LMFDB - Embedded newform 1152.2.w.b.1007.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1152.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1007.8
Character	$\chi$	$=$	1152.1007
Dual form			1152.2.w.b.143.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32268 + 3.19322i) q^{5} +(2.32913 + 2.32913i) q^{7} +O(q^{10})$	$q+(1.32268 + 3.19322i) q^{5} +(2.32913 + 2.32913i) q^{7} +(-1.47061 - 3.55036i) q^{11} +(4.49745 + 1.86291i) q^{13} +4.93452 q^{17} +(1.98599 - 4.79460i) q^{19} +(-1.08935 - 1.08935i) q^{23} +(-4.91167 + 4.91167i) q^{25} +(-3.43073 - 1.42105i) q^{29} +8.82364i q^{31} +(-4.35675 + 10.5181i) q^{35} +(1.94208 - 0.804437i) q^{37} +(-5.87486 + 5.87486i) q^{41} +(2.44320 - 1.01201i) q^{43} -1.61865i q^{47} +3.84969i q^{49} +(-5.62320 + 2.32921i) q^{53} +(9.39195 - 9.39195i) q^{55} +(-7.67495 + 3.17907i) q^{59} +(3.16892 - 7.65045i) q^{61} +16.8254i q^{65} +(-3.31324 - 1.37239i) q^{67} +(-2.13686 + 2.13686i) q^{71} +(-1.81541 - 1.81541i) q^{73} +(4.84401 - 11.6945i) q^{77} -1.42339 q^{79} +(-1.04174 - 0.431504i) q^{83} +(6.52678 + 15.7570i) q^{85} +(-0.708782 - 0.708782i) q^{89} +(6.13620 + 14.8141i) q^{91} +17.9370 q^{95} +12.2142 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 8 q^{11} - 16 q^{29} - 24 q^{35} - 16 q^{53} + 32 q^{55} - 32 q^{59} + 32 q^{61} + 16 q^{67} - 16 q^{71} - 16 q^{77} + 32 q^{79} + 40 q^{83} + 48 q^{91} + 80 q^{95}+O(q^{100}) $ 32 * q + 8 * q^11 - 16 * q^29 - 24 * q^35 - 16 * q^53 + 32 * q^55 - 32 * q^59 + 32 * q^61 + 16 * q^67 - 16 * q^71 - 16 * q^77 + 32 * q^79 + 40 * q^83 + 48 * q^91 + 80 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.32268	+	3.19322i	0.591519	+	1.42805i	0.882035	+	0.471183i	$0.156173\pi$
$5$	1.32268	+	3.19322i	0.591519	+	1.42805i	−0.290517	+	0.956870i	$0.593827\pi$
$6$		0			0
$7$	2.32913	+	2.32913i	0.880328	+	0.880328i	0.993568	−	0.113239i	$-0.0361227\pi$
$7$	2.32913	+	2.32913i	0.880328	+	0.880328i	−0.113239	+	0.993568i	$0.536123\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.47061	−	3.55036i	−0.443405	−	1.07047i	−0.974746	−	0.223316i	$-0.928312\pi$
$11$	−1.47061	−	3.55036i	−0.443405	−	1.07047i	0.531341	−	0.847158i	$-0.321688\pi$
$12$		0			0
$13$	4.49745	+	1.86291i	1.24737	+	0.516677i	0.906010	−	0.423256i	$-0.139113\pi$
$13$	4.49745	+	1.86291i	1.24737	+	0.516677i	0.341358	+	0.939933i	$0.389113\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.93452			1.19680			0.598399	−	0.801199i	$-0.295804\pi$
$17$	4.93452			1.19680			0.598399	+	0.801199i	$0.295804\pi$
$18$		0			0
$19$	1.98599	−	4.79460i	0.455617	−	1.09996i	−0.514538	−	0.857468i	$-0.672036\pi$
$19$	1.98599	−	4.79460i	0.455617	−	1.09996i	0.970154	−	0.242488i	$-0.0779635\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.08935	−	1.08935i	−0.227144	−	0.227144i	0.584354	−	0.811499i	$-0.301348\pi$
$23$	−1.08935	−	1.08935i	−0.227144	−	0.227144i	−0.811499	+	0.584354i	$0.801348\pi$
$24$		0			0
$25$	−4.91167	+	4.91167i	−0.982334	+	0.982334i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.43073	−	1.42105i	−0.637070	−	0.263883i	0.0406838	−	0.999172i	$-0.487046\pi$
$29$	−3.43073	−	1.42105i	−0.637070	−	0.263883i	−0.677754	+	0.735289i	$0.737046\pi$
$30$		0			0
$31$			8.82364i			1.58477i	0.610019	+	0.792387i	$0.291162\pi$
$31$			8.82364i			1.58477i	−0.610019	+	0.792387i	$0.708838\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.35675	+	10.5181i	−0.736425	+	1.77789i
$36$		0			0
$37$	1.94208	−	0.804437i	0.319276	−	0.132249i	−0.217289	−	0.976107i	$-0.569721\pi$
$37$	1.94208	−	0.804437i	0.319276	−	0.132249i	0.536565	+	0.843859i	$0.319721\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5.87486	+	5.87486i	−0.917498	+	0.917498i	−0.996847	−	0.0793485i	$-0.974716\pi$
$41$	−5.87486	+	5.87486i	−0.917498	+	0.917498i	0.0793485	+	0.996847i	$0.474716\pi$
$42$		0			0
$43$	2.44320	−	1.01201i	0.372585	−	0.154330i	−0.188530	−	0.982067i	$-0.560372\pi$
$43$	2.44320	−	1.01201i	0.372585	−	0.154330i	0.561115	+	0.827738i	$0.310372\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	1.61865i		−	0.236105i	−0.993007	−	0.118052i	$-0.962335\pi$
$47$		−	1.61865i		−	0.236105i	0.993007	−	0.118052i	$-0.0376651\pi$
$48$		0			0
$49$			3.84969i			0.549956i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−5.62320	+	2.32921i	−0.772407	+	0.319941i	−0.733847	−	0.679315i	$-0.762277\pi$
$53$	−5.62320	+	2.32921i	−0.772407	+	0.319941i	−0.0385598	+	0.999256i	$0.512277\pi$
$54$		0			0
$55$	9.39195	−	9.39195i	1.26641	−	1.26641i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−7.67495	+	3.17907i	−0.999193	+	0.413879i	−0.821501	−	0.570207i	$-0.806863\pi$
$59$	−7.67495	+	3.17907i	−0.999193	+	0.413879i	−0.177692	+	0.984086i	$0.556863\pi$
$60$		0			0
$61$	3.16892	−	7.65045i	0.405738	−	0.979539i	−0.580508	−	0.814255i	$-0.697146\pi$
$61$	3.16892	−	7.65045i	0.405738	−	0.979539i	0.986246	−	0.165284i	$-0.0528542\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			16.8254i			2.08693i
$66$		0			0
$67$	−3.31324	−	1.37239i	−0.404777	−	0.167664i	0.171000	−	0.985271i	$-0.445300\pi$
$67$	−3.31324	−	1.37239i	−0.404777	−	0.167664i	−0.575777	+	0.817607i	$0.695300\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−2.13686	+	2.13686i	−0.253599	+	0.253599i	−0.822444	−	0.568846i	$-0.807390\pi$
$71$	−2.13686	+	2.13686i	−0.253599	+	0.253599i	0.568846	+	0.822444i	$0.307390\pi$
$72$		0			0
$73$	−1.81541	−	1.81541i	−0.212478	−	0.212478i	0.592841	−	0.805319i	$-0.298006\pi$
$73$	−1.81541	−	1.81541i	−0.212478	−	0.212478i	−0.805319	+	0.592841i	$0.798006\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.84401	−	11.6945i	0.552027	−	1.33271i
$78$		0			0
$79$	−1.42339			−0.160144			−0.0800721	−	0.996789i	$-0.525515\pi$
$79$	−1.42339			−0.160144			−0.0800721	+	0.996789i	$0.525515\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.04174	−	0.431504i	−0.114346	−	0.0473637i	0.324777	−	0.945791i	$-0.394711\pi$
$83$	−1.04174	−	0.431504i	−0.114346	−	0.0473637i	−0.439123	+	0.898427i	$0.644711\pi$
$84$		0			0
$85$	6.52678	+	15.7570i	0.707928	+	1.70909i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.708782	−	0.708782i	−0.0751308	−	0.0751308i	0.668543	−	0.743674i	$-0.266918\pi$
$89$	−0.708782	−	0.708782i	−0.0751308	−	0.0751308i	−0.743674	+	0.668543i	$0.766918\pi$
$90$		0			0
$91$	6.13620	+	14.8141i	0.643248	+	1.55294i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	17.9370			1.84030
$96$		0			0
$97$	12.2142			1.24016			0.620082	−	0.784537i	$-0.287099\pi$
$97$	12.2142			1.24016			0.620082	+	0.784537i	$0.287099\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.13564	−	14.8127i	−0.610519	−	1.47392i	−0.862432	−	0.506173i	$-0.831060\pi$
$101$	−6.13564	−	14.8127i	−0.610519	−	1.47392i	0.251913	−	0.967750i	$-0.418940\pi$
$102$		0			0
$103$	9.45184	+	9.45184i	0.931318	+	0.931318i	0.997788	−	0.0664707i	$-0.0211739\pi$
$103$	9.45184	+	9.45184i	0.931318	+	0.931318i	−0.0664707	+	0.997788i	$0.521174\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.93527	+	9.50057i	0.380436	+	0.918455i	0.991881	+	0.127168i	$0.0405887\pi$
$107$	3.93527	+	9.50057i	0.380436	+	0.918455i	−0.611445	+	0.791287i	$0.709411\pi$
$108$		0			0
$109$	−10.8399	−	4.49003i	−1.03827	−	0.430067i	−0.202582	−	0.979265i	$-0.564933\pi$
$109$	−10.8399	−	4.49003i	−1.03827	−	0.430067i	−0.835692	+	0.549198i	$0.814933\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	9.42620			0.886742			0.443371	−	0.896338i	$-0.353782\pi$
$113$	9.42620			0.886742			0.443371	+	0.896338i	$0.353782\pi$
$114$		0			0
$115$	2.03767	−	4.91937i	0.190014	−	0.458734i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	11.4931	+	11.4931i	1.05357	+	1.05357i
$120$		0			0
$121$	−2.66419	+	2.66419i	−0.242199	+	0.242199i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−6.21449	−	2.57413i	−0.555841	−	0.230237i
$126$		0			0
$127$		−	6.69360i		−	0.593961i	−0.954884	−	0.296980i	$-0.904020\pi$
$127$		−	6.69360i		−	0.593961i	0.954884	−	0.296980i	$-0.0959796\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	5.25325	−	12.6825i	0.458979	−	1.10807i	−0.509833	−	0.860273i	$-0.670293\pi$
$131$	5.25325	−	12.6825i	0.458979	−	1.10807i	0.968811	−	0.247799i	$-0.0797072\pi$
$132$		0			0
$133$	15.7929	−	6.54162i	1.36941	−	0.567230i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.46480	−	3.46480i	0.296018	−	0.296018i	−0.543434	−	0.839452i	$-0.682876\pi$
$137$	3.46480	−	3.46480i	0.296018	−	0.296018i	0.839452	+	0.543434i	$0.182876\pi$
$138$		0			0
$139$	−15.2400	+	6.31262i	−1.29264	+	0.535429i	−0.919771	−	0.392455i	$-0.871626\pi$
$139$	−15.2400	+	6.31262i	−1.29264	+	0.535429i	−0.372869	+	0.927884i	$0.621626\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	18.7072i		−	1.56437i
$144$		0			0
$145$		−	12.8347i		−	1.06586i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−8.66511	+	3.58921i	−0.709873	+	0.294039i	−0.708252	−	0.705959i	$-0.750516\pi$
$149$	−8.66511	+	3.58921i	−0.709873	+	0.294039i	−0.00162119	+	0.999999i	$0.500516\pi$
$150$		0			0
$151$	−16.6619	+	16.6619i	−1.35592	+	1.35592i	−0.477045	+	0.878879i	$0.658292\pi$
$151$	−16.6619	+	16.6619i	−1.35592	+	1.35592i	−0.878879	+	0.477045i	$0.841708\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−28.1759	+	11.6708i	−2.26314	+	0.937423i
$156$		0			0
$157$	3.37611	−	8.15066i	0.269443	−	0.650493i	−0.730014	−	0.683432i	$-0.760487\pi$
$157$	3.37611	−	8.15066i	0.269443	−	0.650493i	0.999457	+	0.0329386i	$0.0104866\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	5.07445i		−	0.399923i
$162$		0			0
$163$	−14.2435	−	5.89984i	−1.11564	−	0.462112i	−0.252761	−	0.967529i	$-0.581339\pi$
$163$	−14.2435	−	5.89984i	−1.11564	−	0.462112i	−0.862875	+	0.505417i	$0.831339\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	10.0550	−	10.0550i	0.778080	−	0.778080i	−0.201424	−	0.979504i	$-0.564557\pi$
$167$	10.0550	−	10.0550i	0.778080	−	0.778080i	0.979504	+	0.201424i	$0.0645568\pi$
$168$		0			0
$169$	7.56426	+	7.56426i	0.581866	+	0.581866i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	3.57483	−	8.63040i	0.271789	−	0.656157i	−0.727771	−	0.685820i	$-0.759444\pi$
$173$	3.57483	−	8.63040i	0.271789	−	0.656157i	0.999560	+	0.0296634i	$0.00944353\pi$
$174$		0			0
$175$	−22.8798			−1.72955
$176$		0			0
$177$		0			0
$178$		0			0
$179$	6.36855	+	2.63794i	0.476008	+	0.197169i	0.607771	−	0.794112i	$-0.292064\pi$
$179$	6.36855	+	2.63794i	0.476008	+	0.197169i	−0.131763	+	0.991281i	$0.542064\pi$
$180$		0			0
$181$	−2.04004	−	4.92510i	−0.151635	−	0.366080i	0.829748	−	0.558138i	$-0.188484\pi$
$181$	−2.04004	−	4.92510i	−0.151635	−	0.366080i	−0.981384	+	0.192058i	$0.938484\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	5.13749	+	5.13749i	0.377716	+	0.377716i
$186$		0			0
$187$	−7.25674	−	17.5193i	−0.530665	−	1.28114i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−9.91926			−0.717732			−0.358866	−	0.933389i	$-0.616837\pi$
$191$	−9.91926			−0.717732			−0.358866	+	0.933389i	$0.616837\pi$
$192$		0			0
$193$	−20.8089			−1.49785			−0.748927	−	0.662653i	$-0.769431\pi$
$193$	−20.8089			−1.49785			−0.748927	+	0.662653i	$0.769431\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2.99573	+	7.23234i	0.213437	+	0.515283i	0.993947	−	0.109861i	$-0.0350405\pi$
$197$	2.99573	+	7.23234i	0.213437	+	0.515283i	−0.780510	+	0.625143i	$0.785040\pi$
$198$		0			0
$199$	16.3928	+	16.3928i	1.16205	+	1.16205i	0.984026	+	0.178027i	$0.0569713\pi$
$199$	16.3928	+	16.3928i	1.16205	+	1.16205i	0.178027	+	0.984026i	$0.443029\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−4.68079	−	11.3004i	−0.328527	−	0.793134i
$204$		0			0
$205$	−26.5303	−	10.9892i	−1.85295	−	0.767519i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−19.9431			−1.37950
$210$		0			0
$211$	9.39938	−	22.6921i	0.647080	−	1.56219i	−0.169861	−	0.985468i	$-0.554332\pi$
$211$	9.39938	−	22.6921i	0.647080	−	1.56219i	0.816941	−	0.576721i	$-0.195668\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	6.46314	+	6.46314i	0.440782	+	0.440782i
$216$		0			0
$217$	−20.5514	+	20.5514i	−1.39512	+	1.39512i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	22.1928	+	9.19255i	1.49285	+	0.618358i
$222$		0			0
$223$		−	13.0361i		−	0.872961i	−0.899714	−	0.436480i	$-0.856225\pi$
$223$		−	13.0361i		−	0.872961i	0.899714	−	0.436480i	$-0.143775\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.970105	−	2.34204i	0.0643882	−	0.155447i	−0.888410	−	0.459050i	$-0.848190\pi$
$227$	0.970105	−	2.34204i	0.0643882	−	0.155447i	0.952798	+	0.303603i	$0.0981898\pi$
$228$		0			0
$229$	10.5855	−	4.38467i	0.699512	−	0.289747i	−0.00444500	−	0.999990i	$-0.501415\pi$
$229$	10.5855	−	4.38467i	0.699512	−	0.289747i	0.703957	+	0.710243i	$0.251415\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	15.0433	−	15.0433i	0.985522	−	0.985522i	−0.0143751	−	0.999897i	$-0.504576\pi$
$233$	15.0433	−	15.0433i	0.985522	−	0.985522i	0.999897	+	0.0143751i	$0.00457589\pi$
$234$		0			0
$235$	5.16872	−	2.14095i	0.337170	−	0.139660i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	10.1723i		−	0.657989i	−0.944332	−	0.328995i	$-0.893290\pi$
$239$		−	10.1723i		−	0.657989i	0.944332	−	0.328995i	$-0.106710\pi$
$240$		0			0
$241$		−	20.6542i		−	1.33045i	−0.746642	−	0.665227i	$-0.768335\pi$
$241$		−	20.6542i		−	1.33045i	0.746642	−	0.665227i	$-0.231665\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−12.2929	+	5.09190i	−0.785366	+	0.325309i
$246$		0			0
$247$	17.8638	−	17.8638i	1.13664	−	1.13664i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	18.5479	−	7.68280i	1.17073	−	0.484934i	0.289299	−	0.957239i	$-0.406578\pi$
$251$	18.5479	−	7.68280i	1.17073	−	0.484934i	0.881435	+	0.472304i	$0.156578\pi$
$252$		0			0
$253$	−2.26557	+	5.46957i	−0.142435	+	0.343869i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			7.80823i			0.487064i	0.969893	+	0.243532i	$0.0783061\pi$
$257$			7.80823i			0.487064i	−0.969893	+	0.243532i	$0.921694\pi$
$258$		0			0
$259$	6.39700	+	2.64972i	0.397490	+	0.164646i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−19.5761	+	19.5761i	−1.20711	+	1.20711i	−0.235158	+	0.971957i	$0.575561\pi$
$263$	−19.5761	+	19.5761i	−1.20711	+	1.20711i	−0.971957	+	0.235158i	$0.924439\pi$
$264$		0			0
$265$	−14.8754	−	14.8754i	−0.913786	−	0.913786i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.69145	+	4.08353i	−0.103130	+	0.248977i	−0.967019	−	0.254705i	$-0.918022\pi$
$269$	−1.69145	+	4.08353i	−0.103130	+	0.248977i	0.863889	+	0.503682i	$0.168022\pi$
$270$		0			0
$271$	−6.31185			−0.383418			−0.191709	−	0.981452i	$-0.561403\pi$
$271$	−6.31185			−0.383418			−0.191709	+	0.981452i	$0.561403\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	24.6613	+	10.2151i	1.48713	+	0.615991i
$276$		0			0
$277$	7.53180	+	18.1834i	0.452542	+	1.09253i	0.971352	+	0.237644i	$0.0763751\pi$
$277$	7.53180	+	18.1834i	0.452542	+	1.09253i	−0.518810	+	0.854889i	$0.673625\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−16.2957	−	16.2957i	−0.972118	−	0.972118i	0.0275040	−	0.999622i	$-0.491244\pi$
$281$	−16.2957	−	16.2957i	−0.972118	−	0.972118i	−0.999622	+	0.0275040i	$0.991244\pi$
$282$		0			0
$283$	3.93995	+	9.51187i	0.234206	+	0.565422i	0.996664	−	0.0816150i	$-0.0260078\pi$
$283$	3.93995	+	9.51187i	0.234206	+	0.565422i	−0.762458	+	0.647037i	$0.776008\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−27.3666			−1.61540
$288$		0			0
$289$	7.34950			0.432324
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−5.02532	−	12.1322i	−0.293582	−	0.708770i	−1.00000		0.000974464i	$-0.999690\pi$
$293$	−5.02532	−	12.1322i	−0.293582	−	0.708770i	0.706417	−	0.707795i	$-0.250310\pi$
$294$		0			0
$295$	−20.3029	−	20.3029i	−1.18208	−	1.18208i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.86993	−	6.92862i	−0.165972	−	0.400693i
$300$		0			0
$301$	8.04764	+	3.33344i	0.463858	+	0.192136i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	28.6210			1.63884
$306$		0			0
$307$	5.19514	−	12.5422i	0.296502	−	0.715820i	−0.703485	−	0.710710i	$-0.748374\pi$
$307$	5.19514	−	12.5422i	0.296502	−	0.715820i	0.999987	−	0.00510930i	$-0.00162635\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−5.27753	−	5.27753i	−0.299261	−	0.299261i	0.541463	−	0.840725i	$-0.317871\pi$
$311$	−5.27753	−	5.27753i	−0.299261	−	0.299261i	−0.840725	+	0.541463i	$0.817871\pi$
$312$		0			0
$313$	−18.5402	+	18.5402i	−1.04795	+	1.04795i	−0.0491617	+	0.998791i	$0.515655\pi$
$313$	−18.5402	+	18.5402i	−1.04795	+	1.04795i	−0.998791	+	0.0491617i	$0.984345\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	11.2977	+	4.67965i	0.634540	+	0.262835i	0.676681	−	0.736276i	$-0.263418\pi$
$317$	11.2977	+	4.67965i	0.634540	+	0.262835i	−0.0421404	+	0.999112i	$0.513418\pi$
$318$		0			0
$319$			14.2701i			0.798973i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	9.79989	−	23.6590i	0.545281	−	1.31642i
$324$		0			0
$325$	−31.2400	+	12.9400i	−1.73288	+	0.717783i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	3.77005	−	3.77005i	0.207850	−	0.207850i
$330$		0			0
$331$	−26.3575	+	10.9176i	−1.44874	+	0.600087i	−0.961899	−	0.273405i	$-0.911850\pi$
$331$	−26.3575	+	10.9176i	−1.44874	+	0.600087i	−0.486839	+	0.873492i	$0.661850\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		−	12.3952i		−	0.677219i
$336$		0			0
$337$		−	8.96574i		−	0.488395i	−0.969726	−	0.244197i	$-0.921475\pi$
$337$		−	8.96574i		−	0.488395i	0.969726	−	0.244197i	$-0.0785245\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	31.3271	−	12.9761i	1.69646	−	0.702696i
$342$		0			0
$343$	7.33747	−	7.33747i	0.396186	−	0.396186i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.0344829	−	0.0142833i	0.00185114	−	0.000766767i	−0.381758	−	0.924262i	$-0.624681\pi$
$347$	0.0344829	−	0.0142833i	0.00185114	−	0.000766767i	0.383609	+	0.923496i	$0.374681\pi$
$348$		0			0
$349$	−1.36920	+	3.30553i	−0.0732914	+	0.176941i	−0.956280	−	0.292454i	$-0.905528\pi$
$349$	−1.36920	+	3.30553i	−0.0732914	+	0.176941i	0.882988	+	0.469395i	$0.155528\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			10.2214i			0.544031i	0.962293	+	0.272016i	$0.0876902\pi$
$353$			10.2214i			0.544031i	−0.962293	+	0.272016i	$0.912310\pi$
$354$		0			0
$355$	−9.64984	−	3.99710i	−0.512161	−	0.212144i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	21.7022	−	21.7022i	1.14540	−	1.14540i	0.157953	−	0.987447i	$-0.449511\pi$
$359$	21.7022	−	21.7022i	1.14540	−	1.14540i	0.987447	−	0.157953i	$-0.0504894\pi$
$360$		0			0
$361$	−5.60898	−	5.60898i	−0.295210	−	0.295210i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	3.39581	−	8.19821i	0.177745	−	0.429114i
$366$		0			0
$367$	2.68336			0.140070			0.0700350	−	0.997545i	$-0.477689\pi$
$367$	2.68336			0.140070			0.0700350	+	0.997545i	$0.477689\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−18.5222	−	7.67215i	−0.961625	−	0.398318i
$372$		0			0
$373$	−3.60763	−	8.70959i	−0.186796	−	0.450965i	0.802543	−	0.596594i	$-0.203480\pi$
$373$	−3.60763	−	8.70959i	−0.186796	−	0.450965i	−0.989339	+	0.145628i	$0.953480\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−12.7822	−	12.7822i	−0.658318	−	0.658318i
$378$		0			0
$379$	7.30210	+	17.6288i	0.375083	+	0.905532i	0.992872	+	0.119187i	$0.0380289\pi$
$379$	7.30210	+	17.6288i	0.375083	+	0.905532i	−0.617788	+	0.786344i	$0.711971\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	17.7992			0.909497			0.454748	−	0.890620i	$-0.349729\pi$
$383$	17.7992			0.909497			0.454748	+	0.890620i	$0.349729\pi$
$384$		0			0
$385$	43.7502			2.22971
$386$		0			0
$387$		0			0
$388$		0			0
$389$	10.4216	+	25.1599i	0.528396	+	1.27566i	0.932574	+	0.360979i	$0.117558\pi$
$389$	10.4216	+	25.1599i	0.528396	+	1.27566i	−0.404178	+	0.914680i	$0.632442\pi$
$390$		0			0
$391$	−5.37540	−	5.37540i	−0.271846	−	0.271846i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−1.88269	−	4.54521i	−0.0947284	−	0.228695i
$396$		0			0
$397$	−6.35478	−	2.63224i	−0.318938	−	0.132108i	0.217471	−	0.976067i	$-0.430219\pi$
$397$	−6.35478	−	2.63224i	−0.318938	−	0.132108i	−0.536408	+	0.843959i	$0.680219\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	14.1764			0.707935			0.353968	−	0.935258i	$-0.384832\pi$
$401$	14.1764			0.707935			0.353968	+	0.935258i	$0.384832\pi$
$402$		0			0
$403$	−16.4376	+	39.6839i	−0.818816	+	1.97680i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.71208	−	5.71208i	−0.283137	−	0.283137i
$408$		0			0
$409$	23.0001	−	23.0001i	1.13728	−	1.13728i	0.148347	−	0.988935i	$-0.452605\pi$
$409$	23.0001	−	23.0001i	1.13728	−	1.13728i	0.988935	−	0.148347i	$-0.0473951\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−25.2804	−	10.4715i	−1.24397	−	0.515268i
$414$		0			0
$415$		−	3.89725i		−	0.191309i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−3.33096	+	8.04166i	−0.162728	+	0.392861i	−0.984120	−	0.177503i	$-0.943198\pi$
$419$	−3.33096	+	8.04166i	−0.162728	+	0.392861i	0.821392	+	0.570364i	$0.193198\pi$
$420$		0			0
$421$	−6.91049	+	2.86242i	−0.336797	+	0.139506i	−0.544671	−	0.838650i	$-0.683346\pi$
$421$	−6.91049	+	2.86242i	−0.336797	+	0.139506i	0.207874	+	0.978156i	$0.433346\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−24.2367	+	24.2367i	−1.17565	+	1.17565i
$426$		0			0
$427$	25.1997	−	10.4381i	1.21950	−	0.505133i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			18.8488i			0.907917i	0.891023	+	0.453958i	$0.149989\pi$
$431$			18.8488i			0.907917i	−0.891023	+	0.453958i	$0.850011\pi$
$432$		0			0
$433$			32.1408i			1.54459i	0.635264	+	0.772295i	$0.280891\pi$
$433$			32.1408i			1.54459i	−0.635264	+	0.772295i	$0.719109\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−7.38640	+	3.05955i	−0.353339	+	0.146358i
$438$		0			0
$439$	19.4979	−	19.4979i	0.930584	−	0.930584i	−0.0671583	−	0.997742i	$-0.521393\pi$
$439$	19.4979	−	19.4979i	0.930584	−	0.930584i	0.997742	+	0.0671583i	$0.0213933\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	12.4270	−	5.14742i	0.590424	−	0.244561i	−0.0674092	−	0.997725i	$-0.521473\pi$
$443$	12.4270	−	5.14742i	0.590424	−	0.244561i	0.657833	+	0.753164i	$0.271473\pi$
$444$		0			0
$445$	1.32581	−	3.20079i	0.0628494	−	0.151732i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	16.8751i		−	0.796387i	−0.917301	−	0.398194i	$-0.869637\pi$
$449$		−	16.8751i		−	0.796387i	0.917301	−	0.398194i	$-0.130363\pi$
$450$		0			0
$451$	29.4975	+	12.2182i	1.38898	+	0.575335i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−39.1885	+	39.1885i	−1.83719	+	1.83719i
$456$		0			0
$457$	19.1686	+	19.1686i	0.896670	+	0.896670i	0.995140	−	0.0984696i	$-0.0313947\pi$
$457$	19.1686	+	19.1686i	0.896670	+	0.896670i	−0.0984696	+	0.995140i	$0.531395\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−6.32718	+	15.2752i	−0.294686	+	0.711436i	0.705311	+	0.708898i	$0.250808\pi$
$461$	−6.32718	+	15.2752i	−0.294686	+	0.711436i	−0.999997	+	0.00253708i	$0.999192\pi$
$462$		0			0
$463$	−32.5710			−1.51370			−0.756852	−	0.653587i	$-0.773263\pi$
$463$	−32.5710			−1.51370			−0.756852	+	0.653587i	$0.773263\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	5.84384	+	2.42060i	0.270420	+	0.112012i	0.513773	−	0.857926i	$-0.328247\pi$
$467$	5.84384	+	2.42060i	0.270420	+	0.112012i	−0.243353	+	0.969938i	$0.578247\pi$
$468$		0			0
$469$	−4.52050	−	10.9134i	−0.208737	−	0.503936i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−7.18598	−	7.18598i	−0.330412	−	0.330412i
$474$		0			0
$475$	13.7950	+	33.3040i	0.632956	+	1.52809i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	7.92963			0.362314			0.181157	−	0.983454i	$-0.442016\pi$
$479$	7.92963			0.362314			0.181157	+	0.983454i	$0.442016\pi$
$480$		0			0
$481$	10.2330			0.466585
$482$		0			0
$483$		0			0
$484$		0			0
$485$	16.1554	+	39.0027i	0.733581	+	1.77102i
$486$		0			0
$487$	−10.7904	−	10.7904i	−0.488961	−	0.488961i	0.419017	−	0.907978i	$-0.362375\pi$
$487$	−10.7904	−	10.7904i	−0.488961	−	0.488961i	−0.907978	+	0.419017i	$0.862375\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1.68219	+	4.06116i	0.0759160	+	0.183277i	0.957282	−	0.289158i	$-0.0933752\pi$
$491$	1.68219	+	4.06116i	0.0759160	+	0.183277i	−0.881366	+	0.472435i	$0.843375\pi$
$492$		0			0
$493$	−16.9290	−	7.01222i	−0.762443	−	0.315814i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−9.95405			−0.446500
$498$		0			0
$499$	15.0645	−	36.3690i	0.674380	−	1.62810i	−0.0997053	−	0.995017i	$-0.531790\pi$
$499$	15.0645	−	36.3690i	0.674380	−	1.62810i	0.774086	−	0.633081i	$-0.218210\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−8.41533	−	8.41533i	−0.375221	−	0.375221i	0.494153	−	0.869375i	$-0.335478\pi$
$503$	−8.41533	−	8.41533i	−0.375221	−	0.375221i	−0.869375	+	0.494153i	$0.835478\pi$
$504$		0			0
$505$	39.1849	−	39.1849i	1.74371	−	1.74371i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	16.2989	+	6.75122i	0.722436	+	0.299243i	0.713440	−	0.700717i	$-0.247136\pi$
$509$	16.2989	+	6.75122i	0.722436	+	0.299243i	0.00899639	+	0.999960i	$0.497136\pi$
$510$		0			0
$511$		−	8.45666i		−	0.374100i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−17.6801	+	42.6836i	−0.779079	+	1.88086i
$516$		0			0
$517$	−5.74680	+	2.38040i	−0.252744	+	0.104690i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−17.7934	+	17.7934i	−0.779542	+	0.779542i	−0.979753	−	0.200211i	$-0.935837\pi$
$521$	−17.7934	+	17.7934i	−0.779542	+	0.779542i	0.200211	+	0.979753i	$0.435837\pi$
$522$		0			0
$523$	−10.5763	+	4.38083i	−0.462468	+	0.191560i	−0.601737	−	0.798694i	$-0.705525\pi$
$523$	−10.5763	+	4.38083i	−0.462468	+	0.191560i	0.139270	+	0.990254i	$0.455525\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			43.5405i			1.89665i
$528$		0			0
$529$		−	20.6267i		−	0.896811i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−37.3662	+	15.4776i	−1.61851	+	0.670408i
$534$		0			0
$535$	−25.1324	+	25.1324i	−1.08657	+	1.08657i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	13.6678	−	5.66139i	0.588714	−	0.243853i
$540$		0			0
$541$	−0.161261	+	0.389318i	−0.00693315	+	0.0167381i	−0.927308	−	0.374299i	$-0.877883\pi$
$541$	−0.161261	+	0.389318i	−0.00693315	+	0.0167381i	0.920375	+	0.391037i	$0.127883\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		−	40.5531i		−	1.73710i
$546$		0			0
$547$	−2.37145	−	0.982285i	−0.101396	−	0.0419995i	0.331409	−	0.943487i	$-0.392476\pi$
$547$	−2.37145	−	0.982285i	−0.101396	−	0.0419995i	−0.432805	+	0.901488i	$0.642476\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−13.6268	+	13.6268i	−0.580519	+	0.580519i
$552$		0			0
$553$	−3.31527	−	3.31527i	−0.140980	−	0.140980i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.975580	+	2.35526i	−0.0413366	+	0.0997955i	−0.943199	−	0.332227i	$-0.892200\pi$
$557$	−0.975580	+	2.35526i	−0.0413366	+	0.0997955i	0.901863	+	0.432023i	$0.142200\pi$
$558$		0			0
$559$	12.8735			0.544489
$560$		0			0
$561$		0			0
$562$		0			0
$563$	9.62858	+	3.98829i	0.405796	+	0.168086i	0.576239	−	0.817281i	$-0.304520\pi$
$563$	9.62858	+	3.98829i	0.405796	+	0.168086i	−0.170443	+	0.985368i	$0.554520\pi$
$564$		0			0
$565$	12.4678	+	30.1000i	0.524525	+	1.26631i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−18.8578	−	18.8578i	−0.790559	−	0.790559i	0.191026	−	0.981585i	$-0.438819\pi$
$569$	−18.8578	−	18.8578i	−0.790559	−	0.790559i	−0.981585	+	0.191026i	$0.938819\pi$
$570$		0			0
$571$	−2.27949	−	5.50317i	−0.0953936	−	0.230300i	0.868979	−	0.494850i	$-0.164777\pi$
$571$	−2.27949	−	5.50317i	−0.0953936	−	0.230300i	−0.964372	+	0.264549i	$0.914777\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	10.7010			0.446263
$576$		0			0
$577$	−2.80878			−0.116931			−0.0584655	−	0.998289i	$-0.518621\pi$
$577$	−2.80878			−0.116931			−0.0584655	+	0.998289i	$0.518621\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.42132	−	3.43138i	−0.0589665	−	0.142358i
$582$		0			0
$583$	16.5390	+	16.5390i	0.684977	+	0.684977i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−10.2932	−	24.8501i	−0.424848	−	1.02567i	−0.980898	−	0.194524i	$-0.937684\pi$
$587$	−10.2932	−	24.8501i	−0.424848	−	1.02567i	0.556050	−	0.831149i	$-0.312316\pi$
$588$		0			0
$589$	42.3058	+	17.5236i	1.74318	+	0.722049i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−40.3079			−1.65525			−0.827624	−	0.561283i	$-0.810308\pi$
$593$	−40.3079			−1.65525			−0.827624	+	0.561283i	$0.810308\pi$
$594$		0			0
$595$	−21.4985	+	51.9019i	−0.881351	+	2.12777i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	12.4557	+	12.4557i	0.508926	+	0.508926i	0.914197	−	0.405271i	$-0.132823\pi$
$599$	12.4557	+	12.4557i	0.508926	+	0.508926i	−0.405271	+	0.914197i	$0.632823\pi$
$600$		0			0
$601$	6.85263	−	6.85263i	0.279525	−	0.279525i	−0.553395	−	0.832919i	$-0.686668\pi$
$601$	6.85263	−	6.85263i	0.279525	−	0.279525i	0.832919	+	0.553395i	$0.186668\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−12.0312	−	4.98349i	−0.489139	−	0.202608i
$606$		0			0
$607$			5.54311i			0.224988i	0.993652	+	0.112494i	$0.0358839\pi$
$607$			5.54311i			0.224988i	−0.993652	+	0.112494i	$0.964116\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	3.01540	−	7.27981i	0.121990	−	0.294510i
$612$		0			0
$613$	1.34403	−	0.556714i	0.0542847	−	0.0224855i	−0.355376	−	0.934723i	$-0.615647\pi$
$613$	1.34403	−	0.556714i	0.0542847	−	0.0224855i	0.409661	+	0.912238i	$0.365647\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	27.3420	−	27.3420i	1.10075	−	1.10075i	0.106429	−	0.994320i	$-0.466058\pi$
$617$	27.3420	−	27.3420i	1.10075	−	1.10075i	0.994320	−	0.106429i	$-0.0339417\pi$
$618$		0			0
$619$	27.2304	−	11.2792i	1.09448	−	0.453350i	0.238916	−	0.971040i	$-0.423208\pi$
$619$	27.2304	−	11.2792i	1.09448	−	0.453350i	0.855568	+	0.517690i	$0.173208\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		−	3.30169i		−	0.132280i
$624$		0			0
$625$			11.4818i			0.459270i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	9.58325	−	3.96951i	0.382109	−	0.158275i
$630$		0			0
$631$	6.25063	−	6.25063i	0.248834	−	0.248834i	−0.571658	−	0.820492i	$-0.693700\pi$
$631$	6.25063	−	6.25063i	0.248834	−	0.248834i	0.820492	+	0.571658i	$0.193700\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	21.3741	−	8.85346i	0.848207	−	0.351339i
$636$		0			0
$637$	−7.17161	+	17.3138i	−0.284150	+	0.685998i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	13.6953i		−	0.540934i	−0.962729	−	0.270467i	$-0.912822\pi$
$641$		−	13.6953i		−	0.540934i	0.962729	−	0.270467i	$-0.0871781\pi$
$642$		0			0
$643$	−17.4338	−	7.22130i	−0.687520	−	0.284780i	0.0114464	−	0.999934i	$-0.496356\pi$
$643$	−17.4338	−	7.22130i	−0.687520	−	0.284780i	−0.698967	+	0.715154i	$0.746356\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−2.78525	+	2.78525i	−0.109500	+	0.109500i	−0.759734	−	0.650234i	$-0.774671\pi$
$647$	−2.78525	+	2.78525i	−0.109500	+	0.109500i	0.650234	+	0.759734i	$0.274671\pi$
$648$		0			0
$649$	22.5737	+	22.5737i	0.886094	+	0.886094i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.42546	−	8.26978i	0.134048	−	0.323622i	−0.842575	−	0.538579i	$-0.818961\pi$
$653$	3.42546	−	8.26978i	0.134048	−	0.323622i	0.976623	+	0.214957i	$0.0689613\pi$
$654$		0			0
$655$	47.4463			1.85388
$656$		0			0
$657$		0			0
$658$		0			0
$659$	44.7390	+	18.5315i	1.74278	+	0.721885i	0.998542	+	0.0539756i	$0.0171893\pi$
$659$	44.7390	+	18.5315i	1.74278	+	0.721885i	0.744243	+	0.667909i	$0.232811\pi$
$660$		0			0
$661$	−5.04994	−	12.1916i	−0.196420	−	0.474200i	0.794727	−	0.606967i	$-0.207614\pi$
$661$	−5.04994	−	12.1916i	−0.196420	−	0.474200i	−0.991147	+	0.132767i	$0.957614\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	41.7777	+	41.7777i	1.62007	+	1.62007i
$666$		0			0
$667$	2.18923	+	5.28526i	0.0847672	+	0.204646i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−31.8221			−1.22848
$672$		0			0
$673$	−38.7728			−1.49458			−0.747291	−	0.664497i	$-0.768646\pi$
$673$	−38.7728			−1.49458			−0.747291	+	0.664497i	$0.768646\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	3.27320	+	7.90221i	0.125799	+	0.303706i	0.974214	−	0.225626i	$-0.0724426\pi$
$677$	3.27320	+	7.90221i	0.125799	+	0.303706i	−0.848415	+	0.529332i	$0.822443\pi$
$678$		0			0
$679$	28.4485	+	28.4485i	1.09175	+	1.09175i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	19.5003	+	47.0778i	0.746157	+	1.80138i	0.578769	+	0.815491i	$0.303533\pi$
$683$	19.5003	+	47.0778i	0.746157	+	1.80138i	0.167388	+	0.985891i	$0.446467\pi$
$684$		0			0
$685$	15.6467	+	6.48108i	0.597830	+	0.247629i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−29.6292			−1.12878
$690$		0			0
$691$	−5.45976	+	13.1810i	−0.207699	+	0.501430i	−0.993060	−	0.117608i	$-0.962477\pi$
$691$	−5.45976	+	13.1810i	−0.207699	+	0.501430i	0.785361	+	0.619038i	$0.212477\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−40.3152	−	40.3152i	−1.52924	−	1.52924i
$696$		0			0
$697$	−28.9896	+	28.9896i	−1.09806	+	1.09806i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	6.06309	+	2.51141i	0.229000	+	0.0948547i	0.494233	−	0.869330i	$-0.335449\pi$
$701$	6.06309	+	2.51141i	0.229000	+	0.0948547i	−0.265233	+	0.964184i	$0.585449\pi$
$702$		0			0
$703$		−	10.9091i		−	0.411445i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	20.2101	−	48.7915i	0.760079	−	1.83499i
$708$		0			0
$709$	17.0266	−	7.05266i	0.639448	−	0.264868i	−0.0393132	−	0.999227i	$-0.512517\pi$
$709$	17.0266	−	7.05266i	0.639448	−	0.264868i	0.678762	+	0.734359i	$0.262517\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	9.61199	−	9.61199i	0.359972	−	0.359972i
$714$		0			0
$715$	59.7362	−	24.7435i	2.23401	−	0.925356i
$716$		0			0
$717$		0			0
$718$		0			0
$719$			40.0842i			1.49489i	0.664324	+	0.747445i	$0.268719\pi$
$719$			40.0842i			1.49489i	−0.664324	+	0.747445i	$0.731281\pi$
$720$		0			0
$721$			44.0291i			1.63973i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	23.8303	−	9.87085i	0.885036	−	0.366594i
$726$		0			0
$727$	−17.6896	+	17.6896i	−0.656073	+	0.656073i	−0.954448	−	0.298376i	$-0.903555\pi$
$727$	−17.6896	+	17.6896i	−0.656073	+	0.656073i	0.298376	+	0.954448i	$0.403555\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	12.0560	−	4.99378i	0.445909	−	0.184701i
$732$		0			0
$733$	−2.68410	+	6.47999i	−0.0991395	+	0.239344i	−0.965666	−	0.259787i	$-0.916348\pi$
$733$	−2.68410	+	6.47999i	−0.0991395	+	0.239344i	0.866526	+	0.499131i	$0.166348\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			13.7814i			0.507646i
$738$		0			0
$739$	8.93406	+	3.70061i	0.328645	+	0.136129i	0.540904	−	0.841084i	$-0.318082\pi$
$739$	8.93406	+	3.70061i	0.328645	+	0.136129i	−0.212259	+	0.977213i	$0.568082\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	32.3436	−	32.3436i	1.18657	−	1.18657i	0.208565	−	0.978009i	$-0.433121\pi$
$743$	32.3436	−	32.3436i	1.18657	−	1.18657i	0.978009	−	0.208565i	$-0.0668791\pi$
$744$		0			0
$745$	−22.9223	−	22.9223i	−0.839807	−	0.839807i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−12.9623	+	31.2938i	−0.473633	+	1.14345i
$750$		0			0
$751$	34.4295			1.25635			0.628175	−	0.778072i	$-0.283802\pi$
$751$	34.4295			1.25635			0.628175	+	0.778072i	$0.283802\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−75.2433	−	31.1668i	−2.73839	−	1.13428i
$756$		0			0
$757$	2.48272	+	5.99382i	0.0902361	+	0.217849i	0.962554	−	0.271090i	$-0.0873840\pi$
$757$	2.48272	+	5.99382i	0.0902361	+	0.217849i	−0.872318	+	0.488939i	$0.837384\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	4.40886	+	4.40886i	0.159821	+	0.159821i	0.782488	−	0.622666i	$-0.213951\pi$
$761$	4.40886	+	4.40886i	0.159821	+	0.159821i	−0.622666	+	0.782488i	$0.713951\pi$
$762$		0			0
$763$	−14.7897	−	35.7054i	−0.535422	−	1.29262i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−40.4400			−1.46020
$768$		0			0
$769$	−16.9600			−0.611592			−0.305796	−	0.952097i	$-0.598923\pi$
$769$	−16.9600			−0.611592			−0.305796	+	0.952097i	$0.598923\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−12.5028	−	30.1845i	−0.449695	−	1.08566i	−0.972436	−	0.233169i	$-0.925090\pi$
$773$	−12.5028	−	30.1845i	−0.449695	−	1.08566i	0.522741	−	0.852492i	$-0.324910\pi$
$774$		0			0
$775$	−43.3388	−	43.3388i	−1.55678	−	1.55678i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	16.5002	+	39.8350i	0.591180	+	1.42724i
$780$		0			0
$781$	10.7291	+	4.44414i	0.383917	+	0.159024i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	30.4924			1.08832
$786$		0			0
$787$	−0.0428254	+	0.103390i	−0.00152656	+	0.00368545i	−0.924641	−	0.380840i	$-0.875635\pi$
$787$	−0.0428254	+	0.103390i	−0.00152656	+	0.00368545i	0.923114	+	0.384525i	$0.125635\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	21.9548	+	21.9548i	0.780624	+	0.780624i
$792$		0			0
$793$	28.5041	−	28.5041i	1.01221	−	1.01221i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	32.6670	+	13.5311i	1.15712	+	0.479297i	0.876917	−	0.480642i	$-0.159597\pi$
$797$	32.6670	+	13.5311i	1.15712	+	0.479297i	0.280208	+	0.959939i	$0.409597\pi$
$798$		0			0
$799$		−	7.98728i		−	0.282569i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.77560	+	9.11512i	−0.133238	+	0.321665i
$804$		0			0
$805$	16.2039	−	6.71186i	0.571111	−	0.236562i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−22.4803	+	22.4803i	−0.790364	+	0.790364i	−0.981553	−	0.191189i	$-0.938766\pi$
$809$	−22.4803	+	22.4803i	−0.790364	+	0.790364i	0.191189	+	0.981553i	$0.438766\pi$
$810$		0			0
$811$	−41.9112	+	17.3602i	−1.47170	+	0.609598i	−0.967246	−	0.253840i	$-0.918306\pi$
$811$	−41.9112	+	17.3602i	−1.47170	+	0.609598i	−0.504454	+	0.863438i	$0.668306\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		−	53.2862i		−	1.86653i
$816$		0			0
$817$		−	13.7240i		−	0.480142i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	2.66376	−	1.10337i	0.0929660	−	0.0385078i	−0.335716	−	0.941963i	$-0.608978\pi$
$821$	2.66376	−	1.10337i	0.0929660	−	0.0385078i	0.428682	+	0.903456i	$0.358978\pi$
$822$		0			0
$823$	−27.8538	+	27.8538i	−0.970924	+	0.970924i	−0.999589	−	0.0286650i	$-0.990874\pi$
$823$	−27.8538	+	27.8538i	−0.970924	+	0.970924i	0.0286650	+	0.999589i	$0.490874\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−31.9381	+	13.2292i	−1.11060	+	0.460024i	−0.861143	−	0.508362i	$-0.830251\pi$
$827$	−31.9381	+	13.2292i	−1.11060	+	0.460024i	−0.249454	+	0.968387i	$0.580251\pi$
$828$		0			0
$829$	4.80176	−	11.5925i	0.166772	−	0.402623i	−0.818294	−	0.574800i	$-0.805080\pi$
$829$	4.80176	−	11.5925i	0.166772	−	0.402623i	0.985066	+	0.172176i	$0.0550799\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$			18.9964i			0.658186i
$834$		0			0
$835$	45.4074	+	18.8084i	1.57139	+	0.650891i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−13.8057	+	13.8057i	−0.476627	+	0.476627i	−0.904051	−	0.427424i	$-0.859421\pi$
$839$	−13.8057	+	13.8057i	−0.476627	+	0.476627i	0.427424	+	0.904051i	$0.359421\pi$
$840$		0			0
$841$	−10.7556	−	10.7556i	−0.370883	−	0.370883i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−14.1493	+	34.1594i	−0.486751	+	1.17512i
$846$		0			0
$847$	−12.4105			−0.426430
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−2.99191	−	1.23929i	−0.102561	−	0.0424823i
$852$		0			0
$853$	−18.1917	−	43.9187i	−0.622873	−	1.50375i	−0.848315	−	0.529492i	$-0.822383\pi$
$853$	−18.1917	−	43.9187i	−0.622873	−	1.50375i	0.225442	−	0.974257i	$-0.427617\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.432800	+	0.432800i	0.0147842	+	0.0147842i	0.714460	−	0.699676i	$-0.246672\pi$
$857$	0.432800	+	0.432800i	0.0147842	+	0.0147842i	−0.699676	+	0.714460i	$0.746672\pi$
$858$		0			0
$859$	−17.5314	−	42.3246i	−0.598164	−	1.44410i	−0.875450	−	0.483309i	$-0.839435\pi$
$859$	−17.5314	−	42.3246i	−0.598164	−	1.44410i	0.277285	−	0.960788i	$-0.410565\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−14.7658			−0.502635			−0.251318	−	0.967905i	$-0.580864\pi$
$863$	−14.7658			−0.502635			−0.251318	+	0.967905i	$0.580864\pi$
$864$		0			0
$865$	32.2871			1.09780
$866$		0			0
$867$		0			0
$868$		0			0
$869$	2.09325	+	5.05356i	0.0710087	+	0.171430i
$870$		0			0
$871$	−12.3445	−	12.3445i	−0.418278	−	0.418278i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−8.47888	−	20.4698i	−0.286638	−	0.692006i
$876$		0			0
$877$	12.3930	+	5.13334i	0.418481	+	0.173341i	0.581980	−	0.813203i	$-0.302278\pi$
$877$	12.3930	+	5.13334i	0.418481	+	0.173341i	−0.163499	+	0.986544i	$0.552278\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−35.8699			−1.20849			−0.604243	−	0.796800i	$-0.706524\pi$
$881$	−35.8699			−1.20849			−0.604243	+	0.796800i	$0.706524\pi$
$882$		0			0
$883$	1.07109	−	2.58584i	0.0360450	−	0.0870203i	−0.904832	−	0.425769i	$-0.860004\pi$
$883$	1.07109	−	2.58584i	0.0360450	−	0.0870203i	0.940877	+	0.338749i	$0.110004\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	4.02213	+	4.02213i	0.135050	+	0.135050i	0.771400	−	0.636350i	$-0.219557\pi$
$887$	4.02213	+	4.02213i	0.135050	+	0.135050i	−0.636350	+	0.771400i	$0.719557\pi$
$888$		0			0
$889$	15.5903	−	15.5903i	0.522880	−	0.522880i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−7.76079	−	3.21462i	−0.259705	−	0.107573i
$894$		0			0
$895$			23.8254i			0.796394i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	12.5389	−	30.2715i	0.418195	−	1.00961i
$900$		0			0
$901$	−27.7478	+	11.4935i	−0.924414	+	0.382905i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	13.0286	−	13.0286i	0.433086	−	0.433086i
$906$		0			0
$907$	−32.7275	+	13.5562i	−1.08670	+	0.450125i	−0.852854	−	0.522150i	$-0.825130\pi$
$907$	−32.7275	+	13.5562i	−1.08670	+	0.450125i	−0.233843	+	0.972274i	$0.575130\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			0.767731i			0.0254361i	0.999919	+	0.0127180i	$0.00404838\pi$
$911$			0.767731i			0.0254361i	−0.999919	+	0.0127180i	$0.995952\pi$
$912$		0			0
$913$			4.33313i			0.143406i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	41.7746	−	17.3036i	1.37952	−	0.571416i
$918$		0			0
$919$	1.32571	−	1.32571i	0.0437311	−	0.0437311i	−0.684903	−	0.728634i	$-0.740155\pi$
$919$	1.32571	−	1.32571i	0.0437311	−	0.0437311i	0.728634	+	0.684903i	$0.240155\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−13.5912	+	5.62965i	−0.447359	+	0.185302i
$924$		0			0
$925$	−5.58774	+	13.4900i	−0.183724	+	0.443548i
$926$		0			0
$927$		0			0
$928$		0			0
$929$			33.4339i			1.09693i	0.836173	+	0.548465i	$0.184788\pi$
$929$			33.4339i			1.09693i	−0.836173	+	0.548465i	$0.815212\pi$
$930$		0			0
$931$	18.4577	+	7.64544i	0.604927	+	0.250569i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	46.3448	−	46.3448i	1.51564	−	1.51564i
$936$		0			0
$937$	37.9699	+	37.9699i	1.24042	+	1.24042i	0.959826	+	0.280597i	$0.0905324\pi$
$937$	37.9699	+	37.9699i	1.24042	+	1.24042i	0.280597	+	0.959826i	$0.409468\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−19.1634	+	46.2645i	−0.624709	+	1.50818i	0.221407	+	0.975181i	$0.428935\pi$
$941$	−19.1634	+	46.2645i	−0.624709	+	1.50818i	−0.846116	+	0.532999i	$0.821065\pi$
$942$		0			0
$943$	12.7995			0.416809
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−35.5194	−	14.7126i	−1.15422	−	0.478096i	−0.278277	−	0.960501i	$-0.589763\pi$
$947$	−35.5194	−	14.7126i	−1.15422	−	0.478096i	−0.875948	+	0.482405i	$0.839763\pi$
$948$		0			0
$949$	−4.78278	−	11.5467i	−0.155256	−	0.374820i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	34.4673	+	34.4673i	1.11650	+	1.11650i	0.992250	+	0.124254i	$0.0396538\pi$
$953$	34.4673	+	34.4673i	1.11650	+	1.11650i	0.124254	+	0.992250i	$0.460346\pi$
$954$		0			0
$955$	−13.1200	−	31.6744i	−0.424552	−	1.02496i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	16.1400			0.521186
$960$		0			0
$961$	−46.8567			−1.51151
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−27.5234	−	66.4473i	−0.886009	−	2.13901i
$966$		0			0
$967$	−36.1443	−	36.1443i	−1.16232	−	1.16232i	−0.983966	−	0.178358i	$-0.942921\pi$
$967$	−36.1443	−	36.1443i	−1.16232	−	1.16232i	−0.178358	−	0.983966i	$-0.557079\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−9.45955	−	22.8374i	−0.303571	−	0.732886i	−0.999885	−	0.0151489i	$-0.995178\pi$
$971$	−9.45955	−	22.8374i	−0.303571	−	0.732886i	0.696314	−	0.717738i	$-0.254822\pi$
$972$		0			0
$973$	−50.1989	−	20.7930i	−1.60930	−	0.666594i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	22.6982			0.726179			0.363090	−	0.931754i	$-0.381722\pi$
$977$	22.6982			0.726179			0.363090	+	0.931754i	$0.381722\pi$
$978$		0			0
$979$	−1.47409	+	3.55877i	−0.0471122	+	0.113739i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	12.1156	+	12.1156i	0.386428	+	0.386428i	0.873411	−	0.486984i	$-0.161903\pi$
$983$	12.1156	+	12.1156i	0.386428	+	0.386428i	−0.486984	+	0.873411i	$0.661903\pi$
$984$		0			0
$985$	−19.1321	+	19.1321i	−0.609599	+	0.609599i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−3.76392	−	1.55907i	−0.119686	−	0.0495754i
$990$		0			0
$991$		−	18.9701i		−	0.602604i	−0.953529	−	0.301302i	$-0.902579\pi$
$991$		−	18.9701i		−	0.602604i	0.953529	−	0.301302i	$-0.0974213\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−30.6634	+	74.0281i	−0.972096	+	2.34685i
$996$		0			0
$997$	−42.6036	+	17.6470i	−1.34927	+	0.558885i	−0.936089	−	0.351764i	$-0.885582\pi$
$997$	−42.6036	+	17.6470i	−1.34927	+	0.558885i	−0.413179	+	0.910650i	$0.635582\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.w.b.1007.8		32
3.2	odd	2		1152.2.w.a.1007.1		32
4.3	odd	2		288.2.w.a.179.4	✓	32
12.11	even	2		288.2.w.b.179.5	yes	32
32.5	even	8		288.2.w.b.251.5	yes	32
32.27	odd	8		1152.2.w.a.143.1		32
96.5	odd	8		288.2.w.a.251.4	yes	32
96.59	even	8	inner	1152.2.w.b.143.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.179.4	✓	32	4.3	odd	2
288.2.w.a.251.4	yes	32	96.5	odd	8
288.2.w.b.179.5	yes	32	12.11	even	2
288.2.w.b.251.5	yes	32	32.5	even	8
1152.2.w.a.143.1		32	32.27	odd	8
1152.2.w.a.1007.1		32	3.2	odd	2
1152.2.w.b.143.8		32	96.59	even	8	inner
1152.2.w.b.1007.8		32	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(1.32268 + 3.19322i) q^{5} +(2.32913 + 2.32913i) q^{7} +O(q^{10})\)	\(q+(1.32268 + 3.19322i) q^{5} +(2.32913 + 2.32913i) q^{7} +(-1.47061 - 3.55036i) q^{11} +(4.49745 + 1.86291i) q^{13} +4.93452 q^{17} +(1.98599 - 4.79460i) q^{19} +(-1.08935 - 1.08935i) q^{23} +(-4.91167 + 4.91167i) q^{25} +(-3.43073 - 1.42105i) q^{29} +8.82364i q^{31} +(-4.35675 + 10.5181i) q^{35} +(1.94208 - 0.804437i) q^{37} +(-5.87486 + 5.87486i) q^{41} +(2.44320 - 1.01201i) q^{43} -1.61865i q^{47} +3.84969i q^{49} +(-5.62320 + 2.32921i) q^{53} +(9.39195 - 9.39195i) q^{55} +(-7.67495 + 3.17907i) q^{59} +(3.16892 - 7.65045i) q^{61} +16.8254i q^{65} +(-3.31324 - 1.37239i) q^{67} +(-2.13686 + 2.13686i) q^{71} +(-1.81541 - 1.81541i) q^{73} +(4.84401 - 11.6945i) q^{77} -1.42339 q^{79} +(-1.04174 - 0.431504i) q^{83} +(6.52678 + 15.7570i) q^{85} +(-0.708782 - 0.708782i) q^{89} +(6.13620 + 14.8141i) q^{91} +17.9370 q^{95} +12.2142 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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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