LMFDB - Embedded newform 1152.2.w.b.719.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1152,2,Mod(143,1152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [32,0,0,0,0,0,0,0,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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			719.7
Character	$\chi$	$=$	1152.719
Dual form			1152.2.w.b.431.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.78959 + 0.741273i) q^{5} +(2.33709 - 2.33709i) q^{7} +(0.683332 + 0.283045i) q^{11} +(2.43602 + 5.88107i) q^{13} +0.967834 q^{17} +(2.52772 - 1.04702i) q^{19} +(-5.00283 + 5.00283i) q^{23} +(-0.882385 - 0.882385i) q^{25} +(-0.563403 - 1.36018i) q^{29} -7.28582i q^{31} +(5.91486 - 2.45001i) q^{35} +(3.26572 - 7.88415i) q^{37} +(6.80014 + 6.80014i) q^{41} +(-1.36517 + 3.29581i) q^{43} +3.69279i q^{47} -3.92399i q^{49} +(1.85469 - 4.47761i) q^{53} +(1.01307 + 1.01307i) q^{55} +(-4.05615 + 9.79242i) q^{59} +(10.8180 - 4.48097i) q^{61} +12.3305i q^{65} +(-1.49290 - 3.60418i) q^{67} +(-9.85675 - 9.85675i) q^{71} +(-4.81362 + 4.81362i) q^{73} +(2.25851 - 0.935506i) q^{77} +11.0160 q^{79} +(1.15064 + 2.77789i) q^{83} +(1.73203 + 0.717429i) q^{85} +(-6.82624 + 6.82624i) q^{89} +(19.4378 + 8.05140i) q^{91} +5.29971 q^{95} +7.67976 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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

Character values

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

$n$	$127$	$641$	$901$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{8}\right)$

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
$5$	1.78959	+	0.741273i	0.800329	+	0.331507i	0.745088	−	0.666966i	$-0.232407\pi$
$5$	1.78959	+	0.741273i	0.800329	+	0.331507i	0.0552409	+	0.998473i	$0.482407\pi$
$6$		0			0
$7$	2.33709	−	2.33709i	0.883337	−	0.883337i	−0.110535	−	0.993872i	$-0.535256\pi$
$7$	2.33709	−	2.33709i	0.883337	−	0.883337i	0.993872	+	0.110535i	$0.0352564\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.683332	+	0.283045i	0.206032	+	0.0853413i	0.483313	−	0.875448i	$-0.339433\pi$
$11$	0.683332	+	0.283045i	0.206032	+	0.0853413i	−0.277281	+	0.960789i	$0.589433\pi$
$12$		0			0
$13$	2.43602	+	5.88107i	0.675630	+	1.63112i	0.771888	+	0.635759i	$0.219313\pi$
$13$	2.43602	+	5.88107i	0.675630	+	1.63112i	−0.0962579	+	0.995356i	$0.530687\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.967834			0.234734			0.117367	−	0.993089i	$-0.462555\pi$
$17$	0.967834			0.234734			0.117367	+	0.993089i	$0.462555\pi$
$18$		0			0
$19$	2.52772	−	1.04702i	0.579899	−	0.240202i	−0.0733991	−	0.997303i	$-0.523385\pi$
$19$	2.52772	−	1.04702i	0.579899	−	0.240202i	0.653298	+	0.757100i	$0.273385\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−5.00283	+	5.00283i	−1.04316	+	1.04316i	−0.0441370	+	0.999025i	$0.514054\pi$
$23$	−5.00283	+	5.00283i	−1.04316	+	1.04316i	−0.999025	+	0.0441370i	$0.985946\pi$
$24$		0			0
$25$	−0.882385	−	0.882385i	−0.176477	−	0.176477i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.563403	−	1.36018i	−0.104621	−	0.252578i	0.862897	−	0.505380i	$-0.168648\pi$
$29$	−0.563403	−	1.36018i	−0.104621	−	0.252578i	−0.967518	+	0.252802i	$0.918648\pi$
$30$		0			0
$31$		−	7.28582i		−	1.30857i	−0.756247	−	0.654286i	$-0.772969\pi$
$31$		−	7.28582i		−	1.30857i	0.756247	−	0.654286i	$-0.227031\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	5.91486	−	2.45001i	0.999793	−	0.414128i
$36$		0			0
$37$	3.26572	−	7.88415i	0.536881	−	1.29615i	−0.390008	−	0.920812i	$-0.627528\pi$
$37$	3.26572	−	7.88415i	0.536881	−	1.29615i	0.926889	−	0.375335i	$-0.122472\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	6.80014	+	6.80014i	1.06200	+	1.06200i	0.997946	+	0.0640576i	$0.0204041\pi$
$41$	6.80014	+	6.80014i	1.06200	+	1.06200i	0.0640576	+	0.997946i	$0.479596\pi$
$42$		0			0
$43$	−1.36517	+	3.29581i	−0.208187	+	0.502607i	−0.993138	−	0.116951i	$-0.962688\pi$
$43$	−1.36517	+	3.29581i	−0.208187	+	0.502607i	0.784951	+	0.619558i	$0.212688\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			3.69279i			0.538649i	0.963050	+	0.269324i	$0.0868004\pi$
$47$			3.69279i			0.538649i	−0.963050	+	0.269324i	$0.913200\pi$
$48$		0			0
$49$		−	3.92399i		−	0.560570i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.85469	−	4.47761i	0.254761	−	0.615047i	−0.743816	−	0.668385i	$-0.766986\pi$
$53$	1.85469	−	4.47761i	0.254761	−	0.615047i	0.998577	+	0.0533378i	$0.0169860\pi$
$54$		0			0
$55$	1.01307	+	1.01307i	0.136602	+	0.136602i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.05615	+	9.79242i	−0.528066	+	1.27486i	0.404722	+	0.914440i	$0.367368\pi$
$59$	−4.05615	+	9.79242i	−0.528066	+	1.27486i	−0.932788	+	0.360425i	$0.882632\pi$
$60$		0			0
$61$	10.8180	−	4.48097i	1.38511	−	0.573730i	0.439265	−	0.898358i	$-0.355239\pi$
$61$	10.8180	−	4.48097i	1.38511	−	0.573730i	0.945842	+	0.324628i	$0.105239\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			12.3305i			1.52941i
$66$		0			0
$67$	−1.49290	−	3.60418i	−0.182387	−	0.440320i	0.806071	−	0.591819i	$-0.201590\pi$
$67$	−1.49290	−	3.60418i	−0.182387	−	0.440320i	−0.988457	+	0.151499i	$0.951590\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−9.85675	−	9.85675i	−1.16978	−	1.16978i	−0.982261	−	0.187520i	$-0.939955\pi$
$71$	−9.85675	−	9.85675i	−1.16978	−	1.16978i	−0.187520	−	0.982261i	$-0.560045\pi$
$72$		0			0
$73$	−4.81362	+	4.81362i	−0.563391	+	0.563391i	−0.930269	−	0.366878i	$-0.880427\pi$
$73$	−4.81362	+	4.81362i	−0.563391	+	0.563391i	0.366878	+	0.930269i	$0.380427\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.25851	−	0.935506i	0.257381	−	0.106611i
$78$		0			0
$79$	11.0160			1.23940			0.619700	−	0.784839i	$-0.287254\pi$
$79$	11.0160			1.23940			0.619700	+	0.784839i	$0.287254\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.15064	+	2.77789i	0.126299	+	0.304913i	0.974363	−	0.224981i	$-0.0722319\pi$
$83$	1.15064	+	2.77789i	0.126299	+	0.304913i	−0.848064	+	0.529894i	$0.822232\pi$
$84$		0			0
$85$	1.73203	+	0.717429i	0.187865	+	0.0778161i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−6.82624	+	6.82624i	−0.723580	+	0.723580i	−0.969333	−	0.245753i	$-0.920965\pi$
$89$	−6.82624	+	6.82624i	−0.723580	+	0.723580i	0.245753	+	0.969333i	$0.420965\pi$
$90$		0			0
$91$	19.4378	+	8.05140i	2.03763	+	0.844016i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	5.29971			0.543739
$96$		0			0
$97$	7.67976			0.779762			0.389881	−	0.920865i	$-0.372516\pi$
$97$	7.67976			0.779762			0.389881	+	0.920865i	$0.372516\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.05030	−	0.435049i	−0.104509	−	0.0432890i	0.329816	−	0.944045i	$-0.393013\pi$
$101$	−1.05030	−	0.435049i	−0.104509	−	0.0432890i	−0.434325	+	0.900756i	$0.643013\pi$
$102$		0			0
$103$	−7.06356	+	7.06356i	−0.695993	+	0.695993i	−0.963544	−	0.267551i	$-0.913786\pi$
$103$	−7.06356	+	7.06356i	−0.695993	+	0.695993i	0.267551	+	0.963544i	$0.413786\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	16.1346	+	6.68316i	1.55979	+	0.646086i	0.985053	−	0.172253i	$-0.0551045\pi$
$107$	16.1346	+	6.68316i	1.55979	+	0.646086i	0.574737	+	0.818338i	$0.305105\pi$
$108$		0			0
$109$	0.771406	+	1.86234i	0.0738873	+	0.178380i	0.956508	−	0.291706i	$-0.0942230\pi$
$109$	0.771406	+	1.86234i	0.0738873	+	0.178380i	−0.882621	+	0.470086i	$0.844223\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.726213			−0.0683163			−0.0341582	−	0.999416i	$-0.510875\pi$
$113$	−0.726213			−0.0683163			−0.0341582	+	0.999416i	$0.510875\pi$
$114$		0			0
$115$	−12.6615	+	5.24456i	−1.18069	+	0.489058i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.26192	−	2.26192i	0.207350	−	0.207350i
$120$		0			0
$121$	−7.39135	−	7.39135i	−0.671941	−	0.671941i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−4.63138	−	11.1811i	−0.414243	−	1.00007i
$126$		0			0
$127$		−	11.5686i		−	1.02654i	−0.858226	−	0.513272i	$-0.828433\pi$
$127$		−	11.5686i		−	1.02654i	0.858226	−	0.513272i	$-0.171567\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	17.9241	−	7.42442i	1.56604	−	0.648674i	0.579913	−	0.814678i	$-0.303087\pi$
$131$	17.9241	−	7.42442i	1.56604	−	0.648674i	0.986125	+	0.166004i	$0.0530866\pi$
$132$		0			0
$133$	3.46054	−	8.35449i	0.300067	−	0.724426i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−15.9867	−	15.9867i	−1.36584	−	1.36584i	−0.866283	−	0.499553i	$-0.833497\pi$
$137$	−15.9867	−	15.9867i	−1.36584	−	1.36584i	−0.499553	−	0.866283i	$-0.666503\pi$
$138$		0			0
$139$	−0.0365308	+	0.0881933i	−0.00309851	+	0.00748046i	−0.925421	−	0.378940i	$-0.876289\pi$
$139$	−0.0365308	+	0.0881933i	−0.00309851	+	0.00748046i	0.922323	+	0.386421i	$0.126289\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			4.70822i			0.393721i
$144$		0			0
$145$		−	2.85179i		−	0.236828i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	5.79476	−	13.9898i	0.474725	−	1.14609i	−0.487326	−	0.873220i	$-0.662028\pi$
$149$	5.79476	−	13.9898i	0.474725	−	1.14609i	0.962051	−	0.272868i	$-0.0879722\pi$
$150$		0			0
$151$	−7.47087	−	7.47087i	−0.607971	−	0.607971i	0.334445	−	0.942415i	$-0.391451\pi$
$151$	−7.47087	−	7.47087i	−0.607971	−	0.607971i	−0.942415	+	0.334445i	$0.891451\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	5.40078	−	13.0386i	0.433801	−	1.04729i
$156$		0			0
$157$	−11.0372	+	4.57177i	−0.880867	+	0.364867i	−0.776833	−	0.629707i	$-0.783175\pi$
$157$	−11.0372	+	4.57177i	−0.880867	+	0.364867i	−0.104034	+	0.994574i	$0.533175\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			23.3841i			1.84293i
$162$		0			0
$163$	3.29972	+	7.96624i	0.258454	+	0.623964i	0.998837	−	0.0482221i	$-0.0153555\pi$
$163$	3.29972	+	7.96624i	0.258454	+	0.623964i	−0.740382	+	0.672186i	$0.765356\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.0751100	+	0.0751100i	0.00581218	+	0.00581218i	0.710007	−	0.704195i	$-0.248692\pi$
$167$	0.0751100	+	0.0751100i	0.00581218	+	0.00581218i	−0.704195	+	0.710007i	$0.748692\pi$
$168$		0			0
$169$	−19.4604	+	19.4604i	−1.49695	+	1.49695i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−21.0041	+	8.70018i	−1.59691	+	0.661463i	−0.990975	−	0.134050i	$-0.957202\pi$
$173$	−21.0041	+	8.70018i	−1.59691	+	0.661463i	−0.605937	+	0.795512i	$0.707202\pi$
$174$		0			0
$175$	−4.12443			−0.311777
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−4.35530	−	10.5146i	−0.325530	−	0.785900i	−0.998913	−	0.0466061i	$-0.985159\pi$
$179$	−4.35530	−	10.5146i	−0.325530	−	0.785900i	0.673383	−	0.739294i	$-0.264841\pi$
$180$		0			0
$181$	−4.28737	−	1.77589i	−0.318677	−	0.132001i	0.217610	−	0.976036i	$-0.430174\pi$
$181$	−4.28737	−	1.77589i	−0.318677	−	0.132001i	−0.536288	+	0.844035i	$0.680174\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	11.6886	−	11.6886i	0.859364	−	0.859364i
$186$		0			0
$187$	0.661352	+	0.273941i	0.0483628	+	0.0200325i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−22.2718			−1.61153			−0.805766	−	0.592234i	$-0.798246\pi$
$191$	−22.2718			−1.61153			−0.805766	+	0.592234i	$0.798246\pi$
$192$		0			0
$193$	10.8858			0.783575			0.391787	−	0.920056i	$-0.371857\pi$
$193$	10.8858			0.783575			0.391787	+	0.920056i	$0.371857\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	6.10110	+	2.52716i	0.434686	+	0.180053i	0.589286	−	0.807924i	$-0.299409\pi$
$197$	6.10110	+	2.52716i	0.434686	+	0.180053i	−0.154601	+	0.987977i	$0.549409\pi$
$198$		0			0
$199$	−10.1086	+	10.1086i	−0.716582	+	0.716582i	−0.967904	−	0.251322i	$-0.919135\pi$
$199$	−10.1086	+	10.1086i	−0.716582	+	0.716582i	0.251322	+	0.967904i	$0.419135\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−4.49558	−	1.86213i	−0.315528	−	0.130696i
$204$		0			0
$205$	7.12871	+	17.2102i	0.497891	+	1.20201i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.02363			0.139977
$210$		0			0
$211$	−18.8236	+	7.79698i	−1.29587	+	0.536766i	−0.920729	−	0.390202i	$-0.872405\pi$
$211$	−18.8236	+	7.79698i	−1.29587	+	0.536766i	−0.375139	+	0.926969i	$0.622405\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−4.88619	+	4.88619i	−0.333236	+	0.333236i
$216$		0			0
$217$	−17.0276	−	17.0276i	−1.15591	−	1.15591i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.35766	+	5.69190i	0.158593	+	0.382879i
$222$		0			0
$223$		−	14.8162i		−	0.992164i	−0.868276	−	0.496082i	$-0.834771\pi$
$223$		−	14.8162i		−	0.992164i	0.868276	−	0.496082i	$-0.165229\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−11.9755	+	4.96040i	−0.794839	+	0.329233i	−0.742887	−	0.669416i	$-0.766544\pi$
$227$	−11.9755	+	4.96040i	−0.794839	+	0.329233i	−0.0519519	+	0.998650i	$0.516544\pi$
$228$		0			0
$229$	−2.65080	+	6.39960i	−0.175170	+	0.422897i	−0.986942	−	0.161077i	$-0.948503\pi$
$229$	−2.65080	+	6.39960i	−0.175170	+	0.422897i	0.811772	+	0.583975i	$0.198503\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−8.35926	−	8.35926i	−0.547634	−	0.547634i	0.378122	−	0.925756i	$-0.376570\pi$
$233$	−8.35926	−	8.35926i	−0.547634	−	0.547634i	−0.925756	+	0.378122i	$0.876570\pi$
$234$		0			0
$235$	−2.73736	+	6.60858i	−0.178566	+	0.431096i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	2.44122i		−	0.157909i	−0.996878	−	0.0789547i	$-0.974842\pi$
$239$		−	2.44122i		−	0.157909i	0.996878	−	0.0789547i	$-0.0251582\pi$
$240$		0			0
$241$			1.86406i			0.120074i	0.998196	+	0.0600372i	$0.0191219\pi$
$241$			1.86406i			0.120074i	−0.998196	+	0.0600372i	$0.980878\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.90874	−	7.02233i	0.185833	−	0.448640i
$246$		0			0
$247$	12.3152	+	12.3152i	0.783595	+	0.783595i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−6.30926	+	15.2319i	−0.398237	+	0.961430i	0.589847	+	0.807515i	$0.299188\pi$
$251$	−6.30926	+	15.2319i	−0.398237	+	0.961430i	−0.988084	+	0.153915i	$0.950812\pi$
$252$		0			0
$253$	−4.83462	+	2.00257i	−0.303950	+	0.125900i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	5.84660i		−	0.364701i	−0.983234	−	0.182350i	$-0.941629\pi$
$257$		−	5.84660i		−	0.364701i	0.983234	−	0.182350i	$-0.0583705\pi$
$258$		0			0
$259$	−10.7937	−	26.0583i	−0.670687	−	1.61918i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−11.4239	−	11.4239i	−0.704427	−	0.704427i	0.260930	−	0.965358i	$-0.415971\pi$
$263$	−11.4239	−	11.4239i	−0.704427	−	0.704427i	−0.965358	+	0.260930i	$0.915971\pi$
$264$		0			0
$265$	6.63826	−	6.63826i	0.407785	−	0.407785i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	2.42511	−	1.00451i	0.147862	−	0.0612463i	−0.307525	−	0.951540i	$-0.599501\pi$
$269$	2.42511	−	1.00451i	0.147862	−	0.0612463i	0.455387	+	0.890294i	$0.349501\pi$
$270$		0			0
$271$	10.6956			0.649711			0.324856	−	0.945764i	$-0.394684\pi$
$271$	10.6956			0.649711			0.324856	+	0.945764i	$0.394684\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.353207	−	0.852716i	−0.0212992	−	0.0514207i
$276$		0			0
$277$	−13.7497	−	5.69533i	−0.826142	−	0.342199i	−0.0707678	−	0.997493i	$-0.522545\pi$
$277$	−13.7497	−	5.69533i	−0.826142	−	0.342199i	−0.755374	+	0.655294i	$0.772545\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.63475	−	1.63475i	0.0975211	−	0.0975211i	−0.656663	−	0.754184i	$-0.728033\pi$
$281$	1.63475	−	1.63475i	0.0975211	−	0.0975211i	0.754184	+	0.656663i	$0.228033\pi$
$282$		0			0
$283$	4.75108	+	1.96796i	0.282423	+	0.116983i	0.519398	−	0.854532i	$-0.326156\pi$
$283$	4.75108	+	1.96796i	0.282423	+	0.116983i	−0.236976	+	0.971516i	$0.576156\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	31.7851			1.87622
$288$		0			0
$289$	−16.0633			−0.944900
$290$		0			0
$291$		0			0
$292$		0			0
$293$	13.0434	+	5.40274i	0.762001	+	0.315631i	0.729628	−	0.683845i	$-0.239693\pi$
$293$	13.0434	+	5.40274i	0.762001	+	0.315631i	0.0323737	+	0.999476i	$0.489693\pi$
$294$		0			0
$295$	−14.5177	+	14.5177i	−0.845254	+	0.845254i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−41.6090	−	17.2350i	−2.40631	−	0.996726i
$300$		0			0
$301$	4.51209	+	10.8931i	0.260072	+	0.627870i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	22.6815			1.29874
$306$		0			0
$307$	−13.7332	+	5.68846i	−0.783793	+	0.324658i	−0.738445	−	0.674313i	$-0.764440\pi$
$307$	−13.7332	+	5.68846i	−0.783793	+	0.324658i	−0.0453480	+	0.998971i	$0.514440\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1.93693	−	1.93693i	0.109833	−	0.109833i	−0.650055	−	0.759888i	$-0.725254\pi$
$311$	1.93693	−	1.93693i	0.109833	−	0.109833i	0.759888	+	0.650055i	$0.225254\pi$
$312$		0			0
$313$	20.8065	+	20.8065i	1.17606	+	1.17606i	0.980741	+	0.195315i	$0.0625728\pi$
$313$	20.8065	+	20.8065i	1.17606	+	1.17606i	0.195315	+	0.980741i	$0.437427\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.99169	−	16.8794i	−0.392692	−	0.948043i	−0.989351	−	0.145548i	$-0.953505\pi$
$317$	−6.99169	−	16.8794i	−0.392692	−	0.948043i	0.596659	−	0.802495i	$-0.296495\pi$
$318$		0			0
$319$		−	1.08892i		−	0.0609678i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	2.44642	−	1.01334i	0.136122	−	0.0563837i
$324$		0			0
$325$	3.03986	−	7.33887i	0.168621	−	0.407087i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	8.63039	+	8.63039i	0.475809	+	0.475809i
$330$		0			0
$331$	−7.57715	+	18.2929i	−0.416478	+	1.00547i	0.566882	+	0.823799i	$0.308150\pi$
$331$	−7.57715	+	18.2929i	−0.416478	+	1.00547i	−0.983360	+	0.181668i	$0.941850\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		−	7.55664i		−	0.412863i
$336$		0			0
$337$			6.73391i			0.366820i	0.983037	+	0.183410i	$0.0587135\pi$
$337$			6.73391i			0.366820i	−0.983037	+	0.183410i	$0.941286\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	2.06222	−	4.97863i	0.111675	−	0.269608i
$342$		0			0
$343$	7.18892	+	7.18892i	0.388165	+	0.388165i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.79644	+	6.75121i	−0.150121	+	0.362424i	−0.980994	−	0.194038i	$-0.937842\pi$
$347$	−2.79644	+	6.75121i	−0.150121	+	0.362424i	0.830873	+	0.556462i	$0.187842\pi$
$348$		0			0
$349$	−3.16816	+	1.31229i	−0.169588	+	0.0702455i	−0.465862	−	0.884857i	$-0.654256\pi$
$349$	−3.16816	+	1.31229i	−0.169588	+	0.0702455i	0.296274	+	0.955103i	$0.404256\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	29.8578i		−	1.58917i	−0.607151	−	0.794586i	$-0.707688\pi$
$353$		−	29.8578i		−	1.58917i	0.607151	−	0.794586i	$-0.292312\pi$
$354$		0			0
$355$	−10.3330	−	24.9461i	−0.548419	−	1.32400i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−9.44266	−	9.44266i	−0.498365	−	0.498365i	0.412564	−	0.910929i	$-0.364633\pi$
$359$	−9.44266	−	9.44266i	−0.498365	−	0.498365i	−0.910929	+	0.412564i	$0.864633\pi$
$360$		0			0
$361$	−8.14189	+	8.14189i	−0.428521	+	0.428521i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−12.1826	+	5.04620i	−0.637667	+	0.264130i
$366$		0			0
$367$	−26.8327			−1.40065			−0.700327	−	0.713822i	$-0.746962\pi$
$367$	−26.8327			−1.40065			−0.700327	+	0.713822i	$0.746962\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−6.13001	−	14.7991i	−0.318254	−	0.768334i
$372$		0			0
$373$	−12.3312	−	5.10777i	−0.638487	−	0.264470i	0.0398670	−	0.999205i	$-0.487307\pi$
$373$	−12.3312	−	5.10777i	−0.638487	−	0.264470i	−0.678354	+	0.734735i	$0.737307\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	6.62683	−	6.62683i	0.341299	−	0.341299i
$378$		0			0
$379$	5.26078	+	2.17909i	0.270228	+	0.111932i	0.513683	−	0.857980i	$-0.328281\pi$
$379$	5.26078	+	2.17909i	0.270228	+	0.111932i	−0.243455	+	0.969912i	$0.578281\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	8.14683			0.416283			0.208142	−	0.978099i	$-0.433258\pi$
$383$	8.14683			0.416283			0.208142	+	0.978099i	$0.433258\pi$
$384$		0			0
$385$	4.73527			0.241332
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−8.22236	−	3.40581i	−0.416890	−	0.172682i	0.164371	−	0.986399i	$-0.447441\pi$
$389$	−8.22236	−	3.40581i	−0.416890	−	0.172682i	−0.581261	+	0.813717i	$0.697441\pi$
$390$		0			0
$391$	−4.84191	+	4.84191i	−0.244866	+	0.244866i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	19.7142	+	8.16588i	0.991927	+	0.410870i
$396$		0			0
$397$	−0.328403	−	0.792834i	−0.0164821	−	0.0397912i	0.915424	−	0.402490i	$-0.131855\pi$
$397$	−0.328403	−	0.792834i	−0.0164821	−	0.0397912i	−0.931906	+	0.362699i	$0.881855\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−17.3098			−0.864411			−0.432206	−	0.901775i	$-0.642265\pi$
$401$	−17.3098			−0.864411			−0.432206	+	0.901775i	$0.642265\pi$
$402$		0			0
$403$	42.8484	−	17.7484i	2.13443	−	0.884111i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.46314	−	4.46314i	0.221230	−	0.221230i
$408$		0			0
$409$	5.00972	+	5.00972i	0.247715	+	0.247715i	0.820032	−	0.572317i	$-0.193955\pi$
$409$	5.00972	+	5.00972i	0.247715	+	0.247715i	−0.572317	+	0.820032i	$0.693955\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	13.4062	+	32.3654i	0.659675	+	1.59260i
$414$		0			0
$415$			5.82422i			0.285900i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	7.01103	−	2.90406i	0.342511	−	0.141873i	−0.204796	−	0.978805i	$-0.565653\pi$
$419$	7.01103	−	2.90406i	0.342511	−	0.141873i	0.547307	+	0.836932i	$0.315653\pi$
$420$		0			0
$421$	3.94749	−	9.53009i	0.192389	−	0.464468i	−0.798021	−	0.602630i	$-0.794119\pi$
$421$	3.94749	−	9.53009i	0.192389	−	0.464468i	0.990410	+	0.138162i	$0.0441195\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.854002	−	0.854002i	−0.0414252	−	0.0414252i
$426$		0			0
$427$	14.8103	−	35.7552i	0.716719	−	1.73031i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			11.8098i			0.568858i	0.958697	+	0.284429i	$0.0918040\pi$
$431$			11.8098i			0.568858i	−0.958697	+	0.284429i	$0.908196\pi$
$432$		0			0
$433$			3.26662i			0.156984i	0.996915	+	0.0784919i	$0.0250105\pi$
$433$			3.26662i			0.156984i	−0.996915	+	0.0784919i	$0.974990\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−7.40772	+	17.8838i	−0.354359	+	0.855499i
$438$		0			0
$439$	−13.7003	−	13.7003i	−0.653877	−	0.653877i	0.300047	−	0.953924i	$-0.402998\pi$
$439$	−13.7003	−	13.7003i	−0.653877	−	0.653877i	−0.953924	+	0.300047i	$0.902998\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−7.53737	+	18.1968i	−0.358111	+	0.864557i	0.637454	+	0.770488i	$0.279988\pi$
$443$	−7.53737	+	18.1968i	−0.358111	+	0.864557i	−0.995566	+	0.0940692i	$0.970012\pi$
$444$		0			0
$445$	−17.2763	+	7.15607i	−0.818974	+	0.339230i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	2.46488i		−	0.116325i	−0.998307	−	0.0581625i	$-0.981476\pi$
$449$		−	2.46488i		−	0.116325i	0.998307	−	0.0581625i	$-0.0185241\pi$
$450$		0			0
$451$	2.72200	+	6.57150i	0.128174	+	0.309440i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	28.8174	+	28.8174i	1.35098	+	1.35098i
$456$		0			0
$457$	3.04617	−	3.04617i	0.142494	−	0.142494i	−0.632261	−	0.774755i	$-0.717873\pi$
$457$	3.04617	−	3.04617i	0.142494	−	0.142494i	0.774755	+	0.632261i	$0.217873\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	9.85993	−	4.08412i	0.459223	−	0.190216i	−0.141065	−	0.990000i	$-0.545053\pi$
$461$	9.85993	−	4.08412i	0.459223	−	0.190216i	0.600288	+	0.799784i	$0.295053\pi$
$462$		0			0
$463$	28.1511			1.30829			0.654147	−	0.756367i	$-0.273028\pi$
$463$	28.1511			1.30829			0.654147	+	0.756367i	$0.273028\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	0.133756	+	0.322916i	0.00618951	+	0.0149428i	0.926944	−	0.375200i	$-0.122426\pi$
$467$	0.133756	+	0.322916i	0.00618951	+	0.0149428i	−0.920755	+	0.390142i	$0.872426\pi$
$468$		0			0
$469$	−11.9123	−	4.93425i	−0.550060	−	0.227842i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.86573	+	1.86573i	−0.0857863	+	0.0857863i
$474$		0			0
$475$	−3.15430	−	1.30655i	−0.144729	−	0.0599487i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	25.3551			1.15850			0.579251	−	0.815149i	$-0.303345\pi$
$479$	25.3551			1.15850			0.579251	+	0.815149i	$0.303345\pi$
$480$		0			0
$481$	54.3226			2.47690
$482$		0			0
$483$		0			0
$484$		0			0
$485$	13.7436	+	5.69280i	0.624066	+	0.258497i
$486$		0			0
$487$	15.5211	−	15.5211i	0.703327	−	0.703327i	−0.261796	−	0.965123i	$-0.584315\pi$
$487$	15.5211	−	15.5211i	0.703327	−	0.703327i	0.965123	+	0.261796i	$0.0843149\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−7.79527	−	3.22890i	−0.351795	−	0.145718i	0.199786	−	0.979840i	$-0.435975\pi$
$491$	−7.79527	−	3.22890i	−0.351795	−	0.145718i	−0.551581	+	0.834121i	$0.685975\pi$
$492$		0			0
$493$	−0.545281	−	1.31642i	−0.0245582	−	0.0592888i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−46.0722			−2.06662
$498$		0			0
$499$	2.14784	−	0.889664i	0.0961504	−	0.0398268i	−0.334090	−	0.942541i	$-0.608429\pi$
$499$	2.14784	−	0.889664i	0.0961504	−	0.0398268i	0.430240	+	0.902714i	$0.358429\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−10.4975	+	10.4975i	−0.468062	+	0.468062i	−0.901286	−	0.433224i	$-0.857376\pi$
$503$	−10.4975	+	10.4975i	−0.468062	+	0.468062i	0.433224	+	0.901286i	$0.357376\pi$
$504$		0			0
$505$	−1.55712	−	1.55712i	−0.0692908	−	0.0692908i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	8.62373	+	20.8195i	0.382240	+	0.922810i	0.991532	+	0.129863i	$0.0414539\pi$
$509$	8.62373	+	20.8195i	0.382240	+	0.922810i	−0.609292	+	0.792946i	$0.708546\pi$
$510$		0			0
$511$			22.4997i			0.995329i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−17.8769	+	7.40485i	−0.787750	+	0.326297i
$516$		0			0
$517$	−1.04523	+	2.52340i	−0.0459690	+	0.110979i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−23.6260	−	23.6260i	−1.03508	−	1.03508i	−0.999362	−	0.0357139i	$-0.988630\pi$
$521$	−23.6260	−	23.6260i	−1.03508	−	1.03508i	−0.0357139	−	0.999362i	$-0.511370\pi$
$522$		0			0
$523$	0.967311	−	2.33529i	0.0422975	−	0.102115i	−0.901319	−	0.433156i	$-0.857400\pi$
$523$	0.967311	−	2.33529i	0.0422975	−	0.102115i	0.943616	+	0.331041i	$0.107400\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	7.05147i		−	0.307167i
$528$		0			0
$529$		−	27.0566i		−	1.17638i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−23.4268	+	56.5574i	−1.01473	+	2.44977i
$534$		0			0
$535$	23.9203	+	23.9203i	1.03416	+	1.03416i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.11067	−	2.68138i	0.0478398	−	0.115495i
$540$		0			0
$541$	13.3578	−	5.53299i	0.574298	−	0.237882i	−0.0765813	−	0.997063i	$-0.524400\pi$
$541$	13.3578	−	5.53299i	0.574298	−	0.237882i	0.650879	+	0.759181i	$0.274400\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$			3.90464i			0.167257i
$546$		0			0
$547$	16.5682	+	39.9992i	0.708406	+	1.71024i	0.703945	+	0.710254i	$0.251420\pi$
$547$	16.5682	+	39.9992i	0.708406	+	1.71024i	0.00446097	+	0.999990i	$0.498580\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.84825	−	2.84825i	−0.121340	−	0.121340i
$552$		0			0
$553$	25.7454	−	25.7454i	1.09481	−	1.09481i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−5.70924	+	2.36484i	−0.241908	+	0.100202i	−0.500344	−	0.865827i	$-0.666793\pi$
$557$	−5.70924	+	2.36484i	−0.241908	+	0.100202i	0.258436	+	0.966029i	$0.416793\pi$
$558$		0			0
$559$	−22.7085			−0.960467
$560$		0			0
$561$		0			0
$562$		0			0
$563$	5.89410	+	14.2296i	0.248407	+	0.599707i	0.998069	−	0.0621133i	$-0.0197840\pi$
$563$	5.89410	+	14.2296i	0.248407	+	0.599707i	−0.749662	+	0.661821i	$0.769784\pi$
$564$		0			0
$565$	−1.29962	−	0.538322i	−0.0546756	−	0.0226474i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−0.242674	+	0.242674i	−0.0101734	+	0.0101734i	−0.712175	−	0.702002i	$-0.752290\pi$
$569$	−0.242674	+	0.242674i	−0.0101734	+	0.0101734i	0.702002	+	0.712175i	$0.252290\pi$
$570$		0			0
$571$	−25.8985	−	10.7275i	−1.08382	−	0.448933i	−0.231972	−	0.972722i	$-0.574518\pi$
$571$	−25.8985	−	10.7275i	−1.08382	−	0.448933i	−0.851848	+	0.523789i	$0.824518\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	8.82885			0.368188
$576$		0			0
$577$	17.7896			0.740589			0.370294	−	0.928914i	$-0.379257\pi$
$577$	17.7896			0.740589			0.370294	+	0.928914i	$0.379257\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	9.18133	+	3.80303i	0.380906	+	0.157776i
$582$		0			0
$583$	2.53473	−	2.53473i	0.104978	−	0.104978i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	30.9718	+	12.8289i	1.27834	+	0.529507i	0.915490	−	0.402340i	$-0.131803\pi$
$587$	30.9718	+	12.8289i	1.27834	+	0.529507i	0.362852	+	0.931847i	$0.381803\pi$
$588$		0			0
$589$	−7.62838	−	18.4165i	−0.314322	−	0.758840i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	41.4635			1.70270			0.851351	−	0.524596i	$-0.175784\pi$
$593$	41.4635			1.70270			0.851351	+	0.524596i	$0.175784\pi$
$594$		0			0
$595$	5.72460	−	2.37121i	0.234686	−	0.0972100i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	32.9148	−	32.9148i	1.34486	−	1.34486i	0.453719	−	0.891145i	$-0.350097\pi$
$599$	32.9148	−	32.9148i	1.34486	−	1.34486i	0.891145	−	0.453719i	$-0.149903\pi$
$600$		0			0
$601$	−12.5748	−	12.5748i	−0.512936	−	0.512936i	0.402489	−	0.915425i	$-0.368145\pi$
$601$	−12.5748	−	12.5748i	−0.512936	−	0.512936i	−0.915425	+	0.402489i	$0.868145\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−7.74848	−	18.7065i	−0.315021	−	0.760527i
$606$		0			0
$607$			46.0240i			1.86806i	0.357198	+	0.934029i	$0.383732\pi$
$607$			46.0240i			1.86806i	−0.357198	+	0.934029i	$0.616268\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−21.7176	+	8.99570i	−0.878598	+	0.363927i
$612$		0			0
$613$	3.81762	−	9.21655i	0.154192	−	0.372253i	−0.827841	−	0.560963i	$-0.810431\pi$
$613$	3.81762	−	9.21655i	0.154192	−	0.372253i	0.982033	+	0.188711i	$0.0604308\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	9.42700	+	9.42700i	0.379517	+	0.379517i	0.870928	−	0.491411i	$-0.163519\pi$
$617$	9.42700	+	9.42700i	0.379517	+	0.379517i	−0.491411	+	0.870928i	$0.663519\pi$
$618$		0			0
$619$	10.4213	−	25.1593i	0.418868	−	1.01124i	−0.563808	−	0.825906i	$-0.690664\pi$
$619$	10.4213	−	25.1593i	0.418868	−	1.01124i	0.982676	−	0.185332i	$-0.0593359\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$			31.9071i			1.27833i
$624$		0			0
$625$		−	17.2034i		−	0.688136i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	3.16068	−	7.63055i	0.126024	−	0.304250i
$630$		0			0
$631$	−15.7973	−	15.7973i	−0.628879	−	0.628879i	0.318907	−	0.947786i	$-0.396684\pi$
$631$	−15.7973	−	15.7973i	−0.628879	−	0.628879i	−0.947786	+	0.318907i	$0.896684\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	8.57545	−	20.7030i	0.340307	−	0.821573i
$636$		0			0
$637$	23.0772	−	9.55891i	0.914354	−	0.378738i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	11.2466i		−	0.444215i	−0.975022	−	0.222107i	$-0.928706\pi$
$641$		−	11.2466i		−	0.444215i	0.975022	−	0.222107i	$-0.0712936\pi$
$642$		0			0
$643$	−4.46309	−	10.7749i	−0.176007	−	0.424919i	0.811115	−	0.584886i	$-0.198861\pi$
$643$	−4.46309	−	10.7749i	−0.176007	−	0.424919i	−0.987122	+	0.159968i	$0.948861\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	22.9908	+	22.9908i	0.903861	+	0.903861i	0.995768	−	0.0919063i	$-0.0292960\pi$
$647$	22.9908	+	22.9908i	0.903861	+	0.903861i	−0.0919063	+	0.995768i	$0.529296\pi$
$648$		0			0
$649$	−5.54340	+	5.54340i	−0.217597	+	0.217597i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.731559	−	0.303022i	0.0286281	−	0.0118582i	−0.368323	−	0.929698i	$-0.620068\pi$
$653$	0.731559	−	0.303022i	0.0286281	−	0.0118582i	0.396952	+	0.917840i	$0.370068\pi$
$654$		0			0
$655$	37.5804			1.46839
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−3.48735	−	8.41921i	−0.135848	−	0.327966i	0.841286	−	0.540590i	$-0.181799\pi$
$659$	−3.48735	−	8.41921i	−0.135848	−	0.327966i	−0.977134	+	0.212624i	$0.931799\pi$
$660$		0			0
$661$	22.6551	+	9.38406i	0.881182	+	0.364998i	0.776955	−	0.629556i	$-0.216763\pi$
$661$	22.6551	+	9.38406i	0.881182	+	0.364998i	0.104227	+	0.994554i	$0.466763\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	12.3859	−	12.3859i	0.480305	−	0.480305i
$666$		0			0
$667$	9.62334	+	3.98612i	0.372617	+	0.154343i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	8.66062			0.334340
$672$		0			0
$673$	−17.3835			−0.670084			−0.335042	−	0.942203i	$-0.608751\pi$
$673$	−17.3835			−0.670084			−0.335042	+	0.942203i	$0.608751\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−39.4502	−	16.3408i	−1.51620	−	0.628029i	−0.539371	−	0.842068i	$-0.681338\pi$
$677$	−39.4502	−	16.3408i	−1.51620	−	0.628029i	−0.976825	+	0.214040i	$0.931338\pi$
$678$		0			0
$679$	17.9483	−	17.9483i	0.688793	−	0.688793i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−40.6471	−	16.8366i	−1.55532	−	0.644234i	−0.571049	−	0.820916i	$-0.693464\pi$
$683$	−40.6471	−	16.8366i	−1.55532	−	0.644234i	−0.984268	+	0.176682i	$0.943464\pi$
$684$		0			0
$685$	−16.7591	−	40.4602i	−0.640334	−	1.54590i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	30.8512			1.17534
$690$		0			0
$691$	0.769203	−	0.318614i	0.0292619	−	0.0121207i	−0.368005	−	0.929824i	$-0.619959\pi$
$691$	0.769203	−	0.318614i	0.0292619	−	0.0121207i	0.397266	+	0.917703i	$0.369959\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.130751	+	0.130751i	−0.00495965	+	0.00495965i
$696$		0			0
$697$	6.58141	+	6.58141i	0.249289	+	0.249289i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	10.7572	+	25.9701i	0.406292	+	0.980876i	0.986105	+	0.166126i	$0.0531259\pi$
$701$	10.7572	+	25.9701i	0.406292	+	0.980876i	−0.579812	+	0.814750i	$0.696874\pi$
$702$		0			0
$703$		−	23.3482i		−	0.880595i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.47140	+	1.43790i	−0.130555	+	0.0540778i
$708$		0			0
$709$	−13.7081	+	33.0944i	−0.514820	+	1.24289i	0.426229	+	0.904615i	$0.359842\pi$
$709$	−13.7081	+	33.0944i	−0.514820	+	1.24289i	−0.941049	+	0.338270i	$0.890158\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	36.4497	+	36.4497i	1.36505	+	1.36505i
$714$		0			0
$715$	−3.49008	+	8.42579i	−0.130522	+	0.315107i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	24.7319i		−	0.922345i	−0.887311	−	0.461172i	$-0.847429\pi$
$719$		−	24.7319i		−	0.922345i	0.887311	−	0.461172i	$-0.152571\pi$
$720$		0			0
$721$			33.0163i			1.22959i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.703060	+	1.69734i	−0.0261110	+	0.0630375i
$726$		0			0
$727$	−4.89101	−	4.89101i	−0.181397	−	0.181397i	0.610567	−	0.791965i	$-0.290942\pi$
$727$	−4.89101	−	4.89101i	−0.181397	−	0.181397i	−0.791965	+	0.610567i	$0.790942\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.32126	+	3.18980i	−0.0488685	+	0.117979i
$732$		0			0
$733$	−10.2058	+	4.22736i	−0.376958	+	0.156141i	−0.563114	−	0.826379i	$-0.690397\pi$
$733$	−10.2058	+	4.22736i	−0.376958	+	0.156141i	0.186156	+	0.982520i	$0.440397\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	2.88540i		−	0.106285i
$738$		0			0
$739$	−1.71029	−	4.12900i	−0.0629139	−	0.151888i	0.889296	−	0.457332i	$-0.151195\pi$
$739$	−1.71029	−	4.12900i	−0.0629139	−	0.151888i	−0.952210	+	0.305445i	$0.901195\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	12.6977	+	12.6977i	0.465832	+	0.465832i	0.900561	−	0.434729i	$-0.143156\pi$
$743$	12.6977	+	12.6977i	0.465832	+	0.465832i	−0.434729	+	0.900561i	$0.643156\pi$
$744$		0			0
$745$	20.7405	−	20.7405i	0.759873	−	0.759873i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	53.3272	−	22.0888i	1.94853	−	0.807108i
$750$		0			0
$751$	25.3864			0.926362			0.463181	−	0.886264i	$-0.346708\pi$
$751$	25.3864			0.926362			0.463181	+	0.886264i	$0.346708\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−7.83185	−	18.9078i	−0.285030	−	0.688123i
$756$		0			0
$757$	48.9351	+	20.2696i	1.77858	+	0.736711i	0.993023	+	0.117918i	$0.0376220\pi$
$757$	48.9351	+	20.2696i	1.77858	+	0.736711i	0.785554	+	0.618793i	$0.212378\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−7.18378	+	7.18378i	−0.260412	+	0.260412i	−0.825221	−	0.564809i	$-0.808950\pi$
$761$	−7.18378	+	7.18378i	−0.260412	+	0.260412i	0.564809	+	0.825221i	$0.308950\pi$
$762$		0			0
$763$	6.15530	+	2.54961i	0.222837	+	0.0923020i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−67.4708			−2.43623
$768$		0			0
$769$	−48.6570			−1.75462			−0.877309	−	0.479926i	$-0.840663\pi$
$769$	−48.6570			−1.75462			−0.877309	+	0.479926i	$0.840663\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−7.43579	−	3.08000i	−0.267447	−	0.110780i	0.244930	−	0.969541i	$-0.421235\pi$
$773$	−7.43579	−	3.08000i	−0.267447	−	0.110780i	−0.512377	+	0.858761i	$0.671235\pi$
$774$		0			0
$775$	−6.42890	+	6.42890i	−0.230933	+	0.230933i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	24.3087	+	10.0690i	0.870951	+	0.360760i
$780$		0			0
$781$	−3.94552	−	9.52534i	−0.141182	−	0.340843i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−23.1411			−0.825940
$786$		0			0
$787$	−14.9915	+	6.20966i	−0.534388	+	0.221351i	−0.633524	−	0.773723i	$-0.718392\pi$
$787$	−14.9915	+	6.20966i	−0.534388	+	0.221351i	0.0991360	+	0.995074i	$0.468392\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−1.69722	+	1.69722i	−0.0603464	+	0.0603464i
$792$		0			0
$793$	52.7058	+	52.7058i	1.87164	+	1.87164i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−2.43692	−	5.88325i	−0.0863202	−	0.208395i	0.874825	−	0.484439i	$-0.160976\pi$
$797$	−2.43692	−	5.88325i	−0.0863202	−	0.208395i	−0.961145	+	0.276044i	$0.910976\pi$
$798$		0			0
$799$			3.57401i			0.126439i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−4.65177	+	1.92682i	−0.164157	+	0.0679962i
$804$		0			0
$805$	−17.3340	+	41.8480i	−0.610944	+	1.47495i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−9.30765	−	9.30765i	−0.327240	−	0.327240i	0.524296	−	0.851536i	$-0.324328\pi$
$809$	−9.30765	−	9.30765i	−0.327240	−	0.327240i	−0.851536	+	0.524296i	$0.824328\pi$
$810$		0			0
$811$	8.10599	−	19.5696i	0.284640	−	0.687181i	−0.715292	−	0.698825i	$-0.753706\pi$
$811$	8.10599	−	19.5696i	0.284640	−	0.687181i	0.999932	+	0.0116440i	$0.00370648\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$			16.7023i			0.585056i
$816$		0			0
$817$			9.76026i			0.341468i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−3.81353	+	9.20668i	−0.133093	+	0.321315i	−0.976350	−	0.216195i	$-0.930635\pi$
$821$	−3.81353	+	9.20668i	−0.133093	+	0.321315i	0.843257	+	0.537511i	$0.180635\pi$
$822$		0			0
$823$	16.5761	+	16.5761i	0.577808	+	0.577808i	0.934299	−	0.356491i	$-0.116027\pi$
$823$	16.5761	+	16.5761i	0.577808	+	0.577808i	−0.356491	+	0.934299i	$0.616027\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−11.1677	+	26.9613i	−0.388340	+	0.937537i	0.601951	+	0.798533i	$0.294390\pi$
$827$	−11.1677	+	26.9613i	−0.388340	+	0.937537i	−0.990292	+	0.139004i	$0.955610\pi$
$828$		0			0
$829$	8.82768	−	3.65654i	0.306598	−	0.126997i	−0.224080	−	0.974571i	$-0.571938\pi$
$829$	8.82768	−	3.65654i	0.306598	−	0.126997i	0.530678	+	0.847574i	$0.321938\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		−	3.79777i		−	0.131585i
$834$		0			0
$835$	0.0787391	+	0.190093i	0.00272488	+	0.00657844i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−4.55814	−	4.55814i	−0.157364	−	0.157364i	0.624033	−	0.781398i	$-0.285493\pi$
$839$	−4.55814	−	4.55814i	−0.157364	−	0.157364i	−0.781398	+	0.624033i	$0.785493\pi$
$840$		0			0
$841$	18.9734	−	18.9734i	0.654257	−	0.654257i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−49.2516	+	20.4007i	−1.69431	+	0.701805i
$846$		0			0
$847$	−34.5485			−1.18710
$848$		0			0
$849$		0			0
$850$		0			0
$851$	23.1052	+	55.7809i	0.792037	+	1.91215i
$852$		0			0
$853$	13.7268	+	5.68583i	0.469997	+	0.194679i	0.605095	−	0.796153i	$-0.293135\pi$
$853$	13.7268	+	5.68583i	0.469997	+	0.194679i	−0.135098	+	0.990832i	$0.543135\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−11.1744	+	11.1744i	−0.381711	+	0.381711i	−0.871718	−	0.490007i	$-0.836994\pi$
$857$	−11.1744	+	11.1744i	−0.381711	+	0.381711i	0.490007	+	0.871718i	$0.336994\pi$
$858$		0			0
$859$	−39.1836	−	16.2304i	−1.33693	−	0.553773i	−0.404304	−	0.914625i	$-0.632486\pi$
$859$	−39.1836	−	16.2304i	−1.33693	−	0.553773i	−0.932623	+	0.360851i	$0.882486\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	22.2298			0.756710			0.378355	−	0.925661i	$-0.376490\pi$
$863$	22.2298			0.756710			0.378355	+	0.925661i	$0.376490\pi$
$864$		0			0
$865$	−44.0379			−1.49733
$866$		0			0
$867$		0			0
$868$		0			0
$869$	7.52760	+	3.11803i	0.255356	+	0.105772i
$870$		0			0
$871$	17.5597	−	17.5597i	0.594987	−	0.594987i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−36.9553	−	15.3074i	−1.24932	−	0.517484i
$876$		0			0
$877$	3.13025	+	7.55709i	0.105701	+	0.255185i	0.967877	−	0.251424i	$-0.0808989\pi$
$877$	3.13025	+	7.55709i	0.105701	+	0.255185i	−0.862176	+	0.506609i	$0.830899\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−4.77921			−0.161016			−0.0805078	−	0.996754i	$-0.525654\pi$
$881$	−4.77921			−0.161016			−0.0805078	+	0.996754i	$0.525654\pi$
$882$		0			0
$883$	45.1752	−	18.7122i	1.52027	−	0.629716i	0.542622	−	0.839977i	$-0.317431\pi$
$883$	45.1752	−	18.7122i	1.52027	−	0.629716i	0.977645	+	0.210261i	$0.0674314\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−6.92890	+	6.92890i	−0.232650	+	0.232650i	−0.813798	−	0.581148i	$-0.802604\pi$
$887$	−6.92890	+	6.92890i	−0.232650	+	0.232650i	0.581148	+	0.813798i	$0.302604\pi$
$888$		0			0
$889$	−27.0368	−	27.0368i	−0.906784	−	0.906784i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	3.86641	+	9.33435i	0.129385	+	0.312362i
$894$		0			0
$895$		−	22.0453i		−	0.736894i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−9.91000	+	4.10486i	−0.330517	+	0.136905i
$900$		0			0
$901$	1.79503	−	4.33358i	0.0598011	−	0.144373i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−6.35622	−	6.35622i	−0.211288	−	0.211288i
$906$		0			0
$907$	−14.4242	+	34.8230i	−0.478946	+	1.15628i	0.481157	+	0.876634i	$0.340217\pi$
$907$	−14.4242	+	34.8230i	−0.478946	+	1.15628i	−0.960104	+	0.279644i	$0.909783\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	44.7402i		−	1.48231i	−0.671335	−	0.741154i	$-0.734279\pi$
$911$		−	44.7402i		−	1.48231i	0.671335	−	0.741154i	$-0.265721\pi$
$912$		0			0
$913$			2.22390i			0.0736004i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	24.5388	−	59.2418i	0.810342	−	1.95634i
$918$		0			0
$919$	−25.4709	−	25.4709i	−0.840207	−	0.840207i	0.148678	−	0.988886i	$-0.452498\pi$
$919$	−25.4709	−	25.4709i	−0.840207	−	0.840207i	−0.988886	+	0.148678i	$0.952498\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	33.9570	−	81.9795i	1.11771	−	2.69839i
$924$		0			0
$925$	−9.83848	+	4.07523i	−0.323487	+	0.133993i
$926$		0			0
$927$		0			0
$928$		0			0
$929$		−	23.0747i		−	0.757058i	−0.925589	−	0.378529i	$-0.876430\pi$
$929$		−	23.0747i		−	0.757058i	0.925589	−	0.378529i	$-0.123570\pi$
$930$		0			0
$931$	−4.10848	−	9.91875i	−0.134650	−	0.325074i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.980484	+	0.980484i	0.0320652	+	0.0320652i
$936$		0			0
$937$	6.57961	−	6.57961i	0.214947	−	0.214947i	−0.591418	−	0.806365i	$-0.701432\pi$
$937$	6.57961	−	6.57961i	0.214947	−	0.214947i	0.806365	+	0.591418i	$0.201432\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	40.5076	−	16.7788i	1.32051	−	0.546973i	0.392577	−	0.919719i	$-0.371584\pi$
$941$	40.5076	−	16.7788i	1.32051	−	0.546973i	0.927934	+	0.372746i	$0.121584\pi$
$942$		0			0
$943$	−68.0399			−2.21569
$944$		0			0
$945$		0			0
$946$		0			0
$947$	21.7966	+	52.6218i	0.708296	+	1.70998i	0.704216	+	0.709986i	$0.251299\pi$
$947$	21.7966	+	52.6218i	0.708296	+	1.70998i	0.00407986	+	0.999992i	$0.498701\pi$
$948$		0			0
$949$	−40.0353	−	16.5831i	−1.29960	−	0.538312i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−24.5821	+	24.5821i	−0.796293	+	0.796293i	−0.982509	−	0.186216i	$-0.940378\pi$
$953$	−24.5821	+	24.5821i	−0.796293	+	0.796293i	0.186216	+	0.982509i	$0.440378\pi$
$954$		0			0
$955$	−39.8574	−	16.5095i	−1.28976	−	0.534234i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−74.7248			−2.41299
$960$		0			0
$961$	−22.0832			−0.712362
$962$		0			0
$963$		0			0
$964$		0			0
$965$	19.4811	+	8.06932i	0.627118	+	0.259761i
$966$		0			0
$967$	19.1878	−	19.1878i	0.617037	−	0.617037i	−0.327734	−	0.944770i	$-0.606285\pi$
$967$	19.1878	−	19.1878i	0.617037	−	0.617037i	0.944770	+	0.327734i	$0.106285\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	35.5982	+	14.7453i	1.14240	+	0.473198i	0.871979	−	0.489544i	$-0.162837\pi$
$971$	35.5982	+	14.7453i	1.14240	+	0.473198i	0.270422	+	0.962742i	$0.412837\pi$
$972$		0			0
$973$	0.120740	+	0.291492i	0.00387074	+	0.00934479i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−10.7488			−0.343885			−0.171943	−	0.985107i	$-0.555004\pi$
$977$	−10.7488			−0.343885			−0.171943	+	0.985107i	$0.555004\pi$
$978$		0			0
$979$	−6.59672	+	2.73245i	−0.210832	+	0.0873295i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−15.2745	+	15.2745i	−0.487181	+	0.487181i	−0.907416	−	0.420234i	$-0.861948\pi$
$983$	−15.2745	+	15.2745i	−0.487181	+	0.487181i	0.420234	+	0.907416i	$0.361948\pi$
$984$		0			0
$985$	9.04516	+	9.04516i	0.288203	+	0.288203i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−9.65868	−	23.3181i	−0.307128	−	0.741473i
$990$		0			0
$991$			15.5708i			0.494622i	0.968936	+	0.247311i	$0.0795469\pi$
$991$			15.5708i			0.494622i	−0.968936	+	0.247311i	$0.920453\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−25.5836	+	10.5971i	−0.811053	+	0.335949i
$996$		0			0
$997$	−1.71754	+	4.14652i	−0.0543951	+	0.131321i	−0.948741	−	0.316055i	$-0.897642\pi$
$997$	−1.71754	+	4.14652i	−0.0543951	+	0.131321i	0.894346	+	0.447376i	$0.147642\pi$
$998$		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.719.7		32
3.2	odd	2		1152.2.w.a.719.2		32
4.3	odd	2		288.2.w.a.107.6	yes	32
12.11	even	2		288.2.w.b.107.3	yes	32
32.3	odd	8		1152.2.w.a.431.2		32
32.29	even	8		288.2.w.b.35.3	yes	32
96.29	odd	8		288.2.w.a.35.6	✓	32
96.35	even	8	inner	1152.2.w.b.431.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.35.6	✓	32	96.29	odd	8
288.2.w.a.107.6	yes	32	4.3	odd	2
288.2.w.b.35.3	yes	32	32.29	even	8
288.2.w.b.107.3	yes	32	12.11	even	2
1152.2.w.a.431.2		32	32.3	odd	8
1152.2.w.a.719.2		32	3.2	odd	2
1152.2.w.b.431.7		32	96.35	even	8	inner
1152.2.w.b.719.7		32	1.1	even	1	trivial

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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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(1.78959 + 0.741273i) q^{5} +(2.33709 - 2.33709i) q^{7} +(0.683332 + 0.283045i) q^{11} +(2.43602 + 5.88107i) q^{13} +0.967834 q^{17} +(2.52772 - 1.04702i) q^{19} +(-5.00283 + 5.00283i) q^{23} +(-0.882385 - 0.882385i) q^{25} +(-0.563403 - 1.36018i) q^{29} -7.28582i q^{31} +(5.91486 - 2.45001i) q^{35} +(3.26572 - 7.88415i) q^{37} +(6.80014 + 6.80014i) q^{41} +(-1.36517 + 3.29581i) q^{43} +3.69279i q^{47} -3.92399i q^{49} +(1.85469 - 4.47761i) q^{53} +(1.01307 + 1.01307i) q^{55} +(-4.05615 + 9.79242i) q^{59} +(10.8180 - 4.48097i) q^{61} +12.3305i q^{65} +(-1.49290 - 3.60418i) q^{67} +(-9.85675 - 9.85675i) q^{71} +(-4.81362 + 4.81362i) q^{73} +(2.25851 - 0.935506i) q^{77} +11.0160 q^{79} +(1.15064 + 2.77789i) q^{83} +(1.73203 + 0.717429i) q^{85} +(-6.82624 + 6.82624i) q^{89} +(19.4378 + 8.05140i) q^{91} +5.29971 q^{95} +7.67976 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{11} - 16 q^{29} - 24 q^{35} - 16 q^{53} + 32 q^{55} - 32 q^{59} + 32 q^{61} + 16 q^{67} - 16 q^{71} - 16 q^{77} + 32 q^{79} + 40 q^{83} + 48 q^{91} + 80 q^{95}+O(q^{100}) \) 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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