LMFDB - Embedded newform 3311.1.ex.a.237.1

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			237.1
Root			$0.983930 + 0.178557i$ of defining polynomial
Character	$\chi$	$=$	3311.237
Dual form			3311.1.ex.a.475.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.202174 + 1.49251i) q^{2} +(-1.22275 - 0.337459i) q^{4} +(0.809017 - 0.587785i) q^{7} +(0.158919 - 0.371810i) q^{8} +(-0.936235 - 0.351375i) q^{9} +O(q^{10})$	\(q+(-0.202174 + 1.49251i) q^{2} +(-1.22275 - 0.337459i) q^{4} +(0.809017 - 0.587785i) q^{7} +(0.158919 - 0.371810i) q^{8} +(-0.936235 - 0.351375i) q^{9} +(-0.134233 - 0.990950i) q^{11} +(0.713714 + 1.32630i) q^{14} +(-0.566112 - 0.338236i) q^{16} +(0.713714 - 1.32630i) q^{18} +1.50614 q^{22} +(0.490094 - 0.614559i) q^{23} +(-0.983930 - 0.178557i) q^{25} +(-1.18758 + 0.445707i) q^{28} +(1.84238 - 0.334342i) q^{29} +(0.871382 - 1.09268i) q^{32} +(1.02621 + 0.745586i) q^{36} +(-1.08097 - 1.48783i) q^{37} +(-0.550897 + 0.834573i) q^{43} +(-0.170270 + 1.25699i) q^{44} +(0.818152 + 0.855720i) q^{46} +(0.309017 - 0.951057i) q^{49} +(0.465424 - 1.43243i) q^{50} +(1.98393 - 0.178557i) q^{53} +(-0.0899761 - 0.394211i) q^{56} +(0.126528 + 2.81737i) q^{58} +(-0.963963 + 0.266037i) q^{63} +(0.998937 + 1.04481i) q^{64} +(0.167386 + 0.209896i) q^{67} +(-0.668355 - 1.78082i) q^{71} +(-0.279430 + 0.292261i) q^{72} +(2.43914 - 1.31256i) q^{74} +(-0.691063 - 0.722795i) q^{77} +(1.58745 - 0.515795i) q^{79} +(0.753071 + 0.657939i) q^{81} +(-1.13423 - 0.990950i) q^{86} +(-0.389777 - 0.107572i) q^{88} +(-0.806653 + 0.586068i) q^{92} +(1.35699 + 0.653491i) q^{98} +(-0.222521 + 0.974928i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3311\mathbb{Z}\right)^\times$.

$n$	$904$	$1893$	$2927$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$	$e\left(\frac{5}{14}\right)$

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 $

$2$	−0.202174	+	1.49251i	−0.202174	+	1.49251i	0.550897	+	0.834573i	$0.314286\pi$
$2$	−0.202174	+	1.49251i	−0.202174	+	1.49251i	−0.753071	+	0.657939i	$0.771429\pi$
$3$		0			0		0.178557	−	0.983930i	$-0.442857\pi$
$3$		0			0		−0.178557	+	0.983930i	$0.557143\pi$
$4$	−1.22275	−	0.337459i	−1.22275	−	0.337459i
$5$		0			0		0.0896393	−	0.995974i	$-0.471429\pi$
$5$		0			0		−0.0896393	+	0.995974i	$0.528571\pi$
$6$		0			0
$7$	0.809017	−	0.587785i	0.809017	−	0.587785i
$7$	0.809017	−	0.587785i	0.809017	−	0.587785i
$8$	0.158919	−	0.371810i	0.158919	−	0.371810i
$9$	−0.936235	−	0.351375i	−0.936235	−	0.351375i
$10$		0			0
$11$	−0.134233	−	0.990950i	−0.134233	−	0.990950i
$11$	−0.134233	−	0.990950i	−0.134233	−	0.990950i
$12$		0			0
$13$		0			0		−0.512899	−	0.858449i	$-0.671429\pi$
$13$		0			0		0.512899	+	0.858449i	$0.328571\pi$
$14$	0.713714	+	1.32630i	0.713714	+	1.32630i
$15$		0			0
$16$	−0.566112	−	0.338236i	−0.566112	−	0.338236i
$17$		0			0		0.512899	−	0.858449i	$-0.328571\pi$
$17$		0			0		−0.512899	+	0.858449i	$0.671429\pi$
$18$	0.713714	−	1.32630i	0.713714	−	1.32630i
$19$		0			0		−0.0448648	−	0.998993i	$-0.514286\pi$
$19$		0			0		0.0448648	+	0.998993i	$0.485714\pi$
$20$		0			0
$21$		0			0
$22$	1.50614			1.50614
$23$	0.490094	−	0.614559i	0.490094	−	0.614559i	−0.473869	−	0.880596i	$-0.657143\pi$
$23$	0.490094	−	0.614559i	0.490094	−	0.614559i	0.963963	+	0.266037i	$0.0857143\pi$
$24$		0			0
$25$	−0.983930	−	0.178557i	−0.983930	−	0.178557i
$26$		0			0
$27$		0			0
$28$	−1.18758	+	0.445707i	−1.18758	+	0.445707i
$29$	1.84238	−	0.334342i	1.84238	−	0.334342i	0.858449	−	0.512899i	$-0.171429\pi$
$29$	1.84238	−	0.334342i	1.84238	−	0.334342i	0.983930	+	0.178557i	$0.0571429\pi$
$30$		0			0
$31$		0			0		0.134233	−	0.990950i	$-0.457143\pi$
$31$		0			0		−0.134233	+	0.990950i	$0.542857\pi$
$32$	0.871382	−	1.09268i	0.871382	−	1.09268i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	1.02621	+	0.745586i	1.02621	+	0.745586i
$37$	−1.08097	−	1.48783i	−1.08097	−	1.48783i	−0.858449	−	0.512899i	$-0.828571\pi$
$37$	−1.08097	−	1.48783i	−1.08097	−	1.48783i	−0.222521	−	0.974928i	$-0.571429\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.880596	−	0.473869i	$-0.157143\pi$
$41$		0			0		−0.880596	+	0.473869i	$0.842857\pi$
$42$		0			0
$43$	−0.550897	+	0.834573i	−0.550897	+	0.834573i
$43$	−0.550897	+	0.834573i	−0.550897	+	0.834573i
$44$	−0.170270	+	1.25699i	−0.170270	+	1.25699i
$45$		0			0
$46$	0.818152	+	0.855720i	0.818152	+	0.855720i
$47$		0			0		−0.0448648	−	0.998993i	$-0.514286\pi$
$47$		0			0		0.0448648	+	0.998993i	$0.485714\pi$
$48$		0			0
$49$	0.309017	−	0.951057i	0.309017	−	0.951057i
$50$	0.465424	−	1.43243i	0.465424	−	1.43243i
$51$		0			0
$52$		0			0
$53$	1.98393	−	0.178557i	1.98393	−	0.178557i	0.983930	−	0.178557i	$-0.0571429\pi$
$53$	1.98393	−	0.178557i	1.98393	−	0.178557i	1.00000			$0$
$54$		0			0
$55$		0			0
$56$	−0.0899761	−	0.394211i	−0.0899761	−	0.394211i
$57$		0			0
$58$	0.126528	+	2.81737i	0.126528	+	2.81737i
$59$		0			0		−0.393025	−	0.919528i	$-0.628571\pi$
$59$		0			0		0.393025	+	0.919528i	$0.371429\pi$
$60$		0			0
$61$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$61$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$62$		0			0
$63$	−0.963963	+	0.266037i	−0.963963	+	0.266037i
$64$	0.998937	+	1.04481i	0.998937	+	1.04481i
$65$		0			0
$66$		0			0
$67$	0.167386	+	0.209896i	0.167386	+	0.209896i	0.858449	−	0.512899i	$-0.171429\pi$
$67$	0.167386	+	0.209896i	0.167386	+	0.209896i	−0.691063	+	0.722795i	$0.742857\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.668355	−	1.78082i	−0.668355	−	1.78082i	−0.623490	−	0.781831i	$-0.714286\pi$
$71$	−0.668355	−	1.78082i	−0.668355	−	1.78082i	−0.0448648	−	0.998993i	$-0.514286\pi$
$72$	−0.279430	+	0.292261i	−0.279430	+	0.292261i
$73$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$73$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$74$	2.43914	−	1.31256i	2.43914	−	1.31256i
$75$		0			0
$76$		0			0
$77$	−0.691063	−	0.722795i	−0.691063	−	0.722795i
$78$		0			0
$79$	1.58745	−	0.515795i	1.58745	−	0.515795i	0.623490	−	0.781831i	$-0.285714\pi$
$79$	1.58745	−	0.515795i	1.58745	−	0.515795i	0.963963	+	0.266037i	$0.0857143\pi$
$80$		0			0
$81$	0.753071	+	0.657939i	0.753071	+	0.657939i
$82$		0			0
$83$		0			0		0.990950	−	0.134233i	$-0.0428571\pi$
$83$		0			0		−0.990950	+	0.134233i	$0.957143\pi$
$84$		0			0
$85$		0			0
$86$	−1.13423	−	0.990950i	−1.13423	−	0.990950i
$87$		0			0
$88$	−0.389777	−	0.107572i	−0.389777	−	0.107572i
$89$		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
$92$	−0.806653	+	0.586068i	−0.806653	+	0.586068i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.936235	−	0.351375i	$-0.885714\pi$
$97$		0			0		0.936235	+	0.351375i	$0.114286\pi$
$98$	1.35699	+	0.653491i	1.35699	+	0.653491i
$99$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$100$	1.14285	+	0.550367i	1.14285	+	0.550367i
$101$		0			0		−0.834573	−	0.550897i	$-0.814286\pi$
$101$		0			0		0.834573	+	0.550897i	$0.185714\pi$
$102$		0			0
$103$		0			0		−0.393025	−	0.919528i	$-0.628571\pi$
$103$		0			0		0.393025	+	0.919528i	$0.371429\pi$
$104$		0			0
$105$		0			0
$106$	−0.134602	+	2.99714i	−0.134602	+	2.99714i
$107$	0.0950054	−	0.523523i	0.0950054	−	0.523523i	−0.900969	−	0.433884i	$-0.857143\pi$
$107$	0.0950054	−	0.523523i	0.0950054	−	0.523523i	0.995974	−	0.0896393i	$-0.0285714\pi$
$108$		0			0
$109$	−0.919098	−	0.732956i	−0.919098	−	0.732956i	0.0448648	−	0.998993i	$-0.485714\pi$
$109$	−0.919098	−	0.732956i	−0.919098	−	0.732956i	−0.963963	+	0.266037i	$0.914286\pi$
$110$		0			0
$111$		0			0
$112$	−0.656804	+	0.0591135i	−0.656804	+	0.0591135i
$113$	0.951109	+	1.08863i	0.951109	+	1.08863i	0.995974	+	0.0896393i	$0.0285714\pi$
$113$	0.951109	+	1.08863i	0.951109	+	1.08863i	−0.0448648	+	0.998993i	$0.514286\pi$
$114$		0			0
$115$		0			0
$116$	−2.36560	−	0.212908i	−2.36560	−	0.212908i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.963963	+	0.266037i	−0.963963	+	0.266037i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−0.202174	−	1.49251i	−0.202174	−	1.49251i
$127$	0.849696	+	0.812393i	0.849696	+	0.812393i	0.983930	−	0.178557i	$-0.0571429\pi$
$127$	0.849696	+	0.812393i	0.849696	+	0.812393i	−0.134233	+	0.990950i	$0.542857\pi$
$128$	−0.630673	+	0.458211i	−0.630673	+	0.458211i
$129$		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
$134$	−0.347113	+	0.207390i	−0.347113	+	0.207390i
$135$		0			0
$136$		0			0
$137$	0.0320114	−	0.355676i	0.0320114	−	0.355676i	−0.963963	−	0.266037i	$-0.914286\pi$
$137$	0.0320114	−	0.355676i	0.0320114	−	0.355676i	0.995974	−	0.0896393i	$-0.0285714\pi$
$138$		0			0
$139$		0			0		0.919528	−	0.393025i	$-0.128571\pi$
$139$		0			0		−0.919528	+	0.393025i	$0.871429\pi$
$140$		0			0
$141$		0			0
$142$	2.79303	−	0.637490i	2.79303	−	0.637490i
$143$		0			0
$144$	0.411166	+	0.515586i	0.411166	+	0.515586i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	0.819680	+	2.18403i	0.819680	+	2.18403i
$149$	−0.686957	−	1.04070i	−0.686957	−	1.04070i	−0.995974	−	0.0896393i	$-0.971429\pi$
$149$	−0.686957	−	1.04070i	−0.686957	−	1.04070i	0.309017	−	0.951057i	$-0.400000\pi$
$150$		0			0
$151$	−1.93623	−	0.351375i	−1.93623	−	0.351375i	−0.936235	−	0.351375i	$-0.885714\pi$
$151$	−1.93623	−	0.351375i	−1.93623	−	0.351375i	−1.00000			$\pi$
$152$		0			0
$153$		0			0
$154$	1.21850	−	0.885289i	1.21850	−	0.885289i
$155$		0			0
$156$		0			0
$157$		0			0		0.998993	−	0.0448648i	$-0.0142857\pi$
$157$		0			0		−0.998993	+	0.0448648i	$0.985714\pi$
$158$	0.448887	+	2.47357i	0.448887	+	2.47357i
$159$		0			0
$160$		0			0
$161$	0.0352660	−	0.785259i	0.0352660	−	0.785259i
$162$	−1.13423	+	0.990950i	−1.13423	+	0.990950i
$163$	−0.618838	+	1.64889i	−0.618838	+	1.64889i	0.134233	+	0.990950i	$0.457143\pi$
$163$	−0.618838	+	1.64889i	−0.618838	+	1.64889i	−0.753071	+	0.657939i	$0.771429\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.512899	−	0.858449i	$-0.671429\pi$
$167$		0			0		0.512899	+	0.858449i	$0.328571\pi$
$168$		0			0
$169$	−0.473869	+	0.880596i	−0.473869	+	0.880596i
$170$		0			0
$171$		0			0
$172$	0.955246	−	0.834573i	0.955246	−	0.834573i
$173$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$173$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$174$		0			0
$175$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$176$	−0.259184	+	0.606391i	−0.259184	+	0.606391i
$177$		0			0
$178$		0			0
$179$	−0.773453	+	1.06457i	−0.773453	+	1.06457i	0.222521	+	0.974928i	$0.428571\pi$
$179$	−0.773453	+	1.06457i	−0.773453	+	1.06457i	−0.995974	+	0.0896393i	$0.971429\pi$
$180$		0			0
$181$		0			0		−0.550897	−	0.834573i	$-0.685714\pi$
$181$		0			0		0.550897	+	0.834573i	$0.314286\pi$
$182$		0			0
$183$		0			0
$184$	−0.150614	−	0.279887i	−0.150614	−	0.279887i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.384580	+	1.39349i	−0.384580	+	1.39349i	0.473869	+	0.880596i	$0.342857\pi$
$191$	−0.384580	+	1.39349i	−0.384580	+	1.39349i	−0.858449	+	0.512899i	$0.828571\pi$
$192$		0			0
$193$	0.696390	−	0.0943324i	0.696390	−	0.0943324i	0.222521	−	0.974928i	$-0.428571\pi$
$193$	0.696390	−	0.0943324i	0.696390	−	0.0943324i	0.473869	+	0.880596i	$0.342857\pi$
$194$		0			0
$195$		0			0
$196$	−0.698794	+	1.05863i	−0.698794	+	1.05863i
$197$	0.154946	+	0.321748i	0.154946	+	0.321748i	0.963963	−	0.266037i	$-0.0857143\pi$
$197$	0.154946	+	0.321748i	0.154946	+	0.321748i	−0.809017	+	0.587785i	$0.800000\pi$
$198$	−1.41010	−	0.529221i	−1.41010	−	0.529221i
$199$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$199$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$200$	−0.222755	+	0.337459i	−0.222755	+	0.337459i
$201$		0			0
$202$		0			0
$203$	1.29399	−	1.35341i	1.29399	−	1.35341i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.674784	+	0.403165i	−0.674784	+	0.403165i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.0494318	−	0.0748860i	0.0494318	−	0.0748860i	−0.809017	−	0.587785i	$-0.800000\pi$
$211$	0.0494318	−	0.0748860i	0.0494318	−	0.0748860i	0.858449	+	0.512899i	$0.171429\pi$
$212$	−2.48611	−	0.451163i	−2.48611	−	0.451163i
$213$		0			0
$214$	0.762157	+	0.247640i	0.762157	+	0.247640i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	1.27976	−	1.22358i	1.27976	−	1.22358i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.919528	−	0.393025i	$-0.871429\pi$
$223$		0			0		0.919528	+	0.393025i	$0.128571\pi$
$224$	0.0627026	−	1.39618i	0.0627026	−	1.39618i
$225$	0.858449	+	0.512899i	0.858449	+	0.512899i
$226$	−1.81709	+	1.19945i	−1.81709	+	1.19945i
$227$		0			0		0.983930	−	0.178557i	$-0.0571429\pi$
$227$		0			0		−0.983930	+	0.178557i	$0.942857\pi$
$228$		0			0
$229$		0			0		0.134233	−	0.990950i	$-0.457143\pi$
$229$		0			0		−0.134233	+	0.990950i	$0.542857\pi$
$230$		0			0
$231$		0			0
$232$	0.168478	−	0.738148i	0.168478	−	0.738148i
$233$	1.38213	+	1.44559i	1.38213	+	1.44559i	0.691063	+	0.722795i	$0.257143\pi$
$233$	1.38213	+	1.44559i	1.38213	+	1.44559i	0.691063	+	0.722795i	$0.257143\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.179098	+	0.00804330i	−0.179098	+	0.00804330i	−0.134233	−	0.990950i	$-0.542857\pi$
$239$	−0.179098	+	0.00804330i	−0.179098	+	0.00804330i	−0.0448648	+	0.998993i	$0.514286\pi$
$240$		0			0
$241$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$241$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$242$	−0.202174	−	1.49251i	−0.202174	−	1.49251i
$243$		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		−0.309017	−	0.951057i	$-0.600000\pi$
$251$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$252$	1.26847			1.26847
$253$	−0.674784	−	0.403165i	−0.674784	−	0.403165i
$254$	−1.38429	+	1.10394i	−1.38429	+	1.10394i
$255$		0			0
$256$	0.128602	+	0.238983i	0.128602	+	0.238983i
$257$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$257$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$258$		0			0
$259$	−1.74905	−	0.568299i	−1.74905	−	0.568299i
$260$		0			0
$261$	−1.84238	−	0.334342i	−1.84238	−	0.334342i
$262$		0			0
$263$	−0.416664	−	1.82552i	−0.416664	−	1.82552i	−0.550897	−	0.834573i	$-0.685714\pi$
$263$	−0.416664	−	1.82552i	−0.416664	−	1.82552i	0.134233	−	0.990950i	$-0.457143\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−0.133841	−	0.313137i	−0.133841	−	0.313137i
$269$		0			0		−0.550897	−	0.834573i	$-0.685714\pi$
$269$		0			0		0.550897	+	0.834573i	$0.314286\pi$
$270$		0			0
$271$		0			0		0.657939	−	0.753071i	$-0.271429\pi$
$271$		0			0		−0.657939	+	0.753071i	$0.728571\pi$
$272$		0			0
$273$		0			0
$274$	0.524379	+	0.119686i	0.524379	+	0.119686i
$275$	−0.0448648	+	0.998993i	−0.0448648	+	0.998993i
$276$		0			0
$277$	−0.891370	+	1.35037i	−0.891370	+	1.35037i	0.0448648	+	0.998993i	$0.485714\pi$
$277$	−0.891370	+	1.35037i	−0.891370	+	1.35037i	−0.936235	+	0.351375i	$0.885714\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.39303	−	0.919528i	1.39303	−	0.919528i	0.393025	−	0.919528i	$-0.371429\pi$
$281$	1.39303	−	0.919528i	1.39303	−	0.919528i	1.00000			$0$
$282$		0			0
$283$		0			0		0.178557	−	0.983930i	$-0.442857\pi$
$283$		0			0		−0.178557	+	0.983930i	$0.557143\pi$
$284$	0.216279	+	2.40305i	0.216279	+	2.40305i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−1.19976	+	0.716822i	−1.19976	+	0.716822i
$289$	−0.473869	−	0.880596i	−0.473869	−	0.880596i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.657939	−	0.753071i	$-0.271429\pi$
$293$		0			0		−0.657939	+	0.753071i	$0.728571\pi$
$294$		0			0
$295$		0			0
$296$	−0.724976	+	0.165471i	−0.724976	+	0.165471i
$297$		0			0
$298$	1.69214	−	0.814890i	1.69214	−	0.814890i
$299$		0			0
$300$		0			0
$301$	0.0448648	+	0.998993i	0.0448648	+	0.998993i
$302$	0.915888	−	2.81881i	0.915888	−	2.81881i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$	0.601087	+	1.11701i	0.601087	+	1.11701i
$309$		0			0
$310$		0			0
$311$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$311$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$312$		0			0
$313$		0			0		−0.722795	−	0.691063i	$-0.757143\pi$
$313$		0			0		0.722795	+	0.691063i	$0.242857\pi$
$314$		0			0
$315$		0			0
$316$	−2.11512	+	0.0949904i	−2.11512	+	0.0949904i
$317$	1.09736	−	0.0987640i	1.09736	−	0.0987640i	0.473869	−	0.880596i	$-0.342857\pi$
$317$	1.09736	−	0.0987640i	1.09736	−	0.0987640i	0.623490	+	0.781831i	$0.285714\pi$
$318$		0			0
$319$	−0.578625	−	1.78082i	−0.578625	−	1.78082i
$320$		0			0
$321$		0			0
$322$	1.16488	+	0.211394i	1.16488	+	0.211394i
$323$		0			0
$324$	−0.698794	−	1.05863i	−0.698794	−	1.05863i
$325$		0			0
$326$	−2.33587	−	1.25699i	−2.33587	−	1.25699i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.348160	+	0.0794653i	−0.348160	+	0.0794653i	−0.393025	−	0.919528i	$-0.628571\pi$
$331$	−0.348160	+	0.0794653i	−0.348160	+	0.0794653i	0.0448648	+	0.998993i	$0.485714\pi$
$332$		0			0
$333$	0.489257	+	1.77278i	0.489257	+	1.77278i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.773453	−	1.06457i	−0.773453	−	1.06457i	−0.995974	−	0.0896393i	$-0.971429\pi$
$337$	−0.773453	−	1.06457i	−0.773453	−	1.06457i	0.222521	−	0.974928i	$-0.428571\pi$
$338$	−1.21850	−	0.885289i	−1.21850	−	0.885289i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$344$	0.222755	+	0.337459i	0.222755	+	0.337459i
$345$		0			0
$346$		0			0
$347$	−0.185527	−	1.36962i	−0.185527	−	1.36962i	−0.809017	−	0.587785i	$-0.800000\pi$
$347$	−0.185527	−	1.36962i	−0.185527	−	1.36962i	0.623490	−	0.781831i	$-0.285714\pi$
$348$		0			0
$349$		0			0		0.393025	−	0.919528i	$-0.371429\pi$
$349$		0			0		−0.393025	+	0.919528i	$0.628571\pi$
$350$	−0.465424	−	1.43243i	−0.465424	−	1.43243i
$351$		0			0
$352$	−1.19976	−	0.716822i	−1.19976	−	0.716822i
$353$		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
$358$	−1.43251	−	1.36962i	−1.43251	−	1.36962i
$359$	0.350072	−	1.26846i	0.350072	−	1.26846i	−0.550897	−	0.834573i	$-0.685714\pi$
$359$	0.350072	−	1.26846i	0.350072	−	1.26846i	0.900969	−	0.433884i	$-0.142857\pi$
$360$		0			0
$361$	−0.995974	+	0.0896393i	−0.995974	+	0.0896393i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.0448648	−	0.998993i	$-0.485714\pi$
$367$		0			0		−0.0448648	+	0.998993i	$0.514286\pi$
$368$	−0.485314	+	0.182141i	−0.485314	+	0.182141i
$369$		0			0
$370$		0			0
$371$	1.50008	−	1.31058i	1.50008	−	1.31058i
$372$		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
$379$	−0.782886	−	0.0704610i	−0.782886	−	0.0704610i	−0.309017	−	0.951057i	$-0.600000\pi$
$379$	−0.782886	−	0.0704610i	−0.782886	−	0.0704610i	−0.473869	+	0.880596i	$0.657143\pi$
$380$		0			0
$381$		0			0
$382$	−2.00206	−	0.855720i	−2.00206	−	0.855720i
$383$		0			0		−0.834573	−	0.550897i	$-0.814286\pi$
$383$		0			0		0.834573	+	0.550897i	$0.185714\pi$
$384$		0			0
$385$		0			0
$386$			1.05844i			1.05844i
$387$	0.809017	−	0.587785i	0.809017	−	0.587785i
$388$		0			0
$389$	0.314473	+	1.73289i	0.314473	+	1.73289i	0.623490	+	0.781831i	$0.285714\pi$
$389$	0.314473	+	1.73289i	0.314473	+	1.73289i	−0.309017	+	0.951057i	$0.600000\pi$
$390$		0			0
$391$		0			0
$392$	−0.304504	−	0.266037i	−0.304504	−	0.266037i
$393$		0			0
$394$	−0.511539	+	0.166209i	−0.511539	+	0.166209i
$395$		0			0
$396$	0.601087	−	1.11701i	0.601087	−	1.11701i
$397$		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
$400$	0.496620	+	0.433884i	0.496620	+	0.433884i
$401$	−1.35991	+	1.42236i	−1.35991	+	1.42236i	−0.550897	+	0.834573i	$0.685714\pi$
$401$	−1.35991	+	1.42236i	−1.35991	+	1.42236i	−0.809017	+	0.587785i	$0.800000\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	1.75837	+	2.20493i	1.75837	+	2.20493i
$407$	−1.32926	+	1.27090i	−1.32926	+	1.27090i
$408$		0			0
$409$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$409$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−0.465304	−	1.08863i	−0.465304	−	1.08863i
$415$		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
$421$	0.531538	+	1.92598i	0.531538	+	1.92598i	0.309017	+	0.951057i	$0.400000\pi$
$421$	0.531538	+	1.92598i	0.531538	+	1.92598i	0.222521	+	0.974928i	$0.428571\pi$
$422$	0.101774	+	0.0889176i	0.101774	+	0.0889176i
$423$		0			0
$424$	0.248895	−	0.766021i	0.248895	−	0.766021i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.292836	+	0.608080i	−0.292836	+	0.608080i
$429$		0			0
$430$		0			0
$431$	0.506032	−	0.164420i	0.506032	−	0.164420i	−0.0448648	−	0.998993i	$-0.514286\pi$
$431$	0.506032	−	0.164420i	0.506032	−	0.164420i	0.550897	+	0.834573i	$0.314286\pi$
$432$		0			0
$433$		0			0		−0.880596	−	0.473869i	$-0.842857\pi$
$433$		0			0		0.880596	+	0.473869i	$0.157143\pi$
$434$		0			0
$435$		0			0
$436$	0.876489	+	1.20638i	0.876489	+	1.20638i
$437$		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
$443$	0.242903	−	0.568299i	0.242903	−	0.568299i	−0.753071	−	0.657939i	$-0.771429\pi$
$443$	0.242903	−	0.568299i	0.242903	−	0.568299i	0.995974	+	0.0896393i	$0.0285714\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	1.42228	+	0.258106i	1.42228	+	0.258106i
$449$	1.66747	+	1.10068i	1.66747	+	1.10068i	0.858449	+	0.512899i	$0.171429\pi$
$449$	1.66747	+	1.10068i	1.66747	+	1.10068i	0.809017	+	0.587785i	$0.200000\pi$
$450$	−0.939065	+	1.17755i	−0.939065	+	1.17755i
$451$		0			0
$452$	−0.795605	−	1.65209i	−0.795605	−	1.65209i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.65503	−	0.988832i	−1.65503	−	0.988832i	−0.963963	−	0.266037i	$-0.914286\pi$
$457$	−1.65503	−	0.988832i	−1.65503	−	0.988832i	−0.691063	−	0.722795i	$-0.742857\pi$
$458$		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
$463$	0.685130	+	0.156377i	0.685130	+	0.156377i	0.550897	−	0.834573i	$-0.314286\pi$
$463$	0.685130	+	0.156377i	0.685130	+	0.156377i	0.134233	+	0.990950i	$0.457143\pi$
$464$	−1.15608	−	0.433884i	−1.15608	−	0.433884i
$465$		0			0
$466$	−2.43699	+	1.77058i	−2.43699	+	1.77058i
$467$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$467$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$468$		0			0
$469$	0.258792	+	0.0714220i	0.258792	+	0.0714220i
$470$		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
$477$	−1.92016	−	0.529932i	−1.92016	−	0.529932i
$478$	0.0242043	−	0.268932i	0.0242043	−	0.268932i
$479$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$479$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	1.26847			1.26847
$485$		0			0
$486$		0			0
$487$	−0.522106	−	0.970235i	−0.522106	−	0.970235i	−0.995974	−	0.0896393i	$-0.971429\pi$
$487$	−0.522106	−	0.970235i	−0.522106	−	0.970235i	0.473869	−	0.880596i	$-0.342857\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.590905	−	1.09808i	0.590905	−	1.09808i	−0.393025	−	0.919528i	$-0.628571\pi$
$491$	0.590905	−	1.09808i	0.590905	−	1.09808i	0.983930	−	0.178557i	$-0.0571429\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.58745	−	1.04787i	−1.58745	−	1.04787i
$498$		0			0
$499$	1.53483	−	0.656016i	1.53483	−	0.656016i	0.550897	−	0.834573i	$-0.314286\pi$
$499$	1.53483	−	0.656016i	1.53483	−	0.656016i	0.983930	+	0.178557i	$0.0571429\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.393025	−	0.919528i	$-0.371429\pi$
$503$		0			0		−0.393025	+	0.919528i	$0.628571\pi$
$504$	−0.0542771	+	0.400690i	−0.0542771	+	0.400690i
$505$		0			0
$506$	0.738152	−	0.925613i	0.738152	−	0.925613i
$507$		0			0
$508$	−0.764821	−	1.28009i	−0.764821	−	1.28009i
$509$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$509$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$510$		0			0
$511$		0			0
$512$	−1.11253	+	0.417540i	−1.11253	+	0.417540i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	1.20181	−	2.49558i	1.20181	−	2.49558i
$519$		0			0
$520$		0			0
$521$		0			0		0.657939	−	0.753071i	$-0.271429\pi$
$521$		0			0		−0.657939	+	0.753071i	$0.728571\pi$
$522$	0.871492	−	2.68218i	0.871492	−	2.68218i
$523$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$523$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$524$		0			0
$525$		0			0
$526$	2.80885	−	0.252801i	2.80885	−	0.252801i
$527$		0			0
$528$		0			0
$529$	0.0850309	+	0.372545i	0.0850309	+	0.372545i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	0.104642	−	0.0288794i	0.104642	−	0.0288794i
$537$		0			0
$538$		0			0
$539$	−0.983930	−	0.178557i	−0.983930	−	0.178557i
$540$		0			0
$541$	1.44413	−	1.38073i	1.44413	−	1.38073i	0.691063	−	0.722795i	$-0.257143\pi$
$541$	1.44413	−	1.38073i	1.44413	−	1.38073i	0.753071	−	0.657939i	$-0.228571\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	1.71703	−	0.923976i	1.71703	−	0.923976i	0.753071	−	0.657939i	$-0.228571\pi$
$547$	1.71703	−	0.923976i	1.71703	−	0.923976i	0.963963	−	0.266037i	$-0.0857143\pi$
$548$	−0.159168	+	0.424102i	−0.159168	+	0.424102i
$549$		0			0
$550$	−1.48194	−	0.268932i	−1.48194	−	0.268932i
$551$		0			0
$552$		0			0
$553$	0.981100	−	1.35037i	0.981100	−	1.35037i
$554$	−1.83523	−	1.60339i	−1.83523	−	1.60339i
$555$		0			0
$556$		0			0
$557$	0.125481	+	0.691456i	0.125481	+	0.691456i	0.983930	+	0.178557i	$0.0571429\pi$
$557$	0.125481	+	0.691456i	0.125481	+	0.691456i	−0.858449	+	0.512899i	$0.828571\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	1.09077	+	2.26501i	1.09077	+	2.26501i
$563$		0			0		−0.834573	−	0.550897i	$-0.814286\pi$
$563$		0			0		0.834573	+	0.550897i	$0.185714\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.995974	+	0.0896393i	0.995974	+	0.0896393i
$568$	−0.768343	−	0.0345063i	−0.768343	−	0.0345063i
$569$	1.28289	+	1.46838i	1.28289	+	1.46838i	0.809017	+	0.587785i	$0.200000\pi$
$569$	1.28289	+	1.46838i	1.28289	+	1.46838i	0.473869	+	0.880596i	$0.342857\pi$
$570$		0			0
$571$	0.0808436	+	0.0389322i	0.0808436	+	0.0389322i	0.473869	−	0.880596i	$-0.342857\pi$
$571$	0.0808436	+	0.0389322i	0.0808436	+	0.0389322i	−0.393025	+	0.919528i	$0.628571\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.591952	+	0.517173i	−0.591952	+	0.517173i
$576$	−0.568121	−	1.32919i	−0.568121	−	1.32919i
$577$		0			0		0.990950	−	0.134233i	$-0.0428571\pi$
$577$		0			0		−0.990950	+	0.134233i	$0.957143\pi$
$578$	1.41010	−	0.529221i	1.41010	−	0.529221i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.443250	−	1.94201i	−0.443250	−	1.94201i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.266037	−	0.963963i	$-0.414286\pi$
$587$		0			0		−0.266037	+	0.963963i	$0.585714\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.108713	+	1.20790i	0.108713	+	1.20790i
$593$		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
$596$	0.488788	+	1.50434i	0.488788	+	1.50434i
$597$		0			0
$598$		0			0
$599$	0.0120447	+	0.0889176i	0.0120447	+	0.0889176i	0.995974	−	0.0896393i	$-0.0285714\pi$
$599$	0.0120447	+	0.0889176i	0.0120447	+	0.0889176i	−0.983930	+	0.178557i	$0.942857\pi$
$600$		0			0
$601$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$601$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$602$	−1.50008	−	0.135010i	−1.50008	−	0.135010i
$603$	−0.0829607	−	0.255327i	−0.0829607	−	0.255327i
$604$	2.24897	+	1.08304i	2.24897	+	1.08304i
$605$		0			0
$606$		0			0
$607$		0			0		0.858449	−	0.512899i	$-0.171429\pi$
$607$		0			0		−0.858449	+	0.512899i	$0.828571\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.272900	+	0.988832i	0.272900	+	0.988832i	0.963963	+	0.266037i	$0.0857143\pi$
$613$	0.272900	+	0.988832i	0.272900	+	0.988832i	−0.691063	+	0.722795i	$0.742857\pi$
$614$		0			0
$615$		0			0
$616$	−0.378566	+	0.142078i	−0.378566	+	0.142078i
$617$	−1.24196	−	1.55737i	−1.24196	−	1.55737i	−0.691063	−	0.722795i	$-0.742857\pi$
$617$	−1.24196	−	1.55737i	−1.24196	−	1.55737i	−0.550897	−	0.834573i	$-0.685714\pi$
$618$		0			0
$619$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$619$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.936235	+	0.351375i	0.936235	+	0.351375i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−0.234959	−	1.29473i	−0.234959	−	1.29473i	−0.858449	−	0.512899i	$-0.828571\pi$
$631$	−0.234959	−	1.29473i	−0.234959	−	1.29473i	0.623490	−	0.781831i	$-0.285714\pi$
$632$	0.0604992	−	0.672201i	0.0604992	−	0.672201i
$633$		0			0
$634$	−0.0744514	+	1.65779i	−0.0744514	+	1.65779i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	2.77489	−	0.503567i	2.77489	−	0.503567i
$639$			1.90211i			1.90211i
$640$		0			0
$641$	−0.702042	+	0.0315287i	−0.702042	+	0.0315287i	−0.393025	−	0.919528i	$-0.628571\pi$
$641$	−0.702042	+	0.0315287i	−0.702042	+	0.0315287i	−0.309017	+	0.951057i	$0.600000\pi$
$642$		0			0
$643$		0			0		0.691063	−	0.722795i	$-0.257143\pi$
$643$		0			0		−0.691063	+	0.722795i	$0.742857\pi$
$644$	−0.308114	+	0.948278i	−0.308114	+	0.948278i
$645$		0			0
$646$		0			0
$647$		0			0		−0.990950	−	0.134233i	$-0.957143\pi$
$647$		0			0		0.990950	+	0.134233i	$0.0428571\pi$
$648$	0.364306	−	0.175440i	0.364306	−	0.175440i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	1.31312	−	1.80735i	1.31312	−	1.80735i
$653$	1.20999	−	1.38494i	1.20999	−	1.38494i	0.309017	−	0.951057i	$-0.400000\pi$
$653$	1.20999	−	1.38494i	1.20999	−	1.38494i	0.900969	−	0.433884i	$-0.142857\pi$
$654$		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	$0.571429\pi$
$662$	−0.0482138	−	0.535699i	−0.0482138	−	0.535699i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−2.74481	+	0.371810i	−2.74481	+	0.371810i
$667$	0.697466	−	1.29611i	0.697466	−	1.29611i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.147897	−	0.224055i	0.147897	−	0.224055i	−0.753071	−	0.657939i	$-0.771429\pi$
$673$	0.147897	−	0.224055i	0.147897	−	0.224055i	0.900969	+	0.433884i	$0.142857\pi$
$674$	1.74525	−	0.939160i	1.74525	−	0.939160i
$675$		0			0
$676$	0.876590	−	0.916841i	0.876590	−	0.916841i
$677$		0			0		−0.550897	−	0.834573i	$-0.685714\pi$
$677$		0			0		0.550897	+	0.834573i	$0.314286\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.360046	+	1.57747i	0.360046	+	1.57747i	0.753071	+	0.657939i	$0.228571\pi$
$683$	0.360046	+	1.57747i	0.360046	+	1.57747i	−0.393025	+	0.919528i	$0.628571\pi$
$684$		0			0
$685$		0			0
$686$	1.48194	−	0.268932i	1.48194	−	0.268932i
$687$		0			0
$688$	0.594152	−	0.286129i	0.594152	−	0.286129i
$689$		0			0
$690$		0			0
$691$		0			0		0.722795	−	0.691063i	$-0.242857\pi$
$691$		0			0		−0.722795	+	0.691063i	$0.757143\pi$
$692$		0			0
$693$	0.393025	+	0.919528i	0.393025	+	0.919528i
$694$	2.08168			2.08168
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	1.24808	−	0.226493i	1.24808	−	0.226493i
$701$	0.489257	+	0.209118i	0.489257	+	0.209118i	0.623490	−	0.781831i	$-0.285714\pi$
$701$	0.489257	+	0.209118i	0.489257	+	0.209118i	−0.134233	+	0.990950i	$0.542857\pi$
$702$		0			0
$703$		0			0
$704$	0.901260	−	1.13014i	0.901260	−	1.13014i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.267386	+	1.97392i	0.267386	+	1.97392i	0.222521	+	0.974928i	$0.428571\pi$
$709$	0.267386	+	1.97392i	0.267386	+	1.97392i	0.0448648	+	0.998993i	$0.485714\pi$
$710$		0			0
$711$	−1.66747	−	0.0748860i	−1.66747	−	0.0748860i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.30499	−	1.04070i	1.30499	−	1.04070i
$717$		0			0
$718$	1.82241	+	0.778936i	1.82241	+	0.778936i
$719$		0			0		0.983930	−	0.178557i	$-0.0571429\pi$
$719$		0			0		−0.983930	+	0.178557i	$0.942857\pi$
$720$		0			0
$721$		0			0
$722$	0.0675728	−	1.50463i	0.0675728	−	1.50463i
$723$		0			0
$724$		0			0
$725$	−1.87247			−1.87247
$726$		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
$729$	−0.473869	−	0.880596i	−0.473869	−	0.880596i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.983930	−	0.178557i	$-0.0571429\pi$
$733$		0			0		−0.983930	+	0.178557i	$0.942857\pi$
$734$		0			0
$735$		0			0
$736$	−0.244456	−	1.07103i	−0.244456	−	1.07103i
$737$	0.185527	−	0.194046i	0.185527	−	0.194046i
$738$		0			0
$739$	−1.47387	+	0.880596i	−1.47387	+	0.880596i	−0.473869	+	0.880596i	$0.657143\pi$
$739$	−1.47387	+	0.880596i	−1.47387	+	0.880596i	−1.00000			$\pi$
$740$		0			0
$741$		0			0
$742$	1.65278	+	2.50385i	1.65278	+	2.50385i
$743$	1.18648	−	1.24096i	1.18648	−	1.24096i	0.222521	−	0.974928i	$-0.428571\pi$
$743$	1.18648	−	1.24096i	1.18648	−	1.24096i	0.963963	−	0.266037i	$-0.0857143\pi$
$744$		0			0
$745$		0			0
$746$	−0.369264	+	0.559412i	−0.369264	+	0.559412i
$747$		0			0
$748$		0			0
$749$	−0.230858	−	0.479382i	−0.230858	−	0.479382i
$750$		0			0
$751$	−0.531538	−	1.92598i	−0.531538	−	1.92598i	−0.309017	−	0.951057i	$-0.600000\pi$
$751$	−0.531538	−	1.92598i	−0.531538	−	1.92598i	−0.222521	−	0.974928i	$-0.571429\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	0.170504	+	1.89446i	0.170504	+	1.89446i	0.393025	+	0.919528i	$0.371429\pi$
$757$	0.170504	+	1.89446i	0.170504	+	1.89446i	−0.222521	+	0.974928i	$0.571429\pi$
$758$	0.263443	−	1.15422i	0.263443	−	1.15422i
$759$		0			0
$760$		0			0
$761$		0			0		0.858449	−	0.512899i	$-0.171429\pi$
$761$		0			0		−0.858449	+	0.512899i	$0.828571\pi$
$762$		0			0
$763$	−1.17439	−	0.0527418i	−1.17439	−	0.0527418i
$764$	0.940494	−	1.57412i	0.940494	−	1.57412i
$765$		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
$772$	−0.883347	−	0.119657i	−0.883347	−	0.119657i
$773$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$773$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$774$	0.713714	+	1.32630i	0.713714	+	1.32630i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−2.64993	+	0.119009i	−2.64993	+	0.119009i
$779$		0			0
$780$		0			0
$781$	−1.67499	+	0.901352i	−1.67499	+	0.901352i
$782$		0			0
$783$		0			0
$784$	−0.496620	+	0.433884i	−0.496620	+	0.433884i
$785$		0			0
$786$		0			0
$787$		0			0		0.0896393	−	0.995974i	$-0.471429\pi$
$787$		0			0		−0.0896393	+	0.995974i	$0.528571\pi$
$788$	−0.0808839	−	0.445707i	−0.0808839	−	0.445707i
$789$		0			0
$790$		0			0
$791$	1.40935	+	0.321674i	1.40935	+	0.321674i
$792$	0.327125	+	0.237670i	0.327125	+	0.237670i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.550897	−	0.834573i	$-0.685714\pi$
$797$		0			0		0.550897	+	0.834573i	$0.314286\pi$
$798$		0			0
$799$		0			0
$800$	−1.05248	+	0.919528i	−1.05248	+	0.919528i
$801$		0			0
$802$	−1.84795	−	2.31725i	−1.84795	−	2.31725i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.157872	+	1.75410i	−0.157872	+	1.75410i	0.393025	+	0.919528i	$0.371429\pi$
$809$	−0.157872	+	1.75410i	−0.157872	+	1.75410i	−0.550897	+	0.834573i	$0.685714\pi$
$810$		0			0
$811$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$811$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$812$	−2.03896	+	1.21822i	−2.03896	+	1.21822i
$813$		0			0
$814$	−1.62809	−	2.24088i	−1.62809	−	2.24088i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.415992	+	1.50731i	−0.415992	+	1.50731i	0.393025	+	0.919528i	$0.371429\pi$
$821$	−0.415992	+	1.50731i	−0.415992	+	1.50731i	−0.809017	+	0.587785i	$0.800000\pi$
$822$		0			0
$823$	0.427100	+	1.31448i	0.427100	+	1.31448i	0.900969	+	0.433884i	$0.142857\pi$
$823$	0.427100	+	1.31448i	0.427100	+	1.31448i	−0.473869	+	0.880596i	$0.657143\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.0777861	+	0.864274i	0.0777861	+	0.864274i	0.936235	+	0.351375i	$0.114286\pi$
$827$	0.0777861	+	0.864274i	0.0777861	+	0.864274i	−0.858449	+	0.512899i	$0.828571\pi$
$828$	0.961146	−	0.265260i	0.961146	−	0.265260i
$829$		0			0		−0.178557	−	0.983930i	$-0.557143\pi$
$829$		0			0		0.178557	+	0.983930i	$0.442857\pi$
$830$		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		0.178557	−	0.983930i	$-0.442857\pi$
$839$		0			0		−0.178557	+	0.983930i	$0.557143\pi$
$840$		0			0
$841$	2.34634	−	0.880596i	2.34634	−	0.880596i
$842$	−2.98202	+	0.403942i	−2.98202	+	0.403942i
$843$		0			0
$844$	−0.0857139	+	0.0748860i	−0.0857139	+	0.0748860i
$845$		0			0
$846$		0			0
$847$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$848$	−1.18352	−	0.569953i	−1.18352	−	0.569953i
$849$		0			0
$850$		0			0
$851$	−1.44413	−	0.0648561i	−1.44413	−	0.0648561i
$852$		0			0
$853$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$853$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$854$		0			0
$855$		0			0
$856$	−0.179553	−	0.118522i	−0.179553	−	0.118522i
$857$		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
$862$	0.143092	+	0.788501i	0.143092	+	0.788501i
$863$	1.54951	−	0.209896i	1.54951	−	0.209896i	0.691063	−	0.722795i	$-0.257143\pi$
$863$	1.54951	−	0.209896i	1.54951	−	0.209896i	0.858449	+	0.512899i	$0.171429\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.724216	−	1.50385i	−0.724216	−	1.50385i
$870$		0			0
$871$		0			0
$872$	−0.418583	+	0.225249i	−0.418583	+	0.225249i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.30397	+	1.49251i	1.30397	+	1.49251i	0.753071	+	0.657939i	$0.228571\pi$
$877$	1.30397	+	1.49251i	1.30397	+	1.49251i	0.550897	+	0.834573i	$0.314286\pi$
$878$		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	$0.857143\pi$
$882$	−1.04084	−	1.08863i	−1.04084	−	1.08863i
$883$	0.429004	−	0.118398i	0.429004	−	0.118398i	−0.0448648	−	0.998993i	$-0.514286\pi$
$883$	0.429004	−	0.118398i	0.429004	−	0.118398i	0.473869	+	0.880596i	$0.342857\pi$
$884$		0			0
$885$		0			0
$886$	0.799085	+	0.477431i	0.799085	+	0.477431i
$887$		0			0		−0.393025	−	0.919528i	$-0.628571\pi$
$887$		0			0		0.393025	+	0.919528i	$0.371429\pi$
$888$		0			0
$889$	1.16493	+	0.157801i	1.16493	+	0.157801i
$890$		0			0
$891$	0.550897	−	0.834573i	0.550897	−	0.834573i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−0.240896	+	0.741401i	−0.240896	+	0.741401i
$897$		0			0
$898$	−1.97990	+	2.26618i	−1.97990	+	2.26618i
$899$		0			0
$900$	−0.876590	−	0.916841i	−0.876590	−	0.916841i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.555914	−	0.180627i	0.555914	−	0.180627i
$905$		0			0
$906$		0			0
$907$	−1.75307	+	0.657939i	−1.75307	+	0.657939i	−0.753071	+	0.657939i	$0.771429\pi$
$907$	−1.75307	+	0.657939i	−1.75307	+	0.657939i	−1.00000			$1.00000\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.445077	−	0.744934i	−0.445077	−	0.744934i	0.550897	−	0.834573i	$-0.314286\pi$
$911$	−0.445077	−	0.744934i	−0.445077	−	0.744934i	−0.995974	+	0.0896393i	$0.971429\pi$
$912$		0			0
$913$		0			0
$914$	1.81045	−	2.27023i	1.81045	−	2.27023i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−1.01651	+	1.70136i	−1.01651	+	1.70136i	−0.393025	+	0.919528i	$0.628571\pi$
$919$	−1.01651	+	1.70136i	−1.01651	+	1.70136i	−0.623490	+	0.781831i	$0.714286\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	0.797936	+	1.65693i	0.797936	+	1.65693i
$926$	−0.371910	+	0.990950i	−0.371910	+	0.990950i
$927$		0			0
$928$	1.24009	−	2.30447i	1.24009	−	2.30447i
$929$		0			0		0.512899	−	0.858449i	$-0.328571\pi$
$929$		0			0		−0.512899	+	0.858449i	$0.671429\pi$
$930$		0			0
$931$		0			0
$932$	−1.20217	−	2.23401i	−1.20217	−	2.23401i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.936235	−	0.351375i	$-0.885714\pi$
$937$		0			0		0.936235	+	0.351375i	$0.114286\pi$
$938$	−0.158919	+	0.371810i	−0.158919	+	0.371810i
$939$		0			0
$940$		0			0
$941$		0			0		0.0896393	−	0.995974i	$-0.471429\pi$
$941$		0			0		−0.0896393	+	0.995974i	$0.528571\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−0.829730	+	1.25699i	−0.829730	+	1.25699i
$947$	−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
$953$	−1.59203	+	1.15668i	−1.59203	+	1.15668i	−0.691063	+	0.722795i	$0.742857\pi$
$953$	−1.59203	+	1.15668i	−1.59203	+	1.15668i	−0.900969	+	0.433884i	$0.857143\pi$
$954$	1.17914	−	2.75873i	1.17914	−	2.75873i
$955$		0			0
$956$	0.221707	+	0.0506032i	0.221707	+	0.0506032i
$957$		0			0
$958$		0			0
$959$	−0.183163	−	0.306564i	−0.183163	−	0.306564i
$960$		0			0
$961$	−0.963963	−	0.266037i	−0.963963	−	0.266037i
$962$		0			0
$963$	−0.272900	+	0.456758i	−0.272900	+	0.456758i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−0.797936	−	1.65693i	−0.797936	−	1.65693i	−0.753071	−	0.657939i	$-0.771429\pi$
$967$	−0.797936	−	1.65693i	−0.797936	−	1.65693i	−0.0448648	−	0.998993i	$-0.514286\pi$
$968$	−0.0542771	+	0.400690i	−0.0542771	+	0.400690i
$969$		0			0
$970$		0			0
$971$		0			0		−0.983930	−	0.178557i	$-0.942857\pi$
$971$		0			0		0.983930	+	0.178557i	$0.0571429\pi$
$972$		0			0
$973$		0			0
$974$	1.55364	−	0.583092i	1.55364	−	0.583092i
$975$		0			0
$976$		0			0
$977$	0.202174	−	1.49251i	0.202174	−	1.49251i	−0.550897	−	0.834573i	$-0.685714\pi$
$977$	0.202174	−	1.49251i	0.202174	−	1.49251i	0.753071	−	0.657939i	$-0.228571\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.602949	+	1.00917i	0.602949	+	1.00917i
$982$	1.51944	+	1.10394i	1.51944	+	1.10394i
$983$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$983$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.242903	+	0.747578i	0.242903	+	0.747578i
$990$		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
$994$	1.88490	−	2.15744i	1.88490	−	2.15744i
$995$		0			0
$996$		0			0
$997$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$997$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$998$	0.668810	+	2.42338i	0.668810	+	2.42338i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3311.1.ex.a.237.1	✓	24
7.6	odd	2	CM	3311.1.ex.a.237.1	✓	24
11.2	odd	10		3311.1.ex.b.3247.1	yes	24
43.2	odd	14		3311.1.ex.b.776.1	yes	24
77.13	even	10		3311.1.ex.b.3247.1	yes	24
301.174	even	14		3311.1.ex.b.776.1	yes	24
473.2	even	70	inner	3311.1.ex.a.475.1	yes	24
3311.475	odd	70	inner	3311.1.ex.a.475.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3311.1.ex.a.237.1	✓	24	1.1	even	1	trivial
3311.1.ex.a.237.1	✓	24	7.6	odd	2	CM
3311.1.ex.a.475.1	yes	24	473.2	even	70	inner
3311.1.ex.a.475.1	yes	24	3311.475	odd	70	inner
3311.1.ex.b.776.1	yes	24	43.2	odd	14
3311.1.ex.b.776.1	yes	24	301.174	even	14
3311.1.ex.b.3247.1	yes	24	11.2	odd	10
3311.1.ex.b.3247.1	yes	24	77.13	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)

\(f(q)\)	\(=\)	\(q+(-0.202174 + 1.49251i) q^{2} +(-1.22275 - 0.337459i) q^{4} +(0.809017 - 0.587785i) q^{7} +(0.158919 - 0.371810i) q^{8} +(-0.936235 - 0.351375i) q^{9} +O(q^{10})\)	\(q+(-0.202174 + 1.49251i) q^{2} +(-1.22275 - 0.337459i) q^{4} +(0.809017 - 0.587785i) q^{7} +(0.158919 - 0.371810i) q^{8} +(-0.936235 - 0.351375i) q^{9} +(-0.134233 - 0.990950i) q^{11} +(0.713714 + 1.32630i) q^{14} +(-0.566112 - 0.338236i) q^{16} +(0.713714 - 1.32630i) q^{18} +1.50614 q^{22} +(0.490094 - 0.614559i) q^{23} +(-0.983930 - 0.178557i) q^{25} +(-1.18758 + 0.445707i) q^{28} +(1.84238 - 0.334342i) q^{29} +(0.871382 - 1.09268i) q^{32} +(1.02621 + 0.745586i) q^{36} +(-1.08097 - 1.48783i) q^{37} +(-0.550897 + 0.834573i) q^{43} +(-0.170270 + 1.25699i) q^{44} +(0.818152 + 0.855720i) q^{46} +(0.309017 - 0.951057i) q^{49} +(0.465424 - 1.43243i) q^{50} +(1.98393 - 0.178557i) q^{53} +(-0.0899761 - 0.394211i) q^{56} +(0.126528 + 2.81737i) q^{58} +(-0.963963 + 0.266037i) q^{63} +(0.998937 + 1.04481i) q^{64} +(0.167386 + 0.209896i) q^{67} +(-0.668355 - 1.78082i) q^{71} +(-0.279430 + 0.292261i) q^{72} +(2.43914 - 1.31256i) q^{74} +(-0.691063 - 0.722795i) q^{77} +(1.58745 - 0.515795i) q^{79} +(0.753071 + 0.657939i) q^{81} +(-1.13423 - 0.990950i) q^{86} +(-0.389777 - 0.107572i) q^{88} +(-0.806653 + 0.586068i) q^{92} +(1.35699 + 0.653491i) q^{98} +(-0.222521 + 0.974928i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 3 q^{4} + 6 q^{7} + 8 q^{8} - q^{9}+O(q^{10}) \) 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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