.391181i
$25$	−0.937818	−	0.222267i	−0.187564	−	0.0444534i
$26$	8.38496	+	4.06558i	1.64443	+	0.797326i
$27$	−1.23247	−	5.04787i	−0.237188	−	0.971464i
$28$	−5.03746	+	3.97345i	−0.951991	+	0.750911i
$29$	−1.18331	+	0.354259i	−0.219735	+	0.0657843i	−0.394778	−	0.918776i	$-0.629179\pi$
$29$	−1.18331	+	0.354259i	−0.219735	+	0.0657843i	0.175043	+	0.984561i	$0.443993\pi$
$30$	4.49440	+	3.94755i	0.820562	+	0.720720i
$31$	3.24150	+	4.92846i	0.582190	+	0.885177i	0.999724	−	0.0234844i	$-0.00747601\pi$
$31$	3.24150	+	4.92846i	0.582190	+	0.885177i	−0.417534	+	0.908661i	$0.637106\pi$
$32$	5.43765	+	1.55948i	0.961249	+	0.275680i
$33$	6.48988	+	2.20425i	1.12974	+	0.383711i
$34$	0.0541450	+	0.0302613i	0.00928579	+	0.00518976i
$35$	−7.36169	+	2.67944i	−1.24435	+	0.452907i
$36$	−2.12536	−	5.61096i	−0.354227	−	0.935159i
$37$	4.55219	+	1.65686i	0.748376	+	0.272387i	0.687922	−	0.725784i	$-0.258523\pi$
$37$	4.55219	+	1.65686i	0.748376	+	0.272387i	0.0604539	+	0.998171i	$0.480745\pi$
$38$	−4.22686	−	4.89695i	−0.685687	−	0.794390i
$39$	−3.50914	−	10.8601i	−0.561912	−	1.73900i
$40$	5.70824	+	3.88926i	0.902553	+	0.614946i
$41$	−0.981017	+	0.925542i	−0.153209	+	0.144545i	−0.759030	−	0.651056i	$-0.774326\pi$
$41$	−0.981017	+	0.925542i	−0.153209	+	0.144545i	0.605821	+	0.795601i	$0.292845\pi$
$42$	7.78217	+	1.08821i	1.20082	+	0.167915i
$43$	−1.26027	+	0.938234i	−0.192189	+	0.143079i	−0.688952	−	0.724807i	$-0.741929\pi$
$43$	−1.26027	+	0.938234i	−0.192189	+	0.143079i	0.496763	+	0.867886i	$0.334522\pi$
$44$	7.74891	+	1.60957i	1.16819	+	0.242652i
$45$	−0.317068	−	7.31940i	−0.0472657	−	1.09111i
$46$	2.98303	+	6.65841i	0.439824	+	0.981729i
$47$	5.76986	+	3.79489i	0.841620	+	0.553542i	0.895529	−	0.445004i	$-0.146798\pi$
$47$	5.76986	+	3.79489i	0.841620	+	0.553542i	−0.0539087	+	0.998546i	$0.517168\pi$
$48$	−3.22817	−	6.13016i	−0.465947	−	0.884813i
$49$	−1.96529	+	2.63985i	−0.280756	+	0.377121i
$50$	0.829112	+	1.08184i	0.117254	+	0.152996i
$51$	−0.0191153	−	0.0735238i	−0.00267667	−	0.0102954i
$52$	−5.55536	−	11.9504i	−0.770390	−	1.65722i
$53$	−8.53190	+	4.92589i	−1.17195	+	0.676623i	−0.954138	−	0.299368i	$-0.903224\pi$
$53$	−8.53190	+	4.92589i	−1.17195	+	0.676623i	−0.217808	+	0.975992i	$0.569891\pi$
$54$	−3.16127	+	6.63373i	−0.430194	+	0.902737i
$55$	8.36904	+	4.83187i	1.12848	+	0.651529i
$56$	9.07230	+	0.148041i	1.21234	+	0.0197827i
$57$	−0.749236	+	7.88723i	−0.0992387	+	1.04469i
$58$	1.61347	+	0.669439i	0.211859	+	0.0879016i
$59$	4.33789	+	10.0564i	0.564745	+	1.30923i	0.926269	+	0.376863i	$0.122997\pi$
$59$	4.33789	+	10.0564i	0.564745	+	1.30923i	−0.361524	+	0.932363i	$0.617744\pi$
$60$	−1.39710	−	8.34348i	−0.180365	−	1.07714i
$61$	−0.185066	+	3.17746i	−0.0236953	+	0.406832i	0.965517	+	0.260341i	$0.0838350\pi$
$61$	−0.185066	+	3.17746i	−0.0236953	+	0.406832i	−0.989212	+	0.146491i	$0.953202\pi$
$62$	0.852772	−	8.29860i	0.108302	−	1.05392i
$63$	−5.63146	−	7.80425i	−0.709497	−	0.983243i
$64$	−4.56536	−	6.56944i	−0.570670	−	0.821180i
$65$	−1.86811	−	15.9827i	−0.231711	−	1.98241i
$66$	−5.14221	−	8.21658i	−0.632963	−	1.01139i
$67$	−1.14811	−	0.343723i	−0.140264	−	0.0419924i	0.215901	−	0.976415i	$-0.430731\pi$
$67$	−1.14811	−	0.343723i	−0.140264	−	0.0419924i	−0.356166	+	0.934423i	$0.615916\pi$
$68$	−0.0322905	−	0.0815609i	−0.00391580	−	0.00989071i
$69$	3.36089	−	8.27972i	0.404603	−	0.996761i
$70$	10.4629	+	3.64366i	1.25055	+	0.435501i
$71$	11.5777	−	9.71483i	1.37402	−	1.15294i	0.402651	−	0.915353i	$-0.368089\pi$
$71$	11.5777	−	9.71483i	1.37402	−	1.15294i	0.971367	−	0.237585i	$-0.0763557\pi$
$72$	−2.68602	+	8.04893i	−0.316550	+	0.948576i
$73$	−6.54463	−	5.49160i	−0.765991	−	0.642743i	0.173688	−	0.984801i	$-0.444432\pi$
$73$	−6.54463	−	5.49160i	−0.765991	−	0.642743i	−0.939679	+	0.342058i	$0.888876\pi$
$74$	−3.50792	−	5.88471i	−0.407788	−	0.684084i
$75$	0.254228	−	1.64987i	0.0293558	−	0.190511i
$76$	0.255275	+	9.14482i	0.0292821	+	1.04898i
$77$	12.6730	−	0.738116i	1.44422	−	0.0841162i
$78$	−5.86131	+	15.0384i	−0.663663	+	1.70277i
$79$	−1.32576	−	1.25079i	−0.149159	−	0.140724i	0.608045	−	0.793902i	$-0.291954\pi$
$79$	−1.32576	−	1.25079i	−0.149159	−	0.140724i	−0.757204	+	0.653178i	$0.773435\pi$
$80$	−2.77948	−	9.36457i	−0.310755	−	1.04699i
$81$	8.54512	−	2.82507i	0.949457	−	0.313896i
$82$	1.90241	−	0.137462i	0.210086	−	0.0151801i
$83$	−5.72637	+	6.06959i	−0.628550	+	0.666225i	−0.960888	−	0.276936i	$-0.910681\pi$
$83$	−5.72637	+	6.06959i	−0.628550	+	0.666225i	0.332338	+	0.943160i	$0.392163\pi$
$84$	−7.55603	−	8.14858i	−0.824430	−	0.889083i
$85$	−0.00622792	−	0.106929i	−0.000675512	−	0.0115981i
$86$	2.21979	+	0.0982318i	0.239366	+	0.0105926i
$87$	−0.775070	−	1.99410i	−0.0830963	−	0.213790i
$88$	−7.05357	−	8.69022i	−0.751913	−	0.926380i
$89$	1.91594	−	2.28333i	0.203089	−	0.242032i	−0.654881	−	0.755732i	$-0.727281\pi$
$89$	1.91594	−	2.28333i	0.203089	−	0.242032i	0.857970	+	0.513700i	$0.171726\pi$
$90$	−6.19485	+	8.30495i	−0.652994	+	0.875419i
$91$	−13.5873	−	16.1927i	−1.42434	−	1.69746i
$92$	2.68233	−	9.96348i	0.279652	−	1.03876i
$93$	−8.06147	+	6.27724i	−0.835935	+	0.650919i
$94$	−2.93135	−	9.31623i	−0.302345	−	0.960896i
$95$	−3.20376	+	10.7013i	−0.328699	+	1.09793i
$96$	−1.94150	+	9.60368i	−0.198153	+	0.980171i
$97$	17.9553	−	2.09867i	1.82308	−	0.213087i	0.865431	−	0.501027i	$-0.167044\pi$
$97$	17.9553	−	2.09867i	1.82308	−	0.213087i	0.957649	+	0.287940i	$0.0929703\pi$
$98$	4.51341	−	1.13644i	0.455923	−	0.114798i
$99$	−2.90939	+	11.5094i	−0.292405	+	1.15674i
$100$	0.0583397	−	1.92671i	0.00583397	−	0.192671i
$101$	−5.65398	−	0.329307i	−0.562592	−	0.0327672i	−0.225507	−	0.974242i	$-0.572404\pi$
$101$	−5.65398	−	0.329307i	−0.562592	−	0.0327672i	−0.337085	+	0.941474i	$0.609441\pi$
$102$	−0.0447691	+	0.0976627i	−0.00443280	+	0.00967005i
$103$	11.4395	−	4.93452i	1.12717	−	0.486212i	0.250888	−	0.968016i	$-0.419277\pi$
$103$	11.4395	−	4.93452i	1.12717	−	0.486212i	0.876279	+	0.481804i	$0.160018\pi$
$104$	−4.59335	+	18.0623i	−0.450415	+	1.77116i
$105$	−5.64288	−	12.3402i	−0.550688	−	1.20428i
$106$	13.7533	+	2.22767i	1.33584	+	0.216371i
$107$	−3.52738	+	6.10960i	−0.341005	+	0.590638i	−0.984620	−	0.174712i	$-0.944101\pi$
$107$	−3.52738	+	6.10960i	−0.341005	+	0.590638i	0.643615	+	0.765350i	$0.277434\pi$
$108$	9.39398	−	4.44445i	0.903936	−	0.427668i
$109$	−6.52977	−	11.3099i	−0.625438	−	1.08329i	−0.988456	−	0.151509i	$-0.951587\pi$
$109$	−6.52977	−	11.3099i	−0.625438	−	1.08329i	0.363018	−	0.931782i	$-0.381746\pi$
$110$	−4.85298	−	12.7759i	−0.462714	−	1.21814i
$111$	−2.23192	+	8.08836i	−0.211845	+	0.767713i
$112$	−9.81028	−	8.27138i	−0.926984	−	0.781572i
$113$	10.4405	+	7.77270i	0.982164	+	0.731194i	0.963244	−	0.268627i	$-0.0865700\pi$
$113$	10.4405	+	7.77270i	0.982164	+	0.731194i	0.0189195	+	0.999821i	$0.493977\pi$
$114$	7.87098	−	7.97415i	0.737185	−	0.746847i
$115$	6.92327	−	10.5263i	0.645598	−	0.981584i
$116$	−1.16988	−	2.17583i	−0.108621	−	0.202021i
$117$	18.2656	−	7.55856i	1.68866	−	0.698789i
$118$	4.23469	−	14.8984i	0.389835	−	1.37151i
$119$	−0.0840215	−	0.112860i	−0.00770223	−	0.0103459i
$120$	−5.92657	+	10.3926i	−0.541019	+	0.948714i
$121$	−3.19727	−	3.38890i	−0.290661	−	0.308082i
$122$	3.04294	−	3.31685i	0.275495	−	0.300294i
$123$	−1.73347	−	1.56593i	−0.156302	−	0.141195i
$124$	−8.35215	+	8.33244i	−0.750045	+	0.748275i
$125$	−3.37121	+	9.26233i	−0.301530	+	0.828448i
$126$	−0.804032	+	13.5865i	−0.0716288	+	1.21038i
$127$	7.08474	+	19.4652i	0.628669	+	1.72725i	0.684699	+	0.728825i	$0.259933\pi$
$127$	7.08474	+	19.4652i	0.628669	+	1.72725i	−0.0560302	+	0.998429i	$0.517844\pi$
$128$	−0.868679	+	11.2803i	−0.0767811	+	0.997048i
$129$	−1.79395	−	2.04632i	−0.157949	−	0.180168i
$130$	−12.2386	+	19.1857i	−1.07340	+	1.68270i
$131$	10.7598	−	7.07682i	0.940087	−	0.618305i	0.0157476	−	0.999876i	$-0.494987\pi$
$131$	10.7598	−	7.07682i	0.940087	−	0.618305i	0.924340	+	0.381571i	$0.124617\pi$
$132$	−1.70876	+	13.6011i	−0.148729	+	1.18382i
$133$	4.20851	+	14.0574i	0.364924	+	1.21893i
$134$	0.951021	+	1.40292i	0.0821557	+	0.121194i
$135$	12.5934	−	1.55832i	1.08387	−	0.134119i
$136$	−0.0375137	+	0.118247i	−0.00321678	+	0.0101396i
$137$	1.40758	−	5.93904i	0.120258	−	0.507406i	−0.879260	−	0.476342i	$-0.841962\pi$
$137$	1.40758	−	5.93904i	0.120258	−	0.507406i	0.999517	−	0.0310640i	$-0.00988958\pi$
$138$	−11.0840	+	6.06991i	−0.943532	+	0.516705i
$139$	0.423999	−	0.844251i	0.0359631	−	0.0716084i	−0.874934	−	0.484243i	$-0.839095\pi$
$139$	0.423999	−	0.844251i	0.0359631	−	0.0716084i	0.910897	+	0.412635i	$0.135391\pi$
$140$	−8.20973	−	13.3453i	−0.693849	−	1.12788i
$141$	−5.75514	+	10.4860i	−0.484670	+	0.883079i
$142$	−21.3718	+	0.298236i	−1.79348	+	0.0250274i
$143$	−4.52783	+	25.6786i	−0.378636	+	2.14735i
$144$	10.1381	−	6.42020i	0.844841	−	0.535017i
$145$	−0.523804	−	2.97064i	−0.0434996	−	0.246698i
$146$	2.26387	+	11.8682i	0.187360	+	0.982221i
$147$	−4.82922	−	3.02855i	−0.398307	−	0.249791i
$148$	−1.41552	+	9.58473i	−0.116355	+	0.787860i
$149$	4.05523	+	17.1104i	0.332218	+	1.40174i	0.841090	+	0.540895i	$0.181914\pi$
$149$	4.05523	+	17.1104i	0.332218	+	1.40174i	−0.508873	+	0.860842i	$0.669938\pi$
$150$	−1.75333	+	1.58091i	−0.143159	+	0.129080i
$151$	15.0417	+	6.48836i	1.22408	+	0.528015i	0.907300	−	0.420484i	$-0.138140\pi$
$151$	15.0417	+	6.48836i	1.22408	+	0.528015i	0.316778	+	0.948500i	$0.397399\pi$
$152$	7.89419	−	10.2502i	0.640303	−	0.831405i
$153$	0.124301	−	0.0431577i	0.0100492	−	0.00348909i
$154$	−14.5484	−	10.5186i	−1.17235	−	0.847614i
$155$	−12.8733	+	6.46523i	−1.03401	+	0.519300i
$156$	19.8655	−	11.2420i	1.59051	−	0.900082i
$157$	4.75036	+	0.555237i	0.379120	+	0.0443127i	0.303519	−	0.952825i	$-0.401838\pi$
$157$	4.75036	+	0.555237i	0.379120	+	0.0443127i	0.0756008	+	0.997138i	$0.475913\pi$
$158$	0.334939	+	2.55578i	0.0266463	+	0.203327i
$159$	−9.68308	−	14.0503i	−0.767918	−	1.11426i
$160$	−5.32427	+	12.7473i	−0.420920	+	1.00776i
$161$		−	16.5503i		−	1.30434i
$162$	−11.8900	−	4.54184i	−0.934165	−	0.356841i
$163$		−	2.37358i		−	0.185913i	−0.995670	−	0.0929567i	$-0.970368\pi$
$163$		−	2.37358i		−	0.185913i	0.995670	−	0.0929567i	$-0.0296318\pi$
$164$	−2.20777	−	1.54979i	−0.172398	−	0.121018i
$165$	−7.18653	+	15.1168i	−0.559470	+	1.17684i
$166$	11.7009	−	1.53342i	0.908166	−	0.119017i
$167$	−14.8779	−	1.73898i	−1.15129	−	0.134566i	−0.481036	−	0.876701i	$-0.659739\pi$
$167$	−14.8779	−	1.73898i	−1.15129	−	0.134566i	−0.670251	+	0.742135i	$0.733813\pi$
$168$	0.997393	+	15.6841i	0.0769505	+	1.21005i
$169$	27.1827	−	13.6517i	2.09098	−	1.05013i
$170$	−0.0887516	+	0.122754i	−0.00680694	+	0.00941476i
$171$	−13.7211	−	0.204266i	−1.04928	−	0.0156206i
$172$	−2.34493	−	2.09178i	−0.178799	−	0.159497i
$173$	3.66361	+	1.58033i	0.278539	+	0.120150i	0.530767	−	0.847518i	$-0.321904\pi$
$173$	3.66361	+	1.58033i	0.278539	+	0.120150i	−0.252228	+	0.967668i	$0.581163\pi$
$174$	−0.932971	+	2.87817i	−0.0707283	+	0.218194i
$175$	−0.713026	−	3.00849i	−0.0538997	−	0.227421i
$176$	−0.0373976	+	15.8286i	−0.00281895	+	1.19312i
$177$	−16.7635	+	8.87841i	−1.26002	+	0.667343i
$178$	−4.14065	+	0.789833i	−0.310355	+	0.0592005i
$179$	−3.08085	−	17.4724i	−0.230273	−	1.30595i	−0.852343	−	0.522983i	$-0.824819\pi$
$179$	−3.08085	−	17.4724i	−0.230273	−	1.30595i	0.622069	−	0.782962i	$-0.286292\pi$
$180$	14.2124	−	3.56447i	1.05933	−	0.265680i
$181$	−3.04539	+	17.2712i	−0.226362	+	1.28376i	0.633703	+	0.773576i	$0.281534\pi$
$181$	−3.04539	+	17.2712i	−0.226362	+	1.28376i	−0.860065	+	0.510185i	$0.829577\pi$
$182$	0.417117	+	29.8909i	0.0309188	+	2.21566i
$183$	−5.51156	+	0.119321i	−0.407426	+	0.00882047i
$184$	−11.8453	+	8.52171i	−0.873250	+	0.628229i
$185$	−5.30944	+	10.5720i	−0.390358	+	0.777266i
$186$	14.4456	+	0.326209i	1.05920	+	0.0239188i
$187$	−0.0400260	+	0.168883i	−0.00292699	+	0.0123500i
$188$	−5.11462	+	12.8301i	−0.373022	+	0.935729i
$189$	12.6966	−	10.8008i	0.923538	−	0.785640i
$190$	13.0763	−	8.86424i	0.948653	−	0.643079i
$191$	−0.665145	−	2.22174i	−0.0481282	−	0.160759i	0.930547	−	0.366172i	$-0.119332\pi$
$191$	−0.665145	−	2.22174i	−0.0481282	−	0.160759i	−0.978676	+	0.205412i	$0.934146\pi$
$192$	10.7118	−	8.78957i	0.773060	−	0.634332i
$193$	−9.33270	+	6.13821i	−0.671782	+	0.441838i	−0.839036	−	0.544076i	$-0.816880\pi$
$193$	−9.33270	+	6.13821i	−0.671782	+	0.441838i	0.167254	+	0.985914i	$0.446510\pi$
$194$	−21.5535	−	13.7490i	−1.54745	−	0.987123i
$195$	27.3368	−	5.43277i	1.95763	−	0.389048i
$196$	−5.96216	−	2.78878i	−0.425869	−	0.199199i
$197$	−1.65484	−	4.54665i	−0.117903	−	0.323935i	0.866677	−	0.498869i	$-0.166251\pi$
$197$	−1.65484	−	4.54665i	−0.117903	−	0.323935i	−0.984580	+	0.174934i	$0.944029\pi$
$198$	13.4760	−	10.0130i	0.957699	−	0.711594i
$199$	8.01569	−	22.0229i	0.568217	−	1.56116i	−0.239069	−	0.971003i	$-0.576842\pi$
$199$	8.01569	−	22.0229i	0.568217	−	1.56116i	0.807286	−	0.590161i	$-0.200936\pi$
$200$	−1.78610	+	2.05939i	−0.126296	+	0.145621i
$201$	0.434882	−	2.02973i	0.0306742	−	0.143166i
$202$	5.90201	+	5.41461i	0.415264	+	0.380971i
$203$	−2.71922	−	2.88221i	−0.190852	−	0.202291i
$204$	0.136358	−	0.0670153i	0.00954697	−	0.00469201i
$205$	−1.96685	−	2.64193i	−0.137370	−	0.184520i
$206$	−16.9475	−	4.81713i	−1.18079	−	0.335625i
$207$	14.7594	+	4.65917i	1.02585	+	0.323834i
$208$	21.1787	−	15.6893i	1.46848	−	1.08786i
$209$	9.94655	−	15.1230i	0.688017	−	1.04608i
$210$	−4.84586	+	18.5677i	−0.334396	+	1.28130i
$211$	−11.8542	−	8.82513i	−0.816077	−	0.607547i	0.106082	−	0.994357i	$-0.466169\pi$
$211$	−11.8542	−	8.82513i	−0.816077	−	0.607547i	−0.922159	+	0.386810i	$0.873577\pi$
$212$	−13.0815	−	14.7345i	−0.898438	−	1.01197i
$213$	18.3720	+	18.6476i	1.25883	+	1.27771i
$214$	9.32673	−	3.54280i	0.637562	−	0.242181i
$215$	−1.91846	−	3.32287i	−0.130838	−	0.226618i
$216$	−14.2677	−	3.52586i	−0.970797	−	0.239904i
$217$	−9.46174	+	16.3882i	−0.642305	+	1.11250i
$218$	−2.95300	+	18.2314i	−0.200003	+	1.23478i
$219$	8.57755	−	12.0580i	0.579617	−	0.814804i
$220$	−6.10102	+	18.3393i	−0.411331	+	1.23643i
$221$	0.265370	−	0.114469i	0.0178507	−	0.00770004i
$222$	9.67568	−	6.86930i	0.649389	−	0.461037i
$223$	−2.97643	−	0.173357i	−0.199316	−	0.0116088i	−0.0418037	−	0.999126i	$-0.513310\pi$
$223$	−2.97643	−	0.173357i	−0.199316	−	0.0116088i	−0.157512	+	0.987517i	$0.550347\pi$
$224$	3.35813	+	17.8336i	0.224374	+	1.19156i
$225$	2.88368	+	0.211067i	0.192245	+	0.0140712i
$226$	−4.49459	−	17.8504i	−0.298976	−	1.18739i
$227$	−7.27305	+	0.850097i	−0.482729	+	0.0564229i	−0.353978	−	0.935254i	$-0.615171\pi$
$227$	−7.27305	+	0.850097i	−0.482729	+	0.0564229i	−0.128752	+	0.991677i	$0.541097\pi$
$228$	−15.7536	+	1.70375i	−1.04331	+	0.112833i
$229$	2.24530	−	7.49983i	0.148374	−	0.495603i	−0.851199	−	0.524844i	$-0.824124\pi$
$229$	2.24530	−	7.49983i	0.148374	−	0.495603i	0.999572	+	0.0292409i	$0.00930898\pi$
$230$	−16.9962	+	5.34784i	−1.12070	+	0.352626i
$231$	3.02467	+	21.7784i	0.199009	+	1.43291i
$232$	−0.662725	+	3.43024i	−0.0435100	+	0.225206i
$233$	−5.32136	−	6.34175i	−0.348614	−	0.415462i	0.563034	−	0.826434i	$-0.309634\pi$
$233$	−5.32136	−	6.34175i	−0.348614	−	0.415462i	−0.911648	+	0.410972i	$0.865189\pi$
$234$	−26.7739	−	8.04278i	−1.75027	−	0.525773i
$235$	−10.8406	+	12.9193i	−0.707164	+	0.842765i
$236$	−17.9576	+	12.5425i	−1.16894	+	0.816446i
$237$	1.97642	−	2.46171i	0.128383	−	0.159905i
$238$	−0.00879693	+	0.198788i	−0.000570220	+	0.0128855i
$239$	−1.12133	−	19.2525i	−0.0725328	−	1.24534i	−0.816587	−	0.577222i	$-0.804137\pi$
$239$	−1.12133	−	19.2525i	−0.0725328	−	1.24534i	0.744054	−	0.668119i	$-0.232900\pi$
$240$	15.7844	−	6.09222i	1.01888	−	0.393251i
$241$	16.0114	−	16.9711i	1.03138	−	1.09320i	0.0357962	−	0.999359i	$-0.488603\pi$
$241$	16.0114	−	16.9711i	1.03138	−	1.09320i	0.995587	−	0.0938432i	$-0.0299152\pi$
$242$	0.474859	+	6.57182i	0.0305251	+	0.422453i
$243$	6.05776	+	14.3633i	0.388605	+	0.921404i
$244$	−6.29957	+	0.915150i	−0.403288	+	0.0585865i
$245$	−5.84597	−	5.51539i	−0.373485	−	0.352365i
$246$	0.500077	+	3.26559i	0.0318837	+	0.208206i
$247$	−30.0895	+	1.75251i	−1.91455	+	0.111510i
$248$	16.6012	−	1.66633i	1.05418	−	0.105812i
$249$	−11.2702	−	9.04849i	−0.714223	−	0.573425i
$250$	11.9736	−	7.13755i	0.757277	−	0.451418i
$251$	11.5892	+	9.72449i	0.731504	+	0.613804i	0.930541	−	0.366188i	$-0.119337\pi$
$251$	11.5892	+	9.72449i	0.731504	+	0.613804i	−0.199038	+	0.979992i	$0.563782\pi$
$252$	13.0252	−	14.1712i	0.820513	−	0.892699i
$253$	−15.6391	+	13.1228i	−0.983223	+	0.825022i
$254$	9.63426	−	27.6650i	0.604507	−	1.73586i
$255$	0.183757	−	0.0255209i	0.0115073	−	0.00159818i
$256$	11.0347	−	11.5860i	0.689671	−	0.724123i
$257$	−7.28722	−	2.18165i	−0.454564	−	0.136088i	0.0513326	−	0.998682i	$-0.483653\pi$
$257$	−7.28722	−	2.18165i	−0.454564	−	0.136088i	−0.505897	+	0.862594i	$0.668838\pi$
$258$	0.136978	+	3.84611i	0.00852788	+	0.239449i
$259$	1.80414	+	15.4354i	0.112104	+	0.959111i
$260$	30.5615	−	10.0869i	1.89534	−	0.625564i
$261$	3.33583	−	1.61359i	0.206483	−	0.0998790i
$262$	−18.1175	−	1.86177i	−1.11930	−	0.115020i
$263$	0.544710	−	9.35231i	0.0335883	−	0.576688i	−0.938966	−	0.344011i	$-0.888214\pi$
$263$	0.544710	−	9.35231i	0.0335883	−	0.576688i	0.972554	−	0.232677i	$-0.0747486\pi$
$264$	14.0298	−	13.3785i	0.863474	−	0.823388i
$265$	−9.52926	−	22.0913i	−0.585378	−	1.35706i
$266$	7.95276	−	19.1676i	0.487615	−	1.17524i
$267$	4.20686	+	2.99258i	0.257456	+	0.183143i
$268$	0.211726	−	2.38755i	0.0129332	−	0.145843i
$269$	1.61221	+	0.930808i	0.0982980	+	0.0567524i	0.548343	−	0.836253i	$-0.315259\pi$
$269$	1.61221	+	0.930808i	0.0982980	+	0.0567524i	−0.450045	+	0.893006i	$0.648592\pi$
$270$	−15.1944	−	9.54862i	−0.924700	−	0.581110i
$271$	−3.03568	+	1.75265i	−0.184404	+	0.106466i	−0.589360	−	0.807870i	$-0.700620\pi$
$271$	−3.03568	+	1.75265i	−0.184404	+	0.106466i	0.404956	+	0.914336i	$0.367287\pi$
$272$	0.146806	−	0.0960596i	0.00890141	−	0.00582447i
$273$	26.0808	−	25.6954i	1.57848	−	1.55516i
$274$	−6.85112	+	5.25063i	−0.413891	+	0.317202i
$275$	−2.27750	+	3.05922i	−0.137339	+	0.184478i
$276$	17.5728	+	3.25506i	1.05776	+	0.195931i
$277$	−12.8197	−	8.43165i	−0.770261	−	0.506609i	0.102514	−	0.994732i	$-0.467311\pi$
$277$	−12.8197	−	8.43165i	−0.770261	−	0.506609i	−0.872775	+	0.488123i	$0.837682\pi$
$278$	−1.21929	+	0.546255i	−0.0731283	+	0.0327622i
$279$	−11.9513	−	13.0514i	−0.715503	−	0.781370i
$280$	−2.93116	+	21.9636i	−0.175171	+	1.31258i
$281$	−13.3962	+	9.97313i	−0.799153	+	0.594947i	−0.917368	−	0.398041i	$-0.869690\pi$
$281$	−13.3962	+	9.97313i	−0.799153	+	0.594947i	0.118215	+	0.992988i	$0.462283\pi$
$282$	15.6799	−	6.34775i	0.933727	−	0.378003i
$283$	19.4859	−	18.3840i	1.15832	−	1.09281i	0.163987	−	0.986463i	$-0.447565\pi$
$283$	19.4859	−	18.3840i	1.15832	−	1.09281i	0.994329	−	0.106352i	$-0.0339169\pi$
$284$	23.6885	+	18.7760i	1.40565	+	1.11415i
$285$	−18.9187	−	4.05343i	−1.12064	−	0.240104i
$286$	27.9146	−	24.0948i	1.65062	−	1.42475i
$287$	−4.06570	−	1.47979i	−0.239991	−	0.0873494i
$288$	−16.8492	−	2.02569i	−0.992850	−	0.119365i
$289$	−15.9730	+	5.81368i	−0.939586	+	0.341981i
$290$	−2.08121	+	3.72381i	−0.122213	+	0.218669i
$291$	6.10325	+	30.7105i	0.357779	+	1.80028i
$292$	8.12717	−	15.0303i	0.475607	−	0.879579i
$293$	2.27945	+	3.46574i	0.133167	+	0.202471i	0.895915	−	0.444225i	$-0.146521\pi$
$293$	2.27945	+	3.46574i	0.133167	+	0.202471i	−0.762748	+	0.646695i	$0.776150\pi$
$294$	2.58546	+	7.63560i	0.150787	+	0.445317i
$295$	−25.6223	+	7.67081i	−1.49179	+	0.446612i
$296$	10.1185	−	9.23894i	0.588124	−	0.537002i
$297$	−20.2733	−	3.43359i	−1.17638	−	0.199237i
$298$	10.8496	−	22.3765i	0.628500	−	1.29623i
$299$	33.0784	+	7.83972i	1.91297	+	0.453383i
$300$	3.33459	−	0.165376i	0.192523	−	0.00954797i
$301$	−4.50413	−	2.26206i	−0.259614	−	0.130383i
$302$	−10.6851	−	20.5556i	−0.614860	−	1.18284i
$303$	−0.212320	−	9.80727i	−0.0121975	−	0.563413i
$304$	−17.8135	+	4.17745i	−1.02167	+	0.239593i
$305$	−7.65471	−	1.34973i	−0.438307	−	0.0772854i
$306$	−0.174801	−	0.0638071i	−0.00999273	−	0.00364761i
$307$	−0.00915717	+	0.00161466i	−0.000522628	+	9.21533e-5i	−0.173909	−	0.984762i	$-0.555640\pi$
$307$	−0.00915717	+	0.00161466i	−0.000522628	+	9.21533e-5i	0.173387	+	0.984854i	$0.444529\pi$
$308$	6.54215	+	24.5315i	0.372774	+	1.39781i
$309$	10.0995	+	19.0692i	0.574543	+	1.08481i
$310$	19.8871	+	4.42119i	1.12951	+	0.251107i
$311$	−14.1188	+	3.34622i	−0.800605	+	0.189747i	−0.610499	−	0.792017i	$-0.709031\pi$
$311$	−14.1188	+	3.34622i	−0.800605	+	0.189747i	−0.190106	+	0.981764i	$0.560883\pi$
$312$	−31.8196	−	5.43597i	−1.80143	−	0.307751i
$313$	−9.42637	+	21.8528i	−0.532810	+	1.23519i	0.413077	+	0.910696i	$0.364454\pi$
$313$	−9.42637	+	21.8528i	−0.532810	+	1.23519i	−0.945887	+	0.324496i	$0.894805\pi$
$314$	−4.70976	−	4.85453i	−0.265787	−	0.273957i
$315$	20.5264	−	11.4469i	1.15653	−	0.644962i
$316$	1.91737	−	3.10033i	0.107861	−	0.174407i
$317$	−3.56886	−	7.10619i	−0.200447	−	0.399123i	0.770842	−	0.637027i	$-0.219836\pi$
$317$	−3.56886	−	7.10619i	−0.200447	−	0.399123i	−0.971289	+	0.237904i	$0.923540\pi$
$318$	−1.94667	+	24.0532i	−0.109164	+	1.34884i
$319$	−0.567449	+	4.85483i	−0.0317710	+	0.271818i
$320$	17.2290	−	9.21113i	0.963130	−	0.514918i
$321$	−11.0356	−	5.24634i	−0.615948	−	0.292822i
$322$	−14.7932	+	18.1379i	−0.824393	+	1.01079i
$323$	−0.200625			−0.0111631
$324$	8.97092	+	15.6052i	0.498385	+	0.866956i
$325$	6.35070			0.352274
$326$	−2.12159	+	2.60128i	−0.117504	+	0.144072i
$327$	18.6251	−	12.8359i	1.02997	−	0.709827i
$328$	1.03431	+	3.67184i	0.0571100	+	0.202743i
$329$	−2.57194	+	22.0044i	−0.141796	+	1.21314i
$330$	21.3878	−	10.1434i	1.17736	−	0.558373i
$331$	−4.17737	−	8.31784i	−0.229609	−	0.457190i	0.749096	−	0.662462i	$-0.230488\pi$
$331$	−4.17737	−	8.31784i	−0.229609	−	0.457190i	−0.978705	+	0.205272i	$0.934192\pi$
$332$	−14.1940	−	8.77814i	−0.778996	−	0.481763i
$333$	−14.2731	−	2.73640i	−0.782161	−	0.149954i
$334$	14.7508	+	15.2042i	0.807126	+	0.831935i
$335$	1.15923	−	2.68739i	0.0633353	−	0.146828i
$336$	12.9259	−	18.0802i	0.705166	−	0.986354i
$337$	12.7585	−	3.02382i	0.694999	−	0.164718i	0.132091	−	0.991238i	$-0.457831\pi$
$337$	12.7585	−	3.02382i	0.694999	−	0.164718i	0.562908	+	0.826520i	$0.309683\pi$
$338$	−41.9927	−	9.33558i	−2.28410	−	0.507789i
$339$	−11.9779	+	19.0995i	−0.650549	+	1.03734i
$340$	0.206987	−	0.0551999i	0.0112254	−	0.00299364i
$341$	22.9882	−	4.05345i	1.24488	−	0.219506i
$342$	14.8547	+	12.4882i	0.803251	+	0.675285i
$343$	11.7174	+	2.06609i	0.632678	+	0.111558i
$344$	0.700172	+	4.38842i	0.0377508	+	0.236608i
$345$	19.1302	+	10.4995i	1.02994	+	0.565272i
$346$	−2.60251	−	5.00658i	−0.139912	−	0.269156i
$347$	11.7054	+	5.87866i	0.628378	+	0.315583i	0.734335	−	0.678787i	$-0.237494\pi$
$347$	11.7054	+	5.87866i	0.628378	+	0.315583i	−0.105957	+	0.994371i	$0.533791\pi$
$348$	3.59508	−	2.32035i	0.192717	−	0.124384i
$349$	10.5756	+	2.50647i	0.566101	+	0.134168i	0.503694	−	0.863882i	$-0.331974\pi$
$349$	10.5756	+	2.50647i	0.566101	+	0.134168i	0.0624074	+	0.998051i	$0.480122\pi$
$350$	−1.90767	+	3.93442i	−0.101969	+	0.210304i
$351$	15.5728	+	30.4923i	0.831215	+	1.62756i
$352$	14.1891	−	17.3136i	0.756282	−	0.922817i
$353$	−11.4119	+	3.41651i	−0.607396	+	0.181842i	−0.575708	−	0.817655i	$-0.695274\pi$
$353$	−11.4119	+	3.41651i	−0.607396	+	0.181842i	−0.0316882	+	0.999498i	$0.510088\pi$
$354$	26.3075	+	5.25371i	1.39823	+	0.279231i
$355$	20.2817	+	30.8368i	1.07644	+	1.63665i
$356$	5.24384	+	2.83545i	0.277923	+	0.150279i
$357$	0.183253	−	0.160653i	0.00969879	−	0.00850268i
$358$	−12.2410	+	21.9022i	−0.646957	+	1.15757i
$359$	−0.456242	+	0.166059i	−0.0240795	+	0.00876424i	−0.354032	−	0.935233i	$-0.615190\pi$
$359$	−0.456242	+	0.166059i	−0.0240795	+	0.00876424i	0.329952	+	0.943998i	$0.392967\pi$
$360$	−18.7618	−	8.79709i	−0.988833	−	0.463647i
$361$	1.80724	+	0.657782i	0.0951179	+	0.0346201i
$362$	18.7752	−	16.2060i	0.986800	−	0.851768i
$363$	5.40948	−	5.98824i	0.283924	−	0.314301i
$364$	26.2604	−	33.1312i	1.37642	−	1.73654i
$365$	15.1758	−	14.3176i	0.794335	−	0.749417i
$366$	6.14693	+	4.79565i	0.321305	+	0.250673i
$367$	11.5321	−	8.58531i	0.601969	−	0.448150i	−0.252539	−	0.967587i	$-0.581266\pi$
$367$	11.5321	−	8.58531i	0.601969	−	0.448150i	0.854509	+	0.519437i	$0.173858\pi$
$368$	20.5986	+	1.24857i	1.07378	+	0.0650864i
$369$	2.46423	−	3.20917i	0.128283	−	0.167063i
$370$	15.2683	−	6.84036i	0.793763	−	0.355613i
$371$	−26.4050	−	17.3668i	−1.37088	−	0.901640i
$372$	−15.5398	−	13.2695i	−0.805700	−	0.687990i
$373$	8.29281	−	11.1392i	0.429385	−	0.576765i	−0.533797	−	0.845612i	$-0.679235\pi$
$373$	8.29281	−	11.1392i	0.429385	−	0.576765i	0.963183	+	0.268848i	$0.0866429\pi$
$374$	0.194819	−	0.149307i	0.0100739	−	0.00772050i
$375$	−16.4573	−	4.54128i	−0.849854	−	0.234511i
$376$	17.0732	−	9.48922i	0.880483	−	0.489369i
$377$	7.04862	−	4.06952i	0.363023	−	0.209591i
$378$	−23.5686	+	0.488263i	−1.21224	+	0.0251135i
$379$	−28.3794	−	16.3849i	−1.45775	−	0.841634i	−0.458852	−	0.888513i	$-0.651739\pi$
$379$	−28.3794	−	16.3849i	−1.45775	−	0.841634i	−0.998901	+	0.0468784i	$0.985073\pi$
$380$	−22.2538	−	1.97345i	−1.14160	−	0.101236i
$381$	−32.6288	+	14.9204i	−1.67163	+	0.764397i
$382$	−1.25691	+	3.02940i	−0.0643093	+	0.154997i
$383$	3.62436	+	8.40221i	0.185196	+	0.429333i	0.985369	−	0.170437i	$-0.0545179\pi$
$383$	3.62436	+	8.40221i	0.185196	+	0.429333i	−0.800172	+	0.599770i	$0.795259\pi$
$384$	−19.5958	+	0.0581370i	−0.999996	+	0.00296679i
$385$	−1.80255	+	30.9485i	−0.0918662	+	1.57728i
$386$	15.7145	+	1.61484i	0.799848	+	0.0821931i
$387$	3.28527	−	3.37994i	0.167000	−	0.171812i
$388$	11.3318	+	34.3333i	0.575285	+	1.74301i
$389$	−0.350109	−	2.99537i	−0.0177512	−	0.151871i	0.981456	−	0.191689i	$-0.0613964\pi$
$389$	−0.350109	−	2.99537i	−0.0177512	−	0.151871i	−0.999207	+	0.0398175i	$0.987322\pi$
$390$	−34.8151	−	18.4806i	−1.76293	−	0.935801i
$391$	0.216773	+	0.0648977i	0.0109627	+	0.00328202i
$392$	4.04140	+	8.38549i	0.204121	+	0.423531i
$393$	13.7044	+	17.5998i	0.691298	+	0.887791i
$394$	−2.25036	+	6.46196i	−0.113371	+	0.325549i
$395$	3.40974	−	2.86111i	0.171563	−	0.143958i
$396$	−23.7187	−	1.07177i	−1.19191	−	0.0538587i
$397$	3.50581	+	2.94172i	0.175952	+	0.147641i	0.726510	−	0.687155i	$-0.241141\pi$
$397$	3.50581	+	2.94172i	0.175952	+	0.147641i	−0.550559	+	0.834796i	$0.685585\pi$
$398$	−28.4695	+	16.9709i	−1.42705	+	0.850672i
$399$	−23.6894	+	9.20764i	−1.18595	+	0.460959i
$400$	3.79819	−	0.660475i	0.189910	−	0.0330237i
$401$	1.47771	−	0.0860670i	0.0737935	−	0.00429798i	−0.0212083	−	0.999775i	$-0.506751\pi$
$401$	1.47771	−	0.0860670i	0.0737935	−	0.00429798i	0.0950019	+	0.995477i	$0.469714\pi$
$402$	−2.29084	+	1.83573i	−0.114257	+	0.0915579i
$403$	−28.2725	−	26.6737i	−1.40835	−	1.32871i
$404$	−1.62842	−	11.2095i	−0.0810169	−	0.557691i
$405$	4.42980	+	21.5278i	0.220118	+	1.06972i
$406$	0.403860	+	5.58923i	0.0200432	+	0.277389i
$407$	13.1551	−	13.9436i	0.652076	−	0.691160i
$408$	−0.209339	−	0.0484375i	−0.0103638	−	0.00239801i
$409$	−1.33743	−	22.9628i	−0.0661318	−	1.13544i	−0.854232	−	0.519892i	$-0.825972\pi$
$409$	−1.33743	−	22.9628i	−0.0661318	−	1.13544i	0.788100	−	0.615547i	$-0.211065\pi$
$410$	−0.205926	+	4.65340i	−0.0101700	+	0.229815i
$411$	10.4484	+	1.60998i	0.515380	+	0.0794146i
$412$	14.2676	+	20.4275i	0.702912	+	1.00639i
$413$	−22.5836	+	26.9141i	−1.11127	+	1.32436i
$414$	−12.0107	−	18.2986i	−0.590296	−	0.899326i
$415$	−13.0988	−	15.6105i	−0.642994	−	0.766291i
$416$	−37.2340	−	1.73586i	−1.82555	−	0.0851075i
$417$	1.51619	+	0.615448i	0.0742481	+	0.0301386i
$418$	−24.4182	+	7.68316i	−1.19433	+	0.375796i
$419$	−3.81061	+	12.7283i	−0.186160	+	0.621819i	0.813054	+	0.582188i	$0.197803\pi$
$419$	−3.81061	+	12.7283i	−0.186160	+	0.621819i	−0.999214	+	0.0396309i	$0.987382\pi$
$420$	21.9072	−	16.0175i	1.06896	−	0.781575i
$421$	3.78364	−	0.442244i	0.184403	−	0.0215536i	−0.0233900	−	0.999726i	$-0.507446\pi$
$421$	3.78364	−	0.442244i	0.184403	−	0.0215536i	0.207793	+	0.978173i	$0.433372\pi$
$422$	5.10317	+	20.2674i	0.248418	+	0.986602i
$423$	−18.8993	−	8.48821i	−0.918914	−	0.412711i
$424$	1.16613	+	27.8406i	0.0566320	+	1.35206i
$425$	0.0422008	+	0.00245792i	0.00204704	+	0.000119226i
$426$	−3.46660	−	36.8579i	−0.167957	−	1.78577i
$427$	−9.37542	+	4.04416i	−0.453709	+	0.195711i
$428$	−13.3881	−	4.45390i	−0.647139	−	0.215287i
$429$	−44.9603	−	4.27094i	−2.17071	−	0.206203i
$430$	−0.867599	+	5.35642i	−0.0418394	+	0.258309i
$431$	13.7184	−	23.7610i	0.660793	−	1.14453i	−0.319615	−	0.947547i	$-0.603554\pi$
$431$	13.7184	−	23.7610i	0.660793	−	1.14453i	0.980408	−	0.196979i	$-0.0631130\pi$
$432$	12.4849	+	16.6171i	0.600680	+	0.799490i
$433$	4.47373	+	7.74873i	0.214994	+	0.372380i	0.953271	−	0.302118i	$-0.0976935\pi$
$433$	4.47373	+	7.74873i	0.214994	+	0.372380i	−0.738277	+	0.674498i	$0.764360\pi$
$434$	25.0177	−	9.50310i	1.20089	−	0.456163i
$435$	5.05658	−	1.31465i	0.242444	−	0.0630325i
$436$	19.5321	−	17.3408i	0.935418	−	0.830473i
$437$	−18.9291	−	14.0922i	−0.905502	−	0.674122i
$438$	−20.1782	+	5.54780i	−0.964154	+	0.265084i
$439$	−18.3003	+	27.8243i	−0.873427	+	1.32798i	0.0703927	+	0.997519i	$0.477575\pi$
$439$	−18.3003	+	27.8243i	−0.873427	+	1.32798i	−0.943819	+	0.330462i	$0.892796\pi$
$440$	23.0785	−	14.6452i	1.10023	−	0.698184i
$441$	4.56194	−	8.75610i	0.217235	−	0.416957i
$442$	−0.393143	−	0.111746i	−0.0186999	−	0.00531523i
$443$	−3.19745	−	4.29493i	−0.151916	−	0.204058i	0.719650	−	0.694337i	$-0.244302\pi$
$443$	−3.19745	−	4.29493i	−0.151916	−	0.204058i	−0.871566	+	0.490279i	$0.836895\pi$
$444$	−16.7439	−	1.12019i	−0.794629	−	0.0531619i
$445$	4.99520	+	5.29460i	0.236795	+	0.250988i
$446$	3.10700	+	2.85042i	0.147121	+	0.134971i
$447$	−28.9816	+	9.36465i	−1.37078	+	0.442933i
$448$	12.2600	−	22.5460i	0.579231	−	1.06520i
$449$	−5.73466	+	15.7558i	−0.270635	+	0.743565i	0.727700	+	0.685895i	$0.240589\pi$
$449$	−5.73466	+	15.7558i	−0.270635	+	0.743565i	−0.998336	+	0.0576694i	$0.981633\pi$
$450$	−2.97165	−	2.80884i	−0.140085	−	0.132410i
$451$	1.82538	+	5.01520i	0.0859539	+	0.236157i
$452$	−11.0296	+	23.5802i	−0.518788	+	1.10912i
$453$	−9.12495	+	26.8662i	−0.428728	+	1.26228i
$454$	8.73059	+	5.56925i	0.409747	+	0.261378i
$455$	43.1289	−	28.3663i	2.02191	−	1.32983i
$456$	18.7877	+	12.2139i	0.879815	+	0.571969i
$457$	−6.43068	−	21.4800i	−0.300814	−	1.00479i	−0.966093	−	0.258195i	$-0.916872\pi$
$457$	−6.43068	−	21.4800i	−0.300814	−	1.00479i	0.665278	−	0.746595i	$-0.268313\pi$
$458$	−9.16430	+	6.21235i	−0.428219	+	0.290284i
$459$	0.0916807	+	0.208650i	0.00427929	+	0.00973896i
$460$	23.4067	+	9.33092i	1.09134	+	0.435056i
$461$	4.15296	−	17.5227i	0.193423	−	0.816115i	−0.786637	−	0.617415i	$-0.788180\pi$
$461$	4.15296	−	17.5227i	0.193423	−	0.816115i	0.980060	−	0.198700i	$-0.0636720\pi$
$462$	16.1514	−	26.5711i	0.751433	−	1.23620i
$463$	−4.62177	+	9.20270i	−0.214792	+	0.427686i	−0.975066	−	0.221917i	$-0.928769\pi$
$463$	−4.62177	+	9.20270i	−0.214792	+	0.427686i	0.760274	+	0.649603i	$0.225065\pi$
$464$	3.79237	−	3.16694i	0.176056	−	0.147021i
$465$	−12.9404	−	21.3334i	−0.600097	−	0.989311i
$466$	0.163360	+	11.7065i	0.00756752	+	0.542294i
$467$	1.49638	−	8.48642i	0.0692444	−	0.392705i	−0.930413	−	0.366514i	$-0.880551\pi$
$467$	1.49638	−	8.48642i	0.0692444	−	0.392705i	0.999657	−	0.0261906i	$-0.00833769\pi$
$468$	22.1534	+	32.7458i	1.02404	+	1.51367i
$469$	−0.667613	−	3.78622i	−0.0308275	−	0.174832i
$470$	23.4283	−	4.46897i	1.08067	−	0.206138i
$471$	−0.302557	+	8.27834i	−0.0139411	+	0.381446i
$472$	30.8912	+	2.30547i	1.42188	+	0.106118i
$473$	1.43382	+	6.04976i	0.0659270	+	0.278168i
$474$	−4.36638	+	0.931267i	−0.200555	+	0.0427745i
$475$	−4.04804	−	1.74615i	−0.185737	−	0.0801191i
$476$	0.187325	−	0.209995i	0.00858601	−	0.00962510i
$477$	22.9210	−	18.6587i	1.04948	−	0.854323i
$478$	−15.9796	+	22.1017i	−0.730892	+	1.01091i
$479$	31.5489	−	15.8444i	1.44151	−	0.723951i	0.455434	−	0.890270i	$-0.349484\pi$
$479$	31.5489	−	15.8444i	1.44151	−	0.723951i	0.986072	+	0.166318i	$0.0531880\pi$
$480$	−22.7440	−	7.43198i	−1.03812	−	0.339222i
$481$	−31.7048	−	3.70576i	−1.44561	−	0.168968i
$482$	−32.7166	+	4.28757i	−1.49020	+	0.195293i
$483$	28.5746	−	2.28579i	1.30019	−	0.104007i
$484$	5.35371	−	7.62670i	0.243350	−	0.346668i
$485$			44.1468i			2.00460i
$486$	6.19951	−	21.1558i	0.281215	−	0.959645i
$487$			36.5213i			1.65494i	0.561513	+	0.827468i	$0.310220\pi$
$487$			36.5213i			1.65494i	−0.561513	+	0.827468i	$0.689780\pi$
$488$	7.72187	+	4.62783i	0.349553	+	0.209492i
$489$	4.09808	−	0.327820i	0.185322	−	0.0148245i
$490$	1.47693	+	11.2698i	0.0667207	+	0.509118i
$491$	8.96130	+	1.04743i	0.404418	+	0.0472697i	0.315870	−	0.948802i	$-0.397703\pi$
$491$	8.96130	+	1.04743i	0.404418	+	0.0472697i	0.0885473	+	0.996072i	$0.471778\pi$
$492$	2.37084	−	4.02584i	0.106886	−	0.181499i
$493$	0.0484135	−	0.0243142i	0.00218044	−	0.00109506i
$494$	34.5424	+	24.9744i	1.55414	+	1.12365i
$495$	−27.0922	−	10.3200i	−1.21770	−	0.463849i
$496$	−19.6831	−	13.0125i	−0.883799	−	0.584280i
$497$	44.5187	+	19.2035i	1.99694	+	0.861395i
$498$	4.26354	+	19.9902i	0.191054	+	0.895784i
$499$	−0.409918	−	1.72958i	−0.0183505	−	0.0774266i	0.963099	−	0.269147i	$-0.0867416\pi$
$499$	−0.409918	−	1.72958i	−0.0183505	−	0.0774266i	−0.981450	+	0.191720i	$0.938593\pi$
$500$	−19.5020	−	2.88016i	−0.872156	−	0.128805i
$501$	0.947595	−	25.9274i	0.0423354	−	1.15835i
$502$	−4.00886	−	21.0162i	−0.178924	−	0.937998i
$503$	−5.68735	−	32.2546i	−0.253587	−	1.43816i	−0.799675	−	0.600433i	$-0.794995\pi$
$503$	−5.68735	−	32.2546i	−0.253587	−	1.43816i	0.546088	−	0.837728i	$-0.316116\pi$
$504$	−26.9414	+	3.88819i	−1.20007	+	0.173194i
$505$	2.40171	−	13.6208i	0.106875	−	0.606117i
$506$	28.8690	−	0.402856i	1.28338	−	0.0179091i
$507$	27.3244	+	45.0465i	1.21352	+	2.00059i
$508$	−35.2864	+	21.7075i	−1.56558	+	0.963114i
$509$	−4.11496	+	8.19355i	−0.182392	+	0.363173i	−0.966185	−	0.257850i	$-0.916986\pi$
$509$	−4.11496	+	8.19355i	−0.182392	+	0.363173i	0.783793	+	0.621022i	$0.213282\pi$
$510$	−0.224196	−	0.136279i	−0.00992756	−	0.00603454i
$511$	6.32049	−	26.6683i	0.279602	−	1.17973i
$512$	−22.4492	+	2.83417i	−0.992125	+	0.125254i
$513$	−1.54236	−	23.7181i	−0.0680971	−	1.04718i
$514$	6.03624	+	8.90450i	0.266247	+	0.392761i
$515$	8.72584	+	29.1464i	0.384507	+	1.28434i
$516$	3.28767	−	4.33750i	0.144732	−	0.190948i
$517$	22.8322	−	15.0170i	1.00416	−	0.660447i
$518$	11.8195	−	18.5287i	0.519319	−	0.814106i
$519$	−2.22250	+	6.54361i	−0.0975571	+	0.287233i
$520$	−42.5093	−	16.2624i	−1.86415	−	0.713151i
$521$	−8.51499	−	23.3947i	−0.373049	−	1.02494i	−0.974176	−	0.225789i	$-0.927504\pi$
$521$	−8.51499	−	23.3947i	−0.373049	−	1.02494i	0.601128	−	0.799153i	$-0.294718\pi$
$522$	−5.09812	−	1.21330i	−0.223139	−	0.0531046i
$523$	1.18937	−	3.26776i	0.0520074	−	0.142889i	−0.910969	−	0.412475i	$-0.864665\pi$
$523$	1.18937	−	3.26776i	0.0520074	−	0.142889i	0.962976	+	0.269586i	$0.0868867\pi$
$524$	18.1914	+	18.2344i	0.794693	+	0.796573i
$525$	5.09579	−	1.64657i	0.222399	−	0.0718623i
$526$	−8.95638	+	9.76259i	−0.390517	+	0.425669i
$527$	−0.177549	−	0.188191i	−0.00773415	−	0.00819772i
$528$	−27.3338	+	2.12154i	−1.18955	+	0.0923283i
$529$	2.15959	+	2.90083i	0.0938951	+	0.126123i
$530$	−9.30257	+	32.7281i	−0.404078	+	1.42162i
$531$	−17.6441	−	27.7166i	−0.765690	−	1.20280i
$532$	−25.8484	+	13.8979i	−1.12067	+	0.602551i
$533$	4.88349	−	7.42498i	0.211527	−	0.321612i
$534$	−1.93555	−	7.03990i	−0.0837593	−	0.304646i
$535$	−13.8193	−	10.2881i	−0.597459	−	0.444792i
$536$	−2.36612	+	2.42734i	−0.102201	+	0.104845i
$537$	29.7412	−	7.73233i	1.28343	−	0.333675i
$538$	−0.934876	−	2.46115i	−0.0403054	−	0.106107i
$539$	6.51165	+	11.2785i	0.280477	+	0.485800i
$540$	8.11708	+	24.0459i	0.349303	+	1.03477i
$541$	−18.6219	+	32.2541i	−0.800619	+	1.38671i	0.118590	+	0.992943i	$0.462162\pi$
$541$	−18.6219	+	32.2541i	−0.800619	+	1.38671i	−0.919209	+	0.393769i	$0.871171\pi$
$542$	4.89347	+	0.792613i	0.210192	+	0.0340457i
$543$	−30.2400	−	2.87261i	−1.29772	−	0.123275i
$544$	−0.246750	−	0.0259456i	−0.0105793	−	0.00111241i
$545$	29.2842	−	12.6320i	1.25440	−	0.541095i
$546$	−51.5501	+	4.84845i	−2.20614	+	0.207494i
$547$	3.02145	+	0.175979i	0.129188	+	0.00752434i	0.122617	−	0.992454i	$-0.460871\pi$
$547$	3.02145	+	0.175979i	0.129188	+	0.00752434i	0.00657096	+	0.999978i	$0.497908\pi$
$548$	12.2015	+	0.369455i	0.521224	+	0.0157823i
$549$	−0.967223	−	9.49943i	−0.0412801	−	0.405426i
$550$	5.23041	−	1.31697i	0.223026	−	0.0561560i
$551$	−5.61184	+	0.655930i	−0.239072	+	0.0279436i
$552$	−16.3490	−	19.2744i	−0.695860	−	0.820375i
$553$	1.67695	−	5.60141i	0.0713112	−	0.238196i
$554$	6.51299	+	20.6992i	0.276710	+	0.879424i
$555$	−18.9862	−	7.70682i	−0.805918	−	0.327136i
$556$	1.82452	+	0.491189i	0.0773769	+	0.0208311i
$557$	−19.3406	−	23.0492i	−0.819487	−	0.976627i	0.180489	−	0.983577i	$-0.442232\pi$
$557$	−19.3406	−	23.0492i	−0.819487	−	0.976627i	−0.999976	+	0.00695029i	$0.997788\pi$
$558$	1.43189	+	24.9859i	0.0606169	+	1.05774i
$559$	6.65465	−	7.93070i	0.281462	−	0.335433i
$560$	22.8442	−	21.4506i	0.965342	−	0.906452i
$561$	−0.297111	−	0.0457817i	−0.0125440	−	0.00193290i
$562$	23.5957	+	1.04417i	0.995323	+	0.0440458i
$563$	−0.278730	−	4.78561i	−0.0117471	−	0.201690i	−0.999075	−	0.0429974i	$-0.986309\pi$
$563$	−0.278730	−	4.78561i	−0.0117471	−	0.201690i	0.987328	−	0.158692i	$-0.0507278\pi$
$564$	−22.8580	−	7.05858i	−0.962493	−	0.297220i
$565$	−21.8133	+	23.1207i	−0.917691	+	0.972695i
$566$	−37.7874	+	2.73039i	−1.58832	+	0.114767i
$567$	20.4014	+	20.4293i	0.856780	+	0.857952i
$568$	−9.17833	−	41.7507i	−0.385114	−	1.75182i
$569$	18.5756	+	17.5252i	0.778731	+	0.734695i	0.969006	−	0.247036i	$-0.0794567\pi$
$569$	18.5756	+	17.5252i	0.778731	+	0.734695i	−0.190276	+	0.981731i	$0.560938\pi$
$570$	17.1104	+	21.3524i	0.716676	+	0.894354i
$571$	24.6821	−	1.43757i	1.03291	−	0.0601603i	0.466697	−	0.884417i	$-0.345444\pi$
$571$	24.6821	−	1.43757i	1.03291	−	0.0601603i	0.566216	+	0.824257i	$0.308407\pi$
$572$	−52.1291	+	1.45517i	−2.17963	+	0.0608437i
$573$	3.74405	−	1.45524i	0.156410	−	0.0607937i
$574$	3.13303	+	5.25581i	0.130770	+	0.219373i
$575$	3.80903	+	3.19616i	0.158848	+	0.133289i
$576$	16.6549	+	17.2804i	0.693956	+	0.720018i
$577$	3.60364	−	3.02381i	0.150021	−	0.125883i	−0.564688	−	0.825305i	$-0.691003\pi$
$577$	3.60364	−	3.02381i	0.150021	−	0.125883i	0.714709	+	0.699422i	$0.246559\pi$
$578$	22.7017	+	7.90580i	0.944267	+	0.328838i
$579$	−11.8868	−	15.2655i	−0.493998	−	0.634411i
$580$	5.60932	−	2.22077i	0.232914	−	0.0922126i
$581$	−25.6444	−	7.67744i	−1.06391	−	0.318514i
$582$	20.7614	−	39.1119i	0.860587	−	1.62124i
$583$	4.52589	+	38.7215i	0.187443	+	1.60368i
$584$	−22.3414	+	9.20775i	−0.924492	+	0.381019i
$585$	13.1554	+	46.4475i	0.543908	+	1.92037i
$586$	0.599678	−	5.83566i	0.0247725	−	0.241069i
$587$	0.219084	−	3.76152i	0.00904255	−	0.155255i	−0.990764	−	0.135596i	$-0.956705\pi$
$587$	0.219084	−	3.76152i	0.00904255	−	0.155255i	0.999807	−	0.0196585i	$-0.00625791\pi$
$588$	3.99149	−	10.6790i	0.164606	−	0.440396i
$589$	10.6873	+	24.7759i	0.440362	+	1.02087i
$590$	34.9366	+	14.4954i	1.43832	+	0.596766i
$591$	7.62140	−	3.48509i	0.313502	−	0.143358i
$592$	−19.3472	+	1.08099i	−0.795165	+	0.0444283i
$593$	−14.9986	−	8.65945i	−0.615919	−	0.355601i	0.159360	−	0.987221i	$-0.449057\pi$
$593$	−14.9986	−	8.65945i	−0.615919	−	0.355601i	−0.775278	+	0.631620i	$0.782390\pi$
$594$	19.1490	+	21.8839i	0.785694	+	0.897908i
$595$	0.297572	−	0.171803i	0.0121993	−	0.00704326i
$596$	−31.8912	+	14.8253i	−1.30632	+	0.607267i
$597$	39.1304	+	10.7977i	1.60150	+	0.441922i
$598$	−29.2441	−	38.1583i	−1.19588	−	1.56041i
$599$	19.0239	−	25.5535i	0.777295	−	1.04409i	−0.220345	−	0.975422i	$-0.570718\pi$
$599$	19.0239	−	25.5535i	0.777295	−	1.04409i	0.997640	−	0.0686662i	$-0.0218743\pi$
$600$	−3.80230	−	2.79933i	−0.155228	−	0.114282i
$601$	−10.5162	−	6.91663i	−0.428966	−	0.282135i	0.316610	−	0.948556i	$-0.397455\pi$
$601$	−10.5162	−	6.91663i	−0.428966	−	0.282135i	−0.745576	+	0.666421i	$0.767826\pi$
$602$	2.91430	+	6.50500i	0.118778	+	0.265124i
$603$	3.56447	+	0.470509i	0.145156	+	0.0191606i
$604$	−6.66313	+	32.0782i	−0.271119	+	1.30524i
$605$	9.12650	−	6.79443i	0.371045	−	0.276233i
$606$	−8.53339	+	10.9379i	−0.346645	+	0.444320i
$607$	−20.4626	+	19.3055i	−0.830552	+	0.783585i	−0.978682	−	0.205383i	$-0.934156\pi$
$607$	−20.4626	+	19.3055i	−0.830552	+	0.783585i	0.148130	+	0.988968i	$0.452675\pi$
$608$	23.2563	+	11.3441i	0.943166	+	0.460065i
$609$	4.60068	−	5.09290i	0.186429	−	0.206375i
$610$	7.18258	+	8.32125i	0.290814	+	0.336918i
$611$	−42.7609	−	15.5637i	−1.72992	−	0.629640i
$612$	0.134537	+	0.226171i	0.00543833	+	0.00914244i
$613$	15.3157	−	5.57444i	0.618594	−	0.225150i	−0.0136655	−	0.999907i	$-0.504350\pi$
$613$	15.3157	−	5.57444i	0.618594	−	0.225150i	0.632259	+	0.774757i	$0.282128\pi$
$614$	0.0114788	+	0.00641545i	0.000463249	+	0.000258906i
$615$	4.28974	−	3.76071i	0.172979	−	0.151646i
$616$	14.7574	−	32.7324i	0.594592	−	1.31883i
$617$	3.27680	+	4.98213i	0.131919	+	0.200573i	0.895407	−	0.445249i	$-0.146885\pi$
$617$	3.27680	+	4.98213i	0.131919	+	0.200573i	−0.763488	+	0.645822i	$0.776515\pi$
$618$	5.97630	−	29.9258i	0.240402	−	1.20379i
$619$	45.5653	−	13.6414i	1.83143	−	0.548293i	0.831453	−	0.555596i	$-0.187510\pi$
$619$	45.5653	−	13.6414i	1.83143	−	0.548293i	0.999973	+	0.00730285i	$0.00232459\pi$
$620$	−17.8431	−	22.6211i	−0.716594	−	0.908485i
$621$	−6.00577	+	26.1261i	−0.241003	+	1.04841i
$622$	18.4642	+	8.95267i	0.740347	+	0.358969i
$623$	9.30417	+	2.20513i	0.372764	+	0.0883466i
$624$	30.0132	+	34.3989i	1.20149	+	1.37706i
$625$	−25.8171	−	12.9658i	−1.03268	−	0.518634i
$626$	29.8634	−	15.5235i	1.19358	−	0.620443i
$627$	27.4841	+	15.0844i	1.09761	+	0.602413i
$628$	0.822421	+	9.52997i	0.0328182	+	0.380287i
$629$	−0.209246	−	0.0368957i	−0.00834317	−	0.00147113i
$630$	−32.7271	−	5.80214i	−1.30388	−	0.231163i
$631$	−17.2343	+	3.03887i	−0.686087	+	0.120976i	−0.505816	−	0.862641i	$-0.668809\pi$
$631$	−17.2343	+	3.03887i	−0.686087	+	0.120976i	−0.180271	+	0.983617i	$0.557697\pi$
$632$	−4.87249	+	1.68393i	−0.193817	+	0.0669832i
$633$	13.5997	−	21.6856i	0.540539	−	0.861924i
$634$	−2.44053	+	10.9778i	−0.0969260	+	0.435986i
$635$	−49.2228	+	11.6660i	−1.95335	+	0.462952i
$636$	23.6330	−	24.6206i	0.937109	−	0.976271i
$637$	8.58927	−	19.9122i	0.340319	−	0.788949i
$638$	4.96130	−	4.81335i	0.196420	−	0.190562i
$639$	−29.6583	+	34.2954i	−1.17326	+	1.35670i
$640$	−27.1150	−	5.30512i	−1.07181	−	0.209703i
$641$	18.1965	+	36.2322i	0.718719	+	1.43109i	0.894688	+	0.446692i	$0.147398\pi$
$641$	18.1965	+	36.2322i	0.718719	+	1.43109i	−0.175969	+	0.984396i	$0.556306\pi$
$642$	7.40490	+	15.6136i	0.292248	+	0.616221i
$643$	2.92109	−	24.9915i	0.115196	−	0.985568i	−0.804774	−	0.593581i	$-0.797714\pi$
$643$	2.92109	−	24.9915i	0.115196	−	0.985568i	0.919971	−	0.391987i	$-0.128212\pi$
$644$	32.4246	−	6.65521i	1.27771	−	0.262252i
$645$	5.47210	−	3.77122i	0.215464	−	0.148492i
$646$	0.219870	+	0.179325i	0.00865069	+	0.00705546i
$647$	26.8998			1.05754			0.528769	−	0.848765i	$-0.322654\pi$
$647$	26.8998			1.05754			0.528769	+	0.848765i	$0.322654\pi$
$648$	4.11697	−	25.1207i	0.161730	−	0.986835i
$649$	43.3390			1.70120
$650$	−6.95992	−	5.67648i	−0.272991	−	0.222650i
$651$	−29.6016	−	14.0726i	−1.16018	−	0.551550i
$652$	4.65023	−	0.954468i	0.182117	−	0.0373799i
$653$	4.49346	−	38.4440i	0.175843	−	1.50443i	−0.560689	−	0.828027i	$-0.689464\pi$
$653$	4.49346	−	38.4440i	0.175843	−	1.50443i	0.736531	−	0.676403i	$-0.236462\pi$
$654$	−31.8849	−	2.58050i	−1.24680	−	0.100906i
$655$	14.1149	+	28.1050i	0.551514	+	1.09815i
$656$	2.14849	−	4.94857i	0.0838843	−	0.193209i
$657$	22.0032	+	13.1441i	0.858427	+	0.512800i
$658$	22.4869	−	21.8163i	0.876631	−	0.850489i
$659$	−7.92625	+	18.3751i	−0.308763	+	0.715793i	−0.999976	−	0.00685758i	$-0.997817\pi$
$659$	−7.92625	+	18.3751i	−0.308763	+	0.715793i	0.691214	+	0.722651i	$0.257076\pi$
$660$	−32.5060	−	8.00077i	−1.26529	−	0.311429i
$661$	−1.11888	+	0.265179i	−0.0435193	+	0.0103143i	−0.252318	−	0.967644i	$-0.581193\pi$
$661$	−1.11888	+	0.265179i	−0.0435193	+	0.0103143i	0.208799	+	0.977959i	$0.433045\pi$
$662$	−2.85666	+	12.8496i	−0.111027	+	0.499415i
$663$	0.234286	+	0.442361i	0.00909891	+	0.0171799i
$664$	7.70940	+	22.3073i	0.299183	+	0.865691i
$665$	−35.2905	+	6.22266i	−1.36851	+	0.241305i
$666$	13.1964	+	15.7567i	0.511351	+	0.610559i
$667$	6.27572	+	1.10658i	0.242997	+	0.0428469i
$668$	−2.57579	−	29.8474i	−0.0996601	−	1.15483i
$669$	−0.111772	−	5.16285i	−0.00432134	−	0.199607i
$670$	−3.67251	+	1.90903i	−0.141881	+	0.0737523i
$671$	11.2553	+	5.65264i	0.434507	+	0.218218i
$672$	−30.3266	+	8.26096i	−1.16987	+	0.318673i
$673$	46.4101	+	10.9994i	1.78898	+	0.423996i	0.985267	−	0.171023i	$-0.0547074\pi$
$673$	46.4101	+	10.9994i	1.78898	+	0.423996i	0.803712	+	0.595019i	$0.202856\pi$
$674$	−16.6852	−	8.09008i	−0.642689	−	0.311618i
$675$	0.0338538	+	5.00792i	0.00130303	+	0.192755i
$676$	37.6766	+	47.7657i	1.44910	+	1.83714i
$677$	42.6657	−	12.7733i	1.63978	−	0.490917i	0.671542	−	0.740966i	$-0.265632\pi$
$677$	42.6657	−	12.7733i	1.63978	−	0.490917i	0.968233	+	0.250050i	$0.0804470\pi$
$678$	30.1987	−	10.2254i	1.15977	−	0.392705i
$679$	31.8672	+	48.4516i	1.22295	+	1.85940i
$680$	−0.276182	−	0.124517i	−0.0105911	−	0.00477499i
$681$	−2.47222	−	12.4398i	−0.0947355	−	0.476693i
$682$	−28.8166	−	16.1054i	−1.10344	−	0.616707i
$683$	2.17028	−	0.789918i	0.0830435	−	0.0302254i	−0.300164	−	0.953888i	$-0.597042\pi$
$683$	2.17028	−	0.789918i	0.0830435	−	0.0302254i	0.383208	+	0.923662i	$0.374819\pi$
$684$	−5.11734	−	26.9638i	−0.195666	−	1.03099i
$685$	14.0065	+	5.09796i	0.535162	+	0.194783i
$686$	−10.9947	−	12.7377i	−0.419778	−	0.486326i
$687$	13.2588	+	2.84078i	0.505856	+	0.108383i
$688$	3.15518	−	5.43523i	0.120290	−	0.207216i
$689$	47.2181	−	44.5480i	1.79887	−	1.69714i
$690$	−11.5806	−	28.6059i	−0.440867	−	1.08901i
$691$	−37.0974	+	27.6180i	−1.41125	+	1.05064i	−0.421655	+	0.906756i	$0.638551\pi$
$691$	−37.0974	+	27.6180i	−1.41125	+	1.05064i	−0.989595	+	0.143880i	$0.954042\pi$
$692$	−1.62289	+	7.81307i	−0.0616932	+	0.297008i
$693$	−37.1834	+	8.23004i	−1.41248	+	0.312634i
$694$	−7.57372	−	16.9053i	−0.287494	−	0.641715i
$695$	1.92759	+	1.26779i	0.0731176	+	0.0480902i
$696$	−6.01396	−	0.670462i	−0.227959	−	0.0254138i
$697$	0.0353247	−	0.0474493i	0.00133802	−	0.00179727i
$698$	−9.34978	−	12.1998i	−0.353894	−	0.461769i
$699$	10.2143	−	10.0634i	0.386341	−	0.380632i
$700$	5.60739	−	2.60671i	0.211939	−	0.0985243i
$701$	−20.8180	+	12.0193i	−0.786286	+	0.453962i	−0.838653	−	0.544666i	$-0.816657\pi$
$701$	−20.8180	+	12.0193i	−0.786286	+	0.453962i	0.0523675	+	0.998628i	$0.483323\pi$
$702$	10.1884	−	47.3369i	0.384535	−	1.78662i
$703$	19.1902	+	11.0795i	0.723773	+	0.417870i
$704$	−31.0257	+	6.29174i	−1.16933	+	0.237129i
$705$	−23.8029	−	16.9324i	−0.896469	−	0.637711i
$706$	15.5605	+	6.45613i	0.585626	+	0.242980i
$707$	−7.19619	−	16.6826i	−0.270640	−	0.627415i
$708$	−24.1352	−	29.2722i	−0.907056	−	1.10012i
$709$	−0.221573	+	3.80426i	−0.00832134	+	0.142872i	0.991588	+	0.129432i	$0.0413153\pi$
$709$	−0.221573	+	3.80426i	−0.00832134	+	0.142872i	−0.999910	+	0.0134401i	$0.995722\pi$
$710$	5.33570	−	51.9234i	0.200245	−	1.94865i
$711$	4.52320	+	3.07238i	0.169633	+	0.115223i
$712$	−3.21245	−	7.79458i	−0.120392	−	0.292114i
$713$	−3.53306	−	30.2273i	−0.132314	−	1.13202i
$714$	−0.344430	+	0.0122668i	−0.0128900	+	0.000459072i
$715$	−61.0017	−	18.2627i	−2.28133	−	0.682986i
$716$	32.9922	−	13.0619i	1.23298	−	0.488145i
$717$	33.0853	−	4.59501i	1.23559	−	0.171604i
$718$	0.648438	+	0.225817i	0.0241995	+	0.00842740i
$719$	15.4778	−	12.9875i	0.577226	−	0.484350i	−0.306809	−	0.951771i	$-0.599261\pi$
$719$	15.4778	−	12.9875i	0.577226	−	0.484350i	0.884035	+	0.467421i	$0.154817\pi$
$720$	12.6984	+	26.4109i	0.473243	+	0.984277i
$721$	30.6158	+	25.6897i	1.14019	+	0.956736i
$722$	−1.39266	−	2.33626i	−0.0518294	−	0.0869464i
$723$	31.5125	+	25.3003i	1.17196	+	0.940928i
$724$	−35.0617	+	0.978738i	−1.30306	+	0.0363745i
$725$	1.18847	−	0.0692204i	0.0441386	−	0.00257078i
$726$	−11.2809	+	1.72751i	−0.418674	+	0.0641137i
$727$	−12.1138	−	11.4288i	−0.449275	−	0.423869i	0.428058	−	0.903751i	$-0.359198\pi$
$727$	−12.1138	−	11.4288i	−0.449275	−	0.423869i	−0.877333	+	0.479882i	$0.840679\pi$
$728$	−58.3933	+	12.8370i	−2.16420	+	0.475770i
$729$	−23.9621	+	12.4427i	−0.887483	+	0.460840i
$730$	−29.4291	+	2.12645i	−1.08922	+	0.0787035i
$731$	0.0472900	−	0.0501244i	0.00174908	−	0.00185392i
$732$	−2.45008	−	10.7500i	−0.0905577	−	0.397333i
$733$	0.309515	+	5.31417i	0.0114322	+	0.196283i	0.999188	+	0.0402785i	$0.0128245\pi$
$733$	0.309515	+	5.31417i	0.0114322	+	0.196283i	−0.987756	+	0.156005i	$0.950138\pi$
$734$	−20.3122	−	0.898870i	−0.749736	−	0.0331779i
$735$	8.71512	−	10.8550i	0.321462	−	0.400393i
$736$	−21.4586	−	19.7801i	−0.790976	−	0.729105i
$737$	−3.04842	+	3.63297i	−0.112290	+	0.133822i
$738$	−5.56909	+	1.31442i	−0.205001	+	0.0483843i
$739$	11.2624	+	13.4220i	0.414293	+	0.493735i	0.932323	−	0.361627i	$-0.117779\pi$
$739$	11.2624	+	13.4220i	0.414293	+	0.493735i	−0.518030	+	0.855363i	$0.673334\pi$
$740$	−22.8472	−	6.15082i	−0.839879	−	0.226109i
$741$	−7.18149	−	51.7086i	−0.263819	−	1.89956i
$742$	13.4149	+	42.6344i	0.492477	+	1.56516i
$743$	−0.845153	+	2.82301i	−0.0310057	+	0.103566i	−0.972092	−	0.234601i	$-0.924622\pi$
$743$	−0.845153	+	2.82301i	−0.0310057	+	0.103566i	0.941086	+	0.338167i	$0.109807\pi$
$744$	5.16979	+	28.4324i	0.189534	+	1.04238i
$745$	−42.6522	+	4.98533i	−1.56266	+	0.182648i
$746$	−19.0449	+	4.79535i	−0.697284	+	0.175570i
$747$	14.0660	−	20.7082i	0.514648	−	0.757673i
$748$	−0.346964	−	0.0105059i	−0.0126863	−	0.000384132i
$749$	−22.5932	−	1.31590i	−0.825537	−	0.0480820i
$750$	13.9769	+	19.6871i	0.510365	+	0.718870i
$751$	28.2803	−	12.1989i	1.03196	−	0.445145i	0.188352	−	0.982102i	$-0.439686\pi$
$751$	28.2803	−	12.1989i	1.03196	−	0.445145i	0.843610	+	0.536957i	$0.180426\pi$
$752$	−27.1928	−	4.86110i	−0.991620	−	0.177266i
$753$	−15.1891	+	21.3522i	−0.553521	+	0.778118i
$754$	−11.3623	−	1.84039i	−0.413789	−	0.0670230i
$755$	−20.0025	+	34.6453i	−0.727965	+	1.26087i
$756$	26.2660	+	20.5313i	0.955284	+	0.746717i
$757$	−21.1776	−	36.6808i	−0.769715	−	1.33318i	−0.937718	−	0.347398i	$-0.887065\pi$
$757$	−21.1776	−	36.6808i	−0.769715	−	1.33318i	0.168003	−	0.985786i	$-0.446268\pi$
$758$	16.4565	+	43.3231i	0.597726	+	1.57357i
$759$	−24.8169	−	25.1891i	−0.900796	−	0.914306i
$760$	22.6247	+	22.0540i	0.820683	+	0.799983i
$761$	−11.8395	−	8.81419i	−0.429182	−	0.319514i	0.360801	−	0.932643i	$-0.382503\pi$
$761$	−11.8395	−	8.81419i	−0.429182	−	0.319514i	−0.789983	+	0.613129i	$0.789911\pi$
$762$	49.0953	+	12.8130i	1.77853	+	0.464167i
$763$	23.0215	−	35.0024i	0.833433	−	1.26717i
$764$	4.08527	−	2.19653i	0.147800	−	0.0794677i
$765$	0.0694417	+	0.313738i	0.00251067	+	0.0113432i
$766$	3.53814	−	12.4478i	0.127838	−	0.449758i
$767$	−43.0945	−	57.8859i	−1.55605	−	2.09014i
$768$	21.5276	+	17.4517i	0.776811	+	0.629734i
$769$	−8.25389	−	8.74861i	−0.297643	−	0.315483i	0.561242	−	0.827652i	$-0.310324\pi$
$769$	−8.25389	−	8.74861i	−0.297643	−	0.315483i	−0.858885	+	0.512169i	$0.828842\pi$
$770$	29.6383	−	32.3062i	1.06809	−	1.16423i
$771$	2.76025	−	12.8830i	0.0994079	−	0.463968i
$772$	−15.7786	−	15.8159i	−0.567884	−	0.569227i
$773$	4.37064	−	12.0082i	0.157201	−	0.431906i	−0.835941	−	0.548819i	$-0.815078\pi$
$773$	4.37064	−	12.0082i	0.157201	−	0.431906i	0.993142	+	0.116913i	$0.0372998\pi$
$774$	−6.62153	+	0.767690i	−0.238006	+	0.0275941i
$775$	−1.94450	−	5.34247i	−0.0698485	−	0.191907i
$776$	18.2694	−	47.7556i	0.655833	−	1.71433i
$777$	−26.4007	+	5.24673i	−0.947118	+	0.188225i
$778$	−2.29367	+	3.59565i	−0.0822320	+	0.128910i
$779$	−5.15434	+	3.39007i	−0.184674	+	0.121462i
$780$	21.6363	+	51.3724i	0.774705	+	1.83943i
$781$	−17.1528	−	57.2943i	−0.613776	−	2.05015i
$782$	−0.179560	−	0.264883i	−0.00642107	−	0.00947219i
$783$	3.24665	+	5.53658i	0.116026	+	0.197861i
$784$	3.06615	−	12.8022i	0.109505	−	0.457223i
$785$	−2.69354	+	11.3649i	−0.0961365	+	0.405632i
$786$	0.712178	−	31.5376i	0.0254025	−	1.12491i
$787$	−0.689558	+	1.37302i	−0.0245801	+	0.0489430i	−0.905588	−	0.424159i	$-0.860570\pi$
$787$	−0.689558	+	1.37302i	−0.0245801	+	0.0489430i	0.881007	+	0.473102i	$0.156866\pi$
$788$	8.24215	−	5.07040i	0.293615	−	0.180626i
$789$	16.2223	−	0.351201i	0.577530	−	0.0125031i
$790$	−6.29419	+	0.0878333i	−0.223937	+	0.00312497i
$791$	−7.25074	+	41.1210i	−0.257807	+	1.46210i
$792$	25.0361	+	22.3752i	0.889618	+	0.795068i
$793$	−3.64185	−	20.6540i	−0.129326	−	0.733444i
$794$	−1.21271	−	6.35753i	−0.0430373	−	0.225620i
$795$	36.8253	−	19.5037i	1.30606	−	0.691724i
$796$	46.3696	+	6.84812i	1.64353	+	0.242725i
$797$	6.77953	+	28.6051i	0.240143	+	1.01324i	0.950824	+	0.309730i	$0.100239\pi$
$797$	6.77953	+	28.6051i	0.240143	+	1.01324i	−0.710681	+	0.703514i	$0.751613\pi$
$798$	34.1920	+	11.0835i	1.21038	+	0.392350i
$799$	−0.278125	−	0.119971i	−0.00983935	−	0.00424428i
$800$	−4.75290	−	2.67112i	−0.168040	−	0.0944383i
$801$	−4.58579	+	7.67661i	−0.162031	+	0.271240i
$802$	−1.69640	−	1.22651i	−0.0599019	−	0.0433095i
$803$	−30.2116	+	15.1728i	−1.06614	+	0.535438i
$804$	4.15144	+	0.0358041i	0.146410	+	0.00126271i
$805$	40.1440	+	4.69216i	1.41489	+	0.165377i
$806$	7.14277	+	54.5035i	0.251593	+	1.91980i
$807$	−1.38441	+	2.91209i	−0.0487335	+	0.102510i
$808$	−8.23476	+	13.7403i	−0.289698	+	0.483382i
$809$		−	24.4449i		−	0.859437i	−0.902963	−	0.429718i	$-0.858613\pi$
$809$		−	24.4449i		−	0.859437i	0.902963	−	0.429718i	$-0.141387\pi$
$810$	14.3875	−	27.5524i	0.505525	−	0.968093i
$811$		−	1.62195i		−	0.0569544i	−0.999594	−	0.0284772i	$-0.990934\pi$
$811$		−	1.62195i		−	0.0569544i	0.999594	−	0.0284772i	$-0.00906579\pi$
$812$	4.55324	−	6.48638i	0.159788	−	0.227627i
$813$	−3.44527	−	4.99915i	−0.120831	−	0.175328i
$814$	−26.8804	+	3.52272i	−0.942157	+	0.123471i
$815$	5.75731	+	0.672933i	0.201670	+	0.0235718i
$816$	0.186126	+	0.240199i	0.00651571	+	0.00840863i
$817$	−6.42237	+	3.22543i	−0.224690	+	0.112844i
$818$	−19.0592	+	26.3611i	−0.666390	+	0.921693i
$819$	47.9661	+	41.4806i	1.67607	+	1.44945i
$820$	4.38505	−	4.91574i	0.153133	−	0.171665i
$821$	−20.2122	−	8.71871i	−0.705412	−	0.304285i	0.0129878	−	0.999916i	$-0.495866\pi$
$821$	−20.2122	−	8.71871i	−0.705412	−	0.304285i	−0.718400	+	0.695631i	$0.755125\pi$
$822$	−10.0116	−	11.1035i	−0.349195	−	0.387280i
$823$	−7.19336	−	30.3512i	−0.250745	−	1.05797i	−0.942066	−	0.335427i	$-0.891119\pi$
$823$	−7.19336	−	30.3512i	−0.250745	−	1.05797i	0.691321	−	0.722547i	$-0.257029\pi$
$824$	2.62257	−	35.1399i	0.0913615	−	1.22416i
$825$	−5.59639	−	3.50967i	−0.194841	−	0.122191i
$826$	48.8068	−	9.30994i	1.69820	−	0.323934i
$827$	4.06791	+	23.0703i	0.141455	+	0.802232i	0.970145	+	0.242524i	$0.0779754\pi$
$827$	4.06791	+	23.0703i	0.141455	+	0.802232i	−0.828690	+	0.559708i	$0.810913\pi$
$828$	−3.19297	+	30.7896i	−0.110963	+	1.07001i
$829$	5.21908	−	29.5988i	0.181266	−	1.02801i	−0.749394	−	0.662125i	$-0.769655\pi$
$829$	5.21908	−	29.5988i	0.181266	−	1.02801i	0.930660	−	0.365886i	$-0.119234\pi$
$830$	0.402120	+	28.8162i	0.0139578	+	1.00022i
$831$	12.7870	−	23.2982i	0.443576	−	0.808205i
$832$	39.2543	+	35.1834i	1.36090	+	1.21977i
$833$	0.0647828	−	0.128993i	0.00224459	−	0.00446935i
$834$	−1.11153	−	2.02971i	−0.0384890	−	0.0702831i
$835$	8.43604	−	35.5945i	0.291941	−	1.23180i
$836$	33.6280	+	13.4056i	1.16305	+	0.463642i
$837$	20.8832	−	22.4368i	0.721828	−	0.775530i
$838$	15.5532	−	10.5433i	0.537275	−	0.364212i
$839$	13.0775	+	43.6818i	0.451485	+	1.50806i	0.816656	+	0.577124i	$0.195825\pi$
$839$	13.0775	+	43.6818i	0.451485	+	1.50806i	−0.365171	+	0.930940i	$0.618990\pi$
$840$	−38.3257	−	2.02733i	−1.32236	−	0.0699497i
$841$	−22.9544	+	15.0974i	−0.791532	+	0.520599i
$842$	−4.54189	−	2.89728i	−0.156524	−	0.0998468i
$843$	−19.0691	−	21.7517i	−0.656776	−	0.749168i
$844$	12.5230	−	26.7730i	0.431059	−	0.921566i
$845$	25.4067	+	69.8042i	0.874015	+	2.40134i
$846$	13.1252	+	26.1953i	0.451254	+	0.900613i
$847$	5.11192	−	14.0449i	0.175648	−	0.482588i
$848$	23.6069	−	31.5537i	0.810665	−	1.08356i
$849$	34.4318	+	31.1040i	1.18170	+	1.06749i
$850$	−0.0440521	−	0.0404142i	−0.00151097	−	0.00138620i
$851$	−17.1509	−	18.1789i	−0.587925	−	0.623165i
$852$	−29.1457	+	43.4922i	−0.998516	+	1.49002i
$853$	−20.6049	−	27.6772i	−0.705498	−	0.947648i	0.294470	−	0.955661i	$-0.404857\pi$
$853$	−20.6049	−	27.6772i	−0.705498	−	0.947648i	−0.999968	+	0.00801267i	$0.997449\pi$
$854$	13.8896	+	3.94796i	0.475293	+	0.135096i
$855$	4.38551	−	33.2235i	0.149981	−	1.13622i
$856$	10.6914	+	16.8479i	0.365424	+	0.575849i
$857$	−1.85316	+	2.81759i	−0.0633028	+	0.0962472i	−0.865752	−	0.500473i	$-0.833159\pi$
$857$	−1.85316	+	2.81759i	−0.0633028	+	0.0962472i	0.802449	+	0.596720i	$0.203530\pi$
$858$	45.4558	+	44.8677i	1.55184	+	1.53176i
$859$	−20.1595	−	15.0082i	−0.687833	−	0.512073i	0.195568	−	0.980690i	$-0.437345\pi$
$859$	−20.1595	−	15.0082i	−0.687833	−	0.512073i	−0.883401	+	0.468617i	$0.844752\pi$
$860$	5.73858	−	5.09477i	0.195684	−	0.173730i
$861$	1.99340	−	7.22395i	0.0679347	−	0.246192i
$862$	−36.2728	+	13.7784i	−1.23546	+	0.469293i
$863$	6.07199	+	10.5170i	0.206693	+	0.358003i	0.950671	−	0.310202i	$-0.100397\pi$
$863$	6.07199	+	10.5170i	0.206693	+	0.358003i	−0.743978	+	0.668204i	$0.767063\pi$
$864$	1.17035	−	29.3706i	0.0398161	−	0.999207i
$865$	−4.87187	+	8.43833i	−0.165649	+	0.286912i
$866$	2.02319	−	12.4908i	0.0687507	−	0.424456i
$867$	−12.2436	−	26.7750i	−0.415814	−	0.909325i
$868$	−35.9119	−	11.9470i	−1.21893	−	0.405507i
$869$	−6.62269	+	2.85675i	−0.224659	+	0.0969086i
$870$	−6.71673	−	3.07898i	−0.227718	−	0.104387i
$871$	7.88361	+	0.459168i	0.267126	+	0.0155583i
$872$	−36.9056	+	1.54582i	−1.24978	+	0.0523479i
$873$	−52.1799	+	14.7790i	−1.76602	+	0.500192i
$874$	8.14888	+	32.3635i	0.275640	+	1.09471i
$875$	−31.4064	+	3.67088i	−1.06173	+	0.124098i
$876$	27.0727	+	11.9560i	0.914703	+	0.403956i
$877$	−8.22976	+	27.4893i	−0.277899	+	0.928248i	0.699103	+	0.715021i	$0.253583\pi$
$877$	−8.22976	+	27.4893i	−0.277899	+	0.928248i	−0.977003	+	0.213227i	$0.931603\pi$
$878$	44.9262	−	14.1360i	1.51618	−	0.477067i
$879$	−5.66890	+	4.41421i	−0.191207	+	0.148888i
$880$	−38.3828	−	4.57826i	−1.29389	−	0.154333i
$881$	22.6735	+	27.0212i	0.763889	+	0.910368i	0.998087	−	0.0618211i	$-0.0196908\pi$
$881$	22.6735	+	27.0212i	0.763889	+	0.910368i	−0.234198	+	0.972189i	$0.575246\pi$
$882$	−12.8261	+	5.51845i	−0.431876	+	0.185816i
$883$	19.0825	−	22.7417i	0.642178	−	0.765318i	−0.342535	−	0.939505i	$-0.611285\pi$
$883$	19.0825	−	22.7417i	0.642178	−	0.765318i	0.984712	+	0.174188i	$0.0557299\pi$
$884$	0.330974	+	0.473870i	0.0111319	+	0.0159380i
$885$	−16.7827	−	43.1783i	−0.564143	−	1.45142i
$886$	−0.334769	+	7.56493i	−0.0112468	+	0.254149i
$887$	0.905852	+	15.5529i	0.0304155	+	0.522215i	0.978765	+	0.204987i	$0.0657151\pi$
$887$	0.905852	+	15.5529i	0.0304155	+	0.522215i	−0.948349	+	0.317228i	$0.897248\pi$
$888$	17.3488	+	16.1939i	0.582189	+	0.543431i
$889$	−45.6016	+	48.3348i	−1.52943	+	1.62110i
$890$	−0.741888	−	10.2674i	−0.0248681	−	0.344164i
$891$	3.12823	−	35.4768i	0.104800	−	1.18852i
$892$	−0.857249	−	5.90100i	−0.0287028	−	0.197580i
$893$	22.9772	+	21.6779i	0.768902	+	0.725422i
$894$	40.1322	+	15.6418i	1.34222	+	0.523139i
$895$	43.2540	−	2.51926i	1.44582	−	0.0842095i
$896$	−33.5885	+	13.7504i	−1.12211	+	0.459368i
$897$	−8.96704	+	58.1937i	−0.299401	+	1.94303i
$898$	20.3679	−	12.1415i	0.679686	−	0.405166i
$899$	−5.58164	−	4.68356i	−0.186158	−	0.156205i
$900$	0.746073	+	5.73445i	0.0248691	+	0.191148i
$901$	0.331008	−	0.277749i	0.0110275	−	0.00925316i
$902$	2.48227	−	7.12789i	0.0826504	−	0.237333i
$903$	3.28345	−	8.08896i	0.109266	−	0.269184i
$904$	33.1645	−	15.9837i	1.10303	−	0.531608i
$905$	−41.0293	−	12.2834i	−1.36386	−	0.408313i
$906$	34.0142	−	21.2872i	1.13005	−	0.707221i
$907$	2.71183	+	23.2012i	0.0900448	+	0.770382i	0.960528	+	0.278184i	$0.0897325\pi$
$907$	2.71183	+	23.2012i	0.0900448	+	0.770382i	−0.870483	+	0.492198i	$0.836193\pi$
$908$	−4.59012	−	13.9072i	−0.152328	−	0.461527i
$909$	16.9033	−	1.72108i	0.560646	−	0.0570845i
$910$	−72.6210	−	7.46260i	−2.40736	−	0.247383i
$911$	−0.752067	+	12.9125i	−0.0249171	+	0.427810i	0.962664	+	0.270699i	$0.0872549\pi$
$911$	−0.752067	+	12.9125i	−0.0249171	+	0.427810i	−0.987581	+	0.157111i	$0.949782\pi$
$912$	−9.67276	−	30.1787i	−0.320297	−	0.999316i
$913$	13.0788	+	30.3201i	0.432845	+	1.00345i
$914$	−12.1520	+	29.2885i	−0.401951	+	0.968777i
$915$	1.27316	−	13.4025i	0.0420892	−	0.443074i
$916$	15.5962	+	1.38306i	0.515314	+	0.0456976i
$917$	35.7787	+	20.6568i	1.18152	+	0.682149i
$918$	0.0860231	−	0.310613i	0.00283918	−	0.0102518i
$919$	−47.1233	+	27.2066i	−1.55445	+	0.897464i	−0.556683	+	0.830725i	$0.687926\pi$
$919$	−47.1233	+	27.2066i	−1.55445	+	0.897464i	−0.997770	+	0.0667391i	$0.978740\pi$
$920$	−17.3118	−	31.1477i	−0.570753	−	1.02691i
$921$	−0.00405247	−	0.0155872i	−0.000133534	−	0.000513615i
$922$	−20.2138	+	15.4916i	−0.665705	+	0.510189i
$923$	−59.4694	+	79.8813i	−1.95746	+	2.62932i
$924$	−41.4510	+	14.6833i	−1.36364	+	0.483047i
$925$	−3.90086	−	2.56564i	−0.128260	−	0.0843577i
$926$	13.2908	−	5.95441i	0.436764	−	0.195674i
$927$	−31.5288	+	20.0709i	−1.03554	+	0.659215i
$928$	−6.98688	+	0.0809891i	−0.229356	+	0.00265860i
$929$	−47.2762	+	35.1959i	−1.55108	+	1.15474i	−0.623084	+	0.782155i	$0.714121\pi$
$929$	−47.2762	+	35.1959i	−1.55108	+	1.15474i	−0.927999	+	0.372584i	$0.878472\pi$
$930$	−4.88671	+	34.9464i	−0.160241	+	1.14594i
$931$	−10.9499	+	10.3307i	−0.358868	+	0.338574i
$932$	10.2847	−	12.9755i	0.336885	−	0.425027i
$933$	−7.72735	−	23.9145i	−0.252982	−	0.782926i
$934$	−9.22538	+	7.96299i	−0.301864	+	0.260557i
$935$	−0.398291	−	0.144966i	−0.0130255	−	0.00474090i
$936$	4.99073	−	55.6885i	0.163127	−	1.82023i
$937$	−13.1332	+	4.78010i	−0.429044	+	0.156159i	−0.547510	−	0.836799i	$-0.684424\pi$
$937$	−13.1332	+	4.78010i	−0.429044	+	0.156159i	0.118467	+	0.992958i	$0.462202\pi$
$938$	−2.65260	+	4.74617i	−0.0866104	+	0.154968i
$939$	−39.0315	−	13.2568i	−1.27374	−	0.432621i
$940$	−29.6703	−	16.0433i	−0.967737	−	0.523276i
$941$	−29.7533	−	45.2378i	−0.969931	−	1.47471i	−0.877838	−	0.478959i	$-0.841014\pi$
$941$	−29.7533	−	45.2378i	−0.969931	−	1.47471i	−0.0920938	−	0.995750i	$-0.529356\pi$
$942$	7.73105	−	8.80204i	0.251891	−	0.286786i
$943$	6.66584	−	1.99562i	0.217070	−	0.0649864i
$944$	−31.7938	−	30.1382i	−1.03480	−	0.980916i
$945$	22.5985	+	33.8586i	0.735129	+	1.10142i
$946$	3.83612	−	7.91170i	0.124723	−	0.257232i
$947$	23.6467	+	5.60436i	0.768413	+	0.182117i	0.596084	−	0.802922i	$-0.296723\pi$
$947$	23.6467	+	5.60436i	0.768413	+	0.182117i	0.172329	+	0.985039i	$0.444871\pi$
$948$	5.61765	+	2.88222i	0.182453	+	0.0936102i
$949$	50.3068	+	25.2650i	1.63303	+	0.820137i
$950$	2.87559	+	5.53194i	0.0932966	+	0.179480i
$951$	11.7762	−	7.14321i	0.381869	−	0.231635i
$952$	−0.392995	+	0.0627024i	−0.0127370	+	0.00203220i
$953$	−5.35751	−	0.944673i	−0.173547	−	0.0306010i	0.0861994	−	0.996278i	$-0.472528\pi$
$953$	−5.35751	−	0.944673i	−0.173547	−	0.0306010i	−0.259746	+	0.965677i	$0.583639\pi$
$954$	−41.7976	−	0.0389625i	−1.35325	−	0.00126146i
$955$	5.57757	−	0.983476i	0.180486	−	0.0318245i
$956$	37.2678	−	9.93870i	1.20533	−	0.321441i
$957$	−8.46041	−	0.309212i	−0.273486	−	0.00999539i
$958$	−48.7377	−	10.8351i	−1.57464	−	0.350066i
$959$	19.0523	−	4.51547i	0.615230	−	0.145812i
$960$	18.2829	+	28.4743i	0.590077	+	0.919004i
$961$	−1.50390	+	3.48644i	−0.0485130	+	0.112466i
$962$	31.4339	+	32.4001i	1.01347	+	1.04462i
$963$	7.53385	−	19.7780i	0.242775	−	0.637336i
$964$	39.6875	+	24.5444i	1.27825	+	0.790521i
$965$	−12.2428	−	24.3774i	−0.394109	−	0.784736i
$966$	−33.3589	−	23.0359i	−1.07330	−	0.741169i
$967$	6.56209	−	56.1422i	0.211022	−	1.80541i	−0.308788	−	0.951131i	$-0.599923\pi$
$967$	6.56209	−	56.1422i	0.211022	−	1.80541i	0.519810	−	0.854282i	$-0.326003\pi$
$968$	−12.6843	+	3.57299i	−0.407688	+	0.114840i
$969$	−0.0277086	−	0.346386i	−0.000890128	−	0.0111275i
$970$	39.4599	−	48.3818i	1.26698	−	1.55345i
$971$	24.4690			0.785249			0.392624	−	0.919699i	$-0.371567\pi$
$971$	24.4690			0.785249			0.392624	+	0.919699i	$0.371567\pi$
$972$	−25.7040	+	17.6439i	−0.824455	+	0.565928i
$973$	3.03070			0.0971598
$974$	32.6440	−	40.0247i	1.04598	−	1.28247i
$975$	0.877106	+	10.9647i	0.0280899	+	0.351152i
$976$	−4.32611	−	11.9738i	−0.138475	−	0.383273i
$977$	−3.55947	+	30.4532i	−0.113878	+	0.974286i	0.808633	+	0.588314i	$0.200208\pi$
$977$	−3.55947	+	30.4532i	−0.113878	+	0.974286i	−0.922511	+	0.385972i	$0.873866\pi$
$978$	−4.78422	−	3.30374i	−0.152982	−	0.105642i
$979$	−5.29358	−	10.5404i	−0.169184	−	0.336872i
$980$	8.45473	−	13.6710i	0.270076	−	0.436705i
$981$	24.7340	+	30.3841i	0.789695	+	0.970089i
$982$	−8.88472	−	9.15782i	−0.283523	−	0.292238i
$983$	−14.2475	+	33.0294i	−0.454425	+	1.05348i	0.524897	+	0.851166i	$0.324104\pi$
$983$	−14.2475	+	33.0294i	−0.454425	+	1.05348i	−0.979322	+	0.202310i	$0.935155\pi$
$984$	−6.19671	+	2.29289i	−0.197544	+	0.0730947i
$985$	11.4974	−	2.72493i	0.366338	−	0.0868236i
$986$	−0.0747906	−	0.0166270i	−0.00238182	−	0.000529513i
$987$	−38.3465	−	1.40149i	−1.22058	−	0.0446099i
$988$	−15.5331	−	58.2454i	−0.494173	−	1.85303i
$989$	7.98267	−	1.40756i	0.253834	−	0.0447578i
$990$	20.4668	+	35.5259i	0.650476	+	1.12909i
$991$	9.10143	+	1.60483i	0.289116	+	0.0509790i	0.316325	−	0.948651i	$-0.397551\pi$
$991$	9.10143	+	1.60483i	0.289116	+	0.0509790i	−0.0272090	+	0.999630i	$0.508662\pi$
$992$	9.94028	+	31.8543i	0.315604	+	1.01137i
$993$	13.7841	−	8.36117i	0.437425	−	0.265334i
$994$	−31.6246	−	60.8381i	−1.00307	−	1.92967i
$995$	51.1457	+	25.6864i	1.62143	+	0.814312i
$996$	13.1954	−	25.7188i	0.418113	−	0.814931i
$997$	−40.8978	−	9.69295i	−1.29525	−	0.306979i	−0.475504	−	0.879713i	$-0.657734\pi$
$997$	−40.8978	−	9.69295i	−1.29525	−	0.306979i	−0.819741	+	0.572734i	$0.805883\pi$
$998$	−1.09672	+	2.26190i	−0.0347160	+	0.0715991i
$999$	2.75321	−	25.0209i	0.0871077	−	0.791627i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.p.a.11.12	✓	936
3.2	odd	2		972.2.p.a.359.41		936
4.3	odd	2	inner	324.2.p.a.11.15	yes	936
12.11	even	2		972.2.p.a.359.38		936
81.22	even	27		972.2.p.a.287.38		936
81.59	odd	54	inner	324.2.p.a.59.15	yes	936
324.59	even	54	inner	324.2.p.a.59.12	yes	936
324.103	odd	54		972.2.p.a.287.41		936

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.p.a.11.12	✓	936	1.1	even	1	trivial
324.2.p.a.11.15	yes	936	4.3	odd	2	inner
324.2.p.a.59.12	yes	936	324.59	even	54	inner
324.2.p.a.59.15	yes	936	81.59	odd	54	inner
972.2.p.a.287.38		936	81.22	even	27
972.2.p.a.287.41		936	324.103	odd	54
972.2.p.a.359.38		936	12.11	even	2
972.2.p.a.359.41		936	3.2	odd	2

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.p (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09593 - 0.893834i) q^{2} +(0.138112 + 1.72654i) q^{3} +(0.402121 + 1.95916i) q^{4} +(-0.283509 + 2.42558i) q^{5} +(1.39188 - 2.01561i) q^{6} +(1.43973 + 2.86675i) q^{7} +(1.31047 - 2.50653i) q^{8} +(-2.96185 + 0.476909i) q^{9} +O(q^{10})\)	\(q+(-1.09593 - 0.893834i) q^{2} +(0.138112 + 1.72654i) q^{3} +(0.402121 + 1.95916i) q^{4} +(-0.283509 + 2.42558i) q^{5} +(1.39188 - 2.01561i) q^{6} +(1.43973 + 2.86675i) q^{7} +(1.31047 - 2.50653i) q^{8} +(-2.96185 + 0.476909i) q^{9} +(2.47877 - 2.40485i) q^{10} +(1.56735 - 3.63353i) q^{11} +(-3.32702 + 0.964859i) q^{12} +(-6.41164 + 1.51959i) q^{13} +(0.984550 - 4.42864i) q^{14} +(-4.22700 - 0.154489i) q^{15} +(-3.67660 + 1.57564i) q^{16} +(-0.0431938 + 0.00761624i) q^{17} +(3.67226 + 2.12474i) q^{18} +(4.50470 + 0.794300i) q^{19} +(-4.86609 + 0.419936i) q^{20} +(-4.75070 + 2.88168i) q^{21} +(-4.96547 + 2.58114i) q^{22} +(-4.61035 - 2.31541i) q^{23} +(4.50860 + 1.91639i) q^{24} +(-0.937818 - 0.222267i) q^{25} +(8.38496 + 4.06558i) q^{26} +(-1.23247 - 5.04787i) q^{27} +(-5.03746 + 3.97345i) q^{28} +(-1.18331 + 0.354259i) q^{29} +(4.49440 + 3.94755i) q^{30} +(3.24150 + 4.92846i) q^{31} +(5.43765 + 1.55948i) q^{32} +(6.48988 + 2.20425i) q^{33} +(0.0541450 + 0.0302613i) q^{34} +(-7.36169 + 2.67944i) q^{35} +(-2.12536 - 5.61096i) q^{36} +(4.55219 + 1.65686i) q^{37} +(-4.22686 - 4.89695i) q^{38} +(-3.50914 - 10.8601i) q^{39} +(5.70824 + 3.88926i) q^{40} +(-0.981017 + 0.925542i) q^{41} +(7.78217 + 1.08821i) q^{42} +(-1.26027 + 0.938234i) q^{43} +(7.74891 + 1.60957i) q^{44} +(-0.317068 - 7.31940i) q^{45} +(2.98303 + 6.65841i) q^{46} +(5.76986 + 3.79489i) q^{47} +(-3.22817 - 6.13016i) q^{48} +(-1.96529 + 2.63985i) q^{49} +(0.829112 + 1.08184i) q^{50} +(-0.0191153 - 0.0735238i) q^{51} +(-5.55536 - 11.9504i) q^{52} +(-8.53190 + 4.92589i) q^{53} +(-3.16127 + 6.63373i) q^{54} +(8.36904 + 4.83187i) q^{55} +(9.07230 + 0.148041i) q^{56} +(-0.749236 + 7.88723i) q^{57} +(1.61347 + 0.669439i) q^{58} +(4.33789 + 10.0564i) q^{59} +(-1.39710 - 8.34348i) q^{60} +(-0.185066 + 3.17746i) q^{61} +(0.852772 - 8.29860i) q^{62} +(-5.63146 - 7.80425i) q^{63} +(-4.56536 - 6.56944i) q^{64} +(-1.86811 - 15.9827i) q^{65} +(-5.14221 - 8.21658i) q^{66} +(-1.14811 - 0.343723i) q^{67} +(-0.0322905 - 0.0815609i) q^{68} +(3.36089 - 8.27972i) q^{69} +(10.4629 + 3.64366i) q^{70} +(11.5777 - 9.71483i) q^{71} +(-2.68602 + 8.04893i) q^{72} +(-6.54463 - 5.49160i) q^{73} +(-3.50792 - 5.88471i) q^{74} +(0.254228 - 1.64987i) q^{75} +(0.255275 + 9.14482i) q^{76} +(12.6730 - 0.738116i) q^{77} +(-5.86131 + 15.0384i) q^{78} +(-1.32576 - 1.25079i) q^{79} +(-2.77948 - 9.36457i) q^{80} +(8.54512 - 2.82507i) q^{81} +(1.90241 - 0.137462i) q^{82} +(-5.72637 + 6.06959i) q^{83} +(-7.55603 - 8.14858i) q^{84} +(-0.00622792 - 0.106929i) q^{85} +(2.21979 + 0.0982318i) q^{86} +(-0.775070 - 1.99410i) q^{87} +(-7.05357 - 8.69022i) q^{88} +(1.91594 - 2.28333i) q^{89} +(-6.19485 + 8.30495i) q^{90} +(-13.5873 - 16.1927i) q^{91} +(2.68233 - 9.96348i) q^{92} +(-8.06147 + 6.27724i) q^{93} +(-2.93135 - 9.31623i) q^{94} +(-3.20376 + 10.7013i) q^{95} +(-1.94150 + 9.60368i) q^{96} +(17.9553 - 2.09867i) q^{97} +(4.51341 - 1.13644i) q^{98} +(-2.90939 + 11.5094i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Introduction

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