LMFDB - Embedded newform 3311.1.ex.a.2631.1

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			2631.1
Root			$0.753071 + 0.657939i$ of defining polynomial
Character	$\chi$	$=$	3311.2631
Dual form			3311.1.ex.a.930.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.65503 + 0.988832i) q^{2} +(1.28745 + 2.39249i) q^{4} +(0.809017 + 0.587785i) q^{7} +(-0.148505 + 3.30672i) q^{8} +(-0.134233 - 0.990950i) q^{9} +O(q^{10})$	\(q+(1.65503 + 0.988832i) q^{2} +(1.28745 + 2.39249i) q^{4} +(0.809017 + 0.587785i) q^{7} +(-0.148505 + 3.30672i) q^{8} +(-0.134233 - 0.990950i) q^{9} +(-0.858449 + 0.512899i) q^{11} +(0.757723 + 1.77278i) q^{14} +(-2.01884 + 3.05841i) q^{16} +(0.757723 - 1.77278i) q^{18} -1.92793 q^{22} +(-0.0808436 + 0.0389322i) q^{23} +(-0.753071 - 0.657939i) q^{25} +(-0.364698 + 2.69231i) q^{28} +(0.202174 - 0.176635i) q^{29} +(-3.38322 + 1.62927i) q^{32} +(2.19802 - 1.59695i) q^{36} +(1.17439 - 1.61640i) q^{37} +(-0.691063 + 0.722795i) q^{43} +(-2.33232 - 1.39349i) q^{44} +(-0.172296 - 0.0155069i) q^{46} +(0.309017 + 0.951057i) q^{49} +(-0.595762 - 1.83357i) q^{50} +(1.75307 - 0.657939i) q^{53} +(-2.06378 + 2.58790i) q^{56} +(0.509266 - 0.0924181i) q^{58} +(0.473869 - 0.880596i) q^{63} +(-3.56051 - 0.320452i) q^{64} +(-1.54687 - 0.744934i) q^{67} +(1.88490 + 0.255327i) q^{71} +(3.29673 - 0.296711i) q^{72} +(3.54199 - 1.51392i) q^{74} +(-0.995974 - 0.0896393i) q^{77} +(-1.37484 - 0.446712i) q^{79} +(-0.963963 + 0.266037i) q^{81} +(-1.85845 + 0.512899i) q^{86} +(-1.56853 - 2.91482i) q^{88} +(-0.197227 - 0.143294i) q^{92} +(-0.429004 + 1.87959i) q^{98} +(0.623490 + 0.781831i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3311\mathbb{Z}\right)^\times$.

$n$	$904$	$1893$	$2927$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$	$e\left(\frac{13}{14}\right)$

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 $

$2$	1.65503	+	0.988832i	1.65503	+	0.988832i	0.963963	+	0.266037i	$0.0857143\pi$
$2$	1.65503	+	0.988832i	1.65503	+	0.988832i	0.691063	+	0.722795i	$0.257143\pi$
$3$		0			0		0.657939	−	0.753071i	$-0.271429\pi$
$3$		0			0		−0.657939	+	0.753071i	$0.728571\pi$
$4$	1.28745	+	2.39249i	1.28745	+	2.39249i
$5$		0			0		0.351375	−	0.936235i	$-0.385714\pi$
$5$		0			0		−0.351375	+	0.936235i	$0.614286\pi$
$6$		0			0
$7$	0.809017	+	0.587785i	0.809017	+	0.587785i
$7$	0.809017	+	0.587785i	0.809017	+	0.587785i
$8$	−0.148505	+	3.30672i	−0.148505	+	3.30672i
$9$	−0.134233	−	0.990950i	−0.134233	−	0.990950i
$10$		0			0
$11$	−0.858449	+	0.512899i	−0.858449	+	0.512899i
$11$	−0.858449	+	0.512899i	−0.858449	+	0.512899i
$12$		0			0
$13$		0			0		0.834573	−	0.550897i	$-0.185714\pi$
$13$		0			0		−0.834573	+	0.550897i	$0.814286\pi$
$14$	0.757723	+	1.77278i	0.757723	+	1.77278i
$15$		0			0
$16$	−2.01884	+	3.05841i	−2.01884	+	3.05841i
$17$		0			0		−0.834573	−	0.550897i	$-0.814286\pi$
$17$		0			0		0.834573	+	0.550897i	$0.185714\pi$
$18$	0.757723	−	1.77278i	0.757723	−	1.77278i
$19$		0			0		0.983930	−	0.178557i	$-0.0571429\pi$
$19$		0			0		−0.983930	+	0.178557i	$0.942857\pi$
$20$		0			0
$21$		0			0
$22$	−1.92793			−1.92793
$23$	−0.0808436	+	0.0389322i	−0.0808436	+	0.0389322i	−0.473869	−	0.880596i	$-0.657143\pi$
$23$	−0.0808436	+	0.0389322i	−0.0808436	+	0.0389322i	0.393025	+	0.919528i	$0.371429\pi$
$24$		0			0
$25$	−0.753071	−	0.657939i	−0.753071	−	0.657939i
$26$		0			0
$27$		0			0
$28$	−0.364698	+	2.69231i	−0.364698	+	2.69231i
$29$	0.202174	−	0.176635i	0.202174	−	0.176635i	−0.550897	−	0.834573i	$-0.685714\pi$
$29$	0.202174	−	0.176635i	0.202174	−	0.176635i	0.753071	+	0.657939i	$0.228571\pi$
$30$		0			0
$31$		0			0		−0.858449	−	0.512899i	$-0.828571\pi$
$31$		0			0		0.858449	+	0.512899i	$0.171429\pi$
$32$	−3.38322	+	1.62927i	−3.38322	+	1.62927i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	2.19802	−	1.59695i	2.19802	−	1.59695i
$37$	1.17439	−	1.61640i	1.17439	−	1.61640i	0.550897	−	0.834573i	$-0.314286\pi$
$37$	1.17439	−	1.61640i	1.17439	−	1.61640i	0.623490	−	0.781831i	$-0.285714\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.919528	−	0.393025i	$-0.128571\pi$
$41$		0			0		−0.919528	+	0.393025i	$0.871429\pi$
$42$		0			0
$43$	−0.691063	+	0.722795i	−0.691063	+	0.722795i
$43$	−0.691063	+	0.722795i	−0.691063	+	0.722795i
$44$	−2.33232	−	1.39349i	−2.33232	−	1.39349i
$45$		0			0
$46$	−0.172296	−	0.0155069i	−0.172296	−	0.0155069i
$47$		0			0		0.983930	−	0.178557i	$-0.0571429\pi$
$47$		0			0		−0.983930	+	0.178557i	$0.942857\pi$
$48$		0			0
$49$	0.309017	+	0.951057i	0.309017	+	0.951057i
$50$	−0.595762	−	1.83357i	−0.595762	−	1.83357i
$51$		0			0
$52$		0			0
$53$	1.75307	−	0.657939i	1.75307	−	0.657939i	0.753071	−	0.657939i	$-0.228571\pi$
$53$	1.75307	−	0.657939i	1.75307	−	0.657939i	1.00000			$0$
$54$		0			0
$55$		0			0
$56$	−2.06378	+	2.58790i	−2.06378	+	2.58790i
$57$		0			0
$58$	0.509266	−	0.0924181i	0.509266	−	0.0924181i
$59$		0			0		−0.0448648	−	0.998993i	$-0.514286\pi$
$59$		0			0		0.0448648	+	0.998993i	$0.485714\pi$
$60$		0			0
$61$		0			0		0.858449	−	0.512899i	$-0.171429\pi$
$61$		0			0		−0.858449	+	0.512899i	$0.828571\pi$
$62$		0			0
$63$	0.473869	−	0.880596i	0.473869	−	0.880596i
$64$	−3.56051	−	0.320452i	−3.56051	−	0.320452i
$65$		0			0
$66$		0			0
$67$	−1.54687	−	0.744934i	−1.54687	−	0.744934i	−0.550897	−	0.834573i	$-0.685714\pi$
$67$	−1.54687	−	0.744934i	−1.54687	−	0.744934i	−0.995974	+	0.0896393i	$0.971429\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.88490	+	0.255327i	1.88490	+	0.255327i	0.983930	−	0.178557i	$-0.0571429\pi$
$71$	1.88490	+	0.255327i	1.88490	+	0.255327i	0.900969	+	0.433884i	$0.142857\pi$
$72$	3.29673	−	0.296711i	3.29673	−	0.296711i
$73$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$73$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$74$	3.54199	−	1.51392i	3.54199	−	1.51392i
$75$		0			0
$76$		0			0
$77$	−0.995974	−	0.0896393i	−0.995974	−	0.0896393i
$78$		0			0
$79$	−1.37484	−	0.446712i	−1.37484	−	0.446712i	−0.473869	−	0.880596i	$-0.657143\pi$
$79$	−1.37484	−	0.446712i	−1.37484	−	0.446712i	−0.900969	+	0.433884i	$0.857143\pi$
$80$		0			0
$81$	−0.963963	+	0.266037i	−0.963963	+	0.266037i
$82$		0			0
$83$		0			0		−0.512899	−	0.858449i	$-0.671429\pi$
$83$		0			0		0.512899	+	0.858449i	$0.328571\pi$
$84$		0			0
$85$		0			0
$86$	−1.85845	+	0.512899i	−1.85845	+	0.512899i
$87$		0			0
$88$	−1.56853	−	2.91482i	−1.56853	−	2.91482i
$89$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$89$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$90$		0			0
$91$		0			0
$92$	−0.197227	−	0.143294i	−0.197227	−	0.143294i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$97$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$98$	−0.429004	+	1.87959i	−0.429004	+	1.87959i
$99$	0.623490	+	0.781831i	0.623490	+	0.781831i
$100$	0.604567	−	2.64878i	0.604567	−	2.64878i
$101$		0			0		−0.722795	−	0.691063i	$-0.757143\pi$
$101$		0			0		0.722795	+	0.691063i	$0.242857\pi$
$102$		0			0
$103$		0			0		−0.0448648	−	0.998993i	$-0.514286\pi$
$103$		0			0		0.0448648	+	0.998993i	$0.485714\pi$
$104$		0			0
$105$		0			0
$106$	3.55197	+	0.644587i	3.55197	+	0.644587i
$107$	−1.15876	+	1.32630i	−1.15876	+	1.32630i	−0.222521	+	0.974928i	$0.571429\pi$
$107$	−1.15876	+	1.32630i	−1.15876	+	1.32630i	−0.936235	+	0.351375i	$0.885714\pi$
$108$		0			0
$109$	−0.510061	−	1.05915i	−0.510061	−	1.05915i	−0.983930	−	0.178557i	$-0.942857\pi$
$109$	−0.510061	−	1.05915i	−0.510061	−	1.05915i	0.473869	−	0.880596i	$-0.342857\pi$
$110$		0			0
$111$		0			0
$112$	−3.43096	+	1.28766i	−3.43096	+	1.28766i
$113$	0.0476947	−	0.172818i	0.0476947	−	0.172818i	−0.936235	−	0.351375i	$-0.885714\pi$
$113$	0.0476947	−	0.172818i	0.0476947	−	0.172818i	0.983930	+	0.178557i	$0.0571429\pi$
$114$		0			0
$115$		0			0
$116$	0.682886	+	0.256291i	0.682886	+	0.256291i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.473869	−	0.880596i	0.473869	−	0.880596i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	1.65503	−	0.988832i	1.65503	−	0.988832i
$127$	−0.105377	−	1.17084i	−0.105377	−	1.17084i	−0.858449	−	0.512899i	$-0.828571\pi$
$127$	−0.105377	−	1.17084i	−0.105377	−	1.17084i	0.753071	−	0.657939i	$-0.228571\pi$
$128$	−2.53793	−	1.84392i	−2.53793	−	1.84392i
$129$		0			0
$130$		0			0
$131$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$131$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$132$		0			0
$133$		0			0
$134$	−1.82350	−	2.76248i	−1.82350	−	2.76248i
$135$		0			0
$136$		0			0
$137$	−0.462366	+	1.23197i	−0.462366	+	1.23197i	0.473869	+	0.880596i	$0.342857\pi$
$137$	−0.462366	+	1.23197i	−0.462366	+	1.23197i	−0.936235	+	0.351375i	$0.885714\pi$
$138$		0			0
$139$		0			0		0.998993	−	0.0448648i	$-0.0142857\pi$
$139$		0			0		−0.998993	+	0.0448648i	$0.985714\pi$
$140$		0			0
$141$		0			0
$142$	2.86708	+	2.28642i	2.86708	+	2.28642i
$143$		0			0
$144$	3.30172	+	1.59003i	3.30172	+	1.59003i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	5.37920	+	0.728662i	5.37920	+	0.728662i
$149$	1.24525	+	1.30243i	1.24525	+	1.30243i	0.936235	+	0.351375i	$0.114286\pi$
$149$	1.24525	+	1.30243i	1.24525	+	1.30243i	0.309017	+	0.951057i	$0.400000\pi$
$150$		0			0
$151$	−1.13423	−	0.990950i	−1.13423	−	0.990950i	−0.134233	−	0.990950i	$-0.542857\pi$
$151$	−1.13423	−	0.990950i	−1.13423	−	0.990950i	−1.00000			$\pi$
$152$		0			0
$153$		0			0
$154$	−1.55972	−	1.13321i	−1.55972	−	1.13321i
$155$		0			0
$156$		0			0
$157$		0			0		−0.178557	−	0.983930i	$-0.557143\pi$
$157$		0			0		0.178557	+	0.983930i	$0.442857\pi$
$158$	−1.83367	−	2.09880i	−1.83367	−	2.09880i
$159$		0			0
$160$		0			0
$161$	−0.0882877	−	0.0160218i	−0.0882877	−	0.0160218i
$162$	−1.85845	−	0.512899i	−1.85845	−	0.512899i
$163$	1.82241	−	0.246862i	1.82241	−	0.246862i	0.858449	−	0.512899i	$-0.171429\pi$
$163$	1.82241	−	0.246862i	1.82241	−	0.246862i	0.963963	+	0.266037i	$0.0857143\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.834573	−	0.550897i	$-0.185714\pi$
$167$		0			0		−0.834573	+	0.550897i	$0.814286\pi$
$168$		0			0
$169$	0.393025	−	0.919528i	0.393025	−	0.919528i
$170$		0			0
$171$		0			0
$172$	−2.61899	−	0.722795i	−2.61899	−	0.722795i
$173$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$173$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$174$		0			0
$175$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$176$	0.164413	−	3.66094i	0.164413	−	3.66094i
$177$		0			0
$178$		0			0
$179$	0.312745	+	0.430457i	0.312745	+	0.430457i	0.936235	−	0.351375i	$-0.114286\pi$
$179$	0.312745	+	0.430457i	0.312745	+	0.430457i	−0.623490	+	0.781831i	$0.714286\pi$
$180$		0			0
$181$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$181$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$182$		0			0
$183$		0			0
$184$	−0.116732	−	0.273109i	−0.116732	−	0.273109i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.157872	−	0.0849545i	0.157872	−	0.0849545i	−0.393025	−	0.919528i	$-0.628571\pi$
$191$	0.157872	−	0.0849545i	0.157872	−	0.0849545i	0.550897	+	0.834573i	$0.314286\pi$
$192$		0			0
$193$	−1.01651	−	1.70136i	−1.01651	−	1.70136i	−0.623490	−	0.781831i	$-0.714286\pi$
$193$	−1.01651	−	1.70136i	−1.01651	−	1.70136i	−0.393025	−	0.919528i	$-0.628571\pi$
$194$		0			0
$195$		0			0
$196$	−1.87755	+	1.96376i	−1.87755	+	1.96376i
$197$	−1.28289	+	0.292810i	−1.28289	+	0.292810i	−0.809017	−	0.587785i	$-0.800000\pi$
$197$	−1.28289	+	0.292810i	−1.28289	+	0.292810i	−0.473869	+	0.880596i	$0.657143\pi$
$198$	0.258792	+	1.91048i	0.258792	+	1.91048i
$199$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$199$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$200$	2.28745	−	2.39249i	2.28745	−	2.39249i
$201$		0			0
$202$		0			0
$203$	0.267386	−	0.0240652i	0.267386	−	0.0240652i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.0494318	+	0.0748860i	0.0494318	+	0.0748860i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−1.35991	+	1.42236i	−1.35991	+	1.42236i	−0.550897	+	0.834573i	$0.685714\pi$
$211$	−1.35991	+	1.42236i	−1.35991	+	1.42236i	−0.809017	+	0.587785i	$0.800000\pi$
$212$	3.83111	+	3.34714i	3.83111	+	3.34714i
$213$		0			0
$214$	−3.22926	+	1.04925i	−3.22926	+	1.04925i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	0.203160	−	2.25729i	0.203160	−	2.25729i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.998993	−	0.0448648i	$-0.985714\pi$
$223$		0			0		0.998993	+	0.0448648i	$0.0142857\pi$
$224$	−3.69475	−	0.670498i	−3.69475	−	0.670498i
$225$	−0.550897	+	0.834573i	−0.550897	+	0.834573i
$226$	0.249824	−	0.238856i	0.249824	−	0.238856i
$227$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$227$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$228$		0			0
$229$		0			0		−0.858449	−	0.512899i	$-0.828571\pi$
$229$		0			0		0.858449	+	0.512899i	$0.171429\pi$
$230$		0			0
$231$		0			0
$232$	0.554057	+	0.694765i	0.554057	+	0.694765i
$233$	1.99195	+	0.179279i	1.99195	+	0.179279i	0.995974	+	0.0896393i	$0.0285714\pi$
$233$	1.99195	+	0.179279i	1.99195	+	0.179279i	0.995974	+	0.0896393i	$0.0285714\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.125481	+	0.691456i	0.125481	+	0.691456i	0.983930	+	0.178557i	$0.0571429\pi$
$239$	0.125481	+	0.691456i	0.125481	+	0.691456i	−0.858449	+	0.512899i	$0.828571\pi$
$240$		0			0
$241$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$241$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$242$	1.65503	−	0.988832i	1.65503	−	0.988832i
$243$		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	$-0.400000\pi$
$251$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$252$	2.71690			2.71690
$253$	0.0494318	−	0.0748860i	0.0494318	−	0.0748860i
$254$	0.983360	−	2.04197i	0.983360	−	2.04197i
$255$		0			0
$256$	−0.971995	−	2.27409i	−0.971995	−	2.27409i
$257$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$257$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$258$		0			0
$259$	1.90020	−	0.617412i	1.90020	−	0.617412i
$260$		0			0
$261$	−0.202174	−	0.176635i	−0.202174	−	0.176635i
$262$		0			0
$263$	0.167386	−	0.209896i	0.167386	−	0.209896i	−0.691063	−	0.722795i	$-0.742857\pi$
$263$	0.167386	−	0.209896i	0.167386	−	0.209896i	0.858449	+	0.512899i	$0.171429\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−0.209278	−	4.65994i	−0.209278	−	4.65994i
$269$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$269$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$270$		0			0
$271$		0			0		−0.266037	−	0.963963i	$-0.585714\pi$
$271$		0			0		0.266037	+	0.963963i	$0.414286\pi$
$272$		0			0
$273$		0			0
$274$	−1.98344	+	1.58174i	−1.98344	+	1.58174i
$275$	0.983930	+	0.178557i	0.983930	+	0.178557i
$276$		0			0
$277$	−1.11816	+	1.16951i	−1.11816	+	1.16951i	−0.134233	+	0.990950i	$0.542857\pi$
$277$	−1.11816	+	1.16951i	−1.11816	+	1.16951i	−0.983930	+	0.178557i	$0.942857\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.04486	−	0.998993i	1.04486	−	0.998993i	0.0448648	−	0.998993i	$-0.485714\pi$
$281$	1.04486	−	0.998993i	1.04486	−	0.998993i	1.00000			$0$
$282$		0			0
$283$		0			0		0.657939	−	0.753071i	$-0.271429\pi$
$283$		0			0		−0.657939	+	0.753071i	$0.728571\pi$
$284$	1.81585	+	4.83832i	1.81585	+	4.83832i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	2.06867	+	3.13390i	2.06867	+	3.13390i
$289$	0.393025	+	0.919528i	0.393025	+	0.919528i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.266037	−	0.963963i	$-0.585714\pi$
$293$		0			0		0.266037	+	0.963963i	$0.414286\pi$
$294$		0			0
$295$		0			0
$296$	5.17059	+	4.12341i	5.17059	+	4.12341i
$297$		0			0
$298$	0.773038	+	3.38690i	0.773038	+	3.38690i
$299$		0			0
$300$		0			0
$301$	−0.983930	+	0.178557i	−0.983930	+	0.178557i
$302$	−0.897302	−	2.76161i	−0.897302	−	2.76161i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$	−1.06781	−	2.49826i	−1.06781	−	2.49826i
$309$		0			0
$310$		0			0
$311$		0			0		−0.963963	−	0.266037i	$-0.914286\pi$
$311$		0			0		0.963963	+	0.266037i	$0.0857143\pi$
$312$		0			0
$313$		0			0		−0.0896393	−	0.995974i	$-0.528571\pi$
$313$		0			0		0.0896393	+	0.995974i	$0.471429\pi$
$314$		0			0
$315$		0			0
$316$	−0.701286	−	3.86440i	−0.701286	−	3.86440i
$317$	−1.29399	+	0.485644i	−1.29399	+	0.485644i	−0.900969	−	0.433884i	$-0.857143\pi$
$317$	−1.29399	+	0.485644i	−1.29399	+	0.485644i	−0.393025	+	0.919528i	$0.628571\pi$
$318$		0			0
$319$	−0.0829607	+	0.255327i	−0.0829607	+	0.255327i
$320$		0			0
$321$		0			0
$322$	−0.130275	−	0.113818i	−0.130275	−	0.113818i
$323$		0			0
$324$	−1.87755	−	1.96376i	−1.87755	−	1.96376i
$325$		0			0
$326$	3.26024	+	1.39349i	3.26024	+	1.39349i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.02879	−	0.820436i	−1.02879	−	0.820436i	−0.0448648	−	0.998993i	$-0.514286\pi$
$331$	−1.02879	−	0.820436i	−1.02879	−	0.820436i	−0.983930	+	0.178557i	$0.942857\pi$
$332$		0			0
$333$	−1.75942	−	0.946783i	−1.75942	−	0.946783i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.312745	−	0.430457i	0.312745	−	0.430457i	−0.623490	−	0.781831i	$-0.714286\pi$
$337$	0.312745	−	0.430457i	0.312745	−	0.430457i	0.936235	+	0.351375i	$0.114286\pi$
$338$	1.55972	−	1.13321i	1.55972	−	1.13321i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$344$	−2.28745	−	2.39249i	−2.28745	−	2.39249i
$345$		0			0
$346$		0			0
$347$	−1.70999	+	1.02167i	−1.70999	+	1.02167i	−0.809017	+	0.587785i	$0.800000\pi$
$347$	−1.70999	+	1.02167i	−1.70999	+	1.02167i	−0.900969	+	0.433884i	$0.857143\pi$
$348$		0			0
$349$		0			0		0.0448648	−	0.998993i	$-0.485714\pi$
$349$		0			0		−0.0448648	+	0.998993i	$0.514286\pi$
$350$	0.595762	−	1.83357i	0.595762	−	1.83357i
$351$		0			0
$352$	2.06867	−	3.13390i	2.06867	−	3.13390i
$353$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$353$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.0919519	+	1.02167i	0.0919519	+	1.02167i
$359$	−0.468542	+	0.252133i	−0.468542	+	0.252133i	−0.691063	−	0.722795i	$-0.742857\pi$
$359$	−0.468542	+	0.252133i	−0.468542	+	0.252133i	0.222521	+	0.974928i	$0.428571\pi$
$360$		0			0
$361$	0.936235	−	0.351375i	0.936235	−	0.351375i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.983930	−	0.178557i	$-0.942857\pi$
$367$		0			0		0.983930	+	0.178557i	$0.0571429\pi$
$368$	0.0441394	−	0.325850i	0.0441394	−	0.325850i
$369$		0			0
$370$		0			0
$371$	1.80499	+	0.498146i	1.80499	+	0.498146i
$372$		0			0
$373$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$373$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.0840080	+	0.0315287i	0.0840080	+	0.0315287i	0.393025	−	0.919528i	$-0.371429\pi$
$379$	0.0840080	+	0.0315287i	0.0840080	+	0.0315287i	−0.309017	+	0.951057i	$0.600000\pi$
$380$		0			0
$381$		0			0
$382$	0.345288	+	0.0155069i	0.345288	+	0.0155069i
$383$		0			0		−0.722795	−	0.691063i	$-0.757143\pi$
$383$		0			0		0.722795	+	0.691063i	$0.242857\pi$
$384$		0			0
$385$		0			0
$386$		−	3.82096i		−	3.82096i
$387$	0.809017	+	0.587785i	0.809017	+	0.587785i
$388$		0			0
$389$	−1.20999	−	1.38494i	−1.20999	−	1.38494i	−0.900969	−	0.433884i	$-0.857143\pi$
$389$	−1.20999	−	1.38494i	−1.20999	−	1.38494i	−0.309017	−	0.951057i	$-0.600000\pi$
$390$		0			0
$391$		0			0
$392$	−3.19077	+	0.880596i	−3.19077	+	0.880596i
$393$		0			0
$394$	−2.41275	−	0.783950i	−2.41275	−	0.783950i
$395$		0			0
$396$	−1.06781	+	2.49826i	−1.06781	+	2.49826i
$397$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$397$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$398$		0			0
$399$		0			0
$400$	3.53257	−	0.974928i	3.53257	−	0.974928i
$401$	−1.50008	+	0.135010i	−1.50008	+	0.135010i	−0.809017	−	0.587785i	$-0.800000\pi$
$401$	−1.50008	+	0.135010i	−1.50008	+	0.135010i	−0.691063	+	0.722795i	$0.742857\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	0.466327	+	0.224571i	0.466327	+	0.224571i
$407$	−0.179098	+	1.98994i	−0.179098	+	1.98994i
$408$		0			0
$409$		0			0		−0.995974	−	0.0896393i	$-0.971429\pi$
$409$		0			0		0.995974	+	0.0896393i	$0.0285714\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.00776126	+	0.172818i	0.00776126	+	0.172818i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$419$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$420$		0			0
$421$	−0.314473	−	0.169225i	−0.314473	−	0.169225i	0.309017	−	0.951057i	$-0.400000\pi$
$421$	−0.314473	−	0.169225i	−0.314473	−	0.169225i	−0.623490	+	0.781831i	$0.714286\pi$
$422$	−3.65717	+	1.00931i	−3.65717	+	1.00931i
$423$		0			0
$424$	1.91528	+	5.89462i	1.91528	+	5.89462i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−4.66501	−	1.06476i	−4.66501	−	1.06476i
$429$		0			0
$430$		0			0
$431$	1.67499	+	0.544238i	1.67499	+	0.544238i	0.983930	−	0.178557i	$-0.0571429\pi$
$431$	1.67499	+	0.544238i	1.67499	+	0.544238i	0.691063	+	0.722795i	$0.257143\pi$
$432$		0			0
$433$		0			0		−0.919528	−	0.393025i	$-0.871429\pi$
$433$		0			0		0.919528	+	0.393025i	$0.128571\pi$
$434$		0			0
$435$		0			0
$436$	1.87733	−	2.58392i	1.87733	−	2.58392i
$437$		0			0
$438$		0			0
$439$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$439$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$440$		0			0
$441$	0.900969	−	0.433884i	0.900969	−	0.433884i
$442$		0			0
$443$	0.0277280	−	0.617412i	0.0277280	−	0.617412i	−0.936235	−	0.351375i	$-0.885714\pi$
$443$	0.0277280	−	0.617412i	0.0277280	−	0.617412i	0.963963	−	0.266037i	$-0.0857143\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−2.69216	−	2.35207i	−2.69216	−	2.35207i
$449$	0.258120	+	0.246788i	0.258120	+	0.246788i	0.809017	−	0.587785i	$-0.200000\pi$
$449$	0.258120	+	0.246788i	0.258120	+	0.246788i	−0.550897	+	0.834573i	$0.685714\pi$
$450$	−1.73700	+	0.836496i	−1.73700	+	0.836496i
$451$		0			0
$452$	0.474869	−	0.108386i	0.474869	−	0.108386i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.522106	+	0.790956i	−0.522106	+	0.790956i	−0.995974	−	0.0896393i	$-0.971429\pi$
$457$	−0.522106	+	0.790956i	−0.522106	+	0.790956i	0.473869	+	0.880596i	$0.342857\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$461$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$462$		0			0
$463$	1.54951	−	1.23569i	1.54951	−	1.23569i	0.691063	−	0.722795i	$-0.257143\pi$
$463$	1.54951	−	1.23569i	1.54951	−	1.23569i	0.858449	−	0.512899i	$-0.171429\pi$
$464$	0.132063	+	0.974928i	0.132063	+	0.974928i
$465$		0			0
$466$	3.11945	+	2.26641i	3.11945	+	2.26641i
$467$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$467$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$468$		0			0
$469$	−0.813584	−	1.51189i	−0.813584	−	1.51189i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.222521	−	0.974928i	0.222521	−	0.974928i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.887305	−	1.64889i	−0.887305	−	1.64889i
$478$	−0.476060	+	1.26846i	−0.476060	+	1.26846i
$479$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$479$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	2.71690			2.71690
$485$		0			0
$486$		0			0
$487$	0.543210	+	1.27090i	0.543210	+	1.27090i	0.936235	+	0.351375i	$0.114286\pi$
$487$	0.543210	+	1.27090i	0.543210	+	1.27090i	−0.393025	+	0.919528i	$0.628571\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.708207	−	1.65693i	0.708207	−	1.65693i	−0.0448648	−	0.998993i	$-0.514286\pi$
$491$	0.708207	−	1.65693i	0.708207	−	1.65693i	0.753071	−	0.657939i	$-0.228571\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.37484	+	1.31448i	1.37484	+	1.31448i
$498$		0			0
$499$	1.44413	−	0.0648561i	1.44413	−	0.0648561i	0.691063	−	0.722795i	$-0.257143\pi$
$499$	1.44413	−	0.0648561i	1.44413	−	0.0648561i	0.753071	+	0.657939i	$0.228571\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.0448648	−	0.998993i	$-0.485714\pi$
$503$		0			0		−0.0448648	+	0.998993i	$0.514286\pi$
$504$	2.84151	+	1.69772i	2.84151	+	1.69772i
$505$		0			0
$506$	0.155861	−	0.0750585i	0.155861	−	0.0750585i
$507$		0			0
$508$	2.66555	−	1.75951i	2.66555	−	1.75951i
$509$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$509$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$510$		0			0
$511$		0			0
$512$	0.218923	−	1.61616i	0.218923	−	1.61616i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	3.75539	+	0.857144i	3.75539	+	0.857144i
$519$		0			0
$520$		0			0
$521$		0			0		−0.266037	−	0.963963i	$-0.585714\pi$
$521$		0			0		0.266037	+	0.963963i	$0.414286\pi$
$522$	−0.159942	−	0.492251i	−0.159942	−	0.492251i
$523$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$523$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$524$		0			0
$525$		0			0
$526$	0.484580	−	0.181866i	0.484580	−	0.181866i
$527$		0			0
$528$		0			0
$529$	−0.618470	+	0.775537i	−0.618470	+	0.775537i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	2.69300	−	5.00444i	2.69300	−	5.00444i
$537$		0			0
$538$		0			0
$539$	−0.753071	−	0.657939i	−0.753071	−	0.657939i
$540$		0			0
$541$	0.0320114	−	0.355676i	0.0320114	−	0.355676i	−0.963963	−	0.266037i	$-0.914286\pi$
$541$	0.0320114	−	0.355676i	0.0320114	−	0.355676i	0.995974	−	0.0896393i	$-0.0285714\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.43783	+	0.614559i	−1.43783	+	0.614559i	−0.963963	−	0.266037i	$-0.914286\pi$
$547$	−1.43783	+	0.614559i	−1.43783	+	0.614559i	−0.473869	+	0.880596i	$0.657143\pi$
$548$	−3.54275	+	0.479898i	−3.54275	+	0.479898i
$549$		0			0
$550$	1.45187	+	1.26846i	1.45187	+	1.26846i
$551$		0			0
$552$		0			0
$553$	−0.849696	−	1.16951i	−0.849696	−	1.16951i
$554$	−3.00703	+	0.829888i	−3.00703	+	0.829888i
$555$		0			0
$556$		0			0
$557$	1.30397	+	1.49251i	1.30397	+	1.49251i	0.753071	+	0.657939i	$0.228571\pi$
$557$	1.30397	+	1.49251i	1.30397	+	1.49251i	0.550897	+	0.834573i	$0.314286\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	2.71711	−	0.620164i	2.71711	−	0.620164i
$563$		0			0		−0.722795	−	0.691063i	$-0.757143\pi$
$563$		0			0		0.722795	+	0.691063i	$0.242857\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.936235	−	0.351375i	−0.936235	−	0.351375i
$568$	−1.12421	+	6.19491i	−1.12421	+	6.19491i
$569$	0.415992	−	1.50731i	0.415992	−	1.50731i	−0.393025	−	0.919528i	$-0.628571\pi$
$569$	0.415992	−	1.50731i	0.415992	−	1.50731i	0.809017	−	0.587785i	$-0.200000\pi$
$570$		0			0
$571$	−0.437890	+	1.91852i	−0.437890	+	1.91852i	−0.0448648	+	0.998993i	$0.514286\pi$
$571$	−0.437890	+	1.91852i	−0.437890	+	1.91852i	−0.393025	+	0.919528i	$0.628571\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.0864961	+	0.0238714i	0.0864961	+	0.0238714i
$576$	0.160388	+	3.57131i	0.160388	+	3.57131i
$577$		0			0		−0.512899	−	0.858449i	$-0.671429\pi$
$577$		0			0		0.512899	+	0.858449i	$0.328571\pi$
$578$	−0.258792	+	1.91048i	−0.258792	+	1.91048i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−1.16747	+	1.46396i	−1.16747	+	1.46396i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.880596	−	0.473869i	$-0.157143\pi$
$587$		0			0		−0.880596	+	0.473869i	$0.842857\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	2.57273	+	6.85501i	2.57273	+	6.85501i
$593$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$593$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$594$		0			0
$595$		0			0
$596$	−1.51285	+	4.65607i	−1.51285	+	4.65607i
$597$		0			0
$598$		0			0
$599$	−1.68931	+	1.00931i	−1.68931	+	1.00931i	−0.753071	+	0.657939i	$0.771429\pi$
$599$	−1.68931	+	1.00931i	−1.68931	+	1.00931i	−0.936235	+	0.351375i	$0.885714\pi$
$600$		0			0
$601$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$601$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$602$	−1.80499	−	0.677425i	−1.80499	−	0.677425i
$603$	−0.530551	+	1.63287i	−0.530551	+	1.63287i
$604$	0.910564	−	3.98944i	0.910564	−	3.98944i
$605$		0			0
$606$		0			0
$607$		0			0		−0.550897	−	0.834573i	$-0.685714\pi$
$607$		0			0		0.550897	+	0.834573i	$0.314286\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−1.46984	−	0.790956i	−1.46984	−	0.790956i	−0.473869	−	0.880596i	$-0.657143\pi$
$613$	−1.46984	−	0.790956i	−1.46984	−	0.790956i	−0.995974	+	0.0896393i	$0.971429\pi$
$614$		0			0
$615$		0			0
$616$	0.444319	−	3.28009i	0.444319	−	3.28009i
$617$	−1.68704	−	0.812434i	−1.68704	−	0.812434i	−0.995974	−	0.0896393i	$-0.971429\pi$
$617$	−1.68704	−	0.812434i	−1.68704	−	0.812434i	−0.691063	−	0.722795i	$-0.742857\pi$
$618$		0			0
$619$		0			0		−0.963963	−	0.266037i	$-0.914286\pi$
$619$		0			0		0.963963	+	0.266037i	$0.0857143\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.134233	+	0.990950i	0.134233	+	0.990950i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−0.350072	−	0.400690i	−0.350072	−	0.400690i	0.550897	−	0.834573i	$-0.314286\pi$
$631$	−0.350072	−	0.400690i	−0.350072	−	0.400690i	−0.900969	+	0.433884i	$0.857143\pi$
$632$	1.68132	−	4.47986i	1.68132	−	4.47986i
$633$		0			0
$634$	−2.62181	−	0.475789i	−2.62181	−	0.475789i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−0.389777	+	0.340538i	−0.389777	+	0.340538i
$639$		−	1.90211i		−	1.90211i
$640$		0			0
$641$	−0.353882	−	1.95005i	−0.353882	−	1.95005i	−0.309017	−	0.951057i	$-0.600000\pi$
$641$	−0.353882	−	1.95005i	−0.353882	−	1.95005i	−0.0448648	−	0.998993i	$-0.514286\pi$
$642$		0			0
$643$		0			0		0.995974	−	0.0896393i	$-0.0285714\pi$
$643$		0			0		−0.995974	+	0.0896393i	$0.971429\pi$
$644$	−0.0753341	−	0.231855i	−0.0753341	−	0.231855i
$645$		0			0
$646$		0			0
$647$		0			0		0.512899	−	0.858449i	$-0.328571\pi$
$647$		0			0		−0.512899	+	0.858449i	$0.671429\pi$
$648$	−0.736556	−	3.22706i	−0.736556	−	3.22706i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	2.93688	+	4.04227i	2.93688	+	4.04227i
$653$	0.531538	+	1.92598i	0.531538	+	1.92598i	0.309017	+	0.951057i	$0.400000\pi$
$653$	0.531538	+	1.92598i	0.531538	+	1.92598i	0.222521	+	0.974928i	$0.428571\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.846011	−	0.193096i	−0.846011	−	0.193096i	−0.222521	−	0.974928i	$-0.571429\pi$
$659$	−0.846011	−	0.193096i	−0.846011	−	0.193096i	−0.623490	+	0.781831i	$0.714286\pi$
$660$		0			0
$661$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$661$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$662$	−0.891408	−	2.37515i	−0.891408	−	2.37515i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−1.97567	−	3.30672i	−1.97567	−	3.30672i
$667$	−0.00946774	+	0.0221509i	−0.00946774	+	0.0221509i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.18648	−	1.24096i	1.18648	−	1.24096i	0.222521	−	0.974928i	$-0.428571\pi$
$673$	1.18648	−	1.24096i	1.18648	−	1.24096i	0.963963	−	0.266037i	$-0.0857143\pi$
$674$	0.943250	−	0.403165i	0.943250	−	0.403165i
$675$		0			0
$676$	2.70596	−	0.243541i	2.70596	−	0.243541i
$677$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$677$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.00883	+	1.26503i	−1.00883	+	1.26503i	−0.0448648	+	0.998993i	$0.514286\pi$
$683$	−1.00883	+	1.26503i	−1.00883	+	1.26503i	−0.963963	+	0.266037i	$0.914286\pi$
$684$		0			0
$685$		0			0
$686$	−1.45187	+	1.26846i	−1.45187	+	1.26846i
$687$		0			0
$688$	−0.815458	−	3.57275i	−0.815458	−	3.57275i
$689$		0			0
$690$		0			0
$691$		0			0		0.0896393	−	0.995974i	$-0.471429\pi$
$691$		0			0		−0.0896393	+	0.995974i	$0.528571\pi$
$692$		0			0
$693$	0.0448648	+	0.998993i	0.0448648	+	0.998993i
$694$	−3.84033			−3.84033
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	2.04602	−	1.78755i	2.04602	−	1.78755i
$701$	−1.75942	−	0.0790155i	−1.75942	−	0.0790155i	−0.858449	−	0.512899i	$-0.828571\pi$
$701$	−1.75942	−	0.0790155i	−1.75942	−	0.0790155i	−0.900969	+	0.433884i	$0.857143\pi$
$702$		0			0
$703$		0			0
$704$	3.22088	−	1.55109i	3.22088	−	1.55109i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−1.60742	+	0.960388i	−1.60742	+	0.960388i	−0.623490	+	0.781831i	$0.714286\pi$
$709$	−1.60742	+	0.960388i	−1.60742	+	0.960388i	−0.983930	+	0.178557i	$0.942857\pi$
$710$		0			0
$711$	−0.258120	+	1.42236i	−0.258120	+	1.42236i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.627218	+	1.30243i	−0.627218	+	1.30243i
$717$		0			0
$718$	−1.02477	−	0.0460223i	−1.02477	−	0.0460223i
$719$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$719$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$720$		0			0
$721$		0			0
$722$	1.89694	+	0.344244i	1.89694	+	0.344244i
$723$		0			0
$724$		0			0
$725$	−0.268467			−0.268467
$726$		0			0
$727$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$727$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$728$		0			0
$729$	0.393025	+	0.919528i	0.393025	+	0.919528i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$733$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$734$		0			0
$735$		0			0
$736$	0.210081	−	0.263433i	0.210081	−	0.263433i
$737$	1.70999	−	0.153902i	1.70999	−	0.153902i
$738$		0			0
$739$	−0.606975	−	0.919528i	−0.606975	−	0.919528i	0.393025	−	0.919528i	$-0.371429\pi$
$739$	−0.606975	−	0.919528i	−0.606975	−	0.919528i	−1.00000			$\pi$
$740$		0			0
$741$		0			0
$742$	2.49472	+	2.60928i	2.49472	+	2.60928i
$743$	−1.09736	+	0.0987640i	−1.09736	+	0.0987640i	−0.623490	−	0.781831i	$-0.714286\pi$
$743$	−1.09736	+	0.0987640i	−1.09736	+	0.0987640i	−0.473869	+	0.880596i	$0.657143\pi$
$744$		0			0
$745$		0			0
$746$	−1.66137	+	1.73766i	−1.66137	+	1.73766i
$747$		0			0
$748$		0			0
$749$	−1.71703	+	0.391902i	−1.71703	+	0.391902i
$750$		0			0
$751$	0.314473	+	0.169225i	0.314473	+	0.169225i	0.623490	−	0.781831i	$-0.285714\pi$
$751$	0.314473	+	0.169225i	0.314473	+	0.169225i	−0.309017	+	0.951057i	$0.600000\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	0.668355	+	1.78082i	0.668355	+	1.78082i	0.623490	+	0.781831i	$0.285714\pi$
$757$	0.668355	+	1.78082i	0.668355	+	1.78082i	0.0448648	+	0.998993i	$0.485714\pi$
$758$	0.107859	+	0.135251i	0.107859	+	0.135251i
$759$		0			0
$760$		0			0
$761$		0			0		−0.550897	−	0.834573i	$-0.685714\pi$
$761$		0			0		0.550897	+	0.834573i	$0.314286\pi$
$762$		0			0
$763$	0.209906	−	1.15668i	0.209906	−	1.15668i
$764$	0.406505	+	0.268332i	0.406505	+	0.268332i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$769$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$770$		0			0
$771$		0			0
$772$	2.76177	−	4.62242i	2.76177	−	4.62242i
$773$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$773$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$774$	0.757723	+	1.77278i	0.757723	+	1.77278i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.633085	−	3.48858i	−0.633085	−	3.48858i
$779$		0			0
$780$		0			0
$781$	−1.74905	+	0.747578i	−1.74905	+	0.747578i
$782$		0			0
$783$		0			0
$784$	−3.53257	−	0.974928i	−3.53257	−	0.974928i
$785$		0			0
$786$		0			0
$787$		0			0		0.351375	−	0.936235i	$-0.385714\pi$
$787$		0			0		−0.351375	+	0.936235i	$0.614286\pi$
$788$	−2.35220	−	2.69231i	−2.35220	−	2.69231i
$789$		0			0
$790$		0			0
$791$	0.140166	−	0.111778i	0.140166	−	0.111778i
$792$	−2.67789	+	1.94560i	−2.67789	+	1.94560i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$797$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$798$		0			0
$799$		0			0
$800$	3.61977	+	0.998993i	3.61977	+	0.998993i
$801$		0			0
$802$	−2.61617	−	1.25988i	−2.61617	−	1.25988i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.646198	+	1.72179i	−0.646198	+	1.72179i	0.0448648	+	0.998993i	$0.485714\pi$
$809$	−0.646198	+	1.72179i	−0.646198	+	1.72179i	−0.691063	+	0.722795i	$0.742857\pi$
$810$		0			0
$811$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$811$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$812$	0.401822	+	0.608734i	0.401822	+	0.608734i
$813$		0			0
$814$	−2.26413	+	3.11631i	−2.26413	+	3.11631i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.764152	+	0.411208i	−0.764152	+	0.411208i	−0.809017	−	0.587785i	$-0.800000\pi$
$821$	−0.764152	+	0.411208i	−0.764152	+	0.411208i	0.0448648	+	0.998993i	$0.485714\pi$
$822$		0			0
$823$	0.615546	−	1.89446i	0.615546	−	1.89446i	0.222521	−	0.974928i	$-0.428571\pi$
$823$	0.615546	−	1.89446i	0.615546	−	1.89446i	0.393025	−	0.919528i	$-0.371429\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.685130	+	1.82552i	0.685130	+	1.82552i	0.550897	+	0.834573i	$0.314286\pi$
$827$	0.685130	+	1.82552i	0.685130	+	1.82552i	0.134233	+	0.990950i	$0.457143\pi$
$828$	−0.115523	+	0.214677i	−0.115523	+	0.214677i
$829$		0			0		−0.657939	−	0.753071i	$-0.728571\pi$
$829$		0			0		0.657939	+	0.753071i	$0.271429\pi$
$830$		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		0.657939	−	0.753071i	$-0.271429\pi$
$839$		0			0		−0.657939	+	0.753071i	$0.728571\pi$
$840$		0			0
$841$	−0.124559	+	0.919528i	−0.124559	+	0.919528i
$842$	−0.353125	−	0.591032i	−0.353125	−	0.591032i
$843$		0			0
$844$	−5.15380	−	1.42236i	−5.15380	−	1.42236i
$845$		0			0
$846$		0			0
$847$	0.900969	−	0.433884i	0.900969	−	0.433884i
$848$	−1.52692	+	6.68988i	−1.52692	+	6.68988i
$849$		0			0
$850$		0			0
$851$	−0.0320114	+	0.176398i	−0.0320114	+	0.176398i
$852$		0			0
$853$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$853$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$854$		0			0
$855$		0			0
$856$	−4.21363	−	4.02864i	−4.21363	−	4.02864i
$857$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$857$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$858$		0			0
$859$		0			0			−	1.00000i	$-0.5\pi$
$859$		0			0				1.00000i	$0.5\pi$
$860$		0			0
$861$		0			0
$862$	2.23400	+	2.55701i	2.23400	+	2.55701i
$863$	0.445077	+	0.744934i	0.445077	+	0.744934i	0.995974	−	0.0896393i	$-0.0285714\pi$
$863$	0.445077	+	0.744934i	0.445077	+	0.744934i	−0.550897	+	0.834573i	$0.685714\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1.40935	−	0.321674i	1.40935	−	0.321674i
$870$		0			0
$871$		0			0
$872$	3.57806	−	1.52934i	3.57806	−	1.52934i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.272900	+	0.988832i	−0.272900	+	0.988832i	0.691063	+	0.722795i	$0.257143\pi$
$877$	−0.272900	+	0.988832i	−0.272900	+	0.988832i	−0.963963	+	0.266037i	$0.914286\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$881$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$882$	1.92016	+	0.172818i	1.92016	+	0.172818i
$883$	0.590905	−	1.09808i	0.590905	−	1.09808i	−0.393025	−	0.919528i	$-0.628571\pi$
$883$	0.590905	−	1.09808i	0.590905	−	1.09808i	0.983930	−	0.178557i	$-0.0571429\pi$
$884$		0			0
$885$		0			0
$886$	0.656407	−	0.994414i	0.656407	−	0.994414i
$887$		0			0		−0.0448648	−	0.998993i	$-0.514286\pi$
$887$		0			0		0.0448648	+	0.998993i	$0.485714\pi$
$888$		0			0
$889$	0.602949	−	1.00917i	0.602949	−	1.00917i
$890$		0			0
$891$	0.691063	−	0.722795i	0.691063	−	0.722795i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−0.969405	−	2.98352i	−0.969405	−	2.98352i
$897$		0			0
$898$	0.183163	+	0.663678i	0.183163	+	0.663678i
$899$		0			0
$900$	−2.70596	−	0.243541i	−2.70596	−	0.243541i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.564377	+	0.183377i	0.564377	+	0.183377i
$905$		0			0
$906$		0			0
$907$	−0.0360371	+	0.266037i	−0.0360371	+	0.266037i	0.963963	+	0.266037i	$0.0857143\pi$
$907$	−0.0360371	+	0.266037i	−0.0360371	+	0.266037i	−1.00000			$1.00000\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.62730	−	1.07417i	1.62730	−	1.07417i	0.691063	−	0.722795i	$-0.257143\pi$
$911$	1.62730	−	1.07417i	1.62730	−	1.07417i	0.936235	−	0.351375i	$-0.114286\pi$
$912$		0			0
$913$		0			0
$914$	−1.64622	+	0.792778i	−1.64622	+	0.792778i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	0.856104	+	0.565109i	0.856104	+	0.565109i	0.900969	−	0.433884i	$-0.142857\pi$
$919$	0.856104	+	0.565109i	0.856104	+	0.565109i	−0.0448648	+	0.998993i	$0.514286\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−1.94789	+	0.444594i	−1.94789	+	0.444594i
$926$	3.78637	−	0.512899i	3.78637	−	0.512899i
$927$		0			0
$928$	−0.396215	+	0.926991i	−0.396215	+	0.926991i
$929$		0			0		−0.834573	−	0.550897i	$-0.814286\pi$
$929$		0			0		0.834573	+	0.550897i	$0.185714\pi$
$930$		0			0
$931$		0			0
$932$	2.13562	+	4.99653i	2.13562	+	4.99653i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$937$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$938$	0.148505	−	3.30672i	0.148505	−	3.30672i
$939$		0			0
$940$		0			0
$941$		0			0		0.351375	−	0.936235i	$-0.385714\pi$
$941$		0			0		−0.351375	+	0.936235i	$0.614286\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	1.33232	−	1.39349i	1.33232	−	1.39349i
$947$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$947$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1.21850	−	0.885289i	−1.21850	−	0.885289i	−0.222521	−	0.974928i	$-0.571429\pi$
$953$	−1.21850	−	0.885289i	−1.21850	−	0.885289i	−0.995974	+	0.0896393i	$0.971429\pi$
$954$	0.161961	−	3.60635i	0.161961	−	3.60635i
$955$		0			0
$956$	−1.49275	+	1.19043i	−1.49275	+	1.19043i
$957$		0			0
$958$		0			0
$959$	−1.09820	+	0.724913i	−1.09820	+	0.724913i
$960$		0			0
$961$	0.473869	+	0.880596i	0.473869	+	0.880596i
$962$		0			0
$963$	1.46984	+	0.970235i	1.46984	+	0.970235i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	1.94789	−	0.444594i	1.94789	−	0.444594i	0.963963	−	0.266037i	$-0.0857143\pi$
$967$	1.94789	−	0.444594i	1.94789	−	0.444594i	0.983930	−	0.178557i	$-0.0571429\pi$
$968$	2.84151	+	1.69772i	2.84151	+	1.69772i
$969$		0			0
$970$		0			0
$971$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$971$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$972$		0			0
$973$		0			0
$974$	−0.357683	+	2.64052i	−0.357683	+	2.64052i
$975$		0			0
$976$		0			0
$977$	−1.65503	−	0.988832i	−1.65503	−	0.988832i	−0.963963	−	0.266037i	$-0.914286\pi$
$977$	−1.65503	−	0.988832i	−1.65503	−	0.988832i	−0.691063	−	0.722795i	$-0.742857\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−0.981100	+	0.647618i	−0.981100	+	0.647618i
$982$	2.81053	−	2.04197i	2.81053	−	2.04197i
$983$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$983$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.0277280	−	0.0853380i	0.0277280	−	0.0853380i
$990$		0			0
$991$	−0.846011	−	0.193096i	−0.846011	−	0.193096i	−0.222521	−	0.974928i	$-0.571429\pi$
$991$	−0.846011	−	0.193096i	−0.846011	−	0.193096i	−0.623490	+	0.781831i	$0.714286\pi$
$992$		0			0
$993$		0			0
$994$	0.975592	+	3.53498i	0.975592	+	3.53498i
$995$		0			0
$996$		0			0
$997$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$997$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$998$	2.45421	+	1.32067i	2.45421	+	1.32067i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3311.1.ex.a.2631.1	yes	24
7.6	odd	2	CM	3311.1.ex.a.2631.1	yes	24
11.6	odd	10		3311.1.ex.b.2932.1	yes	24
43.27	odd	14		3311.1.ex.b.629.1	yes	24
77.6	even	10		3311.1.ex.b.2932.1	yes	24
301.27	even	14		3311.1.ex.b.629.1	yes	24
473.457	even	70	inner	3311.1.ex.a.930.1	✓	24
3311.930	odd	70	inner	3311.1.ex.a.930.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3311.1.ex.a.930.1	✓	24	473.457	even	70	inner
3311.1.ex.a.930.1	✓	24	3311.930	odd	70	inner
3311.1.ex.a.2631.1	yes	24	1.1	even	1	trivial
3311.1.ex.a.2631.1	yes	24	7.6	odd	2	CM
3311.1.ex.b.629.1	yes	24	43.27	odd	14
3311.1.ex.b.629.1	yes	24	301.27	even	14
3311.1.ex.b.2932.1	yes	24	11.6	odd	10
3311.1.ex.b.2932.1	yes	24	77.6	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)

\(f(q)\)	\(=\)	\(q+(1.65503 + 0.988832i) q^{2} +(1.28745 + 2.39249i) q^{4} +(0.809017 + 0.587785i) q^{7} +(-0.148505 + 3.30672i) q^{8} +(-0.134233 - 0.990950i) q^{9} +O(q^{10})\)	\(q+(1.65503 + 0.988832i) q^{2} +(1.28745 + 2.39249i) q^{4} +(0.809017 + 0.587785i) q^{7} +(-0.148505 + 3.30672i) q^{8} +(-0.134233 - 0.990950i) q^{9} +(-0.858449 + 0.512899i) q^{11} +(0.757723 + 1.77278i) q^{14} +(-2.01884 + 3.05841i) q^{16} +(0.757723 - 1.77278i) q^{18} -1.92793 q^{22} +(-0.0808436 + 0.0389322i) q^{23} +(-0.753071 - 0.657939i) q^{25} +(-0.364698 + 2.69231i) q^{28} +(0.202174 - 0.176635i) q^{29} +(-3.38322 + 1.62927i) q^{32} +(2.19802 - 1.59695i) q^{36} +(1.17439 - 1.61640i) q^{37} +(-0.691063 + 0.722795i) q^{43} +(-2.33232 - 1.39349i) q^{44} +(-0.172296 - 0.0155069i) q^{46} +(0.309017 + 0.951057i) q^{49} +(-0.595762 - 1.83357i) q^{50} +(1.75307 - 0.657939i) q^{53} +(-2.06378 + 2.58790i) q^{56} +(0.509266 - 0.0924181i) q^{58} +(0.473869 - 0.880596i) q^{63} +(-3.56051 - 0.320452i) q^{64} +(-1.54687 - 0.744934i) q^{67} +(1.88490 + 0.255327i) q^{71} +(3.29673 - 0.296711i) q^{72} +(3.54199 - 1.51392i) q^{74} +(-0.995974 - 0.0896393i) q^{77} +(-1.37484 - 0.446712i) q^{79} +(-0.963963 + 0.266037i) q^{81} +(-1.85845 + 0.512899i) q^{86} +(-1.56853 - 2.91482i) q^{88} +(-0.197227 - 0.143294i) q^{92} +(-0.429004 + 1.87959i) q^{98} +(0.623490 + 0.781831i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 3 q^{4} + 6 q^{7} + 8 q^{8} - q^{9}+O(q^{10}) \) 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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