LMFDB - Embedded newform 855.2.dl.a.523.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [855,2,Mod(127,855)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(855, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([0, 9, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("855.127"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.dl (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,12,0,0,12,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			523.7
Character	$\chi$	$=$	855.523
Dual form			855.2.dl.a.667.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.06046 - 1.51450i) q^{2} +(-0.485079 - 1.33274i) q^{4} +(0.767519 - 2.10022i) q^{5} +(1.17582 + 4.38823i) q^{7} +(1.03888 + 0.278366i) q^{8} +(-2.36685 - 3.38961i) q^{10} +(0.761040 + 1.31816i) q^{11} +(0.138155 - 0.0120870i) q^{13} +(7.89287 + 2.87277i) q^{14} +(3.69620 - 3.10148i) q^{16} +(4.15164 + 2.90701i) q^{17} +(4.14601 - 1.34559i) q^{19} +(-3.17136 - 0.00413488i) q^{20} +(2.80340 + 0.245266i) q^{22} +(-6.70821 - 3.12809i) q^{23} +(-3.82183 - 3.22391i) q^{25} +(0.128202 - 0.222052i) q^{26} +(5.27802 - 3.69571i) q^{28} +(-0.346487 + 1.96502i) q^{29} +(-1.08369 - 0.625668i) q^{31} +(-0.590025 - 6.74402i) q^{32} +(8.80531 - 3.20487i) q^{34} +(10.1187 + 0.898567i) q^{35} +(-2.05676 - 2.05676i) q^{37} +(2.35879 - 7.70606i) q^{38} +(1.38199 - 1.96821i) q^{40} +(-1.05100 - 1.25253i) q^{41} +(-0.373752 - 0.801514i) q^{43} +(1.38761 - 1.65368i) q^{44} +(-11.8513 + 6.84234i) q^{46} +(-1.41793 - 2.02502i) q^{47} +(-11.8118 + 6.81954i) q^{49} +(-8.93551 + 2.36931i) q^{50} +(-0.0831248 - 0.178262i) q^{52} +(-4.74246 + 10.1702i) q^{53} +(3.35254 - 0.586637i) q^{55} +4.88613i q^{56} +(2.60859 + 2.60859i) q^{58} +(-1.86831 - 10.5957i) q^{59} +(-2.79178 + 1.01612i) q^{61} +(-2.09678 + 0.977745i) q^{62} +(-2.48226 - 1.43314i) q^{64} +(0.0806511 - 0.299432i) q^{65} +(11.6415 - 8.15144i) q^{67} +(1.86043 - 6.94321i) q^{68} +(12.0914 - 14.3718i) q^{70} +(1.79203 - 4.92356i) q^{71} +(-6.01690 - 0.526410i) q^{73} +(-5.29607 + 0.933839i) q^{74} +(-3.80447 - 4.87285i) q^{76} +(-4.88954 + 4.88954i) q^{77} +(-4.43572 + 3.72201i) q^{79} +(-3.67688 - 10.1433i) q^{80} +(-3.01150 + 0.263472i) q^{82} +(-0.458159 + 0.122763i) q^{83} +(9.29182 - 6.48816i) q^{85} +(-1.61024 - 0.283929i) q^{86} +(0.423695 + 1.58125i) q^{88} +(1.43212 + 1.20169i) q^{89} +(0.215486 + 0.592042i) q^{91} +(-0.914930 + 10.4577i) q^{92} -4.57054 q^{94} +(0.356111 - 9.74029i) q^{95} +(-0.682796 + 0.975134i) q^{97} +(-2.19778 + 25.1208i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{2} + 12 q^{5} + 18 q^{8} - 12 q^{10} + 12 q^{11} - 12 q^{13} + 12 q^{16} + 30 q^{17} + 84 q^{20} - 24 q^{22} + 12 q^{25} + 48 q^{26} - 36 q^{31} - 18 q^{32} + 30 q^{35} - 54 q^{38} + 54 q^{40}+ \cdots + 90 q^{98}+O(q^{100}) $ 96 * q + 12 * q^2 + 12 * q^5 + 18 * q^8 - 12 * q^10 + 12 * q^11 - 12 * q^13 + 12 * q^16 + 30 * q^17 + 84 * q^20 - 24 * q^22 + 12 * q^25 + 48 * q^26 - 36 * q^31 - 18 * q^32 + 30 * q^35 - 54 * q^38 + 54 * q^40 - 12 * q^41 + 48 * q^43 - 36 * q^46 + 24 * q^47 - 126 * q^50 + 30 * q^53 + 18 * q^55 + 120 * q^58 - 48 * q^61 - 60 * q^62 - 72 * q^65 + 108 * q^67 - 18 * q^68 + 36 * q^70 + 24 * q^71 + 6 * q^73 + 60 * q^76 - 168 * q^77 + 60 * q^80 + 60 * q^82 - 36 * q^85 + 180 * q^86 - 198 * q^88 - 24 * q^91 + 72 * q^92 + 24 * q^95 - 72 * q^97 + 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{17}{18}\right)$

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 $

$2$	1.06046	−	1.51450i	0.749860	−	1.07091i	−0.244988	−	0.969526i	$-0.578784\pi$
$2$	1.06046	−	1.51450i	0.749860	−	1.07091i	0.994847	−	0.101384i	$-0.0323272\pi$
$3$		0			0
$3$		0			0
$4$	−0.485079	−	1.33274i	−0.242540	−	0.666372i
$5$	0.767519	−	2.10022i	0.343245	−	0.939246i
$5$	0.767519	−	2.10022i	0.343245	−	0.939246i
$6$		0			0
$7$	1.17582	+	4.38823i	0.444419	+	1.65859i	0.717466	+	0.696593i	$0.245302\pi$
$7$	1.17582	+	4.38823i	0.444419	+	1.65859i	−0.273048	+	0.962001i	$0.588032\pi$
$8$	1.03888	+	0.278366i	0.367298	+	0.0984172i
$9$		0			0
$10$	−2.36685	−	3.38961i	−0.748463	−	1.07189i
$11$	0.761040	+	1.31816i	0.229462	+	0.397440i	0.957649	−	0.287939i	$-0.0929699\pi$
$11$	0.761040	+	1.31816i	0.229462	+	0.397440i	−0.728187	+	0.685379i	$0.759637\pi$
$12$		0			0
$13$	0.138155	−	0.0120870i	0.0383172	−	0.00335232i	−0.0679810	−	0.997687i	$-0.521656\pi$
$13$	0.138155	−	0.0120870i	0.0383172	−	0.00335232i	0.106298	+	0.994334i	$0.466100\pi$
$14$	7.89287	+	2.87277i	2.10946	+	0.767780i
$15$		0			0
$16$	3.69620	−	3.10148i	0.924050	−	0.775370i
$17$	4.15164	+	2.90701i	1.00692	+	0.705054i	0.955915	−	0.293645i	$-0.0948683\pi$
$17$	4.15164	+	2.90701i	1.00692	+	0.705054i	0.0510063	+	0.998698i	$0.483757\pi$
$18$		0			0
$19$	4.14601	−	1.34559i	0.951160	−	0.308699i
$19$	4.14601	−	1.34559i	0.951160	−	0.308699i
$20$	−3.17136	−	0.00413488i	−0.709138	−	0.000924588i
$21$		0			0
$22$	2.80340	+	0.245266i	0.597687	+	0.0522909i
$23$	−6.70821	−	3.12809i	−1.39876	−	0.652252i	−0.430589	−	0.902548i	$-0.641694\pi$
$23$	−6.70821	−	3.12809i	−1.39876	−	0.652252i	−0.968169	+	0.250297i	$0.919472\pi$
$24$		0			0
$25$	−3.82183	−	3.22391i	−0.764366	−	0.644783i
$26$	0.128202	−	0.222052i	0.0251425	−	0.0435481i
$27$		0			0
$28$	5.27802	−	3.69571i	0.997452	−	0.698423i
$29$	−0.346487	+	1.96502i	−0.0643410	+	0.364896i	0.935589	+	0.353090i	$0.114869\pi$
$29$	−0.346487	+	1.96502i	−0.0643410	+	0.364896i	−0.999930	+	0.0118058i	$0.996242\pi$
$30$		0			0
$31$	−1.08369	−	0.625668i	−0.194636	−	0.112373i	0.399515	−	0.916727i	$-0.369179\pi$
$31$	−1.08369	−	0.625668i	−0.194636	−	0.112373i	−0.594151	+	0.804353i	$0.702512\pi$
$32$	−0.590025	−	6.74402i	−0.104303	−	1.19218i
$33$		0			0
$34$	8.80531	−	3.20487i	1.51010	−	0.549631i
$35$	10.1187	+	0.898567i	1.71037	+	0.151885i
$36$		0			0
$37$	−2.05676	−	2.05676i	−0.338129	−	0.338129i	0.517534	−	0.855663i	$-0.326850\pi$
$37$	−2.05676	−	2.05676i	−0.338129	−	0.338129i	−0.855663	+	0.517534i	$0.826850\pi$
$38$	2.35879	−	7.70606i	0.382647	−	1.25009i
$39$		0			0
$40$	1.38199	−	1.96821i	0.218511	−	0.311202i
$41$	−1.05100	−	1.25253i	−0.164138	−	0.195613i	0.677706	−	0.735333i	$-0.262974\pi$
$41$	−1.05100	−	1.25253i	−0.164138	−	0.195613i	−0.841844	+	0.539721i	$0.818530\pi$
$42$		0			0
$43$	−0.373752	−	0.801514i	−0.0569966	−	0.122230i	0.875747	−	0.482771i	$-0.160370\pi$
$43$	−0.373752	−	0.801514i	−0.0569966	−	0.122230i	−0.932743	+	0.360541i	$0.882592\pi$
$44$	1.38761	−	1.65368i	0.209190	−	0.249302i
$45$		0			0
$46$	−11.8513	+	6.84234i	−1.74738	+	1.00885i
$47$	−1.41793	−	2.02502i	−0.206827	−	0.295379i	0.702315	−	0.711866i	$-0.252150\pi$
$47$	−1.41793	−	2.02502i	−0.206827	−	0.295379i	−0.909141	+	0.416488i	$0.863261\pi$
$48$		0			0
$49$	−11.8118	+	6.81954i	−1.68740	+	0.974220i
$50$	−8.93551	+	2.36931i	−1.26367	+	0.335071i
$51$		0			0
$52$	−0.0831248	−	0.178262i	−0.0115273	−	0.0247205i
$53$	−4.74246	+	10.1702i	−0.651427	+	1.39699i	0.251780	+	0.967784i	$0.418984\pi$
$53$	−4.74246	+	10.1702i	−0.651427	+	1.39699i	−0.903207	+	0.429205i	$0.858794\pi$
$54$		0			0
$55$	3.35254	−	0.586637i	0.452056	−	0.0791021i
$56$			4.88613i			0.652936i
$57$		0			0
$58$	2.60859	+	2.60859i	0.342524	+	0.342524i
$59$	−1.86831	−	10.5957i	−0.243233	−	1.37944i	−0.824561	−	0.565773i	$-0.808578\pi$
$59$	−1.86831	−	10.5957i	−0.243233	−	1.37944i	0.581328	−	0.813669i	$-0.302533\pi$
$60$		0			0
$61$	−2.79178	+	1.01612i	−0.357451	+	0.130101i	−0.514502	−	0.857489i	$-0.672023\pi$
$61$	−2.79178	+	1.01612i	−0.357451	+	0.130101i	0.157052	+	0.987590i	$0.449801\pi$
$62$	−2.09678	+	0.977745i	−0.266292	+	0.124174i
$63$		0			0
$64$	−2.48226	−	1.43314i	−0.310283	−	0.179142i
$65$	0.0806511	−	0.299432i	0.0100035	−	0.0371399i
$66$		0			0
$67$	11.6415	−	8.15144i	1.42223	−	0.995857i	0.426411	−	0.904530i	$-0.359778\pi$
$67$	11.6415	−	8.15144i	1.42223	−	0.995857i	0.995821	−	0.0913279i	$-0.0291111\pi$
$68$	1.86043	−	6.94321i	0.225610	−	0.841988i
$69$		0			0
$70$	12.0914	−	14.3718i	1.44519	−	1.71776i
$71$	1.79203	−	4.92356i	0.212675	−	0.584319i	−0.786784	−	0.617229i	$-0.788255\pi$
$71$	1.79203	−	4.92356i	0.212675	−	0.584319i	0.999458	+	0.0329100i	$0.0104775\pi$
$72$		0			0
$73$	−6.01690	−	0.526410i	−0.704225	−	0.0616117i	−0.270582	−	0.962697i	$-0.587216\pi$
$73$	−6.01690	−	0.526410i	−0.704225	−	0.0616117i	−0.433642	+	0.901085i	$0.642772\pi$
$74$	−5.29607	+	0.933839i	−0.615655	+	0.108557i
$75$		0			0
$76$	−3.80447	−	4.87285i	−0.436403	−	0.558955i
$77$	−4.88954	+	4.88954i	−0.557215	+	0.557215i
$78$		0			0
$79$	−4.43572	+	3.72201i	−0.499058	+	0.418759i	−0.857259	−	0.514885i	$-0.827835\pi$
$79$	−4.43572	+	3.72201i	−0.499058	+	0.418759i	0.358201	+	0.933644i	$0.383390\pi$
$80$	−3.67688	−	10.1433i	−0.411087	−	1.13405i
$81$		0			0
$82$	−3.01150	+	0.263472i	−0.332564	+	0.0290956i
$83$	−0.458159	+	0.122763i	−0.0502895	+	0.0134750i	−0.283876	−	0.958861i	$-0.591620\pi$
$83$	−0.458159	+	0.122763i	−0.0502895	+	0.0134750i	0.233587	+	0.972336i	$0.424954\pi$
$84$		0			0
$85$	9.29182	−	6.48816i	1.00784	−	0.703740i
$86$	−1.61024	−	0.283929i	−0.173636	−	0.0306168i
$87$		0			0
$88$	0.423695	+	1.58125i	0.0451661	+	0.168562i
$89$	1.43212	+	1.20169i	0.151805	+	0.127379i	0.715527	−	0.698585i	$-0.246187\pi$
$89$	1.43212	+	1.20169i	0.151805	+	0.127379i	−0.563722	+	0.825964i	$0.690631\pi$
$90$		0			0
$91$	0.215486	+	0.592042i	0.0225890	+	0.0620628i
$92$	−0.914930	+	10.4577i	−0.0953881	+	1.09029i
$93$		0			0
$94$	−4.57054			−0.471415
$95$	0.356111	−	9.74029i	0.0365363	−	0.999332i
$96$		0			0
$97$	−0.682796	+	0.975134i	−0.0693274	+	0.0990098i	−0.852318	−	0.523023i	$-0.824804\pi$
$97$	−0.682796	+	0.975134i	−0.0693274	+	0.0990098i	0.782991	+	0.622033i	$0.213693\pi$
$98$	−2.19778	+	25.1208i	−0.222010	+	2.53758i
$99$		0			0
$100$	−2.44277	+	6.65738i	−0.244277	+	0.665738i
$101$	0.589039	+	0.494263i	0.0586116	+	0.0491810i	0.671623	−	0.740893i	$-0.265598\pi$
$101$	0.589039	+	0.494263i	0.0586116	+	0.0491810i	−0.613011	+	0.790074i	$0.710042\pi$
$102$		0			0
$103$	−3.83402	−	1.02732i	−0.377777	−	0.101225i	0.0649337	−	0.997890i	$-0.479316\pi$
$103$	−3.83402	−	1.02732i	−0.377777	−	0.101225i	−0.442711	+	0.896665i	$0.645983\pi$
$104$	0.146890	+	0.0259007i	0.0144038	+	0.00253977i
$105$		0			0
$106$	10.3736	+	17.9676i	1.00757	+	1.74517i
$107$	14.6290	−	3.91983i	1.41424	−	0.378944i	0.530802	−	0.847496i	$-0.321891\pi$
$107$	14.6290	−	3.91983i	1.41424	−	0.378944i	0.883436	+	0.468552i	$0.155224\pi$
$108$		0			0
$109$	−8.35240	−	3.04003i	−0.800015	−	0.291182i	−0.0905223	−	0.995894i	$-0.528854\pi$
$109$	−8.35240	−	3.04003i	−0.800015	−	0.291182i	−0.709493	+	0.704713i	$0.751076\pi$
$110$	2.66678	−	5.69951i	0.254267	−	0.543427i
$111$		0			0
$112$	17.9561	+	12.5730i	1.69669	+	1.18803i
$113$	−3.03272	+	3.03272i	−0.285294	+	0.285294i	−0.835216	−	0.549922i	$-0.814658\pi$
$113$	−3.03272	+	3.03272i	−0.285294	+	0.285294i	0.549922	+	0.835216i	$0.314658\pi$
$114$		0			0
$115$	−11.7183	+	11.6878i	−1.09274	+	1.08990i
$116$	2.78695	−	0.491414i	0.258762	−	0.0456267i
$117$		0			0
$118$	−18.0284	−	8.40679i	−1.65965	−	0.773907i
$119$	−7.87503	+	21.6365i	−0.721903	+	1.98341i
$120$		0			0
$121$	4.34164	−	7.51993i	0.394694	−	0.683630i
$122$	−1.42166	+	5.30570i	−0.128711	+	0.480355i
$123$		0			0
$124$	−0.308181	+	1.74778i	−0.0276754	+	0.156955i
$125$	−9.70425	+	5.55225i	−0.867975	+	0.496609i
$126$		0			0
$127$	1.16792	+	13.3493i	0.103636	+	1.18456i	0.852822	+	0.522202i	$0.174889\pi$
$127$	1.16792	+	13.3493i	0.103636	+	1.18456i	−0.749186	+	0.662360i	$0.769555\pi$
$128$	7.46818	−	3.48247i	0.660100	−	0.307810i
$129$		0			0
$130$	−0.367961	−	0.439682i	−0.0322723	−	0.0385626i
$131$	1.85946	+	10.5455i	0.162462	+	0.921369i	0.951643	+	0.307207i	$0.0993945\pi$
$131$	1.85946	+	10.5455i	0.162462	+	0.921369i	−0.789180	+	0.614161i	$0.789494\pi$
$132$		0			0
$133$	10.7797	+	16.6115i	0.934720	+	1.44040i
$134$		−	26.2753i		−	2.26984i
$135$		0			0
$136$	3.50383	+	4.17570i	0.300451	+	0.358063i
$137$	−8.82158	+	18.9179i	−0.753679	+	1.61627i	0.0334197	+	0.999441i	$0.489360\pi$
$137$	−8.82158	+	18.9179i	−0.753679	+	1.61627i	−0.787098	+	0.616828i	$0.788418\pi$
$138$		0			0
$139$	4.32307	−	5.15204i	0.366678	−	0.436990i	−0.550884	−	0.834582i	$-0.685709\pi$
$139$	4.32307	−	5.15204i	0.366678	−	0.436990i	0.917562	+	0.397592i	$0.130154\pi$
$140$	−3.71081	−	13.9215i	−0.313621	−	1.17658i
$141$		0			0
$142$	−5.55633	−	7.93526i	−0.466277	−	0.665913i
$143$	0.121074	+	0.172911i	0.0101247	+	0.0144596i
$144$		0			0
$145$	3.86104	+	2.23589i	0.320642	+	0.185681i
$146$	−7.17794	+	8.55433i	−0.594050	+	0.707961i
$147$		0			0
$148$	−1.74344	+	3.73883i	−0.143310	+	0.307330i
$149$	−5.56213	−	6.62869i	−0.455668	−	0.543043i	0.488476	−	0.872577i	$-0.337553\pi$
$149$	−5.56213	−	6.62869i	−0.455668	−	0.543043i	−0.944144	+	0.329534i	$0.893108\pi$
$150$		0			0
$151$		−	10.4228i		−	0.848193i	−0.905617	−	0.424097i	$-0.860592\pi$
$151$		−	10.4228i		−	0.848193i	0.905617	−	0.424097i	$-0.139408\pi$
$152$	4.68175	−	0.243792i	0.379740	−	0.0197742i
$153$		0			0
$154$	2.22002	+	12.5904i	0.178894	+	1.01456i
$155$	−2.14579	+	1.79577i	−0.172354	+	0.144240i
$156$		0			0
$157$	−14.7648	+	6.88494i	−1.17836	+	0.549478i	−0.910310	−	0.413927i	$-0.864157\pi$
$157$	−14.7648	+	6.88494i	−1.17836	+	0.549478i	−0.268049	+	0.963405i	$0.586379\pi$
$158$	0.933061	+	10.6649i	0.0742304	+	0.848457i
$159$		0			0
$160$	−14.6168	−	3.93698i	−1.15556	−	0.311246i
$161$	5.83910	−	33.1152i	0.460186	−	2.60984i
$162$		0			0
$163$	1.53732	−	5.73737i	0.120413	−	0.449386i	−0.879222	−	0.476412i	$-0.841937\pi$
$163$	1.53732	−	5.73737i	0.120413	−	0.449386i	0.999635	+	0.0270262i	$0.00860377\pi$
$164$	−1.15949	+	2.00829i	−0.0905407	+	0.156821i
$165$		0			0
$166$	−0.299935	+	0.824066i	−0.0232795	+	0.0639599i
$167$	13.5351	+	6.31154i	1.04738	+	0.488402i	0.868614	−	0.495490i	$-0.165011\pi$
$167$	13.5351	+	6.31154i	1.04738	+	0.488402i	0.178767	+	0.983891i	$0.442789\pi$
$168$		0			0
$169$	−12.7836	+	2.25409i	−0.983351	+	0.173391i
$170$	0.0273188	−	20.9529i	0.00209525	−	1.60701i
$171$		0			0
$172$	−0.886914	+	0.886914i	−0.0676265	+	0.0676265i
$173$	11.2602	+	7.88448i	0.856098	+	0.599446i	0.917085	−	0.398692i	$-0.130536\pi$
$173$	11.2602	+	7.88448i	0.856098	+	0.599446i	−0.0609868	+	0.998139i	$0.519425\pi$
$174$		0			0
$175$	9.65348	−	20.5618i	0.729734	−	1.55433i
$176$	6.90120	+	2.51183i	0.520198	+	0.189336i
$177$		0			0
$178$	3.33867	−	0.894595i	0.250244	−	0.0670527i
$179$	−2.00568	−	3.47394i	−0.149912	−	0.259654i	0.781283	−	0.624177i	$-0.214566\pi$
$179$	−2.00568	−	3.47394i	−0.149912	−	0.259654i	−0.931195	+	0.364523i	$0.881232\pi$
$180$		0			0
$181$	−22.2392	−	3.92137i	−1.65303	−	0.291473i	−0.732096	−	0.681202i	$-0.761458\pi$
$181$	−22.2392	−	3.92137i	−1.65303	−	0.291473i	−0.920930	+	0.389729i	$0.872569\pi$
$182$	1.12516	+	0.301485i	0.0834023	+	0.0223476i
$183$		0			0
$184$	−6.09824	−	5.11703i	−0.449568	−	0.377232i
$185$	−5.89824	+	2.74104i	−0.433647	+	0.201525i
$186$		0			0
$187$	−0.672340	+	7.68488i	−0.0491664	+	0.561974i
$188$	−2.01102	+	2.87203i	−0.146669	+	0.209465i
$189$		0			0
$190$	−14.3740	−	10.8685i	−1.04280	−	0.788486i
$191$	−12.6937			−0.918482			−0.459241	−	0.888312i	$-0.651879\pi$
$191$	−12.6937			−0.918482			−0.459241	+	0.888312i	$0.651879\pi$
$192$		0			0
$193$	−1.30105	+	14.8711i	−0.0936519	+	1.07045i	0.793376	+	0.608731i	$0.208321\pi$
$193$	−1.30105	+	14.8711i	−0.0936519	+	1.07045i	−0.887028	+	0.461715i	$0.847234\pi$
$194$	0.752757	+	2.06818i	0.0540448	+	0.148487i
$195$		0			0
$196$	14.8184	+	12.4341i	1.05845	+	0.888149i
$197$	1.63548	+	6.10369i	0.116523	+	0.434870i	0.999396	−	0.0347415i	$-0.0110608\pi$
$197$	1.63548	+	6.10369i	0.116523	+	0.434870i	−0.882873	+	0.469611i	$0.844394\pi$
$198$		0			0
$199$	−12.5304	−	2.20944i	−0.888254	−	0.156623i	−0.289140	−	0.957287i	$-0.593369\pi$
$199$	−12.5304	−	2.20944i	−0.888254	−	0.156623i	−0.599114	+	0.800664i	$0.704480\pi$
$200$	−3.07298	−	4.41311i	−0.217292	−	0.312054i
$201$		0			0
$202$	1.37321	−	0.367951i	0.0966189	−	0.0258890i
$203$	−9.03038	+	0.790056i	−0.633808	+	0.0554510i
$204$		0			0
$205$	−3.43725	+	1.24598i	−0.240068	+	0.0870233i
$206$	−5.62170	+	4.71717i	−0.391683	+	0.328661i
$207$		0			0
$208$	0.473160	−	0.473160i	0.0328077	−	0.0328077i
$209$	4.92898	+	4.44106i	0.340945	+	0.307194i
$210$		0			0
$211$	16.9039	−	2.98061i	1.16371	−	0.205193i	0.441756	−	0.897135i	$-0.354356\pi$
$211$	16.9039	−	2.98061i	1.16371	−	0.205193i	0.721953	+	0.691942i	$0.243245\pi$
$212$	15.8548	+	1.38712i	1.08891	+	0.0952675i
$213$		0			0
$214$	9.57692	−	26.3124i	0.654665	−	1.79868i
$215$	−1.97021	+	0.169783i	−0.134368	+	0.0115791i
$216$		0			0
$217$	1.47135	−	5.49114i	0.0998816	−	0.372763i
$218$	−13.4615	+	9.42585i	−0.911728	+	0.638399i
$219$		0			0
$220$	−2.40808	−	4.18351i	−0.162353	−	0.282052i
$221$	0.608705	+	0.351436i	0.0409460	+	0.0236402i
$222$		0			0
$223$	17.0209	−	7.93699i	1.13981	−	0.531500i	0.241295	−	0.970452i	$-0.422428\pi$
$223$	17.0209	−	7.93699i	1.13981	−	0.531500i	0.898511	+	0.438952i	$0.144650\pi$
$224$	28.9005	−	10.5189i	1.93100	−	0.702825i
$225$		0			0
$226$	1.37696	+	7.80913i	0.0915940	+	0.519456i
$227$	0.0653385	+	0.0653385i	0.00433667	+	0.00433667i	0.709272	−	0.704935i	$-0.249024\pi$
$227$	0.0653385	+	0.0653385i	0.00433667	+	0.00433667i	−0.704935	+	0.709272i	$0.749024\pi$
$228$		0			0
$229$			10.2958i			0.680367i	0.940359	+	0.340184i	$0.110489\pi$
$229$			10.2958i			0.680367i	−0.940359	+	0.340184i	$0.889511\pi$
$230$	5.27431	+	30.1419i	0.347778	+	1.98750i
$231$		0			0
$232$	−0.906952	+	1.94497i	−0.0595443	+	0.127693i
$233$	−9.16084	−	19.6455i	−0.600146	−	1.28702i	−0.938266	−	0.345915i	$-0.887569\pi$
$233$	−9.16084	−	19.6455i	−0.600146	−	1.28702i	0.338119	−	0.941103i	$-0.390209\pi$
$234$		0			0
$235$	−5.34126	+	1.42373i	−0.348426	+	0.0928736i
$236$	−13.2151	+	7.62973i	−0.860229	+	0.496653i
$237$		0			0
$238$	24.4172	+	34.8713i	1.58273	+	2.26037i
$239$	8.88903	−	5.13208i	0.574984	−	0.331967i	−0.184154	−	0.982897i	$-0.558954\pi$
$239$	8.88903	−	5.13208i	0.574984	−	0.331967i	0.759137	+	0.650931i	$0.225621\pi$
$240$		0			0
$241$	−12.7247	+	15.1647i	−0.819672	+	0.976847i	−0.999977	−	0.00676413i	$-0.997847\pi$
$241$	−12.7247	+	15.1647i	−0.819672	+	0.976847i	0.180306	+	0.983611i	$0.442291\pi$
$242$	−6.78477	−	14.5500i	−0.436142	−	0.935309i
$243$		0			0
$244$	2.70847	+	3.22783i	0.173392	+	0.206640i
$245$	5.25674	+	30.0415i	0.335841	+	1.91928i
$246$		0			0
$247$	0.556526	−	0.236012i	0.0354109	−	0.0150171i
$248$	−0.951653	−	0.951653i	−0.0604300	−	0.0604300i
$249$		0			0
$250$	−1.88212	+	20.5850i	−0.119035	+	1.30191i
$251$	−5.76397	+	2.09791i	−0.363819	+	0.132419i	−0.517460	−	0.855708i	$-0.673122\pi$
$251$	−5.76397	+	2.09791i	−0.363819	+	0.132419i	0.153641	+	0.988127i	$0.450900\pi$
$252$		0			0
$253$	−0.981894	−	11.2231i	−0.0617311	−	0.705590i
$254$	21.4560	+	12.3877i	1.34627	+	0.777270i
$255$		0			0
$256$	3.64098	−	20.6490i	0.227561	−	1.29056i
$257$	19.0585	−	13.3449i	1.18883	−	0.832430i	0.199759	−	0.979845i	$-0.435984\pi$
$257$	19.0585	−	13.3449i	1.18883	−	0.832430i	0.989075	+	0.147415i	$0.0470952\pi$
$258$		0			0
$259$	6.60714	−	11.4439i	0.410548	−	0.711090i
$260$	−0.438188	+	0.0377609i	−0.0271753	+	0.00234183i
$261$		0			0
$262$	17.9431	+	8.36700i	1.10853	+	0.516915i
$263$	−12.5544	−	1.09837i	−0.774140	−	0.0677285i	−0.306762	−	0.951786i	$-0.599246\pi$
$263$	−12.5544	−	1.09837i	−0.774140	−	0.0677285i	−0.467378	+	0.884058i	$0.654801\pi$
$264$		0			0
$265$	17.7198	+	17.7660i	1.08852	+	1.09136i
$266$	36.5895	+	1.28997i	2.24344	+	0.0790930i
$267$		0			0
$268$	−16.5108	−	11.5610i	−1.00856	−	0.706201i
$269$	−13.4512	+	11.2869i	−0.820136	+	0.688176i	−0.953004	−	0.302958i	$-0.902026\pi$
$269$	−13.4512	+	11.2869i	−0.820136	+	0.688176i	0.132868	+	0.991134i	$0.457581\pi$
$270$		0			0
$271$	−15.7503	−	5.73264i	−0.956762	−	0.348233i	−0.183998	−	0.982927i	$-0.558904\pi$
$271$	−15.7503	−	5.73264i	−0.956762	−	0.348233i	−0.772764	+	0.634694i	$0.781126\pi$
$272$	24.3613	−	2.13134i	1.47712	−	0.129231i
$273$		0			0
$274$	19.2962	+	33.4220i	1.16573	+	2.01910i
$275$	1.34107	−	7.49131i	0.0808697	−	0.451743i
$276$		0			0
$277$	29.0963	+	7.79634i	1.74823	+	0.468437i	0.984247	−	0.176800i	$-0.0565747\pi$
$277$	29.0963	+	7.79634i	1.74823	+	0.468437i	0.763982	+	0.645237i	$0.223241\pi$
$278$	−3.21829	−	12.0108i	−0.193020	−	0.720361i
$279$		0			0
$280$	10.2619	+	3.75020i	0.613268	+	0.224117i
$281$	−9.59450	−	26.3607i	−0.572360	−	1.57255i	−0.800764	−	0.598980i	$-0.795573\pi$
$281$	−9.59450	−	26.3607i	−0.572360	−	1.57255i	0.228404	−	0.973566i	$-0.426649\pi$
$282$		0			0
$283$	−11.2068	+	16.0049i	−0.666173	+	0.951394i	0.333789	+	0.942648i	$0.391673\pi$
$283$	−11.2068	+	16.0049i	−0.666173	+	0.951394i	−0.999962	+	0.00874584i	$0.997216\pi$
$284$	−7.43112			−0.440956
$285$		0			0
$286$	0.390268			0.0230770
$287$	4.26061	−	6.08478i	0.251496	−	0.359173i
$288$		0			0
$289$	2.97107	+	8.16296i	0.174769	+	0.480174i
$290$	7.48074	−	3.47646i	0.439284	−	0.204145i
$291$		0			0
$292$	2.21710	+	8.27434i	0.129746	+	0.484219i
$293$	5.41159	+	1.45003i	0.316148	+	0.0847117i	0.413404	−	0.910548i	$-0.364340\pi$
$293$	5.41159	+	1.45003i	0.316148	+	0.0847117i	−0.0972556	+	0.995259i	$0.531006\pi$
$294$		0			0
$295$	−23.6872	−	4.20855i	−1.37912	−	0.245031i
$296$	−1.56418	−	2.70925i	−0.0909164	−	0.157472i
$297$		0			0
$298$	−15.9376	+	1.39436i	−0.923238	+	0.0807728i
$299$	−0.964579	−	0.351078i	−0.0557831	−	0.0203034i
$300$		0			0
$301$	3.07776	−	2.58254i	0.177399	−	0.148855i
$302$	−15.7853	−	11.0530i	−0.908339	−	0.636026i
$303$		0			0
$304$	11.1512	−	17.8323i	0.639563	−	1.02275i
$305$	−0.00866158	+	6.64324i	−0.000495961	+	0.380391i
$306$		0			0
$307$	−16.2726	−	1.42367i	−0.928725	−	0.0812529i	−0.387255	−	0.921973i	$-0.626577\pi$
$307$	−16.2726	−	1.42367i	−0.928725	−	0.0812529i	−0.541470	+	0.840720i	$0.682132\pi$
$308$	8.88832	+	4.14469i	0.506459	+	0.236166i
$309$		0			0
$310$	0.444158	+	5.15414i	0.0252265	+	0.292735i
$311$	−0.890255	+	1.54197i	−0.0504817	+	0.0874369i	−0.890162	−	0.455644i	$-0.849409\pi$
$311$	−0.890255	+	1.54197i	−0.0504817	+	0.0874369i	0.839680	+	0.543081i	$0.182742\pi$
$312$		0			0
$313$	−3.59819	+	2.51948i	−0.203382	+	0.142409i	−0.670830	−	0.741611i	$-0.734062\pi$
$313$	−3.59819	+	2.51948i	−0.203382	+	0.142409i	0.467449	+	0.884020i	$0.345173\pi$
$314$	−5.23029	+	29.6624i	−0.295162	+	1.67395i
$315$		0			0
$316$	7.11217	+	4.10622i	0.400091	+	0.230993i
$317$	−0.800161	−	9.14589i	−0.0449415	−	0.513684i	−0.984986	−	0.172633i	$-0.944773\pi$
$317$	−0.800161	−	9.14589i	−0.0449415	−	0.513684i	0.940045	−	0.341051i	$-0.110783\pi$
$318$		0			0
$319$	−2.85391	+	1.03874i	−0.159788	+	0.0581581i
$320$	−4.91508	+	4.11334i	−0.274761	+	0.229942i
$321$		0			0
$322$	−43.9607	−	43.9607i	−2.44983	−	2.44983i
$323$	21.1244	+	6.46609i	1.17539	+	0.359783i
$324$		0			0
$325$	−0.566971	−	0.399205i	−0.0314499	−	0.0221439i
$326$	−7.05896	−	8.41254i	−0.390959	−	0.465927i
$327$		0			0
$328$	−0.743195	−	1.59379i	−0.0410361	−	0.0880021i
$329$	7.21899	−	8.60326i	0.397996	−	0.474313i
$330$		0			0
$331$	9.85862	−	5.69188i	0.541879	−	0.312854i	−0.203961	−	0.978979i	$-0.565382\pi$
$331$	9.85862	−	5.69188i	0.541879	−	0.312854i	0.745840	+	0.666125i	$0.232048\pi$
$332$	0.385856	+	0.551059i	0.0211766	+	0.0302433i
$333$		0			0
$334$	23.9123	−	13.8058i	1.30842	−	0.755418i
$335$	−8.18476	−	30.7060i	−0.447181	−	1.67765i
$336$		0			0
$337$	−6.59306	−	14.1389i	−0.359147	−	0.770193i	−0.999997	−	0.00252652i	$-0.999196\pi$
$337$	−6.59306	−	14.1389i	−0.359147	−	0.770193i	0.640850	−	0.767666i	$-0.278582\pi$
$338$	−10.1427	+	21.7510i	−0.551688	+	1.18310i
$339$		0			0
$340$	−13.1543	−	9.23635i	−0.713394	−	0.500911i
$341$		−	1.90463i		−	0.103142i
$342$		0			0
$343$	−21.3274	−	21.3274i	−1.15157	−	1.15157i
$344$	−0.165168	−	0.936712i	−0.00890524	−	0.0505041i
$345$		0			0
$346$	23.8820	−	8.69235i	1.28391	−	0.467304i
$347$	−12.7342	+	5.93804i	−0.683606	+	0.318770i	−0.733214	−	0.679998i	$-0.761981\pi$
$347$	−12.7342	+	5.93804i	−0.683606	+	0.318770i	0.0496082	+	0.998769i	$0.484203\pi$
$348$		0			0
$349$	20.6061	+	11.8969i	1.10302	+	0.636829i	0.937012	−	0.349296i	$-0.113579\pi$
$349$	20.6061	+	11.8969i	1.10302	+	0.636829i	0.166007	+	0.986125i	$0.446913\pi$
$350$	−20.9036	−	36.4252i	−1.11735	−	1.94701i
$351$		0			0
$352$	8.44066	−	5.91022i	0.449889	−	0.315016i
$353$	−3.32012	+	12.3909i	−0.176712	+	0.659499i	0.819542	+	0.573020i	$0.194228\pi$
$353$	−3.32012	+	12.3909i	−0.176712	+	0.659499i	−0.996254	+	0.0864789i	$0.972438\pi$
$354$		0			0
$355$	−8.96513	−	7.54258i	−0.475820	−	0.400318i
$356$	0.906858	−	2.49157i	0.0480634	−	0.132053i
$357$		0			0
$358$	−7.38821	−	0.646385i	−0.390479	−	0.0341625i
$359$	1.62390	−	0.286337i	0.0857062	−	0.0151123i	−0.130631	−	0.991431i	$-0.541700\pi$
$359$	1.62390	−	0.286337i	0.0857062	−	0.0151123i	0.216337	+	0.976319i	$0.430589\pi$
$360$		0			0
$361$	15.3788	−	11.1576i	0.809409	−	0.587245i
$362$	−29.5227	+	29.5227i	−1.55168	+	1.55168i
$363$		0			0
$364$	0.684513	−	0.574375i	0.0358782	−	0.0301054i
$365$	−5.72366	+	12.2328i	−0.299590	+	0.640292i
$366$		0			0
$367$	17.6746	−	1.54633i	0.922606	−	0.0807176i	0.384055	−	0.923310i	$-0.374527\pi$
$367$	17.6746	−	1.54633i	0.922606	−	0.0807176i	0.538551	+	0.842593i	$0.318972\pi$
$368$	−34.4966	+	9.24333i	−1.79826	+	0.481842i
$369$		0			0
$370$	−2.10357	+	11.8396i	−0.109359	+	0.615513i
$371$	−50.2056	−	8.85260i	−2.60654	−	0.459604i
$372$		0			0
$373$	−3.36965	−	12.5757i	−0.174474	−	0.651145i	−0.996641	−	0.0818983i	$-0.973902\pi$
$373$	−3.36965	−	12.5757i	−0.174474	−	0.651145i	0.822167	−	0.569246i	$-0.192765\pi$
$374$	10.9257	+	9.16778i	0.564956	+	0.474054i
$375$		0			0
$376$	−0.909359	−	2.49844i	−0.0468966	−	0.128847i
$377$	−0.0241176	+	0.275665i	−0.00124212	+	0.0141975i
$378$		0			0
$379$	−19.2818			−0.990442			−0.495221	−	0.868767i	$-0.664913\pi$
$379$	−19.2818			−0.990442			−0.495221	+	0.868767i	$0.664913\pi$
$380$	−13.1541	+	4.25021i	−0.674789	+	0.218031i
$381$		0			0
$382$	−13.4612	+	19.2245i	−0.688733	+	0.983612i
$383$	1.30745	−	14.9442i	0.0668074	−	0.763612i	−0.886720	−	0.462306i	$-0.847022\pi$
$383$	1.30745	−	14.9442i	0.0668074	−	0.763612i	0.953528	−	0.301305i	$-0.0974224\pi$
$384$		0			0
$385$	6.51628	+	14.0219i	0.332100	+	0.714623i
$386$	21.1425	+	17.7407i	1.07613	+	0.902977i
$387$		0			0
$388$	1.63081	+	0.436975i	0.0827921	+	0.0221841i
$389$	13.3902	+	2.36105i	0.678909	+	0.119710i	0.502461	−	0.864600i	$-0.332428\pi$
$389$	13.3902	+	2.36105i	0.678909	+	0.119710i	0.176448	+	0.984310i	$0.443539\pi$
$390$		0			0
$391$	−18.7567	−	32.4875i	−0.948566	−	1.64297i
$392$	−14.1693	+	3.79666i	−0.715658	+	0.191760i
$393$		0			0
$394$	10.9784	+	3.99580i	0.553082	+	0.201306i
$395$	4.41254	+	12.1727i	0.222019	+	0.612475i
$396$		0			0
$397$	−3.83927	−	2.68829i	−0.192687	−	0.134921i	0.473252	−	0.880927i	$-0.343080\pi$
$397$	−3.83927	−	2.68829i	−0.192687	−	0.134921i	−0.665939	+	0.746006i	$0.731969\pi$
$398$	−16.6342	+	16.6342i	−0.833795	+	0.833795i
$399$		0			0
$400$	−24.1251	−	0.0629097i	−1.20626	−	0.00314549i
$401$	29.5512	−	5.21067i	1.47572	−	0.260209i	0.622851	−	0.782340i	$-0.285974\pi$
$401$	29.5512	−	5.21067i	1.47572	−	0.260209i	0.852865	+	0.522132i	$0.174863\pi$
$402$		0			0
$403$	−0.157279	−	0.0733404i	−0.00783463	−	0.00365335i
$404$	0.372995	−	1.02480i	0.0185572	−	0.0509855i
$405$		0			0
$406$	−8.37983	+	14.5143i	−0.415884	+	0.720333i
$407$	1.14586	−	4.27641i	0.0567982	−	0.211974i
$408$		0			0
$409$	5.94508	−	33.7162i	0.293965	−	1.66716i	−0.377414	−	0.926045i	$-0.623187\pi$
$409$	5.94508	−	33.7162i	0.293965	−	1.66716i	0.671379	−	0.741114i	$-0.265702\pi$
$410$	−1.75803	+	6.52702i	−0.0868231	+	0.322347i
$411$		0			0
$412$	0.490645	+	5.60810i	0.0241723	+	0.276291i
$413$	44.2995	−	20.6572i	2.17984	−	1.01647i
$414$		0			0
$415$	−0.0938161	+	1.05646i	−0.00460525	+	0.0518594i
$416$	−0.163029	−	0.924586i	−0.00799317	−	0.0453315i
$417$		0			0
$418$	11.9530	−	2.75535i	0.584638	−	0.134769i
$419$			7.01480i			0.342696i	0.985211	+	0.171348i	$0.0548122\pi$
$419$			7.01480i			0.342696i	−0.985211	+	0.171348i	$0.945188\pi$
$420$		0			0
$421$	−2.21994	−	2.64562i	−0.108193	−	0.128939i	0.709230	−	0.704977i	$-0.249043\pi$
$421$	−2.21994	−	2.64562i	−0.108193	−	0.128939i	−0.817423	+	0.576037i	$0.804598\pi$
$422$	13.4118	−	28.7616i	0.652875	−	1.40009i
$423$		0			0
$424$	−7.75787	+	9.24547i	−0.376755	+	0.449000i
$425$	−6.49491	−	24.4946i	−0.315049	−	1.18816i
$426$		0			0
$427$	−7.74162	−	11.0562i	−0.374643	−	0.535046i
$428$	−12.3203	−	17.5953i	−0.595526	−	0.850500i
$429$		0			0
$430$	−1.83220	+	3.16393i	−0.0883566	+	0.152578i
$431$	6.73534	−	8.02687i	0.324430	−	0.386641i	−0.579035	−	0.815303i	$-0.696571\pi$
$431$	6.73534	−	8.02687i	0.324430	−	0.386641i	0.903465	+	0.428662i	$0.141015\pi$
$432$		0			0
$433$	−10.0690	+	21.5929i	−0.483883	+	1.03769i	0.501156	+	0.865357i	$0.332908\pi$
$433$	−10.0690	+	21.5929i	−0.483883	+	1.03769i	−0.985039	+	0.172333i	$0.944869\pi$
$434$	−6.75601	−	8.05150i	−0.324299	−	0.386484i
$435$		0			0
$436$			12.6063i			0.603731i
$437$	−32.0214	−	3.94259i	−1.53179	−	0.188600i
$438$		0			0
$439$	−0.100282	−	0.568729i	−0.00478621	−	0.0271439i	0.982321	−	0.187204i	$-0.0599424\pi$
$439$	−0.100282	−	0.568729i	−0.00478621	−	0.0271439i	−0.987107	+	0.160060i	$0.948831\pi$
$440$	3.64617	+	0.323789i	0.173824	+	0.0154360i
$441$		0			0
$442$	1.17776	−	0.549197i	0.0560202	−	0.0261227i
$443$	0.740596	+	8.46505i	0.0351868	+	0.402187i	0.993281	+	0.115732i	$0.0369213\pi$
$443$	0.740596	+	8.46505i	0.0351868	+	0.402187i	−0.958094	+	0.286455i	$0.907523\pi$
$444$		0			0
$445$	3.62300	−	2.08545i	0.171747	−	0.0988597i
$446$	6.02950	−	34.1950i	0.285505	−	1.61918i
$447$		0			0
$448$	3.37022	−	12.5778i	0.159228	−	0.594247i
$449$	4.27636	−	7.40687i	0.201814	−	0.349552i	−0.747299	−	0.664488i	$-0.768650\pi$
$449$	4.27636	−	7.40687i	0.201814	−	0.349552i	0.949113	+	0.314936i	$0.101983\pi$
$450$		0			0
$451$	0.851185	−	2.33861i	0.0400807	−	0.110121i
$452$	5.51295	+	2.57073i	0.259308	+	0.120917i
$453$		0			0
$454$	0.168244	−	0.0296659i	0.00789608	−	0.00139229i
$455$	1.40881	+	0.00183683i	0.0660458	+	8.61118e-5i
$456$		0			0
$457$	1.00342	−	1.00342i	0.0469379	−	0.0469379i	−0.683248	−	0.730186i	$-0.739433\pi$
$457$	1.00342	−	1.00342i	0.0469379	−	0.0469379i	0.730186	+	0.683248i	$0.239433\pi$
$458$	15.5930	+	10.9183i	0.728612	+	0.510180i
$459$		0			0
$460$	21.2612	+	9.94804i	0.991309	+	0.463830i
$461$	0.708319	+	0.257807i	0.0329897	+	0.0120073i	0.358462	−	0.933544i	$-0.383301\pi$
$461$	0.708319	+	0.257807i	0.0329897	+	0.0120073i	−0.325473	+	0.945551i	$0.605523\pi$
$462$		0			0
$463$	21.1144	−	5.65758i	0.981269	−	0.262930i	0.267690	−	0.963505i	$-0.413740\pi$
$463$	21.1144	−	5.65758i	0.981269	−	0.262930i	0.713579	+	0.700575i	$0.247073\pi$
$464$	4.81380	+	8.33774i	0.223475	+	0.387070i
$465$		0			0
$466$	−39.4677	−	6.95922i	−1.82831	−	0.322380i
$467$	−3.02917	−	0.811663i	−0.140173	−	0.0375593i	0.188050	−	0.982159i	$-0.439783\pi$
$467$	−3.02917	−	0.811663i	−0.140173	−	0.0375593i	−0.328223	+	0.944600i	$0.606450\pi$
$468$		0			0
$469$	49.4587	+	41.5008i	2.28379	+	1.91633i
$470$	−3.50798	+	9.59913i	−0.161811	+	0.442775i
$471$		0			0
$472$	1.00854	−	11.5277i	0.0464219	−	0.530605i
$473$	0.772083	−	1.10265i	0.0355004	−	0.0506999i
$474$		0			0
$475$	−20.1834	−	8.22377i	−0.926078	−	0.377332i
$476$	32.6559			1.49678
$477$		0			0
$478$	1.65395	−	18.9048i	0.0756501	−	0.864684i
$479$	−9.80127	−	26.9288i	−0.447831	−	1.23041i	−0.934230	−	0.356670i	$-0.883912\pi$
$479$	−9.80127	−	26.9288i	−0.447831	−	1.23041i	0.486399	−	0.873737i	$-0.338310\pi$
$480$		0			0
$481$	−0.309011	−	0.259291i	−0.0140897	−	0.0118226i
$482$	9.47285	+	35.3532i	0.431477	+	1.61029i
$483$		0			0
$484$	−12.1282	−	2.13853i	−0.551281	−	0.0972058i
$485$	1.52393	+	2.18245i	0.0691983	+	0.0991001i
$486$		0			0
$487$	−9.40703	+	2.52061i	−0.426273	+	0.114220i	−0.465576	−	0.885008i	$-0.654153\pi$
$487$	−9.40703	+	2.52061i	−0.426273	+	0.114220i	0.0393029	+	0.999227i	$0.487486\pi$
$488$	−3.18316	+	0.278491i	−0.144095	+	0.0126067i
$489$		0			0
$490$	51.0723	+	23.8965i	2.30721	+	1.07953i
$491$	−6.63665	+	5.56881i	−0.299508	+	0.251317i	−0.780139	−	0.625606i	$-0.784852\pi$
$491$	−6.63665	+	5.56881i	−0.299508	+	0.251317i	0.480631	+	0.876923i	$0.340407\pi$
$492$		0			0
$493$	−7.15084	+	7.15084i	−0.322057	+	0.322057i
$494$	0.232735	−	1.09314i	0.0104713	−	0.0491826i
$495$		0			0
$496$	−5.94602	+	1.04844i	−0.266984	+	0.0470765i
$497$	23.7128	+	2.07460i	1.06366	+	0.0930586i
$498$		0			0
$499$	0.511920	−	1.40649i	0.0229167	−	0.0629631i	−0.927707	−	0.373310i	$-0.878223\pi$
$499$	0.511920	−	1.40649i	0.0229167	−	0.0629631i	0.950623	+	0.310347i	$0.100445\pi$
$500$	12.1071	+	10.2400i	0.541445	+	0.457947i
$501$		0			0
$502$	−2.93519	+	10.9543i	−0.131004	+	0.488913i
$503$	−6.48967	+	4.54411i	−0.289360	+	0.202612i	−0.709239	−	0.704968i	$-0.750961\pi$
$503$	−6.48967	+	4.54411i	−0.289360	+	0.202612i	0.419879	+	0.907580i	$0.362072\pi$
$504$		0			0
$505$	1.49016	−	0.857755i	0.0663112	−	0.0381696i
$506$	−18.0386	−	10.4146i	−0.801913	−	0.462985i
$507$		0			0
$508$	17.2247	−	8.03202i	0.764223	−	0.356363i
$509$	−31.2055	+	11.3579i	−1.38316	+	0.503430i	−0.923135	−	0.384476i	$-0.874382\pi$
$509$	−31.2055	+	11.3579i	−1.38316	+	0.503430i	−0.460026	+	0.887905i	$0.652160\pi$
$510$		0			0
$511$	−4.76479	−	27.0225i	−0.210782	−	1.19540i
$512$	−15.7583	−	15.7583i	−0.696424	−	0.696424i
$513$		0			0
$514$		−	43.0157i		−	1.89734i
$515$	−5.10028	+	7.26378i	−0.224745	+	0.320080i
$516$		0			0
$517$	1.59019	−	3.41018i	0.0699366	−	0.149979i
$518$	−10.3251	−	22.1423i	−0.453660	−	0.972877i
$519$		0			0
$520$	0.167138	−	0.288622i	0.00732949	−	0.0126569i
$521$	−26.1470	+	15.0960i	−1.14552	+	0.661367i	−0.947792	−	0.318890i	$-0.896690\pi$
$521$	−26.1470	+	15.0960i	−1.14552	+	0.661367i	−0.197729	+	0.980257i	$0.563357\pi$
$522$		0			0
$523$	4.88803	+	6.98083i	0.213739	+	0.305250i	0.911677	−	0.410907i	$-0.134788\pi$
$523$	4.88803	+	6.98083i	0.213739	+	0.305250i	−0.697939	+	0.716158i	$0.745899\pi$
$524$	13.1525	−	7.59362i	0.574571	−	0.331729i
$525$		0			0
$526$	−14.9770	+	17.8489i	−0.653028	+	0.778248i
$527$	−2.68026	−	5.74784i	−0.116754	−	0.250380i
$528$		0			0
$529$	20.4310	+	24.3487i	0.888304	+	1.05864i
$530$	45.6978	−	7.99633i	1.98498	−	0.347338i
$531$		0			0
$532$	16.9098	−	22.4245i	0.733133	−	0.972225i
$533$	−0.160340	−	0.160340i	−0.00694508	−	0.00694508i
$534$		0			0
$535$	2.99554	−	33.7326i	0.129509	−	1.45839i
$536$	14.3631	−	5.22775i	0.620392	−	0.225804i
$537$		0			0
$538$	2.82949	+	32.3412i	0.121988	+	1.39433i
$539$	−17.9785	−	10.3799i	−0.774389	−	0.447094i
$540$		0			0
$541$	3.84885	−	21.8279i	0.165475	−	0.938454i	−0.783099	−	0.621897i	$-0.786362\pi$
$541$	3.84885	−	21.8279i	0.165475	−	0.938454i	0.948574	−	0.316557i	$-0.102527\pi$
$542$	−25.3846	+	17.7745i	−1.09036	+	0.763481i
$543$		0			0
$544$	17.1554	−	29.7139i	0.735530	−	1.27397i
$545$	−12.7953	+	15.2086i	−0.548092	+	0.651464i
$546$		0			0
$547$	28.6999	+	13.3830i	1.22712	+	0.572216i	0.924605	−	0.380928i	$-0.124396\pi$
$547$	28.6999	+	13.3830i	1.22712	+	0.572216i	0.302516	+	0.953144i	$0.402173\pi$
$548$	29.4920	+	2.58021i	1.25983	+	0.110221i
$549$		0			0
$550$	−9.92341	−	9.97530i	−0.423136	−	0.425348i
$551$	1.20758	+	8.61324i	0.0514446	+	0.366936i
$552$		0			0
$553$	−21.5487	−	15.0885i	−0.916342	−	0.641630i
$554$	42.6631	−	35.7986i	1.81258	−	1.52094i
$555$		0			0
$556$	−8.96338	−	3.26240i	−0.380132	−	0.138357i
$557$	0.255505	−	0.0223538i	0.0108261	−	0.000947162i	−0.0817414	−	0.996654i	$-0.526048\pi$
$557$	0.255505	−	0.0223538i	0.0108261	−	0.000947162i	0.0925675	+	0.995706i	$0.470493\pi$
$558$		0			0
$559$	−0.0613234	−	0.106215i	−0.00259370	−	0.00449243i
$560$	40.1876	−	28.0616i	1.69824	−	1.18582i
$561$		0			0
$562$	−50.0978	−	13.4237i	−2.11325	−	0.566243i
$563$	1.38026	+	5.15121i	0.0581711	+	0.217097i	0.988893	−	0.148631i	$-0.0474866\pi$
$563$	1.38026	+	5.15121i	0.0581711	+	0.217097i	−0.930722	+	0.365728i	$0.880820\pi$
$564$		0			0
$565$	4.04170	+	8.69705i	0.170036	+	0.365888i
$566$	12.3550	+	33.9452i	0.519321	+	1.42682i
$567$		0			0
$568$	3.23224	−	4.61612i	0.135622	−	0.193688i
$569$	20.8877			0.875659			0.437830	−	0.899058i	$-0.355747\pi$
$569$	20.8877			0.875659			0.437830	+	0.899058i	$0.355747\pi$
$570$		0			0
$571$	−14.0563			−0.588237			−0.294118	−	0.955769i	$-0.595026\pi$
$571$	−14.0563			−0.588237			−0.294118	+	0.955769i	$0.595026\pi$
$572$	0.171716	−	0.245236i	0.00717982	−	0.0102538i
$573$		0			0
$574$	−4.69716	−	12.9053i	−0.196056	−	0.538659i
$575$	15.5529	+	33.5817i	0.648602	+	1.40045i
$576$		0			0
$577$	−7.13342	−	26.6223i	−0.296968	−	1.10830i	−0.939642	−	0.342160i	$-0.888841\pi$
$577$	−7.13342	−	26.6223i	−0.296968	−	1.10830i	0.642673	−	0.766140i	$-0.277825\pi$
$578$	15.5135	+	4.15682i	0.645275	+	0.172901i
$579$		0			0
$580$	1.10696	−	6.23037i	0.0459640	−	0.258702i
$581$	−1.07743	−	1.86616i	−0.0446992	−	0.0774212i
$582$		0			0
$583$	−17.0152	+	1.48864i	−0.704698	+	0.0616531i
$584$	−6.10427	−	2.22177i	−0.252597	−	0.0919376i
$585$		0			0
$586$	7.93484	−	6.65812i	0.327785	−	0.275045i
$587$	13.4922	+	9.44733i	0.556882	+	0.389933i	0.817865	−	0.575410i	$-0.195158\pi$
$587$	13.4922	+	9.44733i	0.556882	+	0.389933i	−0.260983	+	0.965343i	$0.584047\pi$
$588$		0			0
$589$	−5.33487	−	1.13583i	−0.219820	−	0.0468009i
$590$	−31.4932	+	31.4112i	−1.29656	+	1.29318i
$591$		0			0
$592$	−13.9812	−	1.22319i	−0.574623	−	0.0502730i
$593$	−17.2159	−	8.02791i	−0.706972	−	0.329667i	0.0356619	−	0.999364i	$-0.488646\pi$
$593$	−17.2159	−	8.02791i	−0.706972	−	0.329667i	−0.742634	+	0.669697i	$0.766424\pi$
$594$		0			0
$595$	39.3971	+	33.1457i	1.61512	+	1.35884i
$596$	−6.13628	+	10.6283i	−0.251352	+	0.435354i
$597$		0			0
$598$	−1.55461	+	1.08855i	−0.0635726	+	0.0445140i
$599$	6.72471	−	38.1377i	0.274764	−	1.55826i	−0.464946	−	0.885339i	$-0.653926\pi$
$599$	6.72471	−	38.1377i	0.274764	−	1.55826i	0.739710	−	0.672926i	$-0.234963\pi$
$600$		0			0
$601$	24.2204	+	13.9836i	0.987970	+	0.570405i	0.904667	−	0.426120i	$-0.140120\pi$
$601$	24.2204	+	13.9836i	0.987970	+	0.570405i	0.0833031	+	0.996524i	$0.473453\pi$
$602$	−0.647411	−	7.39994i	−0.0263865	−	0.301599i
$603$		0			0
$604$	−13.8909	+	5.05587i	−0.565213	+	0.205721i
$605$	−12.4612	−	14.8901i	−0.506620	−	0.605368i
$606$		0			0
$607$	31.1811	+	31.1811i	1.26560	+	1.26560i	0.948338	+	0.317263i	$0.102764\pi$
$607$	31.1811	+	31.1811i	1.26560	+	1.26560i	0.317263	+	0.948338i	$0.397236\pi$
$608$	−11.5209	−	27.1668i	−0.467235	−	1.10176i
$609$		0			0
$610$	10.0520	+	7.05802i	0.406992	+	0.285771i
$611$	−0.220370	−	0.262627i	−0.00891522	−	0.0106247i
$612$		0			0
$613$	6.16710	+	13.2254i	0.249087	+	0.534169i	0.990603	−	0.136766i	$-0.0436709\pi$
$613$	6.16710	+	13.2254i	0.249087	+	0.534169i	−0.741516	+	0.670935i	$0.765893\pi$
$614$	−19.4126	+	23.1350i	−0.783428	+	0.933653i
$615$		0			0
$616$	−6.44070	+	3.71854i	−0.259503	+	0.149824i
$617$	−3.52558	−	5.03505i	−0.141935	−	0.202704i	0.741891	−	0.670521i	$-0.233929\pi$
$617$	−3.52558	−	5.03505i	−0.141935	−	0.202704i	−0.883825	+	0.467817i	$0.845040\pi$
$618$		0			0
$619$	−19.4464	+	11.2274i	−0.781618	+	0.451268i	−0.837003	−	0.547198i	$-0.815695\pi$
$619$	−19.4464	+	11.2274i	−0.781618	+	0.451268i	0.0553852	+	0.998465i	$0.482361\pi$
$620$	3.43418	+	1.98870i	0.137920	+	0.0798681i
$621$		0			0
$622$	1.39122	+	2.98348i	0.0557829	+	0.119627i
$623$	−3.58938	+	7.69746i	−0.143806	+	0.308392i
$624$		0			0
$625$	4.21274	+	24.6425i	0.168510	+	0.985700i
$626$			8.12126i			0.324591i
$627$		0			0
$628$	16.3380	+	16.3380i	0.651956	+	0.651956i
$629$	−2.55990	−	14.5179i	−0.102070	−	0.578868i
$630$		0			0
$631$	12.9935	−	4.72926i	0.517264	−	0.188269i	−0.0701787	−	0.997534i	$-0.522357\pi$
$631$	12.9935	−	4.72926i	0.517264	−	0.188269i	0.587443	+	0.809266i	$0.300135\pi$
$632$	−5.64425	+	2.63196i	−0.224516	+	0.104694i
$633$		0			0
$634$	−14.7000	−	8.48702i	−0.583810	−	0.337063i
$635$	28.9329	+	7.79299i	1.14817	+	0.309255i
$636$		0			0
$637$	−1.54943	+	1.08492i	−0.0613905	+	0.0429861i
$638$	−1.45330	+	5.42377i	−0.0575365	+	0.214729i
$639$		0			0
$640$	−1.58197	−	18.3577i	−0.0625329	−	0.725650i
$641$	−10.3038	+	28.3093i	−0.406974	+	1.11815i	0.551799	+	0.833977i	$0.313942\pi$
$641$	−10.3038	+	28.3093i	−0.406974	+	1.11815i	−0.958773	+	0.284174i	$0.908281\pi$
$642$		0			0
$643$	−25.5226	−	2.23293i	−1.00651	−	0.0880584i	−0.428039	−	0.903760i	$-0.640795\pi$
$643$	−25.5226	−	2.23293i	−1.00651	−	0.0880584i	−0.578473	+	0.815702i	$0.696351\pi$
$644$	−46.9665	+	8.28147i	−1.85074	+	0.326336i
$645$		0			0
$646$	32.1945	−	25.1358i	1.26667	−	0.988953i
$647$	5.87443	−	5.87443i	0.230948	−	0.230948i	−0.582141	−	0.813088i	$-0.697785\pi$
$647$	5.87443	−	5.87443i	0.230948	−	0.230948i	0.813088	+	0.582141i	$0.197785\pi$
$648$		0			0
$649$	12.5450	−	10.5265i	0.492433	−	0.413200i
$650$	−1.20584	+	0.435334i	−0.0472971	+	0.0170752i
$651$		0			0
$652$	−8.39218	+	0.734220i	−0.328663	+	0.0287543i
$653$	5.27313	−	1.41293i	0.206353	−	0.0552922i	−0.154162	−	0.988046i	$-0.549268\pi$
$653$	5.27313	−	1.41293i	0.206353	−	0.0552922i	0.360515	+	0.932753i	$0.382601\pi$
$654$		0			0
$655$	23.5751	+	4.18863i	0.921156	+	0.163663i
$656$	−7.76940	−	1.36995i	−0.303344	−	0.0534878i
$657$		0			0
$658$	−5.37414	−	20.0566i	−0.209506	−	0.781886i
$659$	22.7331	+	19.0754i	0.885557	+	0.743071i	0.967314	−	0.253582i	$-0.0816087\pi$
$659$	22.7331	+	19.0754i	0.885557	+	0.743071i	−0.0817569	+	0.996652i	$0.526053\pi$
$660$		0			0
$661$	8.70685	+	23.9219i	0.338657	+	0.930454i	0.985776	+	0.168064i	$0.0537516\pi$
$661$	8.70685	+	23.9219i	0.338657	+	0.930454i	−0.647119	+	0.762389i	$0.724026\pi$
$662$	1.83436	−	20.9669i	0.0712945	−	0.814900i
$663$		0			0
$664$	−0.510143			−0.0197974
$665$	43.1613	−	9.89014i	1.67372	−	0.383523i
$666$		0			0
$667$	8.47108	−	12.0980i	0.328001	−	0.468435i
$668$	1.84605	−	21.1005i	0.0714259	−	0.816402i
$669$		0			0
$670$	−55.1838	−	20.1668i	−2.13193	−	0.779110i
$671$	−3.46407	−	2.90670i	−0.133729	−	0.112212i
$672$		0			0
$673$	37.3907	+	10.0188i	1.44131	+	0.386197i	0.892991	−	0.450075i	$-0.148603\pi$
$673$	37.3907	+	10.0188i	1.44131	+	0.386197i	0.548315	+	0.836272i	$0.315269\pi$
$674$	−28.4049	−	5.00855i	−1.09412	−	0.192922i
$675$		0			0
$676$	9.20516	+	15.9438i	0.354045	+	0.613224i
$677$	13.0692	−	3.50187i	0.502289	−	0.134588i	0.00122697	−	0.999999i	$-0.499609\pi$
$677$	13.0692	−	3.50187i	0.502289	−	0.134588i	0.501062	+	0.865411i	$0.332943\pi$
$678$		0			0
$679$	−5.08195	−	1.84968i	−0.195027	−	0.0709842i
$680$	11.4591	−	4.15387i	0.439437	−	0.159294i
$681$		0			0
$682$	−2.88456	−	2.01979i	−0.110456	−	0.0773418i
$683$	8.52271	−	8.52271i	0.326112	−	0.326112i	−0.524994	−	0.851106i	$-0.675932\pi$
$683$	8.52271	−	8.52271i	0.326112	−	0.326112i	0.851106	+	0.524994i	$0.175932\pi$
$684$		0			0
$685$	32.9611	+	33.0471i	1.25938	+	1.26267i
$686$	−54.9172	+	9.68339i	−2.09675	+	0.369714i
$687$		0			0
$688$	−3.86734	−	1.80337i	−0.147441	−	0.0687528i
$689$	−0.532265	+	1.46239i	−0.0202777	+	0.0557125i
$690$		0			0
$691$	−26.0866	+	45.1834i	−0.992383	+	1.71886i	−0.389504	+	0.921025i	$0.627354\pi$
$691$	−26.0866	+	45.1834i	−0.992383	+	1.71886i	−0.602878	+	0.797833i	$0.705980\pi$
$692$	5.04591	−	18.8316i	0.191817	−	0.715869i
$693$		0			0
$694$	−4.51095	+	25.5829i	−0.171233	+	0.971113i
$695$	−7.50236	−	13.0337i	−0.284581	−	0.494396i
$696$		0			0
$697$	−0.722248	−	8.25533i	−0.0273571	−	0.312693i
$698$	39.8698	−	18.5916i	1.50910	−	0.703703i
$699$		0			0
$700$	−32.0863	−	2.89152i	−1.21275	−	0.109289i
$701$	4.07872	+	23.1316i	0.154051	+	0.873668i	0.959648	+	0.281204i	$0.0907337\pi$
$701$	4.07872	+	23.1316i	0.154051	+	0.873668i	−0.805597	+	0.592464i	$0.798155\pi$
$702$		0			0
$703$	−11.2949	−	5.75979i	−0.425995	−	0.217234i
$704$		−	4.36270i		−	0.164425i
$705$		0			0
$706$	15.2450	+	18.1683i	0.573755	+	0.683774i
$707$	−1.47633	+	3.16600i	−0.0555232	+	0.119070i
$708$		0			0
$709$	8.49230	−	10.1207i	0.318935	−	0.380092i	−0.582629	−	0.812739i	$-0.697976\pi$
$709$	8.49230	−	10.1207i	0.318935	−	0.380092i	0.901564	+	0.432647i	$0.142420\pi$
$710$	−20.9304	+	5.57904i	−0.785503	+	0.209378i
$711$		0			0
$712$	1.15329	+	1.64706i	0.0432213	+	0.0617264i
$713$	5.31246	+	7.58698i	0.198953	+	0.284135i
$714$		0			0
$715$	0.456078	−	0.121569i	0.0170563	−	0.00454641i
$716$	−3.65696	+	4.35819i	−0.136667	+	0.162873i
$717$		0			0
$718$	1.28843	−	2.76304i	0.0480837	−	0.103116i
$719$	30.9997	+	36.9440i	1.15609	+	1.37778i	0.913092	+	0.407753i	$0.133687\pi$
$719$	30.9997	+	36.9440i	1.15609	+	1.37778i	0.243001	+	0.970026i	$0.421868\pi$
$720$		0			0
$721$		−	18.0325i		−	0.671565i
$722$	−0.589612	−	35.1234i	−0.0219431	−	1.30716i
$723$		0			0
$724$	5.56159	+	31.5413i	0.206695	+	1.17222i
$725$	7.65929	−	6.39294i	0.284459	−	0.237428i
$726$		0			0
$727$	−5.18618	+	2.41835i	−0.192345	+	0.0896918i	−0.516404	−	0.856345i	$-0.672730\pi$
$727$	−5.18618	+	2.41835i	−0.192345	+	0.0896918i	0.324060	+	0.946037i	$0.394952\pi$
$728$	0.0590585	+	0.675041i	0.00218885	+	0.0250187i
$729$		0			0
$730$	12.4568	+	21.6408i	0.461045	+	0.800963i
$731$	0.778324	−	4.41410i	0.0287874	−	0.163261i
$732$		0			0
$733$	−3.88782	+	14.5096i	−0.143600	+	0.535923i	0.856214	+	0.516622i	$0.172811\pi$
$733$	−3.88782	+	14.5096i	−0.143600	+	0.535923i	−0.999814	+	0.0193008i	$0.993856\pi$
$734$	16.4013	−	28.4079i	0.605384	−	1.04856i
$735$		0			0
$736$	−17.1379	+	47.0859i	−0.631710	+	1.73561i
$737$	19.6045	+	9.14175i	0.722142	+	0.336741i
$738$		0			0
$739$	37.0848	−	6.53906i	1.36419	−	0.240543i	0.556840	−	0.830620i	$-0.312014\pi$
$739$	37.0848	−	6.53906i	1.36419	−	0.240543i	0.807347	+	0.590077i	$0.200902\pi$
$740$	6.51422	+	6.53123i	0.239468	+	0.240093i
$741$		0			0
$742$	−66.6483	+	66.6483i	−2.44674	+	2.44674i
$743$	−5.49028	−	3.84433i	−0.201419	−	0.141035i	0.468516	−	0.883455i	$-0.344789\pi$
$743$	−5.49028	−	3.84433i	−0.201419	−	0.141035i	−0.669934	+	0.742420i	$0.733678\pi$
$744$		0			0
$745$	−18.1907	+	6.59404i	−0.666457	+	0.241587i
$746$	−22.6192	−	8.23272i	−0.828148	−	0.301421i
$747$		0			0
$748$	10.5681	−	2.83172i	0.386409	−	0.103538i
$749$	34.4022	+	59.5863i	1.25703	+	2.17724i
$750$		0			0
$751$	16.8825	+	2.97683i	0.616050	+	0.108626i	0.472960	−	0.881084i	$-0.343185\pi$
$751$	16.8825	+	2.97683i	0.616050	+	0.108626i	0.143089	+	0.989710i	$0.454296\pi$
$752$	−11.5215	−	3.08718i	−0.420146	−	0.112578i
$753$		0			0
$754$	0.391918	+	0.328858i	0.0142728	+	0.0119763i
$755$	−21.8901	−	7.99968i	−0.796662	−	0.291138i
$756$		0			0
$757$	0.579501	−	6.62372i	0.0210623	−	0.240743i	−0.978364	−	0.206889i	$-0.933666\pi$
$757$	0.579501	−	6.62372i	0.0210623	−	0.240743i	0.999427	−	0.0338545i	$-0.0107783\pi$
$758$	−20.4477	+	29.2023i	−0.742692	+	1.06067i
$759$		0			0
$760$	3.08132	−	10.0198i	0.111771	−	0.363457i
$761$	46.7690			1.69538			0.847688	−	0.530495i	$-0.177994\pi$
$761$	46.7690			1.69538			0.847688	+	0.530495i	$0.177994\pi$
$762$		0			0
$763$	3.51938	−	40.2268i	0.127410	−	1.45631i
$764$	6.15744	+	16.9174i	0.222768	+	0.612051i
$765$		0			0
$766$	−21.2464	−	17.8278i	−0.767664	−	0.644146i
$767$	−0.386185	−	1.44126i	−0.0139443	−	0.0520410i
$768$		0			0
$769$	−48.7943	−	8.60376i	−1.75957	−	0.310259i	−0.801756	−	0.597652i	$-0.796101\pi$
$769$	−48.7943	−	8.60376i	−1.75957	−	0.310259i	−0.957813	+	0.287392i	$0.907212\pi$
$770$	28.1464	+	5.00082i	1.01433	+	0.180217i
$771$		0			0
$772$	20.4505	−	5.47970i	0.736030	−	0.197219i
$773$	14.1733	−	1.24000i	0.509778	−	0.0445998i	0.170634	−	0.985334i	$-0.445418\pi$
$773$	14.1733	−	1.24000i	0.509778	−	0.0445998i	0.339144	+	0.940735i	$0.389863\pi$
$774$		0			0
$775$	2.12457	+	5.88492i	0.0763169	+	0.211392i
$776$	−0.980784	+	0.822975i	−0.0352081	+	0.0295431i
$777$		0			0
$778$	17.7756	−	17.7756i	0.637285	−	0.637285i
$779$	−6.04284	−	3.77880i	−0.216507	−	0.135389i
$780$		0			0
$781$	7.85385	−	1.38484i	0.281033	−	0.0495536i
$782$	−69.0930	−	6.04485i	−2.47076	−	0.216163i
$783$		0			0
$784$	−22.5081	+	61.8404i	−0.803860	+	2.20859i
$785$	3.12760	+	36.2936i	0.111629	+	1.29537i
$786$		0			0
$787$	−5.51072	+	20.5663i	−0.196436	+	0.733110i	0.795454	+	0.606014i	$0.207232\pi$
$787$	−5.51072	+	20.5663i	−0.196436	+	0.733110i	−0.991890	+	0.127096i	$0.959434\pi$
$788$	7.34132	−	5.14045i	0.261524	−	0.183121i
$789$		0			0
$790$	23.1148	+	6.22591i	0.822389	+	0.221508i
$791$	−16.8742	−	9.74233i	−0.599978	−	0.346397i
$792$		0			0
$793$	−0.373415	+	0.174126i	−0.0132604	+	0.00618341i
$794$	−8.14280	+	2.96374i	−0.288977	+	0.105179i
$795$		0			0
$796$	3.13360	+	17.7715i	0.111068	+	0.629895i
$797$	2.03401	+	2.03401i	0.0720484	+	0.0720484i	0.742213	−	0.670164i	$-0.233776\pi$
$797$	2.03401	+	2.03401i	0.0720484	+	0.0720484i	−0.670164	+	0.742213i	$0.733776\pi$
$798$		0			0
$799$		−	12.5291i		−	0.443247i
$800$	−19.4872	+	27.6767i	−0.688975	+	0.978518i
$801$		0			0
$802$	23.4464	−	50.2809i	0.827920	−	1.77548i
$803$	−3.88521	−	8.33186i	−0.137106	−	0.294025i
$804$		0			0
$805$	−65.0675	−	37.6799i	−2.29333	−	1.32804i
$806$	−0.277862	+	0.160424i	−0.00978728	+	0.00565069i
$807$		0			0
$808$	0.474353	+	0.677446i	0.0166877	+	0.0238325i
$809$	−8.61084	+	4.97147i	−0.302741	+	0.174788i	−0.643674	−	0.765300i	$-0.722591\pi$
$809$	−8.61084	+	4.97147i	−0.302741	+	0.174788i	0.340932	+	0.940088i	$0.389257\pi$
$810$		0			0
$811$	4.70296	−	5.60477i	0.165143	−	0.196810i	−0.677126	−	0.735867i	$-0.736775\pi$
$811$	4.70296	−	5.60477i	0.165143	−	0.196810i	0.842269	+	0.539057i	$0.181219\pi$
$812$	5.43339	+	11.6520i	0.190675	+	0.408903i
$813$		0			0
$814$	−5.26147	−	6.27038i	−0.184414	−	0.219777i
$815$	−10.8698	−	7.63226i	−0.380753	−	0.267346i
$816$		0			0
$817$	−2.62809	−	2.82017i	−0.0919451	−	0.0986651i
$818$	−44.7585	−	44.7585i	−1.56495	−	1.56495i
$819$		0			0
$820$	3.32792	+	3.97658i	0.116216	+	0.138868i
$821$	42.9758	−	15.6419i	1.49986	−	0.545906i	0.543839	−	0.839190i	$-0.316970\pi$
$821$	42.9758	−	15.6419i	1.49986	−	0.545906i	0.956025	+	0.293284i	$0.0947481\pi$
$822$		0			0
$823$	4.37934	+	50.0561i	0.152654	+	1.74485i	0.557245	+	0.830348i	$0.311858\pi$
$823$	4.37934	+	50.0561i	0.152654	+	1.74485i	−0.404591	+	0.914498i	$0.632586\pi$
$824$	−3.69709	−	2.13452i	−0.128794	−	0.0743595i
$825$		0			0
$826$	15.6927	−	88.9976i	0.546018	−	3.09662i
$827$	40.0530	−	28.0454i	1.39278	−	0.975234i	0.394364	−	0.918954i	$-0.370965\pi$
$827$	40.0530	−	28.0454i	1.39278	−	0.975234i	0.998415	−	0.0562800i	$-0.0179240\pi$
$828$		0			0
$829$	−17.1185	+	29.6501i	−0.594549	+	1.02979i	0.399061	+	0.916924i	$0.369336\pi$
$829$	−17.1185	+	29.6501i	−0.594549	+	1.02979i	−0.993610	+	0.112865i	$0.963997\pi$
$830$	1.50051	+	1.26242i	0.0520835	+	0.0438191i
$831$		0			0
$832$	−0.360259	−	0.167991i	−0.0124897	−	0.00582405i
$833$	−68.8628	−	6.02472i	−2.38596	−	0.208744i
$834$		0			0
$835$	23.6441	−	23.5825i	0.818237	−	0.816107i
$836$	3.52785	−	8.72334i	0.122013	−	0.301703i
$837$		0			0
$838$	10.6239	+	7.43893i	0.366996	+	0.256974i
$839$	−20.4137	+	17.1291i	−0.704758	+	0.591362i	−0.923123	−	0.384505i	$-0.874372\pi$
$839$	−20.4137	+	17.1291i	−0.704758	+	0.591362i	0.218365	+	0.975867i	$0.429928\pi$
$840$		0			0
$841$	23.5098	+	8.55687i	0.810683	+	0.295065i
$842$	−6.36093	+	0.556510i	−0.219212	+	0.0191786i
$843$		0			0
$844$	−12.1721	−	21.0827i	−0.418981	−	0.725696i
$845$	−5.07756	+	28.5783i	−0.174673	+	0.983124i
$846$		0			0
$847$	38.1042	+	10.2100i	1.30927	+	0.350819i
$848$	14.0137	+	52.2998i	0.481232	+	1.79598i
$849$		0			0
$850$	−43.9846	−	16.1391i	−1.50866	−	0.553567i
$851$	7.36344	+	20.2309i	0.252415	+	0.693506i
$852$		0			0
$853$	−8.83275	+	12.6145i	−0.302427	+	0.431911i	−0.941387	−	0.337329i	$-0.890476\pi$
$853$	−8.83275	+	12.6145i	−0.302427	+	0.431911i	0.638959	+	0.769241i	$0.279365\pi$
$854$	−24.9542			−0.853916
$855$		0			0
$856$	16.2888			0.556741
$857$	20.1332	−	28.7532i	0.687737	−	0.982191i	−0.311750	−	0.950164i	$-0.600915\pi$
$857$	20.1332	−	28.7532i	0.687737	−	0.982191i	0.999487	−	0.0320266i	$-0.0101961\pi$
$858$		0			0
$859$	−13.2030	−	36.2749i	−0.450480	−	1.23768i	−0.932387	−	0.361462i	$-0.882278\pi$
$859$	−13.2030	−	36.2749i	−0.450480	−	1.23768i	0.481907	−	0.876223i	$-0.339944\pi$
$860$	1.18199	+	2.54343i	0.0403055	+	0.0867304i
$861$		0			0
$862$	−5.01409	−	18.7128i	−0.170781	−	0.637362i
$863$	31.9550	+	8.56232i	1.08776	+	0.291465i	0.757772	−	0.652520i	$-0.226288\pi$
$863$	31.9550	+	8.56232i	1.08776	+	0.291465i	0.329989	+	0.943985i	$0.392955\pi$
$864$		0			0
$865$	25.2016	−	17.5974i	0.856879	−	0.598329i
$866$	22.0247	+	38.1479i	0.748429	+	1.29632i
$867$		0			0
$868$	−8.03201	+	0.702710i	−0.272624	+	0.0238515i
$869$	−8.28198	−	3.01439i	−0.280947	−	0.102256i
$870$		0			0
$871$	1.50980	−	1.26687i	0.0511575	−	0.0429263i
$872$	−7.83086	−	5.48323i	−0.265187	−	0.185686i
$873$		0			0
$874$	−39.9285	+	44.3153i	−1.35060	+	1.49899i
$875$	−35.7750	−	36.0560i	−1.20942	−	1.21891i
$876$		0			0
$877$	−34.7538	−	3.04056i	−1.17355	−	0.102672i	−0.516343	−	0.856382i	$-0.672707\pi$
$877$	−34.7538	−	3.04056i	−1.17355	−	0.102672i	−0.657208	+	0.753709i	$0.728263\pi$
$878$	−0.967683	−	0.451238i	−0.0326577	−	0.0152285i
$879$		0			0
$880$	10.5722	−	12.5661i	0.356389	−	0.423605i
$881$	4.01849	−	6.96024i	0.135387	−	0.234496i	−0.790359	−	0.612645i	$-0.790106\pi$
$881$	4.01849	−	6.96024i	0.135387	−	0.234496i	0.925745	+	0.378148i	$0.123439\pi$
$882$		0			0
$883$	5.32719	−	3.73014i	0.179274	−	0.125529i	−0.480495	−	0.876997i	$-0.659543\pi$
$883$	5.32719	−	3.73014i	0.179274	−	0.125529i	0.659769	+	0.751468i	$0.270654\pi$
$884$	0.173104	−	0.981724i	0.00582213	−	0.0330189i
$885$		0			0
$886$	13.6057	+	7.85523i	0.457091	+	0.263902i
$887$	4.17511	+	47.7217i	0.140186	+	1.60234i	0.662151	+	0.749370i	$0.269644\pi$
$887$	4.17511	+	47.7217i	0.140186	+	1.60234i	−0.521965	+	0.852967i	$0.674801\pi$
$888$		0			0
$889$	−57.2066	+	20.8215i	−1.91865	+	0.698331i
$890$	0.683652	−	7.69856i	0.0229161	−	0.258056i
$891$		0			0
$892$	−18.8345	−	18.8345i	−0.630625	−	0.630625i
$893$	−8.60359	−	6.48778i	−0.287908	−	0.217105i
$894$		0			0
$895$	−8.83543	+	1.54605i	−0.295336	+	0.0516787i
$896$	24.0631	+	28.6773i	0.803892	+	0.958041i
$897$		0			0
$898$	−6.68276	−	14.3312i	−0.223007	−	0.478239i
$899$	1.60494	−	1.91269i	0.0535276	−	0.0637918i
$900$		0			0
$901$	−49.2540	+	28.4368i	−1.64089	+	0.947367i
$902$	−2.63917	−	3.76913i	−0.0878747	−	0.125498i
$903$		0			0
$904$	−3.99483	+	2.30641i	−0.132866	+	0.0767102i
$905$	−25.3047	+	43.6974i	−0.841158	+	1.45255i
$906$		0			0
$907$	11.6361	+	24.9537i	0.386370	+	0.828574i	0.999262	+	0.0384071i	$0.0122284\pi$
$907$	11.6361	+	24.9537i	0.386370	+	0.828574i	−0.612892	+	0.790167i	$0.709994\pi$
$908$	0.0553852	−	0.118774i	0.00183802	−	0.00394165i
$909$		0			0
$910$	1.49677	−	2.13168i	0.0496173	−	0.0706646i
$911$		−	50.4735i		−	1.67226i	−0.548529	−	0.836132i	$-0.684812\pi$
$911$		−	50.4735i		−	1.67226i	0.548529	−	0.836132i	$-0.315188\pi$
$912$		0			0
$913$	−0.510499	−	0.510499i	−0.0168951	−	0.0168951i
$914$	−0.455586	−	2.58376i	−0.0150694	−	0.0854631i
$915$		0			0
$916$	13.7217	−	4.99429i	0.453378	−	0.165016i
$917$	−44.0898	+	20.5594i	−1.45598	+	0.678932i
$918$		0			0
$919$	−22.3948	−	12.9296i	−0.738736	−	0.426510i	0.0828733	−	0.996560i	$-0.473590\pi$
$919$	−22.3948	−	12.9296i	−0.738736	−	0.426510i	−0.821610	+	0.570050i	$0.806924\pi$
$920$	−15.4274	+	8.88021i	−0.508626	+	0.292772i
$921$		0			0
$922$	1.14159	−	0.799352i	0.0375964	−	0.0263252i
$923$	0.188066	−	0.701873i	0.00619027	−	0.0231024i
$924$		0			0
$925$	1.22976	+	14.4914i	0.0404344	+	0.476474i
$926$	13.8226	−	37.9773i	0.454239	−	1.24801i
$927$		0			0
$928$	13.4566	+	1.17730i	0.441734	+	0.0386467i
$929$	−49.5361	+	8.73454i	−1.62523	+	0.286571i	−0.910709	−	0.413048i	$-0.864464\pi$
$929$	−49.5361	+	8.73454i	−1.62523	+	0.286571i	−0.714516	+	0.699619i	$0.753353\pi$
$930$		0			0
$931$	−39.7955	+	44.1677i	−1.30424	+	1.44754i
$932$	−21.7387	+	21.7387i	−0.712074	+	0.712074i
$933$		0			0
$934$	−4.44157	+	3.72692i	−0.145333	+	0.121949i
$935$	15.6239	+	7.31035i	0.510956	+	0.239074i
$936$		0			0
$937$	33.6752	−	2.94620i	1.10012	−	0.0962482i	0.477396	−	0.878688i	$-0.341581\pi$
$937$	33.6752	−	2.94620i	1.10012	−	0.0962482i	0.622726	+	0.782440i	$0.286025\pi$
$938$	115.302	−	30.8950i	3.76474	−	1.00876i
$939$		0			0
$940$	4.48840	+	6.42792i	0.146395	+	0.209656i
$941$	20.3861	+	3.59461i	0.664567	+	0.117181i	0.495748	−	0.868466i	$-0.334894\pi$
$941$	20.3861	+	3.59461i	0.664567	+	0.117181i	0.168818	+	0.985647i	$0.446005\pi$
$942$		0			0
$943$	3.13229	+	11.6899i	0.102001	+	0.380674i
$944$	−39.7680	−	33.3693i	−1.29434	−	1.08608i
$945$		0			0
$946$	−0.851193	−	2.33863i	−0.0276747	−	0.0760355i
$947$	3.20227	−	36.6021i	0.104060	−	1.18941i	−0.747177	−	0.664625i	$-0.768591\pi$
$947$	3.20227	−	36.6021i	0.104060	−	1.18941i	0.851237	−	0.524782i	$-0.175853\pi$
$948$		0			0
$949$	−0.837625			−0.0271905
$950$	−33.8586	+	21.8467i	−1.09852	+	0.708800i
$951$		0			0
$952$	−14.2040	+	20.2855i	−0.460355	+	0.657455i
$953$	−1.19399	+	13.6473i	−0.0386770	+	0.442080i	0.952024	+	0.306023i	$0.0989986\pi$
$953$	−1.19399	+	13.6473i	−0.0386770	+	0.442080i	−0.990701	+	0.136057i	$0.956557\pi$
$954$		0			0
$955$	−9.74264	+	26.6595i	−0.315265	+	0.862681i
$956$	−11.1516	−	9.35734i	−0.360670	−	0.302638i
$957$		0			0
$958$	−51.1774	−	13.7129i	−1.65347	−	0.443045i
$959$	−93.3888	−	16.4670i	−3.01568	−	0.531746i
$960$		0			0
$961$	−14.7171	−	25.4907i	−0.474744	−	0.822282i
$962$	−0.720389	+	0.193028i	−0.0232263	+	0.00622346i
$963$		0			0
$964$	26.3832	+	9.60271i	0.849746	+	0.309282i
$965$	30.2340	+	14.1464i	0.973267	+	0.455388i
$966$		0			0
$967$	0.256099	+	0.179322i	0.00823557	+	0.00576661i	0.577687	−	0.816258i	$-0.303955\pi$
$967$	0.256099	+	0.179322i	0.00823557	+	0.00576661i	−0.569451	+	0.822025i	$0.692844\pi$
$968$	6.60371	−	6.60371i	0.212251	−	0.212251i
$969$		0			0
$970$	4.92139	+	0.00641660i	0.158016	+	0.000206025i
$971$	38.3652	−	6.76482i	1.23120	−	0.217093i	0.480058	−	0.877237i	$-0.340616\pi$
$971$	38.3652	−	6.76482i	1.23120	−	0.217093i	0.751140	+	0.660143i	$0.229504\pi$
$972$		0			0
$973$	27.6915	+	12.9127i	0.887748	+	0.413963i
$974$	−6.15835	+	16.9199i	−0.197326	+	0.542149i
$975$		0			0
$976$	−7.16748	+	12.4144i	−0.229425	+	0.397376i
$977$	−4.32385	+	16.1368i	−0.138332	+	0.516262i	0.861630	+	0.507537i	$0.169444\pi$
$977$	−4.32385	+	16.1368i	−0.138332	+	0.516262i	−0.999962	+	0.00872521i	$0.997223\pi$
$978$		0			0
$979$	−0.494122	+	2.80231i	−0.0157922	+	0.0895621i
$980$	37.4877	−	21.5784i	1.19750	−	0.689297i
$981$		0			0
$982$	1.39603	+	15.9567i	0.0445491	+	0.509199i
$983$	−19.8575	+	9.25970i	−0.633355	+	0.295338i	−0.712657	−	0.701512i	$-0.752509\pi$
$983$	−19.8575	+	9.25970i	−0.633355	+	0.295338i	0.0793022	+	0.996851i	$0.474731\pi$
$984$		0			0
$985$	14.0743	+	1.24984i	0.448445	+	0.0398231i
$986$	3.24673	+	18.4131i	0.103397	+	0.586393i
$987$		0			0
$988$	−0.584503	−	0.627223i	−0.0185955	−	0.0199546i
$989$			6.54585i			0.208146i
$990$		0			0
$991$	20.3243	+	24.2215i	0.645622	+	0.769422i	0.985247	−	0.171139i	$-0.0547446\pi$
$991$	20.3243	+	24.2215i	0.645622	+	0.769422i	−0.339625	+	0.940561i	$0.610300\pi$
$992$	−3.58011	+	7.67757i	−0.113669	+	0.243763i
$993$		0			0
$994$	28.2885	−	33.7129i	0.897256	−	1.06931i
$995$	−14.2576	+	24.6207i	−0.451996	+	0.780529i
$996$		0			0
$997$	−20.1485	−	28.7750i	−0.638109	−	0.911314i	0.361671	−	0.932306i	$-0.382206\pi$
$997$	−20.1485	−	28.7750i	−0.638109	−	0.911314i	−0.999780	+	0.0209919i	$0.993318\pi$
$998$	−1.58725	−	2.26683i	−0.0502436	−	0.0717553i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.dl.a.523.7		96
3.2	odd	2		95.2.r.a.48.2	yes	96
5.2	odd	4	inner	855.2.dl.a.352.7		96
15.2	even	4		95.2.r.a.67.2	yes	96
15.8	even	4		475.2.bb.b.257.7		96
15.14	odd	2		475.2.bb.b.143.7		96
19.2	odd	18	inner	855.2.dl.a.838.7		96
57.2	even	18		95.2.r.a.78.2	yes	96
95.2	even	36	inner	855.2.dl.a.667.7		96
285.2	odd	36		95.2.r.a.2.2	✓	96
285.59	even	18		475.2.bb.b.268.7		96
285.173	odd	36		475.2.bb.b.382.7		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.r.a.2.2	✓	96	285.2	odd	36
95.2.r.a.48.2	yes	96	3.2	odd	2
95.2.r.a.67.2	yes	96	15.2	even	4
95.2.r.a.78.2	yes	96	57.2	even	18
475.2.bb.b.143.7		96	15.14	odd	2
475.2.bb.b.257.7		96	15.8	even	4
475.2.bb.b.268.7		96	285.59	even	18
475.2.bb.b.382.7		96	285.173	odd	36
855.2.dl.a.352.7		96	5.2	odd	4	inner
855.2.dl.a.523.7		96	1.1	even	1	trivial
855.2.dl.a.667.7		96	95.2	even	36	inner
855.2.dl.a.838.7		96	19.2	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.dl (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06046 - 1.51450i) q^{2} +(-0.485079 - 1.33274i) q^{4} +(0.767519 - 2.10022i) q^{5} +(1.17582 + 4.38823i) q^{7} +(1.03888 + 0.278366i) q^{8} +(-2.36685 - 3.38961i) q^{10} +(0.761040 + 1.31816i) q^{11} +(0.138155 - 0.0120870i) q^{13} +(7.89287 + 2.87277i) q^{14} +(3.69620 - 3.10148i) q^{16} +(4.15164 + 2.90701i) q^{17} +(4.14601 - 1.34559i) q^{19} +(-3.17136 - 0.00413488i) q^{20} +(2.80340 + 0.245266i) q^{22} +(-6.70821 - 3.12809i) q^{23} +(-3.82183 - 3.22391i) q^{25} +(0.128202 - 0.222052i) q^{26} +(5.27802 - 3.69571i) q^{28} +(-0.346487 + 1.96502i) q^{29} +(-1.08369 - 0.625668i) q^{31} +(-0.590025 - 6.74402i) q^{32} +(8.80531 - 3.20487i) q^{34} +(10.1187 + 0.898567i) q^{35} +(-2.05676 - 2.05676i) q^{37} +(2.35879 - 7.70606i) q^{38} +(1.38199 - 1.96821i) q^{40} +(-1.05100 - 1.25253i) q^{41} +(-0.373752 - 0.801514i) q^{43} +(1.38761 - 1.65368i) q^{44} +(-11.8513 + 6.84234i) q^{46} +(-1.41793 - 2.02502i) q^{47} +(-11.8118 + 6.81954i) q^{49} +(-8.93551 + 2.36931i) q^{50} +(-0.0831248 - 0.178262i) q^{52} +(-4.74246 + 10.1702i) q^{53} +(3.35254 - 0.586637i) q^{55} +4.88613i q^{56} +(2.60859 + 2.60859i) q^{58} +(-1.86831 - 10.5957i) q^{59} +(-2.79178 + 1.01612i) q^{61} +(-2.09678 + 0.977745i) q^{62} +(-2.48226 - 1.43314i) q^{64} +(0.0806511 - 0.299432i) q^{65} +(11.6415 - 8.15144i) q^{67} +(1.86043 - 6.94321i) q^{68} +(12.0914 - 14.3718i) q^{70} +(1.79203 - 4.92356i) q^{71} +(-6.01690 - 0.526410i) q^{73} +(-5.29607 + 0.933839i) q^{74} +(-3.80447 - 4.87285i) q^{76} +(-4.88954 + 4.88954i) q^{77} +(-4.43572 + 3.72201i) q^{79} +(-3.67688 - 10.1433i) q^{80} +(-3.01150 + 0.263472i) q^{82} +(-0.458159 + 0.122763i) q^{83} +(9.29182 - 6.48816i) q^{85} +(-1.61024 - 0.283929i) q^{86} +(0.423695 + 1.58125i) q^{88} +(1.43212 + 1.20169i) q^{89} +(0.215486 + 0.592042i) q^{91} +(-0.914930 + 10.4577i) q^{92} -4.57054 q^{94} +(0.356111 - 9.74029i) q^{95} +(-0.682796 + 0.975134i) q^{97} +(-2.19778 + 25.1208i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{2} + 12 q^{5} + 18 q^{8} - 12 q^{10} + 12 q^{11} - 12 q^{13} + 12 q^{16} + 30 q^{17} + 84 q^{20} - 24 q^{22} + 12 q^{25} + 48 q^{26} - 36 q^{31} - 18 q^{32} + 30 q^{35} - 54 q^{38} + 54 q^{40}+ \cdots + 90 q^{98}+O(q^{100}) \) 96 * q + 12 * q^2 + 12 * q^5 + 18 * q^8 - 12 * q^10 + 12 * q^11 - 12 * q^13 + 12 * q^16 + 30 * q^17 + 84 * q^20 - 24 * q^22 + 12 * q^25 + 48 * q^26 - 36 * q^31 - 18 * q^32 + 30 * q^35 - 54 * q^38 + 54 * q^40 - 12 * q^41 + 48 * q^43 - 36 * q^46 + 24 * q^47 - 126 * q^50 + 30 * q^53 + 18 * q^55 + 120 * q^58 - 48 * q^61 - 60 * q^62 - 72 * q^65 + 108 * q^67 - 18 * q^68 + 36 * q^70 + 24 * q^71 + 6 * q^73 + 60 * q^76 - 168 * q^77 + 60 * q^80 + 60 * q^82 - 36 * q^85 + 180 * q^86 - 198 * q^88 - 24 * q^91 + 72 * q^92 + 24 * q^95 - 72 * q^97 + 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more