LMFDB - Embedded newform 1152.2.w.a.143.1

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			143.1
Character	$\chi$	$=$	1152.143
Dual form			1152.2.w.a.1007.1

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

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

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
$5$	−1.32268	+	3.19322i	−0.591519	+	1.42805i	0.290517	+	0.956870i	$0.406173\pi$
$5$	−1.32268	+	3.19322i	−0.591519	+	1.42805i	−0.882035	+	0.471183i	$0.843827\pi$
$6$		0			0
$7$	2.32913	−	2.32913i	0.880328	−	0.880328i	−0.113239	−	0.993568i	$-0.536123\pi$
$7$	2.32913	−	2.32913i	0.880328	−	0.880328i	0.993568	+	0.113239i	$0.0361227\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.47061	−	3.55036i	0.443405	−	1.07047i	−0.531341	−	0.847158i	$-0.678312\pi$
$11$	1.47061	−	3.55036i	0.443405	−	1.07047i	0.974746	−	0.223316i	$-0.0716881\pi$
$12$		0			0
$13$	4.49745	−	1.86291i	1.24737	−	0.516677i	0.341358	−	0.939933i	$-0.389113\pi$
$13$	4.49745	−	1.86291i	1.24737	−	0.516677i	0.906010	+	0.423256i	$0.139113\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.93452			−1.19680			−0.598399	−	0.801199i	$-0.704196\pi$
$17$	−4.93452			−1.19680			−0.598399	+	0.801199i	$0.704196\pi$
$18$		0			0
$19$	1.98599	+	4.79460i	0.455617	+	1.09996i	0.970154	+	0.242488i	$0.0779635\pi$
$19$	1.98599	+	4.79460i	0.455617	+	1.09996i	−0.514538	+	0.857468i	$0.672036\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.08935	−	1.08935i	0.227144	−	0.227144i	−0.584354	−	0.811499i	$-0.698652\pi$
$23$	1.08935	−	1.08935i	0.227144	−	0.227144i	0.811499	+	0.584354i	$0.198652\pi$
$24$		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	$-0.512954\pi$
$29$	3.43073	−	1.42105i	0.637070	−	0.263883i	0.677754	+	0.735289i	$0.262954\pi$
$30$		0			0
$31$		−	8.82364i		−	1.58477i	−0.610019	−	0.792387i	$-0.708838\pi$
$31$		−	8.82364i		−	1.58477i	0.610019	−	0.792387i	$-0.291162\pi$
$32$		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	0.536565	−	0.843859i	$-0.319721\pi$
$37$	1.94208	+	0.804437i	0.319276	+	0.132249i	−0.217289	+	0.976107i	$0.569721\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.87486	+	5.87486i	0.917498	+	0.917498i	0.996847	−	0.0793485i	$-0.0252840\pi$
$41$	5.87486	+	5.87486i	0.917498	+	0.917498i	−0.0793485	+	0.996847i	$0.525284\pi$
$42$		0			0
$43$	2.44320	+	1.01201i	0.372585	+	0.154330i	0.561115	−	0.827738i	$-0.310372\pi$
$43$	2.44320	+	1.01201i	0.372585	+	0.154330i	−0.188530	+	0.982067i	$0.560372\pi$
$44$		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	$-0.237723\pi$
$53$	5.62320	+	2.32921i	0.772407	+	0.319941i	0.0385598	+	0.999256i	$0.487723\pi$
$54$		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	$-0.193137\pi$
$59$	7.67495	+	3.17907i	0.999193	+	0.413879i	0.177692	+	0.984086i	$0.443137\pi$
$60$		0			0
$61$	3.16892	+	7.65045i	0.405738	+	0.979539i	0.986246	+	0.165284i	$0.0528542\pi$
$61$	3.16892	+	7.65045i	0.405738	+	0.979539i	−0.580508	+	0.814255i	$0.697146\pi$
$62$		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	−0.575777	−	0.817607i	$-0.695300\pi$
$67$	−3.31324	+	1.37239i	−0.404777	+	0.167664i	0.171000	+	0.985271i	$0.445300\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	2.13686	+	2.13686i	0.253599	+	0.253599i	0.822444	−	0.568846i	$-0.192610\pi$
$71$	2.13686	+	2.13686i	0.253599	+	0.253599i	−0.568846	+	0.822444i	$0.692610\pi$
$72$		0			0
$73$	−1.81541	+	1.81541i	−0.212478	+	0.212478i	−0.805319	−	0.592841i	$-0.798006\pi$
$73$	−1.81541	+	1.81541i	−0.212478	+	0.212478i	0.592841	+	0.805319i	$0.298006\pi$
$74$		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	$-0.605289\pi$
$83$	1.04174	−	0.431504i	0.114346	−	0.0473637i	0.439123	+	0.898427i	$0.355289\pi$
$84$		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	$-0.733082\pi$
$89$	0.708782	−	0.708782i	0.0751308	−	0.0751308i	0.743674	+	0.668543i	$0.233082\pi$
$90$		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	−0.251913	−	0.967750i	$-0.581060\pi$
$101$	6.13564	−	14.8127i	0.610519	−	1.47392i	0.862432	−	0.506173i	$-0.168940\pi$
$102$		0			0
$103$	9.45184	−	9.45184i	0.931318	−	0.931318i	−0.0664707	−	0.997788i	$-0.521174\pi$
$103$	9.45184	−	9.45184i	0.931318	−	0.931318i	0.997788	+	0.0664707i	$0.0211739\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.93527	+	9.50057i	−0.380436	+	0.918455i	0.611445	+	0.791287i	$0.290589\pi$
$107$	−3.93527	+	9.50057i	−0.380436	+	0.918455i	−0.991881	+	0.127168i	$0.959411\pi$
$108$		0			0
$109$	−10.8399	+	4.49003i	−1.03827	+	0.430067i	−0.835692	−	0.549198i	$-0.814933\pi$
$109$	−10.8399	+	4.49003i	−1.03827	+	0.430067i	−0.202582	+	0.979265i	$0.564933\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−9.42620			−0.886742			−0.443371	−	0.896338i	$-0.646218\pi$
$113$	−9.42620			−0.886742			−0.443371	+	0.896338i	$0.646218\pi$
$114$		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	$0.0959796\pi$
$127$			6.69360i			0.593961i	−0.954884	+	0.296980i	$0.904020\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.25325	−	12.6825i	−0.458979	−	1.10807i	−0.968811	−	0.247799i	$-0.920293\pi$
$131$	−5.25325	−	12.6825i	−0.458979	−	1.10807i	0.509833	−	0.860273i	$-0.329707\pi$
$132$		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	$-0.317124\pi$
$137$	−3.46480	−	3.46480i	−0.296018	−	0.296018i	−0.839452	+	0.543434i	$0.817124\pi$
$138$		0			0
$139$	−15.2400	−	6.31262i	−1.29264	−	0.535429i	−0.372869	−	0.927884i	$-0.621626\pi$
$139$	−15.2400	−	6.31262i	−1.29264	−	0.535429i	−0.919771	+	0.392455i	$0.871626\pi$
$140$		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	$-0.249484\pi$
$149$	8.66511	+	3.58921i	0.709873	+	0.294039i	0.00162119	+	0.999999i	$0.499484\pi$
$150$		0			0
$151$	−16.6619	−	16.6619i	−1.35592	−	1.35592i	−0.878879	−	0.477045i	$-0.841708\pi$
$151$	−16.6619	−	16.6619i	−1.35592	−	1.35592i	−0.477045	−	0.878879i	$-0.658292\pi$
$152$		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	0.999457	−	0.0329386i	$-0.0104866\pi$
$157$	3.37611	+	8.15066i	0.269443	+	0.650493i	−0.730014	+	0.683432i	$0.760487\pi$
$158$		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	−0.862875	−	0.505417i	$-0.831339\pi$
$163$	−14.2435	+	5.89984i	−1.11564	+	0.462112i	−0.252761	+	0.967529i	$0.581339\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−10.0550	−	10.0550i	−0.778080	−	0.778080i	0.201424	−	0.979504i	$-0.435443\pi$
$167$	−10.0550	−	10.0550i	−0.778080	−	0.778080i	−0.979504	+	0.201424i	$0.935443\pi$
$168$		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	$-0.240556\pi$
$173$	−3.57483	−	8.63040i	−0.271789	−	0.656157i	−0.999560	+	0.0296634i	$0.990556\pi$
$174$		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	$-0.707936\pi$
$179$	−6.36855	+	2.63794i	−0.476008	+	0.197169i	0.131763	+	0.991281i	$0.457936\pi$
$180$		0			0
$181$	−2.04004	+	4.92510i	−0.151635	+	0.366080i	−0.981384	−	0.192058i	$-0.938484\pi$
$181$	−2.04004	+	4.92510i	−0.151635	+	0.366080i	0.829748	+	0.558138i	$0.188484\pi$
$182$		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	$-0.383163\pi$
$191$	9.91926			0.717732			0.358866	+	0.933389i	$0.383163\pi$
$192$		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	$-0.964960\pi$
$197$	−2.99573	+	7.23234i	−0.213437	+	0.515283i	0.780510	+	0.625143i	$0.214960\pi$
$198$		0			0
$199$	16.3928	−	16.3928i	1.16205	−	1.16205i	0.178027	−	0.984026i	$-0.443029\pi$
$199$	16.3928	−	16.3928i	1.16205	−	1.16205i	0.984026	−	0.178027i	$-0.0569713\pi$
$200$		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	0.816941	+	0.576721i	$0.195668\pi$
$211$	9.39938	+	22.6921i	0.647080	+	1.56219i	−0.169861	+	0.985468i	$0.554332\pi$
$212$		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	$0.143775\pi$
$223$			13.0361i			0.872961i	−0.899714	+	0.436480i	$0.856225\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−0.970105	−	2.34204i	−0.0643882	−	0.155447i	0.888410	−	0.459050i	$-0.151810\pi$
$227$	−0.970105	−	2.34204i	−0.0643882	−	0.155447i	−0.952798	+	0.303603i	$0.901810\pi$
$228$		0			0
$229$	10.5855	+	4.38467i	0.699512	+	0.289747i	0.703957	−	0.710243i	$-0.251415\pi$
$229$	10.5855	+	4.38467i	0.699512	+	0.289747i	−0.00444500	+	0.999990i	$0.501415\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−15.0433	−	15.0433i	−0.985522	−	0.985522i	0.0143751	−	0.999897i	$-0.495424\pi$
$233$	−15.0433	−	15.0433i	−0.985522	−	0.985522i	−0.999897	+	0.0143751i	$0.995424\pi$
$234$		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	$0.231665\pi$
$241$			20.6542i			1.33045i	−0.746642	+	0.665227i	$0.768335\pi$
$242$		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	$-0.593422\pi$
$251$	−18.5479	−	7.68280i	−1.17073	−	0.484934i	−0.881435	+	0.472304i	$0.843422\pi$
$252$		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	0.971957	+	0.235158i	$0.0755606\pi$
$263$	19.5761	+	19.5761i	1.20711	+	1.20711i	0.235158	+	0.971957i	$0.424439\pi$
$264$		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	$-0.0819783\pi$
$269$	1.69145	+	4.08353i	0.103130	+	0.248977i	−0.863889	+	0.503682i	$0.831978\pi$
$270$		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	−0.518810	−	0.854889i	$-0.673625\pi$
$277$	7.53180	−	18.1834i	0.452542	−	1.09253i	0.971352	−	0.237644i	$-0.0763751\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	16.2957	−	16.2957i	0.972118	−	0.972118i	−0.0275040	−	0.999622i	$-0.508756\pi$
$281$	16.2957	−	16.2957i	0.972118	−	0.972118i	0.999622	+	0.0275040i	$0.00875591\pi$
$282$		0			0
$283$	3.93995	−	9.51187i	0.234206	−	0.565422i	−0.762458	−	0.647037i	$-0.776008\pi$
$283$	3.93995	−	9.51187i	0.234206	−	0.565422i	0.996664	+	0.0816150i	$0.0260078\pi$
$284$		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	−0.706417	−	0.707795i	$-0.749690\pi$
$293$	5.02532	−	12.1322i	0.293582	−	0.708770i	1.00000		0.000974464i	$-0.000310182\pi$
$294$		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	0.999987	+	0.00510930i	$0.00162635\pi$
$307$	5.19514	+	12.5422i	0.296502	+	0.715820i	−0.703485	+	0.710710i	$0.748374\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	5.27753	−	5.27753i	0.299261	−	0.299261i	−0.541463	−	0.840725i	$-0.682129\pi$
$311$	5.27753	−	5.27753i	0.299261	−	0.299261i	0.840725	+	0.541463i	$0.182129\pi$
$312$		0			0
$313$	−18.5402	−	18.5402i	−1.04795	−	1.04795i	−0.998791	−	0.0491617i	$-0.984345\pi$
$313$	−18.5402	−	18.5402i	−1.04795	−	1.04795i	−0.0491617	−	0.998791i	$-0.515655\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−11.2977	+	4.67965i	−0.634540	+	0.262835i	−0.676681	−	0.736276i	$-0.736582\pi$
$317$	−11.2977	+	4.67965i	−0.634540	+	0.262835i	0.0421404	+	0.999112i	$0.486582\pi$
$318$		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	−0.486839	−	0.873492i	$-0.661850\pi$
$331$	−26.3575	−	10.9176i	−1.44874	−	0.600087i	−0.961899	+	0.273405i	$0.911850\pi$
$332$		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	$0.0785245\pi$
$337$			8.96574i			0.488395i	−0.969726	+	0.244197i	$0.921475\pi$
$338$		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	$-0.375319\pi$
$347$	−0.0344829	−	0.0142833i	−0.00185114	−	0.000766767i	−0.383609	+	0.923496i	$0.625319\pi$
$348$		0			0
$349$	−1.36920	−	3.30553i	−0.0732914	−	0.176941i	0.882988	−	0.469395i	$-0.155528\pi$
$349$	−1.36920	−	3.30553i	−0.0732914	−	0.176941i	−0.956280	+	0.292454i	$0.905528\pi$
$350$		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	−0.987447	−	0.157953i	$-0.949511\pi$
$359$	−21.7022	−	21.7022i	−1.14540	−	1.14540i	−0.157953	−	0.987447i	$-0.550489\pi$
$360$		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	−0.989339	−	0.145628i	$-0.953480\pi$
$373$	−3.60763	+	8.70959i	−0.186796	+	0.450965i	0.802543	+	0.596594i	$0.203480\pi$
$374$		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	−0.617788	−	0.786344i	$-0.711971\pi$
$379$	7.30210	−	17.6288i	0.375083	−	0.905532i	0.992872	−	0.119187i	$-0.0380289\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−17.7992			−0.909497			−0.454748	−	0.890620i	$-0.650271\pi$
$383$	−17.7992			−0.909497			−0.454748	+	0.890620i	$0.650271\pi$
$384$		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	0.404178	+	0.914680i	$0.367558\pi$
$389$	−10.4216	+	25.1599i	−0.528396	+	1.27566i	−0.932574	+	0.360979i	$0.882442\pi$
$390$		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	−0.536408	−	0.843959i	$-0.680219\pi$
$397$	−6.35478	+	2.63224i	−0.318938	+	0.132108i	0.217471	+	0.976067i	$0.430219\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−14.1764			−0.707935			−0.353968	−	0.935258i	$-0.615168\pi$
$401$	−14.1764			−0.707935			−0.353968	+	0.935258i	$0.615168\pi$
$402$		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	0.988935	+	0.148347i	$0.0473951\pi$
$409$	23.0001	+	23.0001i	1.13728	+	1.13728i	0.148347	+	0.988935i	$0.452605\pi$
$410$		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	$-0.0568021\pi$
$419$	3.33096	+	8.04166i	0.162728	+	0.392861i	−0.821392	+	0.570364i	$0.806802\pi$
$420$		0			0
$421$	−6.91049	−	2.86242i	−0.336797	−	0.139506i	0.207874	−	0.978156i	$-0.433346\pi$
$421$	−6.91049	−	2.86242i	−0.336797	−	0.139506i	−0.544671	+	0.838650i	$0.683346\pi$
$422$		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	$-0.719109\pi$
$433$		−	32.1408i		−	1.54459i	0.635264	−	0.772295i	$-0.280891\pi$
$434$		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	0.997742	−	0.0671583i	$-0.0213933\pi$
$439$	19.4979	+	19.4979i	0.930584	+	0.930584i	−0.0671583	+	0.997742i	$0.521393\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−12.4270	−	5.14742i	−0.590424	−	0.244561i	0.0674092	−	0.997725i	$-0.478527\pi$
$443$	−12.4270	−	5.14742i	−0.590424	−	0.244561i	−0.657833	+	0.753164i	$0.728527\pi$
$444$		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	−0.0984696	−	0.995140i	$-0.531395\pi$
$457$	19.1686	−	19.1686i	0.896670	−	0.896670i	0.995140	+	0.0984696i	$0.0313947\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	6.32718	+	15.2752i	0.294686	+	0.711436i	0.999997	+	0.00253708i	$0.000807579\pi$
$461$	6.32718	+	15.2752i	0.294686	+	0.711436i	−0.705311	+	0.708898i	$0.749192\pi$
$462$		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	$-0.671753\pi$
$467$	−5.84384	+	2.42060i	−0.270420	+	0.112012i	0.243353	+	0.969938i	$0.421753\pi$
$468$		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	$-0.557984\pi$
$479$	−7.92963			−0.362314			−0.181157	+	0.983454i	$0.557984\pi$
$480$		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	−0.907978	−	0.419017i	$-0.862375\pi$
$487$	−10.7904	+	10.7904i	−0.488961	+	0.488961i	0.419017	+	0.907978i	$0.362375\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.68219	+	4.06116i	−0.0759160	+	0.183277i	−0.957282	−	0.289158i	$-0.906625\pi$
$491$	−1.68219	+	4.06116i	−0.0759160	+	0.183277i	0.881366	+	0.472435i	$0.156625\pi$
$492$		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	0.774086	+	0.633081i	$0.218210\pi$
$499$	15.0645	+	36.3690i	0.674380	+	1.62810i	−0.0997053	+	0.995017i	$0.531790\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	8.41533	−	8.41533i	0.375221	−	0.375221i	−0.494153	−	0.869375i	$-0.664522\pi$
$503$	8.41533	−	8.41533i	0.375221	−	0.375221i	0.869375	+	0.494153i	$0.164522\pi$
$504$		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	$-0.752864\pi$
$509$	−16.2989	+	6.75122i	−0.722436	+	0.299243i	−0.00899639	+	0.999960i	$0.502864\pi$
$510$		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	$-0.0641628\pi$
$521$	17.7934	+	17.7934i	0.779542	+	0.779542i	−0.200211	+	0.979753i	$0.564163\pi$
$522$		0			0
$523$	−10.5763	−	4.38083i	−0.462468	−	0.191560i	0.139270	−	0.990254i	$-0.455525\pi$
$523$	−10.5763	−	4.38083i	−0.462468	−	0.191560i	−0.601737	+	0.798694i	$0.705525\pi$
$524$		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	0.920375	−	0.391037i	$-0.127883\pi$
$541$	−0.161261	−	0.389318i	−0.00693315	−	0.0167381i	−0.927308	+	0.374299i	$0.877883\pi$
$542$		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	−0.432805	−	0.901488i	$-0.642476\pi$
$547$	−2.37145	+	0.982285i	−0.101396	+	0.0419995i	0.331409	+	0.943487i	$0.392476\pi$
$548$		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	$-0.107800\pi$
$557$	0.975580	+	2.35526i	0.0413366	+	0.0997955i	−0.901863	+	0.432023i	$0.857800\pi$
$558$		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	$-0.695480\pi$
$563$	−9.62858	+	3.98829i	−0.405796	+	0.168086i	0.170443	+	0.985368i	$0.445480\pi$
$564$		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	$-0.561181\pi$
$569$	18.8578	−	18.8578i	0.790559	−	0.790559i	0.981585	+	0.191026i	$0.0611814\pi$
$570$		0			0
$571$	−2.27949	+	5.50317i	−0.0953936	+	0.230300i	−0.964372	−	0.264549i	$-0.914777\pi$
$571$	−2.27949	+	5.50317i	−0.0953936	+	0.230300i	0.868979	+	0.494850i	$0.164777\pi$
$572$		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	−0.556050	−	0.831149i	$-0.687684\pi$
$587$	10.2932	−	24.8501i	0.424848	−	1.02567i	0.980898	−	0.194524i	$-0.0623162\pi$
$588$		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	$-0.189692\pi$
$593$	40.3079			1.65525			0.827624	+	0.561283i	$0.189692\pi$
$594$		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	$-0.867177\pi$
$599$	−12.4557	+	12.4557i	−0.508926	+	0.508926i	0.405271	+	0.914197i	$0.367177\pi$
$600$		0			0
$601$	6.85263	+	6.85263i	0.279525	+	0.279525i	0.832919	−	0.553395i	$-0.186668\pi$
$601$	6.85263	+	6.85263i	0.279525	+	0.279525i	−0.553395	+	0.832919i	$0.686668\pi$
$602$		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	$-0.964116\pi$
$607$		−	5.54311i		−	0.224988i	0.993652	−	0.112494i	$-0.0358839\pi$
$608$		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	0.409661	−	0.912238i	$-0.365647\pi$
$613$	1.34403	+	0.556714i	0.0542847	+	0.0224855i	−0.355376	+	0.934723i	$0.615647\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−27.3420	−	27.3420i	−1.10075	−	1.10075i	−0.994320	−	0.106429i	$-0.966058\pi$
$617$	−27.3420	−	27.3420i	−1.10075	−	1.10075i	−0.106429	−	0.994320i	$-0.533942\pi$
$618$		0			0
$619$	27.2304	+	11.2792i	1.09448	+	0.453350i	0.855568	−	0.517690i	$-0.173208\pi$
$619$	27.2304	+	11.2792i	1.09448	+	0.453350i	0.238916	+	0.971040i	$0.423208\pi$
$620$		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	0.820492	−	0.571658i	$-0.193700\pi$
$631$	6.25063	+	6.25063i	0.248834	+	0.248834i	−0.571658	+	0.820492i	$0.693700\pi$
$632$		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	−0.698967	−	0.715154i	$-0.746356\pi$
$643$	−17.4338	+	7.22130i	−0.687520	+	0.284780i	0.0114464	+	0.999934i	$0.496356\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	2.78525	+	2.78525i	0.109500	+	0.109500i	0.759734	−	0.650234i	$-0.225329\pi$
$647$	2.78525	+	2.78525i	0.109500	+	0.109500i	−0.650234	+	0.759734i	$0.725329\pi$
$648$		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	$-0.181039\pi$
$653$	−3.42546	−	8.26978i	−0.134048	−	0.323622i	−0.976623	+	0.214957i	$0.931039\pi$
$654$		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	−0.744243	+	0.667909i	$0.767189\pi$
$659$	−44.7390	+	18.5315i	−1.74278	+	0.721885i	−0.998542	+	0.0539756i	$0.982811\pi$
$660$		0			0
$661$	−5.04994	+	12.1916i	−0.196420	+	0.474200i	−0.991147	−	0.132767i	$-0.957614\pi$
$661$	−5.04994	+	12.1916i	−0.196420	+	0.474200i	0.794727	+	0.606967i	$0.207614\pi$
$662$		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	$-0.927557\pi$
$677$	−3.27320	+	7.90221i	−0.125799	+	0.303706i	0.848415	+	0.529332i	$0.177557\pi$
$678$		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	−0.167388	+	0.985891i	$0.553533\pi$
$683$	−19.5003	+	47.0778i	−0.746157	+	1.80138i	−0.578769	+	0.815491i	$0.696467\pi$
$684$		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	0.785361	−	0.619038i	$-0.212477\pi$
$691$	−5.45976	−	13.1810i	−0.207699	−	0.501430i	−0.993060	+	0.117608i	$0.962477\pi$
$692$		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	$-0.664551\pi$
$701$	−6.06309	+	2.51141i	−0.229000	+	0.0948547i	0.265233	+	0.964184i	$0.414551\pi$
$702$		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	0.678762	−	0.734359i	$-0.262517\pi$
$709$	17.0266	+	7.05266i	0.639448	+	0.264868i	−0.0393132	+	0.999227i	$0.512517\pi$
$710$		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	0.298376	−	0.954448i	$-0.403555\pi$
$727$	−17.6896	−	17.6896i	−0.656073	−	0.656073i	−0.954448	+	0.298376i	$0.903555\pi$
$728$		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	0.866526	−	0.499131i	$-0.166348\pi$
$733$	−2.68410	−	6.47999i	−0.0991395	−	0.239344i	−0.965666	+	0.259787i	$0.916348\pi$
$734$		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	−0.212259	−	0.977213i	$-0.568082\pi$
$739$	8.93406	−	3.70061i	0.328645	−	0.136129i	0.540904	+	0.841084i	$0.318082\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−32.3436	−	32.3436i	−1.18657	−	1.18657i	−0.978009	−	0.208565i	$-0.933121\pi$
$743$	−32.3436	−	32.3436i	−1.18657	−	1.18657i	−0.208565	−	0.978009i	$-0.566879\pi$
$744$		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	−0.872318	−	0.488939i	$-0.837384\pi$
$757$	2.48272	−	5.99382i	0.0902361	−	0.217849i	0.962554	+	0.271090i	$0.0873840\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−4.40886	+	4.40886i	−0.159821	+	0.159821i	−0.782488	−	0.622666i	$-0.786049\pi$
$761$	−4.40886	+	4.40886i	−0.159821	+	0.159821i	0.622666	+	0.782488i	$0.286049\pi$
$762$		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	−0.522741	−	0.852492i	$-0.675090\pi$
$773$	12.5028	−	30.1845i	0.449695	−	1.08566i	0.972436	−	0.233169i	$-0.0749096\pi$
$774$		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	0.923114	−	0.384525i	$-0.125635\pi$
$787$	−0.0428254	−	0.103390i	−0.00152656	−	0.00368545i	−0.924641	+	0.380840i	$0.875635\pi$
$788$		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	$-0.840403\pi$
$797$	−32.6670	+	13.5311i	−1.15712	+	0.479297i	−0.280208	+	0.959939i	$0.590403\pi$
$798$		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	$-0.0612345\pi$
$809$	22.4803	+	22.4803i	0.790364	+	0.790364i	−0.191189	+	0.981553i	$0.561234\pi$
$810$		0			0
$811$	−41.9112	−	17.3602i	−1.47170	−	0.609598i	−0.504454	−	0.863438i	$-0.668306\pi$
$811$	−41.9112	−	17.3602i	−1.47170	−	0.609598i	−0.967246	+	0.253840i	$0.918306\pi$
$812$		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	$-0.391022\pi$
$821$	−2.66376	−	1.10337i	−0.0929660	−	0.0385078i	−0.428682	+	0.903456i	$0.641022\pi$
$822$		0			0
$823$	−27.8538	−	27.8538i	−0.970924	−	0.970924i	0.0286650	−	0.999589i	$-0.490874\pi$
$823$	−27.8538	−	27.8538i	−0.970924	−	0.970924i	−0.999589	+	0.0286650i	$0.990874\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	31.9381	+	13.2292i	1.11060	+	0.460024i	0.861143	−	0.508362i	$-0.169749\pi$
$827$	31.9381	+	13.2292i	1.11060	+	0.460024i	0.249454	+	0.968387i	$0.419749\pi$
$828$		0			0
$829$	4.80176	+	11.5925i	0.166772	+	0.402623i	0.985066	−	0.172176i	$-0.0550799\pi$
$829$	4.80176	+	11.5925i	0.166772	+	0.402623i	−0.818294	+	0.574800i	$0.805080\pi$
$830$		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	$-0.140579\pi$
$839$	13.8057	+	13.8057i	0.476627	+	0.476627i	−0.427424	+	0.904051i	$0.640579\pi$
$840$		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	0.225442	+	0.974257i	$0.427617\pi$
$853$	−18.1917	+	43.9187i	−0.622873	+	1.50375i	−0.848315	+	0.529492i	$0.822383\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.432800	+	0.432800i	−0.0147842	+	0.0147842i	−0.714460	−	0.699676i	$-0.753328\pi$
$857$	−0.432800	+	0.432800i	−0.0147842	+	0.0147842i	0.699676	+	0.714460i	$0.253328\pi$
$858$		0			0
$859$	−17.5314	+	42.3246i	−0.598164	+	1.44410i	0.277285	+	0.960788i	$0.410565\pi$
$859$	−17.5314	+	42.3246i	−0.598164	+	1.44410i	−0.875450	+	0.483309i	$0.839435\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	14.7658			0.502635			0.251318	−	0.967905i	$-0.419136\pi$
$863$	14.7658			0.502635			0.251318	+	0.967905i	$0.419136\pi$
$864$		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	−0.163499	−	0.986544i	$-0.552278\pi$
$877$	12.3930	−	5.13334i	0.418481	−	0.173341i	0.581980	+	0.813203i	$0.302278\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	35.8699			1.20849			0.604243	−	0.796800i	$-0.293476\pi$
$881$	35.8699			1.20849			0.604243	+	0.796800i	$0.293476\pi$
$882$		0			0
$883$	1.07109	+	2.58584i	0.0360450	+	0.0870203i	0.940877	−	0.338749i	$-0.110004\pi$
$883$	1.07109	+	2.58584i	0.0360450	+	0.0870203i	−0.904832	+	0.425769i	$0.860004\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−4.02213	+	4.02213i	−0.135050	+	0.135050i	−0.771400	−	0.636350i	$-0.780443\pi$
$887$	−4.02213	+	4.02213i	−0.135050	+	0.135050i	0.636350	+	0.771400i	$0.280443\pi$
$888$		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	−0.233843	−	0.972274i	$-0.575130\pi$
$907$	−32.7275	−	13.5562i	−1.08670	−	0.450125i	−0.852854	+	0.522150i	$0.825130\pi$
$908$		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	0.728634	−	0.684903i	$-0.240155\pi$
$919$	1.32571	+	1.32571i	0.0437311	+	0.0437311i	−0.684903	+	0.728634i	$0.740155\pi$
$920$		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	0.280597	−	0.959826i	$-0.409468\pi$
$937$	37.9699	−	37.9699i	1.24042	−	1.24042i	0.959826	−	0.280597i	$-0.0905324\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	19.1634	+	46.2645i	0.624709	+	1.50818i	0.846116	+	0.532999i	$0.178935\pi$
$941$	19.1634	+	46.2645i	0.624709	+	1.50818i	−0.221407	+	0.975181i	$0.571065\pi$
$942$		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	$-0.410237\pi$
$947$	35.5194	−	14.7126i	1.15422	−	0.478096i	0.875948	+	0.482405i	$0.160237\pi$
$948$		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	−0.124254	+	0.992250i	$0.539654\pi$
$953$	−34.4673	+	34.4673i	−1.11650	+	1.11650i	−0.992250	+	0.124254i	$0.960346\pi$
$954$		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	−0.178358	+	0.983966i	$0.557079\pi$
$967$	−36.1443	+	36.1443i	−1.16232	+	1.16232i	−0.983966	+	0.178358i	$0.942921\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	9.45955	−	22.8374i	0.303571	−	0.732886i	−0.696314	−	0.717738i	$-0.745178\pi$
$971$	9.45955	−	22.8374i	0.303571	−	0.732886i	0.999885	−	0.0151489i	$-0.00482222\pi$
$972$		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	$-0.618278\pi$
$977$	−22.6982			−0.726179			−0.363090	+	0.931754i	$0.618278\pi$
$978$		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	$-0.838097\pi$
$983$	−12.1156	+	12.1156i	−0.386428	+	0.386428i	0.486984	+	0.873411i	$0.338097\pi$
$984$		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	$0.0974213\pi$
$991$			18.9701i			0.602604i	−0.953529	+	0.301302i	$0.902579\pi$
$992$		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	−0.413179	−	0.910650i	$-0.635582\pi$
$997$	−42.6036	−	17.6470i	−1.34927	−	0.558885i	−0.936089	+	0.351764i	$0.885582\pi$
$998$		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.143.1		32
3.2	odd	2		1152.2.w.b.143.8		32
4.3	odd	2		288.2.w.b.251.5	yes	32
12.11	even	2		288.2.w.a.251.4	yes	32
32.13	even	8		288.2.w.a.179.4	✓	32
32.19	odd	8		1152.2.w.b.1007.8		32
96.77	odd	8		288.2.w.b.179.5	yes	32
96.83	even	8	inner	1152.2.w.a.1007.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.179.4	✓	32	32.13	even	8
288.2.w.a.251.4	yes	32	12.11	even	2
288.2.w.b.179.5	yes	32	96.77	odd	8
288.2.w.b.251.5	yes	32	4.3	odd	2
1152.2.w.a.143.1		32	1.1	even	1	trivial
1152.2.w.a.1007.1		32	96.83	even	8	inner
1152.2.w.b.143.8		32	3.2	odd	2
1152.2.w.b.1007.8		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)

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