LMFDB - Embedded newform 3311.1.ex.a.426.1

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			426.1
Root			$-0.550897 + 0.834573i$ of defining polynomial
Character	$\chi$	$=$	3311.426
Dual form			3311.1.ex.a.2526.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0620088 + 1.38073i) q^{2} +(-0.906606 - 0.0815960i) q^{4} +(-0.309017 + 0.951057i) q^{7} +(-0.0166473 + 0.122895i) q^{8} +(0.393025 + 0.919528i) q^{9} +O(q^{10})$	\(q+(-0.0620088 + 1.38073i) q^{2} +(-0.906606 - 0.0815960i) q^{4} +(-0.309017 + 0.951057i) q^{7} +(-0.0166473 + 0.122895i) q^{8} +(0.393025 + 0.919528i) q^{9} +(0.0448648 + 0.998993i) q^{11} +(-1.29399 - 0.485644i) q^{14} +(-1.06430 - 0.193141i) q^{16} +(-1.29399 + 0.485644i) q^{18} -1.38213 q^{22} +(0.0597394 - 0.261736i) q^{23} +(0.550897 - 0.834573i) q^{25} +(0.357759 - 0.837019i) q^{28} +(0.433033 + 0.656016i) q^{29} +(0.305076 - 1.33662i) q^{32} +(-0.281289 - 0.865719i) q^{36} +(-1.88490 - 0.612441i) q^{37} +(0.753071 + 0.657939i) q^{43} +(0.0408391 - 0.909354i) q^{44} +(0.357683 + 0.0987141i) q^{46} +(-0.809017 - 0.587785i) q^{49} +(1.11816 + 0.812393i) q^{50} +(0.449103 - 0.834573i) q^{53} +(-0.111736 - 0.0538092i) q^{56} +(-0.932636 + 0.557224i) q^{58} +(-0.995974 + 0.0896393i) q^{63} +(0.783906 + 0.216344i) q^{64} +(0.0199667 + 0.0874800i) q^{67} +(1.08097 + 0.462029i) q^{71} +(-0.119548 + 0.0329933i) q^{72} +(0.962498 - 2.56457i) q^{74} +(-0.963963 - 0.266037i) q^{77} +(0.773453 + 1.06457i) q^{79} +(-0.691063 + 0.722795i) q^{81} +(-0.955135 + 0.998993i) q^{86} +(-0.123518 - 0.0111169i) q^{88} +(-0.0755167 + 0.232416i) q^{92} +(0.861741 - 1.08059i) q^{98} +(-0.900969 + 0.433884i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3311\mathbb{Z}\right)^\times$.

$n$	$904$	$1893$	$2927$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{11}{14}\right)$

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 $

$2$	−0.0620088	+	1.38073i	−0.0620088	+	1.38073i	0.691063	+	0.722795i	$0.257143\pi$
$2$	−0.0620088	+	1.38073i	−0.0620088	+	1.38073i	−0.753071	+	0.657939i	$0.771429\pi$
$3$		0			0		−0.834573	−	0.550897i	$-0.814286\pi$
$3$		0			0		0.834573	+	0.550897i	$0.185714\pi$
$4$	−0.906606	−	0.0815960i	−0.906606	−	0.0815960i
$5$		0			0		0.880596	−	0.473869i	$-0.157143\pi$
$5$		0			0		−0.880596	+	0.473869i	$0.842857\pi$
$6$		0			0
$7$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$7$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$8$	−0.0166473	+	0.122895i	−0.0166473	+	0.122895i
$9$	0.393025	+	0.919528i	0.393025	+	0.919528i
$10$		0			0
$11$	0.0448648	+	0.998993i	0.0448648	+	0.998993i
$11$	0.0448648	+	0.998993i	0.0448648	+	0.998993i
$12$		0			0
$13$		0			0		−0.178557	−	0.983930i	$-0.557143\pi$
$13$		0			0		0.178557	+	0.983930i	$0.442857\pi$
$14$	−1.29399	−	0.485644i	−1.29399	−	0.485644i
$15$		0			0
$16$	−1.06430	−	0.193141i	−1.06430	−	0.193141i
$17$		0			0		0.178557	−	0.983930i	$-0.442857\pi$
$17$		0			0		−0.178557	+	0.983930i	$0.557143\pi$
$18$	−1.29399	+	0.485644i	−1.29399	+	0.485644i
$19$		0			0		0.858449	−	0.512899i	$-0.171429\pi$
$19$		0			0		−0.858449	+	0.512899i	$0.828571\pi$
$20$		0			0
$21$		0			0
$22$	−1.38213			−1.38213
$23$	0.0597394	−	0.261736i	0.0597394	−	0.261736i	−0.936235	−	0.351375i	$-0.885714\pi$
$23$	0.0597394	−	0.261736i	0.0597394	−	0.261736i	0.995974	+	0.0896393i	$0.0285714\pi$
$24$		0			0
$25$	0.550897	−	0.834573i	0.550897	−	0.834573i
$26$		0			0
$27$		0			0
$28$	0.357759	−	0.837019i	0.357759	−	0.837019i
$29$	0.433033	+	0.656016i	0.433033	+	0.656016i	0.983930	−	0.178557i	$-0.0571429\pi$
$29$	0.433033	+	0.656016i	0.433033	+	0.656016i	−0.550897	+	0.834573i	$0.685714\pi$
$30$		0			0
$31$		0			0		0.0448648	−	0.998993i	$-0.485714\pi$
$31$		0			0		−0.0448648	+	0.998993i	$0.514286\pi$
$32$	0.305076	−	1.33662i	0.305076	−	1.33662i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−0.281289	−	0.865719i	−0.281289	−	0.865719i
$37$	−1.88490	−	0.612441i	−1.88490	−	0.612441i	−0.983930	−	0.178557i	$-0.942857\pi$
$37$	−1.88490	−	0.612441i	−1.88490	−	0.612441i	−0.900969	−	0.433884i	$-0.857143\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.351375	−	0.936235i	$-0.385714\pi$
$41$		0			0		−0.351375	+	0.936235i	$0.614286\pi$
$42$		0			0
$43$	0.753071	+	0.657939i	0.753071	+	0.657939i
$43$	0.753071	+	0.657939i	0.753071	+	0.657939i
$44$	0.0408391	−	0.909354i	0.0408391	−	0.909354i
$45$		0			0
$46$	0.357683	+	0.0987141i	0.357683	+	0.0987141i
$47$		0			0		0.858449	−	0.512899i	$-0.171429\pi$
$47$		0			0		−0.858449	+	0.512899i	$0.828571\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$50$	1.11816	+	0.812393i	1.11816	+	0.812393i
$51$		0			0
$52$		0			0
$53$	0.449103	−	0.834573i	0.449103	−	0.834573i	−0.550897	−	0.834573i	$-0.685714\pi$
$53$	0.449103	−	0.834573i	0.449103	−	0.834573i	1.00000			$0$
$54$		0			0
$55$		0			0
$56$	−0.111736	−	0.0538092i	−0.111736	−	0.0538092i
$57$		0			0
$58$	−0.932636	+	0.557224i	−0.932636	+	0.557224i
$59$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$59$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$60$		0			0
$61$		0			0		−0.0448648	−	0.998993i	$-0.514286\pi$
$61$		0			0		0.0448648	+	0.998993i	$0.485714\pi$
$62$		0			0
$63$	−0.995974	+	0.0896393i	−0.995974	+	0.0896393i
$64$	0.783906	+	0.216344i	0.783906	+	0.216344i
$65$		0			0
$66$		0			0
$67$	0.0199667	+	0.0874800i	0.0199667	+	0.0874800i	0.983930	−	0.178557i	$-0.0571429\pi$
$67$	0.0199667	+	0.0874800i	0.0199667	+	0.0874800i	−0.963963	+	0.266037i	$0.914286\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.08097	+	0.462029i	1.08097	+	0.462029i	0.858449	−	0.512899i	$-0.171429\pi$
$71$	1.08097	+	0.462029i	1.08097	+	0.462029i	0.222521	+	0.974928i	$0.428571\pi$
$72$	−0.119548	+	0.0329933i	−0.119548	+	0.0329933i
$73$		0			0		0.691063	−	0.722795i	$-0.257143\pi$
$73$		0			0		−0.691063	+	0.722795i	$0.742857\pi$
$74$	0.962498	−	2.56457i	0.962498	−	2.56457i
$75$		0			0
$76$		0			0
$77$	−0.963963	−	0.266037i	−0.963963	−	0.266037i
$78$		0			0
$79$	0.773453	+	1.06457i	0.773453	+	1.06457i	0.995974	+	0.0896393i	$0.0285714\pi$
$79$	0.773453	+	1.06457i	0.773453	+	1.06457i	−0.222521	+	0.974928i	$0.571429\pi$
$80$		0			0
$81$	−0.691063	+	0.722795i	−0.691063	+	0.722795i
$82$		0			0
$83$		0			0		0.998993	−	0.0448648i	$-0.0142857\pi$
$83$		0			0		−0.998993	+	0.0448648i	$0.985714\pi$
$84$		0			0
$85$		0			0
$86$	−0.955135	+	0.998993i	−0.955135	+	0.998993i
$87$		0			0
$88$	−0.123518	−	0.0111169i	−0.123518	−	0.0111169i
$89$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$89$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$90$		0			0
$91$		0			0
$92$	−0.0755167	+	0.232416i	−0.0755167	+	0.232416i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.393025	−	0.919528i	$-0.628571\pi$
$97$		0			0		0.393025	+	0.919528i	$0.371429\pi$
$98$	0.861741	−	1.08059i	0.861741	−	1.08059i
$99$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$100$	−0.567544	+	0.711678i	−0.567544	+	0.711678i
$101$		0			0		0.657939	−	0.753071i	$-0.271429\pi$
$101$		0			0		−0.657939	+	0.753071i	$0.728571\pi$
$102$		0			0
$103$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$103$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$104$		0			0
$105$		0			0
$106$	1.12447	+	0.671843i	1.12447	+	0.671843i
$107$	0.149621	+	0.0987640i	0.149621	+	0.0987640i	0.623490	−	0.781831i	$-0.285714\pi$
$107$	0.149621	+	0.0987640i	0.149621	+	0.0987640i	−0.473869	+	0.880596i	$0.657143\pi$
$108$		0			0
$109$	−1.85442	−	0.423260i	−1.85442	−	0.423260i	−0.858449	−	0.512899i	$-0.828571\pi$
$109$	−1.85442	−	0.423260i	−1.85442	−	0.423260i	−0.995974	+	0.0896393i	$0.971429\pi$
$110$		0			0
$111$		0			0
$112$	0.512573	−	0.952521i	0.512573	−	0.952521i
$113$	0.384580	−	0.367696i	0.384580	−	0.367696i	−0.473869	−	0.880596i	$-0.657143\pi$
$113$	0.384580	−	0.367696i	0.384580	−	0.367696i	0.858449	+	0.512899i	$0.171429\pi$
$114$		0			0
$115$		0			0
$116$	−0.339062	−	0.630082i	−0.339062	−	0.630082i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.995974	+	0.0896393i	−0.995974	+	0.0896393i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−0.0620088	−	1.38073i	−0.0620088	−	1.38073i
$127$	−0.506032	−	1.83357i	−0.506032	−	1.83357i	−0.550897	−	0.834573i	$-0.685714\pi$
$127$	−0.506032	−	1.83357i	−0.506032	−	1.83357i	0.0448648	−	0.998993i	$-0.485714\pi$
$128$	0.0763386	−	0.234946i	0.0763386	−	0.234946i
$129$		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
$134$	−0.122025	+	0.0221442i	−0.122025	+	0.0221442i
$135$		0			0
$136$		0			0
$137$	−1.46984	+	0.790956i	−1.46984	+	0.790956i	−0.995974	−	0.0896393i	$-0.971429\pi$
$137$	−1.46984	+	0.790956i	−1.46984	+	0.790956i	−0.473869	+	0.880596i	$0.657143\pi$
$138$		0			0
$139$		0			0		0.990950	−	0.134233i	$-0.0428571\pi$
$139$		0			0		−0.990950	+	0.134233i	$0.957143\pi$
$140$		0			0
$141$		0			0
$142$	−0.704968	+	1.46388i	−0.704968	+	1.46388i
$143$		0			0
$144$	−0.240696	−	1.05456i	−0.240696	−	1.05456i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	1.65889	+	0.709042i	1.65889	+	0.709042i
$149$	−0.335148	+	0.292810i	−0.335148	+	0.292810i	−0.809017	−	0.587785i	$-0.800000\pi$
$149$	−0.335148	+	0.292810i	−0.335148	+	0.292810i	0.473869	+	0.880596i	$0.342857\pi$
$150$		0			0
$151$	−0.606975	+	0.919528i	−0.606975	+	0.919528i	0.393025	+	0.919528i	$0.371429\pi$
$151$	−0.606975	+	0.919528i	−0.606975	+	0.919528i	−1.00000			$\pi$
$152$		0			0
$153$		0			0
$154$	0.427100	−	1.31448i	0.427100	−	1.31448i
$155$		0			0
$156$		0			0
$157$		0			0		−0.512899	−	0.858449i	$-0.671429\pi$
$157$		0			0		0.512899	+	0.858449i	$0.328571\pi$
$158$	−1.51784	+	1.00192i	−1.51784	+	1.00192i
$159$		0			0
$160$		0			0
$161$	0.230465	+	0.137696i	0.230465	+	0.137696i
$162$	−0.955135	−	0.998993i	−0.955135	−	0.998993i
$163$	0.646198	−	0.276198i	0.646198	−	0.276198i	−0.0448648	−	0.998993i	$-0.514286\pi$
$163$	0.646198	−	0.276198i	0.646198	−	0.276198i	0.691063	+	0.722795i	$0.257143\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.178557	−	0.983930i	$-0.557143\pi$
$167$		0			0		0.178557	+	0.983930i	$0.442857\pi$
$168$		0			0
$169$	−0.936235	+	0.351375i	−0.936235	+	0.351375i
$170$		0			0
$171$		0			0
$172$	−0.629054	−	0.657939i	−0.629054	−	0.657939i
$173$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$173$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$174$		0			0
$175$	0.623490	+	0.781831i	0.623490	+	0.781831i
$176$	0.145197	−	1.07189i	0.145197	−	1.07189i
$177$		0			0
$178$		0			0
$179$	1.37484	−	0.446712i	1.37484	−	0.446712i	0.473869	−	0.880596i	$-0.342857\pi$
$179$	1.37484	−	0.446712i	1.37484	−	0.446712i	0.900969	+	0.433884i	$0.142857\pi$
$180$		0			0
$181$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$181$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$182$		0			0
$183$		0			0
$184$	0.0311716	+	0.0116989i	0.0311716	+	0.0116989i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.0476947	+	0.529932i	−0.0476947	+	0.529932i	0.936235	+	0.351375i	$0.114286\pi$
$191$	−0.0476947	+	0.529932i	−0.0476947	+	0.529932i	−0.983930	+	0.178557i	$0.942857\pi$
$192$		0			0
$193$	1.83720	−	0.0825089i	1.83720	−	0.0825089i	0.900969	−	0.433884i	$-0.142857\pi$
$193$	1.83720	−	0.0825089i	1.83720	−	0.0825089i	0.936235	+	0.351375i	$0.114286\pi$
$194$		0			0
$195$		0			0
$196$	0.685499	+	0.598902i	0.685499	+	0.598902i
$197$	1.30499	−	1.04070i	1.30499	−	1.04070i	0.309017	−	0.951057i	$-0.400000\pi$
$197$	1.30499	−	1.04070i	1.30499	−	1.04070i	0.995974	−	0.0896393i	$-0.0285714\pi$
$198$	−0.543210	−	1.27090i	−0.543210	−	1.27090i
$199$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$199$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$200$	0.0933941	+	0.0815960i	0.0933941	+	0.0815960i
$201$		0			0
$202$		0			0
$203$	−0.757723	+	0.209118i	−0.757723	+	0.209118i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.264152	−	0.0479366i	0.264152	−	0.0479366i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	1.29295	+	1.12961i	1.29295	+	1.12961i	0.983930	+	0.178557i	$0.0571429\pi$
$211$	1.29295	+	1.12961i	1.29295	+	1.12961i	0.309017	+	0.951057i	$0.400000\pi$
$212$	−0.475257	+	0.719984i	−0.475257	+	0.719984i
$213$		0			0
$214$	−0.145645	+	0.200463i	−0.145645	+	0.200463i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	0.699400	−	2.53422i	0.699400	−	2.53422i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.990950	−	0.134233i	$-0.957143\pi$
$223$		0			0		0.990950	+	0.134233i	$0.0428571\pi$
$224$	1.17693	+	0.703183i	1.17693	+	0.703183i
$225$	0.983930	+	0.178557i	0.983930	+	0.178557i
$226$	0.483843	+	0.553803i	0.483843	+	0.553803i
$227$		0			0		−0.550897	−	0.834573i	$-0.685714\pi$
$227$		0			0		0.550897	+	0.834573i	$0.314286\pi$
$228$		0			0
$229$		0			0		0.0448648	−	0.998993i	$-0.485714\pi$
$229$		0			0		−0.0448648	+	0.998993i	$0.514286\pi$
$230$		0			0
$231$		0			0
$232$	−0.0878301	+	0.0422968i	−0.0878301	+	0.0422968i
$233$	1.92793	+	0.532074i	1.92793	+	0.532074i	0.963963	+	0.266037i	$0.0857143\pi$
$233$	1.92793	+	0.532074i	1.92793	+	0.532074i	0.963963	+	0.266037i	$0.0857143\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.903314	+	1.51189i	0.903314	+	1.51189i	0.858449	+	0.512899i	$0.171429\pi$
$239$	0.903314	+	1.51189i	0.903314	+	1.51189i	0.0448648	+	0.998993i	$0.485714\pi$
$240$		0			0
$241$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$241$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$242$	−0.0620088	−	1.38073i	−0.0620088	−	1.38073i
$243$		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	$-0.200000\pi$
$251$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$252$	0.910270			0.910270
$253$	0.264152	+	0.0479366i	0.264152	+	0.0479366i
$254$	2.56305	−	0.584998i	2.56305	−	0.584998i
$255$		0			0
$256$	1.08102	+	0.405714i	1.08102	+	0.405714i
$257$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$257$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$258$		0			0
$259$	1.16493	−	1.60339i	1.16493	−	1.60339i
$260$		0			0
$261$	−0.433033	+	0.656016i	−0.433033	+	0.656016i
$262$		0			0
$263$	0.708207	+	0.341054i	0.708207	+	0.341054i	0.753071	−	0.657939i	$-0.228571\pi$
$263$	0.708207	+	0.341054i	0.708207	+	0.341054i	−0.0448648	+	0.998993i	$0.514286\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−0.0109639	−	0.0809390i	−0.0109639	−	0.0809390i
$269$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$269$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$270$		0			0
$271$		0			0		−0.722795	−	0.691063i	$-0.757143\pi$
$271$		0			0		0.722795	+	0.691063i	$0.242857\pi$
$272$		0			0
$273$		0			0
$274$	−1.00096	−	2.07851i	−1.00096	−	2.07851i
$275$	0.858449	+	0.512899i	0.858449	+	0.512899i
$276$		0			0
$277$	−0.465424	−	0.406628i	−0.465424	−	0.406628i	0.393025	−	0.919528i	$-0.371429\pi$
$277$	−0.465424	−	0.406628i	−0.465424	−	0.406628i	−0.858449	+	0.512899i	$0.828571\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.865767	+	0.990950i	0.865767	+	0.990950i	1.00000			$0$
$281$	0.865767	+	0.990950i	0.865767	+	0.990950i	−0.134233	+	0.990950i	$0.542857\pi$
$282$		0			0
$283$		0			0		−0.834573	−	0.550897i	$-0.814286\pi$
$283$		0			0		0.834573	+	0.550897i	$0.185714\pi$
$284$	−0.942314	−	0.507081i	−0.942314	−	0.507081i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	1.34896	−	0.244801i	1.34896	−	0.244801i
$289$	−0.936235	−	0.351375i	−0.936235	−	0.351375i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.722795	−	0.691063i	$-0.757143\pi$
$293$		0			0		0.722795	+	0.691063i	$0.242857\pi$
$294$		0			0
$295$		0			0
$296$	0.106644	−	0.221450i	0.106644	−	0.221450i
$297$		0			0
$298$	−0.383511	−	0.480907i	−0.383511	−	0.480907i
$299$		0			0
$300$		0			0
$301$	−0.858449	+	0.512899i	−0.858449	+	0.512899i
$302$	−1.23199	−	0.895090i	−1.23199	−	0.895090i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$	0.852227	+	0.319846i	0.852227	+	0.319846i
$309$		0			0
$310$		0			0
$311$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$311$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$312$		0			0
$313$		0			0		−0.266037	−	0.963963i	$-0.585714\pi$
$313$		0			0		0.266037	+	0.963963i	$0.414286\pi$
$314$		0			0
$315$		0			0
$316$	−0.614353	−	1.02825i	−0.614353	−	1.02825i
$317$	0.713714	−	1.32630i	0.713714	−	1.32630i	−0.222521	−	0.974928i	$-0.571429\pi$
$317$	0.713714	−	1.32630i	0.713714	−	1.32630i	0.936235	−	0.351375i	$-0.114286\pi$
$318$		0			0
$319$	−0.635928	+	0.462029i	−0.635928	+	0.462029i
$320$		0			0
$321$		0			0
$322$	−0.204413	+	0.309672i	−0.204413	+	0.309672i
$323$		0			0
$324$	0.685499	−	0.598902i	0.685499	−	0.598902i
$325$		0			0
$326$	0.341286	+	0.909354i	0.341286	+	0.909354i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.724216	+	1.50385i	−0.724216	+	1.50385i	0.134233	+	0.990950i	$0.457143\pi$
$331$	−0.724216	+	1.50385i	−0.724216	+	1.50385i	−0.858449	+	0.512899i	$0.828571\pi$
$332$		0			0
$333$	−0.177656	−	1.97392i	−0.177656	−	1.97392i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.37484	+	0.446712i	1.37484	+	0.446712i	0.900969	−	0.433884i	$-0.142857\pi$
$337$	1.37484	+	0.446712i	1.37484	+	0.446712i	0.473869	+	0.880596i	$0.342857\pi$
$338$	−0.427100	−	1.31448i	−0.427100	−	1.31448i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.809017	−	0.587785i	0.809017	−	0.587785i
$344$	−0.0933941	+	0.0815960i	−0.0933941	+	0.0815960i
$345$		0			0
$346$		0			0
$347$	0.0864961	+	1.92598i	0.0864961	+	1.92598i	0.309017	+	0.951057i	$0.400000\pi$
$347$	0.0864961	+	1.92598i	0.0864961	+	1.92598i	−0.222521	+	0.974928i	$0.571429\pi$
$348$		0			0
$349$		0			0		0.134233	−	0.990950i	$-0.457143\pi$
$349$		0			0		−0.134233	+	0.990950i	$0.542857\pi$
$350$	−1.11816	+	0.812393i	−1.11816	+	0.812393i
$351$		0			0
$352$	1.34896	+	0.244801i	1.34896	+	0.244801i
$353$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$353$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.531538	+	1.92598i	0.531538	+	1.92598i
$359$	0.129582	−	1.43977i	0.129582	−	1.43977i	−0.623490	−	0.781831i	$-0.714286\pi$
$359$	0.129582	−	1.43977i	0.129582	−	1.43977i	0.753071	−	0.657939i	$-0.228571\pi$
$360$		0			0
$361$	0.473869	−	0.880596i	0.473869	−	0.880596i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.858449	−	0.512899i	$-0.828571\pi$
$367$		0			0		0.858449	+	0.512899i	$0.171429\pi$
$368$	−0.114132	+	0.267026i	−0.114132	+	0.267026i
$369$		0			0
$370$		0			0
$371$	0.654946	+	0.685020i	0.654946	+	0.685020i
$372$		0			0
$373$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$373$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.127218	−	0.236410i	−0.127218	−	0.236410i	0.809017	−	0.587785i	$-0.200000\pi$
$379$	−0.127218	−	0.236410i	−0.127218	−	0.236410i	−0.936235	+	0.351375i	$0.885714\pi$
$380$		0			0
$381$		0			0
$382$	−0.728737	−	0.0987141i	−0.728737	−	0.0987141i
$383$		0			0		0.657939	−	0.753071i	$-0.271429\pi$
$383$		0			0		−0.657939	+	0.753071i	$0.728571\pi$
$384$		0			0
$385$		0			0
$386$			2.54181i			2.54181i
$387$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$388$		0			0
$389$	0.586496	−	0.387143i	0.586496	−	0.387143i	−0.222521	−	0.974928i	$-0.571429\pi$
$389$	0.586496	−	0.387143i	0.586496	−	0.387143i	0.809017	+	0.587785i	$0.200000\pi$
$390$		0			0
$391$		0			0
$392$	0.0857040	−	0.0896393i	0.0857040	−	0.0896393i
$393$		0			0
$394$	1.35600	+	1.86638i	1.35600	+	1.86638i
$395$		0			0
$396$	0.852227	−	0.319846i	0.852227	−	0.319846i
$397$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$397$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$398$		0			0
$399$		0			0
$400$	−0.747507	+	0.781831i	−0.747507	+	0.781831i
$401$	1.06209	−	0.293118i	1.06209	−	0.293118i	0.309017	−	0.951057i	$-0.400000\pi$
$401$	1.06209	−	0.293118i	1.06209	−	0.293118i	0.753071	+	0.657939i	$0.228571\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−0.241751	−	1.05918i	−0.241751	−	1.05918i
$407$	0.527258	−	1.91048i	0.527258	−	1.91048i
$408$		0			0
$409$		0			0		−0.963963	−	0.266037i	$-0.914286\pi$
$409$		0			0		0.963963	+	0.266037i	$0.0857143\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.0498078	+	0.367696i	0.0498078	+	0.367696i
$415$		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
$421$	0.0919519	+	1.02167i	0.0919519	+	1.02167i	0.900969	+	0.433884i	$0.142857\pi$
$421$	0.0919519	+	1.02167i	0.0919519	+	1.02167i	−0.809017	+	0.587785i	$0.800000\pi$
$422$	−1.63987	+	1.71517i	−1.63987	+	1.71517i
$423$		0			0
$424$	0.0950887	+	0.0690860i	0.0950887	+	0.0690860i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.127589	−	0.101749i	−0.127589	−	0.101749i
$429$		0			0
$430$		0			0
$431$	0.105377	+	0.145039i	0.105377	+	0.145039i	0.858449	−	0.512899i	$-0.171429\pi$
$431$	0.105377	+	0.145039i	0.105377	+	0.145039i	−0.753071	+	0.657939i	$0.771429\pi$
$432$		0			0
$433$		0			0		−0.351375	−	0.936235i	$-0.614286\pi$
$433$		0			0		0.351375	+	0.936235i	$0.385714\pi$
$434$		0			0
$435$		0			0
$436$	1.64669	+	0.535043i	1.64669	+	0.535043i
$437$		0			0
$438$		0			0
$439$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$439$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$440$		0			0
$441$	0.222521	−	0.974928i	0.222521	−	0.974928i
$442$		0			0
$443$	0.217194	−	1.60339i	0.217194	−	1.60339i	−0.473869	−	0.880596i	$-0.657143\pi$
$443$	0.217194	−	1.60339i	0.217194	−	1.60339i	0.691063	−	0.722795i	$-0.257143\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.447996	+	0.678685i	−0.447996	+	0.678685i
$449$	0.674913	−	0.772500i	0.674913	−	0.772500i	−0.309017	−	0.951057i	$-0.600000\pi$
$449$	0.674913	−	0.772500i	0.674913	−	0.772500i	0.983930	+	0.178557i	$0.0571429\pi$
$450$	−0.307552	+	1.34747i	−0.307552	+	1.34747i
$451$		0			0
$452$	−0.378665	+	0.301975i	−0.378665	+	0.301975i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.95994	−	0.355676i	−1.95994	−	0.355676i	−0.995974	−	0.0896393i	$-0.971429\pi$
$457$	−1.95994	−	0.355676i	−1.95994	−	0.355676i	−0.963963	−	0.266037i	$-0.914286\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$461$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$462$		0			0
$463$	−0.797936	−	1.65693i	−0.797936	−	1.65693i	−0.753071	−	0.657939i	$-0.771429\pi$
$463$	−0.797936	−	1.65693i	−0.797936	−	1.65693i	−0.0448648	−	0.998993i	$-0.514286\pi$
$464$	−0.334171	−	0.781831i	−0.334171	−	0.781831i
$465$		0			0
$466$	−0.854200	+	2.62896i	−0.854200	+	2.62896i
$467$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$467$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$468$		0			0
$469$	−0.0893684	−	0.00804330i	−0.0893684	−	0.00804330i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.943922	+	0.0849545i	0.943922	+	0.0849545i
$478$	−2.14353	+	1.15348i	−2.14353	+	1.15348i
$479$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$479$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.910270			0.910270
$485$		0			0
$486$		0			0
$487$	1.41010	+	0.529221i	1.41010	+	0.529221i	0.936235	−	0.351375i	$-0.114286\pi$
$487$	1.41010	+	0.529221i	1.41010	+	0.529221i	0.473869	+	0.880596i	$0.342857\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−0.416664	+	0.156377i	−0.416664	+	0.156377i	−0.550897	−	0.834573i	$-0.685714\pi$
$491$	−0.416664	+	0.156377i	−0.416664	+	0.156377i	0.134233	+	0.990950i	$0.457143\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.773453	+	0.885289i	−0.773453	+	0.885289i
$498$		0			0
$499$	−1.30397	+	0.176635i	−1.30397	+	0.176635i	−0.753071	−	0.657939i	$-0.771429\pi$
$499$	−1.30397	+	0.176635i	−1.30397	+	0.176635i	−0.550897	+	0.834573i	$0.685714\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.134233	−	0.990950i	$-0.457143\pi$
$503$		0			0		−0.134233	+	0.990950i	$0.542857\pi$
$504$	0.00556403	−	0.123893i	0.00556403	−	0.123893i
$505$		0			0
$506$	−0.0825674	+	0.361751i	−0.0825674	+	0.361751i
$507$		0			0
$508$	0.309160	+	1.70361i	0.309160	+	1.70361i
$509$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$509$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$510$		0			0
$511$		0			0
$512$	−0.530124	+	1.24029i	−0.530124	+	1.24029i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	2.14162	+	1.70788i	2.14162	+	1.70788i
$519$		0			0
$520$		0			0
$521$		0			0		−0.722795	−	0.691063i	$-0.757143\pi$
$521$		0			0		0.722795	+	0.691063i	$0.242857\pi$
$522$	−0.878932	−	0.638581i	−0.878932	−	0.638581i
$523$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$523$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$524$		0			0
$525$		0			0
$526$	−0.514820	+	0.956696i	−0.514820	+	0.956696i
$527$		0			0
$528$		0			0
$529$	0.836032	+	0.402612i	0.836032	+	0.402612i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−0.0110833		0.000997512i	−0.0110833		0.000997512i
$537$		0			0
$538$		0			0
$539$	0.550897	−	0.834573i	0.550897	−	0.834573i
$540$		0			0
$541$	0.272900	−	0.988832i	0.272900	−	0.988832i	−0.691063	−	0.722795i	$-0.742857\pi$
$541$	0.272900	−	0.988832i	0.272900	−	0.988832i	0.963963	−	0.266037i	$-0.0857143\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.304912	−	0.812434i	0.304912	−	0.812434i	−0.691063	−	0.722795i	$-0.742857\pi$
$547$	0.304912	−	0.812434i	0.304912	−	0.812434i	0.995974	−	0.0896393i	$-0.0285714\pi$
$548$	1.39711	−	0.597152i	1.39711	−	0.597152i
$549$		0			0
$550$	−0.761409	+	1.15348i	−0.761409	+	1.15348i
$551$		0			0
$552$		0			0
$553$	−1.25147	+	0.406628i	−1.25147	+	0.406628i
$554$	0.590306	−	0.617412i	0.590306	−	0.617412i
$555$		0			0
$556$		0			0
$557$	−1.53483	+	1.01313i	−1.53483	+	1.01313i	−0.550897	+	0.834573i	$0.685714\pi$
$557$	−1.53483	+	1.01313i	−1.53483	+	1.01313i	−0.983930	+	0.178557i	$0.942857\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−1.42192	+	1.13395i	−1.42192	+	1.13395i
$563$		0			0		0.657939	−	0.753071i	$-0.271429\pi$
$563$		0			0		−0.657939	+	0.753071i	$0.728571\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.473869	−	0.880596i	−0.473869	−	0.880596i
$568$	−0.0747763	+	0.125155i	−0.0747763	+	0.125155i
$569$	0.627218	−	0.599682i	0.627218	−	0.599682i	−0.309017	−	0.951057i	$-0.600000\pi$
$569$	0.627218	−	0.599682i	0.627218	−	0.599682i	0.936235	+	0.351375i	$0.114286\pi$
$570$		0			0
$571$	1.07047	−	1.34232i	1.07047	−	1.34232i	0.134233	−	0.990950i	$-0.457143\pi$
$571$	1.07047	−	1.34232i	1.07047	−	1.34232i	0.936235	−	0.351375i	$-0.114286\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.185527	−	0.194046i	−0.185527	−	0.194046i
$576$	0.109160	+	0.805852i	0.109160	+	0.805852i
$577$		0			0		0.998993	−	0.0448648i	$-0.0142857\pi$
$577$		0			0		−0.998993	+	0.0448648i	$0.985714\pi$
$578$	0.543210	−	1.27090i	0.543210	−	1.27090i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	0.853882	+	0.411208i	0.853882	+	0.411208i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.0896393	−	0.995974i	$-0.471429\pi$
$587$		0			0		−0.0896393	+	0.995974i	$0.528571\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	1.88780	+	1.01587i	1.88780	+	1.01587i
$593$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$593$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$594$		0			0
$595$		0			0
$596$	0.327740	−	0.238117i	0.327740	−	0.238117i
$597$		0			0
$598$		0			0
$599$	0.0770283	+	1.71517i	0.0770283	+	1.71517i	0.550897	+	0.834573i	$0.314286\pi$
$599$	0.0770283	+	1.71517i	0.0770283	+	1.71517i	−0.473869	+	0.880596i	$0.657143\pi$
$600$		0			0
$601$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$601$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$602$	−0.654946	−	1.21709i	−0.654946	−	1.21709i
$603$	−0.0725928	+	0.0527418i	−0.0725928	+	0.0527418i
$604$	0.625317	−	0.784123i	0.625317	−	0.784123i
$605$		0			0
$606$		0			0
$607$		0			0		0.983930	−	0.178557i	$-0.0571429\pi$
$607$		0			0		−0.983930	+	0.178557i	$0.942857\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.0320114	+	0.355676i	0.0320114	+	0.355676i	0.995974	+	0.0896393i	$0.0285714\pi$
$613$	0.0320114	+	0.355676i	0.0320114	+	0.355676i	−0.963963	+	0.266037i	$0.914286\pi$
$614$		0			0
$615$		0			0
$616$	0.0487420	−	0.114038i	0.0487420	−	0.114038i
$617$	−0.210891	−	0.923976i	−0.210891	−	0.923976i	−0.963963	−	0.266037i	$-0.914286\pi$
$617$	−0.210891	−	0.923976i	−0.210891	−	0.923976i	0.753071	−	0.657939i	$-0.228571\pi$
$618$		0			0
$619$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$619$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.393025	−	0.919528i	−0.393025	−	0.919528i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−1.20645	+	0.796371i	−1.20645	+	0.796371i	−0.983930	−	0.178557i	$-0.942857\pi$
$631$	−1.20645	+	0.796371i	−1.20645	+	0.796371i	−0.222521	+	0.974928i	$0.571429\pi$
$632$	−0.143706	+	0.0773316i	−0.143706	+	0.0773316i
$633$		0			0
$634$	1.78701	+	1.06769i	1.78701	+	1.06769i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−0.598505	−	0.906697i	−0.598505	−	0.906697i
$639$			1.17557i			1.17557i
$640$		0			0
$641$	0.943250	+	1.57874i	0.943250	+	1.57874i	0.809017	+	0.587785i	$0.200000\pi$
$641$	0.943250	+	1.57874i	0.943250	+	1.57874i	0.134233	+	0.990950i	$0.457143\pi$
$642$		0			0
$643$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$643$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$644$	−0.197705	−	0.143641i	−0.197705	−	0.143641i
$645$		0			0
$646$		0			0
$647$		0			0		−0.998993	−	0.0448648i	$-0.985714\pi$
$647$		0			0		0.998993	+	0.0448648i	$0.0142857\pi$
$648$	−0.0773237	−	0.0969609i	−0.0773237	−	0.0969609i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.608383	+	0.197676i	−0.608383	+	0.197676i
$653$	−1.43251	−	1.36962i	−1.43251	−	1.36962i	−0.809017	−	0.587785i	$-0.800000\pi$
$653$	−1.43251	−	1.36962i	−1.43251	−	1.36962i	−0.623490	−	0.781831i	$-0.714286\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.52446	+	1.21572i	1.52446	+	1.21572i	0.900969	+	0.433884i	$0.142857\pi$
$659$	1.52446	+	1.21572i	1.52446	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$660$		0			0
$661$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$661$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$662$	−2.03151	−	1.09320i	−2.03151	−	1.09320i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	2.73648	−	0.122895i	2.73648	−	0.122895i
$667$	0.197572	−	0.0741500i	0.197572	−	0.0741500i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.0675728	+	0.0590366i	0.0675728	+	0.0590366i	0.691063	−	0.722795i	$-0.257143\pi$
$673$	0.0675728	+	0.0590366i	0.0675728	+	0.0590366i	−0.623490	+	0.781831i	$0.714286\pi$
$674$	−0.702042	+	1.87058i	−0.702042	+	1.87058i
$675$		0			0
$676$	0.877467	−	0.242165i	0.877467	−	0.242165i
$677$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$677$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.556829	−	0.268155i	−0.556829	−	0.268155i	0.134233	−	0.990950i	$-0.457143\pi$
$683$	−0.556829	−	0.268155i	−0.556829	−	0.268155i	−0.691063	+	0.722795i	$0.742857\pi$
$684$		0			0
$685$		0			0
$686$	0.761409	+	1.15348i	0.761409	+	1.15348i
$687$		0			0
$688$	−0.674415	−	0.845690i	−0.674415	−	0.845690i
$689$		0			0
$690$		0			0
$691$		0			0		0.266037	−	0.963963i	$-0.414286\pi$
$691$		0			0		−0.266037	+	0.963963i	$0.585714\pi$
$692$		0			0
$693$	−0.134233	−	0.990950i	−0.134233	−	0.990950i
$694$	−2.66463			−2.66463
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.501465	−	0.759687i	−0.501465	−	0.759687i
$701$	−0.177656	−	0.0240652i	−0.177656	−	0.0240652i	0.0448648	−	0.998993i	$-0.485714\pi$
$701$	−0.177656	−	0.0240652i	−0.177656	−	0.0240652i	−0.222521	+	0.974928i	$0.571429\pi$
$702$		0			0
$703$		0			0
$704$	−0.180957	+	0.792823i	−0.180957	+	0.792823i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.0425201	+	0.946783i	0.0425201	+	0.946783i	0.900969	+	0.433884i	$0.142857\pi$
$709$	0.0425201	+	0.946783i	0.0425201	+	0.946783i	−0.858449	+	0.512899i	$0.828571\pi$
$710$		0			0
$711$	−0.674913	+	1.12961i	−0.674913	+	1.12961i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.28289	+	0.292810i	−1.28289	+	0.292810i
$717$		0			0
$718$	1.97990	+	0.268196i	1.97990	+	0.268196i
$719$		0			0		−0.550897	−	0.834573i	$-0.685714\pi$
$719$		0			0		0.550897	+	0.834573i	$0.314286\pi$
$720$		0			0
$721$		0			0
$722$	1.18648	+	0.708891i	1.18648	+	0.708891i
$723$		0			0
$724$		0			0
$725$	0.786050			0.786050
$726$		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
$729$	−0.936235	−	0.351375i	−0.936235	−	0.351375i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.550897	−	0.834573i	$-0.685714\pi$
$733$		0			0		0.550897	+	0.834573i	$0.314286\pi$
$734$		0			0
$735$		0			0
$736$	−0.331617	−	0.159698i	−0.331617	−	0.159698i
$737$	−0.0864961	+	0.0238714i	−0.0864961	+	0.0238714i
$738$		0			0
$739$	−1.93623	+	0.351375i	−1.93623	+	0.351375i	−0.936235	+	0.351375i	$0.885714\pi$
$739$	−1.93623	+	0.351375i	−1.93623	+	0.351375i	−1.00000			$\pi$
$740$		0			0
$741$		0			0
$742$	−0.986442	+	0.861828i	−0.986442	+	0.861828i
$743$	1.89694	−	0.523523i	1.89694	−	0.523523i	0.900969	−	0.433884i	$-0.142857\pi$
$743$	1.89694	−	0.523523i	1.89694	−	0.523523i	0.995974	−	0.0896393i	$-0.0285714\pi$
$744$		0			0
$745$		0			0
$746$	−1.87553	−	1.63860i	−1.87553	−	1.63860i
$747$		0			0
$748$		0			0
$749$	−0.140166	+	0.111778i	−0.140166	+	0.111778i
$750$		0			0
$751$	−0.0919519	−	1.02167i	−0.0919519	−	1.02167i	−0.900969	−	0.433884i	$-0.857143\pi$
$751$	−0.0919519	−	1.02167i	−0.0919519	−	1.02167i	0.809017	−	0.587785i	$-0.200000\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.03520	−	0.557066i	−1.03520	−	0.557066i	−0.134233	−	0.990950i	$-0.542857\pi$
$757$	−1.03520	−	0.557066i	−1.03520	−	0.557066i	−0.900969	+	0.433884i	$0.857143\pi$
$758$	0.334308	−	0.160994i	0.334308	−	0.160994i
$759$		0			0
$760$		0			0
$761$		0			0		0.983930	−	0.178557i	$-0.0571429\pi$
$761$		0			0		−0.983930	+	0.178557i	$0.942857\pi$
$762$		0			0
$763$	0.975592	−	1.63287i	0.975592	−	1.63287i
$764$	0.0864806	−	0.476548i	0.0864806	−	0.476548i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$769$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$770$		0			0
$771$		0			0
$772$	−1.67235	−	0.0751054i	−1.67235	−	0.0751054i
$773$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$773$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$774$	−1.29399	−	0.485644i	−1.29399	−	0.485644i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	0.498173	+	0.833801i	0.498173	+	0.833801i
$779$		0			0
$780$		0			0
$781$	−0.413066	+	1.10061i	−0.413066	+	1.10061i
$782$		0			0
$783$		0			0
$784$	0.747507	+	0.781831i	0.747507	+	0.781831i
$785$		0			0
$786$		0			0
$787$		0			0		0.880596	−	0.473869i	$-0.157143\pi$
$787$		0			0		−0.880596	+	0.473869i	$0.842857\pi$
$788$	−1.26803	+	0.837019i	−1.26803	+	0.837019i
$789$		0			0
$790$		0			0
$791$	0.230858	+	0.479382i	0.230858	+	0.479382i
$792$	−0.0383236	−	0.117948i	−0.0383236	−	0.117948i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$797$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$798$		0			0
$799$		0			0
$800$	−0.947445	−	0.990950i	−0.947445	−	0.990950i
$801$		0			0
$802$	0.338859	+	1.48464i	0.338859	+	1.48464i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.618838	−	0.333011i	0.618838	−	0.333011i	−0.134233	−	0.990950i	$-0.542857\pi$
$809$	0.618838	−	0.333011i	0.618838	−	0.333011i	0.753071	+	0.657939i	$0.228571\pi$
$810$		0			0
$811$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$811$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$812$	0.704019	−	0.127761i	0.704019	−	0.127761i
$813$		0			0
$814$	2.60517	+	0.846470i	2.60517	+	0.846470i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.174784	−	1.94201i	0.174784	−	1.94201i	−0.134233	−	0.990950i	$-0.542857\pi$
$821$	0.174784	−	1.94201i	0.174784	−	1.94201i	0.309017	−	0.951057i	$-0.400000\pi$
$822$		0			0
$823$	−1.55972	+	1.13321i	−1.55972	+	1.13321i	−0.623490	+	0.781831i	$0.714286\pi$
$823$	−1.55972	+	1.13321i	−1.55972	+	1.13321i	−0.936235	+	0.351375i	$0.885714\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.37695	−	0.740971i	−1.37695	−	0.740971i	−0.393025	−	0.919528i	$-0.628571\pi$
$827$	−1.37695	−	0.740971i	−1.37695	−	0.740971i	−0.983930	+	0.178557i	$0.942857\pi$
$828$	−0.243393	+	0.0219058i	−0.243393	+	0.0219058i
$829$		0			0		0.834573	−	0.550897i	$-0.185714\pi$
$829$		0			0		−0.834573	+	0.550897i	$0.814286\pi$
$830$		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		−0.834573	−	0.550897i	$-0.814286\pi$
$839$		0			0		0.834573	+	0.550897i	$0.185714\pi$
$840$		0			0
$841$	0.150185	−	0.351375i	0.150185	−	0.351375i
$842$	−1.41635	+	0.0636086i	−1.41635	+	0.0636086i
$843$		0			0
$844$	−1.08002	−	1.12961i	−1.08002	−	1.12961i
$845$		0			0
$846$		0			0
$847$	0.222521	−	0.974928i	0.222521	−	0.974928i
$848$	−0.639169	+	0.801492i	−0.639169	+	0.801492i
$849$		0			0
$850$		0			0
$851$	−0.272900	+	0.456758i	−0.272900	+	0.456758i
$852$		0			0
$853$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$853$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$854$		0			0
$855$		0			0
$856$	−0.0146284	+	0.0167436i	−0.0146284	+	0.0167436i
$857$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$857$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$858$		0			0
$859$		0			0			−	1.00000i	$-0.5\pi$
$859$		0			0				1.00000i	$0.5\pi$
$860$		0			0
$861$		0			0
$862$	−0.206795	+	0.136504i	−0.206795	+	0.136504i
$863$	1.94789	−	0.0874800i	1.94789	−	0.0874800i	0.963963	−	0.266037i	$-0.0857143\pi$
$863$	1.94789	−	0.0874800i	1.94789	−	0.0874800i	0.983930	+	0.178557i	$0.0571429\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.02879	+	0.820436i	−1.02879	+	0.820436i
$870$		0			0
$871$		0			0
$872$	0.0828878	−	0.220854i	0.0828878	−	0.220854i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.44413	+	1.38073i	−1.44413	+	1.38073i	−0.691063	+	0.722795i	$0.742857\pi$
$877$	−1.44413	+	1.38073i	−1.44413	+	1.38073i	−0.753071	+	0.657939i	$0.771429\pi$
$878$		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	$0.285714\pi$
$882$	1.33232	+	0.367696i	1.33232	+	0.367696i
$883$	1.79468	−	0.161524i	1.79468	−	0.161524i	0.858449	−	0.512899i	$-0.171429\pi$
$883$	1.79468	−	0.161524i	1.79468	−	0.161524i	0.936235	+	0.351375i	$0.114286\pi$
$884$		0			0
$885$		0			0
$886$	2.20039	+	0.399311i	2.20039	+	0.399311i
$887$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$887$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$888$		0			0
$889$	1.90020	+	0.0853380i	1.90020	+	0.0853380i
$890$		0			0
$891$	−0.753071	−	0.657939i	−0.753071	−	0.657939i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	0.199857	+	0.145205i	0.199857	+	0.145205i
$897$		0			0
$898$	1.02477	+	0.979776i	1.02477	+	0.979776i
$899$		0			0
$900$	−0.877467	−	0.242165i	−0.877467	−	0.242165i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.0387859	+	0.0533842i	0.0387859	+	0.0533842i
$905$		0			0
$906$		0			0
$907$	−0.308937	+	0.722795i	−0.308937	+	0.722795i	0.691063	+	0.722795i	$0.257143\pi$
$907$	−0.308937	+	0.722795i	−0.308937	+	0.722795i	−1.00000			$\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.279203	−	1.53853i	−0.279203	−	1.53853i	−0.753071	−	0.657939i	$-0.771429\pi$
$911$	−0.279203	−	1.53853i	−0.279203	−	1.53853i	0.473869	−	0.880596i	$-0.342857\pi$
$912$		0			0
$913$		0			0
$914$	0.612627	−	2.68410i	0.612627	−	2.68410i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	0.356754	−	1.96588i	0.356754	−	1.96588i	0.134233	−	0.990950i	$-0.457143\pi$
$919$	0.356754	−	1.96588i	0.356754	−	1.96588i	0.222521	−	0.974928i	$-0.428571\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−1.54951	+	1.23569i	−1.54951	+	1.23569i
$926$	2.33726	−	0.998993i	2.33726	−	0.998993i
$927$		0			0
$928$	1.00895	−	0.378667i	1.00895	−	0.378667i
$929$		0			0		0.178557	−	0.983930i	$-0.442857\pi$
$929$		0			0		−0.178557	+	0.983930i	$0.557143\pi$
$930$		0			0
$931$		0			0
$932$	−1.70445	−	0.639692i	−1.70445	−	0.639692i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.393025	−	0.919528i	$-0.628571\pi$
$937$		0			0		0.393025	+	0.919528i	$0.371429\pi$
$938$	0.0166473	−	0.122895i	0.0166473	−	0.122895i
$939$		0			0
$940$		0			0
$941$		0			0		0.880596	−	0.473869i	$-0.157143\pi$
$941$		0			0		−0.880596	+	0.473869i	$0.842857\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−1.04084	−	0.909354i	−1.04084	−	0.909354i
$947$	1.24698			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$947$	1.24698			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.340473	+	1.04787i	−0.340473	+	1.04787i	0.623490	+	0.781831i	$0.285714\pi$
$953$	−0.340473	+	1.04787i	−0.340473	+	1.04787i	−0.963963	+	0.266037i	$0.914286\pi$
$954$	−0.175831	+	1.29804i	−0.175831	+	1.29804i
$955$		0			0
$956$	−0.695585	−	1.44440i	−0.695585	−	1.44440i
$957$		0			0
$958$		0			0
$959$	−0.298038	−	1.64232i	−0.298038	−	1.64232i
$960$		0			0
$961$	−0.995974	−	0.0896393i	−0.995974	−	0.0896393i
$962$		0			0
$963$	−0.0320114	+	0.176398i	−0.0320114	+	0.176398i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	1.54951	−	1.23569i	1.54951	−	1.23569i	0.691063	−	0.722795i	$-0.257143\pi$
$967$	1.54951	−	1.23569i	1.54951	−	1.23569i	0.858449	−	0.512899i	$-0.171429\pi$
$968$	0.00556403	−	0.123893i	0.00556403	−	0.123893i
$969$		0			0
$970$		0			0
$971$		0			0		0.550897	−	0.834573i	$-0.314286\pi$
$971$		0			0		−0.550897	+	0.834573i	$0.685714\pi$
$972$		0			0
$973$		0			0
$974$	−0.818152	+	1.91416i	−0.818152	+	1.91416i
$975$		0			0
$976$		0			0
$977$	0.0620088	−	1.38073i	0.0620088	−	1.38073i	−0.691063	−	0.722795i	$-0.742857\pi$
$977$	0.0620088	−	1.38073i	0.0620088	−	1.38073i	0.753071	−	0.657939i	$-0.228571\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−0.339635	−	1.87155i	−0.339635	−	1.87155i
$982$	−0.190077	−	0.584998i	−0.190077	−	0.584998i
$983$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$983$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.217194	−	0.157801i	0.217194	−	0.157801i
$990$		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
$994$	−1.17439	−	1.12283i	−1.17439	−	1.12283i
$995$		0			0
$996$		0			0
$997$		0			0		0.691063	−	0.722795i	$-0.257143\pi$
$997$		0			0		−0.691063	+	0.722795i	$0.742857\pi$
$998$	−0.163028	−	1.81139i	−0.163028	−	1.81139i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3311.1.ex.a.426.1	✓	24
7.6	odd	2	CM	3311.1.ex.a.426.1	✓	24
11.7	odd	10		3311.1.ex.b.2834.1	yes	24
43.32	odd	14		3311.1.ex.b.118.1	yes	24
77.62	even	10		3311.1.ex.b.2834.1	yes	24
301.118	even	14		3311.1.ex.b.118.1	yes	24
473.161	even	70	inner	3311.1.ex.a.2526.1	yes	24
3311.2526	odd	70	inner	3311.1.ex.a.2526.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3311.1.ex.a.426.1	✓	24	1.1	even	1	trivial
3311.1.ex.a.426.1	✓	24	7.6	odd	2	CM
3311.1.ex.a.2526.1	yes	24	473.161	even	70	inner
3311.1.ex.a.2526.1	yes	24	3311.2526	odd	70	inner
3311.1.ex.b.118.1	yes	24	43.32	odd	14
3311.1.ex.b.118.1	yes	24	301.118	even	14
3311.1.ex.b.2834.1	yes	24	11.7	odd	10
3311.1.ex.b.2834.1	yes	24	77.62	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)

\(f(q)\)	\(=\)	\(q+(-0.0620088 + 1.38073i) q^{2} +(-0.906606 - 0.0815960i) q^{4} +(-0.309017 + 0.951057i) q^{7} +(-0.0166473 + 0.122895i) q^{8} +(0.393025 + 0.919528i) q^{9} +O(q^{10})\)	\(q+(-0.0620088 + 1.38073i) q^{2} +(-0.906606 - 0.0815960i) q^{4} +(-0.309017 + 0.951057i) q^{7} +(-0.0166473 + 0.122895i) q^{8} +(0.393025 + 0.919528i) q^{9} +(0.0448648 + 0.998993i) q^{11} +(-1.29399 - 0.485644i) q^{14} +(-1.06430 - 0.193141i) q^{16} +(-1.29399 + 0.485644i) q^{18} -1.38213 q^{22} +(0.0597394 - 0.261736i) q^{23} +(0.550897 - 0.834573i) q^{25} +(0.357759 - 0.837019i) q^{28} +(0.433033 + 0.656016i) q^{29} +(0.305076 - 1.33662i) q^{32} +(-0.281289 - 0.865719i) q^{36} +(-1.88490 - 0.612441i) q^{37} +(0.753071 + 0.657939i) q^{43} +(0.0408391 - 0.909354i) q^{44} +(0.357683 + 0.0987141i) q^{46} +(-0.809017 - 0.587785i) q^{49} +(1.11816 + 0.812393i) q^{50} +(0.449103 - 0.834573i) q^{53} +(-0.111736 - 0.0538092i) q^{56} +(-0.932636 + 0.557224i) q^{58} +(-0.995974 + 0.0896393i) q^{63} +(0.783906 + 0.216344i) q^{64} +(0.0199667 + 0.0874800i) q^{67} +(1.08097 + 0.462029i) q^{71} +(-0.119548 + 0.0329933i) q^{72} +(0.962498 - 2.56457i) q^{74} +(-0.963963 - 0.266037i) q^{77} +(0.773453 + 1.06457i) q^{79} +(-0.691063 + 0.722795i) q^{81} +(-0.955135 + 0.998993i) q^{86} +(-0.123518 - 0.0111169i) q^{88} +(-0.0755167 + 0.232416i) q^{92} +(0.861741 - 1.08059i) q^{98} +(-0.900969 + 0.433884i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 3 q^{4} + 6 q^{7} + 8 q^{8} - q^{9}+O(q^{10}) \) 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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