LMFDB - Embedded newform 3311.1.gb.a.62.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3311,1,Mod(62,3311)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3311, base_ring=CyclotomicField(210))

chi = DirichletCharacter(H, H._module([105, 147, 95]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("3311.62");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3311 = 7 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3311.gb (of order $210$, degree $48$, 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:	$1.65240425683$
Analytic rank:	$0$
Dimension:	$48$
Coefficient field:	$\Q(\zeta_{210})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{48} - x^{47} + x^{46} + x^{43} - x^{42} + 2 x^{41} - x^{40} + x^{39} + x^{36} - x^{35} + x^{34} + \cdots + 1 $ x^48 - x^47 + x^46 + x^43 - x^42 + 2x^41 - x^40 + x^39 + x^36 - x^35 + x^34 - x^33 + x^32 - x^31 - x^28 - x^26 - x^24 - x^22 - x^20 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 + x^9 - x^8 + 2x^7 - x^6 + x^5 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{210}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{210} - \cdots)$

Embedding invariants

Embedding label			62.1
Root			$-0.791071 + 0.611724i$ of defining polynomial
Character	$\chi$	$=$	3311.62
Dual form			3311.1.gb.a.3044.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87296 + 0.516904i) q^{2} +(2.38234 - 1.42338i) q^{4} +(0.669131 - 0.743145i) q^{7} +(-2.38356 + 2.49301i) q^{8} +(0.946327 + 0.323210i) q^{9} +O(q^{10})$	\(q+(-1.87296 + 0.516904i) q^{2} +(2.38234 - 1.42338i) q^{4} +(0.669131 - 0.743145i) q^{7} +(-2.38356 + 2.49301i) q^{8} +(0.946327 + 0.323210i) q^{9} +(-0.473869 + 0.880596i) q^{11} +(-0.869121 + 1.73776i) q^{14} +(1.86060 - 3.45758i) q^{16} +(-1.93950 - 0.116198i) q^{18} +(0.432354 - 1.89427i) q^{22} +(1.15979 + 1.07613i) q^{23} +(0.772417 + 0.635116i) q^{25} +(0.536318 - 2.72286i) q^{28} +(-0.196523 - 1.18344i) q^{29} +(-0.930094 + 4.07501i) q^{32} +(2.71453 - 0.576991i) q^{36} +(-0.412060 + 1.93859i) q^{37} +(-0.193256 + 0.981148i) q^{43} +(0.124508 + 2.77238i) q^{44} +(-2.72850 - 1.41605i) q^{46} +(-0.104528 - 0.994522i) q^{49} +(-1.77500 - 0.790281i) q^{50} +(-0.612807 + 0.722962i) q^{53} +(0.257753 + 3.43948i) q^{56} +(0.979804 + 2.11495i) q^{58} +(0.873408 - 0.486989i) q^{63} +(-0.188202 - 4.19065i) q^{64} +(-1.61056 - 0.496793i) q^{67} +(-0.798138 - 0.157209i) q^{71} +(-3.06139 + 1.58881i) q^{72} +(-0.230293 - 3.84390i) q^{74} +(0.337330 + 0.941386i) q^{77} +(1.95155 + 0.205116i) q^{79} +(0.791071 + 0.611724i) q^{81} +(-0.145199 - 1.93755i) q^{86} +(-1.06584 - 3.28031i) q^{88} +(4.29477 + 0.912881i) q^{92} +(0.709850 + 1.80867i) q^{98} +(-0.733052 + 0.680173i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{2} + 6 q^{7} - 21 q^{8} + q^{9}+O(q^{10}) $ 48 * q - 2 * q^2 + 6 * q^7 - 21 * q^8 + q^9	$ 48 q - 2 q^{2} + 6 q^{7} - 21 q^{8} + q^{9} - 2 q^{11} - 9 q^{14} + 3 q^{16} - 6 q^{18} + 2 q^{22} - q^{23} + q^{25} - 10 q^{28} - q^{29} - 4 q^{32} - 7 q^{36} - 5 q^{37} + q^{43} + 23 q^{44} + 4 q^{46} + 6 q^{49} - q^{50} + 10 q^{53} - 15 q^{56} + 4 q^{58} + q^{63} - 21 q^{64} + q^{67} - 7 q^{71} - 4 q^{72} - 14 q^{74} + q^{77} + 2 q^{79} - q^{81} + 13 q^{86} - 7 q^{88} + 20 q^{92} + q^{98} + 4 q^{99}+O(q^{100}) $ 48 * q - 2 * q^2 + 6 * q^7 - 21 * q^8 + q^9 - 2 * q^11 - 9 * q^14 + 3 * q^16 - 6 * q^18 + 2 * q^22 - q^23 + q^25 - 10 * q^28 - q^29 - 4 * q^32 - 7 * q^36 - 5 * q^37 + q^43 + 23 * q^44 + 4 * q^46 + 6 * q^49 - q^50 + 10 * q^53 - 15 * q^56 + 4 * q^58 + q^63 - 21 * q^64 + q^67 - 7 * q^71 - 4 * q^72 - 14 * q^74 + q^77 + 2 * q^79 - q^81 + 13 * q^86 - 7 * q^88 + 20 * q^92 + q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3311\mathbb{Z}\right)^\times$.

$n$	$904$	$1893$	$2927$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{19}{42}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.87296	+	0.516904i	−1.87296	+	0.516904i	−0.873408	+	0.486989i	$0.838095\pi$
$2$	−1.87296	+	0.516904i	−1.87296	+	0.516904i	−0.999552	+	0.0299155i	$0.990476\pi$
$3$		0			0		−0.986491	−	0.163818i	$-0.947619\pi$
$3$		0			0		0.986491	+	0.163818i	$0.0523810\pi$
$4$	2.38234	−	1.42338i	2.38234	−	1.42338i
$5$		0			0		−0.941386	−	0.337330i	$-0.890476\pi$
$5$		0			0		0.941386	+	0.337330i	$0.109524\pi$
$6$		0			0
$7$	0.669131	−	0.743145i	0.669131	−	0.743145i
$7$	0.669131	−	0.743145i	0.669131	−	0.743145i
$8$	−2.38356	+	2.49301i	−2.38356	+	2.49301i
$9$	0.946327	+	0.323210i	0.946327	+	0.323210i
$10$		0			0
$11$	−0.473869	+	0.880596i	−0.473869	+	0.880596i
$11$	−0.473869	+	0.880596i	−0.473869	+	0.880596i
$12$		0			0
$13$		0			0		−0.850680	−	0.525684i	$-0.823810\pi$
$13$		0			0		0.850680	+	0.525684i	$0.176190\pi$
$14$	−0.869121	+	1.73776i	−0.869121	+	1.73776i
$15$		0			0
$16$	1.86060	−	3.45758i	1.86060	−	3.45758i
$17$		0			0		−0.0299155	−	0.999552i	$-0.509524\pi$
$17$		0			0		0.0299155	+	0.999552i	$0.490476\pi$
$18$	−1.93950	−	0.116198i	−1.93950	−	0.116198i
$19$		0			0		0.575617	−	0.817719i	$-0.304762\pi$
$19$		0			0		−0.575617	+	0.817719i	$0.695238\pi$
$20$		0			0
$21$		0			0
$22$	0.432354	−	1.89427i	0.432354	−	1.89427i
$23$	1.15979	+	1.07613i	1.15979	+	1.07613i	0.995974	+	0.0896393i	$0.0285714\pi$
$23$	1.15979	+	1.07613i	1.15979	+	1.07613i	0.163818	+	0.986491i	$0.447619\pi$
$24$		0			0
$25$	0.772417	+	0.635116i	0.772417	+	0.635116i
$26$		0			0
$27$		0			0
$28$	0.536318	−	2.72286i	0.536318	−	2.72286i
$29$	−0.196523	−	1.18344i	−0.196523	−	1.18344i	−0.887586	−	0.460642i	$-0.847619\pi$
$29$	−0.196523	−	1.18344i	−0.196523	−	1.18344i	0.691063	−	0.722795i	$-0.257143\pi$
$30$		0			0
$31$		0			0		0.251587	−	0.967835i	$-0.419048\pi$
$31$		0			0		−0.251587	+	0.967835i	$0.580952\pi$
$32$	−0.930094	+	4.07501i	−0.930094	+	4.07501i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	2.71453	−	0.576991i	2.71453	−	0.576991i
$37$	−0.412060	+	1.93859i	−0.412060	+	1.93859i	−0.0747301	+	0.997204i	$0.523810\pi$
$37$	−0.412060	+	1.93859i	−0.412060	+	1.93859i	−0.337330	+	0.941386i	$0.609524\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.834573	−	0.550897i	$-0.185714\pi$
$41$		0			0		−0.834573	+	0.550897i	$0.814286\pi$
$42$		0			0
$43$	−0.193256	+	0.981148i	−0.193256	+	0.981148i
$43$	−0.193256	+	0.981148i	−0.193256	+	0.981148i
$44$	0.124508	+	2.77238i	0.124508	+	2.77238i
$45$		0			0
$46$	−2.72850	−	1.41605i	−2.72850	−	1.41605i
$47$		0			0		−0.995974	−	0.0896393i	$-0.971429\pi$
$47$		0			0		0.995974	+	0.0896393i	$0.0285714\pi$
$48$		0			0
$49$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$50$	−1.77500	−	0.790281i	−1.77500	−	0.790281i
$51$		0			0
$52$		0			0
$53$	−0.612807	+	0.722962i	−0.612807	+	0.722962i	−0.978148	−	0.207912i	$-0.933333\pi$
$53$	−0.612807	+	0.722962i	−0.612807	+	0.722962i	0.365341	+	0.930874i	$0.380952\pi$
$54$		0			0
$55$		0			0
$56$	0.257753	+	3.43948i	0.257753	+	3.43948i
$57$		0			0
$58$	0.979804	+	2.11495i	0.979804	+	2.11495i
$59$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$59$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$60$		0			0
$61$		0			0		−0.251587	−	0.967835i	$-0.580952\pi$
$61$		0			0		0.251587	+	0.967835i	$0.419048\pi$
$62$		0			0
$63$	0.873408	−	0.486989i	0.873408	−	0.486989i
$64$	−0.188202	−	4.19065i	−0.188202	−	4.19065i
$65$		0			0
$66$		0			0
$67$	−1.61056	−	0.496793i	−1.61056	−	0.496793i	−0.646600	−	0.762830i	$-0.723810\pi$
$67$	−1.61056	−	0.496793i	−1.61056	−	0.496793i	−0.963963	+	0.266037i	$0.914286\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.798138	−	0.157209i	−0.798138	−	0.157209i	−0.222521	−	0.974928i	$-0.571429\pi$
$71$	−0.798138	−	0.157209i	−0.798138	−	0.157209i	−0.575617	+	0.817719i	$0.695238\pi$
$72$	−3.06139	+	1.58881i	−3.06139	+	1.58881i
$73$		0			0		0.925304	−	0.379225i	$-0.123810\pi$
$73$		0			0		−0.925304	+	0.379225i	$0.876190\pi$
$74$	−0.230293	−	3.84390i	−0.230293	−	3.84390i
$75$		0			0
$76$		0			0
$77$	0.337330	+	0.941386i	0.337330	+	0.941386i
$78$		0			0
$79$	1.95155	+	0.205116i	1.95155	+	0.205116i	0.995974	−	0.0896393i	$-0.0285714\pi$
$79$	1.95155	+	0.205116i	1.95155	+	0.205116i	0.955573	+	0.294755i	$0.0952381\pi$
$80$		0			0
$81$	0.791071	+	0.611724i	0.791071	+	0.611724i
$82$		0			0
$83$		0			0		−0.701798	−	0.712376i	$-0.747619\pi$
$83$		0			0		0.701798	+	0.712376i	$0.252381\pi$
$84$		0			0
$85$		0			0
$86$	−0.145199	−	1.93755i	−0.145199	−	1.93755i
$87$		0			0
$88$	−1.06584	−	3.28031i	−1.06584	−	3.28031i
$89$		0			0		−0.149042	−	0.988831i	$-0.547619\pi$
$89$		0			0		0.149042	+	0.988831i	$0.452381\pi$
$90$		0			0
$91$		0			0
$92$	4.29477	+	0.912881i	4.29477	+	0.912881i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$97$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$98$	0.709850	+	1.80867i	0.709850	+	1.80867i
$99$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$100$	2.74418	+	0.413618i	2.74418	+	0.413618i
$101$		0			0		−0.119394	−	0.992847i	$-0.538095\pi$
$101$		0			0		0.119394	+	0.992847i	$0.461905\pi$
$102$		0			0
$103$		0			0		0.280427	−	0.959875i	$-0.409524\pi$
$103$		0			0		−0.280427	+	0.959875i	$0.590476\pi$
$104$		0			0
$105$		0			0
$106$	0.774060	−	1.67084i	0.774060	−	1.67084i
$107$	0.0629940	+	0.167847i	0.0629940	+	0.167847i	0.963963	−	0.266037i	$-0.0857143\pi$
$107$	0.0629940	+	0.167847i	0.0629940	+	0.167847i	−0.900969	+	0.433884i	$0.857143\pi$
$108$		0			0
$109$	0.282832	−	0.304820i	0.282832	−	0.304820i	−0.575617	−	0.817719i	$-0.695238\pi$
$109$	0.282832	−	0.304820i	0.282832	−	0.304820i	0.858449	+	0.512899i	$0.171429\pi$
$110$		0			0
$111$		0			0
$112$	−1.32449	−	3.69627i	−1.32449	−	3.69627i
$113$	1.91815	−	0.259831i	1.91815	−	0.259831i	0.925304	−	0.379225i	$-0.123810\pi$
$113$	1.91815	−	0.259831i	1.91815	−	0.259831i	0.992847	+	0.119394i	$0.0380952\pi$
$114$		0			0
$115$		0			0
$116$	−2.15267	−	2.53963i	−2.15267	−	2.53963i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.550897	−	0.834573i	−0.550897	−	0.834573i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−1.38413	+	1.36358i	−1.38413	+	1.36358i
$127$	−1.48479	−	0.0666821i	−1.48479	−	0.0666821i	−0.712376	−	0.701798i	$-0.752381\pi$
$127$	−1.48479	−	0.0666821i	−1.48479	−	0.0666821i	−0.772417	+	0.635116i	$0.780952\pi$
$128$	1.22703	+	3.77641i	1.22703	+	3.77641i
$129$		0			0
$130$		0			0
$131$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$131$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$132$		0			0
$133$		0			0
$134$	3.27331	+	0.0979666i	3.27331	+	0.0979666i
$135$		0			0
$136$		0			0
$137$	−0.319395	−	1.76001i	−0.319395	−	1.76001i	−0.599822	−	0.800134i	$-0.704762\pi$
$137$	−0.319395	−	1.76001i	−0.319395	−	1.76001i	0.280427	−	0.959875i	$-0.409524\pi$
$138$		0			0
$139$		0			0		−0.237080	−	0.971490i	$-0.576190\pi$
$139$		0			0		0.237080	+	0.971490i	$0.423810\pi$
$140$		0			0
$141$		0			0
$142$	1.57614	−	0.118116i	1.57614	−	0.118116i
$143$		0			0
$144$	2.87826	−	2.67063i	2.87826	−	2.67063i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	1.77769	+	5.20491i	1.77769	+	5.20491i
$149$	1.45562	+	0.175044i	1.45562	+	0.175044i	0.809017	−	0.587785i	$-0.200000\pi$
$149$	1.45562	+	0.175044i	1.45562	+	0.175044i	0.646600	+	0.762830i	$0.276190\pi$
$150$		0			0
$151$	−0.837580	+	0.314349i	−0.837580	+	0.314349i	−0.733052	−	0.680173i	$-0.761905\pi$
$151$	−0.837580	+	0.314349i	−0.837580	+	0.314349i	−0.104528	+	0.994522i	$0.533333\pi$
$152$		0			0
$153$		0			0
$154$	−1.11841	−	1.58881i	−1.11841	−	1.58881i
$155$		0			0
$156$		0			0
$157$		0			0		0.907359	−	0.420357i	$-0.138095\pi$
$157$		0			0		−0.907359	+	0.420357i	$0.861905\pi$
$158$	−3.76120	+	0.624589i	−3.76120	+	0.624589i
$159$		0			0
$160$		0			0
$161$	1.57577	−	0.141822i	1.57577	−	0.141822i
$162$	−1.79785	−	0.736828i	−1.79785	−	0.736828i
$163$	0.410551	−	1.20205i	0.410551	−	1.20205i	−0.525684	−	0.850680i	$-0.676190\pi$
$163$	0.410551	−	1.20205i	0.410551	−	1.20205i	0.936235	−	0.351375i	$-0.114286\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.0299155	−	0.999552i	$-0.490476\pi$
$167$		0			0		−0.0299155	+	0.999552i	$0.509524\pi$
$168$		0			0
$169$	0.447313	+	0.894377i	0.447313	+	0.894377i
$170$		0			0
$171$		0			0
$172$	0.936149	+	2.61251i	0.936149	+	2.61251i
$173$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$173$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$174$		0			0
$175$	0.988831	−	0.149042i	0.988831	−	0.149042i
$176$	2.16305	+	3.27687i	2.16305	+	3.27687i
$177$		0			0
$178$		0			0
$179$	−0.399139	−	1.87780i	−0.399139	−	1.87780i	−0.473869	−	0.880596i	$-0.657143\pi$
$179$	−0.399139	−	1.87780i	−0.399139	−	1.87780i	0.0747301	−	0.997204i	$-0.476190\pi$
$180$		0			0
$181$		0			0		0.599822	−	0.800134i	$-0.295238\pi$
$181$		0			0		−0.599822	+	0.800134i	$0.704762\pi$
$182$		0			0
$183$		0			0
$184$	−5.44724	+	0.326351i	−5.44724	+	0.326351i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.532014	−	0.00795951i	0.532014	−	0.00795951i	0.251587	−	0.967835i	$-0.419048\pi$
$191$	0.532014	−	0.00795951i	0.532014	−	0.00795951i	0.280427	+	0.959875i	$0.409524\pi$
$192$		0			0
$193$	0.0635265	−	0.230183i	0.0635265	−	0.230183i	−0.925304	−	0.379225i	$-0.876190\pi$
$193$	0.0635265	−	0.230183i	0.0635265	−	0.230183i	0.988831	+	0.149042i	$0.0476190\pi$
$194$		0			0
$195$		0			0
$196$	−1.66461	−	2.22051i	−1.66461	−	2.22051i
$197$	0.111340	+	0.0436978i	0.111340	+	0.0436978i	0.420357	−	0.907359i	$-0.361905\pi$
$197$	0.111340	+	0.0436978i	0.111340	+	0.0436978i	−0.309017	+	0.951057i	$0.600000\pi$
$198$	1.02139	−	1.65285i	1.02139	−	1.65285i
$199$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$199$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$200$	−3.42445	+	0.411805i	−3.42445	+	0.411805i
$201$		0			0
$202$		0			0
$203$	−1.01096	−	0.645829i	−1.01096	−	0.645829i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.749728	+	1.39323i	0.749728	+	1.39323i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.686543	+	1.60625i	−0.686543	+	1.60625i	0.104528	+	0.994522i	$0.466667\pi$
$211$	−0.686543	+	1.60625i	−0.686543	+	1.60625i	−0.791071	+	0.611724i	$0.790476\pi$
$212$	−0.430863	+	2.59460i	−0.430863	+	2.59460i
$213$		0			0
$214$	−0.204746	−	0.281809i	−0.204746	−	0.281809i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−0.372170	+	0.717113i	−0.372170	+	0.717113i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.722795	−	0.691063i	$-0.757143\pi$
$223$		0			0		0.722795	+	0.691063i	$0.242857\pi$
$224$	2.40597	+	3.41791i	2.40597	+	3.41791i
$225$	0.525684	+	0.850680i	0.525684	+	0.850680i
$226$	−3.45831	+	1.47815i	−3.45831	+	1.47815i
$227$		0			0		0.772417	−	0.635116i	$-0.219048\pi$
$227$		0			0		−0.772417	+	0.635116i	$0.780952\pi$
$228$		0			0
$229$		0			0		−0.712376	−	0.701798i	$-0.752381\pi$
$229$		0			0		0.712376	+	0.701798i	$0.247619\pi$
$230$		0			0
$231$		0			0
$232$	3.41874	+	2.33086i	3.41874	+	2.33086i
$233$	0.842721	−	0.538351i	0.842721	−	0.538351i	−0.0448648	−	0.998993i	$-0.514286\pi$
$233$	0.842721	−	0.538351i	0.842721	−	0.538351i	0.887586	+	0.460642i	$0.152381\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.39124	+	0.979332i	1.39124	+	0.979332i	0.998210	+	0.0598042i	$0.0190476\pi$
$239$	1.39124	+	0.979332i	1.39124	+	0.979332i	0.393025	+	0.919528i	$0.371429\pi$
$240$		0			0
$241$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$241$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$242$	1.46320	+	1.27836i	1.46320	+	1.27836i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$251$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$252$	1.38759	−	2.40337i	1.38759	−	2.40337i
$253$	−1.49722	+	0.511364i	−1.49722	+	0.511364i
$254$	2.81543	−	0.642603i	2.81543	−	0.642603i
$255$		0			0
$256$	−1.93927	−	2.93788i	−1.93927	−	2.93788i
$257$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$257$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$258$		0			0
$259$	1.16493	+	1.60339i	1.16493	+	1.60339i
$260$		0			0
$261$	0.196523	−	1.18344i	0.196523	−	1.18344i
$262$		0			0
$263$	−1.64066	+	1.11858i	−1.64066	+	1.11858i	−0.753071	+	0.657939i	$0.771429\pi$
$263$	−1.64066	+	1.11858i	−1.64066	+	1.11858i	−0.887586	+	0.460642i	$0.847619\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−4.54404	+	1.10892i	−4.54404	+	1.10892i
$269$		0			0		−0.393025	−	0.919528i	$-0.628571\pi$
$269$		0			0		0.393025	+	0.919528i	$0.371429\pi$
$270$		0			0
$271$		0			0		−0.379225	−	0.925304i	$-0.623810\pi$
$271$		0			0		0.379225	+	0.925304i	$0.376190\pi$
$272$		0			0
$273$		0			0
$274$	1.50797	+	3.13133i	1.50797	+	3.13133i
$275$	−0.925304	+	0.379225i	−0.925304	+	0.379225i
$276$		0			0
$277$	1.17343	+	1.56530i	1.17343	+	1.56530i	0.753071	+	0.657939i	$0.228571\pi$
$277$	1.17343	+	1.56530i	1.17343	+	1.56530i	0.420357	+	0.907359i	$0.361905\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.0771787	−	0.641795i	0.0771787	−	0.641795i	−0.900969	−	0.433884i	$-0.857143\pi$
$281$	0.0771787	−	0.641795i	0.0771787	−	0.641795i	0.978148	−	0.207912i	$-0.0666667\pi$
$282$		0			0
$283$		0			0		0.635116	−	0.772417i	$-0.280952\pi$
$283$		0			0		−0.635116	+	0.772417i	$0.719048\pi$
$284$	−2.12521	+	0.761532i	−2.12521	+	0.761532i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−2.19726	+	3.55568i	−2.19726	+	3.55568i
$289$	−0.998210	+	0.0598042i	−0.998210	+	0.0598042i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.990950	−	0.134233i	$-0.957143\pi$
$293$		0			0		0.990950	+	0.134233i	$0.0428571\pi$
$294$		0			0
$295$		0			0
$296$	−3.85075	−	5.64802i	−3.85075	−	5.64802i
$297$		0			0
$298$	−2.81679	+	0.424563i	−2.81679	+	0.424563i
$299$		0			0
$300$		0			0
$301$	0.599822	+	0.800134i	0.599822	+	0.800134i
$302$	1.40627	−	1.02171i	1.40627	−	1.02171i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$307$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$308$	2.14359	+	1.76256i	2.14359	+	1.76256i
$309$		0			0
$310$		0			0
$311$		0			0		−0.925304	−	0.379225i	$-0.876190\pi$
$311$		0			0		0.925304	+	0.379225i	$0.123810\pi$
$312$		0			0
$313$		0			0		0.538351	−	0.842721i	$-0.319048\pi$
$313$		0			0		−0.538351	+	0.842721i	$0.680952\pi$
$314$		0			0
$315$		0			0
$316$	4.94121	−	2.28914i	4.94121	−	2.28914i
$317$	0.380300	+	0.0690144i	0.380300	+	0.0690144i	0.365341	−	0.930874i	$-0.380952\pi$
$317$	0.380300	+	0.0690144i	0.380300	+	0.0690144i	0.0149594	+	0.999888i	$0.495238\pi$
$318$		0			0
$319$	1.13526	+	0.387736i	1.13526	+	0.387736i
$320$		0			0
$321$		0			0
$322$	−2.87805	+	1.08015i	−2.87805	+	1.08015i
$323$		0			0
$324$	2.75532	+	0.331339i	2.75532	+	0.331339i
$325$		0			0
$326$	−0.147599	+	2.46362i	−0.147599	+	2.46362i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1.66448	−	0.124735i	1.66448	−	0.124735i	0.791071	−	0.611724i	$-0.209524\pi$
$331$	1.66448	−	0.124735i	1.66448	−	0.124735i	0.873408	+	0.486989i	$0.161905\pi$
$332$		0			0
$333$	−1.01651	+	1.70136i	−1.01651	+	1.70136i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.352370	−	0.317275i	−0.352370	−	0.317275i	0.473869	−	0.880596i	$-0.342857\pi$
$337$	−0.352370	−	0.317275i	−0.352370	−	0.317275i	−0.826239	+	0.563320i	$0.809524\pi$
$338$	−1.30011	−	1.44392i	−1.30011	−	1.44392i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$344$	−1.98537	−	2.82041i	−1.98537	−	2.82041i
$345$		0			0
$346$		0			0
$347$	−1.01496	+	0.999888i	−1.01496	+	0.999888i	−0.0149594	+	0.999888i	$0.504762\pi$
$347$	−1.01496	+	0.999888i	−1.01496	+	0.999888i	−1.00000			$\pi$
$348$		0			0
$349$		0			0		−0.280427	−	0.959875i	$-0.590476\pi$
$349$		0			0		0.280427	+	0.959875i	$0.409524\pi$
$350$	−1.77500	+	0.790281i	−1.77500	+	0.790281i
$351$		0			0
$352$	−3.14769	−	2.75006i	−3.14769	−	2.75006i
$353$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$353$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	1.71821	+	3.31073i	1.71821	+	3.31073i
$359$	−0.703986	+	1.26259i	−0.703986	+	1.26259i	0.251587	+	0.967835i	$0.419048\pi$
$359$	−0.703986	+	1.26259i	−0.703986	+	1.26259i	−0.955573	+	0.294755i	$0.904762\pi$
$360$		0			0
$361$	−0.337330	−	0.941386i	−0.337330	−	0.941386i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.420357	−	0.907359i	$-0.361905\pi$
$367$		0			0		−0.420357	+	0.907359i	$0.638095\pi$
$368$	5.87871	−	2.00782i	5.87871	−	2.00782i
$369$		0			0
$370$		0			0
$371$	0.127218	+	0.939160i	0.127218	+	0.939160i
$372$		0			0
$373$	1.63402	+	0.246289i	1.63402	+	0.246289i	0.900969	−	0.433884i	$-0.142857\pi$
$373$	1.63402	+	0.246289i	1.63402	+	0.246289i	0.733052	+	0.680173i	$0.238095\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.82087	−	0.330439i	1.82087	−	0.330439i	0.842721	−	0.538351i	$-0.180952\pi$
$379$	1.82087	−	0.330439i	1.82087	−	0.330439i	0.978148	+	0.207912i	$0.0666667\pi$
$380$		0			0
$381$		0			0
$382$	−0.992327	+	0.289908i	−0.992327	+	0.289908i
$383$		0			0		−0.919528	−	0.393025i	$-0.871429\pi$
$383$		0			0		0.919528	+	0.393025i	$0.128571\pi$
$384$		0			0
$385$		0			0
$386$			0.463961i			0.463961i
$387$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$388$		0			0
$389$	0.693256	−	1.84717i	0.693256	−	1.84717i	0.193256	−	0.981148i	$-0.438095\pi$
$389$	0.693256	−	1.84717i	0.693256	−	1.84717i	0.500000	−	0.866025i	$-0.333333\pi$
$390$		0			0
$391$		0			0
$392$	2.72850	+	2.10991i	2.72850	+	2.10991i
$393$		0			0
$394$	−0.231123	−	0.0242921i	−0.231123	−	0.0242921i
$395$		0			0
$396$	−0.778234	+	2.66382i	−0.778234	+	2.66382i
$397$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$397$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$398$		0			0
$399$		0			0
$400$	3.63312	−	1.48899i	3.63312	−	1.48899i
$401$	1.77199	−	0.919636i	1.77199	−	0.919636i	0.858449	−	0.512899i	$-0.171429\pi$
$401$	1.77199	−	0.919636i	1.77199	−	0.919636i	0.913545	−	0.406737i	$-0.133333\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	2.22733	+	0.687040i	2.22733	+	0.687040i
$407$	−1.51185	−	1.28150i	−1.51185	−	1.28150i
$408$		0			0
$409$		0			0		−0.0448648	−	0.998993i	$-0.514286\pi$
$409$		0			0		0.0448648	+	0.998993i	$0.485714\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−2.12438	−	2.22192i	−2.12438	−	2.22192i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$419$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$420$		0			0
$421$	−1.02568	−	0.0153453i	−1.02568	−	0.0153453i	−0.500000	−	0.866025i	$-0.666667\pi$
$421$	−1.02568	−	0.0153453i	−1.02568	−	0.0153453i	−0.525684	+	0.850680i	$0.676190\pi$
$422$	0.455592	−	3.36331i	0.455592	−	3.36331i
$423$		0			0
$424$	−0.341689	−	3.25096i	−0.341689	−	3.25096i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.388984	+	0.310204i	0.388984	+	0.310204i
$429$		0			0
$430$		0			0
$431$	0.961287	−	1.32310i	0.961287	−	1.32310i	0.0149594	−	0.999888i	$-0.495238\pi$
$431$	0.961287	−	1.32310i	0.961287	−	1.32310i	0.946327	−	0.323210i	$-0.104762\pi$
$432$		0			0
$433$		0			0		0.894377	−	0.447313i	$-0.147619\pi$
$433$		0			0		−0.894377	+	0.447313i	$0.852381\pi$
$434$		0			0
$435$		0			0
$436$	0.239926	−	1.12876i	0.239926	−	1.12876i
$437$		0			0
$438$		0			0
$439$		0			0		−0.294755	−	0.955573i	$-0.595238\pi$
$439$		0			0		0.294755	+	0.955573i	$0.404762\pi$
$440$		0			0
$441$	0.222521	−	0.974928i	0.222521	−	0.974928i
$442$		0			0
$443$	0.203097	+	0.0495633i	0.203097	+	0.0495633i	0.337330	−	0.941386i	$-0.390476\pi$
$443$	0.203097	+	0.0495633i	0.203097	+	0.0495633i	−0.134233	+	0.990950i	$0.542857\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−3.24019	−	2.66423i	−3.24019	−	2.66423i
$449$	−0.779312	+	0.584213i	−0.779312	+	0.584213i	−0.913545	−	0.406737i	$-0.866667\pi$
$449$	−0.779312	+	0.584213i	−0.779312	+	0.584213i	0.134233	+	0.990950i	$0.457143\pi$
$450$	−1.42431	−	1.32156i	−1.42431	−	1.32156i
$451$		0			0
$452$	4.19985	−	3.34927i	4.19985	−	3.34927i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.943922	−	1.75410i	0.943922	−	1.75410i	0.393025	−	0.919528i	$-0.371429\pi$
$457$	0.943922	−	1.75410i	0.943922	−	1.75410i	0.550897	−	0.834573i	$-0.314286\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.930874	−	0.365341i	$-0.119048\pi$
$461$		0			0		−0.930874	+	0.365341i	$0.880952\pi$
$462$		0			0
$463$	−1.59579	−	0.119588i	−1.59579	−	0.119588i	−0.753071	−	0.657939i	$-0.771429\pi$
$463$	−1.59579	−	0.119588i	−1.59579	−	0.119588i	−0.842721	+	0.538351i	$0.819048\pi$
$464$	−4.45747	−	1.52241i	−4.45747	−	1.52241i
$465$		0			0
$466$	−1.30011	+	1.44392i	−1.30011	+	1.44392i
$467$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$467$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$468$		0			0
$469$	−1.44687	+	0.864462i	−1.44687	+	0.864462i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.772417	−	0.635116i	−0.772417	−	0.635116i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.813584	+	0.486094i	−0.813584	+	0.486094i
$478$	−3.11195	−	1.11511i	−3.11195	−	1.11511i
$479$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$479$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−2.50034	−	1.20410i	−2.50034	−	1.20410i
$485$		0			0
$486$		0			0
$487$	0.846609	−	1.69275i	0.846609	−	1.69275i	0.134233	−	0.990950i	$-0.457143\pi$
$487$	0.846609	−	1.69275i	0.846609	−	1.69275i	0.712376	−	0.701798i	$-0.247619\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.90772	−	0.114294i	−1.90772	−	0.114294i	−0.936235	−	0.351375i	$-0.885714\pi$
$491$	−1.90772	−	0.114294i	−1.90772	−	0.114294i	−0.971490	+	0.237080i	$0.923810\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.650887	+	0.487939i	−0.650887	+	0.487939i
$498$		0			0
$499$	−1.26308	−	0.369008i	−1.26308	−	0.369008i	−0.420357	−	0.907359i	$-0.638095\pi$
$499$	−1.26308	−	0.369008i	−1.26308	−	0.369008i	−0.842721	+	0.538351i	$0.819048\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.971490	−	0.237080i	$-0.923810\pi$
$503$		0			0		0.971490	+	0.237080i	$0.0761905\pi$
$504$	−0.867754	+	3.33818i	−0.867754	+	3.33818i
$505$		0			0
$506$	2.53992	−	1.73169i	2.53992	−	1.73169i
$507$		0			0
$508$	−3.63220	+	1.95457i	−3.63220	+	1.95457i
$509$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$509$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$510$		0			0
$511$		0			0
$512$	2.16053	+	1.88760i	2.16053	+	1.88760i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−3.01067	−	2.40093i	−3.01067	−	2.40093i
$519$		0			0
$520$		0			0
$521$		0			0		0.611724	−	0.791071i	$-0.290476\pi$
$521$		0			0		−0.611724	+	0.791071i	$0.709524\pi$
$522$	0.243644	+	2.31812i	0.243644	+	2.31812i
$523$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$523$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$524$		0			0
$525$		0			0
$526$	2.49469	−	2.94312i	2.49469	−	2.94312i
$527$		0			0
$528$		0			0
$529$	0.112332	+	1.49897i	0.112332	+	1.49897i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	5.07738	−	2.83101i	5.07738	−	2.83101i
$537$		0			0
$538$		0			0
$539$	0.925304	+	0.379225i	0.925304	+	0.379225i
$540$		0			0
$541$	0.552239	+	0.864462i	0.552239	+	0.864462i	0.999552	−	0.0299155i	$-0.00952381\pi$
$541$	0.552239	+	0.864462i	0.552239	+	0.864462i	−0.447313	+	0.894377i	$0.647619\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.119274	−	1.99084i	−0.119274	−	1.99084i	−0.134233	−	0.990950i	$-0.542857\pi$
$547$	−0.119274	−	1.99084i	−0.119274	−	1.99084i	0.0149594	−	0.999888i	$-0.495238\pi$
$548$	−3.26607	−	3.73832i	−3.26607	−	3.73832i
$549$		0			0
$550$	1.53704	−	1.18857i	1.53704	−	1.18857i
$551$		0			0
$552$		0			0
$553$	1.45827	−	1.31303i	1.45827	−	1.31303i
$554$	−3.00689	−	2.32519i	−3.00689	−	2.32519i
$555$		0			0
$556$		0			0
$557$	−0.646198	+	1.72179i	−0.646198	+	1.72179i	0.0448648	+	0.998993i	$0.485714\pi$
$557$	−0.646198	+	1.72179i	−0.646198	+	1.72179i	−0.691063	+	0.722795i	$0.742857\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.187194	+	1.24195i	0.187194	+	1.24195i
$563$		0			0		−0.919528	−	0.393025i	$-0.871429\pi$
$563$		0			0		0.919528	+	0.393025i	$0.128571\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.983930	−	0.178557i	0.983930	−	0.178557i
$568$	2.29433	−	1.61505i	2.29433	−	1.61505i
$569$	−0.427251	+	1.04248i	−0.427251	+	1.04248i	0.550897	+	0.834573i	$0.314286\pi$
$569$	−0.427251	+	1.04248i	−0.427251	+	1.04248i	−0.978148	+	0.207912i	$0.933333\pi$
$570$		0			0
$571$	−0.627253	−	1.59821i	−0.627253	−	1.59821i	−0.791071	−	0.611724i	$-0.790476\pi$
$571$	−0.627253	−	1.59821i	−0.627253	−	1.59821i	0.163818	−	0.986491i	$-0.447619\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.212376	+	1.56782i	0.212376	+	1.56782i
$576$	1.17636	−	4.02655i	1.17636	−	4.02655i
$577$		0			0		0.967835	−	0.251587i	$-0.0809524\pi$
$577$		0			0		−0.967835	+	0.251587i	$0.919048\pi$
$578$	1.83870	−	0.627990i	1.83870	−	0.627990i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.346247	−	0.882224i	−0.346247	−	0.882224i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.486989	−	0.873408i	$-0.338095\pi$
$587$		0			0		−0.486989	+	0.873408i	$0.661905\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	5.93614	+	5.03167i	5.93614	+	5.03167i
$593$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$593$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$594$		0			0
$595$		0			0
$596$	3.71693	−	1.65489i	3.71693	−	1.65489i
$597$		0			0
$598$		0			0
$599$	−1.22308	+	1.20492i	−1.22308	+	1.20492i	−0.251587	+	0.967835i	$0.580952\pi$
$599$	−1.22308	+	1.20492i	−1.22308	+	1.20492i	−0.971490	+	0.237080i	$0.923810\pi$
$600$		0			0
$601$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$601$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$602$	−1.53704	−	1.18857i	−1.53704	−	1.18857i
$603$	−1.36355	−	0.990678i	−1.36355	−	0.990678i
$604$	−1.54796	+	1.94109i	−1.54796	+	1.94109i
$605$		0			0
$606$		0			0
$607$		0			0		−0.999552	−	0.0299155i	$-0.990476\pi$
$607$		0			0		0.999552	+	0.0299155i	$0.00952381\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.965673	−	1.61626i	0.965673	−	1.61626i	0.193256	−	0.981148i	$-0.438095\pi$
$613$	0.965673	−	1.61626i	0.965673	−	1.61626i	0.772417	−	0.635116i	$-0.219048\pi$
$614$		0			0
$615$		0			0
$616$	−3.15093	−	1.40288i	−3.15093	−	1.40288i
$617$	−0.770707	+	0.715112i	−0.770707	+	0.715112i	−0.963963	−	0.266037i	$-0.914286\pi$
$617$	−0.770707	+	0.715112i	−0.770707	+	0.715112i	0.193256	+	0.981148i	$0.438095\pi$
$618$		0			0
$619$		0			0		0.791071	−	0.611724i	$-0.209524\pi$
$619$		0			0		−0.791071	+	0.611724i	$0.790476\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.193256	+	0.981148i	0.193256	+	0.981148i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−1.42606	+	0.236813i	−1.42606	+	0.236813i	−0.826239	−	0.563320i	$-0.809524\pi$
$631$	−1.42606	+	0.236813i	−1.42606	+	0.236813i	−0.599822	+	0.800134i	$0.704762\pi$
$632$	−5.16299	+	4.37632i	−5.16299	+	4.37632i
$633$		0			0
$634$	−0.747962	+	0.0673178i	−0.747962	+	0.0673178i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−2.32671	−	0.139397i	−2.32671	−	0.139397i
$639$	−0.704489	−	0.406737i	−0.704489	−	0.406737i
$640$		0			0
$641$	0.164852	−	1.83165i	0.164852	−	1.83165i	−0.309017	−	0.951057i	$-0.600000\pi$
$641$	0.164852	−	1.83165i	0.164852	−	1.83165i	0.473869	−	0.880596i	$-0.342857\pi$
$642$		0			0
$643$		0			0		0.0448648	−	0.998993i	$-0.485714\pi$
$643$		0			0		−0.0448648	+	0.998993i	$0.514286\pi$
$644$	3.55216	−	2.58080i	3.55216	−	2.58080i
$645$		0			0
$646$		0			0
$647$		0			0		−0.266037	−	0.963963i	$-0.585714\pi$
$647$		0			0		0.266037	+	0.963963i	$0.414286\pi$
$648$	−3.41060	+	0.514065i	−3.41060	+	0.514065i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.732912	−	3.44808i	−0.732912	−	3.44808i
$653$	−1.21238	−	0.164228i	−1.21238	−	0.164228i	−0.500000	−	0.866025i	$-0.666667\pi$
$653$	−1.21238	−	0.164228i	−1.21238	−	0.164228i	−0.712376	+	0.701798i	$0.752381\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	0.202749	−	1.34515i	0.202749	−	1.34515i	−0.623490	−	0.781831i	$-0.714286\pi$
$659$	0.202749	−	1.34515i	0.202749	−	1.34515i	0.826239	−	0.563320i	$-0.190476\pi$
$660$		0			0
$661$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$661$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$662$	−3.05303	+	1.09400i	−3.05303	+	1.09400i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	1.02445	−	3.71202i	1.02445	−	3.71202i
$667$	1.04561	−	1.58403i	1.04561	−	1.58403i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.0890878	+	0.0107132i	−0.0890878	+	0.0107132i	−0.163818	−	0.986491i	$-0.552381\pi$
$673$	−0.0890878	+	0.0107132i	−0.0890878	+	0.0107132i	0.0747301	+	0.997204i	$0.476190\pi$
$674$	0.823976	+	0.412103i	0.823976	+	0.412103i
$675$		0			0
$676$	2.33870	+	1.49402i	2.33870	+	1.49402i
$677$		0			0		−0.393025	−	0.919528i	$-0.628571\pi$
$677$		0			0		0.393025	+	0.919528i	$0.371429\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.10572	−	0.753869i	1.10572	−	0.753869i	0.134233	−	0.990950i	$-0.457143\pi$
$683$	1.10572	−	0.753869i	1.10572	−	0.753869i	0.971490	+	0.237080i	$0.0761905\pi$
$684$		0			0
$685$		0			0
$686$	1.81909	+	0.682714i	1.81909	+	0.682714i
$687$		0			0
$688$	3.03282	+	2.49372i	3.03282	+	2.49372i
$689$		0			0
$690$		0			0
$691$		0			0		0.460642	−	0.887586i	$-0.347619\pi$
$691$		0			0		−0.460642	+	0.887586i	$0.652381\pi$
$692$		0			0
$693$	0.0149594	+	0.999888i	0.0149594	+	0.999888i
$694$	1.38413	−	2.39739i	1.38413	−	2.39739i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	2.14359	−	1.76256i	2.14359	−	1.76256i
$701$	0.430234	−	1.76298i	0.430234	−	1.76298i	−0.193256	−	0.981148i	$-0.561905\pi$
$701$	0.430234	−	1.76298i	0.430234	−	1.76298i	0.623490	−	0.781831i	$-0.285714\pi$
$702$		0			0
$703$		0			0
$704$	3.77945	+	1.82009i	3.77945	+	1.82009i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−1.92706	−	0.531836i	−1.92706	−	0.531836i	−0.971490	−	0.237080i	$-0.923810\pi$
$709$	−1.92706	−	0.531836i	−1.92706	−	0.531836i	−0.955573	−	0.294755i	$-0.904762\pi$
$710$		0			0
$711$	1.78051	+	0.824866i	1.78051	+	0.824866i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−3.62371	−	3.90543i	−3.62371	−	3.90543i
$717$		0			0
$718$	0.665900	−	2.72867i	0.665900	−	2.72867i
$719$		0			0		0.772417	−	0.635116i	$-0.219048\pi$
$719$		0			0		−0.772417	+	0.635116i	$0.780952\pi$
$720$		0			0
$721$		0			0
$722$	1.11841	+	1.58881i	1.11841	+	1.58881i
$723$		0			0
$724$		0			0
$725$	0.599822	−	1.03892i	0.599822	−	1.03892i
$726$		0			0
$727$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$727$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$728$		0			0
$729$	0.550897	+	0.834573i	0.550897	+	0.834573i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.936235	−	0.351375i	$-0.885714\pi$
$733$		0			0		0.936235	+	0.351375i	$0.114286\pi$
$734$		0			0
$735$		0			0
$736$	−5.46395	+	3.72526i	−5.46395	+	3.72526i
$737$	1.20067	−	1.18284i	1.20067	−	1.18284i
$738$		0			0
$739$	0.932507	+	1.73289i	0.932507	+	1.73289i	0.623490	+	0.781831i	$0.285714\pi$
$739$	0.932507	+	1.73289i	0.932507	+	1.73289i	0.309017	+	0.951057i	$0.400000\pi$
$740$		0			0
$741$		0			0
$742$	−0.723730	−	1.69325i	−0.723730	−	1.69325i
$743$	0.568550	+	0.363204i	0.568550	+	0.363204i	0.791071	−	0.611724i	$-0.209524\pi$
$743$	0.568550	+	0.363204i	0.568550	+	0.363204i	−0.222521	+	0.974928i	$0.571429\pi$
$744$		0			0
$745$		0			0
$746$	−3.18776	+	0.383343i	−3.18776	+	0.383343i
$747$		0			0
$748$		0			0
$749$	0.166886	+	0.0654978i	0.166886	+	0.0654978i
$750$		0			0
$751$	0.973869	+	1.74662i	0.973869	+	1.74662i	0.500000	+	0.866025i	$0.333333\pi$
$751$	0.973869	+	1.74662i	0.973869	+	1.74662i	0.473869	+	0.880596i	$0.342857\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1.87246	−	0.670964i	1.87246	−	0.670964i	0.900969	−	0.433884i	$-0.142857\pi$
$757$	1.87246	−	0.670964i	1.87246	−	0.670964i	0.971490	−	0.237080i	$-0.0761905\pi$
$758$	−3.23961	+	1.56011i	−3.23961	+	1.56011i
$759$		0			0
$760$		0			0
$761$		0			0		0.525684	−	0.850680i	$-0.323810\pi$
$761$		0			0		−0.525684	+	0.850680i	$0.676190\pi$
$762$		0			0
$763$	−0.0372741	−	0.414149i	−0.0372741	−	0.414149i
$764$	1.25611	−	0.776222i	1.25611	−	0.776222i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		−0.563320	−	0.826239i	$-0.690476\pi$
$769$		0			0		0.563320	+	0.826239i	$0.309524\pi$
$770$		0			0
$771$		0			0
$772$	−0.176297	−	0.638798i	−0.176297	−	0.638798i
$773$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$773$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$774$	0.488828	−	1.88048i	0.488828	−	1.88048i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.343629	+	3.81803i	−0.343629	+	3.81803i
$779$		0			0
$780$		0			0
$781$	0.516650	−	0.628341i	0.516650	−	0.628341i
$782$		0			0
$783$		0			0
$784$	−3.63312	−	1.48899i	−3.63312	−	1.48899i
$785$		0			0
$786$		0			0
$787$		0			0		0.762830	−	0.646600i	$-0.223810\pi$
$787$		0			0		−0.762830	+	0.646600i	$0.776190\pi$
$788$	0.327449	−	0.0543767i	0.327449	−	0.0543767i
$789$		0			0
$790$		0			0
$791$	1.09040	−	1.59933i	1.09040	−	1.59933i
$792$	0.0515968	−	3.44874i	0.0515968	−	3.44874i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.992847	−	0.119394i	$-0.961905\pi$
$797$		0			0		0.992847	+	0.119394i	$0.0380952\pi$
$798$		0			0
$799$		0			0
$800$	−3.30652	+	2.55689i	−3.30652	+	2.55689i
$801$		0			0
$802$	−2.84351	+	2.63839i	−2.84351	+	2.63839i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.352289	−	1.94127i	−0.352289	−	1.94127i	−0.337330	−	0.941386i	$-0.609524\pi$
$809$	−0.352289	−	1.94127i	−0.352289	−	1.94127i	−0.0149594	−	0.999888i	$-0.504762\pi$
$810$		0			0
$811$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$811$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$812$	−3.32773	−	0.0995951i	−3.32773	−	0.0995951i
$813$		0			0
$814$	3.49405	+	1.61871i	3.49405	+	1.61871i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.302359	+	0.506064i	0.302359	+	0.506064i	0.971490	−	0.237080i	$-0.0761905\pi$
$821$	0.302359	+	0.506064i	0.302359	+	0.506064i	−0.669131	+	0.743145i	$0.733333\pi$
$822$		0			0
$823$	−1.30158	+	0.579499i	−1.30158	+	0.579499i	−0.936235	−	0.351375i	$-0.885714\pi$
$823$	−1.30158	+	0.579499i	−1.30158	+	0.579499i	−0.365341	+	0.930874i	$0.619048\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.227388	−	0.192741i	−0.227388	−	0.192741i	0.525684	−	0.850680i	$-0.323810\pi$
$827$	−0.227388	−	0.192741i	−0.227388	−	0.192741i	−0.753071	+	0.657939i	$0.771429\pi$
$828$	3.76920	+	2.25199i	3.76920	+	2.25199i
$829$		0			0		−0.635116	−	0.772417i	$-0.719048\pi$
$829$		0			0		0.635116	+	0.772417i	$0.280952\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.351375	−	0.936235i	$-0.614286\pi$
$839$		0			0		0.351375	+	0.936235i	$0.385714\pi$
$840$		0			0
$841$	−0.415575	+	0.141936i	−0.415575	+	0.141936i
$842$	1.92900	−	0.501439i	1.92900	−	0.501439i
$843$		0			0
$844$	0.650725	+	4.80384i	0.650725	+	4.80384i
$845$		0			0
$846$		0			0
$847$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$848$	1.35951	+	3.46397i	1.35951	+	3.46397i
$849$		0			0
$850$		0			0
$851$	−2.56408	+	1.80493i	−2.56408	+	1.80493i
$852$		0			0
$853$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$853$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$854$		0			0
$855$		0			0
$856$	−0.568594	−	0.243029i	−0.568594	−	0.243029i
$857$		0			0		−0.149042	−	0.988831i	$-0.547619\pi$
$857$		0			0		0.149042	+	0.988831i	$0.452381\pi$
$858$		0			0
$859$		0			0			−	1.00000i	$-0.5\pi$
$859$		0			0				1.00000i	$0.5\pi$
$860$		0			0
$861$		0			0
$862$	−1.11654	+	2.97500i	−1.11654	+	2.97500i
$863$	−0.954688	−	0.969078i	−0.954688	−	0.969078i	0.0448648	−	0.998993i	$-0.485714\pi$
$863$	−0.954688	−	0.969078i	−0.954688	−	0.969078i	−0.999552	+	0.0299155i	$0.990476\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.10540	+	1.62133i	−1.10540	+	1.62133i
$870$		0			0
$871$		0			0
$872$	0.0857727	+	1.43166i	0.0857727	+	1.43166i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.563572	−	0.728802i	−0.563572	−	0.728802i	0.420357	−	0.907359i	$-0.361905\pi$
$877$	−0.563572	−	0.728802i	−0.563572	−	0.728802i	−0.983930	+	0.178557i	$0.942857\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$881$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$882$	0.0871715	+	1.94102i	0.0871715	+	1.94102i
$883$	1.57383	−	0.877524i	1.57383	−	0.877524i	0.575617	−	0.817719i	$-0.304762\pi$
$883$	1.57383	−	0.877524i	1.57383	−	0.877524i	0.998210	−	0.0598042i	$-0.0190476\pi$
$884$		0			0
$885$		0			0
$886$	−0.406012	+	0.0121515i	−0.406012	+	0.0121515i
$887$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$887$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$888$		0			0
$889$	−1.04307	+	1.05880i	−1.04307	+	1.05880i
$890$		0			0
$891$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	3.62746	+	1.61505i	3.62746	+	1.61505i
$897$		0			0
$898$	1.15764	−	1.49704i	1.15764	−	1.49704i
$899$		0			0
$900$	2.46320	+	1.27836i	2.46320	+	1.27836i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−3.92427	+	5.40129i	−3.92427	+	5.40129i
$905$		0			0
$906$		0			0
$907$	−1.49537	−	1.30646i	−1.49537	−	1.30646i	−0.826239	−	0.563320i	$-0.809524\pi$
$907$	−1.49537	−	1.30646i	−1.49537	−	1.30646i	−0.669131	−	0.743145i	$-0.733333\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1.63945	+	0.882224i	−1.63945	+	0.882224i	−0.646600	+	0.762830i	$0.723810\pi$
$911$	−1.63945	+	0.882224i	−1.63945	+	0.882224i	−0.992847	+	0.119394i	$0.961905\pi$
$912$		0			0
$913$		0			0
$914$	−0.861226	+	3.77328i	−0.861226	+	3.77328i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−0.948138	−	0.510215i	−0.948138	−	0.510215i	−0.0747301	−	0.997204i	$-0.523810\pi$
$919$	−0.948138	−	0.510215i	−0.948138	−	0.510215i	−0.873408	+	0.486989i	$0.838095\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−1.54951	+	1.23569i	−1.54951	+	1.23569i
$926$	3.05067	−	0.600888i	3.05067	−	0.600888i
$927$		0			0
$928$	5.00530	+	0.299875i	5.00530	+	0.299875i
$929$		0			0		−0.0299155	−	0.999552i	$-0.509524\pi$
$929$		0			0		0.0299155	+	0.999552i	$0.490476\pi$
$930$		0			0
$931$		0			0
$932$	1.24137	−	2.48205i	1.24137	−	2.48205i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.946327	−	0.323210i	$-0.895238\pi$
$937$		0			0		0.946327	+	0.323210i	$0.104762\pi$
$938$	2.26308	−	2.36699i	2.26308	−	2.36699i
$939$		0			0
$940$		0			0
$941$		0			0		−0.941386	−	0.337330i	$-0.890476\pi$
$941$		0			0		0.941386	+	0.337330i	$0.109524\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	1.77500	+	0.790281i	1.77500	+	0.790281i
$947$	−1.97766			−1.97766			−0.988831	−	0.149042i	$-0.952381\pi$
$947$	−1.97766			−1.97766			−0.988831	+	0.149042i	$0.952381\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.737244	−	0.818792i	0.737244	−	0.818792i	−0.251587	−	0.967835i	$-0.580952\pi$
$953$	0.737244	−	0.818792i	0.737244	−	0.818792i	0.988831	+	0.149042i	$0.0476190\pi$
$954$	1.27255	−	1.33098i	1.27255	−	1.33098i
$955$		0			0
$956$	4.70836	+	0.352843i	4.70836	+	0.352843i
$957$		0			0
$958$		0			0
$959$	−1.52166	−	0.940319i	−1.52166	−	0.940319i
$960$		0			0
$961$	−0.873408	−	0.486989i	−0.873408	−	0.486989i
$962$		0			0
$963$	0.00536320	+	0.179198i	0.00536320	+	0.179198i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.592981	−	0.472886i	0.592981	−	0.472886i	−0.280427	−	0.959875i	$-0.590476\pi$
$967$	0.592981	−	0.472886i	0.592981	−	0.472886i	0.873408	+	0.486989i	$0.161905\pi$
$968$	3.39369	+	0.615865i	3.39369	+	0.615865i
$969$		0			0
$970$		0			0
$971$		0			0		−0.772417	−	0.635116i	$-0.780952\pi$
$971$		0			0		0.772417	+	0.635116i	$0.219048\pi$
$972$		0			0
$973$		0			0
$974$	−0.710677	+	3.60807i	−0.710677	+	3.60807i
$975$		0			0
$976$		0			0
$977$	−0.347724	+	1.33767i	−0.347724	+	1.33767i	0.525684	+	0.850680i	$0.323810\pi$
$977$	−0.347724	+	1.33767i	−0.347724	+	1.33767i	−0.873408	+	0.486989i	$0.838095\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.366172	−	0.197046i	0.366172	−	0.197046i
$982$	3.63217	−	0.772042i	3.63217	−	0.772042i
$983$		0			0		0.207912	−	0.978148i	$-0.433333\pi$
$983$		0			0		−0.207912	+	0.978148i	$0.566667\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1.27998	+	0.929960i	−1.27998	+	0.929960i
$990$		0			0
$991$	1.52446	+	1.21572i	1.52446	+	1.21572i	0.900969	+	0.433884i	$0.142857\pi$
$991$	1.52446	+	1.21572i	1.52446	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$992$		0			0
$993$		0			0
$994$	0.966868	−	1.25034i	0.966868	−	1.25034i
$995$		0			0
$996$		0			0
$997$		0			0		0.134233	−	0.990950i	$-0.457143\pi$
$997$		0			0		−0.134233	+	0.990950i	$0.542857\pi$
$998$	2.55644	+	0.0382471i	2.55644	+	0.0382471i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3311.1.gb.a.62.1	✓	48
7.6	odd	2	CM	3311.1.gb.a.62.1	✓	48
11.8	odd	10		3311.1.gb.b.965.1	yes	48
43.34	odd	42		3311.1.gb.b.2141.1	yes	48
77.41	even	10		3311.1.gb.b.965.1	yes	48
301.34	even	42		3311.1.gb.b.2141.1	yes	48
473.206	even	210	inner	3311.1.gb.a.3044.1	yes	48
3311.3044	odd	210	inner	3311.1.gb.a.3044.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3311.1.gb.a.62.1	✓	48	1.1	even	1	trivial
3311.1.gb.a.62.1	✓	48	7.6	odd	2	CM
3311.1.gb.a.3044.1	yes	48	473.206	even	210	inner
3311.1.gb.a.3044.1	yes	48	3311.3044	odd	210	inner
3311.1.gb.b.965.1	yes	48	11.8	odd	10
3311.1.gb.b.965.1	yes	48	77.41	even	10
3311.1.gb.b.2141.1	yes	48	43.34	odd	42
3311.1.gb.b.2141.1	yes	48	301.34	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:	\( N \)	\(=\)	\( 3311 = 7 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3311.gb (of order \(210\), degree \(48\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.87296 + 0.516904i) q^{2} +(2.38234 - 1.42338i) q^{4} +(0.669131 - 0.743145i) q^{7} +(-2.38356 + 2.49301i) q^{8} +(0.946327 + 0.323210i) q^{9} +O(q^{10})\)	\(q+(-1.87296 + 0.516904i) q^{2} +(2.38234 - 1.42338i) q^{4} +(0.669131 - 0.743145i) q^{7} +(-2.38356 + 2.49301i) q^{8} +(0.946327 + 0.323210i) q^{9} +(-0.473869 + 0.880596i) q^{11} +(-0.869121 + 1.73776i) q^{14} +(1.86060 - 3.45758i) q^{16} +(-1.93950 - 0.116198i) q^{18} +(0.432354 - 1.89427i) q^{22} +(1.15979 + 1.07613i) q^{23} +(0.772417 + 0.635116i) q^{25} +(0.536318 - 2.72286i) q^{28} +(-0.196523 - 1.18344i) q^{29} +(-0.930094 + 4.07501i) q^{32} +(2.71453 - 0.576991i) q^{36} +(-0.412060 + 1.93859i) q^{37} +(-0.193256 + 0.981148i) q^{43} +(0.124508 + 2.77238i) q^{44} +(-2.72850 - 1.41605i) q^{46} +(-0.104528 - 0.994522i) q^{49} +(-1.77500 - 0.790281i) q^{50} +(-0.612807 + 0.722962i) q^{53} +(0.257753 + 3.43948i) q^{56} +(0.979804 + 2.11495i) q^{58} +(0.873408 - 0.486989i) q^{63} +(-0.188202 - 4.19065i) q^{64} +(-1.61056 - 0.496793i) q^{67} +(-0.798138 - 0.157209i) q^{71} +(-3.06139 + 1.58881i) q^{72} +(-0.230293 - 3.84390i) q^{74} +(0.337330 + 0.941386i) q^{77} +(1.95155 + 0.205116i) q^{79} +(0.791071 + 0.611724i) q^{81} +(-0.145199 - 1.93755i) q^{86} +(-1.06584 - 3.28031i) q^{88} +(4.29477 + 0.912881i) q^{92} +(0.709850 + 1.80867i) q^{98} +(-0.733052 + 0.680173i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{2} + 6 q^{7} - 21 q^{8} + q^{9}+O(q^{10}) \) 48 * q - 2 * q^2 + 6 * q^7 - 21 * q^8 + q^9	\( 48 q - 2 q^{2} + 6 q^{7} - 21 q^{8} + q^{9} - 2 q^{11} - 9 q^{14} + 3 q^{16} - 6 q^{18} + 2 q^{22} - q^{23} + q^{25} - 10 q^{28} - q^{29} - 4 q^{32} - 7 q^{36} - 5 q^{37} + q^{43} + 23 q^{44} + 4 q^{46} + 6 q^{49} - q^{50} + 10 q^{53} - 15 q^{56} + 4 q^{58} + q^{63} - 21 q^{64} + q^{67} - 7 q^{71} - 4 q^{72} - 14 q^{74} + q^{77} + 2 q^{79} - q^{81} + 13 q^{86} - 7 q^{88} + 20 q^{92} + q^{98} + 4 q^{99}+O(q^{100}) \) 48 * q - 2 * q^2 + 6 * q^7 - 21 * q^8 + q^9 - 2 * q^11 - 9 * q^14 + 3 * q^16 - 6 * q^18 + 2 * q^22 - q^23 + q^25 - 10 * q^28 - q^29 - 4 * q^32 - 7 * q^36 - 5 * q^37 + q^43 + 23 * q^44 + 4 * q^46 + 6 * q^49 - q^50 + 10 * q^53 - 15 * q^56 + 4 * q^58 + q^63 - 21 * q^64 + q^67 - 7 * q^71 - 4 * q^72 - 14 * q^74 + q^77 + 2 * q^79 - q^81 + 13 * q^86 - 7 * q^88 + 20 * q^92 + q^98 + 4 * q^99

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