LMFDB - Embedded newform 3311.1.ex.a.1140.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3311,1,Mod(118,3311)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3311, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([35, 21, 15]))

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

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

chi := DirichletCharacter("3311.118");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3311 = 7 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3311.ex (of order $70$, degree $24$, 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:	$24$
Coefficient field:	$\Q(\zeta_{35})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{24} - x^{23} + x^{19} - x^{18} + x^{17} - x^{16} + x^{14} - x^{13} + x^{12} - x^{11} + x^{10} + \cdots + 1 $ x^24 - x^23 + x^19 - x^18 + x^17 - x^16 + x^14 - x^13 + x^12 - x^11 + x^10 - x^8 + x^7 - x^6 + x^5 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{70}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{70} - \cdots)$

Embedding invariants

Embedding label			1140.1
Root			$0.134233 + 0.990950i$ of defining polynomial
Character	$\chi$	$=$	3311.1140
Dual form			3311.1.ex.a.2582.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.813584 - 1.51189i) q^{2} +(-1.07300 + 1.62553i) q^{4} +(-0.309017 - 0.951057i) q^{7} +(1.62062 + 0.145858i) q^{8} +(0.963963 - 0.266037i) q^{9} +O(q^{10})$	\(q+(-0.813584 - 1.51189i) q^{2} +(-1.07300 + 1.62553i) q^{4} +(-0.309017 - 0.951057i) q^{7} +(1.62062 + 0.145858i) q^{8} +(0.963963 - 0.266037i) q^{9} +(-0.473869 + 0.880596i) q^{11} +(-1.18648 + 1.24096i) q^{14} +(-0.332477 - 0.777868i) q^{16} +(-1.18648 - 1.24096i) q^{18} +1.71690 q^{22} +(1.24196 - 1.55737i) q^{23} +(-0.134233 - 0.990950i) q^{25} +(1.87755 + 0.518170i) q^{28} +(-0.258792 + 1.91048i) q^{29} +(0.108967 - 0.136641i) q^{32} +(-0.601884 + 1.85241i) q^{36} +(0.170504 - 0.0554001i) q^{37} +(-0.0448648 - 0.998993i) q^{43} +(-0.922972 - 1.71517i) q^{44} +(-3.36501 - 0.610660i) q^{46} +(-0.809017 + 0.587785i) q^{49} +(-1.38900 + 1.00917i) q^{50} +(1.13423 - 0.990950i) q^{53} +(-0.362079 - 1.58637i) q^{56} +(3.09899 - 1.16307i) q^{58} +(-0.550897 - 0.834573i) q^{63} +(-1.12759 - 0.204627i) q^{64} +(0.590905 + 0.740971i) q^{67} +(0.312745 - 1.13321i) q^{71} +(1.60102 - 0.290542i) q^{72} +(-0.222478 - 0.212711i) q^{74} +(0.983930 + 0.178557i) q^{77} +(1.17439 - 1.61640i) q^{79} +(0.858449 - 0.512899i) q^{81} +(-1.47387 + 0.880596i) q^{86} +(-0.896402 + 1.35799i) q^{88} +(1.19892 + 3.68990i) q^{92} +(1.54687 + 0.744934i) q^{98} +(-0.222521 + 0.974928i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} + 3 q^{4} + 6 q^{7} + 8 q^{8} - q^{9}+O(q^{10}) $ 24 * q - 2 * q^2 + 3 * q^4 + 6 * q^7 + 8 * q^8 - q^9	$ 24 q - 2 q^{2} + 3 q^{4} + 6 q^{7} + 8 q^{8} - q^{9} - q^{11} - 3 q^{14} - 3 q^{18} + 2 q^{22} - 2 q^{23} - q^{25} + 2 q^{28} + 2 q^{29} + 11 q^{32} + 4 q^{36} - 5 q^{37} + q^{43} - 26 q^{44} - 8 q^{46} - 6 q^{49} + 2 q^{50} + 25 q^{53} - 3 q^{56} + 8 q^{58} + q^{63} - 5 q^{64} + 2 q^{67} + 5 q^{71} - q^{72} + 7 q^{74} + q^{77} - 5 q^{79} + q^{81} - 25 q^{86} - 8 q^{88} + 4 q^{92} - 2 q^{98} - 4 q^{99}+O(q^{100}) $ 24 * q - 2 * q^2 + 3 * q^4 + 6 * q^7 + 8 * q^8 - q^9 - q^11 - 3 * q^14 - 3 * q^18 + 2 * q^22 - 2 * q^23 - q^25 + 2 * q^28 + 2 * q^29 + 11 * q^32 + 4 * q^36 - 5 * q^37 + q^43 - 26 * q^44 - 8 * q^46 - 6 * q^49 + 2 * q^50 + 25 * q^53 - 3 * q^56 + 8 * q^58 + q^63 - 5 * q^64 + 2 * q^67 + 5 * q^71 - q^72 + 7 * q^74 + q^77 - 5 * q^79 + q^81 - 25 * q^86 - 8 * q^88 + 4 * q^92 - 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$904$	$1893$	$2927$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{5}{14}\right)$

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 $

$2$	−0.813584	−	1.51189i	−0.813584	−	1.51189i	−0.858449	−	0.512899i	$-0.828571\pi$
$2$	−0.813584	−	1.51189i	−0.813584	−	1.51189i	0.0448648	−	0.998993i	$-0.485714\pi$
$3$		0			0		0.990950	−	0.134233i	$-0.0428571\pi$
$3$		0			0		−0.990950	+	0.134233i	$0.957143\pi$
$4$	−1.07300	+	1.62553i	−1.07300	+	1.62553i
$5$		0			0		0.657939	−	0.753071i	$-0.271429\pi$
$5$		0			0		−0.657939	+	0.753071i	$0.728571\pi$
$6$		0			0
$7$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$7$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$8$	1.62062	+	0.145858i	1.62062	+	0.145858i
$9$	0.963963	−	0.266037i	0.963963	−	0.266037i
$10$		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		−0.919528	−	0.393025i	$-0.871429\pi$
$13$		0			0		0.919528	+	0.393025i	$0.128571\pi$
$14$	−1.18648	+	1.24096i	−1.18648	+	1.24096i
$15$		0			0
$16$	−0.332477	−	0.777868i	−0.332477	−	0.777868i
$17$		0			0		0.919528	−	0.393025i	$-0.128571\pi$
$17$		0			0		−0.919528	+	0.393025i	$0.871429\pi$
$18$	−1.18648	−	1.24096i	−1.18648	−	1.24096i
$19$		0			0		0.936235	−	0.351375i	$-0.114286\pi$
$19$		0			0		−0.936235	+	0.351375i	$0.885714\pi$
$20$		0			0
$21$		0			0
$22$	1.71690			1.71690
$23$	1.24196	−	1.55737i	1.24196	−	1.55737i	0.550897	−	0.834573i	$-0.314286\pi$
$23$	1.24196	−	1.55737i	1.24196	−	1.55737i	0.691063	−	0.722795i	$-0.257143\pi$
$24$		0			0
$25$	−0.134233	−	0.990950i	−0.134233	−	0.990950i
$26$		0			0
$27$		0			0
$28$	1.87755	+	0.518170i	1.87755	+	0.518170i
$29$	−0.258792	+	1.91048i	−0.258792	+	1.91048i	0.134233	+	0.990950i	$0.457143\pi$
$29$	−0.258792	+	1.91048i	−0.258792	+	1.91048i	−0.393025	+	0.919528i	$0.628571\pi$
$30$		0			0
$31$		0			0		−0.473869	−	0.880596i	$-0.657143\pi$
$31$		0			0		0.473869	+	0.880596i	$0.342857\pi$
$32$	0.108967	−	0.136641i	0.108967	−	0.136641i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−0.601884	+	1.85241i	−0.601884	+	1.85241i
$37$	0.170504	−	0.0554001i	0.170504	−	0.0554001i	−0.222521	−	0.974928i	$-0.571429\pi$
$37$	0.170504	−	0.0554001i	0.170504	−	0.0554001i	0.393025	+	0.919528i	$0.371429\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.722795	−	0.691063i	$-0.757143\pi$
$41$		0			0		0.722795	+	0.691063i	$0.242857\pi$
$42$		0			0
$43$	−0.0448648	−	0.998993i	−0.0448648	−	0.998993i
$43$	−0.0448648	−	0.998993i	−0.0448648	−	0.998993i
$44$	−0.922972	−	1.71517i	−0.922972	−	1.71517i
$45$		0			0
$46$	−3.36501	−	0.610660i	−3.36501	−	0.610660i
$47$		0			0		0.936235	−	0.351375i	$-0.114286\pi$
$47$		0			0		−0.936235	+	0.351375i	$0.885714\pi$
$48$		0			0
$49$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$50$	−1.38900	+	1.00917i	−1.38900	+	1.00917i
$51$		0			0
$52$		0			0
$53$	1.13423	−	0.990950i	1.13423	−	0.990950i	0.134233	−	0.990950i	$-0.457143\pi$
$53$	1.13423	−	0.990950i	1.13423	−	0.990950i	1.00000			$0$
$54$		0			0
$55$		0			0
$56$	−0.362079	−	1.58637i	−0.362079	−	1.58637i
$57$		0			0
$58$	3.09899	−	1.16307i	3.09899	−	1.16307i
$59$		0			0		0.995974	−	0.0896393i	$-0.0285714\pi$
$59$		0			0		−0.995974	+	0.0896393i	$0.971429\pi$
$60$		0			0
$61$		0			0		0.473869	−	0.880596i	$-0.342857\pi$
$61$		0			0		−0.473869	+	0.880596i	$0.657143\pi$
$62$		0			0
$63$	−0.550897	−	0.834573i	−0.550897	−	0.834573i
$64$	−1.12759	−	0.204627i	−1.12759	−	0.204627i
$65$		0			0
$66$		0			0
$67$	0.590905	+	0.740971i	0.590905	+	0.740971i	0.983930	−	0.178557i	$-0.0571429\pi$
$67$	0.590905	+	0.740971i	0.590905	+	0.740971i	−0.393025	+	0.919528i	$0.628571\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.312745	−	1.13321i	0.312745	−	1.13321i	−0.623490	−	0.781831i	$-0.714286\pi$
$71$	0.312745	−	1.13321i	0.312745	−	1.13321i	0.936235	−	0.351375i	$-0.114286\pi$
$72$	1.60102	−	0.290542i	1.60102	−	0.290542i
$73$		0			0		0.858449	−	0.512899i	$-0.171429\pi$
$73$		0			0		−0.858449	+	0.512899i	$0.828571\pi$
$74$	−0.222478	−	0.212711i	−0.222478	−	0.212711i
$75$		0			0
$76$		0			0
$77$	0.983930	+	0.178557i	0.983930	+	0.178557i
$78$		0			0
$79$	1.17439	−	1.61640i	1.17439	−	1.61640i	0.550897	−	0.834573i	$-0.314286\pi$
$79$	1.17439	−	1.61640i	1.17439	−	1.61640i	0.623490	−	0.781831i	$-0.285714\pi$
$80$		0			0
$81$	0.858449	−	0.512899i	0.858449	−	0.512899i
$82$		0			0
$83$		0			0		−0.880596	−	0.473869i	$-0.842857\pi$
$83$		0			0		0.880596	+	0.473869i	$0.157143\pi$
$84$		0			0
$85$		0			0
$86$	−1.47387	+	0.880596i	−1.47387	+	0.880596i
$87$		0			0
$88$	−0.896402	+	1.35799i	−0.896402	+	1.35799i
$89$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$89$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$90$		0			0
$91$		0			0
$92$	1.19892	+	3.68990i	1.19892	+	3.68990i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$97$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$98$	1.54687	+	0.744934i	1.54687	+	0.744934i
$99$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$100$	1.75485	+	0.845092i	1.75485	+	0.845092i
$101$		0			0		0.998993	−	0.0448648i	$-0.0142857\pi$
$101$		0			0		−0.998993	+	0.0448648i	$0.985714\pi$
$102$		0			0
$103$		0			0		0.995974	−	0.0896393i	$-0.0285714\pi$
$103$		0			0		−0.995974	+	0.0896393i	$0.971429\pi$
$104$		0			0
$105$		0			0
$106$	−2.42100	−	0.908618i	−2.42100	−	0.908618i
$107$	−1.65404	+	0.224055i	−1.65404	+	0.224055i	−0.900969	−	0.433884i	$-0.857143\pi$
$107$	−1.65404	+	0.224055i	−1.65404	+	0.224055i	−0.753071	+	0.657939i	$0.771429\pi$
$108$		0			0
$109$	−1.48713	−	1.18595i	−1.48713	−	1.18595i	−0.936235	−	0.351375i	$-0.885714\pi$
$109$	−1.48713	−	1.18595i	−1.48713	−	1.18595i	−0.550897	−	0.834573i	$-0.685714\pi$
$110$		0			0
$111$		0			0
$112$	−0.637056	+	0.556579i	−0.637056	+	0.556579i
$113$	0.183163	−	0.306564i	0.183163	−	0.306564i	−0.753071	−	0.657939i	$-0.771429\pi$
$113$	0.183163	−	0.306564i	0.183163	−	0.306564i	0.936235	+	0.351375i	$0.114286\pi$
$114$		0			0
$115$		0			0
$116$	−2.82785	−	2.47062i	−2.82785	−	2.47062i
$117$		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
$126$	−0.813584	+	1.51189i	−0.813584	+	1.51189i
$127$	−0.339635	−	1.87155i	−0.339635	−	1.87155i	−0.473869	−	0.880596i	$-0.657143\pi$
$127$	−0.339635	−	1.87155i	−0.339635	−	1.87155i	0.134233	−	0.990950i	$-0.457143\pi$
$128$	0.554007	+	1.70506i	0.554007	+	1.70506i
$129$		0			0
$130$		0			0
$131$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$131$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$132$		0			0
$133$		0			0
$134$	0.639518	−	1.49623i	0.639518	−	1.49623i
$135$		0			0
$136$		0			0
$137$	−1.30397	+	1.49251i	−1.30397	+	1.49251i	−0.550897	+	0.834573i	$0.685714\pi$
$137$	−1.30397	+	1.49251i	−1.30397	+	1.49251i	−0.753071	+	0.657939i	$0.771429\pi$
$138$		0			0
$139$		0			0		−0.0896393	−	0.995974i	$-0.528571\pi$
$139$		0			0		0.0896393	+	0.995974i	$0.471429\pi$
$140$		0			0
$141$		0			0
$142$	−1.96773	+	0.449122i	−1.96773	+	0.449122i
$143$		0			0
$144$	−0.527437	−	0.661385i	−0.527437	−	0.661385i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−0.0928968	+	0.336604i	−0.0928968	+	0.336604i
$149$	−0.0559455	+	1.24572i	−0.0559455	+	1.24572i	0.753071	+	0.657939i	$0.228571\pi$
$149$	−0.0559455	+	1.24572i	−0.0559455	+	1.24572i	−0.809017	+	0.587785i	$0.800000\pi$
$150$		0			0
$151$	−0.0360371	−	0.266037i	−0.0360371	−	0.266037i	0.963963	−	0.266037i	$-0.0857143\pi$
$151$	−0.0360371	−	0.266037i	−0.0360371	−	0.266037i	−1.00000			$\pi$
$152$		0			0
$153$		0			0
$154$	−0.530551	−	1.63287i	−0.530551	−	1.63287i
$155$		0			0
$156$		0			0
$157$		0			0		−0.351375	−	0.936235i	$-0.614286\pi$
$157$		0			0		0.351375	+	0.936235i	$0.385714\pi$
$158$	−3.39929	−	0.460465i	−3.39929	−	0.460465i
$159$		0			0
$160$		0			0
$161$	−1.86493	−	0.699921i	−1.86493	−	0.699921i
$162$	−1.47387	−	0.880596i	−1.47387	−	0.880596i
$163$	−0.384580	−	1.39349i	−0.384580	−	1.39349i	−0.858449	−	0.512899i	$-0.828571\pi$
$163$	−0.384580	−	1.39349i	−0.384580	−	1.39349i	0.473869	−	0.880596i	$-0.342857\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.919528	−	0.393025i	$-0.871429\pi$
$167$		0			0		0.919528	+	0.393025i	$0.128571\pi$
$168$		0			0
$169$	0.691063	+	0.722795i	0.691063	+	0.722795i
$170$		0			0
$171$		0			0
$172$	1.67203	+	0.998993i	1.67203	+	0.998993i
$173$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$173$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$174$		0			0
$175$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$176$	0.842538	+	0.0758298i	0.842538	+	0.0758298i
$177$		0			0
$178$		0			0
$179$	0.975592	+	0.316989i	0.975592	+	0.316989i	0.753071	−	0.657939i	$-0.228571\pi$
$179$	0.975592	+	0.316989i	0.975592	+	0.316989i	0.222521	+	0.974928i	$0.428571\pi$
$180$		0			0
$181$		0			0		0.0448648	−	0.998993i	$-0.485714\pi$
$181$		0			0		−0.0448648	+	0.998993i	$0.514286\pi$
$182$		0			0
$183$		0			0
$184$	2.23990	−	2.34275i	2.23990	−	2.34275i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.298038	−	0.196733i	−0.298038	−	0.196733i	0.393025	−	0.919528i	$-0.371429\pi$
$191$	−0.298038	−	0.196733i	−0.298038	−	0.196733i	−0.691063	+	0.722795i	$0.742857\pi$
$192$		0			0
$193$	−0.468542	−	0.252133i	−0.468542	−	0.252133i	0.222521	−	0.974928i	$-0.428571\pi$
$193$	−0.468542	−	0.252133i	−0.468542	−	0.252133i	−0.691063	+	0.722795i	$0.742857\pi$
$194$		0			0
$195$		0			0
$196$	−0.0873849	−	1.94578i	−0.0873849	−	1.94578i
$197$	0.859914	+	1.78563i	0.859914	+	1.78563i	0.550897	+	0.834573i	$0.314286\pi$
$197$	0.859914	+	1.78563i	0.859914	+	1.78563i	0.309017	+	0.951057i	$0.400000\pi$
$198$	1.65503	−	0.456758i	1.65503	−	0.456758i
$199$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$199$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$200$	−0.0730026	−	1.62553i	−0.0730026	−	1.62553i
$201$		0			0
$202$		0			0
$203$	1.89694	−	0.344244i	1.89694	−	0.344244i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.782886	−	1.83165i	0.782886	−	1.83165i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.0840080	−	1.87058i	−0.0840080	−	1.87058i	−0.393025	−	0.919528i	$-0.628571\pi$
$211$	−0.0840080	−	1.87058i	−0.0840080	−	1.87058i	0.309017	−	0.951057i	$-0.400000\pi$
$212$	0.393783	+	2.90702i	0.393783	+	2.90702i
$213$		0			0
$214$	1.68445	+	2.31844i	1.68445	+	2.31844i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−0.583119	+	3.21325i	−0.583119	+	3.21325i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.0896393	−	0.995974i	$-0.471429\pi$
$223$		0			0		−0.0896393	+	0.995974i	$0.528571\pi$
$224$	−0.163626	−	0.0614097i	−0.163626	−	0.0614097i
$225$	−0.393025	−	0.919528i	−0.393025	−	0.919528i
$226$	−0.612510	−	0.0275079i	−0.612510	−	0.0275079i
$227$		0			0		0.134233	−	0.990950i	$-0.457143\pi$
$227$		0			0		−0.134233	+	0.990950i	$0.542857\pi$
$228$		0			0
$229$		0			0		−0.473869	−	0.880596i	$-0.657143\pi$
$229$		0			0		0.473869	+	0.880596i	$0.342857\pi$
$230$		0			0
$231$		0			0
$232$	−0.698061	+	3.05841i	−0.698061	+	3.05841i
$233$	−1.96786	−	0.357114i	−1.96786	−	0.357114i	−0.983930	−	0.178557i	$-0.942857\pi$
$233$	−1.96786	−	0.357114i	−1.96786	−	0.357114i	−0.983930	−	0.178557i	$-0.942857\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.462366	+	1.23197i	0.462366	+	1.23197i	0.936235	+	0.351375i	$0.114286\pi$
$239$	0.462366	+	1.23197i	0.462366	+	1.23197i	−0.473869	+	0.880596i	$0.657143\pi$
$240$		0			0
$241$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$241$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$242$	−0.813584	+	1.51189i	−0.813584	+	1.51189i
$243$		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		−0.809017	−	0.587785i	$-0.800000\pi$
$251$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$252$	1.94774			1.94774
$253$	0.782886	+	1.83165i	0.782886	+	1.83165i
$254$	−2.55325	+	2.03615i	−2.55325	+	2.03615i
$255$		0			0
$256$	1.33517	−	1.39648i	1.33517	−	1.39648i
$257$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$257$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$258$		0			0
$259$	−0.105377	−	0.145039i	−0.105377	−	0.145039i
$260$		0			0
$261$	0.258792	+	1.91048i	0.258792	+	1.91048i
$262$		0			0
$263$	0.429004	+	1.87959i	0.429004	+	1.87959i	0.473869	+	0.880596i	$0.342857\pi$
$263$	0.429004	+	1.87959i	0.429004	+	1.87959i	−0.0448648	+	0.998993i	$0.514286\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−1.83851	+	0.165469i	−1.83851	+	0.165469i
$269$		0			0		0.0448648	−	0.998993i	$-0.485714\pi$
$269$		0			0		−0.0448648	+	0.998993i	$0.514286\pi$
$270$		0			0
$271$		0			0		−0.512899	−	0.858449i	$-0.671429\pi$
$271$		0			0		0.512899	+	0.858449i	$0.328571\pi$
$272$		0			0
$273$		0			0
$274$	3.31741	+	0.757176i	3.31741	+	0.757176i
$275$	0.936235	+	0.351375i	0.936235	+	0.351375i
$276$		0			0
$277$	0.0277280	+	0.617412i	0.0277280	+	0.617412i	0.963963	+	0.266037i	$0.0857143\pi$
$277$	0.0277280	+	0.617412i	0.0277280	+	0.617412i	−0.936235	+	0.351375i	$0.885714\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.99597	+	0.0896393i	1.99597	+	0.0896393i	1.00000			$0$
$281$	1.99597	+	0.0896393i	1.99597	+	0.0896393i	0.995974	+	0.0896393i	$0.0285714\pi$
$282$		0			0
$283$		0			0		0.990950	−	0.134233i	$-0.0428571\pi$
$283$		0			0		−0.990950	+	0.134233i	$0.957143\pi$
$284$	1.50648	+	1.72431i	1.50648	+	1.72431i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.0686889	−	0.160706i	0.0686889	−	0.160706i
$289$	0.691063	−	0.722795i	0.691063	−	0.722795i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.512899	−	0.858449i	$-0.671429\pi$
$293$		0			0		0.512899	+	0.858449i	$0.328571\pi$
$294$		0			0
$295$		0			0
$296$	0.284402	−	0.0649130i	0.284402	−	0.0649130i
$297$		0			0
$298$	1.92892	−	0.928917i	1.92892	−	0.928917i
$299$		0			0
$300$		0			0
$301$	−0.936235	+	0.351375i	−0.936235	+	0.351375i
$302$	−0.372900	+	0.270928i	−0.372900	+	0.270928i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$	−1.34601	+	1.40781i	−1.34601	+	1.40781i
$309$		0			0
$310$		0			0
$311$		0			0		−0.858449	−	0.512899i	$-0.828571\pi$
$311$		0			0		0.858449	+	0.512899i	$0.171429\pi$
$312$		0			0
$313$		0			0		−0.178557	−	0.983930i	$-0.557143\pi$
$313$		0			0		0.178557	+	0.983930i	$0.442857\pi$
$314$		0			0
$315$		0			0
$316$	1.36739	+	3.64341i	1.36739	+	3.64341i
$317$	−0.0675728	+	0.0590366i	−0.0675728	+	0.0590366i	−0.691063	−	0.722795i	$-0.742857\pi$
$317$	−0.0675728	+	0.0590366i	−0.0675728	+	0.0590366i	0.623490	+	0.781831i	$0.285714\pi$
$318$		0			0
$319$	−1.55972	−	1.13321i	−1.55972	−	1.13321i
$320$		0			0
$321$		0			0
$322$	0.459074	+	3.38902i	0.459074	+	3.38902i
$323$		0			0
$324$	−0.0873849	+	1.94578i	−0.0873849	+	1.94578i
$325$		0			0
$326$	−1.79393	+	1.71517i	−1.79393	+	1.71517i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.93221	+	0.441014i	−1.93221	+	0.441014i	−0.936235	+	0.351375i	$0.885714\pi$
$331$	−1.93221	+	0.441014i	−1.93221	+	0.441014i	−0.995974	+	0.0896393i	$0.971429\pi$
$332$		0			0
$333$	0.149621	−	0.0987640i	0.149621	−	0.0987640i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.975592	−	0.316989i	0.975592	−	0.316989i	0.222521	−	0.974928i	$-0.428571\pi$
$337$	0.975592	−	0.316989i	0.975592	−	0.316989i	0.753071	+	0.657939i	$0.228571\pi$
$338$	0.530551	−	1.63287i	0.530551	−	1.63287i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.809017	+	0.587785i	0.809017	+	0.587785i
$344$	0.0730026	−	1.62553i	0.0730026	−	1.62553i
$345$		0			0
$346$		0			0
$347$	0.932507	−	1.73289i	0.932507	−	1.73289i	0.309017	−	0.951057i	$-0.400000\pi$
$347$	0.932507	−	1.73289i	0.932507	−	1.73289i	0.623490	−	0.781831i	$-0.285714\pi$
$348$		0			0
$349$		0			0		−0.995974	−	0.0896393i	$-0.971429\pi$
$349$		0			0		0.995974	+	0.0896393i	$0.0285714\pi$
$350$	1.38900	+	1.00917i	1.38900	+	1.00917i
$351$		0			0
$352$	0.0686889	+	0.160706i	0.0686889	+	0.160706i
$353$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$353$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−0.314473	−	1.73289i	−0.314473	−	1.73289i
$359$	0.856104	+	0.565109i	0.856104	+	0.565109i	0.900969	−	0.433884i	$-0.142857\pi$
$359$	0.856104	+	0.565109i	0.856104	+	0.565109i	−0.0448648	+	0.998993i	$0.514286\pi$
$360$		0			0
$361$	0.753071	−	0.657939i	0.753071	−	0.657939i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.936235	−	0.351375i	$-0.885714\pi$
$367$		0			0		0.936235	+	0.351375i	$0.114286\pi$
$368$	−1.62435	−	0.448292i	−1.62435	−	0.448292i
$369$		0			0
$370$		0			0
$371$	−1.29295	−	0.772500i	−1.29295	−	0.772500i
$372$		0			0
$373$	0.400969	+	0.193096i	0.400969	+	0.193096i	0.623490	−	0.781831i	$-0.285714\pi$
$373$	0.400969	+	0.193096i	0.400969	+	0.193096i	−0.222521	+	0.974928i	$0.571429\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.50008	+	1.31058i	1.50008	+	1.31058i	0.809017	+	0.587785i	$0.200000\pi$
$379$	1.50008	+	1.31058i	1.50008	+	1.31058i	0.691063	+	0.722795i	$0.257143\pi$
$380$		0			0
$381$		0			0
$382$	−0.0549604	+	0.610660i	−0.0549604	+	0.610660i
$383$		0			0		0.998993	−	0.0448648i	$-0.0142857\pi$
$383$		0			0		−0.998993	+	0.0448648i	$0.985714\pi$
$384$		0			0
$385$		0			0
$386$			0.913516i			0.913516i
$387$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$388$		0			0
$389$	1.43251	+	0.194046i	1.43251	+	0.194046i	0.809017	−	0.587785i	$-0.200000\pi$
$389$	1.43251	+	0.194046i	1.43251	+	0.194046i	0.623490	+	0.781831i	$0.285714\pi$
$390$		0			0
$391$		0			0
$392$	−1.39684	+	0.834573i	−1.39684	+	0.834573i
$393$		0			0
$394$	2.00007	−	2.75286i	2.00007	−	2.75286i
$395$		0			0
$396$	−1.34601	−	1.40781i	−1.34601	−	1.40781i
$397$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$397$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$398$		0			0
$399$		0			0
$400$	−0.726199	+	0.433884i	−0.726199	+	0.433884i
$401$	0.264152	−	0.0479366i	0.264152	−	0.0479366i	−0.0448648	−	0.998993i	$-0.514286\pi$
$401$	0.264152	−	0.0479366i	0.264152	−	0.0479366i	0.309017	+	0.951057i	$0.400000\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−2.06378	−	2.58790i	−2.06378	−	2.58790i
$407$	−0.0320114	+	0.176398i	−0.0320114	+	0.176398i
$408$		0			0
$409$		0			0		−0.983930	−	0.178557i	$-0.942857\pi$
$409$		0			0		0.983930	+	0.178557i	$0.0571429\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−3.40620	+	0.306564i	−3.40620	+	0.306564i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$419$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$420$		0			0
$421$	−0.586496	+	0.387143i	−0.586496	+	0.387143i	−0.809017	−	0.587785i	$-0.800000\pi$
$421$	−0.586496	+	0.387143i	−0.586496	+	0.387143i	0.222521	+	0.974928i	$0.428571\pi$
$422$	−2.75977	+	1.64889i	−2.75977	+	1.64889i
$423$		0			0
$424$	1.98270	−	1.44051i	1.98270	−	1.44051i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	1.41058	−	2.92910i	1.41058	−	2.92910i
$429$		0			0
$430$		0			0
$431$	0.981100	−	1.35037i	0.981100	−	1.35037i	0.0448648	−	0.998993i	$-0.485714\pi$
$431$	0.981100	−	1.35037i	0.981100	−	1.35037i	0.936235	−	0.351375i	$-0.114286\pi$
$432$		0			0
$433$		0			0		0.722795	−	0.691063i	$-0.242857\pi$
$433$		0			0		−0.722795	+	0.691063i	$0.757143\pi$
$434$		0			0
$435$		0			0
$436$	3.52349	−	1.14485i	3.52349	−	1.14485i
$437$		0			0
$438$		0			0
$439$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$439$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$440$		0			0
$441$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$442$		0			0
$443$	−1.61152	−	0.145039i	−1.61152	−	0.145039i	−0.753071	−	0.657939i	$-0.771429\pi$
$443$	−1.61152	−	0.145039i	−1.61152	−	0.145039i	−0.858449	+	0.512899i	$0.828571\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	0.153832	+	1.13563i	0.153832	+	1.13563i
$449$	−0.702042	+	0.0315287i	−0.702042	+	0.0315287i	−0.393025	−	0.919528i	$-0.628571\pi$
$449$	−0.702042	+	0.0315287i	−0.702042	+	0.0315287i	−0.309017	+	0.951057i	$0.600000\pi$
$450$	−1.07047	+	1.34232i	−1.07047	+	1.34232i
$451$		0			0
$452$	0.301794	+	0.626681i	0.301794	+	0.626681i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.433033	+	1.01313i	0.433033	+	1.01313i	0.983930	+	0.178557i	$0.0571429\pi$
$457$	0.433033	+	1.01313i	0.433033	+	1.01313i	−0.550897	+	0.834573i	$0.685714\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$461$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$462$		0			0
$463$	0.518733	+	0.118398i	0.518733	+	0.118398i	0.473869	−	0.880596i	$-0.342857\pi$
$463$	0.518733	+	0.118398i	0.518733	+	0.118398i	0.0448648	+	0.998993i	$0.485714\pi$
$464$	1.57214	−	0.433884i	1.57214	−	0.433884i
$465$		0			0
$466$	1.06110	+	3.26573i	1.06110	+	3.26573i
$467$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$467$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$468$		0			0
$469$	0.522106	−	0.790956i	0.522106	−	0.790956i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.900969	+	0.433884i	0.900969	+	0.433884i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.829730	−	1.25699i	0.829730	−	1.25699i
$478$	1.48643	−	1.70136i	1.48643	−	1.70136i
$479$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$479$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	1.94774			1.94774
$485$		0			0
$486$		0			0
$487$	0.0620088	−	0.0648561i	0.0620088	−	0.0648561i	−0.691063	−	0.722795i	$-0.742857\pi$
$487$	0.0620088	−	0.0648561i	0.0620088	−	0.0648561i	0.753071	+	0.657939i	$0.228571\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−0.861741	−	0.901310i	−0.861741	−	0.901310i	0.134233	−	0.990950i	$-0.457143\pi$
$491$	−0.861741	−	0.901310i	−0.861741	−	0.901310i	−0.995974	+	0.0896393i	$0.971429\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.17439	+	0.0527418i	−1.17439	+	0.0527418i
$498$		0			0
$499$	0.179098	+	1.98994i	0.179098	+	1.98994i	0.134233	+	0.990950i	$0.457143\pi$
$499$	0.179098	+	1.98994i	0.179098	+	1.98994i	0.0448648	+	0.998993i	$0.485714\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.995974	−	0.0896393i	$-0.971429\pi$
$503$		0			0		0.995974	+	0.0896393i	$0.0285714\pi$
$504$	−0.771064	−	1.43288i	−0.771064	−	1.43288i
$505$		0			0
$506$	2.13232	−	2.67384i	2.13232	−	2.67384i
$507$		0			0
$508$	3.40668	+	1.45609i	3.40668	+	1.45609i
$509$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$509$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$510$		0			0
$511$		0			0
$512$	−1.46940	−	0.405530i	−1.46940	−	0.405530i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−0.133551	+	0.277321i	−0.133551	+	0.277321i
$519$		0			0
$520$		0			0
$521$		0			0		−0.512899	−	0.858449i	$-0.671429\pi$
$521$		0			0		0.512899	+	0.858449i	$0.328571\pi$
$522$	2.67789	−	1.94560i	2.67789	−	1.94560i
$523$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$523$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$524$		0			0
$525$		0			0
$526$	2.49270	−	2.17781i	2.49270	−	2.17781i
$527$		0			0
$528$		0			0
$529$	−0.660411	−	2.89345i	−0.660411	−	2.89345i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	0.849554	+	1.28702i	0.849554	+	1.28702i
$537$		0			0
$538$		0			0
$539$	−0.134233	−	0.990950i	−0.134233	−	0.990950i
$540$		0			0
$541$	−0.125481	+	0.691456i	−0.125481	+	0.691456i	0.858449	+	0.512899i	$0.171429\pi$
$541$	−0.125481	+	0.691456i	−0.125481	+	0.691456i	−0.983930	+	0.178557i	$0.942857\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	1.40935	+	1.34747i	1.40935	+	1.34747i	0.858449	+	0.512899i	$0.171429\pi$
$547$	1.40935	+	1.34747i	1.40935	+	1.34747i	0.550897	+	0.834573i	$0.314286\pi$
$548$	−1.02696	−	3.72111i	−1.02696	−	3.72111i
$549$		0			0
$550$	−0.230465	−	1.70136i	−0.230465	−	1.70136i
$551$		0			0
$552$		0			0
$553$	−1.90020	−	0.617412i	−1.90020	−	0.617412i
$554$	0.910901	−	0.544238i	0.910901	−	0.544238i
$555$		0			0
$556$		0			0
$557$	0.527258	+	0.0714220i	0.527258	+	0.0714220i	0.393025	−	0.919528i	$-0.371429\pi$
$557$	0.527258	+	0.0714220i	0.527258	+	0.0714220i	0.134233	+	0.990950i	$0.457143\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−1.48837	−	3.09063i	−1.48837	−	3.09063i
$563$		0			0		0.998993	−	0.0448648i	$-0.0142857\pi$
$563$		0			0		−0.998993	+	0.0448648i	$0.985714\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.753071	−	0.657939i	−0.753071	−	0.657939i
$568$	0.672128	−	1.79088i	0.672128	−	1.79088i
$569$	−1.00008	+	1.67385i	−1.00008	+	1.67385i	−0.309017	+	0.951057i	$0.600000\pi$
$569$	−1.00008	+	1.67385i	−1.00008	+	1.67385i	−0.691063	+	0.722795i	$0.742857\pi$
$570$		0			0
$571$	−1.68704	−	0.812434i	−1.68704	−	0.812434i	−0.995974	−	0.0896393i	$-0.971429\pi$
$571$	−1.68704	−	0.812434i	−1.68704	−	0.812434i	−0.691063	−	0.722795i	$-0.742857\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.70999	−	1.02167i	−1.70999	−	1.02167i
$576$	−1.14139	+	0.102727i	−1.14139	+	0.102727i
$577$		0			0		−0.880596	−	0.473869i	$-0.842857\pi$
$577$		0			0		0.880596	+	0.473869i	$0.157143\pi$
$578$	−1.65503	−	0.456758i	−1.65503	−	0.456758i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	0.335148	+	1.46838i	0.335148	+	1.46838i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.834573	−	0.550897i	$-0.814286\pi$
$587$		0			0		0.834573	+	0.550897i	$0.185714\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.0997827	−	0.114210i	−0.0997827	−	0.114210i
$593$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$593$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$594$		0			0
$595$		0			0
$596$	−1.96493	−	1.42761i	−1.96493	−	1.42761i
$597$		0			0
$598$		0			0
$599$	−0.887305	+	1.64889i	−0.887305	+	1.64889i	−0.134233	+	0.990950i	$0.542857\pi$
$599$	−0.887305	+	1.64889i	−0.887305	+	1.64889i	−0.753071	+	0.657939i	$0.771429\pi$
$600$		0			0
$601$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$601$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$602$	1.29295	+	1.12961i	1.29295	+	1.12961i
$603$	0.766736	+	0.557066i	0.766736	+	0.557066i
$604$	0.471119	+	0.226879i	0.471119	+	0.226879i
$605$		0			0
$606$		0			0
$607$		0			0		0.393025	−	0.919528i	$-0.371429\pi$
$607$		0			0		−0.393025	+	0.919528i	$0.628571\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	1.53483	−	1.01313i	1.53483	−	1.01313i	0.550897	−	0.834573i	$-0.314286\pi$
$613$	1.53483	−	1.01313i	1.53483	−	1.01313i	0.983930	−	0.178557i	$-0.0571429\pi$
$614$		0			0
$615$		0			0
$616$	1.56853	+	0.432887i	1.56853	+	0.432887i
$617$	0.939065	+	1.17755i	0.939065	+	1.17755i	0.983930	+	0.178557i	$0.0571429\pi$
$617$	0.939065	+	1.17755i	0.939065	+	1.17755i	−0.0448648	+	0.998993i	$0.514286\pi$
$618$		0			0
$619$		0			0		−0.858449	−	0.512899i	$-0.828571\pi$
$619$		0			0		0.858449	+	0.512899i	$0.171429\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.963963	+	0.266037i	−0.963963	+	0.266037i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	1.01651	+	0.137696i	1.01651	+	0.137696i	0.623490	−	0.781831i	$-0.285714\pi$
$631$	1.01651	+	0.137696i	1.01651	+	0.137696i	0.393025	+	0.919528i	$0.371429\pi$
$632$	2.13900	−	2.44828i	2.13900	−	2.44828i
$633$		0			0
$634$	0.144233	+	0.0541316i	0.144233	+	0.0541316i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−0.444319	+	3.28009i	−0.444319	+	3.28009i
$639$		−	1.17557i		−	1.17557i
$640$		0			0
$641$	−0.186957	−	0.498146i	−0.186957	−	0.498146i	0.809017	−	0.587785i	$-0.200000\pi$
$641$	−0.186957	−	0.498146i	−0.186957	−	0.498146i	−0.995974	+	0.0896393i	$0.971429\pi$
$642$		0			0
$643$		0			0		0.983930	−	0.178557i	$-0.0571429\pi$
$643$		0			0		−0.983930	+	0.178557i	$0.942857\pi$
$644$	3.13882	−	2.28048i	3.13882	−	2.28048i
$645$		0			0
$646$		0			0
$647$		0			0		0.880596	−	0.473869i	$-0.157143\pi$
$647$		0			0		−0.880596	+	0.473869i	$0.842857\pi$
$648$	1.46603	−	0.706002i	1.46603	−	0.706002i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	2.67782	+	0.870077i	2.67782	+	0.870077i
$653$	0.0919519	+	0.153902i	0.0919519	+	0.153902i	0.900969	−	0.433884i	$-0.142857\pi$
$653$	0.0919519	+	0.153902i	0.0919519	+	0.153902i	−0.809017	+	0.587785i	$0.800000\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.678448	+	1.40881i	−0.678448	+	1.40881i	0.222521	+	0.974928i	$0.428571\pi$
$659$	−0.678448	+	1.40881i	−0.678448	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$660$		0			0
$661$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$661$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$662$	2.23878	+	2.56249i	2.23878	+	2.56249i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−0.271050	−	0.145858i	−0.271050	−	0.145858i
$667$	2.65391	+	2.77577i	2.65391	+	2.77577i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.0425201	+	0.946783i	0.0425201	+	0.946783i	0.900969	+	0.433884i	$0.142857\pi$
$673$	0.0425201	+	0.946783i	0.0425201	+	0.946783i	−0.858449	+	0.512899i	$0.828571\pi$
$674$	−1.27298	−	1.21709i	−1.27298	−	1.21709i
$675$		0			0
$676$	−1.91644	+	0.347782i	−1.91644	+	0.347782i
$677$		0			0		0.0448648	−	0.998993i	$-0.485714\pi$
$677$		0			0		−0.0448648	+	0.998993i	$0.514286\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.137526	−	0.602539i	−0.137526	−	0.602539i	−0.995974	−	0.0896393i	$-0.971429\pi$
$683$	−0.137526	−	0.602539i	−0.137526	−	0.602539i	0.858449	−	0.512899i	$-0.171429\pi$
$684$		0			0
$685$		0			0
$686$	0.230465	−	1.70136i	0.230465	−	1.70136i
$687$		0			0
$688$	−0.762169	+	0.367041i	−0.762169	+	0.367041i
$689$		0			0
$690$		0			0
$691$		0			0		0.178557	−	0.983930i	$-0.442857\pi$
$691$		0			0		−0.178557	+	0.983930i	$0.557143\pi$
$692$		0			0
$693$	0.995974	−	0.0896393i	0.995974	−	0.0896393i
$694$	−3.37861			−3.37861
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	0.261451	−	1.93011i	0.261451	−	1.93011i
$701$	0.149621	−	1.66243i	0.149621	−	1.66243i	−0.473869	−	0.880596i	$-0.657143\pi$
$701$	0.149621	−	1.66243i	0.149621	−	1.66243i	0.623490	−	0.781831i	$-0.285714\pi$
$702$		0			0
$703$		0			0
$704$	0.714523	−	0.895983i	0.714523	−	0.895983i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.713714	+	1.32630i	−0.713714	+	1.32630i	0.222521	+	0.974928i	$0.428571\pi$
$709$	−0.713714	+	1.32630i	−0.713714	+	1.32630i	−0.936235	+	0.351375i	$0.885714\pi$
$710$		0			0
$711$	0.702042	−	1.87058i	0.702042	−	1.87058i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.56209	+	1.24572i	−1.56209	+	1.24572i
$717$		0			0
$718$	0.157872	−	1.75410i	0.157872	−	1.75410i
$719$		0			0		0.134233	−	0.990950i	$-0.457143\pi$
$719$		0			0		−0.134233	+	0.990950i	$0.542857\pi$
$720$		0			0
$721$		0			0
$722$	−1.60742	−	0.603275i	−1.60742	−	0.603275i
$723$		0			0
$724$		0			0
$725$	1.92793			1.92793
$726$		0			0
$727$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$727$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$728$		0			0
$729$	0.691063	−	0.722795i	0.691063	−	0.722795i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.134233	−	0.990950i	$-0.457143\pi$
$733$		0			0		−0.134233	+	0.990950i	$0.542857\pi$
$734$		0			0
$735$		0			0
$736$	−0.0774668	−	0.339404i	−0.0774668	−	0.339404i
$737$	−0.932507	+	0.169225i	−0.932507	+	0.169225i
$738$		0			0
$739$	−0.308937	+	0.722795i	−0.308937	+	0.722795i	0.691063	+	0.722795i	$0.257143\pi$
$739$	−0.308937	+	0.722795i	−0.308937	+	0.722795i	−1.00000			$\pi$
$740$		0			0
$741$		0			0
$742$	−0.116016	+	2.58329i	−0.116016	+	2.58329i
$743$	0.773418	−	0.140355i	0.773418	−	0.140355i	0.222521	−	0.974928i	$-0.428571\pi$
$743$	0.773418	−	0.140355i	0.773418	−	0.140355i	0.550897	+	0.834573i	$0.314286\pi$
$744$		0			0
$745$		0			0
$746$	−0.0342808	−	0.763322i	−0.0342808	−	0.763322i
$747$		0			0
$748$		0			0
$749$	0.724216	+	1.50385i	0.724216	+	1.50385i
$750$		0			0
$751$	0.586496	−	0.387143i	0.586496	−	0.387143i	−0.222521	−	0.974928i	$-0.571429\pi$
$751$	0.586496	−	0.387143i	0.586496	−	0.387143i	0.809017	+	0.587785i	$0.200000\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	0.773453	+	0.885289i	0.773453	+	0.885289i	0.995974	−	0.0896393i	$-0.0285714\pi$
$757$	0.773453	+	0.885289i	0.773453	+	0.885289i	−0.222521	+	0.974928i	$0.571429\pi$
$758$	0.761015	−	3.33423i	0.761015	−	3.33423i
$759$		0			0
$760$		0			0
$761$		0			0		0.393025	−	0.919528i	$-0.371429\pi$
$761$		0			0		−0.393025	+	0.919528i	$0.628571\pi$
$762$		0			0
$763$	−0.668355	+	1.78082i	−0.668355	+	1.78082i
$764$	0.639590	−	0.273374i	0.639590	−	0.273374i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$769$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$770$		0			0
$771$		0			0
$772$	0.912596	−	0.491089i	0.912596	−	0.491089i
$773$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$773$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$774$	−1.18648	+	1.24096i	−1.18648	+	1.24096i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.872088	−	2.32367i	−0.872088	−	2.32367i
$779$		0			0
$780$		0			0
$781$	0.849696	+	0.812393i	0.849696	+	0.812393i
$782$		0			0
$783$		0			0
$784$	0.726199	+	0.433884i	0.726199	+	0.433884i
$785$		0			0
$786$		0			0
$787$		0			0		0.657939	−	0.753071i	$-0.271429\pi$
$787$		0			0		−0.657939	+	0.753071i	$0.728571\pi$
$788$	−3.82528	−	0.518170i	−3.82528	−	0.518170i
$789$		0			0
$790$		0			0
$791$	−0.348160	−	0.0794653i	−0.348160	−	0.0794653i
$792$	−0.502823	+	1.54753i	−0.502823	+	1.54753i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.0448648	−	0.998993i	$-0.485714\pi$
$797$		0			0		−0.0448648	+	0.998993i	$0.514286\pi$
$798$		0			0
$799$		0			0
$800$	−0.150031	−	0.0896393i	−0.150031	−	0.0896393i
$801$		0			0
$802$	−0.287385	−	0.360369i	−0.287385	−	0.360369i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.951109	−	1.08863i	0.951109	−	1.08863i	−0.0448648	−	0.998993i	$-0.514286\pi$
$809$	0.951109	−	1.08863i	0.951109	−	1.08863i	0.995974	−	0.0896393i	$-0.0285714\pi$
$810$		0			0
$811$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$811$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$812$	−1.47585	+	3.45291i	−1.47585	+	3.45291i
$813$		0			0
$814$	0.292738	−	0.0951164i	0.292738	−	0.0951164i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.30499	+	0.861417i	1.30499	+	0.861417i	0.995974	−	0.0896393i	$-0.0285714\pi$
$821$	1.30499	+	0.861417i	1.30499	+	0.861417i	0.309017	+	0.951057i	$0.400000\pi$
$822$		0			0
$823$	1.59203	+	1.15668i	1.59203	+	1.15668i	0.900969	+	0.433884i	$0.142857\pi$
$823$	1.59203	+	1.15668i	1.59203	+	1.15668i	0.691063	+	0.722795i	$0.257143\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.570938	−	0.653491i	−0.570938	−	0.653491i	0.393025	−	0.919528i	$-0.371429\pi$
$827$	−0.570938	−	0.653491i	−0.570938	−	0.653491i	−0.963963	+	0.266037i	$0.914286\pi$
$828$	2.13737	+	3.23797i	2.13737	+	3.23797i
$829$		0			0		−0.990950	−	0.134233i	$-0.957143\pi$
$829$		0			0		0.990950	+	0.134233i	$0.0428571\pi$
$830$		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		0.990950	−	0.134233i	$-0.0428571\pi$
$839$		0			0		−0.990950	+	0.134233i	$0.957143\pi$
$840$		0			0
$841$	−2.61899	−	0.722795i	−2.61899	−	0.722795i
$842$	1.06248	+	0.571746i	1.06248	+	0.571746i
$843$		0			0
$844$	3.13083	+	1.87058i	3.13083	+	1.87058i
$845$		0			0
$846$		0			0
$847$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$848$	−1.14793	−	0.552816i	−1.14793	−	0.552816i
$849$		0			0
$850$		0			0
$851$	0.125481	−	0.334342i	0.125481	−	0.334342i
$852$		0			0
$853$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$853$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$854$		0			0
$855$		0			0
$856$	−2.71325	+	0.121852i	−2.71325	+	0.121852i
$857$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$857$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$858$		0			0
$859$		0			0			−	1.00000i	$-0.5\pi$
$859$		0			0				1.00000i	$0.5\pi$
$860$		0			0
$861$		0			0
$862$	−2.83982	−	0.384679i	−2.83982	−	0.384679i
$863$	−1.37695	−	0.740971i	−1.37695	−	0.740971i	−0.393025	−	0.919528i	$-0.628571\pi$
$863$	−1.37695	−	0.740971i	−1.37695	−	0.740971i	−0.983930	+	0.178557i	$0.942857\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.866894	+	1.80012i	0.866894	+	1.80012i
$870$		0			0
$871$		0			0
$872$	−2.23709	−	2.13888i	−2.23709	−	2.13888i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.903314	−	1.51189i	0.903314	−	1.51189i	0.0448648	−	0.998993i	$-0.485714\pi$
$877$	0.903314	−	1.51189i	0.903314	−	1.51189i	0.858449	−	0.512899i	$-0.171429\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$881$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$882$	1.68931	+	0.306564i	1.68931	+	0.306564i
$883$	0.245172	+	0.371420i	0.245172	+	0.371420i	0.936235	−	0.351375i	$-0.114286\pi$
$883$	0.245172	+	0.371420i	0.245172	+	0.371420i	−0.691063	+	0.722795i	$0.742857\pi$
$884$		0			0
$885$		0			0
$886$	1.09182	+	2.55445i	1.09182	+	2.55445i
$887$		0			0		0.995974	−	0.0896393i	$-0.0285714\pi$
$887$		0			0		−0.995974	+	0.0896393i	$0.971429\pi$
$888$		0			0
$889$	−1.67499	+	0.901352i	−1.67499	+	0.901352i
$890$		0			0
$891$	0.0448648	+	0.998993i	0.0448648	+	0.998993i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	1.45041	−	1.05378i	1.45041	−	1.05378i
$897$		0			0
$898$	0.618838	+	1.03576i	0.618838	+	1.03576i
$899$		0			0
$900$	1.91644	+	0.347782i	1.91644	+	0.347782i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.341553	−	0.470107i	0.341553	−	0.470107i
$905$		0			0
$906$		0			0
$907$	−1.85845	−	0.512899i	−1.85845	−	0.512899i	−0.858449	−	0.512899i	$-0.828571\pi$
$907$	−1.85845	−	0.512899i	−1.85845	−	0.512899i	−1.00000			$\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	0.797936	+	0.341054i	0.797936	+	0.341054i	0.753071	−	0.657939i	$-0.228571\pi$
$911$	0.797936	+	0.341054i	0.797936	+	0.341054i	0.0448648	+	0.998993i	$0.485714\pi$
$912$		0			0
$913$		0			0
$914$	1.17944	−	1.47897i	1.17944	−	1.47897i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−1.61946	+	0.692192i	−1.61946	+	0.692192i	−0.995974	−	0.0896393i	$-0.971429\pi$
$919$	−1.61946	+	0.692192i	−1.61946	+	0.692192i	−0.623490	+	0.781831i	$0.714286\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.0777861	−	0.161524i	−0.0777861	−	0.161524i
$926$	−0.243029	−	0.880596i	−0.243029	−	0.880596i
$927$		0			0
$928$	0.232849	+	0.243541i	0.232849	+	0.243541i
$929$		0			0		0.919528	−	0.393025i	$-0.128571\pi$
$929$		0			0		−0.919528	+	0.393025i	$0.871429\pi$
$930$		0			0
$931$		0			0
$932$	2.69202	−	2.81563i	2.69202	−	2.81563i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$937$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$938$	−1.62062	−	0.145858i	−1.62062	−	0.145858i
$939$		0			0
$940$		0			0
$941$		0			0		0.657939	−	0.753071i	$-0.271429\pi$
$941$		0			0		−0.657939	+	0.753071i	$0.728571\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−0.0770283	−	1.71517i	−0.0770283	−	1.71517i
$947$	−1.80194			−1.80194			−0.900969	−	0.433884i	$-0.857143\pi$
$947$	−1.80194			−1.80194			−0.900969	+	0.433884i	$0.857143\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.0829607	+	0.255327i	0.0829607	+	0.255327i	0.983930	−	0.178557i	$-0.0571429\pi$
$953$	0.0829607	+	0.255327i	0.0829607	+	0.255327i	−0.900969	+	0.433884i	$0.857143\pi$
$954$	−2.57548	−	0.231798i	−2.57548	−	0.231798i
$955$		0			0
$956$	−2.49872	−	0.570318i	−2.49872	−	0.570318i
$957$		0			0
$958$		0			0
$959$	1.82241	+	0.778936i	1.82241	+	0.778936i
$960$		0			0
$961$	−0.550897	+	0.834573i	−0.550897	+	0.834573i
$962$		0			0
$963$	−1.53483	+	0.656016i	−1.53483	+	0.656016i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.0777861	+	0.161524i	0.0777861	+	0.161524i	0.936235	−	0.351375i	$-0.114286\pi$
$967$	0.0777861	+	0.161524i	0.0777861	+	0.161524i	−0.858449	+	0.512899i	$0.828571\pi$
$968$	−0.771064	−	1.43288i	−0.771064	−	1.43288i
$969$		0			0
$970$		0			0
$971$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$971$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$972$		0			0
$973$		0			0
$974$	−0.148505	−	0.0409847i	−0.148505	−	0.0409847i
$975$		0			0
$976$		0			0
$977$	0.813584	+	1.51189i	0.813584	+	1.51189i	0.858449	+	0.512899i	$0.171429\pi$
$977$	0.813584	+	1.51189i	0.813584	+	1.51189i	−0.0448648	+	0.998993i	$0.514286\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−1.74905	−	0.747578i	−1.74905	−	0.747578i
$982$	−0.661586	+	2.03615i	−0.661586	+	2.03615i
$983$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$983$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1.61152	−	1.17084i	−1.61152	−	1.17084i
$990$		0			0
$991$	−0.678448	+	1.40881i	−0.678448	+	1.40881i	0.222521	+	0.974928i	$0.428571\pi$
$991$	−0.678448	+	1.40881i	−0.678448	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$992$		0			0
$993$		0			0
$994$	1.03520	+	1.73264i	1.03520	+	1.73264i
$995$		0			0
$996$		0			0
$997$		0			0		0.858449	−	0.512899i	$-0.171429\pi$
$997$		0			0		−0.858449	+	0.512899i	$0.828571\pi$
$998$	2.86287	−	1.88976i	2.86287	−	1.88976i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3311.1.ex.a.1140.1	✓	24
7.6	odd	2	CM	3311.1.ex.a.1140.1	✓	24
11.8	odd	10		3311.1.ex.b.2043.1	yes	24
43.2	odd	14		3311.1.ex.b.1679.1	yes	24
77.41	even	10		3311.1.ex.b.2043.1	yes	24
301.174	even	14		3311.1.ex.b.1679.1	yes	24
473.217	even	70	inner	3311.1.ex.a.2582.1	yes	24
3311.2582	odd	70	inner	3311.1.ex.a.2582.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3311.1.ex.a.1140.1	✓	24	1.1	even	1	trivial
3311.1.ex.a.1140.1	✓	24	7.6	odd	2	CM
3311.1.ex.a.2582.1	yes	24	473.217	even	70	inner
3311.1.ex.a.2582.1	yes	24	3311.2582	odd	70	inner
3311.1.ex.b.1679.1	yes	24	43.2	odd	14
3311.1.ex.b.1679.1	yes	24	301.174	even	14
3311.1.ex.b.2043.1	yes	24	11.8	odd	10
3311.1.ex.b.2043.1	yes	24	77.41	even	10

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.ex (of order \(70\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.813584 - 1.51189i) q^{2} +(-1.07300 + 1.62553i) q^{4} +(-0.309017 - 0.951057i) q^{7} +(1.62062 + 0.145858i) q^{8} +(0.963963 - 0.266037i) q^{9} +O(q^{10})\)	\(q+(-0.813584 - 1.51189i) q^{2} +(-1.07300 + 1.62553i) q^{4} +(-0.309017 - 0.951057i) q^{7} +(1.62062 + 0.145858i) q^{8} +(0.963963 - 0.266037i) q^{9} +(-0.473869 + 0.880596i) q^{11} +(-1.18648 + 1.24096i) q^{14} +(-0.332477 - 0.777868i) q^{16} +(-1.18648 - 1.24096i) q^{18} +1.71690 q^{22} +(1.24196 - 1.55737i) q^{23} +(-0.134233 - 0.990950i) q^{25} +(1.87755 + 0.518170i) q^{28} +(-0.258792 + 1.91048i) q^{29} +(0.108967 - 0.136641i) q^{32} +(-0.601884 + 1.85241i) q^{36} +(0.170504 - 0.0554001i) q^{37} +(-0.0448648 - 0.998993i) q^{43} +(-0.922972 - 1.71517i) q^{44} +(-3.36501 - 0.610660i) q^{46} +(-0.809017 + 0.587785i) q^{49} +(-1.38900 + 1.00917i) q^{50} +(1.13423 - 0.990950i) q^{53} +(-0.362079 - 1.58637i) q^{56} +(3.09899 - 1.16307i) q^{58} +(-0.550897 - 0.834573i) q^{63} +(-1.12759 - 0.204627i) q^{64} +(0.590905 + 0.740971i) q^{67} +(0.312745 - 1.13321i) q^{71} +(1.60102 - 0.290542i) q^{72} +(-0.222478 - 0.212711i) q^{74} +(0.983930 + 0.178557i) q^{77} +(1.17439 - 1.61640i) q^{79} +(0.858449 - 0.512899i) q^{81} +(-1.47387 + 0.880596i) q^{86} +(-0.896402 + 1.35799i) q^{88} +(1.19892 + 3.68990i) q^{92} +(1.54687 + 0.744934i) q^{98} +(-0.222521 + 0.974928i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 3 q^{4} + 6 q^{7} + 8 q^{8} - q^{9}+O(q^{10}) \) 24 * q - 2 * q^2 + 3 * q^4 + 6 * q^7 + 8 * q^8 - q^9	\( 24 q - 2 q^{2} + 3 q^{4} + 6 q^{7} + 8 q^{8} - q^{9} - q^{11} - 3 q^{14} - 3 q^{18} + 2 q^{22} - 2 q^{23} - q^{25} + 2 q^{28} + 2 q^{29} + 11 q^{32} + 4 q^{36} - 5 q^{37} + q^{43} - 26 q^{44} - 8 q^{46} - 6 q^{49} + 2 q^{50} + 25 q^{53} - 3 q^{56} + 8 q^{58} + q^{63} - 5 q^{64} + 2 q^{67} + 5 q^{71} - q^{72} + 7 q^{74} + q^{77} - 5 q^{79} + q^{81} - 25 q^{86} - 8 q^{88} + 4 q^{92} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) 24 * q - 2 * q^2 + 3 * q^4 + 6 * q^7 + 8 * q^8 - q^9 - q^11 - 3 * q^14 - 3 * q^18 + 2 * q^22 - 2 * q^23 - q^25 + 2 * q^28 + 2 * q^29 + 11 * q^32 + 4 * q^36 - 5 * q^37 + q^43 - 26 * q^44 - 8 * q^46 - 6 * q^49 + 2 * q^50 + 25 * q^53 - 3 * q^56 + 8 * q^58 + q^63 - 5 * q^64 + 2 * q^67 + 5 * q^71 - q^72 + 7 * q^74 + q^77 - 5 * q^79 + q^81 - 25 * q^86 - 8 * q^88 + 4 * q^92 - 2 * q^98 - 4 * q^99

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