LMFDB - Embedded newform 441.2.bg.a.395.3

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			395.3
Character	$\chi$	$=$	441.395
Dual form			441.2.bg.a.278.3

$q$-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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

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

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	$-0.670652\pi$
$2$	−2.07888	−	0.815901i	−1.46999	−	0.576929i	−0.959188	+	0.282769i	$0.908747\pi$
$3$		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	$-0.497716\pi$
$5$	−2.05954	−	1.40417i	−0.921054	−	0.627964i	−0.928229	+	0.372010i	$0.878669\pi$
$6$		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	0.999639	+	0.0268550i	$0.00854922\pi$
$11$	0.173548	+	1.15142i	0.0523268	+	0.347166i	−0.947313	+	0.320311i	$0.896213\pi$
$12$		0			0
$13$	1.20405	−	0.960194i	0.333942	−	0.266310i	−0.442134	−	0.896949i	$-0.645779\pi$
$13$	1.20405	−	0.960194i	0.333942	−	0.266310i	0.776076	+	0.630639i	$0.217207\pi$
$14$	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	$-0.302244\pi$
$17$	2.49422	+	0.769366i	0.604938	+	0.186599i	0.0228697	+	0.999738i	$0.492720\pi$
$18$		0			0
$19$	0.129636	−	0.0748453i	0.0297405	−	0.0171707i	−0.485056	−	0.874483i	$-0.661201\pi$
$19$	0.129636	−	0.0748453i	0.0297405	−	0.0171707i	0.514797	+	0.857312i	$0.327867\pi$
$20$	−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	$-0.0535617\pi$
$23$	0.369109	+	1.19662i	0.0769645	+	0.249513i	−0.908912	+	0.416989i	$0.863085\pi$
$24$		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	$-0.546984\pi$
$29$	0.805580	−	0.183868i	0.149592	−	0.0341435i	0.296661	+	0.954983i	$0.404127\pi$
$30$		0			0
$31$	8.87043	+	5.12134i	1.59318	+	0.919820i	0.992758	+	0.120134i	$0.0383323\pi$
$31$	8.87043	+	5.12134i	1.59318	+	0.919820i	0.600418	+	0.799687i	$0.295001\pi$
$32$	−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	0.611533	−	0.791219i	$-0.290553\pi$
$37$	8.79713	−	8.16255i	1.44624	−	1.34191i	0.834706	−	0.550695i	$-0.185637\pi$
$38$	−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	$-0.439587\pi$
$41$	6.87743	−	3.31199i	1.07407	−	0.517247i	0.885418	+	0.464797i	$0.153873\pi$
$42$		0			0
$43$	−9.17465	−	4.41828i	−1.39912	−	0.673781i	−0.426138	−	0.904658i	$-0.640126\pi$
$43$	−9.17465	−	4.41828i	−1.39912	−	0.673781i	−0.972983	+	0.230877i	$0.925841\pi$
$44$	−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	$-0.788495\pi$
$47$	1.43464	−	3.65541i	0.209264	−	0.533196i	0.996513	+	0.0834395i	$0.0265905\pi$
$48$		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	$-0.836151\pi$
$53$	−2.28911	+	2.46707i	−0.314433	+	0.338879i	0.555984	+	0.831193i	$0.312342\pi$
$54$		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	$-0.444144\pi$
$59$	8.87123	−	6.04830i	1.15494	−	0.787422i	0.980359	+	0.197222i	$0.0631920\pi$
$60$		0			0
$61$	2.83787	+	3.05850i	0.363352	+	0.391601i	0.888095	−	0.459660i	$-0.152029\pi$
$61$	2.83787	+	3.05850i	0.363352	+	0.391601i	−0.524742	+	0.851261i	$0.675838\pi$
$62$	−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	0.487410	+	0.873173i	$0.337942\pi$
$67$	−4.19487	+	7.26573i	−0.512485	+	0.887650i	−0.999895	+	0.0144772i	$0.995392\pi$
$68$	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	$-0.0927492\pi$
$71$	14.2924	+	3.26215i	1.69620	+	0.387146i	0.738348	+	0.674420i	$0.235606\pi$
$72$		0			0
$73$	10.1462	−	3.98209i	1.18752	−	0.466068i	0.312391	−	0.949954i	$-0.398870\pi$
$73$	10.1462	−	3.98209i	1.18752	−	0.466068i	0.875131	+	0.483885i	$0.160775\pi$
$74$	−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	0.833386	−	0.552692i	$-0.186399\pi$
$79$	−0.550642	−	0.953740i	−0.0619521	−	0.107304i	−0.895338	+	0.445387i	$0.853066\pi$
$80$	−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	$-0.891616\pi$
$83$	−3.71031	+	4.65258i	−0.407260	+	0.510687i	0.535329	+	0.844644i	$0.320188\pi$
$84$		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	$-0.292905\pi$
$89$	8.96124	+	1.35069i	0.949889	+	0.143173i	0.344220	+	0.938889i	$0.388143\pi$
$90$		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	$0.163854\pi$
$97$			9.69774i			0.984656i	−0.870410	+	0.492328i	$0.836146\pi$
$98$	−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	0.840482	+	0.541840i	$0.182272\pi$
$101$	−0.717255	+	9.57110i	−0.0713695	+	0.952360i	−0.911851	+	0.410521i	$0.865347\pi$
$102$		0			0
$103$	−7.09042	+	10.3997i	−0.698640	+	1.02472i	0.298877	+	0.954292i	$0.403388\pi$
$103$	−7.09042	+	10.3997i	−0.698640	+	1.02472i	−0.997517	+	0.0704251i	$0.977564\pi$
$104$	−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	0.795913	+	0.605411i	$0.206991\pi$
$107$	−1.48011	+	9.81990i	−0.143088	+	0.949325i	−0.939001	+	0.343915i	$0.888247\pi$
$108$		0			0
$109$	−9.55463	+	1.44013i	−0.915168	+	0.137939i	−0.589708	−	0.807617i	$-0.700757\pi$
$109$	−9.55463	+	1.44013i	−0.915168	+	0.137939i	−0.325460	+	0.945556i	$0.605519\pi$
$110$	−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	$-0.467319\pi$
$113$	−8.97715	−	7.15904i	−0.844500	−	0.673466i	−0.946988	+	0.321268i	$0.895891\pi$
$114$		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	0.996226	+	0.0867987i	$0.0276637\pi$
$127$	1.53622	+	6.73064i	0.136318	+	0.597248i	−0.859908	+	0.510449i	$0.829479\pi$
$128$	−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	−0.864358	−	0.502877i	$-0.832275\pi$
$131$	−0.968337	−	12.9216i	−0.0846040	−	1.12896i	0.779754	−	0.626086i	$-0.215344\pi$
$132$		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	−0.839831	−	0.542848i	$-0.817346\pi$
$137$	−12.1533	−	17.8257i	−1.03833	−	1.52295i	−0.198498	−	0.980101i	$-0.563606\pi$
$138$		0			0
$139$	−1.62745	−	3.37944i	−0.138039	−	0.286640i	0.820477	−	0.571679i	$-0.193708\pi$
$139$	−1.62745	−	3.37944i	−0.138039	−	0.286640i	−0.958516	+	0.285039i	$0.907993\pi$
$140$	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	$-0.242181\pi$
$149$	9.59664	+	3.76640i	0.786188	+	0.308556i	0.0619256	+	0.998081i	$0.480276\pi$
$150$		0			0
$151$	9.91135	+	9.19639i	0.806575	+	0.748392i	0.971277	−	0.237951i	$-0.0764759\pi$
$151$	9.91135	+	9.19639i	0.806575	+	0.748392i	−0.164703	+	0.986343i	$0.552666\pi$
$152$	−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	0.992477	+	0.122432i	$0.0390692\pi$
$157$	9.32045	+	13.6706i	0.743853	+	1.09103i	−0.248624	+	0.968600i	$0.579978\pi$
$158$	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	0.999998	−	0.00194228i	$-0.000618246\pi$
$163$	0.138902	+	1.85352i	0.0108797	+	0.145179i	−0.989118	+	0.147121i	$0.952999\pi$
$164$	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	0.971652	+	0.236416i	$0.0759730\pi$
$167$	2.56908	+	11.2559i	0.198801	+	0.871004i	−0.772851	+	0.634588i	$0.781170\pi$
$168$		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	$-0.538679\pi$
$173$	4.44305	−	1.37050i	0.337799	−	0.104197i	0.459014	+	0.888429i	$0.348203\pi$
$174$		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	−0.342355	−	0.939571i	$-0.611224\pi$
$179$	6.28538	−	20.3767i	0.469791	−	1.52303i	0.812146	−	0.583454i	$-0.198299\pi$
$180$		0			0
$181$	−7.58961	−	6.05251i	−0.564132	−	0.449880i	0.299434	−	0.954117i	$-0.403202\pi$
$181$	−7.58961	−	6.05251i	−0.564132	−	0.449880i	−0.863565	+	0.504237i	$0.831774\pi$
$182$	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	$-0.624971\pi$
$191$	8.53026	−	12.5116i	0.617228	−	0.905308i	0.999827	+	0.0186070i	$0.00592315\pi$
$192$		0			0
$193$	0.567028	−	7.56646i	0.0408155	−	0.544645i	−0.938892	−	0.344212i	$-0.888146\pi$
$193$	0.567028	−	7.56646i	0.0408155	−	0.544645i	0.979707	−	0.200433i	$-0.0642350\pi$
$194$	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	−0.341074	−	0.940036i	$-0.610791\pi$
$199$	−11.5456	−	0.865220i	−0.818443	−	0.0613339i	−0.477370	+	0.878703i	$0.658410\pi$
$200$	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	−0.486817	−	0.873504i	$-0.661842\pi$
$211$	6.87238	−	8.61769i	0.473114	−	0.593266i	0.959931	+	0.280238i	$0.0904134\pi$
$212$	−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	0.994936	−	0.100506i	$-0.0320462\pi$
$223$	27.5926	+	6.29782i	1.84774	+	0.421733i	0.852799	+	0.522240i	$0.174903\pi$
$224$	−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	$-0.819824\pi$
$227$	0.639251	−	1.10722i	0.0424286	−	0.0734885i	0.886460	+	0.462806i	$0.153157\pi$
$228$		0			0
$229$	−19.7036	+	1.47658i	−1.30205	+	0.0975752i	−0.707632	−	0.706581i	$-0.750237\pi$
$229$	−19.7036	+	1.47658i	−1.30205	+	0.0975752i	−0.594418	+	0.804156i	$0.702618\pi$
$230$	−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	$-0.256910\pi$
$233$	−1.22666	−	1.32202i	−0.0803610	−	0.0866085i	−0.771952	+	0.635681i	$0.780720\pi$
$234$		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	$-0.982549\pi$
$239$	−5.14965	+	10.6934i	−0.333103	+	0.691696i	0.665394	+	0.746492i	$0.268263\pi$
$240$		0			0
$241$	11.4016	−	12.2880i	0.734443	−	0.791541i	−0.249813	−	0.968294i	$-0.580369\pi$
$241$	11.4016	−	12.2880i	0.734443	−	0.791541i	0.984255	+	0.176753i	$0.0565595\pi$
$242$	−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	$-0.0328560\pi$
$251$	24.3077	+	11.7060i	1.53429	+	0.738876i	0.539614	+	0.841913i	$0.318570\pi$
$252$		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	$-0.549604\pi$
$257$	13.1186	−	12.1723i	0.818317	−	0.759287i	0.973522	+	0.228595i	$0.0734133\pi$
$258$		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	$-0.259772\pi$
$263$	6.43376	+	3.71453i	0.396722	+	0.229048i	−0.288346	+	0.957526i	$0.593105\pi$
$264$		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	$-0.236918\pi$
$269$	−4.33700	−	11.0505i	−0.264431	−	0.673760i	−0.999993	+	0.00369739i	$0.998823\pi$
$270$		0			0
$271$	−1.31490	−	4.26279i	−0.0798742	−	0.258946i	0.906824	−	0.421510i	$-0.138500\pi$
$271$	−1.31490	−	4.26279i	−0.0798742	−	0.258946i	−0.986698	+	0.162564i	$0.948024\pi$
$272$	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	0.260575	−	0.965453i	$-0.416088\pi$
$277$	−1.13152	−	0.349027i	−0.0679863	−	0.0209710i	−0.328562	+	0.944482i	$0.606564\pi$
$278$	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	−0.368925	+	0.929459i	$0.620274\pi$
$281$	−22.7504	+	18.1428i	−1.35717	+	1.08231i	−0.988249	+	0.152851i	$0.951154\pi$
$282$		0			0
$283$	−0.0238140	−	0.157995i	−0.00141559	−	0.00939185i	0.988112	−	0.153737i	$-0.0491307\pi$
$283$	−0.0238140	−	0.157995i	−0.00141559	−	0.00939185i	−0.989527	+	0.144345i	$0.953893\pi$
$284$	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	$-0.803916\pi$
$293$	−27.9417			−1.63237			−0.816186	+	0.577789i	$0.803916\pi$
$294$		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	−0.181811	−	0.983334i	$-0.558196\pi$
$307$	12.9030	−	10.2898i	0.736412	−	0.587269i	0.918223	+	0.396065i	$0.129624\pi$
$308$	−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	$-0.561092\pi$
$311$	−15.8952	−	4.90301i	−0.901333	−	0.278024i	−0.710582	+	0.703614i	$0.751568\pi$
$312$		0			0
$313$	19.7180	−	11.3842i	1.11452	−	0.643471i	0.174527	−	0.984652i	$-0.444160\pi$
$313$	19.7180	−	11.3842i	1.11452	−	0.643471i	0.939998	+	0.341181i	$0.110827\pi$
$314$	−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	$-0.122091\pi$
$317$	−0.884400	−	2.86715i	−0.0496729	−	0.161035i	−0.977011	+	0.213189i	$0.931615\pi$
$318$		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	0.161304	−	0.986905i	$-0.448430\pi$
$331$	21.0589	−	19.5398i	1.15750	−	1.07401i	0.996199	−	0.0871010i	$-0.0277603\pi$
$332$	−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	−0.115246	−	0.993337i	$-0.536766\pi$
$337$	−17.6916	−	8.51983i	−0.963723	−	0.464105i	−0.848477	+	0.529232i	$0.822480\pi$
$338$	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	$-0.814472\pi$
$347$	−4.16587	+	4.48974i	−0.223636	+	0.241022i	0.611260	+	0.791430i	$0.290663\pi$
$348$		0			0
$349$	0.995638	−	2.06746i	0.0532953	−	0.110669i	−0.872620	−	0.488399i	$-0.837581\pi$
$349$	0.995638	−	2.06746i	0.0532953	−	0.110669i	0.925916	+	0.377730i	$0.123295\pi$
$350$	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	$-0.443383\pi$
$353$	21.7523	−	14.8305i	1.15776	−	0.789346i	0.980827	+	0.194878i	$0.0624311\pi$
$354$		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	$-0.838672\pi$
$359$	−31.5751	+	2.36623i	−1.66647	+	0.124885i	−0.792179	+	0.610289i	$0.791053\pi$
$360$		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	−0.411448	−	0.911433i	$-0.634977\pi$
$367$	−1.78408	+	0.700199i	−0.0931280	+	0.0365501i	0.318320	+	0.947983i	$0.396881\pi$
$368$	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	0.856450	−	0.516231i	$-0.172665\pi$
$373$	−0.363940	−	0.630362i	−0.0188441	−	0.0326389i	−0.875294	+	0.483592i	$0.839332\pi$
$374$	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	0.624886	−	0.780716i	$-0.285145\pi$
$379$	−5.35964	−	6.72077i	−0.275306	−	0.345223i	−0.900192	+	0.435493i	$0.856574\pi$
$380$	−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	$-0.263457\pi$
$383$	21.6463	+	3.26266i	1.10608	+	0.166714i	0.429485	+	0.903074i	$0.358695\pi$
$384$		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	$-0.512724\pi$
$389$	−4.50483	−	0.337591i	−0.228404	−	0.0171165i	−0.188441	+	0.982085i	$0.560343\pi$
$390$		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	−0.241200	−	0.970475i	$-0.577541\pi$
$397$	14.9498	−	21.9274i	0.750311	−	1.10050i	0.991510	−	0.130028i	$-0.0415067\pi$
$398$	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	−0.943007	−	0.332772i	$-0.892016\pi$
$401$	1.12523	−	7.46539i	0.0561911	−	0.372804i	0.999198	−	0.0400316i	$-0.0127459\pi$
$402$		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	−0.997327	−	0.0730615i	$-0.976723\pi$
$409$	−2.67236	+	8.66359i	−0.132140	+	0.428387i	0.865188	+	0.501448i	$0.167199\pi$
$410$	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	0.886614	+	0.462510i	$0.153051\pi$
$419$	−2.31046	+	10.1228i	−0.112873	+	0.494530i	−0.999487	+	0.0320196i	$0.989806\pi$
$420$		0			0
$421$	−1.40068	−	6.13680i	−0.0682652	−	0.299089i	0.929258	−	0.369432i	$-0.120448\pi$
$421$	−1.40068	−	6.13680i	−0.0682652	−	0.299089i	−0.997523	+	0.0703429i	$0.977591\pi$
$422$	−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	0.902217	+	0.431282i	$0.141939\pi$
$431$	20.2222	+	29.6605i	0.974070	+	1.42870i	0.0718526	+	0.997415i	$0.477109\pi$
$432$		0			0
$433$	−7.73903	−	16.0703i	−0.371914	−	0.772287i	0.628069	−	0.778158i	$-0.283846\pi$
$433$	−7.73903	−	16.0703i	−0.371914	−	0.772287i	−0.999983	+	0.00587067i	$0.998131\pi$
$434$	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	0.379597	−	0.925152i	$-0.376063\pi$
$439$	0.599199	+	0.235168i	0.0285982	+	0.0112240i	−0.350999	+	0.936376i	$0.614158\pi$
$440$	−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	$-0.591448\pi$
$443$	−24.0651	−	9.44487i	−1.14337	−	0.448739i	−0.860011	+	0.510275i	$0.829544\pi$
$444$		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	$-0.145646\pi$
$449$	−0.161075	−	0.334476i	−0.00760160	−	0.0157849i	−0.904735	+	0.425975i	$0.859931\pi$
$450$		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	−0.970576	−	0.240796i	$-0.922592\pi$
$457$	−0.998957	−	13.3302i	−0.0467292	−	0.623558i	0.923847	−	0.382763i	$-0.125027\pi$
$458$	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	0.941087	+	0.338165i	$0.109806\pi$
$461$	5.15133	+	22.5694i	0.239921	+	1.05116i	−0.701165	+	0.712999i	$0.747337\pi$
$462$		0			0
$463$	0.200977	−	0.880537i	0.00934018	−	0.0409220i	−0.970043	−	0.242933i	$-0.921891\pi$
$463$	0.200977	−	0.880537i	0.00934018	−	0.0409220i	0.979383	+	0.202011i	$0.0647476\pi$
$464$	−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	$-0.559819\pi$
$467$	4.58606	−	1.41461i	0.212218	−	0.0654605i	0.399041	+	0.916933i	$0.369343\pi$
$468$		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	$-0.311926\pi$
$479$	29.1998	−	4.40117i	1.33417	−	0.201094i	0.777105	+	0.629371i	$0.216688\pi$
$480$		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	0.966706	+	0.255890i	$0.0823684\pi$
$487$	−0.603365	+	8.05135i	−0.0273411	+	0.364842i	−0.994047	+	0.108952i	$0.965251\pi$
$488$	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	−0.510062	−	0.860138i	$-0.670377\pi$
$499$	−27.9451	−	4.21204i	−1.25099	−	0.188557i	−0.740931	+	0.671581i	$0.765616\pi$
$500$	−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	$-0.102911\pi$
$503$	9.58702	+	12.0217i	0.427464	+	0.536023i	−0.520727	+	0.853723i	$0.674339\pi$
$504$		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	−0.999829	−	0.0184959i	$-0.994112\pi$
$509$	−11.6400	−	20.1610i	−0.515932	−	0.893621i	0.483897	−	0.875125i	$-0.339221\pi$
$510$		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	−0.228787	+	0.973477i	$0.573476\pi$
$521$	−21.8542	+	37.8525i	−0.957449	+	1.65835i	−0.728662	+	0.684874i	$0.759857\pi$
$522$		0			0
$523$	2.70012	−	0.202346i	0.118068	−	0.00884796i	−0.0155651	−	0.999879i	$-0.504955\pi$
$523$	2.70012	−	0.202346i	0.118068	−	0.00884796i	0.133633	+	0.991031i	$0.457336\pi$
$524$	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	−0.733195	−	0.680018i	$-0.761972\pi$
$541$	6.20572	−	15.8119i	0.266805	−	0.679807i	1.00000		0.000210854i	$6.71170e-5\pi$
$542$	−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	−0.356485	−	0.934301i	$-0.616025\pi$
$547$	3.54836	−	1.70880i	0.151717	−	0.0730629i	0.508201	+	0.861238i	$0.330311\pi$
$548$	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	$-0.611616\pi$
$557$	−31.3559	−	18.1034i	−1.32859	−	0.767064i	−0.985082	+	0.172085i	$0.944950\pi$
$558$		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	−0.746695	−	0.665167i	$-0.768360\pi$
$563$	−15.4646	−	39.4033i	−0.651757	−	1.66065i	0.0949374	−	0.995483i	$-0.469735\pi$
$564$		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	$-0.589346\pi$
$569$	9.93757	−	5.73746i	0.416605	−	0.240527i	0.693624	+	0.720338i	$0.256013\pi$
$570$		0			0
$571$	13.1509	+	4.05652i	0.550348	+	0.169760i	0.557443	−	0.830215i	$-0.311782\pi$
$571$	13.1509	+	4.05652i	0.550348	+	0.169760i	−0.00709536	+	0.999975i	$0.502259\pi$
$572$	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	0.973492	+	0.228721i	$0.0734544\pi$
$577$	2.65830	+	17.6366i	0.110666	+	0.734223i	−0.862826	+	0.505502i	$0.831307\pi$
$578$	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	$-0.736550\pi$
$587$	−32.7857			−1.35321			−0.676606	+	0.736345i	$0.736550\pi$
$588$		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	$-0.305169\pi$
$593$	0.550480	+	0.375311i	0.0226055	+	0.0154122i	−0.551965	+	0.833868i	$0.686122\pi$
$594$		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	0.997975	+	0.0636149i	$0.0202629\pi$
$599$	1.54405	+	10.2441i	0.0630880	+	0.418562i	−0.934886	+	0.354947i	$0.884499\pi$
$600$		0			0
$601$	−37.7417	+	30.0980i	−1.53952	+	1.22772i	−0.660614	+	0.750726i	$0.729704\pi$
$601$	−37.7417	+	30.0980i	−1.53952	+	1.22772i	−0.878904	+	0.476999i	$0.841725\pi$
$602$	−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	−0.953853	−	0.300275i	$-0.902921\pi$
$607$	−28.8438	+	16.6530i	−1.17073	+	0.675923i	−0.216880	+	0.976198i	$0.569588\pi$
$608$	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	0.987824	−	0.155577i	$-0.0497236\pi$
$613$	3.90889	+	9.95969i	0.157879	+	0.402268i	−0.829945	+	0.557845i	$0.811628\pi$
$614$	−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	$-0.639871\pi$
$617$	−10.3341	+	2.35868i	−0.416033	+	0.0949569i	0.00938006	+	0.999956i	$0.497014\pi$
$618$		0			0
$619$	19.2455	+	11.1114i	0.773542	+	0.446605i	0.834137	−	0.551558i	$-0.185966\pi$
$619$	19.2455	+	11.1114i	0.773542	+	0.446605i	−0.0605948	+	0.998162i	$0.519300\pi$
$620$	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	−0.0748589	−	0.997194i	$-0.523851\pi$
$631$	−22.6371	−	10.9015i	−0.901170	−	0.433981i	−0.826312	+	0.563213i	$0.809565\pi$
$632$	−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	$-0.701451\pi$
$641$	6.50188	−	7.00737i	0.256809	−	0.276774i	0.848275	+	0.529555i	$0.177641\pi$
$642$		0			0
$643$	0.0302707	−	0.0628578i	0.00119376	−	0.00247887i	−0.900371	−	0.435123i	$-0.856705\pi$
$643$	0.0302707	−	0.0628578i	0.00119376	−	0.00247887i	0.901565	+	0.432644i	$0.142419\pi$
$644$	−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	$-0.599255\pi$
$647$	11.8815	−	8.10068i	0.467110	−	0.318471i	0.773901	+	0.633307i	$0.218303\pi$
$648$		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	$-0.565887\pi$
$653$	−6.71743	+	0.503402i	−0.262873	+	0.0196996i	−0.0573585	+	0.998354i	$0.518268\pi$
$654$		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	$-0.342805\pi$
$659$	13.3244	+	3.04120i	0.519043	+	0.118468i	0.0450293	+	0.998986i	$0.485662\pi$
$660$		0			0
$661$	−14.5956	+	5.72834i	−0.567702	+	0.222807i	−0.631793	−	0.775137i	$-0.717681\pi$
$661$	−14.5956	+	5.72834i	−0.567702	+	0.222807i	0.0640904	+	0.997944i	$0.479585\pi$
$662$	−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	0.894293	+	0.447481i	$0.147679\pi$
$673$	29.3551	+	36.8101i	1.13156	+	1.41893i	0.237263	+	0.971446i	$0.423750\pi$
$674$	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	$-0.149734\pi$
$677$	41.8799	+	6.31238i	1.60957	+	0.242604i	0.718188	+	0.695849i	$0.244972\pi$
$678$		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	$-0.623906\pi$
$683$	−23.3292	−	1.74828i	−0.892668	−	0.0668962i	−0.513160	+	0.858293i	$0.671525\pi$
$684$		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	−0.950149	−	0.311796i	$-0.899069\pi$
$691$	−8.22195	+	12.0594i	−0.312778	+	0.458761i	0.637371	+	0.770557i	$0.280022\pi$
$692$	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	$-0.102095\pi$
$701$	22.5793	+	18.0064i	0.852809	+	0.680093i	−0.0961928	+	0.995363i	$0.530667\pi$
$702$		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	−0.402198	−	0.915553i	$-0.631754\pi$
$709$	−5.82495	+	1.79676i	−0.218761	+	0.0674788i	0.183437	+	0.983031i	$0.441278\pi$
$710$	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	−0.999698	−	0.0245915i	$-0.992171\pi$
$719$	−0.397680	−	5.30667i	−0.0148310	−	0.197906i	0.984867	−	0.173314i	$-0.0554476\pi$
$720$		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	−0.966317	−	0.257354i	$-0.917149\pi$
$727$	−15.2350	−	31.6359i	−0.565036	−	1.17331i	0.401281	−	0.915955i	$-0.368565\pi$
$728$	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	0.974530	−	0.224256i	$-0.0719951\pi$
$733$	41.5959	+	16.3252i	1.53638	+	0.602984i	0.561849	+	0.827240i	$0.310090\pi$
$734$	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	0.999202	−	0.0399408i	$-0.0127169\pi$
$739$	28.1100	+	26.0823i	1.03404	+	0.959452i	0.0348413	+	0.999393i	$0.488907\pi$
$740$	−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	0.992610	+	0.121351i	$0.0387228\pi$
$743$	12.7732	+	26.5239i	0.468604	+	0.973066i	−0.524006	+	0.851715i	$0.675563\pi$
$744$		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	0.858921	+	0.512108i	$0.171135\pi$
$751$	2.35456	+	31.4194i	0.0859191	+	1.14651i	−0.773002	+	0.634404i	$0.781246\pi$
$752$	−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	−0.547855	−	0.836573i	$-0.684555\pi$
$757$	8.49403	−	37.2148i	0.308721	−	1.35259i	0.856576	−	0.516021i	$-0.172587\pi$
$758$	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	$-0.640109\pi$
$761$	−7.40735	+	2.28487i	−0.268516	+	0.0828263i	0.157573	+	0.987507i	$0.449633\pi$
$762$		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	0.220497	−	0.975388i	$-0.429232\pi$
$769$	−18.8950	−	15.0682i	−0.681370	−	0.543375i	−0.901867	+	0.432013i	$0.857804\pi$
$770$	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	$-0.552595\pi$
$773$	−0.859499	+	0.129549i	−0.0309140	+	0.00465954i	0.133567	+	0.991040i	$0.457357\pi$
$774$		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	0.610918	−	0.791694i	$-0.290801\pi$
$787$	30.7752	+	2.30628i	1.09702	+	0.0822100i	0.486098	+	0.873904i	$0.338420\pi$
$788$	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	$-0.0422006\pi$
$797$	18.1183	+	22.7196i	0.641782	+	0.804769i	−0.349443	+	0.936958i	$0.613629\pi$
$798$		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	$-0.755673\pi$
$809$	−22.0374	+	8.64903i	−0.774793	+	0.304084i	−0.0551955	+	0.998476i	$0.517578\pi$
$810$		0			0
$811$	−21.6873	−	4.94998i	−0.761544	−	0.173817i	−0.175925	−	0.984404i	$-0.556292\pi$
$811$	−21.6873	−	4.94998i	−0.761544	−	0.173817i	−0.585619	+	0.810586i	$0.699149\pi$
$812$	−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	$-0.290309\pi$
$821$	−6.36511	−	6.85996i	−0.222144	−	0.239414i	−0.834284	+	0.551335i	$0.814118\pi$
$822$		0			0
$823$	8.80774	−	6.00502i	0.307019	−	0.209322i	−0.400003	−	0.916514i	$-0.630991\pi$
$823$	8.80774	−	6.00502i	0.307019	−	0.209322i	0.707021	+	0.707192i	$0.250038\pi$
$824$	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	−0.556104	−	0.831113i	$-0.687704\pi$
$827$	12.6652	−	26.2995i	0.440411	−	0.914523i	0.996515	−	0.0834105i	$-0.0265813\pi$
$828$		0			0
$829$	18.2651	−	19.6851i	0.634373	−	0.683691i	−0.331278	−	0.943533i	$-0.607480\pi$
$829$	18.2651	−	19.6851i	0.634373	−	0.683691i	0.965651	+	0.259842i	$0.0836704\pi$
$830$	−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	$-0.519347\pi$
$839$	−25.4608	−	12.2613i	−0.879006	−	0.423307i	−0.818261	+	0.574847i	$0.805062\pi$
$840$		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	−0.517371	−	0.855761i	$-0.673089\pi$
$853$	−17.8802	+	4.08103i	−0.612205	+	0.139732i	−0.0948340	+	0.995493i	$0.530232\pi$
$854$	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	0.744194	+	0.667964i	$0.232834\pi$
$857$	19.1161	+	48.7069i	0.652992	+	1.66380i	−0.0912015	+	0.995832i	$0.529071\pi$
$858$		0			0
$859$	2.72148	+	8.82283i	0.0928558	+	0.301031i	0.990072	−	0.140560i	$-0.0448903\pi$
$859$	2.72148	+	8.82283i	0.0928558	+	0.301031i	−0.897216	+	0.441591i	$0.854414\pi$
$860$	−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	$-0.705291\pi$
$863$	−6.15895	+	3.55587i	−0.209653	+	0.121043i	0.391497	+	0.920179i	$0.371957\pi$
$864$		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	0.0378639	−	0.999283i	$-0.487945\pi$
$877$	−26.0163	−	17.7376i	−0.878509	−	0.598957i	−0.916373	+	0.400326i	$0.868897\pi$
$878$	−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	$-0.348514\pi$
$881$	27.1971			0.916293			0.458146	+	0.888877i	$0.348514\pi$
$882$		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	$-0.460204\pi$
$887$	−22.4368	−	15.2971i	−0.753353	−	0.513628i	−0.878051	+	0.478567i	$0.841156\pi$
$888$		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	0.839758	−	0.542960i	$-0.182697\pi$
$907$	−4.37094	−	11.1370i	−0.145135	−	0.369797i	−0.984893	+	0.173163i	$0.944601\pi$
$908$	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	$-0.740402\pi$
$911$	−29.7947	+	6.80044i	−0.987141	+	0.225308i	−0.301673	+	0.953411i	$0.597545\pi$
$912$		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	−0.865142	−	0.501527i	$-0.832772\pi$
$919$	−13.0254	+	12.0858i	−0.429669	+	0.398675i	0.435473	+	0.900202i	$0.356581\pi$
$920$	−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	$-0.957861\pi$
$929$	−5.32876	+	13.5775i	−0.174831	+	0.445462i	0.816419	+	0.577460i	$0.195956\pi$
$930$		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	−0.929724	−	0.368258i	$-0.879954\pi$
$937$	−1.90198	+	3.94950i	−0.0621349	+	0.129024i	0.867589	+	0.497282i	$0.165669\pi$
$938$	−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	$-0.693426\pi$
$941$	−0.469715	+	0.320246i	−0.0153123	+	0.0104397i	0.555640	+	0.831423i	$0.312473\pi$
$942$		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	$-0.617059\pi$
$947$	−17.7237	+	1.32821i	−0.575943	+	0.0431610i	−0.216425	+	0.976299i	$0.569440\pi$
$948$		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	$-0.552399\pi$
$953$	−22.8300	−	5.21080i	−0.739536	−	0.168794i	−0.575663	+	0.817687i	$0.695256\pi$
$954$		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	0.946169	−	0.323674i	$-0.104918\pi$
$967$	13.0627	+	16.3801i	0.420068	+	0.526748i	−0.526101	+	0.850422i	$0.676347\pi$
$968$	−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	$-0.634163\pi$
$971$	−33.3115	−	5.02090i	−1.06902	−	0.161128i	−0.659900	+	0.751354i	$0.729401\pi$
$972$		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	$-0.291074\pi$
$977$	34.2447	+	2.56628i	1.09558	+	0.0821027i	0.485347	+	0.874322i	$0.338693\pi$
$978$		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	−0.772560	−	0.634942i	$-0.781024\pi$
$983$	2.69648	−	35.9820i	0.0860044	−	1.14765i	0.858564	−	0.512706i	$-0.171357\pi$
$984$		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	−0.221868	−	0.975077i	$-0.571216\pi$
$991$	−4.61093	+	0.694986i	−0.146471	+	0.0220770i	0.0753974	+	0.997154i	$0.475977\pi$
$992$	−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	0.694577	+	0.719418i	$0.255592\pi$
$997$	−8.98546	+	29.1301i	−0.284572	+	0.922561i	−0.979149	+	0.203142i	$0.934885\pi$
$998$	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.395.3	yes	216
3.2	odd	2	inner	441.2.bg.a.395.16	yes	216
49.33	odd	42	inner	441.2.bg.a.278.16	yes	216
147.131	even	42	inner	441.2.bg.a.278.3	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bg.a.278.3	✓	216	147.131	even	42	inner
441.2.bg.a.278.16	yes	216	49.33	odd	42	inner
441.2.bg.a.395.3	yes	216	1.1	even	1	trivial
441.2.bg.a.395.16	yes	216	3.2	odd	2	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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