LMFDB - Embedded newform 621.2.s.a.44.11

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			44.11
Character	$\chi$	$=$	621.44
Dual form			621.2.s.a.494.11

$q$-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 $\left(\mathbb{Z}/621\mathbb{Z}\right)^\times$.

$n$	$28$	$461$
$\chi(n)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{5}{6}\right)$

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	0.139861	−	0.990171i	$-0.455334\pi$
$2$	0.261583	+	0.0124607i	0.184967	+	0.00881107i	0.0451060	+	0.998982i	$0.485637\pi$
$3$		0			0
$3$		0			0
$4$	−1.92267	−	0.183593i	−0.961337	−	0.0917965i
$5$	3.04369	−	2.90215i	1.36118	−	1.29788i	0.445886	−	0.895090i	$-0.352889\pi$
$5$	3.04369	−	2.90215i	1.36118	−	1.29788i	0.915292	−	0.402791i	$-0.131960\pi$
$6$		0			0
$7$	−0.702638	+	3.64563i	−0.265572	+	1.37792i	0.566869	+	0.823808i	$0.308154\pi$
$7$	−0.702638	+	3.64563i	−0.265572	+	1.37792i	−0.832442	+	0.554113i	$0.813058\pi$
$8$	−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	0.892616	−	0.450817i	$-0.148867\pi$
$11$	3.45977	+	1.78363i	1.04316	+	0.537786i	0.150543	+	0.988603i	$0.451898\pi$
$12$		0			0
$13$	0.259083	−	0.0499342i	0.0718568	−	0.0138493i	−0.153196	−	0.988196i	$-0.548957\pi$
$13$	0.259083	−	0.0499342i	0.0718568	−	0.0138493i	0.225053	+	0.974347i	$0.427744\pi$
$14$	−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	−0.702028	−	0.712149i	$-0.747722\pi$
$17$	1.22006	−	2.67157i	0.295909	−	0.647950i	0.997937	+	0.0641992i	$0.0204493\pi$
$18$		0			0
$19$	1.48734	−	0.679244i	0.341218	−	0.155829i	−0.237434	−	0.971404i	$-0.576306\pi$
$19$	1.48734	−	0.679244i	0.341218	−	0.155829i	0.578652	+	0.815575i	$0.303579\pi$
$20$	−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	−0.990837	−	0.135063i	$-0.956876\pi$
$29$	−0.234074	−	2.45134i	−0.0434665	−	0.455201i	0.947371	−	0.320139i	$-0.103730\pi$
$30$		0			0
$31$	0.601339	+	0.472898i	0.108004	+	0.0849350i	0.670700	−	0.741728i	$-0.265994\pi$
$31$	0.601339	+	0.472898i	0.108004	+	0.0849350i	−0.562697	+	0.826663i	$0.690236\pi$
$32$	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	0.999654	+	0.0263193i	$0.00837867\pi$
$37$	1.05184	+	3.58222i	0.172921	+	0.588914i	−0.826733	+	0.562595i	$0.809803\pi$
$38$	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	0.472369	−	0.881401i	$-0.343399\pi$
$41$	−2.75661	−	2.89105i	−0.430510	−	0.451506i	−0.902879	+	0.429895i	$0.858550\pi$
$42$		0			0
$43$	−4.40550	−	5.60205i	−0.671833	−	0.854305i	0.323947	−	0.946075i	$-0.394990\pi$
$43$	−4.40550	−	5.60205i	−0.671833	−	0.854305i	−0.995780	+	0.0917702i	$0.970747\pi$
$44$	−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	−0.111061	−	0.993814i	$-0.535425\pi$
$47$	4.75835	−	2.74724i	0.694077	−	0.400726i	0.805138	+	0.593088i	$0.202091\pi$
$48$		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	−0.845202	−	0.534447i	$-0.820520\pi$
$53$	−1.42625	+	1.64598i	−0.195910	+	0.226092i	0.649292	+	0.760539i	$0.275065\pi$
$54$		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	0.882144	+	0.470979i	$0.156099\pi$
$59$	1.82992	+	9.49452i	0.238235	+	1.23608i	−0.643909	+	0.765102i	$0.722689\pi$
$60$		0			0
$61$	1.51839	+	3.79277i	0.194411	+	0.485614i	0.993259	−	0.115919i	$-0.0369812\pi$
$61$	1.51839	+	3.79277i	0.194411	+	0.485614i	−0.798848	+	0.601533i	$0.794557\pi$
$62$	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	0.885766	+	0.464132i	$0.153634\pi$
$67$	6.13936	+	11.9087i	0.750042	+	1.45488i	−0.135724	+	0.990747i	$0.543336\pi$
$68$	−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	−0.821249	−	0.570569i	$-0.806723\pi$
$71$	0.327930	−	0.510270i	0.0389182	−	0.0605579i	0.860168	+	0.510012i	$0.170359\pi$
$72$		0			0
$73$	6.89379	+	15.0953i	0.806857	+	1.76677i	0.620365	+	0.784313i	$0.286984\pi$
$73$	6.89379	+	15.0953i	0.806857	+	1.76677i	0.186492	+	0.982457i	$0.440288\pi$
$74$	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	0.437189	−	0.899370i	$-0.355974\pi$
$79$	1.99885	+	0.691809i	0.224888	+	0.0778346i	−0.212300	+	0.977205i	$0.568095\pi$
$80$	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	0.0359043	−	0.999355i	$-0.488569\pi$
$83$	−8.75158	−	8.34461i	−0.960611	−	0.915940i	−0.996515	+	0.0834149i	$0.973417\pi$
$84$		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	−0.955028	−	0.296515i	$-0.904175\pi$
$89$	−1.15305	−	8.01966i	−0.122223	−	0.850082i	0.832805	−	0.553567i	$-0.186734\pi$
$90$		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	−0.522603	−	0.852576i	$-0.675039\pi$
$97$	−5.87423	+	1.42507i	−0.596438	+	0.144694i	−0.0738351	+	0.997270i	$0.523524\pi$
$98$	−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	−0.747819	−	0.663903i	$-0.768899\pi$
$101$	−0.493298	+	0.517356i	−0.0490850	+	0.0514789i	0.698734	+	0.715382i	$0.253747\pi$
$102$		0			0
$103$	−16.2006	+	0.771732i	−1.59630	+	0.0760410i	−0.826758	−	0.562558i	$-0.809817\pi$
$103$	−16.2006	+	0.771732i	−1.59630	+	0.0760410i	−0.769539	+	0.638599i	$0.779514\pi$
$104$	−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	0.731069	+	0.682304i	$0.239022\pi$
$107$	−1.68209	+	11.6992i	−0.162614	+	1.13100i	−0.893683	+	0.448700i	$0.851887\pi$
$108$		0			0
$109$	−18.0521	−	8.24414i	−1.72908	−	0.789645i	−0.993710	−	0.111981i	$-0.964280\pi$
$109$	−18.0521	−	8.24414i	−1.72908	−	0.789645i	−0.735372	−	0.677664i	$-0.762992\pi$
$110$	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	−0.470899	−	0.882187i	$-0.656070\pi$
$113$	−0.270422	+	0.139412i	−0.0254392	+	0.0131148i	0.445460	+	0.895302i	$0.353040\pi$
$114$		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	−0.492934	−	0.870067i	$-0.664075\pi$
$127$	1.05634	−	0.678868i	0.0937349	−	0.0602398i	0.586669	+	0.809827i	$0.300439\pi$
$128$	−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	−0.601300	−	0.799023i	$-0.705350\pi$
$131$	−6.63876	+	2.29770i	−0.580031	+	0.200751i	0.0212693	+	0.999774i	$0.493229\pi$
$132$		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	0.866000	−	0.500044i	$-0.166683\pi$
$137$	−0.000589825	−	0.00102161i	−5.03921e−5	−	8.72817e-5i	−0.866051	+	0.499956i	$0.833349\pi$
$138$		0			0
$139$	4.03809	−	6.99418i	0.342507	−	0.593239i	−0.642391	−	0.766377i	$-0.722057\pi$
$139$	4.03809	−	6.99418i	0.342507	−	0.593239i	0.984898	+	0.173138i	$0.0553908\pi$
$140$	−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	0.997765	+	0.0668258i	$0.0212872\pi$
$149$	0.132687	+	2.78545i	0.0108702	+	0.228193i	−0.986895	+	0.161367i	$0.948410\pi$
$150$		0			0
$151$	−3.05152	+	8.81680i	−0.248329	+	0.717501i	0.750092	+	0.661334i	$0.230009\pi$
$151$	−3.05152	+	8.81680i	−0.248329	+	0.717501i	−0.998421	+	0.0561671i	$0.982112\pi$
$152$	−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	−0.962927	−	0.269761i	$-0.913055\pi$
$157$	0.421650	−	4.41572i	0.0336514	−	0.352413i	0.996579	−	0.0826514i	$-0.0263388\pi$
$158$	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	0.575603	−	0.817729i	$-0.304767\pi$
$163$	0.905001	+	0.581609i	0.0708852	+	0.0455551i	−0.504718	+	0.863284i	$0.668404\pi$
$164$	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	−0.956052	−	0.293196i	$-0.905281\pi$
$167$	−12.8153	+	9.12572i	−0.991676	+	0.706169i	−0.0356238	+	0.999365i	$0.511342\pi$
$168$		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	−0.356488	−	0.934300i	$-0.616026\pi$
$173$	8.04110	−	15.5976i	0.611353	−	1.18586i	0.967842	−	0.251560i	$-0.0809437\pi$
$174$		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	−0.613239	−	0.789898i	$-0.710134\pi$
$179$	4.41110	−	15.0228i	0.329701	−	1.12286i	0.942940	−	0.332962i	$-0.108048\pi$
$180$		0			0
$181$	−2.90054	+	0.417035i	−0.215596	+	0.0309980i	−0.249266	−	0.968435i	$-0.580189\pi$
$181$	−2.90054	+	0.417035i	−0.215596	+	0.0309980i	0.0336705	+	0.999433i	$0.489280\pi$
$182$	−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	0.681829	−	0.731512i	$-0.261185\pi$
$191$	14.4137	+	2.77802i	1.04294	+	0.201010i	0.361112	+	0.932522i	$0.382397\pi$
$192$		0			0
$193$	−2.84923	+	11.7447i	−0.205092	+	0.845400i	0.772521	+	0.634989i	$0.218995\pi$
$193$	−2.84923	+	11.7447i	−0.205092	+	0.845400i	−0.977613	+	0.210411i	$0.932520\pi$
$194$	−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	−0.758431	−	0.651753i	$-0.774034\pi$
$197$	−3.10535	+	2.69081i	−0.221247	+	0.191712i	0.537184	+	0.843465i	$0.319488\pi$
$198$		0			0
$199$	16.4077	+	2.35908i	1.16311	+	0.167230i	0.696717	−	0.717346i	$-0.254643\pi$
$199$	16.4077	+	2.35908i	1.16311	+	0.167230i	0.466396	+	0.884576i	$0.345552\pi$
$200$	−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	0.442838	−	0.896602i	$-0.353972\pi$
$211$	10.2841	+	0.982017i	0.707990	+	0.0676048i	0.265152	+	0.964207i	$0.414578\pi$
$212$	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	−0.438102	−	0.898925i	$-0.644349\pi$
$223$	−17.6050	−	3.39309i	−1.17892	−	0.227218i	−0.740817	+	0.671707i	$0.765561\pi$
$224$	−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	−0.975515	−	0.219933i	$-0.929416\pi$
$227$	−14.9425	+	11.7509i	−0.991767	+	0.779935i	−0.0162526	+	0.999868i	$0.505174\pi$
$228$		0			0
$229$	−13.9991	−	8.08237i	−0.925085	−	0.534098i	−0.0398315	−	0.999206i	$-0.512682\pi$
$229$	−13.9991	−	8.08237i	−0.925085	−	0.534098i	−0.885254	+	0.465108i	$0.846015\pi$
$230$	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	0.282260	−	0.959338i	$-0.408916\pi$
$233$	12.5681	−	1.80702i	0.823363	−	0.118382i	0.541103	+	0.840956i	$0.318007\pi$
$234$		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	0.0653221	−	0.997864i	$-0.479193\pi$
$239$	−5.16143	−	1.25215i	−0.333865	−	0.0809948i	−0.399187	+	0.916869i	$0.630708\pi$
$240$		0			0
$241$	2.66476	−	5.16892i	0.171653	−	0.332959i	−0.787279	−	0.616597i	$-0.788511\pi$
$241$	2.66476	−	5.16892i	0.171653	−	0.332959i	0.958932	+	0.283637i	$0.0915412\pi$
$242$	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	0.811131	−	0.584864i	$-0.198852\pi$
$251$	9.76049	+	6.27268i	0.616076	+	0.395928i	−0.195055	+	0.980792i	$0.562488\pi$
$252$		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	−0.991590	−	0.129420i	$-0.958688\pi$
$257$	0.105383	−	1.10362i	0.00657362	−	0.0688421i	0.998163	+	0.0605782i	$0.0192944\pi$
$258$		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	0.717646	+	0.696409i	$0.245220\pi$
$263$	−4.49143	+	12.9771i	−0.276953	+	0.800204i	−0.994599	+	0.103795i	$0.966901\pi$
$264$		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	0.886767	−	0.462216i	$-0.152946\pi$
$269$	9.11016	+	7.89400i	0.555456	+	0.481305i	−0.331311	+	0.943522i	$0.607491\pi$
$270$		0			0
$271$	−16.1529	−	4.74293i	−0.981222	−	0.288113i	−0.248493	−	0.968634i	$-0.579935\pi$
$271$	−16.1529	−	4.74293i	−0.981222	−	0.288113i	−0.732729	+	0.680521i	$0.761754\pi$
$272$	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	0.878954	+	0.476907i	$0.158242\pi$
$277$	14.1883	+	24.5748i	0.852490	+	1.47656i	−0.0264633	+	0.999650i	$0.508425\pi$
$278$	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	0.957415	−	0.288717i	$-0.0932285\pi$
$281$	−0.433611	−	1.78737i	−0.0258671	−	0.106625i	−0.983282	+	0.182091i	$0.941713\pi$
$282$		0			0
$283$	−11.9314	+	4.12950i	−0.709249	+	0.245473i	−0.657790	−	0.753202i	$-0.728508\pi$
$283$	−11.9314	+	4.12950i	−0.709249	+	0.245473i	−0.0514592	+	0.998675i	$0.516387\pi$
$284$	−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	0.810542	−	0.585681i	$-0.199173\pi$
$293$	−0.137444	−	0.193013i	−0.00802954	−	0.0112759i	−0.818571	+	0.574405i	$0.805233\pi$
$294$		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	−0.546460	−	0.837485i	$-0.684025\pi$
$307$	3.74628	−	26.0559i	0.213811	−	1.48709i	0.760271	−	0.649606i	$-0.225066\pi$
$308$	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	−0.444345	−	0.895856i	$-0.646564\pi$
$311$	−14.1350	+	0.673333i	−0.801522	+	0.0381812i	−0.357177	+	0.934037i	$0.616261\pi$
$312$		0			0
$313$	−1.05571	+	1.10720i	−0.0596722	+	0.0625824i	−0.752893	−	0.658143i	$-0.771342\pi$
$313$	−1.05571	+	1.10720i	−0.0596722	+	0.0625824i	0.693221	+	0.720725i	$0.256191\pi$
$314$	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	−0.712520	−	0.701652i	$-0.752446\pi$
$317$	−18.2374	+	4.42435i	−1.02432	+	0.248496i	−0.311797	+	0.950149i	$0.600931\pi$
$318$		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	0.210040	−	0.977693i	$-0.432641\pi$
$331$	−13.7642	−	13.1242i	−0.756552	−	0.721370i	−0.966591	+	0.256322i	$0.917489\pi$
$332$	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	−0.935235	−	0.354028i	$-0.884812\pi$
$337$	−6.80507	+	8.65335i	−0.370696	+	0.471378i	0.564539	+	0.825407i	$0.309054\pi$
$338$	−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	0.671613	−	0.740902i	$-0.265602\pi$
$347$	−5.98854	−	11.6161i	−0.321482	−	0.623588i	−0.993095	+	0.117315i	$0.962571\pi$
$348$		0			0
$349$	−1.25044	+	1.75600i	−0.0669348	+	0.0939967i	−0.846686	−	0.532092i	$-0.821406\pi$
$349$	−1.25044	+	1.75600i	−0.0669348	+	0.0939967i	0.779752	+	0.626089i	$0.215345\pi$
$350$	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	−0.955285	−	0.295687i	$-0.904452\pi$
$353$	−8.79217	−	21.9618i	−0.467960	−	1.16891i	0.487325	−	0.873221i	$-0.337973\pi$
$354$		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	0.672037	−	0.740518i	$-0.265420\pi$
$359$	31.0308	−	9.11147i	1.63774	−	0.480885i	0.965707	+	0.259633i	$0.0836015\pi$
$360$		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	−0.164525	−	0.986373i	$-0.552609\pi$
$367$	11.6368	−	6.71851i	0.607436	−	0.350703i	0.771961	+	0.635670i	$0.219276\pi$
$368$	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	0.999969	+	0.00793156i	$0.00252472\pi$
$373$	18.5467	+	19.4512i	0.960311	+	1.00714i	−0.0396578	+	0.999213i	$0.512627\pi$
$374$	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	0.464046	−	0.885811i	$-0.346397\pi$
$379$	−10.4054	−	16.1911i	−0.534487	−	0.831679i	−0.998534	+	0.0541323i	$0.982761\pi$
$380$	−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	0.159926	−	0.987129i	$-0.448875\pi$
$383$	−14.9063	−	11.7224i	−0.761674	−	0.598987i	−0.921600	+	0.388142i	$0.873117\pi$
$384$		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	−0.426035	−	0.904707i	$-0.640090\pi$
$389$	1.65809	−	34.8077i	0.0840687	−	1.76482i	0.510104	−	0.860113i	$-0.329607\pi$
$390$		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	−0.441224	−	0.897397i	$-0.645456\pi$
$397$	10.4790	−	22.9457i	0.525924	−	1.15161i	0.967148	−	0.254215i	$-0.0818172\pi$
$398$	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	−0.833447	−	0.552599i	$-0.813636\pi$
$401$	−28.0713	+	5.41030i	−1.40181	+	0.270177i	−0.568365	+	0.822776i	$0.692424\pi$
$402$		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	0.0709013	−	0.997483i	$-0.477412\pi$
$409$	21.6521	−	20.6453i	1.07063	−	1.02084i	0.999727	−	0.0233589i	$-0.00743603\pi$
$410$	−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	−0.884207	−	0.467095i	$-0.845301\pi$
$419$	−9.41010	+	8.97251i	−0.459713	+	0.438336i	0.424494	+	0.905431i	$0.360452\pi$
$420$		0			0
$421$	−0.793744	+	4.11834i	−0.0386847	+	0.200715i	−0.996129	−	0.0879025i	$-0.971984\pi$
$421$	−0.793744	+	4.11834i	−0.0386847	+	0.200715i	0.957444	+	0.288618i	$0.0931957\pi$
$422$	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	0.601123	+	0.799157i	$0.294720\pi$
$431$	−8.23138	+	18.0242i	−0.396491	+	0.868195i	−0.997614	+	0.0690383i	$0.978007\pi$
$432$		0			0
$433$	−2.39698	+	1.09467i	−0.115192	+	0.0526063i	−0.472177	−	0.881504i	$-0.656532\pi$
$433$	−2.39698	+	1.09467i	−0.115192	+	0.0526063i	0.356986	+	0.934110i	$0.383805\pi$
$434$	−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	−0.982138	−	0.188160i	$-0.939748\pi$
$439$	0.281569	−	5.91086i	0.0134386	−	0.282110i	0.995577	−	0.0939499i	$-0.0299494\pi$
$440$	−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	0.991138	+	0.132834i	$0.0424076\pi$
$443$	0.906099	+	9.48910i	0.0430501	+	0.450841i	−0.948088	+	0.318007i	$0.896986\pi$
$444$		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	0.612370	−	0.790571i	$-0.290216\pi$
$449$	−7.65255	−	11.9076i	−0.361146	−	0.561954i	−0.973517	+	0.228617i	$0.926580\pi$
$450$		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	0.965271	+	0.261251i	$0.0841350\pi$
$457$	21.1977	+	26.9551i	0.991586	+	1.26090i	0.0263154	+	0.999654i	$0.491623\pi$
$458$	−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	−0.940352	−	0.340203i	$-0.889504\pi$
$461$	−23.9595	+	13.8330i	−1.11590	+	0.644267i	−0.175551	+	0.984470i	$0.556171\pi$
$462$		0			0
$463$	0.173922	+	0.0696279i	0.00808285	+	0.00323588i	0.375700	−	0.926741i	$-0.377402\pi$
$463$	0.173922	+	0.0696279i	0.00808285	+	0.00323588i	−0.367618	+	0.929977i	$0.619826\pi$
$464$	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	0.127201	+	0.991877i	$0.459401\pi$
$467$	−18.8588	+	21.7643i	−0.872683	+	1.00713i	−0.999884	+	0.0152530i	$0.995145\pi$
$468$		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	−0.586574	−	0.809895i	$-0.699524\pi$
$479$	8.11157	−	11.3911i	0.370627	−	0.520473i	0.957201	+	0.289422i	$0.0934632\pi$
$480$		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	0.994339	−	0.106252i	$-0.0338850\pi$
$487$	5.80138	+	12.7033i	0.262886	+	0.575639i	−0.731454	+	0.681891i	$0.761158\pi$
$488$	−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	−0.561201	−	0.827679i	$-0.689661\pi$
$491$	8.31954	−	10.5792i	0.375455	−	0.477430i	0.936657	+	0.350249i	$0.113903\pi$
$492$		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	−0.999469	−	0.0325903i	$-0.989624\pi$
$499$	−5.22670	−	15.1016i	−0.233979	−	0.676039i	0.765490	−	0.643448i	$-0.222497\pi$
$500$	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	0.989373	+	0.145402i	$0.0464476\pi$
$503$	1.81756	+	12.6414i	0.0810410	+	0.563653i	−0.908332	+	0.418251i	$0.862643\pi$
$504$		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	−0.764274	−	0.644891i	$-0.776903\pi$
$509$	5.27664	−	13.1804i	0.233883	−	0.584211i	0.998157	+	0.0606799i	$0.0193269\pi$
$510$		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	−0.369390	−	0.929274i	$-0.620433\pi$
$521$	5.63432	−	39.1875i	0.246844	−	1.71684i	0.616234	−	0.787563i	$-0.288657\pi$
$522$		0			0
$523$	10.2065	+	4.66115i	0.446299	+	0.203818i	0.625870	−	0.779927i	$-0.284744\pi$
$523$	10.2065	+	4.66115i	0.446299	+	0.203818i	−0.179572	+	0.983745i	$0.557471\pi$
$524$	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	−0.905822	−	0.423659i	$-0.860745\pi$
$541$	−20.8576	+	13.4044i	−0.896739	+	0.576299i	0.00908220	+	0.999959i	$0.497109\pi$
$542$	−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	−0.904553	−	0.426360i	$-0.859796\pi$
$547$	−6.92108	−	28.5291i	−0.295924	−	1.21981i	0.608630	−	0.793455i	$-0.291720\pi$
$548$	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	0.249152	−	0.968464i	$-0.419848\pi$
$557$	−1.53026	−	0.449323i	−0.0648390	−	0.0190384i	−0.313991	+	0.949426i	$0.601666\pi$
$558$		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	0.911651	+	0.410966i	$0.134808\pi$
$563$	1.02486	+	21.5145i	0.0431928	+	0.906728i	−0.868458	+	0.495763i	$0.834889\pi$
$564$		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	0.562250	−	0.826967i	$-0.309936\pi$
$569$	30.3144	−	2.89467i	1.27084	−	0.121351i	0.708594	+	0.705616i	$0.249330\pi$
$570$		0			0
$571$	−2.97623	+	31.1685i	−0.124551	+	1.30436i	0.689805	+	0.723996i	$0.257696\pi$
$571$	−2.97623	+	31.1685i	−0.124551	+	1.30436i	−0.814356	+	0.580366i	$0.802910\pi$
$572$	−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	0.956917	−	0.290362i	$-0.0937758\pi$
$577$	26.1902	+	16.8314i	1.09031	+	0.700701i	0.133395	+	0.991063i	$0.457412\pi$
$578$	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	−0.572963	−	0.819581i	$-0.694206\pi$
$587$	10.3454	−	20.0672i	0.426999	−	0.828262i	0.999962	−	0.00868140i	$-0.00276341\pi$
$588$		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	−0.950198	−	0.311646i	$-0.899120\pi$
$593$	0.429753	−	1.46360i	0.0176478	−	0.0601030i	0.967846	+	0.251543i	$0.0809379\pi$
$594$		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	−0.100185	−	0.994969i	$-0.531943\pi$
$599$	−24.7668	−	14.2991i	−1.01195	−	0.584247i	−0.911761	+	0.410722i	$0.865277\pi$
$600$		0			0
$601$	−7.53928	+	5.92896i	−0.307534	+	0.241847i	−0.759983	−	0.649943i	$-0.774793\pi$
$601$	−7.53928	+	5.92896i	−0.307534	+	0.241847i	0.452449	+	0.891790i	$0.350550\pi$
$602$	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	0.306657	+	0.951820i	$0.400790\pi$
$607$	−9.90570	+	40.8318i	−0.402060	+	1.65731i	−0.708717	+	0.705493i	$0.750726\pi$
$608$	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	−0.161451	−	0.986881i	$-0.551618\pi$
$613$	−14.7166	−	2.11593i	−0.594399	−	0.0854617i	−0.432948	+	0.901419i	$0.642527\pi$
$614$	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	0.601775	−	0.798666i	$-0.294461\pi$
$617$	25.8710	+	2.47038i	1.04153	+	0.0994536i	0.439751	+	0.898120i	$0.355067\pi$
$618$		0			0
$619$	14.9413	+	0.711739i	0.600540	+	0.0286072i	0.345651	−	0.938363i	$-0.387658\pi$
$619$	14.9413	+	0.711739i	0.600540	+	0.0286072i	0.254889	+	0.966970i	$0.417961\pi$
$620$	−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	−0.618035	−	0.786151i	$-0.712071\pi$
$631$	1.81259	−	1.57062i	0.0721583	−	0.0625255i	0.690193	+	0.723625i	$0.257526\pi$
$632$	−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	−0.599062	−	0.800703i	$-0.704460\pi$
$641$	0.957930	−	0.753324i	0.0378360	−	0.0297545i	0.636898	+	0.770948i	$0.280217\pi$
$642$		0			0
$643$	14.1568	+	8.17341i	0.558288	+	0.322328i	0.752458	−	0.658640i	$-0.228868\pi$
$643$	14.1568	+	8.17341i	0.558288	+	0.322328i	−0.194170	+	0.980968i	$0.562201\pi$
$644$	−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	0.175396	−	0.984498i	$-0.443879\pi$
$647$	15.7972	−	2.27130i	0.621053	−	0.0892939i	0.445657	+	0.895204i	$0.352970\pi$
$648$		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	−0.400843	−	0.916147i	$-0.631283\pi$
$653$	−30.0751	−	7.29613i	−1.17693	−	0.285520i	−0.776086	+	0.630627i	$0.782798\pi$
$654$		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	−0.214292	−	0.976770i	$-0.568744\pi$
$659$	7.82109	−	3.13109i	0.304666	−	0.121970i	0.518958	+	0.854800i	$0.326320\pi$
$660$		0			0
$661$	9.30455	−	6.62574i	0.361905	−	0.257712i	−0.384611	−	0.923079i	$-0.625664\pi$
$661$	9.30455	−	6.62574i	0.361905	−	0.257712i	0.746516	+	0.665367i	$0.231725\pi$
$662$	−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	−0.447655	−	0.894206i	$-0.647741\pi$
$673$	−18.6263	+	1.77859i	−0.717990	+	0.0685598i	−0.270335	+	0.962766i	$0.587135\pi$
$674$	−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	0.254992	+	0.966943i	$0.417927\pi$
$677$	−14.1329	+	40.8342i	−0.543170	+	1.56939i	−0.798162	+	0.602443i	$0.794194\pi$
$678$		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	0.128412	−	0.991721i	$-0.459012\pi$
$683$	−21.8205	−	18.9076i	−0.834940	−	0.723479i	−0.963352	+	0.268241i	$0.913558\pi$
$684$		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	0.975037	−	0.222043i	$-0.0712726\pi$
$691$	7.76050	+	13.4416i	0.295223	+	0.511342i	−0.679813	+	0.733385i	$0.737939\pi$
$692$	−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	−0.347494	−	0.937682i	$-0.612967\pi$
$701$	9.56055	−	6.14419i	0.361097	−	0.232063i	0.708591	+	0.705619i	$0.249331\pi$
$702$		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	0.326242	−	0.945286i	$-0.394218\pi$
$709$	−12.2578	−	8.72875i	−0.460352	−	0.327815i	−0.786593	+	0.617471i	$0.788157\pi$
$710$	−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	0.691776	−	0.722112i	$-0.256829\pi$
$719$	16.0632	+	7.33582i	0.599057	+	0.273580i	−0.0927192	+	0.995692i	$0.529556\pi$
$720$		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	0.00678467	−	0.999977i	$-0.497840\pi$
$727$	27.1060	−	28.4280i	1.00531	−	1.05433i	0.998522	−	0.0543578i	$-0.0173112\pi$
$728$	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	−0.999709	−	0.0241032i	$-0.992327\pi$
$733$	−7.02712	+	17.5529i	−0.259553	+	0.648331i	0.740157	+	0.672434i	$0.234751\pi$
$734$	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	0.858169	+	0.513368i	$0.171602\pi$
$739$	4.87676	+	33.9186i	0.179394	+	1.24772i	−0.678774	+	0.734347i	$0.737488\pi$
$740$	−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	0.784120	+	0.620609i	$0.213114\pi$
$743$	15.0299	+	43.4262i	0.551395	+	1.59315i	−0.232725	+	0.972542i	$0.574764\pi$
$744$		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	−0.996241	−	0.0866245i	$-0.972392\pi$
$751$	−18.5579	+	23.5982i	−0.677186	+	0.861112i	0.319055	+	0.947736i	$0.396634\pi$
$752$	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	−0.929995	−	0.367572i	$-0.880189\pi$
$757$	−5.75878	+	8.96084i	−0.209306	+	0.325687i	0.720689	+	0.693259i	$0.243826\pi$
$758$	−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	−0.983981	−	0.178276i	$-0.942948\pi$
$761$	−15.4051	−	29.8818i	−0.558435	−	1.08321i	0.425545	−	0.904937i	$-0.360082\pi$
$762$		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	−0.984631	−	0.174647i	$-0.944122\pi$
$769$	−3.75589	−	19.4874i	−0.135441	−	0.702734i	0.849190	−	0.528087i	$-0.177091\pi$
$770$	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	−0.220660	−	0.975351i	$-0.570821\pi$
$773$	3.36480	−	0.987993i	0.121023	−	0.0355357i	0.341683	+	0.939815i	$0.389003\pi$
$774$		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	0.998106	−	0.0615100i	$-0.0195916\pi$
$787$	24.9445	+	26.1610i	0.889174	+	0.932539i	−0.108932	+	0.994049i	$0.534743\pi$
$788$	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	0.126892	−	0.991917i	$-0.459500\pi$
$797$	−22.7868	−	17.9197i	−0.807149	−	0.634749i	−0.934040	+	0.357168i	$0.883742\pi$
$798$		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	−0.884422	−	0.466689i	$-0.845447\pi$
$809$	−31.5971	+	14.4299i	−1.11089	+	0.507328i	−0.226473	+	0.974017i	$0.572719\pi$
$810$		0			0
$811$	−2.55975	+	5.60508i	−0.0898851	+	0.196821i	−0.949236	−	0.314566i	$-0.898141\pi$
$811$	−2.55975	+	5.60508i	−0.0898851	+	0.196821i	0.859350	+	0.511387i	$0.170868\pi$
$812$	−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	−0.860568	−	0.509336i	$-0.829891\pi$
$821$	3.65776	−	18.9783i	0.127657	−	0.662346i	0.988225	−	0.153010i	$-0.0488967\pi$
$822$		0			0
$823$	4.72951	−	4.50958i	0.164860	−	0.157194i	−0.603158	−	0.797622i	$-0.706091\pi$
$823$	4.72951	−	4.50958i	0.164860	−	0.157194i	0.768019	+	0.640427i	$0.221243\pi$
$824$	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	0.147214	−	0.989105i	$-0.452969\pi$
$839$	−16.6000	−	8.55787i	−0.573094	−	0.295451i	−0.720308	+	0.693654i	$0.756000\pi$
$840$		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	−0.967051	−	0.254584i	$-0.918062\pi$
$853$	0.578891	−	12.1524i	0.0198208	−	0.416091i	0.986872	−	0.161507i	$-0.0516354\pi$
$854$	−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	0.931103	+	0.364758i	$0.118848\pi$
$857$	2.51343	+	26.3218i	0.0858570	+	0.899136i	−0.845245	+	0.534378i	$0.820546\pi$
$858$		0			0
$859$	−17.6671	−	13.8936i	−0.602794	−	0.474042i	0.269516	−	0.962996i	$-0.413136\pi$
$859$	−17.6671	−	13.8936i	−0.602794	−	0.474042i	−0.872310	+	0.488954i	$0.837379\pi$
$860$	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	0.970604	+	0.240681i	$0.0773707\pi$
$863$	23.1000	+	35.9442i	0.786332	+	1.22356i	−0.184273	+	0.982875i	$0.558993\pi$
$864$		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	−0.292444	−	0.956283i	$-0.594469\pi$
$877$	−34.4711	−	13.8001i	−1.16401	−	0.465998i	−0.871562	+	0.490285i	$0.836893\pi$
$878$	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	−0.153213	−	0.988193i	$-0.548962\pi$
$881$	25.1322	−	29.0041i	0.846726	−	0.977174i	0.999939	+	0.0110188i	$0.00350745\pi$
$882$		0			0
$883$	8.16884	−	2.39859i	0.274903	−	0.0807189i	−0.141375	−	0.989956i	$-0.545152\pi$
$883$	8.16884	−	2.39859i	0.274903	−	0.0807189i	0.416278	+	0.909237i	$0.363334\pi$
$884$	−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	0.998861	−	0.0477233i	$-0.0151966\pi$
$887$	1.60270	+	8.31561i	0.0538135	+	0.279211i	−0.945047	+	0.326934i	$0.893984\pi$
$888$		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	0.923178	−	0.384373i	$-0.125582\pi$
$907$	42.5015	+	14.7099i	1.41124	+	0.488435i	0.488063	+	0.872808i	$0.337704\pi$
$908$	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	0.132861	−	0.991135i	$-0.457584\pi$
$911$	−25.6804	−	24.4862i	−0.850829	−	0.811264i	−0.983690	+	0.179871i	$0.942432\pi$
$912$		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	$0.191361\pi$
$919$			34.2932i			1.13123i	−0.824670	+	0.565614i	$0.808639\pi$
$920$	−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	−0.107643	−	0.994190i	$-0.534330\pi$
$929$	27.1433	−	28.4671i	0.890543	−	0.933974i	0.998185	+	0.0602154i	$0.0191788\pi$
$930$		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	0.854009	−	0.520258i	$-0.174164\pi$
$937$	31.2252	+	14.2601i	1.02008	+	0.465856i	0.166072	+	0.986114i	$0.446891\pi$
$938$	−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	−0.115619	−	0.993294i	$-0.536885\pi$
$941$	19.2162	−	9.90662i	0.626429	−	0.322947i	0.742048	+	0.670347i	$0.233855\pi$
$942$		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	0.657635	−	0.753337i	$-0.271557\pi$
$947$	4.94905	+	3.52420i	0.160822	+	0.114521i	−0.496813	+	0.867858i	$0.665496\pi$
$948$		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	0.991906	+	0.126973i	$0.0405263\pi$
$953$	30.1429	+	34.7868i	0.976424	+	1.12685i	−0.0154819	+	0.999880i	$0.504928\pi$
$954$		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	0.287670	+	0.957729i	$0.407119\pi$
$967$	−21.3193	+	36.9261i	−0.685583	+	1.18746i	−0.973253	+	0.229735i	$0.926214\pi$
$968$	−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	0.826508	−	0.562925i	$-0.190324\pi$
$971$	37.9374	+	11.1394i	1.21747	+	0.357481i	0.390962	+	0.920407i	$0.372142\pi$
$972$		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	−0.855363	−	0.518029i	$-0.826666\pi$
$977$	−1.66021	−	34.8522i	−0.0531149	−	1.11502i	0.802248	−	0.596991i	$-0.203637\pi$
$978$		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	−0.203016	−	0.979175i	$-0.565074\pi$
$983$	−6.80522	+	0.649820i	−0.217053	+	0.0207260i	−0.0140370	+	0.999901i	$0.504468\pi$
$984$		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	0.0931073	−	0.995656i	$-0.470320\pi$
$991$	−24.3623	−	15.6567i	−0.773895	−	0.497352i	−0.867002	+	0.498304i	$0.833956\pi$
$992$	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	−0.735604	−	0.677412i	$-0.763101\pi$
$997$	−25.2766	+	10.1192i	−0.800517	+	0.320479i	−0.0649137	+	0.997891i	$0.520677\pi$
$998$	−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.44.11		440
3.2	odd	2		207.2.o.a.113.12	yes	440
9.2	odd	6	inner	621.2.s.a.251.11		440
9.7	even	3		207.2.o.a.182.12	yes	440
23.11	odd	22	inner	621.2.s.a.287.11		440
69.11	even	22		207.2.o.a.149.12	yes	440
207.11	even	66	inner	621.2.s.a.494.11		440
207.34	odd	66		207.2.o.a.11.12	✓	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.12	✓	440	207.34	odd	66
207.2.o.a.113.12	yes	440	3.2	odd	2
207.2.o.a.149.12	yes	440	69.11	even	22
207.2.o.a.182.12	yes	440	9.7	even	3
621.2.s.a.44.11		440	1.1	even	1	trivial
621.2.s.a.251.11		440	9.2	odd	6	inner
621.2.s.a.287.11		440	23.11	odd	22	inner
621.2.s.a.494.11		440	207.11	even	66	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:	\( N \)	\(=\)	\( 621 = 3^{3} \cdot 23 \)
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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