LMFDB - Embedded newform 847.1.bb.a.328.1

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			328.1
Root			$-0.736741 - 0.676175i$ of defining polynomial
Character	$\chi$	$=$	847.328
Dual form			847.1.bb.a.643.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.687626 + 0.631097i) q^{2} +(-0.0110295 - 0.128414i) q^{4} +(-0.466667 + 0.884433i) q^{7} +(0.643396 - 0.834371i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.687626 + 0.631097i) q^{2} +(-0.0110295 - 0.128414i) q^{4} +(-0.466667 + 0.884433i) q^{7} +(0.643396 - 0.834371i) q^{8} +(0.309017 - 0.951057i) q^{9} +(0.993482 + 0.113991i) q^{11} +(-0.879056 + 0.313647i) q^{14} +(0.841987 - 0.145712i) q^{16} +(0.812697 - 0.458951i) q^{18} +(0.611204 + 0.705367i) q^{22} +(-0.198369 + 1.37969i) q^{23} +(-0.998369 + 0.0570888i) q^{25} +(0.118720 + 0.0501716i) q^{28} +(0.0570190 + 0.00326046i) q^{29} +(-0.215439 - 0.138454i) q^{32} +(-0.125537 - 0.0291924i) q^{36} +(-1.57598 + 0.366479i) q^{37} +(1.89088 - 0.555213i) q^{43} +(0.00368049 - 0.128834i) q^{44} +(-1.00712 + 0.823519i) q^{46} +(-0.564443 - 0.825472i) q^{49} +(-0.722533 - 0.590812i) q^{50} +(-1.52561 - 0.264017i) q^{53} +(0.437693 + 0.958414i) q^{56} +(0.0371501 + 0.0382265i) q^{58} +(0.696938 + 0.717132i) q^{63} +(-0.277993 - 1.05760i) q^{64} +(-0.211212 + 0.462490i) q^{67} +(-1.42616 - 1.16617i) q^{71} +(-0.594714 - 0.869741i) q^{72} +(-1.31497 - 0.742599i) q^{74} +(-0.564443 + 0.825472i) q^{77} +(-0.582954 + 0.852543i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(1.65061 + 0.811551i) q^{86} +(0.734314 - 0.755591i) q^{88} +(0.179359 + 0.0102561i) q^{92} +(0.132827 - 0.923835i) q^{98} +(0.415415 - 0.909632i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$-1$	$e\left(\frac{13}{55}\right)$

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 $

$2$	0.687626	+	0.631097i	0.687626	+	0.631097i	0.941844	−	0.336049i	$-0.109091\pi$
$2$	0.687626	+	0.631097i	0.687626	+	0.631097i	−0.254218	+	0.967147i	$0.581818\pi$
$3$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$3$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$4$	−0.0110295	−	0.128414i	−0.0110295	−	0.128414i
$5$		0			0		−0.0285561	−	0.999592i	$-0.509091\pi$
$5$		0			0		0.0285561	+	0.999592i	$0.490909\pi$
$6$		0			0
$7$	−0.466667	+	0.884433i	−0.466667	+	0.884433i
$7$	−0.466667	+	0.884433i	−0.466667	+	0.884433i
$8$	0.643396	−	0.834371i	0.643396	−	0.834371i
$9$	0.309017	−	0.951057i	0.309017	−	0.951057i
$10$		0			0
$11$	0.993482	+	0.113991i	0.993482	+	0.113991i
$11$	0.993482	+	0.113991i	0.993482	+	0.113991i
$12$		0			0
$13$		0			0		0.921124	−	0.389270i	$-0.127273\pi$
$13$		0			0		−0.921124	+	0.389270i	$0.872727\pi$
$14$	−0.879056	+	0.313647i	−0.879056	+	0.313647i
$15$		0			0
$16$	0.841987	−	0.145712i	0.841987	−	0.145712i
$17$		0			0		0.254218	−	0.967147i	$-0.418182\pi$
$17$		0			0		−0.254218	+	0.967147i	$0.581818\pi$
$18$	0.812697	−	0.458951i	0.812697	−	0.458951i
$19$		0			0		0.362808	−	0.931864i	$-0.381818\pi$
$19$		0			0		−0.362808	+	0.931864i	$0.618182\pi$
$20$		0			0
$21$		0			0
$22$	0.611204	+	0.705367i	0.611204	+	0.705367i
$23$	−0.198369	+	1.37969i	−0.198369	+	1.37969i	0.610648	+	0.791902i	$0.290909\pi$
$23$	−0.198369	+	1.37969i	−0.198369	+	1.37969i	−0.809017	+	0.587785i	$0.800000\pi$
$24$		0			0
$25$	−0.998369	+	0.0570888i	−0.998369	+	0.0570888i
$26$		0			0
$27$		0			0
$28$	0.118720	+	0.0501716i	0.118720	+	0.0501716i
$29$	0.0570190	+	0.00326046i	0.0570190	+	0.00326046i	0.0855750	−	0.996332i	$-0.472727\pi$
$29$	0.0570190	+	0.00326046i	0.0570190	+	0.00326046i	−0.0285561	+	0.999592i	$0.509091\pi$
$30$		0			0
$31$		0			0		−0.516397	−	0.856349i	$-0.672727\pi$
$31$		0			0		0.516397	+	0.856349i	$0.327273\pi$
$32$	−0.215439	−	0.138454i	−0.215439	−	0.138454i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−0.125537	−	0.0291924i	−0.125537	−	0.0291924i
$37$	−1.57598	+	0.366479i	−1.57598	+	0.366479i	−0.921124	−	0.389270i	$-0.872727\pi$
$37$	−1.57598	+	0.366479i	−1.57598	+	0.366479i	−0.654861	+	0.755750i	$0.727273\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.198590	−	0.980083i	$-0.563636\pi$
$41$		0			0		0.198590	+	0.980083i	$0.436364\pi$
$42$		0			0
$43$	1.89088	−	0.555213i	1.89088	−	0.555213i	0.897398	−	0.441221i	$-0.145455\pi$
$43$	1.89088	−	0.555213i	1.89088	−	0.555213i	0.993482	−	0.113991i	$-0.0363636\pi$
$44$	0.00368049	−	0.128834i	0.00368049	−	0.128834i
$45$		0			0
$46$	−1.00712	+	0.823519i	−1.00712	+	0.823519i
$47$		0			0		−0.870746	−	0.491733i	$-0.836364\pi$
$47$		0			0		0.870746	+	0.491733i	$0.163636\pi$
$48$		0			0
$49$	−0.564443	−	0.825472i	−0.564443	−	0.825472i
$50$	−0.722533	−	0.590812i	−0.722533	−	0.590812i
$51$		0			0
$52$		0			0
$53$	−1.52561	−	0.264017i	−1.52561	−	0.264017i	−0.654861	−	0.755750i	$-0.727273\pi$
$53$	−1.52561	−	0.264017i	−1.52561	−	0.264017i	−0.870746	+	0.491733i	$0.836364\pi$
$54$		0			0
$55$		0			0
$56$	0.437693	+	0.958414i	0.437693	+	0.958414i
$57$		0			0
$58$	0.0371501	+	0.0382265i	0.0371501	+	0.0382265i
$59$		0			0		0.198590	−	0.980083i	$-0.436364\pi$
$59$		0			0		−0.198590	+	0.980083i	$0.563636\pi$
$60$		0			0
$61$		0			0		0.736741	−	0.676175i	$-0.236364\pi$
$61$		0			0		−0.736741	+	0.676175i	$0.763636\pi$
$62$		0			0
$63$	0.696938	+	0.717132i	0.696938	+	0.717132i
$64$	−0.277993	−	1.05760i	−0.277993	−	1.05760i
$65$		0			0
$66$		0			0
$67$	−0.211212	+	0.462490i	−0.211212	+	0.462490i	−0.985354	−	0.170522i	$-0.945455\pi$
$67$	−0.211212	+	0.462490i	−0.211212	+	0.462490i	0.774142	+	0.633012i	$0.218182\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.42616	−	1.16617i	−1.42616	−	1.16617i	−0.959493	−	0.281733i	$-0.909091\pi$
$71$	−1.42616	−	1.16617i	−1.42616	−	1.16617i	−0.466667	−	0.884433i	$-0.654545\pi$
$72$	−0.594714	−	0.869741i	−0.594714	−	0.869741i
$73$		0			0		0.696938	−	0.717132i	$-0.254545\pi$
$73$		0			0		−0.696938	+	0.717132i	$0.745455\pi$
$74$	−1.31497	−	0.742599i	−1.31497	−	0.742599i
$75$		0			0
$76$		0			0
$77$	−0.564443	+	0.825472i	−0.564443	+	0.825472i
$78$		0			0
$79$	−0.582954	+	0.852543i	−0.582954	+	0.852543i	−0.998369	−	0.0570888i	$-0.981818\pi$
$79$	−0.582954	+	0.852543i	−0.582954	+	0.852543i	0.415415	+	0.909632i	$0.363636\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$82$		0			0
$83$		0			0		0.897398	−	0.441221i	$-0.145455\pi$
$83$		0			0		−0.897398	+	0.441221i	$0.854545\pi$
$84$		0			0
$85$		0			0
$86$	1.65061	+	0.811551i	1.65061	+	0.811551i
$87$		0			0
$88$	0.734314	−	0.755591i	0.734314	−	0.755591i
$89$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$89$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$90$		0			0
$91$		0			0
$92$	0.179359	+	0.0102561i	0.179359	+	0.0102561i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.0285561	−	0.999592i	$-0.490909\pi$
$97$		0			0		−0.0285561	+	0.999592i	$0.509091\pi$
$98$	0.132827	−	0.923835i	0.132827	−	0.923835i
$99$	0.415415	−	0.909632i	0.415415	−	0.909632i
$100$	0.0183425	+	0.127575i	0.0183425	+	0.127575i
$101$		0			0		0.993482	−	0.113991i	$-0.0363636\pi$
$101$		0			0		−0.993482	+	0.113991i	$0.963636\pi$
$102$		0			0
$103$		0			0		0.870746	−	0.491733i	$-0.163636\pi$
$103$		0			0		−0.870746	+	0.491733i	$0.836364\pi$
$104$		0			0
$105$		0			0
$106$	−0.882427	−	1.14435i	−0.882427	−	1.14435i
$107$	−1.88062	+	0.671003i	−1.88062	+	0.671003i	−0.921124	+	0.389270i	$0.872727\pi$
$107$	−1.88062	+	0.671003i	−1.88062	+	0.671003i	−0.959493	+	0.281733i	$0.909091\pi$
$108$		0			0
$109$	1.14043	+	1.31613i	1.14043	+	1.31613i	0.941844	+	0.336049i	$0.109091\pi$
$109$	1.14043	+	1.31613i	1.14043	+	1.31613i	0.198590	+	0.980083i	$0.436364\pi$
$110$		0			0
$111$		0			0
$112$	−0.264056	+	0.812680i	−0.264056	+	0.812680i
$113$	−0.899779	+	1.16685i	−0.899779	+	1.16685i	0.0855750	+	0.996332i	$0.472727\pi$
$113$	−0.899779	+	1.16685i	−0.899779	+	1.16685i	−0.985354	+	0.170522i	$0.945455\pi$
$114$		0			0
$115$		0			0
$116$	−0.000210200	−	0.00735797i	−0.000210200	−	0.00735797i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.974012	+	0.226497i	0.974012	+	0.226497i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	0.0266524	+	0.932954i	0.0266524	+	0.932954i
$127$	1.87141	+	0.214724i	1.87141	+	0.214724i	0.974012	−	0.226497i	$-0.0727273\pi$
$127$	1.87141	+	0.214724i	1.87141	+	0.214724i	0.897398	+	0.441221i	$0.145455\pi$
$128$	0.356781	−	0.676175i	0.356781	−	0.676175i
$129$		0			0
$130$		0			0
$131$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$131$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$132$		0			0
$133$		0			0
$134$	−0.437111	+	0.184725i	−0.437111	+	0.184725i
$135$		0			0
$136$		0			0
$137$	−0.168643	+	0.0291849i	−0.168643	+	0.0291849i	−0.254218	−	0.967147i	$-0.581818\pi$
$137$	−0.168643	+	0.0291849i	−0.168643	+	0.0291849i	0.0855750	+	0.996332i	$0.472727\pi$
$138$		0			0
$139$		0			0		0.870746	−	0.491733i	$-0.163636\pi$
$139$		0			0		−0.870746	+	0.491733i	$0.836364\pi$
$140$		0			0
$141$		0			0
$142$	−0.244701	−	1.70193i	−0.244701	−	1.70193i
$143$		0			0
$144$	0.121608	−	0.845804i	0.121608	−	0.845804i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	0.0644432	+	0.198336i	0.0644432	+	0.198336i
$149$	−0.765297	−	0.323417i	−0.765297	−	0.323417i	−0.0285561	−	0.999592i	$-0.509091\pi$
$149$	−0.765297	−	0.323417i	−0.765297	−	0.323417i	−0.736741	+	0.676175i	$0.763636\pi$
$150$		0			0
$151$	0.104512	−	1.21682i	0.104512	−	1.21682i	−0.736741	−	0.676175i	$-0.763636\pi$
$151$	0.104512	−	1.21682i	0.104512	−	1.21682i	0.841254	−	0.540641i	$-0.181818\pi$
$152$		0			0
$153$		0			0
$154$	−0.909079	+	0.211397i	−0.909079	+	0.211397i
$155$		0			0
$156$		0			0
$157$		0			0		−0.974012	−	0.226497i	$-0.927273\pi$
$157$		0			0		0.974012	+	0.226497i	$0.0727273\pi$
$158$	−0.938892	+	0.218330i	−0.938892	+	0.218330i
$159$		0			0
$160$		0			0
$161$	−1.12767	−	0.819299i	−1.12767	−	0.819299i
$162$	−0.185351	−	0.914745i	−0.185351	−	0.914745i
$163$	1.12705	−	1.64825i	1.12705	−	1.64825i	0.516397	−	0.856349i	$-0.327273\pi$
$163$	1.12705	−	1.64825i	1.12705	−	1.64825i	0.610648	−	0.791902i	$-0.290909\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.774142	−	0.633012i	$-0.218182\pi$
$167$		0			0		−0.774142	+	0.633012i	$0.781818\pi$
$168$		0			0
$169$	0.696938	−	0.717132i	0.696938	−	0.717132i
$170$		0			0
$171$		0			0
$172$	−0.0921522	−	0.236691i	−0.0921522	−	0.236691i
$173$		0			0		−0.466667	−	0.884433i	$-0.654545\pi$
$173$		0			0		0.466667	+	0.884433i	$0.345455\pi$
$174$		0			0
$175$	0.415415	−	0.909632i	0.415415	−	0.909632i
$176$	0.853108	−	0.0487825i	0.853108	−	0.0487825i
$177$		0			0
$178$		0			0
$179$	1.31281	+	1.35085i	1.31281	+	1.35085i	0.897398	+	0.441221i	$0.145455\pi$
$179$	1.31281	+	1.35085i	1.31281	+	1.35085i	0.415415	+	0.909632i	$0.363636\pi$
$180$		0			0
$181$		0			0		0.736741	−	0.676175i	$-0.236364\pi$
$181$		0			0		−0.736741	+	0.676175i	$0.763636\pi$
$182$		0			0
$183$		0			0
$184$	1.02354	+	1.05320i	1.02354	+	1.05320i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.374706	−	0.962424i	−0.374706	−	0.962424i	−0.985354	−	0.170522i	$-0.945455\pi$
$191$	−0.374706	−	0.962424i	−0.374706	−	0.962424i	0.610648	−	0.791902i	$-0.290909\pi$
$192$		0			0
$193$	0.831697	+	1.21632i	0.831697	+	1.21632i	0.974012	+	0.226497i	$0.0727273\pi$
$193$	0.831697	+	1.21632i	0.831697	+	1.21632i	−0.142315	+	0.989821i	$0.545455\pi$
$194$		0			0
$195$		0			0
$196$	−0.0997764	+	0.0815867i	−0.0997764	+	0.0815867i
$197$	−0.164217	−	0.0482185i	−0.164217	−	0.0482185i	0.198590	−	0.980083i	$-0.436364\pi$
$197$	−0.164217	−	0.0482185i	−0.164217	−	0.0482185i	−0.362808	+	0.931864i	$0.618182\pi$
$198$	0.859717	−	0.363319i	0.859717	−	0.363319i
$199$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$199$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$200$	−0.594714	+	0.869741i	−0.594714	+	0.869741i
$201$		0			0
$202$		0			0
$203$	−0.0294925	+	0.0489079i	−0.0294925	+	0.0489079i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.25086	+	0.615007i	1.25086	+	0.615007i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	1.00595	+	1.66819i	1.00595	+	1.66819i	0.696938	+	0.717132i	$0.254545\pi$
$211$	1.00595	+	1.66819i	1.00595	+	1.66819i	0.309017	+	0.951057i	$0.400000\pi$
$212$	−0.0170767	+	0.198821i	−0.0170767	+	0.198821i
$213$		0			0
$214$	−1.71663	−	0.725453i	−1.71663	−	0.725453i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−0.0464149	+	1.62473i	−0.0464149	+	1.62473i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.362808	−	0.931864i	$-0.381818\pi$
$223$		0			0		−0.362808	+	0.931864i	$0.618182\pi$
$224$	0.222992	−	0.125929i	0.222992	−	0.125929i
$225$	−0.254218	+	0.967147i	−0.254218	+	0.967147i
$226$	−1.35511	+	0.234511i	−1.35511	+	0.234511i
$227$		0			0		−0.610648	−	0.791902i	$-0.709091\pi$
$227$		0			0		0.610648	+	0.791902i	$0.290909\pi$
$228$		0			0
$229$		0			0		0.921124	−	0.389270i	$-0.127273\pi$
$229$		0			0		−0.921124	+	0.389270i	$0.872727\pi$
$230$		0			0
$231$		0			0
$232$	0.0394062	−	0.0454772i	0.0394062	−	0.0454772i
$233$	0.519923	−	1.60016i	0.519923	−	1.60016i	−0.254218	−	0.967147i	$-0.581818\pi$
$233$	0.519923	−	1.60016i	0.519923	−	1.60016i	0.774142	−	0.633012i	$-0.218182\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.411334	−	0.298852i	0.411334	−	0.298852i	−0.362808	−	0.931864i	$-0.618182\pi$
$239$	0.411334	−	0.298852i	0.411334	−	0.298852i	0.774142	+	0.633012i	$0.218182\pi$
$240$		0			0
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$	0.526814	+	0.770442i	0.526814	+	0.770442i
$243$		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	$0.600000\pi$
$252$	0.0844027	−	0.0974059i	0.0844027	−	0.0974059i
$253$	−0.354349	+	1.34808i	−0.354349	+	1.34808i
$254$	1.15132	+	1.32869i	1.15132	+	1.32869i
$255$		0			0
$256$	−0.357863	+	0.127685i	−0.357863	+	0.127685i
$257$		0			0		−0.610648	−	0.791902i	$-0.709091\pi$
$257$		0			0		0.610648	+	0.791902i	$0.290909\pi$
$258$		0			0
$259$	0.411334	−	1.56488i	0.411334	−	1.56488i
$260$		0			0
$261$	0.0207207	−	0.0532207i	0.0207207	−	0.0532207i
$262$		0			0
$263$	0.262179	+	1.82350i	0.262179	+	1.82350i	0.516397	+	0.856349i	$0.327273\pi$
$263$	0.262179	+	1.82350i	0.262179	+	1.82350i	−0.254218	+	0.967147i	$0.581818\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	0.0617196	+	0.0220215i	0.0617196	+	0.0220215i
$269$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$269$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$270$		0			0
$271$		0			0		−0.998369	−	0.0570888i	$-0.981818\pi$
$271$		0			0		0.998369	+	0.0570888i	$0.0181818\pi$
$272$		0			0
$273$		0			0
$274$	−0.134382	−	0.0863621i	−0.134382	−	0.0863621i
$275$	−0.998369	−	0.0570888i	−0.998369	−	0.0570888i
$276$		0			0
$277$	−0.651166	−	0.320157i	−0.651166	−	0.320157i	0.0855750	−	0.996332i	$-0.472727\pi$
$277$	−0.651166	−	0.320157i	−0.651166	−	0.320157i	−0.736741	+	0.676175i	$0.763636\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.799530	−	1.32587i	0.799530	−	1.32587i	−0.142315	−	0.989821i	$-0.545455\pi$
$281$	0.799530	−	1.32587i	0.799530	−	1.32587i	0.941844	−	0.336049i	$-0.109091\pi$
$282$		0			0
$283$		0			0		−0.198590	−	0.980083i	$-0.563636\pi$
$283$		0			0		0.198590	+	0.980083i	$0.436364\pi$
$284$	−0.134022	+	0.196001i	−0.134022	+	0.196001i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.198252	+	0.162110i	−0.198252	+	0.162110i
$289$	−0.870746	−	0.491733i	−0.870746	−	0.491733i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.362808	−	0.931864i	$-0.618182\pi$
$293$		0			0		0.362808	+	0.931864i	$0.381818\pi$
$294$		0			0
$295$		0			0
$296$	−0.708203	+	1.55075i	−0.708203	+	1.55075i
$297$		0			0
$298$	−0.322130	−	0.705367i	−0.322130	−	0.705367i
$299$		0			0
$300$		0			0
$301$	−0.391364	+	1.93146i	−0.391364	+	1.93146i
$302$	0.839795	−	0.770757i	0.839795	−	0.770757i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$307$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$308$	0.112227	+	0.0633777i	0.112227	+	0.0633777i
$309$		0			0
$310$		0			0
$311$		0			0		−0.466667	−	0.884433i	$-0.654545\pi$
$311$		0			0		0.466667	+	0.884433i	$0.345455\pi$
$312$		0			0
$313$		0			0		−0.774142	−	0.633012i	$-0.781818\pi$
$313$		0			0		0.774142	+	0.633012i	$0.218182\pi$
$314$		0			0
$315$		0			0
$316$	0.115908	+	0.0654562i	0.115908	+	0.0654562i
$317$	0.478446	−	0.391223i	0.478446	−	0.391223i	−0.362808	−	0.931864i	$-0.618182\pi$
$317$	0.478446	−	0.391223i	0.478446	−	0.391223i	0.841254	+	0.540641i	$0.181818\pi$
$318$		0			0
$319$	0.0562756	+	0.00973888i	0.0562756	+	0.00973888i
$320$		0			0
$321$		0			0
$322$	−0.258357	−	1.27504i	−0.258357	−	1.27504i
$323$		0			0
$324$	−0.0665566	+	0.110372i	−0.0665566	+	0.110372i
$325$		0			0
$326$	1.81519	−	0.422105i	1.81519	−	0.422105i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.334130	+	0.214732i	0.334130	+	0.214732i	0.696938	−	0.717132i	$-0.254545\pi$
$331$	0.334130	+	0.214732i	0.334130	+	0.214732i	−0.362808	+	0.931864i	$0.618182\pi$
$332$		0			0
$333$	−0.138463	+	1.61210i	−0.138463	+	1.61210i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.374083	+	0.133472i	0.374083	+	0.133472i	0.516397	−	0.856349i	$-0.327273\pi$
$337$	0.374083	+	0.133472i	0.374083	+	0.133472i	−0.142315	+	0.989821i	$0.545455\pi$
$338$	0.931812	−	0.0532830i	0.931812	−	0.0532830i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.993482	−	0.113991i	0.993482	−	0.113991i
$344$	0.753332	−	1.93492i	0.753332	−	1.93492i
$345$		0			0
$346$		0			0
$347$	−1.76851	+	0.306053i	−1.76851	+	0.306053i	−0.959493	−	0.281733i	$-0.909091\pi$
$347$	−1.76851	+	0.306053i	−1.76851	+	0.306053i	−0.809017	+	0.587785i	$0.800000\pi$
$348$		0			0
$349$		0			0		0.941844	−	0.336049i	$-0.109091\pi$
$349$		0			0		−0.941844	+	0.336049i	$0.890909\pi$
$350$	0.859717	−	0.363319i	0.859717	−	0.363319i
$351$		0			0
$352$	−0.198252	−	0.162110i	−0.198252	−	0.162110i
$353$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$353$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.0502047	+	1.75739i	0.0502047	+	1.75739i
$359$	0.0339888	+	0.395724i	0.0339888	+	0.395724i	0.993482	+	0.113991i	$0.0363636\pi$
$359$	0.0339888	+	0.395724i	0.0339888	+	0.395724i	−0.959493	+	0.281733i	$0.909091\pi$
$360$		0			0
$361$	−0.736741	−	0.676175i	−0.736741	−	0.676175i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.0855750	−	0.996332i	$-0.527273\pi$
$367$		0			0		0.0855750	+	0.996332i	$0.472727\pi$
$368$	0.0340122	+	1.19058i	0.0340122	+	1.19058i
$369$		0			0
$370$		0			0
$371$	0.945456	−	1.22609i	0.945456	−	1.22609i
$372$		0			0
$373$	0.186393	−	0.215109i	0.186393	−	0.215109i	−0.654861	−	0.755750i	$-0.727273\pi$
$373$	0.186393	−	0.215109i	0.186393	−	0.215109i	0.841254	+	0.540641i	$0.181818\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.20341	+	0.208258i	−1.20341	+	0.208258i	−0.736741	−	0.676175i	$-0.763636\pi$
$379$	−1.20341	+	0.208258i	−1.20341	+	0.208258i	−0.466667	+	0.884433i	$0.654545\pi$
$380$		0			0
$381$		0			0
$382$	0.349726	−	0.898264i	0.349726	−	0.898264i
$383$		0			0		0.993482	−	0.113991i	$-0.0363636\pi$
$383$		0			0		−0.993482	+	0.113991i	$0.963636\pi$
$384$		0			0
$385$		0			0
$386$	−0.195719	+	1.36125i	−0.195719	+	1.36125i
$387$	0.0562756	−	1.96990i	0.0562756	−	1.96990i
$388$		0			0
$389$	1.15027	+	0.410416i	1.15027	+	0.410416i	0.841254	−	0.540641i	$-0.181818\pi$
$389$	1.15027	+	0.410416i	1.15027	+	0.410416i	0.309017	+	0.951057i	$0.400000\pi$
$390$		0			0
$391$		0			0
$392$	−1.05191	−	0.0601504i	−1.05191	−	0.0601504i
$393$		0			0
$394$	−0.0824895	−	0.136793i	−0.0824895	−	0.136793i
$395$		0			0
$396$	−0.121391	−	0.0433122i	−0.121391	−	0.0433122i
$397$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$397$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$398$		0			0
$399$		0			0
$400$	−0.832295	+	0.193542i	−0.832295	+	0.193542i
$401$	1.74815	−	0.859509i	1.74815	−	0.859509i	0.774142	−	0.633012i	$-0.218182\pi$
$401$	1.74815	−	0.859509i	1.74815	−	0.859509i	0.974012	−	0.226497i	$-0.0727273\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−0.0511455	+	0.0150177i	−0.0511455	+	0.0150177i
$407$	−1.60749	+	0.184442i	−1.60749	+	0.184442i
$408$		0			0
$409$		0			0		0.774142	−	0.633012i	$-0.218182\pi$
$409$		0			0		−0.774142	+	0.633012i	$0.781818\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.471995	+	1.21231i	0.471995	+	1.21231i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$419$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$420$		0			0
$421$	0.276810	+	0.284831i	0.276810	+	0.284831i	0.841254	−	0.540641i	$-0.181818\pi$
$421$	0.276810	+	0.284831i	0.276810	+	0.284831i	−0.564443	+	0.825472i	$0.690909\pi$
$422$	−0.361069	+	1.78195i	−0.361069	+	1.78195i
$423$		0			0
$424$	−1.20186	+	1.10305i	−1.20186	+	1.10305i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.106908	+	0.234096i	0.106908	+	0.234096i
$429$		0			0
$430$		0			0
$431$	0.714988	+	0.123734i	0.714988	+	0.123734i	0.516397	−	0.856349i	$-0.327273\pi$
$431$	0.714988	+	0.123734i	0.714988	+	0.123734i	0.198590	+	0.980083i	$0.436364\pi$
$432$		0			0
$433$		0			0		−0.362808	−	0.931864i	$-0.618182\pi$
$433$		0			0		0.362808	+	0.931864i	$0.381818\pi$
$434$		0			0
$435$		0			0
$436$	0.156431	−	0.160964i	0.156431	−	0.160964i
$437$		0			0
$438$		0			0
$439$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$439$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$440$		0			0
$441$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$442$		0			0
$443$	0.356430	+	1.75905i	0.356430	+	1.75905i	0.610648	+	0.791902i	$0.290909\pi$
$443$	0.356430	+	1.75905i	0.356430	+	1.75905i	−0.254218	+	0.967147i	$0.581818\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	1.06510	+	0.247679i	1.06510	+	0.247679i
$449$	−1.56281	−	0.768383i	−1.56281	−	0.768383i	−0.564443	−	0.825472i	$-0.690909\pi$
$449$	−1.56281	−	0.768383i	−1.56281	−	0.768383i	−0.998369	+	0.0570888i	$0.981818\pi$
$450$	−0.785171	+	0.504599i	−0.785171	+	0.504599i
$451$		0			0
$452$	0.159764	+	0.102674i	0.159764	+	0.102674i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$457$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$461$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$462$		0			0
$463$	−0.282774	−	1.96674i	−0.282774	−	1.96674i	−0.254218	−	0.967147i	$-0.581818\pi$
$463$	−0.282774	−	1.96674i	−0.282774	−	1.96674i	−0.0285561	−	0.999592i	$-0.509091\pi$
$464$	0.0484843	−	0.00556305i	0.0484843	−	0.00556305i
$465$		0			0
$466$	1.36737	−	0.772189i	1.36737	−	0.772189i
$467$		0			0		0.254218	−	0.967147i	$-0.418182\pi$
$467$		0			0		−0.254218	+	0.967147i	$0.581818\pi$
$468$		0			0
$469$	−0.310476	−	0.402632i	−0.310476	−	0.402632i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.94184	−	0.336049i	1.94184	−	0.336049i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.722533	+	1.36935i	−0.722533	+	1.36935i
$478$	0.471448	+	0.0540937i	0.471448	+	0.0540937i
$479$		0			0		−0.0285561	−	0.999592i	$-0.509091\pi$
$479$		0			0		0.0285561	+	0.999592i	$0.490909\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.0183425	−	0.127575i	0.0183425	−	0.127575i
$485$		0			0
$486$		0			0
$487$	1.59434	−	1.15835i	1.59434	−	1.15835i	0.696938	−	0.717132i	$-0.254545\pi$
$487$	1.59434	−	1.15835i	1.59434	−	1.15835i	0.897398	−	0.441221i	$-0.145455\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.132827	−	0.251736i	0.132827	−	0.251736i	−0.809017	−	0.587785i	$-0.800000\pi$
$491$	0.132827	−	0.251736i	0.132827	−	0.251736i	0.941844	+	0.336049i	$0.109091\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.69694	−	0.717132i	1.69694	−	0.717132i
$498$		0			0
$499$	0.377401	+	0.489423i	0.377401	+	0.489423i	0.941844	−	0.336049i	$-0.109091\pi$
$499$	0.377401	+	0.489423i	0.377401	+	0.489423i	−0.564443	+	0.825472i	$0.690909\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.362808	−	0.931864i	$-0.381818\pi$
$503$		0			0		−0.362808	+	0.931864i	$0.618182\pi$
$504$	1.04676	−	0.120105i	1.04676	−	0.120105i
$505$		0			0
$506$	−1.09443	+	0.703348i	−1.09443	+	0.703348i
$507$		0			0
$508$	0.00693289	−	0.242683i	0.00693289	−	0.242683i
$509$		0			0		0.998369	−	0.0570888i	$-0.0181818\pi$
$509$		0			0		−0.998369	+	0.0570888i	$0.981818\pi$
$510$		0			0
$511$		0			0
$512$	−1.03088	−	0.435655i	−1.03088	−	0.435655i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	1.27043	−	0.816458i	1.27043	−	0.816458i
$519$		0			0
$520$		0			0
$521$		0			0		0.974012	−	0.226497i	$-0.0727273\pi$
$521$		0			0		−0.974012	+	0.226497i	$0.927273\pi$
$522$	0.0478356	−	0.0235192i	0.0478356	−	0.0235192i
$523$		0			0		0.516397	−	0.856349i	$-0.327273\pi$
$523$		0			0		−0.516397	+	0.856349i	$0.672727\pi$
$524$		0			0
$525$		0			0
$526$	−0.970522	+	1.41934i	−0.970522	+	1.41934i
$527$		0			0
$528$		0			0
$529$	−0.904694	−	0.265642i	−0.904694	−	0.265642i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	0.249995	+	0.473794i	0.249995	+	0.473794i
$537$		0			0
$538$		0			0
$539$	−0.466667	−	0.884433i	−0.466667	−	0.884433i
$540$		0			0
$541$	−0.495223	−	1.88403i	−0.495223	−	1.88403i	−0.466667	−	0.884433i	$-0.654545\pi$
$541$	−0.495223	−	1.88403i	−0.495223	−	1.88403i	−0.0285561	−	0.999592i	$-0.509091\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	1.17260	+	1.20658i	1.17260	+	1.20658i	0.974012	+	0.226497i	$0.0727273\pi$
$547$	1.17260	+	1.20658i	1.17260	+	1.20658i	0.198590	+	0.980083i	$0.436364\pi$
$548$	0.00560778	+	0.0213342i	0.00560778	+	0.0213342i
$549$		0			0
$550$	−0.650476	−	0.669324i	−0.650476	−	0.669324i
$551$		0			0
$552$		0			0
$553$	−0.481972	−	0.913438i	−0.481972	−	0.913438i
$554$	−0.245709	−	0.631097i	−0.245709	−	0.631097i
$555$		0			0
$556$		0			0
$557$	0.430731	−	0.443212i	0.430731	−	0.443212i	−0.466667	−	0.884433i	$-0.654545\pi$
$557$	0.430731	−	0.443212i	0.430731	−	0.443212i	0.897398	+	0.441221i	$0.145455\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	1.38653	−	0.407122i	1.38653	−	0.407122i
$563$		0			0		0.564443	−	0.825472i	$-0.309091\pi$
$563$		0			0		−0.564443	+	0.825472i	$0.690909\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.897398	−	0.441221i	0.897398	−	0.441221i
$568$	−1.89060	+	0.439640i	−1.89060	+	0.439640i
$569$	−1.86912	−	0.434644i	−1.86912	−	0.434644i	−0.870746	−	0.491733i	$-0.836364\pi$
$569$	−1.86912	−	0.434644i	−1.86912	−	0.434644i	−0.998369	+	0.0570888i	$0.981818\pi$
$570$		0			0
$571$	0.143981	−	0.0925307i	0.143981	−	0.0925307i	−0.466667	−	0.884433i	$-0.654545\pi$
$571$	0.143981	−	0.0925307i	0.143981	−	0.0925307i	0.610648	+	0.791902i	$0.290909\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.119281	−	1.38876i	0.119281	−	1.38876i
$576$	−1.09174	−	0.0624279i	−1.09174	−	0.0624279i
$577$		0			0		−0.921124	−	0.389270i	$-0.872727\pi$
$577$		0			0		0.921124	+	0.389270i	$0.127273\pi$
$578$	−0.288416	−	0.887654i	−0.288416	−	0.887654i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−1.48557	−	0.436202i	−1.48557	−	0.436202i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.870746	−	0.491733i	$-0.163636\pi$
$587$		0			0		−0.870746	+	0.491733i	$0.836364\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−1.27356	+	0.538210i	−1.27356	+	0.538210i
$593$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$593$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$594$		0			0
$595$		0			0
$596$	−0.0330904	+	0.101842i	−0.0330904	+	0.101842i
$597$		0			0
$598$		0			0
$599$	−1.73014	−	0.198515i	−1.73014	−	0.198515i	−0.809017	−	0.587785i	$-0.800000\pi$
$599$	−1.73014	−	0.198515i	−1.73014	−	0.198515i	−0.921124	+	0.389270i	$0.872727\pi$
$600$		0			0
$601$		0			0		−0.0855750	−	0.996332i	$-0.527273\pi$
$601$		0			0		0.0855750	+	0.996332i	$0.472727\pi$
$602$	−1.48805	+	1.08113i	−1.48805	+	1.08113i
$603$	0.374586	+	0.343792i	0.374586	+	0.343792i
$604$	−0.157408			−0.157408
$605$		0			0
$606$		0			0
$607$		0			0		−0.736741	−	0.676175i	$-0.763636\pi$
$607$		0			0		0.736741	+	0.676175i	$0.236364\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	1.09599	−	1.42130i	1.09599	−	1.42130i	0.198590	−	0.980083i	$-0.436364\pi$
$613$	1.09599	−	1.42130i	1.09599	−	1.42130i	0.897398	−	0.441221i	$-0.145455\pi$
$614$		0			0
$615$		0			0
$616$	0.325589	+	1.00206i	0.325589	+	1.00206i
$617$	−1.30118	−	1.50165i	−1.30118	−	1.50165i	−0.736741	−	0.676175i	$-0.763636\pi$
$617$	−1.30118	−	1.50165i	−1.30118	−	1.50165i	−0.564443	−	0.825472i	$-0.690909\pi$
$618$		0			0
$619$		0			0		0.941844	−	0.336049i	$-0.109091\pi$
$619$		0			0		−0.941844	+	0.336049i	$0.890909\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.993482	−	0.113991i	0.993482	−	0.113991i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	1.83474	+	0.654632i	1.83474	+	0.654632i	0.993482	+	0.113991i	$0.0363636\pi$
$631$	1.83474	+	0.654632i	1.83474	+	0.654632i	0.841254	+	0.540641i	$0.181818\pi$
$632$	0.336267	+	1.03492i	0.336267	+	1.03492i
$633$		0			0
$634$	0.575892	+	0.0329307i	0.575892	+	0.0329307i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	0.0325504	+	0.0422121i	0.0325504	+	0.0422121i
$639$	−1.54980	+	0.995994i	−1.54980	+	0.995994i
$640$		0			0
$641$	1.74815	+	0.406516i	1.74815	+	0.406516i	0.974012	−	0.226497i	$-0.0727273\pi$
$641$	1.74815	+	0.406516i	1.74815	+	0.406516i	0.774142	+	0.633012i	$0.218182\pi$
$642$		0			0
$643$		0			0		0.897398	−	0.441221i	$-0.145455\pi$
$643$		0			0		−0.897398	+	0.441221i	$0.854545\pi$
$644$	−0.0927716	+	0.153844i	−0.0927716	+	0.153844i
$645$		0			0
$646$		0			0
$647$		0			0		0.564443	−	0.825472i	$-0.309091\pi$
$647$		0			0		−0.564443	+	0.825472i	$0.690909\pi$
$648$	−1.01095	+	0.296842i	−1.01095	+	0.296842i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.224089	−	0.126549i	−0.224089	−	0.126549i
$653$	1.31281	−	1.35085i	1.31281	−	1.35085i	0.415415	−	0.909632i	$-0.363636\pi$
$653$	1.31281	−	1.35085i	1.31281	−	1.35085i	0.897398	−	0.441221i	$-0.145455\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.142315	+	0.989821i	$0.545455\pi$
$659$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.654861	+	0.755750i	$0.727273\pi$
$660$		0			0
$661$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$661$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$662$	0.0942394	+	0.358524i	0.0942394	+	0.358524i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−1.11260	+	1.02114i	−1.11260	+	1.02114i
$667$	−0.0158092	+	0.0780216i	−0.0158092	+	0.0780216i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−1.76851	−	0.306053i	−1.76851	−	0.306053i	−0.809017	−	0.587785i	$-0.800000\pi$
$673$	−1.76851	−	0.306053i	−1.76851	−	0.306053i	−0.959493	+	0.281733i	$0.909091\pi$
$674$	0.172995	+	0.327862i	0.172995	+	0.327862i
$675$		0			0
$676$	−0.0997764	−	0.0815867i	−0.0997764	−	0.0815867i
$677$		0			0		−0.564443	−	0.825472i	$-0.690909\pi$
$677$		0			0		0.564443	+	0.825472i	$0.309091\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.86912	+	0.548822i	−1.86912	+	0.548822i	−0.870746	+	0.491733i	$0.836364\pi$
$683$	−1.86912	+	0.548822i	−1.86912	+	0.548822i	−0.998369	+	0.0570888i	$0.981818\pi$
$684$		0			0
$685$		0			0
$686$	0.755084	+	0.548600i	0.755084	+	0.548600i
$687$		0			0
$688$	1.51120	−	0.743005i	1.51120	−	0.743005i
$689$		0			0
$690$		0			0
$691$		0			0		−0.897398	−	0.441221i	$-0.854545\pi$
$691$		0			0		0.897398	+	0.441221i	$0.145455\pi$
$692$		0			0
$693$	0.610648	+	0.791902i	0.610648	+	0.791902i
$694$	−1.40922	−	0.905652i	−1.40922	−	0.905652i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.121391	−	0.0433122i	−0.121391	−	0.0433122i
$701$	−1.21930	+	0.0697223i	−1.21930	+	0.0697223i	−0.654861	−	0.755750i	$-0.727273\pi$
$701$	−1.21930	+	0.0697223i	−1.21930	+	0.0697223i	−0.564443	+	0.825472i	$0.690909\pi$
$702$		0			0
$703$		0			0
$704$	−0.155624	−	1.08239i	−0.155624	−	1.08239i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.456270	+	1.73583i	−0.456270	+	1.73583i	0.198590	+	0.980083i	$0.436364\pi$
$709$	−0.456270	+	1.73583i	−0.456270	+	1.73583i	−0.654861	+	0.755750i	$0.727273\pi$
$710$		0			0
$711$	0.630674	+	0.817873i	0.630674	+	0.817873i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.158988	−	0.183482i	0.158988	−	0.183482i
$717$		0			0
$718$	−0.226369	+	0.293560i	−0.226369	+	0.293560i
$719$		0			0		0.466667	−	0.884433i	$-0.345455\pi$
$719$		0			0		−0.466667	+	0.884433i	$0.654545\pi$
$720$		0			0
$721$		0			0
$722$	−0.0798701	−	0.929911i	−0.0798701	−	0.929911i
$723$		0			0
$724$		0			0
$725$	−0.0571121			−0.0571121
$726$		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		0.466667	−	0.884433i	$-0.345455\pi$
$733$		0			0		−0.466667	+	0.884433i	$0.654545\pi$
$734$		0			0
$735$		0			0
$736$	0.233760	−	0.269773i	0.233760	−	0.269773i
$737$	−0.262555	+	0.435399i	−0.262555	+	0.435399i
$738$		0			0
$739$	−0.569286	+	0.240582i	−0.569286	+	0.240582i	−0.654861	−	0.755750i	$-0.727273\pi$
$739$	−0.569286	+	0.240582i	−0.569286	+	0.240582i	0.0855750	+	0.996332i	$0.472727\pi$
$740$		0			0
$741$		0			0
$742$	1.42390	−	0.246416i	1.42390	−	0.246416i
$743$	−0.157116	+	0.597730i	−0.157116	+	0.597730i	0.841254	+	0.540641i	$0.181818\pi$
$743$	−0.157116	+	0.597730i	−0.157116	+	0.597730i	−0.998369	+	0.0570888i	$0.981818\pi$
$744$		0			0
$745$		0			0
$746$	0.263923	−	0.0302824i	0.263923	−	0.0302824i
$747$		0			0
$748$		0			0
$749$	0.284165	−	1.97641i	0.284165	−	1.97641i
$750$		0			0
$751$	−0.170871	+	0.00977075i	−0.170871	+	0.00977075i	−0.142315	−	0.989821i	$-0.545455\pi$
$751$	−0.170871	+	0.00977075i	−0.170871	+	0.00977075i	−0.0285561	+	0.999592i	$0.509091\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1.02606	+	1.70153i	1.02606	+	1.70153i	0.610648	+	0.791902i	$0.290909\pi$
$757$	1.02606	+	1.70153i	1.02606	+	1.70153i	0.415415	+	0.909632i	$0.363636\pi$
$758$	−0.958926	−	0.616264i	−0.958926	−	0.616264i
$759$		0			0
$760$		0			0
$761$		0			0		−0.897398	−	0.441221i	$-0.854545\pi$
$761$		0			0		0.897398	+	0.441221i	$0.145455\pi$
$762$		0			0
$763$	−1.69623	+	0.394442i	−1.69623	+	0.394442i
$764$	−0.119456	+	0.0587324i	−0.119456	+	0.0587324i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$769$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$770$		0			0
$771$		0			0
$772$	0.147019	−	0.120217i	0.147019	−	0.120217i
$773$		0			0		−0.870746	−	0.491733i	$-0.836364\pi$
$773$		0			0		0.870746	+	0.491733i	$0.163636\pi$
$774$	1.28190	−	1.31904i	1.28190	−	1.31904i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	0.531944	+	1.00815i	0.531944	+	1.00815i
$779$		0			0
$780$		0			0
$781$	−1.28393	−	1.32113i	−1.28393	−	1.32113i
$782$		0			0
$783$		0			0
$784$	−0.595534	−	0.612790i	−0.595534	−	0.612790i
$785$		0			0
$786$		0			0
$787$		0			0		0.736741	−	0.676175i	$-0.236364\pi$
$787$		0			0		−0.736741	+	0.676175i	$0.763636\pi$
$788$	−0.00438069	+	0.0216196i	−0.00438069	+	0.0216196i
$789$		0			0
$790$		0			0
$791$	−0.612107	−	1.34033i	−0.612107	−	1.34033i
$792$	−0.491694	−	0.931864i	−0.491694	−	0.931864i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.774142	−	0.633012i	$-0.781818\pi$
$797$		0			0		0.774142	+	0.633012i	$0.218182\pi$
$798$		0			0
$799$		0			0
$800$	0.222992	+	0.125929i	0.222992	+	0.125929i
$801$		0			0
$802$	1.74451	+	0.512234i	1.74451	+	0.512234i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.69042	−	0.831123i	1.69042	−	0.831123i	0.696938	−	0.717132i	$-0.254545\pi$
$809$	1.69042	−	0.831123i	1.69042	−	0.831123i	0.993482	−	0.113991i	$-0.0363636\pi$
$810$		0			0
$811$		0			0		−0.974012	−	0.226497i	$-0.927273\pi$
$811$		0			0		0.974012	+	0.226497i	$0.0727273\pi$
$812$	0.00660573	+	0.00324782i	0.00660573	+	0.00324782i
$813$		0			0
$814$	−1.22175	−	0.887654i	−1.22175	−	0.887654i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.23355	−	0.440131i	−1.23355	−	0.440131i	−0.362808	−	0.931864i	$-0.618182\pi$
$821$	−1.23355	−	0.440131i	−1.23355	−	0.440131i	−0.870746	+	0.491733i	$0.836364\pi$
$822$		0			0
$823$	−0.0176486	+	0.617782i	−0.0176486	+	0.617782i	0.941844	+	0.336049i	$0.109091\pi$
$823$	−0.0176486	+	0.617782i	−0.0176486	+	0.617782i	−0.959493	+	0.281733i	$0.909091\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.825414	−	0.0947075i	0.825414	−	0.0947075i	0.309017	−	0.951057i	$-0.400000\pi$
$827$	0.825414	−	0.0947075i	0.825414	−	0.0947075i	0.516397	+	0.856349i	$0.327273\pi$
$828$	0.0651790	−	0.167411i	0.0651790	−	0.167411i
$829$		0			0		0.870746	−	0.491733i	$-0.163636\pi$
$829$		0			0		−0.870746	+	0.491733i	$0.836364\pi$
$830$		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		0.610648	−	0.791902i	$-0.290909\pi$
$839$		0			0		−0.610648	+	0.791902i	$0.709091\pi$
$840$		0			0
$841$	−0.990241	−	0.113620i	−0.990241	−	0.113620i
$842$	0.0105858	+	0.370552i	0.0105858	+	0.370552i
$843$		0			0
$844$	0.203123	−	0.147578i	0.203123	−	0.147578i
$845$		0			0
$846$		0			0
$847$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$848$	−1.32301			−1.32301
$849$		0			0
$850$		0			0
$851$	−0.193001	−	2.24706i	−0.193001	−	2.24706i
$852$		0			0
$853$		0			0		−0.993482	−	0.113991i	$-0.963636\pi$
$853$		0			0		0.993482	+	0.113991i	$0.0363636\pi$
$854$		0			0
$855$		0			0
$856$	−0.650116	+	2.00085i	−0.650116	+	2.00085i
$857$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$857$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$858$		0			0
$859$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$859$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$860$		0			0
$861$		0			0
$862$	0.413556	+	0.536309i	0.413556	+	0.536309i
$863$	1.29054	−	0.223337i	1.29054	−	0.223337i	0.516397	−	0.856349i	$-0.327273\pi$
$863$	1.29054	−	0.223337i	1.29054	−	0.223337i	0.774142	+	0.633012i	$0.218182\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.676337	+	0.780534i	−0.676337	+	0.780534i
$870$		0			0
$871$		0			0
$872$	1.83189	−	0.104751i	1.83189	−	0.104751i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.157650	+	1.83549i	−0.157650	+	1.83549i	0.309017	+	0.951057i	$0.400000\pi$
$877$	−0.157650	+	1.83549i	−0.157650	+	1.83549i	−0.466667	+	0.884433i	$0.654545\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$881$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$882$	−0.837573	−	0.411807i	−0.837573	−	0.411807i
$883$	1.63878	+	0.381082i	1.63878	+	0.381082i	0.941844	−	0.336049i	$-0.109091\pi$
$883$	1.63878	+	0.381082i	1.63878	+	0.381082i	0.696938	+	0.717132i	$0.254545\pi$
$884$		0			0
$885$		0			0
$886$	−0.865041	+	1.43451i	−0.865041	+	1.43451i
$887$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$887$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$888$		0			0
$889$	−1.06324	+	1.55493i	−1.06324	+	1.55493i
$890$		0			0
$891$	−0.736741	−	0.676175i	−0.736741	−	0.676175i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	0.431533	+	0.631097i	0.431533	+	0.631097i
$897$		0			0
$898$	−0.589706	−	1.51465i	−0.589706	−	1.51465i
$899$		0			0
$900$	0.126999	+	0.0219780i	0.126999	+	0.0219780i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.394675	+	1.50150i	0.394675	+	1.50150i
$905$		0			0
$906$		0			0
$907$	1.08558	−	0.996332i	1.08558	−	0.996332i	0.0855750	−	0.996332i	$-0.472727\pi$
$907$	1.08558	−	0.996332i	1.08558	−	0.996332i	1.00000			$0$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.211212	−	0.803535i	−0.211212	−	0.803535i	−0.985354	−	0.170522i	$-0.945455\pi$
$911$	−0.211212	−	0.803535i	−0.211212	−	0.803535i	0.774142	−	0.633012i	$-0.218182\pi$
$912$		0			0
$913$		0			0
$914$	0.627346	−	1.37370i	0.627346	−	1.37370i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	0.637192	+	0.931864i	0.637192	+	0.931864i	1.00000			$0$
$919$	0.637192	+	0.931864i	0.637192	+	0.931864i	−0.362808	+	0.931864i	$0.618182\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	1.55249	−	0.455853i	1.55249	−	0.455853i
$926$	1.04676	−	1.53084i	1.04676	−	1.53084i
$927$		0			0
$928$	−0.0118327	−	0.00859694i	−0.0118327	−	0.00859694i
$929$		0			0		0.516397	−	0.856349i	$-0.327273\pi$
$929$		0			0		−0.516397	+	0.856349i	$0.672727\pi$
$930$		0			0
$931$		0			0
$932$	−0.211217	−	0.0491164i	−0.211217	−	0.0491164i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.516397	−	0.856349i	$-0.672727\pi$
$937$		0			0		0.516397	+	0.856349i	$0.327273\pi$
$938$	0.0406089	−	0.472801i	0.0406089	−	0.472801i
$939$		0			0
$940$		0			0
$941$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$941$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	1.54734	+	0.994417i	1.54734	+	0.994417i
$947$	0.273100	+	1.89945i	0.273100	+	1.89945i	0.415415	+	0.909632i	$0.363636\pi$
$947$	0.273100	+	1.89945i	0.273100	+	1.89945i	−0.142315	+	0.989821i	$0.545455\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1.18956	+	1.54264i	1.18956	+	1.54264i	0.774142	+	0.633012i	$0.218182\pi$
$953$	1.18956	+	1.54264i	1.18956	+	1.54264i	0.415415	+	0.909632i	$0.363636\pi$
$954$	−1.36103	+	0.485614i	−1.36103	+	0.485614i
$955$		0			0
$956$	−0.0429134	−	0.0495247i	−0.0429134	−	0.0495247i
$957$		0			0
$958$		0			0
$959$	0.0528883	−	0.162773i	0.0528883	−	0.162773i
$960$		0			0
$961$	−0.466667	+	0.884433i	−0.466667	+	0.884433i
$962$		0			0
$963$	0.0570190	+	1.99592i	0.0570190	+	1.99592i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−1.74149			−1.74149			−0.870746	−	0.491733i	$-0.836364\pi$
$967$	−1.74149			−1.74149			−0.870746	+	0.491733i	$0.836364\pi$
$968$	0.815658	−	0.666960i	0.815658	−	0.666960i
$969$		0			0
$970$		0			0
$971$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$971$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$972$		0			0
$973$		0			0
$974$	1.82734	+	0.209668i	1.82734	+	0.209668i
$975$		0			0
$976$		0			0
$977$	0.122736	−	0.377742i	0.122736	−	0.377742i	−0.870746	−	0.491733i	$-0.836364\pi$
$977$	0.122736	−	0.377742i	0.122736	−	0.377742i	0.993482	+	0.113991i	$0.0363636\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	1.60413	−	0.677911i	1.60413	−	0.677911i
$982$	0.250205	−	0.0892731i	0.250205	−	0.0892731i
$983$		0			0		−0.610648	−	0.791902i	$-0.709091\pi$
$983$		0			0		0.610648	+	0.791902i	$0.290909\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.390928	+	2.71896i	0.390928	+	2.71896i
$990$		0			0
$991$	0.273100	−	1.89945i	0.273100	−	1.89945i	−0.142315	−	0.989821i	$-0.545455\pi$
$991$	0.273100	−	1.89945i	0.273100	−	1.89945i	0.415415	−	0.909632i	$-0.363636\pi$
$992$		0			0
$993$		0			0
$994$	1.61944	+	0.577814i	1.61944	+	0.577814i
$995$		0			0
$996$		0			0
$997$		0			0		−0.998369	−	0.0570888i	$-0.981818\pi$
$997$		0			0		0.998369	+	0.0570888i	$0.0181818\pi$
$998$	−0.0493624	+	0.574717i	−0.0493624	+	0.574717i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.1.bb.a.328.1	✓	40
7.6	odd	2	CM	847.1.bb.a.328.1	✓	40
121.38	even	55	inner	847.1.bb.a.643.1	yes	40
847.643	odd	110	inner	847.1.bb.a.643.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.1.bb.a.328.1	✓	40	1.1	even	1	trivial
847.1.bb.a.328.1	✓	40	7.6	odd	2	CM
847.1.bb.a.643.1	yes	40	121.38	even	55	inner
847.1.bb.a.643.1	yes	40	847.643	odd	110	inner

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)

\(f(q)\)	\(=\)	\(q+(0.687626 + 0.631097i) q^{2} +(-0.0110295 - 0.128414i) q^{4} +(-0.466667 + 0.884433i) q^{7} +(0.643396 - 0.834371i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.687626 + 0.631097i) q^{2} +(-0.0110295 - 0.128414i) q^{4} +(-0.466667 + 0.884433i) q^{7} +(0.643396 - 0.834371i) q^{8} +(0.309017 - 0.951057i) q^{9} +(0.993482 + 0.113991i) q^{11} +(-0.879056 + 0.313647i) q^{14} +(0.841987 - 0.145712i) q^{16} +(0.812697 - 0.458951i) q^{18} +(0.611204 + 0.705367i) q^{22} +(-0.198369 + 1.37969i) q^{23} +(-0.998369 + 0.0570888i) q^{25} +(0.118720 + 0.0501716i) q^{28} +(0.0570190 + 0.00326046i) q^{29} +(-0.215439 - 0.138454i) q^{32} +(-0.125537 - 0.0291924i) q^{36} +(-1.57598 + 0.366479i) q^{37} +(1.89088 - 0.555213i) q^{43} +(0.00368049 - 0.128834i) q^{44} +(-1.00712 + 0.823519i) q^{46} +(-0.564443 - 0.825472i) q^{49} +(-0.722533 - 0.590812i) q^{50} +(-1.52561 - 0.264017i) q^{53} +(0.437693 + 0.958414i) q^{56} +(0.0371501 + 0.0382265i) q^{58} +(0.696938 + 0.717132i) q^{63} +(-0.277993 - 1.05760i) q^{64} +(-0.211212 + 0.462490i) q^{67} +(-1.42616 - 1.16617i) q^{71} +(-0.594714 - 0.869741i) q^{72} +(-1.31497 - 0.742599i) q^{74} +(-0.564443 + 0.825472i) q^{77} +(-0.582954 + 0.852543i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(1.65061 + 0.811551i) q^{86} +(0.734314 - 0.755591i) q^{88} +(0.179359 + 0.0102561i) q^{92} +(0.132827 - 0.923835i) q^{98} +(0.415415 - 0.909632i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 2 q^{2} + 3 q^{4} + q^{7} - q^{8} - 10 q^{9}+O(q^{10}) \) 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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