LMFDB - Embedded newform 1152.2.w.b.719.2

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			719.2
Character	$\chi$	$=$	1152.719
Dual form			1152.2.w.b.431.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.70076 - 1.11869i) q^{5} +(1.06647 - 1.06647i) q^{7} +O(q^{10})$	$q+(-2.70076 - 1.11869i) q^{5} +(1.06647 - 1.06647i) q^{7} +(-5.29504 - 2.19328i) q^{11} +(1.67540 + 4.04478i) q^{13} +3.44484 q^{17} +(-3.23205 + 1.33876i) q^{19} +(-0.703083 + 0.703083i) q^{23} +(2.50711 + 2.50711i) q^{25} +(3.94721 + 9.52941i) q^{29} +4.23846i q^{31} +(-4.07335 + 1.68724i) q^{35} +(-2.04600 + 4.93947i) q^{37} +(-3.53573 - 3.53573i) q^{41} +(3.38340 - 8.16825i) q^{43} +4.33671i q^{47} +4.72526i q^{49} +(-0.541366 + 1.30697i) q^{53} +(11.8470 + 11.8470i) q^{55} +(-3.66093 + 8.83827i) q^{59} +(-1.97197 + 0.816817i) q^{61} -12.7983i q^{65} +(3.55849 + 8.59096i) q^{67} +(1.76501 + 1.76501i) q^{71} +(-1.16342 + 1.16342i) q^{73} +(-7.98610 + 3.30795i) q^{77} -14.4770 q^{79} +(-4.27230 - 10.3143i) q^{83} +(-9.30371 - 3.85372i) q^{85} +(-7.99481 + 7.99481i) q^{89} +(6.10044 + 2.52688i) q^{91} +10.2267 q^{95} +12.8450 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−2.70076	−	1.11869i	−1.20782	−	0.500294i	−0.314300	−	0.949324i	$-0.601770\pi$
$5$	−2.70076	−	1.11869i	−1.20782	−	0.500294i	−0.893517	+	0.449029i	$0.851770\pi$
$6$		0			0
$7$	1.06647	−	1.06647i	0.403090	−	0.403090i	−0.476231	−	0.879320i	$-0.657997\pi$
$7$	1.06647	−	1.06647i	0.403090	−	0.403090i	0.879320	+	0.476231i	$0.157997\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−5.29504	−	2.19328i	−1.59651	−	0.661297i	−0.605596	−	0.795772i	$-0.707065\pi$
$11$	−5.29504	−	2.19328i	−1.59651	−	0.661297i	−0.990917	+	0.134475i	$0.957065\pi$
$12$		0			0
$13$	1.67540	+	4.04478i	0.464674	+	1.12182i	0.966457	+	0.256828i	$0.0826774\pi$
$13$	1.67540	+	4.04478i	0.464674	+	1.12182i	−0.501783	+	0.864993i	$0.667323\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.44484			0.835498			0.417749	−	0.908563i	$-0.362819\pi$
$17$	3.44484			0.835498			0.417749	+	0.908563i	$0.362819\pi$
$18$		0			0
$19$	−3.23205	+	1.33876i	−0.741483	+	0.307132i	−0.721261	−	0.692663i	$-0.756437\pi$
$19$	−3.23205	+	1.33876i	−0.741483	+	0.307132i	−0.0202218	+	0.999796i	$0.506437\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.703083	+	0.703083i	−0.146603	+	0.146603i	−0.776599	−	0.629996i	$-0.783057\pi$
$23$	−0.703083	+	0.703083i	−0.146603	+	0.146603i	0.629996	+	0.776599i	$0.283057\pi$
$24$		0			0
$25$	2.50711	+	2.50711i	0.501422	+	0.501422i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.94721	+	9.52941i	0.732979	+	1.76957i	0.632405	+	0.774638i	$0.282068\pi$
$29$	3.94721	+	9.52941i	0.732979	+	1.76957i	0.100574	+	0.994930i	$0.467932\pi$
$30$		0			0
$31$			4.23846i			0.761250i	0.924729	+	0.380625i	$0.124291\pi$
$31$			4.23846i			0.761250i	−0.924729	+	0.380625i	$0.875709\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.07335	+	1.68724i	−0.688522	+	0.285195i
$36$		0			0
$37$	−2.04600	+	4.93947i	−0.336360	+	0.812044i	0.661699	+	0.749769i	$0.269836\pi$
$37$	−2.04600	+	4.93947i	−0.336360	+	0.812044i	−0.998059	+	0.0622749i	$0.980164\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.53573	−	3.53573i	−0.552188	−	0.552188i	0.374884	−	0.927072i	$-0.377683\pi$
$41$	−3.53573	−	3.53573i	−0.552188	−	0.552188i	−0.927072	+	0.374884i	$0.877683\pi$
$42$		0			0
$43$	3.38340	−	8.16825i	0.515963	−	1.24565i	−0.424400	−	0.905475i	$-0.639515\pi$
$43$	3.38340	−	8.16825i	0.515963	−	1.24565i	0.940364	−	0.340171i	$-0.110485\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			4.33671i			0.632575i	0.948663	+	0.316287i	$0.102436\pi$
$47$			4.33671i			0.632575i	−0.948663	+	0.316287i	$0.897564\pi$
$48$		0			0
$49$			4.72526i			0.675038i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.541366	+	1.30697i	−0.0743624	+	0.179527i	−0.956690	−	0.291110i	$-0.905976\pi$
$53$	−0.541366	+	1.30697i	−0.0743624	+	0.179527i	0.882327	+	0.470636i	$0.155976\pi$
$54$		0			0
$55$	11.8470	+	11.8470i	1.59745	+	1.59745i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.66093	+	8.83827i	−0.476613	+	1.15064i	0.484575	+	0.874750i	$0.338974\pi$
$59$	−3.66093	+	8.83827i	−0.476613	+	1.15064i	−0.961188	+	0.275895i	$0.911026\pi$
$60$		0			0
$61$	−1.97197	+	0.816817i	−0.252485	+	0.104583i	−0.505336	−	0.862922i	$-0.668632\pi$
$61$	−1.97197	+	0.816817i	−0.252485	+	0.104583i	0.252851	+	0.967505i	$0.418632\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	12.7983i		−	1.58743i
$66$		0			0
$67$	3.55849	+	8.59096i	0.434739	+	1.04955i	0.977740	+	0.209821i	$0.0672880\pi$
$67$	3.55849	+	8.59096i	0.434739	+	1.04955i	−0.543001	+	0.839732i	$0.682712\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.76501	+	1.76501i	0.209468	+	0.209468i	0.804041	−	0.594574i	$-0.202679\pi$
$71$	1.76501	+	1.76501i	0.209468	+	0.209468i	−0.594574	+	0.804041i	$0.702679\pi$
$72$		0			0
$73$	−1.16342	+	1.16342i	−0.136168	+	0.136168i	−0.771905	−	0.635737i	$-0.780696\pi$
$73$	−1.16342	+	1.16342i	−0.136168	+	0.136168i	0.635737	+	0.771905i	$0.280696\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.98610	+	3.30795i	−0.910100	+	0.376976i
$78$		0			0
$79$	−14.4770			−1.62879			−0.814393	−	0.580314i	$-0.802930\pi$
$79$	−14.4770			−1.62879			−0.814393	+	0.580314i	$0.802930\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.27230	−	10.3143i	−0.468946	−	1.13214i	−0.964624	−	0.263630i	$-0.915080\pi$
$83$	−4.27230	−	10.3143i	−0.468946	−	1.13214i	0.495678	−	0.868507i	$-0.334920\pi$
$84$		0			0
$85$	−9.30371	−	3.85372i	−1.00913	−	0.417995i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−7.99481	+	7.99481i	−0.847448	+	0.847448i	−0.989814	−	0.142366i	$-0.954529\pi$
$89$	−7.99481	+	7.99481i	−0.847448	+	0.847448i	0.142366	+	0.989814i	$0.454529\pi$
$90$		0			0
$91$	6.10044	+	2.52688i	0.639500	+	0.264889i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	10.2267			1.04923
$96$		0			0
$97$	12.8450			1.30421			0.652107	−	0.758127i	$-0.273885\pi$
$97$	12.8450			1.30421			0.652107	+	0.758127i	$0.273885\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.195046	−	0.0807908i	−0.0194078	−	0.00803898i	0.372958	−	0.927848i	$-0.378343\pi$
$101$	−0.195046	−	0.0807908i	−0.0194078	−	0.00803898i	−0.392366	+	0.919809i	$0.628343\pi$
$102$		0			0
$103$	−7.52990	+	7.52990i	−0.741943	+	0.741943i	−0.972952	−	0.231009i	$-0.925797\pi$
$103$	−7.52990	+	7.52990i	−0.741943	+	0.741943i	0.231009	+	0.972952i	$0.425797\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.43177	+	2.66413i	0.621783	+	0.257551i	0.671257	−	0.741225i	$-0.265755\pi$
$107$	6.43177	+	2.66413i	0.621783	+	0.257551i	−0.0494744	+	0.998775i	$0.515755\pi$
$108$		0			0
$109$	−4.89484	−	11.8172i	−0.468840	−	1.13188i	−0.964670	−	0.263461i	$-0.915136\pi$
$109$	−4.89484	−	11.8172i	−0.468840	−	1.13188i	0.495830	−	0.868420i	$-0.334864\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.983568			−0.0925263			−0.0462631	−	0.998929i	$-0.514731\pi$
$113$	−0.983568			−0.0925263			−0.0462631	+	0.998929i	$0.514731\pi$
$114$		0			0
$115$	2.68539	−	1.11233i	0.250414	−	0.103725i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	3.67384	−	3.67384i	0.336780	−	0.336780i
$120$		0			0
$121$	15.4488	+	15.4488i	1.40443	+	1.40443i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.62704	+	3.92802i	0.145527	+	0.351333i
$126$		0			0
$127$		−	5.32766i		−	0.472754i	−0.971661	−	0.236377i	$-0.924040\pi$
$127$		−	5.32766i		−	0.472754i	0.971661	−	0.236377i	$-0.0759600\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−17.7023	+	7.33252i	−1.54666	+	0.640646i	−0.982707	−	0.185165i	$-0.940718\pi$
$131$	−17.7023	+	7.33252i	−1.54666	+	0.640646i	−0.563948	+	0.825811i	$0.690718\pi$
$132$		0			0
$133$	−2.01915	+	4.87465i	−0.175082	+	0.422686i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−10.0787	−	10.0787i	−0.861079	−	0.861079i	0.130384	−	0.991464i	$-0.458379\pi$
$137$	−10.0787	−	10.0787i	−0.861079	−	0.861079i	−0.991464	+	0.130384i	$0.958379\pi$
$138$		0			0
$139$	4.57378	−	11.0421i	0.387943	−	0.936578i	−0.602432	−	0.798170i	$-0.705802\pi$
$139$	4.57378	−	11.0421i	0.387943	−	0.936578i	0.990375	−	0.138408i	$-0.0441984\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	25.0919i		−	2.09829i
$144$		0			0
$145$		−	30.1524i		−	2.50402i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2.47497	+	5.97511i	−0.202758	+	0.489500i	−0.992250	−	0.124261i	$-0.960344\pi$
$149$	−2.47497	+	5.97511i	−0.202758	+	0.489500i	0.789492	+	0.613761i	$0.210344\pi$
$150$		0			0
$151$	5.28519	+	5.28519i	0.430103	+	0.430103i	0.888663	−	0.458560i	$-0.151635\pi$
$151$	5.28519	+	5.28519i	0.430103	+	0.430103i	−0.458560	+	0.888663i	$0.651635\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.74153	−	11.4471i	0.380849	−	0.919451i
$156$		0			0
$157$	19.9431	−	8.26070i	1.59163	−	0.659276i	0.601431	−	0.798924i	$-0.294597\pi$
$157$	19.9431	−	8.26070i	1.59163	−	0.659276i	0.990201	+	0.139649i	$0.0445973\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			1.49964i			0.118188i
$162$		0			0
$163$	−4.75817	−	11.4872i	−0.372689	−	0.899751i	−0.993293	−	0.115626i	$-0.963112\pi$
$163$	−4.75817	−	11.4872i	−0.372689	−	0.899751i	0.620604	−	0.784124i	$-0.286888\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	13.4711	+	13.4711i	1.04243	+	1.04243i	0.999059	+	0.0433679i	$0.0138088\pi$
$167$	13.4711	+	13.4711i	1.04243	+	1.04243i	0.0433679	+	0.999059i	$0.486191\pi$
$168$		0			0
$169$	−4.36092	+	4.36092i	−0.335455	+	0.335455i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.48659	+	0.615768i	−0.113024	+	0.0468160i	−0.438479	−	0.898742i	$-0.644483\pi$
$173$	−1.48659	+	0.615768i	−0.113024	+	0.0468160i	0.325455	+	0.945558i	$0.394483\pi$
$174$		0			0
$175$	5.34754			0.404236
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−0.188898	−	0.456040i	−0.0141189	−	0.0340860i	0.916663	−	0.399661i	$-0.130872\pi$
$179$	−0.188898	−	0.456040i	−0.0141189	−	0.0340860i	−0.930782	+	0.365575i	$0.880872\pi$
$180$		0			0
$181$	−20.2286	−	8.37896i	−1.50358	−	0.622803i	−0.529358	−	0.848398i	$-0.677567\pi$
$181$	−20.2286	−	8.37896i	−1.50358	−	0.622803i	−0.974221	+	0.225596i	$0.927567\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	11.0515	−	11.0515i	0.812522	−	0.812522i
$186$		0			0
$187$	−18.2406	−	7.55549i	−1.33388	−	0.552512i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	23.3059			1.68636			0.843180	−	0.537632i	$-0.180681\pi$
$191$	23.3059			1.68636			0.843180	+	0.537632i	$0.180681\pi$
$192$		0			0
$193$	−27.0699			−1.94854			−0.974268	−	0.225392i	$-0.927634\pi$
$193$	−27.0699			−1.94854			−0.974268	+	0.225392i	$0.927634\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	0.234504	+	0.0971345i	0.0167077	+	0.00692055i	0.391022	−	0.920381i	$-0.372122\pi$
$197$	0.234504	+	0.0971345i	0.0167077	+	0.00692055i	−0.374314	+	0.927302i	$0.622122\pi$
$198$		0			0
$199$	2.87064	−	2.87064i	0.203494	−	0.203494i	−0.598001	−	0.801495i	$-0.704038\pi$
$199$	2.87064	−	2.87064i	0.203494	−	0.203494i	0.801495	+	0.598001i	$0.204038\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	14.3725	+	5.95328i	1.00875	+	0.417838i
$204$		0			0
$205$	5.59377	+	13.5045i	0.390686	+	0.943199i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	20.0501			1.38689
$210$		0			0
$211$	−21.3966	+	8.86277i	−1.47300	+	0.610138i	−0.967542	−	0.252710i	$-0.918678\pi$
$211$	−21.3966	+	8.86277i	−1.47300	+	0.610138i	−0.505462	+	0.862849i	$0.668678\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−18.2755	+	18.2755i	−1.24638	+	1.24638i
$216$		0			0
$217$	4.52021	+	4.52021i	0.306852	+	0.306852i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	5.77151	+	13.9337i	0.388234	+	0.937279i
$222$		0			0
$223$			6.32748i			0.423720i	0.977300	+	0.211860i	$0.0679520\pi$
$223$			6.32748i			0.423720i	−0.977300	+	0.211860i	$0.932048\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.62883	−	2.74575i	0.439971	−	0.182242i	−0.151691	−	0.988428i	$-0.548472\pi$
$227$	6.62883	−	2.74575i	0.439971	−	0.182242i	0.591662	+	0.806186i	$0.298472\pi$
$228$		0			0
$229$	−2.56839	+	6.20065i	−0.169724	+	0.409751i	−0.985739	−	0.168280i	$-0.946179\pi$
$229$	−2.56839	+	6.20065i	−0.169724	+	0.409751i	0.816015	+	0.578031i	$0.196179\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	4.72679	+	4.72679i	0.309662	+	0.309662i	0.844779	−	0.535116i	$-0.179732\pi$
$233$	4.72679	+	4.72679i	0.309662	+	0.309662i	−0.535116	+	0.844779i	$0.679732\pi$
$234$		0			0
$235$	4.85145	−	11.7124i	0.316474	−	0.764035i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			5.76879i			0.373152i	0.982441	+	0.186576i	$0.0597390\pi$
$239$			5.76879i			0.373152i	−0.982441	+	0.186576i	$0.940261\pi$
$240$		0			0
$241$		−	20.1679i		−	1.29913i	−0.760308	−	0.649563i	$-0.774952\pi$
$241$		−	20.1679i		−	1.29913i	0.760308	−	0.649563i	$-0.225048\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	5.28612	−	12.7618i	0.337718	−	0.815322i
$246$		0			0
$247$	−10.8300	−	10.8300i	−0.689095	−	0.689095i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−0.288817	+	0.697266i	−0.0182300	+	0.0440110i	−0.932732	−	0.360569i	$-0.882582\pi$
$251$	−0.288817	+	0.697266i	−0.0182300	+	0.0440110i	0.914502	+	0.404580i	$0.132582\pi$
$252$		0			0
$253$	5.26491	−	2.18080i	0.331002	−	0.137105i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			6.89560i			0.430136i	0.976599	+	0.215068i	$0.0689973\pi$
$257$			6.89560i			0.430136i	−0.976599	+	0.215068i	$0.931003\pi$
$258$		0			0
$259$	3.08582	+	7.44983i	0.191743	+	0.462910i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−3.11571	−	3.11571i	−0.192123	−	0.192123i	0.604490	−	0.796613i	$-0.293377\pi$
$263$	−3.11571	−	3.11571i	−0.192123	−	0.192123i	−0.796613	+	0.604490i	$0.793377\pi$
$264$		0			0
$265$	2.92420	−	2.92420i	0.179632	−	0.179632i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	12.4085	−	5.13977i	0.756560	−	0.313378i	0.0291452	−	0.999575i	$-0.490721\pi$
$269$	12.4085	−	5.13977i	0.756560	−	0.313378i	0.727415	+	0.686198i	$0.240721\pi$
$270$		0			0
$271$	−5.94627			−0.361210			−0.180605	−	0.983556i	$-0.557806\pi$
$271$	−5.94627			−0.361210			−0.180605	+	0.983556i	$0.557806\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−7.77645	−	18.7740i	−0.468938	−	1.13212i
$276$		0			0
$277$	−8.48544	−	3.51479i	−0.509841	−	0.211183i	0.112907	−	0.993606i	$-0.463984\pi$
$277$	−8.48544	−	3.51479i	−0.509841	−	0.211183i	−0.622748	+	0.782423i	$0.713984\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	12.5190	−	12.5190i	0.746823	−	0.746823i	−0.227058	−	0.973881i	$-0.572911\pi$
$281$	12.5190	−	12.5190i	0.746823	−	0.746823i	0.973881	+	0.227058i	$0.0729107\pi$
$282$		0			0
$283$	16.8466	+	6.97810i	1.00143	+	0.414805i	0.822321	−	0.569024i	$-0.192679\pi$
$283$	16.8466	+	6.97810i	1.00143	+	0.414805i	0.179107	+	0.983830i	$0.442679\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−7.54153			−0.445162
$288$		0			0
$289$	−5.13305			−0.301944
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.86190	+	0.771224i	0.108773	+	0.0450554i	0.436406	−	0.899750i	$-0.356251\pi$
$293$	1.86190	+	0.771224i	0.108773	+	0.0450554i	−0.327633	+	0.944805i	$0.606251\pi$
$294$		0			0
$295$	19.7746	−	19.7746i	1.15132	−	1.15132i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−4.02177	−	1.66587i	−0.232585	−	0.0963398i
$300$		0			0
$301$	−5.10292	−	12.3195i	−0.294127	−	0.710086i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	6.23959			0.357278
$306$		0			0
$307$	3.70099	−	1.53300i	0.211227	−	0.0874930i	−0.274561	−	0.961570i	$-0.588533\pi$
$307$	3.70099	−	1.53300i	0.211227	−	0.0874930i	0.485788	+	0.874077i	$0.338533\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−9.17785	+	9.17785i	−0.520428	+	0.520428i	−0.917701	−	0.397273i	$-0.869957\pi$
$311$	−9.17785	+	9.17785i	−0.520428	+	0.520428i	0.397273	+	0.917701i	$0.369957\pi$
$312$		0			0
$313$	−8.66154	−	8.66154i	−0.489579	−	0.489579i	0.418594	−	0.908173i	$-0.362523\pi$
$313$	−8.66154	−	8.66154i	−0.489579	−	0.489579i	−0.908173	+	0.418594i	$0.862523\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.41379	−	17.8985i	−0.416400	−	1.00528i	−0.983382	−	0.181548i	$-0.941889\pi$
$317$	−7.41379	−	17.8985i	−0.416400	−	1.00528i	0.566982	−	0.823730i	$-0.308111\pi$
$318$		0			0
$319$		−	59.1159i		−	3.30986i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−11.1339	+	4.61182i	−0.619507	+	0.256608i
$324$		0			0
$325$	−5.94030	+	14.3411i	−0.329508	+	0.795503i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	4.62500	+	4.62500i	0.254984	+	0.254984i
$330$		0			0
$331$	3.96293	−	9.56736i	0.217822	−	0.525870i	−0.776763	−	0.629793i	$-0.783140\pi$
$331$	3.96293	−	9.56736i	0.217822	−	0.525870i	0.994585	+	0.103923i	$0.0331397\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		−	27.1830i		−	1.48517i
$336$		0			0
$337$			7.50723i			0.408945i	0.978872	+	0.204472i	$0.0655479\pi$
$337$			7.50723i			0.408945i	−0.978872	+	0.204472i	$0.934452\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	9.29611	−	22.4428i	0.503413	−	1.21535i
$342$		0			0
$343$	12.5047	+	12.5047i	0.675190	+	0.675190i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.18203	+	2.85368i	−0.0634548	+	0.153194i	−0.952426	−	0.304769i	$-0.901421\pi$
$347$	−1.18203	+	2.85368i	−0.0634548	+	0.153194i	0.888971	+	0.457963i	$0.151421\pi$
$348$		0			0
$349$	3.41473	−	1.41443i	0.182786	−	0.0757126i	−0.289413	−	0.957204i	$-0.593460\pi$
$349$	3.41473	−	1.41443i	0.182786	−	0.0757126i	0.472200	+	0.881492i	$0.343460\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	6.81226i		−	0.362580i	−0.983430	−	0.181290i	$-0.941973\pi$
$353$		−	6.81226i		−	0.362580i	0.983430	−	0.181290i	$-0.0580273\pi$
$354$		0			0
$355$	−2.79236	−	6.74136i	−0.148203	−	0.357794i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5.31414	−	5.31414i	−0.280469	−	0.280469i	0.552827	−	0.833296i	$-0.313549\pi$
$359$	−5.31414	−	5.31414i	−0.280469	−	0.280469i	−0.833296	+	0.552827i	$0.813549\pi$
$360$		0			0
$361$	−4.78116	+	4.78116i	−0.251640	+	0.251640i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	4.44363	−	1.84061i	0.232590	−	0.0963420i
$366$		0			0
$367$	−29.3775			−1.53349			−0.766745	−	0.641951i	$-0.778125\pi$
$367$	−29.3775			−1.53349			−0.766745	+	0.641951i	$0.778125\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.816501	+	1.97121i	0.0423906	+	0.102340i
$372$		0			0
$373$	14.6798	+	6.08058i	0.760092	+	0.314840i	0.728852	−	0.684671i	$-0.240054\pi$
$373$	14.6798	+	6.08058i	0.760092	+	0.314840i	0.0312402	+	0.999512i	$0.490054\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−31.9312	+	31.9312i	−1.64454	+	1.64454i
$378$		0			0
$379$	1.25001	+	0.517769i	0.0642085	+	0.0265960i	0.414557	−	0.910024i	$-0.363937\pi$
$379$	1.25001	+	0.517769i	0.0642085	+	0.0265960i	−0.350348	+	0.936620i	$0.613937\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−35.2581			−1.80160			−0.900802	−	0.434230i	$-0.857020\pi$
$383$	−35.2581			−1.80160			−0.900802	+	0.434230i	$0.857020\pi$
$384$		0			0
$385$	25.2691			1.28783
$386$		0			0
$387$		0			0
$388$		0			0
$389$	3.34556	+	1.38578i	0.169627	+	0.0702616i	0.465881	−	0.884848i	$-0.345738\pi$
$389$	3.34556	+	1.38578i	0.169627	+	0.0702616i	−0.296254	+	0.955109i	$0.595738\pi$
$390$		0			0
$391$	−2.42201	+	2.42201i	−0.122486	+	0.122486i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	39.0988	+	16.1953i	1.96728	+	0.814872i
$396$		0			0
$397$	−2.21822	−	5.35526i	−0.111329	−	0.268773i	0.858389	−	0.513000i	$-0.171466\pi$
$397$	−2.21822	−	5.35526i	−0.111329	−	0.268773i	−0.969718	+	0.244227i	$0.921466\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5.97617			−0.298436			−0.149218	−	0.988804i	$-0.547676\pi$
$401$	−5.97617			−0.298436			−0.149218	+	0.988804i	$0.547676\pi$
$402$		0			0
$403$	−17.1437	+	7.10114i	−0.853987	+	0.353733i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	21.6672	−	21.6672i	1.07401	−	1.07401i
$408$		0			0
$409$	−5.91961	−	5.91961i	−0.292706	−	0.292706i	0.545443	−	0.838148i	$-0.316362\pi$
$409$	−5.91961	−	5.91961i	−0.292706	−	0.292706i	−0.838148	+	0.545443i	$0.816362\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	5.52150	+	13.3301i	0.271695	+	0.655931i
$414$		0			0
$415$			32.6357i			1.60203i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	30.7382	−	12.7322i	1.50166	−	0.622007i	0.527841	−	0.849343i	$-0.323002\pi$
$419$	30.7382	−	12.7322i	1.50166	−	0.622007i	0.973816	+	0.227336i	$0.0730017\pi$
$420$		0			0
$421$	7.98264	−	19.2718i	0.389050	−	0.939249i	−0.601092	−	0.799180i	$-0.705267\pi$
$421$	7.98264	−	19.2718i	0.389050	−	0.939249i	0.990142	−	0.140069i	$-0.0447326\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	8.63660	+	8.63660i	0.418937	+	0.418937i
$426$		0			0
$427$	−1.23194	+	2.97417i	−0.0596179	+	0.143930i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			29.2128i			1.40713i	0.710630	+	0.703565i	$0.248410\pi$
$431$			29.2128i			1.40713i	−0.710630	+	0.703565i	$0.751590\pi$
$432$		0			0
$433$			17.9410i			0.862190i	0.902306	+	0.431095i	$0.141873\pi$
$433$			17.9410i			0.862190i	−0.902306	+	0.431095i	$0.858127\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.33114	−	3.21366i	0.0636771	−	0.153730i
$438$		0			0
$439$	8.96708	+	8.96708i	0.427975	+	0.427975i	0.887938	−	0.459963i	$-0.152137\pi$
$439$	8.96708	+	8.96708i	0.427975	+	0.427975i	−0.459963	+	0.887938i	$0.652137\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−6.09257	+	14.7088i	−0.289467	+	0.698835i	−0.999988	−	0.00484090i	$-0.998459\pi$
$443$	−6.09257	+	14.7088i	−0.289467	+	0.698835i	0.710522	+	0.703675i	$0.248459\pi$
$444$		0			0
$445$	30.5358	−	12.6484i	1.44754	−	0.599589i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	3.66413i		−	0.172921i	−0.996255	−	0.0864604i	$-0.972444\pi$
$449$		−	3.66413i		−	0.172921i	0.996255	−	0.0864604i	$-0.0275556\pi$
$450$		0			0
$451$	10.9670	+	26.4766i	0.516415	+	1.24674i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−13.6490	−	13.6490i	−0.639876	−	0.639876i
$456$		0			0
$457$	−13.9728	+	13.9728i	−0.653622	+	0.653622i	−0.953863	−	0.300241i	$-0.902933\pi$
$457$	−13.9728	+	13.9728i	−0.653622	+	0.653622i	0.300241	+	0.953863i	$0.402933\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2.25638	−	0.934623i	0.105090	−	0.0435297i	−0.329519	−	0.944149i	$-0.606887\pi$
$461$	2.25638	−	0.934623i	0.105090	−	0.0435297i	0.434609	+	0.900619i	$0.356887\pi$
$462$		0			0
$463$	−16.4302			−0.763575			−0.381788	−	0.924250i	$-0.624691\pi$
$463$	−16.4302			−0.763575			−0.381788	+	0.924250i	$0.624691\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	8.14599	+	19.6662i	0.376951	+	0.910041i	0.992534	+	0.121969i	$0.0389208\pi$
$467$	8.14599	+	19.6662i	0.376951	+	0.910041i	−0.615582	+	0.788072i	$0.711079\pi$
$468$		0			0
$469$	12.9571	+	5.36700i	0.598303	+	0.247825i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−35.8304	+	35.8304i	−1.64748	+	1.64748i
$474$		0			0
$475$	−11.4595	−	4.74669i	−0.525799	−	0.217793i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−4.35772			−0.199109			−0.0995545	−	0.995032i	$-0.531742\pi$
$479$	−4.35772			−0.199109			−0.0995545	+	0.995032i	$0.531742\pi$
$480$		0			0
$481$	−23.4070			−1.06727
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−34.6914	−	14.3696i	−1.57525	−	0.652491i
$486$		0			0
$487$	−10.1865	+	10.1865i	−0.461594	+	0.461594i	−0.899178	−	0.437584i	$-0.855834\pi$
$487$	−10.1865	+	10.1865i	−0.461594	+	0.461594i	0.437584	+	0.899178i	$0.355834\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−28.0848	−	11.6331i	−1.26745	−	0.524994i	−0.355260	−	0.934768i	$-0.615608\pi$
$491$	−28.0848	−	11.6331i	−1.26745	−	0.524994i	−0.912187	+	0.409774i	$0.865608\pi$
$492$		0			0
$493$	13.5975	+	32.8273i	0.612402	+	1.47847i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.76467			0.168869
$498$		0			0
$499$	20.5327	−	8.50493i	0.919170	−	0.380733i	0.127610	−	0.991824i	$-0.459269\pi$
$499$	20.5327	−	8.50493i	0.919170	−	0.380733i	0.791560	+	0.611092i	$0.209269\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−6.66355	+	6.66355i	−0.297113	+	0.297113i	−0.839882	−	0.542769i	$-0.817376\pi$
$503$	−6.66355	+	6.66355i	−0.297113	+	0.297113i	0.542769	+	0.839882i	$0.317376\pi$
$504$		0			0
$505$	0.436393	+	0.436393i	0.0194192	+	0.0194192i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	4.13590	+	9.98494i	0.183320	+	0.442575i	0.988647	−	0.150257i	$-0.0480101\pi$
$509$	4.13590	+	9.98494i	0.183320	+	0.442575i	−0.805327	+	0.592831i	$0.798010\pi$
$510$		0			0
$511$			2.48152i			0.109776i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	28.7601	−	11.9128i	1.26732	−	0.524942i
$516$		0			0
$517$	9.51161	−	22.9631i	0.418320	−	1.00991i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−2.91587	−	2.91587i	−0.127746	−	0.127746i	0.640343	−	0.768089i	$-0.278792\pi$
$521$	−2.91587	−	2.91587i	−0.127746	−	0.127746i	−0.768089	+	0.640343i	$0.778792\pi$
$522$		0			0
$523$	−14.2159	+	34.3201i	−0.621616	+	1.50071i	0.228189	+	0.973617i	$0.426720\pi$
$523$	−14.2159	+	34.3201i	−0.621616	+	1.50071i	−0.849805	+	0.527097i	$0.823280\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			14.6008i			0.636023i
$528$		0			0
$529$			22.0113i			0.957015i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	8.37748	−	20.2250i	0.362869	−	0.876043i
$534$		0			0
$535$	−14.3903	−	14.3903i	−0.622149	−	0.622149i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	10.3638	−	25.0204i	0.446401	−	1.07771i
$540$		0			0
$541$	−29.5435	+	12.2373i	−1.27017	+	0.526123i	−0.913017	−	0.407921i	$-0.866254\pi$
$541$	−29.5435	+	12.2373i	−1.27017	+	0.526123i	−0.357157	+	0.934044i	$0.616254\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$			37.3912i			1.60166i
$546$		0			0
$547$	11.8740	+	28.6664i	0.507696	+	1.22569i	0.945206	+	0.326474i	$0.105860\pi$
$547$	11.8740	+	28.6664i	0.507696	+	1.22569i	−0.437510	+	0.899213i	$0.644140\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−25.5152	−	25.5152i	−1.08698	−	1.08698i
$552$		0			0
$553$	−15.4393	+	15.4393i	−0.656546	+	0.656546i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−16.2393	+	6.72656i	−0.688083	+	0.285013i	−0.699201	−	0.714925i	$-0.746461\pi$
$557$	−16.2393	+	6.72656i	−0.688083	+	0.285013i	0.0111181	+	0.999938i	$0.496461\pi$
$558$		0			0
$559$	38.7074			1.63715
$560$		0			0
$561$		0			0
$562$		0			0
$563$	15.7698	+	38.0718i	0.664620	+	1.60453i	0.790481	+	0.612486i	$0.209830\pi$
$563$	15.7698	+	38.0718i	0.664620	+	1.60453i	−0.125862	+	0.992048i	$0.540170\pi$
$564$		0			0
$565$	2.65638	+	1.10031i	0.111755	+	0.0462904i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	11.0276	−	11.0276i	0.462302	−	0.462302i	−0.437107	−	0.899409i	$-0.643997\pi$
$569$	11.0276	−	11.0276i	0.462302	−	0.462302i	0.899409	+	0.437107i	$0.143997\pi$
$570$		0			0
$571$	31.3409	+	12.9818i	1.31157	+	0.543272i	0.925343	−	0.379130i	$-0.123777\pi$
$571$	31.3409	+	12.9818i	1.31157	+	0.543272i	0.386231	+	0.922402i	$0.373777\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−3.52541			−0.147020
$576$		0			0
$577$	−2.28631			−0.0951802			−0.0475901	−	0.998867i	$-0.515154\pi$
$577$	−2.28631			−0.0951802			−0.0475901	+	0.998867i	$0.515154\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−15.5562	−	6.44359i	−0.645380	−	0.267325i
$582$		0			0
$583$	5.73311	−	5.73311i	0.237441	−	0.237441i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	5.89005	+	2.43974i	0.243108	+	0.100699i	0.500911	−	0.865499i	$-0.332998\pi$
$587$	5.89005	+	2.43974i	0.243108	+	0.100699i	−0.257803	+	0.966198i	$0.582998\pi$
$588$		0			0
$589$	−5.67428	−	13.6989i	−0.233805	−	0.564454i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−10.9801			−0.450897			−0.225449	−	0.974255i	$-0.572385\pi$
$593$	−10.9801			−0.450897			−0.225449	+	0.974255i	$0.572385\pi$
$594$		0			0
$595$	−14.0321	+	5.81227i	−0.575259	+	0.238280i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−3.54515	+	3.54515i	−0.144851	+	0.144851i	−0.775813	−	0.630962i	$-0.782660\pi$
$599$	−3.54515	+	3.54515i	−0.144851	+	0.144851i	0.630962	+	0.775813i	$0.282660\pi$
$600$		0			0
$601$	0.844578	+	0.844578i	0.0344511	+	0.0344511i	0.724122	−	0.689671i	$-0.242245\pi$
$601$	0.844578	+	0.844578i	0.0344511	+	0.0344511i	−0.689671	+	0.724122i	$0.742245\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−24.4410	−	59.0059i	−0.993669	−	2.39893i
$606$		0			0
$607$			17.9859i			0.730024i	0.931003	+	0.365012i	$0.118935\pi$
$607$			17.9859i			0.730024i	−0.931003	+	0.365012i	$0.881065\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−17.5411	+	7.26575i	−0.709636	+	0.293941i
$612$		0			0
$613$	−6.72419	+	16.2336i	−0.271588	+	0.655671i	−0.999552	−	0.0299448i	$-0.990467\pi$
$613$	−6.72419	+	16.2336i	−0.271588	+	0.655671i	0.727964	+	0.685615i	$0.240467\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−8.70935	−	8.70935i	−0.350625	−	0.350625i	0.509717	−	0.860342i	$-0.329750\pi$
$617$	−8.70935	−	8.70935i	−0.350625	−	0.350625i	−0.860342	+	0.509717i	$0.829750\pi$
$618$		0			0
$619$	3.38639	−	8.17546i	0.136110	−	0.328600i	−0.841098	−	0.540883i	$-0.818090\pi$
$619$	3.38639	−	8.17546i	0.136110	−	0.328600i	0.977208	+	0.212284i	$0.0680901\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$			17.0525i			0.683195i
$624$		0			0
$625$		−	30.1567i		−	1.20627i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−7.04814	+	17.0157i	−0.281028	+	0.678461i
$630$		0			0
$631$	−2.69060	−	2.69060i	−0.107111	−	0.107111i	0.651520	−	0.758631i	$-0.274132\pi$
$631$	−2.69060	−	2.69060i	−0.107111	−	0.107111i	−0.758631	+	0.651520i	$0.774132\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−5.96002	+	14.3888i	−0.236516	+	0.571000i
$636$		0			0
$637$	−19.1127	+	7.91673i	−0.757272	+	0.313672i
$638$		0			0
$639$		0			0
$640$		0			0
$641$			37.2166i			1.46997i	0.678084	+	0.734984i	$0.262811\pi$
$641$			37.2166i			1.46997i	−0.678084	+	0.734984i	$0.737189\pi$
$642$		0			0
$643$	11.0037	+	26.5652i	0.433942	+	1.04763i	0.978005	+	0.208583i	$0.0668853\pi$
$643$	11.0037	+	26.5652i	0.433942	+	1.04763i	−0.544063	+	0.839044i	$0.683115\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	30.0988	+	30.0988i	1.18331	+	1.18331i	0.978882	+	0.204426i	$0.0655327\pi$
$647$	30.0988	+	30.0988i	1.18331	+	1.18331i	0.204426	+	0.978882i	$0.434467\pi$
$648$		0			0
$649$	38.7695	−	38.7695i	1.52184	−	1.52184i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	4.00245	−	1.65787i	0.156628	−	0.0648775i	−0.302992	−	0.952993i	$-0.597986\pi$
$653$	4.00245	−	1.65787i	0.156628	−	0.0648775i	0.459620	+	0.888116i	$0.347986\pi$
$654$		0			0
$655$	56.0125			2.18859
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−2.32569	−	5.61472i	−0.0905962	−	0.218719i	0.872086	−	0.489352i	$-0.162767\pi$
$659$	−2.32569	−	5.61472i	−0.0905962	−	0.218719i	−0.962682	+	0.270634i	$0.912767\pi$
$660$		0			0
$661$	37.0965	+	15.3659i	1.44288	+	0.597662i	0.960496	−	0.278295i	$-0.0897692\pi$
$661$	37.0965	+	15.3659i	1.44288	+	0.597662i	0.482389	+	0.875957i	$0.339769\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	10.9065	−	10.9065i	0.422935	−	0.422935i
$666$		0			0
$667$	−9.47519	−	3.92475i	−0.366881	−	0.151967i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	12.2332			0.472256
$672$		0			0
$673$	−13.6208			−0.525043			−0.262521	−	0.964926i	$-0.584554\pi$
$673$	−13.6208			−0.525043			−0.262521	+	0.964926i	$0.584554\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	11.5314	+	4.77647i	0.443189	+	0.183575i	0.593107	−	0.805124i	$-0.297901\pi$
$677$	11.5314	+	4.77647i	0.443189	+	0.183575i	−0.149918	+	0.988698i	$0.547901\pi$
$678$		0			0
$679$	13.6989	−	13.6989i	0.525715	−	0.525715i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−37.0003	−	15.3260i	−1.41578	−	0.586435i	−0.461982	−	0.886889i	$-0.652862\pi$
$683$	−37.0003	−	15.3260i	−1.41578	−	0.586435i	−0.953796	+	0.300454i	$0.902862\pi$
$684$		0			0
$685$	15.9452	+	38.4950i	0.609233	+	1.47082i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−6.19344			−0.235951
$690$		0			0
$691$	−6.40367	+	2.65249i	−0.243607	+	0.100905i	−0.501147	−	0.865362i	$-0.667088\pi$
$691$	−6.40367	+	2.65249i	−0.243607	+	0.100905i	0.257539	+	0.966268i	$0.417088\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−24.7054	+	24.7054i	−0.937129	+	0.937129i
$696$		0			0
$697$	−12.1800	−	12.1800i	−0.461352	−	0.461352i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	7.95095	+	19.1953i	0.300303	+	0.724996i	0.999945	+	0.0105021i	$0.00334297\pi$
$701$	7.95095	+	19.1953i	0.300303	+	0.724996i	−0.699642	+	0.714494i	$0.746657\pi$
$702$		0			0
$703$		−	18.7037i		−	0.705424i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.294173	+	0.121850i	−0.0110635	+	0.00458266i
$708$		0			0
$709$	0.602133	−	1.45368i	0.0226136	−	0.0545940i	−0.912169	−	0.409813i	$-0.865594\pi$
$709$	0.602133	−	1.45368i	0.0226136	−	0.0545940i	0.934783	+	0.355219i	$0.115594\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−2.97999	−	2.97999i	−0.111602	−	0.111602i
$714$		0			0
$715$	−28.0701	+	67.7673i	−1.04976	+	2.53435i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	36.1660i		−	1.34877i	−0.738382	−	0.674383i	$-0.764410\pi$
$719$		−	36.1660i		−	1.34877i	0.738382	−	0.674383i	$-0.235590\pi$
$720$		0			0
$721$			16.0609i			0.598139i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−13.9952	+	33.7874i	−0.519768	+	1.25483i
$726$		0			0
$727$	3.48345	+	3.48345i	0.129194	+	0.129194i	0.768747	−	0.639553i	$-0.220881\pi$
$727$	3.48345	+	3.48345i	0.129194	+	0.129194i	−0.639553	+	0.768747i	$0.720881\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	11.6553	−	28.1383i	0.431086	−	1.04073i
$732$		0			0
$733$	−9.32567	+	3.86282i	−0.344452	+	0.142677i	−0.548201	−	0.836347i	$-0.684687\pi$
$733$	−9.32567	+	3.86282i	−0.344452	+	0.142677i	0.203750	+	0.979023i	$0.434687\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	53.2942i		−	1.96312i
$738$		0			0
$739$	−18.2859	−	44.1460i	−0.672657	−	1.62394i	−0.777078	−	0.629404i	$-0.783299\pi$
$739$	−18.2859	−	44.1460i	−0.672657	−	1.62394i	0.104421	−	0.994533i	$-0.466701\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−26.3660	−	26.3660i	−0.967273	−	0.967273i	0.0322079	−	0.999481i	$-0.489746\pi$
$743$	−26.3660	−	26.3660i	−0.967273	−	0.967273i	−0.999481	+	0.0322079i	$0.989746\pi$
$744$		0			0
$745$	13.3686	−	13.3686i	0.489789	−	0.489789i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	9.70055	−	4.01810i	0.354450	−	0.146818i
$750$		0			0
$751$	−31.9193			−1.16475			−0.582377	−	0.812919i	$-0.697877\pi$
$751$	−31.9193			−1.16475			−0.582377	+	0.812919i	$0.697877\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−8.36155	−	20.1866i	−0.304308	−	0.734664i
$756$		0			0
$757$	25.8156	+	10.6932i	0.938284	+	0.388650i	0.798815	−	0.601577i	$-0.205461\pi$
$757$	25.8156	+	10.6932i	0.938284	+	0.388650i	0.139469	+	0.990226i	$0.455461\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	14.4436	−	14.4436i	0.523579	−	0.523579i	−0.395072	−	0.918650i	$-0.629280\pi$
$761$	14.4436	−	14.4436i	0.523579	−	0.523579i	0.918650	+	0.395072i	$0.129280\pi$
$762$		0			0
$763$	−17.8229	−	7.38250i	−0.645234	−	0.267265i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−41.8824			−1.51229
$768$		0			0
$769$	21.6737			0.781574			0.390787	−	0.920481i	$-0.372203\pi$
$769$	21.6737			0.781574			0.390787	+	0.920481i	$0.372203\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−5.45257	−	2.25853i	−0.196115	−	0.0812336i	0.282464	−	0.959278i	$-0.408848\pi$
$773$	−5.45257	−	2.25853i	−0.196115	−	0.0812336i	−0.478580	+	0.878044i	$0.658848\pi$
$774$		0			0
$775$	−10.6263	+	10.6263i	−0.381708	+	0.381708i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	16.1611	+	6.69416i	0.579033	+	0.239843i
$780$		0			0
$781$	−5.47463	−	13.2169i	−0.195898	−	0.472939i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−63.1027			−2.25223
$786$		0			0
$787$	38.9288	−	16.1249i	1.38766	−	0.574789i	0.441144	−	0.897436i	$-0.354573\pi$
$787$	38.9288	−	16.1249i	1.38766	−	0.574789i	0.946519	+	0.322647i	$0.104573\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−1.04895	+	1.04895i	−0.0372964	+	0.0372964i
$792$		0			0
$793$	−6.60770	−	6.60770i	−0.234646	−	0.234646i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−13.4105	−	32.3759i	−0.475025	−	1.14681i	−0.961915	−	0.273349i	$-0.911869\pi$
$797$	−13.4105	−	32.3759i	−0.475025	−	1.14681i	0.486890	−	0.873463i	$-0.338131\pi$
$798$		0			0
$799$			14.9393i			0.528515i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	8.71205	−	3.60865i	0.307442	−	0.127346i
$804$		0			0
$805$	1.67764	−	4.05017i	0.0591289	−	0.142750i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	23.3959	+	23.3959i	0.822557	+	0.822557i	0.986474	−	0.163917i	$-0.0524130\pi$
$809$	23.3959	+	23.3959i	0.822557	+	0.822557i	−0.163917	+	0.986474i	$0.552413\pi$
$810$		0			0
$811$	14.5916	−	35.2272i	0.512380	−	1.23699i	−0.430115	−	0.902774i	$-0.641527\pi$
$811$	14.5916	−	35.2272i	0.512380	−	1.23699i	0.942495	−	0.334221i	$-0.108473\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$			36.3473i			1.27319i
$816$		0			0
$817$			30.9297i			1.08209i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−6.11371	+	14.7598i	−0.213370	+	0.515120i	−0.993937	−	0.109952i	$-0.964930\pi$
$821$	−6.11371	+	14.7598i	−0.213370	+	0.515120i	0.780567	+	0.625072i	$0.214930\pi$
$822$		0			0
$823$	−17.5536	−	17.5536i	−0.611879	−	0.611879i	0.331557	−	0.943435i	$-0.392426\pi$
$823$	−17.5536	−	17.5536i	−0.611879	−	0.611879i	−0.943435	+	0.331557i	$0.892426\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−4.15220	+	10.0243i	−0.144386	+	0.348579i	−0.979484	−	0.201522i	$-0.935411\pi$
$827$	−4.15220	+	10.0243i	−0.144386	+	0.348579i	0.835098	+	0.550102i	$0.185411\pi$
$828$		0			0
$829$	3.68500	−	1.52638i	0.127985	−	0.0530132i	−0.317772	−	0.948167i	$-0.602935\pi$
$829$	3.68500	−	1.52638i	0.127985	−	0.0530132i	0.445757	+	0.895154i	$0.352935\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$			16.2778i			0.563992i
$834$		0			0
$835$	−21.3123	−	51.4524i	−0.737541	−	1.78058i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	4.96619	+	4.96619i	0.171452	+	0.171452i	0.787617	−	0.616165i	$-0.211315\pi$
$839$	4.96619	+	4.96619i	0.171452	+	0.171452i	−0.616165	+	0.787617i	$0.711315\pi$
$840$		0			0
$841$	−54.7231	+	54.7231i	−1.88700	+	1.88700i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	16.6563	−	6.89927i	0.572995	−	0.237342i
$846$		0			0
$847$	32.9514			1.13223
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−2.03435	−	4.91137i	−0.0697368	−	0.168359i
$852$		0			0
$853$	−7.27599	−	3.01381i	−0.249125	−	0.103191i	0.254627	−	0.967039i	$-0.418047\pi$
$853$	−7.27599	−	3.01381i	−0.249125	−	0.103191i	−0.503752	+	0.863848i	$0.668047\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	36.1746	−	36.1746i	1.23570	−	1.23570i	0.273961	−	0.961741i	$-0.411666\pi$
$857$	36.1746	−	36.1746i	1.23570	−	1.23570i	0.961741	−	0.273961i	$-0.0883341\pi$
$858$		0			0
$859$	28.2133	+	11.6863i	0.962627	+	0.398733i	0.807962	−	0.589234i	$-0.200570\pi$
$859$	28.2133	+	11.6863i	0.962627	+	0.398733i	0.154664	+	0.987967i	$0.450570\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	6.56021			0.223312			0.111656	−	0.993747i	$-0.464384\pi$
$863$	6.56021			0.223312			0.111656	+	0.993747i	$0.464384\pi$
$864$		0			0
$865$	4.70379			0.159934
$866$		0			0
$867$		0			0
$868$		0			0
$869$	76.6560	+	31.7520i	2.60038	+	1.07711i
$870$		0			0
$871$	−28.7867	+	28.7867i	−0.975399	+	0.975399i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	5.92433	+	2.45394i	0.200279	+	0.0829582i
$876$		0			0
$877$	−9.62481	−	23.2364i	−0.325007	−	0.784636i	−0.998948	−	0.0458511i	$-0.985400\pi$
$877$	−9.62481	−	23.2364i	−0.325007	−	0.784636i	0.673941	−	0.738785i	$-0.264600\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	36.6081			1.23336			0.616679	−	0.787215i	$-0.288478\pi$
$881$	36.6081			1.23336			0.616679	+	0.787215i	$0.288478\pi$
$882$		0			0
$883$	−1.40699	+	0.582794i	−0.0473489	+	0.0196126i	−0.406232	−	0.913770i	$-0.633158\pi$
$883$	−1.40699	+	0.582794i	−0.0473489	+	0.0196126i	0.358883	+	0.933382i	$0.383158\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	32.4795	−	32.4795i	1.09056	−	1.09056i	0.0950860	−	0.995469i	$-0.469687\pi$
$887$	32.4795	−	32.4795i	1.09056	−	1.09056i	0.995469	−	0.0950860i	$-0.0303126\pi$
$888$		0			0
$889$	−5.68182	−	5.68182i	−0.190562	−	0.190562i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−5.80581	−	14.0165i	−0.194284	−	0.469044i
$894$		0			0
$895$			1.44297i			0.0482333i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−40.3901	+	16.7301i	−1.34708	+	0.557980i
$900$		0			0
$901$	−1.86492	+	4.50232i	−0.0621296	+	0.149994i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	45.2591	+	45.2591i	1.50446	+	1.50446i
$906$		0			0
$907$	−10.6402	+	25.6878i	−0.353303	+	0.852950i	0.642905	+	0.765946i	$0.277729\pi$
$907$	−10.6402	+	25.6878i	−0.353303	+	0.852950i	−0.996208	+	0.0870037i	$0.972271\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	9.64671i		−	0.319610i	−0.987149	−	0.159805i	$-0.948914\pi$
$911$		−	9.64671i		−	0.319610i	0.987149	−	0.159805i	$-0.0510865\pi$
$912$		0			0
$913$			63.9847i			2.11758i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−11.0591	+	26.6990i	−0.365203	+	0.881678i
$918$		0			0
$919$	−36.1191	−	36.1191i	−1.19146	−	1.19146i	−0.976657	−	0.214803i	$-0.931089\pi$
$919$	−36.1191	−	36.1191i	−1.19146	−	1.19146i	−0.214803	−	0.976657i	$-0.568911\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−4.18197	+	10.0962i	−0.137651	+	0.332320i
$924$		0			0
$925$	−17.5133	+	7.25426i	−0.575835	+	0.238519i
$926$		0			0
$927$		0			0
$928$		0			0
$929$			16.6303i			0.545622i	0.962068	+	0.272811i	$0.0879534\pi$
$929$			16.6303i			0.545622i	−0.962068	+	0.272811i	$0.912047\pi$
$930$		0			0
$931$	−6.32599	−	15.2723i	−0.207326	−	0.500529i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	40.8112	+	40.8112i	1.33467	+	1.33467i
$936$		0			0
$937$	39.4807	−	39.4807i	1.28978	−	1.28978i	0.354860	−	0.934920i	$-0.384529\pi$
$937$	39.4807	−	39.4807i	1.28978	−	1.28978i	0.934920	−	0.354860i	$-0.115471\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−38.4855	+	15.9412i	−1.25459	+	0.519669i	−0.908246	−	0.418437i	$-0.862578\pi$
$941$	−38.4855	+	15.9412i	−1.25459	+	0.519669i	−0.346347	+	0.938107i	$0.612578\pi$
$942$		0			0
$943$	4.97182			0.161905
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.88812	−	4.55832i	−0.0613556	−	0.148125i	0.890228	−	0.455515i	$-0.150545\pi$
$947$	−1.88812	−	4.55832i	−0.0613556	−	0.148125i	−0.951584	+	0.307389i	$0.900545\pi$
$948$		0			0
$949$	−6.65498	−	2.75658i	−0.216030	−	0.0894825i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	3.89115	−	3.89115i	0.126047	−	0.126047i	−0.641269	−	0.767316i	$-0.721592\pi$
$953$	3.89115	−	3.89115i	0.126047	−	0.126047i	0.767316	+	0.641269i	$0.221592\pi$
$954$		0			0
$955$	−62.9438	−	26.0722i	−2.03681	−	0.843676i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−21.4973			−0.694184
$960$		0			0
$961$	13.0354			0.420498
$962$		0			0
$963$		0			0
$964$		0			0
$965$	73.1094	+	30.2829i	2.35348	+	0.974842i
$966$		0			0
$967$	−11.3033	+	11.3033i	−0.363488	+	0.363488i	−0.865095	−	0.501607i	$-0.832742\pi$
$967$	−11.3033	+	11.3033i	−0.363488	+	0.363488i	0.501607	+	0.865095i	$0.332742\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	19.3675	+	8.02226i	0.621531	+	0.257447i	0.671150	−	0.741322i	$-0.265801\pi$
$971$	19.3675	+	8.02226i	0.621531	+	0.257447i	−0.0496188	+	0.998768i	$0.515801\pi$
$972$		0			0
$973$	−6.89828	−	16.6539i	−0.221149	−	0.533900i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2.98023			−0.0953461			−0.0476730	−	0.998863i	$-0.515181\pi$
$977$	−2.98023			−0.0953461			−0.0476730	+	0.998863i	$0.515181\pi$
$978$		0			0
$979$	59.8676	−	24.7980i	1.91338	−	0.792547i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	35.5614	−	35.5614i	1.13423	−	1.13423i	0.144767	−	0.989466i	$-0.453757\pi$
$983$	35.5614	−	35.5614i	1.13423	−	1.13423i	0.989466	−	0.144767i	$-0.0462432\pi$
$984$		0			0
$985$	−0.524675	−	0.524675i	−0.0167175	−	0.0167175i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	3.36415	+	8.12177i	0.106974	+	0.258257i
$990$		0			0
$991$			7.45023i			0.236664i	0.992974	+	0.118332i	$0.0377548\pi$
$991$			7.45023i			0.236664i	−0.992974	+	0.118332i	$0.962245\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−10.9643	+	4.54156i	−0.347591	+	0.143977i
$996$		0			0
$997$	0.482816	−	1.16562i	0.0152909	−	0.0369156i	−0.916050	−	0.401065i	$-0.868640\pi$
$997$	0.482816	−	1.16562i	0.0152909	−	0.0369156i	0.931341	+	0.364149i	$0.118640\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.w.b.719.2		32
3.2	odd	2		1152.2.w.a.719.7		32
4.3	odd	2		288.2.w.a.107.2	yes	32
12.11	even	2		288.2.w.b.107.7	yes	32
32.3	odd	8		1152.2.w.a.431.7		32
32.29	even	8		288.2.w.b.35.7	yes	32
96.29	odd	8		288.2.w.a.35.2	✓	32
96.35	even	8	inner	1152.2.w.b.431.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.35.2	✓	32	96.29	odd	8
288.2.w.a.107.2	yes	32	4.3	odd	2
288.2.w.b.35.7	yes	32	32.29	even	8
288.2.w.b.107.7	yes	32	12.11	even	2
1152.2.w.a.431.7		32	32.3	odd	8
1152.2.w.a.719.7		32	3.2	odd	2
1152.2.w.b.431.2		32	96.35	even	8	inner
1152.2.w.b.719.2		32	1.1	even	1	trivial

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Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.70076 - 1.11869i) q^{5} +(1.06647 - 1.06647i) q^{7} +O(q^{10})\)	\(q+(-2.70076 - 1.11869i) q^{5} +(1.06647 - 1.06647i) q^{7} +(-5.29504 - 2.19328i) q^{11} +(1.67540 + 4.04478i) q^{13} +3.44484 q^{17} +(-3.23205 + 1.33876i) q^{19} +(-0.703083 + 0.703083i) q^{23} +(2.50711 + 2.50711i) q^{25} +(3.94721 + 9.52941i) q^{29} +4.23846i q^{31} +(-4.07335 + 1.68724i) q^{35} +(-2.04600 + 4.93947i) q^{37} +(-3.53573 - 3.53573i) q^{41} +(3.38340 - 8.16825i) q^{43} +4.33671i q^{47} +4.72526i q^{49} +(-0.541366 + 1.30697i) q^{53} +(11.8470 + 11.8470i) q^{55} +(-3.66093 + 8.83827i) q^{59} +(-1.97197 + 0.816817i) q^{61} -12.7983i q^{65} +(3.55849 + 8.59096i) q^{67} +(1.76501 + 1.76501i) q^{71} +(-1.16342 + 1.16342i) q^{73} +(-7.98610 + 3.30795i) q^{77} -14.4770 q^{79} +(-4.27230 - 10.3143i) q^{83} +(-9.30371 - 3.85372i) q^{85} +(-7.99481 + 7.99481i) q^{89} +(6.10044 + 2.52688i) q^{91} +10.2267 q^{95} +12.8450 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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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