LMFDB - Embedded newform 162.2.g.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$4$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	162.13
Dual form			162.2.g.a.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.893633 - 0.448799i) q^{2} +(-1.71649 + 0.231626i) q^{3} +(0.597159 + 0.802123i) q^{4} +(-0.267154 - 0.892356i) q^{5} +(1.63787 + 0.563372i) q^{6} +(1.11188 + 2.57764i) q^{7} +(-0.173648 - 0.984808i) q^{8} +(2.89270 - 0.795169i) q^{9} +O(q^{10})$	\(q+(-0.893633 - 0.448799i) q^{2} +(-1.71649 + 0.231626i) q^{3} +(0.597159 + 0.802123i) q^{4} +(-0.267154 - 0.892356i) q^{5} +(1.63787 + 0.563372i) q^{6} +(1.11188 + 2.57764i) q^{7} +(-0.173648 - 0.984808i) q^{8} +(2.89270 - 0.795169i) q^{9} +(-0.161751 + 0.917337i) q^{10} +(4.46341 - 1.05785i) q^{11} +(-1.21081 - 1.23852i) q^{12} +(1.47403 + 0.969483i) q^{13} +(0.163226 - 2.80247i) q^{14} +(0.665260 + 1.46984i) q^{15} +(-0.286803 + 0.957990i) q^{16} +(1.42569 - 0.518907i) q^{17} +(-2.94188 - 0.587652i) q^{18} +(4.12421 + 1.50109i) q^{19} +(0.556246 - 0.747168i) q^{20} +(-2.50559 - 4.16696i) q^{21} +(-4.46341 - 1.05785i) q^{22} +(-2.92223 + 6.77448i) q^{23} +(0.526173 + 1.65019i) q^{24} +(3.45251 - 2.27075i) q^{25} +(-0.882135 - 1.52790i) q^{26} +(-4.78112 + 2.03493i) q^{27} +(-1.40361 + 2.43113i) q^{28} +(-0.418954 - 7.19315i) q^{29} +(0.0651659 - 1.61207i) q^{30} +(-6.24778 + 0.730261i) q^{31} +(0.686242 - 0.727374i) q^{32} +(-7.41639 + 2.84963i) q^{33} +(-1.50693 - 0.176134i) q^{34} +(2.00313 - 1.68082i) q^{35} +(2.36522 + 1.84546i) q^{36} +(-0.516723 - 0.433582i) q^{37} +(-3.01184 - 3.19236i) q^{38} +(-2.75471 - 1.32269i) q^{39} +(-0.832408 + 0.418051i) q^{40} +(-8.46317 + 4.25037i) q^{41} +(0.368950 + 4.84823i) q^{42} +(3.77539 + 4.00168i) q^{43} +(3.51389 + 2.94850i) q^{44} +(-1.48237 - 2.36888i) q^{45} +(5.65178 - 4.74241i) q^{46} +(5.01677 + 0.586377i) q^{47} +(0.270401 - 1.71081i) q^{48} +(-0.604237 + 0.640453i) q^{49} +(-4.10439 + 0.479734i) q^{50} +(-2.32699 + 1.22093i) q^{51} +(0.102583 + 1.76129i) q^{52} +(-1.33883 + 2.31892i) q^{53} +(5.18583 + 0.327285i) q^{54} +(-2.13639 - 3.70034i) q^{55} +(2.34540 - 1.54259i) q^{56} +(-7.42686 - 1.62134i) q^{57} +(-2.85389 + 6.61606i) q^{58} +(4.89941 + 1.16118i) q^{59} +(-0.781729 + 1.41135i) q^{60} +(3.14866 - 4.22938i) q^{61} +(5.91096 + 2.15141i) q^{62} +(5.26600 + 6.57219i) q^{63} +(-0.939693 + 0.342020i) q^{64} +(0.471331 - 1.57436i) q^{65} +(7.90644 + 0.781947i) q^{66} +(0.832311 - 14.2902i) q^{67} +(1.26759 + 0.833706i) q^{68} +(3.44684 - 12.3052i) q^{69} +(-2.54441 + 0.603036i) q^{70} +(-0.0492509 + 0.279316i) q^{71} +(-1.28540 - 2.71067i) q^{72} +(-2.01050 - 11.4021i) q^{73} +(0.267169 + 0.619368i) q^{74} +(-5.40025 + 4.69742i) q^{75} +(1.25875 + 4.20451i) q^{76} +(7.68955 + 10.3289i) q^{77} +(1.86808 + 2.41831i) q^{78} +(3.17920 + 1.59665i) q^{79} +0.931488 q^{80} +(7.73541 - 4.60037i) q^{81} +9.47053 q^{82} +(-9.56164 - 4.80204i) q^{83} +(1.84618 - 4.49813i) q^{84} +(-0.843927 - 1.13359i) q^{85} +(-1.57786 - 5.27043i) q^{86} +(2.38525 + 12.2500i) q^{87} +(-1.81684 - 4.21191i) q^{88} +(1.74720 + 9.90888i) q^{89} +(0.261540 + 2.78220i) q^{90} +(-0.860028 + 4.87746i) q^{91} +(-7.17900 + 1.70145i) q^{92} +(10.5551 - 2.70064i) q^{93} +(-4.21999 - 2.77553i) q^{94} +(0.237708 - 4.08128i) q^{95} +(-1.00945 + 1.40748i) q^{96} +(-4.96298 + 16.5775i) q^{97} +(0.827401 - 0.301149i) q^{98} +(12.0701 - 6.60920i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 9 q^{6}+O(q^{10}) $ 72 * q + 9 * q^6	$ 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) $ 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{4}{27}\right)$

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 $

$2$	−0.893633	−	0.448799i	−0.631894	−	0.317349i
$2$	−0.893633	−	0.448799i	−0.631894	−	0.317349i
$3$	−1.71649	+	0.231626i	−0.991018	+	0.133729i
$3$	−1.71649	+	0.231626i	−0.991018	+	0.133729i
$4$	0.597159	+	0.802123i	0.298579	+	0.401062i
$5$	−0.267154	−	0.892356i	−0.119475	−	0.399074i	0.877241	−	0.480050i	$-0.159381\pi$
$5$	−0.267154	−	0.892356i	−0.119475	−	0.399074i	−0.996716	+	0.0809762i	$0.974196\pi$
$6$	1.63787	+	0.563372i	0.668657	+	0.229996i
$7$	1.11188	+	2.57764i	0.420253	+	0.974255i	0.988476	+	0.151381i	$0.0483719\pi$
$7$	1.11188	+	2.57764i	0.420253	+	0.974255i	−0.568223	+	0.822875i	$0.692369\pi$
$8$	−0.173648	−	0.984808i	−0.0613939	−	0.348182i
$9$	2.89270	−	0.795169i	0.964233	−	0.265056i
$10$	−0.161751	+	0.917337i	−0.0511502	+	0.290087i
$11$	4.46341	−	1.05785i	1.34577	−	0.318953i	0.506299	−	0.862358i	$-0.331013\pi$
$11$	4.46341	−	1.05785i	1.34577	−	0.318953i	0.839471	+	0.543405i	$0.182865\pi$
$12$	−1.21081	−	1.23852i	−0.349531	−	0.357530i
$13$	1.47403	+	0.969483i	0.408821	+	0.268886i	0.737219	−	0.675653i	$-0.236138\pi$
$13$	1.47403	+	0.969483i	0.408821	+	0.268886i	−0.328398	+	0.944539i	$0.606509\pi$
$14$	0.163226	−	2.80247i	0.0436239	−	0.748993i
$15$	0.665260	+	1.46984i	0.171769	+	0.379512i
$16$	−0.286803	+	0.957990i	−0.0717008	+	0.239497i
$17$	1.42569	−	0.518907i	0.345780	−	0.125854i	−0.163292	−	0.986578i	$-0.552211\pi$
$17$	1.42569	−	0.518907i	0.345780	−	0.125854i	0.509071	+	0.860724i	$0.329989\pi$
$18$	−2.94188	−	0.587652i	−0.693408	−	0.138511i
$19$	4.12421	+	1.50109i	0.946158	+	0.344373i	0.768595	−	0.639736i	$-0.220956\pi$
$19$	4.12421	+	1.50109i	0.946158	+	0.344373i	0.177563	+	0.984109i	$0.443179\pi$
$20$	0.556246	−	0.747168i	0.124380	−	0.167072i
$21$	−2.50559	−	4.16696i	−0.546764	−	0.909304i
$22$	−4.46341	−	1.05785i	−0.951603	−	0.225534i
$23$	−2.92223	+	6.77448i	−0.609326	+	1.41258i	0.282088	+	0.959388i	$0.408973\pi$
$23$	−2.92223	+	6.77448i	−0.609326	+	1.41258i	−0.891415	+	0.453189i	$0.850286\pi$
$24$	0.526173	+	1.65019i	0.107405	+	0.336845i
$25$	3.45251	−	2.27075i	0.690502	−	0.454151i
$26$	−0.882135	−	1.52790i	−0.173001	−	0.299646i
$27$	−4.78112	+	2.03493i	−0.920126	+	0.391622i
$28$	−1.40361	+	2.43113i	−0.265258	+	0.459440i
$29$	−0.418954	−	7.19315i	−0.0777977	−	1.33574i	−0.780904	−	0.624651i	$-0.785241\pi$
$29$	−0.418954	−	7.19315i	−0.0777977	−	1.33574i	0.703107	−	0.711085i	$-0.251796\pi$
$30$	0.0651659	−	1.61207i	0.0118976	−	0.294322i
$31$	−6.24778	+	0.730261i	−1.12213	+	0.131159i	−0.656863	−	0.754010i	$-0.728117\pi$
$31$	−6.24778	+	0.730261i	−1.12213	+	0.131159i	−0.465271	+	0.885168i	$0.654043\pi$
$32$	0.686242	−	0.727374i	0.121312	−	0.128583i
$33$	−7.41639	+	2.84963i	−1.29103	+	0.496057i
$34$	−1.50693	−	0.176134i	−0.258436	−	0.0302068i
$35$	2.00313	−	1.68082i	0.338590	−	0.284111i
$36$	2.36522	+	1.84546i	0.394204	+	0.307576i
$37$	−0.516723	−	0.433582i	−0.0849487	−	0.0712804i	0.599324	−	0.800506i	$-0.295436\pi$
$37$	−0.516723	−	0.433582i	−0.0849487	−	0.0712804i	−0.684273	+	0.729226i	$0.739880\pi$
$38$	−3.01184	−	3.19236i	−0.488585	−	0.517870i
$39$	−2.75471	−	1.32269i	−0.441107	−	0.211800i
$40$	−0.832408	+	0.418051i	−0.131615	+	0.0660997i
$41$	−8.46317	+	4.25037i	−1.32173	+	0.663796i	−0.962963	−	0.269633i	$-0.913098\pi$
$41$	−8.46317	+	4.25037i	−1.32173	+	0.663796i	−0.358763	+	0.933429i	$0.616801\pi$
$42$	0.368950	+	4.84823i	0.0569302	+	0.748099i
$43$	3.77539	+	4.00168i	0.575742	+	0.610251i	0.948152	−	0.317817i	$-0.102950\pi$
$43$	3.77539	+	4.00168i	0.575742	+	0.610251i	−0.372410	+	0.928068i	$0.621468\pi$
$44$	3.51389	+	2.94850i	0.529739	+	0.444504i
$45$	−1.48237	−	2.36888i	−0.220978	−	0.353132i
$46$	5.65178	−	4.74241i	0.833309	−	0.699230i
$47$	5.01677	+	0.586377i	0.731772	+	0.0855319i	0.473815	−	0.880625i	$-0.342877\pi$
$47$	5.01677	+	0.586377i	0.731772	+	0.0855319i	0.257957	+	0.966156i	$0.416951\pi$
$48$	0.270401	−	1.71081i	0.0390290	−	0.246935i
$49$	−0.604237	+	0.640453i	−0.0863195	+	0.0914934i
$50$	−4.10439	+	0.479734i	−0.580448	+	0.0678447i
$51$	−2.32699	+	1.22093i	−0.325844	+	0.170964i
$52$	0.102583	+	1.76129i	0.0142257	+	0.244246i
$53$	−1.33883	+	2.31892i	−0.183903	+	0.318529i	−0.943206	−	0.332208i	$-0.892206\pi$
$53$	−1.33883	+	2.31892i	−0.183903	+	0.318529i	0.759304	+	0.650737i	$0.225540\pi$
$54$	5.18583	+	0.327285i	0.705703	+	0.0445378i
$55$	−2.13639	−	3.70034i	−0.288071	−	0.498954i
$56$	2.34540	−	1.54259i	0.313417	−	0.206138i
$57$	−7.42686	−	1.62134i	−0.983712	−	0.214751i
$58$	−2.85389	+	6.61606i	−0.374734	+	0.868732i
$59$	4.89941	+	1.16118i	0.637849	+	0.151173i	0.536802	−	0.843708i	$-0.319632\pi$
$59$	4.89941	+	1.16118i	0.637849	+	0.151173i	0.101048	+	0.994882i	$0.467781\pi$
$60$	−0.781729	+	1.41135i	−0.100921	+	0.182205i
$61$	3.14866	−	4.22938i	0.403144	−	0.541517i	−0.553472	−	0.832868i	$-0.686697\pi$
$61$	3.14866	−	4.22938i	0.403144	−	0.541517i	0.956616	+	0.291351i	$0.0941048\pi$
$62$	5.91096	+	2.15141i	0.750693	+	0.273230i
$63$	5.26600	+	6.57219i	0.663454	+	0.828019i
$64$	−0.939693	+	0.342020i	−0.117462	+	0.0427525i
$65$	0.471331	−	1.57436i	0.0584615	−	0.195275i
$66$	7.90644	+	0.781947i	0.973216	+	0.0962511i
$67$	0.832311	−	14.2902i	0.101683	−	1.74583i	−0.433554	−	0.901127i	$-0.642741\pi$
$67$	0.832311	−	14.2902i	0.101683	−	1.74583i	0.535237	−	0.844702i	$-0.320222\pi$
$68$	1.26759	+	0.833706i	0.153718	+	0.101102i
$69$	3.44684	−	12.3052i	0.414950	−	1.48137i
$70$	−2.54441	+	0.603036i	−0.304115	+	0.0720766i
$71$	−0.0492509	+	0.279316i	−0.00584501	+	0.0331487i	−0.987591	−	0.157049i	$-0.949802\pi$
$71$	−0.0492509	+	0.279316i	−0.00584501	+	0.0331487i	0.981746	+	0.190198i	$0.0609130\pi$
$72$	−1.28540	−	2.71067i	−0.151486	−	0.319456i
$73$	−2.01050	−	11.4021i	−0.235312	−	1.33452i	−0.841957	−	0.539545i	$-0.818596\pi$
$73$	−2.01050	−	11.4021i	−0.235312	−	1.33452i	0.606645	−	0.794973i	$-0.292515\pi$
$74$	0.267169	+	0.619368i	0.0310578	+	0.0720000i
$75$	−5.40025	+	4.69742i	−0.623567	+	0.542412i
$76$	1.25875	+	4.20451i	0.144388	+	0.482290i
$77$	7.68955	+	10.3289i	0.876305	+	1.17708i
$78$	1.86808	+	2.41831i	0.211519	+	0.273820i
$79$	3.17920	+	1.59665i	0.357687	+	0.179637i	0.618563	−	0.785735i	$-0.287715\pi$
$79$	3.17920	+	1.59665i	0.357687	+	0.179637i	−0.260876	+	0.965372i	$0.584011\pi$
$80$	0.931488			0.104144
$81$	7.73541	−	4.60037i	0.859490	−	0.511152i
$82$	9.47053			1.04584
$83$	−9.56164	−	4.80204i	−1.04953	−	0.527092i	−0.161494	−	0.986874i	$-0.551631\pi$
$83$	−9.56164	−	4.80204i	−1.04953	−	0.527092i	−0.888032	+	0.459782i	$0.847928\pi$
$84$	1.84618	−	4.49813i	0.201435	−	0.490786i
$85$	−0.843927	−	1.13359i	−0.0915368	−	0.122955i
$86$	−1.57786	−	5.27043i	−0.170145	−	0.568325i
$87$	2.38525	+	12.2500i	0.255726	+	1.31333i
$88$	−1.81684	−	4.21191i	−0.193676	−	0.448991i
$89$	1.74720	+	9.90888i	0.185203	+	1.05034i	0.925694	+	0.378273i	$0.123482\pi$
$89$	1.74720	+	9.90888i	0.185203	+	1.05034i	−0.740491	+	0.672066i	$0.765407\pi$
$90$	0.261540	+	2.78220i	0.0275687	+	0.293269i
$91$	−0.860028	+	4.87746i	−0.0901554	+	0.511297i
$92$	−7.17900	+	1.70145i	−0.748463	+	0.177389i
$93$	10.5551	−	2.70064i	1.09452	−	0.280043i
$94$	−4.21999	−	2.77553i	−0.435259	−	0.286274i
$95$	0.237708	−	4.08128i	0.0243883	−	0.418731i
$96$	−1.00945	+	1.40748i	−0.103027	+	0.143651i
$97$	−4.96298	+	16.5775i	−0.503914	+	1.68319i	0.205711	+	0.978613i	$0.434049\pi$
$97$	−4.96298	+	16.5775i	−0.503914	+	1.68319i	−0.709626	+	0.704579i	$0.751136\pi$
$98$	0.827401	−	0.301149i	0.0835801	−	0.0304207i
$99$	12.0701	−	6.60920i	1.21309	−	0.664250i
$100$	3.88312	+	1.41334i	0.388312	+	0.141334i
$101$	−3.77928	+	5.07645i	−0.376052	+	0.505126i	−0.949350	−	0.314222i	$-0.898257\pi$
$101$	−3.77928	+	5.07645i	−0.376052	+	0.505126i	0.573298	+	0.819347i	$0.305664\pi$
$102$	2.62742	−	0.0467096i	0.260154	−	0.00462494i
$103$	−18.1237	−	4.29540i	−1.78578	−	0.423238i	−0.801234	−	0.598350i	$-0.795823\pi$
$103$	−18.1237	−	4.29540i	−1.78578	−	0.423238i	−0.984548	+	0.175112i	$0.943971\pi$
$104$	0.698792	−	1.61998i	0.0685222	−	0.158852i
$105$	−3.04903	+	3.34909i	−0.297555	+	0.326838i
$106$	2.23715	−	1.47140i	0.217292	−	0.142915i
$107$	−0.530621	−	0.919062i	−0.0512970	−	0.0888491i	0.839237	−	0.543766i	$-0.183002\pi$
$107$	−0.530621	−	0.919062i	−0.0512970	−	0.0888491i	−0.890534	+	0.454917i	$0.849669\pi$
$108$	−4.48735	−	2.61987i	−0.431795	−	0.252097i
$109$	6.12250	−	10.6045i	0.586429	−	1.01573i	−0.408266	−	0.912863i	$-0.633866\pi$
$109$	6.12250	−	10.6045i	0.586429	−	1.01573i	0.994696	−	0.102863i	$-0.0328002\pi$
$110$	0.248441	+	4.26556i	0.0236879	+	0.406705i
$111$	0.987380	+	0.624554i	0.0937179	+	0.0592800i
$112$	−2.78824	+	0.325899i	−0.263464	+	0.0307945i
$113$	−4.67396	+	4.95410i	−0.439689	+	0.466043i	−0.908882	−	0.417052i	$-0.863063\pi$
$113$	−4.67396	+	4.95410i	−0.439689	+	0.466043i	0.469194	+	0.883095i	$0.344545\pi$
$114$	5.90923	+	4.78205i	0.553450	+	0.447880i
$115$	6.82593	+	0.797837i	0.636521	+	0.0743987i
$116$	5.51961	−	4.63151i	0.512483	−	0.430025i
$117$	5.03482	+	1.63232i	0.465469	+	0.150908i
$118$	−3.85714	−	3.23652i	−0.355078	−	0.297946i
$119$	2.92275	+	3.09794i	0.267928	+	0.283987i
$120$	1.33199	−	0.910389i	0.121594	−	0.0831068i
$121$	8.97305	−	4.50643i	0.815732	−	0.409676i
$122$	−4.71189	+	2.36640i	−0.426594	+	0.214244i
$123$	13.5425	−	9.25601i	1.22108	−	0.834587i
$124$	−4.31667	−	4.57541i	−0.387649	−	0.410884i
$125$	−6.51648	−	5.46797i	−0.582851	−	0.489070i
$126$	−1.75628	−	8.23650i	−0.156462	−	0.733766i
$127$	−6.52630	+	5.47622i	−0.579116	+	0.485936i	−0.884657	−	0.466243i	$-0.845607\pi$
$127$	−6.52630	+	5.47622i	−0.579116	+	0.485936i	0.305541	+	0.952179i	$0.401163\pi$
$128$	0.993238	+	0.116093i	0.0877907	+	0.0102613i
$129$	−7.40733	−	5.99438i	−0.652179	−	0.527776i
$130$	−1.12777	+	1.19536i	−0.0989117	+	0.104840i
$131$	−15.8598	+	1.85375i	−1.38568	+	0.161963i	−0.776024	−	0.630703i	$-0.782766\pi$
$131$	−15.8598	+	1.85375i	−1.38568	+	0.161963i	−0.609656	+	0.792666i	$0.708692\pi$
$132$	−6.71452	−	4.24718i	−0.584424	−	0.369669i
$133$	0.716379	+	12.2997i	0.0621179	+	1.06652i
$134$	−7.15722	+	12.3967i	−0.618290	+	1.07091i
$135$	3.09317	+	3.72282i	0.266218	+	0.320409i
$136$	−0.758592	−	1.31392i	−0.0650487	−	0.112668i
$137$	8.99273	−	5.91461i	0.768301	−	0.505319i	−0.103828	−	0.994595i	$-0.533109\pi$
$137$	8.99273	−	5.91461i	0.768301	−	0.505319i	0.872129	+	0.489276i	$0.162739\pi$
$138$	−8.60278	+	9.44941i	−0.732317	+	0.804387i
$139$	2.55292	−	5.91833i	0.216536	−	0.501986i	−0.774978	−	0.631988i	$-0.782239\pi$
$139$	2.55292	−	5.91833i	0.216536	−	0.501986i	0.991514	+	0.130002i	$0.0414984\pi$
$140$	2.54441	+	0.603036i	0.215042	+	0.0509659i
$141$	−8.74708	+	0.155503i	−0.736637	+	0.0130957i
$142$	0.169369	−	0.227502i	0.0142131	−	0.0190916i
$143$	7.60475	+	2.76790i	0.635941	+	0.231464i
$144$	−0.0678720	+	2.99923i	−0.00565600	+	0.249936i
$145$	−6.30693	+	2.29553i	−0.523762	+	0.190634i
$146$	−3.32061	+	11.0916i	−0.274816	+	0.917949i
$147$	0.888823	−	1.23929i	0.0733089	−	0.102215i
$148$	0.0392206	−	0.673392i	0.00322392	−	0.0553525i
$149$	−0.0289210	−	0.0190217i	−0.00236930	−	0.00155831i	0.548324	−	0.836266i	$-0.315266\pi$
$149$	−0.0289210	−	0.0190217i	−0.00236930	−	0.00155831i	−0.550693	+	0.834708i	$0.685637\pi$
$150$	6.93404	−	1.77414i	0.566162	−	0.144858i
$151$	−22.1823	+	5.25731i	−1.80517	+	0.427834i	−0.988745	−	0.149613i	$-0.952197\pi$
$151$	−22.1823	+	5.25731i	−1.80517	+	0.427834i	−0.816429	+	0.577446i	$0.804049\pi$
$152$	0.762123	−	4.32221i	0.0618163	−	0.350578i
$153$	3.71146	−	2.63470i	0.300054	−	0.213003i
$154$	−2.23605	−	12.6813i	−0.180186	−	1.02189i
$155$	2.32077	+	5.38015i	0.186409	+	0.432144i
$156$	−0.584043	−	2.99947i	−0.0467609	−	0.240150i
$157$	2.53198	+	8.45740i	0.202074	+	0.674974i	0.997612	+	0.0690700i	$0.0220032\pi$
$157$	2.53198	+	8.45740i	0.202074	+	0.674974i	−0.795538	+	0.605904i	$0.792812\pi$
$158$	−2.12446	−	2.85364i	−0.169013	−	0.227023i
$159$	1.76097	−	4.29053i	0.139654	−	0.340261i
$160$	−0.832408	−	0.418051i	−0.0658076	−	0.0330498i
$161$	−20.7113			−1.63228
$162$	−8.97726	+	0.639391i	−0.705320	+	0.0502353i
$163$	−21.2225			−1.66227			−0.831137	−	0.556067i	$-0.812310\pi$
$163$	−21.2225			−1.66227			−0.831137	+	0.556067i	$0.812310\pi$
$164$	−8.46317	−	4.25037i	−0.660863	−	0.331898i
$165$	4.52420	+	5.85677i	0.352209	+	0.455949i
$166$	6.38944	+	8.58251i	0.495917	+	0.666132i
$167$	−4.59344	−	15.3431i	−0.355451	−	1.18729i	−0.929610	−	0.368544i	$-0.879856\pi$
$167$	−4.59344	−	15.3431i	−0.355451	−	1.18729i	0.574159	−	0.818744i	$-0.305329\pi$
$168$	−3.66856	+	3.19111i	−0.283036	+	0.246199i
$169$	−3.91618	−	9.07872i	−0.301245	−	0.698363i
$170$	0.245406	+	1.39177i	0.0188218	+	0.106744i
$171$	13.1237	+	1.06276i	1.00359	+	0.0812710i
$172$	−0.955334	+	5.41797i	−0.0728436	+	0.413116i
$173$	−10.9871	+	2.60399i	−0.835334	+	0.197978i	−0.625957	−	0.779857i	$-0.715292\pi$
$173$	−10.9871	+	2.60399i	−0.835334	+	0.197978i	−0.209376	+	0.977835i	$0.567143\pi$
$174$	3.36623	−	12.0175i	0.255194	−	0.911042i
$175$	9.69197	+	6.37451i	0.732644	+	0.481868i
$176$	−0.266714	+	4.57930i	−0.0201043	+	0.345177i
$177$	−8.67877	−	0.858331i	−0.652336	−	0.0645161i
$178$	2.88574	−	9.63905i	0.216295	−	0.722477i
$179$	18.7430	−	6.82191i	1.40092	−	0.509893i	0.472469	−	0.881347i	$-0.343363\pi$
$179$	18.7430	−	6.82191i	1.40092	−	0.509893i	0.928451	+	0.371454i	$0.121141\pi$
$180$	1.01493	−	2.60364i	0.0756482	−	0.194064i
$181$	19.9989	+	7.27900i	1.48651	+	0.541044i	0.952527	−	0.304454i	$-0.0984739\pi$
$181$	19.9989	+	7.27900i	1.48651	+	0.541044i	0.533979	+	0.845498i	$0.320696\pi$
$182$	2.95755	−	3.97268i	0.219228	−	0.294474i
$183$	−4.42502	+	7.98902i	−0.327107	+	0.590565i
$184$	7.17900	+	1.70145i	0.529243	+	0.125433i
$185$	−0.248865	+	0.576933i	−0.0182969	+	0.0424170i
$186$	−10.6444	−	2.32376i	−0.780489	−	0.170386i
$187$	5.81450	−	3.82426i	0.425198	−	0.279657i
$188$	2.52546	+	4.37423i	0.184188	+	0.319024i
$189$	−10.5613	−	10.0614i	−0.768225	−	0.731858i
$190$	−2.04410	+	3.54048i	−0.148294	+	0.256854i
$191$	−1.03657	−	17.7972i	−0.0750033	−	1.28776i	−0.800417	−	0.599444i	$-0.795388\pi$
$191$	−1.03657	−	17.7972i	−0.0750033	−	1.28776i	0.725414	−	0.688313i	$-0.241649\pi$
$192$	1.53376	−	0.804732i	0.110689	−	0.0580766i
$193$	22.1969	−	2.59445i	1.59777	−	0.186753i	0.729904	−	0.683550i	$-0.239565\pi$
$193$	22.1969	−	2.59445i	1.59777	−	0.186753i	0.867866	+	0.496798i	$0.165491\pi$
$194$	11.8751	−	12.5868i	0.852579	−	0.903681i
$195$	−0.444375	+	2.81155i	−0.0318224	+	0.201339i
$196$	−0.874548	−	0.102220i	−0.0624677	−	0.00730143i
$197$	−3.12785	+	2.62458i	−0.222850	+	0.186994i	−0.747377	−	0.664401i	$-0.768687\pi$
$197$	−3.12785	+	2.62458i	−0.222850	+	0.186994i	0.524526	+	0.851394i	$0.324242\pi$
$198$	−13.7525	+	0.489130i	−0.977346	+	0.0347610i
$199$	−0.620215	−	0.520423i	−0.0439659	−	0.0368918i	0.620540	−	0.784175i	$-0.286913\pi$
$199$	−0.620215	−	0.520423i	−0.0439659	−	0.0368918i	−0.664506	+	0.747283i	$0.731358\pi$
$200$	−2.83578	−	3.00575i	−0.200520	−	0.212538i
$201$	1.88133	+	24.7219i	0.132699	+	1.74375i
$202$	5.65559	−	2.84035i	0.397926	−	0.199846i
$203$	18.0755	−	9.07787i	1.26865	−	0.637141i
$204$	−2.36892	−	1.13744i	−0.165857	−	0.0796370i
$205$	6.05381	+	6.41666i	0.422816	+	0.448159i
$206$	14.2682	+	11.9724i	0.994111	+	0.834158i
$207$	−3.06626	+	21.9202i	−0.213120	+	1.52356i
$208$	−1.35151	+	1.13405i	−0.0937103	+	0.0786323i
$209$	19.9960	+	2.33719i	1.38315	+	0.161667i
$210$	4.22778	−	1.62446i	0.291745	−	0.112098i
$211$	−7.80319	+	8.27090i	−0.537194	+	0.569392i	−0.937940	−	0.346797i	$-0.887269\pi$
$211$	−7.80319	+	8.27090i	−0.537194	+	0.569392i	0.400746	+	0.916189i	$0.368751\pi$
$212$	−2.65956	+	0.310858i	−0.182659	+	0.0213498i
$213$	0.0198421	−	0.490852i	0.00135956	−	0.0336326i
$214$	0.0617057	+	1.05945i	0.00421811	+	0.0724222i
$215$	2.56231	−	4.43806i	0.174748	−	0.302673i
$216$	2.83424	+	4.35512i	0.192846	+	0.296328i
$217$	−8.82916	−	15.2925i	−0.599362	−	1.03813i
$218$	−10.2306	+	6.72874i	−0.692900	+	0.455728i
$219$	6.09204	+	19.1060i	0.411662	+	1.29106i
$220$	1.69236	−	3.92334i	0.114099	−	0.264512i
$221$	2.60457	+	0.617295i	0.175202	+	0.0415237i
$222$	−0.602055	−	1.00126i	−0.0404073	−	0.0672000i
$223$	10.6088	−	14.2500i	0.710415	−	0.954252i	−0.289581	−	0.957153i	$-0.593516\pi$
$223$	10.6088	−	14.2500i	0.710415	−	0.954252i	0.999996	+	0.00290107i	$0.000923440\pi$
$224$	2.63793	+	0.960127i	0.176254	+	0.0641512i
$225$	8.18144	−	9.31393i	0.545430	−	0.620929i
$226$	6.40020	−	2.32948i	0.425735	−	0.154955i
$227$	0.718661	−	2.40050i	0.0476992	−	0.159327i	−0.930822	−	0.365473i	$-0.880907\pi$
$227$	0.718661	−	2.40050i	0.0476992	−	0.159327i	0.978521	+	0.206147i	$0.0660924\pi$
$228$	−3.13451	−	6.92545i	−0.207588	−	0.458649i
$229$	−0.262629	+	4.50916i	−0.0173550	+	0.297974i	0.978451	+	0.206480i	$0.0662010\pi$
$229$	−0.262629	+	4.50916i	−0.0173550	+	0.297974i	−0.995806	+	0.0914931i	$0.970836\pi$
$230$	−5.74181	−	3.77645i	−0.378604	−	0.249011i
$231$	−15.5915	−	15.9483i	−1.02584	−	1.04932i
$232$	−7.01112	+	1.66167i	−0.460303	+	0.109094i
$233$	2.12497	−	12.0513i	0.139212	−	0.789508i	−0.832622	−	0.553841i	$-0.813161\pi$
$233$	2.12497	−	12.0513i	0.139212	−	0.789508i	0.971834	−	0.235667i	$-0.0757275\pi$
$234$	−3.76669	−	3.71832i	−0.246236	−	0.243074i
$235$	−0.816993	−	4.63340i	−0.0532948	−	0.302250i
$236$	1.99432	+	4.62334i	0.129819	+	0.300954i
$237$	−5.82689	−	2.00426i	−0.378497	−	0.130191i
$238$	−1.22152	−	4.08015i	−0.0791791	−	0.264477i
$239$	15.8275	+	21.2601i	1.02380	+	1.37520i	0.924946	+	0.380098i	$0.124110\pi$
$239$	15.8275	+	21.2601i	1.02380	+	1.37520i	0.0988519	+	0.995102i	$0.468483\pi$
$240$	−1.59889	+	0.215757i	−0.103208	+	0.0139270i
$241$	−4.87872	−	2.45019i	−0.314266	−	0.157830i	0.284674	−	0.958625i	$-0.408115\pi$
$241$	−4.87872	−	2.45019i	−0.314266	−	0.157830i	−0.598940	+	0.800794i	$0.704411\pi$
$242$	−10.0411			−0.645466
$243$	−12.2122	+	9.68822i	−0.783414	+	0.621500i
$244$	5.27273			0.337552
$245$	0.732936	+	0.368094i	0.0468256	+	0.0235167i
$246$	−16.2561	+	2.19362i	−1.03645	+	0.139860i
$247$	4.62391	+	6.21099i	0.294212	+	0.395196i
$248$	1.80408	+	6.02605i	0.114559	+	0.382655i
$249$	17.5248	+	6.02794i	1.11059	+	0.382005i
$250$	3.36931	+	7.81095i	0.213094	+	0.494008i
$251$	0.521714	+	2.95878i	0.0329303	+	0.186757i	0.996836	−	0.0794874i	$-0.0253283\pi$
$251$	0.521714	+	2.95878i	0.0329303	+	0.186757i	−0.963906	+	0.266244i	$0.914217\pi$
$252$	−2.12707	+	8.14862i	−0.133993	+	0.513315i
$253$	−5.87673	+	33.3286i	−0.369467	+	2.09535i
$254$	8.28984	−	1.96473i	0.520151	−	0.123278i
$255$	1.71116	+	1.75033i	0.107157	+	0.109610i
$256$	−0.835488	−	0.549509i	−0.0522180	−	0.0343443i
$257$	0.761444	−	13.0735i	0.0474975	−	0.815501i	−0.887491	−	0.460824i	$-0.847554\pi$
$257$	0.761444	−	13.0735i	0.0474975	−	0.815501i	0.934989	−	0.354677i	$-0.115409\pi$
$258$	3.92916	+	8.68118i	0.244619	+	0.540467i
$259$	0.543081	−	1.81402i	0.0337454	−	0.112717i
$260$	1.54429	−	0.562075i	0.0957727	−	0.0348584i
$261$	−6.93168	−	20.4745i	−0.429060	−	1.26734i
$262$	15.0048	+	5.46131i	0.927001	+	0.337401i
$263$	−1.87795	+	2.52252i	−0.115799	+	0.155545i	−0.856244	−	0.516572i	$-0.827208\pi$
$263$	−1.87795	+	2.52252i	−0.115799	+	0.155545i	0.740444	+	0.672118i	$0.234615\pi$
$264$	4.09418	+	6.80889i	0.251979	+	0.419058i
$265$	2.42698	+	0.575204i	0.149088	+	0.0353345i
$266$	4.87994	−	11.3130i	0.299208	−	0.693642i
$267$	−5.29422	−	16.6038i	−0.324001	−	1.01614i
$268$	11.9595	−	7.86592i	0.730545	−	0.480487i
$269$	−10.1021	−	17.4974i	−0.615938	−	1.06684i	−0.990219	−	0.139520i	$-0.955444\pi$
$269$	−10.1021	−	17.4974i	−0.615938	−	1.06684i	0.374282	−	0.927315i	$-0.377889\pi$
$270$	−1.09336	−	4.71504i	−0.0665398	−	0.286948i
$271$	−14.8899	+	25.7901i	−0.904500	+	1.56664i	−0.0829129	+	0.996557i	$0.526422\pi$
$271$	−14.8899	+	25.7901i	−0.904500	+	1.56664i	−0.821587	+	0.570083i	$0.806911\pi$
$272$	0.0882164	+	1.51462i	0.00534890	+	0.0918371i
$273$	0.346486	−	8.57133i	0.0209703	−	0.518760i
$274$	−10.6907	+	1.24956i	−0.645847	+	0.0754887i
$275$	13.0079	−	13.7875i	0.784404	−	0.831420i
$276$	11.9286	−	4.58338i	0.718018	−	0.275887i
$277$	−4.36989	−	0.510767i	−0.262561	−	0.0306890i	−0.0162063	−	0.999869i	$-0.505159\pi$
$277$	−4.36989	−	0.510767i	−0.262561	−	0.0306890i	−0.246355	+	0.969180i	$0.579233\pi$
$278$	−4.93751	+	4.14306i	−0.296132	+	0.248484i
$279$	−17.4923	+	7.08046i	−1.04723	+	0.423896i
$280$	−2.00313	−	1.68082i	−0.119710	−	0.100448i
$281$	19.4042	+	20.5672i	1.15755	+	1.22694i	0.969583	+	0.244762i	$0.0787098\pi$
$281$	19.4042	+	20.5672i	1.15755	+	1.22694i	0.187972	+	0.982174i	$0.439809\pi$
$282$	7.88647	+	3.78672i	0.469632	+	0.225496i
$283$	6.51124	−	3.27007i	0.387053	−	0.194385i	−0.244622	−	0.969618i	$-0.578664\pi$
$283$	6.51124	−	3.27007i	0.387053	−	0.194385i	0.631675	+	0.775233i	$0.282368\pi$
$284$	−0.253456	+	0.127291i	−0.0150399	+	0.00755331i
$285$	0.537307	+	7.06055i	0.0318273	+	0.418231i
$286$	−5.55362	−	5.88650i	−0.328393	−	0.348076i
$287$	−20.3660	−	17.0891i	−1.20217	−	1.00874i
$288$	1.40671	−	2.64975i	0.0828909	−	0.156138i
$289$	−11.2594	+	9.44779i	−0.662320	+	0.555752i
$290$	6.66631	+	0.779180i	0.391459	+	0.0457550i
$291$	4.67914	−	29.6047i	0.274296	−	1.73546i
$292$	7.94532	−	8.42155i	0.464965	−	0.492834i
$293$	−0.386477	+	0.0451727i	−0.0225782	+	0.00263902i	−0.127375	−	0.991855i	$-0.540655\pi$
$293$	−0.386477	+	0.0451727i	−0.0225782	+	0.00263902i	0.104796	+	0.994494i	$0.466581\pi$
$294$	−1.35047	+	0.708568i	−0.0787612	+	0.0413245i
$295$	−0.272709	−	4.68223i	−0.0158777	−	0.272610i
$296$	−0.337267	+	0.584163i	−0.0196032	+	0.0339538i
$297$	−19.1875	+	14.1404i	−1.11337	+	0.820510i
$298$	0.0173079	+	0.0299781i	0.00100262	+	0.00173658i
$299$	−10.8752	+	7.15272i	−0.628928	+	0.413652i
$300$	−6.99272	−	1.52656i	−0.403725	−	0.0881358i
$301$	−6.11709	+	14.1810i	−0.352583	+	0.817380i
$302$	22.1823	+	5.25731i	1.27645	+	0.302524i
$303$	5.31127	−	9.58907i	0.305124	−	0.550878i
$304$	−2.62086	+	3.52043i	−0.150317	+	0.201910i
$305$	−4.61529	−	1.67983i	−0.264271	−	0.0961866i
$306$	−4.49914	+	0.688756i	−0.257199	+	0.0393736i
$307$	15.8628	−	5.77360i	0.905340	−	0.329517i	0.152949	−	0.988234i	$-0.451123\pi$
$307$	15.8628	−	5.77360i	0.905340	−	0.329517i	0.752391	+	0.658717i	$0.228901\pi$
$308$	−3.69313	+	12.3359i	−0.210436	+	0.702905i
$309$	32.1042	+	3.17510i	1.82634	+	0.180625i
$310$	0.340691	−	5.84944i	0.0193499	−	0.332226i
$311$	−20.9613	−	13.7865i	−1.18861	−	0.781760i	−0.208074	−	0.978113i	$-0.566720\pi$
$311$	−20.9613	−	13.7865i	−1.18861	−	0.781760i	−0.980533	+	0.196353i	$0.937090\pi$
$312$	−0.824242	+	2.94255i	−0.0466635	+	0.166589i
$313$	9.15572	−	2.16994i	0.517512	−	0.122653i	0.0364435	−	0.999336i	$-0.488397\pi$
$313$	9.15572	−	2.16994i	0.517512	−	0.122653i	0.481068	+	0.876683i	$0.340249\pi$
$314$	1.53301	−	8.69416i	0.0865130	−	0.490640i
$315$	4.45790	−	6.45493i	0.251174	−	0.363694i
$316$	0.617772	+	3.50356i	0.0347524	+	0.197091i
$317$	−5.32798	−	12.3516i	−0.299249	−	0.693737i	0.700554	−	0.713600i	$-0.252936\pi$
$317$	−5.32798	−	12.3516i	−0.299249	−	0.693737i	−0.999803	+	0.0198626i	$0.993677\pi$
$318$	−3.49925	+	3.04383i	−0.196228	+	0.170690i
$319$	−9.47923	−	31.6628i	−0.530735	−	1.77278i
$320$	0.556246	+	0.747168i	0.0310951	+	0.0417680i
$321$	1.12369	+	1.45466i	0.0627180	+	0.0811911i
$322$	18.5083	+	9.29523i	1.03143	+	0.518003i
$323$	6.65875			0.370503
$324$	8.30933	+	3.45761i	0.461629	+	0.192089i
$325$	7.29055			0.404407
$326$	18.9651	+	9.52464i	1.05038	+	0.527521i
$327$	−8.05296	+	19.6207i	−0.445330	+	1.08503i
$328$	5.65541	+	7.59653i	0.312268	+	0.419448i
$329$	4.06661	+	13.5834i	0.224199	+	0.748878i
$330$	−1.41446	−	7.26426i	−0.0778635	−	0.399884i
$331$	−5.56619	−	12.9039i	−0.305946	−	0.709262i	0.693997	−	0.719978i	$-0.255848\pi$
$331$	−5.56619	−	12.9039i	−0.305946	−	0.709262i	−0.999943	+	0.0107163i	$0.996589\pi$
$332$	−1.85799	−	10.5372i	−0.101971	−	0.578303i
$333$	−1.83949	−	0.843340i	−0.100804	−	0.0462147i
$334$	−2.78115	+	15.7727i	−0.152178	+	0.863042i
$335$	−12.9743	+	3.07497i	−0.708863	+	0.168004i
$336$	4.71051	−	1.20523i	0.256979	−	0.0657508i
$337$	5.45623	+	3.58862i	0.297220	+	0.195485i	0.689356	−	0.724423i	$-0.257894\pi$
$337$	5.45623	+	3.58862i	0.297220	+	0.195485i	−0.392136	+	0.919907i	$0.628264\pi$
$338$	−0.574898	+	9.87062i	−0.0312703	+	0.536891i
$339$	6.87532	−	9.58630i	0.373416	−	0.520656i
$340$	0.405321	−	1.35387i	0.0219816	−	0.0734238i
$341$	−27.1139	+	9.86866i	−1.46830	+	0.534418i
$342$	−11.2508	−	6.83962i	−0.608374	−	0.369844i
$343$	16.1428	+	5.87549i	0.871629	+	0.317247i
$344$	3.28530	−	4.41292i	0.177131	−	0.237929i
$345$	−11.9015	+	0.211581i	−0.640753	+	0.0113911i
$346$	10.9871	+	2.60399i	0.590670	+	0.139991i
$347$	10.6690	−	24.7336i	0.572744	−	1.32777i	−0.347961	−	0.937509i	$-0.613126\pi$
$347$	10.6690	−	24.7336i	0.572744	−	1.32777i	0.920705	−	0.390260i	$-0.127615\pi$
$348$	−8.40160	+	9.22844i	−0.450373	+	0.494696i
$349$	−21.0859	+	13.8684i	−1.12870	+	0.742359i	−0.969550	−	0.244895i	$-0.921247\pi$
$349$	−21.0859	+	13.8684i	−1.12870	+	0.742359i	−0.159153	+	0.987254i	$0.550876\pi$
$350$	−5.80019	−	10.0462i	−0.310033	−	0.536993i
$351$	−9.02032	−	1.63567i	−0.481469	−	0.0873058i
$352$	2.29353	−	3.97251i	0.122245	−	0.211735i
$353$	−0.0557860	−	0.957808i	−0.00296919	−	0.0509790i	0.996498	−	0.0836154i	$-0.0266467\pi$
$353$	−0.0557860	−	0.957808i	−0.00296919	−	0.0509790i	−0.999467	+	0.0326364i	$0.989610\pi$
$354$	7.37042	+	4.66206i	0.391733	+	0.247786i
$355$	0.262407	−	0.0306710i	0.0139271	−	0.00162785i
$356$	−6.90479	+	7.31865i	−0.365953	+	0.387888i
$357$	−5.73445	−	4.64060i	−0.303499	−	0.245607i
$358$	−19.8111	−	2.31558i	−1.04705	−	0.122382i
$359$	−12.5985	+	10.5714i	−0.664925	+	0.557939i	−0.911559	−	0.411170i	$-0.865120\pi$
$359$	−12.5985	+	10.5714i	−0.664925	+	0.557939i	0.246633	+	0.969109i	$0.420676\pi$
$360$	−2.07548	+	1.87120i	−0.109388	+	0.0986209i
$361$	0.200968	+	0.168633i	0.0105773	+	0.00887540i
$362$	−14.6049	−	15.4802i	−0.767614	−	0.813623i
$363$	−14.3584	+	9.81365i	−0.753619	+	0.515083i
$364$	−4.42590	+	2.22277i	−0.231980	+	0.116505i
$365$	−9.63764	+	4.84020i	−0.504457	+	0.253348i
$366$	7.53980	−	5.15330i	0.394112	−	0.269367i
$367$	−1.16969	−	1.23980i	−0.0610575	−	0.0647172i	0.696125	−	0.717921i	$-0.254906\pi$
$367$	−1.16969	−	1.23980i	−0.0610575	−	0.0647172i	−0.757182	+	0.653204i	$0.773425\pi$
$368$	−5.65178	−	4.74241i	−0.294619	−	0.247215i
$369$	−21.1017	+	19.0247i	−1.09851	+	0.990385i
$370$	0.481321	−	0.403876i	0.0250227	−	0.0209965i
$371$	−7.46597	−	0.872647i	−0.387614	−	0.0453056i
$372$	8.46933	+	6.85380i	0.439114	+	0.355353i
$373$	−9.80490	+	10.3926i	−0.507678	+	0.538108i	−0.929622	−	0.368514i	$-0.879866\pi$
$373$	−9.80490	+	10.3926i	−0.507678	+	0.538108i	0.421944	+	0.906622i	$0.361348\pi$
$374$	−6.91235	+	0.807938i	−0.357429	+	0.0417775i
$375$	12.4520	+	7.87635i	0.643019	+	0.406733i
$376$	−0.293685	−	5.04238i	−0.0151457	−	0.260041i
$377$	6.35609	−	11.0091i	0.327355	−	0.566996i
$378$	4.92243	+	13.7311i	0.253182	+	0.706252i
$379$	−12.0604	−	20.8893i	−0.619504	−	1.07301i	−0.989576	−	0.144009i	$-0.954001\pi$
$379$	−12.0604	−	20.8893i	−0.619504	−	1.07301i	0.370073	−	0.929003i	$-0.379333\pi$
$380$	3.41564	−	2.24650i	0.175219	−	0.115243i
$381$	9.93392	−	10.9116i	0.508930	−	0.559016i
$382$	−7.06104	+	16.3693i	−0.361274	+	0.837528i
$383$	5.64393	+	1.33764i	0.288391	+	0.0683500i	0.372265	−	0.928126i	$-0.378581\pi$
$383$	5.64393	+	1.33764i	0.288391	+	0.0683500i	−0.0838739	+	0.996476i	$0.526729\pi$
$384$	−1.73178	+	0.0307871i	−0.0883744	+	0.00157110i
$385$	7.16272	−	9.62120i	0.365046	−	0.490342i
$386$	−21.0003	−	7.64348i	−1.06889	−	0.389043i
$387$	14.1031	+	8.57359i	0.716900	+	0.435820i
$388$	−16.2609	+	5.91848i	−0.825522	+	0.300465i
$389$	−5.89390	+	19.6870i	−0.298833	+	0.998170i	0.668299	+	0.743893i	$0.267023\pi$
$389$	−5.89390	+	19.6870i	−0.298833	+	0.998170i	−0.967131	+	0.254277i	$0.918162\pi$
$390$	1.65893	−	2.31305i	0.0840031	−	0.117126i
$391$	−0.650849	+	11.1747i	−0.0329149	+	0.565126i
$392$	0.735648	+	0.483843i	0.0371558	+	0.0244378i
$393$	26.7939	−	6.85550i	1.35157	−	0.345814i
$394$	3.97306	−	0.941633i	0.200160	−	0.0474388i
$395$	0.575447	−	3.26352i	0.0289539	−	0.164206i
$396$	12.5092	+	5.73500i	0.628610	+	0.288194i
$397$	−2.54727	−	14.4463i	−0.127844	−	0.725039i	−0.979578	−	0.201065i	$-0.935560\pi$
$397$	−2.54727	−	14.4463i	−0.127844	−	0.725039i	0.851734	−	0.523974i	$-0.175551\pi$
$398$	0.320680	+	0.743419i	0.0160742	+	0.0372642i
$399$	−4.07860	−	20.9465i	−0.204185	−	1.04864i
$400$	1.18517	+	3.95873i	0.0592583	+	0.197936i
$401$	15.9451	+	21.4180i	0.796262	+	1.06957i	0.995968	+	0.0897093i	$0.0285938\pi$
$401$	15.9451	+	21.4180i	0.796262	+	1.06957i	−0.199706	+	0.979856i	$0.563999\pi$
$402$	9.41393	−	22.9366i	0.469524	−	1.14397i
$403$	−9.91737	−	4.98069i	−0.494019	−	0.248106i
$404$	−6.32877			−0.314868
$405$	−6.17171	−	5.67373i	−0.306675	−	0.281930i
$406$	−20.2270			−1.00385
$407$	−2.76501	−	1.38864i	−0.137056	−	0.0688323i
$408$	1.60646	+	2.07962i	0.0795314	+	0.102957i
$409$	−5.81400	−	7.80956i	−0.287484	−	0.386158i	0.634796	−	0.772679i	$-0.281084\pi$
$409$	−5.81400	−	7.80956i	−0.287484	−	0.386158i	−0.922280	+	0.386521i	$0.873677\pi$
$410$	−2.53009	−	8.45108i	−0.124952	−	0.417369i
$411$	−14.0660	+	12.2353i	−0.693824	+	0.603525i
$412$	−7.37729	−	17.1025i	−0.363453	−	0.842579i
$413$	2.45447	+	13.9200i	0.120777	+	0.684959i
$414$	12.5779	−	18.2125i	0.618169	−	0.895094i
$415$	−1.73070	+	9.81527i	−0.0849565	+	0.481812i
$416$	1.71671	−	0.406869i	0.0841688	−	0.0199484i
$417$	−3.01123	+	10.7501i	−0.147460	+	0.526434i
$418$	−16.8201	−	11.0628i	−0.822698	−	0.541097i
$419$	0.515542	−	8.85151i	0.0251859	−	0.432425i	−0.962021	−	0.272977i	$-0.911992\pi$
$419$	0.515542	−	8.85151i	0.0251859	−	0.432425i	0.987206	−	0.159448i	$-0.0509713\pi$
$420$	−4.50714	−	0.445756i	−0.219926	−	0.0217507i
$421$	3.31057	−	11.0581i	0.161347	−	0.538938i	−0.838636	−	0.544692i	$-0.816646\pi$
$421$	3.31057	−	11.0581i	0.161347	−	0.538938i	0.999983	+	0.00575434i	$0.00183167\pi$
$422$	10.6852	−	3.88908i	0.520145	−	0.189317i
$423$	14.9783	−	2.29297i	0.728269	−	0.111488i
$424$	2.51618	+	0.915814i	0.122196	+	0.0444759i
$425$	3.74389	−	5.02891i	0.181605	−	0.243938i
$426$	−0.238025	+	0.429736i	−0.0115324	+	0.0208208i
$427$	14.4028	+	3.41352i	0.696998	+	0.165192i
$428$	0.420336	−	0.974449i	0.0203177	−	0.0471018i
$429$	−13.6946	−	2.98963i	−0.661183	−	0.144341i
$430$	−4.28156	+	2.81603i	−0.206475	+	0.135801i
$431$	13.5607	+	23.4878i	0.653196	+	1.13137i	0.982343	+	0.187090i	$0.0599056\pi$
$431$	13.5607	+	23.4878i	0.653196	+	1.13137i	−0.329147	+	0.944279i	$0.606761\pi$
$432$	−0.578198	−	5.16388i	−0.0278186	−	0.248447i
$433$	0.933229	−	1.61640i	0.0448481	−	0.0776792i	−0.842730	−	0.538337i	$-0.819053\pi$
$433$	0.933229	−	1.61640i	0.0448481	−	0.0776792i	0.887578	+	0.460657i	$0.152386\pi$
$434$	1.02674	+	17.6284i	0.0492851	+	0.846192i
$435$	10.2941	−	5.40112i	0.493564	−	0.258964i
$436$	12.1622	−	1.42156i	0.582464	−	0.0680803i
$437$	−22.2210	+	23.5528i	−1.06297	+	1.12669i
$438$	3.13070	−	19.8078i	0.149591	−	0.946455i
$439$	5.43863	+	0.635684i	0.259571	+	0.0303396i	0.244883	−	0.969553i	$-0.421250\pi$
$439$	5.43863	+	0.635684i	0.259571	+	0.0303396i	0.0146882	+	0.999892i	$0.495324\pi$
$440$	−3.27315	+	2.74650i	−0.156041	+	0.130934i
$441$	−1.23861	+	2.33311i	−0.0589812	+	0.111100i
$442$	−2.05049	−	1.72056i	−0.0975318	−	0.0818389i
$443$	7.84510	+	8.31532i	0.372732	+	0.395073i	0.886403	−	0.462914i	$-0.153196\pi$
$443$	7.84510	+	8.31532i	0.372732	+	0.395073i	−0.513671	+	0.857987i	$0.671715\pi$
$444$	0.0886532	+	1.16496i	0.00420729	+	0.0552865i
$445$	8.37548	−	4.20632i	0.397036	−	0.199399i
$446$	−15.8757	+	7.97309i	−0.751737	+	0.377537i
$447$	0.0540486	+	0.0259517i	0.00255641	+	0.00122747i
$448$	−1.92643	−	2.04190i	−0.0910154	−	0.0964707i
$449$	−0.447406	−	0.375418i	−0.0211144	−	0.0177171i	0.632169	−	0.774830i	$-0.282165\pi$
$449$	−0.447406	−	0.375418i	−0.0211144	−	0.0177171i	−0.653284	+	0.757113i	$0.726609\pi$
$450$	−11.4913	+	4.65141i	−0.541705	+	0.219270i
$451$	−33.2784	+	27.9239i	−1.56702	+	1.31488i
$452$	−6.76489	−	0.790703i	−0.318194	−	0.0371915i
$453$	36.8581	−	14.1621i	1.73175	−	0.665396i
$454$	−1.71956	+	1.82263i	−0.0807029	+	0.0855401i
$455$	4.58219	−	0.535581i	0.214816	−	0.0251084i
$456$	−0.307042	+	7.59558i	−0.0143786	+	0.355695i
$457$	−0.759073	−	13.0328i	−0.0355079	−	0.609648i	−0.968386	−	0.249456i	$-0.919748\pi$
$457$	−0.759073	−	13.0328i	−0.0355079	−	0.609648i	0.932878	−	0.360192i	$-0.117289\pi$
$458$	2.25840	−	3.91166i	0.105528	−	0.182780i
$459$	−5.76043	+	5.38212i	−0.268874	+	0.251216i
$460$	3.43620	+	5.95167i	0.160214	+	0.277498i
$461$	9.75285	−	6.41455i	0.454236	−	0.298756i	−0.301698	−	0.953403i	$-0.597553\pi$
$461$	9.75285	−	6.41455i	0.454236	−	0.298756i	0.755934	+	0.654648i	$0.227183\pi$
$462$	6.77547	+	21.2494i	0.315224	+	0.988611i
$463$	3.89577	−	9.03140i	0.181052	−	0.419725i	−0.803386	−	0.595458i	$-0.796970\pi$
$463$	3.89577	−	9.03140i	0.181052	−	0.419725i	0.984438	+	0.175734i	$0.0562297\pi$
$464$	7.01112	+	1.66167i	0.325483	+	0.0771409i
$465$	−5.22977	−	8.69744i	−0.242525	−	0.403334i
$466$	−7.30757	+	9.81577i	−0.338517	+	0.454707i
$467$	16.7575	+	6.09922i	0.775444	+	0.282238i	0.699271	−	0.714856i	$-0.253508\pi$
$467$	16.7575	+	6.09922i	0.775444	+	0.282238i	0.0761723	+	0.997095i	$0.475730\pi$
$468$	1.69726	+	5.01330i	0.0784559	+	0.231740i
$469$	37.7605	−	13.7437i	1.74362	−	0.634624i
$470$	−1.34937	+	4.50722i	−0.0622420	+	0.207903i
$471$	−6.30508	−	13.9306i	−0.290523	−	0.641888i
$472$	0.292767	−	5.02662i	0.0134757	−	0.231369i
$473$	21.0843	+	13.8674i	0.969458	+	0.637622i
$474$	4.30759	+	4.40618i	0.197854	+	0.202382i
$475$	17.6475	−	4.18253i	0.809722	−	0.191908i
$476$	−0.739580	+	4.19437i	−0.0338986	+	0.192249i
$477$	−2.02890	+	7.77254i	−0.0928969	+	0.355880i
$478$	−4.60250	−	26.1021i	−0.210513	−	1.19388i
$479$	14.2659	+	33.0722i	0.651827	+	1.51111i	0.847700	+	0.530476i	$0.177987\pi$
$479$	14.2659	+	33.0722i	0.651827	+	1.51111i	−0.195873	+	0.980629i	$0.562754\pi$
$480$	1.52565	+	0.524774i	0.0696363	+	0.0239526i
$481$	−0.341313	−	1.14006i	−0.0155625	−	0.0519825i
$482$	3.26014	+	4.37913i	0.148496	+	0.199464i
$483$	35.5509	−	4.79728i	1.61762	−	0.218284i
$484$	8.97305	+	4.50643i	0.407866	+	0.204838i
$485$	16.1189			0.731922
$486$	15.2613	−	3.17688i	0.692267	−	0.144106i
$487$	28.2800			1.28149			0.640744	−	0.767754i	$-0.278626\pi$
$487$	28.2800			1.28149			0.640744	+	0.767754i	$0.278626\pi$
$488$	−4.71189	−	2.36640i	−0.213297	−	0.107122i
$489$	36.4283	−	4.91568i	1.64734	−	0.222295i
$490$	−0.489775	−	0.657882i	−0.0221258	−	0.0297201i
$491$	−1.26149	−	4.21368i	−0.0569303	−	0.190161i	0.924794	−	0.380467i	$-0.124237\pi$
$491$	−1.26149	−	4.21368i	−0.0569303	−	0.190161i	−0.981725	+	0.190307i	$0.939052\pi$
$492$	15.5115	+	5.33543i	0.699311	+	0.240540i
$493$	−4.32988	−	10.0378i	−0.195008	−	0.452079i
$494$	−1.34459	−	7.62555i	−0.0604960	−	0.343090i
$495$	−9.12234	−	9.00518i	−0.410019	−	0.404753i
$496$	1.09230	−	6.19475i	0.0490458	−	0.278152i
$497$	−0.774737	+	0.183616i	−0.0347517	+	0.00823630i
$498$	−12.9554	−	13.2519i	−0.580544	−	0.593830i
$499$	−13.2375	−	8.70642i	−0.592590	−	0.389753i	0.217498	−	0.976061i	$-0.430210\pi$
$499$	−13.2375	−	8.70642i	−0.592590	−	0.389753i	−0.810088	+	0.586308i	$0.800581\pi$
$500$	0.494618	−	8.49226i	0.0221200	−	0.379786i
$501$	11.4385	+	25.2724i	0.511033	+	1.12909i
$502$	0.861680	−	2.87821i	0.0384587	−	0.128461i
$503$	−12.5996	+	4.58586i	−0.561786	+	0.204473i	−0.607275	−	0.794491i	$-0.707738\pi$
$503$	−12.5996	+	4.58586i	−0.561786	+	0.204473i	0.0454892	+	0.998965i	$0.485515\pi$
$504$	5.55791	−	6.32725i	0.247569	−	0.281838i
$505$	5.53965	+	2.01627i	0.246511	+	0.0897227i
$506$	20.2095	−	27.1460i	0.898421	−	1.20679i
$507$	8.82496	+	14.6765i	0.391930	+	0.651805i
$508$	−8.28984	−	1.96473i	−0.367802	−	0.0871707i
$509$	−5.98696	+	13.8793i	−0.265367	+	0.615191i	−0.997846	−	0.0655993i	$-0.979104\pi$
$509$	−5.98696	+	13.8793i	−0.265367	+	0.615191i	0.732479	+	0.680790i	$0.238363\pi$
$510$	−0.743608	−	2.33212i	−0.0329275	−	0.103268i
$511$	27.1551	−	17.8602i	1.20127	−	0.790088i
$512$	0.500000	+	0.866025i	0.0220971	+	0.0382733i
$513$	−22.7729	+	1.21558i	−1.00545	+	0.0536690i
$514$	−6.54782	+	11.3412i	−0.288812	+	0.500237i
$515$	1.00879	+	17.3203i	0.0444528	+	0.763225i
$516$	0.384883	−	9.52119i	0.0169435	−	0.419147i
$517$	23.0122	−	2.68974i	1.01208	−	0.118295i
$518$	−1.29944	+	1.37733i	−0.0570943	+	0.0605164i
$519$	18.2561	−	7.01463i	0.801355	−	0.307908i
$520$	−1.63228	−	0.190787i	−0.0715804	−	0.00836655i
$521$	1.94311	−	1.63047i	0.0851294	−	0.0714321i	−0.599230	−	0.800577i	$-0.704526\pi$
$521$	1.94311	−	1.63047i	0.0851294	−	0.0714321i	0.684359	+	0.729145i	$0.260082\pi$
$522$	−2.99456	+	21.4076i	−0.131068	+	0.936985i
$523$	−14.0884	−	11.8216i	−0.616042	−	0.516921i	0.280514	−	0.959850i	$-0.409495\pi$
$523$	−14.0884	−	11.8216i	−0.616042	−	0.516921i	−0.896557	+	0.442929i	$0.853939\pi$
$524$	−10.9578	−	11.6146i	−0.478692	−	0.507384i
$525$	−18.1127	−	8.69689i	−0.790503	−	0.379563i
$526$	2.81030	−	1.41139i	0.122535	−	0.0615394i
$527$	−8.52844	+	4.28314i	−0.371505	+	0.186577i
$528$	−0.602872	−	7.92211i	−0.0262366	−	0.344766i
$529$	−21.5707	−	22.8636i	−0.937854	−	0.994068i
$530$	−1.91068	−	1.60325i	−0.0829945	−	0.0696406i
$531$	15.0959	−	0.536910i	0.655105	−	0.0232999i
$532$	−9.43812	+	7.91952i	−0.409194	+	0.343355i
$533$	−16.5956	−	1.93975i	−0.718835	−	0.0840198i
$534$	−2.72070	+	17.2138i	−0.117736	+	0.744913i
$535$	−0.678373	+	0.719033i	−0.0293286	+	0.0310865i
$536$	−14.2177	+	1.66181i	−0.614109	+	0.0717791i
$537$	−30.5922	+	16.0511i	−1.32015	+	0.692658i
$538$	1.17477	+	20.1701i	0.0506481	+	0.869594i
$539$	−2.01945	+	3.49780i	−0.0869841	+	0.150661i
$540$	−1.13905	+	4.70422i	−0.0490167	+	0.202437i
$541$	−7.56562	−	13.1040i	−0.325271	−	0.563386i	0.656296	−	0.754504i	$-0.272122\pi$
$541$	−7.56562	−	13.1040i	−0.325271	−	0.563386i	−0.981567	+	0.191117i	$0.938789\pi$
$542$	24.8807	−	16.3643i	1.06872	−	0.702908i
$543$	−36.0140	−	7.86210i	−1.54551	−	0.337395i
$544$	0.600926	−	1.39310i	0.0257645	−	0.0597288i
$545$	−11.0986	−	2.63042i	−0.475413	−	0.112675i
$546$	−4.15644	+	7.50412i	−0.177879	+	0.321147i
$547$	−10.5461	+	14.1659i	−0.450920	+	0.605690i	−0.968216	−	0.250116i	$-0.919531\pi$
$547$	−10.5461	+	14.1659i	−0.450920	+	0.605690i	0.517296	+	0.855806i	$0.326939\pi$
$548$	10.1143	+	3.68132i	0.432063	+	0.157258i
$549$	5.74505	−	14.7380i	0.245193	−	0.629004i
$550$	−17.8121	+	6.48307i	−0.759510	+	0.276439i
$551$	9.06971	−	30.2949i	0.386383	−	1.29061i
$552$	−12.7168	−	1.25769i	−0.541263	−	0.0535310i
$553$	−0.580693	+	9.97011i	−0.0246936	+	0.423972i
$554$	3.67584	+	2.41764i	0.156172	+	0.102716i
$555$	0.293542	−	1.04795i	0.0124602	−	0.0444828i
$556$	6.27172	−	1.48643i	0.265980	−	0.0630385i
$557$	2.15648	−	12.2300i	0.0913731	−	0.518203i	−0.904425	−	0.426632i	$-0.859700\pi$
$557$	2.15648	−	12.2300i	0.0913731	−	0.518203i	0.995799	−	0.0915710i	$-0.0291888\pi$
$558$	18.8094	+	1.52318i	0.796264	+	0.0644814i
$559$	1.68547	+	9.55877i	0.0712877	+	0.404293i
$560$	1.03571	+	2.40104i	0.0437666	+	0.101462i
$561$	−9.09475	+	7.91110i	−0.383981	+	0.334007i
$562$	−8.10964	−	27.0881i	−0.342085	−	1.14264i
$563$	−15.6180	−	20.9785i	−0.658218	−	0.884140i	0.340201	−	0.940353i	$-0.389505\pi$
$563$	−15.6180	−	20.9785i	−0.658218	−	0.884140i	−0.998419	+	0.0562125i	$0.982098\pi$
$564$	−5.34813	−	6.92338i	−0.225197	−	0.291527i
$565$	5.66949	+	2.84732i	0.238517	+	0.119788i
$566$	−7.28626			−0.306264
$567$	20.4590	+	14.8240i	0.859196	+	0.622550i
$568$	0.283625			0.0119006
$569$	13.1704	+	6.61443i	0.552133	+	0.277291i	0.702913	−	0.711276i	$-0.251882\pi$
$569$	13.1704	+	6.61443i	0.552133	+	0.277291i	−0.150780	+	0.988567i	$0.548179\pi$
$570$	2.68861	−	6.55068i	0.112614	−	0.274378i
$571$	3.97285	+	5.33646i	0.166259	+	0.223324i	0.877442	−	0.479682i	$-0.159248\pi$
$571$	3.97285	+	5.33646i	0.166259	+	0.223324i	−0.711184	+	0.703006i	$0.751841\pi$
$572$	2.32104	+	7.75283i	0.0970477	+	0.324162i
$573$	5.90154	+	30.3086i	0.246540	+	1.26616i
$574$	10.5301	+	24.4116i	0.439519	+	1.01892i
$575$	5.29415	+	30.0246i	0.220781	+	1.25211i
$576$	−2.44628	+	1.73658i	−0.101929	+	0.0723573i
$577$	5.41335	−	30.7007i	0.225361	−	1.27809i	−0.636633	−	0.771167i	$-0.719673\pi$
$577$	5.41335	−	30.7007i	0.225361	−	1.27809i	0.861994	−	0.506918i	$-0.169215\pi$
$578$	14.3020	−	3.38963i	0.594883	−	0.140990i
$579$	−37.4999	+	9.59474i	−1.55844	+	0.398744i
$580$	−5.60754	−	3.68813i	−0.232840	−	0.153141i
$581$	1.74647	−	29.9858i	0.0724558	−	1.24402i
$582$	−17.4680	+	24.3558i	−0.724073	+	1.00958i
$583$	−3.52269	+	11.7666i	−0.145895	+	0.487322i
$584$	−10.8798	+	3.95992i	−0.450209	+	0.163863i
$585$	0.111541	−	4.92893i	0.00461164	−	0.203786i
$586$	0.365642	+	0.133083i	0.0151045	+	0.00549760i
$587$	−25.5016	+	34.2546i	−1.05256	+	1.41384i	−0.147248	+	0.989100i	$0.547042\pi$
$587$	−25.5016	+	34.2546i	−1.05256	+	1.41384i	−0.905316	+	0.424739i	$0.860366\pi$
$588$	1.52483	−	0.0271080i	0.0628830	−	0.00111792i
$589$	−26.8633	−	6.36672i	−1.10688	−	0.262336i
$590$	−1.85768	+	4.30659i	−0.0764795	+	0.177299i
$591$	4.76102	−	5.22957i	0.195842	−	0.215116i
$592$	0.563564	−	0.370662i	0.0231624	−	0.0152341i
$593$	6.95785	+	12.0513i	0.285725	+	0.494890i	0.972785	−	0.231711i	$-0.0744324\pi$
$593$	6.95785	+	12.0513i	0.285725	+	0.494890i	−0.687060	+	0.726601i	$0.741099\pi$
$594$	23.4927	−	4.02502i	0.963919	−	0.165149i
$595$	1.98364	−	3.43576i	0.0813212	−	0.140852i
$596$	−0.00201273	−	0.0345572i	−8.24445e−5	−	0.00141552i
$597$	1.18514	+	0.749644i	0.0485045	+	0.0306809i
$598$	12.9286	−	1.51113i	0.528688	−	0.0617947i
$599$	−4.87779	+	5.17016i	−0.199301	+	0.211247i	−0.819314	−	0.573344i	$-0.805646\pi$
$599$	−4.87779	+	5.17016i	−0.199301	+	0.211247i	0.620013	+	0.784591i	$0.287127\pi$
$600$	5.56380	+	4.50251i	0.227141	+	0.183814i
$601$	−22.4454	−	2.62349i	−0.915567	−	0.107014i	−0.354757	−	0.934959i	$-0.615436\pi$
$601$	−22.4454	−	2.62349i	−0.915567	−	0.107014i	−0.560811	+	0.827944i	$0.689510\pi$
$602$	11.8309	−	9.92726i	0.482190	−	0.404605i
$603$	−8.95552	−	41.9992i	−0.364697	−	1.71034i
$604$	−17.4634	−	14.6535i	−0.710575	−	0.596243i
$605$	−6.41852	−	6.80324i	−0.260950	−	0.276591i
$606$	−9.04989	+	6.18542i	−0.367627	+	0.251265i
$607$	−28.7677	+	14.4477i	−1.16765	+	0.586414i	−0.923603	−	0.383350i	$-0.874770\pi$
$607$	−28.7677	+	14.4477i	−1.16765	+	0.586414i	−0.244043	+	0.969764i	$0.578474\pi$
$608$	3.92205	−	1.96973i	0.159060	−	0.0798831i
$609$	−28.9238	+	19.7689i	−1.17205	+	0.801074i
$610$	3.37047	+	3.57249i	0.136466	+	0.144646i
$611$	6.82638	+	5.72801i	0.276166	+	0.231730i
$612$	4.32969	+	1.40371i	0.175017	+	0.0567418i
$613$	−17.0259	+	14.2864i	−0.687670	+	0.577024i	−0.918236	−	0.396033i	$-0.870387\pi$
$613$	−17.0259	+	14.2864i	−0.687670	+	0.577024i	0.230566	+	0.973057i	$0.425942\pi$
$614$	−16.7667	−	1.95975i	−0.676650	−	0.0790891i
$615$	−11.8776	−	9.61194i	−0.478950	−	0.387591i
$616$	8.83666	−	9.36631i	0.356039	−	0.377379i
$617$	33.2913	−	3.89120i	1.34026	−	0.156654i	0.584441	−	0.811437i	$-0.301314\pi$
$617$	33.2913	−	3.89120i	1.34026	−	0.156654i	0.755817	+	0.654783i	$0.227240\pi$
$618$	−27.2643	−	17.2457i	−1.09673	−	0.693724i
$619$	0.202006	+	3.46831i	0.00811931	+	0.139403i	0.999932	+	0.0116986i	$0.00372387\pi$
$619$	0.202006	+	3.46831i	0.00811931	+	0.139403i	−0.991812	+	0.127704i	$0.959239\pi$
$620$	−2.92968	+	5.07435i	−0.117659	+	0.203791i
$621$	0.185935	−	38.3361i	0.00746133	−	1.53838i
$622$	12.5444	+	21.7275i	0.502983	+	0.871192i
$623$	−23.5988	+	15.5212i	−0.945467	+	0.621843i
$624$	2.05718	−	2.25964i	0.0823532	−	0.0904578i
$625$	5.04519	−	11.6961i	0.201807	−	0.467842i
$626$	−9.15572	−	2.16994i	−0.365936	−	0.0867284i
$627$	−34.8643	+	0.619807i	−1.39235	+	0.0247527i
$628$	−5.27188	+	7.08137i	−0.210371	+	0.282577i
$629$	−0.961673	−	0.350020i	−0.0383444	−	0.0139562i
$630$	−6.88069	+	3.76764i	−0.274133	+	0.150106i
$631$	38.5574	−	14.0337i	1.53494	−	0.558674i	0.570118	−	0.821563i	$-0.306897\pi$
$631$	38.5574	−	14.0337i	1.53494	−	0.558674i	0.964826	+	0.262888i	$0.0846751\pi$
$632$	1.02033	−	3.40815i	0.0405867	−	0.135569i
$633$	11.4784	−	16.0044i	0.456224	−	0.636116i
$634$	−0.782151	+	13.4290i	−0.0310632	+	0.533334i
$635$	6.63026	+	4.36079i	0.263114	+	0.173053i
$636$	4.49311	−	1.14961i	0.178163	−	0.0455849i
$637$	−1.51157	+	0.358249i	−0.0598906	+	0.0141943i
$638$	−5.73930	+	32.5492i	−0.227221	+	1.28864i
$639$	0.0796352	+	0.847140i	0.00315032	+	0.0335123i
$640$	−0.161751	−	0.917337i	−0.00639378	−	0.0362609i
$641$	−9.47251	−	21.9598i	−0.374142	−	0.867358i	−0.996418	−	0.0845606i	$-0.973051\pi$
$641$	−9.47251	−	21.9598i	−0.374142	−	0.867358i	0.622277	−	0.782797i	$-0.286208\pi$
$642$	−0.351313	−	1.80424i	−0.0138652	−	0.0712076i
$643$	5.06218	+	16.9089i	0.199633	+	0.666821i	0.997915	+	0.0645373i	$0.0205572\pi$
$643$	5.06218	+	16.9089i	0.199633	+	0.666821i	−0.798282	+	0.602284i	$0.794258\pi$
$644$	−12.3680	−	16.6130i	−0.487366	−	0.654646i
$645$	−3.37023	+	8.21140i	−0.132703	+	0.323323i
$646$	−5.95048	−	2.98844i	−0.234118	−	0.117579i
$647$	28.7326			1.12959			0.564797	−	0.825230i	$-0.308954\pi$
$647$	28.7326			1.12959			0.564797	+	0.825230i	$0.308954\pi$
$648$	−5.87372	−	6.81905i	−0.230741	−	0.267878i
$649$	23.0965			0.906615
$650$	−6.51507	−	3.27199i	−0.255542	−	0.128338i
$651$	18.6973	+	24.2045i	0.732806	+	0.948649i
$652$	−12.6732	−	17.0231i	−0.496321	−	0.666675i
$653$	−5.44267	−	18.1798i	−0.212988	−	0.711430i	−0.995994	−	0.0894161i	$-0.971500\pi$
$653$	−5.44267	−	18.1798i	−0.212988	−	0.711430i	0.783006	−	0.622014i	$-0.213685\pi$
$654$	16.0021	−	13.9195i	0.625733	−	0.544296i
$655$	5.89122	+	13.6574i	0.230189	+	0.533638i
$656$	−1.64454	−	9.32665i	−0.0642085	−	0.364145i
$657$	−14.8824	−	31.3842i	−0.580618	−	1.22442i
$658$	2.46217	−	13.9637i	0.0959854	−	0.544360i
$659$	−28.0969	+	6.65909i	−1.09450	+	0.259401i	−0.737937	−	0.674870i	$-0.764200\pi$
$659$	−28.0969	+	6.65909i	−1.09450	+	0.259401i	−0.356564	+	0.934271i	$0.616052\pi$
$660$	−1.99619	+	7.12639i	−0.0777014	+	0.277394i
$661$	28.6512	+	18.8442i	1.11440	+	0.732955i	0.966658	−	0.256070i	$-0.0824278\pi$
$661$	28.6512	+	18.8442i	1.11440	+	0.732955i	0.147746	+	0.989025i	$0.452798\pi$
$662$	−0.817122	+	14.0294i	−0.0317583	+	0.545270i
$663$	−4.61371	−	0.456296i	−0.179182	−	0.0177211i
$664$	−3.06872	+	10.2502i	−0.119089	+	0.397787i
$665$	10.7844	−	3.92519i	0.418200	−	0.152212i
$666$	1.26534	+	1.57920i	0.0490310	+	0.0611927i
$667$	49.9542	+	18.1818i	1.93423	+	0.704003i
$668$	9.56408	−	12.8468i	0.370045	−	0.497057i
$669$	−14.9092	+	26.9173i	−0.576422	+	1.04068i
$670$	12.9743	+	3.07497i	0.501242	+	0.118796i
$671$	9.57971	−	22.2083i	0.369821	−	0.857341i
$672$	−4.75037	−	1.03704i	−0.183250	−	0.0400047i
$673$	−36.5808	+	24.0596i	−1.41009	+	0.927429i	−0.410207	+	0.911992i	$0.634544\pi$
$673$	−36.5808	+	24.0596i	−1.41009	+	0.927429i	−0.999881	+	0.0154368i	$0.995086\pi$
$674$	−3.26530	−	5.65566i	−0.125775	−	0.217848i
$675$	−11.8860	+	17.8823i	−0.457494	+	0.688292i
$676$	4.94367	−	8.56270i	0.190141	−	0.329334i
$677$	−2.24011	−	38.4612i	−0.0860945	−	1.47819i	−0.714137	−	0.700006i	$-0.753181\pi$
$677$	−2.24011	−	38.4612i	−0.0860945	−	1.47819i	0.628042	−	0.778179i	$-0.283857\pi$
$678$	−10.4463	+	5.48099i	−0.401189	+	0.210496i
$679$	−48.2491	+	5.63951i	−1.85163	+	0.216424i
$680$	−0.969823	+	1.02795i	−0.0371910	+	0.0394202i
$681$	−0.677560	+	4.28690i	−0.0259642	+	0.164274i
$682$	28.6589	+	3.34975i	1.09741	+	0.128268i
$683$	4.17850	−	3.50618i	0.159886	−	0.134160i	−0.559335	−	0.828942i	$-0.688943\pi$
$683$	4.17850	−	3.50618i	0.159886	−	0.134160i	0.719221	+	0.694782i	$0.244499\pi$
$684$	6.98447	+	11.1615i	0.267058	+	0.426769i
$685$	−7.68038	−	6.44460i	−0.293452	−	0.246236i
$686$	−11.7888	−	12.4954i	−0.450099	−	0.477077i
$687$	−0.593638	−	7.80077i	−0.0226487	−	0.297618i
$688$	−4.91637	+	2.46909i	−0.187435	+	0.0941332i
$689$	−4.22163	+	2.12018i	−0.160831	+	0.0807725i
$690$	10.7305	+	5.15229i	0.408503	+	0.196144i
$691$	17.2210	+	18.2532i	0.655117	+	0.694384i	0.966722	−	0.255828i	$-0.0823481\pi$
$691$	17.2210	+	18.2532i	0.655117	+	0.694384i	−0.311605	+	0.950212i	$0.600867\pi$
$692$	−8.64976	−	7.25801i	−0.328815	−	0.275908i
$693$	30.4567	+	23.7638i	1.15696	+	0.902711i
$694$	−20.6346	+	17.3145i	−0.783279	+	0.657250i
$695$	−5.96327	−	0.697007i	−0.226200	−	0.0264390i
$696$	11.6497	−	4.47620i	0.441579	−	0.169670i
$697$	−9.86028	+	10.4513i	−0.373485	+	0.395871i
$698$	25.0672	−	2.92993i	0.948807	−	0.110900i
$699$	−0.856104	+	21.1782i	−0.0323808	+	0.801033i
$700$	0.674502	+	11.5807i	0.0254938	+	0.437711i
$701$	−3.42730	+	5.93625i	−0.129447	+	0.224209i	−0.923463	−	0.383689i	$-0.874654\pi$
$701$	−3.42730	+	5.93625i	−0.129447	+	0.224209i	0.794015	+	0.607898i	$0.207987\pi$
$702$	7.32676	+	5.51000i	0.276531	+	0.207962i
$703$	−1.48023	−	2.56383i	−0.0558278	−	0.0966966i
$704$	−3.83243	+	2.52063i	−0.144440	+	0.0949998i
$705$	2.47558	+	7.76396i	0.0932357	+	0.292408i
$706$	−0.380011	+	0.880965i	−0.0143019	+	0.0331556i
$707$	−17.2874	−	4.09718i	−0.650158	−	0.154090i
$708$	−4.49412	−	7.47400i	−0.168899	−	0.280890i
$709$	−17.0943	+	22.9617i	−0.641991	+	0.862344i	−0.997377	−	0.0723754i	$-0.976942\pi$
$709$	−17.0943	+	22.9617i	−0.641991	+	0.862344i	0.355386	+	0.934720i	$0.384349\pi$
$710$	−0.248260	−	0.0903594i	−0.00931705	−	0.00339113i
$711$	10.4661	+	2.09064i	0.392508	+	0.0784050i
$712$	9.45495	−	3.44132i	0.354339	−	0.128969i
$713$	13.3103	−	44.4595i	0.498474	−	1.66502i
$714$	3.04179	+	6.72061i	0.113836	+	0.251513i
$715$	0.438316	−	7.52560i	0.0163921	−	0.281442i
$716$	16.6646	+	10.9605i	0.622785	+	0.409612i
$717$	−32.0922	−	32.8267i	−1.19851	−	1.22594i
$718$	16.0029	−	3.79276i	0.597223	−	0.141545i
$719$	−1.27419	+	7.22626i	−0.0475191	+	0.269494i	−0.999305	−	0.0372680i	$-0.988134\pi$
$719$	−1.27419	+	7.22626i	−0.0475191	+	0.269494i	0.951786	+	0.306762i	$0.0992456\pi$
$720$	2.69451	−	0.740690i	0.100419	−	0.0276039i
$721$	−9.07949	−	51.4924i	−0.338138	−	1.91768i
$722$	−0.103910	−	0.240890i	−0.00386712	−	0.00896500i
$723$	8.94182	+	3.07569i	0.332550	+	0.114386i
$724$	6.10386	+	20.3883i	0.226848	+	0.757725i
$725$	−17.7803	−	23.8831i	−0.660344	−	0.886996i
$726$	17.2355	−	2.32578i	0.639668	−	0.0863177i
$727$	13.3751	+	6.71724i	0.496056	+	0.249129i	0.679194	−	0.733958i	$-0.262329\pi$
$727$	13.3751	+	6.71724i	0.496056	+	0.249129i	−0.183138	+	0.983087i	$0.558626\pi$
$728$	4.95270			0.183559
$729$	18.7182	−	19.4584i	0.693265	−	0.720683i
$730$	10.7848			0.399163
$731$	7.45903	+	3.74607i	0.275882	+	0.138553i
$732$	−9.05061	+	1.22130i	−0.334520	+	0.0451406i
$733$	0.198111	+	0.266109i	0.00731738	+	0.00982895i	0.805767	−	0.592233i	$-0.201753\pi$
$733$	0.198111	+	0.266109i	0.00731738	+	0.00982895i	−0.798449	+	0.602062i	$0.794346\pi$
$734$	0.488854	+	1.63289i	0.0180439	+	0.0602709i
$735$	−1.34334	−	0.462065i	−0.0495499	−	0.0170435i
$736$	2.92223	+	6.77448i	0.107715	+	0.249711i
$737$	−11.4019	−	64.6636i	−0.419996	−	2.38192i
$738$	27.3954	−	7.53067i	1.00844	−	0.277208i
$739$	0.921946	−	5.22861i	0.0339143	−	0.192338i	−0.963144	−	0.268987i	$-0.913311\pi$
$739$	0.921946	−	5.22861i	0.0339143	−	0.192338i	0.997058	+	0.0766494i	$0.0244222\pi$
$740$	−0.611383	+	0.144901i	−0.0224749	+	0.00532665i
$741$	−9.37554	−	9.59011i	−0.344419	−	0.352301i
$742$	6.28019	+	4.13055i	0.230553	+	0.151637i
$743$	−1.43288	+	24.6016i	−0.0525673	+	0.902547i	0.864206	+	0.503138i	$0.167821\pi$
$743$	−1.43288	+	24.6016i	−0.0525673	+	0.902547i	−0.916773	+	0.399408i	$0.869216\pi$
$744$	−4.49249	−	9.92581i	−0.164703	−	0.363898i
$745$	−0.00924772	+	0.0308895i	−0.000338810	+	0.00113171i
$746$	13.4262	−	4.88672i	0.491567	−	0.178916i
$747$	−31.4774	−	6.28773i	−1.15170	−	0.230056i
$748$	6.53970	+	2.38026i	0.239115	+	0.0870308i
$749$	1.77902	−	2.38964i	0.0650040	−	0.0873155i
$750$	−7.59262	−	12.6270i	−0.277243	−	0.461074i
$751$	38.8862	+	9.21620i	1.41898	+	0.336304i	0.867314	−	0.497762i	$-0.165845\pi$
$751$	38.8862	+	9.21620i	1.41898	+	0.336304i	0.551665	+	0.834066i	$0.313993\pi$
$752$	−2.00057	+	4.63784i	−0.0729533	+	0.169125i
$753$	−1.58085	−	4.95789i	−0.0576093	−	0.180676i
$754$	−10.6209	+	6.98546i	−0.386789	+	0.254395i
$755$	10.6175	+	18.3900i	0.386410	+	0.669282i
$756$	1.76367	−	14.4797i	0.0641440	−	0.526623i
$757$	−1.35834	+	2.35271i	−0.0493695	+	0.0855105i	−0.889654	−	0.456635i	$-0.849055\pi$
$757$	−1.35834	+	2.35271i	−0.0493695	+	0.0855105i	0.840285	+	0.542146i	$0.182388\pi$
$758$	1.40251	+	24.0801i	0.0509413	+	0.874628i
$759$	2.36760	−	58.5695i	0.0859385	−	2.12594i
$760$	−4.06055	+	0.474611i	−0.147292	+	0.0172159i
$761$	−5.86783	+	6.21954i	−0.212709	+	0.225458i	−0.824939	−	0.565221i	$-0.808791\pi$
$761$	−5.86783	+	6.21954i	−0.212709	+	0.225458i	0.612231	+	0.790679i	$0.290272\pi$
$762$	−13.7744	+	5.29258i	−0.498993	+	0.191730i
$763$	34.1420	+	3.99063i	1.23602	+	0.144471i
$764$	13.6565	−	11.4592i	0.494075	−	0.414579i
$765$	−3.34262	−	2.60807i	−0.120853	−	0.0942951i
$766$	−4.44327	−	3.72835i	−0.160542	−	0.134711i
$767$	6.09612	+	6.46151i

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.893633 - 0.448799i) q^{2} +(-1.71649 + 0.231626i) q^{3} +(0.597159 + 0.802123i) q^{4} +(-0.267154 - 0.892356i) q^{5} +(1.63787 + 0.563372i) q^{6} +(1.11188 + 2.57764i) q^{7} +(-0.173648 - 0.984808i) q^{8} +(2.89270 - 0.795169i) q^{9} +O(q^{10})\)	\(q+(-0.893633 - 0.448799i) q^{2} +(-1.71649 + 0.231626i) q^{3} +(0.597159 + 0.802123i) q^{4} +(-0.267154 - 0.892356i) q^{5} +(1.63787 + 0.563372i) q^{6} +(1.11188 + 2.57764i) q^{7} +(-0.173648 - 0.984808i) q^{8} +(2.89270 - 0.795169i) q^{9} +(-0.161751 + 0.917337i) q^{10} +(4.46341 - 1.05785i) q^{11} +(-1.21081 - 1.23852i) q^{12} +(1.47403 + 0.969483i) q^{13} +(0.163226 - 2.80247i) q^{14} +(0.665260 + 1.46984i) q^{15} +(-0.286803 + 0.957990i) q^{16} +(1.42569 - 0.518907i) q^{17} +(-2.94188 - 0.587652i) q^{18} +(4.12421 + 1.50109i) q^{19} +(0.556246 - 0.747168i) q^{20} +(-2.50559 - 4.16696i) q^{21} +(-4.46341 - 1.05785i) q^{22} +(-2.92223 + 6.77448i) q^{23} +(0.526173 + 1.65019i) q^{24} +(3.45251 - 2.27075i) q^{25} +(-0.882135 - 1.52790i) q^{26} +(-4.78112 + 2.03493i) q^{27} +(-1.40361 + 2.43113i) q^{28} +(-0.418954 - 7.19315i) q^{29} +(0.0651659 - 1.61207i) q^{30} +(-6.24778 + 0.730261i) q^{31} +(0.686242 - 0.727374i) q^{32} +(-7.41639 + 2.84963i) q^{33} +(-1.50693 - 0.176134i) q^{34} +(2.00313 - 1.68082i) q^{35} +(2.36522 + 1.84546i) q^{36} +(-0.516723 - 0.433582i) q^{37} +(-3.01184 - 3.19236i) q^{38} +(-2.75471 - 1.32269i) q^{39} +(-0.832408 + 0.418051i) q^{40} +(-8.46317 + 4.25037i) q^{41} +(0.368950 + 4.84823i) q^{42} +(3.77539 + 4.00168i) q^{43} +(3.51389 + 2.94850i) q^{44} +(-1.48237 - 2.36888i) q^{45} +(5.65178 - 4.74241i) q^{46} +(5.01677 + 0.586377i) q^{47} +(0.270401 - 1.71081i) q^{48} +(-0.604237 + 0.640453i) q^{49} +(-4.10439 + 0.479734i) q^{50} +(-2.32699 + 1.22093i) q^{51} +(0.102583 + 1.76129i) q^{52} +(-1.33883 + 2.31892i) q^{53} +(5.18583 + 0.327285i) q^{54} +(-2.13639 - 3.70034i) q^{55} +(2.34540 - 1.54259i) q^{56} +(-7.42686 - 1.62134i) q^{57} +(-2.85389 + 6.61606i) q^{58} +(4.89941 + 1.16118i) q^{59} +(-0.781729 + 1.41135i) q^{60} +(3.14866 - 4.22938i) q^{61} +(5.91096 + 2.15141i) q^{62} +(5.26600 + 6.57219i) q^{63} +(-0.939693 + 0.342020i) q^{64} +(0.471331 - 1.57436i) q^{65} +(7.90644 + 0.781947i) q^{66} +(0.832311 - 14.2902i) q^{67} +(1.26759 + 0.833706i) q^{68} +(3.44684 - 12.3052i) q^{69} +(-2.54441 + 0.603036i) q^{70} +(-0.0492509 + 0.279316i) q^{71} +(-1.28540 - 2.71067i) q^{72} +(-2.01050 - 11.4021i) q^{73} +(0.267169 + 0.619368i) q^{74} +(-5.40025 + 4.69742i) q^{75} +(1.25875 + 4.20451i) q^{76} +(7.68955 + 10.3289i) q^{77} +(1.86808 + 2.41831i) q^{78} +(3.17920 + 1.59665i) q^{79} +0.931488 q^{80} +(7.73541 - 4.60037i) q^{81} +9.47053 q^{82} +(-9.56164 - 4.80204i) q^{83} +(1.84618 - 4.49813i) q^{84} +(-0.843927 - 1.13359i) q^{85} +(-1.57786 - 5.27043i) q^{86} +(2.38525 + 12.2500i) q^{87} +(-1.81684 - 4.21191i) q^{88} +(1.74720 + 9.90888i) q^{89} +(0.261540 + 2.78220i) q^{90} +(-0.860028 + 4.87746i) q^{91} +(-7.17900 + 1.70145i) q^{92} +(10.5551 - 2.70064i) q^{93} +(-4.21999 - 2.77553i) q^{94} +(0.237708 - 4.08128i) q^{95} +(-1.00945 + 1.40748i) q^{96} +(-4.96298 + 16.5775i) q^{97} +(0.827401 - 0.301149i) q^{98} +(12.0701 - 6.60920i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 9 q^{6}+O(q^{10}) \) 72 * q + 9 * q^6	\( 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) \) 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

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