LMFDB - Embedded newform 243.2.g.a.10.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,2,Mod(10,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("243.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.g (of order $27$, degree $18$, not 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:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			10.2
Character	$\chi$	$=$	243.10
Dual form			243.2.g.a.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38037 - 0.693250i) q^{2} +(0.230520 + 0.309643i) q^{4} +(-0.145961 - 0.487543i) q^{5} +(1.57975 + 3.66226i) q^{7} +(0.432916 + 2.45519i) q^{8} +O(q^{10})$	\(q+(-1.38037 - 0.693250i) q^{2} +(0.230520 + 0.309643i) q^{4} +(-0.145961 - 0.487543i) q^{5} +(1.57975 + 3.66226i) q^{7} +(0.432916 + 2.45519i) q^{8} +(-0.136509 + 0.774179i) q^{10} +(3.72537 - 0.882929i) q^{11} +(-2.60109 - 1.71076i) q^{13} +(0.358223 - 6.15045i) q^{14} +(1.32590 - 4.42882i) q^{16} +(1.41129 - 0.513668i) q^{17} +(6.30242 + 2.29389i) q^{19} +(0.117317 - 0.157584i) q^{20} +(-5.75450 - 1.36384i) q^{22} +(0.469931 - 1.08942i) q^{23} +(3.96105 - 2.60522i) q^{25} +(2.40449 + 4.16470i) q^{26} +(-0.769829 + 1.33338i) q^{28} +(0.402098 + 6.90375i) q^{29} +(0.0460395 - 0.00538124i) q^{31} +(-1.47883 + 1.56747i) q^{32} +(-2.30421 - 0.269324i) q^{34} +(1.55493 - 1.30474i) q^{35} +(-2.33905 - 1.96269i) q^{37} +(-7.10946 - 7.53559i) q^{38} +(1.13382 - 0.569427i) q^{40} +(5.30934 - 2.66645i) q^{41} +(-0.163456 - 0.173253i) q^{43} +(1.13217 + 0.950001i) q^{44} +(-1.40392 + 1.17803i) q^{46} +(-4.70556 - 0.550002i) q^{47} +(-6.11287 + 6.47927i) q^{49} +(-7.27379 + 0.850185i) q^{50} +(-0.0698789 - 1.19977i) q^{52} +(-6.81173 + 11.7983i) q^{53} +(-0.974224 - 1.68741i) q^{55} +(-8.30765 + 5.46403i) q^{56} +(4.23098 - 9.80852i) q^{58} +(1.35914 + 0.322122i) q^{59} +(-0.187500 + 0.251856i) q^{61} +(-0.0672822 - 0.0244887i) q^{62} +(-5.56048 + 2.02385i) q^{64} +(-0.454414 + 1.51785i) q^{65} +(-0.319359 + 5.48318i) q^{67} +(0.484385 + 0.318585i) q^{68} +(-3.05090 + 0.723076i) q^{70} +(2.03991 - 11.5689i) q^{71} +(2.70207 + 15.3242i) q^{73} +(1.86812 + 4.33080i) q^{74} +(0.742550 + 2.48029i) q^{76} +(9.11866 + 12.2485i) q^{77} +(-12.5080 - 6.28175i) q^{79} -2.35277 q^{80} -9.17740 q^{82} +(-0.628222 - 0.315505i) q^{83} +(-0.456428 - 0.613090i) q^{85} +(0.105523 + 0.352470i) q^{86} +(3.78053 + 8.76426i) q^{88} +(-2.00921 - 11.3948i) q^{89} +(2.15620 - 12.2284i) q^{91} +(0.445661 - 0.105624i) q^{92} +(6.11415 + 4.02134i) q^{94} +(0.198465 - 3.40752i) q^{95} +(3.73131 - 12.4634i) q^{97} +(12.9298 - 4.70606i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8}+O(q^{10}) $ 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8	$ 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26} - 9 q^{28} - 9 q^{29} - 18 q^{31} - 36 q^{32} - 18 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} - 18 q^{40} - 18 q^{43} - 54 q^{44} - 18 q^{46} - 36 q^{47} - 18 q^{49} - 99 q^{50} - 45 q^{53} - 9 q^{55} - 126 q^{56} - 18 q^{58} - 45 q^{59} - 18 q^{61} - 81 q^{62} - 18 q^{64} + 9 q^{67} + 99 q^{68} + 36 q^{70} + 90 q^{71} - 18 q^{73} + 162 q^{74} + 63 q^{76} + 162 q^{77} + 36 q^{79} + 288 q^{80} - 36 q^{82} + 90 q^{83} + 36 q^{85} + 162 q^{86} + 63 q^{88} + 81 q^{89} - 18 q^{91} + 144 q^{92} + 36 q^{94} - 18 q^{95} + 9 q^{97} - 81 q^{98}+O(q^{100}) $ 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{27}\right)$

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 $

$2$	−1.38037	−	0.693250i	−0.976072	−	0.490202i	−0.112076	−	0.993700i	$-0.535750\pi$
$2$	−1.38037	−	0.693250i	−0.976072	−	0.490202i	−0.863996	+	0.503498i	$0.832046\pi$
$3$		0			0
$3$		0			0
$4$	0.230520	+	0.309643i	0.115260	+	0.154821i
$5$	−0.145961	−	0.487543i	−0.0652757	−	0.218036i	0.919128	−	0.393958i	$-0.128894\pi$
$5$	−0.145961	−	0.487543i	−0.0652757	−	0.218036i	−0.984404	+	0.175922i	$0.943709\pi$
$6$		0			0
$7$	1.57975	+	3.66226i	0.597088	+	1.38420i	0.901963	+	0.431813i	$0.142126\pi$
$7$	1.57975	+	3.66226i	0.597088	+	1.38420i	−0.304876	+	0.952392i	$0.598615\pi$
$8$	0.432916	+	2.45519i	0.153059	+	0.868041i
$9$		0			0
$10$	−0.136509	+	0.774179i	−0.0431678	+	0.244817i
$11$	3.72537	−	0.882929i	1.12324	−	0.266213i	0.373296	−	0.927712i	$-0.378228\pi$
$11$	3.72537	−	0.882929i	1.12324	−	0.266213i	0.749946	+	0.661499i	$0.230079\pi$
$12$		0			0
$13$	−2.60109	−	1.71076i	−0.721412	−	0.474480i	0.134952	−	0.990852i	$-0.456912\pi$
$13$	−2.60109	−	1.71076i	−0.721412	−	0.474480i	−0.856365	+	0.516372i	$0.827282\pi$
$14$	0.358223	−	6.15045i	0.0957391	−	1.64378i
$15$		0			0
$16$	1.32590	−	4.42882i	0.331476	−	1.10721i
$17$	1.41129	−	0.513668i	0.342288	−	0.124583i	−0.165156	−	0.986268i	$-0.552813\pi$
$17$	1.41129	−	0.513668i	0.342288	−	0.124583i	0.507444	+	0.861685i	$0.330590\pi$
$18$		0			0
$19$	6.30242	+	2.29389i	1.44587	+	0.526255i	0.941436	−	0.337192i	$-0.109477\pi$
$19$	6.30242	+	2.29389i	1.44587	+	0.526255i	0.504439	+	0.863447i	$0.331699\pi$
$20$	0.117317	−	0.157584i	0.0262329	−	0.0352369i
$21$		0			0
$22$	−5.75450	−	1.36384i	−1.22686	−	0.290772i
$23$	0.469931	−	1.08942i	0.0979874	−	0.227160i	−0.862171	−	0.506618i	$-0.830895\pi$
$23$	0.469931	−	1.08942i	0.0979874	−	0.227160i	0.960158	+	0.279458i	$0.0901547\pi$
$24$		0			0
$25$	3.96105	−	2.60522i	0.792209	−	0.521044i
$26$	2.40449	+	4.16470i	0.471559	+	0.816765i
$27$		0			0
$28$	−0.769829	+	1.33338i	−0.145484	+	0.251986i
$29$	0.402098	+	6.90375i	0.0746677	+	1.28199i	0.802671	+	0.596422i	$0.203411\pi$
$29$	0.402098	+	6.90375i	0.0746677	+	1.28199i	−0.728004	+	0.685573i	$0.759552\pi$
$30$		0			0
$31$	0.0460395	−	0.00538124i	0.00826893	−	0.000966499i	−0.111957	−	0.993713i	$-0.535712\pi$
$31$	0.0460395	−	0.00538124i	0.00826893	−	0.000966499i	0.120226	+	0.992747i	$0.461638\pi$
$32$	−1.47883	+	1.56747i	−0.261423	+	0.277093i
$33$		0			0
$34$	−2.30421	−	0.269324i	−0.395169	−	0.0461886i
$35$	1.55493	−	1.30474i	0.262831	−	0.220541i
$36$		0			0
$37$	−2.33905	−	1.96269i	−0.384537	−	0.322665i	0.429943	−	0.902856i	$-0.358533\pi$
$37$	−2.33905	−	1.96269i	−0.384537	−	0.322665i	−0.814481	+	0.580191i	$0.802978\pi$
$38$	−7.10946	−	7.53559i	−1.15331	−	1.22243i
$39$		0			0
$40$	1.13382	−	0.569427i	0.179273	−	0.0900343i
$41$	5.30934	−	2.66645i	0.829180	−	0.416430i	0.0170132	−	0.999855i	$-0.494584\pi$
$41$	5.30934	−	2.66645i	0.829180	−	0.416430i	0.812167	+	0.583425i	$0.198288\pi$
$42$		0			0
$43$	−0.163456	−	0.173253i	−0.0249268	−	0.0264208i	0.714790	−	0.699339i	$-0.246522\pi$
$43$	−0.163456	−	0.173253i	−0.0249268	−	0.0264208i	−0.739717	+	0.672918i	$0.765041\pi$
$44$	1.13217	+	0.950001i	0.170681	+	0.143218i
$45$		0			0
$46$	−1.40392	+	1.17803i	−0.206997	+	0.173691i
$47$	−4.70556	−	0.550002i	−0.686377	−	0.0802260i	−0.234246	−	0.972177i	$-0.575262\pi$
$47$	−4.70556	−	0.550002i	−0.686377	−	0.0802260i	−0.452131	+	0.891951i	$0.649336\pi$
$48$		0			0
$49$	−6.11287	+	6.47927i	−0.873268	+	0.925610i
$50$	−7.27379	+	0.850185i	−1.02867	+	0.120234i
$51$		0			0
$52$	−0.0698789	−	1.19977i	−0.00969046	−	0.166379i
$53$	−6.81173	+	11.7983i	−0.935663	+	1.62062i	−0.162216	+	0.986755i	$0.551864\pi$
$53$	−6.81173	+	11.7983i	−0.935663	+	1.62062i	−0.773447	+	0.633860i	$0.781469\pi$
$54$		0			0
$55$	−0.974224	−	1.68741i	−0.131364	−	0.227530i
$56$	−8.30765	+	5.46403i	−1.11016	+	0.730161i
$57$		0			0
$58$	4.23098	−	9.80852i	0.555555	−	1.28792i
$59$	1.35914	+	0.322122i	0.176945	+	0.0419368i	0.318133	−	0.948046i	$-0.396944\pi$
$59$	1.35914	+	0.322122i	0.176945	+	0.0419368i	−0.141188	+	0.989983i	$0.545092\pi$
$60$		0			0
$61$	−0.187500	+	0.251856i	−0.0240069	+	0.0322469i	−0.813965	−	0.580914i	$-0.802695\pi$
$61$	−0.187500	+	0.251856i	−0.0240069	+	0.0322469i	0.789958	+	0.613161i	$0.210102\pi$
$62$	−0.0672822	−	0.0244887i	−0.00854485	−	0.00311007i
$63$		0			0
$64$	−5.56048	+	2.02385i	−0.695060	+	0.252981i
$65$	−0.454414	+	1.51785i	−0.0563631	+	0.188266i
$66$		0			0
$67$	−0.319359	+	5.48318i	−0.0390159	+	0.669878i	0.920936	+	0.389713i	$0.127426\pi$
$67$	−0.319359	+	5.48318i	−0.0390159	+	0.669878i	−0.959952	+	0.280164i	$0.909611\pi$
$68$	0.484385	+	0.318585i	0.0587403	+	0.0386341i
$69$		0			0
$70$	−3.05090	+	0.723076i	−0.364652	+	0.0864241i
$71$	2.03991	−	11.5689i	0.242093	−	1.37298i	−0.585054	−	0.810994i	$-0.698927\pi$
$71$	2.03991	−	11.5689i	0.242093	−	1.37298i	0.827147	−	0.561985i	$-0.189962\pi$
$72$		0			0
$73$	2.70207	+	15.3242i	0.316253	+	1.79356i	0.565106	+	0.825019i	$0.308835\pi$
$73$	2.70207	+	15.3242i	0.316253	+	1.79356i	−0.248853	+	0.968541i	$0.580053\pi$
$74$	1.86812	+	4.33080i	0.217165	+	0.503445i
$75$		0			0
$76$	0.742550	+	2.48029i	0.0851763	+	0.284509i
$77$	9.11866	+	12.2485i	1.03917	+	1.39584i
$78$		0			0
$79$	−12.5080	−	6.28175i	−1.40726	−	0.706752i	−0.426960	−	0.904271i	$-0.640415\pi$
$79$	−12.5080	−	6.28175i	−1.40726	−	0.706752i	−0.980299	+	0.197519i	$0.936712\pi$
$80$	−2.35277			−0.263048
$81$		0			0
$82$	−9.17740			−1.01347
$83$	−0.628222	−	0.315505i	−0.0689563	−	0.0346312i	0.413987	−	0.910283i	$-0.364136\pi$
$83$	−0.628222	−	0.315505i	−0.0689563	−	0.0346312i	−0.482943	+	0.875652i	$0.660432\pi$
$84$		0			0
$85$	−0.456428	−	0.613090i	−0.0495066	−	0.0664989i
$86$	0.105523	+	0.352470i	0.0113788	+	0.0380078i
$87$		0			0
$88$	3.78053	+	8.76426i	0.403006	+	0.934273i
$89$	−2.00921	−	11.3948i	−0.212976	−	1.20785i	−0.884384	−	0.466760i	$-0.845421\pi$
$89$	−2.00921	−	11.3948i	−0.212976	−	1.20785i	0.671408	−	0.741088i	$-0.265690\pi$
$90$		0			0
$91$	2.15620	−	12.2284i	0.226032	−	1.28189i
$92$	0.445661	−	0.105624i	0.0464633	−	0.0110120i
$93$		0			0
$94$	6.11415	+	4.02134i	0.630627	+	0.414770i
$95$	0.198465	−	3.40752i	0.0203621	−	0.349604i
$96$		0			0
$97$	3.73131	−	12.4634i	0.378857	−	1.26547i	−0.529870	−	0.848079i	$-0.677759\pi$
$97$	3.73131	−	12.4634i	0.378857	−	1.26547i	0.908727	−	0.417391i	$-0.137055\pi$
$98$	12.9298	−	4.70606i	1.30611	−	0.475384i
$99$		0			0
$100$	1.71979	+	0.625952i	0.171979	+	0.0625952i
$101$	7.38327	−	9.91745i	0.734663	−	0.986823i	−0.265082	−	0.964226i	$-0.585399\pi$
$101$	7.38327	−	9.91745i	0.734663	−	0.986823i	0.999745	−	0.0225975i	$-0.00719361\pi$
$102$		0			0
$103$	−2.03381	−	0.482021i	−0.200397	−	0.0474949i	0.129192	−	0.991620i	$-0.458762\pi$
$103$	−2.03381	−	0.482021i	−0.200397	−	0.0474949i	−0.329588	+	0.944125i	$0.606910\pi$
$104$	3.07420	−	7.12679i	0.301450	−	0.698839i
$105$		0			0
$106$	17.5819	−	11.5638i	1.70770	−	1.12317i
$107$	−0.831363	−	1.43996i	−0.0803709	−	0.139207i	0.823038	−	0.567986i	$-0.192277\pi$
$107$	−0.831363	−	1.43996i	−0.0803709	−	0.139207i	−0.903409	+	0.428779i	$0.858944\pi$
$108$		0			0
$109$	−2.14981	+	3.72357i	−0.205914	+	0.356654i	−0.950424	−	0.310958i	$-0.899350\pi$
$109$	−2.14981	+	3.72357i	−0.205914	+	0.356654i	0.744510	+	0.667612i	$0.232683\pi$
$110$	0.175000	+	3.00463i	0.0166856	+	0.286480i
$111$		0			0
$112$	18.3141	−	2.14061i	1.73052	−	0.202269i
$113$	−9.76830	+	10.3538i	−0.918924	+	0.974003i	−0.999742	−	0.0227261i	$-0.992765\pi$
$113$	−9.76830	+	10.3538i	−0.918924	+	0.974003i	0.0808175	+	0.996729i	$0.474247\pi$
$114$		0			0
$115$	−0.599732	−	0.0700986i	−0.0559253	−	0.00653673i
$116$	−2.04501	+	1.71596i	−0.189874	+	0.159323i
$117$		0			0
$118$	−1.65281	−	1.38687i	−0.152154	−	0.127672i
$119$	4.11067	+	4.35705i	0.376824	+	0.399410i
$120$		0			0
$121$	3.26887	−	1.64169i	0.297170	−	0.149244i
$122$	0.433420	−	0.217672i	0.0392400	−	0.0197071i
$123$		0			0
$124$	0.0122793	+	0.0130153i	0.00110271	+	0.00116881i
$125$	−3.79760	−	3.18657i	−0.339668	−	0.285015i
$126$		0			0
$127$	14.1754	−	11.8946i	1.25787	−	1.05548i	0.261961	−	0.965078i	$-0.415631\pi$
$127$	14.1754	−	11.8946i	1.25787	−	1.05548i	0.995906	−	0.0903976i	$-0.0288138\pi$
$128$	13.3594	+	1.56149i	1.18081	+	0.138017i
$129$		0			0
$130$	1.67951	−	1.78018i	0.147303	−	0.156132i
$131$	−5.51565	+	0.644687i	−0.481904	+	0.0563265i	−0.353577	−	0.935405i	$-0.615035\pi$
$131$	−5.51565	+	0.644687i	−0.481904	+	0.0563265i	−0.128327	+	0.991732i	$0.540961\pi$
$132$		0			0
$133$	1.55538	+	26.7049i	0.134869	+	2.31561i
$134$	4.24205	−	7.34745i	0.366458	−	0.634723i
$135$		0			0
$136$	1.87212	+	3.24261i	0.160533	+	0.278052i
$137$	2.49276	−	1.63952i	0.212971	−	0.140073i	−0.438542	−	0.898711i	$-0.644505\pi$
$137$	2.49276	−	1.63952i	0.212971	−	0.140073i	0.651513	+	0.758637i	$0.274135\pi$
$138$		0			0
$139$	−2.33438	+	5.41169i	−0.197999	+	0.459014i	−0.988071	−	0.154001i	$-0.950784\pi$
$139$	−2.33438	+	5.41169i	−0.197999	+	0.459014i	0.790072	+	0.613015i	$0.210043\pi$
$140$	0.762446	+	0.180703i	0.0644385	+	0.0152722i
$141$		0			0
$142$	−10.8360	+	14.5553i	−0.909337	+	1.22145i
$143$	−11.2005	−	4.07665i	−0.936633	−	0.340907i
$144$		0			0
$145$	3.30719	−	1.20372i	0.274647	−	0.0999633i
$146$	6.89363	−	23.0263i	0.570521	−	1.90567i
$147$		0			0
$148$	0.0685356	−	1.17671i	0.00563359	−	0.0967250i
$149$	4.54998	+	2.99257i	0.372748	+	0.245161i	0.722037	−	0.691855i	$-0.243206\pi$
$149$	4.54998	+	2.99257i	0.372748	+	0.245161i	−0.349288	+	0.937015i	$0.613577\pi$
$150$		0			0
$151$	−14.5098	+	3.43888i	−1.18079	+	0.279852i	−0.773709	−	0.633541i	$-0.781601\pi$
$151$	−14.5098	+	3.43888i	−1.18079	+	0.279852i	−0.407079	+	0.913393i	$0.633453\pi$
$152$	−2.90352	+	16.4667i	−0.235507	+	1.33563i
$153$		0			0
$154$	−4.09590	−	23.2290i	−0.330057	−	1.87185i
$155$	−0.00934354	−	0.0216608i	−0.000750491	−	0.00173983i
$156$		0			0
$157$	−2.40470	−	8.03227i	−0.191916	−	0.641045i	−0.998737	−	0.0502483i	$-0.983999\pi$
$157$	−2.40470	−	8.03227i	−0.191916	−	0.641045i	0.806821	−	0.590797i	$-0.201186\pi$
$158$	12.9109	+	17.3423i	1.02713	+	1.37968i
$159$		0			0
$160$	0.980062	+	0.492206i	0.0774807	+	0.0389123i
$161$	4.73212			0.372944
$162$		0			0
$163$	3.04537			0.238531			0.119266	−	0.992862i	$-0.461946\pi$
$163$	3.04537			0.238531			0.119266	+	0.992862i	$0.461946\pi$
$164$	2.04956	+	1.02933i	0.160044	+	0.0803770i
$165$		0			0
$166$	0.648458	+	0.871030i	0.0503301	+	0.0676050i
$167$	−6.05264	−	20.2172i	−0.468367	−	1.56445i	−0.787233	−	0.616655i	$-0.788487\pi$
$167$	−6.05264	−	20.2172i	−0.468367	−	1.56445i	0.318866	−	0.947800i	$-0.396698\pi$
$168$		0			0
$169$	−1.31008	−	3.03711i	−0.100776	−	0.233624i
$170$	0.205018	+	1.16271i	0.0157241	+	0.0891760i
$171$		0			0
$172$	0.0159666	−	0.0905513i	0.00121744	−	0.00690447i
$173$	−1.64906	+	0.390835i	−0.125376	+	0.0297146i	−0.292825	−	0.956166i	$-0.594595\pi$
$173$	−1.64906	+	0.390835i	−0.125376	+	0.0297146i	0.167449	+	0.985881i	$0.446447\pi$
$174$		0			0
$175$	15.7984	+	10.3908i	1.19425	+	0.785471i
$176$	1.02914	−	17.6697i	0.0775745	−	1.33190i
$177$		0			0
$178$	−5.12599	+	17.1220i	−0.384209	+	1.28335i
$179$	−11.3362	+	4.12604i	−0.847308	+	0.308395i	−0.728942	−	0.684575i	$-0.759988\pi$
$179$	−11.3362	+	4.12604i	−0.847308	+	0.308395i	−0.118366	+	0.992970i	$0.537765\pi$
$180$		0			0
$181$	−7.09567	−	2.58261i	−0.527417	−	0.191964i	0.0645678	−	0.997913i	$-0.479433\pi$
$181$	−7.09567	−	2.58261i	−0.527417	−	0.191964i	−0.591985	+	0.805949i	$0.701655\pi$
$182$	−11.4537	+	15.3850i	−0.849007	+	1.14041i
$183$		0			0
$184$	2.87818	+	0.682141i	0.212182	+	0.0502881i
$185$	−0.615488	+	1.42686i	−0.0452516	+	0.104905i
$186$		0			0
$187$	4.80405	−	3.15967i	0.351307	−	0.231058i
$188$	−0.914425	−	1.58383i	−0.0666913	−	0.115513i
$189$		0			0
$190$	−2.63622	+	4.56607i	−0.191251	+	0.331257i
$191$	−0.753015	−	12.9288i	−0.0544863	−	0.935493i	−0.909191	−	0.416379i	$-0.863299\pi$
$191$	−0.753015	−	12.9288i	−0.0544863	−	0.935493i	0.854705	−	0.519114i	$-0.173738\pi$
$192$		0			0
$193$	−17.9568	+	2.09885i	−1.29256	+	0.151079i	−0.734435	−	0.678679i	$-0.762553\pi$
$193$	−17.9568	+	2.09885i	−1.29256	+	0.151079i	−0.558125	+	0.829757i	$0.688479\pi$
$194$	−13.7909	+	14.6175i	−0.990127	+	1.04947i
$195$		0			0
$196$	−3.41540	−	0.399203i	−0.243957	−	0.0285145i
$197$	−7.47510	+	6.27235i	−0.532579	+	0.446886i	−0.868991	−	0.494828i	$-0.835231\pi$
$197$	−7.47510	+	6.27235i	−0.532579	+	0.446886i	0.336412	+	0.941715i	$0.390786\pi$
$198$		0			0
$199$	−6.35460	−	5.33214i	−0.450465	−	0.377985i	0.389143	−	0.921177i	$-0.372771\pi$
$199$	−6.35460	−	5.33214i	−0.450465	−	0.377985i	−0.839609	+	0.543192i	$0.817216\pi$
$200$	8.11111	+	8.59728i	0.573542	+	0.607919i
$201$		0			0
$202$	−17.0670	+	8.57134i	−1.20083	+	0.603078i
$203$	−24.6481	+	12.3788i	−1.72996	+	0.868819i
$204$		0			0
$205$	−2.07497	−	2.19933i	−0.144922	−	0.153608i
$206$	2.47325	+	2.07530i	0.172320	+	0.144593i
$207$		0			0
$208$	−11.0255	+	9.25146i	−0.764478	+	0.641473i
$209$	25.5042	+	2.98101i	1.76416	+	0.206201i
$210$		0			0
$211$	7.78139	−	8.24779i	0.535693	−	0.567802i	−0.401835	−	0.915712i	$-0.631627\pi$
$211$	7.78139	−	8.24779i	0.535693	−	0.567802i	0.937528	+	0.347911i	$0.113109\pi$
$212$	−5.22349	+	0.610538i	−0.358751	+	0.0419319i
$213$		0			0
$214$	0.149338	+	2.56403i	0.0102085	+	0.175274i
$215$	−0.0606102	+	0.104980i	−0.00413358	+	0.00715957i
$216$		0			0
$217$	0.0924381	+	0.160108i	0.00627511	+	0.0108688i
$218$	5.54890	−	3.64957i	0.375819	−	0.247180i
$219$		0			0
$220$	0.297914	−	0.690643i	0.0200854	−	0.0465631i
$221$	−4.54966	−	1.07829i	−0.306043	−	0.0725336i
$222$		0			0
$223$	11.3015	−	15.1805i	0.756803	−	1.01656i	−0.242124	−	0.970245i	$-0.577844\pi$
$223$	11.3015	−	15.1805i	0.756803	−	1.01656i	0.998927	−	0.0463177i	$-0.0147486\pi$
$224$	−8.07667	−	2.93967i	−0.539646	−	0.196415i
$225$		0			0
$226$	20.6617	−	7.52023i	1.37439	−	0.500239i
$227$	−3.18314	+	10.6324i	−0.211272	+	0.705699i	0.785005	+	0.619490i	$0.212661\pi$
$227$	−3.18314	+	10.6324i	−0.211272	+	0.705699i	−0.996277	+	0.0862092i	$0.972525\pi$
$228$		0			0
$229$	−0.177059	+	3.03999i	−0.0117004	+	0.200888i	0.987392	+	0.158294i	$0.0505994\pi$
$229$	−0.177059	+	3.03999i	−0.0117004	+	0.200888i	−0.999092	+	0.0425944i	$0.986438\pi$
$230$	0.779259	+	0.512527i	0.0513828	+	0.0337950i
$231$		0			0
$232$	−16.7760	+	3.97597i	−1.10140	+	0.261035i
$233$	2.47370	−	14.0290i	0.162057	−	0.919073i	−0.789989	−	0.613121i	$-0.789914\pi$
$233$	2.47370	−	14.0290i	0.162057	−	0.919073i	0.952047	−	0.305953i	$-0.0989750\pi$
$234$		0			0
$235$	0.418679	+	2.37444i	0.0273116	+	0.154892i
$236$	0.213567	+	0.495104i	0.0139020	+	0.0322285i
$237$		0			0
$238$	−2.65373	−	8.86408i	−0.172016	−	0.574573i
$239$	4.74520	+	6.37391i	0.306942	+	0.412294i	0.928651	−	0.370953i	$-0.120969\pi$
$239$	4.74520	+	6.37391i	0.306942	+	0.412294i	−0.621710	+	0.783248i	$0.713562\pi$
$240$		0			0
$241$	3.23832	+	1.62634i	0.208598	+	0.104762i	0.550031	−	0.835144i	$-0.314616\pi$
$241$	3.23832	+	1.62634i	0.208598	+	0.104762i	−0.341433	+	0.939906i	$0.610912\pi$
$242$	−5.65036			−0.363219
$243$		0			0
$244$	−0.121208			−0.00775955
$245$	4.05116	+	2.03457i	0.258819	+	0.129984i
$246$		0			0
$247$	−12.4689	−	16.7486i	−0.793374	−	1.06569i
$248$	0.0331432	+	0.110706i	0.00210459	+	0.00702984i
$249$		0			0
$250$	3.03303	+	7.03134i	0.191825	+	0.444701i
$251$	0.441351	+	2.50303i	0.0278578	+	0.157990i	0.995563	−	0.0940939i	$-0.0299954\pi$
$251$	0.441351	+	2.50303i	0.0278578	+	0.157990i	−0.967706	+	0.252083i	$0.918884\pi$
$252$		0			0
$253$	0.788785	−	4.47342i	0.0495905	−	0.281242i
$254$	−27.8134	+	6.59189i	−1.74517	+	0.413612i
$255$		0			0
$256$	−7.47072	−	4.91357i	−0.466920	−	0.307098i
$257$	−1.62804	+	27.9523i	−0.101554	+	1.74362i	0.435606	+	0.900138i	$0.356534\pi$
$257$	−1.62804	+	27.9523i	−0.101554	+	1.74362i	−0.537160	+	0.843480i	$0.680503\pi$
$258$		0			0
$259$	3.49280	−	11.6668i	0.217032	−	0.724937i
$260$	−0.574742	+	0.209189i	−0.0356440	+	0.0129733i
$261$		0			0
$262$	8.06059	+	2.93381i	0.497985	+	0.181252i
$263$	1.46939	−	1.97374i	0.0906067	−	0.121706i	−0.754508	−	0.656291i	$-0.772125\pi$
$263$	1.46939	−	1.97374i	0.0906067	−	0.121706i	0.845115	+	0.534585i	$0.179532\pi$
$264$		0			0
$265$	6.74641	+	1.59893i	0.414428	+	0.0982213i
$266$	16.3662	−	37.9410i	1.00347	−	2.32631i
$267$		0			0
$268$	−1.77145	+	1.16510i	−0.108208	+	0.0711697i
$269$	5.65271	+	9.79078i	0.344652	+	0.596954i	0.985290	−	0.170888i	$-0.0546637\pi$
$269$	5.65271	+	9.79078i	0.344652	+	0.596954i	−0.640639	+	0.767842i	$0.721330\pi$
$270$		0			0
$271$	2.14084	−	3.70804i	0.130047	−	0.225248i	−0.793648	−	0.608378i	$-0.791821\pi$
$271$	2.14084	−	3.70804i	0.130047	−	0.225248i	0.923694	+	0.383130i	$0.125154\pi$
$272$	−0.403710	−	6.93143i	−0.0244785	−	0.420280i
$273$		0			0
$274$	−4.57754	+	0.535038i	−0.276540	+	0.0323228i
$275$	12.4561	−	13.2027i	0.751134	−	0.796155i
$276$		0			0
$277$	−18.6953	−	2.18516i	−1.12329	−	0.131294i	−0.465895	−	0.884840i	$-0.654268\pi$
$277$	−18.6953	−	2.18516i	−1.12329	−	0.131294i	−0.657395	+	0.753546i	$0.728342\pi$
$278$	6.97397	−	5.85185i	0.418271	−	0.350971i
$279$		0			0
$280$	3.87654	+	3.25280i	0.231668	+	0.194392i
$281$	−9.33535	−	9.89489i	−0.556900	−	0.590280i	0.386354	−	0.922350i	$-0.373734\pi$
$281$	−9.33535	−	9.89489i	−0.556900	−	0.590280i	−0.943254	+	0.332071i	$0.892253\pi$
$282$		0			0
$283$	14.9150	−	7.49059i	0.886605	−	0.445270i	0.0536172	−	0.998562i	$-0.482925\pi$
$283$	14.9150	−	7.49059i	0.886605	−	0.445270i	0.832987	+	0.553292i	$0.186629\pi$
$284$	4.05248	−	2.03523i	0.240470	−	0.120769i
$285$		0			0
$286$	12.6348	+	13.3921i	0.747109	+	0.791889i
$287$	18.1527	+	15.2319i	1.07152	+	0.899110i
$288$		0			0
$289$	−11.2949	+	9.47752i	−0.664404	+	0.557501i
$290$	−5.39963	−	0.631127i	−0.317077	−	0.0370610i
$291$		0			0
$292$	−4.12214	+	4.36921i	−0.241230	+	0.255689i
$293$	−25.2376	+	2.94986i	−1.47440	+	0.172333i	−0.815000	−	0.579461i	$-0.803263\pi$
$293$	−25.2376	+	2.94986i	−1.47440	+	0.172333i	−0.659399	+	0.751793i	$0.729189\pi$
$294$		0			0
$295$	−0.0413328	−	0.709657i	−0.00240649	−	0.0413178i
$296$	3.80617	−	6.59249i	0.221229	−	0.383181i
$297$		0			0
$298$	−4.20607	−	7.28513i	−0.243651	−	0.422016i
$299$	−3.08608	+	2.02975i	−0.178473	+	0.117383i
$300$		0			0
$301$	0.376279	−	0.872314i	0.0216884	−	0.0502793i
$302$	22.4129	+	5.31196i	1.28972	+	0.305669i
$303$		0			0
$304$	18.5156	−	24.8708i	1.06195	−	1.42644i
$305$	0.150158	+	0.0546532i	0.00859805	+	0.00312943i
$306$		0			0
$307$	−9.43080	+	3.43253i	−0.538244	+	0.195905i	−0.596816	−	0.802378i	$-0.703568\pi$
$307$	−9.43080	+	3.43253i	−0.538244	+	0.195905i	0.0585714	+	0.998283i	$0.481345\pi$
$308$	−1.69062	+	5.64705i	−0.0963318	+	0.321771i
$309$		0			0
$310$	−0.00211874	+	0.0363774i	−0.000120336	+	0.00206610i
$311$	22.5173	+	14.8099i	1.27684	+	0.839791i	0.992888	−	0.119048i	$-0.0379843\pi$
$311$	22.5173	+	14.8099i	1.27684	+	0.839791i	0.283951	+	0.958839i	$0.408355\pi$
$312$		0			0
$313$	12.6801	−	3.00523i	0.716720	−	0.169866i	0.143954	−	0.989584i	$-0.454018\pi$
$313$	12.6801	−	3.00523i	0.716720	−	0.169866i	0.572767	+	0.819719i	$0.305870\pi$
$314$	−2.24898	+	12.7546i	−0.126917	+	0.719784i
$315$		0			0
$316$	−0.938250	−	5.32108i	−0.0527807	−	0.299334i
$317$	−3.76028	−	8.71730i	−0.211198	−	0.489612i	0.779382	−	0.626550i	$-0.215533\pi$
$317$	−3.76028	−	8.71730i	−0.211198	−	0.489612i	−0.990580	+	0.136937i	$0.956274\pi$
$318$		0			0
$319$	7.59349	+	25.3640i	0.425154	+	1.42011i
$320$	1.79832	+	2.41557i	0.100529	+	0.135034i
$321$		0			0
$322$	−6.53210	−	3.28055i	−0.364020	−	0.182818i
$323$	10.0729			0.560468
$324$		0			0
$325$	−14.7599			−0.818735
$326$	−4.20374	−	2.11120i	−0.232824	−	0.116929i
$327$		0			0
$328$	8.84514	+	11.8811i	0.488391	+	0.656024i
$329$	−5.41934	−	18.1019i	−0.298778	−	0.997988i
$330$		0			0
$331$	−9.31346	−	21.5910i	−0.511914	−	1.18675i	−0.956690	−	0.291108i	$-0.905976\pi$
$331$	−9.31346	−	21.5910i	−0.511914	−	1.18675i	0.444776	−	0.895642i	$-0.353283\pi$
$332$	−0.0471242	−	0.267255i	−0.00258628	−	0.0146675i
$333$		0			0
$334$	−5.66068	+	32.1033i	−0.309739	+	1.75661i
$335$	2.71990	−	0.644629i	0.148604	−	0.0352198i
$336$		0			0
$337$	2.59680	+	1.70794i	0.141457	+	0.0930376i	0.618265	−	0.785970i	$-0.287836\pi$
$337$	2.59680	+	1.70794i	0.141457	+	0.0930376i	−0.476808	+	0.879007i	$0.658206\pi$
$338$	−0.297074	+	5.10057i	−0.0161587	+	0.277434i
$339$		0			0
$340$	0.0846227	−	0.282659i	0.00458931	−	0.0153294i
$341$	0.166763	−	0.0606967i	0.00903071	−	0.00328691i
$342$		0			0
$343$	−7.15012	−	2.60243i	−0.386070	−	0.140518i
$344$	0.354606	−	0.476319i	0.0191191	−	0.0256814i
$345$		0			0
$346$	2.54727	+	0.603714i	0.136942	+	0.0324559i
$347$	8.83048	−	20.4714i	0.474045	−	1.09896i	−0.498636	−	0.866812i	$-0.666165\pi$
$347$	8.83048	−	20.4714i	0.474045	−	1.09896i	0.972680	−	0.232148i	$-0.0745754\pi$
$348$		0			0
$349$	−2.51713	+	1.65554i	−0.134739	+	0.0886192i	−0.615089	−	0.788458i	$-0.710880\pi$
$349$	−2.51713	+	1.65554i	−0.134739	+	0.0886192i	0.480350	+	0.877077i	$0.340510\pi$
$350$	−14.6043	−	25.2955i	−0.780635	−	1.35210i
$351$		0			0
$352$	−4.12524	+	7.14512i	−0.219876	+	0.380836i
$353$	0.125841	+	2.16060i	0.00669783	+	0.114997i	1.00000		0.000549684i	$-0.000174970\pi$
$353$	0.125841	+	2.16060i	0.00669783	+	0.114997i	−0.993302	+	0.115547i	$0.963138\pi$
$354$		0			0
$355$	−5.93810	+	0.694064i	−0.315161	+	0.0368371i
$356$	3.06516	−	3.24888i	0.162453	−	0.172190i
$357$		0			0
$358$	18.5086	+	2.16334i	0.978209	+	0.114336i
$359$	0.496794	−	0.416860i	0.0262198	−	0.0220010i	−0.629584	−	0.776933i	$-0.716774\pi$
$359$	0.496794	−	0.416860i	0.0262198	−	0.0220010i	0.655803	+	0.754932i	$0.272330\pi$
$360$		0			0
$361$	19.9037	+	16.7012i	1.04756	+	0.879011i
$362$	8.00428	+	8.48404i	0.420696	+	0.445911i
$363$		0			0
$364$	4.28350	−	2.15125i	0.224516	−	0.112756i
$365$	7.07680	−	3.55410i	0.370417	−	0.186030i
$366$		0			0
$367$	6.49821	+	6.88770i	0.339204	+	0.359535i	0.874411	−	0.485186i	$-0.161248\pi$
$367$	6.49821	+	6.88770i	0.339204	+	0.359535i	−0.535207	+	0.844721i	$0.679767\pi$
$368$	−4.20178	−	3.52571i	−0.219033	−	0.183790i
$369$		0			0
$370$	1.83878	−	1.54292i	0.0955935	−	0.0802124i
$371$	−53.9691	−	6.30809i	−2.80194	−	0.327499i
$372$		0			0
$373$	3.35002	−	3.55082i	0.173458	−	0.183854i	−0.634813	−	0.772666i	$-0.718923\pi$
$373$	3.35002	−	3.55082i	0.173458	−	0.183854i	0.808270	+	0.588812i	$0.200404\pi$
$374$	−8.82183	+	1.03112i	−0.456166	+	0.0533182i
$375$		0			0
$376$	−0.686757	−	11.7912i	−0.0354168	−	0.608083i
$377$	10.7648	−	18.6452i	0.554415	−	0.960275i
$378$		0			0
$379$	13.0190	+	22.5495i	0.668739	+	1.15829i	0.978257	+	0.207396i	$0.0664989\pi$
$379$	13.0190	+	22.5495i	0.668739	+	1.15829i	−0.309518	+	0.950894i	$0.600168\pi$
$380$	1.10086	−	0.724050i	0.0564731	−	0.0371430i
$381$		0			0
$382$	−7.92343	+	18.3686i	−0.405398	+	0.939818i
$383$	7.81450	+	1.85207i	0.399302	+	0.0946364i	0.425360	−	0.905024i	$-0.360147\pi$
$383$	7.81450	+	1.85207i	0.399302	+	0.0946364i	−0.0260580	+	0.999660i	$0.508295\pi$
$384$		0			0
$385$	4.64070	−	6.23354i	0.236512	−	0.317690i
$386$	26.2422	+	9.55136i	1.33569	+	0.486152i
$387$		0			0
$388$	4.71935	−	1.71770i	0.239589	−	0.0872032i
$389$	−6.52364	+	21.7905i	−0.330762	+	1.10482i	0.617298	+	0.786729i	$0.288227\pi$
$389$	−6.52364	+	21.7905i	−0.330762	+	1.10482i	−0.948060	+	0.318092i	$0.896958\pi$
$390$		0			0
$391$	0.103608	−	1.77888i	0.00523968	−	0.0899619i
$392$	−18.5542	−	12.2033i	−0.937128	−	0.616359i
$393$		0			0
$394$	14.6667	−	3.47608i	0.738900	−	0.175122i
$395$	−1.23695	+	7.01507i	−0.0622375	+	0.352967i
$396$		0			0
$397$	4.29294	+	24.3465i	0.215456	+	1.22191i	0.880113	+	0.474765i	$0.157467\pi$
$397$	4.29294	+	24.3465i	0.215456	+	1.22191i	−0.664656	+	0.747149i	$0.731422\pi$
$398$	5.07522	+	11.7657i	0.254398	+	0.589760i
$399$		0			0
$400$	−6.28610	−	20.9970i	−0.314305	−	1.04985i
$401$	10.1376	+	13.6172i	0.506249	+	0.680010i	0.979622	−	0.200852i	$-0.0643710\pi$
$401$	10.1376	+	13.6172i	0.506249	+	0.680010i	−0.473373	+	0.880862i	$0.656964\pi$
$402$		0			0
$403$	−0.128959	−	0.0647655i	−0.00642389	−	0.00322620i
$404$	4.77286			0.237459
$405$		0			0
$406$	42.6052			2.11446
$407$	−10.4467	−	5.24655i	−0.517826	−	0.260062i
$408$		0			0
$409$	6.74707	+	9.06289i	0.333621	+	0.448131i	0.937003	−	0.349321i	$-0.113588\pi$
$409$	6.74707	+	9.06289i	0.333621	+	0.448131i	−0.603382	+	0.797453i	$0.706180\pi$
$410$	1.33954	+	4.47438i	0.0661552	+	0.220974i
$411$		0			0
$412$	−0.319580	−	0.740869i	−0.0157446	−	0.0365000i
$413$	0.967401	+	5.48640i	0.0476027	+	0.269968i
$414$		0			0
$415$	−0.0621265	+	0.352337i	−0.00304967	+	0.0172955i
$416$	6.52815	−	1.54720i	0.320069	−	0.0758578i
$417$		0			0
$418$	−33.1388	−	21.7957i	−1.62087	−	1.06606i
$419$	1.88570	−	32.3762i	0.0921223	−	1.58168i	−0.563194	−	0.826325i	$-0.690428\pi$
$419$	1.88570	−	32.3762i	0.0921223	−	1.58168i	0.655316	−	0.755355i	$-0.272535\pi$
$420$		0			0
$421$	0.190554	−	0.636493i	0.00928701	−	0.0310208i	−0.953220	−	0.302276i	$-0.902254\pi$
$421$	0.190554	−	0.636493i	0.00928701	−	0.0310208i	0.962507	+	0.271255i	$0.0874388\pi$
$422$	−16.4590	+	5.99059i	−0.801212	+	0.291617i
$423$		0			0
$424$	−31.9159	−	11.6164i	−1.54997	−	0.564144i
$425$	4.25197	−	5.71139i	0.206251	−	0.277043i
$426$		0			0
$427$	−1.21857	−	0.288806i	−0.0589706	−	0.0139763i
$428$	0.254228	−	0.589367i	0.0122886	−	0.0284881i
$429$		0			0
$430$	0.156442	−	0.102894i	0.00754430	−	0.00496197i
$431$	15.1861	+	26.3031i	0.731488	+	1.26698i	0.956247	+	0.292561i	$0.0945073\pi$
$431$	15.1861	+	26.3031i	0.731488	+	1.26698i	−0.224759	+	0.974414i	$0.572159\pi$
$432$		0			0
$433$	5.68299	−	9.84323i	0.273107	−	0.473035i	−0.696549	−	0.717510i	$-0.745282\pi$
$433$	5.68299	−	9.84323i	0.273107	−	0.473035i	0.969656	+	0.244474i	$0.0786153\pi$
$434$	−0.0166047	−	0.285091i	−0.000797049	−	0.0136848i
$435$		0			0
$436$	−1.64855	+	0.192688i	−0.0789513	+	0.00922808i
$437$	5.46073	−	5.78803i	0.261222	−	0.276879i
$438$		0			0
$439$	7.12292	+	0.832550i	0.339958	+	0.0397354i	0.284359	−	0.958718i	$-0.408219\pi$
$439$	7.12292	+	0.832550i	0.339958	+	0.0397354i	0.0555990	+	0.998453i	$0.482293\pi$
$440$	3.72114	−	3.12241i	0.177399	−	0.148855i
$441$		0			0
$442$	5.53271	+	4.64249i	0.263164	+	0.220821i
$443$	−1.19860	−	1.27044i	−0.0569470	−	0.0603603i	0.698274	−	0.715831i	$-0.253952\pi$
$443$	−1.19860	−	1.27044i	−0.0569470	−	0.0603603i	−0.755221	+	0.655471i	$0.772470\pi$
$444$		0			0
$445$	−5.26220	+	2.64277i	−0.249452	+	0.125280i
$446$	−26.1242	+	13.1201i	−1.23702	+	0.621253i
$447$		0			0
$448$	−16.1960	−	17.1668i	−0.765189	−	0.811053i
$449$	−25.6694	−	21.5392i	−1.21142	−	1.01650i	−0.999229	−	0.0392691i	$-0.987497\pi$
$449$	−25.6694	−	21.5392i	−1.21142	−	1.01650i	−0.212187	−	0.977229i	$-0.568059\pi$
$450$		0			0
$451$	17.4250	−	14.6213i	0.820510	−	0.688490i
$452$	−5.45777	−	0.637922i	−0.256712	−	0.0300053i
$453$		0			0
$454$	11.7649	−	12.4700i	0.552152	−	0.585247i
$455$	−6.27661	+	0.733631i	−0.294252	+	0.0343931i
$456$		0			0
$457$	−0.664425	−	11.4077i	−0.0310805	−	0.533631i	−0.977532	−	0.210786i	$-0.932398\pi$
$457$	−0.664425	−	11.4077i	−0.0310805	−	0.533631i	0.946452	−	0.322845i	$-0.104639\pi$
$458$	2.35188	−	4.07358i	0.109896	−	0.190346i
$459$		0			0
$460$	−0.116545	−	0.201862i	−0.00543394	−	0.00941186i
$461$	13.9090	−	9.14809i	0.647806	−	0.426069i	−0.182631	−	0.983182i	$-0.558461\pi$
$461$	13.9090	−	9.14809i	0.647806	−	0.426069i	0.830437	+	0.557113i	$0.188091\pi$
$462$		0			0
$463$	−1.81262	+	4.20212i	−0.0842396	+	0.195289i	−0.955129	−	0.296189i	$-0.904284\pi$
$463$	−1.81262	+	4.20212i	−0.0842396	+	0.195289i	0.870890	+	0.491478i	$0.163543\pi$
$464$	31.1087	+	7.37289i	1.44418	+	0.342278i
$465$		0			0
$466$	−13.1403	+	17.6504i	−0.608711	+	0.817641i
$467$	31.8531	+	11.5936i	1.47398	+	0.536486i	0.949179	−	0.314736i	$-0.101916\pi$
$467$	31.8531	+	11.5936i	1.47398	+	0.536486i	0.524805	+	0.851222i	$0.324138\pi$
$468$		0			0
$469$	−20.5854	+	7.49246i	−0.950544	+	0.345970i
$470$	1.06815	−	3.56787i	0.0492701	−	0.164574i
$471$		0			0
$472$	−0.202477	+	3.47640i	−0.00931978	+	0.160014i
$473$	−0.761904	−	0.501112i	−0.0350324	−	0.0230412i
$474$		0			0
$475$	30.9403	−	7.33298i	1.41964	−	0.336460i
$476$	−0.401537	+	2.27723i	−0.0184044	+	0.104377i
$477$		0			0
$478$	−2.13144	−	12.0880i	−0.0974898	−	0.552892i
$479$	−3.43926	−	7.97309i	−0.157144	−	0.364300i	0.821396	−	0.570358i	$-0.193196\pi$
$479$	−3.43926	−	7.97309i	−0.157144	−	0.364300i	−0.978540	+	0.206058i	$0.933936\pi$
$480$		0			0
$481$	2.72637	+	9.10670i	0.124312	+	0.415230i
$482$	−3.34262	−	4.48992i	−0.152252	−	0.204510i
$483$		0			0
$484$	1.26188	+	0.633739i	0.0573581	+	0.0288063i
$485$	−6.62108			−0.300648
$486$		0			0
$487$	−21.3432			−0.967154			−0.483577	−	0.875302i	$-0.660663\pi$
$487$	−21.3432			−0.967154			−0.483577	+	0.875302i	$0.660663\pi$
$488$	−0.699527	−	0.351316i	−0.0316661	−	0.0159033i
$489$		0			0
$490$	−4.18165	−	5.61694i	−0.188908	−	0.253747i
$491$	1.20892	+	4.03808i	0.0545579	+	0.182236i	0.980925	−	0.194385i	$-0.0622711\pi$
$491$	1.20892	+	4.03808i	0.0545579	+	0.182236i	−0.926367	+	0.376621i	$0.877086\pi$
$492$		0			0
$493$	4.11371	+	9.53666i	0.185272	+	0.429510i
$494$	5.60073	+	31.7633i	0.251989	+	1.42910i
$495$		0			0
$496$	0.0372113	−	0.211036i	0.00167084	−	0.00947578i
$497$	45.5910	−	10.8053i	2.04504	−	0.484682i
$498$		0			0
$499$	−25.4197	−	16.7188i	−1.13794	−	0.748435i	−0.166575	−	0.986029i	$-0.553271\pi$
$499$	−25.4197	−	16.7188i	−1.13794	−	0.748435i	−0.971365	+	0.237594i	$0.923641\pi$
$500$	0.111272	−	1.91047i	0.00497624	−	0.0854388i
$501$		0			0
$502$	1.12599	−	3.76108i	0.0502555	−	0.167865i
$503$	11.9111	−	4.33528i	0.531089	−	0.193301i	−0.0625356	−	0.998043i	$-0.519919\pi$
$503$	11.9111	−	4.33528i	0.531089	−	0.193301i	0.593624	+	0.804742i	$0.297696\pi$
$504$		0			0
$505$	−5.91285	−	2.15210i	−0.263118	−	0.0957673i
$506$	−4.19002	+	5.62817i	−0.186269	+	0.250203i
$507$		0			0
$508$	6.95081	+	1.64737i	0.308392	+	0.0730903i
$509$	1.39112	−	3.22498i	0.0616604	−	0.142945i	−0.884600	−	0.466350i	$-0.845569\pi$
$509$	1.39112	−	3.22498i	0.0616604	−	0.142945i	0.946260	+	0.323406i	$0.104828\pi$
$510$		0			0
$511$	−51.8526	+	34.1040i	−2.29382	+	1.50867i
$512$	−6.54427	−	11.3350i	−0.289219	−	0.500941i
$513$		0			0
$514$	21.6252	−	37.4560i	0.953849	−	1.65211i
$515$	0.0618500	+	1.06192i	0.00272544	+	0.0467940i
$516$		0			0
$517$	−18.0156	+	2.10572i	−0.792325	+	0.0926095i
$518$	−12.9094	+	13.6831i	−0.567204	+	0.601202i
$519$		0			0
$520$	−3.92333	−	0.458571i	−0.172049	−	0.0201097i
$521$	−6.50992	+	5.46247i	−0.285205	+	0.239315i	−0.774154	−	0.632997i	$-0.781825\pi$
$521$	−6.50992	+	5.46247i	−0.285205	+	0.239315i	0.488950	+	0.872312i	$0.337380\pi$
$522$		0			0
$523$	−9.72249	−	8.15814i	−0.425135	−	0.356730i	0.404978	−	0.914327i	$-0.367279\pi$
$523$	−9.72249	−	8.15814i	−0.425135	−	0.356730i	−0.830112	+	0.557596i	$0.811724\pi$
$524$	−1.47109	−	1.55927i	−0.0642649	−	0.0681169i
$525$		0			0
$526$	−3.39661	+	1.70584i	−0.148099	+	0.0743782i
$527$	0.0622109	−	0.0312435i	0.00270995	−	0.00136099i
$528$		0			0
$529$	14.8176	+	15.7057i	0.644241	+	0.682856i
$530$	−8.20411	−	6.88406i	−0.356364	−	0.299025i
$531$		0			0
$532$	−7.91043	+	6.63763i	−0.342960	+	0.287778i
$533$	−18.3717	−	2.14735i	−0.795768	−	0.0930120i
$534$		0			0
$535$	−0.580698	+	0.615504i	−0.0251058	+	0.0266105i
$536$	−13.6005	+	1.58967i	−0.587453	+	0.0686634i
$537$		0			0
$538$	−1.01540	−	17.4337i	−0.0437768	−	0.751619i
$539$	−17.0520	+	29.5349i	−0.734481	+	1.27216i
$540$		0			0
$541$	−6.14520	−	10.6438i	−0.264203	−	0.457612i	0.703152	−	0.711040i	$-0.251775\pi$
$541$	−6.14520	−	10.6438i	−0.264203	−	0.457612i	−0.967354	+	0.253427i	$0.918442\pi$
$542$	−5.52576	+	3.63435i	−0.237352	+	0.156109i
$543$		0			0
$544$	−1.28190	+	2.97179i	−0.0549612	+	0.127414i
$545$	2.12919	+	0.504627i	0.0912045	+	0.0216159i
$546$		0			0
$547$	−16.0599	+	21.5722i	−0.686673	+	0.922362i	−0.999624	−	0.0274073i	$-0.991275\pi$
$547$	−16.0599	+	21.5722i	−0.686673	+	0.922362i	0.312951	+	0.949769i	$0.398682\pi$
$548$	1.08230	+	0.393924i	0.0462335	+	0.0168276i
$549$		0			0
$550$	−26.3469	+	9.58950i	−1.12344	+	0.408898i
$551$	−13.3023	+	44.4327i	−0.566697	+	1.89290i
$552$		0			0
$553$	3.24597	−	55.7311i	0.138033	−	2.36993i
$554$	24.2916	+	15.9768i	1.03205	+	0.678791i
$555$		0			0
$556$	−2.21381	+	0.524683i	−0.0938866	+	0.0222515i
$557$	−3.81879	+	21.6574i	−0.161807	+	0.917654i	0.790488	+	0.612477i	$0.209827\pi$
$557$	−3.81879	+	21.6574i	−0.161807	+	0.917654i	−0.952296	+	0.305177i	$0.901284\pi$
$558$		0			0
$559$	0.128768	+	0.730281i	0.00544631	+	0.0308876i
$560$	−3.71678	−	8.61647i	−0.157063	−	0.364112i
$561$		0			0
$562$	6.02664	+	20.1304i	0.254219	+	0.849149i
$563$	−28.2743	−	37.9790i	−1.19162	−	1.60062i	−0.649691	−	0.760198i	$-0.725102\pi$
$563$	−28.2743	−	37.9790i	−1.19162	−	1.60062i	−0.541928	−	0.840425i	$-0.682306\pi$
$564$		0			0
$565$	6.47371	+	3.25122i	0.272351	+	0.136780i
$566$	−25.7811			−1.08366
$567$		0			0
$568$	29.2870			1.22886
$569$	15.4894	+	7.77907i	0.649350	+	0.326116i	0.742805	−	0.669508i	$-0.233495\pi$
$569$	15.4894	+	7.77907i	0.649350	+	0.326116i	−0.0934552	+	0.995623i	$0.529791\pi$
$570$		0			0
$571$	21.2908	+	28.5986i	0.890994	+	1.19681i	0.979642	+	0.200750i	$0.0643379\pi$
$571$	21.2908	+	28.5986i	0.890994	+	1.19681i	−0.0886482	+	0.996063i	$0.528255\pi$
$572$	−1.31964	−	4.40791i	−0.0551769	−	0.184304i
$573$		0			0
$574$	−14.4980	−	33.6100i	−0.605133	−	1.40286i
$575$	−0.976768	−	5.53953i	−0.0407341	−	0.231014i
$576$		0			0
$577$	−0.228884	+	1.29807i	−0.00952858	+	0.0540393i	−0.989201	−	0.146563i	$-0.953179\pi$
$577$	−0.228884	+	1.29807i	−0.00952858	+	0.0540393i	0.979673	+	0.200602i	$0.0642899\pi$
$578$	22.1614	−	5.25236i	0.921794	−	0.218469i
$579$		0			0
$580$	1.13510	+	0.746565i	0.0471323	+	0.0309994i
$581$	0.163031	−	2.79913i	0.00676366	−	0.116128i
$582$		0			0
$583$	−14.9592	+	49.9672i	−0.619546	+	2.06943i
$584$	−36.4540	+	13.2682i	−1.50848	+	0.549041i
$585$		0			0
$586$	36.8824	+	13.4241i	1.52360	+	0.554544i
$587$	−3.00838	+	4.04096i	−0.124169	+	0.166788i	−0.859861	−	0.510528i	$-0.829450\pi$
$587$	−3.00838	+	4.04096i	−0.124169	+	0.166788i	0.735692	+	0.677317i	$0.236857\pi$
$588$		0			0
$589$	0.302504	+	0.0716948i	0.0124645	+	0.00295413i
$590$	−0.434915	+	1.00825i	−0.0179052	+	0.0415088i
$591$		0			0
$592$	−11.7938	+	7.75689i	−0.484721	+	0.318806i
$593$	−13.0012	−	22.5187i	−0.533895	−	0.924732i	−0.999216	−	0.0395907i	$-0.987395\pi$
$593$	−13.0012	−	22.5187i	−0.533895	−	0.924732i	0.465321	−	0.885142i	$-0.345939\pi$
$594$		0			0
$595$	1.52425	−	2.64009i	0.0624883	−	0.108233i
$596$	0.122236	+	2.09871i	0.00500699	+	0.0859667i
$597$		0			0
$598$	5.66706	−	0.662385i	0.231743	−	0.0270869i
$599$	−12.3128	+	13.0508i	−0.503087	+	0.533241i	−0.928290	−	0.371857i	$-0.878721\pi$
$599$	−12.3128	+	13.0508i	−0.503087	+	0.533241i	0.425203	+	0.905098i	$0.360203\pi$
$600$		0			0
$601$	34.0693	+	3.98213i	1.38972	+	0.162435i	0.777812	−	0.628497i	$-0.216330\pi$
$601$	34.0693	+	3.98213i	1.38972	+	0.162435i	0.611904	+	0.790932i	$0.290404\pi$
$602$	−1.12414	+	0.943264i	−0.0458164	+	0.0384446i
$603$		0			0
$604$	−4.40962	−	3.70011i	−0.179425	−	0.150555i
$605$	−1.27752	−	1.35409i	−0.0519386	−	0.0550517i
$606$		0			0
$607$	−1.75575	+	0.881768i	−0.0712635	+	0.0357899i	−0.484074	−	0.875027i	$-0.660843\pi$
$607$	−1.75575	+	0.881768i	−0.0712635	+	0.0357899i	0.412811	+	0.910817i	$0.364547\pi$
$608$	−12.9158	+	6.48658i	−0.523807	+	0.263066i
$609$		0			0
$610$	−0.169387	−	0.179539i	−0.00685826	−	0.00726933i
$611$	11.2987	+	9.48071i	0.457095	+	0.383549i
$612$		0			0
$613$	−1.60067	+	1.34312i	−0.0646505	+	0.0542482i	−0.674540	−	0.738238i	$-0.735658\pi$
$613$	−1.60067	+	1.34312i	−0.0646505	+	0.0542482i	0.609890	+	0.792486i	$0.291214\pi$
$614$	15.3976	+	1.79973i	0.621398	+	0.0726310i
$615$		0			0
$616$	−26.1247	+	27.6906i	−1.05260	+	1.11569i
$617$	−41.2858	+	4.82562i	−1.66211	+	0.194272i	−0.894631	−	0.446807i	$-0.852561\pi$
$617$	−41.2858	+	4.82562i	−1.66211	+	0.194272i	−0.767475	+	0.641079i	$0.778487\pi$
$618$		0			0
$619$	0.408859	+	7.01983i	0.0164334	+	0.282151i	0.996507	+	0.0835141i	$0.0266144\pi$
$619$	0.408859	+	7.01983i	0.0164334	+	0.282151i	−0.980073	+	0.198637i	$0.936349\pi$
$620$	0.00455322	−	0.00788641i	0.000182862	−	0.000316726i
$621$		0			0
$622$	−20.8154	−	36.0533i	−0.834620	−	1.44561i
$623$	38.5568	−	25.3592i	1.54474	−	1.01599i
$624$		0			0
$625$	8.38978	−	19.4497i	0.335591	−	0.777988i
$626$	−19.5866	−	4.64212i	−0.782839	−	0.185536i
$627$		0			0
$628$	1.93280	−	2.59620i	0.0771271	−	0.103600i
$629$	−4.30925	−	1.56844i	−0.171821	−	0.0625378i
$630$		0			0
$631$	6.32771	−	2.30310i	0.251902	−	0.0916848i	−0.212983	−	0.977056i	$-0.568318\pi$
$631$	6.32771	−	2.30310i	0.251902	−	0.0916848i	0.464885	+	0.885371i	$0.346096\pi$
$632$	10.0080	−	33.4290i	0.398096	−	1.32973i
$633$		0			0
$634$	−0.852680	+	14.6400i	−0.0338643	+	0.581427i
$635$	−7.86819	−	5.17499i	−0.312240	−	0.205363i
$636$		0			0
$637$	26.9846	−	6.39547i	1.06917	−	0.253398i
$638$	7.10175	−	40.2760i	0.281161	−	1.59454i
$639$		0			0
$640$	−1.18865	−	6.74119i	−0.0469857	−	0.266469i
$641$	−5.18207	−	12.0134i	−0.204680	−	0.474501i	0.784696	−	0.619880i	$-0.212819\pi$
$641$	−5.18207	−	12.0134i	−0.204680	−	0.474501i	−0.989376	+	0.145380i	$0.953560\pi$
$642$		0			0
$643$	0.752226	+	2.51261i	0.0296649	+	0.0990877i	0.971540	−	0.236876i	$-0.0761234\pi$
$643$	0.752226	+	2.51261i	0.0296649	+	0.0990877i	−0.941875	+	0.335963i	$0.890938\pi$
$644$	1.09085	+	1.46527i	0.0429856	+	0.0577396i
$645$		0			0
$646$	−13.9043	−	6.98300i	−0.547058	−	0.274743i
$647$	−2.94663			−0.115844			−0.0579219	−	0.998321i	$-0.518447\pi$
$647$	−2.94663			−0.115844			−0.0579219	+	0.998321i	$0.518447\pi$
$648$		0			0
$649$	5.34772			0.209916
$650$	20.3743	+	10.2323i	0.799144	+	0.401345i
$651$		0			0
$652$	0.702019	+	0.942975i	0.0274932	+	0.0369298i
$653$	10.1039	+	33.7492i	0.395395	+	1.32071i	0.891726	+	0.452577i	$0.149495\pi$
$653$	10.1039	+	33.7492i	0.395395	+	1.32071i	−0.496331	+	0.868133i	$0.665320\pi$
$654$		0			0
$655$	1.11938	+	2.59502i	0.0437378	+	0.101396i
$656$	−4.76957	−	27.0496i	−0.186221	−	1.05611i
$657$		0			0
$658$	−5.06840	+	28.7443i	−0.197587	+	1.12057i
$659$	−16.3509	+	3.87524i	−0.636942	+	0.150958i	−0.536385	−	0.843973i	$-0.680211\pi$
$659$	−16.3509	+	3.87524i	−0.636942	+	0.150958i	−0.100557	+	0.994931i	$0.532062\pi$
$660$		0			0
$661$	2.43154	+	1.59925i	0.0945758	+	0.0622035i	0.595916	−	0.803047i	$-0.296789\pi$
$661$	2.43154	+	1.59925i	0.0945758	+	0.0622035i	−0.501340	+	0.865250i	$0.667159\pi$
$662$	−2.11192	+	36.2603i	−0.0820821	+	1.40930i
$663$		0			0
$664$	0.502657	−	1.67899i	0.0195069	−	0.0651575i
$665$	12.7928	−	4.65618i	0.496082	−	0.180559i
$666$		0			0
$667$	7.71007	+	2.80623i	0.298535	+	0.108658i
$668$	4.86486	−	6.53463i	0.188227	−	0.252833i
$669$		0			0
$670$	−4.20137	−	0.995743i	−0.162313	−	0.0384689i
$671$	−0.476136	+	1.10381i	−0.0183810	+	0.0426120i
$672$		0			0
$673$	−2.54198	+	1.67188i	−0.0979860	+	0.0644464i	−0.597556	−	0.801827i	$-0.703862\pi$
$673$	−2.54198	+	1.67188i	−0.0979860	+	0.0644464i	0.499570	+	0.866273i	$0.333491\pi$
$674$	−2.40053	−	4.15783i	−0.0924648	−	0.160154i
$675$		0			0
$676$	0.638419	−	1.10577i	0.0245546	−	0.0425298i
$677$	2.17657	+	37.3703i	0.0836525	+	1.43626i	0.735303	+	0.677739i	$0.237040\pi$
$677$	2.17657	+	37.3703i	0.0836525	+	1.43626i	−0.651650	+	0.758520i	$0.725923\pi$
$678$		0			0
$679$	51.5389	−	6.02403i	1.97788	−	0.231181i
$680$	1.30766	−	1.38603i	0.0501463	−	0.0531520i
$681$		0			0
$682$	−0.272273	−	0.0318242i	−0.0104259	−	0.00121861i
$683$	23.8512	−	20.0135i	0.912641	−	0.765797i	−0.0599783	−	0.998200i	$-0.519103\pi$
$683$	23.8512	−	20.0135i	0.912641	−	0.765797i	0.972620	+	0.232403i	$0.0746587\pi$
$684$		0			0
$685$	−1.16318	−	0.976025i	−0.0444429	−	0.0372920i
$686$	8.06571	+	8.54915i	0.307950	+	0.326408i
$687$		0			0
$688$	−0.984033	+	0.494200i	−0.0375159	+	0.0188412i
$689$	37.9019	−	19.0351i	1.44395	−	0.725179i
$690$		0			0
$691$	−7.35279	−	7.79351i	−0.279713	−	0.296479i	0.572251	−	0.820078i	$-0.306070\pi$
$691$	−7.35279	−	7.79351i	−0.279713	−	0.296479i	−0.851964	+	0.523600i	$0.824589\pi$
$692$	−0.501162	−	0.420525i	−0.0190513	−	0.0159859i
$693$		0			0
$694$	−26.3811	+	22.1364i	−1.00141	+	0.840286i
$695$	2.97916	+	0.348214i	0.113006	+	0.0132085i
$696$		0			0
$697$	6.12336	−	6.49038i	0.231939	−	0.245841i
$698$	4.62229	−	0.540268i	0.174956	−	0.0204495i
$699$		0			0
$700$	0.424429	+	7.28716i	0.0160419	+	0.275429i
$701$	10.3580	−	17.9406i	0.391216	−	0.677607i	−0.601394	−	0.798953i	$-0.705388\pi$
$701$	10.3580	−	17.9406i	0.391216	−	0.677607i	0.992610	+	0.121346i	$0.0387210\pi$
$702$		0			0
$703$	−10.2395	−	17.7353i	−0.386188	−	0.668898i
$704$	−18.9279	+	12.4491i	−0.713373	+	0.469193i
$705$		0			0
$706$	1.32413	−	3.06968i	0.0498343	−	0.115529i
$707$	47.9840	+	11.3724i	1.80462	+	0.427704i
$708$		0			0
$709$	−10.8621	+	14.5903i	−0.407933	+	0.547949i	−0.957849	−	0.287271i	$-0.907252\pi$
$709$	−10.8621	+	14.5903i	−0.407933	+	0.547949i	0.549917	+	0.835220i	$0.314660\pi$
$710$	8.67796	+	3.15852i	0.325678	+	0.118537i
$711$		0			0
$712$	27.1066	−	9.86600i	1.01586	−	0.369744i
$713$	0.0157729	−	0.0526853i	0.000590701	−	0.00197308i
$714$		0			0
$715$	−0.352708	+	6.05576i	−0.0131905	+	0.226473i
$716$	−3.89083	−	2.55904i	−0.145407	−	0.0956357i
$717$		0			0
$718$	−0.974750	+	0.231020i	−0.0363773	+	0.00862159i
$719$	5.53156	−	31.3710i	0.206292	−	1.16994i	−0.689101	−	0.724666i	$-0.741994\pi$
$719$	5.53156	−	31.3710i	0.206292	−	1.16994i	0.895393	−	0.445277i	$-0.146895\pi$
$720$		0			0
$721$	−1.44761	−	8.20980i	−0.0539118	−	0.305749i
$722$	−15.8965	−	36.8522i	−0.591605	−	1.37150i
$723$		0			0
$724$	−0.836010	−	2.79247i	−0.0310701	−	0.103781i
$725$	19.5785	+	26.2985i	0.727128	+	0.976703i
$726$		0			0
$727$	8.47059	+	4.25409i	0.314157	+	0.157775i	0.598890	−	0.800831i	$-0.295609\pi$
$727$	8.47059	+	4.25409i	0.314157	+	0.157775i	−0.284733	+	0.958607i	$0.591905\pi$
$728$	30.9566			1.14733
$729$		0			0
$730$	−12.2325			−0.452746
$731$	−0.319678	−	0.160548i	−0.0118237	−	0.00593810i
$732$		0			0
$733$	−25.1663	−	33.8042i	−0.929538	−	1.24859i	−0.968415	−	0.249342i	$-0.919786\pi$
$733$	−25.1663	−	33.8042i	−0.929538	−	1.24859i	0.0388776	−	0.999244i	$-0.487622\pi$
$734$	−4.19506	−	14.0125i	−0.154843	−	0.517210i
$735$		0			0
$736$	1.01269	+	2.34768i	0.0373283	+	0.0865366i
$737$	3.65153	+	20.7089i	0.134506	+	0.762821i
$738$		0			0
$739$	8.32565	−	47.2171i	0.306264	−	1.73691i	−0.311232	−	0.950334i	$-0.600742\pi$
$739$	8.32565	−	47.2171i	0.306264	−	1.73691i	0.617496	−	0.786574i	$-0.288147\pi$
$740$	−0.583700	+	0.138340i	−0.0214572	+	0.00508546i
$741$		0			0
$742$	70.1245	+	46.1216i	2.57435	+	1.69318i
$743$	−0.599497	+	10.2930i	−0.0219934	+	0.377612i	0.969295	+	0.245902i	$0.0790840\pi$
$743$	−0.599497	+	10.2930i	−0.0219934	+	0.377612i	−0.991288	+	0.131711i	$0.957953\pi$
$744$		0			0
$745$	0.794887	−	2.65511i	0.0291224	−	0.0972756i
$746$	−7.08589	+	2.57905i	−0.259433	+	0.0944258i
$747$		0			0
$748$	2.08580	+	0.759170i	0.0762645	+	0.0277580i
$749$	3.96018	−	5.31945i	0.144702	−	0.194368i
$750$		0			0
$751$	24.3796	+	5.77806i	0.889623	+	0.210844i	0.649921	−	0.760002i	$-0.274802\pi$
$751$	24.3796	+	5.77806i	0.889623	+	0.210844i	0.239702	+	0.970847i	$0.422950\pi$
$752$	−8.67498	+	20.1109i	−0.316344	+	0.733368i
$753$		0			0
$754$	−27.7852	+	18.2746i	−1.01188	+	0.665523i
$755$	3.79446	+	6.57219i	0.138094	+	0.239187i
$756$		0			0
$757$	3.05875	−	5.29791i	0.111172	−	0.192556i	−0.805071	−	0.593178i	$-0.797873\pi$
$757$	3.05875	−	5.29791i	0.111172	−	0.192556i	0.916243	+	0.400623i	$0.131206\pi$
$758$	−2.33860	−	40.1521i	−0.0849416	−	1.45839i
$759$		0			0
$760$	8.45203	−	0.987900i	0.306587	−	0.0358349i
$761$	30.7810	−	32.6260i	1.11581	−	1.18269i	0.134370	−	0.990931i	$-0.457099\pi$
$761$	30.7810	−	32.6260i	1.11581	−	1.18269i	0.981442	−	0.191761i	$-0.0614197\pi$
$762$		0			0
$763$	−17.0328	−	1.99085i	−0.616630	−	0.0720738i
$764$	3.82972	−	3.21351i	0.138554	−	0.116261i
$765$		0			0
$766$	−9.50299	−	7.97396i	−0.343357	−	0.288111i
$767$	−2.98417	−	3.16304i	−0.107752	−	0.114211i
$768$		0			0
$769$	33.8960	−	17.0232i	1.22232	−	0.613873i	0.283731	−	0.958904i	$-0.408428\pi$
$769$	33.8960	−	17.0232i	1.22232	−	0.613873i	0.938591	+	0.345031i	$0.112131\pi$
$770$	−10.7273	+	5.38745i	−0.386585	+	0.194150i
$771$		0			0
$772$	−4.78931	−	5.07637i	−0.172371	−	0.182703i
$773$	−11.7711	−	9.87712i	−0.423377	−	0.355255i	0.406069	−	0.913842i	$-0.366899\pi$
$773$	−11.7711	−	9.87712i	−0.423377	−	0.355255i	−0.829446	+	0.558587i	$0.811344\pi$
$774$		0			0
$775$	0.168345	−	0.141258i	0.00604713	−	0.00507415i
$776$	32.2154	+	3.76544i	1.15647	+	0.135172i
$777$		0			0
$778$	24.1113	−	25.5565i	0.864432	−	0.916245i
$779$	39.5783	−	4.62604i	1.41804	−	0.165745i
$780$		0			0
$781$	−2.61511	−	44.8997i	−0.0935759	−	1.60664i
$782$	−1.37623	+	2.38370i	−0.0492138	+	0.0852408i
$783$		0			0
$784$	20.5905	+	35.6637i	0.735373	+	1.27370i
$785$	−3.56508	+	2.34479i	−0.127243	+	0.0836892i
$786$		0			0
$787$	−19.5395	+	45.2976i	−0.696507	+	1.61468i	0.0891477	+	0.996018i	$0.471586\pi$
$787$	−19.5395	+	45.2976i	−0.696507	+	1.61468i	−0.785654	+	0.618666i	$0.787674\pi$
$788$	−3.66535	−	0.868704i	−0.130573	−	0.0309463i
$789$		0			0
$790$	6.57065	−	8.82591i	0.233773	−	0.314012i
$791$	−53.3497	−	19.4177i	−1.89690	−	0.690414i
$792$		0			0
$793$	0.918571	−	0.334333i	0.0326194	−	0.0118725i
$794$	10.9523	−	36.5833i	0.388683	−	1.29829i
$795$		0			0
$796$	0.186194	−	3.19682i	0.00659946	−	0.113308i
$797$	−12.7468	−	8.38372i	−0.451516	−	0.296967i	0.303310	−	0.952892i	$-0.401908\pi$
$797$	−12.7468	−	8.38372i	−0.451516	−	0.296967i	−0.754826	+	0.655925i	$0.772279\pi$
$798$		0			0
$799$	−6.92344	+	1.64089i	−0.244934	+	0.0580504i
$800$	−1.77412	+	10.0615i	−0.0627245	+	0.355728i
$801$		0			0
$802$	−4.55360	−	25.8247i	−0.160793	−	0.911903i
$803$	23.5964	+	54.7025i	0.832698	+	1.93041i
$804$		0			0
$805$	−0.690705	−	2.30711i	−0.0243441	−	0.0813151i
$806$	0.133113	+	0.178801i	0.00468869	+	0.00629801i
$807$		0			0
$808$	27.5456	+	13.8339i	0.969050	+	0.486675i
$809$	−30.2451			−1.06336			−0.531681	−	0.846945i	$-0.678439\pi$
$809$	−30.2451			−1.06336			−0.531681	+	0.846945i	$0.678439\pi$
$810$		0			0
$811$	−20.7859			−0.729892			−0.364946	−	0.931029i	$-0.618913\pi$
$811$	−20.7859			−0.729892			−0.364946	+	0.931029i	$0.618913\pi$
$812$	−9.51489	−	4.77856i	−0.333907	−	0.167695i
$813$		0			0
$814$	10.7832	+	14.4844i	0.377952	+	0.507678i
$815$	−0.444504	−	1.48475i	−0.0155703	−	0.0520084i
$816$		0			0
$817$	−0.632743	−	1.46686i	−0.0221369	−	0.0513191i
$818$	−3.03064	−	17.1876i	−0.105964	−	0.600950i
$819$		0			0
$820$	0.202686	−	1.14949i	0.00707810	−	0.0401419i
$821$	−42.6205	+	10.1012i	−1.48747	+	0.352536i	−0.892438	−	0.451169i	$-0.851007\pi$
$821$	−42.6205	+	10.1012i	−1.48747	+	0.352536i	−0.595028	+	0.803705i	$0.702859\pi$
$822$		0			0
$823$	−6.24648	−	4.10838i	−0.217739	−	0.143209i	0.435954	−	0.899969i	$-0.356411\pi$
$823$	−6.24648	−	4.10838i	−0.217739	−	0.143209i	−0.653693	+	0.756760i	$0.726781\pi$
$824$	0.302985	−	5.20205i	0.0105550	−	0.181222i
$825$		0			0
$826$	2.46807	−	8.24394i	0.0858753	−	0.286843i
$827$	36.5331	−	13.2970i	1.27038	−	0.462381i	0.383142	−	0.923690i	$-0.374842\pi$
$827$	36.5331	−	13.2970i	1.27038	−	0.462381i	0.887240	+	0.461309i	$0.152620\pi$
$828$		0			0
$829$	−32.8678	−	11.9629i	−1.14155	−	0.415489i	−0.299075	−	0.954230i	$-0.596678\pi$
$829$	−32.8678	−	11.9629i	−1.14155	−	0.415489i	−0.842471	+	0.538741i	$0.818900\pi$
$830$	0.330015	−	0.443287i	0.0114550	−	0.0153867i
$831$		0			0
$832$	17.9256	+	4.24845i	0.621459	+	0.147289i
$833$	−5.29885	+	12.2841i	−0.183594	+	0.425620i
$834$		0			0
$835$	−8.97331	+	5.90184i	−0.310534	+	0.204242i
$836$	4.95619	+	8.58438i	0.171413	+	0.296897i
$837$		0			0
$838$	−25.0477	+	43.3840i	−0.865260	+	1.49867i
$839$	0.312817	+	5.37086i	0.0107996	+	0.185423i	0.999394	+	0.0348177i	$0.0110851\pi$
$839$	0.312817	+	5.37086i	0.0107996	+	0.185423i	−0.988594	+	0.150605i	$0.951878\pi$
$840$		0			0
$841$	−18.6962	+	2.18528i	−0.644697	+	0.0753543i
$842$	−0.704284	+	0.746498i	−0.0242712	+	0.0257260i
$843$		0			0
$844$	4.34764	+	0.508166i	0.149652	+	0.0174918i
$845$	−1.28950	+	1.08202i	−0.0443602	+	0.0372227i
$846$		0			0
$847$	11.1763	+	9.37801i	0.384021	+	0.322232i
$848$	43.2207	+	45.8113i	1.48421	+	1.57317i
$849$		0			0
$850$	−9.82873	+	4.93617i	−0.337123	+	0.169309i
$851$	−3.23740	+	1.62588i	−0.110976	+	0.0557345i
$852$		0			0
$853$	−13.1558	−	13.9443i	−0.450444	−	0.477443i	0.461862	−	0.886952i	$-0.347182\pi$
$853$	−13.1558	−	13.9443i	−0.450444	−	0.477443i	−0.912306	+	0.409509i	$0.865700\pi$
$854$	1.48186	+	1.24343i	0.0507083	+	0.0425493i
$855$		0			0
$856$	3.17547	−	2.66454i	0.108535	−	0.0910721i
$857$	−31.6463	−	3.69892i	−1.08102	−	0.126353i	−0.443111	−	0.896467i	$-0.646125\pi$
$857$	−31.6463	−	3.69892i	−1.08102	−	0.126353i	−0.637906	+	0.770114i	$0.720199\pi$
$858$		0			0
$859$	−10.8109	+	11.4589i	−0.368863	+	0.390972i	−0.885044	−	0.465507i	$-0.845872\pi$
$859$	−10.8109	+	11.4589i	−0.368863	+	0.390972i	0.516181	+	0.856480i	$0.327353\pi$
$860$	−0.0464781	+	0.00543251i	−0.00158489	+	0.000185247i
$861$		0			0
$862$	−2.72788	−	46.8359i	−0.0929119	−	1.59524i
$863$	−1.55618	+	2.69539i	−0.0529731	+	0.0917521i	−0.891296	−	0.453422i	$-0.850203\pi$
$863$	−1.55618	+	2.69539i	−0.0529731	+	0.0917521i	0.838323	+	0.545174i	$0.183536\pi$
$864$		0			0
$865$	0.431247	+	0.746942i	0.0146628	+	0.0253968i
$866$	−14.6685	+	9.64761i	−0.498455	+	0.327839i
$867$		0			0
$868$	−0.0282673	+	0.0655309i	−0.000959453	+	0.00222426i
$869$	−52.1432	−	12.3582i	−1.76884	−	0.419222i
$870$		0			0
$871$	10.2111	−	13.7159i	0.345990	−	0.464746i
$872$	−10.0728	−	3.66619i	−0.341107	−	0.124153i
$873$		0			0
$874$	−11.5504	+	4.20400i	−0.390698	+	0.142202i
$875$	5.67080	−	18.9418i	0.191708	−	0.640349i
$876$		0			0
$877$	0.446806	−	7.67137i	0.0150876	−	0.259044i	−0.982327	−	0.187175i	$-0.940067\pi$
$877$	0.446806	−	7.67137i	0.0150876	−	0.259044i	0.997414	−	0.0718685i	$-0.0228962\pi$
$878$	−9.25513	−	6.08720i	−0.312346	−	0.205433i
$879$		0			0
$880$	−8.76495	+	2.07733i	−0.295466	+	0.0700268i
$881$	−8.24582	+	46.7644i	−0.277809	+	1.57553i	0.452087	+	0.891974i	$0.350680\pi$
$881$	−8.24582	+	46.7644i	−0.277809	+	1.57553i	−0.729896	+	0.683558i	$0.760432\pi$
$882$		0			0
$883$	5.38476	+	30.5385i	0.181212	+	1.02770i	0.930727	+	0.365715i	$0.119176\pi$
$883$	5.38476	+	30.5385i	0.181212	+	1.02770i	−0.749515	+	0.661987i	$0.769713\pi$
$884$	−0.714905	−	1.65734i	−0.0240449	−	0.0557423i
$885$		0			0
$886$	0.773780	+	2.58461i	0.0259957	+	0.0868315i
$887$	−1.82153	−	2.44674i	−0.0611611	−	0.0821536i	0.770490	−	0.637452i	$-0.220012\pi$
$887$	−1.82153	−	2.44674i	−0.0611611	−	0.0821536i	−0.831651	+	0.555298i	$0.812604\pi$
$888$		0			0
$889$	65.9548	+	33.1237i	2.21205	+	1.11093i
$890$	9.09590			0.304895
$891$		0			0
$892$	7.30576			0.244615
$893$	−28.3948	−	14.2604i	−0.950196	−	0.477206i
$894$		0			0
$895$	3.66626	+	4.92465i	0.122550	+	0.164613i
$896$	15.3858	+	51.3923i	0.514005	+	1.71690i
$897$		0			0
$898$	20.5014	+	47.5275i	0.684139	+	1.58601i
$899$	0.0556631	+	0.315681i	0.00185647	+	0.0105286i
$900$		0			0
$901$	−3.55294	+	20.1497i	−0.118366	+	0.671285i
$902$	−34.1892	+	8.10299i	−1.13838	+	0.269800i
$903$		0			0
$904$	−29.6494	−	19.5007i	−0.986124	−	0.648584i
$905$	−0.223445	+	3.83640i	−0.00742756	+	0.127526i
$906$		0			0
$907$	−4.23822	+	14.1566i	−0.140728	+	0.470063i	−0.999075	−	0.0430062i	$-0.986306\pi$
$907$	−4.23822	+	14.1566i	−0.140728	+	0.470063i	0.858347	+	0.513069i	$0.171492\pi$
$908$	−4.02603	+	1.46536i	−0.133609	+	0.0486296i
$909$		0			0
$910$	9.17266	+	3.33858i	0.304071	+	0.110673i
$911$	−17.9180	+	24.0680i	−0.593649	+	0.797410i	−0.992839	−	0.119459i	$-0.961884\pi$
$911$	−17.9180	+	24.0680i	−0.593649	+	0.797410i	0.399190	+	0.916868i	$0.369291\pi$
$912$		0			0
$913$	−2.61893	−	0.620698i	−0.0866739	−	0.0205421i
$914$	−6.99126	+	16.2076i	−0.231250	+	0.536098i
$915$		0			0
$916$	−0.982127	+	0.645955i	−0.0324504	+	0.0213430i
$917$	−11.0743	−	19.1813i	−0.365707	−	0.633422i
$918$		0			0
$919$	−13.6334	+	23.6138i	−0.449725	+	0.778947i	−0.998368	−	0.0571097i	$-0.981812\pi$
$919$	−13.6334	+	23.6138i	−0.449725	+	0.778947i	0.548642	+	0.836057i	$0.315145\pi$
$920$	−0.0875283	−	1.50280i	−0.00288572	−	0.0495459i
$921$		0			0
$922$	−25.5415	+	2.98538i	−0.841165	+	0.0983181i
$923$	−25.0977	+	26.6020i	−0.826101	+	0.875616i
$924$		0			0
$925$	−14.3783	−	1.68059i	−0.472756	−	0.0552573i
$926$	5.41522	−	4.54391i	0.177955	−	0.149322i
$927$		0			0
$928$	−11.4161	−	9.57923i	−0.374751	−	0.314454i
$929$	−29.5198	−	31.2892i	−0.968514	−	1.02657i	−0.999634	−	0.0270495i	$-0.991389\pi$
$929$	−29.5198	−	31.2892i	−0.968514	−	1.02657i	0.0311198	−	0.999516i	$-0.490093\pi$
$930$		0			0
$931$	−53.3887	+	26.8128i	−1.74974	+	0.878754i
$932$	4.91423	−	2.46802i	0.160971	−	0.0808427i
$933$		0			0
$934$	−35.9319	−	38.0856i	−1.17573	−	1.24620i
$935$	−2.24168	−	1.88099i	−0.0733108	−	0.0615151i
$936$		0			0
$937$	36.7580	−	30.8436i	1.20083	−	1.00762i	0.201226	−	0.979545i	$-0.435507\pi$
$937$	36.7580	−	30.8436i	1.20083	−	1.00762i	0.999606	−	0.0280726i	$-0.00893697\pi$
$938$	33.6097	+	3.92841i	1.09739	+	0.128267i
$939$		0			0
$940$	−0.638715	+	0.676999i	−0.0208326	+	0.0220813i
$941$	28.9644	−	3.38545i	0.944212	−	0.110363i	0.369966	−	0.929045i	$-0.379369\pi$
$941$	28.9644	−	3.38545i	0.944212	−	0.110363i	0.574246	+	0.818683i	$0.305295\pi$
$942$		0			0
$943$	−0.409868	−	7.03717i	−0.0133471	−	0.229162i
$944$	3.22871	−	5.59229i	0.105086	−	0.182014i
$945$		0			0
$946$	0.704316	+	1.21991i	0.0228993	+	0.0396628i
$947$	−43.5980	+	28.6749i	−1.41675	+	0.931809i	−0.417009	+	0.908903i	$0.636921\pi$
$947$	−43.5980	+	28.6749i	−1.41675	+	0.931809i	−0.999738	+	0.0229060i	$0.992708\pi$
$948$		0			0
$949$	19.1877	−	44.4822i	0.622860	−	1.44395i
$950$	−47.7928	−	11.3271i	−1.55060	−	0.367499i
$951$		0			0
$952$	−8.91782	+	11.9787i	−0.289028	+	0.388232i
$953$	−10.4942	−	3.81957i	−0.339940	−	0.123728i	0.166409	−	0.986057i	$-0.446783\pi$
$953$	−10.4942	−	3.81957i	−0.339940	−	0.123728i	−0.506349	+	0.862329i	$0.669005\pi$
$954$		0			0
$955$	−6.19342	+	2.25422i	−0.200414	+	0.0729449i
$956$	−0.879770	+	2.93864i	−0.0284538	+	0.0950423i
$957$		0			0
$958$	−0.779886	+	13.3901i	−0.0251970	+	0.432615i
$959$	9.94228	+	6.53914i	0.321053	+	0.211160i
$960$		0			0
$961$	−30.1623	+	7.14860i	−0.972977	+	0.230600i
$962$	2.54981	−	14.4607i	0.0822093	−	0.466232i
$963$		0			0
$964$	0.242913	+	1.37763i	0.00782369	+	0.0443703i
$965$	3.64427	+	8.44837i	0.117313	+	0.271963i
$966$		0			0
$967$	−15.2140	−	50.8183i	−0.489249	−	1.63421i	−0.744711	−	0.667387i	$-0.767413\pi$
$967$	−15.2140	−	50.8183i	−0.489249	−	1.63421i	0.255462	−	0.966819i	$-0.417772\pi$
$968$	5.44580	+	7.31498i	0.175035	+	0.235112i
$969$		0			0
$970$	9.13957	+	4.59007i	0.293454	+	0.147378i
$971$	45.0507			1.44575			0.722873	−	0.690981i	$-0.242821\pi$
$971$	45.0507			1.44575			0.722873	+	0.690981i	$0.242821\pi$
$972$		0			0
$973$	−23.5068			−0.753592
$974$	29.4616	+	14.7962i	0.944012	+	0.474100i
$975$		0			0
$976$	0.866820	+	1.16434i	0.0277462	+	0.0372697i
$977$	−15.8200	−	52.8426i	−0.506127	−	1.69058i	−0.703870	−	0.710329i	$-0.748546\pi$
$977$	−15.8200	−	52.8426i	−0.506127	−	1.69058i	0.197742	−	0.980254i	$-0.436639\pi$
$978$		0			0
$979$	−17.5459	−	40.6759i	−0.560769	−	1.30001i
$980$	0.303886	+	1.72342i	0.00970728	+	0.0550527i
$981$		0			0
$982$	1.13063	−	6.41214i	0.0360800	−	0.204620i
$983$	37.8649	−	8.97416i	1.20770	−	0.286231i	0.423016	−	0.906122i	$-0.360971\pi$
$983$	37.8649	−	8.97416i	1.20770	−	0.286231i	0.784688	+	0.619891i	$0.212823\pi$
$984$		0			0
$985$	4.14911	+	2.72891i	0.132202	+	0.0869504i
$986$	0.932826	−	16.0160i	0.0297072	−	0.510053i
$987$		0			0
$988$	2.31175	−	7.72178i	0.0735465	−	0.245662i
$989$	−0.265559	+	0.0966555i	−0.00844428	+	0.00307347i
$990$		0			0
$991$	−7.91069	−	2.87925i	−0.251291	−	0.0914625i	0.213303	−	0.976986i	$-0.431578\pi$
$991$	−7.91069	−	2.87925i	−0.251291	−	0.0914625i	−0.464595	+	0.885523i	$0.653800\pi$
$992$	−0.0596498	+	0.0801235i	−0.00189388	+	0.00254392i
$993$		0			0
$994$	−70.4234	−	16.6906i	−2.23369	−	0.529395i
$995$	−1.67213	+	3.87642i	−0.0530099	+	0.122891i
$996$		0			0
$997$	40.8278	−	26.8528i	1.29303	−	0.850438i	0.298450	−	0.954425i	$-0.403530\pi$
$997$	40.8278	−	26.8528i	1.29303	−	0.850438i	0.994579	+	0.103987i	$0.0331601\pi$
$998$	23.4983	+	40.7003i	0.743827	+	1.28835i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.g.a.10.2		144
3.2	odd	2		81.2.g.a.13.7	✓	144
9.2	odd	6		729.2.g.d.514.2		144
9.4	even	3		729.2.g.b.28.7		144
9.5	odd	6		729.2.g.c.28.2		144
9.7	even	3		729.2.g.a.514.7		144
81.2	odd	54		729.2.g.c.703.2		144
81.5	odd	54		6561.2.a.c.1.56		72
81.25	even	27	inner	243.2.g.a.73.2		144
81.29	odd	54		729.2.g.d.217.2		144
81.52	even	27		729.2.g.a.217.7		144
81.56	odd	54		81.2.g.a.25.7	yes	144
81.76	even	27		6561.2.a.d.1.17		72
81.79	even	27		729.2.g.b.703.7		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.7	✓	144	3.2	odd	2
81.2.g.a.25.7	yes	144	81.56	odd	54
243.2.g.a.10.2		144	1.1	even	1	trivial
243.2.g.a.73.2		144	81.25	even	27	inner
729.2.g.a.217.7		144	81.52	even	27
729.2.g.a.514.7		144	9.7	even	3
729.2.g.b.28.7		144	9.4	even	3
729.2.g.b.703.7		144	81.79	even	27
729.2.g.c.28.2		144	9.5	odd	6
729.2.g.c.703.2		144	81.2	odd	54
729.2.g.d.217.2		144	81.29	odd	54
729.2.g.d.514.2		144	9.2	odd	6
6561.2.a.c.1.56		72	81.5	odd	54
6561.2.a.d.1.17		72	81.76	even	27

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.38037 - 0.693250i) q^{2} +(0.230520 + 0.309643i) q^{4} +(-0.145961 - 0.487543i) q^{5} +(1.57975 + 3.66226i) q^{7} +(0.432916 + 2.45519i) q^{8} +O(q^{10})\)	\(q+(-1.38037 - 0.693250i) q^{2} +(0.230520 + 0.309643i) q^{4} +(-0.145961 - 0.487543i) q^{5} +(1.57975 + 3.66226i) q^{7} +(0.432916 + 2.45519i) q^{8} +(-0.136509 + 0.774179i) q^{10} +(3.72537 - 0.882929i) q^{11} +(-2.60109 - 1.71076i) q^{13} +(0.358223 - 6.15045i) q^{14} +(1.32590 - 4.42882i) q^{16} +(1.41129 - 0.513668i) q^{17} +(6.30242 + 2.29389i) q^{19} +(0.117317 - 0.157584i) q^{20} +(-5.75450 - 1.36384i) q^{22} +(0.469931 - 1.08942i) q^{23} +(3.96105 - 2.60522i) q^{25} +(2.40449 + 4.16470i) q^{26} +(-0.769829 + 1.33338i) q^{28} +(0.402098 + 6.90375i) q^{29} +(0.0460395 - 0.00538124i) q^{31} +(-1.47883 + 1.56747i) q^{32} +(-2.30421 - 0.269324i) q^{34} +(1.55493 - 1.30474i) q^{35} +(-2.33905 - 1.96269i) q^{37} +(-7.10946 - 7.53559i) q^{38} +(1.13382 - 0.569427i) q^{40} +(5.30934 - 2.66645i) q^{41} +(-0.163456 - 0.173253i) q^{43} +(1.13217 + 0.950001i) q^{44} +(-1.40392 + 1.17803i) q^{46} +(-4.70556 - 0.550002i) q^{47} +(-6.11287 + 6.47927i) q^{49} +(-7.27379 + 0.850185i) q^{50} +(-0.0698789 - 1.19977i) q^{52} +(-6.81173 + 11.7983i) q^{53} +(-0.974224 - 1.68741i) q^{55} +(-8.30765 + 5.46403i) q^{56} +(4.23098 - 9.80852i) q^{58} +(1.35914 + 0.322122i) q^{59} +(-0.187500 + 0.251856i) q^{61} +(-0.0672822 - 0.0244887i) q^{62} +(-5.56048 + 2.02385i) q^{64} +(-0.454414 + 1.51785i) q^{65} +(-0.319359 + 5.48318i) q^{67} +(0.484385 + 0.318585i) q^{68} +(-3.05090 + 0.723076i) q^{70} +(2.03991 - 11.5689i) q^{71} +(2.70207 + 15.3242i) q^{73} +(1.86812 + 4.33080i) q^{74} +(0.742550 + 2.48029i) q^{76} +(9.11866 + 12.2485i) q^{77} +(-12.5080 - 6.28175i) q^{79} -2.35277 q^{80} -9.17740 q^{82} +(-0.628222 - 0.315505i) q^{83} +(-0.456428 - 0.613090i) q^{85} +(0.105523 + 0.352470i) q^{86} +(3.78053 + 8.76426i) q^{88} +(-2.00921 - 11.3948i) q^{89} +(2.15620 - 12.2284i) q^{91} +(0.445661 - 0.105624i) q^{92} +(6.11415 + 4.02134i) q^{94} +(0.198465 - 3.40752i) q^{95} +(3.73131 - 12.4634i) q^{97} +(12.9298 - 4.70606i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8}+O(q^{10}) \) 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26} - 9 q^{28} - 9 q^{29} - 18 q^{31} - 36 q^{32} - 18 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} - 18 q^{40} - 18 q^{43} - 54 q^{44} - 18 q^{46} - 36 q^{47} - 18 q^{49} - 99 q^{50} - 45 q^{53} - 9 q^{55} - 126 q^{56} - 18 q^{58} - 45 q^{59} - 18 q^{61} - 81 q^{62} - 18 q^{64} + 9 q^{67} + 99 q^{68} + 36 q^{70} + 90 q^{71} - 18 q^{73} + 162 q^{74} + 63 q^{76} + 162 q^{77} + 36 q^{79} + 288 q^{80} - 36 q^{82} + 90 q^{83} + 36 q^{85} + 162 q^{86} + 63 q^{88} + 81 q^{89} - 18 q^{91} + 144 q^{92} + 36 q^{94} - 18 q^{95} + 9 q^{97} - 81 q^{98}+O(q^{100}) \) 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Introduction

L-functions

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