LMFDB - Embedded newform 621.2.s.a.494.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [621,2,Mod(17,621)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("621.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(621, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([55, 21])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 621 = 3^{3} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	621.s (of order $66$, degree $20$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.95870996552$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	no (minimal twist has level 207)
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			494.11
Character	$\chi$	$=$	621.494
Dual form			621.2.s.a.44.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.261583 - 0.0124607i) q^{2} +(-1.92267 + 0.183593i) q^{4} +(3.04369 + 2.90215i) q^{5} +(-0.702638 - 3.64563i) q^{7} +(-1.01908 + 0.146521i) q^{8} +(0.832339 + 0.721226i) q^{10} +(3.45977 - 1.78363i) q^{11} +(0.259083 + 0.0499342i) q^{13} +(-0.229225 - 0.944880i) q^{14} +(3.52828 - 0.680021i) q^{16} +(1.22006 + 2.67157i) q^{17} +(1.48734 + 0.679244i) q^{19} +(-6.38483 - 5.02109i) q^{20} +(0.882791 - 0.509680i) q^{22} +(3.98136 + 2.67373i) q^{23} +(0.603648 + 12.6721i) q^{25} +(0.0683940 + 0.00983357i) q^{26} +(2.02026 + 6.88036i) q^{28} +(-0.234074 + 2.45134i) q^{29} +(0.601339 - 0.472898i) q^{31} +(2.91554 - 0.707302i) q^{32} +(0.352437 + 0.683633i) q^{34} +(8.44156 - 13.1353i) q^{35} +(1.05184 - 3.58222i) q^{37} +(0.397526 + 0.159145i) q^{38} +(-3.52698 - 2.51155i) q^{40} +(-2.75661 + 2.89105i) q^{41} +(-4.40550 + 5.60205i) q^{43} +(-6.32454 + 4.06454i) q^{44} +(1.07477 + 0.649790i) q^{46} +(4.75835 + 2.74724i) q^{47} +(-6.29837 + 2.52149i) q^{49} +(0.315808 + 3.30729i) q^{50} +(-0.507300 - 0.0484413i) q^{52} +(-1.42625 - 1.64598i) q^{53} +(15.7068 + 4.61194i) q^{55} +(1.25021 + 3.61224i) q^{56} +(-0.0306844 + 0.644144i) q^{58} +(1.82992 - 9.49452i) q^{59} +(1.51839 - 3.79277i) q^{61} +(0.151407 - 0.131195i) q^{62} +(-6.14149 + 1.80331i) q^{64} +(0.643652 + 0.903883i) q^{65} +(6.13936 - 11.9087i) q^{67} +(-2.83626 - 4.91255i) q^{68} +(2.04449 - 3.54117i) q^{70} +(0.327930 + 0.510270i) q^{71} +(6.89379 - 15.0953i) q^{73} +(0.230505 - 0.950155i) q^{74} +(-2.98437 - 1.03290i) q^{76} +(-8.93345 - 11.3598i) q^{77} +(1.99885 - 0.691809i) q^{79} +(12.7125 + 8.16984i) q^{80} +(-0.685057 + 0.790598i) q^{82} +(-8.75158 + 8.34461i) q^{83} +(-4.03979 + 11.6722i) q^{85} +(-1.08260 + 1.52030i) q^{86} +(-3.26444 + 2.32459i) q^{88} +(-1.15305 + 8.01966i) q^{89} -0.979609i q^{91} +(-8.14572 - 4.40975i) q^{92} +(1.27894 + 0.659337i) q^{94} +(2.55572 + 6.38388i) q^{95} +(-5.87423 - 1.42507i) q^{97} +(-1.61613 + 0.738060i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q + 27 q^{2} - 29 q^{4} + 33 q^{5} - 11 q^{7} - 44 q^{10} + 33 q^{11} - 9 q^{13} + 33 q^{14} + 3 q^{16} - 44 q^{19} + 33 q^{20} + 27 q^{23} + 11 q^{25} - 44 q^{28} - 27 q^{29} - 3 q^{31} + 33 q^{32}+ \cdots + 22 q^{97}+O(q^{100}) $ 440 * q + 27 * q^2 - 29 * q^4 + 33 * q^5 - 11 * q^7 - 44 * q^10 + 33 * q^11 - 9 * q^13 + 33 * q^14 + 3 * q^16 - 44 * q^19 + 33 * q^20 + 27 * q^23 + 11 * q^25 - 44 * q^28 - 27 * q^29 - 3 * q^31 + 33 * q^32 - 11 * q^34 - 44 * q^37 + 33 * q^38 - 77 * q^40 - 9 * q^41 - 11 * q^43 - 36 * q^46 + 120 * q^47 + 35 * q^49 + 3 * q^50 - 38 * q^52 - 44 * q^55 - 165 * q^56 - 10 * q^58 + 9 * q^59 - 11 * q^61 - 22 * q^64 - 198 * q^65 - 11 * q^67 - 70 * q^70 - 36 * q^73 - 231 * q^74 - 11 * q^76 - 39 * q^77 - 11 * q^79 - 10 * q^82 - 66 * q^83 + q^85 + 33 * q^86 - 99 * q^88 - 63 * q^92 - 42 * q^94 + 93 * q^95 + 22 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/621\mathbb{Z}\right)^\times$.

$n$	$28$	$461$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.261583	−	0.0124607i	0.184967	−	0.00881107i	0.0451060	−	0.998982i	$-0.485637\pi$
$2$	0.261583	−	0.0124607i	0.184967	−	0.00881107i	0.139861	+	0.990171i	$0.455334\pi$
$3$		0			0
$3$		0			0
$4$	−1.92267	+	0.183593i	−0.961337	+	0.0917965i
$5$	3.04369	+	2.90215i	1.36118	+	1.29788i	0.915292	+	0.402791i	$0.131960\pi$
$5$	3.04369	+	2.90215i	1.36118	+	1.29788i	0.445886	+	0.895090i	$0.352889\pi$
$6$		0			0
$7$	−0.702638	−	3.64563i	−0.265572	−	1.37792i	−0.832442	−	0.554113i	$-0.813058\pi$
$7$	−0.702638	−	3.64563i	−0.265572	−	1.37792i	0.566869	−	0.823808i	$-0.308154\pi$
$8$	−1.01908	+	0.146521i	−0.360299	+	0.0518031i
$9$		0			0
$10$	0.832339	+	0.721226i	0.263209	+	0.228072i
$11$	3.45977	−	1.78363i	1.04316	−	0.537786i	0.150543	−	0.988603i	$-0.451898\pi$
$11$	3.45977	−	1.78363i	1.04316	−	0.537786i	0.892616	+	0.450817i	$0.148867\pi$
$12$		0			0
$13$	0.259083	+	0.0499342i	0.0718568	+	0.0138493i	0.225053	−	0.974347i	$-0.427744\pi$
$13$	0.259083	+	0.0499342i	0.0718568	+	0.0138493i	−0.153196	+	0.988196i	$0.548957\pi$
$14$	−0.229225	−	0.944880i	−0.0612631	−	0.252530i
$15$		0			0
$16$	3.52828	−	0.680021i	0.882071	−	0.170005i
$17$	1.22006	+	2.67157i	0.295909	+	0.647950i	0.997937	−	0.0641992i	$-0.0204493\pi$
$17$	1.22006	+	2.67157i	0.295909	+	0.647950i	−0.702028	+	0.712149i	$0.747722\pi$
$18$		0			0
$19$	1.48734	+	0.679244i	0.341218	+	0.155829i	0.578652	−	0.815575i	$-0.303579\pi$
$19$	1.48734	+	0.679244i	0.341218	+	0.155829i	−0.237434	+	0.971404i	$0.576306\pi$
$20$	−6.38483	−	5.02109i	−1.42769	−	1.12275i
$21$		0			0
$22$	0.882791	−	0.509680i	0.188212	−	0.108664i
$23$	3.98136	+	2.67373i	0.830170	+	0.557510i
$23$	3.98136	+	2.67373i	0.830170	+	0.557510i
$24$		0			0
$25$	0.603648	+	12.6721i	0.120730	+	2.53443i
$26$	0.0683940	+	0.00983357i	0.0134132	+	0.00192852i
$27$		0			0
$28$	2.02026	+	6.88036i	0.381793	+	1.30027i
$29$	−0.234074	+	2.45134i	−0.0434665	+	0.455201i	0.947371	+	0.320139i	$0.103730\pi$
$29$	−0.234074	+	2.45134i	−0.0434665	+	0.455201i	−0.990837	+	0.135063i	$0.956876\pi$
$30$		0			0
$31$	0.601339	−	0.472898i	0.108004	−	0.0849350i	−0.562697	−	0.826663i	$-0.690236\pi$
$31$	0.601339	−	0.472898i	0.108004	−	0.0849350i	0.670700	+	0.741728i	$0.265994\pi$
$32$	2.91554	−	0.707302i	0.515399	−	0.125035i
$33$		0			0
$34$	0.352437	+	0.683633i	0.0604425	+	0.117242i
$35$	8.44156	−	13.1353i	1.42688	−	2.22028i
$36$		0			0
$37$	1.05184	−	3.58222i	0.172921	−	0.588914i	−0.826733	−	0.562595i	$-0.809803\pi$
$37$	1.05184	−	3.58222i	0.172921	−	0.588914i	0.999654	−	0.0263193i	$-0.00837867\pi$
$38$	0.397526	+	0.159145i	0.0644872	+	0.0258168i
$39$		0			0
$40$	−3.52698	−	2.51155i	−0.557665	−	0.397111i
$41$	−2.75661	+	2.89105i	−0.430510	+	0.451506i	−0.902879	−	0.429895i	$-0.858550\pi$
$41$	−2.75661	+	2.89105i	−0.430510	+	0.451506i	0.472369	+	0.881401i	$0.343399\pi$
$42$		0			0
$43$	−4.40550	+	5.60205i	−0.671833	+	0.854305i	−0.995780	−	0.0917702i	$-0.970747\pi$
$43$	−4.40550	+	5.60205i	−0.671833	+	0.854305i	0.323947	+	0.946075i	$0.394990\pi$
$44$	−6.32454	+	4.06454i	−0.953461	+	0.612752i
$45$		0			0
$46$	1.07477	+	0.649790i	0.158466	+	0.0958064i
$47$	4.75835	+	2.74724i	0.694077	+	0.400726i	0.805138	−	0.593088i	$-0.202091\pi$
$47$	4.75835	+	2.74724i	0.694077	+	0.400726i	−0.111061	+	0.993814i	$0.535425\pi$
$48$		0			0
$49$	−6.29837	+	2.52149i	−0.899767	+	0.360213i
$50$	0.315808	+	3.30729i	0.0446620	+	0.467721i
$51$		0			0
$52$	−0.507300	−	0.0484413i	−0.0703499	−	0.00671760i
$53$	−1.42625	−	1.64598i	−0.195910	−	0.226092i	0.649292	−	0.760539i	$-0.275065\pi$
$53$	−1.42625	−	1.64598i	−0.195910	−	0.226092i	−0.845202	+	0.534447i	$0.820520\pi$
$54$		0			0
$55$	15.7068	+	4.61194i	2.11791	+	0.621874i
$56$	1.25021	+	3.61224i	0.167066	+	0.482705i
$57$		0			0
$58$	−0.0306844	+	0.644144i	−0.00402905	+	0.0845803i
$59$	1.82992	−	9.49452i	0.238235	−	1.23608i	−0.643909	−	0.765102i	$-0.722689\pi$
$59$	1.82992	−	9.49452i	0.238235	−	1.23608i	0.882144	−	0.470979i	$-0.156099\pi$
$60$		0			0
$61$	1.51839	−	3.79277i	0.194411	−	0.485614i	−0.798848	−	0.601533i	$-0.794557\pi$
$61$	1.51839	−	3.79277i	0.194411	−	0.485614i	0.993259	+	0.115919i	$0.0369812\pi$
$62$	0.151407	−	0.131195i	0.0192287	−	0.0166618i
$63$		0			0
$64$	−6.14149	+	1.80331i	−0.767687	+	0.225413i
$65$	0.643652	+	0.903883i	0.0798352	+	0.112113i
$66$		0			0
$67$	6.13936	−	11.9087i	0.750042	−	1.45488i	−0.135724	−	0.990747i	$-0.543336\pi$
$67$	6.13936	−	11.9087i	0.750042	−	1.45488i	0.885766	−	0.464132i	$-0.153634\pi$
$68$	−2.83626	−	4.91255i	−0.343948	−	0.595735i
$69$		0			0
$70$	2.04449	−	3.54117i	0.244364	−	0.423250i
$71$	0.327930	+	0.510270i	0.0389182	+	0.0605579i	0.860168	−	0.510012i	$-0.170359\pi$
$71$	0.327930	+	0.510270i	0.0389182	+	0.0605579i	−0.821249	+	0.570569i	$0.806723\pi$
$72$		0			0
$73$	6.89379	−	15.0953i	0.806857	−	1.76677i	0.186492	−	0.982457i	$-0.440288\pi$
$73$	6.89379	−	15.0953i	0.806857	−	1.76677i	0.620365	−	0.784313i	$-0.286984\pi$
$74$	0.230505	−	0.950155i	0.0267957	−	0.110453i
$75$		0			0
$76$	−2.98437	−	1.03290i	−0.342330	−	0.118482i
$77$	−8.93345	−	11.3598i	−1.01806	−	1.29457i
$78$		0			0
$79$	1.99885	−	0.691809i	0.224888	−	0.0778346i	−0.212300	−	0.977205i	$-0.568095\pi$
$79$	1.99885	−	0.691809i	0.224888	−	0.0778346i	0.437189	+	0.899370i	$0.355974\pi$
$80$	12.7125	+	8.16984i	1.42130	+	0.913415i
$81$		0			0
$82$	−0.685057	+	0.790598i	−0.0756519	+	0.0873069i
$83$	−8.75158	+	8.34461i	−0.960611	+	0.915940i	−0.996515	−	0.0834149i	$-0.973417\pi$
$83$	−8.75158	+	8.34461i	−0.960611	+	0.915940i	0.0359043	+	0.999355i	$0.488569\pi$
$84$		0			0
$85$	−4.03979	+	11.6722i	−0.438177	+	1.26603i
$86$	−1.08260	+	1.52030i	−0.116740	+	0.163938i
$87$		0			0
$88$	−3.26444	+	2.32459i	−0.347990	+	0.247803i
$89$	−1.15305	+	8.01966i	−0.122223	+	0.850082i	0.832805	+	0.553567i	$0.186734\pi$
$89$	−1.15305	+	8.01966i	−0.122223	+	0.850082i	−0.955028	+	0.296515i	$0.904175\pi$
$90$		0			0
$91$		−	0.979609i		−	0.102691i
$92$	−8.14572	−	4.40975i	−0.849250	−	0.459749i
$93$		0			0
$94$	1.27894	+	0.659337i	0.131912	+	0.0680055i
$95$	2.55572	+	6.38388i	0.262211	+	0.654972i
$96$		0			0
$97$	−5.87423	−	1.42507i	−0.596438	−	0.144694i	−0.0738351	−	0.997270i	$-0.523524\pi$
$97$	−5.87423	−	1.42507i	−0.596438	−	0.144694i	−0.522603	+	0.852576i	$0.675039\pi$
$98$	−1.61613	+	0.738060i	−0.163253	+	0.0745554i
$99$		0			0
$100$	−3.48713	−	24.2535i	−0.348713	−	2.42535i
$101$	−0.493298	−	0.517356i	−0.0490850	−	0.0514789i	0.698734	−	0.715382i	$-0.253747\pi$
$101$	−0.493298	−	0.517356i	−0.0490850	−	0.0514789i	−0.747819	+	0.663903i	$0.768899\pi$
$102$		0			0
$103$	−16.2006	−	0.771732i	−1.59630	−	0.0760410i	−0.769539	−	0.638599i	$-0.779514\pi$
$103$	−16.2006	−	0.771732i	−1.59630	−	0.0760410i	−0.826758	+	0.562558i	$0.809817\pi$
$104$	−0.271343	−	0.0129257i	−0.0266074	−	0.00126746i
$105$		0			0
$106$	−0.393592	−	0.412787i	−0.0382290	−	0.0400934i
$107$	−1.68209	−	11.6992i	−0.162614	−	1.13100i	−0.893683	−	0.448700i	$-0.851887\pi$
$107$	−1.68209	−	11.6992i	−0.162614	−	1.13100i	0.731069	−	0.682304i	$-0.239022\pi$
$108$		0			0
$109$	−18.0521	+	8.24414i	−1.72908	+	0.789645i	−0.735372	+	0.677664i	$0.762992\pi$
$109$	−18.0521	+	8.24414i	−1.72908	+	0.789645i	−0.993710	+	0.111981i	$0.964280\pi$
$110$	4.16611	+	1.01069i	0.397223	+	0.0963651i
$111$		0			0
$112$	−4.95822	−	12.3850i	−0.468507	−	1.17027i
$113$	−0.270422	−	0.139412i	−0.0254392	−	0.0131148i	0.445460	−	0.895302i	$-0.353040\pi$
$113$	−0.270422	−	0.139412i	−0.0254392	−	0.0131148i	−0.470899	+	0.882187i	$0.656070\pi$
$114$		0			0
$115$	4.35844	+	19.6925i	0.406427	+	1.83633i
$116$		−	4.75609i		−	0.441592i
$117$		0			0
$118$	0.360367	−	2.50641i	0.0331745	−	0.230733i
$119$	8.88229	−	6.32505i	0.814238	−	0.579816i
$120$		0			0
$121$	2.40802	−	3.38159i	0.218911	−	0.307418i
$122$	0.349926	−	1.01104i	0.0316808	−	0.0915356i
$123$		0			0
$124$	−1.06936	+	1.01963i	−0.0960311	+	0.0915655i
$125$	−21.1689	+	24.4302i	−1.89340	+	2.18510i
$126$		0			0
$127$	1.05634	+	0.678868i	0.0937349	+	0.0602398i	0.586669	−	0.809827i	$-0.300439\pi$
$127$	1.05634	+	0.678868i	0.0937349	+	0.0602398i	−0.492934	+	0.870067i	$0.664075\pi$
$128$	−7.25425	+	2.51072i	−0.641191	+	0.221918i
$129$		0			0
$130$	0.179631	+	0.228420i	0.0157547	+	0.0200338i
$131$	−6.63876	−	2.29770i	−0.580031	−	0.200751i	0.0212693	−	0.999774i	$-0.493229\pi$
$131$	−6.63876	−	2.29770i	−0.580031	−	0.200751i	−0.601300	+	0.799023i	$0.705350\pi$
$132$		0			0
$133$	1.43121	−	5.89955i	0.124102	−	0.511556i
$134$	1.45756	−	3.19161i	0.125914	−	0.275713i
$135$		0			0
$136$	−1.63478	−	2.54377i	−0.140181	−	0.218127i
$137$	−0.000589825		0.00102161i	−5.03921e−5		8.72817e-5i	−0.866051	−	0.499956i	$-0.833349\pi$
$137$	−0.000589825		0.00102161i	−5.03921e−5		8.72817e-5i	0.866000	+	0.500044i	$0.166683\pi$
$138$		0			0
$139$	4.03809	+	6.99418i	0.342507	+	0.593239i	0.984898	−	0.173138i	$-0.0553908\pi$
$139$	4.03809	+	6.99418i	0.342507	+	0.593239i	−0.642391	+	0.766377i	$0.722057\pi$
$140$	−13.8188	+	26.8048i	−1.16790	+	2.26542i
$141$		0			0
$142$	0.0921393	+	0.129392i	0.00773216	+	0.0108583i
$143$	0.985433	−	0.289349i	0.0824061	−	0.0241966i
$144$		0			0
$145$	−7.82659	+	6.78178i	−0.649963	+	0.563196i
$146$	1.61520	−	4.03457i	0.133675	−	0.333903i
$147$		0			0
$148$	−1.36467	+	7.08056i	−0.112175	+	0.582018i
$149$	0.132687	−	2.78545i	0.0108702	−	0.228193i	−0.986895	−	0.161367i	$-0.948410\pi$
$149$	0.132687	−	2.78545i	0.0108702	−	0.228193i	0.997765	−	0.0668258i	$-0.0212872\pi$
$150$		0			0
$151$	−3.05152	−	8.81680i	−0.248329	−	0.717501i	−0.998421	−	0.0561671i	$-0.982112\pi$
$151$	−3.05152	−	8.81680i	−0.248329	−	0.717501i	0.750092	−	0.661334i	$-0.230009\pi$
$152$	−1.61524	−	0.474276i	−0.131013	−	0.0384689i
$153$		0			0
$154$	−2.47839	−	2.86021i	−0.199714	−	0.230482i
$155$	3.20271	+	0.305821i	0.257248	+	0.0245642i
$156$		0			0
$157$	0.421650	+	4.41572i	0.0336514	+	0.352413i	0.996579	+	0.0826514i	$0.0263388\pi$
$157$	0.421650	+	4.41572i	0.0336514	+	0.352413i	−0.962927	+	0.269761i	$0.913055\pi$
$158$	0.514245	−	0.205873i	0.0409111	−	0.0163784i
$159$		0			0
$160$	10.9267	+	6.30852i	0.863830	+	0.498732i
$161$	6.94997	−	16.3932i	0.547735	−	1.29197i
$162$		0			0
$163$	0.905001	−	0.581609i	0.0708852	−	0.0455551i	−0.504718	−	0.863284i	$-0.668404\pi$
$163$	0.905001	−	0.581609i	0.0708852	−	0.0455551i	0.575603	+	0.817729i	$0.304767\pi$
$164$	4.76928	−	6.06463i	0.372418	−	0.473568i
$165$		0			0
$166$	−2.18528	+	2.29186i	−0.169611	+	0.177883i
$167$	−12.8153	−	9.12572i	−0.991676	−	0.706169i	−0.0356238	−	0.999365i	$-0.511342\pi$
$167$	−12.8153	−	9.12572i	−0.991676	−	0.706169i	−0.956052	+	0.293196i	$0.905281\pi$
$168$		0			0
$169$	−12.0042	−	4.80574i	−0.923396	−	0.369672i
$170$	−0.911296	+	3.10359i	−0.0698932	+	0.238035i
$171$		0			0
$172$	7.44184	−	11.5797i	0.567435	−	0.882947i
$173$	8.04110	+	15.5976i	0.611353	+	1.18586i	0.967842	+	0.251560i	$0.0809437\pi$
$173$	8.04110	+	15.5976i	0.611353	+	1.18586i	−0.356488	+	0.934300i	$0.616026\pi$
$174$		0			0
$175$	45.7738	−	11.1046i	3.46017	−	0.839429i
$176$	10.9941	−	8.64589i	0.828714	−	0.651708i
$177$		0			0
$178$	−0.201688	+	2.11217i	−0.0151172	+	0.158314i
$179$	4.41110	+	15.0228i	0.329701	+	1.12286i	0.942940	+	0.332962i	$0.108048\pi$
$179$	4.41110	+	15.0228i	0.329701	+	1.12286i	−0.613239	+	0.789898i	$0.710134\pi$
$180$		0			0
$181$	−2.90054	−	0.417035i	−0.215596	−	0.0309980i	0.0336705	−	0.999433i	$-0.489280\pi$
$181$	−2.90054	−	0.417035i	−0.215596	−	0.0309980i	−0.249266	+	0.968435i	$0.580189\pi$
$182$	−0.0122066	−	0.256249i	−0.000904817	−	0.0189944i
$183$		0			0
$184$	−4.44907	−	2.14138i	−0.327990	−	0.157865i
$185$	13.5976	−	7.85058i	0.999716	−	0.577186i
$186$		0			0
$187$	8.98623	+	7.06685i	0.657139	+	0.516779i
$188$	−9.65313	−	4.40844i	−0.704027	−	0.321518i
$189$		0			0
$190$	0.748080	+	1.63807i	0.0542714	+	0.118838i
$191$	14.4137	−	2.77802i	1.04294	−	0.201010i	0.361112	−	0.932522i	$-0.382397\pi$
$191$	14.4137	−	2.77802i	1.04294	−	0.201010i	0.681829	+	0.731512i	$0.261185\pi$
$192$		0			0
$193$	−2.84923	−	11.7447i	−0.205092	−	0.845400i	−0.977613	−	0.210411i	$-0.932520\pi$
$193$	−2.84923	−	11.7447i	−0.205092	−	0.845400i	0.772521	−	0.634989i	$-0.218995\pi$
$194$	−1.55436	−	0.299578i	−0.111596	−	0.0215084i
$195$		0			0
$196$	11.6468	−	6.00433i	0.831913	−	0.428881i
$197$	−3.10535	−	2.69081i	−0.221247	−	0.191712i	0.537184	−	0.843465i	$-0.319488\pi$
$197$	−3.10535	−	2.69081i	−0.221247	−	0.191712i	−0.758431	+	0.651753i	$0.774034\pi$
$198$		0			0
$199$	16.4077	−	2.35908i	1.16311	−	0.167230i	0.466396	−	0.884576i	$-0.345552\pi$
$199$	16.4077	−	2.35908i	1.16311	−	0.167230i	0.696717	+	0.717346i	$0.254643\pi$
$200$	−2.47190	−	12.8254i	−0.174790	−	0.906896i
$201$		0			0
$202$	−0.135485	−	0.129185i	−0.00953269	−	0.00908940i
$203$	9.10114	−	0.869054i	0.638775	−	0.0609956i
$204$		0			0
$205$	−16.7805	+	0.799353i	−1.17200	+	0.0558293i
$206$	−4.24743			−0.295932
$207$		0			0
$208$	0.948076			0.0657373
$209$	6.35736	−	0.302839i	0.439748	−	0.0209478i
$210$		0			0
$211$	10.2841	−	0.982017i	0.707990	−	0.0676048i	0.265152	−	0.964207i	$-0.414578\pi$
$211$	10.2841	−	0.982017i	0.707990	−	0.0676048i	0.442838	+	0.896602i	$0.353972\pi$
$212$	3.04440	+	2.90283i	0.209090	+	0.199367i
$213$		0			0
$214$	−0.585786	−	3.03935i	−0.0400435	−	0.207766i
$215$	−29.6670	+	4.26546i	−2.02327	+	0.290902i
$216$		0			0
$217$	−2.14654	−	1.85998i	−0.145716	−	0.126264i
$218$	−4.61941	+	2.38147i	−0.312866	+	0.161293i
$219$		0			0
$220$	−31.0458	−	5.98359i	−2.09311	−	0.403414i
$221$	0.182696	+	0.753081i	0.0122894	+	0.0506577i
$222$		0			0
$223$	−17.6050	+	3.39309i	−1.17892	+	0.227218i	−0.740817	−	0.671707i	$-0.765561\pi$
$223$	−17.6050	+	3.39309i	−1.17892	+	0.227218i	−0.438102	+	0.898925i	$0.644349\pi$
$224$	−4.62713	−	10.1320i	−0.309163	−	0.676973i
$225$		0			0
$226$	−0.0724749	−	0.0330982i	−0.00482096	−	0.00220166i
$227$	−14.9425	−	11.7509i	−0.991767	−	0.779935i	−0.0162526	−	0.999868i	$-0.505174\pi$
$227$	−14.9425	−	11.7509i	−0.991767	−	0.779935i	−0.975515	+	0.219933i	$0.929416\pi$
$228$		0			0
$229$	−13.9991	+	8.08237i	−0.925085	+	0.534098i	−0.885254	−	0.465108i	$-0.846015\pi$
$229$	−13.9991	+	8.08237i	−0.925085	+	0.534098i	−0.0398315	+	0.999206i	$0.512682\pi$
$230$	1.38548	+	5.09690i	0.0913557	+	0.336080i
$231$		0			0
$232$	−0.120633	−	2.53240i	−0.00791995	−	0.166260i
$233$	12.5681	+	1.80702i	0.823363	+	0.118382i	0.541103	−	0.840956i	$-0.318007\pi$
$233$	12.5681	+	1.80702i	0.823363	+	0.118382i	0.282260	+	0.959338i	$0.408916\pi$
$234$		0			0
$235$	6.51004	+	22.1712i	0.424668	+	1.44629i
$236$	−1.77521	+	18.5908i	−0.115556	+	1.21016i
$237$		0			0
$238$	2.24464	−	1.76520i	0.145498	−	0.114421i
$239$	−5.16143	+	1.25215i	−0.333865	+	0.0809948i	−0.399187	−	0.916869i	$-0.630708\pi$
$239$	−5.16143	+	1.25215i	−0.333865	+	0.0809948i	0.0653221	+	0.997864i	$0.479193\pi$
$240$		0			0
$241$	2.66476	+	5.16892i	0.171653	+	0.332959i	0.958932	−	0.283637i	$-0.0915412\pi$
$241$	2.66476	+	5.16892i	0.171653	+	0.332959i	−0.787279	+	0.616597i	$0.788511\pi$
$242$	0.587760	−	0.914573i	0.0377826	−	0.0587910i
$243$		0			0
$244$	−2.22305	+	7.57102i	−0.142316	+	0.484685i
$245$	−26.4880	−	10.6042i	−1.69226	−	0.677477i
$246$		0			0
$247$	0.351427	+	0.250250i	0.0223607	+	0.0159230i
$248$	−0.543522	+	0.570029i	−0.0345137	+	0.0361969i
$249$		0			0
$250$	−5.23300	+	6.65431i	−0.330964	+	0.420855i
$251$	9.76049	−	6.27268i	0.616076	−	0.395928i	−0.195055	−	0.980792i	$-0.562488\pi$
$251$	9.76049	−	6.27268i	0.616076	−	0.395928i	0.811131	+	0.584864i	$0.198852\pi$
$252$		0			0
$253$	18.5435	+	2.14919i	1.16582	+	0.135118i
$254$	0.284779	+	0.164417i	0.0178686	+	0.0103165i
$255$		0			0
$256$	10.0182	−	4.01070i	0.626140	−	0.250669i
$257$	0.105383	+	1.10362i	0.00657362	+	0.0688421i	0.998163	−	0.0605782i	$-0.0192944\pi$
$257$	0.105383	+	1.10362i	0.00657362	+	0.0688421i	−0.991590	+	0.129420i	$0.958688\pi$
$258$		0			0
$259$	−13.7985	−	1.31760i	−0.857400	−	0.0818717i
$260$	−1.40348	−	1.61970i	−0.0870401	−	0.100450i
$261$		0			0
$262$	−1.76522	−	0.518314i	−0.109055	−	0.0320216i
$263$	−4.49143	−	12.9771i	−0.276953	−	0.800204i	−0.994599	−	0.103795i	$-0.966901\pi$
$263$	−4.49143	−	12.9771i	−0.276953	−	0.800204i	0.717646	−	0.696409i	$-0.245220\pi$
$264$		0			0
$265$	0.435821	−	9.14902i	0.0267723	−	0.562020i
$266$	0.300869	−	1.56105i	0.0184474	−	0.0957144i
$267$		0			0
$268$	−9.61763	+	24.0237i	−0.587490	+	1.46748i
$269$	9.11016	−	7.89400i	0.555456	−	0.481305i	−0.331311	−	0.943522i	$-0.607491\pi$
$269$	9.11016	−	7.89400i	0.555456	−	0.481305i	0.886767	+	0.462216i	$0.152946\pi$
$270$		0			0
$271$	−16.1529	+	4.74293i	−0.981222	+	0.288113i	−0.732729	−	0.680521i	$-0.761754\pi$
$271$	−16.1529	+	4.74293i	−0.981222	+	0.288113i	−0.248493	+	0.968634i	$0.579935\pi$
$272$	6.12145	+	8.59637i	0.371167	+	0.521232i
$273$		0			0
$274$	−0.000141558	0	0.000274584i	−8.55184e−6	0	1.65883e-5i
$275$	24.6909	+	42.7659i	1.48892	+	2.57888i
$276$		0			0
$277$	14.1883	−	24.5748i	0.852490	−	1.47656i	−0.0264633	−	0.999650i	$-0.508425\pi$
$277$	14.1883	−	24.5748i	0.852490	−	1.47656i	0.878954	−	0.476907i	$-0.158242\pi$
$278$	1.14345	+	1.77924i	0.0685795	+	0.106712i
$279$		0			0
$280$	−6.67801	+	14.6228i	−0.399087	+	0.873880i
$281$	−0.433611	+	1.78737i	−0.0258671	+	0.106625i	−0.983282	−	0.182091i	$-0.941713\pi$
$281$	−0.433611	+	1.78737i	−0.0258671	+	0.106625i	0.957415	+	0.288717i	$0.0932285\pi$
$282$		0			0
$283$	−11.9314	−	4.12950i	−0.709249	−	0.245473i	−0.0514592	−	0.998675i	$-0.516387\pi$
$283$	−11.9314	−	4.12950i	−0.709249	−	0.245473i	−0.657790	+	0.753202i	$0.728508\pi$
$284$	−0.724185	−	0.920876i	−0.0429725	−	0.0546439i
$285$		0			0
$286$	0.254167	−	0.0879681i	0.0150292	−	0.00520166i
$287$	12.4766	+	8.01822i	0.736470	+	0.473301i
$288$		0			0
$289$	5.48392	−	6.32878i	0.322584	−	0.372281i
$290$	−1.96280	+	1.87152i	−0.115259	+	0.109900i
$291$		0			0
$292$	−10.4831	+	30.2890i	−0.613478	+	1.77253i
$293$	−0.137444	+	0.193013i	−0.00802954	+	0.0112759i	−0.818571	−	0.574405i	$-0.805233\pi$
$293$	−0.137444	+	0.193013i	−0.00802954	+	0.0112759i	0.810542	+	0.585681i	$0.199173\pi$
$294$		0			0
$295$	33.1242	−	23.5876i	1.92857	−	1.37333i
$296$	−0.547031	+	3.80469i	−0.0317955	+	0.221143i
$297$		0			0
$298$		−	0.730278i		−	0.0423039i
$299$	0.897993	+	0.891524i	0.0519323	+	0.0515582i
$300$		0			0
$301$	23.5185	+	12.1246i	1.35558	+	0.698852i
$302$	−0.908090	−	2.26830i	−0.0522547	−	0.130526i
$303$		0			0
$304$	5.70964	+	1.38514i	0.327471	+	0.0794435i
$305$	15.6287	−	7.13739i	0.894896	−	0.408686i
$306$		0			0
$307$	3.74628	+	26.0559i	0.213811	+	1.48709i	0.760271	+	0.649606i	$0.225066\pi$
$307$	3.74628	+	26.0559i	0.213811	+	1.48709i	−0.546460	+	0.837485i	$0.684025\pi$
$308$	19.2617	+	20.2011i	1.09754	+	1.15106i
$309$		0			0
$310$	0.841584	+	0.0400896i	0.0477988	+	0.00227694i
$311$	−14.1350	−	0.673333i	−0.801522	−	0.0381812i	−0.357177	−	0.934037i	$-0.616261\pi$
$311$	−14.1350	−	0.673333i	−0.801522	−	0.0381812i	−0.444345	+	0.895856i	$0.646564\pi$
$312$		0			0
$313$	−1.05571	−	1.10720i	−0.0596722	−	0.0625824i	0.693221	−	0.720725i	$-0.256191\pi$
$313$	−1.05571	−	1.10720i	−0.0596722	−	0.0625824i	−0.752893	+	0.658143i	$0.771342\pi$
$314$	0.165320	+	1.14982i	0.00932952	+	0.0648883i
$315$		0			0
$316$	−3.71613	+	1.69710i	−0.209049	+	0.0954693i
$317$	−18.2374	−	4.42435i	−1.02432	−	0.248496i	−0.311797	−	0.950149i	$-0.600931\pi$
$317$	−18.2374	−	4.42435i	−1.02432	−	0.248496i	−0.712520	+	0.701652i	$0.752446\pi$
$318$		0			0
$319$	3.56244	+	8.89856i	0.199459	+	0.498223i
$320$	−23.9262	−	12.3348i	−1.33752	−	0.689538i
$321$		0			0
$322$	1.61372	−	4.37479i	0.0899293	−	0.243797i
$323$			4.80224i			0.267204i
$324$		0			0
$325$	−0.476378	+	3.31328i	−0.0264247	+	0.183788i
$326$	0.229486	−	0.163416i	0.0127100	−	0.00905077i
$327$		0			0
$328$	2.38560	−	3.35011i	0.131723	−	0.184979i
$329$	6.67202	−	19.2775i	0.367840	−	1.06280i
$330$		0			0
$331$	−13.7642	+	13.1242i	−0.756552	+	0.721370i	−0.966591	−	0.256322i	$-0.917489\pi$
$331$	−13.7642	+	13.1242i	−0.756552	+	0.721370i	0.210040	+	0.977693i	$0.432641\pi$
$332$	15.2944	−	17.6507i	0.839390	−	0.968708i
$333$		0			0
$334$	−3.46597	−	2.22744i	−0.189650	−	0.121880i
$335$	53.2471	−	18.4290i	2.90920	−	1.00688i
$336$		0			0
$337$	−6.80507	−	8.65335i	−0.370696	−	0.471378i	0.564539	−	0.825407i	$-0.309054\pi$
$337$	−6.80507	−	8.65335i	−0.370696	−	0.471378i	−0.935235	+	0.354028i	$0.884812\pi$
$338$	−3.19996	−	1.10752i	−0.174055	−	0.0602411i
$339$		0			0
$340$	5.62426	−	23.1835i	0.305019	−	1.25730i
$341$	1.23702	−	2.70869i	0.0669882	−	0.146684i
$342$		0			0
$343$	−0.432867	−	0.673554i	−0.0233726	−	0.0363685i
$344$	3.66873	−	6.35443i	0.197805	−	0.342608i
$345$		0			0
$346$	2.29777	+	3.97986i	0.123529	+	0.213958i
$347$	−5.98854	+	11.6161i	−0.321482	+	0.623588i	−0.993095	−	0.117315i	$-0.962571\pi$
$347$	−5.98854	+	11.6161i	−0.321482	+	0.623588i	0.671613	+	0.740902i	$0.265602\pi$
$348$		0			0
$349$	−1.25044	−	1.75600i	−0.0669348	−	0.0939967i	0.779752	−	0.626089i	$-0.215345\pi$
$349$	−1.25044	−	1.75600i	−0.0669348	−	0.0939967i	−0.846686	+	0.532092i	$0.821406\pi$
$350$	11.8353	−	3.47515i	0.632622	−	0.185755i
$351$		0			0
$352$	8.82552	−	7.64736i	0.470402	−	0.407605i
$353$	−8.79217	+	21.9618i	−0.467960	+	1.16891i	0.487325	+	0.873221i	$0.337973\pi$
$353$	−8.79217	+	21.9618i	−0.467960	+	1.16891i	−0.955285	+	0.295687i	$0.904452\pi$
$354$		0			0
$355$	−0.482761	+	2.50480i	−0.0256223	+	0.132941i
$356$	0.744591	−	15.6309i	0.0394632	−	0.828435i
$357$		0			0
$358$	1.34106	+	3.87475i	0.0708775	+	0.204787i
$359$	31.0308	+	9.11147i	1.63774	+	0.480885i	0.965707	−	0.259633i	$-0.0836015\pi$
$359$	31.0308	+	9.11147i	1.63774	+	0.480885i	0.672037	+	0.740518i	$0.265420\pi$
$360$		0			0
$361$	−10.6916	−	12.3387i	−0.562714	−	0.649406i
$362$	−0.763929	−	0.0729464i	−0.0401512	−	0.00383398i
$363$		0			0
$364$	0.179849	+	1.88347i	0.00942667	+	0.0987206i
$365$	64.7913	−	25.9385i	3.39133	−	1.35768i
$366$		0			0
$367$	11.6368	+	6.71851i	0.607436	+	0.350703i	0.771961	−	0.635670i	$-0.219276\pi$
$367$	11.6368	+	6.71851i	0.607436	+	0.350703i	−0.164525	+	0.986373i	$0.552609\pi$
$368$	15.8655	+	6.72626i	0.827048	+	0.350631i
$369$		0			0
$370$	3.45908	−	2.22301i	0.179829	−	0.115569i
$371$	−4.99849	+	6.35610i	−0.259509	+	0.329992i
$372$		0			0
$373$	18.5467	−	19.4512i	0.960311	−	1.00714i	−0.0396578	−	0.999213i	$-0.512627\pi$
$373$	18.5467	−	19.4512i	0.960311	−	1.00714i	0.999969	−	0.00793156i	$-0.00252472\pi$
$374$	2.43870	+	1.73659i	0.126102	+	0.0897971i
$375$		0			0
$376$	−5.25166	−	2.10245i	−0.270834	−	0.108426i
$377$	−0.183050	+	0.623412i	−0.00942757	+	0.0321074i
$378$		0			0
$379$	−10.4054	+	16.1911i	−0.534487	+	0.831679i	−0.998534	−	0.0541323i	$-0.982761\pi$
$379$	−10.4054	+	16.1911i	−0.534487	+	0.831679i	0.464046	+	0.885811i	$0.346397\pi$
$380$	−6.08585	−	11.8049i	−0.312197	−	0.605578i
$381$		0			0
$382$	3.73577	−	0.906288i	0.191139	−	0.0463697i
$383$	−14.9063	+	11.7224i	−0.761674	+	0.598987i	−0.921600	−	0.388142i	$-0.873117\pi$
$383$	−14.9063	+	11.7224i	−0.761674	+	0.598987i	0.159926	+	0.987129i	$0.448875\pi$
$384$		0			0
$385$	5.77723	−	60.5019i	0.294435	−	3.08346i
$386$	−0.891656	−	3.03670i	−0.0453841	−	0.154564i
$387$		0			0
$388$	11.5559	+	1.66148i	0.586660	+	0.0843490i
$389$	1.65809	+	34.8077i	0.0840687	+	1.76482i	0.510104	+	0.860113i	$0.329607\pi$
$389$	1.65809	+	34.8077i	0.0840687	+	1.76482i	−0.426035	+	0.904707i	$0.640090\pi$
$390$		0			0
$391$	−2.28553	+	13.8986i	−0.115584	+	0.702881i
$392$	6.04908	−	3.49244i	0.305525	−	0.176395i
$393$		0			0
$394$	−0.845837	−	0.665174i	−0.0426127	−	0.0335110i
$395$	8.09161	+	3.69532i	0.407133	+	0.185932i
$396$		0			0
$397$	10.4790	+	22.9457i	0.525924	+	1.15161i	0.967148	+	0.254215i	$0.0818172\pi$
$397$	10.4790	+	22.9457i	0.525924	+	1.15161i	−0.441224	+	0.897397i	$0.645456\pi$
$398$	4.26259	−	0.821546i	0.213664	−	0.0411804i
$399$		0			0
$400$	10.7472	+	44.3004i	0.537358	+	2.21502i
$401$	−28.0713	−	5.41030i	−1.40181	−	0.270177i	−0.568365	−	0.822776i	$-0.692424\pi$
$401$	−28.0713	−	5.41030i	−1.40181	−	0.270177i	−0.833447	+	0.552599i	$0.813636\pi$
$402$		0			0
$403$	0.179411	−	0.0924927i	0.00893708	−	0.00460739i
$404$	1.04343	+	0.904141i	0.0519128	+	0.0449827i
$405$		0			0
$406$	2.36987	−	0.340736i	0.117615	−	0.0169105i
$407$	−2.75027	−	14.2698i	−0.136326	−	0.707326i
$408$		0			0
$409$	21.6521	+	20.6453i	1.07063	+	1.02084i	0.999727	+	0.0233589i	$0.00743603\pi$
$409$	21.6521	+	20.6453i	1.07063	+	1.02084i	0.0709013	+	0.997483i	$0.477412\pi$
$410$	−4.37953	+	0.418194i	−0.216290	+	0.0206532i
$411$		0			0
$412$	31.2902	−	1.49054i	1.54156	−	0.0734335i
$413$	−35.8993			−1.76649
$414$		0			0
$415$	−50.8544			−2.49634
$416$	0.790686	−	0.0376650i	0.0387666	−	0.00184668i
$417$		0			0
$418$	1.65920	−	0.158435i	0.0811543	−	0.00774930i
$419$	−9.41010	−	8.97251i	−0.459713	−	0.438336i	0.424494	−	0.905431i	$-0.360452\pi$
$419$	−9.41010	−	8.97251i	−0.459713	−	0.438336i	−0.884207	+	0.467095i	$0.845301\pi$
$420$		0			0
$421$	−0.793744	−	4.11834i	−0.0386847	−	0.200715i	0.957444	−	0.288618i	$-0.0931957\pi$
$421$	−0.793744	−	4.11834i	−0.0386847	−	0.200715i	−0.996129	+	0.0879025i	$0.971984\pi$
$422$	2.67792	−	0.385027i	0.130359	−	0.0187428i
$423$		0			0
$424$	1.69463	+	1.46840i	0.0822984	+	0.0713120i
$425$	−33.1179	+	17.0735i	−1.60646	+	0.828185i
$426$		0			0
$427$	−14.8939	−	2.87057i	−0.720768	−	0.138917i
$428$	5.38200	+	22.1849i	0.260149	+	1.07235i
$429$		0			0
$430$	−7.70722	+	1.48544i	−0.371675	+	0.0716345i
$431$	−8.23138	−	18.0242i	−0.396491	−	0.868195i	−0.997614	−	0.0690383i	$-0.978007\pi$
$431$	−8.23138	−	18.0242i	−0.396491	−	0.868195i	0.601123	−	0.799157i	$-0.294720\pi$
$432$		0			0
$433$	−2.39698	−	1.09467i	−0.115192	−	0.0526063i	0.356986	−	0.934110i	$-0.383805\pi$
$433$	−2.39698	−	1.09467i	−0.115192	−	0.0526063i	−0.472177	+	0.881504i	$0.656532\pi$
$434$	−0.584674	−	0.459793i	−0.0280653	−	0.0220708i
$435$		0			0
$436$	33.1948	−	19.1650i	1.58974	−	0.917839i
$437$	4.10550	+	6.68104i	0.196393	+	0.319598i
$438$		0			0
$439$	0.281569	+	5.91086i	0.0134386	+	0.282110i	0.995577	+	0.0939499i	$0.0299494\pi$
$439$	0.281569	+	5.91086i	0.0134386	+	0.282110i	−0.982138	+	0.188160i	$0.939748\pi$
$440$	−16.6822	−	2.39854i	−0.795295	−	0.114346i
$441$		0			0
$442$	0.0571740	+	0.194717i	0.00271949	+	0.00926173i
$443$	0.906099	−	9.48910i	0.0430501	−	0.450841i	−0.948088	−	0.318007i	$-0.896986\pi$
$443$	0.906099	−	9.48910i	0.0430501	−	0.450841i	0.991138	−	0.132834i	$-0.0424076\pi$
$444$		0			0
$445$	−26.7838	+	21.0630i	−1.26967	+	0.998482i
$446$	−4.56289	+	1.10695i	−0.216059	+	0.0524154i
$447$		0			0
$448$	10.8894	+	21.1226i	0.514478	+	0.997947i
$449$	−7.65255	+	11.9076i	−0.361146	+	0.561954i	−0.973517	−	0.228617i	$-0.926580\pi$
$449$	−7.65255	+	11.9076i	−0.361146	+	0.561954i	0.612370	+	0.790571i	$0.290216\pi$
$450$		0			0
$451$	−4.38065	+	14.9191i	−0.206277	+	0.702514i
$452$	0.545528	+	0.218396i	0.0256595	+	0.0102725i
$453$		0			0
$454$	−4.05512	−	2.88764i	−0.190316	−	0.135524i
$455$	2.84297	−	2.98162i	0.133281	−	0.139781i
$456$		0			0
$457$	21.1977	−	26.9551i	0.991586	−	1.26090i	0.0263154	−	0.999654i	$-0.491623\pi$
$457$	21.1977	−	26.9551i	0.991586	−	1.26090i	0.965271	−	0.261251i	$-0.0841350\pi$
$458$	−3.56121	+	2.28865i	−0.166404	+	0.106942i
$459$		0			0
$460$	−11.9953	−	37.0620i	−0.559282	−	1.72803i
$461$	−23.9595	−	13.8330i	−1.11590	−	0.644267i	−0.175551	−	0.984470i	$-0.556171\pi$
$461$	−23.9595	−	13.8330i	−1.11590	−	0.644267i	−0.940352	+	0.340203i	$0.889504\pi$
$462$		0			0
$463$	0.173922	−	0.0696279i	0.00808285	−	0.00323588i	−0.367618	−	0.929977i	$-0.619826\pi$
$463$	0.173922	−	0.0696279i	0.00808285	−	0.00323588i	0.375700	+	0.926741i	$0.377402\pi$
$464$	0.841079	+	8.80818i	0.0390461	+	0.408910i
$465$		0			0
$466$	3.31012	+	0.316078i	0.153338	+	0.0146420i
$467$	−18.8588	−	21.7643i	−0.872683	−	1.00713i	−0.999884	−	0.0152530i	$-0.995145\pi$
$467$	−18.8588	−	21.7643i	−0.872683	−	1.00713i	0.127201	−	0.991877i	$-0.459401\pi$
$468$		0			0
$469$	−47.7285	−	14.0143i	−2.20390	−	0.647122i
$470$	1.97918	+	5.71848i	0.0912930	+	0.263774i
$471$		0			0
$472$	−0.473681	+	9.94379i	−0.0218029	+	0.457700i
$473$	−5.25000	+	27.2396i	−0.241395	+	1.25248i
$474$		0			0
$475$	−7.70964	+	19.2577i	−0.353742	+	0.883606i
$476$	−15.9165	+	13.7917i	−0.729532	+	0.632143i
$477$		0			0
$478$	−1.33454	+	0.391856i	−0.0610404	+	0.0179231i
$479$	8.11157	+	11.3911i	0.370627	+	0.520473i	0.957201	−	0.289422i	$-0.0934632\pi$
$479$	8.11157	+	11.3911i	0.370627	+	0.520473i	−0.586574	+	0.809895i	$0.699524\pi$
$480$		0			0
$481$	0.451389	−	0.875572i	0.0205816	−	0.0399227i
$482$	0.761465	+	1.31890i	0.0346838	+	0.0600741i
$483$		0			0
$484$	−4.00900	+	6.94379i	−0.182227	+	0.315627i
$485$	−13.7436	−	21.3854i	−0.624062	−	0.971060i
$486$		0			0
$487$	5.80138	−	12.7033i	0.262886	−	0.575639i	−0.731454	−	0.681891i	$-0.761158\pi$
$487$	5.80138	−	12.7033i	0.262886	−	0.575639i	0.994339	+	0.106252i	$0.0338850\pi$
$488$	−0.991643	+	4.08761i	−0.0448895	+	0.185037i
$489$		0			0
$490$	−7.06094	−	2.44382i	−0.318981	−	0.110400i
$491$	8.31954	+	10.5792i	0.375455	+	0.477430i	0.936657	−	0.350249i	$-0.113903\pi$
$491$	8.31954	+	10.5792i	0.375455	+	0.477430i	−0.561201	+	0.827679i	$0.689661\pi$
$492$		0			0
$493$	−6.83449	+	2.36544i	−0.307810	+	0.106534i
$494$	0.0950455	+	0.0610820i	0.00427630	+	0.00274821i
$495$		0			0
$496$	1.80011	−	2.07744i	0.0808275	−	0.0932799i
$497$	1.62984	−	1.55405i	0.0731083	−	0.0697086i
$498$		0			0
$499$	−5.22670	+	15.1016i	−0.233979	+	0.676039i	0.765490	+	0.643448i	$0.222497\pi$
$499$	−5.22670	+	15.1016i	−0.233979	+	0.676039i	−0.999469	+	0.0325903i	$0.989624\pi$
$500$	36.2157	−	50.8578i	1.61961	−	2.27443i
$501$		0			0
$502$	2.47501	−	1.76245i	0.110465	−	0.0786620i
$503$	1.81756	−	12.6414i	0.0810410	−	0.563653i	−0.908332	−	0.418251i	$-0.862643\pi$
$503$	1.81756	−	12.6414i	0.0810410	−	0.563653i	0.989373	−	0.145402i	$-0.0464476\pi$
$504$		0			0
$505$		−	3.00630i		−	0.133778i
$506$	4.87745	+	0.331126i	0.216829	+	0.0147203i
$507$		0			0
$508$	−2.15563	−	1.11130i	−0.0956406	−	0.0493062i
$509$	5.27664	+	13.1804i	0.233883	+	0.584211i	0.998157	−	0.0606799i	$-0.0193269\pi$
$509$	5.27664	+	13.1804i	0.233883	+	0.584211i	−0.764274	+	0.644891i	$0.776903\pi$
$510$		0			0
$511$	−59.8757	−	14.5257i	−2.64875	−	0.642579i
$512$	16.5361	−	7.55178i	0.730799	−	0.333745i
$513$		0			0
$514$	0.0413184	+	0.287376i	0.00182248	+	0.0126756i
$515$	−47.0700	−	49.3656i	−2.07415	−	2.17531i
$516$		0			0
$517$	21.3629	+	1.01764i	0.939538	+	0.0447557i
$518$	−3.62588	−	0.172722i	−0.159312	−	0.00758897i
$519$		0			0
$520$	−0.788370	−	0.826819i	−0.0345723	−	0.0362584i
$521$	5.63432	+	39.1875i	0.246844	+	1.71684i	0.616234	+	0.787563i	$0.288657\pi$
$521$	5.63432	+	39.1875i	0.246844	+	1.71684i	−0.369390	+	0.929274i	$0.620433\pi$
$522$		0			0
$523$	10.2065	−	4.66115i	0.446299	−	0.203818i	−0.179572	−	0.983745i	$-0.557471\pi$
$523$	10.2065	−	4.66115i	0.446299	−	0.203818i	0.625870	+	0.779927i	$0.284744\pi$
$524$	13.1860	+	3.19889i	0.576033	+	0.139744i
$525$		0			0
$526$	−1.33658	−	3.33863i	−0.0582779	−	0.145571i
$527$	1.99705	+	1.02955i	0.0869928	+	0.0448479i
$528$		0			0
$529$	8.70238	+	21.2901i	0.378364	+	0.925657i
$530$		−	2.39866i		−	0.104191i
$531$		0			0
$532$	−1.66864	+	11.6057i	−0.0723448	+	0.503169i
$533$	−0.858553	+	0.611373i	−0.0371881	+	0.0264815i
$534$		0			0
$535$	28.8330	−	40.4903i	1.24656	−	1.75055i
$536$	−4.51161	+	13.0354i	−0.194872	+	0.563045i
$537$		0			0
$538$	2.28470	−	2.17845i	0.0985003	−	0.0939198i
$539$	−17.2935	+	19.9578i	−0.744884	+	0.859642i
$540$		0			0
$541$	−20.8576	−	13.4044i	−0.896739	−	0.576299i	0.00908220	−	0.999959i	$-0.497109\pi$
$541$	−20.8576	−	13.4044i	−0.896739	−	0.576299i	−0.905822	+	0.423659i	$0.860745\pi$
$542$	−4.16624	+	1.44195i	−0.178955	+	0.0619370i
$543$		0			0
$544$	5.44674	+	6.92610i	0.233527	+	0.296954i
$545$	−78.8708	−	27.2974i	−3.37845	−	1.16929i
$546$		0			0
$547$	−6.92108	+	28.5291i	−0.295924	+	1.21981i	0.608630	+	0.793455i	$0.291720\pi$
$547$	−6.92108	+	28.5291i	−0.295924	+	1.21981i	−0.904553	+	0.426360i	$0.859796\pi$
$548$	0.000946481	−	0.00207250i	4.04316e−5	−	8.85330e-5i
$549$		0			0
$550$	6.99162	+	10.8792i	0.298124	+	0.463889i
$551$	−2.01320	+	3.48697i	−0.0857652	+	0.148550i
$552$		0			0
$553$	−3.92655	−	6.80099i	−0.166974	−	0.289208i
$554$	3.40519	−	6.60514i	0.144673	−	0.280626i
$555$		0			0
$556$	−9.04802	−	12.7062i	−0.383721	−	0.538861i
$557$	−1.53026	+	0.449323i	−0.0648390	+	0.0190384i	−0.313991	−	0.949426i	$-0.601666\pi$
$557$	−1.53026	+	0.449323i	−0.0648390	+	0.0190384i	0.249152	+	0.968464i	$0.419848\pi$
$558$		0			0
$559$	−1.42113	+	1.23141i	−0.0601073	+	0.0520832i
$560$	20.8519	−	52.0856i	0.881155	−	2.20102i
$561$		0			0
$562$	−0.0911533	+	0.472948i	−0.00384507	+	0.0199501i
$563$	1.02486	−	21.5145i	0.0431928	−	0.906728i	−0.868458	−	0.495763i	$-0.834889\pi$
$563$	1.02486	−	21.5145i	0.0431928	−	0.906728i	0.911651	−	0.410966i	$-0.134808\pi$
$564$		0			0
$565$	−0.418484	−	1.20913i	−0.0176058	−	0.0508685i
$566$	−3.17251	−	0.931533i	−0.133351	−	0.0391553i
$567$		0			0
$568$	−0.408952	−	0.471956i	−0.0171593	−	0.0198028i
$569$	30.3144	+	2.89467i	1.27084	+	0.121351i	0.708594	−	0.705616i	$-0.249330\pi$
$569$	30.3144	+	2.89467i	1.27084	+	0.121351i	0.562250	+	0.826967i	$0.309936\pi$
$570$		0			0
$571$	−2.97623	−	31.1685i	−0.124551	−	1.30436i	−0.814356	−	0.580366i	$-0.802910\pi$
$571$	−2.97623	−	31.1685i	−0.124551	−	1.30436i	0.689805	−	0.723996i	$-0.257696\pi$
$572$	−1.84154	+	0.737243i	−0.0769988	+	0.0308257i
$573$		0			0
$574$	3.36358	+	1.94196i	0.140393	+	0.0810559i
$575$	−31.4785	+	52.0662i	−1.31274	+	2.17131i
$576$		0			0
$577$	26.1902	−	16.8314i	1.09031	−	0.700701i	0.133395	−	0.991063i	$-0.457412\pi$
$577$	26.1902	−	16.8314i	1.09031	−	0.700701i	0.956917	+	0.290362i	$0.0937758\pi$
$578$	1.35564	−	1.72384i	0.0563872	−	0.0717021i
$579$		0			0
$580$	13.8029	−	14.4761i	0.573134	−	0.601085i
$581$	36.5706	+	26.0418i	1.51720	+	1.08040i
$582$		0			0
$583$	−7.87031	−	3.15080i	−0.325955	−	0.130493i
$584$	−4.81353	+	16.3934i	−0.199185	+	0.678363i
$585$		0			0
$586$	−0.0335478	+	0.0522014i	−0.00138585	+	0.00215642i
$587$	10.3454	+	20.0672i	0.426999	+	0.828262i	0.999962	+	0.00868140i	$0.00276341\pi$
$587$	10.3454	+	20.0672i	0.426999	+	0.828262i	−0.572963	+	0.819581i	$0.694206\pi$
$588$		0			0
$589$	1.21561	−	0.294903i	0.0500882	−	0.0121513i
$590$	8.37081	−	6.58288i	0.344621	−	0.271013i
$591$		0			0
$592$	1.27519	−	13.3544i	0.0524099	−	0.548861i
$593$	0.429753	+	1.46360i	0.0176478	+	0.0601030i	0.967846	−	0.251543i	$-0.0809379\pi$
$593$	0.429753	+	1.46360i	0.0176478	+	0.0601030i	−0.950198	+	0.311646i	$0.899120\pi$
$594$		0			0
$595$	45.3911	+	6.52626i	1.86085	+	0.267551i
$596$	0.256274	+	5.37986i	0.0104974	+	0.220368i
$597$		0			0
$598$	0.246009	+	0.222018i	0.0100600	+	0.00907898i
$599$	−24.7668	+	14.2991i	−1.01195	+	0.584247i	−0.911761	−	0.410722i	$-0.865277\pi$
$599$	−24.7668	+	14.2991i	−1.01195	+	0.584247i	−0.100185	+	0.994969i	$0.531943\pi$
$600$		0			0
$601$	−7.53928	−	5.92896i	−0.307534	−	0.241847i	0.452449	−	0.891790i	$-0.350550\pi$
$601$	−7.53928	−	5.92896i	−0.307534	−	0.241847i	−0.759983	+	0.649943i	$0.774793\pi$
$602$	6.30312	+	2.87854i	0.256896	+	0.117320i
$603$		0			0
$604$	7.48578	+	16.3916i	0.304592	+	0.666964i
$605$	17.1431	−	3.30407i	0.696968	−	0.134330i
$606$		0			0
$607$	−9.90570	−	40.8318i	−0.402060	−	1.65731i	−0.708717	−	0.705493i	$-0.750726\pi$
$607$	−9.90570	−	40.8318i	−0.402060	−	1.65731i	0.306657	−	0.951820i	$-0.400790\pi$
$608$	4.81682	+	0.928365i	0.195348	+	0.0376502i
$609$		0			0
$610$	3.99926	−	2.06176i	0.161925	−	0.0834783i
$611$	1.09563	+	0.949368i	0.0443244	+	0.0384073i
$612$		0			0
$613$	−14.7166	+	2.11593i	−0.594399	+	0.0854617i	−0.432948	−	0.901419i	$-0.642527\pi$
$613$	−14.7166	+	2.11593i	−0.594399	+	0.0854617i	−0.161451	+	0.986881i	$0.551618\pi$
$614$	1.30464	+	6.76911i	0.0526509	+	0.273179i
$615$		0			0
$616$	10.7683	+	10.2676i	0.433869	+	0.413693i
$617$	25.8710	−	2.47038i	1.04153	−	0.0994536i	0.439751	−	0.898120i	$-0.355067\pi$
$617$	25.8710	−	2.47038i	1.04153	−	0.0994536i	0.601775	+	0.798666i	$0.294461\pi$
$618$		0			0
$619$	14.9413	−	0.711739i	0.600540	−	0.0286072i	0.254889	−	0.966970i	$-0.417961\pi$
$619$	14.9413	−	0.711739i	0.600540	−	0.0286072i	0.345651	+	0.938363i	$0.387658\pi$
$620$	−6.21391			−0.249557
$621$		0			0
$622$	−3.70586			−0.148592
$623$	30.0469	−	1.43131i	1.20380	−	0.0573443i
$624$		0			0
$625$	−72.1863	+	6.89296i	−2.88745	+	0.275718i
$626$	−0.289952	−	0.276469i	−0.0115888	−	0.0110499i
$627$		0			0
$628$	−1.62139	−	8.41258i	−0.0647006	−	0.335698i
$629$	10.8535	−	1.56049i	0.432756	−	0.0622209i
$630$		0			0
$631$	1.81259	+	1.57062i	0.0721583	+	0.0625255i	0.690193	−	0.723625i	$-0.257526\pi$
$631$	1.81259	+	1.57062i	0.0721583	+	0.0625255i	−0.618035	+	0.786151i	$0.712071\pi$
$632$	−1.93562	+	0.997883i	−0.0769949	+	0.0396937i
$633$		0			0
$634$	−4.82573	−	0.930084i	−0.191654	−	0.0369383i
$635$	1.24499	+	5.13191i	0.0494059	+	0.203654i
$636$		0			0
$637$	−1.75771	+	0.338771i	−0.0696431	+	0.0134226i
$638$	1.04276	+	2.28332i	0.0412831	+	0.0903975i
$639$		0			0
$640$	−29.3661	−	13.4111i	−1.16080	−	0.530119i
$641$	0.957930	+	0.753324i	0.0378360	+	0.0297545i	0.636898	−	0.770948i	$-0.280217\pi$
$641$	0.957930	+	0.753324i	0.0378360	+	0.0297545i	−0.599062	+	0.800703i	$0.704460\pi$
$642$		0			0
$643$	14.1568	−	8.17341i	0.558288	−	0.322328i	−0.194170	−	0.980968i	$-0.562201\pi$
$643$	14.1568	−	8.17341i	0.558288	−	0.322328i	0.752458	+	0.658640i	$0.228868\pi$
$644$	−10.3528	+	32.7948i	−0.407959	+	1.29230i
$645$		0			0
$646$	0.0598394	+	1.25618i	0.00235435	+	0.0494239i
$647$	15.7972	+	2.27130i	0.621053	+	0.0892939i	0.445657	−	0.895204i	$-0.352970\pi$
$647$	15.7972	+	2.27130i	0.621053	+	0.0892939i	0.175396	+	0.984498i	$0.443879\pi$
$648$		0			0
$649$	−10.6037	−	36.1128i	−0.416230	−	1.41755i
$650$	−0.0833264	+	0.872634i	−0.00326833	+	0.0342275i
$651$		0			0
$652$	−1.63324	+	1.28440i	−0.0639627	+	0.0503008i
$653$	−30.0751	+	7.29613i	−1.17693	+	0.285520i	−0.776086	−	0.630627i	$-0.782798\pi$
$653$	−30.0751	+	7.29613i	−1.17693	+	0.285520i	−0.400843	+	0.916147i	$0.631283\pi$
$654$		0			0
$655$	−13.5380	−	26.2601i	−0.528975	−	1.02607i
$656$	−7.76012	+	12.0750i	−0.302982	+	0.471449i
$657$		0			0
$658$	1.50507	−	5.12581i	0.0586739	−	0.199825i
$659$	7.82109	+	3.13109i	0.304666	+	0.121970i	0.518958	−	0.854800i	$-0.326320\pi$
$659$	7.82109	+	3.13109i	0.304666	+	0.121970i	−0.214292	+	0.976770i	$0.568744\pi$
$660$		0			0
$661$	9.30455	+	6.62574i	0.361905	+	0.257712i	0.746516	−	0.665367i	$-0.231725\pi$
$661$	9.30455	+	6.62574i	0.361905	+	0.257712i	−0.384611	+	0.923079i	$0.625664\pi$
$662$	−3.43696	+	3.60458i	−0.133581	+	0.140096i
$663$		0			0
$664$	7.69588	−	9.78611i	0.298658	−	0.379775i
$665$	21.4775	−	13.8028i	0.832863	−	0.535249i
$666$		0			0
$667$	−7.48613	+	9.13379i	−0.289864	+	0.353662i
$668$	26.3150	+	15.1930i	1.01816	+	0.587834i
$669$		0			0
$670$	13.6989	−	5.48421i	0.529234	−	0.211873i
$671$	−1.51162	−	15.8304i	−0.0583553	−	0.611124i
$672$		0			0
$673$	−18.6263	−	1.77859i	−0.717990	−	0.0685598i	−0.270335	−	0.962766i	$-0.587135\pi$
$673$	−18.6263	−	1.77859i	−0.717990	−	0.0685598i	−0.447655	+	0.894206i	$0.647741\pi$
$674$	−1.88792	−	2.17877i	−0.0727199	−	0.0839232i
$675$		0			0
$676$	23.9624	+	7.03599i	0.921629	+	0.270615i
$677$	−14.1329	−	40.8342i	−0.543170	−	1.56939i	−0.798162	−	0.602443i	$-0.794194\pi$
$677$	−14.1329	−	40.8342i	−0.543170	−	1.56939i	0.254992	−	0.966943i	$-0.417927\pi$
$678$		0			0
$679$	−1.06784	+	22.4166i	−0.0409798	+	0.860271i
$680$	2.40664	−	12.4868i	0.0922903	−	0.478848i
$681$		0			0
$682$	0.289830	−	0.723960i	0.0110982	−	0.0277219i
$683$	−21.8205	+	18.9076i	−0.834940	+	0.723479i	−0.963352	−	0.268241i	$-0.913558\pi$
$683$	−21.8205	+	18.9076i	−0.834940	+	0.723479i	0.128412	+	0.991721i	$0.459012\pi$
$684$		0			0
$685$	−0.00476010	+	0.00139769i	−0.000181874	+	5.34030e-5i
$686$	−0.121624	−	0.170796i	−0.00464361	−	0.00652104i
$687$		0			0
$688$	−11.7343	+	22.7615i	−0.447368	+	0.867773i
$689$	−0.287326	−	0.497664i	−0.0109463	−	0.0189595i
$690$		0			0
$691$	7.76050	−	13.4416i	0.295223	−	0.511342i	−0.679813	−	0.733385i	$-0.737939\pi$
$691$	7.76050	−	13.4416i	0.295223	−	0.511342i	0.975037	+	0.222043i	$0.0712726\pi$
$692$	−18.3240	−	28.5127i	−0.696574	−	1.08389i
$693$		0			0
$694$	−1.42175	+	3.11321i	−0.0539691	+	0.118176i
$695$	−8.00747	+	33.0072i	−0.303741	+	1.25204i
$696$		0			0
$697$	−11.0869	−	3.83720i	−0.419945	−	0.145344i
$698$	−0.348976	−	0.443759i	−0.0132089	−	0.0167965i
$699$		0			0
$700$	−85.9693	+	29.7543i	−3.24933	+	1.12461i
$701$	9.56055	+	6.14419i	0.361097	+	0.232063i	0.708591	−	0.705619i	$-0.249331\pi$
$701$	9.56055	+	6.14419i	0.361097	+	0.232063i	−0.347494	+	0.937682i	$0.612967\pi$
$702$		0			0
$703$	3.99764	−	4.61352i	0.150774	−	0.174002i
$704$	−18.0317	+	17.1932i	−0.679596	+	0.647993i
$705$		0			0
$706$	−2.02622	+	5.85438i	−0.0762578	+	0.220333i
$707$	−1.53948	+	2.16190i	−0.0578982	+	0.0813066i
$708$		0			0
$709$	−12.2578	+	8.72875i	−0.460352	+	0.327815i	−0.786593	−	0.617471i	$-0.788157\pi$
$709$	−12.2578	+	8.72875i	−0.460352	+	0.327815i	0.326242	+	0.945286i	$0.394218\pi$
$710$	−0.0950704	+	0.661229i	−0.00356793	+	0.0248155i
$711$		0			0
$712$		−	8.34161i		−	0.312615i
$713$	3.65854	−	0.274960i	0.137014	−	0.0102973i
$714$		0			0
$715$	3.83908	+	1.97919i	0.143574	+	0.0740173i
$716$	−11.2392	−	28.0742i	−0.420029	−	1.04918i
$717$		0			0
$718$	8.23067	+	1.99674i	0.307166	+	0.0745176i
$719$	16.0632	−	7.33582i	0.599057	−	0.273580i	−0.0927192	−	0.995692i	$-0.529556\pi$
$719$	16.0632	−	7.33582i	0.599057	−	0.273580i	0.691776	+	0.722112i	$0.256829\pi$
$720$		0			0
$721$	8.56974	+	59.6039i	0.319154	+	2.21976i
$722$	−2.95048	−	3.09437i	−0.109805	−	0.115161i
$723$		0			0
$724$	5.65336	+	0.269303i	0.210106	+	0.0100086i
$725$	−31.2049	−	1.48647i	−1.15892	−	0.0552063i
$726$		0			0
$727$	27.1060	+	28.4280i	1.00531	+	1.05433i	0.998522	+	0.0543578i	$0.0173112\pi$
$727$	27.1060	+	28.4280i	1.00531	+	1.05433i	0.00678467	+	0.999977i	$0.497840\pi$
$728$	0.143534	+	0.998299i	0.00531971	+	0.0369994i
$729$		0			0
$730$	16.6251	−	7.59242i	0.615322	−	0.281008i
$731$	−20.3412	−	4.93473i	−0.752348	−	0.182518i
$732$		0			0
$733$	−7.02712	−	17.5529i	−0.259553	−	0.648331i	0.740157	−	0.672434i	$-0.234751\pi$
$733$	−7.02712	−	17.5529i	−0.259553	−	0.648331i	−0.999709	+	0.0241032i	$0.992327\pi$
$734$	3.12770	+	1.61244i	0.115446	+	0.0595164i
$735$		0			0
$736$	13.4989	+	4.97933i	0.497577	+	0.183541i
$737$		−	52.1517i		−	1.92103i
$738$		0			0
$739$	4.87676	−	33.9186i	0.179394	−	1.24772i	−0.678774	−	0.734347i	$-0.737488\pi$
$739$	4.87676	−	33.9186i	0.179394	−	1.24772i	0.858169	−	0.513368i	$-0.171602\pi$
$740$	−24.7024	+	17.5905i	−0.908080	+	0.646641i
$741$		0			0
$742$	−1.22832	+	1.72493i	−0.0450930	+	0.0633243i
$743$	15.0299	−	43.4262i	0.551395	−	1.59315i	−0.232725	−	0.972542i	$-0.574764\pi$
$743$	15.0299	−	43.4262i	0.551395	−	1.59315i	0.784120	−	0.620609i	$-0.213114\pi$
$744$		0			0
$745$	8.48764	−	8.09294i	0.310963	−	0.296503i
$746$	4.60912	−	5.31921i	0.168752	−	0.194750i
$747$		0			0
$748$	−18.5750	−	11.9374i	−0.679170	−	0.436476i
$749$	−41.4691	+	14.3526i	−1.51525	+	0.524432i
$750$		0			0
$751$	−18.5579	−	23.5982i	−0.677186	−	0.861112i	0.319055	−	0.947736i	$-0.396634\pi$
$751$	−18.5579	−	23.5982i	−0.677186	−	0.861112i	−0.996241	+	0.0866245i	$0.972392\pi$
$752$	18.6570	+	6.45725i	0.680351	+	0.235472i
$753$		0			0
$754$	−0.0401147	+	0.165355i	−0.00146089	+	0.00602187i
$755$	16.2998	−	35.6915i	0.593210	−	1.29895i
$756$		0			0
$757$	−5.75878	−	8.96084i	−0.209306	−	0.325687i	0.720689	−	0.693259i	$-0.243826\pi$
$757$	−5.75878	−	8.96084i	−0.209306	−	0.325687i	−0.929995	+	0.367572i	$0.880189\pi$
$758$	−2.52011	+	4.36496i	−0.0915346	+	0.158543i
$759$		0			0
$760$	−3.53985	−	6.13121i	−0.128404	−	0.222402i
$761$	−15.4051	+	29.8818i	−0.558435	+	1.08321i	0.425545	+	0.904937i	$0.360082\pi$
$761$	−15.4051	+	29.8818i	−0.558435	+	1.08321i	−0.983981	+	0.178276i	$0.942948\pi$
$762$		0			0
$763$	42.7392	+	60.0189i	1.54726	+	2.17283i
$764$	−27.2029	+	7.98749i	−0.984166	+	0.288977i
$765$		0			0
$766$	−3.75315	+	3.25212i	−0.135607	+	0.117504i
$767$	0.948203	−	2.36850i	0.0342376	−	0.0855215i
$768$		0			0
$769$	−3.75589	+	19.4874i	−0.135441	+	0.702734i	0.849190	+	0.528087i	$0.177091\pi$
$769$	−3.75589	+	19.4874i	−0.135441	+	0.702734i	−0.984631	+	0.174647i	$0.944122\pi$
$770$	0.757327	−	15.8982i	0.0272922	−	0.572933i
$771$		0			0
$772$	7.63437	+	22.0581i	0.274767	+	0.793887i
$773$	3.36480	+	0.987993i	0.121023	+	0.0355357i	0.341683	−	0.939815i	$-0.389003\pi$
$773$	3.36480	+	0.987993i	0.121023	+	0.0355357i	−0.220660	+	0.975351i	$0.570821\pi$
$774$		0			0
$775$	6.35562	+	7.33478i	0.228301	+	0.263473i
$776$	6.19511	+	0.591561i	0.222392	+	0.0212358i
$777$		0			0
$778$	0.867458	+	9.08443i	0.0310999	+	0.325693i
$779$	−6.06373	+	2.42755i	−0.217256	+	0.0869760i
$780$		0			0
$781$	2.04470	+	1.18051i	0.0731650	+	0.0422419i
$782$	−0.424669	+	3.66411i	−0.0151861	+	0.131028i
$783$		0			0
$784$	−20.5078	+	13.1795i	−0.732421	+	0.470698i
$785$	−11.5317	+	14.6638i	−0.411584	+	0.523372i
$786$		0			0
$787$	24.9445	−	26.1610i	0.889174	−	0.932539i	−0.108932	−	0.994049i	$-0.534743\pi$
$787$	24.9445	−	26.1610i	0.889174	−	0.932539i	0.998106	+	0.0615100i	$0.0195916\pi$
$788$	6.46460	+	4.60342i	0.230292	+	0.163990i
$789$		0			0
$790$	2.16267	+	0.865804i	0.0769445	+	0.0308039i
$791$	−0.318237	+	1.08382i	−0.0113152	+	0.0385360i
$792$		0			0
$793$	0.582780	−	0.906823i	0.0206951	−	0.0322022i
$794$	3.02704	+	5.87163i	0.107425	+	0.208376i
$795$		0			0
$796$	−31.1136	+	7.54808i	−1.10279	+	0.267534i
$797$	−22.7868	+	17.9197i	−0.807149	+	0.634749i	−0.934040	−	0.357168i	$-0.883742\pi$
$797$	−22.7868	+	17.9197i	−0.807149	+	0.634749i	0.126892	+	0.991917i	$0.459500\pi$
$798$		0			0
$799$	−1.53393	+	16.0641i	−0.0542666	+	0.568305i
$800$	10.7230	+	36.5191i	0.379115	+	1.29115i
$801$		0			0
$802$	−7.41038	−	1.06545i	−0.261670	−	0.0376224i
$803$	−3.07357	−	64.5222i	−0.108464	−	2.27694i
$804$		0			0
$805$	68.7291	−	29.7260i	2.42238	−	1.04770i
$806$	0.0457783	−	0.0264301i	0.00161247	−	0.000930960i
$807$		0			0
$808$	0.578514	+	0.454948i	0.0203520	+	0.0160050i
$809$	−31.5971	−	14.4299i	−1.11089	−	0.507328i	−0.226473	−	0.974017i	$-0.572719\pi$
$809$	−31.5971	−	14.4299i	−1.11089	−	0.507328i	−0.884422	+	0.466689i	$0.845447\pi$
$810$		0			0
$811$	−2.55975	−	5.60508i	−0.0898851	−	0.196821i	0.859350	−	0.511387i	$-0.170868\pi$
$811$	−2.55975	−	5.60508i	−0.0898851	−	0.196821i	−0.949236	+	0.314566i	$0.898141\pi$
$812$	−17.3390	+	3.34181i	−0.608479	+	0.117275i
$813$		0			0
$814$	−0.897236	−	3.69846i	−0.0314481	−	0.129631i
$815$	4.44246	+	0.856213i	0.155612	+	0.0299918i
$816$		0			0
$817$	−10.3576	+	5.33973i	−0.362367	+	0.186813i
$818$	5.92108	+	5.13064i	0.207026	+	0.179389i
$819$		0			0
$820$	32.1167	−	4.61768i	1.12156	−	0.161256i
$821$	3.65776	+	18.9783i	0.127657	+	0.662346i	0.988225	+	0.153010i	$0.0488967\pi$
$821$	3.65776	+	18.9783i	0.127657	+	0.662346i	−0.860568	+	0.509336i	$0.829891\pi$
$822$		0			0
$823$	4.72951	+	4.50958i	0.164860	+	0.157194i	0.768019	−	0.640427i	$-0.221243\pi$
$823$	4.72951	+	4.50958i	0.164860	+	0.157194i	−0.603158	+	0.797622i	$0.706091\pi$
$824$	16.6228	−	1.58729i	0.579083	−	0.0552957i
$825$		0			0
$826$	−9.39065	+	0.447332i	−0.326742	+	0.0155647i
$827$	53.0645			1.84523			0.922616	−	0.385719i	$-0.126046\pi$
$827$	53.0645			1.84523			0.922616	+	0.385719i	$0.126046\pi$
$828$		0			0
$829$	50.4138			1.75094			0.875472	−	0.483269i	$-0.160551\pi$
$829$	50.4138			1.75094			0.875472	+	0.483269i	$0.160551\pi$
$830$	−13.3026	+	0.633683i	−0.461741	+	0.0219954i
$831$		0			0
$832$	−1.68121	+	0.160536i	−0.0582853	+	0.00556557i
$833$	−14.4207	−	13.7501i	−0.499649	−	0.476414i
$834$		0			0
$835$	−12.5215	−	64.9677i	−0.433324	−	2.24830i
$836$	−12.1675	+	1.74943i	−0.420823	+	0.0605052i
$837$		0			0
$838$	−2.57333	−	2.22980i	−0.0888941	−	0.0770271i
$839$	−16.6000	+	8.55787i	−0.573094	+	0.295451i	−0.720308	−	0.693654i	$-0.756000\pi$
$839$	−16.6000	+	8.55787i	−0.573094	+	0.295451i	0.147214	+	0.989105i	$0.452969\pi$
$840$		0			0
$841$	22.5217	+	4.34070i	0.776610	+	0.149679i
$842$	−0.258947	−	1.06740i	−0.00892392	−	0.0367849i
$843$		0			0
$844$	−19.5928	+	3.77620i	−0.674411	+	0.129982i
$845$	−22.5899	−	49.4650i	−0.777116	−	1.70165i
$846$		0			0
$847$	−14.0200	−	6.40273i	−0.481734	−	0.220000i
$848$	−6.15150	−	4.83759i	−0.211243	−	0.166124i
$849$		0			0
$850$	−8.45034	+	4.87880i	−0.289844	+	0.167342i
$851$	13.7656	−	11.4498i	0.471879	−	0.392494i
$852$		0			0
$853$	0.578891	+	12.1524i	0.0198208	+	0.416091i	0.986872	+	0.161507i	$0.0516354\pi$
$853$	0.578891	+	12.1524i	0.0198208	+	0.416091i	−0.967051	+	0.254584i	$0.918062\pi$
$854$	−3.93177	−	0.565303i	−0.134542	−	0.0193443i
$855$		0			0
$856$	3.42836	+	11.6759i	0.117179	+	0.399075i
$857$	2.51343	−	26.3218i	0.0858570	−	0.899136i	−0.845245	−	0.534378i	$-0.820546\pi$
$857$	2.51343	−	26.3218i	0.0858570	−	0.899136i	0.931103	−	0.364758i	$-0.118848\pi$
$858$		0			0
$859$	−17.6671	+	13.8936i	−0.602794	+	0.474042i	−0.872310	−	0.488954i	$-0.837379\pi$
$859$	−17.6671	+	13.8936i	−0.602794	+	0.474042i	0.269516	+	0.962996i	$0.413136\pi$
$860$	56.2568	−	13.6477i	1.91834	−	0.465384i
$861$		0			0
$862$	−2.37778	−	4.61225i	−0.0809876	−	0.157094i
$863$	23.1000	−	35.9442i	0.786332	−	1.22356i	−0.184273	−	0.982875i	$-0.558993\pi$
$863$	23.1000	−	35.9442i	0.786332	−	1.22356i	0.970604	−	0.240681i	$-0.0773707\pi$
$864$		0			0
$865$	−20.7918	+	70.8105i	−0.706944	+	2.40763i
$866$	−0.640651	−	0.256478i	−0.0217702	−	0.00871547i
$867$		0			0
$868$	4.46857	+	3.18205i	0.151673	+	0.108006i
$869$	5.68163	−	5.95872i	0.192736	−	0.202136i
$870$		0			0
$871$	2.18526	−	2.77878i	0.0740446	−	0.0941554i
$872$	17.1886	−	11.0465i	0.582080	−	0.374080i
$873$		0			0
$874$	1.15718	+	1.69649i	0.0391422	+	0.0573846i
$875$	103.938	+	60.0084i	3.51374	+	2.02866i
$876$		0			0
$877$	−34.4711	+	13.8001i	−1.16401	+	0.465998i	−0.871562	−	0.490285i	$-0.836893\pi$
$877$	−34.4711	+	13.8001i	−1.16401	+	0.465998i	−0.292444	+	0.956283i	$0.594469\pi$
$878$	0.147307	+	1.54267i	0.00497138	+	0.0520627i
$879$		0			0
$880$	58.5544	+	5.59126i	1.97387	+	0.188481i
$881$	25.1322	+	29.0041i	0.846726	+	0.977174i	0.999939	−	0.0110188i	$-0.00350745\pi$
$881$	25.1322	+	29.0041i	0.846726	+	0.977174i	−0.153213	+	0.988193i	$0.548962\pi$
$882$		0			0
$883$	8.16884	+	2.39859i	0.274903	+	0.0807189i	0.416278	−	0.909237i	$-0.363334\pi$
$883$	8.16884	+	2.39859i	0.274903	+	0.0807189i	−0.141375	+	0.989956i	$0.545152\pi$
$884$	−0.489524	−	1.41439i	−0.0164645	−	0.0475710i
$885$		0			0
$886$	0.118779	−	2.49348i	0.00399046	−	0.0837700i
$887$	1.60270	−	8.31561i	0.0538135	−	0.279211i	−0.945047	−	0.326934i	$-0.893984\pi$
$887$	1.60270	−	8.31561i	0.0538135	−	0.279211i	0.998861	+	0.0477233i	$0.0151966\pi$
$888$		0			0
$889$	1.73268	−	4.32802i	0.0581122	−	0.145157i
$890$	−6.74372	+	5.84347i	−0.226050	+	0.195873i
$891$		0			0
$892$	33.2258	−	9.75596i	1.11248	−	0.326654i
$893$	5.21123	+	7.31814i	0.174387	+	0.244892i
$894$		0			0
$895$	−30.1725	+	58.5265i	−1.00856	+	1.95632i
$896$	14.2503	+	24.6822i	0.476068	+	0.824574i
$897$		0			0
$898$	−1.85340	+	3.21018i	−0.0618487	+	0.107125i
$899$	1.01847	+	1.58478i	0.0339680	+	0.0528552i
$900$		0			0
$901$	2.65722	−	5.81851i	0.0885249	−	0.193843i
$902$	−0.960001	+	3.95718i	−0.0319645	+	0.131760i
$903$		0			0
$904$	0.296008	+	0.102449i	0.00984508	+	0.00340742i
$905$	−7.61805	−	9.68713i	−0.253232	−	0.322011i
$906$		0			0
$907$	42.5015	−	14.7099i	1.41124	−	0.488435i	0.488063	−	0.872808i	$-0.337704\pi$
$907$	42.5015	−	14.7099i	1.41124	−	0.488435i	0.923178	+	0.384373i	$0.125582\pi$
$908$	30.8869	+	19.8498i	1.02502	+	0.658739i
$909$		0			0
$910$	0.706520	−	0.815367i	0.0234209	−	0.0270292i
$911$	−25.6804	+	24.4862i	−0.850829	+	0.811264i	−0.983690	−	0.179871i	$-0.942432\pi$
$911$	−25.6804	+	24.4862i	−0.850829	+	0.811264i	0.132861	+	0.991135i	$0.457584\pi$
$912$		0			0
$913$	−15.3947	+	44.4801i	−0.509490	+	1.47207i
$914$	5.20907	−	7.31512i	0.172301	−	0.241963i
$915$		0			0
$916$	25.4318	−	18.1099i	0.840290	−	0.598368i
$917$	−3.71192	+	25.8169i	−0.122578	+	0.852550i
$918$		0			0
$919$		−	34.2932i		−	1.13123i	−0.824670	−	0.565614i	$-0.808639\pi$
$919$		−	34.2932i		−	1.13123i	0.824670	−	0.565614i	$-0.191361\pi$
$920$	−7.32697	−	19.4296i	−0.241563	−	0.640574i
$921$		0			0
$922$	−6.43975	−	3.31992i	−0.212082	−	0.109336i
$923$	0.0594814	+	0.148577i	0.00195785	+	0.00489048i
$924$		0			0
$925$	46.0293	+	11.1666i	1.51344	+	0.367155i
$926$	0.0446274	−	0.0203807i	0.00146655	−	0.000669750i
$927$		0			0
$928$	1.05138	+	7.31252i	0.0345133	+	0.240045i
$929$	27.1433	+	28.4671i	0.890543	+	0.933974i	0.998185	−	0.0602154i	$-0.0191788\pi$
$929$	27.1433	+	28.4671i	0.890543	+	0.933974i	−0.107643	+	0.994190i	$0.534330\pi$
$930$		0			0
$931$	−11.0805	−	0.527829i	−0.363149	−	0.0172989i
$932$	−24.4961	−	1.16689i	−0.802396	−	0.0382228i
$933$		0			0
$934$	−5.20435	−	5.45816i	−0.170292	−	0.178597i
$935$	6.84222	+	47.5887i	0.223764	+	1.55632i
$936$		0			0
$937$	31.2252	−	14.2601i	1.02008	−	0.465856i	0.166072	−	0.986114i	$-0.446891\pi$
$937$	31.2252	−	14.2601i	1.02008	−	0.465856i	0.854009	+	0.520258i	$0.174164\pi$
$938$	−12.6596	−	3.07118i	−0.413350	−	0.100278i
$939$		0			0
$940$	−16.5872	−	41.4327i	−0.541014	−	1.35139i
$941$	19.2162	+	9.90662i	0.626429	+	0.322947i	0.742048	−	0.670347i	$-0.233855\pi$
$941$	19.2162	+	9.90662i	0.626429	+	0.322947i	−0.115619	+	0.993294i	$0.536885\pi$
$942$		0			0
$943$	−18.7049	+	4.13987i	−0.609115	+	0.134813i
$944$		−	34.7437i		−	1.13081i
$945$		0			0
$946$	−1.03389	+	7.19084i	−0.0336145	+	0.233794i
$947$	4.94905	−	3.52420i	0.160822	−	0.114521i	−0.496813	−	0.867858i	$-0.665496\pi$
$947$	4.94905	−	3.52420i	0.160822	−	0.114521i	0.657635	+	0.753337i	$0.271557\pi$
$948$		0			0
$949$	2.53984	−	3.56670i	0.0824466	−	0.115780i
$950$	−1.77674	+	5.13356i	−0.0576452	+	0.166555i
$951$		0			0
$952$	−8.12500	+	7.74717i	−0.263333	+	0.251087i
$953$	30.1429	−	34.7868i	0.976424	−	1.12685i	−0.0154819	−	0.999880i	$-0.504928\pi$
$953$	30.1429	−	34.7868i	0.976424	−	1.12685i	0.991906	−	0.126973i	$-0.0405263\pi$
$954$		0			0
$955$	51.9331	+	33.3754i	1.68052	+	1.08000i
$956$	9.69386	−	3.35508i	0.313522	−	0.108511i
$957$		0			0
$958$	2.26379	+	2.87864i	0.0731397	+	0.0930047i
$959$	0.00413884	+	0.00143247i	0.000133650	+	4.62567e-5i
$960$		0			0
$961$	−7.17055	+	29.5574i	−0.231308	+	0.953465i
$962$	0.107165	−	0.234659i	0.00345515	−	0.00756572i
$963$		0			0
$964$	−6.07245	−	9.44891i	−0.195580	−	0.304329i
$965$	25.4126	−	44.0160i	0.818062	−	1.41692i
$966$		0			0
$967$	−21.3193	−	36.9261i	−0.685583	−	1.18746i	−0.973253	−	0.229735i	$-0.926214\pi$
$967$	−21.3193	−	36.9261i	−0.685583	−	1.18746i	0.287670	−	0.957729i	$-0.407119\pi$
$968$	−1.95849	+	3.79894i	−0.0629482	+	0.122102i
$969$		0			0
$970$	−3.86156	−	5.42280i	−0.123987	−	0.174115i
$971$	37.9374	−	11.1394i	1.21747	−	0.357481i	0.390962	−	0.920407i	$-0.372142\pi$
$971$	37.9374	−	11.1394i	1.21747	−	0.357481i	0.826508	+	0.562925i	$0.190324\pi$
$972$		0			0
$973$	22.6609	−	19.6358i	0.726475	−	0.629494i
$974$	1.35925	−	3.39524i	0.0435532	−	0.108791i
$975$		0			0
$976$	2.77817	−	14.4145i	0.0889270	−	0.461397i
$977$	−1.66021	+	34.8522i	−0.0531149	+	1.11502i	0.802248	+	0.596991i	$0.203637\pi$
$977$	−1.66021	+	34.8522i	−0.0531149	+	1.11502i	−0.855363	+	0.518029i	$0.826666\pi$
$978$		0			0
$979$	10.3148	+	29.8028i	0.329664	+	0.952502i
$980$	52.8746	+	15.5254i	1.68902	+	0.495940i
$981$		0			0
$982$	2.30807	+	2.66366i	0.0736536	+	0.0850007i
$983$	−6.80522	−	0.649820i	−0.217053	−	0.0207260i	−0.0140370	−	0.999901i	$-0.504468\pi$
$983$	−6.80522	−	0.649820i	−0.217053	−	0.0207260i	−0.203016	+	0.979175i	$0.565074\pi$
$984$		0			0
$985$	−1.64261	−	17.2022i	−0.0523378	−	0.548107i
$986$	−1.75831	+	0.703921i	−0.0559960	+	0.0224174i
$987$		0			0
$988$	−0.721623	−	0.416629i	−0.0229579	−	0.0132547i
$989$	−32.5182	+	10.5247i	−1.03402	+	0.334664i
$990$		0			0
$991$	−24.3623	+	15.6567i	−0.773895	+	0.497352i	−0.867002	−	0.498304i	$-0.833956\pi$
$991$	−24.3623	+	15.6567i	−0.773895	+	0.497352i	0.0931073	+	0.995656i	$0.470320\pi$
$992$	1.41874	−	1.80408i	0.0450452	−	0.0572796i
$993$		0			0
$994$	0.406974	−	0.426822i	0.0129084	−	0.0135380i
$995$	56.7864	+	40.4374i	1.80025	+	1.28195i
$996$		0			0
$997$	−25.2766	−	10.1192i	−0.800517	−	0.320479i	−0.0649137	−	0.997891i	$-0.520677\pi$
$997$	−25.2766	−	10.1192i	−0.800517	−	0.320479i	−0.735604	+	0.677412i	$0.763101\pi$
$998$	−1.17904	+	4.01544i	−0.0373218	+	0.127106i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	621.2.s.a.494.11		440
3.2	odd	2		207.2.o.a.11.12	✓	440
9.4	even	3		207.2.o.a.149.12	yes	440
9.5	odd	6	inner	621.2.s.a.287.11		440
23.21	odd	22	inner	621.2.s.a.251.11		440
69.44	even	22		207.2.o.a.182.12	yes	440
207.67	odd	66		207.2.o.a.113.12	yes	440
207.113	even	66	inner	621.2.s.a.44.11		440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.12	✓	440	3.2	odd	2
207.2.o.a.113.12	yes	440	207.67	odd	66
207.2.o.a.149.12	yes	440	9.4	even	3
207.2.o.a.182.12	yes	440	69.44	even	22
621.2.s.a.44.11		440	207.113	even	66	inner
621.2.s.a.251.11		440	23.21	odd	22	inner
621.2.s.a.287.11		440	9.5	odd	6	inner
621.2.s.a.494.11		440	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 621 = 3^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	621.s (of order \(66\), degree \(20\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.261583 - 0.0124607i) q^{2} +(-1.92267 + 0.183593i) q^{4} +(3.04369 + 2.90215i) q^{5} +(-0.702638 - 3.64563i) q^{7} +(-1.01908 + 0.146521i) q^{8} +(0.832339 + 0.721226i) q^{10} +(3.45977 - 1.78363i) q^{11} +(0.259083 + 0.0499342i) q^{13} +(-0.229225 - 0.944880i) q^{14} +(3.52828 - 0.680021i) q^{16} +(1.22006 + 2.67157i) q^{17} +(1.48734 + 0.679244i) q^{19} +(-6.38483 - 5.02109i) q^{20} +(0.882791 - 0.509680i) q^{22} +(3.98136 + 2.67373i) q^{23} +(0.603648 + 12.6721i) q^{25} +(0.0683940 + 0.00983357i) q^{26} +(2.02026 + 6.88036i) q^{28} +(-0.234074 + 2.45134i) q^{29} +(0.601339 - 0.472898i) q^{31} +(2.91554 - 0.707302i) q^{32} +(0.352437 + 0.683633i) q^{34} +(8.44156 - 13.1353i) q^{35} +(1.05184 - 3.58222i) q^{37} +(0.397526 + 0.159145i) q^{38} +(-3.52698 - 2.51155i) q^{40} +(-2.75661 + 2.89105i) q^{41} +(-4.40550 + 5.60205i) q^{43} +(-6.32454 + 4.06454i) q^{44} +(1.07477 + 0.649790i) q^{46} +(4.75835 + 2.74724i) q^{47} +(-6.29837 + 2.52149i) q^{49} +(0.315808 + 3.30729i) q^{50} +(-0.507300 - 0.0484413i) q^{52} +(-1.42625 - 1.64598i) q^{53} +(15.7068 + 4.61194i) q^{55} +(1.25021 + 3.61224i) q^{56} +(-0.0306844 + 0.644144i) q^{58} +(1.82992 - 9.49452i) q^{59} +(1.51839 - 3.79277i) q^{61} +(0.151407 - 0.131195i) q^{62} +(-6.14149 + 1.80331i) q^{64} +(0.643652 + 0.903883i) q^{65} +(6.13936 - 11.9087i) q^{67} +(-2.83626 - 4.91255i) q^{68} +(2.04449 - 3.54117i) q^{70} +(0.327930 + 0.510270i) q^{71} +(6.89379 - 15.0953i) q^{73} +(0.230505 - 0.950155i) q^{74} +(-2.98437 - 1.03290i) q^{76} +(-8.93345 - 11.3598i) q^{77} +(1.99885 - 0.691809i) q^{79} +(12.7125 + 8.16984i) q^{80} +(-0.685057 + 0.790598i) q^{82} +(-8.75158 + 8.34461i) q^{83} +(-4.03979 + 11.6722i) q^{85} +(-1.08260 + 1.52030i) q^{86} +(-3.26444 + 2.32459i) q^{88} +(-1.15305 + 8.01966i) q^{89} -0.979609i q^{91} +(-8.14572 - 4.40975i) q^{92} +(1.27894 + 0.659337i) q^{94} +(2.55572 + 6.38388i) q^{95} +(-5.87423 - 1.42507i) q^{97} +(-1.61613 + 0.738060i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q + 27 q^{2} - 29 q^{4} + 33 q^{5} - 11 q^{7} - 44 q^{10} + 33 q^{11} - 9 q^{13} + 33 q^{14} + 3 q^{16} - 44 q^{19} + 33 q^{20} + 27 q^{23} + 11 q^{25} - 44 q^{28} - 27 q^{29} - 3 q^{31} + 33 q^{32}+ \cdots + 22 q^{97}+O(q^{100}) \) 440 * q + 27 * q^2 - 29 * q^4 + 33 * q^5 - 11 * q^7 - 44 * q^10 + 33 * q^11 - 9 * q^13 + 33 * q^14 + 3 * q^16 - 44 * q^19 + 33 * q^20 + 27 * q^23 + 11 * q^25 - 44 * q^28 - 27 * q^29 - 3 * q^31 + 33 * q^32 - 11 * q^34 - 44 * q^37 + 33 * q^38 - 77 * q^40 - 9 * q^41 - 11 * q^43 - 36 * q^46 + 120 * q^47 + 35 * q^49 + 3 * q^50 - 38 * q^52 - 44 * q^55 - 165 * q^56 - 10 * q^58 + 9 * q^59 - 11 * q^61 - 22 * q^64 - 198 * q^65 - 11 * q^67 - 70 * q^70 - 36 * q^73 - 231 * q^74 - 11 * q^76 - 39 * q^77 - 11 * q^79 - 10 * q^82 - 66 * q^83 + q^85 + 33 * q^86 - 99 * q^88 - 63 * q^92 - 42 * q^94 + 93 * q^95 + 22 * q^97

Introduction

L-functions

Modular forms

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Database

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