LMFDB - Embedded newform 441.2.bb.c.163.3

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			163.3
Character	$\chi$	$=$	441.163
Dual form			441.2.bb.c.46.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.633632 + 1.61447i) q^{2} +(-0.738910 + 0.685609i) q^{4} +(-2.02525 + 1.38079i) q^{5} +(2.55966 + 0.669438i) q^{7} +(1.55011 + 0.746495i) q^{8} +O(q^{10})$	\(q+(0.633632 + 1.61447i) q^{2} +(-0.738910 + 0.685609i) q^{4} +(-2.02525 + 1.38079i) q^{5} +(2.55966 + 0.669438i) q^{7} +(1.55011 + 0.746495i) q^{8} +(-3.51251 - 2.39479i) q^{10} +(1.16365 + 0.175392i) q^{11} +(-3.07468 + 3.85553i) q^{13} +(0.541096 + 4.55666i) q^{14} +(-0.373646 + 4.98596i) q^{16} +(0.121350 - 0.0374315i) q^{17} +(0.786116 - 1.36159i) q^{19} +(0.549795 - 2.40881i) q^{20} +(0.454162 + 1.98981i) q^{22} +(-4.92579 - 1.51941i) q^{23} +(0.368347 - 0.938534i) q^{25} +(-8.17285 - 2.52099i) q^{26} +(-2.35033 + 1.26027i) q^{28} +(-0.371274 + 1.62666i) q^{29} +(-2.64206 - 4.57618i) q^{31} +(-4.99830 + 1.54177i) q^{32} +(0.137323 + 0.172198i) q^{34} +(-6.10831 + 2.17858i) q^{35} +(6.98979 + 6.48558i) q^{37} +(2.69636 + 0.406410i) q^{38} +(-4.17012 + 0.628545i) q^{40} +(5.76353 + 2.77557i) q^{41} +(9.98202 - 4.80709i) q^{43} +(-0.980086 + 0.668211i) q^{44} +(-0.668107 - 8.91527i) q^{46} +(-2.92459 - 7.45174i) q^{47} +(6.10371 + 3.42706i) q^{49} +1.74863 q^{50} +(-0.371470 - 4.95692i) q^{52} +(8.18219 - 7.59196i) q^{53} +(-2.59887 + 1.25155i) q^{55} +(3.46803 + 2.94848i) q^{56} +(-2.86143 + 0.431292i) q^{58} +(5.88187 + 4.01019i) q^{59} +(-9.05562 - 8.40239i) q^{61} +(5.71400 - 7.16513i) q^{62} +(0.578605 + 0.725548i) q^{64} +(0.903317 - 12.0539i) q^{65} +(-2.53046 - 4.38289i) q^{67} +(-0.0640033 + 0.110857i) q^{68} +(-7.38766 - 8.48124i) q^{70} +(-2.08891 - 9.15212i) q^{71} +(-3.24237 + 8.26143i) q^{73} +(-6.04180 + 15.3942i) q^{74} +(0.352651 + 1.54506i) q^{76} +(2.86114 + 1.22794i) q^{77} +(6.33188 - 10.9671i) q^{79} +(-6.12784 - 10.6137i) q^{80} +(-0.829110 + 11.0637i) q^{82} +(10.4034 + 13.0454i) q^{83} +(-0.194079 + 0.243367i) q^{85} +(14.0858 + 13.0697i) q^{86} +(1.67286 + 1.14054i) q^{88} +(-5.91524 + 0.891578i) q^{89} +(-10.4512 + 7.81054i) q^{91} +(4.68143 - 2.25446i) q^{92} +(10.1775 - 9.44332i) q^{94} +(0.287995 + 3.84303i) q^{95} -1.74858 q^{97} +(-1.66538 + 12.0257i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{10}{21}\right)$	$1$

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 $

$2$	0.633632	+	1.61447i	0.448045	+	1.14160i	0.959355	+	0.282204i	$0.0910654\pi$
$2$	0.633632	+	1.61447i	0.448045	+	1.14160i	−0.511309	+	0.859397i	$0.670839\pi$
$3$		0			0
$3$		0			0
$4$	−0.738910	+	0.685609i	−0.369455	+	0.342804i
$5$	−2.02525	+	1.38079i	−0.905720	+	0.617509i	−0.924029	−	0.382323i	$-0.875124\pi$
$5$	−2.02525	+	1.38079i	−0.905720	+	0.617509i	0.0183090	+	0.999832i	$0.494172\pi$
$6$		0			0
$7$	2.55966	+	0.669438i	0.967460	+	0.253024i
$7$	2.55966	+	0.669438i	0.967460	+	0.253024i
$8$	1.55011	+	0.746495i	0.548048	+	0.263926i
$9$		0			0
$10$	−3.51251	−	2.39479i	−1.11075	−	0.757298i
$11$	1.16365	+	0.175392i	0.350855	+	0.0528828i	0.322105	−	0.946704i	$-0.395609\pi$
$11$	1.16365	+	0.175392i	0.350855	+	0.0528828i	0.0287493	+	0.999587i	$0.490848\pi$
$12$		0			0
$13$	−3.07468	+	3.85553i	−0.852764	+	1.06933i	0.144050	+	0.989570i	$0.453987\pi$
$13$	−3.07468	+	3.85553i	−0.852764	+	1.06933i	−0.996814	+	0.0797619i	$0.974584\pi$
$14$	0.541096	+	4.55666i	0.144614	+	1.21782i
$15$		0			0
$16$	−0.373646	+	4.98596i	−0.0934114	+	1.24649i
$17$	0.121350	−	0.0374315i	0.0294317	−	0.00907847i	−0.280004	−	0.959999i	$-0.590336\pi$
$17$	0.121350	−	0.0374315i	0.0294317	−	0.00907847i	0.309436	+	0.950920i	$0.399860\pi$
$18$		0			0
$19$	0.786116	−	1.36159i	0.180347	−	0.312371i	−0.761651	−	0.647987i	$-0.775611\pi$
$19$	0.786116	−	1.36159i	0.180347	−	0.312371i	0.941999	+	0.335616i	$0.108944\pi$
$20$	0.549795	−	2.40881i	0.122938	−	0.538627i
$21$		0			0
$22$	0.454162	+	1.98981i	0.0968277	+	0.424230i
$23$	−4.92579	−	1.51941i	−1.02710	−	0.316818i	−0.264979	−	0.964254i	$-0.585365\pi$
$23$	−4.92579	−	1.51941i	−1.02710	−	0.316818i	−0.762120	+	0.647436i	$0.775841\pi$
$24$		0			0
$25$	0.368347	−	0.938534i	0.0736695	−	0.187707i
$26$	−8.17285	−	2.52099i	−1.60283	−	0.494407i
$27$		0			0
$28$	−2.35033	+	1.26027i	−0.444171	+	0.238169i
$29$	−0.371274	+	1.62666i	−0.0689438	+	0.302063i	−0.997630	−	0.0688033i	$-0.978082\pi$
$29$	−0.371274	+	1.62666i	−0.0689438	+	0.302063i	0.928686	+	0.370866i	$0.120939\pi$
$30$		0			0
$31$	−2.64206	−	4.57618i	−0.474528	−	0.821906i	0.525047	−	0.851073i	$-0.324048\pi$
$31$	−2.64206	−	4.57618i	−0.474528	−	0.821906i	−0.999575	+	0.0291674i	$0.990714\pi$
$32$	−4.99830	+	1.54177i	−0.883582	+	0.272549i
$33$		0			0
$34$	0.137323	+	0.172198i	0.0235507	+	0.0295316i
$35$	−6.10831	+	2.17858i	−1.03249	+	0.368247i
$36$		0			0
$37$	6.98979	+	6.48558i	1.14911	+	1.06622i	0.996964	+	0.0778648i	$0.0248103\pi$
$37$	6.98979	+	6.48558i	1.14911	+	1.06622i	0.152150	+	0.988357i	$0.451380\pi$
$38$	2.69636	+	0.406410i	0.437407	+	0.0659284i
$39$		0			0
$40$	−4.17012	+	0.628545i	−0.659354	+	0.0993817i
$41$	5.76353	+	2.77557i	0.900112	+	0.433471i	0.825929	−	0.563774i	$-0.190651\pi$
$41$	5.76353	+	2.77557i	0.900112	+	0.433471i	0.0741823	+	0.997245i	$0.476365\pi$
$42$		0			0
$43$	9.98202	−	4.80709i	1.52224	−	0.733074i	0.528946	−	0.848656i	$-0.322588\pi$
$43$	9.98202	−	4.80709i	1.52224	−	0.733074i	0.993298	+	0.115582i	$0.0368733\pi$
$44$	−0.980086	+	0.668211i	−0.147754	+	0.100737i
$45$		0			0
$46$	−0.668107	−	8.91527i	−0.0985070	−	1.31448i
$47$	−2.92459	−	7.45174i	−0.426596	−	1.08695i	−0.969050	−	0.246863i	$-0.920600\pi$
$47$	−2.92459	−	7.45174i	−0.426596	−	1.08695i	0.542454	−	0.840085i	$-0.317495\pi$
$48$		0			0
$49$	6.10371	+	3.42706i	0.871958	+	0.489581i
$50$	1.74863			0.247293
$51$		0			0
$52$	−0.371470	−	4.95692i	−0.0515136	−	0.687401i
$53$	8.18219	−	7.59196i	1.12391	−	1.04284i	0.125196	−	0.992132i	$-0.460044\pi$
$53$	8.18219	−	7.59196i	1.12391	−	1.04284i	0.998714	−	0.0507040i	$-0.0161465\pi$
$54$		0			0
$55$	−2.59887	+	1.25155i	−0.350432	+	0.168759i
$56$	3.46803	+	2.94848i	0.463435	+	0.394007i
$57$		0			0
$58$	−2.86143	+	0.431292i	−0.375725	+	0.0566314i
$59$	5.88187	+	4.01019i	0.765754	+	0.522082i	0.882063	−	0.471131i	$-0.156154\pi$
$59$	5.88187	+	4.01019i	0.765754	+	0.522082i	−0.116309	+	0.993213i	$0.537106\pi$
$60$		0			0
$61$	−9.05562	−	8.40239i	−1.15945	−	1.07582i	−0.996008	−	0.0892628i	$-0.971549\pi$
$61$	−9.05562	−	8.40239i	−1.15945	−	1.07582i	−0.163445	−	0.986552i	$-0.552261\pi$
$62$	5.71400	−	7.16513i	0.725678	−	0.909972i
$63$		0			0
$64$	0.578605	+	0.725548i	0.0723256	+	0.0906934i
$65$	0.903317	−	12.0539i	0.112043	−	1.49510i
$66$		0			0
$67$	−2.53046	−	4.38289i	−0.309145	−	0.535456i	0.669030	−	0.743235i	$-0.266710\pi$
$67$	−2.53046	−	4.38289i	−0.309145	−	0.535456i	−0.978176	+	0.207780i	$0.933376\pi$
$68$	−0.0640033	+	0.110857i	−0.00776155	+	0.0134434i
$69$		0			0
$70$	−7.38766	−	8.48124i	−0.882994	−	1.01370i
$71$	−2.08891	−	9.15212i	−0.247908	−	1.08616i	−0.933615	−	0.358279i	$-0.883364\pi$
$71$	−2.08891	−	9.15212i	−0.247908	−	1.08616i	0.685706	−	0.727878i	$-0.259493\pi$
$72$		0			0
$73$	−3.24237	+	8.26143i	−0.379491	+	0.966927i	0.605735	+	0.795667i	$0.292879\pi$
$73$	−3.24237	+	8.26143i	−0.379491	+	0.966927i	−0.985226	+	0.171261i	$0.945216\pi$
$74$	−6.04180	+	15.3942i	−0.702345	+	1.78954i
$75$		0			0
$76$	0.352651	+	1.54506i	0.0404518	+	0.177231i
$77$	2.86114	+	1.22794i	0.326057	+	0.139937i
$78$		0			0
$79$	6.33188	−	10.9671i	0.712393	−	1.23390i	−0.251564	−	0.967841i	$-0.580945\pi$
$79$	6.33188	−	10.9671i	0.712393	−	1.23390i	0.963957	−	0.266060i	$-0.0857218\pi$
$80$	−6.12784	−	10.6137i	−0.685114	−	1.18665i
$81$		0			0
$82$	−0.829110	+	11.0637i	−0.0915599	+	1.22178i
$83$	10.4034	+	13.0454i	1.14192	+	1.43192i	0.885063	+	0.465472i	$0.154115\pi$
$83$	10.4034	+	13.0454i	1.14192	+	1.43192i	0.256857	+	0.966449i	$0.417313\pi$
$84$		0			0
$85$	−0.194079	+	0.243367i	−0.0210508	+	0.0263969i
$86$	14.0858	+	13.0697i	1.51891	+	1.40934i
$87$		0			0
$88$	1.67286	+	1.14054i	0.178328	+	0.121582i
$89$	−5.91524	+	0.891578i	−0.627014	+	0.0945071i	−0.454860	−	0.890563i	$-0.650311\pi$
$89$	−5.91524	+	0.891578i	−0.627014	+	0.0945071i	−0.172154	+	0.985070i	$0.555073\pi$
$90$		0			0
$91$	−10.4512	+	7.81054i	−1.09558	+	0.818767i
$92$	4.68143	−	2.25446i	0.488073	−	0.235044i
$93$		0			0
$94$	10.1775	−	9.44332i	1.04973	−	0.974004i
$95$	0.287995	+	3.84303i	0.0295477	+	0.394287i
$96$		0			0
$97$	−1.74858			−0.177542			−0.0887708	−	0.996052i	$-0.528294\pi$
$97$	−1.74858			−0.177542			−0.0887708	+	0.996052i	$0.528294\pi$
$98$	−1.66538	+	12.0257i	−0.168229	+	1.21478i
$99$		0			0
$100$	0.371291	+	0.946034i	0.0371291	+	0.0946034i
$101$	−1.11204	−	14.8391i	−0.110652	−	1.47655i	−0.725673	−	0.688039i	$-0.758472\pi$
$101$	−1.11204	−	14.8391i	−0.110652	−	1.47655i	0.615021	−	0.788511i	$-0.289147\pi$
$102$		0			0
$103$	2.10798	−	1.43720i	0.207706	−	0.141611i	−0.455000	−	0.890492i	$-0.650361\pi$
$103$	2.10798	−	1.43720i	0.207706	−	0.141611i	0.662705	+	0.748880i	$0.269408\pi$
$104$	−7.64424	+	3.68127i	−0.749580	+	0.360979i
$105$		0			0
$106$	17.4415	+	8.39936i	1.69406	+	0.815818i
$107$	5.98232	−	0.901690i	0.578333	−	0.0871696i	0.146639	−	0.989190i	$-0.453154\pi$
$107$	5.98232	−	0.901690i	0.578333	−	0.0871696i	0.431693	+	0.902020i	$0.357916\pi$
$108$		0			0
$109$	−0.986580	−	0.148703i	−0.0944972	−	0.0142432i	0.101623	−	0.994823i	$-0.467596\pi$
$109$	−0.986580	−	0.148703i	−0.0944972	−	0.0142432i	−0.196121	+	0.980580i	$0.562834\pi$
$110$	−3.66731	−	3.40277i	−0.349664	−	0.324441i
$111$		0			0
$112$	−4.29419	+	12.5122i	−0.405763	+	1.18229i
$113$	−5.99502	−	7.51752i	−0.563964	−	0.707189i	0.415321	−	0.909675i	$-0.363669\pi$
$113$	−5.99502	−	7.51752i	−0.563964	−	0.707189i	−0.979285	+	0.202486i	$0.935098\pi$
$114$		0			0
$115$	12.0739	−	3.72432i	1.12590	−	0.347294i
$116$	−0.840912	−	1.45650i	−0.0780767	−	0.135233i
$117$		0			0
$118$	−2.74738	+	12.0371i	−0.252917	+	1.10810i
$119$	0.335672	−	0.0145756i	0.0307710	−	0.00133615i
$120$		0			0
$121$	−9.18797	−	2.83411i	−0.835270	−	0.257647i
$122$	7.82745	−	19.9440i	0.708664	−	1.80565i
$123$		0			0
$124$	5.08971	+	1.56997i	0.457070	+	0.140987i
$125$	−2.17726	−	9.53919i	−0.194740	−	0.853211i
$126$		0			0
$127$	0.788279	−	3.45368i	0.0699485	−	0.306464i	−0.927836	−	0.372987i	$-0.878333\pi$
$127$	0.788279	−	3.45368i	0.0699485	−	0.306464i	0.997785	+	0.0665231i	$0.0211906\pi$
$128$	−6.03543	+	10.4537i	−0.533462	+	0.923983i
$129$		0			0
$130$	20.0330	−	6.17937i	1.75701	−	0.541967i
$131$	0.183096	−	2.44324i	0.0159972	−	0.213467i	−0.983477	−	0.181034i	$-0.942055\pi$
$131$	0.183096	−	2.44324i	0.0159972	−	0.213467i	0.999474	−	0.0324328i	$-0.0103255\pi$
$132$		0			0
$133$	2.92369	−	2.95896i	0.253516	−	0.256574i
$134$	5.47265	−	6.86249i	0.472765	−	0.592829i
$135$		0			0
$136$	0.216049	+	0.0325641i	0.0185260	+	0.00279235i
$137$	7.54134	+	5.14160i	0.644300	+	0.439277i	0.840888	−	0.541210i	$-0.182034\pi$
$137$	7.54134	+	5.14160i	0.644300	+	0.439277i	−0.196587	+	0.980486i	$0.562986\pi$
$138$		0			0
$139$	10.4571	+	5.03590i	0.886964	+	0.427139i	0.821163	−	0.570694i	$-0.193326\pi$
$139$	10.4571	+	5.03590i	0.886964	+	0.427139i	0.0658005	+	0.997833i	$0.479040\pi$
$140$	3.01984	−	5.79768i	0.255223	−	0.489993i
$141$		0			0
$142$	13.4522	−	9.17155i	1.12888	−	0.769660i
$143$	−4.25410	+	3.94723i	−0.355746	+	0.330084i
$144$		0			0
$145$	−1.49415	−	3.80704i	−0.124083	−	0.316158i
$146$	−15.3923			−1.27387
$147$		0			0
$148$	−9.61139			−0.790052
$149$	4.75361	+	12.1120i	0.389431	+	0.992253i	0.982360	+	0.186999i	$0.0598761\pi$
$149$	4.75361	+	12.1120i	0.389431	+	0.992253i	−0.592929	+	0.805254i	$0.702029\pi$
$150$		0			0
$151$	−11.5510	+	10.7177i	−0.940004	+	0.872196i	−0.991973	−	0.126453i	$-0.959641\pi$
$151$	−11.5510	+	10.7177i	−0.940004	+	0.872196i	0.0519689	+	0.998649i	$0.483450\pi$
$152$	2.23499	−	1.52379i	0.181282	−	0.123596i
$153$		0			0
$154$	−0.169556	+	5.39728i	−0.0136632	+	0.434925i
$155$	11.6696	+	5.61977i	0.937323	+	0.451391i
$156$		0			0
$157$	−6.17975	−	4.21328i	−0.493197	−	0.336256i	0.291047	−	0.956709i	$-0.405997\pi$
$157$	−6.17975	−	4.21328i	−0.493197	−	0.336256i	−0.784244	+	0.620453i	$0.786949\pi$
$158$	21.7182	+	3.27349i	1.72781	+	0.260425i
$159$		0			0
$160$	7.99394	−	10.0241i	0.631976	−	0.792473i
$161$	−11.5912	−	7.18667i	−0.913514	−	0.566389i
$162$		0			0
$163$	−1.24719	+	16.6425i	−0.0976872	+	1.30354i	0.705880	+	0.708331i	$0.250552\pi$
$163$	−1.24719	+	16.6425i	−0.0976872	+	1.30354i	−0.803567	+	0.595214i	$0.797067\pi$
$164$	−6.16168	+	1.90063i	−0.481147	+	0.148414i
$165$		0			0
$166$	−14.4695	+	25.0619i	−1.12305	+	1.94518i
$167$	1.24967	−	5.47515i	0.0967022	−	0.423680i	−0.903283	−	0.429044i	$-0.858850\pi$
$167$	1.24967	−	5.47515i	0.0967022	−	0.423680i	0.999986	+	0.00536440i	$0.00170755\pi$
$168$		0			0
$169$	−2.51867	−	11.0350i	−0.193744	−	0.848848i
$170$	−0.515883	−	0.159129i	−0.0395664	−	0.0122046i
$171$		0			0
$172$	−4.08004	+	10.3958i	−0.311100	+	0.792670i
$173$	15.8216	+	4.88031i	1.20289	+	0.371043i	0.830492	−	0.557030i	$-0.188059\pi$
$173$	15.8216	+	4.88031i	1.20289	+	0.371043i	0.372399	+	0.928073i	$0.378535\pi$
$174$		0			0
$175$	1.57113	−	2.15574i	0.118767	−	0.162959i
$176$	−1.30929	+	5.73639i	−0.0986917	+	0.432397i
$177$		0			0
$178$	−5.18750	−	8.98502i	−0.388820	−	0.673456i
$179$	−5.43964	+	1.67791i	−0.406578	+	0.125413i	−0.491297	−	0.870992i	$-0.663477\pi$
$179$	−5.43964	+	1.67791i	−0.406578	+	0.125413i	0.0847189	+	0.996405i	$0.473001\pi$
$180$		0			0
$181$	−8.76955	−	10.9967i	−0.651835	−	0.817376i	0.340592	−	0.940211i	$-0.389373\pi$
$181$	−8.76955	−	10.9967i	−0.651835	−	0.817376i	−0.992427	+	0.122836i	$0.960801\pi$
$182$	−19.2321	−	11.9241i	−1.42557	−	0.883872i
$183$		0			0
$184$	−6.50130	−	6.03233i	−0.479282	−	0.444709i
$185$	−23.1113	−	3.48347i	−1.69918	−	0.256110i
$186$		0			0
$187$	0.147774	−	0.0222734i	0.0108063	−	0.00162879i
$188$	7.26999	+	3.50104i	0.530219	+	0.255340i
$189$		0			0
$190$	−6.02196	+	2.90003i	−0.436879	+	0.210390i
$191$	−14.5529	+	9.92199i	−1.05301	+	0.717930i	−0.960640	−	0.277795i	$-0.910396\pi$
$191$	−14.5529	+	9.92199i	−1.05301	+	0.717930i	−0.0923695	+	0.995725i	$0.529444\pi$
$192$		0			0
$193$	0.667057	+	8.90125i	0.0480158	+	0.640726i	0.968350	+	0.249594i	$0.0802973\pi$
$193$	0.667057	+	8.90125i	0.0480158	+	0.640726i	−0.920335	+	0.391132i	$0.872084\pi$
$194$	−1.10796	−	2.82303i	−0.0795466	−	0.202681i
$195$		0			0
$196$	−6.85972	+	1.65246i	−0.489980	+	0.118033i
$197$	6.78025			0.483073			0.241536	−	0.970392i	$-0.422349\pi$
$197$	6.78025			0.483073			0.241536	+	0.970392i	$0.422349\pi$
$198$		0			0
$199$	0.531114	+	7.08722i	0.0376497	+	0.502400i	0.983871	+	0.178880i	$0.0572473\pi$
$199$	0.531114	+	7.08722i	0.0376497	+	0.502400i	−0.946221	+	0.323520i	$0.895134\pi$
$200$	1.27159	−	1.17986i	0.0899150	−	0.0834290i
$201$		0			0
$202$	23.2527	−	11.1979i	1.63605	−	0.787882i
$203$	−2.03928	+	3.91514i	−0.143129	+	0.274789i
$204$		0			0
$205$	−15.5051	+	2.33701i	−1.08292	+	0.163224i
$206$	3.65600	+	2.49262i	0.254725	+	0.173669i
$207$		0			0
$208$	−18.0747	−	16.7708i	−1.25325	−	1.16285i
$209$	1.15358	−	1.44654i	0.0797948	−	0.100060i
$210$		0			0
$211$	−15.7447	−	19.7432i	−1.08391	−	1.35918i	−0.928502	−	0.371328i	$-0.878902\pi$
$211$	−15.7447	−	19.7432i	−1.08391	−	1.35918i	−0.155407	−	0.987850i	$-0.549669\pi$
$212$	−0.840789	+	11.2196i	−0.0577457	+	0.770562i
$213$		0			0
$214$	5.24633	+	9.08692i	0.358632	+	0.621169i
$215$	−13.5785	+	23.5187i	−0.926046	+	1.60396i
$216$		0			0
$217$	−3.69930	−	13.4821i	−0.251125	−	0.915228i
$218$	−0.385052	−	1.68702i	−0.0260790	−	0.114260i
$219$		0			0
$220$	1.06226	−	2.70659i	0.0716175	−	0.182478i
$221$	−0.228794	+	0.582959i	−0.0153904	+	0.0392140i
$222$		0			0
$223$	−4.22895	−	18.5282i	−0.283191	−	1.24074i	−0.893676	−	0.448713i	$-0.851882\pi$
$223$	−4.22895	−	18.5282i	−0.283191	−	1.24074i	0.610485	−	0.792028i	$-0.290975\pi$
$224$	−13.8260	+	0.600358i	−0.923792	+	0.0401131i
$225$		0			0
$226$	8.33815	−	14.4421i	0.554645	−	0.960674i
$227$	6.78372	+	11.7497i	0.450251	+	0.779858i	0.998401	−	0.0565218i	$-0.0180010\pi$
$227$	6.78372	+	11.7497i	0.450251	+	0.779858i	−0.548150	+	0.836380i	$0.684668\pi$
$228$		0			0
$229$	1.41612	−	18.8968i	0.0935798	−	1.24874i	−0.730757	−	0.682637i	$-0.760833\pi$
$229$	1.41612	−	18.8968i	0.0935798	−	1.24874i	0.824337	−	0.566099i	$-0.191548\pi$
$230$	13.6632	+	17.1331i	0.900926	+	1.12973i
$231$		0			0
$232$	−1.78981	+	2.24435i	−0.117507	+	0.147349i
$233$	−13.4113	−	12.4439i	−0.878606	−	0.815228i	0.105202	−	0.994451i	$-0.466451\pi$
$233$	−13.4113	−	12.4439i	−0.878606	−	0.815228i	−0.983808	+	0.179223i	$0.942642\pi$
$234$		0			0
$235$	16.2123	+	11.0534i	1.05758	+	0.721044i
$236$	−7.09559	+	1.06949i	−0.461884	+	0.0696178i
$237$		0			0
$238$	0.236225	+	0.532696i	0.0153122	+	0.0345296i
$239$	4.37208	−	2.10548i	0.282806	−	0.136192i	−0.287104	−	0.957900i	$-0.592692\pi$
$239$	4.37208	−	2.10548i	0.282806	−	0.136192i	0.569910	+	0.821707i	$0.306978\pi$
$240$		0			0
$241$	−14.3776	+	13.3405i	−0.926142	+	0.859334i	−0.990348	−	0.138602i	$-0.955739\pi$
$241$	−14.3776	+	13.3405i	−0.926142	+	0.859334i	0.0642061	+	0.997937i	$0.479548\pi$
$242$	−1.24621	−	16.6295i	−0.0801092	−	1.06898i
$243$		0			0
$244$	12.4520			0.797160
$245$	−17.0936	+	1.48729i	−1.09207	+	0.0950194i
$246$		0			0
$247$	2.83261	+	7.21737i	0.180235	+	0.459230i
$248$	−0.679394	−	9.06588i	−0.0431415	−	0.575684i
$249$		0			0
$250$	14.0211	−	9.55944i	0.886774	−	0.604592i
$251$	16.2250	−	7.81356i	1.02412	−	0.493188i	0.155061	−	0.987905i	$-0.450443\pi$
$251$	16.2250	−	7.81356i	1.02412	−	0.493188i	0.869054	+	0.494717i	$0.164728\pi$
$252$		0			0
$253$	−5.46542	−	2.63201i	−0.343608	−	0.165473i
$254$	6.07532	−	0.915708i	0.381200	−	0.0574566i
$255$		0			0
$256$	−18.8661	−	2.84360i	−1.17913	−	0.177725i
$257$	−6.20765	−	5.75986i	−0.387223	−	0.359290i	0.462409	−	0.886667i	$-0.346985\pi$
$257$	−6.20765	−	5.75986i	−0.387223	−	0.359290i	−0.849632	+	0.527377i	$0.823176\pi$
$258$		0			0
$259$	13.5498	+	21.2801i	0.841943	+	1.32228i
$260$	7.59680	+	9.52609i	0.471134	+	0.590783i
$261$		0			0
$262$	4.06055	−	1.25251i	0.250862	−	0.0773806i
$263$	−9.64290	−	16.7020i	−0.594607	−	1.02989i	−0.993602	−	0.112936i	$-0.963974\pi$
$263$	−9.64290	−	16.7020i	−0.594607	−	1.02989i	0.398996	−	0.916953i	$-0.369359\pi$
$264$		0			0
$265$	−6.08806	+	26.6735i	−0.373986	+	1.63854i
$266$	6.62968	+	2.84531i	0.406492	+	0.174457i
$267$		0			0
$268$	4.87474	+	1.50366i	0.297772	+	0.0918505i
$269$	−9.17274	+	23.3718i	−0.559272	+	1.42500i	0.319420	+	0.947613i	$0.396512\pi$
$269$	−9.17274	+	23.3718i	−0.559272	+	1.42500i	−0.878692	+	0.477388i	$0.841583\pi$
$270$		0			0
$271$	9.14079	+	2.81956i	0.555263	+	0.171276i	0.559672	−	0.828714i	$-0.310927\pi$
$271$	9.14079	+	2.81956i	0.555263	+	0.171276i	−0.00440858	+	0.999990i	$0.501403\pi$
$272$	0.141290	+	0.619031i	0.00856696	+	0.0375343i
$273$		0			0
$274$	−3.52251	+	15.4331i	−0.212803	+	0.932349i
$275$	0.593240	−	1.02752i	0.0357737	−	0.0619619i
$276$		0			0
$277$	5.03430	−	1.55287i	0.302482	−	0.0933032i	−0.139799	−	0.990180i	$-0.544646\pi$
$277$	5.03430	−	1.55287i	0.302482	−	0.0933032i	0.442281	+	0.896877i	$0.354169\pi$
$278$	−1.50431	+	20.0736i	−0.0902225	+	1.20394i
$279$		0			0
$280$	−11.0949	−	1.18278i	−0.663045	−	0.0706844i
$281$	6.56607	−	8.23359i	0.391699	−	0.491175i	−0.546409	−	0.837519i	$-0.684005\pi$
$281$	6.56607	−	8.23359i	0.391699	−	0.491175i	0.938108	+	0.346344i	$0.112577\pi$
$282$		0			0
$283$	6.72260	+	1.01327i	0.399617	+	0.0602326i	0.345776	−	0.938317i	$-0.387616\pi$
$283$	6.72260	+	1.01327i	0.399617	+	0.0602326i	0.0538407	+	0.998550i	$0.482854\pi$
$284$	7.81829	+	5.33042i	0.463930	+	0.316302i
$285$		0			0
$286$	−9.06820	−	4.36701i	−0.536214	−	0.258227i
$287$	12.8946	+	10.9628i	0.761144	+	0.647115i
$288$		0			0
$289$	−14.0327	+	9.56736i	−0.825455	+	0.562786i
$290$	5.19960	−	4.82452i	0.305331	−	0.283306i
$291$		0			0
$292$	−3.26829	−	8.32746i	−0.191262	−	0.487327i
$293$	−9.31653			−0.544278			−0.272139	−	0.962258i	$-0.587731\pi$
$293$	−9.31653			−0.544278			−0.272139	+	0.962258i	$0.587731\pi$
$294$		0			0
$295$	−17.4495			−1.01595
$296$	5.99351	+	15.2712i	0.348366	+	0.887622i
$297$		0			0
$298$	−16.5424	+	15.3491i	−0.958274	+	0.889149i
$299$	21.0034	−	14.3199i	1.21466	−	0.828139i
$300$		0			0
$301$	28.7686	−	5.62216i	1.65819	−	0.324056i
$302$	−24.6225	−	11.8576i	−1.41686	−	0.682325i
$303$		0			0
$304$	6.49512	+	4.42829i	0.372520	+	0.253980i
$305$	29.9418	+	4.51301i	1.71447	+	0.258414i
$306$		0			0
$307$	−2.40179	+	3.01175i	−0.137078	+	0.171890i	−0.845632	−	0.533766i	$-0.820776\pi$
$307$	−2.40179	+	3.01175i	−0.137078	+	0.171890i	0.708554	+	0.705656i	$0.249348\pi$
$308$	−2.95601	+	1.05429i	−0.168434	+	0.0600735i
$309$		0			0
$310$	−1.67872	+	22.4010i	−0.0953451	+	1.27229i
$311$	−10.1017	+	3.11597i	−0.572817	+	0.176691i	−0.567612	−	0.823296i	$-0.692133\pi$
$311$	−10.1017	+	3.11597i	−0.572817	+	0.176691i	−0.00520431	+	0.999986i	$0.501657\pi$
$312$		0			0
$313$	2.38127	−	4.12448i	0.134597	−	0.233129i	−0.790846	−	0.612015i	$-0.790359\pi$
$313$	2.38127	−	4.12448i	0.134597	−	0.233129i	0.925444	+	0.378886i	$0.123693\pi$
$314$	2.88652	−	12.6467i	0.162896	−	0.713692i
$315$		0			0
$316$	2.84047	+	12.4449i	0.159789	+	0.700082i
$317$	−26.6724	−	8.22736i	−1.49807	−	0.462095i	−0.566013	−	0.824396i	$-0.691515\pi$
$317$	−26.6724	−	8.22736i	−1.49807	−	0.462095i	−0.932061	+	0.362302i	$0.881991\pi$
$318$		0			0
$319$	−0.717337	+	1.82775i	−0.0401632	+	0.102334i
$320$	−2.17365	−	0.670482i	−0.121511	−	0.0374811i
$321$		0			0
$322$	4.25809	−	23.2673i	0.237294	−	1.29664i
$323$	0.0444287	−	0.194655i	0.00247208	−	0.0108309i
$324$		0			0
$325$	2.48600	+	4.30587i	0.137898	+	0.238847i
$326$	−27.6591	+	8.53170i	−1.53190	+	0.472527i
$327$		0			0
$328$	6.86217	+	8.60489i	0.378900	+	0.475125i
$329$	−2.49749	−	21.0318i	−0.137691	−	1.15952i
$330$		0			0
$331$	2.74197	+	2.54418i	0.150712	+	0.139841i	0.751925	−	0.659248i	$-0.229125\pi$
$331$	2.74197	+	2.54418i	0.150712	+	0.139841i	−0.601213	+	0.799089i	$0.705316\pi$
$332$	−16.6312	−	2.50675i	−0.912757	−	0.137576i
$333$		0			0
$334$	9.63128	−	1.45168i	0.527000	−	0.0794325i
$335$	11.1767	+	5.38241i	0.610648	+	0.294073i
$336$		0			0
$337$	12.6074	−	6.07139i	0.686767	−	0.330730i	−0.0577519	−	0.998331i	$-0.518393\pi$
$337$	12.6074	−	6.07139i	0.686767	−	0.330730i	0.744519	+	0.667601i	$0.232679\pi$
$338$	16.2198	−	11.0585i	0.882240	−	0.601501i
$339$		0			0
$340$	−0.0234478	−	0.312889i	−0.00127163	−	0.0169688i
$341$	−2.27181	−	5.78848i	−0.123025	−	0.313464i
$342$		0			0
$343$	13.3292	+	12.8582i	0.719709	+	0.694276i
$344$	19.0617			1.02774
$345$		0			0
$346$	2.14595	+	28.6357i	0.115367	+	1.53946i
$347$	−21.9050	+	20.3249i	−1.17592	+	1.09110i	−0.181746	+	0.983345i	$0.558175\pi$
$347$	−21.9050	+	20.3249i	−1.17592	+	1.09110i	−0.994178	+	0.107753i	$0.965635\pi$
$348$		0			0
$349$	24.5542	−	11.8247i	1.31436	−	0.632961i	0.360371	−	0.932809i	$-0.382650\pi$
$349$	24.5542	−	11.8247i	1.31436	−	0.632961i	0.953987	+	0.299848i	$0.0969359\pi$
$350$	4.47589	+	1.17060i	0.239246	+	0.0625711i
$351$		0			0
$352$	−6.08670	+	0.917422i	−0.324422	+	0.0488988i
$353$	15.4120	+	10.5077i	0.820298	+	0.559270i	0.899162	−	0.437616i	$-0.144177\pi$
$353$	15.4120	+	10.5077i	0.820298	+	0.559270i	−0.0788640	+	0.996885i	$0.525129\pi$
$354$		0			0
$355$	16.8678	+	15.6510i	0.895247	+	0.830668i
$356$	3.75955	−	4.71433i	0.199256	−	0.249859i
$357$		0			0
$358$	−6.15565	−	7.71894i	−0.325336	−	0.407959i
$359$	−2.01770	+	26.9244i	−0.106490	+	1.42101i	0.646466	+	0.762943i	$0.276246\pi$
$359$	−2.01770	+	26.9244i	−0.106490	+	1.42101i	−0.752956	+	0.658071i	$0.771373\pi$
$360$		0			0
$361$	8.26404	+	14.3137i	0.434950	+	0.753355i
$362$	12.1971	−	21.1260i	0.641065	−	1.11036i
$363$		0			0
$364$	2.36751	−	12.9367i	0.124091	−	0.678068i
$365$	−4.84070	−	21.2085i	−0.253374	−	1.11010i
$366$		0			0
$367$	−0.168245	+	0.428682i	−0.00878233	+	0.0223770i	−0.935198	−	0.354126i	$-0.884778\pi$
$367$	−0.168245	+	0.428682i	−0.00878233	+	0.0223770i	0.926415	+	0.376503i	$0.122874\pi$
$368$	9.41619	−	23.9921i	0.490853	−	1.25067i
$369$		0			0
$370$	−9.02011	−	39.5197i	−0.468933	−	2.05453i
$371$	26.0260	−	13.9554i	1.35120	−	0.724526i
$372$		0			0
$373$	1.06759	−	1.84911i	0.0552775	−	0.0957434i	−0.837063	−	0.547107i	$-0.815729\pi$
$373$	1.06759	−	1.84911i	0.0552775	−	0.0957434i	0.892340	+	0.451364i	$0.149062\pi$
$374$	0.129594	+	0.224464i	0.00670116	+	0.0116067i
$375$		0			0
$376$	1.02924	−	13.7342i	0.0530790	−	0.708289i
$377$	−5.13008	−	6.43292i	−0.264213	−	0.331312i
$378$		0			0
$379$	−10.6248	+	13.3230i	−0.545758	+	0.684359i	−0.975854	−	0.218424i	$-0.929908\pi$
$379$	−10.6248	+	13.3230i	−0.545758	+	0.684359i	0.430096	+	0.902783i	$0.358480\pi$
$380$	−2.84762	−	2.64220i	−0.146080	−	0.135542i
$381$		0			0
$382$	−25.2399	−	17.2083i	−1.29139	−	0.880452i
$383$	−6.79028	+	1.02347i	−0.346967	+	0.0522969i	−0.320214	−	0.947345i	$-0.603755\pi$
$383$	−6.79028	+	1.02347i	−0.346967	+	0.0522969i	−0.0267530	+	0.999642i	$0.508517\pi$
$384$		0			0
$385$	−7.49006	+	1.46376i	−0.381729	+	0.0746001i
$386$	−13.9481	+	6.71706i	−0.709940	+	0.341889i
$387$		0			0
$388$	1.29204	−	1.19884i	0.0655936	−	0.0608620i
$389$	1.72926	+	23.0753i	0.0876769	+	1.16997i	0.851434	+	0.524462i	$0.175734\pi$
$389$	1.72926	+	23.0753i	0.0876769	+	1.16997i	−0.763757	+	0.645504i	$0.776647\pi$
$390$		0			0
$391$	−0.654618			−0.0331054
$392$	6.90315	+	9.86872i	0.348662	+	0.498446i
$393$		0			0
$394$	4.29618	+	10.9465i	0.216438	+	0.551476i
$395$	2.31970	+	30.9542i	0.116717	+	1.55748i
$396$		0			0
$397$	22.2820	−	15.1916i	1.11830	−	0.762443i	0.144421	−	0.989516i	$-0.453868\pi$
$397$	22.2820	−	15.1916i	1.11830	−	0.762443i	0.973878	+	0.227073i	$0.0729156\pi$
$398$	−11.1056	+	5.34815i	−0.556671	+	0.268079i
$399$		0			0
$400$	4.54186	+	2.18724i	0.227093	+	0.109362i
$401$	−16.4236	+	2.47545i	−0.820153	+	0.123618i	−0.545698	−	0.837982i	$-0.683736\pi$
$401$	−16.4236	+	2.47545i	−0.820153	+	0.123618i	−0.274455	+	0.961600i	$0.588497\pi$
$402$		0			0
$403$	25.7671	+	3.88377i	1.28355	+	0.193464i
$404$	10.9955	+	10.2024i	0.547049	+	0.507587i
$405$		0			0
$406$	−7.61302	−	0.811592i	−0.377828	−	0.0402786i
$407$	6.99617	+	8.77292i	0.346787	+	0.434857i
$408$		0			0
$409$	−0.991734	+	0.305909i	−0.0490381	+	0.0151262i	−0.319177	−	0.947695i	$-0.603407\pi$
$409$	−0.991734	+	0.305909i	−0.0490381	+	0.0151262i	0.270139	+	0.962821i	$0.412930\pi$
$410$	−13.5975	−	23.5516i	−0.671534	−	1.16313i
$411$		0			0
$412$	−0.572255	+	2.50721i	−0.0281930	+	0.123522i
$413$	12.3710	+	14.2023i	0.608737	+	0.698847i
$414$		0			0
$415$	−39.0825	−	12.0553i	−1.91848	−	0.591774i
$416$	9.42384	−	24.0115i	0.462042	−	1.17726i
$417$		0			0
$418$	3.06634	+	0.945841i	0.149980	+	0.0462626i
$419$	−4.59136	−	20.1161i	−0.224303	−	0.982734i	−0.954198	−	0.299175i	$-0.903289\pi$
$419$	−4.59136	−	20.1161i	−0.224303	−	0.982734i	0.729896	−	0.683558i	$-0.239569\pi$
$420$		0			0
$421$	1.85136	−	8.11134i	0.0902298	−	0.395323i	−0.909565	−	0.415561i	$-0.863585\pi$
$421$	1.85136	−	8.11134i	0.0902298	−	0.395323i	0.999795	+	0.0202383i	$0.00644249\pi$
$422$	21.8984	−	37.9292i	1.06600	−	1.84636i
$423$		0			0
$424$	18.3507	−	5.66043i	0.891188	−	0.274895i
$425$	0.00956820	−	0.127679i	0.000464126	−	0.00619333i
$426$		0			0
$427$	−17.5544	−	27.5694i	−0.849518	−	1.33418i
$428$	−3.80219	+	4.76780i	−0.183786	+	0.230460i
$429$		0			0
$430$	−46.5739	−	7.01988i	−2.24599	−	0.338529i
$431$	23.2694	+	15.8648i	1.12085	+	0.764180i	0.974351	−	0.225032i	$-0.0722486\pi$
$431$	23.2694	+	15.8648i	1.12085	+	0.764180i	0.146494	+	0.989212i	$0.453201\pi$
$432$		0			0
$433$	3.20101	+	1.54153i	0.153831	+	0.0740810i	0.509215	−	0.860639i	$-0.329936\pi$
$433$	3.20101	+	1.54153i	0.153831	+	0.0740810i	−0.355384	+	0.934720i	$0.615650\pi$
$434$	19.4225	−	14.5151i	0.932309	−	0.696748i
$435$		0			0
$436$	0.830946	−	0.566530i	0.0397951	−	0.0271318i
$437$	−5.94106	+	5.51249i	−0.284199	+	0.263698i
$438$		0			0
$439$	11.8653	+	30.2324i	0.566301	+	1.44291i	0.871391	+	0.490589i	$0.163218\pi$
$439$	11.8653	+	30.2324i	0.566301	+	1.44291i	−0.305090	+	0.952324i	$0.598686\pi$
$440$	−4.96282			−0.236593
$441$		0			0
$442$	−1.08614			−0.0516623
$443$	−0.0677168	−	0.172540i	−0.00321732	−	0.00819760i	0.929256	−	0.369436i	$-0.120449\pi$
$443$	−0.0677168	−	0.172540i	−0.00321732	−	0.00819760i	−0.932473	+	0.361239i	$0.882354\pi$
$444$		0			0
$445$	10.7488	−	9.97338i	0.509540	−	0.472784i
$446$	27.2336	−	18.5676i	1.28955	−	0.879199i
$447$		0			0
$448$	0.995322	+	2.24449i	0.0470246	+	0.106042i
$449$	−18.5722	−	8.94391i	−0.876477	−	0.422089i	−0.0591405	−	0.998250i	$-0.518836\pi$
$449$	−18.5722	−	8.94391i	−0.876477	−	0.422089i	−0.817337	+	0.576161i	$0.804550\pi$
$450$		0			0
$451$	6.21993	+	4.24068i	0.292885	+	0.199686i
$452$	9.58386	+	1.44453i	0.450787	+	0.0679452i
$453$		0			0
$454$	−14.6712	+	18.3971i	−0.688554	+	0.863419i
$455$	10.3815	−	30.2492i	0.486694	−	1.41810i
$456$		0			0
$457$	2.30937	−	30.8164i	0.108028	−	1.44153i	−0.635124	−	0.772410i	$-0.719051\pi$
$457$	2.30937	−	30.8164i	0.108028	−	1.44153i	0.743152	−	0.669122i	$-0.233330\pi$
$458$	31.4056	−	9.68733i	1.46749	−	0.452659i
$459$		0			0
$460$	−6.36814	+	11.0299i	−0.296916	+	0.514273i
$461$	−8.21785	+	36.0047i	−0.382743	+	1.67691i	0.306101	+	0.951999i	$0.400975\pi$
$461$	−8.21785	+	36.0047i	−0.382743	+	1.67691i	−0.688845	+	0.724909i	$0.741882\pi$
$462$		0			0
$463$	−6.81971	−	29.8791i	−0.316939	−	1.38860i	−0.842891	−	0.538085i	$-0.819148\pi$
$463$	−6.81971	−	29.8791i	−0.316939	−	1.38860i	0.525952	−	0.850514i	$-0.323709\pi$
$464$	−7.97171	−	2.45895i	−0.370078	−	0.114154i
$465$		0			0
$466$	11.5924	−	29.5370i	0.537009	−	1.36828i
$467$	24.4538	+	7.54300i	1.13159	+	0.349048i	0.803326	−	0.595539i	$-0.203061\pi$
$467$	24.4538	+	7.54300i	1.13159	+	0.349048i	0.328260	+	0.944587i	$0.393538\pi$
$468$		0			0
$469$	−3.54305	−	12.9127i	−0.163603	−	0.596253i
$470$	−7.57268	+	33.1781i	−0.349302	+	1.53039i
$471$		0			0
$472$	6.12397	+	10.6070i	0.281879	+	0.488228i
$473$	12.4587	−	3.84301i	0.572853	−	0.176702i
$474$		0			0
$475$	−0.988337	−	1.23934i	−0.0453480	−	0.0568646i
$476$	−0.238039	+	0.240910i	−0.0109105	+	0.0110421i
$477$		0			0
$478$	6.16952	+	5.72447i	0.282187	+	0.261831i
$479$	13.0449	+	1.96621i	0.596038	+	0.0898382i	0.440131	−	0.897934i	$-0.354932\pi$
$479$	13.0449	+	1.96621i	0.596038	+	0.0898382i	0.155907	+	0.987772i	$0.450170\pi$
$480$		0			0
$481$	−46.4967	+	7.00826i	−2.12007	+	0.319549i
$482$	−30.6478	−	14.7592i	−1.39597	−	0.672264i
$483$		0			0
$484$	8.73218	−	4.20520i	0.396917	−	0.191145i
$485$	3.54132	−	2.41443i	0.160803	−	0.109634i
$486$		0			0
$487$	−2.54447	−	33.9536i	−0.115301	−	1.53858i	−0.692162	−	0.721742i	$-0.743342\pi$
$487$	−2.54447	−	33.9536i	−0.115301	−	1.53858i	0.576861	−	0.816843i	$-0.304278\pi$
$488$	−7.76489	−	19.7846i	−0.351500	−	0.895608i
$489$		0			0
$490$	−13.2322	−	26.6547i	−0.597771	−	1.20413i
$491$	−13.1160			−0.591915			−0.295957	−	0.955201i	$-0.595639\pi$
$491$	−13.1160			−0.591915			−0.295957	+	0.955201i	$0.595639\pi$
$492$		0			0
$493$	0.0158341	+	0.211292i	0.000713134	+	0.00951611i
$494$	−9.85737	+	9.14630i	−0.443504	+	0.411512i
$495$		0			0
$496$	23.8038	−	11.4633i	1.06882	−	0.514718i
$497$	0.779872	−	24.8247i	0.0349821	−	1.11354i
$498$		0			0
$499$	−26.4685	+	3.98948i	−1.18489	+	0.178594i	−0.711776	−	0.702406i	$-0.752109\pi$
$499$	−26.4685	+	3.98948i	−1.18489	+	0.178594i	−0.473116	+	0.881000i	$0.656871\pi$
$500$	8.14895	+	5.55586i	0.364432	+	0.248466i
$501$		0			0
$502$	22.8954	+	21.2439i	1.02187	+	0.948160i
$503$	14.1123	−	17.6963i	0.629237	−	0.789038i	−0.360375	−	0.932808i	$-0.617351\pi$
$503$	14.1123	−	17.6963i	0.629237	−	0.789038i	0.989611	+	0.143770i	$0.0459226\pi$
$504$		0			0
$505$	22.7419	+	28.5175i	1.01200	+	1.26901i
$506$	0.786226	−	10.4915i	0.0349520	−	0.466402i
$507$		0			0
$508$	1.78540	+	3.09241i	0.0792144	+	0.137203i
$509$	−8.45575	+	14.6458i	−0.374795	+	0.649163i	−0.990296	−	0.138972i	$-0.955620\pi$
$509$	−8.45575	+	14.6458i	−0.374795	+	0.649163i	0.615502	+	0.788136i	$0.288953\pi$
$510$		0			0
$511$	−13.8299	+	18.9759i	−0.611798	+	0.839443i
$512$	−1.99119	−	8.72397i	−0.0879990	−	0.385549i
$513$		0			0
$514$	5.36574	−	13.6717i	0.236673	−	0.603032i
$515$	−2.28472	+	5.82138i	−0.100677	+	0.256521i
$516$		0			0
$517$	−2.09623	−	9.18420i	−0.0921922	−	0.403921i
$518$	−25.7704	+	35.3594i	−1.13229	+	1.55360i
$519$		0			0
$520$	10.3984	−	18.0106i	0.456002	−	0.789818i
$521$	−6.11102	−	10.5846i	−0.267729	−	0.463720i	0.700546	−	0.713607i	$-0.252940\pi$
$521$	−6.11102	−	10.5846i	−0.267729	−	0.463720i	−0.968275	+	0.249887i	$0.919606\pi$
$522$		0			0
$523$	−1.27838	+	17.0588i	−0.0558995	+	0.745927i	0.896882	+	0.442270i	$0.145827\pi$
$523$	−1.27838	+	17.0588i	−0.0558995	+	0.745927i	−0.952781	+	0.303657i	$0.901792\pi$
$524$	1.53982	+	1.93087i	0.0672672	+	0.0843504i
$525$		0			0
$526$	20.8548	−	26.1510i	0.909311	−	1.14024i
$527$	−0.491907	−	0.456423i	−0.0214278	−	0.0198821i
$528$		0			0
$529$	2.95133	+	2.01218i	0.128319	+	0.0874862i
$530$	−46.9211	+	7.07222i	−2.03812	+	0.307198i
$531$		0			0
$532$	−0.131658	+	4.19091i	−0.00570811	+	0.181699i
$533$	−28.4223	+	13.6875i	−1.23111	+	0.592870i
$534$		0			0
$535$	−10.8707	+	10.0865i	−0.469979	+	0.436077i
$536$	−0.650698	−	8.68296i	−0.0281059	−	0.375047i
$537$		0			0
$538$	−43.5451			−1.87736
$539$	6.50152	+	5.05846i	0.280040	+	0.217883i
$540$		0			0
$541$	2.69141	+	6.85759i	0.115713	+	0.294831i	0.976983	−	0.213315i	$-0.0684262\pi$
$541$	2.69141	+	6.85759i	0.115713	+	0.294831i	−0.861271	+	0.508146i	$0.830331\pi$
$542$	1.23981	+	16.5441i	0.0532542	+	0.710628i
$543$		0			0
$544$	−0.548832	+	0.374187i	−0.0235310	+	0.0160431i
$545$	2.20340	−	1.06110i	0.0943833	−	0.0454526i
$546$		0			0
$547$	19.0358	+	9.16716i	0.813913	+	0.391960i	0.794057	−	0.607843i	$-0.207965\pi$
$547$	19.0358	+	9.16716i	0.813913	+	0.391960i	0.0198555	+	0.999803i	$0.493679\pi$
$548$	−9.09750	+	1.37123i	−0.388626	+	0.0585759i
$549$		0			0
$550$	2.03480	+	0.306696i	0.0867640	+	0.0130776i
$551$	1.92298	+	1.78427i	0.0819217	+	0.0760123i
$552$		0			0
$553$	23.5493	−	23.8333i	1.00142	−	1.01350i
$554$	5.69695	+	7.14375i	0.242040	+	0.303509i
$555$		0			0
$556$	−11.1795	+	3.44843i	−0.474118	+	0.146246i
$557$	−5.60469	−	9.70761i	−0.237478	−	0.411325i	0.722512	−	0.691359i	$-0.242988\pi$
$557$	−5.60469	−	9.70761i	−0.237478	−	0.411325i	−0.959990	+	0.280034i	$0.909654\pi$
$558$		0			0
$559$	−12.1577	+	53.2663i	−0.514215	+	2.25292i
$560$	−8.57995	−	31.2698i	−0.362569	−	1.32139i
$561$		0			0
$562$	17.4533	+	5.38364i	0.736224	+	0.227095i
$563$	2.85070	−	7.26345i	0.120143	−	0.306118i	−0.858133	−	0.513428i	$-0.828375\pi$
$563$	2.85070	−	7.26345i	0.120143	−	0.306118i	0.978275	+	0.207310i	$0.0664707\pi$
$564$		0			0
$565$	22.5216	+	6.94698i	0.947489	+	0.292262i
$566$	2.62376	+	11.4955i	0.110285	+	0.483190i
$567$		0			0
$568$	3.59396	−	15.7462i	0.150799	−	0.660695i
$569$	11.9969	−	20.7793i	0.502937	−	0.871113i	−0.497057	−	0.867718i	$-0.665586\pi$
$569$	11.9969	−	20.7793i	0.502937	−	0.871113i	0.999994	−	0.00339495i	$-0.00108065\pi$
$570$		0			0
$571$	−2.96183	+	0.913603i	−0.123949	+	0.0382331i	−0.356109	−	0.934444i	$-0.615897\pi$
$571$	−2.96183	+	0.913603i	−0.123949	+	0.0382331i	0.232160	+	0.972678i	$0.425421\pi$
$572$	0.437145	−	5.83329i	0.0182779	−	0.243902i
$573$		0			0
$574$	−9.52870	+	27.7643i	−0.397720	+	1.15886i
$575$	−3.24041	+	4.06335i	−0.135135	+	0.169453i
$576$		0			0
$577$	6.60442	+	0.995457i	0.274946	+	0.0414414i	0.285068	−	0.958507i	$-0.407984\pi$
$577$	6.60442	+	0.995457i	0.274946	+	0.0414414i	−0.0101220	+	0.999949i	$0.503222\pi$
$578$	−24.3378	−	16.5932i	−1.01232	−	0.690186i
$579$		0			0
$580$	3.71418	+	1.78866i	0.154223	+	0.0742699i
$581$	17.8960	+	40.3563i	0.742451	+	1.67426i
$582$		0			0
$583$	10.8528	−	7.39931i	0.449477	−	0.306448i
$584$	−11.1932	+	10.3857i	−0.463176	+	0.429765i
$585$		0			0
$586$	−5.90325	−	15.0412i	−0.243861	−	0.621347i
$587$	−11.5183			−0.475411			−0.237706	−	0.971337i	$-0.576395\pi$
$587$	−11.5183			−0.475411			−0.237706	+	0.971337i	$0.576395\pi$
$588$		0			0
$589$	−8.30786			−0.342319
$590$	−11.0565	−	28.1716i	−0.455191	−	1.15981i
$591$		0			0
$592$	−34.9485	+	32.4275i	−1.43637	+	1.33276i
$593$	15.2105	−	10.3703i	0.624620	−	0.425859i	−0.209217	−	0.977869i	$-0.567092\pi$
$593$	15.2105	−	10.3703i	0.624620	−	0.425859i	0.833837	+	0.552011i	$0.186139\pi$
$594$		0			0
$595$	−0.659695	+	0.493013i	−0.0270449	+	0.0202116i
$596$	−11.8166	−	5.69056i	−0.484026	−	0.233095i
$597$		0			0
$598$	36.4273	+	24.8357i	1.48962	+	1.01561i
$599$	−13.8989	−	2.09492i	−0.567894	−	0.0855962i	−0.141182	−	0.989984i	$-0.545090\pi$
$599$	−13.8989	−	2.09492i	−0.567894	−	0.0855962i	−0.426712	+	0.904388i	$0.640328\pi$
$600$		0			0
$601$	−3.17752	+	3.98449i	−0.129614	+	0.162531i	−0.842403	−	0.538847i	$-0.818860\pi$
$601$	−3.17752	+	3.98449i	−0.129614	+	0.162531i	0.712790	+	0.701378i	$0.247431\pi$
$602$	27.3055	+	42.8836i	1.11289	+	1.74780i
$603$		0			0
$604$	1.18696	−	15.8389i	0.0482967	−	0.644475i
$605$	22.5213	−	6.94689i	0.915620	−	0.282431i
$606$		0			0
$607$	−4.63944	+	8.03574i	−0.188309	+	0.326161i	−0.944687	−	0.327975i	$-0.893634\pi$
$607$	−4.63944	+	8.03574i	−0.188309	+	0.326161i	0.756378	+	0.654135i	$0.226967\pi$
$608$	−1.82998	+	8.01766i	−0.0742154	+	0.325159i
$609$		0			0
$610$	11.6860	+	51.1997i	0.473152	+	2.07302i
$611$	37.7226	+	11.6359i	1.52609	+	0.470738i
$612$		0			0
$613$	−4.86425	+	12.3939i	−0.196465	+	0.500585i	−0.994826	−	0.101594i	$-0.967606\pi$
$613$	−4.86425	+	12.3939i	−0.196465	+	0.500585i	0.798361	+	0.602180i	$0.205701\pi$
$614$	−6.38423	−	1.96927i	−0.257646	−	0.0794734i
$615$		0			0
$616$	3.51844	+	4.03927i	0.141762	+	0.162747i
$617$	−1.50569	+	6.59687i	−0.0606169	+	0.265580i	−0.996151	−	0.0876571i	$-0.972062\pi$
$617$	−1.50569	+	6.59687i	−0.0606169	+	0.265580i	0.935534	+	0.353237i	$0.114919\pi$
$618$		0			0
$619$	−2.15612	−	3.73451i	−0.0866619	−	0.150103i	0.819436	−	0.573170i	$-0.194287\pi$
$619$	−2.15612	−	3.73451i	−0.0866619	−	0.150103i	−0.906098	+	0.423067i	$0.860953\pi$
$620$	−12.4757	+	3.84826i	−0.501038	+	0.154550i
$621$		0			0
$622$	−11.4314	−	14.3345i	−0.458358	−	0.574762i
$623$	−15.7378	−	1.67774i	−0.630523	−	0.0672174i
$624$		0			0
$625$	21.2766	+	19.7418i	0.851062	+	0.789670i
$626$	8.16768	+	1.23108i	0.326446	+	0.0492039i
$627$		0			0
$628$	7.45494	−	1.12365i	0.297484	−	0.0448386i
$629$	1.09098	+	0.525386i	0.0435000	+	0.0209485i
$630$		0			0
$631$	−5.22495	+	2.51620i	−0.208002	+	0.100168i	−0.534984	−	0.844862i	$-0.679682\pi$
$631$	−5.22495	+	2.51620i	−0.208002	+	0.100168i	0.326982	+	0.945030i	$0.393968\pi$
$632$	18.0021	−	12.2736i	0.716083	−	0.488217i
$633$		0			0
$634$	−3.61770	−	48.2749i	−0.143677	−	1.91724i
$635$	3.17235	+	8.08301i	0.125891	+	0.320765i
$636$		0			0
$637$	−31.9801	+	12.9959i	−1.26710	+	0.514916i
$638$	−3.40536			−0.134820
$639$		0			0
$640$	−2.21109	−	29.5050i	−0.0874011	−	1.16629i
$641$	−18.1434	+	16.8347i	−0.716623	+	0.664929i	−0.951694	−	0.307049i	$-0.900658\pi$
$641$	−18.1434	+	16.8347i	−0.716623	+	0.664929i	0.235071	+	0.971978i	$0.424468\pi$
$642$		0			0
$643$	−6.60846	+	3.18247i	−0.260612	+	0.125504i	−0.559628	−	0.828744i	$-0.689056\pi$
$643$	−6.60846	+	3.18247i	−0.260612	+	0.125504i	0.299016	+	0.954248i	$0.403342\pi$
$644$	13.4921	−	2.63672i	0.531663	−	0.103901i
$645$		0			0
$646$	0.342415	−	0.0516108i	0.0134721	−	0.00203060i
$647$	−24.8894	−	16.9693i	−0.978503	−	0.667132i	−0.0353098	−	0.999376i	$-0.511242\pi$
$647$	−24.8894	−	16.9693i	−0.978503	−	0.667132i	−0.943193	+	0.332244i	$0.892194\pi$
$648$		0			0
$649$	6.14110	+	5.69810i	0.241059	+	0.223670i
$650$	−5.37648	+	6.74189i	−0.210883	+	0.264439i
$651$		0			0
$652$	−10.4887	−	13.1524i	−0.410770	−	0.515089i
$653$	2.28882	−	30.5421i	0.0895683	−	1.19521i	−0.753518	−	0.657427i	$-0.771645\pi$
$653$	2.28882	−	30.5421i	0.0895683	−	1.19521i	0.843086	−	0.537778i	$-0.180736\pi$
$654$		0			0
$655$	3.00280	+	5.20100i	0.117329	+	0.203220i
$656$	−15.9924	+	27.6996i	−0.624397	+	1.08149i
$657$		0			0
$658$	32.3726	−	17.3585i	1.26201	−	0.676704i
$659$	4.71110	+	20.6407i	0.183518	+	0.804047i	0.979938	+	0.199303i	$0.0638676\pi$
$659$	4.71110	+	20.6407i	0.183518	+	0.804047i	−0.796420	+	0.604745i	$0.793275\pi$
$660$		0			0
$661$	−1.51712	+	3.86556i	−0.0590091	+	0.150353i	−0.957338	−	0.288971i	$-0.906687\pi$
$661$	−1.51712	+	3.86556i	−0.0590091	+	0.150353i	0.898329	+	0.439324i	$0.144782\pi$
$662$	−2.37009	+	6.03889i	−0.0921161	+	0.234708i
$663$		0			0
$664$	6.38807	+	27.9880i	0.247905	+	1.08614i
$665$	−1.83550	+	10.0296i	−0.0711776	+	0.388933i
$666$		0			0
$667$	4.30037	−	7.44846i	0.166511	−	0.288405i
$668$	2.83042	+	4.90243i	0.109512	+	0.189681i
$669$		0			0
$670$	−1.60782	+	21.4549i	−0.0621155	+	0.828874i
$671$	−9.06388	−	11.3658i	−0.349907	−	0.438770i
$672$		0			0
$673$	−21.9630	+	27.5407i	−0.846610	+	1.06162i	0.150719	+	0.988577i	$0.451841\pi$
$673$	−21.9630	+	27.5407i	−0.846610	+	1.06162i	−0.997329	+	0.0730387i	$0.976730\pi$
$674$	17.7905	+	16.5071i	0.685264	+	0.635832i
$675$		0			0
$676$	9.42678	+	6.42707i	0.362569	+	0.247195i
$677$	8.35390	−	1.25915i	0.321066	−	0.0483930i	0.0134681	−	0.999909i	$-0.495713\pi$
$677$	8.35390	−	1.25915i	0.321066	−	0.0483930i	0.307598	+	0.951516i	$0.400475\pi$
$678$		0			0
$679$	−4.47577	−	1.17057i	−0.171764	−	0.0449222i
$680$	−0.482517	+	0.232368i	−0.0185037	+	0.00891090i
$681$		0			0
$682$	7.90582	−	7.33553i	0.302729	−	0.280892i
$683$	−0.492221	−	6.56823i	−0.0188343	−	0.251327i	−0.998672	−	0.0515289i	$-0.983591\pi$
$683$	−0.492221	−	6.56823i	−0.0188343	−	0.251327i	0.979837	−	0.199798i	$-0.0640285\pi$
$684$		0			0
$685$	−22.3726			−0.854813
$686$	−12.3133	+	29.6669i	−0.470123	+	1.13269i
$687$		0			0
$688$	20.2382	+	51.5660i	0.771573	+	1.96594i
$689$	4.11340	+	54.8896i	0.156708	+	2.09113i
$690$		0			0
$691$	3.00890	−	2.05144i	0.114464	−	0.0780403i	−0.504735	−	0.863274i	$-0.668410\pi$
$691$	3.00890	−	2.05144i	0.114464	−	0.0780403i	0.619199	+	0.785234i	$0.287457\pi$
$692$	−15.0367	+	7.24129i	−0.571609	+	0.275273i
$693$		0			0
$694$	−46.6936	−	22.4865i	−1.77247	−	0.853574i
$695$	−28.1319	+	4.24020i	−1.06710	+	0.160840i
$696$		0			0
$697$	0.803297	+	0.121078i	0.0304270	+	0.00458614i
$698$	34.6489	+	32.1495i	1.31148	+	1.21688i
$699$		0			0
$700$	0.317068	+	2.67008i	0.0119840	+	0.100920i
$701$	−20.5329	−	25.7474i	−0.775517	−	0.972467i	0.224481	−	0.974478i	$-0.427931\pi$
$701$	−20.5329	−	25.7474i	−0.775517	−	0.972467i	−0.999998	+	0.00201097i	$0.999360\pi$
$702$		0			0
$703$	14.3255	−	4.41883i	0.540297	−	0.166659i
$704$	0.546040	+	0.945769i	0.0205796	+	0.0356450i
$705$		0			0
$706$	−7.19884	+	31.5402i	−0.270932	+	1.18703i
$707$	7.08744	−	38.7276i	0.266551	−	1.45650i
$708$		0			0
$709$	−40.9399	−	12.6283i	−1.53753	−	0.474265i	−0.593697	−	0.804688i	$-0.702332\pi$
$709$	−40.9399	−	12.6283i	−1.53753	−	0.474265i	−0.943833	+	0.330423i	$0.892809\pi$
$710$	−14.5801	+	37.1494i	−0.547180	+	1.39419i
$711$		0			0
$712$	−9.83484	−	3.03365i	−0.368576	−	0.113691i
$713$	6.06115	+	26.5557i	0.226992	+	0.994517i
$714$		0			0
$715$	3.16531	−	13.8681i	0.118376	−	0.518639i
$716$	2.86902	−	4.96929i	0.107220	−	0.185711i
$717$		0			0
$718$	−44.7470	+	13.8026i	−1.66994	+	0.515109i
$719$	−0.118561	+	1.58209i	−0.00442158	+	0.0590019i	−0.998978	−	0.0451964i	$-0.985609\pi$
$719$	−0.118561	+	1.58209i	−0.00442158	+	0.0590019i	0.994557	+	0.104198i	$0.0332277\pi$
$720$		0			0
$721$	6.35783	−	2.26758i	0.236778	−	0.0844489i
$722$	−17.8727	+	22.4117i	−0.665153	+	0.834076i
$723$		0			0
$724$	14.0193	+	2.11307i	0.521024	+	0.0785317i
$725$	1.38991	+	0.947628i	0.0516201	+	0.0351940i
$726$		0			0
$727$	7.31056	+	3.52058i	0.271134	+	0.130571i	0.564511	−	0.825426i	$-0.309065\pi$
$727$	7.31056	+	3.52058i	0.271134	+	0.130571i	−0.293377	+	0.955997i	$0.594779\pi$
$728$	−22.0310	+	4.30546i	−0.816525	+	0.159571i
$729$		0			0
$730$	31.1732	−	21.2535i	1.15377	−	0.786629i
$731$	1.03138	−	0.956981i	0.0381470	−	0.0353952i
$732$		0			0
$733$	−10.8993	−	27.7710i	−0.402575	−	1.02574i	−0.978132	−	0.207983i	$-0.933310\pi$
$733$	−10.8993	−	27.7710i	−0.402575	−	1.02574i	0.575557	−	0.817761i	$-0.304785\pi$
$734$	−0.798698			−0.0294805
$735$		0			0
$736$	26.9631			0.993874
$737$	−2.17586	−	5.54399i	−0.0801487	−	0.204216i
$738$		0			0
$739$	22.7492	−	21.1082i	0.836844	−	0.776478i	−0.140063	−	0.990143i	$-0.544730\pi$
$739$	22.7492	−	21.1082i	0.836844	−	0.776478i	0.976907	+	0.213665i	$0.0685400\pi$
$740$	19.4655	−	13.2713i	0.715565	−	0.487864i
$741$		0			0
$742$	39.0213	+	33.1755i	1.43252	+	1.21791i
$743$	38.9679	+	18.7660i	1.42959	+	0.688456i	0.978922	−	0.204234i	$-0.0654702\pi$
$743$	38.9679	+	18.7660i	1.42959	+	0.688456i	0.450672	+	0.892690i	$0.351185\pi$
$744$		0			0
$745$	−26.3514	−	17.9661i	−0.965441	−	0.658226i
$746$	3.66178	+	0.551925i	0.134067	+	0.0202074i
$747$		0			0
$748$	−0.0939212	+	0.117773i	−0.00343410	+	0.00430622i
$749$	15.9163	+	1.69677i	0.581570	+	0.0619987i
$750$		0			0
$751$	2.63787	−	35.1999i	0.0962571	−	1.28446i	−0.714731	−	0.699399i	$-0.753451\pi$
$751$	2.63787	−	35.1999i	0.0962571	−	1.28446i	0.810988	−	0.585062i	$-0.198930\pi$
$752$	38.2468	−	11.7976i	1.39472	−	0.430214i
$753$		0			0
$754$	7.13515	−	12.3584i	0.259847	−	0.450068i
$755$	8.59464	−	37.6556i	0.312791	−	1.37043i
$756$		0			0
$757$	6.01576	+	26.3568i	0.218646	+	0.957953i	0.958479	+	0.285162i	$0.0920474\pi$
$757$	6.01576	+	26.3568i	0.218646	+	0.957953i	−0.739833	+	0.672791i	$0.765095\pi$
$758$	−28.2418	−	8.71144i	−1.02579	−	0.316414i
$759$		0			0
$760$	−2.42238	+	6.17212i	−0.0878689	+	0.223886i
$761$	−7.12201	−	2.19685i	−0.258173	−	0.0796357i	0.162967	−	0.986632i	$-0.447894\pi$
$761$	−7.12201	−	2.19685i	−0.258173	−	0.0796357i	−0.421140	+	0.906996i	$0.638370\pi$
$762$		0			0
$763$	−2.42576	−	1.04108i	−0.0878185	−	0.0376897i
$764$	3.95068	−	17.3090i	0.142930	−	0.626219i
$765$		0			0
$766$	−5.95489	−	10.3142i	−0.215159	−	0.372666i
$767$	−33.5463	+	10.3477i	−1.21129	+	0.373632i
$768$		0			0
$769$	−6.99772	−	8.77487i	−0.252344	−	0.316430i	0.639483	−	0.768805i	$-0.279148\pi$
$769$	−6.99772	−	8.77487i	−0.252344	−	0.316430i	−0.891828	+	0.452375i	$0.850577\pi$
$770$	−7.10913	−	11.1650i	−0.256195	−	0.402357i
$771$		0			0
$772$	−6.59567	−	6.11989i	−0.237383	−	0.220260i
$773$	−22.9653	−	3.46146i	−0.826005	−	0.124500i	−0.277583	−	0.960702i	$-0.589533\pi$
$773$	−22.9653	−	3.46146i	−0.826005	−	0.124500i	−0.548422	+	0.836201i	$0.684771\pi$
$774$		0			0
$775$	−5.26809	+	0.794037i	−0.189235	+	0.0285227i
$776$	−2.71050	−	1.30531i	−0.0973012	−	0.0468578i
$777$		0			0
$778$	−36.1587	+	17.4131i	−1.29635	+	0.624290i
$779$	8.31000	−	5.66566i	0.297737	−	0.202993i
$780$		0			0
$781$	−0.825556	−	11.0163i	−0.0295407	−	0.394193i
$782$	−0.414786	−	1.05686i	−0.0148327	−	0.0377932i
$783$		0			0
$784$	−19.3678	+	29.1523i	−0.691708	+	1.04115i
$785$	18.3332			0.654340
$786$		0			0
$787$	−3.43430	−	45.8275i	−0.122419	−	1.63357i	−0.633289	−	0.773916i	$-0.718295\pi$
$787$	−3.43430	−	45.8275i	−0.122419	−	1.63357i	0.510869	−	0.859658i	$-0.329324\pi$
$788$	−5.00999	+	4.64860i	−0.178474	+	0.165599i
$789$		0			0
$790$	−48.5048	+	23.3587i	−1.72572	+	0.831064i
$791$	−10.3127	−	23.2556i	−0.366677	−	0.826873i
$792$		0			0
$793$	60.2388	−	9.07954i	2.13914	−	0.322424i
$794$	38.6448	+	26.3476i	1.37145	+	0.935042i
$795$		0			0
$796$	−5.25151	−	4.87269i	−0.186135	−	0.172708i
$797$	−9.71989	+	12.1884i	−0.344296	+	0.431734i	−0.923588	−	0.383386i	$-0.874758\pi$
$797$	−9.71989	+	12.1884i	−0.344296	+	0.431734i	0.579292	+	0.815120i	$0.303329\pi$
$798$		0			0
$799$	−0.633829	−	0.794797i	−0.0224233	−	0.0281179i
$800$	−0.394106	+	5.25898i	−0.0139337	+	0.185933i
$801$		0			0
$802$	−14.4030	−	24.9468i	−0.508588	−	0.880901i
$803$	−5.22199	+	9.04475i	−0.184280	+	0.319182i
$804$		0			0
$805$	33.3984	−	1.45023i	1.17714	−	0.0511140i
$806$	10.0566	+	44.0610i	0.354230	+	1.55198i
$807$		0			0
$808$	9.35356	−	23.8325i	0.329057	−	0.838424i
$809$	8.82433	−	22.4840i	0.310247	−	0.790496i	−0.687673	−	0.726021i	$-0.741368\pi$
$809$	8.82433	−	22.4840i	0.310247	−	0.790496i	0.997919	−	0.0644749i	$-0.0205372\pi$
$810$		0			0
$811$	−7.77036	−	34.0442i	−0.272854	−	1.19545i	−0.906627	−	0.421933i	$-0.861352\pi$
$811$	−7.77036	−	34.0442i	−0.272854	−	1.19545i	0.633773	−	0.773519i	$-0.281505\pi$
$812$	−1.17741	−	4.29109i	−0.0413190	−	0.150588i
$813$		0			0
$814$	−9.73059	+	16.8539i	−0.341057	+	0.590728i
$815$	−20.4540	−	35.4274i	−0.716474	−	1.24097i
$816$		0			0
$817$	1.30173	−	17.3704i	0.0455418	−	0.607713i
$818$	−1.12227	−	1.40729i	−0.0392394	−	0.0492046i
$819$		0			0
$820$	9.85458	−	12.3573i	0.344137	−	0.431534i
$821$	−17.5036	−	16.2410i	−0.610880	−	0.566814i	0.312877	−	0.949794i	$-0.398707\pi$
$821$	−17.5036	−	16.2410i	−0.610880	−	0.566814i	−0.923757	+	0.382980i	$0.874898\pi$
$822$		0			0
$823$	−14.8299	−	10.1109i	−0.516939	−	0.352443i	0.276578	−	0.960992i	$-0.410800\pi$
$823$	−14.8299	−	10.1109i	−0.516939	−	0.352443i	−0.793517	+	0.608548i	$0.791752\pi$
$824$	4.34048	−	0.654221i	0.151208	−	0.0227909i
$825$		0			0
$826$	−15.0904	+	28.9716i	−0.525063	+	1.00805i
$827$	−22.4223	+	10.7980i	−0.779701	+	0.375484i	−0.781013	−	0.624515i	$-0.785297\pi$
$827$	−22.4223	+	10.7980i	−0.779701	+	0.375484i	0.00131191	+	0.999999i	$0.499582\pi$
$828$		0			0
$829$	−39.0799	+	36.2609i	−1.35730	+	1.25939i	−0.421517	+	0.906820i	$0.638502\pi$
$829$	−39.0799	+	36.2609i	−1.35730	+	1.25939i	−0.935785	+	0.352572i	$0.885307\pi$
$830$	−5.30093	−	70.7360i	−0.183998	−	2.45528i
$831$		0			0
$832$	−4.57640			−0.158658
$833$	0.868964	+	0.187403i	0.0301078	+	0.00649313i
$834$		0			0
$835$	5.02916	+	12.8141i	0.174041	+	0.443450i
$836$	0.139371	+	1.85977i	0.00482023	+	0.0643215i
$837$		0			0
$838$	29.5675	−	20.1588i	1.02139	−	0.696373i
$839$	−13.2505	+	6.38111i	−0.457458	+	0.220300i	−0.648398	−	0.761301i	$-0.724561\pi$
$839$	−13.2505	+	6.38111i	−0.457458	+	0.220300i	0.190940	+	0.981602i	$0.438846\pi$
$840$		0			0
$841$	23.6199	+	11.3748i	0.814480	+	0.392233i
$842$	14.2686	−	2.15064i	0.491727	−	0.0741160i
$843$		0			0
$844$	25.1700	+	3.79377i	0.866388	+	0.130587i
$845$	20.3380	+	18.8709i	0.699650	+	0.649180i
$846$		0			0
$847$	−21.6208	−	13.4051i	−0.742900	−	0.460606i
$848$	34.7959	+	43.6327i	1.19490	+	1.49835i
$849$		0			0
$850$	0.212196	−	0.0654537i	0.00727826	−	0.00224505i
$851$	−24.5760	−	42.5669i	−0.842455	−	1.45917i
$852$		0			0
$853$	9.17803	−	40.2116i	0.314250	−	1.37682i	−0.533221	−	0.845976i	$-0.679019\pi$
$853$	9.17803	−	40.2116i	0.314250	−	1.37682i	0.847471	−	0.530842i	$-0.178124\pi$
$854$	33.3869	−	45.8099i	1.14248	−	1.56758i
$855$		0			0
$856$	9.94638	+	3.06805i	0.339960	+	0.104864i
$857$	9.13051	−	23.2642i	0.311892	−	0.794688i	−0.685864	−	0.727730i	$-0.740575\pi$
$857$	9.13051	−	23.2642i	0.311892	−	0.794688i	0.997756	−	0.0669582i	$-0.0213294\pi$
$858$		0			0
$859$	−14.3756	−	4.43427i	−0.490488	−	0.151295i	0.0396385	−	0.999214i	$-0.487379\pi$
$859$	−14.3756	−	4.43427i	−0.490488	−	0.151295i	−0.530126	+	0.847919i	$0.677856\pi$
$860$	−6.09130	−	26.6877i	−0.207711	−	0.910043i
$861$		0			0
$862$	−10.8690	+	47.6200i	−0.370198	+	1.62194i
$863$	1.82348	−	3.15836i	0.0620720	−	0.107512i	−0.833319	−	0.552792i	$-0.813562\pi$
$863$	1.82348	−	3.15836i	0.0620720	−	0.107512i	0.895391	+	0.445280i	$0.146896\pi$
$864$		0			0
$865$	−38.7813	+	11.9625i	−1.31860	+	0.406736i
$866$	−0.460480	+	6.14468i	−0.0156478	+	0.208805i
$867$		0			0
$868$	11.9769	+	7.42583i	0.406523	+	0.252049i
$869$	9.29167	−	11.6514i	0.315198	−	0.395246i
$870$		0			0
$871$	24.6788	+	3.71973i	0.836208	+	0.126038i
$872$	−1.41830	−	0.966984i	−0.0480299	−	0.0327462i
$873$		0			0
$874$	−12.6642	−	6.09875i	−0.428372	−	0.206293i
$875$	0.812855	−	25.8746i	0.0274795	−	0.874721i
$876$		0			0
$877$	8.60845	−	5.86914i	0.290687	−	0.198187i	−0.409193	−	0.912448i	$-0.634190\pi$
$877$	8.60845	−	5.86914i	0.290687	−	0.198187i	0.699879	+	0.714261i	$0.253237\pi$
$878$	−41.2909	+	38.3124i	−1.39350	+	1.29298i
$879$		0			0
$880$	−5.26912	−	13.4255i	−0.177622	−	0.452573i
$881$	−34.2797			−1.15491			−0.577456	−	0.816422i	$-0.695955\pi$
$881$	−34.2797			−1.15491			−0.577456	+	0.816422i	$0.695955\pi$
$882$		0			0
$883$	45.8970			1.54456			0.772278	−	0.635285i	$-0.219117\pi$
$883$	45.8970			1.54456			0.772278	+	0.635285i	$0.219117\pi$
$884$	−0.230623	−	0.587617i	−0.00775669	−	0.0197637i
$885$		0			0
$886$	0.235652	−	0.218653i	0.00791688	−	0.00734579i
$887$	−15.6096	+	10.6425i	−0.524121	+	0.357339i	−0.796295	−	0.604909i	$-0.793210\pi$
$887$	−15.6096	+	10.6425i	−0.524121	+	0.357339i	0.272174	+	0.962248i	$0.412257\pi$
$888$		0			0
$889$	4.32975	−	8.31253i	0.145215	−	0.278793i
$890$	22.9124	+	11.0341i	0.768027	+	0.369862i
$891$		0			0
$892$	15.8279	+	10.7913i	0.529958	+	0.361319i
$893$	−12.4453	−	1.87583i	−0.416467	−	0.0627722i
$894$		0			0
$895$	8.69979	−	10.9092i	0.290802	−	0.364654i
$896$	−22.4467	+	22.7175i	−0.749892	+	0.758938i
$897$		0			0
$898$	2.67170	−	35.6514i	0.0891558	−	1.18970i
$899$	8.42480	−	2.59871i	0.280983	−	0.0866717i
$900$		0			0
$901$	0.708729	−	1.22756i	0.0236112	−	0.0408958i
$902$	−2.90529	+	12.7289i	−0.0967355	+	0.423826i
$903$		0			0
$904$	−3.68117	−	16.1283i	−0.122434	−	0.536418i
$905$	32.9446	+	10.1621i	1.09512	+	0.337799i
$906$		0			0
$907$	−15.5158	+	39.5336i	−0.515193	+	1.31269i	0.402507	+	0.915417i	$0.368139\pi$
$907$	−15.5158	+	39.5336i	−0.515193	+	1.31269i	−0.917700	+	0.397274i	$0.869956\pi$
$908$	−13.0683	−	4.03103i	−0.433686	−	0.133775i
$909$		0			0
$910$	55.4144	−	2.40622i	1.83697	−	0.0797653i
$911$	5.16494	−	22.6291i	0.171122	−	0.749735i	−0.814416	−	0.580282i	$-0.802943\pi$
$911$	5.16494	−	22.6291i	0.171122	−	0.749735i	0.985538	−	0.169454i	$-0.0542003\pi$
$912$		0			0
$913$	9.81786	+	17.0050i	0.324924	+	0.562784i
$914$	51.2154	−	15.7979i	1.69406	−	0.522547i
$915$		0			0
$916$	11.9094	+	14.9339i	0.393499	+	0.493432i
$917$	2.10426	−	6.13130i	0.0694888	−	0.202473i
$918$		0			0
$919$	−9.52703	−	8.83979i	−0.314268	−	0.291598i	0.507229	−	0.861811i	$-0.330670\pi$
$919$	−9.52703	−	8.83979i	−0.314268	−	0.291598i	−0.821496	+	0.570214i	$0.806860\pi$
$920$	21.4962	+	3.24003i	0.708708	+	0.106820i
$921$		0			0
$922$	−63.3355	+	9.54630i	−2.08584	+	0.314391i
$923$	41.7090	+	20.0860i	1.37287	+	0.661139i
$924$		0			0
$925$	8.66160	−	4.17121i	0.284792	−	0.137148i
$926$	43.9176	−	29.9425i	1.44322	−	0.983973i
$927$		0			0
$928$	−0.652194	−	8.70293i	−0.0214093	−	0.285688i
$929$	−7.81392	−	19.9095i	−0.256366	−	0.653211i	0.743513	−	0.668721i	$-0.233158\pi$
$929$	−7.81392	−	19.9095i	−0.256366	−	0.653211i	−0.999880	+	0.0155104i	$0.995063\pi$
$930$		0			0
$931$	9.46449	−	5.61670i	0.310186	−	0.184080i
$932$	18.4414			0.604069
$933$		0			0
$934$	3.31678	+	44.2593i	0.108528	+	1.44821i
$935$	−0.268525	+	0.249155i	−0.00878172	+	0.00814824i
$936$		0			0
$937$	32.7858	−	15.7888i	1.07106	−	0.515797i	0.186615	−	0.982433i	$-0.440248\pi$
$937$	32.7858	−	15.7888i	1.07106	−	0.515797i	0.884450	+	0.466636i	$0.154534\pi$
$938$	18.6021	−	13.9020i	0.607381	−	0.453917i
$939$		0			0
$940$	−19.5578	+	2.94786i	−0.637904	+	0.0961486i
$941$	−22.6250	−	15.4255i	−0.737554	−	0.502856i	0.135320	−	0.990802i	$-0.456794\pi$
$941$	−22.6250	−	15.4255i	−0.737554	−	0.502856i	−0.872874	+	0.487946i	$0.837746\pi$
$942$		0			0
$943$	−24.1727	−	22.4290i	−0.787172	−	0.730389i
$944$	−22.1924	+	27.8283i	−0.722300	+	0.905735i
$945$		0			0
$946$	14.0987	+	17.6792i	0.458387	+	0.574799i
$947$	−0.131691	+	1.75730i	−0.00427940	+	0.0571046i	−0.998935	−	0.0461472i	$-0.985306\pi$
$947$	−0.131691	+	1.75730i	−0.00427940	+	0.0571046i	0.994655	+	0.103252i	$0.0329247\pi$
$948$		0			0
$949$	−21.8829	−	37.9024i	−0.710350	−	1.23036i
$950$	1.37462	−	2.38092i	0.0445987	−	0.0772473i
$951$		0			0
$952$	0.531211	+	0.227984i	0.0172166	+	0.00738900i
$953$	−0.854529	−	3.74394i	−0.0276809	−	0.121278i	0.959200	−	0.282729i	$-0.0912397\pi$
$953$	−0.854529	−	3.74394i	−0.0276809	−	0.121278i	−0.986881	+	0.161451i	$0.948383\pi$
$954$		0			0
$955$	15.7730	−	40.1890i	0.510403	−	1.30049i
$956$	−1.78704	+	4.55330i	−0.0577969	+	0.147264i
$957$		0			0
$958$	5.09130	+	22.3064i	0.164492	+	0.720688i
$959$	15.8613	+	18.2092i	0.512187	+	0.588006i
$960$		0			0
$961$	1.53906	−	2.66573i	0.0496471	−	0.0859914i
$962$	−40.7764	−	70.6268i	−1.31468	−	2.27710i
$963$		0			0
$964$	1.47742	−	19.7148i	0.0475845	−	0.634971i
$965$	−13.6417	−	17.1062i	−0.439143	−	0.550668i
$966$		0			0
$967$	−32.0254	+	40.1586i	−1.02987	+	1.29141i	−0.0741132	+	0.997250i	$0.523613\pi$
$967$	−32.0254	+	40.1586i	−1.02987	+	1.29141i	−0.955755	+	0.294164i	$0.904959\pi$
$968$	−12.1267	−	11.2520i	−0.389768	−	0.361652i
$969$		0			0
$970$	6.14190	+	4.18748i	0.197205	+	0.134452i
$971$	1.49204	−	0.224889i	0.0478819	−	0.00721703i	−0.125058	−	0.992149i	$-0.539912\pi$
$971$	1.49204	−	0.224889i	0.0478819	−	0.00721703i	0.172940	+	0.984932i	$0.444673\pi$
$972$		0			0
$973$	23.3955	+	19.8906i	0.750026	+	0.637663i
$974$	53.2047	−	25.6220i	1.70479	−	0.820983i
$975$		0			0
$976$	45.2775	−	42.0114i	1.44930	−	1.34475i
$977$	−0.748095	−	9.98263i	−0.0239337	−	0.319373i	−0.996302	−	0.0859206i	$-0.972617\pi$
$977$	−0.748095	−	9.98263i	−0.0239337	−	0.319373i	0.972368	−	0.233452i	$-0.0750022\pi$
$978$		0			0
$979$	−7.03966			−0.224988
$980$	11.6109	−	12.8185i	0.370898	−	0.409472i
$981$		0			0
$982$	−8.31068	−	21.1753i	−0.265205	−	0.675730i
$983$	−1.81602	−	24.2331i	−0.0579221	−	0.772916i	−0.948235	−	0.317568i	$-0.897134\pi$
$983$	−1.81602	−	24.2331i	−0.0579221	−	0.772916i	0.890313	−	0.455348i	$-0.150485\pi$
$984$		0			0
$985$	−13.7317	+	9.36211i	−0.437528	+	0.298302i
$986$	−0.331091	+	0.159445i	−0.0105441	+	0.00507776i
$987$		0			0
$988$	−7.04133	−	3.39093i	−0.224015	−	0.107880i
$989$	−56.4732	+	8.51197i	−1.79574	+	0.270665i
$990$		0			0
$991$	−10.6876	−	1.61089i	−0.339502	−	0.0511716i	−0.0229211	−	0.999737i	$-0.507297\pi$
$991$	−10.6876	−	1.61089i	−0.339502	−	0.0511716i	−0.316580	+	0.948566i	$0.602535\pi$
$992$	20.2612	+	18.7996i	0.643294	+	0.596889i
$993$		0			0
$994$	40.5728	−	14.4706i	1.28689	−	0.458981i
$995$	−10.8616	−	13.6200i	−0.344337	−	0.431784i
$996$		0			0
$997$	−38.0593	+	11.7398i	−1.20535	+	0.371802i	−0.831415	−	0.555652i	$-0.812469\pi$
$997$	−38.0593	+	11.7398i	−1.20535	+	0.371802i	−0.373937	+	0.927454i	$0.621992\pi$
$998$	−23.2122	−	40.2046i	−0.734768	−	1.27266i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.c.163.3		48
3.2	odd	2		147.2.m.a.16.2	✓	48
49.46	even	21	inner	441.2.bb.c.46.3		48
147.86	odd	42		7203.2.a.i.1.7		24
147.95	odd	42		147.2.m.a.46.2	yes	48
147.110	even	42		7203.2.a.k.1.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.a.16.2	✓	48	3.2	odd	2
147.2.m.a.46.2	yes	48	147.95	odd	42
441.2.bb.c.46.3		48	49.46	even	21	inner
441.2.bb.c.163.3		48	1.1	even	1	trivial
7203.2.a.i.1.7		24	147.86	odd	42
7203.2.a.k.1.7		24	147.110	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)

\(f(q)\)	\(=\)	\(q+(0.633632 + 1.61447i) q^{2} +(-0.738910 + 0.685609i) q^{4} +(-2.02525 + 1.38079i) q^{5} +(2.55966 + 0.669438i) q^{7} +(1.55011 + 0.746495i) q^{8} +O(q^{10})\)	\(q+(0.633632 + 1.61447i) q^{2} +(-0.738910 + 0.685609i) q^{4} +(-2.02525 + 1.38079i) q^{5} +(2.55966 + 0.669438i) q^{7} +(1.55011 + 0.746495i) q^{8} +(-3.51251 - 2.39479i) q^{10} +(1.16365 + 0.175392i) q^{11} +(-3.07468 + 3.85553i) q^{13} +(0.541096 + 4.55666i) q^{14} +(-0.373646 + 4.98596i) q^{16} +(0.121350 - 0.0374315i) q^{17} +(0.786116 - 1.36159i) q^{19} +(0.549795 - 2.40881i) q^{20} +(0.454162 + 1.98981i) q^{22} +(-4.92579 - 1.51941i) q^{23} +(0.368347 - 0.938534i) q^{25} +(-8.17285 - 2.52099i) q^{26} +(-2.35033 + 1.26027i) q^{28} +(-0.371274 + 1.62666i) q^{29} +(-2.64206 - 4.57618i) q^{31} +(-4.99830 + 1.54177i) q^{32} +(0.137323 + 0.172198i) q^{34} +(-6.10831 + 2.17858i) q^{35} +(6.98979 + 6.48558i) q^{37} +(2.69636 + 0.406410i) q^{38} +(-4.17012 + 0.628545i) q^{40} +(5.76353 + 2.77557i) q^{41} +(9.98202 - 4.80709i) q^{43} +(-0.980086 + 0.668211i) q^{44} +(-0.668107 - 8.91527i) q^{46} +(-2.92459 - 7.45174i) q^{47} +(6.10371 + 3.42706i) q^{49} +1.74863 q^{50} +(-0.371470 - 4.95692i) q^{52} +(8.18219 - 7.59196i) q^{53} +(-2.59887 + 1.25155i) q^{55} +(3.46803 + 2.94848i) q^{56} +(-2.86143 + 0.431292i) q^{58} +(5.88187 + 4.01019i) q^{59} +(-9.05562 - 8.40239i) q^{61} +(5.71400 - 7.16513i) q^{62} +(0.578605 + 0.725548i) q^{64} +(0.903317 - 12.0539i) q^{65} +(-2.53046 - 4.38289i) q^{67} +(-0.0640033 + 0.110857i) q^{68} +(-7.38766 - 8.48124i) q^{70} +(-2.08891 - 9.15212i) q^{71} +(-3.24237 + 8.26143i) q^{73} +(-6.04180 + 15.3942i) q^{74} +(0.352651 + 1.54506i) q^{76} +(2.86114 + 1.22794i) q^{77} +(6.33188 - 10.9671i) q^{79} +(-6.12784 - 10.6137i) q^{80} +(-0.829110 + 11.0637i) q^{82} +(10.4034 + 13.0454i) q^{83} +(-0.194079 + 0.243367i) q^{85} +(14.0858 + 13.0697i) q^{86} +(1.67286 + 1.14054i) q^{88} +(-5.91524 + 0.891578i) q^{89} +(-10.4512 + 7.81054i) q^{91} +(4.68143 - 2.25446i) q^{92} +(10.1775 - 9.44332i) q^{94} +(0.287995 + 3.84303i) q^{95} -1.74858 q^{97} +(-1.66538 + 12.0257i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} + 3 q^{4} - 6 q^{8}+O(q^{10}) \) 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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