LMFDB - Embedded newform 1152.2.w.a.143.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1152.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.19876631285$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366958 + 0.885915i) q^{5} +(-1.21471 + 1.21471i) q^{7} +O(q^{10})$	$q+(-0.366958 + 0.885915i) q^{5} +(-1.21471 + 1.21471i) q^{7} +(0.545272 - 1.31640i) q^{11} +(0.0270492 - 0.0112041i) q^{13} -1.32687 q^{17} +(1.73653 + 4.19236i) q^{19} +(0.934512 - 0.934512i) q^{23} +(2.88535 + 2.88535i) q^{25} +(-9.35195 + 3.87371i) q^{29} +9.74390i q^{31} +(-0.630382 - 1.52188i) q^{35} +(-6.28278 - 2.60241i) q^{37} +(-3.42377 - 3.42377i) q^{41} +(-0.997463 - 0.413163i) q^{43} +6.21143i q^{47} +4.04896i q^{49} +(-2.94741 - 1.22086i) q^{53} +(0.966130 + 0.966130i) q^{55} +(-10.4533 - 4.32990i) q^{59} +(2.76809 + 6.68277i) q^{61} +0.0280747i q^{65} +(10.1069 - 4.18640i) q^{67} +(7.38725 + 7.38725i) q^{71} +(-8.30156 + 8.30156i) q^{73} +(0.936700 + 2.26139i) q^{77} -5.54363 q^{79} +(-11.4571 + 4.74570i) q^{83} +(0.486907 - 1.17550i) q^{85} +(7.93127 - 7.93127i) q^{89} +(-0.0192471 + 0.0464667i) q^{91} -4.35131 q^{95} +12.5582 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{11} + 16 q^{29} + 24 q^{35} + 16 q^{53} + 32 q^{55} + 32 q^{59} + 32 q^{61} + 16 q^{67} + 16 q^{71} + 16 q^{77} + 32 q^{79} - 40 q^{83} + 48 q^{91} - 80 q^{95}+O(q^{100}) $ 32 * q - 8 * q^11 + 16 * q^29 + 24 * q^35 + 16 * q^53 + 32 * q^55 + 32 * q^59 + 32 * q^61 + 16 * q^67 + 16 * q^71 + 16 * q^77 + 32 * q^79 - 40 * q^83 + 48 * q^91 - 80 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.366958	+	0.885915i	−0.164109	+	0.396193i	−0.984446	−	0.175686i	$-0.943786\pi$
$5$	−0.366958	+	0.885915i	−0.164109	+	0.396193i	0.820338	+	0.571880i	$0.193786\pi$
$6$		0			0
$7$	−1.21471	+	1.21471i	−0.459117	+	0.459117i	−0.898366	−	0.439249i	$-0.855245\pi$
$7$	−1.21471	+	1.21471i	−0.459117	+	0.459117i	0.439249	+	0.898366i	$0.355245\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.545272	−	1.31640i	0.164406	−	0.396910i	−0.820110	−	0.572206i	$-0.806088\pi$
$11$	0.545272	−	1.31640i	0.164406	−	0.396910i	0.984516	+	0.175295i	$0.0560879\pi$
$12$		0			0
$13$	0.0270492	−	0.0112041i	0.00750210	−	0.00310747i	−0.378929	−	0.925426i	$-0.623708\pi$
$13$	0.0270492	−	0.0112041i	0.00750210	−	0.00310747i	0.386431	+	0.922318i	$0.373708\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.32687			−0.321814			−0.160907	−	0.986970i	$-0.551442\pi$
$17$	−1.32687			−0.321814			−0.160907	+	0.986970i	$0.551442\pi$
$18$		0			0
$19$	1.73653	+	4.19236i	0.398388	+	0.961793i	0.988049	+	0.154142i	$0.0492614\pi$
$19$	1.73653	+	4.19236i	0.398388	+	0.961793i	−0.589661	+	0.807651i	$0.700739\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.934512	−	0.934512i	0.194859	−	0.194859i	−0.602933	−	0.797792i	$-0.706001\pi$
$23$	0.934512	−	0.934512i	0.194859	−	0.194859i	0.797792	+	0.602933i	$0.206001\pi$
$24$		0			0
$25$	2.88535	+	2.88535i	0.577069	+	0.577069i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−9.35195	+	3.87371i	−1.73661	+	0.719329i	−0.737586	+	0.675253i	$0.764034\pi$
$29$	−9.35195	+	3.87371i	−1.73661	+	0.719329i	−0.999028	+	0.0440761i	$0.985966\pi$
$30$		0			0
$31$			9.74390i			1.75006i	0.484072	+	0.875028i	$0.339157\pi$
$31$			9.74390i			1.75006i	−0.484072	+	0.875028i	$0.660843\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.630382	−	1.52188i	−0.106554	−	0.257244i
$36$		0			0
$37$	−6.28278	−	2.60241i	−1.03288	−	0.427834i	−0.199131	−	0.979973i	$-0.563812\pi$
$37$	−6.28278	−	2.60241i	−1.03288	−	0.427834i	−0.833752	+	0.552139i	$0.813812\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.42377	−	3.42377i	−0.534703	−	0.534703i	0.387266	−	0.921968i	$-0.373420\pi$
$41$	−3.42377	−	3.42377i	−0.534703	−	0.534703i	−0.921968	+	0.387266i	$0.873420\pi$
$42$		0			0
$43$	−0.997463	−	0.413163i	−0.152112	−	0.0630067i	0.305329	−	0.952247i	$-0.401234\pi$
$43$	−0.997463	−	0.413163i	−0.152112	−	0.0630067i	−0.457440	+	0.889240i	$0.651234\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			6.21143i			0.906031i	0.891503	+	0.453015i	$0.149652\pi$
$47$			6.21143i			0.906031i	−0.891503	+	0.453015i	$0.850348\pi$
$48$		0			0
$49$			4.04896i			0.578423i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2.94741	−	1.22086i	−0.404858	−	0.167698i	0.170955	−	0.985279i	$-0.445315\pi$
$53$	−2.94741	−	1.22086i	−0.404858	−	0.167698i	−0.575814	+	0.817581i	$0.695315\pi$
$54$		0			0
$55$	0.966130	+	0.966130i	0.130273	+	0.130273i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−10.4533	−	4.32990i	−1.36090	−	0.563704i	−0.421596	−	0.906784i	$-0.638530\pi$
$59$	−10.4533	−	4.32990i	−1.36090	−	0.563704i	−0.939306	+	0.343079i	$0.888530\pi$
$60$		0			0
$61$	2.76809	+	6.68277i	0.354418	+	0.855641i	0.996064	+	0.0886397i	$0.0282520\pi$
$61$	2.76809	+	6.68277i	0.354418	+	0.855641i	−0.641646	+	0.767001i	$0.721748\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			0.0280747i			0.00348224i
$66$		0			0
$67$	10.1069	−	4.18640i	1.23475	−	0.511450i	0.332680	−	0.943040i	$-0.392047\pi$
$67$	10.1069	−	4.18640i	1.23475	−	0.511450i	0.902070	+	0.431590i	$0.142047\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	7.38725	+	7.38725i	0.876705	+	0.876705i	0.993192	−	0.116487i	$-0.0371633\pi$
$71$	7.38725	+	7.38725i	0.876705	+	0.876705i	−0.116487	+	0.993192i	$0.537163\pi$
$72$		0			0
$73$	−8.30156	+	8.30156i	−0.971625	+	0.971625i	−0.999608	−	0.0279838i	$-0.991091\pi$
$73$	−8.30156	+	8.30156i	−0.971625	+	0.971625i	0.0279838	+	0.999608i	$0.491091\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.936700	+	2.26139i	0.106747	+	0.257710i
$78$		0			0
$79$	−5.54363			−0.623707			−0.311853	−	0.950130i	$-0.600950\pi$
$79$	−5.54363			−0.623707			−0.311853	+	0.950130i	$0.600950\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−11.4571	+	4.74570i	−1.25758	+	0.520909i	−0.909167	−	0.416431i	$-0.863281\pi$
$83$	−11.4571	+	4.74570i	−1.25758	+	0.520909i	−0.348417	+	0.937340i	$0.613281\pi$
$84$		0			0
$85$	0.486907	−	1.17550i	0.0528125	−	0.127501i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	7.93127	−	7.93127i	0.840713	−	0.840713i	−0.148238	−	0.988952i	$-0.547360\pi$
$89$	7.93127	−	7.93127i	0.840713	−	0.840713i	0.988952	+	0.148238i	$0.0473603\pi$
$90$		0			0
$91$	−0.0192471	+	0.0464667i	−0.00201765	+	0.00487103i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−4.35131			−0.446435
$96$		0			0
$97$	12.5582			1.27509			0.637545	−	0.770413i	$-0.279950\pi$
$97$	12.5582			1.27509			0.637545	+	0.770413i	$0.279950\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.67080	+	4.03367i	−0.166251	+	0.401365i	−0.984946	−	0.172864i	$-0.944698\pi$
$101$	−1.67080	+	4.03367i	−0.166251	+	0.401365i	0.818695	+	0.574229i	$0.194698\pi$
$102$		0			0
$103$	2.18742	−	2.18742i	0.215533	−	0.215533i	−0.591080	−	0.806613i	$-0.701298\pi$
$103$	2.18742	−	2.18742i	0.215533	−	0.215533i	0.806613	+	0.591080i	$0.201298\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.09671	−	7.47611i	0.299370	−	0.722743i	−0.700588	−	0.713566i	$-0.747079\pi$
$107$	3.09671	−	7.47611i	0.299370	−	0.722743i	0.999958	−	0.00917704i	$-0.00292118\pi$
$108$		0			0
$109$	−0.499988	+	0.207102i	−0.0478902	+	0.0198368i	−0.406500	−	0.913651i	$-0.633251\pi$
$109$	−0.499988	+	0.207102i	−0.0478902	+	0.0198368i	0.358610	+	0.933488i	$0.383251\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	19.7112			1.85427			0.927137	−	0.374722i	$-0.122262\pi$
$113$	19.7112			1.85427			0.927137	+	0.374722i	$0.122262\pi$
$114$		0			0
$115$	0.484972	+	1.17083i	0.0452239	+	0.109180i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.61177	−	1.61177i	0.147750	−	0.147750i
$120$		0			0
$121$	6.34258	+	6.34258i	0.576598	+	0.576598i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−8.04455	+	3.33216i	−0.719526	+	0.298038i
$126$		0			0
$127$			12.1620i			1.07920i	0.841920	+	0.539602i	$0.181425\pi$
$127$			12.1620i			1.07920i	−0.841920	+	0.539602i	$0.818575\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1.68416	−	4.06591i	−0.147145	−	0.355240i	0.833072	−	0.553165i	$-0.186580\pi$
$131$	−1.68416	−	4.06591i	−0.147145	−	0.355240i	−0.980217	+	0.197924i	$0.936580\pi$
$132$		0			0
$133$	−7.20188	−	2.98312i	−0.624482	−	0.258669i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.05217	−	7.05217i	−0.602508	−	0.602508i	0.338470	−	0.940977i	$-0.390091\pi$
$137$	−7.05217	−	7.05217i	−0.602508	−	0.602508i	−0.940977	+	0.338470i	$0.890091\pi$
$138$		0			0
$139$	−13.5567	−	5.61536i	−1.14986	−	0.476288i	−0.275374	−	0.961337i	$-0.588802\pi$
$139$	−13.5567	−	5.61536i	−1.14986	−	0.476288i	−0.874487	+	0.485049i	$0.838802\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	0.0417169i		−	0.00348855i
$144$		0			0
$145$		−	9.70653i		−	0.806083i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	8.14803	+	3.37503i	0.667513	+	0.276493i	0.690596	−	0.723241i	$-0.257348\pi$
$149$	8.14803	+	3.37503i	0.667513	+	0.276493i	−0.0230832	+	0.999734i	$0.507348\pi$
$150$		0			0
$151$	−13.4470	−	13.4470i	−1.09430	−	1.09430i	−0.995064	−	0.0992395i	$-0.968359\pi$
$151$	−13.4470	−	13.4470i	−1.09430	−	1.09430i	−0.0992395	−	0.995064i	$-0.531641\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−8.63227	−	3.57560i	−0.693361	−	0.287199i
$156$		0			0
$157$	1.17205	+	2.82959i	0.0935400	+	0.225826i	0.963724	−	0.266902i	$-0.0860000\pi$
$157$	1.17205	+	2.82959i	0.0935400	+	0.225826i	−0.870184	+	0.492727i	$0.836000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			2.27032i			0.178926i
$162$		0			0
$163$	14.7015	−	6.08955i	1.15151	−	0.476970i	0.276469	−	0.961023i	$-0.410836\pi$
$163$	14.7015	−	6.08955i	1.15151	−	0.476970i	0.875039	+	0.484052i	$0.160836\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.30270	+	8.30270i	0.642482	+	0.642482i	0.951165	−	0.308683i	$-0.0998882\pi$
$167$	8.30270	+	8.30270i	0.642482	+	0.642482i	−0.308683	+	0.951165i	$0.599888\pi$
$168$		0			0
$169$	−9.19178	+	9.19178i	−0.707060	+	0.707060i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	5.16308	+	12.4648i	0.392542	+	0.947680i	0.989384	+	0.145322i	$0.0464217\pi$
$173$	5.16308	+	12.4648i	0.392542	+	0.947680i	−0.596843	+	0.802358i	$0.703578\pi$
$174$		0			0
$175$	−7.00971			−0.529885
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1.43728	−	0.595340i	0.107427	−	0.0444978i	−0.328323	−	0.944566i	$-0.606483\pi$
$179$	1.43728	−	0.595340i	0.107427	−	0.0444978i	0.435750	+	0.900068i	$0.356483\pi$
$180$		0			0
$181$	5.57818	−	13.4669i	0.414623	−	1.00099i	−0.569258	−	0.822159i	$-0.692769\pi$
$181$	5.57818	−	13.4669i	0.414623	−	1.00099i	0.983880	−	0.178828i	$-0.0572307\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	4.61104	−	4.61104i	0.339010	−	0.339010i
$186$		0			0
$187$	−0.723507	+	1.74670i	−0.0529081	+	0.127731i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−7.01680			−0.507718			−0.253859	−	0.967241i	$-0.581700\pi$
$191$	−7.01680			−0.507718			−0.253859	+	0.967241i	$0.581700\pi$
$192$		0			0
$193$	21.3761			1.53868			0.769342	−	0.638837i	$-0.220584\pi$
$193$	21.3761			1.53868			0.769342	+	0.638837i	$0.220584\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	4.34168	−	10.4817i	0.309332	−	0.746793i	−0.690395	−	0.723432i	$-0.742563\pi$
$197$	4.34168	−	10.4817i	0.309332	−	0.746793i	0.999727	−	0.0233605i	$-0.00743654\pi$
$198$		0			0
$199$	9.04307	−	9.04307i	0.641047	−	0.641047i	−0.309766	−	0.950813i	$-0.600251\pi$
$199$	9.04307	−	9.04307i	0.641047	−	0.641047i	0.950813	+	0.309766i	$0.100251\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	6.65448	−	16.0653i	0.467053	−	1.12757i
$204$		0			0
$205$	4.28955	−	1.77679i	0.299595	−	0.124096i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	6.46572			0.447243
$210$		0			0
$211$	−5.73872	−	13.8545i	−0.395070	−	0.953783i	−0.988817	−	0.149132i	$-0.952352\pi$
$211$	−5.73872	−	13.8545i	−0.395070	−	0.953783i	0.593747	−	0.804652i	$-0.297648\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.732055	−	0.732055i	0.0499257	−	0.0499257i
$216$		0			0
$217$	−11.8360	−	11.8360i	−0.803480	−	0.803480i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.0358909	+	0.0148665i	−0.00241428	+	0.00100003i
$222$		0			0
$223$		−	0.0857822i		−	0.00574440i	−0.999996	−	0.00287220i	$-0.999086\pi$
$223$		−	0.0857822i		−	0.00574440i	0.999996	−	0.00287220i	$-0.000914251\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.62555	+	23.2381i	0.638870	+	1.54237i	0.828187	+	0.560452i	$0.189373\pi$
$227$	9.62555	+	23.2381i	0.638870	+	1.54237i	−0.189317	+	0.981916i	$0.560627\pi$
$228$		0			0
$229$	−24.5201	−	10.1566i	−1.62034	−	0.671165i	−0.626237	−	0.779633i	$-0.715406\pi$
$229$	−24.5201	−	10.1566i	−1.62034	−	0.671165i	−0.994100	+	0.108468i	$0.965406\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.44973	+	2.44973i	0.160487	+	0.160487i	0.782782	−	0.622295i	$-0.213800\pi$
$233$	2.44973	+	2.44973i	0.160487	+	0.160487i	−0.622295	+	0.782782i	$0.713800\pi$
$234$		0			0
$235$	−5.50280	−	2.27934i	−0.358963	−	0.148687i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	11.3256i		−	0.732589i	−0.930499	−	0.366295i	$-0.880626\pi$
$239$		−	11.3256i		−	0.732589i	0.930499	−	0.366295i	$-0.119374\pi$
$240$		0			0
$241$		−	13.4166i		−	0.864239i	−0.901816	−	0.432119i	$-0.857766\pi$
$241$		−	13.4166i		−	0.864239i	0.901816	−	0.432119i	$-0.142234\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.58704	−	1.48580i	−0.229167	−	0.0949243i
$246$		0			0
$247$	0.0939436	+	0.0939436i	0.00597749	+	0.00597749i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	15.2970	+	6.33621i	0.965535	+	0.399938i	0.809048	−	0.587742i	$-0.199983\pi$
$251$	15.2970	+	6.33621i	0.965535	+	0.399938i	0.156487	+	0.987680i	$0.449983\pi$
$252$		0			0
$253$	−0.720632	−	1.73976i	−0.0453057	−	0.109378i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	2.43408i		−	0.151833i	−0.997114	−	0.0759167i	$-0.975812\pi$
$257$		−	2.43408i		−	0.151833i	0.997114	−	0.0759167i	$-0.0241883\pi$
$258$		0			0
$259$	10.7929	−	4.47058i	0.670640	−	0.277788i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	15.2250	+	15.2250i	0.938816	+	0.938816i	0.998233	−	0.0594176i	$-0.0189244\pi$
$263$	15.2250	+	15.2250i	0.938816	+	0.938816i	−0.0594176	+	0.998233i	$0.518924\pi$
$264$		0			0
$265$	2.16316	−	2.16316i	0.132882	−	0.132882i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−2.29849	−	5.54904i	−0.140141	−	0.338331i	0.838190	−	0.545379i	$-0.183614\pi$
$269$	−2.29849	−	5.54904i	−0.140141	−	0.338331i	−0.978331	+	0.207048i	$0.933614\pi$
$270$		0			0
$271$	10.5866			0.643088			0.321544	−	0.946895i	$-0.395798\pi$
$271$	10.5866			0.643088			0.321544	+	0.946895i	$0.395798\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	5.37158	−	2.22498i	0.323918	−	0.134171i
$276$		0			0
$277$	5.91980	−	14.2917i	0.355686	−	0.858702i	−0.640210	−	0.768200i	$-0.721153\pi$
$277$	5.91980	−	14.2917i	0.355686	−	0.858702i	0.995896	−	0.0905024i	$-0.0288473\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−12.0206	+	12.0206i	−0.717087	+	0.717087i	−0.968008	−	0.250921i	$-0.919267\pi$
$281$	−12.0206	+	12.0206i	−0.717087	+	0.717087i	0.250921	+	0.968008i	$0.419267\pi$
$282$		0			0
$283$	5.86696	−	14.1641i	0.348754	−	0.841968i	−0.648013	−	0.761629i	$-0.724400\pi$
$283$	5.86696	−	14.1641i	0.348754	−	0.841968i	0.996768	−	0.0803386i	$-0.0256002\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	8.31776			0.490982
$288$		0			0
$289$	−15.2394			−0.896436
$290$		0			0
$291$		0			0
$292$		0			0
$293$	6.02149	−	14.5372i	0.351779	−	0.849270i	−0.644622	−	0.764502i	$-0.722985\pi$
$293$	6.02149	−	14.5372i	0.351779	−	0.849270i	0.996401	−	0.0847682i	$-0.0270150\pi$
$294$		0			0
$295$	7.67184	−	7.67184i	0.446672	−	0.446672i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.0148074	−	0.0357482i	0.000856334	−	0.00206737i
$300$		0			0
$301$	1.71350	−	0.709755i	0.0987645	−	0.0409096i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−6.93614			−0.397162
$306$		0			0
$307$	10.0677	+	24.3055i	0.574592	+	1.38719i	0.897608	+	0.440795i	$0.145303\pi$
$307$	10.0677	+	24.3055i	0.574592	+	1.38719i	−0.323016	+	0.946394i	$0.604697\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	22.5777	−	22.5777i	1.28027	−	1.28027i	0.339751	−	0.940516i	$-0.389657\pi$
$311$	22.5777	−	22.5777i	1.28027	−	1.28027i	0.940516	−	0.339751i	$-0.110343\pi$
$312$		0			0
$313$	−9.91862	−	9.91862i	−0.560633	−	0.560633i	0.368854	−	0.929487i	$-0.379750\pi$
$313$	−9.91862	−	9.91862i	−0.560633	−	0.560633i	−0.929487	+	0.368854i	$0.879750\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−10.4152	+	4.31414i	−0.584979	+	0.242306i	−0.655489	−	0.755205i	$-0.727537\pi$
$317$	−10.4152	+	4.31414i	−0.584979	+	0.242306i	0.0705101	+	0.997511i	$0.477537\pi$
$318$		0			0
$319$			14.4232i			0.807542i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−2.30416	−	5.56273i	−0.128207	−	0.309519i
$324$		0			0
$325$	0.110374	+	0.0457185i	0.00612245	+	0.00253600i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−7.54509	−	7.54509i	−0.415974	−	0.415974i
$330$		0			0
$331$	−13.0127	−	5.39006i	−0.715245	−	0.296264i	−0.00477208	−	0.999989i	$-0.501519\pi$
$331$	−13.0127	−	5.39006i	−0.715245	−	0.296264i	−0.710473	+	0.703724i	$0.751519\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			10.4901i			0.573133i
$336$		0			0
$337$		−	16.7271i		−	0.911182i	−0.890189	−	0.455591i	$-0.849428\pi$
$337$		−	16.7271i		−	0.911182i	0.890189	−	0.455591i	$-0.150572\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	12.8269	+	5.31308i	0.694616	+	0.287719i
$342$		0			0
$343$	−13.4213	−	13.4213i	−0.724681	−	0.724681i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	17.4060	+	7.20981i	0.934404	+	0.387043i	0.797347	−	0.603521i	$-0.206236\pi$
$347$	17.4060	+	7.20981i	0.934404	+	0.387043i	0.137056	+	0.990563i	$0.456236\pi$
$348$		0			0
$349$	8.01279	+	19.3446i	0.428915	+	1.03549i	0.979632	+	0.200800i	$0.0643541\pi$
$349$	8.01279	+	19.3446i	0.428915	+	1.03549i	−0.550718	+	0.834692i	$0.685646\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			29.2201i			1.55523i	0.628743	+	0.777613i	$0.283570\pi$
$353$			29.2201i			1.55523i	−0.628743	+	0.777613i	$0.716430\pi$
$354$		0			0
$355$	−9.25529	+	3.83367i	−0.491220	+	0.203470i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−23.8752	−	23.8752i	−1.26008	−	1.26008i	−0.951052	−	0.309032i	$-0.899995\pi$
$359$	−23.8752	−	23.8752i	−1.26008	−	1.26008i	−0.309032	−	0.951052i	$-0.600005\pi$
$360$		0			0
$361$	−1.12530	+	1.12530i	−0.0592262	+	0.0592262i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−4.30816	−	10.4008i	−0.225499	−	0.544403i
$366$		0			0
$367$	7.91904			0.413370			0.206685	−	0.978408i	$-0.433732\pi$
$367$	7.91904			0.413370			0.206685	+	0.978408i	$0.433732\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	5.06324	−	2.09726i	0.262870	−	0.108884i
$372$		0			0
$373$	−0.910870	+	2.19904i	−0.0471631	+	0.113862i	−0.945705	−	0.325025i	$-0.894627\pi$
$373$	−0.910870	+	2.19904i	−0.0471631	+	0.113862i	0.898542	+	0.438887i	$0.144627\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.209561	+	0.209561i	−0.0107930	+	0.0107930i
$378$		0			0
$379$	−8.94487	+	21.5948i	−0.459467	+	1.10925i	0.509146	+	0.860680i	$0.329961\pi$
$379$	−8.94487	+	21.5948i	−0.459467	+	1.10925i	−0.968613	+	0.248572i	$0.920039\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−8.41070			−0.429767			−0.214883	−	0.976640i	$-0.568937\pi$
$383$	−8.41070			−0.429767			−0.214883	+	0.976640i	$0.568937\pi$
$384$		0			0
$385$	−2.34713			−0.119621
$386$		0			0
$387$		0			0
$388$		0			0
$389$	4.66887	−	11.2717i	0.236721	−	0.571496i	−0.760219	−	0.649667i	$-0.774908\pi$
$389$	4.66887	−	11.2717i	0.236721	−	0.571496i	0.996940	+	0.0781715i	$0.0249082\pi$
$390$		0			0
$391$	−1.23998	+	1.23998i	−0.0627085	+	0.0627085i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.03428	−	4.91118i	0.102356	−	0.247108i
$396$		0			0
$397$	13.1886	−	5.46289i	0.661916	−	0.274175i	−0.0263285	−	0.999653i	$-0.508382\pi$
$397$	13.1886	−	5.46289i	0.661916	−	0.274175i	0.688245	+	0.725479i	$0.258382\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.87685			−0.193601			−0.0968004	−	0.995304i	$-0.530861\pi$
$401$	−3.87685			−0.193601			−0.0968004	+	0.995304i	$0.530861\pi$
$402$		0			0
$403$	0.109172	+	0.263565i	0.00543825	+	0.0131291i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−6.85165	+	6.85165i	−0.339624	+	0.339624i
$408$		0			0
$409$	6.61246	+	6.61246i	0.326965	+	0.326965i	0.851431	−	0.524466i	$-0.175735\pi$
$409$	6.61246	+	6.61246i	0.326965	+	0.326965i	−0.524466	+	0.851431i	$0.675735\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	17.9573	−	7.43815i	0.883620	−	0.366007i
$414$		0			0
$415$		−	11.8915i		−	0.583732i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	7.69097	+	18.5676i	0.375729	+	0.907089i	0.992756	+	0.120147i	$0.0383367\pi$
$419$	7.69097	+	18.5676i	0.375729	+	0.907089i	−0.617028	+	0.786942i	$0.711663\pi$
$420$		0			0
$421$	15.8875	+	6.58080i	0.774307	+	0.320729i	0.734616	−	0.678483i	$-0.237362\pi$
$421$	15.8875	+	6.58080i	0.774307	+	0.320729i	0.0396916	+	0.999212i	$0.487362\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3.82849	−	3.82849i	−0.185709	−	0.185709i
$426$		0			0
$427$	−11.4800	−	4.75519i	−0.555558	−	0.230120i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	12.7583i		−	0.614548i	−0.951621	−	0.307274i	$-0.900583\pi$
$431$		−	12.7583i		−	0.614548i	0.951621	−	0.307274i	$-0.0994168\pi$
$432$		0			0
$433$		−	1.18066i		−	0.0567390i	−0.999598	−	0.0283695i	$-0.990968\pi$
$433$		−	1.18066i		−	0.0567390i	0.999598	−	0.0283695i	$-0.00903150\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5.54062	+	2.29500i	0.265044	+	0.109785i
$438$		0			0
$439$	8.88783	+	8.88783i	0.424193	+	0.424193i	0.886644	−	0.462452i	$-0.153030\pi$
$439$	8.88783	+	8.88783i	0.424193	+	0.424193i	−0.462452	+	0.886644i	$0.653030\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−12.1498	−	5.03262i	−0.577255	−	0.239107i	0.0749018	−	0.997191i	$-0.476136\pi$
$443$	−12.1498	−	5.03262i	−0.577255	−	0.239107i	−0.652157	+	0.758084i	$0.726136\pi$
$444$		0			0
$445$	4.11599	+	9.93688i	0.195117	+	0.471053i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	0.529631i		−	0.0249948i	−0.999922	−	0.0124974i	$-0.996022\pi$
$449$		−	0.529631i		−	0.0249948i	0.999922	−	0.0124974i	$-0.00397815\pi$
$450$		0			0
$451$	−6.37394	+	2.64017i	−0.300137	+	0.124321i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.0341027	−	0.0341027i	−0.00159876	−	0.00159876i
$456$		0			0
$457$	−5.43494	+	5.43494i	−0.254236	+	0.254236i	−0.822705	−	0.568469i	$-0.807536\pi$
$457$	−5.43494	+	5.43494i	−0.254236	+	0.254236i	0.568469	+	0.822705i	$0.307536\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	7.55433	+	18.2378i	0.351840	+	0.849418i	0.996393	+	0.0848579i	$0.0270436\pi$
$461$	7.55433	+	18.2378i	0.351840	+	0.849418i	−0.644553	+	0.764560i	$0.722956\pi$
$462$		0			0
$463$	−4.63562			−0.215436			−0.107718	−	0.994182i	$-0.534354\pi$
$463$	−4.63562			−0.215436			−0.107718	+	0.994182i	$0.534354\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−18.9494	+	7.84910i	−0.876874	+	0.363213i	−0.775284	−	0.631613i	$-0.782393\pi$
$467$	−18.9494	+	7.84910i	−0.876874	+	0.363213i	−0.101590	+	0.994826i	$0.532393\pi$
$468$		0			0
$469$	−7.19164	+	17.3622i	−0.332079	+	0.801710i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.08778	+	1.08778i	−0.0500161	+	0.0500161i
$474$		0			0
$475$	−7.08591	+	17.1069i	−0.325124	+	0.784918i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−41.5437			−1.89818			−0.949089	−	0.315008i	$-0.897993\pi$
$479$	−41.5437			−1.89818			−0.949089	+	0.315008i	$0.897993\pi$
$480$		0			0
$481$	−0.199102			−0.00907827
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.60833	+	11.1255i	−0.209253	+	0.505182i
$486$		0			0
$487$	18.8137	−	18.8137i	0.852529	−	0.852529i	−0.137915	−	0.990444i	$-0.544040\pi$
$487$	18.8137	−	18.8137i	0.852529	−	0.852529i	0.990444	+	0.137915i	$0.0440400\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−7.29239	+	17.6054i	−0.329101	+	0.794520i	0.669559	+	0.742759i	$0.266483\pi$
$491$	−7.29239	+	17.6054i	−0.329101	+	0.794520i	−0.998660	+	0.0517607i	$0.983517\pi$
$492$		0			0
$493$	12.4089	−	5.13992i	0.558867	−	0.231490i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−17.9467			−0.805020
$498$		0			0
$499$	2.21640	+	5.35086i	0.0992197	+	0.239537i	0.965693	−	0.259685i	$-0.0836189\pi$
$499$	2.21640	+	5.35086i	0.0992197	+	0.239537i	−0.866474	+	0.499223i	$0.833619\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−13.1494	+	13.1494i	−0.586303	+	0.586303i	−0.936628	−	0.350325i	$-0.886071\pi$
$503$	−13.1494	+	13.1494i	−0.586303	+	0.586303i	0.350325	+	0.936628i	$0.386071\pi$
$504$		0			0
$505$	−2.96038	−	2.96038i	−0.131735	−	0.131735i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	11.1362	−	4.61276i	0.493603	−	0.204457i	−0.121975	−	0.992533i	$-0.538923\pi$
$509$	11.1362	−	4.61276i	0.493603	−	0.204457i	0.615578	+	0.788076i	$0.288923\pi$
$510$		0			0
$511$		−	20.1680i		−	0.892179i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.13518	+	2.74056i	0.0500219	+	0.120764i
$516$		0			0
$517$	8.17675	+	3.38692i	0.359613	+	0.148957i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	12.8812	+	12.8812i	0.564338	+	0.564338i	0.930537	−	0.366199i	$-0.119341\pi$
$521$	12.8812	+	12.8812i	0.564338	+	0.564338i	−0.366199	+	0.930537i	$0.619341\pi$
$522$		0			0
$523$	14.3454	+	5.94206i	0.627280	+	0.259828i	0.673597	−	0.739099i	$-0.264748\pi$
$523$	14.3454	+	5.94206i	0.627280	+	0.259828i	−0.0463167	+	0.998927i	$0.514748\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	12.9289i		−	0.563193i
$528$		0			0
$529$			21.2534i			0.924060i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−0.130971	−	0.0542498i	−0.00567296	−	0.00234982i
$534$		0			0
$535$	5.48684	+	5.48684i	0.237217	+	0.237217i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	5.33007	+	2.20779i	0.229582	+	0.0950961i
$540$		0			0
$541$	5.53641	+	13.3661i	0.238029	+	0.574653i	0.997079	−	0.0763798i	$-0.0243361\pi$
$541$	5.53641	+	13.3661i	0.238029	+	0.574653i	−0.759050	+	0.651033i	$0.774336\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		−	0.518945i		−	0.0222292i
$546$		0			0
$547$	−34.8390	+	14.4308i	−1.48961	+	0.617016i	−0.971232	−	0.238137i	$-0.923463\pi$
$547$	−34.8390	+	14.4308i	−1.48961	+	0.617016i	−0.518376	+	0.855153i	$0.673463\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−32.4799	−	32.4799i	−1.38369	−	1.38369i
$552$		0			0
$553$	6.73389	−	6.73389i	0.286354	−	0.286354i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−12.6874	−	30.6300i	−0.537581	−	1.29784i	−0.926407	−	0.376524i	$-0.877119\pi$
$557$	−12.6874	−	30.6300i	−0.537581	−	1.29784i	0.388826	−	0.921311i	$-0.372881\pi$
$558$		0			0
$559$	−0.0316097			−0.00133695
$560$		0			0
$561$		0			0
$562$		0			0
$563$	35.8986	−	14.8697i	1.51294	−	0.626682i	0.536781	−	0.843722i	$-0.319640\pi$
$563$	35.8986	−	14.8697i	1.51294	−	0.626682i	0.976163	+	0.217040i	$0.0696401\pi$
$564$		0			0
$565$	−7.23319	+	17.4625i	−0.304302	+	0.734651i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−19.9044	+	19.9044i	−0.834436	+	0.834436i	−0.988120	−	0.153684i	$-0.950886\pi$
$569$	−19.9044	+	19.9044i	−0.834436	+	0.834436i	0.153684	+	0.988120i	$0.450886\pi$
$570$		0			0
$571$	2.51768	−	6.07821i	0.105361	−	0.254365i	−0.862403	−	0.506223i	$-0.831041\pi$
$571$	2.51768	−	6.07821i	0.105361	−	0.254365i	0.967764	+	0.251857i	$0.0810414\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	5.39278			0.224895
$576$		0			0
$577$	−18.7117			−0.778980			−0.389490	−	0.921031i	$-0.627349\pi$
$577$	−18.7117			−0.778980			−0.389490	+	0.921031i	$0.627349\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	8.15244	−	19.6817i	0.338220	−	0.816536i
$582$		0			0
$583$	−3.21428	+	3.21428i	−0.133122	+	0.133122i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−12.8204	+	30.9512i	−0.529155	+	1.27749i	0.402922	+	0.915234i	$0.367995\pi$
$587$	−12.8204	+	30.9512i	−0.529155	+	1.27749i	−0.932077	+	0.362260i	$0.882005\pi$
$588$		0			0
$589$	−40.8499	+	16.9206i	−1.68319	+	0.697201i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−14.7730			−0.606654			−0.303327	−	0.952887i	$-0.598097\pi$
$593$	−14.7730			−0.606654			−0.303327	+	0.952887i	$0.598097\pi$
$594$		0			0
$595$	0.836437	+	2.01934i	0.0342906	+	0.0827848i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−17.9159	+	17.9159i	−0.732022	+	0.732022i	−0.971020	−	0.238998i	$-0.923181\pi$
$599$	−17.9159	+	17.9159i	−0.732022	+	0.732022i	0.238998	+	0.971020i	$0.423181\pi$
$600$		0			0
$601$	4.12098	+	4.12098i	0.168098	+	0.168098i	0.786143	−	0.618045i	$-0.212075\pi$
$601$	4.12098	+	4.12098i	0.168098	+	0.168098i	−0.618045	+	0.786143i	$0.712075\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−7.94645	+	3.29153i	−0.323069	+	0.133820i
$606$		0			0
$607$			25.4859i			1.03444i	0.855852	+	0.517220i	$0.173033\pi$
$607$			25.4859i			1.03444i	−0.855852	+	0.517220i	$0.826967\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.0695938	+	0.168014i	0.00281546	+	0.00679713i
$612$		0			0
$613$	35.2820	+	14.6143i	1.42503	+	0.590265i	0.956118	−	0.292982i	$-0.0946476\pi$
$613$	35.2820	+	14.6143i	1.42503	+	0.590265i	0.468908	+	0.883247i	$0.344648\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−13.7171	−	13.7171i	−0.552229	−	0.552229i	0.374855	−	0.927084i	$-0.377693\pi$
$617$	−13.7171	−	13.7171i	−0.552229	−	0.552229i	−0.927084	+	0.374855i	$0.877693\pi$
$618$		0			0
$619$	21.5287	+	8.91748i	0.865311	+	0.358424i	0.770782	−	0.637099i	$-0.219866\pi$
$619$	21.5287	+	8.91748i	0.865311	+	0.358424i	0.0945288	+	0.995522i	$0.469866\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$			19.2684i			0.771971i
$624$		0			0
$625$			12.0529i			0.482117i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	8.33646	+	3.45307i	0.332396	+	0.137683i
$630$		0			0
$631$	16.8025	+	16.8025i	0.668896	+	0.668896i	0.957460	−	0.288565i	$-0.0931780\pi$
$631$	16.8025	+	16.8025i	0.668896	+	0.668896i	−0.288565	+	0.957460i	$0.593178\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−10.7745	−	4.46295i	−0.427573	−	0.177107i
$636$		0			0
$637$	0.0453652	+	0.109521i	0.00179743	+	0.00433939i
$638$		0			0
$639$		0			0
$640$		0			0
$641$			10.7233i			0.423546i	0.977319	+	0.211773i	$0.0679238\pi$
$641$			10.7233i			0.423546i	−0.977319	+	0.211773i	$0.932076\pi$
$642$		0			0
$643$	30.3018	−	12.5514i	1.19499	−	0.494980i	0.305612	−	0.952156i	$-0.401139\pi$
$643$	30.3018	−	12.5514i	1.19499	−	0.494980i	0.889376	+	0.457176i	$0.151139\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.94231	+	4.94231i	0.194302	+	0.194302i	0.797552	−	0.603250i	$-0.206128\pi$
$647$	4.94231	+	4.94231i	0.194302	+	0.194302i	−0.603250	+	0.797552i	$0.706128\pi$
$648$		0			0
$649$	−11.3998	+	11.3998i	−0.447480	+	0.447480i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−5.01854	−	12.1158i	−0.196391	−	0.474129i	0.794751	−	0.606935i	$-0.207601\pi$
$653$	−5.01854	−	12.1158i	−0.196391	−	0.474129i	−0.991142	+	0.132806i	$0.957601\pi$
$654$		0			0
$655$	4.22007			0.164892
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−29.1760	+	12.0851i	−1.13653	+	0.470768i	−0.869997	−	0.493057i	$-0.835879\pi$
$659$	−29.1760	+	12.0851i	−1.13653	+	0.470768i	−0.266537	+	0.963825i	$0.585879\pi$
$660$		0			0
$661$	−15.3024	+	36.9433i	−0.595196	+	1.43693i	0.283231	+	0.959052i	$0.408594\pi$
$661$	−15.3024	+	36.9433i	−0.595196	+	1.43693i	−0.878426	+	0.477877i	$0.841406\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	5.28557	−	5.28557i	0.204966	−	0.204966i
$666$		0			0
$667$	−5.11949	+	12.3595i	−0.198227	+	0.478563i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	10.3066			0.397881
$672$		0			0
$673$	−6.49552			−0.250384			−0.125192	−	0.992133i	$-0.539955\pi$
$673$	−6.49552			−0.250384			−0.125192	+	0.992133i	$0.539955\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	2.62635	−	6.34057i	0.100939	−	0.243688i	−0.865340	−	0.501185i	$-0.832898\pi$
$677$	2.62635	−	6.34057i	0.100939	−	0.243688i	0.966279	+	0.257497i	$0.0828977\pi$
$678$		0			0
$679$	−15.2545	+	15.2545i	−0.585415	+	0.585415i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−4.22340	+	10.1962i	−0.161604	+	0.390146i	−0.983852	−	0.178982i	$-0.942719\pi$
$683$	−4.22340	+	10.1962i	−0.161604	+	0.390146i	0.822248	+	0.569129i	$0.192719\pi$
$684$		0			0
$685$	8.83548	−	3.65978i	0.337586	−	0.139833i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.0934039			−0.00355840
$690$		0			0
$691$	2.10014	+	5.07018i	0.0798931	+	0.192879i	0.958779	−	0.284153i	$-0.0917125\pi$
$691$	2.10014	+	5.07018i	0.0798931	+	0.192879i	−0.878886	+	0.477032i	$0.841712\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	9.94946	−	9.94946i	0.377404	−	0.377404i
$696$		0			0
$697$	4.54291	+	4.54291i	0.172075	+	0.172075i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	39.8651	−	16.5127i	1.50568	−	0.623675i	0.531022	−	0.847358i	$-0.321808\pi$
$701$	39.8651	−	16.5127i	1.50568	−	0.623675i	0.974662	+	0.223683i	$0.0718081\pi$
$702$		0			0
$703$		−	30.8588i		−	1.16386i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.87020	−	6.92928i	−0.107945	−	0.260602i
$708$		0			0
$709$	13.6775	+	5.66541i	0.513670	+	0.212769i	0.624434	−	0.781078i	$-0.285330\pi$
$709$	13.6775	+	5.66541i	0.513670	+	0.212769i	−0.110764	+	0.993847i	$0.535330\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	9.10580	+	9.10580i	0.341015	+	0.341015i
$714$		0			0
$715$	0.0369577	+	0.0153084i	0.00138214	+	0.000572501i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	38.0055i		−	1.41736i	−0.705528	−	0.708682i	$-0.749290\pi$
$719$		−	38.0055i		−	1.41736i	0.705528	−	0.708682i	$-0.250710\pi$
$720$		0			0
$721$			5.31416i			0.197910i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−38.1606	−	15.8066i	−1.41725	−	0.587044i
$726$		0			0
$727$	3.50408	+	3.50408i	0.129959	+	0.129959i	0.769094	−	0.639135i	$-0.220708\pi$
$727$	3.50408	+	3.50408i	0.129959	+	0.129959i	−0.639135	+	0.769094i	$0.720708\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	1.32351	+	0.548215i	0.0489517	+	0.0202765i
$732$		0			0
$733$	−18.0521	−	43.5817i	−0.666771	−	1.60973i	−0.786980	−	0.616978i	$-0.788357\pi$
$733$	−18.0521	−	43.5817i	−0.666771	−	1.60973i	0.120210	−	0.992749i	$-0.461643\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	15.5874i		−	0.574170i
$738$		0			0
$739$	−39.4444	+	16.3384i	−1.45098	+	0.601018i	−0.962433	−	0.271518i	$-0.912474\pi$
$739$	−39.4444	+	16.3384i	−1.45098	+	0.601018i	−0.488551	+	0.872535i	$0.662474\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−10.7638	−	10.7638i	−0.394884	−	0.394884i	0.481540	−	0.876424i	$-0.340078\pi$
$743$	−10.7638	−	10.7638i	−0.394884	−	0.394884i	−0.876424	+	0.481540i	$0.840078\pi$
$744$		0			0
$745$	−5.97997	+	5.97997i	−0.219089	+	0.219089i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	5.31970	+	12.8429i	0.194378	+	0.469269i
$750$		0			0
$751$	20.8234			0.759856			0.379928	−	0.925016i	$-0.375949\pi$
$751$	20.8234			0.759856			0.379928	+	0.925016i	$0.375949\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	16.8474	−	6.97843i	0.613140	−	0.253971i
$756$		0			0
$757$	4.51339	−	10.8963i	0.164042	−	0.396032i	−0.820389	−	0.571806i	$-0.806243\pi$
$757$	4.51339	−	10.8963i	0.164042	−	0.396032i	0.984431	+	0.175774i	$0.0562428\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−13.8159	+	13.8159i	−0.500826	+	0.500826i	−0.911695	−	0.410868i	$-0.865226\pi$
$761$	−13.8159	+	13.8159i	−0.500826	+	0.500826i	0.410868	+	0.911695i	$0.365226\pi$
$762$		0			0
$763$	0.355772	−	0.858909i	0.0128798	−	0.0310946i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.331266			−0.0119613
$768$		0			0
$769$	10.2754			0.370539			0.185270	−	0.982688i	$-0.440684\pi$
$769$	10.2754			0.370539			0.185270	+	0.982688i	$0.440684\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−20.3918	+	49.2302i	−0.733442	+	1.77069i	−0.102674	+	0.994715i	$0.532740\pi$
$773$	−20.3918	+	49.2302i	−0.733442	+	1.77069i	−0.630769	+	0.775971i	$0.717260\pi$
$774$		0			0
$775$	−28.1145	+	28.1145i	−1.00990	+	1.00990i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	8.40818	−	20.2991i	0.301254	−	0.727292i
$780$		0			0
$781$	13.7527	−	5.69654i	0.492109	−	0.203838i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−2.93687			−0.104821
$786$		0			0
$787$	−12.3657	−	29.8534i	−0.440789	−	1.06416i	−0.975672	−	0.219233i	$-0.929644\pi$
$787$	−12.3657	−	29.8534i	−0.440789	−	1.06416i	0.534883	−	0.844926i	$-0.320356\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−23.9434	+	23.9434i	−0.851329	+	0.851329i
$792$		0			0
$793$	0.149749	+	0.149749i	0.00531776	+	0.00531776i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	3.74523	−	1.55133i	0.132663	−	0.0549508i	−0.315364	−	0.948971i	$-0.602127\pi$
$797$	3.74523	−	1.55133i	0.132663	−	0.0549508i	0.448027	+	0.894020i	$0.352127\pi$
$798$		0			0
$799$		−	8.24179i		−	0.291574i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	6.40159	+	15.4548i	0.225907	+	0.545389i
$804$		0			0
$805$	−2.01131	−	0.833113i	−0.0708895	−	0.0293634i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	20.1580	+	20.1580i	0.708716	+	0.708716i	0.966265	−	0.257549i	$-0.0829148\pi$
$809$	20.1580	+	20.1580i	0.708716	+	0.708716i	−0.257549	+	0.966265i	$0.582915\pi$
$810$		0			0
$811$	24.3626	+	10.0913i	0.855487	+	0.354354i	0.766941	−	0.641718i	$-0.221778\pi$
$811$	24.3626	+	10.0913i	0.855487	+	0.354354i	0.0885462	+	0.996072i	$0.471778\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$			15.2589i			0.534495i
$816$		0			0
$817$		−	4.89919i		−	0.171401i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−13.0897	−	5.42194i	−0.456834	−	0.189227i	0.142386	−	0.989811i	$-0.454523\pi$
$821$	−13.0897	−	5.42194i	−0.456834	−	0.189227i	−0.599220	+	0.800584i	$0.704523\pi$
$822$		0			0
$823$	25.7815	+	25.7815i	0.898685	+	0.898685i	0.995320	−	0.0966346i	$-0.0308078\pi$
$823$	25.7815	+	25.7815i	0.898685	+	0.898685i	−0.0966346	+	0.995320i	$0.530808\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	38.7610	+	16.0553i	1.34785	+	0.558299i	0.935694	−	0.352813i	$-0.114775\pi$
$827$	38.7610	+	16.0553i	1.34785	+	0.558299i	0.412159	+	0.911112i	$0.364775\pi$
$828$		0			0
$829$	0.355576	+	0.858437i	0.0123497	+	0.0298148i	0.929934	−	0.367726i	$-0.119864\pi$
$829$	0.355576	+	0.858437i	0.0123497	+	0.0298148i	−0.917584	+	0.397541i	$0.869864\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		−	5.37246i		−	0.186145i
$834$		0			0
$835$	−10.4022	+	4.30875i	−0.359984	+	0.149110i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	17.1750	+	17.1750i	0.592947	+	0.592947i	0.938426	−	0.345479i	$-0.112284\pi$
$839$	17.1750	+	17.1750i	0.592947	+	0.592947i	−0.345479	+	0.938426i	$0.612284\pi$
$840$		0			0
$841$	51.9474	−	51.9474i	1.79129	−	1.79129i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−4.77014	−	11.5161i	−0.164098	−	0.396167i
$846$		0			0
$847$	−15.4088			−0.529452
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−8.30333	+	3.43935i	−0.284634	+	0.117899i
$852$		0			0
$853$	16.4371	−	39.6827i	0.562797	−	1.35871i	−0.344724	−	0.938704i	$-0.612028\pi$
$853$	16.4371	−	39.6827i	0.562797	−	1.35871i	0.907521	−	0.420007i	$-0.137972\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−18.0099	+	18.0099i	−0.615208	+	0.615208i	−0.944298	−	0.329090i	$-0.893258\pi$
$857$	−18.0099	+	18.0099i	−0.615208	+	0.615208i	0.329090	+	0.944298i	$0.393258\pi$
$858$		0			0
$859$	7.09982	−	17.1405i	0.242243	−	0.584826i	−0.755262	−	0.655423i	$-0.772490\pi$
$859$	7.09982	−	17.1405i	0.242243	−	0.584826i	0.997505	+	0.0705969i	$0.0224904\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	56.4875			1.92286			0.961429	−	0.275052i	$-0.0886952\pi$
$863$	56.4875			1.92286			0.961429	+	0.275052i	$0.0886952\pi$
$864$		0			0
$865$	−12.9374			−0.439884
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−3.02278	+	7.29765i	−0.102541	+	0.247556i
$870$		0			0
$871$	0.226477	−	0.226477i	0.00767389	−	0.00767389i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	5.72418	−	13.8194i	0.193513	−	0.467181i
$876$		0			0
$877$	−31.8952	+	13.2114i	−1.07702	+	0.446118i	−0.849464	−	0.527646i	$-0.823075\pi$
$877$	−31.8952	+	13.2114i	−1.07702	+	0.446118i	−0.227560	+	0.973764i	$0.573075\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−38.8053			−1.30739			−0.653693	−	0.756760i	$-0.726781\pi$
$881$	−38.8053			−1.30739			−0.653693	+	0.756760i	$0.726781\pi$
$882$		0			0
$883$	−0.251252	−	0.606576i	−0.00845531	−	0.0204129i	0.919595	−	0.392867i	$-0.128517\pi$
$883$	−0.251252	−	0.606576i	−0.00845531	−	0.0204129i	−0.928051	+	0.372454i	$0.878517\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	35.1536	−	35.1536i	1.18034	−	1.18034i	0.200687	−	0.979655i	$-0.435683\pi$
$887$	35.1536	−	35.1536i	1.18034	−	1.18034i	0.979655	−	0.200687i	$-0.0643173\pi$
$888$		0			0
$889$	−14.7733	−	14.7733i	−0.495481	−	0.495481i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−26.0406	+	10.7864i	−0.871414	+	0.360952i
$894$		0			0
$895$			1.49177i			0.0498644i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−37.7450	−	91.1245i	−1.25887	−	3.03917i
$900$		0			0
$901$	3.91085	+	1.61993i	0.130289	+	0.0539676i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	9.88358	+	9.88358i	0.328541	+	0.328541i
$906$		0			0
$907$	24.2246	+	10.0341i	0.804363	+	0.333178i	0.746703	−	0.665158i	$-0.231636\pi$
$907$	24.2246	+	10.0341i	0.804363	+	0.333178i	0.0576607	+	0.998336i	$0.481636\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			21.9666i			0.727787i	0.931441	+	0.363894i	$0.118553\pi$
$911$			21.9666i			0.727787i	−0.931441	+	0.363894i	$0.881447\pi$
$912$		0			0
$913$			17.6699i			0.584789i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	6.98466	+	2.89314i	0.230654	+	0.0955399i
$918$		0			0
$919$	−29.5302	−	29.5302i	−0.974110	−	0.974110i	0.0255634	−	0.999673i	$-0.491862\pi$
$919$	−29.5302	−	29.5302i	−0.974110	−	0.974110i	−0.999673	+	0.0255634i	$0.991862\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	0.282587	+	0.117051i	0.00930146	+	0.00385279i
$924$		0			0
$925$	−10.6191	−	25.6369i	−0.349155	−	0.842935i
$926$		0			0
$927$		0			0
$928$		0			0
$929$		−	39.0425i		−	1.28094i	−0.767983	−	0.640471i	$-0.778739\pi$
$929$		−	39.0425i		−	1.28094i	0.767983	−	0.640471i	$-0.221261\pi$
$930$		0			0
$931$	−16.9747	+	7.03115i	−0.556323	+	0.230437i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.28193	−	1.28193i	−0.0419237	−	0.0419237i
$936$		0			0
$937$	32.3364	−	32.3364i	1.05638	−	1.05638i	0.0580711	−	0.998312i	$-0.481505\pi$
$937$	32.3364	−	32.3364i	1.05638	−	1.05638i	0.998312	−	0.0580711i	$-0.0184950\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	15.7360	+	37.9900i	0.512979	+	1.23844i	0.942142	+	0.335213i	$0.108808\pi$
$941$	15.7360	+	37.9900i	0.512979	+	1.23844i	−0.429164	+	0.903227i	$0.641192\pi$
$942$		0			0
$943$	−6.39911			−0.208384
$944$		0			0
$945$		0			0
$946$		0			0
$947$	38.4816	−	15.9396i	1.25048	−	0.517967i	0.343508	−	0.939150i	$-0.388385\pi$
$947$	38.4816	−	15.9396i	1.25048	−	0.517967i	0.906976	+	0.421182i	$0.138385\pi$
$948$		0			0
$949$	−0.131539	+	0.317563i	−0.00426993	+	0.0103085i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	41.7980	−	41.7980i	1.35397	−	1.35397i	0.472800	−	0.881170i	$-0.343243\pi$
$953$	41.7980	−	41.7980i	1.35397	−	1.35397i	0.881170	−	0.472800i	$-0.156757\pi$
$954$		0			0
$955$	2.57487	−	6.21629i	0.0833209	−	0.201154i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	17.1327			0.553243
$960$		0			0
$961$	−63.9436			−2.06270
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−7.84413	+	18.9374i	−0.252511	+	0.609616i
$966$		0			0
$967$	−31.3866	+	31.3866i	−1.00933	+	1.00933i	−0.00937024	+	0.999956i	$0.502983\pi$
$967$	−31.3866	+	31.3866i	−1.00933	+	1.00933i	−0.999956	+	0.00937024i	$0.997017\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−20.4873	+	49.4608i	−0.657469	+	1.58727i	0.144230	+	0.989544i	$0.453929\pi$
$971$	−20.4873	+	49.4608i	−0.657469	+	1.58727i	−0.801700	+	0.597727i	$0.796071\pi$
$972$		0			0
$973$	23.2884	−	9.64638i	0.746593	−	0.309249i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	15.6979			0.502221			0.251110	−	0.967958i	$-0.419204\pi$
$977$	15.6979			0.502221			0.251110	+	0.967958i	$0.419204\pi$
$978$		0			0
$979$	−6.11605	−	14.7655i	−0.195470	−	0.471906i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−17.7012	+	17.7012i	−0.564581	+	0.564581i	−0.930605	−	0.366024i	$-0.880719\pi$
$983$	−17.7012	+	17.7012i	−0.564581	+	0.564581i	0.366024	+	0.930605i	$0.380719\pi$
$984$		0			0
$985$	7.69271	+	7.69271i	0.245110	+	0.245110i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1.31825	+	0.546036i	−0.0419178	+	0.0173629i
$990$		0			0
$991$		−	58.1793i		−	1.84813i	−0.382240	−	0.924063i	$-0.624847\pi$
$991$		−	58.1793i		−	1.84813i	0.382240	−	0.924063i	$-0.375153\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	4.69297	+	11.3298i	0.148777	+	0.359180i
$996$		0			0
$997$	−9.72099	−	4.02656i	−0.307867	−	0.127523i	0.223401	−	0.974727i	$-0.428284\pi$
$997$	−9.72099	−	4.02656i	−0.307867	−	0.127523i	−0.531268	+	0.847204i	$0.678284\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.w.a.143.3		32
3.2	odd	2		1152.2.w.b.143.6		32
4.3	odd	2		288.2.w.b.251.8	yes	32
12.11	even	2		288.2.w.a.251.1	yes	32
32.13	even	8		288.2.w.a.179.1	✓	32
32.19	odd	8		1152.2.w.b.1007.6		32
96.77	odd	8		288.2.w.b.179.8	yes	32
96.83	even	8	inner	1152.2.w.a.1007.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.179.1	✓	32	32.13	even	8
288.2.w.a.251.1	yes	32	12.11	even	2
288.2.w.b.179.8	yes	32	96.77	odd	8
288.2.w.b.251.8	yes	32	4.3	odd	2
1152.2.w.a.143.3		32	1.1	even	1	trivial
1152.2.w.a.1007.3		32	96.83	even	8	inner
1152.2.w.b.143.6		32	3.2	odd	2
1152.2.w.b.1007.6		32	32.19	odd	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.366958 + 0.885915i) q^{5} +(-1.21471 + 1.21471i) q^{7} +O(q^{10})\)	\(q+(-0.366958 + 0.885915i) q^{5} +(-1.21471 + 1.21471i) q^{7} +(0.545272 - 1.31640i) q^{11} +(0.0270492 - 0.0112041i) q^{13} -1.32687 q^{17} +(1.73653 + 4.19236i) q^{19} +(0.934512 - 0.934512i) q^{23} +(2.88535 + 2.88535i) q^{25} +(-9.35195 + 3.87371i) q^{29} +9.74390i q^{31} +(-0.630382 - 1.52188i) q^{35} +(-6.28278 - 2.60241i) q^{37} +(-3.42377 - 3.42377i) q^{41} +(-0.997463 - 0.413163i) q^{43} +6.21143i q^{47} +4.04896i q^{49} +(-2.94741 - 1.22086i) q^{53} +(0.966130 + 0.966130i) q^{55} +(-10.4533 - 4.32990i) q^{59} +(2.76809 + 6.68277i) q^{61} +0.0280747i q^{65} +(10.1069 - 4.18640i) q^{67} +(7.38725 + 7.38725i) q^{71} +(-8.30156 + 8.30156i) q^{73} +(0.936700 + 2.26139i) q^{77} -5.54363 q^{79} +(-11.4571 + 4.74570i) q^{83} +(0.486907 - 1.17550i) q^{85} +(7.93127 - 7.93127i) q^{89} +(-0.0192471 + 0.0464667i) q^{91} -4.35131 q^{95} +12.5582 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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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