LMFDB - Embedded newform 1152.2.w.b.1007.3

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			1007.3
Character	$\chi$	$=$	1152.1007
Dual form			1152.2.w.b.143.3

$q$-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 $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{8}\right)$

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	−0.998521	−	0.0543661i	$-0.982686\pi$
$5$	−0.739921	−	1.78633i	−0.330903	−	0.798870i	0.667618	−	0.744504i	$-0.267314\pi$
$6$		0			0
$7$	−0.385417	−	0.385417i	−0.145674	−	0.145674i	0.630509	−	0.776182i	$-0.282846\pi$
$7$	−0.385417	−	0.385417i	−0.145674	−	0.145674i	−0.776182	+	0.630509i	$0.782846\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.36398	+	5.70716i	0.712767	+	1.72077i	0.692968	+	0.720969i	$0.256303\pi$
$11$	2.36398	+	5.70716i	0.712767	+	1.72077i	0.0197998	+	0.999804i	$0.493697\pi$
$12$		0			0
$13$	−2.30916	−	0.956485i	−0.640446	−	0.265281i	0.0387383	−	0.999249i	$-0.487666\pi$
$13$	−2.30916	−	0.956485i	−0.640446	−	0.265281i	−0.679184	+	0.733968i	$0.737666\pi$
$14$		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	−0.707942	−	0.706271i	$-0.750376\pi$
$19$	1.27305	−	3.07341i	0.292057	−	0.705089i	0.999999	+	0.00118164i	$0.000376129\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.28291	+	2.28291i	0.476020	+	0.476020i	0.903856	−	0.427837i	$-0.140724\pi$
$23$	2.28291	+	2.28291i	0.476020	+	0.476020i	−0.427837	+	0.903856i	$0.640724\pi$
$24$		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	0.449896	−	0.893081i	$-0.351461\pi$
$29$	0.735171	+	0.304518i	0.136518	+	0.0565475i	−0.313379	+	0.949628i	$0.601461\pi$
$30$		0			0
$31$		−	3.40740i		−	0.611988i	−0.952033	−	0.305994i	$-0.901011\pi$
$31$		−	3.40740i		−	0.611988i	0.952033	−	0.305994i	$-0.0989887\pi$
$32$		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	0.584720	−	0.811235i	$-0.301204\pi$
$37$	9.56094	−	3.96027i	1.57181	−	0.651065i	0.987089	+	0.160170i	$0.0512043\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.27801	−	5.27801i	0.824287	−	0.824287i	−0.162432	−	0.986720i	$-0.551934\pi$
$41$	5.27801	−	5.27801i	0.824287	−	0.824287i	0.986720	+	0.162432i	$0.0519340\pi$
$42$		0			0
$43$	−2.53597	+	1.05043i	−0.386732	+	0.160190i	−0.567574	−	0.823323i	$-0.692118\pi$
$43$	−2.53597	+	1.05043i	−0.386732	+	0.160190i	0.180842	+	0.983512i	$0.442118\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	6.85609i		−	1.00006i	−0.866007	−	0.500031i	$-0.833322\pi$
$47$		−	6.85609i		−	1.00006i	0.866007	−	0.500031i	$-0.166678\pi$
$48$		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	−0.830697	−	0.556725i	$-0.812058\pi$
$53$	−7.45793	+	3.08917i	−1.02442	+	0.424331i	−0.193728	+	0.981055i	$0.562058\pi$
$54$		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	−0.744735	−	0.667361i	$-0.767424\pi$
$59$	−6.14066	+	2.54355i	−0.799446	+	0.331142i	−0.0547117	+	0.998502i	$0.517424\pi$
$60$		0			0
$61$	2.67989	−	6.46983i	0.343125	−	0.828376i	−0.654272	−	0.756260i	$-0.727025\pi$
$61$	2.67989	−	6.46983i	0.343125	−	0.828376i	0.997396	−	0.0721165i	$-0.0229753\pi$
$62$		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	−0.348012	−	0.937490i	$-0.613143\pi$
$67$	−10.2890	−	4.26184i	−1.25700	−	0.520666i	−0.908987	+	0.416824i	$0.863143\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	6.37064	−	6.37064i	0.756056	−	0.756056i	−0.219546	−	0.975602i	$-0.570458\pi$
$71$	6.37064	−	6.37064i	0.756056	−	0.756056i	0.975602	+	0.219546i	$0.0704577\pi$
$72$		0			0
$73$	9.03739	+	9.03739i	1.05775	+	1.05775i	0.998227	+	0.0595198i	$0.0189570\pi$
$73$	9.03739	+	9.03739i	1.05775	+	1.05775i	0.0595198	+	0.998227i	$0.481043\pi$
$74$		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	0.995129	−	0.0985841i	$-0.0314314\pi$
$83$	14.8416	+	6.14761i	1.62908	+	0.674788i	0.633953	+	0.773372i	$0.281431\pi$
$84$		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	0.919778	−	0.392438i	$-0.128368\pi$
$89$	4.97492	+	4.97492i	0.527340	+	0.527340i	−0.392438	+	0.919778i	$0.628368\pi$
$90$		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	0.911172	+	0.412025i	$0.135179\pi$
$101$	5.61006	+	13.5439i	0.558222	+	1.34767i	−0.352950	+	0.935642i	$0.614821\pi$
$102$		0			0
$103$	13.0799	+	13.0799i	1.28880	+	1.28880i	0.935518	+	0.353279i	$0.114933\pi$
$103$	13.0799	+	13.0799i	1.28880	+	1.28880i	0.353279	+	0.935518i	$0.385067\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.16330	+	2.80844i	0.112460	+	0.271502i	0.970082	−	0.242779i	$-0.0780588\pi$
$107$	1.16330	+	2.80844i	0.112460	+	0.271502i	−0.857622	+	0.514281i	$0.828059\pi$
$108$		0			0
$109$	−13.5958	−	5.63158i	−1.30225	−	0.539408i	−0.379634	−	0.925137i	$-0.623950\pi$
$109$	−13.5958	−	5.63158i	−1.30225	−	0.539408i	−0.922612	+	0.385729i	$0.873950\pi$
$110$		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	$0.118482\pi$
$127$			8.19707i			0.727372i	−0.931522	+	0.363686i	$0.881518\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1.61003	−	3.88695i	0.140669	−	0.339604i	−0.837807	−	0.545967i	$-0.816163\pi$
$131$	1.61003	−	3.88695i	0.140669	−	0.339604i	0.978476	+	0.206362i	$0.0661626\pi$
$132$		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	−0.934934	−	0.354821i	$-0.884542\pi$
$137$	−6.79006	+	6.79006i	−0.580114	+	0.580114i	0.354821	+	0.934934i	$0.384542\pi$
$138$		0			0
$139$	3.08589	−	1.27822i	0.261742	−	0.108417i	−0.247954	−	0.968772i	$-0.579758\pi$
$139$	3.08589	−	1.27822i	0.261742	−	0.108417i	0.509695	+	0.860355i	$0.329758\pi$
$140$		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	−0.699474	−	0.714658i	$-0.746582\pi$
$149$	−8.40712	+	3.48234i	−0.688738	+	0.285285i	0.0107364	+	0.999942i	$0.496582\pi$
$150$		0			0
$151$	13.7649	−	13.7649i	1.12017	−	1.12017i	0.128459	−	0.991715i	$-0.458997\pi$
$151$	13.7649	−	13.7649i	1.12017	−	1.12017i	0.991715	−	0.128459i	$-0.0410032\pi$
$152$		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	−0.870424	−	0.492303i	$-0.836155\pi$
$157$	1.16741	−	2.81838i	0.0931694	−	0.224931i	0.963593	+	0.267372i	$0.0861553\pi$
$158$		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	−0.100285	−	0.994959i	$-0.531976\pi$
$163$	−11.1679	−	4.62591i	−0.874740	−	0.362329i	−0.774455	+	0.632630i	$0.781976\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.51551	+	2.51551i	−0.194656	+	0.194656i	−0.797704	−	0.603049i	$-0.793952\pi$
$167$	−2.51551	+	2.51551i	−0.194656	+	0.194656i	0.603049	+	0.797704i	$0.293952\pi$
$168$		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	−0.893359	−	0.449344i	$-0.851658\pi$
$173$	0.737563	−	1.78063i	0.0560759	−	0.135379i	0.949434	+	0.313965i	$0.101658\pi$
$174$		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	−0.000436715	−	1.00000i	$-0.500139\pi$
$179$	−9.47042	−	3.92278i	−0.707852	−	0.293202i	−0.707416	+	0.706798i	$0.750139\pi$
$180$		0			0
$181$	9.91984	+	23.9486i	0.737336	+	1.78009i	0.616410	+	0.787426i	$0.288587\pi$
$181$	9.91984	+	23.9486i	0.737336	+	1.78009i	0.120927	+	0.992661i	$0.461413\pi$
$182$		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	0.767749	−	0.640751i	$-0.221377\pi$
$197$	−3.20309	−	7.73295i	−0.228211	−	0.550950i	−0.995960	+	0.0898012i	$0.971377\pi$
$198$		0			0
$199$	−15.9060	−	15.9060i	−1.12755	−	1.12755i	−0.990575	−	0.136973i	$-0.956263\pi$
$199$	−15.9060	−	15.9060i	−1.12755	−	1.12755i	−0.136973	−	0.990575i	$-0.543737\pi$
$200$		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	−0.984423	−	0.175814i	$-0.943744\pi$
$211$	−2.38241	+	5.75165i	−0.164012	+	0.395960i	0.820412	+	0.571773i	$0.193744\pi$
$212$		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	$0.302196\pi$
$223$			24.2829i			1.62611i	−0.582190	+	0.813053i	$0.697804\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.57334	+	8.62682i	−0.237171	+	0.572582i	−0.996988	−	0.0775552i	$-0.975289\pi$
$227$	−3.57334	+	8.62682i	−0.237171	+	0.572582i	0.759817	+	0.650137i	$0.225289\pi$
$228$		0			0
$229$	14.4317	−	5.97779i	0.953672	−	0.395024i	0.149062	−	0.988828i	$-0.452375\pi$
$229$	14.4317	−	5.97779i	0.953672	−	0.395024i	0.804610	+	0.593804i	$0.202375\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−6.50138	+	6.50138i	−0.425920	+	0.425920i	−0.887236	−	0.461316i	$-0.847377\pi$
$233$	−6.50138	+	6.50138i	−0.425920	+	0.425920i	0.461316	+	0.887236i	$0.347377\pi$
$234$		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	$-0.776374\pi$
$239$		−	19.9787i		−	1.29232i	0.763203	−	0.646159i	$-0.223626\pi$
$240$		0			0
$241$			0.606349i			0.0390584i	0.999809	+	0.0195292i	$0.00621673\pi$
$241$			0.606349i			0.0390584i	−0.999809	+	0.0195292i	$0.993783\pi$
$242$		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	−0.792436	−	0.609955i	$-0.791187\pi$
$251$	−14.5988	+	6.04703i	−0.921470	+	0.381685i	−0.129034	+	0.991640i	$0.541187\pi$
$252$		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	$-0.892787\pi$
$257$		−	10.5962i		−	0.660974i	0.943811	−	0.330487i	$-0.107213\pi$
$258$		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	−0.212979	+	0.977057i	$0.568317\pi$
$263$	−19.2991	+	19.2991i	−1.19004	+	1.19004i	−0.977057	+	0.212979i	$0.931683\pi$
$264$		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	−0.720697	−	0.693250i	$-0.756178\pi$
$269$	4.57782	−	11.0518i	0.279114	−	0.673842i	0.999812	+	0.0194081i	$0.00617818\pi$
$270$		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	0.991438	−	0.130578i	$-0.0416834\pi$
$277$	3.29625	+	7.95785i	0.198053	+	0.478141i	−0.793385	+	0.608720i	$0.791683\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.61069	−	6.61069i	−0.394361	−	0.394361i	0.481878	−	0.876238i	$-0.339955\pi$
$281$	−6.61069	−	6.61069i	−0.394361	−	0.394361i	−0.876238	+	0.481878i	$0.839955\pi$
$282$		0			0
$283$	0.300555	+	0.725605i	0.0178662	+	0.0431327i	0.932561	−	0.361013i	$-0.117569\pi$
$283$	0.300555	+	0.725605i	0.0178662	+	0.0431327i	−0.914695	+	0.404146i	$0.867569\pi$
$284$		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	0.935155	−	0.354239i	$-0.115260\pi$
$293$	0.400806	+	0.967632i	0.0234154	+	0.0565297i	−0.911739	+	0.410769i	$0.865260\pi$
$294$		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	−0.804843	−	0.593488i	$-0.797750\pi$
$307$	3.22266	−	7.78018i	0.183927	−	0.444038i	0.988769	+	0.149450i	$0.0477503\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−7.17660	−	7.17660i	−0.406948	−	0.406948i	0.473725	−	0.880673i	$-0.342909\pi$
$311$	−7.17660	−	7.17660i	−0.406948	−	0.406948i	−0.880673	+	0.473725i	$0.842909\pi$
$312$		0			0
$313$	0.108611	−	0.108611i	0.00613907	−	0.00613907i	−0.704031	−	0.710170i	$-0.748618\pi$
$313$	0.108611	−	0.108611i	0.00613907	−	0.00613907i	0.710170	+	0.704031i	$0.248618\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	9.89983	+	4.10065i	0.556030	+	0.230315i	0.642961	−	0.765899i	$-0.277706\pi$
$317$	9.89983	+	4.10065i	0.556030	+	0.230315i	−0.0869307	+	0.996214i	$0.527706\pi$
$318$		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	0.0606740	−	0.998158i	$-0.480675\pi$
$331$	14.7254	−	6.09946i	0.809381	−	0.335257i	0.748707	+	0.662901i	$0.230675\pi$
$332$		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	$-0.861237\pi$
$337$		−	15.5033i		−	0.844517i	0.906475	−	0.422259i	$-0.138763\pi$
$338$		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	−0.401784	−	0.915735i	$-0.631610\pi$
$347$	−0.714667	+	0.296025i	−0.0383654	+	0.0158914i	0.363418	+	0.931626i	$0.381610\pi$
$348$		0			0
$349$	−3.21246	+	7.75558i	−0.171959	+	0.415146i	−0.986239	−	0.165326i	$-0.947132\pi$
$349$	−3.21246	+	7.75558i	−0.171959	+	0.415146i	0.814280	+	0.580473i	$0.197132\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			11.9668i			0.636927i	0.947935	+	0.318463i	$0.103167\pi$
$353$			11.9668i			0.636927i	−0.947935	+	0.318463i	$0.896833\pi$
$354$		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	−0.391469	−	0.920191i	$-0.628033\pi$
$359$	10.0179	−	10.0179i	0.528723	−	0.528723i	0.920191	+	0.391469i	$0.128033\pi$
$360$		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	0.950092	−	0.311970i	$-0.100989\pi$
$373$	1.11398	+	2.68939i	0.0576797	+	0.139251i	−0.892412	+	0.451221i	$0.850989\pi$
$374$		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	0.980354	−	0.197244i	$-0.0631991\pi$
$379$	2.87476	+	6.94029i	0.147667	+	0.356499i	−0.832688	+	0.553743i	$0.813199\pi$
$380$		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	0.966023	+	0.258458i	$0.0832143\pi$
$389$	9.18501	+	22.1746i	0.465699	+	1.12430i	−0.500324	+	0.865838i	$0.666786\pi$
$390$		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	0.475312	−	0.879817i	$-0.342335\pi$
$397$	3.77144	+	1.56218i	0.189283	+	0.0784037i	−0.286029	+	0.958221i	$0.592335\pi$
$398$		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	−0.973707	−	0.227804i	$-0.926845\pi$
$409$	−15.0850	+	15.0850i	−0.745903	+	0.745903i	0.227804	+	0.973707i	$0.426845\pi$
$410$		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	−0.686167	−	0.727444i	$-0.740708\pi$
$419$	6.41529	−	15.4879i	0.313407	−	0.756632i	0.999574	−	0.0291878i	$-0.00929208\pi$
$420$		0			0
$421$	−13.8675	+	5.74412i	−0.675863	+	0.279951i	−0.694096	−	0.719882i	$-0.744196\pi$
$421$	−13.8675	+	5.74412i	−0.675863	+	0.279951i	0.0182335	+	0.999834i	$0.494196\pi$
$422$		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	$0.392320\pi$
$431$			39.1679i			1.88665i	−0.331870	+	0.943325i	$0.607680\pi$
$432$		0			0
$433$		−	20.6897i		−	0.994283i	−0.867669	−	0.497142i	$-0.834383\pi$
$433$		−	20.6897i		−	0.994283i	0.867669	−	0.497142i	$-0.165617\pi$
$434$		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	−0.505198	−	0.863003i	$-0.668581\pi$
$439$	7.49686	−	7.49686i	0.357805	−	0.357805i	0.863003	+	0.505198i	$0.168581\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−5.58792	+	2.31459i	−0.265490	+	0.109970i	−0.511458	−	0.859308i	$-0.670894\pi$
$443$	−5.58792	+	2.31459i	−0.265490	+	0.109970i	0.245968	+	0.969278i	$0.420894\pi$
$444$		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	$-0.930119\pi$
$449$		−	9.22927i		−	0.435556i	0.975998	−	0.217778i	$-0.0698809\pi$
$450$		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	0.261112	−	0.965309i	$-0.415911\pi$
$457$	−15.0540	−	15.0540i	−0.704197	−	0.704197i	−0.965309	+	0.261112i	$0.915911\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2.11682	+	5.11046i	−0.0985902	+	0.238018i	−0.965478	−	0.260486i	$-0.916117\pi$
$461$	−2.11682	+	5.11046i	−0.0985902	+	0.238018i	0.866887	+	0.498504i	$0.166117\pi$
$462$		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	0.0617775	−	0.998090i	$-0.480323\pi$
$467$	−12.9725	−	5.37338i	−0.600295	−	0.248650i	−0.662073	+	0.749439i	$0.730323\pi$
$468$		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	0.668403	−	0.743799i	$-0.266978\pi$
$487$	−1.66386	−	1.66386i	−0.0753965	−	0.0753965i	−0.743799	+	0.668403i	$0.766978\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−12.2708	−	29.6244i	−0.553775	−	1.33693i	−0.914624	−	0.404306i	$-0.867513\pi$
$491$	−12.2708	−	29.6244i	−0.553775	−	1.33693i	0.360849	−	0.932624i	$-0.382487\pi$
$492$		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	−0.245736	−	0.969337i	$-0.579029\pi$
$499$	13.7034	−	33.0830i	0.613450	−	1.48100i	0.859186	−	0.511663i	$-0.170971\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−23.6161	−	23.6161i	−1.05299	−	1.05299i	−0.998515	−	0.0544742i	$-0.982652\pi$
$503$	−23.6161	−	23.6161i	−1.05299	−	1.05299i	−0.0544742	−	0.998515i	$-0.517348\pi$
$504$		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	0.973474	−	0.228798i	$-0.0734797\pi$
$509$	33.8424	+	14.0180i	1.50004	+	0.621336i	0.526565	+	0.850135i	$0.323480\pi$
$510$		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	−0.677886	−	0.735167i	$-0.737104\pi$
$521$	1.30745	−	1.30745i	0.0572804	−	0.0572804i	0.735167	+	0.677886i	$0.237104\pi$
$522$		0			0
$523$	21.7896	−	9.02554i	0.952792	−	0.394660i	0.148513	−	0.988911i	$-0.452551\pi$
$523$	21.7896	−	9.02554i	0.952792	−	0.394660i	0.804280	+	0.594251i	$0.202551\pi$
$524$		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	−0.975723	−	0.219009i	$-0.929718\pi$
$541$	−3.04512	+	7.35157i	−0.130920	+	0.316069i	0.844803	+	0.535078i	$0.179718\pi$
$542$		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	0.264670	−	0.964339i	$-0.414737\pi$
$547$	−5.38090	−	2.22884i	−0.230071	−	0.0952984i	−0.494741	+	0.869041i	$0.664737\pi$
$548$		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	0.628576	+	0.777748i	$0.283638\pi$
$557$	−8.63425	+	20.8449i	−0.365845	+	0.883228i	−0.994421	+	0.105480i	$0.966362\pi$
$558$		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	−0.00875227	−	0.999962i	$-0.502786\pi$
$563$	−17.1318	−	7.09624i	−0.722021	−	0.299071i	−0.713268	+	0.700891i	$0.752786\pi$
$564$		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	0.952963	−	0.303086i	$-0.0980169\pi$
$569$	15.5020	+	15.5020i	0.649877	+	0.649877i	−0.303086	+	0.952963i	$0.598017\pi$
$570$		0			0
$571$	−11.3574	−	27.4193i	−0.475294	−	1.14746i	−0.961793	−	0.273779i	$-0.911726\pi$
$571$	−11.3574	−	27.4193i	−0.475294	−	1.14746i	0.486499	−	0.873681i	$-0.338274\pi$
$572$		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	0.999532	−	0.0305874i	$-0.00973779\pi$
$587$	6.56890	+	15.8587i	0.271128	+	0.654560i	−0.728404	+	0.685147i	$0.759738\pi$
$588$		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	0.915496	−	0.402326i	$-0.131798\pi$
$599$	12.5596	+	12.5596i	0.513170	+	0.513170i	−0.402326	+	0.915496i	$0.631798\pi$
$600$		0			0
$601$	23.9708	−	23.9708i	0.977791	−	0.977791i	−0.0219673	−	0.999759i	$-0.506993\pi$
$601$	23.9708	−	23.9708i	0.977791	−	0.977791i	0.999759	+	0.0219673i	$0.00699298\pi$
$602$		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	$0.192185\pi$
$607$			27.9757i			1.13550i	−0.823202	+	0.567749i	$0.807815\pi$
$608$		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	−0.897560	−	0.440892i	$-0.854662\pi$
$613$	−30.2175	+	12.5165i	−1.22047	+	0.505537i	−0.322913	+	0.946429i	$0.604662\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−23.4695	+	23.4695i	−0.944848	+	0.944848i	−0.998557	−	0.0537086i	$-0.982896\pi$
$617$	−23.4695	+	23.4695i	−0.944848	+	0.944848i	0.0537086	+	0.998557i	$0.482896\pi$
$618$		0			0
$619$	16.2802	−	6.74349i	0.654357	−	0.271044i	−0.0307046	−	0.999529i	$-0.509775\pi$
$619$	16.2802	−	6.74349i	0.654357	−	0.271044i	0.685062	+	0.728485i	$0.259775\pi$
$620$		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	−0.973584	−	0.228328i	$-0.926674\pi$
$631$	−18.7206	+	18.7206i	−0.745256	+	0.745256i	0.228328	+	0.973584i	$0.426674\pi$
$632$		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	$0.285496\pi$
$641$			39.5671i			1.56281i	−0.624026	+	0.781404i	$0.714504\pi$
$642$		0			0
$643$	32.9323	+	13.6410i	1.29872	+	0.537949i	0.921573	−	0.388204i	$-0.126904\pi$
$643$	32.9323	+	13.6410i	1.29872	+	0.537949i	0.377149	+	0.926153i	$0.376904\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−15.1226	+	15.1226i	−0.594532	+	0.594532i	−0.938852	−	0.344320i	$-0.888109\pi$
$647$	−15.1226	+	15.1226i	−0.594532	+	0.594532i	0.344320	+	0.938852i	$0.388109\pi$
$648$		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	−0.995640	−	0.0932843i	$-0.970263\pi$
$653$	−5.76633	+	13.9212i	−0.225654	+	0.544777i	0.769985	+	0.638061i	$0.220263\pi$
$654$		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	0.767105	−	0.641522i	$-0.221697\pi$
$659$	21.9719	+	9.10108i	0.855905	+	0.354528i	0.0888005	+	0.996049i	$0.471697\pi$
$660$		0			0
$661$	6.04221	+	14.5872i	0.235015	+	0.567376i	0.996754	−	0.0805079i	$-0.0256542\pi$
$661$	6.04221	+	14.5872i	0.235015	+	0.567376i	−0.761739	+	0.647884i	$0.775654\pi$
$662$		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	−0.999347	−	0.0361363i	$-0.988495\pi$
$677$	−8.28073	−	19.9914i	−0.318254	−	0.768333i	0.681093	−	0.732197i	$-0.261505\pi$
$678$		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	0.996571	−	0.0827411i	$-0.0263674\pi$
$683$	6.09927	+	14.7249i	0.233382	+	0.563434i	−0.763189	+	0.646175i	$0.776367\pi$
$684$		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	−0.758232	−	0.651985i	$-0.773937\pi$
$691$	6.28104	−	15.1638i	0.238942	−	0.576857i	0.997174	+	0.0751281i	$0.0239366\pi$
$692$		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	−0.135529	−	0.990773i	$-0.543274\pi$
$701$	−24.6746	−	10.2205i	−0.931946	−	0.386025i	−0.796416	+	0.604749i	$0.793274\pi$
$702$		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	−0.587727	−	0.809060i	$-0.699977\pi$
$709$	−11.4821	+	4.75606i	−0.431221	+	0.178617i	0.156506	+	0.987677i	$0.449977\pi$
$710$		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	$0.148479\pi$
$719$			24.1182i			0.899455i	−0.893166	+	0.449728i	$0.851521\pi$
$720$		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	−0.993929	−	0.110020i	$-0.964908\pi$
$727$	−23.8328	+	23.8328i	−0.883909	+	0.883909i	0.110020	+	0.993929i	$0.464908\pi$
$728$		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	−0.732324	−	0.680956i	$-0.761564\pi$
$733$	7.22918	−	17.4528i	0.267016	−	0.644633i	0.999340	+	0.0363227i	$0.0115644\pi$
$734$		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	0.338621	−	0.940923i	$-0.390039\pi$
$739$	−2.37240	−	0.982682i	−0.0872703	−	0.0361485i	−0.425892	+	0.904774i	$0.640039\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	9.84906	−	9.84906i	0.361327	−	0.361327i	−0.502974	−	0.864301i	$-0.667761\pi$
$743$	9.84906	−	9.84906i	0.361327	−	0.361327i	0.864301	+	0.502974i	$0.167761\pi$
$744$		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	−0.969458	−	0.245257i	$-0.921128\pi$
$757$	−12.5839	−	30.3803i	−0.457371	−	1.10419i	0.512088	−	0.858933i	$-0.328872\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	10.8012	+	10.8012i	0.391543	+	0.391543i	0.875237	−	0.483694i	$-0.160705\pi$
$761$	10.8012	+	10.8012i	0.391543	+	0.391543i	−0.483694	+	0.875237i	$0.660705\pi$
$762$		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	0.999785	−	0.0207297i	$-0.00659894\pi$
$773$	7.73399	+	18.6715i	0.278172	+	0.671567i	−0.721613	+	0.692297i	$0.756599\pi$
$774$		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	−0.998253	−	0.0590900i	$-0.981180\pi$
$787$	−7.03017	+	16.9723i	−0.250598	+	0.604998i	0.747654	+	0.664088i	$0.231180\pi$
$788$		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	−0.566638	−	0.823967i	$-0.691756\pi$
$797$	−43.7568	−	18.1246i	−1.54994	−	0.642008i	−0.983306	+	0.181959i	$0.941756\pi$
$798$		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	−0.586788	−	0.809741i	$-0.699608\pi$
$809$	6.34143	−	6.34143i	0.222953	−	0.222953i	0.809741	+	0.586788i	$0.199608\pi$
$810$		0			0
$811$	12.8711	−	5.33139i	0.451966	−	0.187210i	−0.145076	−	0.989421i	$-0.546343\pi$
$811$	12.8711	−	5.33139i	0.451966	−	0.187210i	0.597042	+	0.802210i	$0.296343\pi$
$812$		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	−0.150341	−	0.988634i	$-0.548037\pi$
$821$	12.6767	−	5.25088i	0.442421	−	0.183257i	0.592763	+	0.805377i	$0.298037\pi$
$822$		0			0
$823$	21.6528	−	21.6528i	0.754770	−	0.754770i	−0.220596	−	0.975365i	$-0.570800\pi$
$823$	21.6528	−	21.6528i	0.754770	−	0.754770i	0.975365	+	0.220596i	$0.0708002\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	26.0418	−	10.7869i	0.905563	−	0.375096i	0.119206	−	0.992869i	$-0.461965\pi$
$827$	26.0418	−	10.7869i	0.905563	−	0.375096i	0.786356	+	0.617773i	$0.211965\pi$
$828$		0			0
$829$	5.29036	−	12.7721i	0.183742	−	0.443592i	−0.804990	−	0.593288i	$-0.797830\pi$
$829$	5.29036	−	12.7721i	0.183742	−	0.443592i	0.988732	+	0.149696i	$0.0478295\pi$
$830$		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	−0.916253	−	0.400600i	$-0.868802\pi$
$839$	−14.9362	+	14.9362i	−0.515654	+	0.515654i	0.400600	+	0.916253i	$0.368802\pi$
$840$		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	0.993059	+	0.117613i	$0.0375243\pi$
$853$	10.9239	+	26.3725i	0.374026	+	0.902978i	−0.619034	+	0.785364i	$0.712476\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−2.77666	−	2.77666i	−0.0948488	−	0.0948488i	0.658090	−	0.752939i	$-0.271365\pi$
$857$	−2.77666	−	2.77666i	−0.0948488	−	0.0948488i	−0.752939	+	0.658090i	$0.771365\pi$
$858$		0			0
$859$	−21.8775	−	52.8170i	−0.746452	−	1.80209i	−0.577352	−	0.816495i	$-0.695914\pi$
$859$	−21.8775	−	52.8170i	−0.746452	−	1.80209i	−0.169100	−	0.985599i	$-0.554086\pi$
$860$		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	0.609609	−	0.792702i	$-0.291326\pi$
$877$	14.2190	+	5.88971i	0.480142	+	0.198882i	−0.129466	+	0.991584i	$0.541326\pi$
$878$		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	0.0383892	+	0.999263i	$0.487777\pi$
$883$	−20.6623	+	49.8832i	−0.695342	+	1.67870i	−0.733731	+	0.679440i	$0.762223\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−24.4215	−	24.4215i	−0.819994	−	0.819994i	0.166112	−	0.986107i	$-0.446879\pi$
$887$	−24.4215	−	24.4215i	−0.819994	−	0.819994i	−0.986107	+	0.166112i	$0.946879\pi$
$888$		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	−0.350994	−	0.936378i	$-0.614156\pi$
$907$	1.89537	−	0.785090i	0.0629349	−	0.0260685i	0.413929	+	0.910309i	$0.364156\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			1.10306i			0.0365460i	0.999833	+	0.0182730i	$0.00581679\pi$
$911$			1.10306i			0.0365460i	−0.999833	+	0.0182730i	$0.994183\pi$
$912$		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	−0.963871	−	0.266370i	$-0.914176\pi$
$919$	−21.1448	+	21.1448i	−0.697501	+	0.697501i	0.266370	+	0.963871i	$0.414176\pi$
$920$		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	$0.0450332\pi$
$929$			8.59550i			0.282009i	−0.990009	+	0.141005i	$0.954967\pi$
$930$		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	0.791349	−	0.611365i	$-0.209379\pi$
$937$	5.50940	+	5.50940i	0.179984	+	0.179984i	−0.611365	+	0.791349i	$0.709379\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	7.60686	−	18.3646i	0.247977	−	0.598669i	−0.750055	−	0.661375i	$-0.769973\pi$
$941$	7.60686	−	18.3646i	0.247977	−	0.598669i	0.998032	+	0.0627064i	$0.0199732\pi$
$942$		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	0.397466	−	0.917617i	$-0.369890\pi$
$947$	0.912836	+	0.378109i	0.0296632	+	0.0122869i	−0.367803	+	0.929904i	$0.619890\pi$
$948$		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	0.998924	+	0.0463673i	$0.0147645\pi$
$953$	32.2689	+	32.2689i	1.04529	+	1.04529i	0.0463673	+	0.998924i	$0.485236\pi$
$954$		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	0.457905	−	0.889001i	$-0.348600\pi$
$967$	−13.4056	−	13.4056i	−0.431097	−	0.431097i	−0.889001	+	0.457905i	$0.848600\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−7.93498	−	19.1567i	−0.254645	−	0.614769i	0.743923	−	0.668266i	$-0.232963\pi$
$971$	−7.93498	−	19.1567i	−0.254645	−	0.614769i	−0.998568	+	0.0534973i	$0.982963\pi$
$972$		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	0.0974212	−	0.995243i	$-0.468941\pi$
$983$	−28.1493	−	28.1493i	−0.897822	−	0.897822i	−0.995243	+	0.0974212i	$0.968941\pi$
$984$		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	$0.128412\pi$
$991$			24.7160i			0.785131i	−0.919724	+	0.392565i	$0.871588\pi$
$992$		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	−0.764411	−	0.644729i	$-0.776970\pi$
$997$	−26.8087	+	11.1045i	−0.849039	+	0.351684i	−0.0846280	+	0.996413i	$0.526970\pi$
$998$		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.1007.3		32
3.2	odd	2		1152.2.w.a.1007.6		32
4.3	odd	2		288.2.w.a.179.6	✓	32
12.11	even	2		288.2.w.b.179.3	yes	32
32.5	even	8		288.2.w.b.251.3	yes	32
32.27	odd	8		1152.2.w.a.143.6		32
96.5	odd	8		288.2.w.a.251.6	yes	32
96.59	even	8	inner	1152.2.w.b.143.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.179.6	✓	32	4.3	odd	2
288.2.w.a.251.6	yes	32	96.5	odd	8
288.2.w.b.179.3	yes	32	12.11	even	2
288.2.w.b.251.3	yes	32	32.5	even	8
1152.2.w.a.143.6		32	32.27	odd	8
1152.2.w.a.1007.6		32	3.2	odd	2
1152.2.w.b.143.3		32	96.59	even	8	inner
1152.2.w.b.1007.3		32	1.1	even	1	trivial

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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:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
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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