LMFDB - Embedded newform 1152.2.w.b.143.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(143,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1152.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.w (of order $8$, degree $4$, not 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:	$9.19876631285$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			143.3
Character	$\chi$	$=$	1152.143
Dual form			1152.2.w.b.1007.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.739921 + 1.78633i) q^{5} +(-0.385417 + 0.385417i) q^{7} +O(q^{10})$	$q+(-0.739921 + 1.78633i) q^{5} +(-0.385417 + 0.385417i) q^{7} +(2.36398 - 5.70716i) q^{11} +(-2.30916 + 0.956485i) q^{13} +5.05518 q^{17} +(1.27305 + 3.07341i) q^{19} +(2.28291 - 2.28291i) q^{23} +(0.892052 + 0.892052i) q^{25} +(0.735171 - 0.304518i) q^{29} +3.40740i q^{31} +(-0.403302 - 0.973658i) q^{35} +(9.56094 + 3.96027i) q^{37} +(5.27801 + 5.27801i) q^{41} +(-2.53597 - 1.05043i) q^{43} +6.85609i q^{47} +6.70291i q^{49} +(-7.45793 - 3.08917i) q^{53} +(8.44569 + 8.44569i) q^{55} +(-6.14066 - 2.54355i) q^{59} +(2.67989 + 6.46983i) q^{61} -4.83264i q^{65} +(-10.2890 + 4.26184i) q^{67} +(6.37064 + 6.37064i) q^{71} +(9.03739 - 9.03739i) q^{73} +(1.28852 + 3.11075i) q^{77} -1.22095 q^{79} +(14.8416 - 6.14761i) q^{83} +(-3.74043 + 9.03021i) q^{85} +(4.97492 - 4.97492i) q^{89} +(0.521343 - 1.25863i) q^{91} -6.43208 q^{95} +1.23680 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 8 q^{11} - 16 q^{29} - 24 q^{35} - 16 q^{53} + 32 q^{55} - 32 q^{59} + 32 q^{61} + 16 q^{67} - 16 q^{71} - 16 q^{77} + 32 q^{79} + 40 q^{83} + 48 q^{91} + 80 q^{95}+O(q^{100}) $ 32 * q + 8 * q^11 - 16 * q^29 - 24 * q^35 - 16 * q^53 + 32 * q^55 - 32 * q^59 + 32 * q^61 + 16 * q^67 - 16 * q^71 - 16 * q^77 + 32 * q^79 + 40 * q^83 + 48 * q^91 + 80 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{8}\right)$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.739921	+	1.78633i	−0.330903	+	0.798870i	0.667618	+	0.744504i	$0.267314\pi$
$5$	−0.739921	+	1.78633i	−0.330903	+	0.798870i	−0.998521	+	0.0543661i	$0.982686\pi$
$6$		0			0
$7$	−0.385417	+	0.385417i	−0.145674	+	0.145674i	−0.776182	−	0.630509i	$-0.782846\pi$
$7$	−0.385417	+	0.385417i	−0.145674	+	0.145674i	0.630509	+	0.776182i	$0.282846\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.36398	−	5.70716i	0.712767	−	1.72077i	0.0197998	−	0.999804i	$-0.493697\pi$
$11$	2.36398	−	5.70716i	0.712767	−	1.72077i	0.692968	−	0.720969i	$-0.256303\pi$
$12$		0			0
$13$	−2.30916	+	0.956485i	−0.640446	+	0.265281i	−0.679184	−	0.733968i	$-0.737666\pi$
$13$	−2.30916	+	0.956485i	−0.640446	+	0.265281i	0.0387383	+	0.999249i	$0.487666\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	5.05518			1.22606			0.613031	−	0.790059i	$-0.289950\pi$
$17$	5.05518			1.22606			0.613031	+	0.790059i	$0.289950\pi$
$18$		0			0
$19$	1.27305	+	3.07341i	0.292057	+	0.705089i	0.999999	−	0.00118164i	$-0.000376129\pi$
$19$	1.27305	+	3.07341i	0.292057	+	0.705089i	−0.707942	+	0.706271i	$0.750376\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.28291	−	2.28291i	0.476020	−	0.476020i	−0.427837	−	0.903856i	$-0.640724\pi$
$23$	2.28291	−	2.28291i	0.476020	−	0.476020i	0.903856	+	0.427837i	$0.140724\pi$
$24$		0			0
$25$	0.892052	+	0.892052i	0.178410	+	0.178410i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.735171	−	0.304518i	0.136518	−	0.0565475i	−0.313379	−	0.949628i	$-0.601461\pi$
$29$	0.735171	−	0.304518i	0.136518	−	0.0565475i	0.449896	+	0.893081i	$0.351461\pi$
$30$		0			0
$31$			3.40740i			0.611988i	0.952033	+	0.305994i	$0.0989887\pi$
$31$			3.40740i			0.611988i	−0.952033	+	0.305994i	$0.901011\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.403302	−	0.973658i	−0.0681705	−	0.164578i
$36$		0			0
$37$	9.56094	+	3.96027i	1.57181	+	0.651065i	0.987089	−	0.160170i	$-0.0512043\pi$
$37$	9.56094	+	3.96027i	1.57181	+	0.651065i	0.584720	+	0.811235i	$0.301204\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.27801	+	5.27801i	0.824287	+	0.824287i	0.986720	−	0.162432i	$-0.0519340\pi$
$41$	5.27801	+	5.27801i	0.824287	+	0.824287i	−0.162432	+	0.986720i	$0.551934\pi$
$42$		0			0
$43$	−2.53597	−	1.05043i	−0.386732	−	0.160190i	0.180842	−	0.983512i	$-0.442118\pi$
$43$	−2.53597	−	1.05043i	−0.386732	−	0.160190i	−0.567574	+	0.823323i	$0.692118\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			6.85609i			1.00006i	0.866007	+	0.500031i	$0.166678\pi$
$47$			6.85609i			1.00006i	−0.866007	+	0.500031i	$0.833322\pi$
$48$		0			0
$49$			6.70291i			0.957558i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−7.45793	−	3.08917i	−1.02442	−	0.424331i	−0.193728	−	0.981055i	$-0.562058\pi$
$53$	−7.45793	−	3.08917i	−1.02442	−	0.424331i	−0.830697	+	0.556725i	$0.812058\pi$
$54$		0			0
$55$	8.44569	+	8.44569i	1.13882	+	1.13882i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.14066	−	2.54355i	−0.799446	−	0.331142i	−0.0547117	−	0.998502i	$-0.517424\pi$
$59$	−6.14066	−	2.54355i	−0.799446	−	0.331142i	−0.744735	+	0.667361i	$0.767424\pi$
$60$		0			0
$61$	2.67989	+	6.46983i	0.343125	+	0.828376i	0.997396	+	0.0721165i	$0.0229753\pi$
$61$	2.67989	+	6.46983i	0.343125	+	0.828376i	−0.654272	+	0.756260i	$0.727025\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	4.83264i		−	0.599415i
$66$		0			0
$67$	−10.2890	+	4.26184i	−1.25700	+	0.520666i	−0.908987	−	0.416824i	$-0.863143\pi$
$67$	−10.2890	+	4.26184i	−1.25700	+	0.520666i	−0.348012	+	0.937490i	$0.613143\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	6.37064	+	6.37064i	0.756056	+	0.756056i	0.975602	−	0.219546i	$-0.0704577\pi$
$71$	6.37064	+	6.37064i	0.756056	+	0.756056i	−0.219546	+	0.975602i	$0.570458\pi$
$72$		0			0
$73$	9.03739	−	9.03739i	1.05775	−	1.05775i	0.0595198	−	0.998227i	$-0.481043\pi$
$73$	9.03739	−	9.03739i	1.05775	−	1.05775i	0.998227	−	0.0595198i	$-0.0189570\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.28852	+	3.11075i	0.146840	+	0.354503i
$78$		0			0
$79$	−1.22095			−0.137367			−0.0686837	−	0.997638i	$-0.521880\pi$
$79$	−1.22095			−0.137367			−0.0686837	+	0.997638i	$0.521880\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	14.8416	−	6.14761i	1.62908	−	0.674788i	0.633953	−	0.773372i	$-0.281431\pi$
$83$	14.8416	−	6.14761i	1.62908	−	0.674788i	0.995129	+	0.0985841i	$0.0314314\pi$
$84$		0			0
$85$	−3.74043	+	9.03021i	−0.405707	+	0.979464i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.97492	−	4.97492i	0.527340	−	0.527340i	−0.392438	−	0.919778i	$-0.628368\pi$
$89$	4.97492	−	4.97492i	0.527340	−	0.527340i	0.919778	+	0.392438i	$0.128368\pi$
$90$		0			0
$91$	0.521343	−	1.25863i	0.0546516	−	0.131941i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−6.43208			−0.659917
$96$		0			0
$97$	1.23680			0.125579			0.0627893	−	0.998027i	$-0.480000\pi$
$97$	1.23680			0.125579			0.0627893	+	0.998027i	$0.480000\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.61006	−	13.5439i	0.558222	−	1.34767i	−0.352950	−	0.935642i	$-0.614821\pi$
$101$	5.61006	−	13.5439i	0.558222	−	1.34767i	0.911172	−	0.412025i	$-0.135179\pi$
$102$		0			0
$103$	13.0799	−	13.0799i	1.28880	−	1.28880i	0.353279	−	0.935518i	$-0.385067\pi$
$103$	13.0799	−	13.0799i	1.28880	−	1.28880i	0.935518	−	0.353279i	$-0.114933\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.16330	−	2.80844i	0.112460	−	0.271502i	−0.857622	−	0.514281i	$-0.828059\pi$
$107$	1.16330	−	2.80844i	0.112460	−	0.271502i	0.970082	+	0.242779i	$0.0780588\pi$
$108$		0			0
$109$	−13.5958	+	5.63158i	−1.30225	+	0.539408i	−0.922612	−	0.385729i	$-0.873950\pi$
$109$	−13.5958	+	5.63158i	−1.30225	+	0.539408i	−0.379634	+	0.925137i	$0.623950\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	13.6829			1.28718			0.643591	−	0.765369i	$-0.277444\pi$
$113$	13.6829			1.28718			0.643591	+	0.765369i	$0.277444\pi$
$114$		0			0
$115$	2.38885	+	5.76720i	0.222761	+	0.537794i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.94835	+	1.94835i	−0.178605	+	0.178605i
$120$		0			0
$121$	−19.2051	−	19.2051i	−1.74591	−	1.74591i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−11.1852	+	4.63305i	−1.00043	+	0.414393i
$126$		0			0
$127$		−	8.19707i		−	0.727372i	−0.931522	−	0.363686i	$-0.881518\pi$
$127$		−	8.19707i		−	0.727372i	0.931522	−	0.363686i	$-0.118482\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1.61003	+	3.88695i	0.140669	+	0.339604i	0.978476	−	0.206362i	$-0.0661626\pi$
$131$	1.61003	+	3.88695i	0.140669	+	0.339604i	−0.837807	+	0.545967i	$0.816163\pi$
$132$		0			0
$133$	−1.67520	−	0.693890i	−0.145258	−	0.0601679i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.79006	−	6.79006i	−0.580114	−	0.580114i	0.354821	−	0.934934i	$-0.384542\pi$
$137$	−6.79006	−	6.79006i	−0.580114	−	0.580114i	−0.934934	+	0.354821i	$0.884542\pi$
$138$		0			0
$139$	3.08589	+	1.27822i	0.261742	+	0.108417i	0.509695	−	0.860355i	$-0.329758\pi$
$139$	3.08589	+	1.27822i	0.261742	+	0.108417i	−0.247954	+	0.968772i	$0.579758\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			15.4399i			1.29115i
$144$		0			0
$145$			1.53857i			0.127772i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−8.40712	−	3.48234i	−0.688738	−	0.285285i	0.0107364	−	0.999942i	$-0.496582\pi$
$149$	−8.40712	−	3.48234i	−0.688738	−	0.285285i	−0.699474	+	0.714658i	$0.746582\pi$
$150$		0			0
$151$	13.7649	+	13.7649i	1.12017	+	1.12017i	0.991715	+	0.128459i	$0.0410032\pi$
$151$	13.7649	+	13.7649i	1.12017	+	1.12017i	0.128459	+	0.991715i	$0.458997\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6.08674	−	2.52121i	−0.488899	−	0.202508i
$156$		0			0
$157$	1.16741	+	2.81838i	0.0931694	+	0.224931i	0.963593	−	0.267372i	$-0.0861553\pi$
$157$	1.16741	+	2.81838i	0.0931694	+	0.224931i	−0.870424	+	0.492303i	$0.836155\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			1.75974i			0.138687i
$162$		0			0
$163$	−11.1679	+	4.62591i	−0.874740	+	0.362329i	−0.774455	−	0.632630i	$-0.781976\pi$
$163$	−11.1679	+	4.62591i	−0.874740	+	0.362329i	−0.100285	+	0.994959i	$0.531976\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.51551	−	2.51551i	−0.194656	−	0.194656i	0.603049	−	0.797704i	$-0.293952\pi$
$167$	−2.51551	−	2.51551i	−0.194656	−	0.194656i	−0.797704	+	0.603049i	$0.793952\pi$
$168$		0			0
$169$	−4.77503	+	4.77503i	−0.367310	+	0.367310i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.737563	+	1.78063i	0.0560759	+	0.135379i	0.949434	−	0.313965i	$-0.101658\pi$
$173$	0.737563	+	1.78063i	0.0560759	+	0.135379i	−0.893359	+	0.449344i	$0.851658\pi$
$174$		0			0
$175$	−0.687623			−0.0519794
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−9.47042	+	3.92278i	−0.707852	+	0.293202i	−0.707416	−	0.706798i	$-0.750139\pi$
$179$	−9.47042	+	3.92278i	−0.707852	+	0.293202i	−0.000436715		1.00000i	$0.500139\pi$
$180$		0			0
$181$	9.91984	−	23.9486i	0.737336	−	1.78009i	0.120927	−	0.992661i	$-0.461413\pi$
$181$	9.91984	−	23.9486i	0.737336	−	1.78009i	0.616410	−	0.787426i	$-0.288587\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−14.1487	+	14.1487i	−1.04023	+	1.04023i
$186$		0			0
$187$	11.9504	−	28.8507i	0.873897	−	2.10977i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	3.03200			0.219388			0.109694	−	0.993965i	$-0.465013\pi$
$191$	3.03200			0.219388			0.109694	+	0.993965i	$0.465013\pi$
$192$		0			0
$193$	4.75813			0.342498			0.171249	−	0.985228i	$-0.445220\pi$
$193$	4.75813			0.342498			0.171249	+	0.985228i	$0.445220\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3.20309	+	7.73295i	−0.228211	+	0.550950i	−0.995960	−	0.0898012i	$-0.971377\pi$
$197$	−3.20309	+	7.73295i	−0.228211	+	0.550950i	0.767749	+	0.640751i	$0.221377\pi$
$198$		0			0
$199$	−15.9060	+	15.9060i	−1.12755	+	1.12755i	−0.136973	+	0.990575i	$0.543737\pi$
$199$	−15.9060	+	15.9060i	−1.12755	+	1.12755i	−0.990575	+	0.136973i	$0.956263\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.165981	+	0.400713i	−0.0116496	+	0.0281245i
$204$		0			0
$205$	−13.3336	+	5.52295i	−0.931257	+	0.385739i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	20.5499			1.42147
$210$		0			0
$211$	−2.38241	−	5.75165i	−0.164012	−	0.395960i	0.820412	−	0.571773i	$-0.193744\pi$
$211$	−2.38241	−	5.75165i	−0.164012	−	0.395960i	−0.984423	+	0.175814i	$0.943744\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	3.75284	−	3.75284i	0.255941	−	0.255941i
$216$		0			0
$217$	−1.31327	−	1.31327i	−0.0891506	−	0.0891506i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−11.6732	+	4.83521i	−0.785226	+	0.325251i
$222$		0			0
$223$		−	24.2829i		−	1.62611i	−0.582190	−	0.813053i	$-0.697804\pi$
$223$		−	24.2829i		−	1.62611i	0.582190	−	0.813053i	$-0.302196\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.57334	−	8.62682i	−0.237171	−	0.572582i	0.759817	−	0.650137i	$-0.225289\pi$
$227$	−3.57334	−	8.62682i	−0.237171	−	0.572582i	−0.996988	+	0.0775552i	$0.975289\pi$
$228$		0			0
$229$	14.4317	+	5.97779i	0.953672	+	0.395024i	0.804610	−	0.593804i	$-0.202375\pi$
$229$	14.4317	+	5.97779i	0.953672	+	0.395024i	0.149062	+	0.988828i	$0.452375\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−6.50138	−	6.50138i	−0.425920	−	0.425920i	0.461316	−	0.887236i	$-0.347377\pi$
$233$	−6.50138	−	6.50138i	−0.425920	−	0.425920i	−0.887236	+	0.461316i	$0.847377\pi$
$234$		0			0
$235$	−12.2472	−	5.07296i	−0.798920	−	0.330923i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			19.9787i			1.29232i	0.763203	+	0.646159i	$0.223626\pi$
$239$			19.9787i			1.29232i	−0.763203	+	0.646159i	$0.776374\pi$
$240$		0			0
$241$		−	0.606349i		−	0.0390584i	−0.999809	−	0.0195292i	$-0.993783\pi$
$241$		−	0.606349i		−	0.0390584i	0.999809	−	0.0195292i	$-0.00621673\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−11.9736	−	4.95962i	−0.764964	−	0.316859i
$246$		0			0
$247$	−5.87935	−	5.87935i	−0.374094	−	0.374094i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−14.5988	−	6.04703i	−0.921470	−	0.381685i	−0.129034	−	0.991640i	$-0.541187\pi$
$251$	−14.5988	−	6.04703i	−0.921470	−	0.381685i	−0.792436	+	0.609955i	$0.791187\pi$
$252$		0			0
$253$	−7.63217	−	18.4257i	−0.479830	−	1.15841i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			10.5962i			0.660974i	0.943811	+	0.330487i	$0.107213\pi$
$257$			10.5962i			0.660974i	−0.943811	+	0.330487i	$0.892787\pi$
$258$		0			0
$259$	−5.21130	+	2.15859i	−0.323815	+	0.134128i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−19.2991	−	19.2991i	−1.19004	−	1.19004i	−0.977057	−	0.212979i	$-0.931683\pi$
$263$	−19.2991	−	19.2991i	−1.19004	−	1.19004i	−0.212979	−	0.977057i	$-0.568317\pi$
$264$		0			0
$265$	11.0366	−	11.0366i	0.677970	−	0.677970i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	4.57782	+	11.0518i	0.279114	+	0.673842i	0.999812	−	0.0194081i	$-0.00617818\pi$
$269$	4.57782	+	11.0518i	0.279114	+	0.673842i	−0.720697	+	0.693250i	$0.756178\pi$
$270$		0			0
$271$	−29.0069			−1.76204			−0.881022	−	0.473075i	$-0.843144\pi$
$271$	−29.0069			−1.76204			−0.881022	+	0.473075i	$0.843144\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	7.19988	−	2.98229i	0.434169	−	0.179839i
$276$		0			0
$277$	3.29625	−	7.95785i	0.198053	−	0.478141i	−0.793385	−	0.608720i	$-0.791683\pi$
$277$	3.29625	−	7.95785i	0.198053	−	0.478141i	0.991438	+	0.130578i	$0.0416834\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.61069	+	6.61069i	−0.394361	+	0.394361i	−0.876238	−	0.481878i	$-0.839955\pi$
$281$	−6.61069	+	6.61069i	−0.394361	+	0.394361i	0.481878	+	0.876238i	$0.339955\pi$
$282$		0			0
$283$	0.300555	−	0.725605i	0.0178662	−	0.0431327i	−0.914695	−	0.404146i	$-0.867569\pi$
$283$	0.300555	−	0.725605i	0.0178662	−	0.0431327i	0.932561	+	0.361013i	$0.117569\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.06847			−0.240154
$288$		0			0
$289$	8.55486			0.503227
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.400806	−	0.967632i	0.0234154	−	0.0565297i	−0.911739	−	0.410769i	$-0.865260\pi$
$293$	0.400806	−	0.967632i	0.0234154	−	0.0565297i	0.935155	+	0.354239i	$0.115260\pi$
$294$		0			0
$295$	9.08721	−	9.08721i	0.529078	−	0.529078i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.08803	+	7.45517i	−0.178586	+	0.431144i
$300$		0			0
$301$	1.38226	−	0.572551i	0.0796721	−	0.0330013i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−13.5401			−0.775306
$306$		0			0
$307$	3.22266	+	7.78018i	0.183927	+	0.444038i	0.988769	−	0.149450i	$-0.0477503\pi$
$307$	3.22266	+	7.78018i	0.183927	+	0.444038i	−0.804843	+	0.593488i	$0.797750\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−7.17660	+	7.17660i	−0.406948	+	0.406948i	−0.880673	−	0.473725i	$-0.842909\pi$
$311$	−7.17660	+	7.17660i	−0.406948	+	0.406948i	0.473725	+	0.880673i	$0.342909\pi$
$312$		0			0
$313$	0.108611	+	0.108611i	0.00613907	+	0.00613907i	0.710170	−	0.704031i	$-0.248618\pi$
$313$	0.108611	+	0.108611i	0.00613907	+	0.00613907i	−0.704031	+	0.710170i	$0.748618\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	9.89983	−	4.10065i	0.556030	−	0.230315i	−0.0869307	−	0.996214i	$-0.527706\pi$
$317$	9.89983	−	4.10065i	0.556030	−	0.230315i	0.642961	+	0.765899i	$0.277706\pi$
$318$		0			0
$319$		−	4.91561i		−	0.275221i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	6.43549	+	15.5367i	0.358080	+	0.864483i
$324$		0			0
$325$	−2.91312	−	1.20666i	−0.161591	−	0.0669332i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−2.64245	−	2.64245i	−0.145683	−	0.145683i
$330$		0			0
$331$	14.7254	+	6.09946i	0.809381	+	0.335257i	0.748707	−	0.662901i	$-0.230675\pi$
$331$	14.7254	+	6.09946i	0.809381	+	0.335257i	0.0606740	+	0.998158i	$0.480675\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		−	21.5329i		−	1.17647i
$336$		0			0
$337$			15.5033i			0.844517i	0.906475	+	0.422259i	$0.138763\pi$
$337$			15.5033i			0.844517i	−0.906475	+	0.422259i	$0.861237\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	19.4466	+	8.05504i	1.05309	+	0.436205i
$342$		0			0
$343$	−5.28133	−	5.28133i	−0.285165	−	0.285165i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−0.714667	−	0.296025i	−0.0383654	−	0.0158914i	0.363418	−	0.931626i	$-0.381610\pi$
$347$	−0.714667	−	0.296025i	−0.0383654	−	0.0158914i	−0.401784	+	0.915735i	$0.631610\pi$
$348$		0			0
$349$	−3.21246	−	7.75558i	−0.171959	−	0.415146i	0.814280	−	0.580473i	$-0.197132\pi$
$349$	−3.21246	−	7.75558i	−0.171959	−	0.415146i	−0.986239	+	0.165326i	$0.947132\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	11.9668i		−	0.636927i	−0.947935	−	0.318463i	$-0.896833\pi$
$353$		−	11.9668i		−	0.636927i	0.947935	−	0.318463i	$-0.103167\pi$
$354$		0			0
$355$	−16.0938	+	6.66628i	−0.854171	+	0.353809i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	10.0179	+	10.0179i	0.528723	+	0.528723i	0.920191	−	0.391469i	$-0.128033\pi$
$359$	10.0179	+	10.0179i	0.528723	+	0.528723i	−0.391469	+	0.920191i	$0.628033\pi$
$360$		0			0
$361$	5.60982	−	5.60982i	0.295254	−	0.295254i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	9.45679	+	22.8307i	0.494991	+	1.19501i
$366$		0			0
$367$	−26.0524			−1.35992			−0.679961	−	0.733248i	$-0.738004\pi$
$367$	−26.0524			−1.35992			−0.679961	+	0.733248i	$0.738004\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	4.06503	−	1.68379i	0.211046	−	0.0874180i
$372$		0			0
$373$	1.11398	−	2.68939i	0.0576797	−	0.139251i	−0.892412	−	0.451221i	$-0.850989\pi$
$373$	1.11398	−	2.68939i	0.0576797	−	0.139251i	0.950092	+	0.311970i	$0.100989\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.40636	+	1.40636i	−0.0724312	+	0.0724312i
$378$		0			0
$379$	2.87476	−	6.94029i	0.147667	−	0.356499i	−0.832688	−	0.553743i	$-0.813199\pi$
$379$	2.87476	−	6.94029i	0.147667	−	0.356499i	0.980354	+	0.197244i	$0.0631991\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−18.2355			−0.931792			−0.465896	−	0.884839i	$-0.654268\pi$
$383$	−18.2355			−0.931792			−0.465896	+	0.884839i	$0.654268\pi$
$384$		0			0
$385$	−6.51022			−0.331791
$386$		0			0
$387$		0			0
$388$		0			0
$389$	9.18501	−	22.1746i	0.465699	−	1.12430i	−0.500324	−	0.865838i	$-0.666786\pi$
$389$	9.18501	−	22.1746i	0.465699	−	1.12430i	0.966023	−	0.258458i	$-0.0832143\pi$
$390$		0			0
$391$	11.5405	−	11.5405i	0.583629	−	0.583629i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.903405	−	2.18101i	0.0454552	−	0.109739i
$396$		0			0
$397$	3.77144	−	1.56218i	0.189283	−	0.0784037i	−0.286029	−	0.958221i	$-0.592335\pi$
$397$	3.77144	−	1.56218i	0.189283	−	0.0784037i	0.475312	+	0.879817i	$0.342335\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−32.5110			−1.62352			−0.811761	−	0.583990i	$-0.801491\pi$
$401$	−32.5110			−1.62352			−0.811761	+	0.583990i	$0.801491\pi$
$402$		0			0
$403$	−3.25913	−	7.86824i	−0.162349	−	0.391945i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	45.2038	−	45.2038i	2.24067	−	2.24067i
$408$		0			0
$409$	−15.0850	−	15.0850i	−0.745903	−	0.745903i	0.227804	−	0.973707i	$-0.426845\pi$
$409$	−15.0850	−	15.0850i	−0.745903	−	0.745903i	−0.973707	+	0.227804i	$0.926845\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	3.34704	−	1.38639i	0.164697	−	0.0682197i
$414$		0			0
$415$			31.0608i			1.52471i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	6.41529	+	15.4879i	0.313407	+	0.756632i	0.999574	+	0.0291878i	$0.00929208\pi$
$419$	6.41529	+	15.4879i	0.313407	+	0.756632i	−0.686167	+	0.727444i	$0.740708\pi$
$420$		0			0
$421$	−13.8675	−	5.74412i	−0.675863	−	0.279951i	0.0182335	−	0.999834i	$-0.494196\pi$
$421$	−13.8675	−	5.74412i	−0.675863	−	0.279951i	−0.694096	+	0.719882i	$0.744196\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	4.50948	+	4.50948i	0.218742	+	0.218742i
$426$		0			0
$427$	−3.52645	−	1.46070i	−0.170657	−	0.0706884i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	39.1679i		−	1.88665i	−0.331870	−	0.943325i	$-0.607680\pi$
$431$		−	39.1679i		−	1.88665i	0.331870	−	0.943325i	$-0.392320\pi$
$432$		0			0
$433$			20.6897i			0.994283i	0.867669	+	0.497142i	$0.165617\pi$
$433$			20.6897i			0.994283i	−0.867669	+	0.497142i	$0.834383\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	9.92258	+	4.11007i	0.474661	+	0.196611i
$438$		0			0
$439$	7.49686	+	7.49686i	0.357805	+	0.357805i	0.863003	−	0.505198i	$-0.168581\pi$
$439$	7.49686	+	7.49686i	0.357805	+	0.357805i	−0.505198	+	0.863003i	$0.668581\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−5.58792	−	2.31459i	−0.265490	−	0.109970i	0.245968	−	0.969278i	$-0.420894\pi$
$443$	−5.58792	−	2.31459i	−0.265490	−	0.109970i	−0.511458	+	0.859308i	$0.670894\pi$
$444$		0			0
$445$	5.20579	+	12.5679i	0.246778	+	0.595775i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			9.22927i			0.435556i	0.975998	+	0.217778i	$0.0698809\pi$
$449$			9.22927i			0.435556i	−0.975998	+	0.217778i	$0.930119\pi$
$450$		0			0
$451$	42.5996	−	17.6453i	2.00594	−	0.830886i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.86258	+	1.86258i	0.0873190	+	0.0873190i
$456$		0			0
$457$	−15.0540	+	15.0540i	−0.704197	+	0.704197i	−0.965309	−	0.261112i	$-0.915911\pi$
$457$	−15.0540	+	15.0540i	−0.704197	+	0.704197i	0.261112	+	0.965309i	$0.415911\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2.11682	−	5.11046i	−0.0985902	−	0.238018i	0.866887	−	0.498504i	$-0.166117\pi$
$461$	−2.11682	−	5.11046i	−0.0985902	−	0.238018i	−0.965478	+	0.260486i	$0.916117\pi$
$462$		0			0
$463$	30.2844			1.40743			0.703717	−	0.710481i	$-0.251522\pi$
$463$	30.2844			1.40743			0.703717	+	0.710481i	$0.251522\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−12.9725	+	5.37338i	−0.600295	+	0.248650i	−0.662073	−	0.749439i	$-0.730323\pi$
$467$	−12.9725	+	5.37338i	−0.600295	+	0.248650i	0.0617775	+	0.998090i	$0.480323\pi$
$468$		0			0
$469$	2.32296	−	5.60813i	0.107264	−	0.258959i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−11.9900	+	11.9900i	−0.551300	+	0.551300i
$474$		0			0
$475$	−1.60602	+	3.87727i	−0.0736891	+	0.177901i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	2.51607			0.114962			0.0574810	−	0.998347i	$-0.481693\pi$
$479$	2.51607			0.114962			0.0574810	+	0.998347i	$0.481693\pi$
$480$		0			0
$481$	−25.8657			−1.17937
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.915138	+	2.20934i	−0.0415543	+	0.100321i
$486$		0			0
$487$	−1.66386	+	1.66386i	−0.0753965	+	0.0753965i	−0.743799	−	0.668403i	$-0.766978\pi$
$487$	−1.66386	+	1.66386i	−0.0753965	+	0.0753965i	0.668403	+	0.743799i	$0.266978\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−12.2708	+	29.6244i	−0.553775	+	1.33693i	0.360849	+	0.932624i	$0.382487\pi$
$491$	−12.2708	+	29.6244i	−0.553775	+	1.33693i	−0.914624	+	0.404306i	$0.867513\pi$
$492$		0			0
$493$	3.71642	−	1.53939i	0.167379	−	0.0693307i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.91070			−0.220275
$498$		0			0
$499$	13.7034	+	33.0830i	0.613450	+	1.48100i	0.859186	+	0.511663i	$0.170971\pi$
$499$	13.7034	+	33.0830i	0.613450	+	1.48100i	−0.245736	+	0.969337i	$0.579029\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−23.6161	+	23.6161i	−1.05299	+	1.05299i	−0.0544742	+	0.998515i	$0.517348\pi$
$503$	−23.6161	+	23.6161i	−1.05299	+	1.05299i	−0.998515	+	0.0544742i	$0.982652\pi$
$504$		0			0
$505$	20.0428	+	20.0428i	0.891894	+	0.891894i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	33.8424	−	14.0180i	1.50004	−	0.621336i	0.526565	−	0.850135i	$-0.323480\pi$
$509$	33.8424	−	14.0180i	1.50004	−	0.621336i	0.973474	+	0.228798i	$0.0734797\pi$
$510$		0			0
$511$			6.96632i			0.308172i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	13.6868	+	33.0430i	0.603115	+	1.45605i
$516$		0			0
$517$	39.1288	+	16.2077i	1.72088	+	0.712812i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.30745	+	1.30745i	0.0572804	+	0.0572804i	0.735167	−	0.677886i	$-0.237104\pi$
$521$	1.30745	+	1.30745i	0.0572804	+	0.0572804i	−0.677886	+	0.735167i	$0.737104\pi$
$522$		0			0
$523$	21.7896	+	9.02554i	0.952792	+	0.394660i	0.804280	−	0.594251i	$-0.202551\pi$
$523$	21.7896	+	9.02554i	0.952792	+	0.394660i	0.148513	+	0.988911i	$0.452551\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			17.2250i			0.750335i
$528$		0			0
$529$			12.5766i			0.546811i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−17.2361	−	7.13943i	−0.746579	−	0.309243i
$534$		0			0
$535$	4.15605	+	4.15605i	0.179682	+	0.179682i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	38.2546	+	15.8456i	1.64774	+	0.682516i
$540$		0			0
$541$	−3.04512	−	7.35157i	−0.130920	−	0.316069i	0.844803	−	0.535078i	$-0.179718\pi$
$541$	−3.04512	−	7.35157i	−0.130920	−	0.316069i	−0.975723	+	0.219009i	$0.929718\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		−	28.4536i		−	1.21882i
$546$		0			0
$547$	−5.38090	+	2.22884i	−0.230071	+	0.0952984i	−0.494741	−	0.869041i	$-0.664737\pi$
$547$	−5.38090	+	2.22884i	−0.230071	+	0.0952984i	0.264670	+	0.964339i	$0.414737\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	1.87182	+	1.87182i	0.0797421	+	0.0797421i
$552$		0			0
$553$	0.470574	−	0.470574i	0.0200108	−	0.0200108i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−8.63425	−	20.8449i	−0.365845	−	0.883228i	−0.994421	−	0.105480i	$-0.966362\pi$
$557$	−8.63425	−	20.8449i	−0.365845	−	0.883228i	0.628576	−	0.777748i	$-0.283638\pi$
$558$		0			0
$559$	6.86069			0.290176
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−17.1318	+	7.09624i	−0.722021	+	0.299071i	−0.713268	−	0.700891i	$-0.752786\pi$
$563$	−17.1318	+	7.09624i	−0.722021	+	0.299071i	−0.00875227	+	0.999962i	$0.502786\pi$
$564$		0			0
$565$	−10.1243	+	24.4422i	−0.425932	+	1.02829i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	15.5020	−	15.5020i	0.649877	−	0.649877i	−0.303086	−	0.952963i	$-0.598017\pi$
$569$	15.5020	−	15.5020i	0.649877	−	0.649877i	0.952963	+	0.303086i	$0.0980169\pi$
$570$		0			0
$571$	−11.3574	+	27.4193i	−0.475294	+	1.14746i	0.486499	+	0.873681i	$0.338274\pi$
$571$	−11.3574	+	27.4193i	−0.475294	+	1.14746i	−0.961793	+	0.273779i	$0.911726\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	4.07295			0.169854
$576$		0			0
$577$	19.6105			0.816396			0.408198	−	0.912893i	$-0.366157\pi$
$577$	19.6105			0.816396			0.408198	+	0.912893i	$0.366157\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−3.35082	+	8.08960i	−0.139016	+	0.335613i
$582$		0			0
$583$	−35.2608	+	35.2608i	−1.46035	+	1.46035i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	6.56890	−	15.8587i	0.271128	−	0.654560i	−0.728404	−	0.685147i	$-0.759738\pi$
$587$	6.56890	−	15.8587i	0.271128	−	0.654560i	0.999532	+	0.0305874i	$0.00973779\pi$
$588$		0			0
$589$	−10.4724	+	4.33779i	−0.431506	+	0.178736i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.287201			0.0117939			0.00589697	−	0.999983i	$-0.498123\pi$
$593$	0.287201			0.0117939			0.00589697	+	0.999983i	$0.498123\pi$
$594$		0			0
$595$	−2.03877	−	4.92202i	−0.0835813	−	0.201783i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	12.5596	−	12.5596i	0.513170	−	0.513170i	−0.402326	−	0.915496i	$-0.631798\pi$
$599$	12.5596	−	12.5596i	0.513170	−	0.513170i	0.915496	+	0.402326i	$0.131798\pi$
$600$		0			0
$601$	23.9708	+	23.9708i	0.977791	+	0.977791i	0.999759	−	0.0219673i	$-0.00699298\pi$
$601$	23.9708	+	23.9708i	0.977791	+	0.977791i	−0.0219673	+	0.999759i	$0.506993\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	48.5168	−	20.0963i	1.97249	−	0.817031i
$606$		0			0
$607$		−	27.9757i		−	1.13550i	−0.823202	−	0.567749i	$-0.807815\pi$
$607$		−	27.9757i		−	1.13550i	0.823202	−	0.567749i	$-0.192185\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−6.55774	−	15.8318i	−0.265298	−	0.640486i
$612$		0			0
$613$	−30.2175	−	12.5165i	−1.22047	−	0.505537i	−0.322913	−	0.946429i	$-0.604662\pi$
$613$	−30.2175	−	12.5165i	−1.22047	−	0.505537i	−0.897560	+	0.440892i	$0.854662\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−23.4695	−	23.4695i	−0.944848	−	0.944848i	0.0537086	−	0.998557i	$-0.482896\pi$
$617$	−23.4695	−	23.4695i	−0.944848	−	0.944848i	−0.998557	+	0.0537086i	$0.982896\pi$
$618$		0			0
$619$	16.2802	+	6.74349i	0.654357	+	0.271044i	0.685062	−	0.728485i	$-0.259775\pi$
$619$	16.2802	+	6.74349i	0.654357	+	0.271044i	−0.0307046	+	0.999529i	$0.509775\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$			3.83483i			0.153639i
$624$		0			0
$625$		−	17.1007i		−	0.684029i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	48.3323	+	20.0199i	1.92714	+	0.798246i
$630$		0			0
$631$	−18.7206	−	18.7206i	−0.745256	−	0.745256i	0.228328	−	0.973584i	$-0.426674\pi$
$631$	−18.7206	−	18.7206i	−0.745256	−	0.745256i	−0.973584	+	0.228328i	$0.926674\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	14.6426	+	6.06518i	0.581076	+	0.240689i
$636$		0			0
$637$	−6.41123	−	15.4781i	−0.254022	−	0.613264i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	39.5671i		−	1.56281i	−0.624026	−	0.781404i	$-0.714504\pi$
$641$		−	39.5671i		−	1.56281i	0.624026	−	0.781404i	$-0.285496\pi$
$642$		0			0
$643$	32.9323	−	13.6410i	1.29872	−	0.537949i	0.377149	−	0.926153i	$-0.376904\pi$
$643$	32.9323	−	13.6410i	1.29872	−	0.537949i	0.921573	+	0.388204i	$0.126904\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−15.1226	−	15.1226i	−0.594532	−	0.594532i	0.344320	−	0.938852i	$-0.388109\pi$
$647$	−15.1226	−	15.1226i	−0.594532	−	0.594532i	−0.938852	+	0.344320i	$0.888109\pi$
$648$		0			0
$649$	−29.0328	+	29.0328i	−1.13964	+	1.13964i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−5.76633	−	13.9212i	−0.225654	−	0.544777i	0.769985	−	0.638061i	$-0.220263\pi$
$653$	−5.76633	−	13.9212i	−0.225654	−	0.544777i	−0.995640	+	0.0932843i	$0.970263\pi$
$654$		0			0
$655$	−8.13465			−0.317847
$656$		0			0
$657$		0			0
$658$		0			0
$659$	21.9719	−	9.10108i	0.855905	−	0.354528i	0.0888005	−	0.996049i	$-0.471697\pi$
$659$	21.9719	−	9.10108i	0.855905	−	0.354528i	0.767105	+	0.641522i	$0.221697\pi$
$660$		0			0
$661$	6.04221	−	14.5872i	0.235015	−	0.567376i	−0.761739	−	0.647884i	$-0.775654\pi$
$661$	6.04221	−	14.5872i	0.235015	−	0.567376i	0.996754	+	0.0805079i	$0.0256542\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.47903	−	2.47903i	0.0961326	−	0.0961326i
$666$		0			0
$667$	0.983142	−	2.37351i	0.0380674	−	0.0919029i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	43.2595			1.67002
$672$		0			0
$673$	23.2501			0.896225			0.448113	−	0.893977i	$-0.352096\pi$
$673$	23.2501			0.896225			0.448113	+	0.893977i	$0.352096\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−8.28073	+	19.9914i	−0.318254	+	0.768333i	0.681093	+	0.732197i	$0.261505\pi$
$677$	−8.28073	+	19.9914i	−0.318254	+	0.768333i	−0.999347	+	0.0361363i	$0.988495\pi$
$678$		0			0
$679$	−0.476685	+	0.476685i	−0.0182935	+	0.0182935i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	6.09927	−	14.7249i	0.233382	−	0.563434i	−0.763189	−	0.646175i	$-0.776367\pi$
$683$	6.09927	−	14.7249i	0.233382	−	0.563434i	0.996571	+	0.0827411i	$0.0263674\pi$
$684$		0			0
$685$	17.1534	−	7.10516i	0.655397	−	0.271474i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	20.1763			0.768655
$690$		0			0
$691$	6.28104	+	15.1638i	0.238942	+	0.576857i	0.997174	−	0.0751281i	$-0.0239366\pi$
$691$	6.28104	+	15.1638i	0.238942	+	0.576857i	−0.758232	+	0.651985i	$0.773937\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.56663	+	4.56663i	−0.173222	+	0.173222i
$696$		0			0
$697$	26.6813	+	26.6813i	1.01063	+	1.01063i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−24.6746	+	10.2205i	−0.931946	+	0.386025i	−0.796416	−	0.604749i	$-0.793274\pi$
$701$	−24.6746	+	10.2205i	−0.931946	+	0.386025i	−0.135529	+	0.990773i	$0.543274\pi$
$702$		0			0
$703$			34.4263i			1.29841i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	3.05783	+	7.38225i	0.115001	+	0.277638i
$708$		0			0
$709$	−11.4821	−	4.75606i	−0.431221	−	0.178617i	0.156506	−	0.987677i	$-0.449977\pi$
$709$	−11.4821	−	4.75606i	−0.431221	−	0.178617i	−0.587727	+	0.809060i	$0.699977\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	7.77879	+	7.77879i	0.291318	+	0.291318i
$714$		0			0
$715$	−27.5806	−	11.4243i	−1.03146	−	0.427243i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	24.1182i		−	0.899455i	−0.893166	−	0.449728i	$-0.851521\pi$
$719$		−	24.1182i		−	0.899455i	0.893166	−	0.449728i	$-0.148479\pi$
$720$		0			0
$721$			10.0824i			0.375488i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	0.927456	+	0.384165i	0.0344449	+	0.0142675i
$726$		0			0
$727$	−23.8328	−	23.8328i	−0.883909	−	0.883909i	0.110020	−	0.993929i	$-0.464908\pi$
$727$	−23.8328	−	23.8328i	−0.883909	−	0.883909i	−0.993929	+	0.110020i	$0.964908\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−12.8198	−	5.31013i	−0.474157	−	0.196402i
$732$		0			0
$733$	7.22918	+	17.4528i	0.267016	+	0.644633i	0.999340	−	0.0363227i	$-0.0115644\pi$
$733$	7.22918	+	17.4528i	0.267016	+	0.644633i	−0.732324	+	0.680956i	$0.761564\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			68.7958i			2.53412i
$738$		0			0
$739$	−2.37240	+	0.982682i	−0.0872703	+	0.0361485i	−0.425892	−	0.904774i	$-0.640039\pi$
$739$	−2.37240	+	0.982682i	−0.0872703	+	0.0361485i	0.338621	+	0.940923i	$0.390039\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	9.84906	+	9.84906i	0.361327	+	0.361327i	0.864301	−	0.502974i	$-0.167761\pi$
$743$	9.84906	+	9.84906i	0.361327	+	0.361327i	−0.502974	+	0.864301i	$0.667761\pi$
$744$		0			0
$745$	12.4412	−	12.4412i	0.455810	−	0.455810i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	0.634067	+	1.53077i	0.0231683	+	0.0559333i
$750$		0			0
$751$	14.4324			0.526644			0.263322	−	0.964708i	$-0.415182\pi$
$751$	14.4324			0.526644			0.263322	+	0.964708i	$0.415182\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−34.7736	+	14.4037i	−1.26554	+	0.524205i
$756$		0			0
$757$	−12.5839	+	30.3803i	−0.457371	+	1.10419i	0.512088	+	0.858933i	$0.328872\pi$
$757$	−12.5839	+	30.3803i	−0.457371	+	1.10419i	−0.969458	+	0.245257i	$0.921128\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	10.8012	−	10.8012i	0.391543	−	0.391543i	−0.483694	−	0.875237i	$-0.660705\pi$
$761$	10.8012	−	10.8012i	0.391543	−	0.391543i	0.875237	+	0.483694i	$0.160705\pi$
$762$		0			0
$763$	3.06956	−	7.41057i	0.111125	−	0.268281i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	16.6126			0.599848
$768$		0			0
$769$	−31.6614			−1.14174			−0.570869	−	0.821041i	$-0.693394\pi$
$769$	−31.6614			−1.14174			−0.570869	+	0.821041i	$0.693394\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	7.73399	−	18.6715i	0.278172	−	0.671567i	−0.721613	−	0.692297i	$-0.756599\pi$
$773$	7.73399	−	18.6715i	0.278172	−	0.671567i	0.999785	+	0.0207297i	$0.00659894\pi$
$774$		0			0
$775$	−3.03958	+	3.03958i	−0.109185	+	0.109185i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−9.50234	+	22.9407i	−0.340457	+	0.821935i
$780$		0			0
$781$	51.4183	−	21.2982i	1.83989	−	0.762108i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−5.89833			−0.210520
$786$		0			0
$787$	−7.03017	−	16.9723i	−0.250598	−	0.604998i	0.747654	−	0.664088i	$-0.231180\pi$
$787$	−7.03017	−	16.9723i	−0.250598	−	0.604998i	−0.998253	+	0.0590900i	$0.981180\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−5.27363	+	5.27363i	−0.187509	+	0.187509i
$792$		0			0
$793$	−12.3766	−	12.3766i	−0.439505	−	0.439505i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−43.7568	+	18.1246i	−1.54994	+	0.642008i	−0.983306	−	0.181959i	$-0.941756\pi$
$797$	−43.7568	+	18.1246i	−1.54994	+	0.642008i	−0.566638	+	0.823967i	$0.691756\pi$
$798$		0			0
$799$			34.6588i			1.22614i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−30.2136	−	72.9421i	−1.06621	−	2.57407i
$804$		0			0
$805$	−3.14348	−	1.30207i	−0.110793	−	0.0458919i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	6.34143	+	6.34143i	0.222953	+	0.222953i	0.809741	−	0.586788i	$-0.199608\pi$
$809$	6.34143	+	6.34143i	0.222953	+	0.222953i	−0.586788	+	0.809741i	$0.699608\pi$
$810$		0			0
$811$	12.8711	+	5.33139i	0.451966	+	0.187210i	0.597042	−	0.802210i	$-0.296343\pi$
$811$	12.8711	+	5.33139i	0.451966	+	0.187210i	−0.145076	+	0.989421i	$0.546343\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		−	23.3724i		−	0.818699i
$816$		0			0
$817$		−	9.13134i		−	0.319465i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	12.6767	+	5.25088i	0.442421	+	0.183257i	0.592763	−	0.805377i	$-0.298037\pi$
$821$	12.6767	+	5.25088i	0.442421	+	0.183257i	−0.150341	+	0.988634i	$0.548037\pi$
$822$		0			0
$823$	21.6528	+	21.6528i	0.754770	+	0.754770i	0.975365	−	0.220596i	$-0.0708002\pi$
$823$	21.6528	+	21.6528i	0.754770	+	0.754770i	−0.220596	+	0.975365i	$0.570800\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	26.0418	+	10.7869i	0.905563	+	0.375096i	0.786356	−	0.617773i	$-0.211965\pi$
$827$	26.0418	+	10.7869i	0.905563	+	0.375096i	0.119206	+	0.992869i	$0.461965\pi$
$828$		0			0
$829$	5.29036	+	12.7721i	0.183742	+	0.443592i	0.988732	−	0.149696i	$-0.0478295\pi$
$829$	5.29036	+	12.7721i	0.183742	+	0.443592i	−0.804990	+	0.593288i	$0.797830\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$			33.8844i			1.17403i
$834$		0			0
$835$	6.35479	−	2.63224i	0.219917	−	0.0910924i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−14.9362	−	14.9362i	−0.515654	−	0.515654i	0.400600	−	0.916253i	$-0.368802\pi$
$839$	−14.9362	−	14.9362i	−0.515654	−	0.515654i	−0.916253	+	0.400600i	$0.868802\pi$
$840$		0			0
$841$	−20.0584	+	20.0584i	−0.691667	+	0.691667i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−4.99663	−	12.0629i	−0.171889	−	0.414977i
$846$		0			0
$847$	14.8039			0.508668
$848$		0			0
$849$		0			0
$850$		0			0
$851$	30.8677	−	12.7858i	1.05813	−	0.438292i
$852$		0			0
$853$	10.9239	−	26.3725i	0.374026	−	0.902978i	−0.619034	−	0.785364i	$-0.712476\pi$
$853$	10.9239	−	26.3725i	0.374026	−	0.902978i	0.993059	−	0.117613i	$-0.0375243\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−2.77666	+	2.77666i	−0.0948488	+	0.0948488i	−0.752939	−	0.658090i	$-0.771365\pi$
$857$	−2.77666	+	2.77666i	−0.0948488	+	0.0948488i	0.658090	+	0.752939i	$0.271365\pi$
$858$		0			0
$859$	−21.8775	+	52.8170i	−0.746452	+	1.80209i	−0.169100	+	0.985599i	$0.554086\pi$
$859$	−21.8775	+	52.8170i	−0.746452	+	1.80209i	−0.577352	+	0.816495i	$0.695914\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−35.8729			−1.22113			−0.610564	−	0.791967i	$-0.709057\pi$
$863$	−35.8729			−1.22113			−0.610564	+	0.791967i	$0.709057\pi$
$864$		0			0
$865$	−3.72653			−0.126706
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2.88630	+	6.96814i	−0.0979110	+	0.236378i
$870$		0			0
$871$	19.6825	−	19.6825i	0.666917	−	0.666917i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	2.52530	−	6.09661i	0.0853707	−	0.206103i
$876$		0			0
$877$	14.2190	−	5.88971i	0.480142	−	0.198882i	−0.129466	−	0.991584i	$-0.541326\pi$
$877$	14.2190	−	5.88971i	0.480142	−	0.198882i	0.609609	+	0.792702i	$0.291326\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−51.9652			−1.75075			−0.875377	−	0.483442i	$-0.839386\pi$
$881$	−51.9652			−1.75075			−0.875377	+	0.483442i	$0.839386\pi$
$882$		0			0
$883$	−20.6623	−	49.8832i	−0.695342	−	1.67870i	−0.733731	−	0.679440i	$-0.762223\pi$
$883$	−20.6623	−	49.8832i	−0.695342	−	1.67870i	0.0383892	−	0.999263i	$-0.487777\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−24.4215	+	24.4215i	−0.819994	+	0.819994i	−0.986107	−	0.166112i	$-0.946879\pi$
$887$	−24.4215	+	24.4215i	−0.819994	+	0.819994i	0.166112	+	0.986107i	$0.446879\pi$
$888$		0			0
$889$	3.15928	+	3.15928i	0.105959	+	0.105959i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−21.0716	+	8.72813i	−0.705133	+	0.292076i
$894$		0			0
$895$		−	19.8198i		−	0.662503i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1.03761	+	2.50502i	0.0346064	+	0.0835472i
$900$		0			0
$901$	−37.7012	−	15.6163i	−1.25601	−	0.520256i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	35.4402	+	35.4402i	1.17807	+	1.17807i
$906$		0			0
$907$	1.89537	+	0.785090i	0.0629349	+	0.0260685i	0.413929	−	0.910309i	$-0.364156\pi$
$907$	1.89537	+	0.785090i	0.0629349	+	0.0260685i	−0.350994	+	0.936378i	$0.614156\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	1.10306i		−	0.0365460i	−0.999833	−	0.0182730i	$-0.994183\pi$
$911$		−	1.10306i		−	0.0365460i	0.999833	−	0.0182730i	$-0.00581679\pi$
$912$		0			0
$913$		−	99.2364i		−	3.28425i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−2.11862	−	0.877563i	−0.0699632	−	0.0289797i
$918$		0			0
$919$	−21.1448	−	21.1448i	−0.697501	−	0.697501i	0.266370	−	0.963871i	$-0.414176\pi$
$919$	−21.1448	−	21.1448i	−0.697501	−	0.697501i	−0.963871	+	0.266370i	$0.914176\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−20.8042	−	8.61740i	−0.684780	−	0.283645i
$924$		0			0
$925$	4.99609	+	12.0616i	0.164270	+	0.396584i
$926$		0			0
$927$		0			0
$928$		0			0
$929$		−	8.59550i		−	0.282009i	−0.990009	−	0.141005i	$-0.954967\pi$
$929$		−	8.59550i		−	0.282009i	0.990009	−	0.141005i	$-0.0450332\pi$
$930$		0			0
$931$	−20.6008	+	8.53313i	−0.675164	+	0.279662i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	42.6945	+	42.6945i	1.39626	+	1.39626i
$936$		0			0
$937$	5.50940	−	5.50940i	0.179984	−	0.179984i	−0.611365	−	0.791349i	$-0.709379\pi$
$937$	5.50940	−	5.50940i	0.179984	−	0.179984i	0.791349	+	0.611365i	$0.209379\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	7.60686	+	18.3646i	0.247977	+	0.598669i	0.998032	−	0.0627064i	$-0.0199732\pi$
$941$	7.60686	+	18.3646i	0.247977	+	0.598669i	−0.750055	+	0.661375i	$0.769973\pi$
$942$		0			0
$943$	24.0985			0.784754
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.912836	−	0.378109i	0.0296632	−	0.0122869i	−0.367803	−	0.929904i	$-0.619890\pi$
$947$	0.912836	−	0.378109i	0.0296632	−	0.0122869i	0.397466	+	0.917617i	$0.369890\pi$
$948$		0			0
$949$	−12.2247	+	29.5129i	−0.396829	+	0.958030i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	32.2689	−	32.2689i	1.04529	−	1.04529i	0.0463673	−	0.998924i	$-0.485236\pi$
$953$	32.2689	−	32.2689i	1.04529	−	1.04529i	0.998924	−	0.0463673i	$-0.0147645\pi$
$954$		0			0
$955$	−2.24344	+	5.41614i	−0.0725960	+	0.175262i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	5.23400			0.169015
$960$		0			0
$961$	19.3896			0.625471
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−3.52064	+	8.49958i	−0.113334	+	0.273611i
$966$		0			0
$967$	−13.4056	+	13.4056i	−0.431097	+	0.431097i	−0.889001	−	0.457905i	$-0.848600\pi$
$967$	−13.4056	+	13.4056i	−0.431097	+	0.431097i	0.457905	+	0.889001i	$0.348600\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−7.93498	+	19.1567i	−0.254645	+	0.614769i	−0.998568	−	0.0534973i	$-0.982963\pi$
$971$	−7.93498	+	19.1567i	−0.254645	+	0.614769i	0.743923	+	0.668266i	$0.232963\pi$
$972$		0			0
$973$	−1.68200	+	0.696707i	−0.0539224	+	0.0223354i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−5.52723			−0.176832			−0.0884159	−	0.996084i	$-0.528180\pi$
$977$	−5.52723			−0.176832			−0.0884159	+	0.996084i	$0.528180\pi$
$978$		0			0
$979$	−16.6320	−	40.1533i	−0.531562	−	1.28330i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−28.1493	+	28.1493i	−0.897822	+	0.897822i	−0.995243	−	0.0974212i	$-0.968941\pi$
$983$	−28.1493	+	28.1493i	−0.897822	+	0.897822i	0.0974212	+	0.995243i	$0.468941\pi$
$984$		0			0
$985$	−11.4435	−	11.4435i	−0.364622	−	0.364622i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−8.18744	+	3.39135i	−0.260345	+	0.107839i
$990$		0			0
$991$		−	24.7160i		−	0.785131i	−0.919724	−	0.392565i	$-0.871588\pi$
$991$		−	24.7160i		−	0.785131i	0.919724	−	0.392565i	$-0.128412\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−16.6442	−	40.1825i	−0.527655	−	1.27387i
$996$		0			0
$997$	−26.8087	−	11.1045i	−0.849039	−	0.351684i	−0.0846280	−	0.996413i	$-0.526970\pi$
$997$	−26.8087	−	11.1045i	−0.849039	−	0.351684i	−0.764411	+	0.644729i	$0.776970\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.w.b.143.3		32
3.2	odd	2		1152.2.w.a.143.6		32
4.3	odd	2		288.2.w.a.251.6	yes	32
12.11	even	2		288.2.w.b.251.3	yes	32
32.13	even	8		288.2.w.b.179.3	yes	32
32.19	odd	8		1152.2.w.a.1007.6		32
96.77	odd	8		288.2.w.a.179.6	✓	32
96.83	even	8	inner	1152.2.w.b.1007.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.179.6	✓	32	96.77	odd	8
288.2.w.a.251.6	yes	32	4.3	odd	2
288.2.w.b.179.3	yes	32	32.13	even	8
288.2.w.b.251.3	yes	32	12.11	even	2
1152.2.w.a.143.6		32	3.2	odd	2
1152.2.w.a.1007.6		32	32.19	odd	8
1152.2.w.b.143.3		32	1.1	even	1	trivial
1152.2.w.b.1007.3		32	96.83	even	8	inner

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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:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.w (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.739921 + 1.78633i) q^{5} +(-0.385417 + 0.385417i) q^{7} +O(q^{10})\)	\(q+(-0.739921 + 1.78633i) q^{5} +(-0.385417 + 0.385417i) q^{7} +(2.36398 - 5.70716i) q^{11} +(-2.30916 + 0.956485i) q^{13} +5.05518 q^{17} +(1.27305 + 3.07341i) q^{19} +(2.28291 - 2.28291i) q^{23} +(0.892052 + 0.892052i) q^{25} +(0.735171 - 0.304518i) q^{29} +3.40740i q^{31} +(-0.403302 - 0.973658i) q^{35} +(9.56094 + 3.96027i) q^{37} +(5.27801 + 5.27801i) q^{41} +(-2.53597 - 1.05043i) q^{43} +6.85609i q^{47} +6.70291i q^{49} +(-7.45793 - 3.08917i) q^{53} +(8.44569 + 8.44569i) q^{55} +(-6.14066 - 2.54355i) q^{59} +(2.67989 + 6.46983i) q^{61} -4.83264i q^{65} +(-10.2890 + 4.26184i) q^{67} +(6.37064 + 6.37064i) q^{71} +(9.03739 - 9.03739i) q^{73} +(1.28852 + 3.11075i) q^{77} -1.22095 q^{79} +(14.8416 - 6.14761i) q^{83} +(-3.74043 + 9.03021i) q^{85} +(4.97492 - 4.97492i) q^{89} +(0.521343 - 1.25863i) q^{91} -6.43208 q^{95} +1.23680 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 8 q^{11} - 16 q^{29} - 24 q^{35} - 16 q^{53} + 32 q^{55} - 32 q^{59} + 32 q^{61} + 16 q^{67} - 16 q^{71} - 16 q^{77} + 32 q^{79} + 40 q^{83} + 48 q^{91} + 80 q^{95}+O(q^{100}) \) 32 * q + 8 * q^11 - 16 * q^29 - 24 * q^35 - 16 * q^53 + 32 * q^55 - 32 * q^59 + 32 * q^61 + 16 * q^67 - 16 * q^71 - 16 * q^77 + 32 * q^79 + 40 * q^83 + 48 * q^91 + 80 * q^95

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