LMFDB - Embedded newform 441.2.bg.a.278.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(17,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 25]))

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

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

chi := DirichletCharacter("441.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bg (of order $42$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			278.16
Character	$\chi$	$=$	441.278
Dual form			441.2.bg.a.395.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.07888 - 0.815901i) q^{2} +(2.18995 - 2.03198i) q^{4} +(2.05954 - 1.40417i) q^{5} +(-1.91279 - 1.82790i) q^{7} +(0.956806 - 1.98683i) q^{8} +O(q^{10})$	\(q+(2.07888 - 0.815901i) q^{2} +(2.18995 - 2.03198i) q^{4} +(2.05954 - 1.40417i) q^{5} +(-1.91279 - 1.82790i) q^{7} +(0.956806 - 1.98683i) q^{8} +(3.13588 - 4.59948i) q^{10} +(-0.173548 + 1.15142i) q^{11} +(1.20405 + 0.960194i) q^{13} +(-5.46786 - 2.23934i) q^{14} +(-0.0784720 + 1.04714i) q^{16} +(-2.49422 + 0.769366i) q^{17} +(0.129636 + 0.0748453i) q^{19} +(1.65705 - 7.26000i) q^{20} +(0.578657 + 2.53526i) q^{22} +(-0.369109 + 1.19662i) q^{23} +(0.443305 - 1.12952i) q^{25} +(3.28649 + 1.01375i) q^{26} +(-7.90317 - 0.116256i) q^{28} +(-0.805580 - 0.183868i) q^{29} +(8.87043 - 5.12134i) q^{31} +(1.99122 + 6.45538i) q^{32} +(-4.55747 + 3.63446i) q^{34} +(-6.50616 - 1.07874i) q^{35} +(8.79713 + 8.16255i) q^{37} +(0.330564 + 0.0498245i) q^{38} +(-0.819266 - 5.43547i) q^{40} +(-6.87743 - 3.31199i) q^{41} +(-9.17465 + 4.41828i) q^{43} +(1.95959 + 2.87420i) q^{44} +(0.208991 + 2.78879i) q^{46} +(-1.43464 - 3.65541i) q^{47} +(0.317563 + 6.99279i) q^{49} -2.70984i q^{50} +(4.58789 - 0.343815i) q^{52} +(2.28911 + 2.46707i) q^{53} +(1.25936 + 2.61508i) q^{55} +(-5.46190 + 2.05145i) q^{56} +(-1.82472 + 0.275033i) q^{58} +(-8.87123 - 6.04830i) q^{59} +(2.83787 - 3.05850i) q^{61} +(14.2621 - 17.8841i) q^{62} +(8.09705 + 10.1534i) q^{64} +(3.82806 + 0.286873i) q^{65} +(-4.19487 - 7.26573i) q^{67} +(-3.89889 + 6.75308i) q^{68} +(-14.4057 + 3.06580i) q^{70} +(-14.2924 + 3.26215i) q^{71} +(10.1462 + 3.98209i) q^{73} +(24.9480 + 9.79138i) q^{74} +(0.435980 - 0.0995096i) q^{76} +(2.43664 - 1.88520i) q^{77} +(-0.550642 + 0.953740i) q^{79} +(1.30874 + 2.26681i) q^{80} +(-16.9996 - 1.27395i) q^{82} +(3.71031 + 4.65258i) q^{83} +(-4.05663 + 5.08686i) q^{85} +(-15.4681 + 16.6707i) q^{86} +(2.12162 + 1.44650i) q^{88} +(-8.96124 + 1.35069i) q^{89} +(-0.547952 - 4.03753i) q^{91} +(1.62318 + 3.37056i) q^{92} +(-5.96490 - 6.42863i) q^{94} +(0.372086 - 0.0278840i) q^{95} -9.69774i q^{97} +(6.36560 + 14.2781i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) $ 216 * q - 16 * q^4 + 2 * q^7	$ 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) $ 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{41}{42}\right)$	$-1$

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 $

$2$	2.07888	−	0.815901i	1.46999	−	0.576929i	0.510803	−	0.859698i	$-0.329348\pi$
$2$	2.07888	−	0.815901i	1.46999	−	0.576929i	0.959188	+	0.282769i	$0.0912529\pi$
$3$		0			0
$3$		0			0
$4$	2.18995	−	2.03198i	1.09498	−	1.01599i
$5$	2.05954	−	1.40417i	0.921054	−	0.627964i	−0.00717441	−	0.999974i	$-0.502284\pi$
$5$	2.05954	−	1.40417i	0.921054	−	0.627964i	0.928229	+	0.372010i	$0.121331\pi$
$6$		0			0
$7$	−1.91279	−	1.82790i	−0.722968	−	0.690881i
$7$	−1.91279	−	1.82790i	−0.722968	−	0.690881i
$8$	0.956806	−	1.98683i	0.338282	−	0.702450i
$9$		0			0
$10$	3.13588	−	4.59948i	0.991651	−	1.45448i
$11$	−0.173548	+	1.15142i	−0.0523268	+	0.347166i	0.947313	+	0.320311i	$0.103787\pi$
$11$	−0.173548	+	1.15142i	−0.0523268	+	0.347166i	−0.999639	+	0.0268550i	$0.991451\pi$
$12$		0			0
$13$	1.20405	+	0.960194i	0.333942	+	0.266310i	0.776076	−	0.630639i	$-0.217207\pi$
$13$	1.20405	+	0.960194i	0.333942	+	0.266310i	−0.442134	+	0.896949i	$0.645779\pi$
$14$	−5.46786	−	2.23934i	−1.46135	−	0.598488i
$15$		0			0
$16$	−0.0784720	+	1.04714i	−0.0196180	+	0.261784i
$17$	−2.49422	+	0.769366i	−0.604938	+	0.186599i	−0.582069	−	0.813140i	$-0.697756\pi$
$17$	−2.49422	+	0.769366i	−0.604938	+	0.186599i	−0.0228697	+	0.999738i	$0.507280\pi$
$18$		0			0
$19$	0.129636	+	0.0748453i	0.0297405	+	0.0171707i	0.514797	−	0.857312i	$-0.327867\pi$
$19$	0.129636	+	0.0748453i	0.0297405	+	0.0171707i	−0.485056	+	0.874483i	$0.661201\pi$
$20$	1.65705	−	7.26000i	0.370527	−	1.62339i
$21$		0			0
$22$	0.578657	+	2.53526i	0.123370	+	0.540519i
$23$	−0.369109	+	1.19662i	−0.0769645	+	0.249513i	−0.985876	−	0.167476i	$-0.946438\pi$
$23$	−0.369109	+	1.19662i	−0.0769645	+	0.249513i	0.908912	+	0.416989i	$0.136915\pi$
$24$		0			0
$25$	0.443305	−	1.12952i	0.0886610	−	0.225904i
$26$	3.28649	+	1.01375i	0.644534	+	0.198812i
$27$		0			0
$28$	−7.90317	−	0.116256i	−1.49356	−	0.0219704i
$29$	−0.805580	−	0.183868i	−0.149592	−	0.0341435i	0.147069	−	0.989126i	$-0.453016\pi$
$29$	−0.805580	−	0.183868i	−0.149592	−	0.0341435i	−0.296661	+	0.954983i	$0.595873\pi$
$30$		0			0
$31$	8.87043	−	5.12134i	1.59318	−	0.919820i	0.600418	−	0.799687i	$-0.295001\pi$
$31$	8.87043	−	5.12134i	1.59318	−	0.919820i	0.992758	−	0.120134i	$-0.0383323\pi$
$32$	1.99122	+	6.45538i	0.352002	+	1.14116i
$33$		0			0
$34$	−4.55747	+	3.63446i	−0.781600	+	0.623305i
$35$	−6.50616	−	1.07874i	−1.09974	−	0.182341i
$36$		0			0
$37$	8.79713	+	8.16255i	1.44624	+	1.34191i	0.834706	+	0.550695i	$0.185637\pi$
$37$	8.79713	+	8.16255i	1.44624	+	1.34191i	0.611533	+	0.791219i	$0.290553\pi$
$38$	0.330564	+	0.0498245i	0.0536246	+	0.00808260i
$39$		0			0
$40$	−0.819266	−	5.43547i	−0.129537	−	0.859424i
$41$	−6.87743	−	3.31199i	−1.07407	−	0.517247i	−0.188656	−	0.982043i	$-0.560413\pi$
$41$	−6.87743	−	3.31199i	−1.07407	−	0.517247i	−0.885418	+	0.464797i	$0.846127\pi$
$42$		0			0
$43$	−9.17465	+	4.41828i	−1.39912	+	0.673781i	−0.972983	−	0.230877i	$-0.925841\pi$
$43$	−9.17465	+	4.41828i	−1.39912	+	0.673781i	−0.426138	+	0.904658i	$0.640126\pi$
$44$	1.95959	+	2.87420i	0.295420	+	0.433301i
$45$		0			0
$46$	0.208991	+	2.78879i	0.0308140	+	0.411185i
$47$	−1.43464	−	3.65541i	−0.209264	−	0.533196i	0.787249	−	0.616635i	$-0.211505\pi$
$47$	−1.43464	−	3.65541i	−0.209264	−	0.533196i	−0.996513	+	0.0834395i	$0.973409\pi$
$48$		0			0
$49$	0.317563	+	6.99279i	0.0453662	+	0.998970i
$50$		−	2.70984i		−	0.383229i
$51$		0			0
$52$	4.58789	−	0.343815i	0.636226	−	0.0476786i
$53$	2.28911	+	2.46707i	0.314433	+	0.338879i	0.870417	−	0.492314i	$-0.163849\pi$
$53$	2.28911	+	2.46707i	0.314433	+	0.338879i	−0.555984	+	0.831193i	$0.687658\pi$
$54$		0			0
$55$	1.25936	+	2.61508i	0.169812	+	0.352618i
$56$	−5.46190	+	2.05145i	−0.729877	+	0.274136i
$57$		0			0
$58$	−1.82472	+	0.275033i	−0.239598	+	0.0361136i
$59$	−8.87123	−	6.04830i	−1.15494	−	0.787422i	−0.174577	−	0.984644i	$-0.555856\pi$
$59$	−8.87123	−	6.04830i	−1.15494	−	0.787422i	−0.980359	+	0.197222i	$0.936808\pi$
$60$		0			0
$61$	2.83787	−	3.05850i	0.363352	−	0.391601i	−0.524742	−	0.851261i	$-0.675838\pi$
$61$	2.83787	−	3.05850i	0.363352	−	0.391601i	0.888095	+	0.459660i	$0.152029\pi$
$62$	14.2621	−	17.8841i	1.81128	−	2.27128i
$63$		0			0
$64$	8.09705	+	10.1534i	1.01213	+	1.26917i
$65$	3.82806	+	0.286873i	0.474812	+	0.0355822i
$66$		0			0
$67$	−4.19487	−	7.26573i	−0.512485	−	0.887650i	−0.999895	−	0.0144772i	$-0.995392\pi$
$67$	−4.19487	−	7.26573i	−0.512485	−	0.887650i	0.487410	−	0.873173i	$-0.337942\pi$
$68$	−3.89889	+	6.75308i	−0.472810	+	0.818931i
$69$		0			0
$70$	−14.4057	+	3.06580i	−1.72181	+	0.366433i
$71$	−14.2924	+	3.26215i	−1.69620	+	0.387146i	−0.957848	−	0.287275i	$-0.907251\pi$
$71$	−14.2924	+	3.26215i	−1.69620	+	0.387146i	−0.738348	+	0.674420i	$0.764394\pi$
$72$		0			0
$73$	10.1462	+	3.98209i	1.18752	+	0.466068i	0.875131	−	0.483885i	$-0.160775\pi$
$73$	10.1462	+	3.98209i	1.18752	+	0.466068i	0.312391	+	0.949954i	$0.398870\pi$
$74$	24.9480	+	9.79138i	2.90015	+	1.13822i
$75$		0			0
$76$	0.435980	−	0.0995096i	0.0500104	−	0.0114145i
$77$	2.43664	−	1.88520i	0.277681	−	0.214838i
$78$		0			0
$79$	−0.550642	+	0.953740i	−0.0619521	+	0.107304i	−0.895338	−	0.445387i	$-0.853066\pi$
$79$	−0.550642	+	0.953740i	−0.0619521	+	0.107304i	0.833386	+	0.552692i	$0.186399\pi$
$80$	1.30874	+	2.26681i	0.146322	+	0.253437i
$81$		0			0
$82$	−16.9996	−	1.27395i	−1.87729	−	0.140684i
$83$	3.71031	+	4.65258i	0.407260	+	0.510687i	0.942589	−	0.333956i	$-0.108384\pi$
$83$	3.71031	+	4.65258i	0.407260	+	0.510687i	−0.535329	+	0.844644i	$0.679812\pi$
$84$		0			0
$85$	−4.05663	+	5.08686i	−0.440004	+	0.551747i
$86$	−15.4681	+	16.6707i	−1.66797	+	1.79765i
$87$		0			0
$88$	2.12162	+	1.44650i	0.226165	+	0.154197i
$89$	−8.96124	+	1.35069i	−0.949889	+	0.143173i	−0.605669	−	0.795716i	$-0.707095\pi$
$89$	−8.96124	+	1.35069i	−0.949889	+	0.143173i	−0.344220	+	0.938889i	$0.611857\pi$
$90$		0			0
$91$	−0.547952	−	4.03753i	−0.0574410	−	0.423248i
$92$	1.62318	+	3.37056i	0.169228	+	0.351405i
$93$		0			0
$94$	−5.96490	−	6.42863i	−0.615232	−	0.663063i
$95$	0.372086	−	0.0278840i	0.0381752	−	0.00286084i
$96$		0			0
$97$		−	9.69774i		−	0.984656i	−0.870410	−	0.492328i	$-0.836146\pi$
$97$		−	9.69774i		−	0.984656i	0.870410	−	0.492328i	$-0.163854\pi$
$98$	6.36560	+	14.2781i	0.643023	+	1.44230i
$99$		0			0
$100$	−1.32435	−	3.37438i	−0.132435	−	0.337438i
$101$	0.717255	+	9.57110i	0.0713695	+	0.952360i	0.911851	+	0.410521i	$0.134653\pi$
$101$	0.717255	+	9.57110i	0.0713695	+	0.952360i	−0.840482	+	0.541840i	$0.817728\pi$
$102$		0			0
$103$	−7.09042	−	10.3997i	−0.698640	−	1.02472i	−0.997517	−	0.0704251i	$-0.977564\pi$
$103$	−7.09042	−	10.3997i	−0.698640	−	1.02472i	0.298877	−	0.954292i	$-0.403388\pi$
$104$	3.05978	−	1.47351i	0.300036	−	0.144490i
$105$		0			0
$106$	6.77167	+	3.26107i	0.657723	+	0.316743i
$107$	1.48011	+	9.81990i	0.143088	+	0.949325i	0.939001	+	0.343915i	$0.111753\pi$
$107$	1.48011	+	9.81990i	0.143088	+	0.949325i	−0.795913	+	0.605411i	$0.793009\pi$
$108$		0			0
$109$	−9.55463	−	1.44013i	−0.915168	−	0.137939i	−0.325460	−	0.945556i	$-0.605519\pi$
$109$	−9.55463	−	1.44013i	−0.915168	−	0.137939i	−0.589708	+	0.807617i	$0.700757\pi$
$110$	4.75170	+	4.40894i	0.453057	+	0.420376i
$111$		0			0
$112$	2.06416	−	1.85952i	0.195045	−	0.175708i
$113$	8.97715	−	7.15904i	0.844500	−	0.673466i	−0.102489	−	0.994734i	$-0.532681\pi$
$113$	8.97715	−	7.15904i	0.844500	−	0.673466i	0.946988	+	0.321268i	$0.104109\pi$
$114$		0			0
$115$	0.920066	+	2.98278i	0.0857966	+	0.278146i
$116$	−2.13780	+	1.23426i	−0.198489	+	0.114598i
$117$		0			0
$118$	−23.3770	−	5.33566i	−2.15203	−	0.491187i
$119$	6.17726	+	3.08755i	0.566269	+	0.283036i
$120$		0			0
$121$	9.21566	+	2.84265i	0.837787	+	0.258423i
$122$	3.40417	−	8.67368i	0.308199	−	0.785278i
$123$		0			0
$124$	9.01934	−	29.2400i	0.809961	−	2.62583i
$125$	2.10032	+	9.20209i	0.187858	+	0.823060i
$126$		0			0
$127$	1.53622	−	6.73064i	0.136318	−	0.597248i	−0.859908	−	0.510449i	$-0.829479\pi$
$127$	1.53622	−	6.73064i	0.136318	−	0.597248i	0.996226	−	0.0867987i	$-0.0276637\pi$
$128$	13.4161	+	7.74577i	1.18582	+	0.684636i
$129$		0			0
$130$	8.19214	−	2.52694i	0.718498	−	0.221627i
$131$	0.968337	−	12.9216i	0.0846040	−	1.12896i	−0.779754	−	0.626086i	$-0.784656\pi$
$131$	0.968337	−	12.9216i	0.0846040	−	1.12896i	0.864358	−	0.502877i	$-0.167725\pi$
$132$		0			0
$133$	−0.111157	−	0.380125i	−0.00963854	−	0.0329610i
$134$	−14.6488	−	11.6820i	−1.26546	−	1.00917i
$135$		0			0
$136$	−0.857891	+	5.69173i	−0.0735635	+	0.488062i
$137$	12.1533	−	17.8257i	1.03833	−	1.52295i	0.198498	−	0.980101i	$-0.436394\pi$
$137$	12.1533	−	17.8257i	1.03833	−	1.52295i	0.839831	−	0.542848i	$-0.182654\pi$
$138$		0			0
$139$	−1.62745	+	3.37944i	−0.138039	+	0.286640i	−0.958516	−	0.285039i	$-0.907993\pi$
$139$	−1.62745	+	3.37944i	−0.138039	+	0.286640i	0.820477	+	0.571679i	$0.193708\pi$
$140$	−16.4401	+	10.8580i	−1.38945	+	0.917666i
$141$		0			0
$142$	−27.0506	+	18.4428i	−2.27004	+	1.54769i
$143$	−1.31455	+	1.21972i	−0.109928	+	0.101998i
$144$		0			0
$145$	−1.91731	+	0.752488i	−0.159224	+	0.0624907i
$146$	24.3417			2.01454
$147$		0			0
$148$	35.8514			2.94697
$149$	−9.59664	+	3.76640i	−0.786188	+	0.308556i	−0.724262	−	0.689525i	$-0.757819\pi$
$149$	−9.59664	+	3.76640i	−0.786188	+	0.308556i	−0.0619256	+	0.998081i	$0.519724\pi$
$150$		0			0
$151$	9.91135	−	9.19639i	0.806575	−	0.748392i	−0.164703	−	0.986343i	$-0.552666\pi$
$151$	9.91135	−	9.19639i	0.806575	−	0.748392i	0.971277	+	0.237951i	$0.0764759\pi$
$152$	0.272741	−	0.185952i	0.0221222	−	0.0150827i
$153$		0			0
$154$	3.52735	−	5.90716i	0.284242	−	0.476012i
$155$	11.0778	−	23.0032i	0.889787	−	1.84766i
$156$		0			0
$157$	9.32045	−	13.6706i	0.743853	−	1.09103i	−0.248624	−	0.968600i	$-0.579978\pi$
$157$	9.32045	−	13.6706i	0.743853	−	1.09103i	0.992477	−	0.122432i	$-0.0390692\pi$
$158$	−0.366562	+	2.43198i	−0.0291621	+	0.193478i
$159$		0			0
$160$	13.1655	+	10.4991i	1.04082	+	0.830027i
$161$	2.89333	−	1.61420i	0.228027	−	0.127216i
$162$		0			0
$163$	0.138902	−	1.85352i	0.0108797	−	0.145179i	−0.989118	−	0.147121i	$-0.952999\pi$
$163$	0.138902	−	1.85352i	0.0108797	−	0.145179i	0.999998	+	0.00194228i	$0.000618246\pi$
$164$	−21.7911	+	6.72167i	−1.70160	+	0.524874i
$165$		0			0
$166$	11.5093	+	6.64492i	0.893299	+	0.515746i
$167$	−2.56908	+	11.2559i	−0.198801	+	0.871004i	0.772851	+	0.634588i	$0.218830\pi$
$167$	−2.56908	+	11.2559i	−0.198801	+	0.871004i	−0.971652	+	0.236416i	$0.924027\pi$
$168$		0			0
$169$	−2.36502	−	10.3618i	−0.181925	−	0.797064i
$170$	−4.28289	+	13.8848i	−0.328483	+	1.06491i
$171$		0			0
$172$	−11.1142	+	28.3185i	−0.847449	+	2.15926i
$173$	−4.44305	−	1.37050i	−0.337799	−	0.104197i	0.121215	−	0.992626i	$-0.461321\pi$
$173$	−4.44305	−	1.37050i	−0.337799	−	0.104197i	−0.459014	+	0.888429i	$0.651797\pi$
$174$		0			0
$175$	−2.91260	+	1.35023i	−0.220172	+	0.102068i
$176$	−1.19207	−	0.272083i	−0.0898559	−	0.0205090i
$177$		0			0
$178$	−17.5273	+	10.1194i	−1.31373	+	0.758481i
$179$	−6.28538	−	20.3767i	−0.469791	−	1.52303i	−0.812146	−	0.583454i	$-0.801701\pi$
$179$	−6.28538	−	20.3767i	−0.469791	−	1.52303i	0.342355	−	0.939571i	$-0.388776\pi$
$180$		0			0
$181$	−7.58961	+	6.05251i	−0.564132	+	0.449880i	−0.863565	−	0.504237i	$-0.831774\pi$
$181$	−7.58961	+	6.05251i	−0.564132	+	0.449880i	0.299434	+	0.954117i	$0.403202\pi$
$182$	−4.43335	−	7.94647i	−0.328622	−	0.589032i
$183$		0			0
$184$	2.02432	+	1.87829i	0.149235	+	0.138469i
$185$	29.5796	+	4.45841i	2.17474	+	0.327789i
$186$		0			0
$187$	−0.452994	−	3.00542i	−0.0331262	−	0.219778i
$188$	−10.5695	−	5.09000i	−0.770860	−	0.371227i
$189$		0			0
$190$	0.750772	−	0.361553i	0.0544667	−	0.0262298i
$191$	−8.53026	−	12.5116i	−0.617228	−	0.905308i	0.382599	−	0.923915i	$-0.375029\pi$
$191$	−8.53026	−	12.5116i	−0.617228	−	0.905308i	−0.999827	+	0.0186070i	$0.994077\pi$
$192$		0			0
$193$	0.567028	+	7.56646i	0.0408155	+	0.544645i	0.979707	+	0.200433i	$0.0642350\pi$
$193$	0.567028	+	7.56646i	0.0408155	+	0.544645i	−0.938892	+	0.344212i	$0.888146\pi$
$194$	−7.91239	−	20.1604i	−0.568077	−	1.44744i
$195$		0			0
$196$	14.9046	+	14.6686i	1.06462	+	1.04776i
$197$		−	12.8332i		−	0.914327i	−0.889383	−	0.457164i	$-0.848865\pi$
$197$		−	12.8332i		−	0.914327i	0.889383	−	0.457164i	$-0.151135\pi$
$198$		0			0
$199$	−11.5456	+	0.865220i	−0.818443	+	0.0613339i	−0.477370	−	0.878703i	$-0.658410\pi$
$199$	−11.5456	+	0.865220i	−0.818443	+	0.0613339i	−0.341074	+	0.940036i	$0.610791\pi$
$200$	−1.82001	−	1.96150i	−0.128694	−	0.138699i
$201$		0			0
$202$	9.30016	+	19.3120i	0.654357	+	1.35879i
$203$	1.20482	+	1.82422i	0.0845615	+	0.128035i
$204$		0			0
$205$	−18.8149	+	2.83590i	−1.31409	+	0.198068i
$206$	−23.2253	−	15.8347i	−1.61818	−	1.10326i
$207$		0			0
$208$	−1.09994	+	1.18545i	−0.0762670	+	0.0821963i
$209$	−0.108676	+	0.136276i	−0.00751730	+	0.00942640i
$210$		0			0
$211$	6.87238	+	8.61769i	0.473114	+	0.593266i	0.959931	−	0.280238i	$-0.0904134\pi$
$211$	6.87238	+	8.61769i	0.473114	+	0.593266i	−0.486817	+	0.873504i	$0.661842\pi$
$212$	10.0261	+	0.751350i	0.688593	+	0.0516029i
$213$		0			0
$214$	11.0890	+	19.2068i	0.758031	+	1.31295i
$215$	−12.6915	+	21.9824i	−0.865556	+	1.49919i
$216$		0			0
$217$	−26.3286	−	6.41818i	−1.78730	−	0.435694i
$218$	−21.0379	+	4.80177i	−1.42487	+	0.325217i
$219$		0			0
$220$	8.07172	+	3.16792i	0.544195	+	0.213581i
$221$	−3.74190	−	1.46859i	−0.251707	−	0.0987879i
$222$		0			0
$223$	27.5926	−	6.29782i	1.84774	−	0.421733i	0.852799	−	0.522240i	$-0.174903\pi$
$223$	27.5926	−	6.29782i	1.84774	−	0.421733i	0.994936	+	0.100506i	$0.0320462\pi$
$224$	7.99100	−	15.9876i	0.533921	−	1.06821i
$225$		0			0
$226$	12.8214	−	22.2073i	0.852865	−	1.47721i
$227$	−0.639251	−	1.10722i	−0.0424286	−	0.0734885i	0.844031	−	0.536294i	$-0.180176\pi$
$227$	−0.639251	−	1.10722i	−0.0424286	−	0.0734885i	−0.886460	+	0.462806i	$0.846843\pi$
$228$		0			0
$229$	−19.7036	−	1.47658i	−1.30205	−	0.0975752i	−0.594418	−	0.804156i	$-0.702618\pi$
$229$	−19.7036	−	1.47658i	−1.30205	−	0.0975752i	−0.707632	+	0.706581i	$0.750237\pi$
$230$	4.34636	+	5.45016i	0.286591	+	0.359373i
$231$		0			0
$232$	−1.13610	+	1.42462i	−0.0745886	+	0.0935311i
$233$	1.22666	−	1.32202i	0.0803610	−	0.0866085i	−0.691591	−	0.722289i	$-0.743090\pi$
$233$	1.22666	−	1.32202i	0.0803610	−	0.0866085i	0.771952	+	0.635681i	$0.219280\pi$
$234$		0			0
$235$	−8.08752	−	5.51398i	−0.527571	−	0.359692i
$236$	−31.7176	+	4.78065i	−2.06464	+	0.311194i
$237$		0			0
$238$	15.3609	+	1.37862i	0.995701	+	0.0893629i
$239$	5.14965	+	10.6934i	0.333103	+	0.691696i	0.998498	−	0.0547961i	$-0.0174509\pi$
$239$	5.14965	+	10.6934i	0.333103	+	0.691696i	−0.665394	+	0.746492i	$0.731737\pi$
$240$		0			0
$241$	11.4016	+	12.2880i	0.734443	+	0.791541i	0.984255	−	0.176753i	$-0.0565595\pi$
$241$	11.4016	+	12.2880i	0.734443	+	0.791541i	−0.249813	+	0.968294i	$0.580369\pi$
$242$	21.4776	−	1.60952i	1.38063	−	0.103464i
$243$		0			0
$244$		−	12.4645i		−	0.797955i
$245$	10.4731	+	13.9560i	0.669102	+	0.891618i
$246$		0			0
$247$	0.0842215	+	0.214593i	0.00535889	+	0.0136542i
$248$	−1.68795	−	22.5242i	−0.107185	−	1.43029i
$249$		0			0
$250$	11.8743	+	17.4164i	0.750997	+	1.10151i
$251$	−24.3077	+	11.7060i	−1.53429	+	0.738876i	−0.994678	−	0.103037i	$-0.967144\pi$
$251$	−24.3077	+	11.7060i	−1.53429	+	0.738876i	−0.539614	+	0.841913i	$0.681430\pi$
$252$		0			0
$253$	−1.31375	−	0.632670i	−0.0825950	−	0.0397756i
$254$	−2.29791	−	15.2456i	−0.144183	−	0.956595i
$255$		0			0
$256$	8.52697	+	1.28523i	0.532936	+	0.0803271i
$257$	−13.1186	−	12.1723i	−0.818317	−	0.759287i	0.155205	−	0.987882i	$-0.450396\pi$
$257$	−13.1186	−	12.1723i	−0.818317	−	0.759287i	−0.973522	+	0.228595i	$0.926587\pi$
$258$		0			0
$259$	−1.90679	−	31.6935i	−0.118482	−	1.96934i
$260$	8.96617	−	7.15028i	0.556058	−	0.443442i
$261$		0			0
$262$	−8.52966	−	27.6525i	−0.526964	−	1.70838i
$263$	−6.43376	+	3.71453i	−0.396722	+	0.229048i	−0.685069	−	0.728478i	$-0.740228\pi$
$263$	−6.43376	+	3.71453i	−0.396722	+	0.229048i	0.288346	+	0.957526i	$0.406895\pi$
$264$		0			0
$265$	8.17870	+	1.86674i	0.502414	+	0.114673i
$266$	−0.541227	−	0.699542i	−0.0331847	−	0.0428917i
$267$		0			0
$268$	−23.9504	−	7.38771i	−1.46300	−	0.451276i
$269$	4.33700	−	11.0505i	0.264431	−	0.673760i	−0.735562	−	0.677458i	$-0.763082\pi$
$269$	4.33700	−	11.0505i	0.264431	−	0.673760i	0.999993	+	0.00369739i	$0.00117692\pi$
$270$		0			0
$271$	−1.31490	+	4.26279i	−0.0798742	+	0.258946i	−0.986698	−	0.162564i	$-0.948024\pi$
$271$	−1.31490	+	4.26279i	−0.0798742	+	0.258946i	0.906824	+	0.421510i	$0.138500\pi$
$272$	−0.609905	−	2.67217i	−0.0369809	−	0.162024i
$273$		0			0
$274$	10.7214	−	46.9734i	0.647701	−	2.83776i
$275$	1.22362	+	0.706456i	0.0737869	+	0.0426009i
$276$		0			0
$277$	−1.13152	+	0.349027i	−0.0679863	+	0.0209710i	−0.328562	−	0.944482i	$-0.606564\pi$
$277$	−1.13152	+	0.349027i	−0.0679863	+	0.0209710i	0.260575	+	0.965453i	$0.416088\pi$
$278$	−0.625993	+	8.35329i	−0.0375446	+	0.500997i
$279$		0			0
$280$	−8.36842	+	11.8945i	−0.500108	+	0.710831i
$281$	22.7504	+	18.1428i	1.35717	+	1.08231i	0.988249	+	0.152851i	$0.0488456\pi$
$281$	22.7504	+	18.1428i	1.35717	+	1.08231i	0.368925	+	0.929459i	$0.379726\pi$
$282$		0			0
$283$	−0.0238140	+	0.157995i	−0.00141559	+	0.00939185i	−0.989527	−	0.144345i	$-0.953893\pi$
$283$	−0.0238140	+	0.157995i	−0.00141559	+	0.00939185i	0.988112	+	0.153737i	$0.0491307\pi$
$284$	−24.6710	+	36.1858i	−1.46396	+	2.14723i
$285$		0			0
$286$	−1.73761	+	3.60819i	−0.102747	+	0.213357i
$287$	7.10111	+	18.9064i	0.419165	+	1.11601i
$288$		0			0
$289$	−8.41683	+	5.73850i	−0.495108	+	0.337559i
$290$	−3.37190	+	3.12866i	−0.198005	+	0.183722i
$291$		0			0
$292$	30.3112	−	11.8963i	1.77383	−	0.696176i
$293$	27.9417			1.63237			0.816186	−	0.577789i	$-0.196084\pi$
$293$	27.9417			1.63237			0.816186	+	0.577789i	$0.196084\pi$
$294$		0			0
$295$	−26.7635			−1.55823
$296$	24.6347	−	9.66842i	1.43186	−	0.561966i
$297$		0			0
$298$	−16.8773	+	15.6598i	−0.977674	+	0.907149i
$299$	−1.59341	+	1.08637i	−0.0921494	+	0.0628264i
$300$		0			0
$301$	25.6254	+	8.31908i	1.47702	+	0.479504i
$302$	13.1012	−	27.2049i	0.753889	−	1.56547i
$303$		0			0
$304$	−0.0885461	+	0.129873i	−0.00507847	+	0.00744874i
$305$	1.55006	−	10.2840i	0.0887560	−	0.588858i
$306$		0			0
$307$	12.9030	+	10.2898i	0.736412	+	0.587269i	0.918223	−	0.396065i	$-0.129624\pi$
$307$	12.9030	+	10.2898i	0.736412	+	0.587269i	−0.181811	+	0.983334i	$0.558196\pi$
$308$	1.50544	−	9.07968i	0.0857806	−	0.517363i
$309$		0			0
$310$	4.26101	−	56.8593i	0.242009	−	3.22939i
$311$	15.8952	−	4.90301i	0.901333	−	0.278024i	0.190751	−	0.981639i	$-0.438908\pi$
$311$	15.8952	−	4.90301i	0.901333	−	0.278024i	0.710582	+	0.703614i	$0.248432\pi$
$312$		0			0
$313$	19.7180	+	11.3842i	1.11452	+	0.643471i	0.939998	−	0.341181i	$-0.110827\pi$
$313$	19.7180	+	11.3842i	1.11452	+	0.643471i	0.174527	+	0.984652i	$0.444160\pi$
$314$	8.22226	−	36.0241i	0.464009	−	2.03296i
$315$		0			0
$316$	0.732099	+	3.20754i	0.0411838	+	0.180438i
$317$	0.884400	−	2.86715i	0.0496729	−	0.161035i	−0.927338	−	0.374225i	$-0.877909\pi$
$317$	0.884400	−	2.86715i	0.0496729	−	0.161035i	0.977011	+	0.213189i	$0.0683851\pi$
$318$		0			0
$319$	0.351517	−	0.895650i	0.0196811	−	0.0501468i
$320$	30.9333	+	9.54165i	1.72922	+	0.533394i
$321$		0			0
$322$	4.69787	−	5.71639i	0.261802	−	0.318562i
$323$	−0.380925	−	0.0869435i	−0.0211952	−	0.00483767i
$324$		0			0
$325$	1.61832	−	0.934337i	0.0897682	−	0.0518277i
$326$	−1.22353	−	3.96659i	−0.0677650	−	0.219689i
$327$		0			0
$328$	−13.1607	+	10.4953i	−0.726680	+	0.579508i
$329$	−3.93754	+	9.61442i	−0.217084	+	0.530060i
$330$		0			0
$331$	21.0589	+	19.5398i	1.15750	+	1.07401i	0.996199	+	0.0871010i	$0.0277603\pi$
$331$	21.0589	+	19.5398i	1.15750	+	1.07401i	0.161304	+	0.986905i	$0.448430\pi$
$332$	17.5793	+	2.64966i	0.964792	+	0.145419i
$333$		0			0
$334$	3.84286	+	25.4957i	0.210272	+	1.39506i
$335$	−18.8418	−	9.07375i	−1.02944	−	0.495752i
$336$		0			0
$337$	−17.6916	+	8.51983i	−0.963723	+	0.464105i	−0.848477	−	0.529232i	$-0.822480\pi$
$337$	−17.6916	+	8.51983i	−0.963723	+	0.464105i	−0.115246	+	0.993337i	$0.536766\pi$
$338$	−13.3708	−	19.6114i	−0.727277	−	1.06672i
$339$		0			0
$340$	1.45255	+	19.3829i	0.0787756	+	1.05119i
$341$	4.35736	+	11.1024i	0.235964	+	0.601227i
$342$		0			0
$343$	12.1747	−	13.9562i	0.657372	−	0.753567i
$344$			22.4559i			1.21074i
$345$		0			0
$346$	−10.3548	+	0.775982i	−0.556676	+	0.0417171i
$347$	4.16587	+	4.48974i	0.223636	+	0.241022i	0.834896	−	0.550407i	$-0.185528\pi$
$347$	4.16587	+	4.48974i	0.223636	+	0.241022i	−0.611260	+	0.791430i	$0.709337\pi$
$348$		0			0
$349$	0.995638	+	2.06746i	0.0532953	+	0.110669i	0.925916	−	0.377730i	$-0.123295\pi$
$349$	0.995638	+	2.06746i	0.0532953	+	0.110669i	−0.872620	+	0.488399i	$0.837581\pi$
$350$	−4.95331	+	5.18336i	−0.264765	+	0.277062i
$351$		0			0
$352$	−7.77842	+	1.17241i	−0.414591	+	0.0624896i
$353$	−21.7523	−	14.8305i	−1.15776	−	0.789346i	−0.176930	−	0.984223i	$-0.556617\pi$
$353$	−21.7523	−	14.8305i	−1.15776	−	0.789346i	−0.980827	+	0.194878i	$0.937569\pi$
$354$		0			0
$355$	−24.8552	+	26.7875i	−1.31918	+	1.42173i
$356$	−16.8801	+	21.1670i	−0.894643	+	1.12185i
$357$		0			0
$358$	−29.6919	−	37.2325i	−1.56927	−	1.96780i
$359$	31.5751	+	2.36623i	1.66647	+	0.124885i	0.874290	−	0.485404i	$-0.161328\pi$
$359$	31.5751	+	2.36623i	1.66647	+	0.124885i	0.792179	+	0.610289i	$0.208947\pi$
$360$		0			0
$361$	−9.48880	−	16.4351i	−0.499410	−	0.865004i
$362$	−10.8397	+	18.7748i	−0.569720	+	0.986783i
$363$		0			0
$364$	−9.40415	−	7.72856i	−0.492912	−	0.405087i
$365$	26.4880	−	6.04572i	1.38645	−	0.316448i
$366$		0			0
$367$	−1.78408	−	0.700199i	−0.0931280	−	0.0365501i	0.318320	−	0.947983i	$-0.396881\pi$
$367$	−1.78408	−	0.700199i	−0.0931280	−	0.0365501i	−0.411448	+	0.911433i	$0.634977\pi$
$368$	−1.22406	−	0.480408i	−0.0638086	−	0.0250430i
$369$		0			0
$370$	65.1302	−	14.8655i	3.38596	−	0.772823i
$371$	0.130968	−	8.90327i	0.00679951	−	0.462235i
$372$		0			0
$373$	−0.363940	+	0.630362i	−0.0188441	+	0.0326389i	−0.875294	−	0.483592i	$-0.839332\pi$
$373$	−0.363940	+	0.630362i	−0.0188441	+	0.0326389i	0.856450	+	0.516231i	$0.172665\pi$
$374$	−3.39384	−	5.87831i	−0.175491	−	0.303960i
$375$		0			0
$376$	−8.63534	−	0.647130i	−0.445334	−	0.0333732i
$377$	−0.793406	−	0.994899i	−0.0408625	−	0.0512399i
$378$		0			0
$379$	−5.35964	+	6.72077i	−0.275306	+	0.345223i	−0.900192	−	0.435493i	$-0.856574\pi$
$379$	−5.35964	+	6.72077i	−0.275306	+	0.345223i	0.624886	+	0.780716i	$0.285145\pi$
$380$	0.758190	−	0.817135i	0.0388943	−	0.0419181i
$381$		0			0
$382$	−27.9416	−	19.0503i	−1.42962	−	0.974697i
$383$	−21.6463	+	3.26266i	−1.10608	+	0.166714i	−0.676590	−	0.736360i	$-0.736543\pi$
$383$	−21.6463	+	3.26266i	−1.10608	+	0.166714i	−0.429485	+	0.903074i	$0.641305\pi$
$384$		0			0
$385$	2.37122	−	7.30410i	0.120848	−	0.372251i
$386$	7.35226	+	15.2671i	0.374220	+	0.777076i
$387$		0			0
$388$	−19.7056	−	21.2376i	−1.00040	−	1.07817i
$389$	4.50483	−	0.337591i	0.228404	−	0.0171165i	0.0399637	−	0.999201i	$-0.487276\pi$
$389$	4.50483	−	0.337591i	0.228404	−	0.0171165i	0.188441	+	0.982085i	$0.439657\pi$
$390$		0			0
$391$		−	3.26862i		−	0.165301i
$392$	14.1973	+	6.05981i	0.717074	+	0.306066i
$393$		0			0
$394$	−10.4706	−	26.6787i	−0.527502	−	1.34405i
$395$	0.205144	+	2.73746i	0.0103219	+	0.137737i
$396$		0			0
$397$	14.9498	+	21.9274i	0.750311	+	1.10050i	0.991510	+	0.130028i	$0.0415067\pi$
$397$	14.9498	+	21.9274i	0.750311	+	1.10050i	−0.241200	+	0.970475i	$0.577541\pi$
$398$	−23.2959	+	11.2187i	−1.16772	+	0.562344i
$399$		0			0
$400$	1.14798	+	0.552836i	0.0573988	+	0.0276418i
$401$	−1.12523	−	7.46539i	−0.0561911	−	0.372804i	−0.999198	−	0.0400316i	$-0.987254\pi$
$401$	−1.12523	−	7.46539i	−0.0561911	−	0.372804i	0.943007	−	0.332772i	$-0.107984\pi$
$402$		0			0
$403$	15.5979	+	2.35100i	0.776986	+	0.117112i
$404$	21.0190	+	19.5028i	1.04573	+	0.970300i
$405$		0			0
$406$	3.99305	+	2.80933i	0.198172	+	0.139425i
$407$	−10.9252	+	8.71258i	−0.541544	+	0.431867i
$408$		0			0
$409$	−2.67236	−	8.66359i	−0.132140	−	0.428387i	0.865188	−	0.501448i	$-0.167199\pi$
$409$	−2.67236	−	8.66359i	−0.132140	−	0.428387i	−0.997327	+	0.0730615i	$0.976723\pi$
$410$	−36.8002	+	21.2466i	−1.81743	+	1.04930i
$411$		0			0
$412$	−36.6597	−	8.36734i	−1.80609	−	0.412229i
$413$	5.91314	+	27.7849i	0.290967	+	1.36720i
$414$		0			0
$415$	14.1746	+	4.37227i	0.695802	+	0.214626i
$416$	−3.80090	+	9.68453i	−0.186354	+	0.474823i
$417$		0			0
$418$	−0.114738	+	0.371971i	−0.00561201	+	0.0181937i
$419$	2.31046	+	10.1228i	0.112873	+	0.494530i	0.999487	+	0.0320196i	$0.0101939\pi$
$419$	2.31046	+	10.1228i	0.112873	+	0.494530i	−0.886614	+	0.462510i	$0.846949\pi$
$420$		0			0
$421$	−1.40068	+	6.13680i	−0.0682652	+	0.299089i	−0.997523	−	0.0703429i	$-0.977591\pi$
$421$	−1.40068	+	6.13680i	−0.0682652	+	0.299089i	0.929258	+	0.369432i	$0.120448\pi$
$422$	21.3180	+	12.3080i	1.03775	+	0.599143i
$423$		0			0
$424$	7.09189	−	2.18756i	0.344412	−	0.106237i
$425$	−0.236685	+	3.15835i	−0.0114809	+	0.153202i
$426$		0			0
$427$	−11.0189	+	0.662932i	−0.533242	+	0.0320816i
$428$	23.1952	+	18.4975i	1.12118	+	0.894112i
$429$		0			0
$430$	−8.44876	+	56.0538i	−0.407435	+	2.70316i
$431$	−20.2222	+	29.6605i	−0.974070	+	1.42870i	−0.0718526	+	0.997415i	$0.522891\pi$
$431$	−20.2222	+	29.6605i	−0.974070	+	1.42870i	−0.902217	+	0.431282i	$0.858061\pi$
$432$		0			0
$433$	−7.73903	+	16.0703i	−0.371914	+	0.772287i	−0.999983	−	0.00587067i	$-0.998131\pi$
$433$	−7.73903	+	16.0703i	−0.371914	+	0.772287i	0.628069	+	0.778158i	$0.283846\pi$
$434$	−59.9706	+	8.13890i	−2.87868	+	0.390680i
$435$		0			0
$436$	−23.8505	+	16.2610i	−1.14223	+	0.778760i
$437$	−0.137411	+	0.127499i	−0.00657327	+	0.00609910i
$438$		0			0
$439$	0.599199	−	0.235168i	0.0285982	−	0.0112240i	−0.350999	−	0.936376i	$-0.614158\pi$
$439$	0.599199	−	0.235168i	0.0285982	−	0.0112240i	0.379597	+	0.925152i	$0.376063\pi$
$440$	6.40069			0.305141
$441$		0			0
$442$	−8.97719			−0.427001
$443$	24.0651	−	9.44487i	1.14337	−	0.448739i	0.283357	−	0.959014i	$-0.408552\pi$
$443$	24.0651	−	9.44487i	1.14337	−	0.448739i	0.860011	+	0.510275i	$0.170456\pi$
$444$		0			0
$445$	−16.5594	+	15.3649i	−0.784992	+	0.728366i
$446$	52.2233	−	35.6052i	2.47284	−	1.68596i
$447$		0			0
$448$	3.07137	−	34.2219i	0.145109	−	1.61683i
$449$	0.161075	−	0.334476i	0.00760160	−	0.0157849i	−0.897134	−	0.441760i	$-0.854354\pi$
$449$	0.161075	−	0.334476i	0.00760160	−	0.0157849i	0.904735	+	0.425975i	$0.140069\pi$
$450$		0			0
$451$	5.00706	−	7.34401i	0.235773	−	0.345816i
$452$	5.11251	−	33.9193i	0.240472	−	1.59543i
$453$		0			0
$454$	−2.23230	−	1.78020i	−0.104767	−	0.0835491i
$455$	−6.79791	−	7.54603i	−0.318691	−	0.353764i
$456$		0			0
$457$	−0.998957	+	13.3302i	−0.0467292	+	0.623558i	0.923847	+	0.382763i	$0.125027\pi$
$457$	−0.998957	+	13.3302i	−0.0467292	+	0.623558i	−0.970576	+	0.240796i	$0.922592\pi$
$458$	−42.1662	+	13.0065i	−1.97030	+	0.607756i
$459$		0			0
$460$	8.07584	+	4.66259i	0.376538	+	0.217394i
$461$	−5.15133	+	22.5694i	−0.239921	+	1.05116i	0.701165	+	0.712999i	$0.252663\pi$
$461$	−5.15133	+	22.5694i	−0.239921	+	1.05116i	−0.941087	+	0.338165i	$0.890194\pi$
$462$		0			0
$463$	0.200977	+	0.880537i	0.00934018	+	0.0409220i	0.979383	−	0.202011i	$-0.0647476\pi$
$463$	0.200977	+	0.880537i	0.00934018	+	0.0409220i	−0.970043	+	0.242933i	$0.921891\pi$
$464$	0.255751	−	0.829124i	0.0118729	−	0.0384911i
$465$		0			0
$466$	1.47144	−	3.74916i	0.0681629	−	0.173676i
$467$	−4.58606	−	1.41461i	−0.212218	−	0.0654605i	0.186823	−	0.982394i	$-0.440181\pi$
$467$	−4.58606	−	1.41461i	−0.212218	−	0.0654605i	−0.399041	+	0.916933i	$0.630657\pi$
$468$		0			0
$469$	−5.25710	+	21.5657i	−0.242750	+	0.995809i
$470$	−21.3118	−	4.86429i	−0.983042	−	0.224373i
$471$		0			0
$472$	−20.5050	+	11.8386i	−0.943819	+	0.544914i
$473$	−3.49504	−	11.3306i	−0.160702	−	0.520984i
$474$		0			0
$475$	0.142008	−	0.113247i	0.00651576	−	0.00519615i
$476$	19.8017	−	5.79047i	0.907611	−	0.265406i
$477$		0			0
$478$	19.4302	+	18.0286i	0.888718	+	0.824610i
$479$	−29.1998	−	4.40117i	−1.33417	−	0.201094i	−0.557070	−	0.830466i	$-0.688074\pi$
$479$	−29.1998	−	4.40117i	−1.33417	−	0.201094i	−0.777105	+	0.629371i	$0.783312\pi$
$480$		0			0
$481$	2.75452	+	18.2750i	0.125595	+	0.833270i
$482$	33.7284	+	16.2427i	1.53629	+	0.739837i
$483$		0			0
$484$	25.9580	−	12.5007i	1.17991	−	0.568215i
$485$	−13.6173	−	19.9729i	−0.618329	−	0.906922i
$486$		0			0
$487$	−0.603365	−	8.05135i	−0.0273411	−	0.364842i	−0.994047	−	0.108952i	$-0.965251\pi$
$487$	−0.603365	−	8.05135i	−0.0273411	−	0.364842i	0.966706	−	0.255890i	$-0.0823684\pi$
$488$	−3.36142	−	8.56476i	−0.152164	−	0.387709i
$489$		0			0
$490$	33.1591	+	20.4679i	1.49797	+	0.924646i
$491$			30.8465i			1.39208i	0.718001	+	0.696042i	$0.245057\pi$
$491$			30.8465i			1.39208i	−0.718001	+	0.696042i	$0.754943\pi$
$492$		0			0
$493$	2.15076	−	0.161177i	0.0968653	−	0.00725905i
$494$	0.350173	+	0.377397i	0.0157550	+	0.0169799i
$495$		0			0
$496$	4.66666	+	9.69043i	0.209539	+	0.435113i
$497$	33.3013	+	19.8853i	1.49377	+	0.891976i
$498$		0			0
$499$	−27.9451	+	4.21204i	−1.25099	+	0.188557i	−0.740931	−	0.671581i	$-0.765616\pi$
$499$	−27.9451	+	4.21204i	−1.25099	+	0.188557i	−0.510062	+	0.860138i	$0.670377\pi$
$500$	23.2980	+	15.8843i	1.04192	+	0.710369i
$501$		0			0
$502$	−40.9820	+	44.1681i	−1.82912	+	1.97132i
$503$	−9.58702	+	12.0217i	−0.427464	+	0.536023i	−0.948191	−	0.317700i	$-0.897089\pi$
$503$	−9.58702	+	12.0217i	−0.427464	+	0.536023i	0.520727	+	0.853723i	$0.325661\pi$
$504$		0			0
$505$	14.9167	+	18.7049i	0.663783	+	0.832358i
$506$	−3.24733	−	0.243354i	−0.144362	−	0.0108184i
$507$		0			0
$508$	−10.3123	−	17.8613i	−0.457532	−	0.792469i
$509$	11.6400	−	20.1610i	0.515932	−	0.893621i	−0.483897	−	0.875125i	$-0.660779\pi$
$509$	11.6400	−	20.1610i	0.515932	−	0.893621i	0.999829	−	0.0184959i	$-0.00588775\pi$
$510$		0			0
$511$	−12.1287	−	26.1632i	−0.536543	−	1.15739i
$512$	−11.4311	+	2.60907i	−0.505187	+	0.115306i
$513$		0			0
$514$	−37.2034	−	14.6013i	−1.64097	−	0.644034i
$515$	−29.2060	−	11.4625i	−1.28697	−	0.505099i
$516$		0			0
$517$	4.45788	−	1.01748i	0.196057	−	0.0447488i
$518$	−29.8228	−	64.3314i	−1.31034	−	2.82656i
$519$		0			0
$520$	4.23268	−	7.33121i	0.185615	−	0.321495i
$521$	21.8542	+	37.8525i	0.957449	+	1.65835i	0.728662	+	0.684874i	$0.240143\pi$
$521$	21.8542	+	37.8525i	0.957449	+	1.65835i	0.228787	+	0.973477i	$0.426524\pi$
$522$		0			0
$523$	2.70012	+	0.202346i	0.118068	+	0.00884796i	0.133633	−	0.991031i	$-0.457336\pi$
$523$	2.70012	+	0.202346i	0.118068	+	0.00884796i	−0.0155651	+	0.999879i	$0.504955\pi$
$524$	−24.1357	−	30.2652i	−1.05437	−	1.32214i
$525$		0			0
$526$	−10.3443	+	12.9714i	−0.451034	+	0.565579i
$527$	−18.1846	+	19.5984i	−0.792135	+	0.853719i
$528$		0			0
$529$	17.7078	+	12.0730i	0.769906	+	0.524913i
$530$	18.5256	−	2.79229i	0.804702	−	0.121289i
$531$		0			0
$532$	−1.01583	−	0.606587i	−0.0440420	−	0.0262989i
$533$	−5.10058	−	10.5915i	−0.220931	−	0.458767i
$534$		0			0
$535$	16.8372	+	18.1461i	0.727934	+	0.784526i
$536$	−18.4494	+	1.38259i	−0.796895	+	0.0597190i
$537$		0			0
$538$		−	26.5112i		−	1.14298i
$539$	−8.10674	−	0.847940i	−0.349182	−	0.0365233i
$540$		0			0
$541$	6.20572	+	15.8119i	0.266805	+	0.679807i	1.00000		0.000210854i	$-6.71170e-5\pi$
$541$	6.20572	+	15.8119i	0.266805	+	0.679807i	−0.733195	+	0.680018i	$0.761972\pi$
$542$	0.744499	+	9.93465i	0.0319790	+	0.426730i
$543$		0			0
$544$	−9.93311	−	14.5692i	−0.425878	−	0.624649i
$545$	−21.7003	+	10.4503i	−0.929540	+	0.447643i
$546$		0			0
$547$	3.54836	+	1.70880i	0.151717	+	0.0730629i	0.508201	−	0.861238i	$-0.330311\pi$
$547$	3.54836	+	1.70880i	0.151717	+	0.0730629i	−0.356485	+	0.934301i	$0.616025\pi$
$548$	−9.60615	−	63.7326i	−0.410354	−	2.72252i
$549$		0			0
$550$	3.12015	+	0.470288i	0.133044	+	0.0200531i
$551$	−0.0906704	−	0.0841299i	−0.00386269	−	0.00358405i
$552$		0			0
$553$	2.79661	−	0.817790i	0.118924	−	0.0347760i
$554$	−2.06752	+	1.64879i	−0.0878404	+	0.0700504i
$555$		0			0
$556$	3.30290	+	10.7077i	0.140074	+	0.454110i
$557$	31.3559	−	18.1034i	1.32859	−	0.767064i	0.343511	−	0.939149i	$-0.388384\pi$
$557$	31.3559	−	18.1034i	1.32859	−	0.767064i	0.985082	+	0.172085i	$0.0550504\pi$
$558$		0			0
$559$	−15.2891	−	3.48964i	−0.646660	−	0.147596i
$560$	1.64014	−	6.72818i	0.0693087	−	0.284318i
$561$		0			0
$562$	62.0981	+	19.1547i	2.61945	+	0.807994i
$563$	15.4646	−	39.4033i	0.651757	−	1.66065i	−0.0949374	−	0.995483i	$-0.530265\pi$
$563$	15.4646	−	39.4033i	0.651757	−	1.66065i	0.746695	−	0.665167i	$-0.231640\pi$
$564$		0			0
$565$	8.43629	−	27.3498i	0.354917	−	1.15061i
$566$	0.0794022	+	0.347884i	0.00333752	+	0.0146226i
$567$		0			0
$568$	−7.19373	+	31.5178i	−0.301842	+	1.32246i
$569$	−9.93757	−	5.73746i	−0.416605	−	0.240527i	0.277019	−	0.960864i	$-0.410654\pi$
$569$	−9.93757	−	5.73746i	−0.416605	−	0.240527i	−0.693624	+	0.720338i	$0.743987\pi$
$570$		0			0
$571$	13.1509	−	4.05652i	0.550348	−	0.169760i	−0.00709536	−	0.999975i	$-0.502259\pi$
$571$	13.1509	−	4.05652i	0.550348	−	0.169760i	0.557443	+	0.830215i	$0.311782\pi$
$572$	−0.400346	+	5.34225i	−0.0167393	+	0.223371i
$573$		0			0
$574$	30.1881	+	33.5104i	1.26003	+	1.39870i
$575$	1.18798	+	0.947384i	0.0495423	+	0.0395087i
$576$		0			0
$577$	2.65830	−	17.6366i	0.110666	−	0.734223i	−0.862826	−	0.505502i	$-0.831307\pi$
$577$	2.65830	−	17.6366i	0.110666	−	0.734223i	0.973492	−	0.228721i	$-0.0734544\pi$
$578$	−12.8155	+	18.7970i	−0.533056	+	0.781850i
$579$		0			0
$580$	−2.66977	+	5.54383i	−0.110856	+	0.230195i
$581$	1.40740	−	15.6815i	0.0583886	−	0.650579i
$582$		0			0
$583$	−3.23790	+	2.20757i	−0.134100	+	0.0914280i
$584$	17.6197	−	16.3487i	0.729108	−	0.676513i
$585$		0			0
$586$	58.0875	−	22.7977i	2.39957	−	0.941763i
$587$	32.7857			1.35321			0.676606	−	0.736345i	$-0.263450\pi$
$587$	32.7857			1.35321			0.676606	+	0.736345i	$0.263450\pi$
$588$		0			0
$589$	1.53323			0.0631758
$590$	−55.6381	+	21.8364i	−2.29059	+	0.898989i
$591$		0			0
$592$	−9.23763	+	8.57126i	−0.379664	+	0.352277i
$593$	−0.550480	+	0.375311i	−0.0226055	+	0.0154122i	−0.574570	−	0.818455i	$-0.694831\pi$
$593$	−0.550480	+	0.375311i	−0.0226055	+	0.0154122i	0.551965	+	0.833868i	$0.313878\pi$
$594$		0			0
$595$	17.0578	−	2.31499i	0.699300	−	0.0949054i
$596$	−13.3629	+	27.7484i	−0.547367	+	1.13662i
$597$		0			0
$598$	−2.42615	+	3.55850i	−0.0992125	+	0.145518i
$599$	−1.54405	+	10.2441i	−0.0630880	+	0.418562i	0.934886	+	0.354947i	$0.115501\pi$
$599$	−1.54405	+	10.2441i	−0.0630880	+	0.418562i	−0.997975	+	0.0636149i	$0.979737\pi$
$600$		0			0
$601$	−37.7417	−	30.0980i	−1.53952	−	1.22772i	−0.878904	−	0.476999i	$-0.841725\pi$
$601$	−37.7417	−	30.0980i	−1.53952	−	1.22772i	−0.660614	−	0.750726i	$-0.729704\pi$
$602$	60.0597	−	3.61338i	2.44785	−	0.147271i
$603$		0			0
$604$	3.01852	−	40.2793i	0.122822	−	1.63894i
$605$	22.9716	−	7.08579i	0.933928	−	0.288079i
$606$		0			0
$607$	−28.8438	−	16.6530i	−1.17073	−	0.675923i	−0.216880	−	0.976198i	$-0.569588\pi$
$607$	−28.8438	−	16.6530i	−1.17073	−	0.675923i	−0.953853	+	0.300275i	$0.902921\pi$
$608$	−0.225021	+	0.985883i	−0.00912582	+	0.0399828i
$609$		0			0
$610$	−5.16831	−	22.6438i	−0.209259	−	0.916822i
$611$	1.78253	−	5.77881i	0.0721133	−	0.233786i
$612$		0			0
$613$	3.90889	−	9.95969i	0.157879	−	0.402268i	−0.829945	−	0.557845i	$-0.811628\pi$
$613$	3.90889	−	9.95969i	0.157879	−	0.402268i	0.987824	+	0.155577i	$0.0497236\pi$
$614$	35.2192	+	10.8637i	1.42133	+	0.438423i
$615$		0			0
$616$	−1.41417	−	6.64496i	−0.0569786	−	0.267733i
$617$	10.3341	+	2.35868i	0.416033	+	0.0949569i	0.425414	−	0.904999i	$-0.360129\pi$
$617$	10.3341	+	2.35868i	0.416033	+	0.0949569i	−0.00938006	+	0.999956i	$0.502986\pi$
$618$		0			0
$619$	19.2455	−	11.1114i	0.773542	−	0.446605i	−0.0605948	−	0.998162i	$-0.519300\pi$
$619$	19.2455	−	11.1114i	0.773542	−	0.446605i	0.834137	+	0.551558i	$0.185966\pi$
$620$	−22.4822	−	72.8856i	−0.902908	−	2.92716i
$621$		0			0
$622$	29.0438	−	23.1617i	1.16455	−	0.928698i
$623$	19.6099	+	13.7967i	0.785655	+	0.552751i
$624$		0			0
$625$	21.6944	+	20.1295i	0.867777	+	0.805179i
$626$	50.2796	+	7.57844i	2.00958	+	0.302895i
$627$		0			0
$628$	−7.36700	−	48.8768i	−0.293975	−	1.95040i
$629$	−28.2220	−	13.5910i	−1.12528	−	0.541909i
$630$		0			0
$631$	−22.6371	+	10.9015i	−0.901170	+	0.433981i	−0.826312	−	0.563213i	$-0.809565\pi$
$631$	−22.6371	+	10.9015i	−0.901170	+	0.433981i	−0.0748589	+	0.997194i	$0.523851\pi$
$632$	1.36806	+	2.00658i	0.0544185	+	0.0798173i
$633$		0			0
$634$	−0.500751	−	6.68206i	−0.0198874	−	0.265378i
$635$	−6.28705	−	16.0191i	−0.249494	−	0.635700i
$636$		0			0
$637$	−6.33208	+	8.72456i	−0.250886	+	0.345680i
$638$		−	2.14875i		−	0.0850699i
$639$		0			0
$640$	38.5073	−	2.88572i	1.52213	−	0.114068i
$641$	−6.50188	−	7.00737i	−0.256809	−	0.276774i	0.591466	−	0.806330i	$-0.298549\pi$
$641$	−6.50188	−	7.00737i	−0.256809	−	0.276774i	−0.848275	+	0.529555i	$0.822359\pi$
$642$		0			0
$643$	0.0302707	+	0.0628578i	0.00119376	+	0.00247887i	0.901565	−	0.432644i	$-0.142419\pi$
$643$	0.0302707	+	0.0628578i	0.00119376	+	0.00247887i	−0.900371	+	0.435123i	$0.856705\pi$
$644$	3.05625	−	9.41419i	0.120433	−	0.370971i
$645$		0			0
$646$	−0.862834	+	0.130051i	−0.0339478	+	0.00511680i
$647$	−11.8815	−	8.10068i	−0.467110	−	0.318471i	0.306791	−	0.951777i	$-0.400745\pi$
$647$	−11.8815	−	8.10068i	−0.467110	−	0.318471i	−0.773901	+	0.633307i	$0.781697\pi$
$648$		0			0
$649$	8.50371	−	9.16482i	0.333800	−	0.359751i
$650$	2.60197	−	3.26277i	0.102058	−	0.127976i
$651$		0			0
$652$	−3.46213	−	4.34137i	−0.135587	−	0.170021i
$653$	6.71743	+	0.503402i	0.262873	+	0.0196996i	0.205515	−	0.978654i	$-0.434113\pi$
$653$	6.71743	+	0.503402i	0.262873	+	0.0196996i	0.0573585	+	0.998354i	$0.481732\pi$
$654$		0			0
$655$	−16.1498	−	27.9722i	−0.631023	−	1.09296i
$656$	4.00780	−	6.94171i	0.156478	−	0.271028i
$657$		0			0
$658$	−0.341273	+	23.1999i	−0.0133042	+	0.904426i
$659$	−13.3244	+	3.04120i	−0.519043	+	0.118468i	−0.474014	−	0.880517i	$-0.657195\pi$
$659$	−13.3244	+	3.04120i	−0.519043	+	0.118468i	−0.0450293	+	0.998986i	$0.514338\pi$
$660$		0			0
$661$	−14.5956	−	5.72834i	−0.567702	−	0.222807i	0.0640904	−	0.997944i	$-0.479585\pi$
$661$	−14.5956	−	5.72834i	−0.567702	−	0.222807i	−0.631793	+	0.775137i	$0.717681\pi$
$662$	59.7216	+	23.4390i	2.32114	+	0.910982i
$663$		0			0
$664$	12.7939	−	2.92013i	0.496501	−	0.113323i
$665$	−0.762693	−	0.626800i	−0.0295760	−	0.0243062i
$666$		0			0
$667$	0.517367	−	0.896107i	0.0200325	−	0.0346974i
$668$	17.2455	+	29.8701i	0.667248	+	1.15571i
$669$		0			0
$670$	−46.5732	−	3.49018i	−1.79928	−	0.134837i
$671$	3.02910	+	3.79838i	0.116937	+	0.146635i
$672$		0			0
$673$	29.3551	−	36.8101i	1.13156	−	1.41893i	0.237263	−	0.971446i	$-0.423750\pi$
$673$	29.3551	−	36.8101i	1.13156	−	1.41893i	0.894293	−	0.447481i	$-0.147679\pi$
$674$	−29.8274	+	32.1463i	−1.14891	+	1.23823i
$675$		0			0
$676$	−26.2343	−	17.8862i	−1.00901	−	0.687932i
$677$	−41.8799	+	6.31238i	−1.60957	+	0.242604i	−0.891386	−	0.453244i	$-0.850266\pi$
$677$	−41.8799	+	6.31238i	−1.60957	+	0.242604i	−0.718188	+	0.695849i	$0.755028\pi$
$678$		0			0
$679$	−17.7265	+	18.5498i	−0.680280	+	0.711875i
$680$	6.22530	+	12.9270i	0.238729	+	0.495727i
$681$		0			0
$682$	18.1169	+	19.5253i	0.693731	+	0.747664i
$683$	23.3292	−	1.74828i	0.892668	−	0.0668962i	0.379507	−	0.925189i	$-0.376094\pi$
$683$	23.3292	−	1.74828i	0.892668	−	0.0668962i	0.513160	+	0.858293i	$0.328475\pi$
$684$		0			0
$685$		−	53.7780i		−	2.05475i
$686$	13.9228	−	38.9467i	0.531576	−	1.48699i
$687$		0			0
$688$	−3.90659	−	9.95382i	−0.148937	−	0.379486i
$689$	0.387322	+	5.16846i	0.0147558	+	0.196903i
$690$		0			0
$691$	−8.22195	−	12.0594i	−0.312778	−	0.458761i	0.637371	−	0.770557i	$-0.280022\pi$
$691$	−8.22195	−	12.0594i	−0.312778	−	0.458761i	−0.950149	+	0.311796i	$0.899069\pi$
$692$	−12.5149	+	6.02685i	−0.475744	+	0.229106i
$693$		0			0
$694$	12.3235	+	5.93471i	0.467795	+	0.225278i
$695$	1.39351	+	9.24531i	0.0528587	+	0.350695i
$696$		0			0
$697$	19.7020	+	2.96960i	0.746266	+	0.112481i
$698$	3.75666	+	3.48567i	0.142192	+	0.131935i
$699$		0			0
$700$	−3.63483	+	8.87527i	−0.137384	+	0.335454i
$701$	−22.5793	+	18.0064i	−0.852809	+	0.680093i	−0.949002	−	0.315270i	$-0.897905\pi$
$701$	−22.5793	+	18.0064i	−0.852809	+	0.680093i	0.0961928	+	0.995363i	$0.469333\pi$
$702$		0			0
$703$	0.529496	+	1.71658i	0.0199703	+	0.0647422i
$704$	−13.0960	+	7.56099i	−0.493575	+	0.284965i
$705$		0			0
$706$	−57.3206	−	13.0831i	−2.15729	−	0.492387i
$707$	16.1231	−	19.6186i	0.606370	−	0.737834i
$708$		0			0
$709$	−5.82495	−	1.79676i	−0.218761	−	0.0674788i	0.183437	−	0.983031i	$-0.441278\pi$
$709$	−5.82495	−	1.79676i	−0.218761	−	0.0674788i	−0.402198	+	0.915553i	$0.631754\pi$
$710$	−29.8150	+	75.9674i	−1.11894	+	2.85100i
$711$		0			0
$712$	−5.89058	+	19.0968i	−0.220759	+	0.715683i
$713$	2.85415	+	12.5049i	0.106889	+	0.468311i
$714$		0			0
$715$	−0.994664	+	4.35791i	−0.0371983	+	0.162977i
$716$	−55.1696	−	31.8522i	−2.06179	−	1.19037i
$717$		0			0
$718$	67.5715	−	20.8430i	2.52174	−	0.777855i
$719$	0.397680	−	5.30667i	0.0148310	−	0.197906i	−0.984867	−	0.173314i	$-0.944552\pi$
$719$	0.397680	−	5.30667i	0.0148310	−	0.197906i	0.999698	−	0.0245915i	$-0.00782851\pi$
$720$		0			0
$721$	−5.44716	+	32.8531i	−0.202863	+	1.22351i
$722$	−33.1355	−	26.4247i	−1.23317	−	0.983424i
$723$		0			0
$724$	−4.32231	+	28.6766i	−0.160637	+	1.06576i
$725$	−0.564801	+	0.828411i	−0.0209762	+	0.0307664i
$726$		0			0
$727$	−15.2350	+	31.6359i	−0.565036	+	1.17331i	0.401281	+	0.915955i	$0.368565\pi$
$727$	−15.2350	+	31.6359i	−0.565036	+	1.17331i	−0.966317	+	0.257354i	$0.917149\pi$
$728$	−8.54616	−	2.77445i	−0.316742	−	0.102828i
$729$		0			0
$730$	50.1328	−	34.1799i	1.85550	−	1.26506i
$731$	19.4844	−	18.0788i	0.720655	−	0.668670i
$732$		0			0
$733$	41.5959	−	16.3252i	1.53638	−	0.602984i	0.561849	−	0.827240i	$-0.310090\pi$
$733$	41.5959	−	16.3252i	1.53638	−	0.602984i	0.974530	+	0.224256i	$0.0719951\pi$
$734$	−4.28018			−0.157984
$735$		0			0
$736$	−8.45962			−0.311826
$737$	9.09391	−	3.56910i	0.334978	−	0.131469i
$738$		0			0
$739$	28.1100	−	26.0823i	1.03404	−	0.959452i	0.0348413	−	0.999393i	$-0.488907\pi$
$739$	28.1100	−	26.0823i	1.03404	−	0.959452i	0.999202	+	0.0399408i	$0.0127169\pi$
$740$	73.8374	−	50.3415i	2.71432	−	1.85059i
$741$		0			0
$742$	−6.99192	−	18.6157i	−0.256681	−	0.683404i
$743$	−12.7732	+	26.5239i	−0.468604	+	0.973066i	0.524006	+	0.851715i	$0.324437\pi$
$743$	−12.7732	+	26.5239i	−0.468604	+	0.973066i	−0.992610	+	0.121351i	$0.961277\pi$
$744$		0			0
$745$	−14.4760	+	21.2324i	−0.530359	+	0.777894i
$746$	−0.242274	+	1.60739i	−0.00887030	+	0.0588506i
$747$		0			0
$748$	−7.09897	−	5.66124i	−0.259564	−	0.206996i
$749$	15.1186	−	21.4889i	0.552423	−	0.785189i
$750$		0			0
$751$	2.35456	−	31.4194i	0.0859191	−	1.14651i	−0.773002	−	0.634404i	$-0.781246\pi$
$751$	2.35456	−	31.4194i	0.0859191	−	1.14651i	0.858921	−	0.512108i	$-0.171135\pi$
$752$	3.94029	−	1.21542i	0.143688	−	0.0443217i
$753$		0			0
$754$	−2.46114	−	1.42094i	−0.0896293	−	0.0517475i
$755$	7.49953	−	32.8576i	0.272936	−	1.19581i
$756$		0			0
$757$	8.49403	+	37.2148i	0.308721	+	1.35259i	0.856576	+	0.516021i	$0.172587\pi$
$757$	8.49403	+	37.2148i	0.308721	+	1.35259i	−0.547855	+	0.836573i	$0.684555\pi$
$758$	−5.65857	+	18.3446i	−0.205528	+	0.666307i
$759$		0			0
$760$	0.300614	−	0.765951i	0.0109044	−	0.0277840i
$761$	7.40735	+	2.28487i	0.268516	+	0.0828263i	0.426090	−	0.904681i	$-0.359891\pi$
$761$	7.40735	+	2.28487i	0.268516	+	0.0828263i	−0.157573	+	0.987507i	$0.550367\pi$
$762$		0			0
$763$	15.6436	+	20.2196i	0.566338	+	0.731998i
$764$	−44.1041	−	10.0665i	−1.59563	−	0.364193i
$765$		0			0
$766$	−42.3381	+	24.4439i	−1.52974	+	0.883195i
$767$	−4.87382	−	15.8005i	−0.175983	−	0.570524i
$768$		0			0
$769$	−18.8950	+	15.0682i	−0.681370	+	0.543375i	−0.901867	−	0.432013i	$-0.857804\pi$
$769$	−18.8950	+	15.0682i	−0.681370	+	0.543375i	0.220497	+	0.975388i	$0.429232\pi$
$770$	−1.02994	−	17.1190i	−0.0371163	−	0.616927i
$771$		0			0
$772$	16.6166	+	15.4180i	0.598046	+	0.554905i
$773$	0.859499	+	0.129549i	0.0309140	+	0.00465954i	0.164481	−	0.986380i	$-0.447405\pi$
$773$	0.859499	+	0.129549i	0.0309140	+	0.00465954i	−0.133567	+	0.991040i	$0.542643\pi$
$774$		0			0
$775$	−1.85237	−	12.2897i	−0.0665390	−	0.441458i
$776$	−19.2677	−	9.27886i	−0.691672	−	0.333092i
$777$		0			0
$778$	9.08958	−	4.37731i	0.325877	−	0.156934i
$779$	−0.643674	−	0.944097i	−0.0230620	−	0.0338258i
$780$		0			0
$781$	−1.27567	−	17.0227i	−0.0456472	−	0.609119i
$782$	−2.66687	−	6.79508i	−0.0953671	−	0.242991i
$783$		0			0
$784$	−7.34733	−	0.216207i	−0.262405	−	0.00772166i
$785$		−	41.2426i		−	1.47201i
$786$		0			0
$787$	30.7752	−	2.30628i	1.09702	−	0.0822100i	0.486098	−	0.873904i	$-0.338420\pi$
$787$	30.7752	−	2.30628i	1.09702	−	0.0822100i	0.610918	+	0.791694i	$0.290801\pi$
$788$	−26.0768	−	28.1041i	−0.928946	−	1.00117i
$789$		0			0
$790$	2.65997	+	5.52348i	0.0946374	+	0.196517i
$791$	−30.2575	−	2.71557i	−1.07583	−	0.0965544i
$792$		0			0
$793$	6.35368	−	0.957664i	0.225626	−	0.0340076i
$794$	48.9695	+	33.3868i	1.73786	+	1.18485i
$795$		0			0
$796$	−23.5261	+	25.3551i	−0.833861	+	0.898688i
$797$	−18.1183	+	22.7196i	−0.641782	+	0.804769i	−0.991225	−	0.132189i	$-0.957799\pi$
$797$	−18.1183	+	22.7196i	−0.641782	+	0.804769i	0.349443	+	0.936958i	$0.386371\pi$
$798$		0			0
$799$	6.39066	+	8.01364i	0.226085	+	0.283502i
$800$	8.17422	+	0.612573i	0.289002	+	0.0216577i
$801$		0			0
$802$	−8.43023	−	14.6016i	−0.297682	−	0.515600i
$803$	−6.34591	+	10.9914i	−0.223942	+	0.387879i
$804$		0			0
$805$	3.69233	−	7.38723i	0.130137	−	0.260366i
$806$	34.3443	−	7.83887i	1.20973	−	0.276112i
$807$		0			0
$808$	19.7024	+	7.73263i	0.693129	+	0.272033i
$809$	22.0374	+	8.64903i	0.774793	+	0.304084i	0.719597	−	0.694392i	$-0.244327\pi$
$809$	22.0374	+	8.64903i	0.774793	+	0.304084i	0.0551955	+	0.998476i	$0.482422\pi$
$810$		0			0
$811$	−21.6873	+	4.94998i	−0.761544	+	0.173817i	−0.585619	−	0.810586i	$-0.699149\pi$
$811$	−21.6873	+	4.94998i	−0.761544	+	0.173817i	−0.175925	+	0.984404i	$0.556292\pi$
$812$	6.34526	+	1.54680i	0.222675	+	0.0542820i
$813$		0			0
$814$	−15.6037	+	27.0263i	−0.546908	+	0.947272i
$815$	−2.31659	−	4.01245i	−0.0811465	−	0.140550i
$816$		0			0
$817$	−1.52005	−	0.113912i	−0.0531799	−	0.00398528i
$818$	−12.6242	−	15.8302i	−0.441393	−	0.553490i
$819$		0			0
$820$	−35.4413	+	44.4420i	−1.23766	+	1.55198i
$821$	6.36511	−	6.85996i	0.222144	−	0.239414i	−0.612140	−	0.790750i	$-0.709691\pi$
$821$	6.36511	−	6.85996i	0.222144	−	0.239414i	0.834284	+	0.551335i	$0.185882\pi$
$822$		0			0
$823$	8.80774	+	6.00502i	0.307019	+	0.209322i	0.707021	−	0.707192i	$-0.250038\pi$
$823$	8.80774	+	6.00502i	0.307019	+	0.209322i	−0.400003	+	0.916514i	$0.630991\pi$
$824$	−27.4467	+	4.13692i	−0.956150	+	0.144116i
$825$		0			0
$826$	34.9624	+	52.9369i	1.21650	+	1.84191i
$827$	−12.6652	−	26.2995i	−0.440411	−	0.914523i	−0.996515	−	0.0834105i	$-0.973419\pi$
$827$	−12.6652	−	26.2995i	−0.440411	−	0.914523i	0.556104	−	0.831113i	$-0.312296\pi$
$828$		0			0
$829$	18.2651	+	19.6851i	0.634373	+	0.683691i	0.965651	−	0.259842i	$-0.0836704\pi$
$829$	18.2651	+	19.6851i	0.634373	+	0.683691i	−0.331278	+	0.943533i	$0.607480\pi$
$830$	33.0346	−	2.47560i	1.14665	−	0.0859293i
$831$		0			0
$832$			19.9999i			0.693371i
$833$	−6.17209	−	17.1973i	−0.213850	−	0.595850i
$834$		0			0
$835$	10.5140	+	26.7893i	0.363853	+	0.927082i
$836$	0.0389136	+	0.519265i	0.00134585	+	0.0179592i
$837$		0			0
$838$	13.0623	+	19.1589i	0.451231	+	0.661834i
$839$	25.4608	−	12.2613i	0.879006	−	0.423307i	0.0607444	−	0.998153i	$-0.480653\pi$
$839$	25.4608	−	12.2613i	0.879006	−	0.423307i	0.818261	+	0.574847i	$0.194938\pi$
$840$		0			0
$841$	−25.5129	−	12.2864i	−0.879757	−	0.423669i
$842$	2.09516	+	13.9005i	0.0722041	+	0.479043i
$843$		0			0
$844$	32.5611	+	4.90780i	1.12080	+	0.168933i
$845$	−19.4206	−	18.0197i	−0.668090	−	0.619897i
$846$		0			0
$847$	−12.4316	−	22.2827i	−0.427154	−	0.765643i
$848$	−2.76299	+	2.20341i	−0.0948816	+	0.0756655i
$849$		0			0
$850$	2.08486	+	6.75894i	0.0715100	+	0.231830i
$851$	−13.0146	+	7.51397i	−0.446134	+	0.257575i
$852$		0			0
$853$	−17.8802	−	4.08103i	−0.612205	−	0.139732i	−0.0948340	−	0.995493i	$-0.530232\pi$
$853$	−17.8802	−	4.08103i	−0.612205	−	0.139732i	−0.517371	+	0.855761i	$0.673089\pi$
$854$	−22.3661	+	10.3685i	−0.765352	+	0.354802i
$855$		0			0
$856$	20.9266	+	6.45501i	0.715258	+	0.220628i
$857$	−19.1161	+	48.7069i	−0.652992	+	1.66380i	0.0912015	+	0.995832i	$0.470929\pi$
$857$	−19.1161	+	48.7069i	−0.652992	+	1.66380i	−0.744194	+	0.667964i	$0.767166\pi$
$858$		0			0
$859$	2.72148	−	8.82283i	0.0928558	−	0.301031i	−0.897216	−	0.441591i	$-0.854414\pi$
$859$	2.72148	−	8.82283i	0.0928558	−	0.301031i	0.990072	+	0.140560i	$0.0448903\pi$
$860$	16.8739	+	73.9293i	0.575394	+	2.52097i
$861$		0			0
$862$	−17.8395	+	78.1601i	−0.607617	+	2.66214i
$863$	6.15895	+	3.55587i	0.209653	+	0.121043i	0.601150	−	0.799136i	$-0.294709\pi$
$863$	6.15895	+	3.55587i	0.209653	+	0.121043i	−0.391497	+	0.920179i	$0.628043\pi$
$864$		0			0
$865$	−11.0751	+	3.41620i	−0.376563	+	0.116154i
$866$	−2.97678	+	39.7224i	−0.101155	+	1.34982i
$867$		0			0
$868$	−70.6999	+	39.4436i	−2.39971	+	1.33880i
$869$	−1.00259	−	0.799539i	−0.0340106	−	0.0271225i
$870$		0			0
$871$	1.92570	−	12.7762i	0.0652498	−	0.432904i
$872$	−12.0032	+	17.6055i	−0.406480	+	0.596197i
$873$		0			0
$874$	−0.181635	+	0.377169i	−0.00614390	+	0.0127579i
$875$	12.8030	−	21.4409i	0.432821	−	0.724834i
$876$		0			0
$877$	−26.0163	+	17.7376i	−0.878509	+	0.598957i	−0.916373	−	0.400326i	$-0.868897\pi$
$877$	−26.0163	+	17.7376i	−0.878509	+	0.598957i	0.0378639	+	0.999283i	$0.487945\pi$
$878$	1.05379	−	0.977774i	0.0355637	−	0.0329983i
$879$		0			0
$880$	−2.83717	+	1.11351i	−0.0956411	+	0.0375364i
$881$	−27.1971			−0.916293			−0.458146	−	0.888877i	$-0.651486\pi$
$881$	−27.1971			−0.916293			−0.458146	+	0.888877i	$0.651486\pi$
$882$		0			0
$883$	−13.4651			−0.453136			−0.226568	−	0.973995i	$-0.572751\pi$
$883$	−13.4651			−0.453136			−0.226568	+	0.973995i	$0.572751\pi$
$884$	−11.1787	+	4.38732i	−0.375981	+	0.147562i
$885$		0			0
$886$	42.3225	−	39.2695i	1.42185	−	1.31929i
$887$	22.4368	−	15.2971i	0.753353	−	0.513628i	−0.124698	−	0.992195i	$-0.539796\pi$
$887$	22.4368	−	15.2971i	0.753353	−	0.513628i	0.878051	+	0.478567i	$0.158844\pi$
$888$		0			0
$889$	−15.2414	+	10.0663i	−0.511181	+	0.337612i
$890$	−21.8889	+	45.4527i	−0.733716	+	1.52358i
$891$		0			0
$892$	47.6293	−	69.8594i	1.59475	−	2.33907i
$893$	0.0876091	−	0.581248i	0.00293173	−	0.0194507i
$894$		0			0
$895$	−41.5573	−	33.1409i	−1.38911	−	1.10778i
$896$	−11.5037	−	39.3393i	−0.384311	−	1.31423i
$897$		0			0
$898$	0.0619568	−	0.826756i	0.00206753	−	0.0275892i
$899$	−8.08749	+	2.49466i	−0.269733	+	0.0832016i
$900$		0			0
$901$	−7.60763	−	4.39227i	−0.253447	−	0.146328i
$902$	4.41710	−	19.3526i	0.147073	−	0.644370i
$903$		0			0
$904$	−5.63439	−	24.6859i	−0.187397	−	0.821040i
$905$	−7.13235	+	23.1225i	−0.237087	+	0.768618i
$906$		0			0
$907$	−4.37094	+	11.1370i	−0.145135	+	0.369797i	−0.984893	−	0.173163i	$-0.944601\pi$
$907$	−4.37094	+	11.1370i	−0.145135	+	0.369797i	0.839758	+	0.542960i	$0.182697\pi$
$908$	−3.64976	−	1.12580i	−0.121122	−	0.0373611i
$909$		0			0
$910$	−20.2889	−	10.1409i	−0.672569	−	0.336167i
$911$	29.7947	+	6.80044i	0.987141	+	0.225308i	0.685468	−	0.728103i	$-0.259598\pi$
$911$	29.7947	+	6.80044i	0.987141	+	0.225308i	0.301673	+	0.953411i	$0.402455\pi$
$912$		0			0
$913$	−6.00099	+	3.46467i	−0.198604	+	0.114664i
$914$	8.79937	+	28.5269i	0.291057	+	0.943585i
$915$		0			0
$916$	−46.1503	+	36.8036i	−1.52485	+	1.21603i
$917$	−25.4716	+	22.9463i	−0.841145	+	0.757753i
$918$		0			0
$919$	−13.0254	−	12.0858i	−0.429669	−	0.398675i	0.435473	−	0.900202i	$-0.356581\pi$
$919$	−13.0254	−	12.0858i	−0.429669	−	0.398675i	−0.865142	+	0.501527i	$0.832772\pi$
$920$	6.80660	+	1.02593i	0.224407	+	0.0338239i
$921$		0			0
$922$	7.70543	+	51.1222i	0.253765	+	1.68362i
$923$	−20.3410	−	9.79571i	−0.669532	−	0.322430i
$924$		0			0
$925$	13.1196	−	6.31806i	0.431369	−	0.207737i
$926$	1.13624	+	1.66655i	0.0373391	+	0.0547664i
$927$		0			0
$928$	−0.417148	−	5.56645i	−0.0136935	−	0.182728i
$929$	5.32876	+	13.5775i	0.174831	+	0.445462i	0.991250	−	0.131998i	$-0.0421392\pi$
$929$	5.32876	+	13.5775i	0.174831	+	0.445462i	−0.816419	+	0.577460i	$0.804044\pi$
$930$		0			0
$931$	−0.482210	+	0.930285i	−0.0158038	+	0.0304889i
$932$		−	5.38770i		−	0.176480i
$933$		0			0
$934$	−10.6881	+	0.800960i	−0.349724	+	0.0262082i
$935$	−5.15308	−	5.55370i	−0.168524	−	0.181625i
$936$		0			0
$937$	−1.90198	−	3.94950i	−0.0621349	−	0.129024i	0.867589	−	0.497282i	$-0.165669\pi$
$937$	−1.90198	−	3.94950i	−0.0621349	−	0.129024i	−0.929724	+	0.368258i	$0.879954\pi$
$938$	6.66654	+	49.1217i	0.217670	+	1.60388i
$939$		0			0
$940$	−28.9155	+	4.35832i	−0.943121	+	0.142153i
$941$	0.469715	+	0.320246i	0.0153123	+	0.0104397i	0.570952	−	0.820983i	$-0.306574\pi$
$941$	0.469715	+	0.320246i	0.0153123	+	0.0104397i	−0.555640	+	0.831423i	$0.687527\pi$
$942$		0			0
$943$	6.50172	−	7.00719i	0.211725	−	0.228185i
$944$	7.02954	−	8.81476i	0.228792	−	0.286896i
$945$		0			0
$946$	−16.5105	−	20.7035i	−0.536801	−	0.673128i
$947$	17.7237	+	1.32821i	0.575943	+	0.0431610i	0.359518	−	0.933138i	$-0.382941\pi$
$947$	17.7237	+	1.32821i	0.575943	+	0.0431610i	0.216425	+	0.976299i	$0.430560\pi$
$948$		0			0
$949$	8.39291	+	14.5369i	0.272445	+	0.471889i
$950$	0.202819	−	0.351292i	0.00658030	−	0.0113974i
$951$		0			0
$952$	12.0449	−	9.31897i	0.390377	−	0.302030i
$953$	22.8300	−	5.21080i	0.739536	−	0.168794i	0.163873	−	0.986481i	$-0.447601\pi$
$953$	22.8300	−	5.21080i	0.739536	−	0.168794i	0.575663	+	0.817687i	$0.304744\pi$
$954$		0			0
$955$	−35.1368	−	13.7902i	−1.13700	−	0.446240i
$956$	33.0061	+	12.9540i	1.06749	+	0.418961i
$957$		0			0
$958$	−64.2939	+	14.6747i	−2.07724	+	0.474117i
$959$	−55.8304	+	11.8818i	−1.80286	+	0.383682i
$960$		0			0
$961$	36.9563	−	64.0102i	1.19214	−	2.06484i
$962$	20.6369	+	35.7442i	0.665361	+	1.15244i
$963$		0			0
$964$	49.9379	+	3.74233i	1.60839	+	0.120532i
$965$	11.7924	+	14.7872i	0.379611	+	0.476017i
$966$		0			0
$967$	13.0627	−	16.3801i	0.420068	−	0.526748i	−0.526101	−	0.850422i	$-0.676347\pi$
$967$	13.0627	−	16.3801i	0.420068	−	0.526748i	0.946169	+	0.323674i	$0.104918\pi$
$968$	14.4655	−	15.5901i	0.464938	−	0.501084i
$969$		0			0
$970$	−44.6046	−	30.4109i	−1.43217	−	0.976435i
$971$	33.3115	−	5.02090i	1.06902	−	0.161128i	0.409117	−	0.912482i	$-0.365837\pi$
$971$	33.3115	−	5.02090i	1.06902	−	0.161128i	0.659900	+	0.751354i	$0.270599\pi$
$972$		0			0
$973$	9.29026	−	3.48935i	0.297832	−	0.111863i
$974$	−7.82343	−	16.2455i	−0.250679	−	0.520540i
$975$		0			0
$976$	2.97997	+	3.21165i	0.0953866	+	0.102802i
$977$	−34.2447	+	2.56628i	−1.09558	+	0.0821027i	−0.610237	−	0.792219i	$-0.708926\pi$
$977$	−34.2447	+	2.56628i	−1.09558	+	0.0821027i	−0.485347	+	0.874322i	$0.661307\pi$
$978$		0			0
$979$		−	10.5525i		−	0.337261i
$980$	51.2939	+	9.28188i	1.63852	+	0.296499i
$981$		0			0
$982$	25.1677	+	64.1262i	0.803133	+	2.04635i
$983$	−2.69648	−	35.9820i	−0.0860044	−	1.14765i	−0.858564	−	0.512706i	$-0.828643\pi$
$983$	−2.69648	−	35.9820i	−0.0860044	−	1.14765i	0.772560	−	0.634942i	$-0.218976\pi$
$984$		0			0
$985$	−18.0200	−	26.4305i	−0.574165	−	0.842145i
$986$	4.33967	−	2.08987i	0.138203	−	0.0665552i
$987$		0			0
$988$	0.620489	+	0.298812i	0.0197404	+	0.00950646i
$989$	−1.90056	−	12.6094i	−0.0604344	−	0.400956i
$990$		0			0
$991$	−4.61093	−	0.694986i	−0.146471	−	0.0220770i	0.0753974	−	0.997154i	$-0.475977\pi$
$991$	−4.61093	−	0.694986i	−0.146471	−	0.0220770i	−0.221868	+	0.975077i	$0.571216\pi$
$992$	50.7232	+	47.0643i	1.61046	+	1.49429i
$993$		0			0
$994$	85.4539	+	14.1685i	2.71043	+	0.449399i
$995$	−22.5636	+	17.9939i	−0.715315	+	0.570445i
$996$		0			0
$997$	−8.98546	−	29.1301i	−0.284572	−	0.922561i	−0.979149	−	0.203142i	$-0.934885\pi$
$997$	−8.98546	−	29.1301i	−0.284572	−	0.922561i	0.694577	−	0.719418i	$-0.255592\pi$
$998$	−54.6579	+	31.5567i	−1.73016	+	0.998911i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bg.a.278.16	yes	216
3.2	odd	2	inner	441.2.bg.a.278.3	✓	216
49.3	odd	42	inner	441.2.bg.a.395.3	yes	216
147.101	even	42	inner	441.2.bg.a.395.16	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bg.a.278.3	✓	216	3.2	odd	2	inner
441.2.bg.a.278.16	yes	216	1.1	even	1	trivial
441.2.bg.a.395.3	yes	216	49.3	odd	42	inner
441.2.bg.a.395.16	yes	216	147.101	even	42	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bg (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.07888 - 0.815901i) q^{2} +(2.18995 - 2.03198i) q^{4} +(2.05954 - 1.40417i) q^{5} +(-1.91279 - 1.82790i) q^{7} +(0.956806 - 1.98683i) q^{8} +O(q^{10})\)	\(q+(2.07888 - 0.815901i) q^{2} +(2.18995 - 2.03198i) q^{4} +(2.05954 - 1.40417i) q^{5} +(-1.91279 - 1.82790i) q^{7} +(0.956806 - 1.98683i) q^{8} +(3.13588 - 4.59948i) q^{10} +(-0.173548 + 1.15142i) q^{11} +(1.20405 + 0.960194i) q^{13} +(-5.46786 - 2.23934i) q^{14} +(-0.0784720 + 1.04714i) q^{16} +(-2.49422 + 0.769366i) q^{17} +(0.129636 + 0.0748453i) q^{19} +(1.65705 - 7.26000i) q^{20} +(0.578657 + 2.53526i) q^{22} +(-0.369109 + 1.19662i) q^{23} +(0.443305 - 1.12952i) q^{25} +(3.28649 + 1.01375i) q^{26} +(-7.90317 - 0.116256i) q^{28} +(-0.805580 - 0.183868i) q^{29} +(8.87043 - 5.12134i) q^{31} +(1.99122 + 6.45538i) q^{32} +(-4.55747 + 3.63446i) q^{34} +(-6.50616 - 1.07874i) q^{35} +(8.79713 + 8.16255i) q^{37} +(0.330564 + 0.0498245i) q^{38} +(-0.819266 - 5.43547i) q^{40} +(-6.87743 - 3.31199i) q^{41} +(-9.17465 + 4.41828i) q^{43} +(1.95959 + 2.87420i) q^{44} +(0.208991 + 2.78879i) q^{46} +(-1.43464 - 3.65541i) q^{47} +(0.317563 + 6.99279i) q^{49} -2.70984i q^{50} +(4.58789 - 0.343815i) q^{52} +(2.28911 + 2.46707i) q^{53} +(1.25936 + 2.61508i) q^{55} +(-5.46190 + 2.05145i) q^{56} +(-1.82472 + 0.275033i) q^{58} +(-8.87123 - 6.04830i) q^{59} +(2.83787 - 3.05850i) q^{61} +(14.2621 - 17.8841i) q^{62} +(8.09705 + 10.1534i) q^{64} +(3.82806 + 0.286873i) q^{65} +(-4.19487 - 7.26573i) q^{67} +(-3.89889 + 6.75308i) q^{68} +(-14.4057 + 3.06580i) q^{70} +(-14.2924 + 3.26215i) q^{71} +(10.1462 + 3.98209i) q^{73} +(24.9480 + 9.79138i) q^{74} +(0.435980 - 0.0995096i) q^{76} +(2.43664 - 1.88520i) q^{77} +(-0.550642 + 0.953740i) q^{79} +(1.30874 + 2.26681i) q^{80} +(-16.9996 - 1.27395i) q^{82} +(3.71031 + 4.65258i) q^{83} +(-4.05663 + 5.08686i) q^{85} +(-15.4681 + 16.6707i) q^{86} +(2.12162 + 1.44650i) q^{88} +(-8.96124 + 1.35069i) q^{89} +(-0.547952 - 4.03753i) q^{91} +(1.62318 + 3.37056i) q^{92} +(-5.96490 - 6.42863i) q^{94} +(0.372086 - 0.0278840i) q^{95} -9.69774i q^{97} +(6.36560 + 14.2781i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) 216 * q - 16 * q^4 + 2 * q^7	\( 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) \) 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Introduction

L-functions

Modular forms

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Database

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