LMFDB - Embedded newform 288.2.w.b.179.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(35,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3, 4]))

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

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

chi := DirichletCharacter("288.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.w (of order $8$, degree $4$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			179.4
Character	$\chi$	$=$	288.179
Dual form			288.2.w.b.251.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.290763 - 1.38400i) q^{2} +(-1.83091 - 0.804831i) q^{4} +(1.12344 + 2.71222i) q^{5} +(3.03150 + 3.03150i) q^{7} +(-1.64625 + 2.29997i) q^{8} +O(q^{10})$	\(q+(0.290763 - 1.38400i) q^{2} +(-1.83091 - 0.804831i) q^{4} +(1.12344 + 2.71222i) q^{5} +(3.03150 + 3.03150i) q^{7} +(-1.64625 + 2.29997i) q^{8} +(4.08037 - 0.766228i) q^{10} +(-0.616847 - 1.48920i) q^{11} +(3.35133 + 1.38816i) q^{13} +(5.07705 - 3.31415i) q^{14} +(2.70449 + 2.94715i) q^{16} -4.76709 q^{17} +(1.13264 - 2.73444i) q^{19} +(0.125961 - 5.87003i) q^{20} +(-2.24041 + 0.420712i) q^{22} +(-4.11192 - 4.11192i) q^{23} +(-2.55851 + 2.55851i) q^{25} +(2.89566 - 4.23461i) q^{26} +(-3.11057 - 7.99027i) q^{28} +(8.16664 + 3.38273i) q^{29} -6.16305i q^{31} +(4.86523 - 2.88610i) q^{32} +(-1.38609 + 6.59765i) q^{34} +(-4.81640 + 11.6278i) q^{35} +(-9.38963 + 3.88931i) q^{37} +(-3.45513 - 2.36265i) q^{38} +(-8.08750 - 1.88112i) q^{40} +(0.169917 - 0.169917i) q^{41} +(7.57687 - 3.13844i) q^{43} +(-0.0691613 + 3.22306i) q^{44} +(-6.88649 + 4.49531i) q^{46} -2.44049i q^{47} +11.3800i q^{49} +(2.79706 + 4.28490i) q^{50} +(-5.01875 - 5.23886i) q^{52} +(-1.99073 + 0.824586i) q^{53} +(3.34605 - 3.34605i) q^{55} +(-11.9630 + 1.98176i) q^{56} +(7.05626 - 10.3191i) q^{58} +(-1.21488 + 0.503218i) q^{59} +(1.04489 - 2.52258i) q^{61} +(-8.52966 - 1.79198i) q^{62} +(-2.57973 - 7.57265i) q^{64} +10.6491i q^{65} +(3.91551 + 1.62186i) q^{67} +(8.72813 + 3.83670i) q^{68} +(14.6925 + 10.0468i) q^{70} +(5.28919 - 5.28919i) q^{71} +(-1.57482 - 1.57482i) q^{73} +(2.65266 + 14.1261i) q^{74} +(-4.27453 + 4.09494i) q^{76} +(2.64454 - 6.38449i) q^{77} -13.7711 q^{79} +(-4.95501 + 10.6461i) q^{80} +(-0.185759 - 0.284570i) q^{82} +(-3.31934 - 1.37492i) q^{83} +(-5.35554 - 12.9294i) q^{85} +(-2.14053 - 11.3989i) q^{86} +(4.44060 + 1.03286i) q^{88} +(-6.99010 - 6.99010i) q^{89} +(5.95133 + 14.3678i) q^{91} +(4.21917 + 10.8380i) q^{92} +(-3.37763 - 0.709602i) q^{94} +8.68886 q^{95} -13.5584 q^{97} +(15.7499 + 3.30888i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} + 4 q^{8}+O(q^{10}) $ 32 * q + 4 * q^2 + 4 * q^8	$ 32 q + 4 q^{2} + 4 q^{8} + 8 q^{10} + 8 q^{11} - 12 q^{14} + 8 q^{16} - 32 q^{20} + 16 q^{22} + 36 q^{26} + 16 q^{29} + 24 q^{32} - 24 q^{35} - 32 q^{38} - 32 q^{40} - 8 q^{44} - 32 q^{46} - 8 q^{50} - 56 q^{52} + 16 q^{53} - 32 q^{55} - 40 q^{56} - 32 q^{58} - 32 q^{59} + 32 q^{61} + 68 q^{62} - 48 q^{64} - 16 q^{67} + 72 q^{68} - 48 q^{70} - 16 q^{71} - 60 q^{74} - 8 q^{76} + 16 q^{77} - 32 q^{79} - 96 q^{80} + 40 q^{82} + 40 q^{83} + 40 q^{86} + 40 q^{88} - 48 q^{91} + 16 q^{92} + 72 q^{94} + 80 q^{95} + 44 q^{98}+O(q^{100}) $ 32 * q + 4 * q^2 + 4 * q^8 + 8 * q^10 + 8 * q^11 - 12 * q^14 + 8 * q^16 - 32 * q^20 + 16 * q^22 + 36 * q^26 + 16 * q^29 + 24 * q^32 - 24 * q^35 - 32 * q^38 - 32 * q^40 - 8 * q^44 - 32 * q^46 - 8 * q^50 - 56 * q^52 + 16 * q^53 - 32 * q^55 - 40 * q^56 - 32 * q^58 - 32 * q^59 + 32 * q^61 + 68 * q^62 - 48 * q^64 - 16 * q^67 + 72 * q^68 - 48 * q^70 - 16 * q^71 - 60 * q^74 - 8 * q^76 + 16 * q^77 - 32 * q^79 - 96 * q^80 + 40 * q^82 + 40 * q^83 + 40 * q^86 + 40 * q^88 - 48 * q^91 + 16 * q^92 + 72 * q^94 + 80 * q^95 + 44 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$-1$	$-1$

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 $

$2$	0.290763	−	1.38400i	0.205600	−	0.978636i
$2$	0.290763	−	1.38400i	0.205600	−	0.978636i
$3$		0			0
$3$		0			0
$4$	−1.83091	−	0.804831i	−0.915457	−	0.402416i
$5$	1.12344	+	2.71222i	0.502418	+	1.21294i	0.948163	+	0.317784i	$0.102939\pi$
$5$	1.12344	+	2.71222i	0.502418	+	1.21294i	−0.445745	+	0.895160i	$0.647061\pi$
$6$		0			0
$7$	3.03150	+	3.03150i	1.14580	+	1.14580i	0.987370	+	0.158430i	$0.0506433\pi$
$7$	3.03150	+	3.03150i	1.14580	+	1.14580i	0.158430	+	0.987370i	$0.449357\pi$
$8$	−1.64625	+	2.29997i	−0.582037	+	0.813163i
$9$		0			0
$10$	4.08037	−	0.766228i	1.29033	−	0.242303i
$11$	−0.616847	−	1.48920i	−0.185986	−	0.449011i	0.803194	−	0.595718i	$-0.203132\pi$
$11$	−0.616847	−	1.48920i	−0.185986	−	0.449011i	−0.989180	+	0.146707i	$0.953132\pi$
$12$		0			0
$13$	3.35133	+	1.38816i	0.929490	+	0.385008i	0.795485	−	0.605973i	$-0.207216\pi$
$13$	3.35133	+	1.38816i	0.929490	+	0.385008i	0.134005	+	0.990981i	$0.457216\pi$
$14$	5.07705	−	3.31415i	1.35690	−	0.885745i
$15$		0			0
$16$	2.70449	+	2.94715i	0.676123	+	0.736789i
$17$	−4.76709			−1.15619			−0.578094	−	0.815970i	$-0.696203\pi$
$17$	−4.76709			−1.15619			−0.578094	+	0.815970i	$0.696203\pi$
$18$		0			0
$19$	1.13264	−	2.73444i	0.259846	−	0.627323i	−0.739082	−	0.673615i	$-0.764741\pi$
$19$	1.13264	−	2.73444i	0.259846	−	0.627323i	0.998928	+	0.0462921i	$0.0147405\pi$
$20$	0.125961	−	5.87003i	0.0281657	−	1.31258i
$21$		0			0
$22$	−2.24041	+	0.420712i	−0.477657	+	0.0896962i
$23$	−4.11192	−	4.11192i	−0.857395	−	0.857395i	0.133636	−	0.991031i	$-0.457335\pi$
$23$	−4.11192	−	4.11192i	−0.857395	−	0.857395i	−0.991031	+	0.133636i	$0.957335\pi$
$24$		0			0
$25$	−2.55851	+	2.55851i	−0.511702	+	0.511702i
$26$	2.89566	−	4.23461i	0.567886	−	0.830475i
$27$		0			0
$28$	−3.11057	−	7.99027i	−0.587843	−	1.51002i
$29$	8.16664	+	3.38273i	1.51651	+	0.628158i	0.976888	−	0.213751i	$-0.0685681\pi$
$29$	8.16664	+	3.38273i	1.51651	+	0.628158i	0.539620	+	0.841909i	$0.318568\pi$
$30$		0			0
$31$		−	6.16305i		−	1.10692i	−0.832877	−	0.553458i	$-0.813308\pi$
$31$		−	6.16305i		−	1.10692i	0.832877	−	0.553458i	$-0.186692\pi$
$32$	4.86523	−	2.88610i	0.860059	−	0.510195i
$33$		0			0
$34$	−1.38609	+	6.59765i	−0.237713	+	1.13149i
$35$	−4.81640	+	11.6278i	−0.814121	+	1.96546i
$36$		0			0
$37$	−9.38963	+	3.88931i	−1.54365	+	0.639399i	−0.982153	−	0.188083i	$-0.939773\pi$
$37$	−9.38963	+	3.88931i	−1.54365	+	0.639399i	−0.561493	+	0.827482i	$0.689773\pi$
$38$	−3.45513	−	2.36265i	−0.560497	−	0.383272i
$39$		0			0
$40$	−8.08750	−	1.88112i	−1.27875	−	0.297431i
$41$	0.169917	−	0.169917i	0.0265365	−	0.0265365i	−0.693714	−	0.720251i	$-0.744027\pi$
$41$	0.169917	−	0.169917i	0.0265365	−	0.0265365i	0.720251	+	0.693714i	$0.244027\pi$
$42$		0			0
$43$	7.57687	−	3.13844i	1.15546	−	0.478608i	0.279100	−	0.960262i	$-0.409964\pi$
$43$	7.57687	−	3.13844i	1.15546	−	0.478608i	0.876361	+	0.481654i	$0.159964\pi$
$44$	−0.0691613	+	3.22306i	−0.0104265	+	0.485894i
$45$		0			0
$46$	−6.88649	+	4.49531i	−1.01536	+	0.662797i
$47$		−	2.44049i		−	0.355981i	−0.984032	−	0.177991i	$-0.943040\pi$
$47$		−	2.44049i		−	0.355981i	0.984032	−	0.177991i	$-0.0569597\pi$
$48$		0			0
$49$			11.3800i			1.62572i
$50$	2.79706	+	4.28490i	0.395564	+	0.605976i
$51$		0			0
$52$	−5.01875	−	5.23886i	−0.695976	−	0.726499i
$53$	−1.99073	+	0.824586i	−0.273447	+	0.113266i	−0.515193	−	0.857074i	$-0.672280\pi$
$53$	−1.99073	+	0.824586i	−0.273447	+	0.113266i	0.241746	+	0.970340i	$0.422280\pi$
$54$		0			0
$55$	3.34605	−	3.34605i	0.451182	−	0.451182i
$56$	−11.9630	+	1.98176i	−1.59862	+	0.264824i
$57$		0			0
$58$	7.05626	−	10.3191i	0.926533	−	1.35496i
$59$	−1.21488	+	0.503218i	−0.158163	+	0.0655134i	−0.460361	−	0.887732i	$-0.652280\pi$
$59$	−1.21488	+	0.503218i	−0.158163	+	0.0655134i	0.302197	+	0.953245i	$0.402280\pi$
$60$		0			0
$61$	1.04489	−	2.52258i	0.133784	−	0.322983i	−0.842764	−	0.538283i	$-0.819073\pi$
$61$	1.04489	−	2.52258i	0.133784	−	0.322983i	0.976548	+	0.215300i	$0.0690731\pi$
$62$	−8.52966	−	1.79198i	−1.08327	−	0.227582i
$63$		0			0
$64$	−2.57973	−	7.57265i	−0.322467	−	0.946581i
$65$			10.6491i			1.32085i
$66$		0			0
$67$	3.91551	+	1.62186i	0.478355	+	0.198141i	0.608815	−	0.793312i	$-0.291645\pi$
$67$	3.91551	+	1.62186i	0.478355	+	0.198141i	−0.130459	+	0.991454i	$0.541645\pi$
$68$	8.72813	+	3.83670i	1.05844	+	0.465268i
$69$		0			0
$70$	14.6925	+	10.0468i	1.75609	+	1.20083i
$71$	5.28919	−	5.28919i	0.627711	−	0.627711i	−0.319781	−	0.947492i	$-0.603609\pi$
$71$	5.28919	−	5.28919i	0.627711	−	0.627711i	0.947492	+	0.319781i	$0.103609\pi$
$72$		0			0
$73$	−1.57482	−	1.57482i	−0.184319	−	0.184319i	0.608916	−	0.793235i	$-0.291605\pi$
$73$	−1.57482	−	1.57482i	−0.184319	−	0.184319i	−0.793235	+	0.608916i	$0.791605\pi$
$74$	2.65266	+	14.1261i	0.308365	+	1.64213i
$75$		0			0
$76$	−4.27453	+	4.09494i	−0.490322	+	0.469721i
$77$	2.64454	−	6.38449i	0.301373	−	0.727580i
$78$		0			0
$79$	−13.7711			−1.54937			−0.774684	−	0.632348i	$-0.782091\pi$
$79$	−13.7711			−1.54937			−0.774684	+	0.632348i	$0.782091\pi$
$80$	−4.95501	+	10.6461i	−0.553987	+	1.19028i
$81$		0			0
$82$	−0.185759	−	0.284570i	−0.0205137	−	0.0314255i
$83$	−3.31934	−	1.37492i	−0.364345	−	0.150917i	0.192997	−	0.981199i	$-0.438179\pi$
$83$	−3.31934	−	1.37492i	−0.364345	−	0.150917i	−0.557343	+	0.830282i	$0.688179\pi$
$84$		0			0
$85$	−5.35554	−	12.9294i	−0.580890	−	1.40239i
$86$	−2.14053	−	11.3989i	−0.230820	−	1.22918i
$87$		0			0
$88$	4.44060	+	1.03286i	0.473370	+	0.110104i
$89$	−6.99010	−	6.99010i	−0.740949	−	0.740949i	0.231811	−	0.972761i	$-0.425535\pi$
$89$	−6.99010	−	6.99010i	−0.740949	−	0.740949i	−0.972761	+	0.231811i	$0.925535\pi$
$90$		0			0
$91$	5.95133	+	14.3678i	0.623869	+	1.50615i
$92$	4.21917	+	10.8380i	0.439879	+	1.12994i
$93$		0			0
$94$	−3.37763	−	0.709602i	−0.348376	−	0.0731899i
$95$	8.68886			0.891459
$96$		0			0
$97$	−13.5584			−1.37665			−0.688323	−	0.725404i	$-0.741653\pi$
$97$	−13.5584			−1.37665			−0.688323	+	0.725404i	$0.741653\pi$
$98$	15.7499	+	3.30888i	1.59099	+	0.334248i
$99$		0			0
$100$	6.74358	−	2.62524i	0.674358	−	0.262524i
$101$	1.10479	+	2.66720i	0.109931	+	0.265396i	0.969265	−	0.246018i	$-0.0791221\pi$
$101$	1.10479	+	2.66720i	0.109931	+	0.265396i	−0.859335	+	0.511413i	$0.829122\pi$
$102$		0			0
$103$	−12.8009	−	12.8009i	−1.26131	−	1.26131i	−0.950459	−	0.310851i	$-0.899386\pi$
$103$	−12.8009	−	12.8009i	−1.26131	−	1.26131i	−0.310851	−	0.950459i	$-0.600614\pi$
$104$	−8.70985	+	5.42269i	−0.854071	+	0.531738i
$105$		0			0
$106$	0.562398	+	2.99492i	0.0546249	+	0.290893i
$107$	0.720677	+	1.73987i	0.0696704	+	0.168199i	0.954879	−	0.296995i	$-0.0959845\pi$
$107$	0.720677	+	1.73987i	0.0696704	+	0.168199i	−0.885209	+	0.465194i	$0.845984\pi$
$108$		0			0
$109$	4.45017	+	1.84332i	0.426249	+	0.176558i	0.585486	−	0.810682i	$-0.300904\pi$
$109$	4.45017	+	1.84332i	0.426249	+	0.176558i	−0.159238	+	0.987240i	$0.550904\pi$
$110$	−3.65803	−	5.60385i	−0.348780	−	0.534306i
$111$		0			0
$112$	−0.735628	+	17.1330i	−0.0695104	+	1.61891i
$113$	13.6612			1.28514			0.642568	−	0.766229i	$-0.277869\pi$
$113$	13.6612			1.28514			0.642568	+	0.766229i	$0.277869\pi$
$114$		0			0
$115$	6.53296	−	15.7720i	0.609201	−	1.47074i
$116$	−12.2299	−	12.7663i	−1.13552	−	1.18532i
$117$		0			0
$118$	0.343213	+	1.82771i	0.0315954	+	0.168254i
$119$	−14.4514	−	14.4514i	−1.32476	−	1.32476i
$120$		0			0
$121$	5.94096	−	5.94096i	0.540087	−	0.540087i
$122$	−3.18743	−	2.17959i	−0.288577	−	0.197331i
$123$		0			0
$124$	−4.96021	+	11.2840i	−0.445440	+	1.01333i
$125$	3.74754	+	1.55228i	0.335190	+	0.138840i
$126$		0			0
$127$			13.2014i			1.17143i	0.810515	+	0.585717i	$0.199187\pi$
$127$			13.2014i			1.17143i	−0.810515	+	0.585717i	$0.800813\pi$
$128$	−11.2306	+	1.36851i	−0.992657	+	0.120960i
$129$		0			0
$130$	14.7383	+	3.09635i	1.29264	+	0.271568i
$131$	2.56553	−	6.19375i	0.224152	−	0.541150i	−0.771294	−	0.636479i	$-0.780390\pi$
$131$	2.56553	−	6.19375i	0.224152	−	0.541150i	0.995446	+	0.0953287i	$0.0303902\pi$
$132$		0			0
$133$	11.7231	−	4.85585i	1.01652	−	0.421056i
$134$	3.38313	−	4.94749i	0.292258	−	0.427398i
$135$		0			0
$136$	7.84781	−	10.9642i	0.672944	−	0.940169i
$137$	−9.77333	+	9.77333i	−0.834992	+	0.834992i	−0.988195	−	0.153203i	$-0.951041\pi$
$137$	−9.77333	+	9.77333i	−0.834992	+	0.834992i	0.153203	+	0.988195i	$0.451041\pi$
$138$		0			0
$139$	−8.26616	+	3.42396i	−0.701127	+	0.290416i	−0.704627	−	0.709578i	$-0.748886\pi$
$139$	−8.26616	+	3.42396i	−0.701127	+	0.290416i	0.00350050	+	0.999994i	$0.498886\pi$
$140$	18.1769	−	17.4132i	1.53623	−	1.47168i
$141$		0			0
$142$	−5.78234	−	8.85814i	−0.485243	−	0.743358i
$143$		−	5.84708i		−	0.488957i
$144$		0			0
$145$			25.9501i			2.15504i
$146$	−2.63745	+	1.72165i	−0.218277	+	0.142485i
$147$		0			0
$148$	20.3219	+	0.436073i	1.67045	+	0.0358449i
$149$	18.9803	−	7.86190i	1.55493	−	0.644072i	0.570729	−	0.821139i	$-0.306661\pi$
$149$	18.9803	−	7.86190i	1.55493	−	0.644072i	0.984199	+	0.177066i	$0.0566607\pi$
$150$		0			0
$151$	7.83326	−	7.83326i	0.637462	−	0.637462i	−0.312467	−	0.949929i	$-0.601155\pi$
$151$	7.83326	−	7.83326i	0.637462	−	0.637462i	0.949929	+	0.312467i	$0.101155\pi$
$152$	4.42452	+	7.10661i	0.358876	+	0.576422i
$153$		0			0
$154$	−8.06720	−	5.51642i	−0.650073	−	0.444526i
$155$	16.7156	−	6.92381i	1.34263	−	0.556134i
$156$		0			0
$157$	3.58014	−	8.64323i	0.285727	−	0.689805i	−0.714222	−	0.699919i	$-0.753219\pi$
$157$	3.58014	−	8.64323i	0.285727	−	0.689805i	0.999949	+	0.0101140i	$0.00321944\pi$
$158$	−4.00412	+	19.0592i	−0.318551	+	1.51627i
$159$		0			0
$160$	13.2935	+	9.95323i	1.05095	+	0.786872i
$161$		−	24.9306i		−	1.96481i
$162$		0			0
$163$	−4.73693	−	1.96210i	−0.371025	−	0.153684i	0.189377	−	0.981904i	$-0.439353\pi$
$163$	−4.73693	−	1.96210i	−0.371025	−	0.153684i	−0.560402	+	0.828221i	$0.689353\pi$
$164$	−0.447857	+	0.174349i	−0.0349718	+	0.0136143i
$165$		0			0
$166$	−2.86803	+	4.19420i	−0.222602	+	0.325533i
$167$	4.55199	−	4.55199i	0.352244	−	0.352244i	−0.508700	−	0.860944i	$-0.669874\pi$
$167$	4.55199	−	4.55199i	0.352244	−	0.352244i	0.860944	+	0.508700i	$0.169874\pi$
$168$		0			0
$169$	0.111994	+	0.111994i	0.00861490	+	0.00861490i
$170$	−19.4515	+	3.65268i	−1.49186	+	0.280147i
$171$		0			0
$172$	−16.3985	−	0.351884i	−1.25037	−	0.0268309i
$173$	4.28444	−	10.3436i	0.325740	−	0.786406i	−0.673159	−	0.739498i	$-0.735063\pi$
$173$	4.28444	−	10.3436i	0.325740	−	0.786406i	0.998899	−	0.0469083i	$-0.0149368\pi$
$174$		0			0
$175$	−15.5123			−1.17262
$176$	2.72064	−	5.84547i	0.205076	−	0.440619i
$177$		0			0
$178$	−11.7068	+	7.64184i	−0.877459	+	0.572780i
$179$	−10.2246	−	4.23519i	−0.764226	−	0.316553i	−0.0336946	−	0.999432i	$-0.510727\pi$
$179$	−10.2246	−	4.23519i	−0.764226	−	0.316553i	−0.730531	+	0.682880i	$0.760727\pi$
$180$		0			0
$181$	−1.33358	−	3.21956i	−0.0991246	−	0.239308i	0.866536	−	0.499114i	$-0.166341\pi$
$181$	−1.33358	−	3.21956i	−0.0991246	−	0.239308i	−0.965661	+	0.259806i	$0.916341\pi$
$182$	21.6154	−	4.05903i	1.60224	−	0.300875i
$183$		0			0
$184$	16.2265	−	2.68806i	1.19624	−	0.198166i
$185$	−21.0974	−	21.0974i	−1.55111	−	1.55111i
$186$		0			0
$187$	2.94056	+	7.09915i	0.215035	+	0.519141i
$188$	−1.96418	+	4.46832i	−0.143253	+	0.325886i
$189$		0			0
$190$	2.52640	−	12.0254i	0.183284	−	0.872414i
$191$	−4.82446			−0.349085			−0.174543	−	0.984650i	$-0.555845\pi$
$191$	−4.82446			−0.349085			−0.174543	+	0.984650i	$0.555845\pi$
$192$		0			0
$193$	0.222878			0.0160431			0.00802155	−	0.999968i	$-0.497447\pi$
$193$	0.222878			0.0160431			0.00802155	+	0.999968i	$0.497447\pi$
$194$	−3.94228	+	18.7648i	−0.283039	+	1.34724i
$195$		0			0
$196$	9.15899	−	20.8358i	0.654214	−	1.48827i
$197$	9.44160	+	22.7940i	0.672686	+	1.62401i	0.777028	+	0.629467i	$0.216727\pi$
$197$	9.44160	+	22.7940i	0.672686	+	1.62401i	−0.104341	+	0.994542i	$0.533273\pi$
$198$		0			0
$199$	14.8710	+	14.8710i	1.05418	+	1.05418i	0.998446	+	0.0557310i	$0.0177489\pi$
$199$	14.8710	+	14.8710i	1.05418	+	1.05418i	0.0557310	+	0.998446i	$0.482251\pi$
$200$	−1.67256	−	10.0964i	−0.118268	−	0.713926i
$201$		0			0
$202$	4.01263	−	0.753507i	0.282328	−	0.0530165i
$203$	14.5024	+	35.0120i	1.01787	+	2.45736i
$204$		0			0
$205$	0.651743	+	0.269961i	0.0455197	+	0.0188549i
$206$	−21.4385	+	13.9944i	−1.49369	+	0.975037i
$207$		0			0
$208$	4.97250	+	13.6312i	0.344781	+	0.945150i
$209$	−4.77079			−0.330003
$210$		0			0
$211$	−0.644000	+	1.55475i	−0.0443348	+	0.107034i	−0.944496	−	0.328524i	$-0.893449\pi$
$211$	−0.644000	+	1.55475i	−0.0443348	+	0.107034i	0.900161	+	0.435558i	$0.143449\pi$
$212$	4.30850	+	0.0924532i	0.295909	+	0.00634971i
$213$		0			0
$214$	2.61752	−	0.491528i	0.178930	−	0.0336002i
$215$	17.0243	+	17.0243i	1.16105	+	1.16105i
$216$		0			0
$217$	18.6833	−	18.6833i	1.26830	−	1.26830i
$218$	3.84510	−	5.62306i	0.260423	−	0.380842i
$219$		0			0
$220$	−8.81935	+	3.43333i	−0.594600	+	0.231475i
$221$	−15.9761	−	6.61750i	−1.07467	−	0.445141i
$222$		0			0
$223$			23.4280i			1.56885i	0.620221	+	0.784427i	$0.287043\pi$
$223$			23.4280i			1.56885i	−0.620221	+	0.784427i	$0.712957\pi$
$224$	23.4982	+	5.99974i	1.57004	+	0.400875i
$225$		0			0
$226$	3.97216	−	18.9071i	0.264224	−	1.25768i
$227$	−5.10690	+	12.3292i	−0.338957	+	0.818315i	0.658859	+	0.752266i	$0.271039\pi$
$227$	−5.10690	+	12.3292i	−0.338957	+	0.818315i	−0.997816	+	0.0660486i	$0.978961\pi$
$228$		0			0
$229$	−7.82666	+	3.24191i	−0.517200	+	0.214231i	−0.625987	−	0.779834i	$-0.715304\pi$
$229$	−7.82666	+	3.24191i	−0.517200	+	0.214231i	0.108786	+	0.994065i	$0.465304\pi$
$230$	−19.9288	−	13.6275i	−1.31407	−	0.898571i
$231$		0			0
$232$	−21.2245	+	13.2142i	−1.39346	+	0.867556i
$233$	−9.66805	+	9.66805i	−0.633375	+	0.633375i	−0.948913	−	0.315538i	$-0.897815\pi$
$233$	−9.66805	+	9.66805i	−0.633375	+	0.633375i	0.315538	+	0.948913i	$0.397815\pi$
$234$		0			0
$235$	6.61915	−	2.74174i	0.431785	−	0.178851i
$236$	2.62934	+	0.0564212i	0.171155	+	0.00367270i
$237$		0			0
$238$	−24.2027	+	15.7989i	−1.56883	+	1.02409i
$239$			25.8579i			1.67261i	0.548268	+	0.836303i	$0.315287\pi$
$239$			25.8579i			1.67261i	−0.548268	+	0.836303i	$0.684713\pi$
$240$		0			0
$241$		−	24.9358i		−	1.60626i	−0.595805	−	0.803129i	$-0.703167\pi$
$241$		−	24.9358i		−	1.60626i	0.595805	−	0.803129i	$-0.296833\pi$
$242$	−6.49488	−	9.94970i	−0.417507	−	0.639591i
$243$		0			0
$244$	−3.94334	+	3.77766i	−0.252447	+	0.241840i
$245$	−30.8652	+	12.7848i	−1.97190	+	0.816789i
$246$		0			0
$247$	7.59170	−	7.59170i	0.483048	−	0.483048i
$248$	14.1748	+	10.1459i	0.900102	+	0.644266i
$249$		0			0
$250$	3.23800	−	4.73525i	0.204789	−	0.299483i
$251$	−11.5486	+	4.78358i	−0.728939	+	0.301937i	−0.716116	−	0.697981i	$-0.754082\pi$
$251$	−11.5486	+	4.78358i	−0.728939	+	0.301937i	−0.0128233	+	0.999918i	$0.504082\pi$
$252$		0			0
$253$	−3.58705	+	8.65990i	−0.225516	+	0.544443i
$254$	18.2707	+	3.83848i	1.14641	+	0.240847i
$255$		0			0
$256$	−1.37144	+	15.9411i	−0.0857148	+	0.996320i
$257$			17.0780i			1.06530i	0.846337	+	0.532648i	$0.178803\pi$
$257$			17.0780i			1.06530i	−0.846337	+	0.532648i	$0.821197\pi$
$258$		0			0
$259$	−40.2552	−	16.6742i	−2.50133	−	1.03609i
$260$	8.57070	−	19.4975i	0.531532	−	1.20919i
$261$		0			0
$262$	−7.82619	−	5.35161i	−0.483503	−	0.330624i
$263$	10.4595	−	10.4595i	0.644963	−	0.644963i	−0.306809	−	0.951771i	$-0.599261\pi$
$263$	10.4595	−	10.4595i	0.644963	−	0.644963i	0.951771	+	0.306809i	$0.0992612\pi$
$264$		0			0
$265$	−4.47292	−	4.47292i	−0.274770	−	0.274770i
$266$	−3.31187	−	17.6366i	−0.203064	−	1.08137i
$267$		0			0
$268$	−5.86364	−	6.12080i	−0.358179	−	0.373888i
$269$	3.47587	−	8.39150i	0.211928	−	0.511639i	−0.781792	−	0.623540i	$-0.785694\pi$
$269$	3.47587	−	8.39150i	0.211928	−	0.511639i	0.993719	+	0.111901i	$0.0356939\pi$
$270$		0			0
$271$	−5.66173			−0.343925			−0.171963	−	0.985103i	$-0.555011\pi$
$271$	−5.66173			−0.343925			−0.171963	+	0.985103i	$0.555011\pi$
$272$	−12.8926	−	14.0493i	−0.781726	−	0.851866i
$273$		0			0
$274$	10.6846	+	16.3680i	0.645479	+	0.988828i
$275$	5.38834	+	2.23192i	0.324929	+	0.134590i
$276$		0			0
$277$	−5.27625	−	12.7380i	−0.317019	−	0.765352i	−0.999409	−	0.0343637i	$-0.989060\pi$
$277$	−5.27625	−	12.7380i	−0.317019	−	0.765352i	0.682390	−	0.730988i	$-0.260940\pi$
$278$	2.33527	+	12.4359i	0.140060	+	0.745858i
$279$		0			0
$280$	−18.8147	−	30.2199i	−1.12439	−	1.80598i
$281$	5.75892	+	5.75892i	0.343548	+	0.343548i	0.857700	−	0.514151i	$-0.171893\pi$
$281$	5.75892	+	5.75892i	0.343548	+	0.343548i	−0.514151	+	0.857700i	$0.671893\pi$
$282$		0			0
$283$	10.4136	+	25.1407i	0.619025	+	1.49446i	0.852837	+	0.522177i	$0.174880\pi$
$283$	10.4136	+	25.1407i	0.619025	+	1.49446i	−0.233812	+	0.972282i	$0.575120\pi$
$284$	−13.9410	+	5.42714i	−0.827243	+	0.322042i
$285$		0			0
$286$	−8.09236	−	1.70011i	−0.478511	−	0.100530i
$287$	1.03021			0.0608111
$288$		0			0
$289$	5.72512			0.336772
$290$	35.9149	+	7.54531i	2.10900	+	0.443076i
$291$		0			0
$292$	1.61590	+	4.15083i	0.0945632	+	0.242909i
$293$	−5.21345	−	12.5864i	−0.304573	−	0.735304i	−0.999863	−	0.0165743i	$-0.994724\pi$
$293$	−5.21345	−	12.5864i	−0.304573	−	0.735304i	0.695290	−	0.718729i	$-0.255276\pi$
$294$		0			0
$295$	−2.72968	−	2.72968i	−0.158928	−	0.158928i
$296$	6.51236	−	27.9987i	0.378523	−	1.62739i
$297$		0			0
$298$	−5.36211	−	28.5547i	−0.310619	−	1.65413i
$299$	−8.07236	−	19.4884i	−0.466837	−	1.12704i
$300$		0			0
$301$	32.4835	+	13.4551i	1.87232	+	0.775539i
$302$	−8.56362	−	13.1189i	−0.492781	−	0.754905i
$303$		0			0
$304$	11.1220	−	4.05720i	0.637892	−	0.232696i
$305$	8.01566			0.458975
$306$		0			0
$307$	−8.98052	+	21.6809i	−0.512545	+	1.23739i	0.429852	+	0.902899i	$0.358566\pi$
$307$	−8.98052	+	21.6809i	−0.512545	+	1.23739i	−0.942398	+	0.334495i	$0.891434\pi$
$308$	−9.98036	+	9.56104i	−0.568684	+	0.544791i
$309$		0			0
$310$	−4.72230	−	25.1475i	−0.268208	−	1.42828i
$311$	−12.7177	−	12.7177i	−0.721157	−	0.721157i	0.247684	−	0.968841i	$-0.420330\pi$
$311$	−12.7177	−	12.7177i	−0.721157	−	0.721157i	−0.968841	+	0.247684i	$0.920330\pi$
$312$		0			0
$313$	10.1388	−	10.1388i	0.573081	−	0.573081i	−0.359907	−	0.932988i	$-0.617192\pi$
$313$	10.1388	−	10.1388i	0.573081	−	0.573081i	0.932988	+	0.359907i	$0.117192\pi$
$314$	−10.9213	−	7.46805i	−0.616323	−	0.421446i
$315$		0			0
$316$	25.2137	+	11.0834i	1.41838	+	0.623490i
$317$	−2.52668	−	1.04659i	−0.141913	−	0.0587822i	0.310597	−	0.950542i	$-0.399471\pi$
$317$	−2.52668	−	1.04659i	−0.141913	−	0.0587822i	−0.452509	+	0.891760i	$0.649471\pi$
$318$		0			0
$319$		−	14.2484i		−	0.797757i
$320$	17.6405	−	15.5042i	0.986136	−	0.866713i
$321$		0			0
$322$	−34.5040	−	7.24889i	−1.92283	−	0.403965i
$323$	−5.39940	+	13.0353i	−0.300431	+	0.725304i
$324$		0			0
$325$	−12.1260	+	5.02277i	−0.672631	+	0.278613i
$326$	−4.09287	+	5.98540i	−0.226683	+	0.331501i
$327$		0			0
$328$	0.111078	+	0.670528i	0.00613327	+	0.0370237i
$329$	7.39834	−	7.39834i	0.407884	−	0.407884i
$330$		0			0
$331$	−5.49794	+	2.27732i	−0.302194	+	0.125173i	−0.528628	−	0.848854i	$-0.677293\pi$
$331$	−5.49794	+	2.27732i	−0.302194	+	0.125173i	0.226434	+	0.974027i	$0.427293\pi$
$332$	4.97086	+	5.18887i	0.272811	+	0.284776i
$333$		0			0
$334$	−4.97641	−	7.62351i	−0.272297	−	0.417140i
$335$			12.4418i			0.679768i
$336$		0			0
$337$			5.85273i			0.318818i	0.987213	+	0.159409i	$0.0509589\pi$
$337$			5.85273i			0.318818i	−0.987213	+	0.159409i	$0.949041\pi$
$338$	0.187563	−	0.122436i	0.0102021	−	0.00665963i
$339$		0			0
$340$	−0.600467	+	27.9829i	−0.0325649	+	1.51759i
$341$	−9.17801	+	3.80166i	−0.497017	+	0.205871i
$342$		0			0
$343$	−13.2780	+	13.2780i	−0.716946	+	0.716946i
$344$	−5.25508	+	22.5932i	−0.283335	+	1.21815i
$345$		0			0
$346$	−13.0697	−	8.93719i	−0.702633	−	0.480466i
$347$	7.23994	−	2.99888i	0.388660	−	0.160988i	−0.179792	−	0.983705i	$-0.557542\pi$
$347$	7.23994	−	2.99888i	0.388660	−	0.160988i	0.568452	+	0.822716i	$0.307542\pi$
$348$		0			0
$349$	−4.01973	+	9.70449i	−0.215171	+	0.519469i	−0.994204	−	0.107515i	$-0.965711\pi$
$349$	−4.01973	+	9.70449i	−0.215171	+	0.519469i	0.779032	+	0.626984i	$0.215711\pi$
$350$	−4.51039	+	21.4690i	−0.241090	+	1.14756i
$351$		0			0
$352$	−7.29908	−	5.46502i	−0.389042	−	0.291286i
$353$			16.6657i			0.887026i	0.896268	+	0.443513i	$0.146268\pi$
$353$			16.6657i			0.887026i	−0.896268	+	0.443513i	$0.853732\pi$
$354$		0			0
$355$	20.2875	+	8.40338i	1.07675	+	0.446005i
$356$	7.17242	+	18.4241i	0.380138	+	0.976477i
$357$		0			0
$358$	−8.83444	+	12.9195i	−0.466915	+	0.682815i
$359$	−9.54649	+	9.54649i	−0.503845	+	0.503845i	−0.912630	−	0.408786i	$-0.865952\pi$
$359$	−9.54649	+	9.54649i	−0.503845	+	0.503845i	0.408786	+	0.912630i	$0.365952\pi$
$360$		0			0
$361$	7.24075	+	7.24075i	0.381092	+	0.381092i
$362$	−4.84363	+	0.909554i	−0.254575	+	0.0478051i
$363$		0			0
$364$	0.667267	−	31.0960i	0.0349743	−	1.62987i
$365$	2.50205	−	6.04049i	0.130963	−	0.316173i
$366$		0			0
$367$	−6.31072			−0.329417			−0.164708	−	0.986342i	$-0.552668\pi$
$367$	−6.31072			−0.329417			−0.164708	+	0.986342i	$0.552668\pi$
$368$	0.997804	−	23.2391i	0.0520141	−	1.21142i
$369$		0			0
$370$	−35.3331	+	23.0644i	−1.83688	+	1.19906i
$371$	−8.53463	−	3.53516i	−0.443096	−	0.183536i
$372$		0			0
$373$	−3.06259	−	7.39375i	−0.158575	−	0.382834i	0.824545	−	0.565797i	$-0.191431\pi$
$373$	−3.06259	−	7.39375i	−0.158575	−	0.382834i	−0.983120	+	0.182963i	$0.941431\pi$
$374$	10.6802	−	2.00557i	0.552261	−	0.103706i
$375$		0			0
$376$	5.61305	+	4.01765i	0.289471	+	0.207194i
$377$	22.6733	+	22.6733i	1.16773	+	1.16773i
$378$		0			0
$379$	−8.31838	−	20.0823i	−0.427286	−	1.03156i	−0.980144	−	0.198285i	$-0.936463\pi$
$379$	−8.31838	−	20.0823i	−0.427286	−	1.03156i	0.552858	−	0.833275i	$-0.313537\pi$
$380$	−15.9086	−	6.99307i	−0.816092	−	0.358737i
$381$		0			0
$382$	−1.40277	+	6.67705i	−0.0717720	+	0.341627i
$383$	7.95308			0.406383			0.203192	−	0.979139i	$-0.434869\pi$
$383$	7.95308			0.406383			0.203192	+	0.979139i	$0.434869\pi$
$384$		0			0
$385$	20.2871			1.03393
$386$	0.0648046	−	0.308463i	0.00329847	−	0.0157004i
$387$		0			0
$388$	24.8243	+	10.9122i	1.26026	+	0.553984i
$389$	2.38215	+	5.75102i	0.120780	+	0.291588i	0.972693	−	0.232094i	$-0.0745578\pi$
$389$	2.38215	+	5.75102i	0.120780	+	0.291588i	−0.851913	+	0.523683i	$0.824558\pi$
$390$		0			0
$391$	19.6019	+	19.6019i	0.991310	+	0.991310i
$392$	−26.1737	−	18.7343i	−1.32197	−	0.946227i
$393$		0			0
$394$	34.2922	−	6.43952i	1.72762	−	0.324418i
$395$	−15.4710	−	37.3503i	−0.778430	−	1.87930i
$396$		0			0
$397$	25.3118	+	10.4845i	1.27036	+	0.526202i	0.913075	−	0.407792i	$-0.133701\pi$
$397$	25.3118	+	10.4845i	1.27036	+	0.526202i	0.357288	+	0.933994i	$0.383701\pi$
$398$	24.9054	−	16.2575i	1.24839	−	0.814916i
$399$		0			0
$400$	−14.4598	−	0.620851i	−0.722990	−	0.0310426i
$401$	1.81017			0.0903954			0.0451977	−	0.998978i	$-0.485608\pi$
$401$	1.81017			0.0903954			0.0451977	+	0.998978i	$0.485608\pi$
$402$		0			0
$403$	8.55532	−	20.6544i	0.426171	−	1.02887i
$404$	0.123870	−	5.77257i	0.00616275	−	0.287196i
$405$		0			0
$406$	52.6734	−	9.89120i	2.61413	−	0.490892i
$407$	11.5839	+	11.5839i	0.574194	+	0.574194i
$408$		0			0
$409$	−14.4331	+	14.4331i	−0.713672	+	0.713672i	−0.967301	−	0.253630i	$-0.918376\pi$
$409$	−14.4331	+	14.4331i	−0.713672	+	0.713672i	0.253630	+	0.967301i	$0.418376\pi$
$410$	0.563129	−	0.823518i	0.0278109	−	0.0406707i
$411$		0			0
$412$	13.1348	+	33.7399i	0.647104	+	1.66225i
$413$	−5.20841	−	2.15739i	−0.256289	−	0.106158i
$414$		0			0
$415$		−	10.5474i		−	0.517754i
$416$	20.3113	−	2.91851i	0.995845	−	0.143092i
$417$		0			0
$418$	−1.38717	+	6.60278i	−0.0678486	+	0.322952i
$419$	1.33902	−	3.23269i	0.0654155	−	0.157927i	−0.887791	−	0.460247i	$-0.847761\pi$
$419$	1.33902	−	3.23269i	0.0654155	−	0.157927i	0.953207	+	0.302320i	$0.0977610\pi$
$420$		0			0
$421$	−10.5557	+	4.37232i	−0.514454	+	0.213094i	−0.624779	−	0.780802i	$-0.714811\pi$
$421$	−10.5557	+	4.37232i	−0.514454	+	0.213094i	0.110325	+	0.993896i	$0.464811\pi$
$422$	1.96453	+	1.34336i	0.0956318	+	0.0653938i
$423$		0			0
$424$	1.38071	−	5.93609i	0.0670530	−	0.288282i
$425$	12.1966	−	12.1966i	0.591624	−	0.591624i
$426$		0			0
$427$	10.8148	−	4.47963i	0.523364	−	0.216784i
$428$	0.0808028	−	3.76557i	0.00390575	−	0.182016i
$429$		0			0
$430$	28.5117	−	18.6116i	1.37496	−	0.897532i
$431$			3.31967i			0.159903i	0.996799	+	0.0799513i	$0.0254765\pi$
$431$			3.31967i			0.159903i	−0.996799	+	0.0799513i	$0.974524\pi$
$432$		0			0
$433$		−	4.53298i		−	0.217841i	−0.994050	−	0.108921i	$-0.965261\pi$
$433$		−	4.53298i		−	0.217841i	0.994050	−	0.108921i	$-0.0347394\pi$
$434$	−20.4253	−	31.2901i	−0.980445	−	1.50197i
$435$		0			0
$436$	−6.66431	−	6.95659i	−0.319163	−	0.333160i
$437$	−15.9011	+	6.58646i	−0.760654	+	0.315073i
$438$		0			0
$439$	20.9703	−	20.9703i	1.00086	−	1.00086i	0.000858061	−	1.00000i	$-0.499727\pi$
$439$	20.9703	−	20.9703i	1.00086	−	1.00086i	1.00000		0.000858061i	$-0.000273129\pi$
$440$	2.18739	+	13.2043i	0.104280	+	0.629489i
$441$		0			0
$442$	−13.8039	+	20.1868i	−0.656583	+	0.960186i
$443$	31.9708	−	13.2427i	1.51898	−	0.629181i	0.541590	−	0.840643i	$-0.317822\pi$
$443$	31.9708	−	13.2427i	1.51898	−	0.629181i	0.977386	+	0.211462i	$0.0678225\pi$
$444$		0			0
$445$	11.1058	−	26.8117i	0.526464	−	1.27100i
$446$	32.4243	+	6.81198i	1.53534	+	0.322557i
$447$		0			0
$448$	15.1360	−	30.7770i	0.715110	−	1.45407i
$449$		−	21.0485i		−	0.993340i	−0.867940	−	0.496670i	$-0.834556\pi$
$449$		−	21.0485i		−	0.993340i	0.867940	−	0.496670i	$-0.165444\pi$
$450$		0			0
$451$	−0.357852	−	0.148227i	−0.0168506	−	0.00697975i
$452$	−25.0125	−	10.9950i	−1.17649	−	0.517159i
$453$		0			0
$454$	15.5787	+	10.6528i	0.731143	+	0.499961i
$455$	−32.2827	+	32.2827i	−1.51344	+	1.51344i
$456$		0			0
$457$	−4.62656	−	4.62656i	−0.216421	−	0.216421i	0.590567	−	0.806988i	$-0.298904\pi$
$457$	−4.62656	−	4.62656i	−0.216421	−	0.216421i	−0.806988	+	0.590567i	$0.798904\pi$
$458$	2.21110	+	11.7747i	0.103318	+	0.550197i
$459$		0			0
$460$	−24.6550	+	23.6192i	−1.14955	+	1.10125i
$461$	−4.84388	+	11.6942i	−0.225602	+	0.544652i	−0.995633	−	0.0933550i	$-0.970241\pi$
$461$	−4.84388	+	11.6942i	−0.225602	+	0.544652i	0.770031	+	0.638007i	$0.220241\pi$
$462$		0			0
$463$	14.2219			0.660950			0.330475	−	0.943815i	$-0.392791\pi$
$463$	14.2219			0.660950			0.330475	+	0.943815i	$0.392791\pi$
$464$	12.1172	+	33.2169i	0.562526	+	1.54206i
$465$		0			0
$466$	10.5695	+	16.1917i	0.489622	+	0.750066i
$467$	34.5241	+	14.3003i	1.59758	+	0.661741i	0.991071	−	0.133333i	$-0.0425681\pi$
$467$	34.5241	+	14.3003i	1.59758	+	0.661741i	0.606512	+	0.795074i	$0.292568\pi$
$468$		0			0
$469$	6.95321	+	16.7865i	0.321069	+	0.775130i
$470$	−1.86997	−	9.95809i	−0.0862552	−	0.459333i
$471$		0			0
$472$	0.842601	−	3.62260i	0.0387838	−	0.166744i
$473$	−9.34754	−	9.34754i	−0.429800	−	0.429800i
$474$		0			0
$475$	4.09821	+	9.89396i	0.188039	+	0.453966i
$476$	14.8284	+	38.0903i	0.679657	+	1.74587i
$477$		0			0
$478$	35.7873	+	7.51850i	1.63687	+	0.343888i
$479$	−13.4016			−0.612333			−0.306167	−	0.951978i	$-0.599046\pi$
$479$	−13.4016			−0.612333			−0.306167	+	0.951978i	$0.599046\pi$
$480$		0			0
$481$	−36.8667			−1.68098
$482$	−34.5112	−	7.25041i	−1.57194	−	0.330247i
$483$		0			0
$484$	−15.6589	+	6.09591i	−0.711766	+	0.277087i
$485$	−15.2320	−	36.7734i	−0.691652	−	1.66979i
$486$		0			0
$487$	1.26750	+	1.26750i	0.0574358	+	0.0574358i	0.735241	−	0.677805i	$-0.237069\pi$
$487$	1.26750	+	1.26750i	0.0574358	+	0.0574358i	−0.677805	+	0.735241i	$0.737069\pi$
$488$	4.08171	+	6.55599i	0.184770	+	0.296776i
$489$		0			0
$490$	8.71969	+	46.4347i	0.393915	+	2.09771i
$491$	−8.81902	−	21.2910i	−0.397997	−	0.960849i	−0.988141	−	0.153551i	$-0.950929\pi$
$491$	−8.81902	−	21.2910i	−0.397997	−	0.960849i	0.590144	−	0.807298i	$-0.299071\pi$
$492$		0			0
$493$	−38.9311	−	16.1258i	−1.75337	−	0.726269i
$494$	−8.29953	−	12.7143i	−0.373414	−	0.572043i
$495$		0			0
$496$	18.1634	−	16.6679i	0.815563	−	0.748411i
$497$	32.0684			1.43846
$498$		0			0
$499$	−2.76574	+	6.67709i	−0.123812	+	0.298908i	−0.973617	−	0.228189i	$-0.926719\pi$
$499$	−2.76574	+	6.67709i	−0.123812	+	0.298908i	0.849805	+	0.527097i	$0.176719\pi$
$500$	−5.61209	−	5.85823i	−0.250980	−	0.261988i
$501$		0			0
$502$	3.26258	+	17.3741i	0.145616	+	0.775445i
$503$	−17.1789	−	17.1789i	−0.765968	−	0.765968i	0.211426	−	0.977394i	$-0.432189\pi$
$503$	−17.1789	−	17.1789i	−0.765968	−	0.765968i	−0.977394	+	0.211426i	$0.932189\pi$
$504$		0			0
$505$	−5.99287	+	5.99287i	−0.266679	+	0.266679i
$506$	10.9423	+	7.48245i	0.486446	+	0.332636i
$507$		0			0
$508$	10.6249	−	24.1706i	0.471404	−	1.07240i
$509$	−0.432418	−	0.179113i	−0.0191666	−	0.00793905i	0.373080	−	0.927799i	$-0.378302\pi$
$509$	−0.432418	−	0.179113i	−0.0191666	−	0.00793905i	−0.392246	+	0.919860i	$0.628302\pi$
$510$		0			0
$511$		−	9.54815i		−	0.422385i
$512$	21.6637	+	6.53315i	0.957411	+	0.288727i
$513$		0			0
$514$	23.6359	+	4.96564i	1.04254	+	0.219025i
$515$	20.3379	−	49.0999i	0.896193	−	2.16360i
$516$		0			0
$517$	−3.63437	+	1.50541i	−0.159839	+	0.0662077i
$518$	−34.7818	+	50.8649i	−1.52823	+	2.23488i
$519$		0			0
$520$	−24.4925	−	17.5310i	−1.07407	−	0.768786i
$521$	20.6495	−	20.6495i	0.904670	−	0.904670i	−0.0911655	−	0.995836i	$-0.529059\pi$
$521$	20.6495	−	20.6495i	0.904670	−	0.904670i	0.995836	+	0.0911655i	$0.0290592\pi$
$522$		0			0
$523$	−40.6453	+	16.8358i	−1.77729	+	0.736180i	−0.783974	+	0.620794i	$0.786810\pi$
$523$	−40.6453	+	16.8358i	−1.77729	+	0.736180i	−0.993321	+	0.115386i	$0.963190\pi$
$524$	−9.68219	+	9.27540i	−0.422969	+	0.405198i
$525$		0			0
$526$	−11.4348	−	17.5172i	−0.498579	−	0.763788i
$527$			29.3798i			1.27980i
$528$		0			0
$529$			10.8158i			0.470252i
$530$	−7.49109	+	4.88997i	−0.325392	+	0.212407i
$531$		0			0
$532$	−25.3721	−	0.544441i	−1.10002	−	0.0236045i
$533$	0.805318	−	0.333574i	0.0348822	−	0.0144487i
$534$		0			0
$535$	−3.90927	+	3.90927i	−0.169013	+	0.169013i
$536$	−10.1761	+	6.33557i	−0.439541	+	0.273655i
$537$		0			0
$538$	−10.6032	−	7.25055i	−0.457136	−	0.312593i
$539$	16.9471	−	7.01973i	0.729964	−	0.302361i
$540$		0			0
$541$	−7.26862	+	17.5480i	−0.312502	+	0.754447i	0.687109	+	0.726555i	$0.258880\pi$
$541$	−7.26862	+	17.5480i	−0.312502	+	0.754447i	−0.999611	+	0.0278925i	$0.991120\pi$
$542$	−1.64622	+	7.83583i	−0.0707111	+	0.336578i
$543$		0			0
$544$	−23.1930	+	13.7583i	−0.994390	+	0.589881i
$545$			14.1407i			0.605721i
$546$		0			0
$547$	−5.22407	−	2.16388i	−0.223365	−	0.0925208i	0.268195	−	0.963365i	$-0.413573\pi$
$547$	−5.22407	−	2.16388i	−0.223365	−	0.0925208i	−0.491560	+	0.870844i	$0.663573\pi$
$548$	25.7600	−	10.0282i	1.10041	−	0.428386i
$549$		0			0
$550$	4.65571	−	6.80851i	0.198520	−	0.290316i
$551$	18.4998	−	18.4998i	0.788116	−	0.788116i
$552$		0			0
$553$	−41.7471	−	41.7471i	−1.77527	−	1.77527i
$554$	−19.1635	+	3.59860i	−0.814180	+	0.152890i
$555$		0			0
$556$	17.8903	+	0.383896i	0.758719	+	0.0162808i
$557$	−7.20051	+	17.3836i	−0.305095	+	0.736565i	0.694755	+	0.719247i	$0.255513\pi$
$557$	−7.20051	+	17.3836i	−0.305095	+	0.736565i	−0.999850	+	0.0173184i	$0.994487\pi$
$558$		0			0
$559$	29.7492			1.25826
$560$	−47.2949	+	17.2527i	−1.99858	+	0.729059i
$561$		0			0
$562$	9.64483	−	6.29587i	0.406843	−	0.265575i
$563$	−43.4445	−	17.9953i	−1.83097	−	0.758411i	−0.966959	−	0.254932i	$-0.917947\pi$
$563$	−43.4445	−	17.9953i	−1.83097	−	0.758411i	−0.864007	−	0.503479i	$-0.832053\pi$
$564$		0			0
$565$	15.3475	+	37.0522i	0.645675	+	1.55880i
$566$	37.8226	−	7.10247i	1.58980	−	0.298539i
$567$		0			0
$568$	3.45766	+	20.8723i	0.145080	+	0.875782i
$569$	5.66061	+	5.66061i	0.237305	+	0.237305i	0.815733	−	0.578428i	$-0.196334\pi$
$569$	5.66061	+	5.66061i	0.237305	+	0.237305i	−0.578428	+	0.815733i	$0.696334\pi$
$570$		0			0
$571$	−13.7365	−	33.1629i	−0.574856	−	1.38783i	−0.897378	−	0.441263i	$-0.854531\pi$
$571$	−13.7365	−	33.1629i	−0.574856	−	1.38783i	0.322522	−	0.946562i	$-0.395469\pi$
$572$	−4.70591	+	10.7055i	−0.196764	+	0.447619i
$573$		0			0
$574$	0.299545	−	1.42581i	0.0125028	−	0.0595120i
$575$	21.0408			0.877461
$576$		0			0
$577$	4.38583			0.182584			0.0912922	−	0.995824i	$-0.470900\pi$
$577$	4.38583			0.182584			0.0912922	+	0.995824i	$0.470900\pi$
$578$	1.66465	−	7.92357i	0.0692404	−	0.329577i
$579$		0			0
$580$	20.8854	−	47.5124i	0.867220	−	1.97284i
$581$	−5.89454	−	14.2307i	−0.244547	−	0.590388i
$582$		0			0
$583$	2.45595	+	2.45595i	0.101715	+	0.101715i
$584$	6.21459	−	1.02950i	0.257162	−	0.0426008i
$585$		0			0
$586$	−18.9354	+	3.55576i	−0.782215	+	0.146887i
$587$	4.24918	+	10.2584i	0.175382	+	0.423411i	0.986988	−	0.160795i	$-0.0514060\pi$
$587$	4.24918	+	10.2584i	0.175382	+	0.423411i	−0.811605	+	0.584206i	$0.801406\pi$
$588$		0			0
$589$	−16.8525	−	6.98052i	−0.694394	−	0.287627i
$590$	−4.57157	+	2.98419i	−0.188208	+	0.122857i
$591$		0			0
$592$	−36.8566	−	17.1541i	−1.51480	−	0.705028i
$593$	−5.76763			−0.236848			−0.118424	−	0.992963i	$-0.537784\pi$
$593$	−5.76763			−0.236848			−0.118424	+	0.992963i	$0.537784\pi$
$594$		0			0
$595$	22.9602	−	55.4309i	0.941277	−	2.27244i
$596$	−41.0788	−	0.881482i	−1.68265	−	0.0361069i
$597$		0			0
$598$	−29.3191	+	5.50565i	−1.19895	+	0.225143i
$599$	13.4401	+	13.4401i	0.549149	+	0.549149i	0.926195	−	0.377045i	$-0.123060\pi$
$599$	13.4401	+	13.4401i	0.549149	+	0.549149i	−0.377045	+	0.926195i	$0.623060\pi$
$600$		0			0
$601$	8.58677	−	8.58677i	0.350262	−	0.350262i	−0.509945	−	0.860207i	$-0.670334\pi$
$601$	8.58677	−	8.58677i	0.350262	−	0.350262i	0.860207	+	0.509945i	$0.170334\pi$
$602$	28.0669	−	41.0449i	1.14392	−	1.67287i
$603$		0			0
$604$	−20.6465	+	8.03757i	−0.840093	+	0.327044i
$605$	22.7875	+	9.43890i	0.926444	+	0.383746i
$606$		0			0
$607$		−	13.3743i		−	0.542847i	−0.962460	−	0.271424i	$-0.912506\pi$
$607$		−	13.3743i		−	0.542847i	0.962460	−	0.271424i	$-0.0874944\pi$
$608$	−2.38129	−	16.5726i	−0.0965742	−	0.672107i
$609$		0			0
$610$	2.33066	−	11.0937i	0.0943655	−	0.449170i
$611$	3.38780	−	8.17886i	0.137056	−	0.330881i
$612$		0			0
$613$	−10.6749	+	4.42168i	−0.431154	+	0.178590i	−0.587697	−	0.809081i	$-0.699965\pi$
$613$	−10.6749	+	4.42168i	−0.431154	+	0.178590i	0.156542	+	0.987671i	$0.449965\pi$
$614$	27.3952	+	18.7330i	1.10558	+	0.756004i
$615$		0			0
$616$	10.3306	+	16.5928i	0.416230	+	0.668544i
$617$	14.8713	−	14.8713i	0.598695	−	0.598695i	−0.341270	−	0.939965i	$-0.610857\pi$
$617$	14.8713	−	14.8713i	0.598695	−	0.598695i	0.939965	+	0.341270i	$0.110857\pi$
$618$		0			0
$619$	−6.25062	+	2.58909i	−0.251234	+	0.104064i	−0.504746	−	0.863268i	$-0.668414\pi$
$619$	−6.25062	+	2.58909i	−0.251234	+	0.104064i	0.253513	+	0.967332i	$0.418414\pi$
$620$	−36.1773	−	0.776303i	−1.45291	−	0.0311771i
$621$		0			0
$622$	−21.2992	+	13.9035i	−0.854020	+	0.557480i
$623$		−	42.3810i		−	1.69796i
$624$		0			0
$625$			29.9995i			1.19998i
$626$	−11.0842	−	16.9801i	−0.443012	−	0.678663i
$627$		0			0
$628$	−13.5113	+	12.9436i	−0.539159	+	0.516506i
$629$	44.7612	−	18.5407i	1.78475	−	0.739266i
$630$		0			0
$631$	−5.78346	+	5.78346i	−0.230236	+	0.230236i	−0.812791	−	0.582555i	$-0.802053\pi$
$631$	−5.78346	+	5.78346i	−0.230236	+	0.230236i	0.582555	+	0.812791i	$0.302053\pi$
$632$	22.6706	−	31.6731i	0.901789	−	1.25989i
$633$		0			0
$634$	−2.18314	+	3.19262i	−0.0867037	+	0.126795i
$635$	−35.8052	+	14.8310i	−1.42088	+	0.588550i
$636$		0			0
$637$	−15.7973	+	38.1381i	−0.625913	+	1.51109i
$638$	−19.7198	−	4.14290i	−0.780714	−	0.164019i
$639$		0			0
$640$	−16.3286	−	28.9226i	−0.645446	−	1.14327i
$641$			29.5203i			1.16598i	0.812479	+	0.582990i	$0.198117\pi$
$641$			29.5203i			1.16598i	−0.812479	+	0.582990i	$0.801883\pi$
$642$		0			0
$643$	10.0660	+	4.16947i	0.396964	+	0.164428i	0.572230	−	0.820093i	$-0.306079\pi$
$643$	10.0660	+	4.16947i	0.396964	+	0.164428i	−0.175266	+	0.984521i	$0.556079\pi$
$644$	−20.0649	+	45.6458i	−0.790669	+	1.79870i
$645$		0			0
$646$	16.4709	+	11.2630i	0.648040	+	0.443135i
$647$	−31.9256	+	31.9256i	−1.25512	+	1.25512i	−0.301730	+	0.953393i	$0.597564\pi$
$647$	−31.9256	+	31.9256i	−1.25512	+	1.25512i	−0.953393	+	0.301730i	$0.902436\pi$
$648$		0			0
$649$	1.49878	+	1.49878i	0.0588324	+	0.0588324i
$650$	3.42571	+	18.2429i	0.134368	+	0.715544i
$651$		0			0
$652$	7.09375	+	7.40486i	0.277813	+	0.289997i
$653$	−6.05626	+	14.6211i	−0.237000	+	0.572168i	−0.996970	−	0.0777900i	$-0.975214\pi$
$653$	−6.05626	+	14.6211i	−0.237000	+	0.572168i	0.759970	+	0.649958i	$0.225214\pi$
$654$		0			0
$655$	19.6811			0.769002
$656$	0.960309	+	0.0412322i	0.0374938	+	0.00160985i
$657$		0			0
$658$	−8.08814	−	12.3905i	−0.315309	−	0.483031i
$659$	−28.2612	−	11.7062i	−1.10090	−	0.456008i	−0.243106	−	0.970000i	$-0.578166\pi$
$659$	−28.2612	−	11.7062i	−1.10090	−	0.456008i	−0.857795	+	0.513992i	$0.828166\pi$
$660$		0			0
$661$	6.64573	+	16.0442i	0.258489	+	0.624047i	0.998839	−	0.0481743i	$-0.0153403\pi$
$661$	6.64573	+	16.0442i	0.258489	+	0.624047i	−0.740350	+	0.672221i	$0.765340\pi$
$662$	1.55322	+	8.27131i	0.0603675	+	0.321474i
$663$		0			0
$664$	8.62674	−	5.37094i	0.334782	−	0.208433i
$665$	26.3403	+	26.3403i	1.02143	+	1.02143i
$666$		0			0
$667$	−19.6711	−	47.4901i	−0.761666	−	1.83883i
$668$	−11.9979	+	4.67072i	−0.464212	+	0.180716i
$669$		0			0
$670$	17.2194	+	3.61761i	0.665245	+	0.139760i
$671$	−4.40116			−0.169905
$672$		0			0
$673$	34.2884			1.32172			0.660860	−	0.750509i	$-0.270192\pi$
$673$	34.2884			1.32172			0.660860	+	0.750509i	$0.270192\pi$
$674$	8.10018	+	1.70176i	0.312007	+	0.0655492i
$675$		0			0
$676$	−0.114915	−	0.295187i	−0.00441980	−	0.0113533i
$677$	16.6560	+	40.2112i	0.640142	+	1.54544i	0.826487	+	0.562956i	$0.190336\pi$
$677$	16.6560	+	40.2112i	0.640142	+	1.54544i	−0.186345	+	0.982484i	$0.559664\pi$
$678$		0			0
$679$	−41.1023	−	41.1023i	−1.57736	−	1.57736i
$680$	38.5538	+	8.96744i	1.47847	+	0.343886i
$681$		0			0
$682$	2.59287	+	13.8077i	0.0992861	+	0.528726i
$683$	5.35596	+	12.9304i	0.204940	+	0.494769i	0.992613	−	0.121325i	$-0.0387142\pi$
$683$	5.35596	+	12.9304i	0.204940	+	0.494769i	−0.787673	+	0.616094i	$0.788714\pi$
$684$		0			0
$685$	−37.4872	−	15.5277i	−1.43231	−	0.593284i
$686$	14.5160	+	22.2376i	0.554225	+	0.849034i
$687$		0			0
$688$	29.7411	+	13.8423i	1.13387	+	0.527733i
$689$	−7.81623			−0.297775
$690$		0			0
$691$	−19.9998	+	48.2837i	−0.760826	+	1.83680i	−0.279929	+	0.960021i	$0.590311\pi$
$691$	−19.9998	+	48.2837i	−0.760826	+	1.83680i	−0.480898	+	0.876777i	$0.659689\pi$
$692$	−16.1693	+	15.4899i	−0.614663	+	0.588838i
$693$		0			0
$694$	−2.04535	−	10.8920i	−0.0776404	−	0.413456i
$695$	−18.5731	−	18.5731i	−0.704517	−	0.704517i
$696$		0			0
$697$	−0.810008	+	0.810008i	−0.0306812	+	0.0306812i
$698$	12.2622	+	8.38501i	0.464132	+	0.317377i
$699$		0			0
$700$	28.4016	+	12.4848i	1.07348	+	0.471879i
$701$	−22.6661	−	9.38859i	−0.856085	−	0.354602i	−0.0889098	−	0.996040i	$-0.528338\pi$
$701$	−22.6661	−	9.38859i	−0.856085	−	0.354602i	−0.767175	+	0.641438i	$0.778338\pi$
$702$		0			0
$703$			30.0806i			1.13451i
$704$	−9.68589	+	8.51290i	−0.365051	+	0.320842i
$705$		0			0
$706$	23.0653	+	4.84577i	0.868076	+	0.182373i
$707$	−4.73644	+	11.4348i	−0.178132	+	0.430049i
$708$		0			0
$709$	−6.91323	+	2.86355i	−0.259632	+	0.107543i	−0.508703	−	0.860942i	$-0.669875\pi$
$709$	−6.91323	+	2.86355i	−0.259632	+	0.107543i	0.249071	+	0.968485i	$0.419875\pi$
$710$	17.5291	−	25.6346i	0.657857	−	0.962049i
$711$		0			0
$712$	27.5845	−	4.56959i	1.03377	−	0.171253i
$713$	−25.3420	+	25.3420i	−0.949064	+	0.949064i
$714$		0			0
$715$	15.8586	−	6.56884i	0.593078	−	0.245661i
$716$	15.3118	+	15.9834i	0.572230	+	0.597327i
$717$		0			0
$718$	10.4366	+	15.9881i	0.389490	+	0.596671i
$719$		−	32.1395i		−	1.19860i	−0.800525	−	0.599300i	$-0.795446\pi$
$719$		−	32.1395i		−	1.19860i	0.800525	−	0.599300i	$-0.204554\pi$
$720$		0			0
$721$		−	77.6119i		−	2.89042i
$722$	12.1265	−	7.91587i	0.451303	−	0.294598i
$723$		0			0
$724$	−0.149522	+	6.96805i	−0.00555696	+	0.258965i
$725$	−29.5492	+	12.2397i	−1.09743	+	0.454570i
$726$		0			0
$727$	24.0313	−	24.0313i	0.891271	−	0.891271i	−0.103372	−	0.994643i	$-0.532963\pi$
$727$	24.0313	−	24.0313i	0.891271	−	0.891271i	0.994643	+	0.103372i	$0.0329632\pi$
$728$	−42.8428	−	9.96505i	−1.58786	−	0.369329i
$729$		0			0
$730$	−7.63253	−	5.21919i	−0.282493	−	0.193171i
$731$	−36.1196	+	14.9612i	−1.33593	+	0.553361i
$732$		0			0
$733$	−3.28110	+	7.92127i	−0.121190	+	0.292579i	−0.972819	−	0.231566i	$-0.925615\pi$
$733$	−3.28110	+	7.92127i	−0.121190	+	0.292579i	0.851629	+	0.524145i	$0.175615\pi$
$734$	−1.83492	+	8.73404i	−0.0677282	+	0.322379i
$735$		0			0
$736$	−31.8728	−	8.13803i	−1.17485	−	0.299972i
$737$		−	6.83141i		−	0.251638i
$738$		0			0
$739$	4.01435	+	1.66280i	0.147670	+	0.0611671i	0.455295	−	0.890341i	$-0.349534\pi$
$739$	4.01435	+	1.66280i	0.147670	+	0.0611671i	−0.307624	+	0.951508i	$0.599534\pi$
$740$	21.6477	+	55.6073i	0.795784	+	2.04417i
$741$		0			0
$742$	−7.37421	+	10.7840i	−0.270716	+	0.395894i
$743$	20.6253	−	20.6253i	0.756669	−	0.756669i	−0.219046	−	0.975715i	$-0.570294\pi$
$743$	20.6253	−	20.6253i	0.756669	−	0.756669i	0.975715	+	0.219046i	$0.0702944\pi$
$744$		0			0
$745$	42.6465	+	42.6465i	1.56245	+	1.56245i
$746$	−11.1234	+	2.08880i	−0.407258	+	0.0764765i
$747$		0			0
$748$	0.329698	−	15.3646i	0.0120550	−	0.561785i
$749$	−3.08968	+	7.45915i	−0.112894	+	0.272551i
$750$		0			0
$751$	13.6475			0.498004			0.249002	−	0.968503i	$-0.419897\pi$
$751$	13.6475			0.498004			0.249002	+	0.968503i	$0.419897\pi$
$752$	7.19249	−	6.60028i	0.262283	−	0.240687i
$753$		0			0
$754$	37.9724	−	24.7873i	1.38287	−	0.902700i
$755$	30.0458	+	12.4454i	1.09348	+	0.452933i
$756$		0			0
$757$	1.50145	+	3.62481i	0.0545710	+	0.131746i	0.948814	−	0.315836i	$-0.102285\pi$
$757$	1.50145	+	3.62481i	0.0545710	+	0.131746i	−0.894243	+	0.447582i	$0.852285\pi$
$758$	−30.2126	+	5.67344i	−1.09737	+	0.206069i
$759$		0			0
$760$	−14.3040	+	19.9841i	−0.518862	+	0.724901i
$761$	10.5824	+	10.5824i	0.383612	+	0.383612i	0.872402	−	0.488790i	$-0.162562\pi$
$761$	10.5824	+	10.5824i	0.383612	+	0.383612i	−0.488790	+	0.872402i	$0.662562\pi$
$762$		0			0
$763$	7.90266	+	19.0787i	0.286096	+	0.690696i
$764$	8.83316	+	3.88287i	0.319573	+	0.140477i
$765$		0			0
$766$	2.31246	−	11.0071i	0.0835525	−	0.397701i
$767$	−4.76999			−0.172234
$768$		0			0
$769$	−42.6343			−1.53743			−0.768715	−	0.639591i	$-0.779104\pi$
$769$	−42.6343			−1.53743			−0.768715	+	0.639591i	$0.779104\pi$
$770$	5.89875	−	28.0774i	0.212576	−	1.01184i
$771$		0			0
$772$	−0.408070	−	0.179379i	−0.0146868	−	0.00645600i
$773$	−13.5374	−	32.6822i	−0.486906	−	1.17550i	−0.956268	−	0.292490i	$-0.905516\pi$
$773$	−13.5374	−	32.6822i	−0.486906	−	1.17550i	0.469362	−	0.883006i	$-0.344484\pi$
$774$		0			0
$775$	15.7682	+	15.7682i	0.566411	+	0.566411i
$776$	22.3205	−	31.1839i	0.801259	−	1.11944i
$777$		0			0
$778$	8.65206	−	1.62472i	0.310191	−	0.0582489i
$779$	−0.272172	−	0.657081i	−0.00975157	−	0.0235424i
$780$		0			0
$781$	−11.1393	−	4.61404i	−0.398595	−	0.165103i
$782$	32.8285	−	21.4295i	1.17395	−	0.766318i
$783$		0			0
$784$	−33.5387	+	30.7772i	−1.19781	+	1.09918i
$785$	27.4645			0.980249
$786$		0			0
$787$	−11.1547	+	26.9298i	−0.397622	+	0.959945i	0.590606	+	0.806960i	$0.298889\pi$
$787$	−11.1547	+	26.9298i	−0.397622	+	0.959945i	−0.988228	+	0.152985i	$0.951111\pi$
$788$	1.05860	−	49.3328i	0.0377110	−	1.75741i
$789$		0			0
$790$	−56.1912	+	10.5518i	−1.99919	+	0.375416i
$791$	41.4139	+	41.4139i	1.47251	+	1.47251i
$792$		0			0
$793$	7.00350	−	7.00350i	0.248702	−	0.248702i
$794$	21.8703	−	31.9830i	0.776147	−	1.13504i
$795$		0			0
$796$	−15.2589	−	39.1962i	−0.540836	−	1.38927i
$797$	−3.44606	−	1.42740i	−0.122066	−	0.0505612i	0.320815	−	0.947142i	$-0.396043\pi$
$797$	−3.44606	−	1.42740i	−0.122066	−	0.0505612i	−0.442880	+	0.896581i	$0.646043\pi$
$798$		0			0
$799$			11.6340i			0.411582i
$800$	−5.06363	+	19.8318i	−0.179026	+	0.701162i
$801$		0			0
$802$	0.526329	−	2.50527i	0.0185853	−	0.0884642i
$803$	−1.37380	+	3.31665i	−0.0484804	+	0.117042i
$804$		0			0
$805$	67.6174	−	28.0080i	2.38320	−	0.987154i
$806$	−26.0981	−	17.8461i	−0.919266	−	0.628602i
$807$		0			0
$808$	−7.95323	−	1.84988i	−0.279794	−	0.0650787i
$809$	−27.7746	+	27.7746i	−0.976503	+	0.976503i	−0.999730	−	0.0232274i	$-0.992606\pi$
$809$	−27.7746	+	27.7746i	−0.976503	+	0.976503i	0.0232274	+	0.999730i	$0.492606\pi$
$810$		0			0
$811$	13.7402	−	5.69137i	0.482483	−	0.199851i	−0.128165	−	0.991753i	$-0.540909\pi$
$811$	13.7402	−	5.69137i	0.482483	−	0.199851i	0.610649	+	0.791902i	$0.290909\pi$
$812$	1.62602	−	75.7759i	0.0570622	−	2.65921i
$813$		0			0
$814$	19.4003	−	12.6640i	0.679982	−	0.443873i
$815$		−	15.0519i		−	0.527246i
$816$		0			0
$817$		−	24.2732i		−	0.849212i
$818$	15.7788	+	24.1721i	0.551694	+	0.845156i
$819$		0			0
$820$	−0.976013	−	1.01882i	−0.0340839	−	0.0355787i
$821$	9.08495	−	3.76311i	0.317067	−	0.131333i	−0.218474	−	0.975843i	$-0.570108\pi$
$821$	9.08495	−	3.76311i	0.317067	−	0.131333i	0.535541	+	0.844509i	$0.320108\pi$
$822$		0			0
$823$	−37.7132	+	37.7132i	−1.31460	+	1.31460i	−0.396615	+	0.917985i	$0.629815\pi$
$823$	−37.7132	+	37.7132i	−1.31460	+	1.31460i	−0.917985	+	0.396615i	$0.870185\pi$
$824$	50.5151	−	8.36823i	1.75978	−	0.291521i
$825$		0			0
$826$	−4.50024	+	6.58115i	−0.156583	+	0.228987i
$827$	−23.6871	+	9.81150i	−0.823680	+	0.341179i	−0.754398	−	0.656418i	$-0.772071\pi$
$827$	−23.6871	+	9.81150i	−0.823680	+	0.341179i	−0.0692824	+	0.997597i	$0.522071\pi$
$828$		0			0
$829$	−6.99320	+	16.8831i	−0.242884	+	0.586374i	−0.997567	−	0.0697159i	$-0.977791\pi$
$829$	−6.99320	+	16.8831i	−0.242884	+	0.586374i	0.754683	+	0.656090i	$0.227791\pi$
$830$	−14.5977	−	3.06680i	−0.506692	−	0.106450i
$831$		0			0
$832$	1.86656	−	28.9595i	0.0647112	−	1.00399i
$833$		−	54.2495i		−	1.87964i
$834$		0			0
$835$	17.4599	+	7.23214i	0.604225	+	0.250278i
$836$	8.73491	+	3.83968i	0.302103	+	0.132798i
$837$		0			0
$838$	−4.08470	−	2.79315i	−0.141104	−	0.0964879i
$839$	9.56749	−	9.56749i	0.330306	−	0.330306i	−0.522396	−	0.852703i	$-0.674962\pi$
$839$	9.56749	−	9.56749i	0.330306	−	0.330306i	0.852703	+	0.522396i	$0.174962\pi$
$840$		0			0
$841$	34.7451	+	34.7451i	1.19811	+	1.19811i
$842$	2.98209	+	15.8804i	0.102769	+	0.547276i
$843$		0			0
$844$	2.43042	−	2.32831i	0.0836586	−	0.0801437i
$845$	−0.177934	+	0.429570i	−0.00612111	+	0.0147777i
$846$		0			0
$847$	36.0201			1.23766
$848$	−7.81409	−	3.63689i	−0.268337	−	0.124891i
$849$		0			0
$850$	−13.3338	−	20.4265i	−0.457347	−	0.700623i
$851$	54.6020	+	22.6169i	1.87173	+	0.775297i
$852$		0			0
$853$	−3.73365	−	9.01383i	−0.127838	−	0.308628i	0.846982	−	0.531621i	$-0.178417\pi$
$853$	−3.73365	−	9.01383i	−0.127838	−	0.308628i	−0.974820	+	0.222994i	$0.928417\pi$
$854$	−3.05527	−	16.2702i	−0.104549	−	0.556753i
$855$		0			0
$856$	−5.18806	−	1.20672i	−0.177324	−	0.0412448i
$857$	−19.7027	−	19.7027i	−0.673032	−	0.673032i	0.285382	−	0.958414i	$-0.407880\pi$
$857$	−19.7027	−	19.7027i	−0.673032	−	0.673032i	−0.958414	+	0.285382i	$0.907880\pi$
$858$		0			0
$859$	8.30760	+	20.0563i	0.283452	+	0.684313i	0.999911	−	0.0133155i	$-0.00423857\pi$
$859$	8.30760	+	20.0563i	0.283452	+	0.684313i	−0.716460	+	0.697629i	$0.754239\pi$
$860$	−17.4684	−	44.8718i	−0.595666	−	1.53011i
$861$		0			0
$862$	4.59442	+	0.965235i	0.156487	+	0.0328760i
$863$	−29.3303			−0.998415			−0.499207	−	0.866483i	$-0.666375\pi$
$863$	−29.3303			−0.998415			−0.499207	+	0.866483i	$0.666375\pi$
$864$		0			0
$865$	32.8674			1.11752
$866$	−6.27364	−	1.31802i	−0.213187	−	0.0447882i
$867$		0			0
$868$	−49.2444	+	19.1706i	−1.67146	+	0.650693i
$869$	8.49465	+	20.5079i	0.288161	+	0.695683i
$870$		0			0
$871$	10.8707	+	10.8707i	0.368341	+	0.368341i
$872$	−11.5657	+	7.20069i	−0.391663	+	0.243846i
$873$		0			0
$874$	4.49221	+	23.9223i	0.151951	+	0.809183i
$875$	6.65492	+	16.0664i	0.224977	+	0.543144i
$876$		0			0
$877$	43.0165	+	17.8180i	1.45256	+	0.601672i	0.962808	−	0.270188i	$-0.0870858\pi$
$877$	43.0165	+	17.8180i	1.45256	+	0.601672i	0.489756	+	0.871859i	$0.337086\pi$
$878$	−22.9255	−	35.1203i	−0.773699	−	1.18525i
$879$		0			0
$880$	18.9107	+	0.811958i	0.637480	+	0.0273711i
$881$	−54.5605			−1.83819			−0.919095	−	0.394035i	$-0.871079\pi$
$881$	−54.5605			−1.83819			−0.919095	+	0.394035i	$0.871079\pi$
$882$		0			0
$883$	−4.61420	+	11.1397i	−0.155280	+	0.374879i	−0.982306	−	0.187285i	$-0.940031\pi$
$883$	−4.61420	+	11.1397i	−0.155280	+	0.374879i	0.827026	+	0.562164i	$0.190031\pi$
$884$	23.9248	+	24.9741i	0.804679	+	0.839970i
$885$		0			0
$886$	−9.03203	−	48.0980i	−0.303437	−	1.61588i
$887$	20.2635	+	20.2635i	0.680383	+	0.680383i	0.960086	−	0.279704i	$-0.0902363\pi$
$887$	20.2635	+	20.2635i	0.680383	+	0.680383i	−0.279704	+	0.960086i	$0.590236\pi$
$888$		0			0
$889$	−40.0201	+	40.0201i	−1.34223	+	1.34223i
$890$	−33.8782	−	23.1662i	−1.13560	−	0.776534i
$891$		0			0
$892$	18.8556	−	42.8946i	0.631331	−	1.43622i
$893$	−6.67336	−	2.76419i	−0.223315	−	0.0925003i
$894$		0			0
$895$		−	32.4895i		−	1.08600i
$896$	−38.1943	−	29.8971i	−1.27598	−	0.998791i
$897$		0			0
$898$	−29.1311	−	6.12012i	−0.972118	−	0.204231i
$899$	20.8479	−	50.3314i	0.695318	−	1.67865i
$900$		0			0
$901$	9.48997	−	3.93087i	0.316157	−	0.130956i
$902$	−0.309197	+	0.452169i	−0.0102951	+	0.0150556i
$903$		0			0
$904$	−22.4897	+	31.4203i	−0.747997	+	1.04502i
$905$	7.23396	−	7.23396i	0.240465	−	0.240465i
$906$		0			0
$907$	31.3520	−	12.9864i	1.04103	−	0.431208i	0.204347	−	0.978899i	$-0.434493\pi$
$907$	31.3520	−	12.9864i	1.04103	−	0.431208i	0.836681	+	0.547691i	$0.184493\pi$
$908$	19.2732	−	18.4634i	0.639603	−	0.612730i
$909$		0			0
$910$	35.2926	+	54.0658i	1.16994	+	1.79226i
$911$			44.6280i			1.47859i	0.673380	+	0.739296i	$0.264842\pi$
$911$			44.6280i			1.47859i	−0.673380	+	0.739296i	$0.735158\pi$
$912$		0			0
$913$			5.79128i			0.191663i
$914$	−7.74839	+	5.05793i	−0.256294	+	0.167301i
$915$		0			0
$916$	16.9391	+	0.363485i	0.559685	+	0.0120099i
$917$	26.5538	−	10.9989i	0.876883	−	0.363217i
$918$		0			0
$919$	7.85821	−	7.85821i	0.259219	−	0.259219i	−0.565518	−	0.824736i	$-0.691324\pi$
$919$	7.85821	−	7.85821i	0.259219	−	0.259219i	0.824736	+	0.565518i	$0.191324\pi$
$920$	25.5202	+	40.9902i	0.841375	+	1.35141i
$921$		0			0
$922$	14.7763	+	10.1042i	0.486632	+	0.332763i
$923$	25.0680	−	10.3835i	0.825125	−	0.341778i
$924$		0			0
$925$	14.0726	−	33.9743i	0.462705	−	1.11707i
$926$	4.13521	−	19.6832i	0.135892	−	0.646830i
$927$		0			0
$928$	49.4955	−	7.11195i	1.62477	−	0.233461i
$929$		−	14.8136i		−	0.486018i	−0.970024	−	0.243009i	$-0.921866\pi$
$929$		−	14.8136i		−	0.486018i	0.970024	−	0.243009i	$-0.0781344\pi$
$930$		0			0
$931$	31.1180	+	12.8895i	1.01985	+	0.422436i
$932$	25.4825	−	9.92022i	0.834708	−	0.324948i
$933$		0			0
$934$	29.8300	−	43.6233i	0.976067	−	1.42740i
$935$	−15.9509	+	15.9509i	−0.521651	+	0.521651i
$936$		0			0
$937$	−10.7125	−	10.7125i	−0.349961	−	0.349961i	0.510134	−	0.860095i	$-0.329596\pi$
$937$	−10.7125	−	10.7125i	−0.349961	−	0.349961i	−0.860095	+	0.510134i	$0.829596\pi$
$938$	25.2543	−	4.74235i	0.824582	−	0.154843i
$939$		0			0
$940$	−14.3257	−	0.307406i	−0.467254	−	0.0100265i
$941$	1.84380	−	4.45134i	0.0601063	−	0.145109i	−0.890973	−	0.454056i	$-0.849977\pi$
$941$	1.84380	−	4.45134i	0.0601063	−	0.145109i	0.951079	+	0.308947i	$0.0999765\pi$
$942$		0			0
$943$	−1.39737			−0.0455046
$944$	−4.76868	−	2.21948i	−0.155207	−	0.0722378i
$945$		0			0
$946$	−15.6549	+	10.2191i	−0.508985	+	0.332251i
$947$	−46.3221	−	19.1872i	−1.50527	−	0.623501i	−0.530691	−	0.847565i	$-0.678068\pi$
$947$	−46.3221	−	19.1872i	−1.50527	−	0.623501i	−0.974574	+	0.224064i	$0.928068\pi$
$948$		0			0
$949$	−3.09163	−	7.46385i	−0.100358	−	0.242287i
$950$	14.8849	−	2.79513i	0.482928	−	0.0906861i
$951$		0			0
$952$	57.0285	−	9.44723i	1.84831	−	0.306186i
$953$	2.40430	+	2.40430i	0.0778828	+	0.0778828i	0.744975	−	0.667092i	$-0.232461\pi$
$953$	2.40430	+	2.40430i	0.0778828	+	0.0778828i	−0.667092	+	0.744975i	$0.732461\pi$
$954$		0			0
$955$	−5.41999	−	13.0850i	−0.175387	−	0.423421i
$956$	20.8112	−	47.3435i	0.673083	−	1.53120i
$957$		0			0
$958$	−3.89668	+	18.5478i	−0.125896	+	0.599251i
$959$	−59.2558			−1.91347
$960$		0			0
$961$	−6.98312			−0.225262
$962$	−10.7195	+	51.0236i	−0.345609	+	1.64507i
$963$		0			0
$964$	−20.0691	+	45.6554i	−0.646383	+	1.47046i
$965$	0.250390	+	0.604495i	0.00806034	+	0.0194594i
$966$		0			0
$967$	−12.6984	−	12.6984i	−0.408354	−	0.408354i	0.472811	−	0.881164i	$-0.343239\pi$
$967$	−12.6984	−	12.6984i	−0.408354	−	0.408354i	−0.881164	+	0.472811i	$0.843239\pi$
$968$	3.88374	+	23.4443i	0.124828	+	0.753529i
$969$		0			0
$970$	−55.3233	+	10.3888i	−1.77633	+	0.333565i
$971$	5.19719	+	12.5471i	0.166786	+	0.402657i	0.985069	−	0.172158i	$-0.0550740\pi$
$971$	5.19719	+	12.5471i	0.166786	+	0.402657i	−0.818283	+	0.574815i	$0.805074\pi$
$972$		0			0
$973$	−35.4386	−	14.6792i	−1.13611	−	0.470592i
$974$	2.12276	−	1.38568i	0.0680175	−	0.0443999i
$975$		0			0
$976$	10.2603	−	3.74285i	0.328424	−	0.119806i
$977$	−20.3021			−0.649521			−0.324761	−	0.945796i	$-0.605284\pi$
$977$	−20.3021			−0.649521			−0.324761	+	0.945796i	$0.605284\pi$
$978$		0			0
$979$	−6.09784	+	14.7215i	−0.194888	+	0.470501i
$980$	66.8010	+	1.43344i	2.13388	+	0.0457895i
$981$		0			0
$982$	−32.0310	+	6.01490i	−1.02215	+	0.191943i
$983$	11.4130	+	11.4130i	0.364017	+	0.364017i	0.865290	−	0.501272i	$-0.167134\pi$
$983$	11.4130	+	11.4130i	0.364017	+	0.364017i	−0.501272	+	0.865290i	$0.667134\pi$
$984$		0			0
$985$	−51.2155	+	51.2155i	−1.63186	+	1.63186i
$986$	−33.6378	+	49.1919i	−1.07125	+	1.56659i
$987$		0			0
$988$	−20.0098	+	7.78971i	−0.636596	+	0.247824i
$989$	−44.0605	−	18.2505i	−1.40104	−	0.580331i
$990$		0			0
$991$		−	12.0390i		−	0.382431i	−0.981548	−	0.191216i	$-0.938757\pi$
$991$		−	12.0390i		−	0.382431i	0.981548	−	0.191216i	$-0.0612430\pi$
$992$	−17.7871	−	29.9846i	−0.564742	−	0.952013i
$993$		0			0
$994$	9.32429	−	44.3826i	0.295748	−	1.40773i
$995$	−23.6268	+	57.0401i	−0.749020	+	1.80829i
$996$		0			0
$997$	17.2248	−	7.13474i	0.545514	−	0.225959i	−0.0928685	−	0.995678i	$-0.529604\pi$
$997$	17.2248	−	7.13474i	0.545514	−	0.225959i	0.638383	+	0.769719i	$0.279604\pi$
$998$	8.43692	+	5.76923i	0.267066	+	0.182622i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.w.b.179.4	yes	32
3.2	odd	2		288.2.w.a.179.5	✓	32
4.3	odd	2		1152.2.w.a.1007.7		32
12.11	even	2		1152.2.w.b.1007.2		32
32.5	even	8		1152.2.w.b.143.2		32
32.27	odd	8		288.2.w.a.251.5	yes	32
96.5	odd	8		1152.2.w.a.143.7		32
96.59	even	8	inner	288.2.w.b.251.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.179.5	✓	32	3.2	odd	2
288.2.w.a.251.5	yes	32	32.27	odd	8
288.2.w.b.179.4	yes	32	1.1	even	1	trivial
288.2.w.b.251.4	yes	32	96.59	even	8	inner
1152.2.w.a.143.7		32	96.5	odd	8
1152.2.w.a.1007.7		32	4.3	odd	2
1152.2.w.b.143.2		32	32.5	even	8
1152.2.w.b.1007.2		32	12.11	even	2

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.290763 - 1.38400i) q^{2} +(-1.83091 - 0.804831i) q^{4} +(1.12344 + 2.71222i) q^{5} +(3.03150 + 3.03150i) q^{7} +(-1.64625 + 2.29997i) q^{8} +O(q^{10})\)	\(q+(0.290763 - 1.38400i) q^{2} +(-1.83091 - 0.804831i) q^{4} +(1.12344 + 2.71222i) q^{5} +(3.03150 + 3.03150i) q^{7} +(-1.64625 + 2.29997i) q^{8} +(4.08037 - 0.766228i) q^{10} +(-0.616847 - 1.48920i) q^{11} +(3.35133 + 1.38816i) q^{13} +(5.07705 - 3.31415i) q^{14} +(2.70449 + 2.94715i) q^{16} -4.76709 q^{17} +(1.13264 - 2.73444i) q^{19} +(0.125961 - 5.87003i) q^{20} +(-2.24041 + 0.420712i) q^{22} +(-4.11192 - 4.11192i) q^{23} +(-2.55851 + 2.55851i) q^{25} +(2.89566 - 4.23461i) q^{26} +(-3.11057 - 7.99027i) q^{28} +(8.16664 + 3.38273i) q^{29} -6.16305i q^{31} +(4.86523 - 2.88610i) q^{32} +(-1.38609 + 6.59765i) q^{34} +(-4.81640 + 11.6278i) q^{35} +(-9.38963 + 3.88931i) q^{37} +(-3.45513 - 2.36265i) q^{38} +(-8.08750 - 1.88112i) q^{40} +(0.169917 - 0.169917i) q^{41} +(7.57687 - 3.13844i) q^{43} +(-0.0691613 + 3.22306i) q^{44} +(-6.88649 + 4.49531i) q^{46} -2.44049i q^{47} +11.3800i q^{49} +(2.79706 + 4.28490i) q^{50} +(-5.01875 - 5.23886i) q^{52} +(-1.99073 + 0.824586i) q^{53} +(3.34605 - 3.34605i) q^{55} +(-11.9630 + 1.98176i) q^{56} +(7.05626 - 10.3191i) q^{58} +(-1.21488 + 0.503218i) q^{59} +(1.04489 - 2.52258i) q^{61} +(-8.52966 - 1.79198i) q^{62} +(-2.57973 - 7.57265i) q^{64} +10.6491i q^{65} +(3.91551 + 1.62186i) q^{67} +(8.72813 + 3.83670i) q^{68} +(14.6925 + 10.0468i) q^{70} +(5.28919 - 5.28919i) q^{71} +(-1.57482 - 1.57482i) q^{73} +(2.65266 + 14.1261i) q^{74} +(-4.27453 + 4.09494i) q^{76} +(2.64454 - 6.38449i) q^{77} -13.7711 q^{79} +(-4.95501 + 10.6461i) q^{80} +(-0.185759 - 0.284570i) q^{82} +(-3.31934 - 1.37492i) q^{83} +(-5.35554 - 12.9294i) q^{85} +(-2.14053 - 11.3989i) q^{86} +(4.44060 + 1.03286i) q^{88} +(-6.99010 - 6.99010i) q^{89} +(5.95133 + 14.3678i) q^{91} +(4.21917 + 10.8380i) q^{92} +(-3.37763 - 0.709602i) q^{94} +8.68886 q^{95} -13.5584 q^{97} +(15.7499 + 3.30888i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} + 4 q^{8}+O(q^{10}) \) 32 * q + 4 * q^2 + 4 * q^8	\( 32 q + 4 q^{2} + 4 q^{8} + 8 q^{10} + 8 q^{11} - 12 q^{14} + 8 q^{16} - 32 q^{20} + 16 q^{22} + 36 q^{26} + 16 q^{29} + 24 q^{32} - 24 q^{35} - 32 q^{38} - 32 q^{40} - 8 q^{44} - 32 q^{46} - 8 q^{50} - 56 q^{52} + 16 q^{53} - 32 q^{55} - 40 q^{56} - 32 q^{58} - 32 q^{59} + 32 q^{61} + 68 q^{62} - 48 q^{64} - 16 q^{67} + 72 q^{68} - 48 q^{70} - 16 q^{71} - 60 q^{74} - 8 q^{76} + 16 q^{77} - 32 q^{79} - 96 q^{80} + 40 q^{82} + 40 q^{83} + 40 q^{86} + 40 q^{88} - 48 q^{91} + 16 q^{92} + 72 q^{94} + 80 q^{95} + 44 q^{98}+O(q^{100}) \) 32 * q + 4 * q^2 + 4 * q^8 + 8 * q^10 + 8 * q^11 - 12 * q^14 + 8 * q^16 - 32 * q^20 + 16 * q^22 + 36 * q^26 + 16 * q^29 + 24 * q^32 - 24 * q^35 - 32 * q^38 - 32 * q^40 - 8 * q^44 - 32 * q^46 - 8 * q^50 - 56 * q^52 + 16 * q^53 - 32 * q^55 - 40 * q^56 - 32 * q^58 - 32 * q^59 + 32 * q^61 + 68 * q^62 - 48 * q^64 - 16 * q^67 + 72 * q^68 - 48 * q^70 - 16 * q^71 - 60 * q^74 - 8 * q^76 + 16 * q^77 - 32 * q^79 - 96 * q^80 + 40 * q^82 + 40 * q^83 + 40 * q^86 + 40 * q^88 - 48 * q^91 + 16 * q^92 + 72 * q^94 + 80 * q^95 + 44 * q^98

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