LMFDB - Embedded newform 441.2.bb.c.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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([0, 32]))

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

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

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, 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:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			37.2
Character	$\chi$	$=$	441.37
Dual form			441.2.bb.c.298.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.449603 + 0.306534i) q^{2} +(-0.622503 + 1.58611i) q^{4} +(-1.43317 - 0.442074i) q^{5} +(0.881776 - 2.49449i) q^{7} +(-0.448490 - 1.96496i) q^{8} +O(q^{10})$	\(q+(-0.449603 + 0.306534i) q^{2} +(-0.622503 + 1.58611i) q^{4} +(-1.43317 - 0.442074i) q^{5} +(0.881776 - 2.49449i) q^{7} +(-0.448490 - 1.96496i) q^{8} +(0.779867 - 0.240557i) q^{10} +(-0.155173 - 2.07065i) q^{11} +(-1.18931 - 0.572740i) q^{13} +(0.368197 + 1.39182i) q^{14} +(-1.69412 - 1.57191i) q^{16} +(2.90096 + 0.437250i) q^{17} +(1.66231 - 2.87921i) q^{19} +(1.59333 - 1.99797i) q^{20} +(0.704489 + 0.883402i) q^{22} +(3.98643 - 0.600858i) q^{23} +(-2.27265 - 1.54947i) q^{25} +(0.710279 - 0.107057i) q^{26} +(3.40763 + 2.95142i) q^{28} +(5.27575 - 6.61558i) q^{29} +(3.76132 + 6.51479i) q^{31} +(5.22949 + 0.788219i) q^{32} +(-1.43831 + 0.692655i) q^{34} +(-2.36648 + 3.18521i) q^{35} +(-2.59163 - 6.60338i) q^{37} +(0.135195 + 1.80406i) q^{38} +(-0.225897 + 3.01439i) q^{40} +(-1.78927 - 7.83931i) q^{41} +(0.550132 - 2.41029i) q^{43} +(3.38087 + 1.04286i) q^{44} +(-1.60813 + 1.49212i) q^{46} +(-7.42968 + 5.06547i) q^{47} +(-5.44494 - 4.39916i) q^{49} +1.49675 q^{50} +(1.64877 - 1.52984i) q^{52} +(-2.17004 + 5.52916i) q^{53} +(-0.692989 + 3.03618i) q^{55} +(-5.29704 - 0.613903i) q^{56} +(-0.344091 + 4.59158i) q^{58} +(-0.718360 + 0.221585i) q^{59} +(-1.68251 - 4.28696i) q^{61} +(-3.68810 - 1.77610i) q^{62} +(1.57155 - 0.756820i) q^{64} +(1.45128 + 1.34659i) q^{65} +(-0.801950 - 1.38902i) q^{67} +(-2.49939 + 4.32906i) q^{68} +(0.0876008 - 2.15749i) q^{70} +(-8.13170 - 10.1968i) q^{71} +(12.2987 + 8.38512i) q^{73} +(3.18936 + 2.17447i) q^{74} +(3.53195 + 4.42893i) q^{76} +(-5.30203 - 1.43877i) q^{77} +(2.96317 - 5.13236i) q^{79} +(1.73305 + 3.00174i) q^{80} +(3.20747 + 2.97610i) q^{82} +(-4.75005 + 2.28751i) q^{83} +(-3.96428 - 1.90909i) q^{85} +(0.491494 + 1.25231i) q^{86} +(-3.99915 + 1.23357i) q^{88} +(-1.10092 + 14.6907i) q^{89} +(-2.47739 + 2.46168i) q^{91} +(-1.52854 + 6.69696i) q^{92} +(1.78767 - 4.55490i) q^{94} +(-3.65520 + 3.39153i) q^{95} -8.41896 q^{97} +(3.79655 + 0.308813i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} + 3 q^{4} - 6 q^{8}+O(q^{10}) $ 48 * q + q^2 + 3 * q^4 - 6 * q^8	$ 48 q + q^{2} + 3 q^{4} - 6 q^{8} + 30 q^{10} + 9 q^{11} + 42 q^{14} + 29 q^{16} + 5 q^{17} - 26 q^{19} + 5 q^{20} + q^{22} + 4 q^{23} - 56 q^{25} + 62 q^{26} + 7 q^{28} - 12 q^{29} - 36 q^{31} + 14 q^{32} - 76 q^{34} - 7 q^{35} - 20 q^{37} + 60 q^{38} + 28 q^{40} - 41 q^{41} + 12 q^{43} - 44 q^{44} + 16 q^{46} - 13 q^{47} - 84 q^{49} + 12 q^{50} + 92 q^{52} - 14 q^{53} - 38 q^{55} - 105 q^{56} + 3 q^{58} - 57 q^{59} + 11 q^{61} + 16 q^{62} - 110 q^{64} - 21 q^{65} + 34 q^{67} - 22 q^{68} - 6 q^{71} - 69 q^{73} + 90 q^{74} - 49 q^{76} + 34 q^{79} - 55 q^{80} + 91 q^{82} - 28 q^{83} - 44 q^{85} + 26 q^{86} + 45 q^{88} - 11 q^{89} - 84 q^{92} + 90 q^{94} - 150 q^{95} + 124 q^{97} - 119 q^{98}+O(q^{100}) $ 48 * q + q^2 + 3 * q^4 - 6 * q^8 + 30 * q^10 + 9 * q^11 + 42 * q^14 + 29 * q^16 + 5 * q^17 - 26 * q^19 + 5 * q^20 + q^22 + 4 * q^23 - 56 * q^25 + 62 * q^26 + 7 * q^28 - 12 * q^29 - 36 * q^31 + 14 * q^32 - 76 * q^34 - 7 * q^35 - 20 * q^37 + 60 * q^38 + 28 * q^40 - 41 * q^41 + 12 * q^43 - 44 * q^44 + 16 * q^46 - 13 * q^47 - 84 * q^49 + 12 * q^50 + 92 * q^52 - 14 * q^53 - 38 * q^55 - 105 * q^56 + 3 * q^58 - 57 * q^59 + 11 * q^61 + 16 * q^62 - 110 * q^64 - 21 * q^65 + 34 * q^67 - 22 * q^68 - 6 * q^71 - 69 * q^73 + 90 * q^74 - 49 * q^76 + 34 * q^79 - 55 * q^80 + 91 * q^82 - 28 * q^83 - 44 * q^85 + 26 * q^86 + 45 * q^88 - 11 * q^89 - 84 * q^92 + 90 * q^94 - 150 * q^95 + 124 * q^97 - 119 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{16}{21}\right)$	$1$

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 $

$2$	−0.449603	+	0.306534i	−0.317917	+	0.216752i	−0.711755	−	0.702428i	$-0.752099\pi$
$2$	−0.449603	+	0.306534i	−0.317917	+	0.216752i	0.393838	+	0.919180i	$0.371147\pi$
$3$		0			0
$3$		0			0
$4$	−0.622503	+	1.58611i	−0.311251	+	0.793055i
$5$	−1.43317	−	0.442074i	−0.640933	−	0.197702i	−0.0427810	−	0.999084i	$-0.513622\pi$
$5$	−1.43317	−	0.442074i	−0.640933	−	0.197702i	−0.598152	+	0.801383i	$0.704098\pi$
$6$		0			0
$7$	0.881776	−	2.49449i	0.333280	−	0.942828i
$7$	0.881776	−	2.49449i	0.333280	−	0.942828i
$8$	−0.448490	−	1.96496i	−0.158565	−	0.694719i
$9$		0			0
$10$	0.779867	−	0.240557i	0.246616	−	0.0760708i
$11$	−0.155173	−	2.07065i	−0.0467866	−	0.624323i	−0.970479	−	0.241187i	$-0.922463\pi$
$11$	−0.155173	−	2.07065i	−0.0467866	−	0.624323i	0.923692	−	0.383136i	$-0.125156\pi$
$12$		0			0
$13$	−1.18931	−	0.572740i	−0.329854	−	0.158849i	0.261625	−	0.965170i	$-0.415742\pi$
$13$	−1.18931	−	0.572740i	−0.329854	−	0.158849i	−0.591479	+	0.806320i	$0.701456\pi$
$14$	0.368197	+	1.39182i	0.0984047	+	0.371980i
$15$		0			0
$16$	−1.69412	−	1.57191i	−0.423529	−	0.392978i
$17$	2.90096	+	0.437250i	0.703587	+	0.106049i	0.491085	−	0.871112i	$-0.336601\pi$
$17$	2.90096	+	0.437250i	0.703587	+	0.106049i	0.212503	+	0.977161i	$0.431839\pi$
$18$		0			0
$19$	1.66231	−	2.87921i	0.381361	−	0.660537i	−0.609896	−	0.792481i	$-0.708789\pi$
$19$	1.66231	−	2.87921i	0.381361	−	0.660537i	0.991257	+	0.131945i	$0.0421222\pi$
$20$	1.59333	−	1.99797i	0.356279	−	0.446760i
$21$		0			0
$22$	0.704489	+	0.883402i	0.150198	+	0.188342i
$23$	3.98643	−	0.600858i	0.831228	−	0.125288i	0.280376	−	0.959890i	$-0.409541\pi$
$23$	3.98643	−	0.600858i	0.831228	−	0.125288i	0.550852	+	0.834603i	$0.314303\pi$
$24$		0			0
$25$	−2.27265	−	1.54947i	−0.454530	−	0.309893i
$26$	0.710279	−	0.107057i	0.139297	−	0.0209957i
$27$		0			0
$28$	3.40763	+	2.95142i	0.643981	+	0.557766i
$29$	5.27575	−	6.61558i	0.979682	−	1.22848i	0.00613897	−	0.999981i	$-0.498046\pi$
$29$	5.27575	−	6.61558i	0.979682	−	1.22848i	0.973543	−	0.228502i	$-0.0733827\pi$
$30$		0			0
$31$	3.76132	+	6.51479i	0.675553	+	1.17009i	0.976307	+	0.216390i	$0.0694283\pi$
$31$	3.76132	+	6.51479i	0.675553	+	1.17009i	−0.300754	+	0.953702i	$0.597238\pi$
$32$	5.22949	+	0.788219i	0.924452	+	0.139339i
$33$		0			0
$34$	−1.43831	+	0.692655i	−0.246669	+	0.118789i
$35$	−2.36648	+	3.18521i	−0.400008	+	0.538399i
$36$		0			0
$37$	−2.59163	−	6.60338i	−0.426062	−	1.08559i	−0.969272	−	0.245992i	$-0.920886\pi$
$37$	−2.59163	−	6.60338i	−0.426062	−	1.08559i	0.543210	−	0.839597i	$-0.317209\pi$
$38$	0.135195	+	1.80406i	0.0219316	+	0.292657i
$39$		0			0
$40$	−0.225897	+	3.01439i	−0.0357175	+	0.476617i
$41$	−1.78927	−	7.83931i	−0.279437	−	1.22429i	−0.898507	−	0.438959i	$-0.855347\pi$
$41$	−1.78927	−	7.83931i	−0.279437	−	1.22429i	0.619070	−	0.785336i	$-0.287510\pi$
$42$		0			0
$43$	0.550132	−	2.41029i	0.0838944	−	0.367565i	−0.915502	−	0.402314i	$-0.868206\pi$
$43$	0.550132	−	2.41029i	0.0838944	−	0.367565i	0.999396	+	0.0347488i	$0.0110631\pi$
$44$	3.38087	+	1.04286i	0.509685	+	0.157217i
$45$		0			0
$46$	−1.60813	+	1.49212i	−0.237105	+	0.220002i
$47$	−7.42968	+	5.06547i	−1.08373	+	0.738875i	−0.967125	−	0.254303i	$-0.918154\pi$
$47$	−7.42968	+	5.06547i	−1.08373	+	0.738875i	−0.116606	+	0.993178i	$0.537202\pi$
$48$		0			0
$49$	−5.44494	−	4.39916i	−0.777849	−	0.628451i
$50$	1.49675			0.211673
$51$		0			0
$52$	1.64877	−	1.52984i	0.228644	−	0.212151i
$53$	−2.17004	+	5.52916i	−0.298077	+	0.759489i	0.700855	+	0.713303i	$0.252802\pi$
$53$	−2.17004	+	5.52916i	−0.298077	+	0.759489i	−0.998933	+	0.0461855i	$0.985293\pi$
$54$		0			0
$55$	−0.692989	+	3.03618i	−0.0934426	+	0.409399i
$56$	−5.29704	−	0.613903i	−0.707847	−	0.0820363i
$57$		0			0
$58$	−0.344091	+	4.59158i	−0.0451814	+	0.602904i
$59$	−0.718360	+	0.221585i	−0.0935225	+	0.0288479i	−0.341163	−	0.940004i	$-0.610821\pi$
$59$	−0.718360	+	0.221585i	−0.0935225	+	0.0288479i	0.247641	+	0.968852i	$0.420345\pi$
$60$		0			0
$61$	−1.68251	−	4.28696i	−0.215423	−	0.548889i	0.781786	−	0.623547i	$-0.214309\pi$
$61$	−1.68251	−	4.28696i	−0.215423	−	0.548889i	−0.997209	+	0.0746575i	$0.976214\pi$
$62$	−3.68810	−	1.77610i	−0.468390	−	0.225565i
$63$		0			0
$64$	1.57155	−	0.756820i	0.196444	−	0.0946025i
$65$	1.45128	+	1.34659i	0.180010	+	0.167024i
$66$		0			0
$67$	−0.801950	−	1.38902i	−0.0979737	−	0.169695i	0.812872	−	0.582442i	$-0.197903\pi$
$67$	−0.801950	−	1.38902i	−0.0979737	−	0.169695i	−0.910846	+	0.412747i	$0.864569\pi$
$68$	−2.49939	+	4.32906i	−0.303095	+	0.524976i
$69$		0			0
$70$	0.0876008	−	2.15749i	0.0104703	−	0.257869i
$71$	−8.13170	−	10.1968i	−0.965056	−	1.21014i	−0.977654	−	0.210221i	$-0.932582\pi$
$71$	−8.13170	−	10.1968i	−0.965056	−	1.21014i	0.0125982	−	0.999921i	$-0.495990\pi$
$72$		0			0
$73$	12.2987	+	8.38512i	1.43946	+	0.981404i	0.996388	+	0.0849154i	$0.0270620\pi$
$73$	12.2987	+	8.38512i	1.43946	+	0.981404i	0.443067	+	0.896489i	$0.353890\pi$
$74$	3.18936	+	2.17447i	0.370756	+	0.252777i
$75$		0			0
$76$	3.53195	+	4.42893i	0.405143	+	0.508033i
$77$	−5.30203	−	1.43877i	−0.604222	−	0.163963i
$78$		0			0
$79$	2.96317	−	5.13236i	0.333383	−	0.577436i	−0.649790	−	0.760114i	$-0.725143\pi$
$79$	2.96317	−	5.13236i	0.333383	−	0.577436i	0.983173	+	0.182678i	$0.0584765\pi$
$80$	1.73305	+	3.00174i	0.193761	+	0.335605i
$81$		0			0
$82$	3.20747	+	2.97610i	0.354206	+	0.328655i
$83$	−4.75005	+	2.28751i	−0.521386	+	0.251086i	−0.676017	−	0.736886i	$-0.736295\pi$
$83$	−4.75005	+	2.28751i	−0.521386	+	0.251086i	0.154631	+	0.987972i	$0.450581\pi$
$84$		0			0
$85$	−3.96428	−	1.90909i	−0.429986	−	0.207070i
$86$	0.491494	+	1.25231i	0.0529991	+	0.135040i
$87$		0			0
$88$	−3.99915	+	1.23357i	−0.426311	+	0.131499i
$89$	−1.10092	+	14.6907i	−0.116697	+	1.55721i	0.564700	+	0.825296i	$0.308992\pi$
$89$	−1.10092	+	14.6907i	−0.116697	+	1.55721i	−0.681397	+	0.731914i	$0.738627\pi$
$90$		0			0
$91$	−2.47739	+	2.46168i	−0.259701	+	0.258054i
$92$	−1.52854	+	6.69696i	−0.159361	+	0.698206i
$93$		0			0
$94$	1.78767	−	4.55490i	0.184384	−	0.469802i
$95$	−3.65520	+	3.39153i	−0.375016	+	0.347964i
$96$		0			0
$97$	−8.41896			−0.854816			−0.427408	−	0.904059i	$-0.640573\pi$
$97$	−8.41896			−0.854816			−0.427408	+	0.904059i	$0.640573\pi$
$98$	3.79655	+	0.308813i	0.383510	+	0.0311948i
$99$		0			0
$100$	3.87236	−	2.64013i	0.387236	−	0.264013i
$101$	1.55409	−	1.44198i	0.154637	−	0.143483i	−0.599060	−	0.800704i	$-0.704459\pi$
$101$	1.55409	−	1.44198i	0.154637	−	0.143483i	0.753697	+	0.657222i	$0.228268\pi$
$102$		0			0
$103$	4.41299	+	1.36123i	0.434825	+	0.134126i	0.504437	−	0.863448i	$-0.331700\pi$
$103$	4.41299	+	1.36123i	0.434825	+	0.134126i	−0.0696122	+	0.997574i	$0.522176\pi$
$104$	−0.592020	+	2.59381i	−0.0580524	+	0.254344i
$105$		0			0
$106$	−0.719221	−	3.15111i	−0.0698570	−	0.306063i
$107$	0.789728	−	10.5382i	0.0763459	−	1.01877i	−0.819116	−	0.573628i	$-0.805536\pi$
$107$	0.789728	−	10.5382i	0.0763459	−	1.01877i	0.895462	−	0.445138i	$-0.146845\pi$
$108$		0			0
$109$	1.03532	+	13.8154i	0.0991661	+	1.32328i	0.795672	+	0.605728i	$0.207118\pi$
$109$	1.03532	+	13.8154i	0.0991661	+	1.32328i	−0.696506	+	0.717551i	$0.745263\pi$
$110$	−0.619123	−	1.57750i	−0.0590311	−	0.150409i
$111$		0			0
$112$	−5.41494	+	2.83988i	−0.511664	+	0.268344i
$113$	3.00328	−	1.44630i	0.282524	−	0.136057i	−0.287255	−	0.957854i	$-0.592743\pi$
$113$	3.00328	−	1.44630i	0.282524	−	0.136057i	0.569780	+	0.821797i	$0.307029\pi$
$114$		0			0
$115$	−5.97885	−	0.901167i	−0.557531	−	0.0840343i
$116$	7.20888	+	12.4861i	0.669328	+	1.15931i
$117$		0			0
$118$	0.255053	−	0.319827i	0.0234795	−	0.0294424i
$119$	3.64871	−	6.85087i	0.334477	−	0.628018i
$120$		0			0
$121$	6.61364	−	0.996846i	0.601240	−	0.0906224i
$122$	2.07056	+	1.41168i	0.187460	+	0.127808i
$123$		0			0
$124$	−12.6746	+	1.91039i	−1.13821	+	0.171558i
$125$	7.24767	+	9.08829i	0.648251	+	0.812881i
$126$		0			0
$127$	−11.4213	+	14.3219i	−1.01348	+	1.27086i	−0.0512325	+	0.998687i	$0.516315\pi$
$127$	−11.4213	+	14.3219i	−1.01348	+	1.27086i	−0.962247	+	0.272177i	$0.912256\pi$
$128$	−5.76314	+	9.98206i	−0.509395	+	0.882297i
$129$		0			0
$130$	−1.06528	−	0.160565i	−0.0934310	−	0.0140825i
$131$	−10.9296	−	10.1412i	−0.954927	−	0.886043i	0.0386440	−	0.999253i	$-0.487696\pi$
$131$	−10.9296	−	10.1412i	−0.954927	−	0.886043i	−0.993571	+	0.113210i	$0.963887\pi$
$132$		0			0
$133$	−5.71637	−	6.68544i	−0.495672	−	0.579701i
$134$	0.786339	+	0.378681i	0.0679294	+	0.0327131i
$135$		0			0
$136$	−0.441873	−	5.89639i	−0.0378903	−	0.505611i
$137$	−8.83286	+	2.72458i	−0.754642	+	0.232776i	−0.648124	−	0.761534i	$-0.724446\pi$
$137$	−8.83286	+	2.72458i	−0.754642	+	0.232776i	−0.106518	+	0.994311i	$0.533970\pi$
$138$		0			0
$139$	−1.99718	−	8.75020i	−0.169398	−	0.742182i	−0.986240	−	0.165320i	$-0.947134\pi$
$139$	−1.99718	−	8.75020i	−0.169398	−	0.742182i	0.816842	−	0.576862i	$-0.195723\pi$
$140$	−3.57896	−	5.73631i	−0.302477	−	0.484806i
$141$		0			0
$142$	6.78171	+	2.09188i	0.569108	+	0.175547i
$143$	−1.00139	+	2.55151i	−0.0837406	+	0.213368i
$144$		0			0
$145$	−10.4856	+	7.14898i	−0.870783	+	0.593690i
$146$	−8.09985			−0.670349
$147$		0			0
$148$	12.0870			0.993544
$149$	19.1481	−	13.0550i	1.56868	−	1.06950i	0.607223	−	0.794531i	$-0.292283\pi$
$149$	19.1481	−	13.0550i	1.56868	−	1.06950i	0.961452	−	0.274973i	$-0.0886691\pi$
$150$		0			0
$151$	−2.00976	+	5.12080i	−0.163552	+	0.416725i	−0.989031	−	0.147709i	$-0.952810\pi$
$151$	−2.00976	+	5.12080i	−0.163552	+	0.416725i	0.825479	+	0.564434i	$0.190905\pi$
$152$	−6.40308	−	1.97509i	−0.519358	−	0.160201i
$153$		0			0
$154$	2.82484	−	0.978379i	0.227632	−	0.0788400i
$155$	−2.51058	−	10.9996i	−0.201655	−	0.883508i
$156$		0			0
$157$	−9.05505	+	2.79311i	−0.722672	+	0.222915i	−0.634206	−	0.773164i	$-0.718673\pi$
$157$	−9.05505	+	2.79311i	−0.722672	+	0.222915i	−0.0884662	+	0.996079i	$0.528197\pi$
$158$	0.240994	+	3.21584i	0.0191724	+	0.255838i
$159$		0			0
$160$	−7.14629	−	3.44147i	−0.564964	−	0.272072i
$161$	2.01630	−	10.4739i	0.158907	−	0.825461i
$162$		0			0
$163$	12.0625	+	11.1924i	0.944809	+	0.876655i	0.992505	−	0.122207i	$-0.0389971\pi$
$163$	12.0625	+	11.1924i	0.944809	+	0.876655i	−0.0476952	+	0.998862i	$0.515188\pi$
$164$	13.5478	+	2.04201i	1.05791	+	0.159454i
$165$		0			0
$166$	1.43444	−	2.48452i	0.111334	−	0.192836i
$167$	−13.6335	+	17.0959i	−1.05499	+	1.32292i	−0.110683	+	0.993856i	$0.535304\pi$
$167$	−13.6335	+	17.0959i	−1.05499	+	1.32292i	−0.944308	+	0.329062i	$0.893268\pi$
$168$		0			0
$169$	−7.01895	−	8.80148i	−0.539919	−	0.677037i
$170$	2.36755	−	0.356851i	0.181583	−	0.0273692i
$171$		0			0
$172$	3.48052	+	2.37298i	0.265387	+	0.180938i
$173$	20.8827	−	3.14755i	1.58768	−	0.239304i	0.704975	−	0.709233i	$-0.250958\pi$
$173$	20.8827	−	3.14755i	1.58768	−	0.239304i	0.882705	+	0.469928i	$0.155720\pi$
$174$		0			0
$175$	−5.86909	+	4.30282i	−0.443662	+	0.325262i
$176$	−2.99199	+	3.75183i	−0.225530	+	0.282805i
$177$		0			0
$178$	−4.00822	−	6.94244i	−0.300429	−	0.520358i
$179$	−3.62751	−	0.546760i	−0.271133	−	0.0408667i	0.0120684	−	0.999927i	$-0.496158\pi$
$179$	−3.62751	−	0.546760i	−0.271133	−	0.0408667i	−0.283201	+	0.959060i	$0.591397\pi$
$180$		0			0
$181$	11.0647	−	5.32847i	0.822431	−	0.396062i	0.0251602	−	0.999683i	$-0.491990\pi$
$181$	11.0647	−	5.32847i	0.822431	−	0.396062i	0.797271	+	0.603621i	$0.206276\pi$
$182$	0.359253	−	1.86618i	0.0266296	−	0.138331i
$183$		0			0
$184$	−2.96854	−	7.56371i	−0.218843	−	0.557604i
$185$	0.795068	+	10.6095i	0.0584546	+	0.780022i
$186$		0			0
$187$	0.455237	−	6.07472i	0.0332903	−	0.444228i
$188$	−3.40940	−	14.9376i	−0.248656	−	1.08943i
$189$		0			0
$190$	0.603769	−	2.64528i	0.0438020	−	0.191909i
$191$	19.5664	+	6.03543i	1.41577	+	0.436708i	0.905882	−	0.423531i	$-0.139209\pi$
$191$	19.5664	+	6.03543i	1.41577	+	0.436708i	0.509891	+	0.860239i	$0.329686\pi$
$192$		0			0
$193$	14.5925	−	13.5399i	1.05039	−	0.974621i	0.0506818	−	0.998715i	$-0.483861\pi$
$193$	14.5925	−	13.5399i	1.05039	−	0.974621i	0.999710	+	0.0240940i	$0.00767010\pi$
$194$	3.78519	−	2.58070i	0.271761	−	0.185283i
$195$		0			0
$196$	10.3670	−	5.89780i	0.740503	−	0.421271i
$197$	14.0362			1.00003			0.500017	−	0.866015i	$-0.333327\pi$
$197$	14.0362			1.00003			0.500017	+	0.866015i	$0.333327\pi$
$198$		0			0
$199$	1.71952	−	1.59548i	0.121894	−	0.113101i	−0.616871	−	0.787064i	$-0.711600\pi$
$199$	1.71952	−	1.59548i	0.121894	−	0.113101i	0.738765	+	0.673964i	$0.235410\pi$
$200$	−2.02538	+	5.16059i	−0.143216	+	0.364909i
$201$		0			0
$202$	−0.256705	+	1.12470i	−0.0180617	+	0.0791336i
$203$	−11.8505	−	18.9938i	−0.831740	−	1.33310i
$204$		0			0
$205$	−0.901228	+	12.0260i	−0.0629445	+	0.839936i
$206$	−2.40135	+	0.740720i	−0.167310	+	0.0516084i
$207$		0			0
$208$	1.11453	+	2.83977i	0.0772786	+	0.196903i
$209$	−6.21978	−	2.99529i	−0.430231	−	0.207188i
$210$		0			0
$211$	21.1916	−	10.2053i	1.45889	−	0.702564i	0.474776	−	0.880107i	$-0.342529\pi$
$211$	21.1916	−	10.2053i	1.45889	−	0.702564i	0.984113	+	0.177543i	$0.0568148\pi$
$212$	−7.41901	−	6.88384i	−0.509540	−	0.472784i
$213$		0			0
$214$	2.87525	+	4.98008i	0.196548	+	0.340431i
$215$	−1.85396	+	3.21115i	−0.126439	+	0.218999i
$216$		0			0
$217$	19.5677	−	3.63798i	1.32834	−	0.246962i
$218$	−4.70039	−	5.89410i	−0.318350	−	0.399199i
$219$		0			0
$220$	−4.38434	−	2.98919i	−0.295592	−	0.201531i
$221$	−3.19970	−	2.18152i	−0.215235	−	0.146745i
$222$		0			0
$223$	1.77541	+	2.22630i	0.118891	+	0.149084i	0.837715	−	0.546107i	$-0.183891\pi$
$223$	1.77541	+	2.22630i	0.118891	+	0.149084i	−0.718825	+	0.695191i	$0.755320\pi$
$224$	6.57744	−	12.3499i	0.439474	−	0.825160i
$225$		0			0
$226$	−0.906940	+	1.57087i	−0.0603287	+	0.104492i
$227$	−1.91275	−	3.31298i	−0.126954	−	0.219891i	0.795541	−	0.605900i	$-0.207187\pi$
$227$	−1.91275	−	3.31298i	−0.126954	−	0.219891i	−0.922495	+	0.386009i	$0.873853\pi$
$228$		0			0
$229$	11.2499	+	10.4384i	0.743415	+	0.689788i	0.957952	−	0.286928i	$-0.0926340\pi$
$229$	11.2499	+	10.4384i	0.743415	+	0.689788i	−0.214538	+	0.976716i	$0.568824\pi$
$230$	2.96435	−	1.42755i	0.195463	−	0.0941301i
$231$		0			0
$232$	−15.3655	−	7.39963i	−1.00879	−	0.485810i
$233$	−4.42460	−	11.2737i	−0.289865	−	0.738565i	−0.999425	−	0.0339192i	$-0.989201\pi$
$233$	−4.42460	−	11.2737i	−0.289865	−	0.738565i	0.709559	−	0.704646i	$-0.248894\pi$
$234$		0			0
$235$	12.8873	−	3.97521i	0.840675	−	0.259314i
$236$	0.0957230	−	1.27734i	0.00623104	−	0.0831474i
$237$		0			0
$238$	0.459551	+	4.19862i	0.0297882	+	0.272156i
$239$	−3.14676	+	13.7869i	−0.203547	+	0.891799i	0.765209	+	0.643782i	$0.222636\pi$
$239$	−3.14676	+	13.7869i	−0.203547	+	0.891799i	−0.968756	+	0.248016i	$0.920221\pi$
$240$		0			0
$241$	−1.29843	+	3.30834i	−0.0836391	+	0.213109i	−0.966575	−	0.256385i	$-0.917468\pi$
$241$	−1.29843	+	3.30834i	−0.0836391	+	0.213109i	0.882936	+	0.469494i	$0.155564\pi$
$242$	−2.66794	+	2.47549i	−0.171502	+	0.159131i
$243$		0			0
$244$	7.84696			0.502350
$245$	5.85877	+	8.71181i	0.374303	+	0.556577i
$246$		0			0
$247$	−3.62604	+	2.47219i	−0.230719	+	0.157302i
$248$	11.1144	−	10.3127i	0.705766	−	0.654855i
$249$		0			0
$250$	−6.04444	−	1.86446i	−0.382284	−	0.117919i
$251$	−2.84907	+	12.4826i	−0.179832	+	0.787895i	0.801874	+	0.597493i	$0.203836\pi$
$251$	−2.84907	+	12.4826i	−0.179832	+	0.787895i	−0.981706	+	0.190402i	$0.939021\pi$
$252$		0			0
$253$	−1.86275	−	8.16125i	−0.117110	−	0.513093i
$254$	0.744914	−	9.94019i	0.0467401	−	0.623703i
$255$		0			0
$256$	−0.208012	−	2.77573i	−0.0130007	−	0.173483i
$257$	−1.81322	−	4.62000i	−0.113105	−	0.288188i	0.863101	−	0.505031i	$-0.168519\pi$
$257$	−1.81322	−	4.62000i	−0.113105	−	0.288188i	−0.976206	+	0.216844i	$0.930424\pi$
$258$		0			0
$259$	−18.7573	+	0.642106i	−1.16552	+	0.0398985i
$260$	−3.03927	+	1.46364i	−0.188488	+	0.0907710i
$261$		0			0
$262$	8.02262	+	1.20922i	0.495639	+	0.0747056i
$263$	−3.43332	−	5.94669i	−0.211708	−	0.366688i	0.740541	−	0.672011i	$-0.234569\pi$
$263$	−3.43332	−	5.94669i	−0.211708	−	0.366688i	−0.952249	+	0.305322i	$0.901236\pi$
$264$		0			0
$265$	5.55433	−	6.96491i	0.341200	−	0.427851i
$266$	4.61941	+	1.25353i	0.283234	+	0.0768588i
$267$		0			0
$268$	2.70235	−	0.407314i	0.165072	−	0.0248807i
$269$	12.8275	+	8.74564i	0.782106	+	0.533231i	0.887284	−	0.461223i	$-0.152589\pi$
$269$	12.8275	+	8.74564i	0.782106	+	0.533231i	−0.105179	+	0.994453i	$0.533541\pi$
$270$		0			0
$271$	−16.5609	+	2.49615i	−1.00600	+	0.151631i	−0.631320	−	0.775522i	$-0.717487\pi$
$271$	−16.5609	+	2.49615i	−1.00600	+	0.151631i	−0.374683	+	0.927153i	$0.622249\pi$
$272$	−4.22725	−	5.30081i	−0.256315	−	0.321409i
$273$		0			0
$274$	3.13610	−	3.93255i	0.189459	−	0.237574i
$275$	−2.85574	+	4.94629i	−0.172208	+	0.298273i
$276$		0			0
$277$	7.38705	+	1.11342i	0.443845	+	0.0668988i	0.367163	−	0.930157i	$-0.380329\pi$
$277$	7.38705	+	1.11342i	0.443845	+	0.0668988i	0.0766821	+	0.997056i	$0.475567\pi$
$278$	3.58017	+	3.32191i	0.214724	+	0.199235i
$279$		0			0
$280$	7.32017	+	3.22151i	0.437464	+	0.192522i
$281$	29.0562	+	13.9927i	1.73335	+	0.834735i	0.985245	+	0.171149i	$0.0547481\pi$
$281$	29.0562	+	13.9927i	1.73335	+	0.834735i	0.748100	+	0.663586i	$0.230966\pi$
$282$		0			0
$283$	0.847328	+	11.3068i	0.0503684	+	0.672120i	0.964055	+	0.265701i	$0.0856035\pi$
$283$	0.847328	+	11.3068i	0.0503684	+	0.672120i	−0.913687	+	0.406419i	$0.866777\pi$
$284$	21.2353	−	6.55023i	1.26008	−	0.388684i
$285$		0			0
$286$	−0.331894	−	1.45412i	−0.0196253	−	0.0859842i
$287$	−21.1328	−	2.44920i	−1.24743	−	0.144571i
$288$		0			0
$289$	−8.02033	−	2.47394i	−0.471784	−	0.145526i
$290$	2.52296	−	6.42840i	0.148153	−	0.377488i
$291$		0			0
$292$	−20.9557	+	14.2874i	−1.22634	+	0.836104i
$293$	7.69626			0.449620			0.224810	−	0.974403i	$-0.427824\pi$
$293$	7.69626			0.449620			0.224810	+	0.974403i	$0.427824\pi$
$294$		0			0
$295$	1.12749			0.0656449
$296$	−11.8131	+	8.05401i	−0.686621	+	0.468130i
$297$		0			0
$298$	−4.60725	+	11.7391i	−0.266891	+	0.680027i
$299$	−5.08522	−	1.56858i	−0.294086	−	0.0907135i
$300$		0			0
$301$	−5.52734	−	3.49763i	−0.318590	−	0.201600i
$302$	−0.666102	−	2.91838i	−0.0383299	−	0.167934i
$303$		0			0
$304$	−7.34202	+	2.26471i	−0.421094	+	0.129890i
$305$	0.516164	+	6.88773i	0.0295555	+	0.394390i
$306$		0			0
$307$	−13.3452	−	6.42669i	−0.761649	−	0.366791i	0.0123947	−	0.999923i	$-0.496055\pi$
$307$	−13.3452	−	6.42669i	−0.761649	−	0.366791i	−0.774043	+	0.633132i	$0.781769\pi$
$308$	5.58257	−	7.51397i	0.318097	−	0.428148i
$309$		0			0
$310$	4.50051	+	4.17586i	0.255612	+	0.237173i
$311$	11.7355	+	1.76884i	0.665458	+	0.100302i	0.473080	−	0.881019i	$-0.343142\pi$
$311$	11.7355	+	1.76884i	0.665458	+	0.100302i	0.192378	+	0.981321i	$0.438380\pi$
$312$		0			0
$313$	10.4618	−	18.1203i	0.591335	−	1.02422i	−0.402718	−	0.915324i	$-0.631934\pi$
$313$	10.4618	−	18.1203i	0.591335	−	1.02422i	0.994053	−	0.108898i	$-0.0347322\pi$
$314$	3.21499	−	4.03147i	0.181432	−	0.227509i
$315$		0			0
$316$	6.29592	+	7.89483i	0.354173	+	0.444119i
$317$	−12.6811	+	1.91137i	−0.712243	+	0.107353i	−0.495163	−	0.868800i	$-0.664891\pi$
$317$	−12.6811	+	1.91137i	−0.712243	+	0.107353i	−0.217080	+	0.976154i	$0.569653\pi$
$318$		0			0
$319$	−14.5172	−	9.89765i	−0.812807	−	0.554162i
$320$	−2.58687	+	0.389908i	−0.144610	+	0.0217965i
$321$		0			0
$322$	2.30408	+	5.32717i	0.128401	+	0.296872i
$323$	6.08125	−	7.62565i	0.338370	−	0.424302i
$324$		0			0
$325$	1.81544	+	3.14443i	0.100702	+	0.174421i
$326$	−8.85418	−	1.33455i	−0.490388	−	0.0739141i
$327$		0			0
$328$	−14.6015	+	7.03170i	−0.806232	+	0.388261i
$329$	6.08445	+	22.9999i	0.335447	+	1.26802i
$330$		0			0
$331$	−3.39747	−	8.65660i	−0.186742	−	0.475810i	0.806589	−	0.591113i	$-0.201311\pi$
$331$	−3.39747	−	8.65660i	−0.186742	−	0.475810i	−0.993330	+	0.115303i	$0.963216\pi$
$332$	−0.671316	−	8.95809i	−0.0368433	−	0.491639i
$333$		0			0
$334$	0.889194	−	11.8655i	0.0486545	−	0.649250i
$335$	0.535281	+	2.34522i	0.0292455	+	0.128133i
$336$		0			0
$337$	4.01949	−	17.6105i	0.218956	−	0.959307i	−0.739296	−	0.673381i	$-0.764841\pi$
$337$	4.01949	−	17.6105i	0.218956	−	0.959307i	0.958252	−	0.285927i	$-0.0923014\pi$
$338$	5.85369	+	1.80562i	0.318399	+	0.0982130i
$339$		0			0
$340$	5.49581	−	5.09936i	0.298052	−	0.276552i
$341$	12.9062	−	8.79928i	0.698909	−	0.476508i
$342$		0			0
$343$	−15.7749	+	9.70328i	−0.851763	+	0.523928i
$344$	−4.98285			−0.268657
$345$		0			0
$346$	−8.42406	+	7.81639i	−0.452881	+	0.420212i
$347$	2.24496	−	5.72008i	0.120516	−	0.307070i	−0.857867	−	0.513872i	$-0.828211\pi$
$347$	2.24496	−	5.72008i	0.120516	−	0.307070i	0.978383	+	0.206802i	$0.0663057\pi$
$348$		0			0
$349$	−3.41209	+	14.9493i	−0.182645	+	0.800219i	0.797720	+	0.603028i	$0.206039\pi$
$349$	−3.41209	+	14.9493i	−0.182645	+	0.800219i	−0.980365	+	0.197191i	$0.936818\pi$
$350$	1.31980	−	3.73363i	0.0705463	−	0.199571i
$351$		0			0
$352$	0.820644	−	10.9507i	0.0437405	−	0.583676i
$353$	−28.3519	+	8.74540i	−1.50902	+	0.465471i	−0.935382	−	0.353639i	$-0.884944\pi$
$353$	−28.3519	+	8.74540i	−1.50902	+	0.465471i	−0.573637	+	0.819110i	$0.694468\pi$
$354$		0			0
$355$	7.14635	+	18.2086i	0.379289	+	0.966412i
$356$	−22.6157	−	10.8912i	−1.19863	−	0.577231i
$357$		0			0
$358$	1.79854	−	0.866131i	0.0950558	−	0.0457764i
$359$	−5.25056	−	4.87181i	−0.277114	−	0.257124i	0.529355	−	0.848400i	$-0.322434\pi$
$359$	−5.25056	−	4.87181i	−0.277114	−	0.257124i	−0.806469	+	0.591276i	$0.798624\pi$
$360$		0			0
$361$	3.97342	+	6.88217i	0.209128	+	0.362220i
$362$	−3.34135	+	5.78739i	−0.175618	+	0.304179i
$363$		0			0
$364$	−2.36232	−	5.46182i	−0.123819	−	0.286277i
$365$	−13.9193	−	17.4542i	−0.728569	−	0.913596i
$366$		0			0
$367$	−23.3421	−	15.9143i	−1.21845	−	0.830722i	−0.228691	−	0.973499i	$-0.573444\pi$
$367$	−23.3421	−	15.9143i	−1.21845	−	0.830722i	−0.989755	+	0.142777i	$0.954397\pi$
$368$	−7.69797	−	5.24839i	−0.401285	−	0.273591i
$369$		0			0
$370$	−3.60962	−	4.52632i	−0.187655	−	0.235312i
$371$	11.8789	+	10.2886i	0.616724	+	0.534158i
$372$		0			0
$373$	−7.62809	+	13.2122i	−0.394967	+	0.684103i	−0.993097	−	0.117296i	$-0.962577\pi$
$373$	−7.62809	+	13.2122i	−0.394967	+	0.684103i	0.598130	+	0.801399i	$0.295911\pi$
$374$	1.65743	+	2.87076i	0.0857037	+	0.148443i
$375$		0			0
$376$	13.2856	+	12.3272i	0.685153	+	0.635729i
$377$	−10.0635	+	4.84632i	−0.518296	+	0.249598i
$378$		0			0
$379$	−0.0443398	−	0.0213529i	−0.00227758	−	0.00109683i	0.432745	−	0.901517i	$-0.357545\pi$
$379$	−0.0443398	−	0.0213529i	−0.00227758	−	0.00109683i	−0.435022	+	0.900420i	$0.643259\pi$
$380$	−3.10397	−	7.90879i	−0.159230	−	0.405713i
$381$		0			0
$382$	−10.6472	+	3.28421i	−0.544756	+	0.168035i
$383$	−2.72437	+	36.3541i	−0.139209	+	1.85761i	0.293352	+	0.956004i	$0.405229\pi$
$383$	−2.72437	+	36.3541i	−0.139209	+	1.85761i	−0.432561	+	0.901605i	$0.642390\pi$
$384$		0			0
$385$	6.96266	+	4.40589i	0.354850	+	0.224545i
$386$	−2.41040	+	10.5607i	−0.122686	+	0.537523i
$387$		0			0
$388$	5.24083	−	13.3534i	0.266063	−	0.677917i
$389$	9.39553	−	8.71778i	0.476372	−	0.442009i	−0.405080	−	0.914281i	$-0.632756\pi$
$389$	9.39553	−	8.71778i	0.476372	−	0.442009i	0.881453	+	0.472272i	$0.156566\pi$
$390$		0			0
$391$	11.8272			0.598128
$392$	−6.20218	+	12.6721i	−0.313257	+	0.640037i
$393$		0			0
$394$	−6.31069	+	4.30256i	−0.317928	+	0.216760i
$395$	−6.51561	+	6.04560i	−0.327836	+	0.304187i
$396$		0			0
$397$	9.59644	+	2.96011i	0.481632	+	0.148564i	0.526057	−	0.850449i	$-0.323670\pi$
$397$	9.59644	+	2.96011i	0.481632	+	0.148564i	−0.0444259	+	0.999013i	$0.514146\pi$
$398$	−0.284032	+	1.24442i	−0.0142372	+	0.0623774i
$399$		0			0
$400$	1.41451	+	6.19738i	0.0707256	+	0.309869i
$401$	−1.57616	+	21.0324i	−0.0787099	+	1.05031i	0.808364	+	0.588683i	$0.200353\pi$
$401$	−1.57616	+	21.0324i	−0.0787099	+	1.05031i	−0.887074	+	0.461627i	$0.847266\pi$
$402$		0			0
$403$	−0.742078	−	9.90234i	−0.0369655	−	0.493271i
$404$	1.31972	+	3.36259i	0.0656585	+	0.167295i
$405$		0			0
$406$	11.1502	+	4.90707i	0.553377	+	0.243534i
$407$	−13.2711	+	6.39103i	−0.657824	+	0.316791i
$408$		0			0
$409$	34.9736	+	5.27143i	1.72934	+	0.260655i	0.936975	−	0.349397i	$-0.113614\pi$
$409$	34.9736	+	5.27143i	1.72934	+	0.260655i	0.792361	+	0.610053i	$0.208852\pi$
$410$	−3.28120	−	5.68320i	−0.162047	−	0.280673i
$411$		0			0
$412$	−4.90616	+	6.15213i	−0.241709	+	0.303093i
$413$	−0.0806918	+	1.98733i	−0.00397058	+	0.0977900i
$414$		0			0
$415$	7.81888	−	1.17851i	0.383814	−	0.0578506i
$416$	−5.76802	−	3.93257i	−0.282800	−	0.192810i
$417$		0			0
$418$	3.71458	−	0.559883i	0.181686	−	0.0273848i
$419$	18.1684	+	22.7824i	0.887584	+	1.11300i	0.992947	+	0.118561i	$0.0378282\pi$
$419$	18.1684	+	22.7824i	0.887584	+	1.11300i	−0.105363	+	0.994434i	$0.533600\pi$
$420$		0			0
$421$	−19.6890	+	24.6892i	−0.959583	+	1.20328i	0.0194988	+	0.999810i	$0.493793\pi$
$421$	−19.6890	+	24.6892i	−0.959583	+	1.20328i	−0.979081	+	0.203469i	$0.934778\pi$
$422$	−6.39951	+	11.0843i	−0.311523	+	0.539574i
$423$		0			0
$424$	11.8378	+	1.78427i	0.574896	+	0.0866517i
$425$	−5.91537	−	5.48866i	−0.286938	−	0.266239i
$426$		0			0
$427$	−12.1774	+	0.416860i	−0.589304	+	0.0201733i
$428$	16.2231	+	7.81265i	0.784174	+	0.377639i
$429$		0			0
$430$	−0.150782	−	2.01204i	−0.00727134	−	0.0970293i
$431$	3.37061	−	1.03970i	0.162357	−	0.0500804i	−0.212511	−	0.977159i	$-0.568164\pi$
$431$	3.37061	−	1.03970i	0.162357	−	0.0500804i	0.374868	+	0.927078i	$0.377688\pi$
$432$		0			0
$433$	2.08103	+	9.11758i	0.100008	+	0.438163i	0.999997	+	0.00225154i	$0.000716687\pi$
$433$	2.08103	+	9.11758i	0.100008	+	0.438163i	−0.899990	+	0.435911i	$0.856426\pi$
$434$	−7.68253	+	7.63381i	−0.368773	+	0.366435i
$435$		0			0
$436$	−22.5573	−	6.95801i	−1.08030	−	0.333228i
$437$	4.89670	−	12.4766i	0.234241	−	0.596837i
$438$		0			0
$439$	20.6147	−	14.0549i	0.983888	−	0.670804i	0.0393569	−	0.999225i	$-0.487469\pi$
$439$	20.6147	−	14.0549i	0.983888	−	0.670804i	0.944531	+	0.328422i	$0.106517\pi$
$440$	6.27679			0.299234
$441$		0			0
$442$	2.10731			0.100234
$443$	−10.3922	+	7.08527i	−0.493747	+	0.336631i	−0.784460	−	0.620179i	$-0.787060\pi$
$443$	−10.3922	+	7.08527i	−0.493747	+	0.336631i	0.290713	+	0.956810i	$0.406108\pi$
$444$		0			0
$445$	8.07217	−	20.5676i	0.382658	−	0.974996i
$446$	−1.48067	−	0.456725i	−0.0701116	−	0.0216266i
$447$		0			0
$448$	−0.502122	−	4.58757i	−0.0237230	−	0.216742i
$449$	−5.22883	−	22.9090i	−0.246764	−	1.08114i	−0.934718	−	0.355390i	$-0.884348\pi$
$449$	−5.22883	−	22.9090i	−0.246764	−	1.08114i	0.687954	−	0.725754i	$-0.258509\pi$
$450$		0			0
$451$	−15.9548	+	4.92140i	−0.751282	+	0.231740i
$452$	0.424447	+	5.66385i	0.0199643	+	0.266405i
$453$		0			0
$454$	1.87552	+	0.903203i	0.0880225	+	0.0423894i
$455$	4.63877	−	2.43282i	0.217469	−	0.114052i
$456$		0			0
$457$	8.89959	+	8.25761i	0.416305	+	0.386275i	0.860328	−	0.509741i	$-0.170259\pi$
$457$	8.89959	+	8.25761i	0.416305	+	0.386275i	−0.444023	+	0.896015i	$0.646449\pi$
$458$	−8.25770	−	1.24465i	−0.385857	−	0.0581586i
$459$		0			0
$460$	5.15120	−	8.92214i	0.240176	−	0.415997i
$461$	18.9293	−	23.7367i	0.881628	−	1.10553i	−0.112100	−	0.993697i	$-0.535758\pi$
$461$	18.9293	−	23.7367i	0.881628	−	1.10553i	0.993727	−	0.111829i	$-0.0356709\pi$
$462$		0			0
$463$	21.0195	+	26.3576i	0.976860	+	1.22494i	0.974371	+	0.224947i	$0.0722208\pi$
$463$	21.0195	+	26.3576i	0.976860	+	1.22494i	0.00248893	+	0.999997i	$0.499208\pi$
$464$	−19.3368	+	2.91456i	−0.897690	+	0.135305i
$465$		0			0
$466$	5.44509	+	3.71240i	0.252239	+	0.171973i
$467$	1.61462	−	0.243365i	0.0747158	−	0.0112616i	−0.111578	−	0.993756i	$-0.535590\pi$
$467$	1.61462	−	0.243365i	0.0747158	−	0.0112616i	0.186294	+	0.982494i	$0.440352\pi$
$468$		0			0
$469$	−4.17203	+	0.775652i	−0.192646	+	0.0358163i
$470$	−4.57563	+	5.73766i	−0.211058	+	0.264658i
$471$		0			0
$472$	0.757583	+	1.31217i	0.0348706	+	0.0603976i
$473$	−5.07622	−	0.765117i	−0.233405	−	0.0351801i
$474$		0			0
$475$	−8.23910	+	3.96774i	−0.378036	+	0.182052i
$476$	8.59490	+	10.0519i	0.393946	+	0.460730i
$477$		0			0
$478$	−2.81135	−	7.16320i	−0.128588	−	0.327637i
$479$	2.43732	+	32.5238i	0.111364	+	1.48605i	0.720760	+	0.693185i	$0.243793\pi$
$479$	2.43732	+	32.5238i	0.111364	+	1.48605i	−0.609395	+	0.792866i	$0.708588\pi$
$480$		0			0
$481$	−0.699769	+	9.33777i	−0.0319067	+	0.425766i
$482$	−0.430342	−	1.88545i	−0.0196015	−	0.0858799i
$483$		0			0
$484$	−2.53590	+	11.1105i	−0.115268	+	0.505023i
$485$	12.0658	+	3.72181i	0.547880	+	0.168999i
$486$		0			0
$487$	−21.6617	+	20.0991i	−0.981584	+	0.910777i	−0.996021	−	0.0891190i	$-0.971595\pi$
$487$	−21.6617	+	20.0991i	−0.981584	+	0.910777i	0.0144370	+	0.999896i	$0.495404\pi$
$488$	−7.66913	+	5.22873i	−0.347165	+	0.236693i
$489$		0			0
$490$	−5.30458	−	2.12094i	−0.239637	−	0.0958142i
$491$	17.6456			0.796334			0.398167	−	0.917313i	$-0.369647\pi$
$491$	17.6456			0.796334			0.398167	+	0.917313i	$0.369647\pi$
$492$		0			0
$493$	18.1974	−	16.8848i	0.819571	−	0.760451i
$494$	0.872466	−	2.22301i	0.0392541	−	0.100018i
$495$		0			0
$496$	3.86856	−	16.9493i	0.173704	−	0.761045i
$497$	−32.6062	+	11.2931i	−1.46259	+	0.506566i
$498$		0			0
$499$	0.407981	−	5.44412i	0.0182637	−	0.243712i	−0.980599	−	0.196026i	$-0.937196\pi$
$499$	0.407981	−	5.44412i	0.0182637	−	0.243712i	0.998862	−	0.0476862i	$-0.0151847\pi$
$500$	−18.9267	+	5.83812i	−0.846429	+	0.261089i
$501$		0			0
$502$	−2.54539	−	6.48555i	−0.113606	−	0.289464i
$503$	21.1579	+	10.1891i	0.943384	+	0.454310i	0.841362	−	0.540472i	$-0.181754\pi$
$503$	21.1579	+	10.1891i	0.943384	+	0.454310i	0.102022	+	0.994782i	$0.467469\pi$
$504$		0			0
$505$	−2.86473	+	1.37958i	−0.127479	+	0.0613906i
$506$	3.33920	+	3.09832i	0.148445	+	0.137737i
$507$		0			0
$508$	−15.6063	−	27.0309i	−0.692418	−	1.19930i
$509$	10.7628	−	18.6417i	0.477053	−	0.826281i	−0.522601	−	0.852578i	$-0.675038\pi$
$509$	10.7628	−	18.6417i	0.477053	−	0.826281i	0.999654	+	0.0262968i	$0.00837149\pi$
$510$		0			0
$511$	31.7613	−	23.2852i	1.40504	−	1.03008i
$512$	−13.4287	−	16.8390i	−0.593469	−	0.744186i
$513$		0			0
$514$	2.23141	+	1.52135i	0.0984235	+	0.0671040i
$515$	−5.72280	−	3.90174i	−0.252177	−	0.171931i
$516$		0			0
$517$	11.6417	+	14.5982i	0.512001	+	0.642029i
$518$	8.23650	−	6.03844i	0.361891	−	0.265314i
$519$		0			0
$520$	1.99512	−	3.45565i	0.0874919	−	0.151540i
$521$	−14.9438	−	25.8835i	−0.654702	−	1.13398i	−0.981969	−	0.189045i	$-0.939461\pi$
$521$	−14.9438	−	25.8835i	−0.654702	−	1.13398i	0.327267	−	0.944932i	$-0.393872\pi$
$522$		0			0
$523$	−21.5103	−	19.9586i	−0.940578	−	0.872729i	0.0514587	−	0.998675i	$-0.483613\pi$
$523$	−21.5103	−	19.9586i	−0.940578	−	0.872729i	−0.992037	+	0.125946i	$0.959803\pi$
$524$	22.8888	−	11.0227i	0.999903	−	0.481528i
$525$		0			0
$526$	3.36649	+	1.62122i	0.146786	+	0.0706884i
$527$	8.06286	+	20.5438i	0.351224	+	0.894903i
$528$		0			0
$529$	−6.44757	+	1.98881i	−0.280329	+	0.0864701i
$530$	−0.362260	+	4.83403i	−0.0157356	+	0.209977i
$531$		0			0
$532$	14.1623	−	4.90510i	0.614014	−	0.212663i
$533$	−2.36189	+	10.3481i	−0.102305	+	0.448227i
$534$		0			0
$535$	−5.79047	+	14.7539i	−0.250344	+	0.637866i
$536$	−2.36970	+	2.19876i	−0.102355	+	0.0949720i
$537$		0			0
$538$	−8.44811			−0.364224
$539$	−8.26419	+	11.9572i	−0.355964	+	0.515032i
$540$		0			0
$541$	−26.5623	+	18.1099i	−1.14200	+	0.778605i	−0.978154	−	0.207880i	$-0.933344\pi$
$541$	−26.5623	+	18.1099i	−1.14200	+	0.778605i	−0.163850	+	0.986485i	$0.552391\pi$
$542$	6.68067	−	6.19876i	0.286959	−	0.266259i
$543$		0			0
$544$	14.8259	+	4.57319i	0.635656	+	0.196074i
$545$	4.62366	−	20.2576i	0.198056	−	0.867738i
$546$		0			0
$547$	−0.228905	−	1.00290i	−0.00978728	−	0.0428809i	0.969798	−	0.243908i	$-0.0784293\pi$
$547$	−0.228905	−	1.00290i	−0.00978728	−	0.0428809i	−0.979586	+	0.201027i	$0.935572\pi$
$548$	1.17700	−	15.7060i	0.0502789	−	0.670925i
$549$		0			0
$550$	−0.232256	−	3.09925i	−0.00990345	−	0.132152i
$551$	−10.2777	−	26.1872i	−0.437845	−	1.11561i
$552$		0			0
$553$	−10.1898	−	11.9172i	−0.433313	−	0.506770i
$554$	−3.66254	+	1.76378i	−0.155606	+	0.0749360i
$555$		0			0
$556$	15.1220	+	2.27928i	0.641317	+	0.0966630i
$557$	−2.74997	−	4.76310i	−0.116520	−	0.201819i	0.801866	−	0.597504i	$-0.203841\pi$
$557$	−2.74997	−	4.76310i	−0.116520	−	0.201819i	−0.918386	+	0.395685i	$0.870507\pi$
$558$		0			0
$559$	−2.03474	+	2.55149i	−0.0860604	+	0.107916i
$560$	9.01597	−	1.67622i	0.380994	−	0.0708334i
$561$		0			0
$562$	−17.3530	+	2.61554i	−0.731991	+	0.110330i
$563$	−25.8475	−	17.6225i	−1.08934	−	0.742701i	−0.121081	−	0.992643i	$-0.538636\pi$
$563$	−25.8475	−	17.6225i	−1.08934	−	0.742701i	−0.968261	+	0.249942i	$0.919588\pi$
$564$		0			0
$565$	−4.94357	+	0.745124i	−0.207978	+	0.0313476i
$566$	−3.84688	−	4.82383i	−0.161696	−	0.202761i
$567$		0			0
$568$	−16.3894	+	20.5517i	−0.687684	+	0.862329i
$569$	2.97113	−	5.14615i	0.124556	−	0.215738i	−0.797003	−	0.603975i	$-0.793583\pi$
$569$	2.97113	−	5.14615i	0.124556	−	0.215738i	0.921559	+	0.388237i	$0.126916\pi$
$570$		0			0
$571$	−20.8141	−	3.13723i	−0.871044	−	0.131289i	−0.301715	−	0.953398i	$-0.597559\pi$
$571$	−20.8141	−	3.13723i	−0.871044	−	0.131289i	−0.569330	+	0.822109i	$0.692797\pi$
$572$	−3.42360	−	3.17664i	−0.143148	−	0.132822i
$573$		0			0
$574$	10.2521	−	5.37675i	0.427915	−	0.224421i
$575$	−9.99077	−	4.81130i	−0.416644	−	0.200645i
$576$		0			0
$577$	0.689895	+	9.20601i	0.0287207	+	0.383251i	0.992979	+	0.118288i	$0.0377407\pi$
$577$	0.689895	+	9.20601i	0.0287207	+	0.383251i	−0.964259	+	0.264963i	$0.914640\pi$
$578$	4.36431	−	1.34621i	0.181531	−	0.0559950i
$579$		0			0
$580$	−4.81174	−	21.0816i	−0.199797	−	0.875366i
$581$	1.51767	+	13.8660i	0.0629637	+	0.575259i
$582$		0			0
$583$	11.7857	+	3.63540i	0.488113	+	0.150563i
$584$	10.9606	−	27.9271i	0.453553	−	1.15563i
$585$		0			0
$586$	−3.46026	+	2.35916i	−0.142942	+	0.0974562i
$587$	28.4418			1.17392			0.586960	−	0.809616i	$-0.300325\pi$
$587$	28.4418			1.17392			0.586960	+	0.809616i	$0.300325\pi$
$588$		0			0
$589$	25.0100			1.03052
$590$	−0.506921	+	0.345613i	−0.0208696	+	0.0142287i
$591$		0			0
$592$	−5.98939	+	15.2607i	−0.246162	+	0.627211i
$593$	35.8289	+	11.0518i	1.47132	+	0.453841i	0.923774	−	0.382937i	$-0.125087\pi$
$593$	35.8289	+	11.0518i	1.47132	+	0.453841i	0.547542	+	0.836778i	$0.315564\pi$
$594$		0			0
$595$	−8.25782	+	8.20545i	−0.338537	+	0.336391i
$596$	8.78687	+	38.4978i	0.359924	+	1.57693i
$597$		0			0
$598$	2.76715	−	0.853553i	0.113157	−	0.0349044i
$599$	−1.13143	−	15.0979i	−0.0462290	−	0.616883i	−0.971418	−	0.237376i	$-0.923713\pi$
$599$	−1.13143	−	15.0979i	−0.0462290	−	0.616883i	0.925189	−	0.379507i	$-0.123906\pi$
$600$		0			0
$601$	16.3540	+	7.87568i	0.667094	+	0.321256i	0.736603	−	0.676326i	$-0.236429\pi$
$601$	16.3540	+	7.87568i	0.667094	+	0.321256i	−0.0695083	+	0.997581i	$0.522143\pi$
$602$	3.55725	−	0.121773i	0.144983	−	0.00496309i
$603$		0			0
$604$	−6.87107	−	6.37542i	−0.279580	−	0.259412i
$605$	−9.91915	−	1.49507i	−0.403271	−	0.0607833i
$606$		0			0
$607$	5.27717	−	9.14033i	0.214194	−	0.370995i	−0.738829	−	0.673893i	$-0.764621\pi$
$607$	5.27717	−	9.14033i	0.214194	−	0.370995i	0.953023	+	0.302898i	$0.0979543\pi$
$608$	10.9625	−	13.7465i	0.444588	−	0.557496i
$609$		0			0
$610$	−2.34339	−	2.93852i	−0.0948812	−	0.118977i
$611$	11.7374	−	1.76912i	0.474843	−	0.0715711i
$612$		0			0
$613$	−26.0096	−	17.7330i	−1.05052	−	0.716230i	−0.0904210	−	0.995904i	$-0.528821\pi$
$613$	−26.0096	−	17.7330i	−1.05052	−	0.716230i	−0.960095	+	0.279674i	$0.909774\pi$
$614$	7.97002	−	1.20129i	0.321644	−	0.0484800i
$615$		0			0
$616$	−0.449216	+	11.0636i	−0.0180994	+	0.445764i
$617$	−16.6775	+	20.9130i	−0.671412	+	0.841925i	−0.994532	−	0.104434i	$-0.966697\pi$
$617$	−16.6775	+	20.9130i	−0.671412	+	0.841925i	0.323119	+	0.946358i	$0.395268\pi$
$618$		0			0
$619$	−13.9341	−	24.1346i	−0.560059	−	0.970050i	−0.997491	−	0.0707987i	$-0.977445\pi$
$619$	−13.9341	−	24.1346i	−0.560059	−	0.970050i	0.437432	−	0.899252i	$-0.355888\pi$
$620$	19.0094	+	2.86521i	0.763436	+	0.115069i
$621$		0			0
$622$	−5.81851	+	2.80205i	−0.233301	+	0.112352i
$623$	35.6750	+	15.7001i	1.42929	+	0.629012i
$624$		0			0
$625$	−1.34490	−	3.42676i	−0.0537962	−	0.137070i
$626$	0.850853	+	11.3538i	0.0340069	+	0.453791i
$627$		0			0
$628$	1.20661	−	16.1010i	0.0481488	−	0.642501i
$629$	−4.63091	−	20.2894i	−0.184647	−	0.808990i
$630$		0			0
$631$	−0.659273	+	2.88846i	−0.0262452	+	0.114988i	−0.986354	−	0.164640i	$-0.947354\pi$
$631$	−0.659273	+	2.88846i	−0.0262452	+	0.114988i	0.960109	+	0.279628i	$0.0902110\pi$
$632$	−11.4139	−	3.52071i	−0.454019	−	0.140046i
$633$		0			0
$634$	5.11557	−	4.74655i	0.203165	−	0.188510i
$635$	22.7000	−	15.4766i	0.900824	−	0.614171i
$636$		0			0
$637$	3.95613	+	8.35048i	0.156748	+	0.330858i
$638$	9.56093			0.378521
$639$		0			0
$640$	12.6724	−	11.7582i	0.500919	−	0.464785i
$641$	8.96743	−	22.8486i	0.354192	−	0.902467i	−0.637099	−	0.770782i	$-0.719866\pi$
$641$	8.96743	−	22.8486i	0.354192	−	0.902467i	0.991292	−	0.131685i	$-0.0420389\pi$
$642$		0			0
$643$	−0.0369094	+	0.161711i	−0.00145557	+	0.00637725i	−0.975650	−	0.219331i	$-0.929613\pi$
$643$	−0.0369094	+	0.161711i	−0.00145557	+	0.00637725i	0.974195	+	0.225708i	$0.0724696\pi$
$644$	15.3577	+	9.71813i	0.605176	+	0.382948i
$645$		0			0
$646$	−0.396627	+	5.29262i	−0.0156051	+	0.208235i
$647$	−27.7438	+	8.55783i	−1.09072	+	0.336443i	−0.787398	−	0.616445i	$-0.788572\pi$
$647$	−27.7438	+	8.55783i	−1.09072	+	0.336443i	−0.303323	+	0.952888i	$0.598096\pi$
$648$		0			0
$649$	0.570294	+	1.45308i	0.0223860	+	0.0570386i
$650$	−1.78010	−	0.857250i	−0.0698212	−	0.0336241i
$651$		0			0
$652$	−25.2613	+	12.1652i	−0.989309	+	0.476426i
$653$	−0.986378	−	0.915225i	−0.0386000	−	0.0358155i	0.660637	−	0.750706i	$-0.270286\pi$
$653$	−0.986378	−	0.915225i	−0.0386000	−	0.0358155i	−0.699237	+	0.714890i	$0.746477\pi$
$654$		0			0
$655$	11.1808	+	19.3658i	0.436872	+	0.756684i
$656$	−9.29146	+	16.0933i	−0.362771	+	0.628337i
$657$		0			0
$658$	−9.78582	−	8.47571i	−0.381491	−	0.330418i
$659$	−11.4683	−	14.3808i	−0.446742	−	0.560196i	0.506564	−	0.862202i	$-0.330915\pi$
$659$	−11.4683	−	14.3808i	−0.446742	−	0.560196i	−0.953306	+	0.302006i	$0.902344\pi$
$660$		0			0
$661$	4.77228	+	3.25369i	0.185620	+	0.126554i	0.652565	−	0.757733i	$-0.273693\pi$
$661$	4.77228	+	3.25369i	0.185620	+	0.126554i	−0.466945	+	0.884286i	$0.654645\pi$
$662$	4.18105	+	2.85059i	0.162501	+	0.110791i
$663$		0			0
$664$	6.62521	+	8.30776i	0.257108	+	0.322403i
$665$	5.23707	+	12.1084i	0.203085	+	0.469545i
$666$		0			0
$667$	17.0564	−	29.5425i	0.660426	−	1.14389i
$668$	−18.6290	−	32.2665i	−0.720779	−	1.24843i
$669$		0			0
$670$	−0.959552	−	0.890334i	−0.0370707	−	0.0343966i
$671$	−8.61570	+	4.14910i	−0.332605	+	0.160174i
$672$		0			0
$673$	3.27366	+	1.57651i	0.126190	+	0.0607701i	0.495914	−	0.868372i	$-0.334833\pi$
$673$	3.27366	+	1.57651i	0.126190	+	0.0607701i	−0.369723	+	0.929142i	$0.620548\pi$
$674$	3.59105	+	9.14985i	0.138322	+	0.352439i
$675$		0			0
$676$	18.3294	−	5.65388i	0.704979	−	0.217457i
$677$	1.22103	−	16.2936i	0.0469282	−	0.626213i	−0.923309	−	0.384057i	$-0.874526\pi$
$677$	1.22103	−	16.2936i	0.0469282	−	0.626213i	0.970237	−	0.242156i	$-0.0778545\pi$
$678$		0			0
$679$	−7.42364	+	21.0010i	−0.284893	+	0.805945i
$680$	−1.97336	+	8.64586i	−0.0756750	+	0.331554i
$681$		0			0
$682$	−3.10537	+	7.91236i	−0.118911	+	0.302980i
$683$	27.3982	−	25.4218i	1.04836	−	0.972737i	0.0487014	−	0.998813i	$-0.484492\pi$
$683$	27.3982	−	25.4218i	1.04836	−	0.972737i	0.999660	+	0.0260762i	$0.00830125\pi$
$684$		0			0
$685$	13.8635			0.529695
$686$	4.11804	−	9.19815i	0.157227	−	0.351187i
$687$		0			0
$688$	−4.72074	+	3.21855i	−0.179977	+	0.122706i
$689$	5.74761	−	5.33300i	0.218966	−	0.203171i
$690$		0			0
$691$	18.1320	+	5.59299i	0.689775	+	0.212767i	0.619775	−	0.784779i	$-0.287224\pi$
$691$	18.1320	+	5.59299i	0.689775	+	0.212767i	0.0700002	+	0.997547i	$0.477700\pi$
$692$	−8.00714	+	35.0816i	−0.304386	+	1.33360i
$693$		0			0
$694$	0.744055	+	3.25992i	0.0282440	+	0.123745i
$695$	−1.00595	+	13.4234i	−0.0381577	+	0.509179i
$696$		0			0
$697$	−1.76287	−	23.5239i	−0.0667736	−	0.891032i
$698$	−3.04839	−	7.76718i	−0.115383	−	0.293992i
$699$		0			0
$700$	−3.17122	−	11.9875i	−0.119861	−	0.453087i
$701$	2.42219	−	1.16647i	0.0914849	−	0.0440568i	−0.387582	−	0.921835i	$-0.626690\pi$
$701$	2.42219	−	1.16647i	0.0914849	−	0.0440568i	0.479067	+	0.877779i	$0.340975\pi$
$702$		0			0
$703$	−23.3206	−	3.51502i	−0.879555	−	0.132572i
$704$	−1.81097	−	3.13669i	−0.0682535	−	0.118218i
$705$		0			0
$706$	10.0663	−	12.6228i	0.378851	−	0.475064i
$707$	−2.22665	−	5.14816i	−0.0837419	−	0.193616i
$708$		0			0
$709$	31.3937	−	4.73183i	1.17901	−	0.177708i	0.469847	−	0.882748i	$-0.344309\pi$
$709$	31.3937	−	4.73183i	1.17901	−	0.177708i	0.709167	+	0.705040i	$0.249071\pi$
$710$	−8.79457	−	5.99604i	−0.330054	−	0.225027i
$711$		0			0
$712$	29.3604	−	4.42537i	1.10033	−	0.165848i
$713$	18.9087	+	23.7108i	0.708136	+	0.887975i
$714$		0			0
$715$	2.56312	−	3.21405i	0.0958552	−	0.120199i
$716$	3.12536	−	5.41328i	0.116800	−	0.202304i
$717$		0			0
$718$	3.85404	+	0.580903i	0.143831	+	0.0216791i
$719$	−28.8237	−	26.7445i	−1.07494	−	0.997402i	−1.00000		0.000213969i	$-0.999932\pi$
$719$	−28.8237	−	26.7445i	−1.07494	−	0.997402i	−0.0749435	−	0.997188i	$-0.523878\pi$
$720$		0			0
$721$	7.28683	−	9.80786i	0.271376	−	0.365264i
$722$	−3.89608	−	1.87625i	−0.144997	−	0.0698269i
$723$		0			0
$724$	1.56375	+	20.8668i	0.0581163	+	0.775508i
$725$	−22.2406	+	6.86030i	−0.825994	+	0.254785i
$726$		0			0
$727$	5.23714	+	22.9454i	0.194235	+	0.850999i	0.974292	+	0.225290i	$0.0723330\pi$
$727$	5.23714	+	22.9454i	0.194235	+	0.850999i	−0.780057	+	0.625709i	$0.784810\pi$
$728$	5.94820	+	3.76395i	0.220455	+	0.139501i
$729$		0			0
$730$	11.6085	+	3.58074i	0.429648	+	0.132529i
$731$	2.64981	−	6.75161i	0.0980068	−	0.249717i
$732$		0			0
$733$	−6.91308	+	4.71326i	−0.255341	+	0.174088i	−0.684225	−	0.729271i	$-0.739859\pi$
$733$	−6.91308	+	4.71326i	−0.255341	+	0.174088i	0.428884	+	0.903360i	$0.358907\pi$
$734$	15.3729			0.567425
$735$		0			0
$736$	21.3206			0.785888
$737$	−2.75172	+	1.87609i	−0.101361	+	0.0691068i
$738$		0			0
$739$	−0.882641	+	2.24893i	−0.0324685	+	0.0827283i	−0.946189	−	0.323616i	$-0.895101\pi$
$739$	−0.882641	+	2.24893i	−0.0324685	+	0.0827283i	0.913720	+	0.406344i	$0.133197\pi$
$740$	−17.3227	−	5.34334i	−0.636795	−	0.196425i
$741$		0			0
$742$	−8.49461	−	0.984487i	−0.311847	−	0.0361416i
$743$	−7.17327	−	31.4282i	−0.263162	−	1.15299i	−0.917799	−	0.397045i	$-0.870036\pi$
$743$	−7.17327	−	31.4282i	−0.263162	−	1.15299i	0.654637	−	0.755943i	$-0.272821\pi$
$744$		0			0
$745$	−33.2138	+	10.2451i	−1.21686	+	0.375351i
$746$	−0.620389	−	8.27852i	−0.0227141	−	0.303098i
$747$		0			0
$748$	9.35179	+	4.50359i	0.341935	+	0.164667i
$749$	−25.5910	−	11.2623i	−0.935076	−	0.411515i
$750$		0			0
$751$	−27.9616	−	25.9445i	−1.02033	−	0.946729i	−0.0217389	−	0.999764i	$-0.506920\pi$
$751$	−27.9616	−	25.9445i	−1.02033	−	0.946729i	−0.998593	+	0.0530343i	$0.983111\pi$
$752$	20.5492	+	3.09730i	0.749353	+	0.112947i
$753$		0			0
$754$	3.03901	−	5.26372i	0.110674	−	0.191693i
$755$	5.14410	−	6.45050i	0.187213	−	0.234758i
$756$		0			0
$757$	−22.7724	−	28.5556i	−0.827676	−	1.03787i	−0.998616	−	0.0525913i	$-0.983252\pi$
$757$	−22.7724	−	28.5556i	−0.827676	−	1.03787i	0.170940	−	0.985281i	$-0.445319\pi$
$758$	0.0264807	−	0.00399132i	0.000961821	−	0.000144971i
$759$		0			0
$760$	8.30356	+	5.66127i	0.301202	+	0.205356i
$761$	9.23438	−	1.39186i	0.334746	−	0.0504548i	0.0204813	−	0.999790i	$-0.493480\pi$
$761$	9.23438	−	1.39186i	0.334746	−	0.0504548i	0.314265	+	0.949335i	$0.398242\pi$
$762$		0			0
$763$	35.3754	+	9.59952i	1.28067	+	0.347526i
$764$	−21.7530	+	27.2774i	−0.786995	+	0.986860i
$765$		0			0
$766$	−9.91889	−	17.1800i	−0.358384	−	0.620739i
$767$	0.981260	+	0.147901i	0.0354312	+	0.00534040i
$768$		0			0
$769$	45.8050	−	22.0585i	1.65177	−	0.795451i	0.652480	−	0.757806i	$-0.273729\pi$
$769$	45.8050	−	22.0585i	1.65177	−	0.795451i	0.999291	−	0.0376451i	$-0.0119856\pi$
$770$	−4.48099	+	0.153395i	−0.161483	+	0.00552796i
$771$		0			0
$772$	12.3919	+	31.5739i	0.445993	+	1.13637i
$773$	2.29757	+	30.6590i	0.0826379	+	1.10273i	0.872231	+	0.489095i	$0.162673\pi$
$773$	2.29757	+	30.6590i	0.0826379	+	1.10273i	−0.789593	+	0.613631i	$0.789708\pi$
$774$		0			0
$775$	1.54630	−	20.6339i	0.0555446	−	0.741191i
$776$	3.77582	+	16.5430i	0.135544	+	0.593857i
$777$		0			0
$778$	−1.55196	+	6.79959i	−0.0556405	+	0.243777i
$779$	−25.5454	−	7.87970i	−0.915258	−	0.282320i
$780$		0			0
$781$	−19.8522	+	18.4202i	−0.710368	+	0.659125i
$782$	−5.31755	+	3.62544i	−0.190155	+	0.129646i
$783$		0			0
$784$	2.30929	+	16.0116i	0.0824746	+	0.571845i
$785$	14.2122			0.507255
$786$		0			0
$787$	0.453442	−	0.420733i	0.0161635	−	0.0149975i	−0.672050	−	0.740506i	$-0.734586\pi$
$787$	0.453442	−	0.420733i	0.0161635	−	0.0149975i	0.688213	+	0.725509i	$0.258395\pi$
$788$	−8.73754	+	22.2629i	−0.311262	+	0.793083i
$789$		0			0
$790$	1.07625	−	4.71537i	0.0382914	−	0.167765i
$791$	−0.959567	−	8.76695i	−0.0341183	−	0.311717i
$792$		0			0
$793$	−0.454295	+	6.06215i	−0.0161325	+	0.215273i
$794$	−5.22196	+	1.61076i	−0.185320	+	0.0571638i
$795$		0			0
$796$	1.46021	+	3.72054i	0.0517556	+	0.131871i
$797$	−12.0025	−	5.78009i	−0.425150	−	0.204741i	0.209059	−	0.977903i	$-0.432960\pi$
$797$	−12.0025	−	5.78009i	−0.425150	−	0.204741i	−0.634209	+	0.773162i	$0.718674\pi$
$798$		0			0
$799$	−23.7681	+	11.4461i	−0.840856	+	0.404935i
$800$	−10.6635	−	9.89427i	−0.377011	−	0.349815i
$801$		0			0
$802$	−5.73851	−	9.93939i	−0.202634	−	0.350972i
$803$	15.4542	−	26.7674i	0.545366	−	0.944602i
$804$		0			0
$805$	−7.51996	+	14.1196i	−0.265044	+	0.497649i
$806$	3.36904	+	4.22465i	0.118669	+	0.148807i
$807$		0			0
$808$	−3.53043	−	2.40701i	−0.124200	−	0.0846783i
$809$	−8.05449	−	5.49146i	−0.283181	−	0.193070i	0.413396	−	0.910551i	$-0.364342\pi$
$809$	−8.05449	−	5.49146i	−0.283181	−	0.193070i	−0.696577	+	0.717482i	$0.745295\pi$
$810$		0			0
$811$	−8.38609	−	10.5158i	−0.294476	−	0.369261i	0.612481	−	0.790486i	$-0.290172\pi$
$811$	−8.38609	−	10.5158i	−0.294476	−	0.369261i	−0.906956	+	0.421225i	$0.861600\pi$
$812$	37.5032	−	6.97249i	1.31610	−	0.244686i
$813$		0			0
$814$	4.00766	−	6.94147i	0.140468	−	0.243298i
$815$	−12.3398	−	21.3731i	−0.432243	−	0.748667i
$816$		0			0
$817$	−6.02523	−	5.59060i	−0.210796	−	0.195590i
$818$	−17.3401	+	8.35056i	−0.606283	+	0.291970i
$819$		0			0
$820$	−18.5136	−	8.91569i	−0.646524	−	0.311349i
$821$	8.37886	+	21.3490i	0.292424	+	0.745085i	0.999288	+	0.0377350i	$0.0120143\pi$
$821$	8.37886	+	21.3490i	0.292424	+	0.745085i	−0.706863	+	0.707350i	$0.749890\pi$
$822$		0			0
$823$	31.5133	−	9.72058i	1.09849	−	0.338838i	0.308042	−	0.951373i	$-0.400326\pi$
$823$	31.5133	−	9.72058i	1.09849	−	0.338838i	0.790444	+	0.612535i	$0.209850\pi$
$824$	0.695579	−	9.28186i	0.0242317	−	0.323349i
$825$		0			0
$826$	−0.572904	−	0.918242i	−0.0199339	−	0.0319497i
$827$	−11.1471	+	48.8387i	−0.387623	+	1.69829i	0.285186	+	0.958472i	$0.407945\pi$
$827$	−11.1471	+	48.8387i	−0.387623	+	1.69829i	−0.672809	+	0.739816i	$0.734912\pi$
$828$		0			0
$829$	9.35345	−	23.8322i	0.324859	−	0.827727i	−0.671383	−	0.741111i	$-0.734299\pi$
$829$	9.35345	−	23.8322i	0.324859	−	0.827727i	0.996242	−	0.0866163i	$-0.0276054\pi$
$830$	−3.15414	+	2.92661i	−0.109482	+	0.101584i
$831$		0			0
$832$	−2.30252			−0.0798254
$833$	−13.8721	−	15.1426i	−0.480638	−	0.524660i
$834$		0			0
$835$	27.0967	−	18.4742i	0.937721	−	0.639328i
$836$	8.62268	−	8.00068i	0.298222	−	0.276709i
$837$		0			0
$838$	−15.1521	−	4.67382i	−0.523422	−	0.161454i
$839$	−3.92700	+	17.2053i	−0.135575	+	0.593993i	0.860802	+	0.508941i	$0.169963\pi$
$839$	−3.92700	+	17.2053i	−0.135575	+	0.593993i	−0.996377	+	0.0850521i	$0.972894\pi$
$840$		0			0
$841$	−9.47928	−	41.5314i	−0.326872	−	1.43212i
$842$	1.28414	−	17.1357i	0.0442544	−	0.590534i
$843$		0			0
$844$	2.99497	+	39.9650i	0.103091	+	1.37565i
$845$	6.16843	+	15.7169i	0.212201	+	0.540678i
$846$		0			0
$847$	3.34513	−	17.3766i	0.114940	−	0.597069i
$848$	12.3676	−	5.95594i	0.424707	−	0.204528i
$849$		0			0
$850$	4.34203	+	0.654455i	0.148930	+	0.0224476i
$851$	−14.2991	−	24.7667i	−0.490166	−	0.848992i
$852$		0			0
$853$	−16.6414	+	20.8676i	−0.569790	+	0.714494i	−0.980334	−	0.197347i	$-0.936768\pi$
$853$	−16.6414	+	20.8676i	−0.569790	+	0.714494i	0.410544	+	0.911841i	$0.365339\pi$
$854$	5.34719	−	3.92020i	0.182977	−	0.134146i
$855$		0			0
$856$	−21.0613	+	3.17449i	−0.719862	+	0.108502i
$857$	3.00982	+	2.05206i	0.102814	+	0.0700971i	0.613635	−	0.789589i	$-0.289706\pi$
$857$	3.00982	+	2.05206i	0.102814	+	0.0700971i	−0.510822	+	0.859687i	$0.670659\pi$
$858$		0			0
$859$	−10.3882	+	1.56577i	−0.354441	+	0.0534233i	−0.323849	−	0.946109i	$-0.604977\pi$
$859$	−10.3882	+	1.56577i	−0.354441	+	0.0534233i	−0.0305913	+	0.999532i	$0.509739\pi$
$860$	−3.93914	−	4.93953i	−0.134324	−	0.168437i
$861$		0			0
$862$	−1.19673	+	1.50066i	−0.0407609	+	0.0511126i
$863$	−4.83352	+	8.37190i	−0.164535	+	0.284983i	−0.936490	−	0.350694i	$-0.885946\pi$
$863$	−4.83352	+	8.37190i	−0.164535	+	0.284983i	0.771955	+	0.635677i	$0.219279\pi$
$864$		0			0
$865$	−31.3198	−	4.72071i	−1.06491	−	0.160509i
$866$	−3.73048	−	3.46138i	−0.126767	−	0.117622i
$867$		0			0
$868$	−6.41072	+	33.3012i	−0.217594	+	1.13032i
$869$	−11.0871	−	5.33927i	−0.376105	−	0.181122i
$870$		0			0
$871$	0.158218	+	2.11128i	0.00536102	+	0.0715378i
$872$	26.6825	−	8.23046i	0.903583	−	0.278719i
$873$		0			0
$874$	1.62293	+	7.11051i	0.0548964	+	0.240517i
$875$	29.0614	−	10.0654i	0.982456	−	0.340272i
$876$		0			0
$877$	−40.3807	−	12.4558i	−1.36356	−	0.420603i	−0.475252	−	0.879850i	$-0.657643\pi$
$877$	−40.3807	−	12.4558i	−1.36356	−	0.420603i	−0.888309	+	0.459247i	$0.848119\pi$
$878$	−4.96014	+	12.6382i	−0.167397	+	0.426520i
$879$		0			0
$880$	5.94661	−	4.05433i	0.200460	−	0.136672i
$881$	−1.78601			−0.0601721			−0.0300860	−	0.999547i	$-0.509578\pi$
$881$	−1.78601			−0.0601721			−0.0300860	+	0.999547i	$0.509578\pi$
$882$		0			0
$883$	−16.8203			−0.566048			−0.283024	−	0.959113i	$-0.591338\pi$
$883$	−16.8203			−0.566048			−0.283024	+	0.959113i	$0.591338\pi$
$884$	5.45196	−	3.71708i	0.183369	−	0.125019i
$885$		0			0
$886$	2.50048	−	6.37111i	0.0840051	−	0.214042i
$887$	15.7442	+	4.85643i	0.528637	+	0.163063i	0.547573	−	0.836758i	$-0.315552\pi$
$887$	15.7442	+	4.85643i	0.528637	+	0.163063i	−0.0189361	+	0.999821i	$0.506028\pi$
$888$		0			0
$889$	25.6548	+	41.1191i	0.860433	+	1.37909i
$890$	2.67538	+	11.7216i	0.0896790	+	0.392910i
$891$		0			0
$892$	−4.63636	+	1.43013i	−0.155237	+	0.0478842i
$893$	2.23410	+	29.8120i	0.0747614	+	0.997622i
$894$		0			0
$895$	4.95713	+	2.38723i	0.165699	+	0.0797963i
$896$	19.8183	+	23.1780i	0.662084	+	0.774323i
$897$		0			0
$898$	9.37329	+	8.69714i	0.312791	+	0.290227i
$899$	62.9429	+	9.48712i	2.09926	+	0.316413i
$900$		0			0
$901$	−8.71282	+	15.0911i	−0.290266	+	0.502756i
$902$	5.66474	−	7.10336i	0.188615	−	0.236516i
$903$		0			0
$904$	−4.18887	−	5.25267i	−0.139320	−	0.174701i
$905$	−18.2131	+	2.74519i	−0.605425	+	0.0912532i
$906$		0			0
$907$	44.8858	+	30.6026i	1.49041	+	1.01614i	0.988500	+	0.151224i	$0.0483214\pi$
$907$	44.8858	+	30.6026i	1.49041	+	1.01614i	0.501910	+	0.864920i	$0.332631\pi$
$908$	6.44545	−	0.971496i	0.213900	−	0.0322402i
$909$		0			0
$910$	−1.33986	+	2.51574i	−0.0444160	+	0.0833960i
$911$	−33.9883	+	42.6199i	−1.12608	+	1.41206i	−0.227212	+	0.973845i	$0.572961\pi$
$911$	−33.9883	+	42.6199i	−1.12608	+	1.41206i	−0.898870	+	0.438216i	$0.855611\pi$
$912$		0			0
$913$	5.47370	+	9.48072i	0.181153	+	0.313766i
$914$	−6.53252	−	0.984618i	−0.216076	−	0.0325683i
$915$		0			0
$916$	−23.5595	+	11.3457i	−0.778429	+	0.374872i
$917$	−34.9347	+	18.3216i	−1.15364	+	0.605032i
$918$		0			0
$919$	2.16355	+	5.51264i	0.0713690	+	0.181845i	0.962107	−	0.272672i	$-0.0879072\pi$
$919$	2.16355	+	5.51264i	0.0713690	+	0.181845i	−0.890738	+	0.454517i	$0.849812\pi$
$920$	0.910696	+	12.1524i	0.0300247	+	0.400652i
$921$		0			0
$922$	−1.23460	+	16.4745i	−0.0406593	+	0.542560i
$923$	3.83095	+	16.7845i	0.126097	+	0.552469i
$924$		0			0
$925$	−4.34183	+	19.0228i	−0.142759	+	0.625466i
$926$	−17.5299	−	5.40727i	−0.576070	−	0.177694i
$927$		0			0
$928$	32.8040	−	30.4377i	1.07684	−	0.999166i
$929$	29.0104	−	19.7789i	0.951800	−	0.648926i	0.0154074	−	0.999881i	$-0.495095\pi$
$929$	29.0104	−	19.7789i	0.951800	−	0.648926i	0.936392	+	0.350955i	$0.114143\pi$
$930$		0			0
$931$	−21.7173	+	8.36437i	−0.711756	+	0.274131i
$932$	20.6357			0.675944
$933$		0			0
$934$	−0.651338	+	0.604354i	−0.0213124	+	0.0197751i
$935$	−3.33791	+	8.50485i	−0.109161	+	0.278138i
$936$		0			0
$937$	−5.27934	+	23.1303i	−0.172468	+	0.755634i	0.812509	+	0.582949i	$0.198101\pi$
$937$	−5.27934	+	23.1303i	−0.172468	+	0.755634i	−0.984977	+	0.172685i	$0.944756\pi$
$938$	1.63799	−	1.62760i	0.0534823	−	0.0531431i
$939$		0			0
$940$	−1.71726	+	22.9153i	−0.0560109	+	0.747414i
$941$	−6.13207	+	1.89149i	−0.199900	+	0.0616609i	−0.393088	−	0.919501i	$-0.628593\pi$
$941$	−6.13207	+	1.89149i	−0.199900	+	0.0616609i	0.193188	+	0.981162i	$0.438117\pi$
$942$		0			0
$943$	−11.8431	−	30.1758i	−0.385665	−	0.982658i
$944$	1.56530	+	0.753807i	0.0509461	+	0.0245343i
$945$		0			0
$946$	2.51681	−	1.21203i	0.0818287	−	0.0394066i
$947$	−6.12127	−	5.67971i	−0.198915	−	0.184566i	0.574426	−	0.818556i	$-0.305225\pi$
$947$	−6.12127	−	5.67971i	−0.198915	−	0.184566i	−0.773341	+	0.633991i	$0.781416\pi$
$948$		0			0
$949$	−9.82444	−	17.0164i	−0.318915	−	0.552377i
$950$	2.48807	−	4.30947i	0.0807238	−	0.139818i
$951$		0			0
$952$	−15.0981	−	4.09704i	−0.489332	−	0.132786i
$953$	2.15510	+	2.70241i	0.0698104	+	0.0875395i	0.815511	−	0.578742i	$-0.196456\pi$
$953$	2.15510	+	2.70241i	0.0698104	+	0.0875395i	−0.745700	+	0.666282i	$0.767885\pi$
$954$		0			0
$955$	−25.3738	−	17.2996i	−0.821077	−	0.559801i
$956$	−19.9086	−	13.5735i	−0.643891	−	0.438998i
$957$		0			0
$958$	−11.0655	−	13.8757i	−0.357509	−	0.448303i
$959$	−0.992176	+	24.4359i	−0.0320390	+	0.789078i
$960$		0			0
$961$	−12.7950	+	22.1616i	−0.412743	+	0.714892i
$962$	−2.54772	−	4.41279i	−0.0821419	−	0.142274i
$963$		0			0
$964$	−4.43912	−	4.11890i	−0.142974	−	0.132661i
$965$	−26.8992	+	12.9539i	−0.865914	+	0.417002i
$966$		0			0
$967$	41.4435	+	19.9581i	1.33273	+	0.641810i	0.958385	−	0.285479i	$-0.0921527\pi$
$967$	41.4435	+	19.9581i	1.33273	+	0.641810i	0.374347	+	0.927289i	$0.377867\pi$
$968$	−4.92492	−	12.5485i	−0.158293	−	0.403324i
$969$		0			0
$970$	−6.56567	+	2.02524i	−0.210811	+	0.0650266i
$971$	3.79426	−	50.6308i	0.121763	−	1.62482i	−0.517396	−	0.855746i	$-0.673098\pi$
$971$	3.79426	−	50.6308i	0.121763	−	1.62482i	0.639159	−	0.769075i	$-0.279283\pi$
$972$		0			0
$973$	−23.5883	−	2.73378i	−0.756207	−	0.0876410i
$974$	3.57809	−	15.6766i	0.114649	−	0.502312i
$975$		0			0
$976$	−3.88835	+	9.90736i	−0.124463	+	0.317127i
$977$	−5.65455	+	5.24666i	−0.180905	+	0.167855i	−0.765427	−	0.643522i	$-0.777472\pi$
$977$	−5.65455	+	5.24666i	−0.180905	+	0.167855i	0.584522	+	0.811378i	$0.301282\pi$
$978$		0			0
$979$	30.5901			0.977662
$980$	−17.4650	+	3.86954i	−0.557899	+	0.123608i
$981$		0			0
$982$	−7.93349	+	5.40896i	−0.253168	+	0.172607i
$983$	−17.7791	+	16.4966i	−0.567066	+	0.526160i	−0.910768	−	0.412918i	$-0.864509\pi$
$983$	−17.7791	+	16.4966i	−0.567066	+	0.526160i	0.343702	+	0.939079i	$0.388319\pi$
$984$		0			0
$985$	−20.1162	−	6.20502i	−0.640955	−	0.197708i
$986$	−3.00587	+	13.1696i	−0.0957262	+	0.419404i
$987$		0			0
$988$	−1.66395	−	7.29025i	−0.0529373	−	0.231934i
$989$	0.744825	−	9.93899i	0.0236840	−	0.316042i
$990$		0			0
$991$	0.954423	+	12.7359i	0.0303182	+	0.404569i	0.991631	+	0.129108i	$0.0412114\pi$
$991$	0.954423	+	12.7359i	0.0303182	+	0.404569i	−0.961312	+	0.275461i	$0.911170\pi$
$992$	14.5347	+	37.0338i	0.461477	+	1.17582i
$993$		0			0
$994$	11.1981	−	15.0723i	0.355183	−	0.478065i
$995$	−3.16969	+	1.52644i	−0.100486	+	0.0483914i
$996$		0			0
$997$	−1.23555	−	0.186229i	−0.0391302	−	0.00589793i	0.129448	−	0.991586i	$-0.458679\pi$
$997$	−1.23555	−	0.186229i	−0.0391302	−	0.00589793i	−0.168578	+	0.985688i	$0.553918\pi$
$998$	1.48538	+	2.57275i	0.0470188	+	0.0814390i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.c.37.2		48
3.2	odd	2		147.2.m.a.37.3	yes	48
49.4	even	21	inner	441.2.bb.c.298.2		48
147.2	odd	42		7203.2.a.i.1.15		24
147.47	even	42		7203.2.a.k.1.15		24
147.53	odd	42		147.2.m.a.4.3	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.a.4.3	✓	48	147.53	odd	42
147.2.m.a.37.3	yes	48	3.2	odd	2
441.2.bb.c.37.2		48	1.1	even	1	trivial
441.2.bb.c.298.2		48	49.4	even	21	inner
7203.2.a.i.1.15		24	147.2	odd	42
7203.2.a.k.1.15		24	147.47	even	42

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.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.449603 + 0.306534i) q^{2} +(-0.622503 + 1.58611i) q^{4} +(-1.43317 - 0.442074i) q^{5} +(0.881776 - 2.49449i) q^{7} +(-0.448490 - 1.96496i) q^{8} +O(q^{10})\)	\(q+(-0.449603 + 0.306534i) q^{2} +(-0.622503 + 1.58611i) q^{4} +(-1.43317 - 0.442074i) q^{5} +(0.881776 - 2.49449i) q^{7} +(-0.448490 - 1.96496i) q^{8} +(0.779867 - 0.240557i) q^{10} +(-0.155173 - 2.07065i) q^{11} +(-1.18931 - 0.572740i) q^{13} +(0.368197 + 1.39182i) q^{14} +(-1.69412 - 1.57191i) q^{16} +(2.90096 + 0.437250i) q^{17} +(1.66231 - 2.87921i) q^{19} +(1.59333 - 1.99797i) q^{20} +(0.704489 + 0.883402i) q^{22} +(3.98643 - 0.600858i) q^{23} +(-2.27265 - 1.54947i) q^{25} +(0.710279 - 0.107057i) q^{26} +(3.40763 + 2.95142i) q^{28} +(5.27575 - 6.61558i) q^{29} +(3.76132 + 6.51479i) q^{31} +(5.22949 + 0.788219i) q^{32} +(-1.43831 + 0.692655i) q^{34} +(-2.36648 + 3.18521i) q^{35} +(-2.59163 - 6.60338i) q^{37} +(0.135195 + 1.80406i) q^{38} +(-0.225897 + 3.01439i) q^{40} +(-1.78927 - 7.83931i) q^{41} +(0.550132 - 2.41029i) q^{43} +(3.38087 + 1.04286i) q^{44} +(-1.60813 + 1.49212i) q^{46} +(-7.42968 + 5.06547i) q^{47} +(-5.44494 - 4.39916i) q^{49} +1.49675 q^{50} +(1.64877 - 1.52984i) q^{52} +(-2.17004 + 5.52916i) q^{53} +(-0.692989 + 3.03618i) q^{55} +(-5.29704 - 0.613903i) q^{56} +(-0.344091 + 4.59158i) q^{58} +(-0.718360 + 0.221585i) q^{59} +(-1.68251 - 4.28696i) q^{61} +(-3.68810 - 1.77610i) q^{62} +(1.57155 - 0.756820i) q^{64} +(1.45128 + 1.34659i) q^{65} +(-0.801950 - 1.38902i) q^{67} +(-2.49939 + 4.32906i) q^{68} +(0.0876008 - 2.15749i) q^{70} +(-8.13170 - 10.1968i) q^{71} +(12.2987 + 8.38512i) q^{73} +(3.18936 + 2.17447i) q^{74} +(3.53195 + 4.42893i) q^{76} +(-5.30203 - 1.43877i) q^{77} +(2.96317 - 5.13236i) q^{79} +(1.73305 + 3.00174i) q^{80} +(3.20747 + 2.97610i) q^{82} +(-4.75005 + 2.28751i) q^{83} +(-3.96428 - 1.90909i) q^{85} +(0.491494 + 1.25231i) q^{86} +(-3.99915 + 1.23357i) q^{88} +(-1.10092 + 14.6907i) q^{89} +(-2.47739 + 2.46168i) q^{91} +(-1.52854 + 6.69696i) q^{92} +(1.78767 - 4.55490i) q^{94} +(-3.65520 + 3.39153i) q^{95} -8.41896 q^{97} +(3.79655 + 0.308813i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} + 3 q^{4} - 6 q^{8}+O(q^{10}) \) 48 * q + q^2 + 3 * q^4 - 6 * q^8	\( 48 q + q^{2} + 3 q^{4} - 6 q^{8} + 30 q^{10} + 9 q^{11} + 42 q^{14} + 29 q^{16} + 5 q^{17} - 26 q^{19} + 5 q^{20} + q^{22} + 4 q^{23} - 56 q^{25} + 62 q^{26} + 7 q^{28} - 12 q^{29} - 36 q^{31} + 14 q^{32} - 76 q^{34} - 7 q^{35} - 20 q^{37} + 60 q^{38} + 28 q^{40} - 41 q^{41} + 12 q^{43} - 44 q^{44} + 16 q^{46} - 13 q^{47} - 84 q^{49} + 12 q^{50} + 92 q^{52} - 14 q^{53} - 38 q^{55} - 105 q^{56} + 3 q^{58} - 57 q^{59} + 11 q^{61} + 16 q^{62} - 110 q^{64} - 21 q^{65} + 34 q^{67} - 22 q^{68} - 6 q^{71} - 69 q^{73} + 90 q^{74} - 49 q^{76} + 34 q^{79} - 55 q^{80} + 91 q^{82} - 28 q^{83} - 44 q^{85} + 26 q^{86} + 45 q^{88} - 11 q^{89} - 84 q^{92} + 90 q^{94} - 150 q^{95} + 124 q^{97} - 119 q^{98}+O(q^{100}) \) 48 * q + q^2 + 3 * q^4 - 6 * q^8 + 30 * q^10 + 9 * q^11 + 42 * q^14 + 29 * q^16 + 5 * q^17 - 26 * q^19 + 5 * q^20 + q^22 + 4 * q^23 - 56 * q^25 + 62 * q^26 + 7 * q^28 - 12 * q^29 - 36 * q^31 + 14 * q^32 - 76 * q^34 - 7 * q^35 - 20 * q^37 + 60 * q^38 + 28 * q^40 - 41 * q^41 + 12 * q^43 - 44 * q^44 + 16 * q^46 - 13 * q^47 - 84 * q^49 + 12 * q^50 + 92 * q^52 - 14 * q^53 - 38 * q^55 - 105 * q^56 + 3 * q^58 - 57 * q^59 + 11 * q^61 + 16 * q^62 - 110 * q^64 - 21 * q^65 + 34 * q^67 - 22 * q^68 - 6 * q^71 - 69 * q^73 + 90 * q^74 - 49 * q^76 + 34 * q^79 - 55 * q^80 + 91 * q^82 - 28 * q^83 - 44 * q^85 + 26 * q^86 + 45 * q^88 - 11 * q^89 - 84 * q^92 + 90 * q^94 - 150 * q^95 + 124 * q^97 - 119 * q^98

Introduction

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