LMFDB - Embedded newform 847.1.bb.a.489.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,1,Mod(20,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(110))

chi = DirichletCharacter(H, H._module([55, 76]))

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

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

chi := DirichletCharacter("847.20");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	847.bb (of order $110$, degree $40$, 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:	$0.422708065700$
Analytic rank:	$0$
Dimension:	$40$
Coefficient field:	$\Q(\zeta_{55})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{40} - x^{39} + x^{35} - x^{34} + x^{30} - x^{28} + x^{25} - x^{23} + x^{20} - x^{17} + x^{15} + \cdots + 1 $ x^40 - x^39 + x^35 - x^34 + x^30 - x^28 + x^25 - x^23 + x^20 - x^17 + x^15 - x^12 + x^10 - x^6 + x^5 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{55}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{55} - \cdots)$

Embedding invariants

Embedding label			489.1
Root			$0.516397 - 0.856349i$ of defining polynomial
Character	$\chi$	$=$	847.489
Dual form			847.1.bb.a.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.630674 - 1.04586i) q^{2} +(-0.229397 - 0.434755i) q^{4} +(0.610648 - 0.791902i) q^{7} +(0.619939 + 0.0354494i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.630674 - 1.04586i) q^{2} +(-0.229397 - 0.434755i) q^{4} +(0.610648 - 0.791902i) q^{7} +(0.619939 + 0.0354494i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-0.921124 + 0.389270i) q^{11} +(-0.443096 - 1.13808i) q^{14} +(0.705514 - 1.03178i) q^{16} +(1.18956 + 0.276620i) q^{18} +(-0.173809 + 1.20886i) q^{22} +(-1.80739 - 0.530696i) q^{23} +(0.198590 - 0.980083i) q^{25} +(-0.484364 - 0.0838225i) q^{28} +(0.307474 + 1.51745i) q^{29} +(-0.376192 - 0.823746i) q^{32} +(0.342589 - 0.352516i) q^{36} +(-1.12767 - 1.16034i) q^{37} +(-0.949680 + 0.610322i) q^{43} +(0.380540 + 0.311166i) q^{44} +(-1.69490 + 1.55557i) q^{46} +(-0.254218 - 0.967147i) q^{49} +(-0.899779 - 0.825810i) q^{50} +(0.831697 + 1.21632i) q^{53} +(0.406637 - 0.469284i) q^{56} +(1.78094 + 0.635440i) q^{58} +(0.941844 + 0.336049i) q^{63} +(0.143008 + 0.0164086i) q^{64} +(-1.30118 - 1.50165i) q^{67} +(1.45190 + 1.33254i) q^{71} +(0.157857 + 0.600551i) q^{72} +(-1.92474 + 0.447580i) q^{74} +(-0.254218 + 0.967147i) q^{77} +(-0.456270 + 1.73583i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(0.0393703 + 1.37814i) q^{86} +(-0.584840 + 0.208670i) q^{88} +(0.183885 + 0.907510i) q^{92} +(-1.17182 - 0.344079i) q^{98} +(-0.654861 - 0.755750i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 2 q^{2} + 3 q^{4} + q^{7} - q^{8} - 10 q^{9}+O(q^{10}) $ 40 * q + 2 * q^2 + 3 * q^4 + q^7 - q^8 - 10 * q^9	$ 40 q + 2 q^{2} + 3 q^{4} + q^{7} - q^{8} - 10 q^{9} + q^{11} - 3 q^{14} - 3 q^{18} + 2 q^{22} - 9 q^{23} + q^{25} - 2 q^{28} + 2 q^{29} - 4 q^{32} + 3 q^{36} - 3 q^{37} + 2 q^{43} - 13 q^{44} - q^{46} + q^{49} + 2 q^{50} - 3 q^{53} - 7 q^{56} - 12 q^{58} + q^{63} - 9 q^{64} + 2 q^{67} - 3 q^{71} - q^{72} + 4 q^{74} + q^{77} - 3 q^{79} - 10 q^{81} - q^{86} - 12 q^{88} - 4 q^{92} - 9 q^{98} - 4 q^{99}+O(q^{100}) $ 40 * q + 2 * q^2 + 3 * q^4 + q^7 - q^8 - 10 * q^9 + q^11 - 3 * q^14 - 3 * q^18 + 2 * q^22 - 9 * q^23 + q^25 - 2 * q^28 + 2 * q^29 - 4 * q^32 + 3 * q^36 - 3 * q^37 + 2 * q^43 - 13 * q^44 - q^46 + q^49 + 2 * q^50 - 3 * q^53 - 7 * q^56 - 12 * q^58 + q^63 - 9 * q^64 + 2 * q^67 - 3 * q^71 - q^72 + 4 * q^74 + q^77 - 3 * q^79 - 10 * q^81 - q^86 - 12 * q^88 - 4 * q^92 - 9 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$-1$	$e\left(\frac{37}{55}\right)$

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 $

$2$	0.630674	−	1.04586i	0.630674	−	1.04586i	−0.362808	−	0.931864i	$-0.618182\pi$
$2$	0.630674	−	1.04586i	0.630674	−	1.04586i	0.993482	−	0.113991i	$-0.0363636\pi$
$3$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$3$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$4$	−0.229397	−	0.434755i	−0.229397	−	0.434755i
$5$		0			0		0.774142	−	0.633012i	$-0.218182\pi$
$5$		0			0		−0.774142	+	0.633012i	$0.781818\pi$
$6$		0			0
$7$	0.610648	−	0.791902i	0.610648	−	0.791902i
$7$	0.610648	−	0.791902i	0.610648	−	0.791902i
$8$	0.619939	+	0.0354494i	0.619939	+	0.0354494i
$9$	0.309017	+	0.951057i	0.309017	+	0.951057i
$10$		0			0
$11$	−0.921124	+	0.389270i	−0.921124	+	0.389270i
$11$	−0.921124	+	0.389270i	−0.921124	+	0.389270i
$12$		0			0
$13$		0			0		0.985354	−	0.170522i	$-0.0545455\pi$
$13$		0			0		−0.985354	+	0.170522i	$0.945455\pi$
$14$	−0.443096	−	1.13808i	−0.443096	−	1.13808i
$15$		0			0
$16$	0.705514	−	1.03178i	0.705514	−	1.03178i
$17$		0			0		0.993482	−	0.113991i	$-0.0363636\pi$
$17$		0			0		−0.993482	+	0.113991i	$0.963636\pi$
$18$	1.18956	+	0.276620i	1.18956	+	0.276620i
$19$		0			0		0.870746	−	0.491733i	$-0.163636\pi$
$19$		0			0		−0.870746	+	0.491733i	$0.836364\pi$
$20$		0			0
$21$		0			0
$22$	−0.173809	+	1.20886i	−0.173809	+	1.20886i
$23$	−1.80739	−	0.530696i	−1.80739	−	0.530696i	−0.809017	−	0.587785i	$-0.800000\pi$
$23$	−1.80739	−	0.530696i	−1.80739	−	0.530696i	−0.998369	+	0.0570888i	$0.981818\pi$
$24$		0			0
$25$	0.198590	−	0.980083i	0.198590	−	0.980083i
$26$		0			0
$27$		0			0
$28$	−0.484364	−	0.0838225i	−0.484364	−	0.0838225i
$29$	0.307474	+	1.51745i	0.307474	+	1.51745i	0.774142	+	0.633012i	$0.218182\pi$
$29$	0.307474	+	1.51745i	0.307474	+	1.51745i	−0.466667	+	0.884433i	$0.654545\pi$
$30$		0			0
$31$		0			0		0.897398	−	0.441221i	$-0.145455\pi$
$31$		0			0		−0.897398	+	0.441221i	$0.854545\pi$
$32$	−0.376192	−	0.823746i	−0.376192	−	0.823746i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.342589	−	0.352516i	0.342589	−	0.352516i
$37$	−1.12767	−	1.16034i	−1.12767	−	1.16034i	−0.985354	−	0.170522i	$-0.945455\pi$
$37$	−1.12767	−	1.16034i	−1.12767	−	1.16034i	−0.142315	−	0.989821i	$-0.545455\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.0855750	−	0.996332i	$-0.527273\pi$
$41$		0			0		0.0855750	+	0.996332i	$0.472727\pi$
$42$		0			0
$43$	−0.949680	+	0.610322i	−0.949680	+	0.610322i	−0.921124	−	0.389270i	$-0.872727\pi$
$43$	−0.949680	+	0.610322i	−0.949680	+	0.610322i	−0.0285561	+	0.999592i	$0.509091\pi$
$44$	0.380540	+	0.311166i	0.380540	+	0.311166i
$45$		0			0
$46$	−1.69490	+	1.55557i	−1.69490	+	1.55557i
$47$		0			0		0.974012	−	0.226497i	$-0.0727273\pi$
$47$		0			0		−0.974012	+	0.226497i	$0.927273\pi$
$48$		0			0
$49$	−0.254218	−	0.967147i	−0.254218	−	0.967147i
$50$	−0.899779	−	0.825810i	−0.899779	−	0.825810i
$51$		0			0
$52$		0			0
$53$	0.831697	+	1.21632i	0.831697	+	1.21632i	0.974012	+	0.226497i	$0.0727273\pi$
$53$	0.831697	+	1.21632i	0.831697	+	1.21632i	−0.142315	+	0.989821i	$0.545455\pi$
$54$		0			0
$55$		0			0
$56$	0.406637	−	0.469284i	0.406637	−	0.469284i
$57$		0			0
$58$	1.78094	+	0.635440i	1.78094	+	0.635440i
$59$		0			0		0.0855750	−	0.996332i	$-0.472727\pi$
$59$		0			0		−0.0855750	+	0.996332i	$0.527273\pi$
$60$		0			0
$61$		0			0		−0.516397	−	0.856349i	$-0.672727\pi$
$61$		0			0		0.516397	+	0.856349i	$0.327273\pi$
$62$		0			0
$63$	0.941844	+	0.336049i	0.941844	+	0.336049i
$64$	0.143008	+	0.0164086i	0.143008	+	0.0164086i
$65$		0			0
$66$		0			0
$67$	−1.30118	−	1.50165i	−1.30118	−	1.50165i	−0.736741	−	0.676175i	$-0.763636\pi$
$67$	−1.30118	−	1.50165i	−1.30118	−	1.50165i	−0.564443	−	0.825472i	$-0.690909\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.45190	+	1.33254i	1.45190	+	1.33254i	0.841254	+	0.540641i	$0.181818\pi$
$71$	1.45190	+	1.33254i	1.45190	+	1.33254i	0.610648	+	0.791902i	$0.290909\pi$
$72$	0.157857	+	0.600551i	0.157857	+	0.600551i
$73$		0			0		0.941844	−	0.336049i	$-0.109091\pi$
$73$		0			0		−0.941844	+	0.336049i	$0.890909\pi$
$74$	−1.92474	+	0.447580i	−1.92474	+	0.447580i
$75$		0			0
$76$		0			0
$77$	−0.254218	+	0.967147i	−0.254218	+	0.967147i
$78$		0			0
$79$	−0.456270	+	1.73583i	−0.456270	+	1.73583i	0.198590	+	0.980083i	$0.436364\pi$
$79$	−0.456270	+	1.73583i	−0.456270	+	1.73583i	−0.654861	+	0.755750i	$0.727273\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$82$		0			0
$83$		0			0		0.0285561	−	0.999592i	$-0.490909\pi$
$83$		0			0		−0.0285561	+	0.999592i	$0.509091\pi$
$84$		0			0
$85$		0			0
$86$	0.0393703	+	1.37814i	0.0393703	+	1.37814i
$87$		0			0
$88$	−0.584840	+	0.208670i	−0.584840	+	0.208670i
$89$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$89$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$90$		0			0
$91$		0			0
$92$	0.183885	+	0.907510i	0.183885	+	0.907510i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.774142	−	0.633012i	$-0.781818\pi$
$97$		0			0		0.774142	+	0.633012i	$0.218182\pi$
$98$	−1.17182	−	0.344079i	−1.17182	−	0.344079i
$99$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$100$	−0.471652	+	0.138489i	−0.471652	+	0.138489i
$101$		0			0		−0.921124	−	0.389270i	$-0.872727\pi$
$101$		0			0		0.921124	+	0.389270i	$0.127273\pi$
$102$		0			0
$103$		0			0		−0.974012	−	0.226497i	$-0.927273\pi$
$103$		0			0		0.974012	+	0.226497i	$0.0727273\pi$
$104$		0			0
$105$		0			0
$106$	1.79662	−	0.102735i	1.79662	−	0.102735i
$107$	−0.144100	−	0.370119i	−0.144100	−	0.370119i	0.841254	−	0.540641i	$-0.181818\pi$
$107$	−0.144100	−	0.370119i	−0.144100	−	0.370119i	−0.985354	+	0.170522i	$0.945455\pi$
$108$		0			0
$109$	−0.277233	+	1.92820i	−0.277233	+	1.92820i	0.0855750	+	0.996332i	$0.472727\pi$
$109$	−0.277233	+	1.92820i	−0.277233	+	1.92820i	−0.362808	+	0.931864i	$0.618182\pi$
$110$		0			0
$111$		0			0
$112$	−0.386249	−	1.18875i	−0.386249	−	1.18875i
$113$	−1.03111	−	0.0589610i	−1.03111	−	0.0589610i	−0.466667	−	0.884433i	$-0.654545\pi$
$113$	−1.03111	−	0.0589610i	−1.03111	−	0.0589610i	−0.564443	+	0.825472i	$0.690909\pi$
$114$		0			0
$115$		0			0
$116$	0.589183	−	0.481773i	0.589183	−	0.481773i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.696938	−	0.717132i	0.696938	−	0.717132i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	0.945456	−	0.773095i	0.945456	−	0.773095i
$127$	0.668382	−	0.282460i	0.668382	−	0.282460i	−0.0285561	−	0.999592i	$-0.509091\pi$
$127$	0.668382	−	0.282460i	0.668382	−	0.282460i	0.696938	+	0.717132i	$0.254545\pi$
$128$	0.660344	−	0.856349i	0.660344	−	0.856349i
$129$		0			0
$130$		0			0
$131$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$131$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$132$		0			0
$133$		0			0
$134$	−2.39113	+	0.413801i	−2.39113	+	0.413801i
$135$		0			0
$136$		0			0
$137$	0.526814	−	0.770442i	0.526814	−	0.770442i	−0.466667	−	0.884433i	$-0.654545\pi$
$137$	0.526814	−	0.770442i	0.526814	−	0.770442i	0.993482	+	0.113991i	$0.0363636\pi$
$138$		0			0
$139$		0			0		−0.974012	−	0.226497i	$-0.927273\pi$
$139$		0			0		0.974012	+	0.226497i	$0.0727273\pi$
$140$		0			0
$141$		0			0
$142$	2.30932	−	0.678079i	2.30932	−	0.678079i
$143$		0			0
$144$	1.19930	+	0.352146i	1.19930	+	0.352146i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−0.245782	+	0.756438i	−0.245782	+	0.756438i
$149$	1.29054	+	0.223337i	1.29054	+	0.223337i	0.774142	−	0.633012i	$-0.218182\pi$
$149$	1.29054	+	0.223337i	1.29054	+	0.223337i	0.516397	+	0.856349i	$0.327273\pi$
$150$		0			0
$151$	0.931812	−	1.76598i	0.931812	−	1.76598i	0.415415	−	0.909632i	$-0.363636\pi$
$151$	0.931812	−	1.76598i	0.931812	−	1.76598i	0.516397	−	0.856349i	$-0.327273\pi$
$152$		0			0
$153$		0			0
$154$	0.851167	+	0.875830i	0.851167	+	0.875830i
$155$		0			0
$156$		0			0
$157$		0			0		0.696938	−	0.717132i	$-0.254545\pi$
$157$		0			0		−0.696938	+	0.717132i	$0.745455\pi$
$158$	1.52767	+	1.57194i	1.52767	+	1.57194i
$159$		0			0
$160$		0			0
$161$	−1.52394	+	1.10720i	−1.52394	+	1.10720i
$162$	0.104512	+	1.21682i	0.104512	+	1.21682i
$163$	−0.100971	+	0.384132i	−0.100971	+	0.384132i	−0.998369	−	0.0570888i	$-0.981818\pi$
$163$	−0.100971	+	0.384132i	−0.100971	+	0.384132i	0.897398	+	0.441221i	$0.145455\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.736741	−	0.676175i	$-0.236364\pi$
$167$		0			0		−0.736741	+	0.676175i	$0.763636\pi$
$168$		0			0
$169$	0.941844	−	0.336049i	0.941844	−	0.336049i
$170$		0			0
$171$		0			0
$172$	0.483194	+	0.272872i	0.483194	+	0.272872i
$173$		0			0		−0.610648	−	0.791902i	$-0.709091\pi$
$173$		0			0		0.610648	+	0.791902i	$0.290909\pi$
$174$		0			0
$175$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$176$	−0.248224	+	1.22503i	−0.248224	+	1.22503i
$177$		0			0
$178$		0			0
$179$	−0.683417	−	0.243843i	−0.683417	−	0.243843i	−0.0285561	−	0.999592i	$-0.509091\pi$
$179$	−0.683417	−	0.243843i	−0.683417	−	0.243843i	−0.654861	+	0.755750i	$0.727273\pi$
$180$		0			0
$181$		0			0		−0.516397	−	0.856349i	$-0.672727\pi$
$181$		0			0		0.516397	+	0.856349i	$0.327273\pi$
$182$		0			0
$183$		0			0
$184$	−1.10166	−	0.393070i	−1.10166	−	0.393070i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.56281	−	0.882561i	−1.56281	−	0.882561i	−0.998369	−	0.0570888i	$-0.981818\pi$
$191$	−1.56281	−	0.882561i	−1.56281	−	0.882561i	−0.564443	−	0.825472i	$-0.690909\pi$
$192$		0			0
$193$	−0.262555	−	0.998864i	−0.262555	−	0.998864i	−0.959493	−	0.281733i	$-0.909091\pi$
$193$	−0.262555	−	0.998864i	−0.262555	−	0.998864i	0.696938	−	0.717132i	$-0.254545\pi$
$194$		0			0
$195$		0			0
$196$	−0.362155	+	0.332383i	−0.362155	+	0.332383i
$197$	−0.785171	−	0.504599i	−0.785171	−	0.504599i	0.0855750	−	0.996332i	$-0.472727\pi$
$197$	−0.785171	−	0.504599i	−0.785171	−	0.504599i	−0.870746	+	0.491733i	$0.836364\pi$
$198$	−1.20341	+	0.208258i	−1.20341	+	0.208258i
$199$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$199$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$200$	0.157857	−	0.600551i	0.157857	−	0.600551i
$201$		0			0
$202$		0			0
$203$	1.38943	+	0.683135i	1.38943	+	0.683135i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.0537907	−	1.88292i	−0.0537907	−	1.88292i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	1.25086	−	0.615007i	1.25086	−	0.615007i	0.309017	−	0.951057i	$-0.400000\pi$
$211$	1.25086	−	0.615007i	1.25086	−	0.615007i	0.941844	+	0.336049i	$0.109091\pi$
$212$	0.338012	−	0.640603i	0.338012	−	0.640603i
$213$		0			0
$214$	−0.477971	−	0.0827161i	−0.477971	−	0.0827161i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	1.84177	+	1.50601i	1.84177	+	1.50601i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.870746	−	0.491733i	$-0.163636\pi$
$223$		0			0		−0.870746	+	0.491733i	$0.836364\pi$
$224$	−0.882047	−	0.205111i	−0.882047	−	0.205111i
$225$	0.993482	−	0.113991i	0.993482	−	0.113991i
$226$	−0.711959	+	1.04121i	−0.711959	+	1.04121i
$227$		0			0		0.998369	−	0.0570888i	$-0.0181818\pi$
$227$		0			0		−0.998369	+	0.0570888i	$0.981818\pi$
$228$		0			0
$229$		0			0		0.985354	−	0.170522i	$-0.0545455\pi$
$229$		0			0		−0.985354	+	0.170522i	$0.945455\pi$
$230$		0			0
$231$		0			0
$232$	0.136823	+	0.951623i	0.136823	+	0.951623i
$233$	0.256741	+	0.790166i	0.256741	+	0.790166i	0.993482	+	0.113991i	$0.0363636\pi$
$233$	0.256741	+	0.790166i	0.256741	+	0.790166i	−0.736741	+	0.676175i	$0.763636\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.60749	−	1.16791i	−1.60749	−	1.16791i	−0.870746	−	0.491733i	$-0.836364\pi$
$239$	−1.60749	−	1.16791i	−1.60749	−	1.16791i	−0.736741	−	0.676175i	$-0.763636\pi$
$240$		0			0
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$	−0.310476	−	1.18117i	−0.310476	−	1.18117i
$243$		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	$0.400000\pi$
$252$	−0.0699568	−	0.486560i	−0.0699568	−	0.486560i
$253$	1.87141	−	0.214724i	1.87141	−	0.214724i
$254$	0.126118	−	0.877171i	0.126118	−	0.877171i
$255$		0			0
$256$	−0.426931	−	1.09656i	−0.426931	−	1.09656i
$257$		0			0		0.998369	−	0.0570888i	$-0.0181818\pi$
$257$		0			0		−0.998369	+	0.0570888i	$0.981818\pi$
$258$		0			0
$259$	−1.60749	+	0.184442i	−1.60749	+	0.184442i
$260$		0			0
$261$	−1.34816	+	0.761342i	−1.34816	+	0.761342i
$262$		0			0
$263$	1.89088	−	0.555213i	1.89088	−	0.555213i	0.897398	−	0.441221i	$-0.145455\pi$
$263$	1.89088	−	0.555213i	1.89088	−	0.555213i	0.993482	−	0.113991i	$-0.0363636\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−0.354361	+	0.910169i	−0.354361	+	0.910169i
$269$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$269$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$270$		0			0
$271$		0			0		−0.198590	−	0.980083i	$-0.563636\pi$
$271$		0			0		0.198590	+	0.980083i	$0.436364\pi$
$272$		0			0
$273$		0			0
$274$	−0.473522	−	1.03687i	−0.473522	−	1.03687i
$275$	0.198590	+	0.980083i	0.198590	+	0.980083i
$276$		0			0
$277$	0.0497301	+	1.74078i	0.0497301	+	1.74078i	0.516397	+	0.856349i	$0.327273\pi$
$277$	0.0497301	+	1.74078i	0.0497301	+	1.74078i	−0.466667	+	0.884433i	$0.654545\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.32230	−	0.650131i	−1.32230	−	0.650131i	−0.362808	−	0.931864i	$-0.618182\pi$
$281$	−1.32230	−	0.650131i	−1.32230	−	0.650131i	−0.959493	+	0.281733i	$0.909091\pi$
$282$		0			0
$283$		0			0		−0.0855750	−	0.996332i	$-0.527273\pi$
$283$		0			0		0.0855750	+	0.996332i	$0.472727\pi$
$284$	0.246268	−	0.936902i	0.246268	−	0.936902i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.667179	−	0.612331i	0.667179	−	0.612331i
$289$	0.974012	−	0.226497i	0.974012	−	0.226497i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.870746	−	0.491733i	$-0.836364\pi$
$293$		0			0		0.870746	+	0.491733i	$0.163636\pi$
$294$		0			0
$295$		0			0
$296$	−0.657952	−	0.759317i	−0.657952	−	0.759317i
$297$		0			0
$298$	1.04749	−	1.20886i	1.04749	−	1.20886i
$299$		0			0
$300$		0			0
$301$	−0.0966045	+	1.12475i	−0.0966045	+	1.12475i
$302$	−1.25929	−	2.08830i	−1.25929	−	2.08830i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$307$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$308$	0.478789	−	0.111338i	0.478789	−	0.111338i
$309$		0			0
$310$		0			0
$311$		0			0		−0.610648	−	0.791902i	$-0.709091\pi$
$311$		0			0		0.610648	+	0.791902i	$0.290909\pi$
$312$		0			0
$313$		0			0		−0.736741	−	0.676175i	$-0.763636\pi$
$313$		0			0		0.736741	+	0.676175i	$0.236364\pi$
$314$		0			0
$315$		0			0
$316$	0.859328	−	0.199828i	0.859328	−	0.199828i
$317$	−0.455331	+	0.417899i	−0.455331	+	0.417899i	−0.870746	−	0.491733i	$-0.836364\pi$
$317$	−0.455331	+	0.417899i	−0.455331	+	0.417899i	0.415415	+	0.909632i	$0.363636\pi$
$318$		0			0
$319$	−0.873918	−	1.27806i	−0.873918	−	1.27806i
$320$		0			0
$321$		0			0
$322$	0.196869	+	2.29210i	0.196869	+	2.29210i
$323$		0			0
$324$	0.441128	+	0.216888i	0.441128	+	0.216888i
$325$		0			0
$326$	0.338067	+	0.347863i	0.338067	+	0.347863i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.0710983	+	0.155684i	0.0710983	+	0.155684i	0.941844	−	0.336049i	$-0.109091\pi$
$331$	0.0710983	+	0.155684i	0.0710983	+	0.155684i	−0.870746	+	0.491733i	$0.836364\pi$
$332$		0			0
$333$	0.755084	−	1.43104i	0.755084	−	1.43104i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.0620945	+	0.159489i	−0.0620945	+	0.159489i	−0.959493	−	0.281733i	$-0.909091\pi$
$337$	−0.0620945	+	0.159489i	−0.0620945	+	0.159489i	0.897398	+	0.441221i	$0.145455\pi$
$338$	0.242538	−	1.19697i	0.242538	−	1.19697i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.921124	−	0.389270i	−0.921124	−	0.389270i
$344$	−0.610379	+	0.344697i	−0.610379	+	0.344697i
$345$		0			0
$346$		0			0
$347$	0.0322365	−	0.0471444i	0.0322365	−	0.0471444i	−0.809017	−	0.587785i	$-0.800000\pi$
$347$	0.0322365	−	0.0471444i	0.0322365	−	0.0471444i	0.841254	+	0.540641i	$0.181818\pi$
$348$		0			0
$349$		0			0		−0.362808	−	0.931864i	$-0.618182\pi$
$349$		0			0		0.362808	+	0.931864i	$0.381818\pi$
$350$	−1.20341	+	0.208258i	−1.20341	+	0.208258i
$351$		0			0
$352$	0.667179	+	0.612331i	0.667179	+	0.612331i
$353$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$353$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−0.686037	+	0.560970i	−0.686037	+	0.560970i
$359$	−0.0798701	−	0.151371i	−0.0798701	−	0.151371i	0.841254	−	0.540641i	$-0.181818\pi$
$359$	−0.0798701	−	0.151371i	−0.0798701	−	0.151371i	−0.921124	+	0.389270i	$0.872727\pi$
$360$		0			0
$361$	0.516397	−	0.856349i	0.516397	−	0.856349i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.466667	−	0.884433i	$-0.654545\pi$
$367$		0			0		0.466667	+	0.884433i	$0.345455\pi$
$368$	−1.82270	+	1.49041i	−1.82270	+	1.49041i
$369$		0			0
$370$		0			0
$371$	1.47108	+	0.0841194i	1.47108	+	0.0841194i
$372$		0			0
$373$	0.273100	+	1.89945i	0.273100	+	1.89945i	0.415415	+	0.909632i	$0.363636\pi$
$373$	0.273100	+	1.89945i	0.273100	+	1.89945i	−0.142315	+	0.989821i	$0.545455\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.12705	−	1.64825i	1.12705	−	1.64825i	0.516397	−	0.856349i	$-0.327273\pi$
$379$	1.12705	−	1.64825i	1.12705	−	1.64825i	0.610648	−	0.791902i	$-0.290909\pi$
$380$		0			0
$381$		0			0
$382$	−1.90866	+	1.07787i	−1.90866	+	1.07787i
$383$		0			0		−0.921124	−	0.389270i	$-0.872727\pi$
$383$		0			0		0.921124	+	0.389270i	$0.127273\pi$
$384$		0			0
$385$		0			0
$386$	−1.21025	−	0.355363i	−1.21025	−	0.355363i
$387$	−0.873918	−	0.714599i	−0.873918	−	0.714599i
$388$		0			0
$389$	0.724432	−	1.86069i	0.724432	−	1.86069i	0.309017	−	0.951057i	$-0.400000\pi$
$389$	0.724432	−	1.86069i	0.724432	−	1.86069i	0.415415	−	0.909632i	$-0.363636\pi$
$390$		0			0
$391$		0			0
$392$	−0.123315	−	0.608584i	−0.123315	−	0.608584i
$393$		0			0
$394$	−1.02292	+	0.502938i	−1.02292	+	0.502938i
$395$		0			0
$396$	−0.178343	+	0.458070i	−0.178343	+	0.458070i
$397$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$397$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$398$		0			0
$399$		0			0
$400$	−0.871122	−	0.896364i	−0.871122	−	0.896364i
$401$	−0.0398036	+	1.39331i	−0.0398036	+	1.39331i	0.696938	+	0.717132i	$0.254545\pi$
$401$	−0.0398036	+	1.39331i	−0.0398036	+	1.39331i	−0.736741	+	0.676175i	$0.763636\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	1.59074	−	1.02230i	1.59074	−	1.02230i
$407$	1.49041	+	0.629852i	1.49041	+	0.629852i
$408$		0			0
$409$		0			0		0.736741	−	0.676175i	$-0.236364\pi$
$409$		0			0		−0.736741	+	0.676175i	$0.763636\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−2.00319	−	1.13125i	−2.00319	−	1.13125i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$419$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$420$		0			0
$421$	0.161197	+	0.0575149i	0.161197	+	0.0575149i	0.415415	−	0.909632i	$-0.363636\pi$
$421$	0.161197	+	0.0575149i	0.161197	+	0.0575149i	−0.254218	+	0.967147i	$0.581818\pi$
$422$	0.145677	−	1.69609i	0.145677	−	1.69609i
$423$		0			0
$424$	0.472484	+	0.783526i	0.472484	+	0.783526i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.127855	+	0.147552i	−0.127855	+	0.147552i
$429$		0			0
$430$		0			0
$431$	0.982973	+	1.43755i	0.982973	+	1.43755i	0.897398	+	0.441221i	$0.145455\pi$
$431$	0.982973	+	1.43755i	0.982973	+	1.43755i	0.0855750	+	0.996332i	$0.472727\pi$
$432$		0			0
$433$		0			0		−0.870746	−	0.491733i	$-0.836364\pi$
$433$		0			0		0.870746	+	0.491733i	$0.163636\pi$
$434$		0			0
$435$		0			0
$436$	0.901889	−	0.321793i	0.901889	−	0.321793i
$437$		0			0
$438$		0			0
$439$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$439$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$440$		0			0
$441$	0.841254	−	0.540641i	0.841254	−	0.540641i
$442$		0			0
$443$	−0.00488737	−	0.0569026i	−0.00488737	−	0.0569026i	0.993482	−	0.113991i	$-0.0363636\pi$
$443$	−0.00488737	−	0.0569026i	−0.00488737	−	0.0569026i	−0.998369	+	0.0570888i	$0.981818\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	0.100322	−	0.103228i	0.100322	−	0.103228i
$449$	−0.0556279	−	1.94723i	−0.0556279	−	1.94723i	−0.254218	−	0.967147i	$-0.581818\pi$
$449$	−0.0556279	−	1.94723i	−0.0556279	−	1.94723i	0.198590	−	0.980083i	$-0.436364\pi$
$450$	0.507345	−	1.11093i	0.507345	−	1.11093i
$451$		0			0
$452$	0.210900	+	0.461806i	0.210900	+	0.461806i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$457$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$461$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$462$		0			0
$463$	1.76762	−	0.519021i	1.76762	−	0.519021i	0.774142	−	0.633012i	$-0.218182\pi$
$463$	1.76762	−	0.519021i	1.76762	−	0.519021i	0.993482	+	0.113991i	$0.0363636\pi$
$464$	1.78260	+	0.753333i	1.78260	+	0.753333i
$465$		0			0
$466$	0.988319	+	0.229824i	0.988319	+	0.229824i
$467$		0			0		0.993482	−	0.113991i	$-0.0363636\pi$
$467$		0			0		−0.993482	+	0.113991i	$0.963636\pi$
$468$		0			0
$469$	−1.98372	+	0.113433i	−1.98372	+	0.113433i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.637192	−	0.931864i	0.637192	−	0.931864i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.899779	+	1.16685i	−0.899779	+	1.16685i
$478$	−2.23526	+	0.944630i	−2.23526	+	0.944630i
$479$		0			0		0.774142	−	0.633012i	$-0.218182\pi$
$479$		0			0		−0.774142	+	0.633012i	$0.781818\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.471652	−	0.138489i	−0.471652	−	0.138489i
$485$		0			0
$486$		0			0
$487$	0.913288	+	0.663543i	0.913288	+	0.663543i	0.941844	−	0.336049i	$-0.109091\pi$
$487$	0.913288	+	0.663543i	0.913288	+	0.663543i	−0.0285561	+	0.999592i	$0.509091\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.17182	+	1.51965i	−1.17182	+	1.51965i	−0.362808	+	0.931864i	$0.618182\pi$
$491$	−1.17182	+	1.51965i	−1.17182	+	1.51965i	−0.809017	+	0.587785i	$0.800000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.94184	−	0.336049i	1.94184	−	0.336049i
$498$		0			0
$499$	−0.617026	+	0.0352828i	−0.617026	+	0.0352828i	−0.362808	−	0.931864i	$-0.618182\pi$
$499$	−0.617026	+	0.0352828i	−0.617026	+	0.0352828i	−0.254218	+	0.967147i	$0.581818\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.870746	−	0.491733i	$-0.163636\pi$
$503$		0			0		−0.870746	+	0.491733i	$0.836364\pi$
$504$	0.571973	+	0.241718i	0.571973	+	0.241718i
$505$		0			0
$506$	0.955679	−	2.09265i	0.955679	−	2.09265i
$507$		0			0
$508$	−0.276125	−	0.225787i	−0.276125	−	0.225787i
$509$		0			0		0.198590	−	0.980083i	$-0.436364\pi$
$509$		0			0		−0.198590	+	0.980083i	$0.563636\pi$
$510$		0			0
$511$		0			0
$512$	−0.350556	−	0.0606661i	−0.350556	−	0.0606661i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−0.820901	+	1.79752i	−0.820901	+	1.79752i
$519$		0			0
$520$		0			0
$521$		0			0		−0.696938	−	0.717132i	$-0.745455\pi$
$521$		0			0		0.696938	+	0.717132i	$0.254545\pi$
$522$	−0.0539970	+	1.89014i	−0.0539970	+	1.89014i
$523$		0			0		−0.897398	−	0.441221i	$-0.854545\pi$
$523$		0			0		0.897398	+	0.441221i	$0.145455\pi$
$524$		0			0
$525$		0			0
$526$	0.611857	−	2.32775i	0.611857	−	2.32775i
$527$		0			0
$528$		0			0
$529$	2.14375	+	1.37771i	2.14375	+	1.37771i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−0.753422	−	0.977055i	−0.753422	−	0.977055i
$537$		0			0
$538$		0			0
$539$	0.610648	+	0.791902i	0.610648	+	0.791902i
$540$		0			0
$541$	1.38479	+	0.158890i	1.38479	+	0.158890i	0.774142	−	0.633012i	$-0.218182\pi$
$541$	1.38479	+	0.158890i	1.38479	+	0.158890i	0.610648	+	0.791902i	$0.290909\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.782513	+	0.279200i	0.782513	+	0.279200i	0.696938	−	0.717132i	$-0.254545\pi$
$547$	0.782513	+	0.279200i	0.782513	+	0.279200i	0.0855750	+	0.996332i	$0.472727\pi$
$548$	−0.455803	−	0.0522985i	−0.455803	−	0.0522985i
$549$		0			0
$550$	1.15027	+	0.410416i	1.15027	+	0.410416i
$551$		0			0
$552$		0			0
$553$	1.09599	+	1.42130i	1.09599	+	1.42130i
$554$	1.85197	+	1.04586i	1.85197	+	1.04586i
$555$		0			0
$556$		0			0
$557$	0.582092	−	0.207690i	0.582092	−	0.207690i	−0.0285561	−	0.999592i	$-0.509091\pi$
$557$	0.582092	−	0.207690i	0.582092	−	0.207690i	0.610648	+	0.791902i	$0.290909\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−1.51388	+	0.972914i	−1.51388	+	0.972914i
$563$		0			0		0.254218	−	0.967147i	$-0.418182\pi$
$563$		0			0		−0.254218	+	0.967147i	$0.581818\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.0285561	+	0.999592i	−0.0285561	+	0.999592i
$568$	0.852852	+	0.877564i	0.852852	+	0.877564i
$569$	1.17260	−	1.20658i	1.17260	−	1.20658i	0.198590	−	0.980083i	$-0.436364\pi$
$569$	1.17260	−	1.20658i	1.17260	−	1.20658i	0.974012	−	0.226497i	$-0.0727273\pi$
$570$		0			0
$571$	−0.387721	+	0.848991i	−0.387721	+	0.848991i	0.610648	+	0.791902i	$0.290909\pi$
$571$	−0.387721	+	0.848991i	−0.387721	+	0.848991i	−0.998369	+	0.0570888i	$0.981818\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.879056	+	1.66600i	−0.879056	+	1.66600i
$576$	0.0285864	+	0.141079i	0.0285864	+	0.141079i
$577$		0			0		−0.985354	−	0.170522i	$-0.945455\pi$
$577$		0			0		0.985354	+	0.170522i	$0.0545455\pi$
$578$	0.377401	−	1.16152i	0.377401	−	1.16152i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−1.23957	−	0.796625i	−1.23957	−	0.796625i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.974012	−	0.226497i	$-0.927273\pi$
$587$		0			0		0.974012	+	0.226497i	$0.0727273\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−1.99281	+	0.344869i	−1.99281	+	0.344869i
$593$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$593$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$594$		0			0
$595$		0			0
$596$	−0.198949	−	0.612301i	−0.198949	−	0.612301i
$597$		0			0
$598$		0			0
$599$	−1.79437	+	0.758307i	−1.79437	+	0.758307i	−0.809017	+	0.587785i	$0.800000\pi$
$599$	−1.79437	+	0.758307i	−1.79437	+	0.758307i	−0.985354	+	0.170522i	$0.945455\pi$
$600$		0			0
$601$		0			0		−0.466667	−	0.884433i	$-0.654545\pi$
$601$		0			0		0.466667	+	0.884433i	$0.345455\pi$
$602$	1.11540	+	0.810382i	1.11540	+	0.810382i
$603$	1.02606	−	1.70153i	1.02606	−	1.70153i
$604$	−0.981523			−0.981523
$605$		0			0
$606$		0			0
$607$		0			0		0.516397	−	0.856349i	$-0.327273\pi$
$607$		0			0		−0.516397	+	0.856349i	$0.672727\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.0570190	+	0.00326046i	0.0570190	+	0.00326046i	0.0855750	−	0.996332i	$-0.472727\pi$
$613$	0.0570190	+	0.00326046i	0.0570190	+	0.00326046i	−0.0285561	+	0.999592i	$0.509091\pi$
$614$		0			0
$615$		0			0
$616$	−0.191885	+	0.590560i	−0.191885	+	0.590560i
$617$	0.262179	−	1.82350i	0.262179	−	1.82350i	−0.254218	−	0.967147i	$-0.581818\pi$
$617$	0.262179	−	1.82350i	0.262179	−	1.82350i	0.516397	−	0.856349i	$-0.327273\pi$
$618$		0			0
$619$		0			0		−0.362808	−	0.931864i	$-0.618182\pi$
$619$		0			0		0.362808	+	0.931864i	$0.381818\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.921124	−	0.389270i	−0.921124	−	0.389270i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−0.505709	+	1.29890i	−0.505709	+	1.29890i	0.415415	+	0.909632i	$0.363636\pi$
$631$	−0.505709	+	1.29890i	−0.505709	+	1.29890i	−0.921124	+	0.389270i	$0.872727\pi$
$632$	−0.344394	+	1.05994i	−0.344394	+	1.05994i
$633$		0			0
$634$	0.149897	+	0.739769i	0.149897	+	0.739769i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−1.88783	+	0.107950i	−1.88783	+	0.107950i
$639$	−0.818662	+	1.79262i	−0.818662	+	1.79262i
$640$		0			0
$641$	−0.0398036	+	0.0409569i	−0.0398036	+	0.0409569i	−0.736741	−	0.676175i	$-0.763636\pi$
$641$	−0.0398036	+	0.0409569i	−0.0398036	+	0.0409569i	0.696938	+	0.717132i	$0.254545\pi$
$642$		0			0
$643$		0			0		0.0285561	−	0.999592i	$-0.490909\pi$
$643$		0			0		−0.0285561	+	0.999592i	$0.509091\pi$
$644$	0.830948	+	0.408550i	0.830948	+	0.408550i
$645$		0			0
$646$		0			0
$647$		0			0		0.254218	−	0.967147i	$-0.418182\pi$
$647$		0			0		−0.254218	+	0.967147i	$0.581818\pi$
$648$	−0.522378	+	0.335712i	−0.522378	+	0.335712i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.190166	−	0.0442211i	0.190166	−	0.0442211i
$653$	−0.683417	+	0.243843i	−0.683417	+	0.243843i	−0.654861	−	0.755750i	$-0.727273\pi$
$653$	−0.683417	+	0.243843i	−0.683417	+	0.243843i	−0.0285561	+	0.999592i	$0.509091\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.959493	−	0.281733i	$-0.909091\pi$
$659$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.142315	−	0.989821i	$-0.545455\pi$
$660$		0			0
$661$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$661$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$662$	0.207662	+	0.0238270i	0.207662	+	0.0238270i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−1.02045	−	1.69223i	−1.02045	−	1.69223i
$667$	0.249578	−	2.90579i	0.249578	−	2.90579i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.0322365	+	0.0471444i	0.0322365	+	0.0471444i	0.841254	−	0.540641i	$-0.181818\pi$
$673$	0.0322365	+	0.0471444i	0.0322365	+	0.0471444i	−0.809017	+	0.587785i	$0.800000\pi$
$674$	0.127641	+	0.165527i	0.127641	+	0.165527i
$675$		0			0
$676$	−0.362155	−	0.332383i	−0.362155	−	0.332383i
$677$		0			0		−0.254218	−	0.967147i	$-0.581818\pi$
$677$		0			0		0.254218	+	0.967147i	$0.418182\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.17260	−	0.753586i	1.17260	−	0.753586i	0.198590	−	0.980083i	$-0.436364\pi$
$683$	1.17260	−	0.753586i	1.17260	−	0.753586i	0.974012	+	0.226497i	$0.0727273\pi$
$684$		0			0
$685$		0			0
$686$	−0.988049	+	0.717860i	−0.988049	+	0.717860i
$687$		0			0
$688$	−0.0402934	+	1.41045i	−0.0402934	+	1.41045i
$689$		0			0
$690$		0			0
$691$		0			0		−0.0285561	−	0.999592i	$-0.509091\pi$
$691$		0			0		0.0285561	+	0.999592i	$0.490909\pi$
$692$		0			0
$693$	−0.998369	+	0.0570888i	−0.998369	+	0.0570888i
$694$	−0.0289755	−	0.0634475i	−0.0289755	−	0.0634475i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.178343	+	0.458070i	−0.178343	+	0.458070i
$701$	−0.396533	+	1.95697i	−0.396533	+	1.95697i	−0.142315	+	0.989821i	$0.545455\pi$
$701$	−0.396533	+	1.95697i	−0.396533	+	1.95697i	−0.254218	+	0.967147i	$0.581818\pi$
$702$		0			0
$703$		0			0
$704$	−0.138115	+	0.0405544i	−0.138115	+	0.0405544i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.0567398	+	0.00651029i	−0.0567398	+	0.00651029i	−0.142315	−	0.989821i	$-0.545455\pi$
$709$	−0.0567398	+	0.00651029i	−0.0567398	+	0.00651029i	0.0855750	+	0.996332i	$0.472727\pi$
$710$		0			0
$711$	−1.79187	+	0.102463i	−1.79187	+	0.102463i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.0507617	+	0.353055i	0.0507617	+	0.353055i
$717$		0			0
$718$	−0.208684	−	0.0119330i	−0.208684	−	0.0119330i
$719$		0			0		0.610648	−	0.791902i	$-0.290909\pi$
$719$		0			0		−0.610648	+	0.791902i	$0.709091\pi$
$720$		0			0
$721$		0			0
$722$	−0.569939	−	1.08015i	−0.569939	−	1.08015i
$723$		0			0
$724$		0			0
$725$	1.54828			1.54828
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.610648	−	0.791902i	$-0.290909\pi$
$733$		0			0		−0.610648	+	0.791902i	$0.709091\pi$
$734$		0			0
$735$		0			0
$736$	0.242765	+	1.68847i	0.242765	+	1.68847i
$737$	1.78310	+	0.876690i	1.78310	+	0.876690i
$738$		0			0
$739$	−0.608982	+	0.105389i	−0.608982	+	0.105389i	−0.466667	−	0.884433i	$-0.654545\pi$
$739$	−0.608982	+	0.105389i	−0.608982	+	0.105389i	−0.142315	+	0.989821i	$0.545455\pi$
$740$		0			0
$741$		0			0
$742$	1.01575	−	1.48548i	1.01575	−	1.48548i
$743$	0.614005	−	0.0704506i	0.614005	−	0.0704506i	0.198590	−	0.980083i	$-0.436364\pi$
$743$	0.614005	−	0.0704506i	0.614005	−	0.0704506i	0.415415	+	0.909632i	$0.363636\pi$
$744$		0			0
$745$		0			0
$746$	2.15879	+	0.912313i	2.15879	+	0.912313i
$747$		0			0
$748$		0			0
$749$	−0.381092	−	0.111899i	−0.381092	−	0.111899i
$750$		0			0
$751$	−0.185351	+	0.914745i	−0.185351	+	0.914745i	0.774142	+	0.633012i	$0.218182\pi$
$751$	−0.185351	+	0.914745i	−0.185351	+	0.914745i	−0.959493	+	0.281733i	$0.909091\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.65323	+	0.812838i	−1.65323	+	0.812838i	−0.654861	+	0.755750i	$0.727273\pi$
$757$	−1.65323	+	0.812838i	−1.65323	+	0.812838i	−0.998369	+	0.0570888i	$0.981818\pi$
$758$	−1.01303	−	2.21824i	−1.01303	−	2.21824i
$759$		0			0
$760$		0			0
$761$		0			0		−0.0285561	−	0.999592i	$-0.509091\pi$
$761$		0			0		0.0285561	+	0.999592i	$0.490909\pi$
$762$		0			0
$763$	1.35765	+	1.39699i	1.35765	+	1.39699i
$764$	−0.0251938	+	0.881897i	−0.0251938	+	0.881897i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$769$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$770$		0			0
$771$		0			0
$772$	−0.374032	+	0.343283i	−0.374032	+	0.343283i
$773$		0			0		0.974012	−	0.226497i	$-0.0727273\pi$
$773$		0			0		−0.974012	+	0.226497i	$0.927273\pi$
$774$	−1.29852	+	0.463313i	−1.29852	+	0.463313i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−1.48913	−	1.93114i	−1.48913	−	1.93114i
$779$		0			0
$780$		0			0
$781$	−1.85610	−	0.662255i	−1.85610	−	0.662255i
$782$		0			0
$783$		0			0
$784$	−1.17724	−	0.420038i	−1.17724	−	0.420038i
$785$		0			0
$786$		0			0
$787$		0			0		−0.516397	−	0.856349i	$-0.672727\pi$
$787$		0			0		0.516397	+	0.856349i	$0.327273\pi$
$788$	−0.0392612	+	0.457110i	−0.0392612	+	0.457110i
$789$		0			0
$790$		0			0
$791$	−0.676337	+	0.780534i	−0.676337	+	0.780534i
$792$	−0.379183	−	0.491733i	−0.379183	−	0.491733i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.736741	−	0.676175i	$-0.763636\pi$
$797$		0			0		0.736741	+	0.676175i	$0.236364\pi$
$798$		0			0
$799$		0			0
$800$	−0.882047	+	0.205111i	−0.882047	+	0.205111i
$801$		0			0
$802$	1.43209	+	0.920351i	1.43209	+	0.920351i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.0207207	−	0.725319i	0.0207207	−	0.725319i	−0.921124	−	0.389270i	$-0.872727\pi$
$809$	0.0207207	−	0.725319i	0.0207207	−	0.725319i	0.941844	−	0.336049i	$-0.109091\pi$
$810$		0			0
$811$		0			0		0.696938	−	0.717132i	$-0.254545\pi$
$811$		0			0		−0.696938	+	0.717132i	$0.745455\pi$
$812$	−0.0217334	−	0.760769i	−0.0217334	−	0.760769i
$813$		0			0
$814$	1.59870	−	1.16152i	1.59870	−	1.16152i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.103266	−	0.265236i	0.103266	−	0.265236i	−0.870746	−	0.491733i	$-0.836364\pi$
$821$	0.103266	−	0.265236i	0.103266	−	0.265236i	0.974012	+	0.226497i	$0.0727273\pi$
$822$		0			0
$823$	0.478446	+	0.391223i	0.478446	+	0.391223i	0.841254	−	0.540641i	$-0.181818\pi$
$823$	0.478446	+	0.391223i	0.478446	+	0.391223i	−0.362808	+	0.931864i	$0.618182\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.20642	+	0.509835i	1.20642	+	0.509835i	0.897398	−	0.441221i	$-0.145455\pi$
$827$	1.20642	+	0.509835i	1.20642	+	0.509835i	0.309017	+	0.951057i	$0.400000\pi$
$828$	−0.806269	+	0.455321i	−0.806269	+	0.455321i
$829$		0			0		−0.974012	−	0.226497i	$-0.927273\pi$
$829$		0			0		0.974012	+	0.226497i	$0.0727273\pi$
$830$		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		−0.998369	−	0.0570888i	$-0.981818\pi$
$839$		0			0		0.998369	+	0.0570888i	$0.0181818\pi$
$840$		0			0
$841$	−1.28698	+	0.543881i	−1.28698	+	0.543881i
$842$	0.161815	−	0.132315i	0.161815	−	0.132315i
$843$		0			0
$844$	−0.554321	−	0.402737i	−0.554321	−	0.402737i
$845$		0			0
$846$		0			0
$847$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$848$	1.84175			1.84175
$849$		0			0
$850$		0			0
$851$	1.42234	+	2.69564i	1.42234	+	2.69564i
$852$		0			0
$853$		0			0		0.921124	−	0.389270i	$-0.127273\pi$
$853$		0			0		−0.921124	+	0.389270i	$0.872727\pi$
$854$		0			0
$855$		0			0
$856$	−0.0762129	−	0.234559i	−0.0762129	−	0.234559i
$857$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$857$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$858$		0			0
$859$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$859$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$860$		0			0
$861$		0			0
$862$	2.12341	−	0.121421i	2.12341	−	0.121421i
$863$	0.160657	−	0.234954i	0.160657	−	0.234954i	−0.736741	−	0.676175i	$-0.763636\pi$
$863$	0.160657	−	0.234954i	0.160657	−	0.234954i	0.897398	+	0.441221i	$0.145455\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.255426	−	1.77653i	−0.255426	−	1.77653i
$870$		0			0
$871$		0			0
$872$	−0.240221	+	1.18554i	−0.240221	+	1.18554i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.919665	−	1.74296i	0.919665	−	1.74296i	0.309017	−	0.951057i	$-0.400000\pi$
$877$	0.919665	−	1.74296i	0.919665	−	1.74296i	0.610648	−	0.791902i	$-0.290909\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$881$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$882$	−0.0348754	−	1.22080i	−0.0348754	−	1.22080i
$883$	0.579037	−	0.595815i	0.579037	−	0.595815i	−0.362808	−	0.931864i	$-0.618182\pi$
$883$	0.579037	−	0.595815i	0.579037	−	0.595815i	0.941844	+	0.336049i	$0.109091\pi$
$884$		0			0
$885$		0			0
$886$	−0.0625942	−	0.0307755i	−0.0625942	−	0.0307755i
$887$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$887$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$888$		0			0
$889$	0.184465	−	0.701777i	0.184465	−	0.701777i
$890$		0			0
$891$	0.516397	−	0.856349i	0.516397	−	0.856349i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−0.274907	−	1.04586i	−0.274907	−	1.04586i
$897$		0			0
$898$	−2.07160	−	1.16989i	−2.07160	−	1.16989i
$899$		0			0
$900$	−0.277460	−	0.405772i	−0.277460	−	0.405772i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−0.637135	−	0.0731045i	−0.637135	−	0.0731045i
$905$		0			0
$906$		0			0
$907$	0.533333	+	0.884433i	0.533333	+	0.884433i	1.00000			$0$
$907$	0.533333	+	0.884433i	0.533333	+	0.884433i	−0.466667	+	0.884433i	$0.654545\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1.30118	−	0.149297i	−1.30118	−	0.149297i	−0.564443	−	0.825472i	$-0.690909\pi$
$911$	−1.30118	−	0.149297i	−1.30118	−	0.149297i	−0.736741	+	0.676175i	$0.763636\pi$
$912$		0			0
$913$		0			0
$914$	1.29407	+	1.49344i	1.29407	+	1.49344i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	0.129254	+	0.491733i	0.129254	+	0.491733i	1.00000			$0$
$919$	0.129254	+	0.491733i	0.129254	+	0.491733i	−0.870746	+	0.491733i	$0.836364\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−1.36118	+	0.874775i	−1.36118	+	0.874775i
$926$	0.571973	−	2.17601i	0.571973	−	2.17601i
$927$		0			0
$928$	1.13432	−	0.824131i	1.13432	−	0.824131i
$929$		0			0		−0.897398	−	0.441221i	$-0.854545\pi$
$929$		0			0		0.897398	+	0.441221i	$0.145455\pi$
$930$		0			0
$931$		0			0
$932$	0.284633	−	0.292881i	0.284633	−	0.292881i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.897398	−	0.441221i	$-0.145455\pi$
$937$		0			0		−0.897398	+	0.441221i	$0.854545\pi$
$938$	−1.13245	+	2.14623i	−1.13245	+	2.14623i
$939$		0			0
$940$		0			0
$941$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$941$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−0.572734	−	1.25411i	−0.572734	−	1.25411i
$947$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.959493	−	0.281733i	$-0.909091\pi$
$947$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.654861	+	0.755750i	$0.727273\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1.39160	+	0.0795747i	−1.39160	+	0.0795747i	−0.736741	−	0.676175i	$-0.763636\pi$
$953$	−1.39160	+	0.0795747i	−1.39160	+	0.0795747i	−0.654861	+	0.755750i	$0.727273\pi$
$954$	0.652893	+	1.67694i	0.652893	+	1.67694i
$955$		0			0
$956$	−0.139002	+	0.966777i	−0.139002	+	0.966777i
$957$		0			0
$958$		0			0
$959$	−0.288416	−	0.887654i	−0.288416	−	0.887654i
$960$		0			0
$961$	0.610648	−	0.791902i	0.610648	−	0.791902i
$962$		0			0
$963$	0.307474	−	0.251420i	0.307474	−	0.251420i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	1.94802			1.94802			0.974012	−	0.226497i	$-0.0727273\pi$
$967$	1.94802			1.94802			0.974012	+	0.226497i	$0.0727273\pi$
$968$	0.457481	−	0.419872i	0.457481	−	0.419872i
$969$		0			0
$970$		0			0
$971$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$971$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$972$		0			0
$973$		0			0
$974$	1.26996	−	0.536688i	1.26996	−	0.536688i
$975$		0			0
$976$		0			0
$977$	0.0528883	+	0.162773i	0.0528883	+	0.162773i	0.974012	−	0.226497i	$-0.0727273\pi$
$977$	0.0528883	+	0.162773i	0.0528883	+	0.162773i	−0.921124	+	0.389270i	$0.872727\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−1.91949	+	0.332181i	−1.91949	+	0.332181i
$982$	0.850294	+	2.18396i	0.850294	+	2.18396i
$983$		0			0		0.998369	−	0.0570888i	$-0.0181818\pi$
$983$		0			0		−0.998369	+	0.0570888i	$0.981818\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.04033	−	0.599096i	2.04033	−	0.599096i
$990$		0			0
$991$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.654861	−	0.755750i	$-0.727273\pi$
$991$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.959493	+	0.281733i	$0.909091\pi$
$992$		0			0
$993$		0			0
$994$	0.873212	−	2.24283i	0.873212	−	2.24283i
$995$		0			0
$996$		0			0
$997$		0			0		−0.198590	−	0.980083i	$-0.563636\pi$
$997$		0			0		0.198590	+	0.980083i	$0.436364\pi$
$998$	−0.352242	+	0.667572i	−0.352242	+	0.667572i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.1.bb.a.489.1	yes	40
7.6	odd	2	CM	847.1.bb.a.489.1	yes	40
121.97	even	55	inner	847.1.bb.a.97.1	✓	40
847.97	odd	110	inner	847.1.bb.a.97.1	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.1.bb.a.97.1	✓	40	121.97	even	55	inner
847.1.bb.a.97.1	✓	40	847.97	odd	110	inner
847.1.bb.a.489.1	yes	40	1.1	even	1	trivial
847.1.bb.a.489.1	yes	40	7.6	odd	2	CM

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	847.bb (of order \(110\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(0.630674 - 1.04586i) q^{2} +(-0.229397 - 0.434755i) q^{4} +(0.610648 - 0.791902i) q^{7} +(0.619939 + 0.0354494i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.630674 - 1.04586i) q^{2} +(-0.229397 - 0.434755i) q^{4} +(0.610648 - 0.791902i) q^{7} +(0.619939 + 0.0354494i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-0.921124 + 0.389270i) q^{11} +(-0.443096 - 1.13808i) q^{14} +(0.705514 - 1.03178i) q^{16} +(1.18956 + 0.276620i) q^{18} +(-0.173809 + 1.20886i) q^{22} +(-1.80739 - 0.530696i) q^{23} +(0.198590 - 0.980083i) q^{25} +(-0.484364 - 0.0838225i) q^{28} +(0.307474 + 1.51745i) q^{29} +(-0.376192 - 0.823746i) q^{32} +(0.342589 - 0.352516i) q^{36} +(-1.12767 - 1.16034i) q^{37} +(-0.949680 + 0.610322i) q^{43} +(0.380540 + 0.311166i) q^{44} +(-1.69490 + 1.55557i) q^{46} +(-0.254218 - 0.967147i) q^{49} +(-0.899779 - 0.825810i) q^{50} +(0.831697 + 1.21632i) q^{53} +(0.406637 - 0.469284i) q^{56} +(1.78094 + 0.635440i) q^{58} +(0.941844 + 0.336049i) q^{63} +(0.143008 + 0.0164086i) q^{64} +(-1.30118 - 1.50165i) q^{67} +(1.45190 + 1.33254i) q^{71} +(0.157857 + 0.600551i) q^{72} +(-1.92474 + 0.447580i) q^{74} +(-0.254218 + 0.967147i) q^{77} +(-0.456270 + 1.73583i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(0.0393703 + 1.37814i) q^{86} +(-0.584840 + 0.208670i) q^{88} +(0.183885 + 0.907510i) q^{92} +(-1.17182 - 0.344079i) q^{98} +(-0.654861 - 0.755750i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 2 q^{2} + 3 q^{4} + q^{7} - q^{8} - 10 q^{9}+O(q^{10}) \) 40 * q + 2 * q^2 + 3 * q^4 + q^7 - q^8 - 10 * q^9	\( 40 q + 2 q^{2} + 3 q^{4} + q^{7} - q^{8} - 10 q^{9} + q^{11} - 3 q^{14} - 3 q^{18} + 2 q^{22} - 9 q^{23} + q^{25} - 2 q^{28} + 2 q^{29} - 4 q^{32} + 3 q^{36} - 3 q^{37} + 2 q^{43} - 13 q^{44} - q^{46} + q^{49} + 2 q^{50} - 3 q^{53} - 7 q^{56} - 12 q^{58} + q^{63} - 9 q^{64} + 2 q^{67} - 3 q^{71} - q^{72} + 4 q^{74} + q^{77} - 3 q^{79} - 10 q^{81} - q^{86} - 12 q^{88} - 4 q^{92} - 9 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q + 2 * q^2 + 3 * q^4 + q^7 - q^8 - 10 * q^9 + q^11 - 3 * q^14 - 3 * q^18 + 2 * q^22 - 9 * q^23 + q^25 - 2 * q^28 + 2 * q^29 - 4 * q^32 + 3 * q^36 - 3 * q^37 + 2 * q^43 - 13 * q^44 - q^46 + q^49 + 2 * q^50 - 3 * q^53 - 7 * q^56 - 12 * q^58 + q^63 - 9 * q^64 + 2 * q^67 - 3 * q^71 - q^72 + 4 * q^74 + q^77 - 3 * q^79 - 10 * q^81 - q^86 - 12 * q^88 - 4 * q^92 - 9 * q^98 - 4 * q^99

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